Answer:
n = 10
Step-by-step explanation:
Factorial is denoted by an exclamation mark "!" placed after the number. It means to multiply all whole numbers from the given number down to 1.
Therefore, n! represents the product of all positive integers from 1 to n.
[tex]\boxed{n!=n \times(n-1) \times(n-2) \times ... \times 1}[/tex]
Given expression:
[tex]n! = (2^8)(3^4)(5^2)(7)[/tex]
The expression for n! has been given as the product of prime factors.
As n! represents the product of all positive integers from 1 to n, begin by writing out the positive integers from 1 in ascending order as the product of primes (using exponents where possible):
[tex]\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}\cline{1-14}\vphantom{\dfrac12}n&1&2&3&4&5&6&7&8&9&10&11&12&13\\\cline{1-14}\vphantom{\dfrac12}\sf Product\;of\;primes&1&2&3&2^2&5&3\cdot 2&7&2^3&3^2&5 \cdot 2&11&2^2\cdot 3&13\\\cline{1-14}\end{aligned}\;\;\sf etc.[/tex]
If we examine the prime products of the given expression, we can see that largest prime number 7 appears only once. Therefore, n must be less than 14, since the next time 7 appears as a prime factor is when 2 · 7 = 14.
The prime number 5 appears twice in the given expression.
From the above table, we can see that the first two times the number 5 is present is (1) on its own, and (2) as a factor of 10. Therefore, n must be equal to or more than 10.
The prime number 3 appears four times in the given expression.
From the above table, we can see that the first four times the number 3 is present is (1) on its own, (2) as a factor of 6, (3) & (4) as both factors of 9.
The 5th time prime number 3 is present is as a prime factor of 12. Therefore, n must be less than 12, else 2⁵ would be a factor of n!.
Therefore, we have determined that 10 ≤ n < 12.
As 11 is a prime number and does not appear in the given expression for n!, we can conclude that n = 10.
We can check this by calculating the given expression and 10!:
[tex]\begin{aligned}n! &= (2^8)(3^4)(5^2)(7)\\&=256 \cdot 81\cdot25\cdot7\\&=20738\cdot25\cdot7\\&=518400\cdot7\\&=3628800\end{aligned}[/tex]
[tex]\begin{aligned}10!&=10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=90 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=720 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=5040 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=30240 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=151200 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=604800 \cdot 3 \cdot 2 \cdot 1\\&=1814400 \cdot 2 \cdot 1\\&=3628800 \cdot 1\\&=3628800\end{aligned}[/tex]
Therefore, this proves that n = 10.
Alg 2 unit 5-5 math questions with g and f
The composition fog is ((3,2), (1,0), (2,7)).
To find the composition fog, we need to apply function g first, and then apply function f to the result.
Let's start by applying function g:
g((-4,1)) = (-2,1)
g((0,4)) = (3,1)
g((1,0)) = (2,8)
Now, let's apply function f to the results:
f((-2,1)) = (3,2)
f((3,1)) = (1,0)
f((2,8)) = (2,7)
Therefore, the composition fog is:
fog = ((-4,1), (0,4), (1,0)) → g → f
= ((3,2), (1,0), (2,7))
So, fog = ((3,2), (1,0), (2,7)).
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The equation of the hyperbola that has a center at (3, 10), a focus at (8, 10), and a vertex at (6, 10), is
Int he above expression, A = 3 (distance from the vertex to the center)
B = 4
C = 3 (distance from focus to center)
D = 10
How is this so?Since the center of the hyperbola is (3,10), we have C=3 and D=10.
The distance from the center to the vertex is A, so we have A= 6-3
A = 3.
The distance from the center to the focus is given by c, so we have c=8-3=5.
We can use the relationship a² + b² = c² to solve for B:
a = 6 - 3 = 3 (distance from vertex to center)
c = 5 (distance from focus to center)
b = ?
b² = c² - a²
b² = 5² - 3²
b² = 16
b = 4
Therefore, the equation of the hyperbola is
((x-3)²/3²) - ((y-10)²/4²) = 1
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Full Quesitn:
The equation of the hyperbola that has a center at (3, 10), a focus at (8, 10), and a vertex at (6, 10), is
((x-C)²/A²) - ((y-D)²)/B²) = 1
Where A = ?
