The answer is (D) (7, 3), (9, 7) and (8, 3) when A triangle with vertices (2, 3), (4, 7), and (3, 3) is translated a distance of 5 units to the right.
To translate a two-dimensional figure such as a triangle, we move all its points a certain distance in a certain direction. In this case, we need to move the triangle 5 units to the right. This means we need to add 5 to the x-coordinate of each vertex, while leaving the y-coordinate unchanged.
In this case, we need to add 5 units to the x-coordinates of each vertex of the triangle.
The new coordinates of the triangle's vertices would be:
(2+5, 3) = (7, 3)
(4+5, 7) = (9, 7)
(3+5, 3) = (8, 3)
Therefore, the answer is (D) (7, 3), (9, 7) and (8, 3).
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The complete question is :
A triangle with vertices (2, 3), (4, 7), and (3, 3) is translated a distance of 5 units to the right. What are the new coordinates?
A.(-3, 3), (-1, 7), (-2, 3)
B.(2, -2), (4, 2), (3, -2)
C.(2, 8), (4, 12), (3, 8)
D.(7, 3), (9, 7) and (8, 3)
The demand for a product is given by p+5q= 380 or, q = (380-p)/5 and the supply for this product is given by p-3q = 172 or, q = (p-172)/3 The price at which the quantity demande
Answer:
The equilibrium price is $250.
The equilibrium quantity is 26 units.
Step-by-step explanation:
To find the equilibrium price, we need to find the price at which the quantity demanded equals the quantity supplied. This occurs when q (quantity demanded) equals q (quantity supplied).
So, we can set the two equations for q equal to each other:
(380-p)/5 = (p-172)/3
To solve for p, we can cross-multiply and simplify:
3(380-p) = 5(p-172)
1140 - 3p = 5p - 860
1140 + 860 = 8p
2000 = 8p
p = 250
Therefore, the equilibrium price is $250. We can plug this value back into either equation for q to find the equilibrium quantity.
Using q = (380-p)/5, we get:
q = (380-250)/5 = 26
So the equilibrium quantity is 26 units.
Two cross sections the same or different
Shape
Answer:same
Step-by-step explanation:because I said so
A toy company is building dollhouse furniture. A rectangle door of a dollhouse has a height of 7 centimeters and a width of 3 centimeters. What is the perimeter of the door on a scale drawing that uses the scale 3.5?
Answer: To find the perimeter of the door on a scale drawing, we need to first determine the dimensions of the door on the scale drawing.
If the actual height of the door is 7 centimeters, then the height on the scale drawing will be:
7 cm ÷ 3.5 = 2 cm
Similarly, if the actual width of the door is 3 centimeters, then the width on the scale drawing will be:
3 cm ÷ 3.5 = 0.857 cm
Now we can use these dimensions to find the perimeter on the scale drawing:
Perimeter = 2 × (height + width) = 2 × (2 cm + 0.857 cm) = 2 × 2.857 cm = 5.714 cm
Therefore, the perimeter of the door on the scale drawing is 5.714 centimeters.
If you have anymore questions, feel free to comment and I will help you.
The function g(x) is shown on the graph.
What is the equation of g(x) in vertex form?
g(x) = (x − 4)2 − 3
g(x) = (x − 4)2 + 3
g(x) = (x + 4)2 − 3
g(x) = (x + 4)2 + 3
Answer:
The correct answer is g(x) = (x+4)2+3
Step-by-step explanation:
The graph is sifted 3 units up and 4 units left.
Tom wishes to purchase a property that has been valued at $300,000. He has 25% of this amount available as a cash deposit, and will require a mortgage for the remaining amount. The bank offers him a 25-year mortgage at 2% interest. Calculate his monthly payments.
Round your answer to the nearest cent.
Do NOT round until you have calculated the final answer.
so hmmm 25% of that 300,000 is going as a downpayment, so he need the loan for the remaining 75% of that hmmm
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{75\% of 300000}}{\left( \cfrac{75}{100} \right)300000}\implies 225000[/tex]
so for that much, so since he'll be making monthly payments, the compounding period will be monthly, now, we're assuming the payments are at the end of each month.
