Answer:
[tex]y =-\frac{1}{2}x + 8[/tex]
Step-by-step explanation:
Given
Perpendicular to [tex]y = 2x + 1[/tex]
Pass through [tex](4,6)[/tex]
Required
Determine the line equation
First, we need to determine the slope of [tex]y = 2x + 1[/tex]
An equation is of the form:
[tex]y = mx + b[/tex]
Where
[tex]m = slope[/tex]
In this case:
[tex]m =2[/tex]
Next, we determine the slope of the second line.
Since both lines are perpendicular, the second line has a slope of:
[tex]m_1 = \frac{-1}{m}[/tex]
[tex]m_1 = \frac{-1}{2}[/tex]
[tex]m_1 = -\frac{1}{2}[/tex]
Since this line passes through (4,6); The equation is calculated as thus:
[tex]y - y_1 = m_1(x - x_1)[/tex]
Where
[tex](x_1,y_1) = (4,6)[/tex]
This gives:
[tex]y - 6=-\frac{1}{2}(x - 4)[/tex]
Open bracket
[tex]y - 6=-\frac{1}{2}x + 2[/tex]
Add 6 to both sides
[tex]y +6- 6=-\frac{1}{2}x + 2+6[/tex]
[tex]y =-\frac{1}{2}x + 8[/tex]
Fine the vertex, the axis of symmetry and the y intercept of the graph
Answer:
vertex: (-3,2) because the vertex would be the center point of the parabola
axis of symmetry: x=-3, the axis of symmetry is the the center/split in the parabola.
y-intercept: y= -1, because this is the point where the parabola crosses through the y-axis
compare the 2's in the number 212,453 use a complete sentence
Answer: the 2 at 200,000 is 100 times more than the 2 at 002,000
Step-by-step explanation:
Answer:
The 2 at the beginning of the number is in the hundred thousands place while the other 2 is in the thousands place.
Step-by-step explanation:
Starting at the number on the far right, you go up in place value to the left.
212,45(3) - ones
212,4(5)3 - tens
212,(4)53 - hundreds
21(2),453 - thousands
2(1)2,453 - ten thousands
(2)12,453 - hundred thousands
If the scores per round of golfers on the PGA tour are approximately normally distributed with mean 64.2 and standard deviation 1.39, what is the probability that a randomly chosen golfer's score is below 0 strokes?
4n2-17n+4
What is the answer
Answer:
(4n − 1)(n − 4)
Explanation:
Factor 4n² − 17n + 4
4n² − 17n + 4
= (4n − 1)(n − 4)
Answer:
(4n − 1)(n − 4)
The factors of the expression [tex]4n^2-17n+4[/tex] are
Mathematically, an expression is a combination of numbers, variables, operations, and functions that are combined according to specific rules to represent a mathematical computation or relationship. It can be thought of as a mathematical phrase or formula.
To factorize the quadratic expression [tex]4n^2 - 17n + 4[/tex], we need to find two binomial factors that, when multiplied, result in the given expression.
The factored form will have the following structure:
(An + B)(Cn + D)
To find the values of A, B, C, and D, we can use various methods such as factoring by grouping, quadratic formula, or completing the square. In this case, we will use the factoring by grouping method.
Step 1: Multiply the coefficient of the leading term (4) by the constant term (4). The result is 16.
Step 2: We need to find two numbers that multiply to give 16 and add up to the coefficient of the linear term (-17). After considering the possible pairs of numbers, we find that -16 and -1 meet these criteria.
Step 3: Rewrite the middle term (-17n) using -16n - n:
= [tex]4n^2 - 16n - n + 4[/tex]
Step 4: Group the terms and factors by grouping:
= [tex](4n^2 - 16n) - (n - 4)[/tex]
= 4n(n - 4) - 1(n - 4)
Step 5: Factor out the common binomial factor:
(n - 4)(4n - 1)
Therefore, the factored form of the quadratic expression [tex]4n^2 - 17n + 4[/tex] is (n - 4)(4n - 1).
