All categories

3 years ago

If VW≅VY, WX = s + 69, and XY = 4s, what is the value of s?

Mathematics

1 answer:

Katen [24]3 years ago

7 0

Answer:

s = 23

Step-by-step explanation:

1. VW ≅ VY is given.

2. XV ≅ VX as it is the same side.

3. ∠WVX ≅ ∠YVX as they are both 90°. ∠WVY is 180° as it is a straight line, so both ∠WVX and ∠YVX are exactly half of that.

Given those three things, you can say that ΔWVX ≅ ΔYVX. Because all corresponding parts of congruent triangles are also congruent, you can be sure that WX ≅ XY. Finally, using that information, you can write an equation and solve for s.

$s+69=4s\\s-s+69=4s-s\\69=3s\\\frac{69}{3}=\frac{3s}{3}\\s=23$

You might be interested in

The ratio of boys to girls is 5:6 if there are72 girls what is the total number of students

Irina18 [472]

72 represents 6 "units", so divide by 6 to get the number of people in one "unit":

72/6 = 12

Now multiply by 5 to get the number of boys:

12 * 5 = 60 boys

5 0

3 years ago

Write the inverse of h(x) = e 2x h -1(x) = log e2 x 2log ex ½log ex

svp [43]

Answer:

Step-by-step explanation:

So we have the function:

$h(x)=e^{2x}$

To find the inverse, switch h(x) and x, change h(x) to h⁻¹(x), and solve for it. Thus: "

$x=e^{2h^{-1}(x)}$

So, take the natural log (log to base e) of both sides:

$\ln(x)=\ln(e^{2h^{-1}(x)})$

The right side will cancel:

$\ln(x)=2h^{-1}(x)$

Divide both sides by 2:

$h^{-1}(x)=\frac{1}{2}\ln(x)$

And we're done!

Our answer is C

Note:

$\ln(x)=\log_ex$

6 0

3 years ago

A local fast food restaurant takes in $9000 in a 4 hour period, where the amount taken in varies directly with the number of hou

Zepler [3.9K]

As per the direct variation formula, it take 11 hours : 6 minutes : 36 seconds to earn $25,000 for the restaurant.

Direct variation:

Direct Variation is said to be the relationship between two variables in which one is a constant multiple of the other.

Direct variation equation: y = kx

Given,

A local fast food restaurant takes in $9000 in a 4 hours period. Write a direct variation equation for the relationship income and number of hours.

Here we need to estimate how many hours it would take the restaurant to earn $25,000.

a) Let us consider income (I) directly varies to number of hours (h) where k is the constant of variation.

I = kh ⇒ Direct variation equation

Solve for k:

9,000 = (k)(4)

k = 9,000/4

k = 2,250

b) When income (I) = 25,000, find the number of hours:

I = kh

25,000 = (2,250) (h)

h = 25,000/2,250

h = 11.11

It will take approximately 11 hours : 6 minutes : 36 seconds for the restaurant to earn $25,000.

To know more about Direct variation here.

brainly.com/question/14254277

#SPJ1

4 0

1 year ago

line y = 2x+1 is transformed by a dialation with a scale factor of two and centered at (0,-4). what is the equation of the image

Gekata [30.6K]

Answer: y = 2x + 6

Step-by-step explanation:

Here the equation of line,

y = 2x + 1

y-intercept of the line is, (0, 1)

And, the slope of the line is 2.

Since, If a point (x,y) is dilated by a scale factor k about a point (a,b),

Then transformed point are get by,

$(x,y)\rightarrow (k(x-a)+a, k(y-b)+b)$

Thus, The transformed point of point (0,1) when dilation is occur by the scale factor 2 about the point (0,-4),

$(0,-4)\rightarrow (2(0-0)+0, 2(1+4)-4)$

$(0,-4)\rightarrow (0, 6)$

Thus, the point of the new line is (0,6)

And, the slope of the new line is 2 ( because in the dilation, the slope of the line does not change)

Thus, the equation of new line,

(y - 6) = 2 (x - 0)

y - 6 = 2x

y = 2x + 6

5 0

3 years ago

Gravel is being dumped from a conveyor belt at a rate of 30 ft3/min, and its coarseness is such that it forms a pile in the shap

pogonyaev

Answer:

Rate of increase in height = $\frac{dh}{dt}=0.3156ft/min$

Step-by-step explanation:

we know that volume of a cone is given by

$V=\frac{1}{12}\pi d^{2}h$

It is Given that diameter equals height thus we have

$V=\frac{1}{12}\pi h^{2}h\\\\V=\frac{1}{12}\pi h^{3}$

Differentiating both sides with respect to time we get

$\frac{dV}{dt}=\frac{1}{12}\pi \frac{dh^{3}}{dt}\\\\\frac{dV}{dt}=\frac{1}{12}\pi(3h^{2}\frac{dh}{dt})$

Applying values and solving for $\frac{dh}{dt}$ we get

$\frac{dh}{dt}=\frac{12\frac{dV}{dt}}{3\pi h^{2}}\\\\\frac{dh}{dt}=0.3156ft/min$

8 0

3 years ago