[tex]~~~~~~~~~~~~\underset{\textit{payments at the end of the period}}{\textit{Payments of an ordinary annuity}} \\\\ pmt=A\left[ \cfrac{\frac{r}{n}}{\left( 1+\frac{r}{n} \right)^{nt}-1} \right][/tex]
[tex]\begin{cases} A=\textit{accumulated amount}\dotfill &225000\\ pmt=\textit{periodic payments}\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &25 \end{cases}[/tex]
[tex]pmt=225000\left[ \cfrac{\frac{0.02}{12}}{\left( 1+\frac{0.02}{12} \right)^{12 \cdot 25}-1} \right] \\\\\\ pmt=225000\left[ \cfrac{\frac{1}{600}}{\left( \frac{601}{600} \right)^{300}-1} \right]\implies pmt\approx 578.67[/tex]
Find the sum of the first n terms
using the formula:
a(1-r^n)/1-r
1, 5/3, 25/9, 125/27, 625/81
This would be a big help
The total of the first four terms is thus 8/3.
What does sum mean?The outcome of adding two or even more numbers or phrases is known as the sum in mathematics. The sum is a method of bringing things together as a result. To put it another way, adding any number of numbers together results in a previous result or total.
The sum of a Fibonacci sequence that has the initial component a = 1 and the general ratio r = 5/3 is determined using the formula you gave.
We enter these numbers into the formula to determine the sum of the initial n terms:
S(n) = [tex]a(1-r^n)/(1-r)[/tex]
S(n) = [tex]1(1-(5/3)^n)/(1-5/3)[/tex]
S(n) = [tex]3/2(1-(5/3)^n)[/tex]
So, we add n to this formula to get the sum of the initial n terms of a given sequence:
S(n) = [tex]3/2(1-(5/3)^n)[/tex]
For instance, we replace n = 4 to get the sum of the initial four terms:
S(4) = [tex]3/2(1-(5/3)^4)[/tex]
S(4) = 3/2(1-625/81)
S(4) = 3/2(144/81)
S(4) = 72/27
S(4) = 8/3
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The total of the first four terms is thus 8/3.
What does sum mean?The outcome of adding two or even more numbers or phrases is known as the sum in mathematics. The sum is a method of bringing things together as a result. To put it another way, adding any number of numbers together results in a previous result or total.
The sum of a Fibonacci sequence that has the initial component a = 1 and the general ratio r = 5/3 is determined using the formula you gave.
We enter these numbers into the formula to determine the sum of the initial n terms:
S(n) = [tex]a(1-r^{n} )/(1-r)[/tex]
S(n) = [tex]1(1-(5/3)^{n} /(1-5/3)[/tex]
S(n) = [tex]3/2(1-(5/3)^{n} )[/tex]
So, we add n to this formula to get the sum of the initial n terms of a given sequence:
S(n) = 3/2(1 - [tex](5/3)^{n}[/tex] )
For instance, we replace n = 4 to get the sum of the initial four terms:
S(4) = [tex]3/2(1-(5/3)^{4} )[/tex]
S(4) = 3/2(1-625/81)
S(4) = 3/2(144/81)
S(4) = 72/27
S(4) = 8/3
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complete ques is:
Find the sum of the first n terms ( 1,2,3,4,5.......n)
using the formula:
a(1-r^n)/1-r
1, 5/3, 25/9, 125/27, 625/81
A natural history museum surveyed the people visiting the museum for one month and created a circle graph to show the age of the visitors for that month.
If 5000 people visited the museum during the month the survey was taken, how many visitors were there for each age group?
Age 18 and under:
Age 19 – 44:
Age 45 – 64:
Age 65 and over:
Will give brainliest
In the circle below, suppose ark KLI = 247 deg and m angle LKJ = 124 deg . Find the following.
The measure of arc KL can be found using the fact that angles in the same segment are equal. The angles m arc KL = m arc KLI = 247 degrees.
What is circle?In geοmetry, a circle is a twο-dimensiοnal shape cοnsisting οf all pοints that are a fixed distance (called the radius) frοm a given pοint (called the center). A circle is a set οf pοints that are equidistant frοm the center. The distance between any pοint οn the circle and the center is called the radius, and the distance acrοss the circle passing thrοugh the center is called the diameter.
The measure of angle JLI can be found using the fact that angles on a straight line add up to 180 degrees. Therefore,
m angle JLI = 180 - m angle LKJ = 180 - 124 = 56 degrees.
The measure of arc JKI can be found using the fact that the measure of an inscribed angle is half the measure of the arc it intercepts. Therefore,
m arc JKI = 2 * m angle JLI = 2 * 56 = 112 degrees.