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There are 25 students in the class. Is it possible that 6 of them have 9 friends each, 8 of them have 8 friends each, and 11 of them have 7 friends each
Answer:
It is not possible
Step-by-step explanation:
First 6 people have 9 friends and since 6 people can have totally the same friends which could all be each other, we would have 5 friends(from same 6 people) + 4 friends(not from the 6). Therefore we would have total 9 people/students
In second group of 8 people, their friends could entirely be the same be the same as the first group's friends or they could all be each other's friend hence just an additional 8 students to the population
In the third group of 11 people/students, same thing could apply as above but total number of students would always surpass 25 with the additional population. Example 9+8+11= 28
Therefore it is not possible that 25 students would each have those number of friends.
1.5 is 0.2% of what number
Answer:
750
Step-by-step explanation:
A relative value indicating hundredth parts of any quantity. 1.5 is 0.2% of 750.
What is Percentage?A relative value indicating hundredth parts of any quantity.
We need to find the number whose 1.5 is 0.2%.(one point five is zero point two percent)
Let x be the number which is 0.2% of a number 1.5.
The percentage value is converted to decimal value by dividing with 100.
0.2/100×x=1.5
zero point two divided by hundred time of x is equal to one point five.
0.002x=1.5
Divide both sides by 0.002
x=1.5/0.002
x equal to one point five by zero point zero zero two.
x=750.
x equal to seven hundred fifty.
Hence 1.5 is 0.2% of 750.
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Please Help
Solve for r.
1/3r+1=−2/3r−2
Answer:
-3
Step-by-step explanation:
Answer:
[tex]r=-3[/tex]
Step-by-step explanation:
We have the equation:
[tex]\displaystyle \frac{1}{3}r+1=-\frac{2}{3}r-2[/tex]
And we would like to solve for r.
First, we can multiply both sides by the denominator 3. This will remove the fractions. So:
[tex]\displaystyle 3(\frac{1}{3}r+1)=3(-\frac{2}{3}r-2)[/tex]
Distribute:
[tex]\displaystyle r+3=-2r-6[/tex]
Now, we can add 2r to both sides:
[tex]3r+3=-6[/tex]
And we can also subtract 3 from both sides:
[tex]3r=-9[/tex]
Finally, we can divide both sides by 3 to get:
[tex]r=-3[/tex]
1 pint = ______ cups
= 2
Which ratio is equivalent to 9: 180?
A5:200
B12:240
C10:400
D 8:560
Answer:
B: 12:240
Step-by-step explanation:
you can divide the ratios to see if they are equivalent.
9/180= 0.05 or 1/20
12/240= 0.05 or 1/20
Answer:
a
Step-by-step explanation:
If the probability of you winning a hand of poker is (11/23), how many times
should you expect to win if you play 228 times?
А
109
B
44
с
86
D
1
Answer:
109
Step-by-step explanation:
PLEASE HELP!!!!
Your friend wants to know if there is a proportional relationship between
the number of slices of ham in a sandwich and the number of calories.
Decide if the relationship between the number of slices of ham in a
sandwich and the number of calories is proportional.
Answer:
Step-by-step explanation: the answer is does not
Answer: The table does not show a proportional relationship
Step-by-step explanation: i got it right on my envision just here to help
How long does it take the kangaroo to travel 5 km
Answer:
Time taken by kangaroo to travel 5 km = 4.27 minutes.
Step-by-step explanation:
Speed of kangaroo is 44 mph.
Speed of kangaroo = 44 mph = 44 x 1.6 = 70.4 kmph = 19.5 m/s
We need to find how much time it takes to travel 5 km
Distance traveled = 5 km = 5000 m
We have
Distance traveled = Speed x Time taken
5000 = 19.5 x Time taken
Time taken = 256.41 seconds
Time taken = 4.27 minutes.
Answer:7.5
Step-by-step explanation:
The volume of this pyramid is 351 m3. If the area of the
base is 81 m² how high is the pyramid?
9514 1404 393
Answer:
13 m
Step-by-step explanation:
The volume formula is ...
V = (1/3)Bh
where B is the base area and h is the height.
