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3 years ago

What is the value of h in the diagram below? If necessary, round your answer

Mathematics

1 answer:

poizon [28]3 years ago

5 0

Answer:

A - 8.1

Step-by-step explanation:

This is an example of similar shapes.

The length of MO is 18, and PO is 5.

So length of MP is 13. (18 - 5)

We need to separate this large triangle into 2 triangles:

Triangle NMP

Triangle NPO

In problems including similar shapes, our unknown needs to be on top of the fraction in an equation.

NP (h) /

${\frac{NP}{MP}$ = $\frac{PO}{NP}$

$\frac{h}{13}$ = $\frac{5}{h}$

Cross multiply

h² = 65

h = √65

h = 8.06

h = 8.1 (rounded)

Drawn out explanation below.

Hope this has answered your question.

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Two cars that are 150 miles apart start driving toward each other on parallel roads. The average speed of the first car is 60 mi

Semmy [17]

Answer:

60T + 55T = 150

Step-by-step explanation:

$T(60+55)=150\\115T=150$

$T=150/115=1.304 hr$

The cars takes 1.304 hrs (1h 18 min aprox) to pass each other

Hope this helps

5 0

2 years ago

What basic trigonometric identity would you use to verify that sin^2x +cos^2x/cos x = sec x

gogolik [260]

<u>Answer:</u>

The basic identity used is $\bold{\sin ^{2} x+\cos ^{2} x=1}$ .

<u>Solution: </u>

In this problem some of the basic trigonometric identities are used to prove the given expression.

Let’s first take the LHS:

$\Rightarrow \frac{\sin ^{2} x+\cos ^{2} x}{\cos x}$

Step one:

The sum of squares of Sine and Cosine is 1 which is:

$\sin ^{2} x+\cos ^{2} x=1$

On substituting the above identity in the given expression, we get,

$\Rightarrow \frac{\sin ^{2} x+\cos ^{2} x}{\cos x}=\frac{1}{\cos x} \rightarrow(1)$

Step two:

The reciprocal of cosine is secant which is:

$\cos x=\frac{1}{\sec x}$

On substituting the above identity in equation (1), we get,

$\Rightarrow \frac{\sin ^{2} x+\cos ^{2} x}{\cos x}=\sec x$

Thus, RHS is obtained.

Using the identity $\sin ^{2} x+\cos ^{2} x=1$ , the given expression is verified.

6 0

3 years ago

Write a quadratic function h whose zeros are 5 and -7

marin [14]

Quadratic function whose zeros are 5 and -7 is x^2+2x-35=0

Step-by-step explanation:

Write a quadratic function h whose zeros are 5 and -7

If 5 and -7 are zeros of quadratic function then:

x=5 and x=-7

or x-5 = 0 and x+7=0

So, Finding quadratic equation:

$(x-5)(x+7)=0\\x(x+7)-5(x+7)=0\\x^2+7x-5x-35=0\\x^2+2x-35=0$

So, quadratic function whose zeros are 5 and -7 is x^2+2x-35=0

Keywords: Quadratic Function

Learn more about Quadratic Function at:

#learnwithBrainly

3 0

3 years ago

Solve 7e^(2x)-5>58. Round to the nearest hundredth.

7nadin3 [17]

Answer:

$x\gtrapprox1.1$

Step-by-step explanation:

$7e^{2x}-5>58$

$7e^{2x}>63$

$e^{2x}>9$

$2x>ln(9)$

$x>\frac{ln(9)}{2}$

$x\gtrapprox1.1$

5 0

3 years ago

devi and her brother had the same amount of money. after devi spent 2/5 of her money and her brother spent 3/10 of his money, th

krok68 [10]

To answer this question you have to create a system of equations. The first equation will be that Devi's money (x) equals her brother's money (y), or x = y. The next equation would be that (3/5)x + (7/10)y = 78. You than can substitute x in for y because x = y. The equation would know be (3/5)x + (7/10)x = 78. You then combine the like terms to create an equation of (13/10)x = 78. Then, multiply both sides by 10 / 13 in order to isolate x. This will create the equation x = 60. This means that Devi and her brother each had 60 dollars. You then find out how much they spent and add it together. You can do so with the equation (2/5)x + (3/10)y = z, with z being total money spent. You substitute 60 in for x and for y then solve. When you solve you see that 24 + 18 = z, or that z equals 42. In other words, they spent 42 dollars altogether.

6 0

3 years ago