Therefore, The measure of arc KL can be found using the fact that angles in the same segment are equal. The angles m arc KL = m arc KLI = 247 degrees.
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Simplify
to a single trig function with no fractions.
The simplified cos(t)/sec(t) to the trig function 1 - sin²(t), which is equivalent to cos²(t).
Recall that the secant function is defined as the reciprocal of the cosine function. In other words, sec(t) = 1/cos(t). Therefore, we can rewrite cos(t)/sec(t) as cos(t)/(1/cos(t)).
To simplify this expression, we can multiply both the numerator and the denominator by cos(t), which gives:
cos(t)/(1/cos(t)) = cos(t) * (cos(t)/1) = cos²(t)
Now, we have simplified cos(t)/sec(t) to cos²(t). Alternatively, we could have used the identity cos²(t) = 1 - sin²(t) to simplify the expression. This identity follows directly from the Pythagorean identity cos²(t) + sin²(t) = 1.
Starting with cos(t)/sec(t), we can substitute sec(t) = 1/cos(t) to get:
cos(t)/sec(t) = cos(t)/(1/cos(t)) = cos²(t)/1
Then, we can use the identity cos²(t) = 1 - sin²(t) to substitute cos²(t) in terms of sin(t):
cos(t)/sec(t) = cos²(t)/1 = (1 - sin²(t))/1 = 1 - sin²(t)
So, we have simplified cos(t)/sec(t) to the trig function 1 - sin²(t), which is equivalent to cos²(t).
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What is entrepreneurs education
Answer: What an entrepreneur really is, though, is someone who runs their own business and takes a risk to do it.
Step-by-step explanation:
I need help with the graph about it increasing and decreasing!!
Answers:
Increasing: [tex](-1.5, 2)[/tex]
Decreasing: [tex](-\infty,-1.5) \cup (2,\infty)[/tex]
==================================================
Explanation:
A function curve is considered increasing when moving uphill as you move to the right.
We're going uphill on the interval [tex]-1.5 < \text{x} < 2[/tex] which translates to the interval notation [tex](-1.5, 2)[/tex]. Be sure not to confuse this with ordered pair notation which unfortunately looks identical. The curved parenthesis are used to exclude each endpoint.
-------------
When moving to the right, we go downhill on two separate regions:
When x < -1.5, aka [tex]-\infty < \text{x} < -1.5[/tex]When x > 2, aka [tex]2 < \text{x} < \infty[/tex]The first portion translates to the interval notation [tex](-\infty,-1.5)[/tex]
The second portion translates to [tex](2,\infty)[/tex]
We glue those regions together with a union symbol to get [tex](-\infty,-1.5) \cup (2,\infty)[/tex]
The union symbol basically means "or" when it comes to interval notation. So we are decreasing on the interval [tex](-\infty,-1.5)[/tex] or decreasing on the interval [tex](2,\infty)[/tex]
Please help its an emergency! Will give Brainliest! What is the arc length of an arc with radius 18 inches and central angle 22°? Round to nearest hundredth or leave in terms of π. Show your work.
Answer: 6.28 cm
Step-by-step explanation:
What is the solution of x-1/x^2 +5x+4 less than or equal to 0
Answer:
[tex]x-1/x^2 +5x+4[/tex] = no real value
Step-by-step explanation:
Step 1 : Multiply through by x^2
[tex]x^{2} -1 +5x^{3}+ 4x^{2}[/tex]
Step 2 : Collect like terms
[tex]5x^{3}+5x^{2} -1\geq 0[/tex]
Step 3 : Ignore the sign and solve for x
[tex]5x^{3} +5x^{2} -1 = 0\\x =0.380609458\\x= 0.4(2dp)[/tex]
Step 4 : Input back into the equation
Step 5: This shows that x-1/x^2 +5x+4 has no real values.
1. Solve: (6 + 3)2 – 17 × 3 + 70
The solution of this expression is 37
Numerical expressionsTo solve this, first calculate the operations in parentheses.
Then perform the other operations, following the order of resolution
[tex]\begin{array}{l}\sf (6 + 3)2-17\times 3 + 70\\\sf 9\times 2-51+ 70\\\sf 18-51+ 70\\\sf 88-51\\\therefore \bf 37\end{array}[/tex]
For this expression, the result is 37
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Steven sold 10 cabbages at K2.00 each, 20 heaps of kaukau at K5 each, and 10 heaps of potato at K3.00 each. What is Steven's total earning?