B = ?
C = ?
D = ?
The points S(-4,-2), T(-4, 5), and
U(-9, -2) form a triangle. Plot the points
then click the "Graph Triangle" button. Then find the perimeter of the triangle.
Round your answer to the nearest tenth if necessary.
The perimeter of the triangle STU is 20.6 units
What is the perimeter of the triangle?To find the perimeter of triangle STU, we need to use the formula of distance between two points and then take the sum of all the sides.
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\\[/tex]
For line ST;
(-4, -2) and (-4, 5)
[tex]d = \sqrt{(-4 - (-4))^2 + (5 - (-2))^2} \\d = 7[/tex]
For line TU;
(-4, 5) and (-9, -2)
[tex]d = \sqrt{(-9 - (-4))^2 - (-2 - 5)^2} \\d = \sqrt{74} \\d = 8.6[/tex]
For line US;
(-9, -2) and (-4, -2)
[tex]d = \sqrt{(-9 - (-4))^2 + (-2 - (-2))^2}\\d = 5[/tex]
The distance between the sides are 7, 8.6 and 5 units.
The perimeter of the triangle = 7 + 8.6 + 5 = 20.6 units
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the table shows how much Eric earns for pruning trees, write an equation that relates x, the number of trees Eric prunes to y the amount he earns. solve your equation to find how much Eric earns if he prunes 7
trees pruned 2 4 6 8
pay in dollars 30 60 90 80
If Eric prunes 7 trees, he would earn $85.
To write an equation that relates the number of trees pruned (x) to the amount Eric earns (y), we can use the given data points to determine the pattern or relationship.
From the table, we observe that Eric's pay increases as the number of trees pruned increases, except for the case where he prunes 8 trees.
Based on the data, we can construct a piecewise equation:
For x = 2, 4, and 6:
y = 30 * x
For x = 8:
y = 80
However, we need to consider the case when x = 7. Since this data point is missing from the table, we can assume that the pay is proportional to the number of trees pruned. Therefore, we can interpolate using the given data points for x = 6 and x = 8:
Using the formula for linear interpolation:
y = y1 + (y2 - y1) * ((x - x1) / (x2 - x1))
Substituting the values, we have:
y = 90 + (80 - 90) * ((7 - 6) / (8 - 6))
y = 90 + (-10) * (1 / 2)
y = 90 - 5
y = 85
Thus, if Eric prunes 7 trees, he would earn $85.
It's important to note that the equation and solution are based on the given data points and the assumption of a linear relationship.
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A restaurant at the food court in a mall is offering a lunch special. The table shows the relationship between the number of side dishes and the total cost of the special.
Restaurant
Number of Side Dishes Total Cost
2 $10.25
4 $13.25
5 $14.75
8 $19.25
Which of the following graphs shows the relationship given in the table?
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 7 and 25 hundredths through the point 3 comma 11 and 75 hundredths
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 7 and 75 hundredths through the point 3 comma 12 and 25 hundredths
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 25 hundredths through the point 3 comma 9 and 75 hundredths
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 5 tenths through the point 5 comma 13
pls use pic for the answer
Graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 5 tenths through the point 5 comma 13
The x-axis of the graph is labeled "number of side dishes," which represents the independent variable in this case.
The y-axis is labeled "cost in dollars," representing the dependent variable.
The line on the graph starts at the point (2, $10.25), indicating that when there are 2 side dishes, the total cost of the lunch special is $10.25.
The line then passes through the point (8, $19.25), which signifies that when there are 8 side dishes, the total cost of the lunch special is $19.25.
This graph correctly illustrates the relationship between the number of side dishes and the total cost, showing that as the number of side dishes increases, the cost of the lunch special also increases.
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I need help!!!!!!!!!
Answer:
its b4 + 7b3 + 4b2 + b5 + 7b4+ 4b3= b5+8b4+11b3+4b2
Answer:
When multiplying, add the exponents, (example) remember if there is "7b" the exponent is one.