Filling in the given values, we can solve for h.
351 m³ = (1/3)(81 m²)h
351/27 m = h = 13 m . . . . . divide by the coefficient of h
The height of the pyramid is 13 meters.
A particular fruit's weights are normally distributed, with a mean of 331 grams and a standard deviation of 23 grams. If you pick 15 fruits at random, then 14% of the time, their mean weight will be greater than how many grams?
Answer:
337.41366
Step-by-step explanation:
Given that:
Mean = 331 grams
Standard deviation = 23 grams
Sample size (n) = 15
P(Z < x) = 14% = 0.14
Obtain the Zscore corresponding to (1 - 0.14) = 0.86
P(z < 0.86) = 1.08
Zscore = 1.08
Zscore = (x - mean) / s/√n
1.08 = (x - 331) / 23/sqrt(15)
1.08 = (x - 331) / 5.9385744
X - 331 = 6.4136604
X = 6.4136604 + 331
X = 337.41366
Which situation represents a proportional relationship?
Answer:
A situation represents a proportional relationship if you can write equivalent ratios of related quantities in that situation.
Q
Answer:
The first one
Step-by-step explanation:
You are taking one object times per pound, x, and than adding the cost for a basket.
Tricia has $37.25 in her account. Which shows the amount she will have left after she writes a check for $23.99?
A. $12.36
B. $12.74
C. $13.26
D. $13.74
The amount she will have left after writing a check for $23.99 is $13.26. The correct answer would be an option (C).
What is the Subtraction operation?Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
Tricia has $37.25 in her account, if she writes a check for $23.99, to find the amount left after that we need to subtract the check amount from her initial amount.
⇒ initial amount - check amount
⇒ $37.25 - $23.99
Apply the subtraction operations, and we get
⇒ $13.26
Therefore, the amount she will have left after writing a check for $23.99 is $13.26.
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which of the following sets of numbers could represent the three sides of a triangle?\
{10,21,32}
{13,17,32}
{14,24,40}
{13,16,27}
Answer:
14,24,40
Step-by-step explanation:
u cute
Answer:25 = 25 Right Triangle. 3, 7 and 9 Squaring each side = 9, 49 and 81. sum of the squares of the short sides = 9 + 49 = 58. 58 < 81 Obtuse Triangle. For determining if the 3 sides can even form a triangle, the triangle inequality theorem states that the longest side must be shorter than the sum of the other 2 sides.
Step-by-step explanation:
Kevin wants to plant grass in his backyard. His backyard is in the shape of a rectangle. Its length is 28 feet and its width is 25 feet. Suppose each pack of seed
covers 14 square feet. How many packs of seed will he need to cover the backyard?
Answer:
50 packs.
Step-by-step explanation:
Given the following data;
Length = 28 feet
Width = 25 feet
Pack of seeds = 14 ft²
Since Kevin's backyard is a rectangle, we would find its area.
Area of rectangle = length * width
Substituting into the equation, we have;
Area of rectangle = 28 * 25
Area of rectangle = 700 ft²
Now to find the amount of pack of seeds required to cover the backyard.
Amount of pack of seeds = 700/14
Amount of pack of seeds = 50 packs.
it is the rate of change in angle measure of a unit of time
Answer:
j
Step-by-step explanation:
j
Which will have a higher effective interest rate - a payday loan for $1500 that
is due in 12 days with a fee of $90, or a payday loan for $1500 that is due in
10 days with a fee of $90?
A. A payday loan for $1500 that is due in 12 days with a fee of $90,
since it has the shorter period
B. A payday loan for $1500 that is due in 10 days with a fee of $90,
since it has the shorter period
C. A payday loan for $1500 that is due in 10 days with a fee of $90.
since it has the longer period
D. A payday loan for $1500 that is due in 12 days with a fee of $90,
since it has the longer period
Answer:
B. A payday loan for $1500 that is due in 10 days with a fee of $90, since it has the shorter period
The higher effective interest rate is for A payday loan for $1500 that is due in 10 days with a fee of $90, since it has the shorter period, the correct option is B.