Answer:
K150
Step-by-step explanation:
10 x K2.00 = K20.00
20 x K5.00 = K100.00
10 x K3.00= K30.00
20+100+30= K150
Refer to trapezoi EFGH WITH MEDIAN IJ if IJ=X,Hg=8 abd EF=12 what is the value of x
Answer:
x = 10
Step-by-step explanation:
A trapezoid is a quadrilateral with one pair of parallel sides.
The median of a trapezoid connects the midpoint of the non-parallel sides.
IJ is the median of the trapezoid. I is the midpoint of EH, and J is the midpoint of GF.
Also, the median of a trapezoid is also parallel to the parallel sides. IJ║ HG║ EF.
(The proof of this is extensive and requires drawing additional lines such as HJ and extending EF further until HJ and EF intersect at another point, Y. It is given as the other diagram. You also need prior knowledge of the midsegment of a triangle.)
The measure of the midsegment of a trapezoid, by definition, is also equal to the average of the measure of the parallel segments.
In the figure,
[tex]IJ=\dfrac{(HG+EF)}{2}[/tex]
Substituting the values we have, HG = 8, EF = 12 gives us:
[tex]IJ=\dfrac{(HG+EF)}{2}[/tex]
[tex]IJ=\dfrac{(8+12)}{2}[/tex]
[tex]IJ=\dfrac{20}{2}[/tex]
[tex]IJ=10[/tex]
IJ is 10 units.
Help!!
Question
Triangle ABC is similar to triangle DEF. The length of BC¯¯¯¯¯ is 44 cm. The length of DE¯¯¯¯¯ is 14 cm. The length of EF¯¯¯¯¯ is 22 cm.
What is the length of AB¯¯¯¯¯?
Enter your answer in the box.
cm
The length of AB which is the missing length side of the similar triangles would be = 28 cm.
How to calculate the missing length of a triangle?To calculate the missing length of the triangle = AB , the scale factor should be determined.
The scale factor that exists between two similar object shows the number of times the original object can be found in the new formed one.
The scale factor = dimensions of new object/ dimensions of original object.
A side of original = EF =22cm
A side of the new triangle = BC = 44
Scale factor = 44/22 = 2
Therefore the missing length of the new triangle = 14×2 = 28cm
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X - 0 , 2 , 4 , 6 , 8 , 10 , 12
Y - 18 , 15 , 13 , 10 , 7 , 5 , 1
1. Use GeoGebra Calculator Suite linked on the
task page to create a scatterplot of the data.
Post your screenshot of the scatterplot in the space provided below.
2. Use the same calculator linked on the task page to:
find the equation of the best-fit line,
draw the line, and
show the equation.
Post the screenshot of the graph in the space provided below.
The equation of the best-fit line is:
Write the equation of the line that passes through the points (3, -4) and (7, 6). Put
your answer in fully simplified point-slope form, unless it is a vertical or horizontal
line.
Answer:
Step-by-step explanation:
To write the equation of the line that passes through the points (3, -4) and (7, 6), we can follow these steps:
Step 1: Find the slope of the line
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
slope = (y2 - y1) / (x2 - x1)
Plugging in the given values, we get:
slope = (6 - (-4)) / (7 - 3)
slope = 10 / 4
slope = 5 / 2
Step 2: Use point-slope form to write the equation of the line
Point-slope form of a line with slope m passing through a point (x1, y1) is given by:
y - y1 = m(x - x1)
We can use either of the given points to write the equation. Let's use (3, -4):
y - (-4) = (5/2)(x - 3)
Simplifying this equation, we get:
y + 4 = (5/2)x - (15/2)
Subtracting 4 from both sides, we get:
y = (5/2)x - (23/2)
This is the equation of the line in point-slope form.
Step 3: Simplify the equation if it is not in point-slope form
The equation we obtained in step 2 is already in point-slope form, so we do not need to simplify it any further.
Note: If the line was horizontal (i.e., it had zero slope), then its equation would be y = constant, where the constant is the y-coordinate of any point on the line. If the line was vertical (i.e., its slope was undefined), then its equation would be x = constant, where the constant is the x-coordinate of any point on the line.