Multiply b^2 * b^3 = b^5 (add the exponent 2 + 3 = 5)
Multiply 7b * b^3 = 7b^4 (the exponent of 7b is one, add 1 + 3 for the exponent to become 4)
Multiply 4 * b^3 = 4b^3 (4 doesn't have a variable, the exponent will be 3)
b^2 * b*2 = b^4 (add exponents)
7b * b^2 = 7b^3 (add the exponents 1 + 2)
4 * b^2 = 4b^2
b^2 + 7b + 4
b^3 b^5 + 7b^4 + 4b^3
+
b^2 b^4 + 7b^3 + 4b^2
b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2
[tex]b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2[/tex]
b^5 + 8b^4 + 11b^3 + 4b^2Drag each number to a box to complete the table. Each number may be used once or not at all. 8,000533,00021,000 Kilometers Meters 1 2,000 5,000 8
Each number should be dragged to a box to complete the table as follows;
Kilometers Meters
1 1,000
2 2,000
3 3,000
5 5,000
8 8,000
What is a conversion factor?In Science and Mathematics, a conversion factor can be defined as a number that is used to convert a number in one set of units to another, either by dividing or multiplying.
Generally speaking, there are one (1) kilometer in one thousand (1,000) meters. This ultimately implies that, a proportion or ratio for the conversion of kilometer to meters would be written as follows;
Conversion:
1 kilometer = 1,000 meters
2 kilometer = 2,000 meters
3 kilometer = 3,000 meters
4 kilometer = 4,000 meters
5 kilometer = 5,000 meters
6 kilometer = 6,000 meters
7 kilometer = 7,000 meters
8 kilometer = 8,000 meters
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
IS THERE ANOTHER WAY TO SOLVE THIS PROBLEM
My family and I own a little country store. It’s called Coomer’s Trading Post. We sell a little of everything, but we do sell a lot of cheeseburgers, French fries, bottle soda, and candy bars daily.
We expect to make $175 for cheeseburger and fries only.
I plan to sell 105 burgers and fries all together.
X= burger $4
Y= fries $ 2
I4x+2=175 (equation)
SOLVE FOR Y
X+Y=105
-Y -Y
X= 105-Y
4(105-Y) + 2 =175
420-4Y+2=175
-420 -420
-4Y+2Y=245
-2Y=-245
-2 -2
Y=122.50
SOLVE FOR X
4X+2(122.50)= 105
4X+245=105
-245 -245
4x= 140
4 4
X=-35
THIS IS FOR CANDY BARS AND BOTTLE SODAS.
We expect to make $ 120 for the candy bars and bottle soda together.
We plan to sell 75.
X= candy bars 1.85
Y= bottle soda 2.49
Solve for y
1.85x+2.49=120
X+Y=75
-Y -Y
X=75-Y
1.85(75-Y)+2.49=120
138.75-1.8Y+2.49=120
-138.75 -138.75
-1.8Y+2.49Y=-18.75
.64Y=-18.75
.64 .64
Y=-29.29
SOLVE FOR X
1.85X+2.49(-29.29)=120
1.85X + -72.93=120
-72.93 -72.93
1.85X =47.07
1.85 1.85
X= 25.44
The values for the Number of cheeseburgers, fries, candy bars, and bottle sodas seem to be inconsistent.The number of fries (Y) is 122.50.The number of cheeseburgers (X) is -17.50
We can calculate the values of X and Y, representing the number of cheeseburgers and fries respectively, and the number of candy bars and bottle sodas respectively.
For cheeseburgers and fries:
We know that the expected revenue from cheeseburgers and fries is $175.
The equation relating the cost of the cheeseburgers (X) and fries (Y) is given as 4X + 2Y = 175.
We also know that the total number of cheeseburgers and fries to be sold is 105, which can be represented as X + Y = 105.