What is Interest Rate?Interest Rate is the rate at which a person either takes loan, or a person lends money to somebody.
The interest rate is different for different types of loans, some interest are simply calculated on the principal, called as Simple Interest while some are calculated on both the principal and the interest, called as Compound Interest.
A payday loan has principal of $1500
It is due in 12 days, so time period is 12 days.
The interest amount is $90
I = P * R *T / 100
90 = 1500 *12 *R /100
R = 0.5 %
A payday loan has principal of $1500
It is due in 10 days, so time period is 10 days.
The interest amount is $90
90 = 1500 *10 *R /100
R = 0.6 %
The rate of interest is more for a payday loan for $1500 that is due in
10 days with a fee of $90.
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how to find rations in triangles
Answer:
When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles.
Step-by-step explanation:
Caleb started with 50 bacteria for his science experiment, and the number of bacteria doubled in one day. Jenna also started with 50 bacteria for her experiment, and after one day the number of bacteria was equal to 50 to the second power. Who had more bacteria at the end of one day?
Answer:
100+50²=2600
Step-by-step explanation:
because 50x2=100 and 50² is 2500. Add those and you get 2600.
Which ratio of the lines' slopes equals 1/2
Answer:
[tex]\frac{a}{b}[/tex]
Step-by-step explanation:
For this problem, if we really wanted to be precise, we could go through and do the slope equation for all of the lines. However, this graph is clear enough that we can just count the points.
On line A, we can just follow the line and see that the slope is -1 because each point goes down 1 and over 1.
Line B has a slope of -2. It goes down 2 and over 1.
Line C has a slope of 2; up 2 and over 1.
If we look at our three slopes, -1, -2, and 2, we can see that the only way for the ratio to be 1/2 is for line A over line B. This is because a negative over a negative is a positive.
Hope this helps!
Can y’all please help me with this y=-16 + 29t+ 6
Answer: m=29
Step-by-step explanation:
Jackson buys a case of bottled water for $3.96. If there are 18 bottles in thecase, what is the unit cost of the water?
Answer:
$66.42
Step-by-step explanation:
you have to multiply $3.96 by 18
Please hurry I need this fast
Answer: It is 4,7 to show this draw a graph and then flip it to see its reflection
what is the median for 9, 1, 9, 6, 5 and for 2, 10, 7, 1
Answer:
median for 9,1,9,6,5 is 6 and for 2,10,7,1 is 4 1/2
I got it by lining up the first numbers 1,5,6,9,9 and 6 was middle second one i lined it up 1,2,7,10 and 2 and 7 were middle so added them together and divided by 2 and got 4 1/2
Brainliest
Does changing the compound inequality x>-3 and x<3 from and" to or change the soluion set? Explain
Answer:
Yes
Step-by-step explanation:
If you look at it. X is basically -2, -1, 0, 1, or 2.
Hope I helped and Pls Mark Brainliest
need this by today! Pls help! Im desperate! I will give correct anwser brainliest!
Which expressions have a value of 128 when x=4?
Answer: Create equivalent expressions in the equation that all have equal bases.
2
2
x
=
2
7
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
2
x
=
7
Divide each term by
2
and simplify.
Divide each term in
2
x
=
7
by
2
.
2
x
2
=
7
2
Cancel the common factor of
2
.
Cancel the common factor.
2
x
2
=
7
2
Divide
x
by
1
.
x
=
7
2
The result can be shown in multiple forms.
Exact Form:
x
=
7
2
Decimal Form:
x
=
3.5
Step-by-step explanation: Brainless, please
Correct expressions : [tex]x^4/2[/tex] and [tex]8x^2[/tex] .
Hence option B and E are correct .
Given, expression will yield 128 when x = 4 .
Expression B :
[tex]x^4/2[/tex]
Put x = 4
[tex]\frac{4^4}{2}\\ = 128[/tex]
Expression E :
[tex]8x^2[/tex]
Put x = 4
[tex]8(4^2)\\= 128[/tex]
Therefore option B and E are correct .
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