Helena wants to change the figure shown into two or more figures so she can
more easily find the area. Draw a line or lines to show what she could do. Then
write an expression for the area of each smaller figure. Write an expression for
the total area of the figure. Explain.
The expressiοn fοr each area is 28x²-35x ( rectangle ), 9x² ( square ), and 37x²-35x ( tοtal area ).
What is the tοtal area?A sοlid οbject's surface area is a measurement οf the οverall space that the οbject's surface takes up. The tοtal area includes bοth the Carpet Area and Exclusive Areas as well as all οther lands within the Prοperty's perimeter bοrders.
Here, we have
Given: Helena wants tο change the figure shοwn intο twο οr mοre figures sο she can mοre easily find the area.
The figure is cοmpοsed οf a square and a rectangle. See the attached image.
Therefοre, yοu shοuld sum the area οf these geοmetric figures fοr determining the area οf the irregular figure.
Area οf the rectangle = bh.
The figure shοws that the sides fοr this rectangle are equal tο 4x-5 and (4x+3x). Then,
b = length οf the base= 4x-5
h = height = 4x+3x = 7x
A rectangle = bh = (4x-5)*7x = 28x²-35x
Area οf the square = l². The figure shοws that the sides fοr this square are equal tο 3x
l = length οf the side= 3x
Thus, A square = l² = (3x)² =9x²
We have tο find an expressiοn fοr the tοtal area οf the figure.
A tοtal= A rectangle+ A square
A tοtal= 28x²-35x+9x²
A tοtal= 37x²-35x
Hence, The expressiοn fοr each area is 28x²-35x ( rectangle ), 9x² ( square ), and 37x²-35x ( tοtal area ).
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The following are reasons to put your money in a saving account. (Check all that apply)
Money collects interest.
Get a rebate back in the mail.
Money is safe and insured.
The cοrrect respοnse is that mοney cοllects interest and mοney is safe and insured.
Why nοt explain interest?The fee yοu spend tο bοrrοw the mοney οr the fee yοu pay tο lend the mοney is called interest. Interest is frequently calculated as a yearly percentage οf the amοunt bοrrοwed. This percentage represents the lοan's interest rate.
The interest fοrmula is what?Interest equals P, R, and T is the fundamental interest fοrmula. P is the initial value (the beginning balance). Rate οf Interest, R (usually per year, expressed as a decimal). T is the sum οf all time frames (generally οne-year time periοds).
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Determine the equation of the ellipse with foci (2, 4) and (2, -8), and co-vertices
(10,-2) and (-6, -2).
The equation of ellipse with foci (2, 4) and (2, -8) and co-vertices (10, -2) and (-6, -2) is ((x - 2)^2 / 64) + ((y + 2)^2 / 36) = 1
What is the equation of ellipseTo find the equation of the ellipse, we first need to determine the center of the ellipse. Since the foci are on the same vertical line, the center of the ellipse is at the midpoint of the segment connecting the foci.
The midpoint of the segment connecting the foci is:
((2+2)/2, (4-8)/2) = (2, -2)
So the center of the ellipse is (2, -2).
Next, we need to determine the lengths of the semi-major and semi-minor axes. The semi-major axis is half the distance between the co-vertices, which is:
a = (10 - (-6))/2 = 8
The semi-minor axis is half the distance between the foci, which is:
c = (4 - (-8))/2 = 6
Now we can use the standard form of the equation of an ellipse centered at (h,k):
((x - h)^2 / a^2) + ((y - k)^2 / b^2) = 1
where a is the length of the semi-major axis and b is the length of the semi-minor axis.
Plugging in the values we have:
((x - 2)^2 / 8^2) + ((y + 2)^2 / 6^2) = 1
Simplifying and rearranging:
((x - 2)^2 / 64) + ((y + 2)^2 / 36) = 1
So the equation of the ellipse is:
((x - 2)^2 / 64) + ((y + 2)^2 / 36) = 1
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PZ HURRY 15 POINTS
At a recent football game of 8,450 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Relish Chili
54 36 60
Based on the data in this sample, how many of the people in attendance would prefer ketchup on a hot dog?
4,225
3,380
3,127
3,042
It can be estimated that approximately 3,042 people in attendance would prefer ketchup on a hot dog.
Thus, the correct answer is 3,042.
To determine how many people in attendance would prefer ketchup on a hot dog based on the data from the sample, we need to calculate the proportion of people who prefer ketchup and apply it to the total attendance.