To solve for Y, we can substitute X = 105 - Y into the first equation:
4(105 - Y) + 2Y = 175
420 - 4Y + 2Y = 175
-2Y = 175 - 420
-2Y = -245
Y = -245 / -2
Y = 122.50
To solve for X, we substitute Y = 122.50 into the equation X + Y = 105:
X + 122.50 = 105
X = 105 - 122.50
X = -17.50
Therefore, the number of cheeseburgers (X) is -17.50. However, since it is not possible to have a negative quantity of cheeseburgers, we can conclude that there might be an error in the calculations or the given information.
Moving on to candy bars and bottle sodas:
We expect to make $120 from the sales of candy bars and bottle sodas.
The equation relating the cost of candy bars (X) and bottle sodas (Y) is given as 1.85X + 2.49Y = 120.
The total number of candy bars and bottle sodas to be sold is 75, which can be represented as X + Y = 75.
To solve for Y, we substitute X = 75 - Y into the first equation:
1.85(75 - Y) + 2.49Y = 120
138.75 - 1.85Y + 2.49Y = 120
0.64Y = 120 - 138.75
0.64Y = -18.75
Y = -18.75 / 0.64
Y = -29.29
Again, we encounter a negative value, which is not possible for the number of bottle sodas. This suggests a mistake in the calculations or the given information.
Similarly, to solve for X, we substitute Y = -29.29 into the equation X + Y = 75:
X - 29.29 = 75
X = 75 + 29.29
X = 104.29
Here, we obtain a non-integer value for the number of candy bars, which may indicate an error in the calculations or the given information.
In conclusion, the calculated values for the number of cheeseburgers, fries, candy bars, and bottle sodas seem to be inconsistent with the given information
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The PTA is holding a raffle. The prize is a camera worth $200. Each raffle ticket costs $5. One hundred tickets are sold and a winner is drawn at random. Find the expected value of the purchase of a ticket.
The expected value of the purchase of a ticket is -$2.95.
To find the expected value of the purchase of a ticket, we need to consider the probability of winning and the amount of money gained or lost.
Given:
The cost of a raffle ticket is $5.
The prize is a camera worth $200.
One hundred tickets are sold.
To calculate the expected value, we multiply the probability of winning by the value gained and subtract the probability of not winning by the cost of the ticket.
Probability of winning:
Since there are 100 tickets sold and only one winner, the probability of winning is 1/100, or 0.01.
Value gained:
If the ticket is a winning ticket, the value gained is $200.
Probability of not winning:
The probability of not winning is 99/100, or 0.99, as there is only one winner out of 100 tickets.
Cost of the ticket:
The cost of a ticket is $5.
Now, let's calculate the expected value:
Expected value = (Probability of winning × Value gained) - (Probability of not winning × Cost of ticket)
= (0.01 × $200) - (0.99 × $5)
= $2 - $4.95
= -$2.95
The expected value of the purchase of a ticket is -$2.95.
This means that, on average, for each raffle ticket purchased, a person can expect to lose approximately $2.95.
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The table shows three unique, discrete functions.
x f(x) g(x) h(x)
-1
0
3
185
15
2
3
0
-25
-10-204
2
3
2
-3
2
3
4
5
6
Which statements can be used to compare the
characteristics of the functions? Select three options.
Of(x) has the greatest maximum.
h(x) has the greatest x-intercept.
g(x) has the smallest minimum value.
All three functions share the same domain.
All three functions share the same y-intercept.
All thre functions share the same y intercept
We can analyze the characteristics of the given functions based on the information provided in the table.
We cannot determine which function has the greatest maximum based on the table alone, as we do not have the complete graph of any of the functions.
We can see from the table that h(x) has an x-intercept of 0, which is the smallest among the three functions. Therefore, we can say that h(x) has the smallest x-intercept.
We can see from the table that g(x) has a minimum value of -204, which is the smallest among the three functions. Therefore, we can say that g(x) has the smallest minimum value.
We cannot determine if all three functions share the same domain based on the table alone. We can only see that all three functions have been evaluated at the same set of input values.
We can see from the table that the y-intercept of f(x) is 2, the y-intercept of g(x) is 3, and the y-intercept of h(x) is 4. Therefore, we can say that all three functions have different y-intercepts.
Therefore, the statements that can be used to compare the characteristics of the functions are:
h(x) has the smallest x-intercept.
g(x) has the smallest minimum value.
All three functions have different y-intercepts.
Which two functions can be used to solve for x?
The expression that should be used is tan 67° = 210/x, tan 23° = x/210.
Given is a figure, we need to find the value of x,
So, the figure is creating a right triangle, the angle of elevation is equal to the angle of depression,
So, the two acute angles in the triangle will be 23° and 67°.
Also, the tangent of an angle is equal to the ratio of the perpendicular side to the base,
Taking 67° as reference angle, we get,
Tan 67° = x / 210
Taking 23° as reference angle, we get,
Tan 23° = 210/x
Hence the expression that should be used is tan 67° = 210/x, tan 23° = x/210.
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y = log₂ X
Compression of ½, down 5 and left 7
Write the equation with the given parent and the given transformation.
Answer:
y = (1/2)log₂ (x - 7) - 5
Brian says the graph shows the circle with a center (-3, 2) and a radius of 2. Mia says the graph shows all possible centers for a circle that passes through (-3, -2) with a radius of 2. Which student is correct? Explain.
Brian is correct, because the graph shows the circle with a center (-3, 2) and a radius of 2.
Since, The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
We have to given that;
Brian says the graph shows the circle with a center (-3, 2) and a radius of 2.
And, Mia says the graph shows all possible centers for a circle that passes through (-3, -2) with a radius of 2.
Now, By given graph we can see that,
Center of circle = (- 3, 2)
And, Radius of circle = - 1 + 3 = 2
Hence, Brian is correct, because the graph shows the circle with a center (-3, 2) and a radius of 2.
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Need the answer quickly!
In the triangle below, b =________. If necessary, round your answer to two
decimal places.
A
42°
C
Answer here
B
41.5%
37
Answer:
b ≈ 54.94
Step-by-step explanation:
using the Sine rule in Δ ABC
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]
where a is the side opposite ∠ A, b is opposite ∠ B , c is opposite ∠ C
we require to calculate ∠ B
∠ B = 180° - (42 + 41.5)° = 180° - 83.5° = 96.5°
to find b using the pair of ratios
[tex]\frac{b}{sinB}[/tex] = [tex]\frac{a}{sinA}[/tex] ( substitute values )
[tex]\frac{b}{sin96.5}[/tex] = [tex]\frac{37}{sin42}[/tex] ( cross- multiply )
b × sin42° = 37 × sin96.5° ( divide both sides by sin42° )
b = [tex]\frac{37sin96.5}{sin42}[/tex] ≈ 54.94 ( to 2 decimal places )
Find the value of x.
12, x, 17, 15, 10; The mean is 12.6.
Answer:x=9
Step-by-step explanation: 12.6x5 then subtract everything else.
4. Determine the lateral and total surface area of the rectangular pyramid. 6 cm 8 cm 6 cm Lateral Surface Area Total Surface Area 6.5 cm
The lateral and the total surface area of the rectangular pyramid are 182 square cm and 278 square cm
Determining the lateral and total surface area of the rectangular pyramid.From the question, we have the following parameters that can be used in our computation:
Length = 6 cm
Width = 8 cm
Height = 6.5 cm
The lateral surface area of the rectangular pyramid is calculated as
LA = 2 *(L + W)H
So, we have
LA = 2 *(6 + 8) * 6.5
Evaluate
LA = 182
The total surface area of the rectangular pyramid is calculated as
TA = 2 * (LW + LH + HW)
So, we have
TA = 2 * (8 * 6 + 8 * 6.5 + 6.5 * 6)
Evalaute
TA = 278
Hence, total surface area of the rectangular pyramid is 278 square cm
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The top of a tree makes angles s and t with Points K and L on the ground, respectively, such that the angles are complementary. Point K is x meters and Point L is y meters from the base of the tree.
a. In terms of x and y, find the height of the tree. Include your work.
b. If s = 38° and y = 3 meters, calculate the height of the tree, rounded to two decimal places.
1. In terms of x and y, the height of the tree is and
2. The height of the tree is 6.71 meters
Since, From the question, we are to determine the height of the tree in terms of x and y
Hence, By Using SOH CAH TOA, we can write that
tan t° = h / y
h = y × tan t°
Also, We get;
tan s° = h / x
h = x × tan s°
2. If m ∠t = 38° and y = 3 meters,
Then, the height of the tree;
h = 3 × tan 38°
h = 3 × 0.78 meters
h = 2.34 meters
Hence, the height of the tree is 2.34 meters.
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You have one red apple and three green apples in a
bowl. You randomly select one apple to eat now and
another apple for your lunch. Use a sample space to
determine whether randomly selecting a green apple
first and randomly selecting a green apple second are
independent events.
Answer: vvvvv
Step-by-step explanation:
Let R1 and G1 represent the red and green apples available for the first selection, respectively. Similarly, let R2, G2a, and G2b represent the red and two green apples available for the second selection, respectively. Then, the sample space for the two selections is:
{(R1, R2), (R1, G2a), (R1, G2b), (G1, R2), (G1, G2a), (G1, G2b)}
Out of these six outcomes, only two involve selecting a green apple first: (G1, R2) and (G1, G2a). And out of these two outcomes, only one involves selecting a green apple second: (G1, G2a).
Therefore, since the probability of selecting a green apple second changes based on whether a green apple was selected first, the events of selecting a green apple first and selecting a green apple second are dependent.
In your drawer you have 10 white socks and 14 black socks. You choose one sock from the drawer and then a second sock (without replacement.)
Event A: You choose a black sock.
Event B: You choose a black sock.
Tell whether the events are independent or dependent. Explain your reasoning.
The events A and B are dependent events.
The probability of event B will be different from the initial probability of selecting a black sock (event A).
Two events are considered independent if the outcome of one event does not affect the probability of the other event.
The outcome of event A (choosing a black sock) directly affects the probability of event B (choosing a black sock again).
To explain further, let's consider the initial scenario:
You have 10 white socks and 14 black socks in your drawer.
The total number of socks is 24.
The first sock, there are two possibilities:
Either it is a black sock or a white sock.
If event A occurs and you select a black sock, the total number of black socks in the drawer decreases to 13, while the total number of socks decreases to 23.
If event B to occur (selecting a black sock again), the probability is now influenced by the fact that you have one less black sock and one less sock in the drawer.
The probability of event B will be different from the initial probability of selecting a black sock (event A).
The outcome of event A affects the probability of event B, the two events are dependent.
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Find the product of (3x + 4)(x − 1). 3x2 + 7x − 4 3x2 + 7x − 3 3x2 − x − 4 3x2 + x − 4
Hello !
Answer:
[tex]\boxed{\sf (3x + 4)(x - 1)=3x^2+x-4}[/tex]
Step-by-step explanation:
We will have to use the distributive property to expand this expression.
Let's remember :
[tex]\sf (a+b)(c+d)=ab+ad+bc+bd)[/tex]
Let's apply this property to our expression :
[tex]\sf (3x + 4)(x -1)\\=3x\times x+3x\times(-1)+4\times x+4\times(-1)[/tex]
Now let's calculate and combine like terms :
[tex]\sf 3x^2-3x+4x-4\\\boxed{\sf =3x^2+x-4}[/tex]
Have a nice day ;)
6:1 scale with dimensions of 24 inches by 36 inches. what are the real dimensions?
The real dimensions of the object are 144 inches by 216 inches.
Given that, 6:1 scale with dimensions of 24 inches by 36 inches.
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
In a 6:1 scale, the real dimensions of an object would be 6 times the scaled dimensions. Therefore, the real dimensions of the object given in the question would be 24 inches x 6 = 144 inches by 36 inches x 6 = 216 inches. So, the real dimensions of the object are 144 inches by 216 inches.
Therefore, the real dimensions of the object are 144 inches by 216 inches.
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need help can someone help me need it to pass math
The measure of segment HI is given as follows:
HI = 7.
How to obtain the measure of segment HI?The measure of segment HI for this problem are obtained considering the triangle midsegment theorem, which states that the length of the midsegment of the triangle is equals to half the length of the base, hence the base has the length that is twice the midsegment.
The lengths are given as follows:
Midsegment HI = -9x + 70.Base EF = -21 + 5x.Hence the value of x is obtained as follows:
EF = 2HI
-21 + 5x = 2(-9x + 70)
-21 + 5x = -18x + 140
23x = 161
x = 7.
Hence the length HI is given as follows:
HI = -9(7) + 70
HI = 7.
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3(x + 4) pleeeeeeeeeeeeaaaase
Answer:
3x + 12
Step-by-step explanation:
Using the distributive property, multiply 3 by x and get 3x. Then multiply 3 by 4 and get 12. Put it together and get 3x + 12
Which equation represents a quadratic function with a leading coefficient of 2 and a constant term of -3?
A - f(x)=2x^3-3
B - f(x)=3x^2-3x+2
C - f(x)=-3x^3+2
D - f(x)=2x^2+3x-3
Answer:
B - f(x)=3x^2-3x+2
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Degree of the quadratic function is 2.The leading co-efficient is the co-efficient of the term with highest degree (that is 2).
f(x) = 2x² + 3x - 3
This function satisfies the given condition.
The leading term is 2x² and its co-efficient is 2 and the constant term is (-3)
Is 4.1 less than or greater than 4.10 
Answer:
4.1 = 4.10
Step-by-step explanation:
Extra 0 at the end of 4.10 doesn't change the quantity of the number, so 4.1 is equal to 4.10
Write the equation of a parabola whose directrix is x = -2 and has a focus at (8,-8).
The equation of the parabola is (x - 3)² = 20(y - k)
Given data ,
To write the equation of a parabola given its directrix and focus, we can use the standard form for a parabola with a vertical axis of symmetry:
(x - h)² = 4p(y - k)
where (h, k) represents the vertex of the parabola, and the distance between the vertex and the focus is equal to the distance between the vertex and the directrix.
In this case, the directrix is x = -2 and the focus is located at (8, -8). Since the directrix is a vertical line, the parabola has a horizontal axis of symmetry.
And , the vertex lies on the axis of symmetry, which is the line equidistant between the directrix and the focus. In this case, the axis of symmetry is the vertical line x = (8 + (-2)) / 2 = 3.
So, the vertex of the parabola is (3, k), where k is yet to be determined
Next, we need to find the value of p, which represents the distance between the vertex and the focus. Since the focus is at (8, -8), and the vertex is at (3, k), the distance between them is given by
p = 8 - 3 = 5
Now, substituting the values into the standard form equation, we have:
(x - 3)² = 4(5)(y - k)
Simplifying further:
(x - 3)² = 20(y - k)
Hence , the equation of the parabola is (x - 3)^2 = 20(y - k), where k is the y-coordinate of the vertex
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Which expression is equivalent to "9 more than the quotient of x and 5
The required expression is (x / 5) + 9
Given that we have to build an equation for the statement "9 more than the quotient of x and 5,
So,
This expression represents the quotient of x divided by 5, and then adding 9 to the result.
Therefore,
"9 more than the quotient of x and 5" can be written mathematically as:
(x / 5) + 9
Hence the required expression is (x / 5) + 9
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Given l ∥ m ∥ n, find the value of x.
Answer:
-x = 17
Step-by-step explanation:
Given m||n we can write the following equation:
(5x - 23)° + (7x - 1)° = 180° because the these angles are supplementary angles.
Add like terms.(12x - 24)° = 180°
Add 24 to both sides.(12x)° = 204°
Divide both sides with 12.x = 17
Evaluate f (x)=5/2x-8 when x=4
Answer:
2
Step-by-step explanation:
f(x) = [tex]\frac{5}{2}[/tex] x - 8 ← substitute x = 4 into f(x) , then
f(4) = [tex]\frac{5}{2}[/tex] × 4 - 8 = 5 × 2 - 8 = 10 - 8 = 2