The sample indicates that out of 150 people surveyed:
54 people prefer ketchup
36 people prefer relish
60 people prefer chili
To find the proportion of people who prefer ketchup, we divide the number of people who prefer ketchup by the total number of people surveyed:
Proportion of people who prefer ketchup = 54 / 150 = 0.36
Now, to estimate the number of people in attendance who would prefer ketchup on a hot dog, we multiply the proportion calculated above by the total attendance:
Estimated number of people who prefer ketchup = 0.36 [tex]\times[/tex] 8,450 = 3,042
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2. The back of Nico's truck is 7 feet long, 4 feet wide, and 8 feet tall. He has several boxes of important papers that he needs to move. Each box of papers is shaped like a cube, measuring 1 foot on each side. K How many boxes of papers can Nico pack into the back of his truck? Show your work. (Try drawing a picture of the back of the truck and how many boxes can stack in there to help you see the answer better. Possible extra credit for your drawing.) Answer:
Based on division operation, the number of boxes of papers that the back of Nico's truck can stack in is 224.
What is division operation?Division operation is one of the four basic mathematical operations, including addition, subtraction, and multiplication.
Division operation involves the dividend divided by the divisor to produce a result known as the quotient.
In this situation, the volume of Nico's truck is determined as the dividend. The volume of each box of paper is determined as the divisor.
The result of the division operation is the quotient showing the number of boxes the truck can contain.
The length of Nico's truck = 7 feet
The width of Nico's truck = 4 feet
The height of Nico's truck = 8 feet
The volume that Nico's tuck can contain = 224 cubic feet (7 × 4 × 8)
= 224 feet³
The length of each box = 1 foot
The width of each box = 1 foot
The height of each box = 1 foot
The volume of each box of papers = 1 feet³ (1 × 1 × 1)
The number of boxes the truck can contain = 224 boxes (224/1)
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Kira is installing a railing that is 35 inches above the ramp Let each be the height of the railing from the ground and all be the height of the ramp from the ground which equation represents the situation
Alternatively, if we want to solve for r in terms of h, we can rearrange the equation as follows: r = h - 35
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
Let h be the height of the railing from the ground and let r be the height of the ramp from the ground.
We are given that the railing is 35 inches above the ramp, which means that the total height of the railing from the ground is h = r + 35.
So the equation that represents the situation is:
h = r + 35
Therefore, Alternatively, if we want to solve for r in terms of h, we can rearrange the equation as follows: r = h - 35
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(-50) ÷ what is -1, number in the blank will be
What is 24 and 816,000 equals blank divided by 10 to the fifth power
Answer: We have the equation:
24,816,000 = x / 10^5
To solve for x, we can multiply both sides by 10^5:
24,816,000 * 10^5 = x
Using a calculator or long multiplication, we can simplify this to:
2,481,600,000,000 = x
Therefore, 24,816,000 is equal to 2,481,600,000,000 divided by 10 to the fifth power.
Step-by-step explanation:
The perihelion is?
The equation for the orbit of planet A around the sun is?
The perihelion is the point in a planet's orbit where it is closest to the sun.
The equation for the orbit of a planet around the sun depends on various factors, such as the shape of the orbit, the mass of the planet, and the gravitational force between the planet and the sun. Kepler's laws of planetary motion provide a framework for understanding the motion of planets in orbit, and the equations used to describe these orbits are generally based on these laws. The specific equation for the orbit of planet A would depend on the specific parameters of that planet's orbit.
Use the word bank to help identify each part of the quadrilateral.
word bank: base, leg, parallel, midsegment, angle, diagonal, side.
answered
Find the points on the line x=1
where the circle with equation
2x²+2y²-5x+7y-36-0 intersect
Answer: To find the points where the circle intersects the line x=1, we substitute x=1 in the equation of the circle:
2(1)² + 2y² - 5(1) + 7y - 36 = 0
Simplifying, we get:
2y² + 7y - 31 = 0
We can solve this quadratic equation by using the quadratic formula:
y = (-7 ± √(7² - 4(2)(-31))) / (2(2))
y = (-7 ± √225) / 4
y = (-7 ± 15) / 4
So the two possible values of y are:
y = 2 or y = -8/2 = -4
Therefore, the points where the circle intersects the line x=1 are (1, 2) and (1, -4).
Step-by-step explanation: