if the driver looks 49 inches above the road bed, at what distances from the tower will the drivers eyes be at the same height as the cable?​

ANSWER

[tex] \frac{237}{10} \: or \: 23 \frac{7}{10} [/tex]

EXPLANATION

We want to simplify:

[tex]\frac{23}{5} + \frac{37}{5} + \frac{117}{10} [/tex]

The LCM of the denominators is 10.

We collect LCD to obtain.

[tex] \frac{23 \times 2 + 37 \times 2 + 117}{10} [/tex]

Carry out the multiplication in the numerator to get,

[tex]\frac{46 +74 + 117}{10} [/tex]

Add the numerator to get:

[tex] \frac{237}{10} = 23 \frac{7}{10} [/tex]

Answer:

Step-by-step explanation:

f(x) = x^2 and g(x) = (3x)^2.  g(x) can be rewritten as 9x^2.

The graph of g(x) is similar to that of f(x), except that the graph of g(x) is the result of vertical stretching of the graph of f(x) by a factor of 9.

Answer: The graph of g(x) is horizontally compressed by a factor of 3.

Step-by-step explanation:

Got this answer right on apex

Answer:

Step-by-step explanation:

[tex]\text{A. The absolute value of the slope of the line is equal to}\ \dfrac{HJ}{FG}\\\bold{FALSE}\\\text{because the slope of the line is equal to}\ \dfrac{HJ}{KJ}\\------------------------------\\\text{B. The absolute value of the slope of the line is equal to}\ \dfrac{FG}{JK}\\\bold{FALSE}\\\text{because the slope of the line is equal to}\ \dfrac{FG}{FK}\\------------------------------[/tex]

[tex]\text{C. Because triangles FGH and HJK are similar, the slope is the same}\\\text{between any two distinct points on the line.}\\\bold{TRUE}\\------------------------------\\\text{D. Because triangles FGH and HJK are not similar, the slope is found}\\\text{by using two distinct points on one of the triangles}\\\bold{FALSE}\\\text{because triangles FGH and HJK are similar (AAA)}[/tex]

Answer:

60 square units.

Step-by-step explanation:

First, work out what the length of of the other leg is

[tex]120 \times 2 = 240 \: 240 \div \: 24 = 10[/tex]

Next, to work out the hypotenuse you add the squares of the legs.

[tex] {24}^{2} + 10 ^{2} = 676[/tex]

Then square root the answer from the previous calculation.

[tex] \sqrt{676} = 26[/tex]

And finally add the sides together.

26+24+10= 60 square units

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side. Then the perimeter of the triangle is 60 units.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

A right triangle has an area of 120 square units and a leg length of 24 units.

Then the other length of the triangle will be

Area = 1/2 (b x h)

120 = 1/2 (24 h)

240 = 24h

h = 10

Then the third length of the triangle will be given by the Pythagoras theorem.

H² = b² + h²

H² = 24² + 10²

H² = 576 + 100

H² = 676

H = 26

Then the perimeter of the right-angle triangle will be

Perimeter = 10 + 24 + 26

Perimeter = 60 units

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Answer: The answer is the third one "1 25/48"

Answer:

C

Step-by-step explanation:

Before multiplying perform the addition in the parenthesis

2 [tex]\frac{1}{6}[/tex] + [tex]\frac{7}{8}[/tex]

Change the mixed number to an improper fraction

2 [tex]\frac{1}{6}[/tex] = [tex]\frac{13}{6}[/tex], thus

[tex]\frac{13}{6}[/tex] + [tex]\frac{7}{8}[/tex]

The fractions require to have a common denominator before adding

The lowest common multiple of 6 and 8 is 24

Multiply numerator/denominator of first fraction by 4

Multiply the numerator/denominator of the second fraction by 3

= [tex]\frac{13(4)}{6(4)}[/tex] + [tex]\frac{7(3)}{8(3)}[/tex]

= [tex]\frac{52}{24}[/tex] + [tex]\frac{21}{24}[/tex] = [tex]\frac{73}{24}[/tex]

Now multiply this result by [tex]\frac{1}{2}[/tex], thus

[tex]\frac{1}{2}[/tex] × [tex]\frac{73}{24}[/tex]

= [tex]\frac{1(73)}{2(24)}[/tex]

= [tex]\frac{73}{48}[/tex]

= 1 [tex]\frac{25}{48}[/tex]

Answer:

a

Step-by-step explanation:

Answer:

C.

but whatever you do, don't put A or E cause it symbolizes a graph that is having a decrease in incline but this graph shows a positive incline

Answer:

55790000  :p :)

Answer: it would be 55,709,000

Step-by-step explanation:

it is true 9x=9x

7x+(2x+7)=9x+7

7x+2x+7=9x+7

-7. -7

7x+2x=9x

9x=9x

Answer:

A on the botton axis and B on the left axis

Answer:A=85 E=73 S=37 L=66.5 (or 65) T=82 P=53 D=10 O=89 C=17

Step-by-step explanation:

I am very good at Pythagorean theorem I did it this year.

To do this it is actually like the easiest thing to do in math. The formula is A²+B²=C². To do this it is easier with a scientific calculator. If you don't have one you can use this online calculator: desmos.com/scientific

Step 1. get the two number and square (²) them ( multiply that number by it) For Example 30 multiplied by 30. Or on the calculator I gave you just do 30²+40²

Step 2. After that you will get 2500. Then on the calculator get this symbol √ and but the number 2500 in front of it. it should look like this. √2500.

Step 3. After that you will get 50 which is your answer. And that is how you do Pythagorean theorem.

I hope that helped you. If you don't have a scientific calculator you can use the link I provided above. If you can't use it I reccomend buying one.

Answer:

The mean would be 14.4 hours.

Step-by-step explanation:

In order to find the mean, or average, of the numbers, you would add all the numbers together.

17 + 15 +14 + 14 + 12 which equals 72

Then, you take the total which is 72, and divide it by how many numbers you added together which is 5.

72/5 = 14.4

Answer:

14.4

Step-by-step explanation:

To find the mean in math, you add all of your numbers together, the divide by how many numbers you added together. So add 17,15,14,14, and 12 together to get 72. Divide 72 by 5 to get 14.4

Answer:

The scale factor is [tex]\frac{1}{60}[/tex]

Step-by-step explanation:

we know that

The scale factor is equal to the ratio between the side length of the scale drawing to the corresponding side length in the actual

so

[tex]\frac{2}{120}=\frac{1}{60}[/tex]

Answer:

1/60

Divide

Step-by-step explanation:

There are 36 sunny days

1:2

1 + 2 = 3

54/3 = 18

1 • 18 = 18

2 • 18 = 36

There are 36 sunny days.

Hope this helps!

If it does then I would appreciate it if you could make me brainliest.

Answer:

A

Step-by-step explanation:

Given the 2 equations

y = x² + 8x + 2 → (1)

y = 7x + 4 → (2)

Substitute y = x² + 8x + 2 into (2)

x² + 8x + 2 = 7x + 4 ( subtract 7x + 4 from both sides )

x² + x - 2 = 0 ← in standard form

(x + 2)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 1 = 0 ⇒ x = 1

Substitute these values into (2) for the corresponding values of y

x = - 2 : y = - 14 + 4 = - 10 ⇒ (- 2, - 10)

x = 1 : y = 7 + 4 = 11 ⇒ (1, 11)

The solutions are (- 2, - 10) and (1, 11) → A

Answer:

c. y= cos2/3x

Step-by-step explanation:

ANSWER

C.

[tex]y = \: \cos( \frac{2}{3}x ) [/tex]

EXPLANATION

The period of a cosine function is calculated using the formula;

[tex]T= \frac{2 \pi}{b} [/tex]

Therefore , if the period is 3π, then

[tex] \frac{2 \pi}{b} = 3\pi[/tex]

We solve b to obtain,

[tex]b = \frac{2}{3} [/tex]

This implies that, the given cosine function must have an equation of the form

[tex]y = a \: \cos( \frac{2}{3}x ) [/tex]

Among the options, the function in this form is:

[tex]y = \: \cos( \frac{2}{3}x ) [/tex]

The correct choice is C.

Answer:

500,000 grams

Step-by-step explanation:

1 kg = 1,000 g

500*1,000=500,000

Answer:

16%

Step-by-step explanation:

What you need to do is add both 48 and 240 together. That gives you a total of 288 flowers. Now you need to divide 48 by 288 because that will give you your percentage. In this case, it's 16%.

Answer:

Here.

Step-by-step explanation:

You add the number of flowers together to get the total number- 48 + 240 is 288.

48 should be 16.66%, as 288 divided by 6 is 48.

(I am not entirely sure about this answer.)

Answer:

Step-by-step explanation:

therefore, force F = m*g  

= 0.02 kg * 9.8 m/s^2  

= 0.196 Newton Force in the MKS system of units is measured in NEWTONS and results from a product of mass in Kg and acceler. the formula is  s o the force=mass x acceleration. and the answer is .02x9.8^2= 1.6928ation in meters/sec^2

The electric force of a charged balloon sticking to the ceiling is due to the interaction between the balloon and the induced positive charge in the ceiling. This force is related to the principle of electrostatics and can theoretically be calculated using Coulomb's Law, but would require more details. However, for the balloon to remain stuck to the ceiling, this electrostatic force must be greater than the weight of the balloon.

To calculate the electric force of a charged balloon sticking to the ceiling, you first need to consider the scenario as an interaction between the charged balloon and the induced charge in the ceiling. This scenario is related to the principle of electrostatics, where like charges repel and different charges attract. It is the electrostatic force that is making the balloon stick to the ceiling.

The balloon gets charged by picking up extra electrons (negative charge) when rubbed. When brought near the ceiling, these extra electrons in the balloon repel the electrons in the ceiling, causing the area of the ceiling near the balloon to be positively charged. This induced positive charge in the ceiling then attracts the negatively charged balloon. The force between the balloon and the ceiling can be caluclated using Coulomb's Law, which states that the force between two charges is directly proportional to the product of their charges, and inversely proportional to the square of the distance between them. However, to accurately calculate this force using Coulomb's law, we need more information such as the amount of charge on the balloon and the distance from the balloon to the ceiling.

Finally, for a balloon to stick to the ceiling, the electrostatic force must be greater than the weight of the balloon. The weight of the balloon can be calculated using the formula Weight = mass x gravity. In this case, the mass of the balloon is 0.020kg and the gravitational force is approximately 9.8 m/s². Therefore, the weight is 0.020kg x 9.8 m/s² = 0.196N. So for the balloon to stick to the ceiling, the electrostatic force must be greater than 0.196 N.

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Answer:

it 100 you would do 20%of 500 and you 100

Step-by-step explanation:

Answer: 100

Step-by-step explanation: 20% of 500 Is equal to 100. It’s also 1/5 in a fraction

The answer is:

D. [tex](x-6)+5[/tex]

The answer is c because it’s the only one showing division

The measure of angle A can be calculated using trigonometry and the components of a known vector. The relationship of the components forms a right triangle, the properties of which can be used to find the measure of angle A.

The measure of angle A can be calculated using trigonometry if we know the distances from the problem. By knowing the scalar components Ax and Ay of vector A, we can find its magnitude and direction angle. In this case, the direction is the angle the vector forms with the positive direction on the x-axis, measured in the counterclockwise direction. The lengths A, Ax, and Ay form a right triangle, related by the Pythagorean theorem.

If the vector A is known, then its magnitude A and its angle are known. To find Ax and Ay, we use the following relationships for a right triangle: Ax = Acose. If the vector lies in the first or the fourth quadrant, where component Ax is positive, angle A is identical to the direction angle. Conversely, when the vector lies in the second or third quadrant, where component Ax is negative, the direction angle is A = 0 + 180°.

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The measure of angle A in the given figure is equal to 20 degrees.

To solve this question we can use the property of a triangle that the sum of all angles in a triangle is equal to 180 degrees.

We have been given three different angles in this figure which are: 90 degrees, 71x-1, and 20x.

Let us find the value of x before finding the value of angle A

71x-1 + 20x + 90 = 180

71x + 20x = 180 - 90 + 1

91x = 91

x = 1

Now we can calculate the value of angle A as:

20x

= 20 (1)

= 20 degrees

The measure of angle A is 20 degrees.

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Answer:

[tex]\frac{2p-1}{3}[/tex]

Step-by-step explanation:

Since you want to get q only and q appears in both side of the equation. Try to isolate q to one side.

1) Expand 2(q+p)

2q + 2p = 1 + 5q

2) Move all q terms to one side

5q - 2q = 2p - 1

3q = 2p - 1

3) Divide 3 on both side (to isolate q)

q = [tex]\frac{2p-1}{3}[/tex]

After making q the subject of the formula in the equation 2(q + p) = 1 + 5q, the resulting solution is:

[tex]q = \frac{2p - 1}{3}[/tex]

The given equation is:

2(q + p) = 1 +5q

To make q the subject of the formula, follow the steps below

Expand the expression using the distributive rule

2q + 2p = 1 + 5q

Collect like terms by subtracting 2q from both sides of the equation

2q - 2q + 2p = 1 + 5q - 2q

2p = 1 + 3q

Subtract 1 from both sides of the equation

2p - 1 = 1 + 3q - 1

2p - 1 = 3q

Divide through by 3

[tex] \frac{2p - 1}{3} = q[/tex]

Therefore after making q the subject if the formula in the equation 2(q + p) = 1 + 5q, the resulting solution is:

[tex] q = \frac{2p - 1}{3}[/tex]

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Answer:

x=9

Step-by-step explanation:

The Slope is given by the following equation

m= (y2-y1) / (x2-x1)

Where x2=4, x1=x, y2=1, y1=-6, m=1 by requirements of this problem

Developing the equation we have this:

[tex]1=\frac{1-(-6)}{4-x}[/tex]

Which leaves to the following equation

[tex]5=4-x[/tex]

Resulting that x=9

Answer:

The number could be [tex]x=-6[/tex]  or [tex]x=-1/3[/tex]

Step-by-step explanation:

Let

x-----> the number

Remember that

The reciprocal of a number is 1 divided by the number

we know that

[tex]x+2(\frac{1}{x})=-\frac{19}{3}[/tex]

Solve for x

Multiply by 3x both sides

[tex]3x^{2} +6=-19x\\ \\ 3x^{2}+19x+6=0[/tex]

Solve the quadratic equation by graphing

The solutions are [tex]x=-6, x=-1/3[/tex]

see the attached figure

Verify both solutions

For [tex]x=-6[/tex]

[tex]-6+2(-\frac{1}{6})=-\frac{19}{3}[/tex]

[tex]-\frac{19}{3}=-\frac{19}{3}[/tex] ----> is true

For [tex]x=-1/3[/tex]

[tex]-(1/3)+2(\frac{1}{(-1/3)})=-\frac{19}{3}[/tex]

[tex]-\frac{19}{3}=-\frac{19}{3}[/tex] ----> is true

The value of x is 5 for the given statement.

An equation is a mathematical statement formed when two algebraic expressions are equated by an equal sign.

The statement given in the question is

Six less than twice a number x is four​

The equation that can be formed by this statement is

2x - 6 = 4

on solving the equation

2x = 10

x=5

The value of x is 5 for the given statement.

The complete question is

Six less than twice a number x is four​ , Determine the value of x.

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Answer:

$54

Step-by-step explanation:

First

45 times .05= 2.25

Second

45 plus 2.25

Third

45 times .15= 6.75

Fourth

45+2.25+6.75

Answer:

$54

Step-by-step explanation:

Okay. if the bill in tax was 5% and the tip is 15% just add them up to make it easier. Now, you have 20%, and you have to now find 20% of 45, make 20% into .20, do .20x45 which equals 9 which represents $9. Finally, add $9 (from tip and tax) to $45 (how much the food cost) = $54

No problem!

Answer:  Option b.

Step-by-step explanation:

First, you need to calculate the ratio of the area. This is:

[tex]ratio=(\frac{64}{28})^2\\\\ratio=\frac{256}{49}[/tex]

You know that the area of the smaller trapezoid is 771 m², then you can set up the following proportion, where "x" is the area of the larger trapezoid. Then you have:

[tex]\frac{256}{49}=\frac{x}{771}[/tex]

Now you must solve for "x". Therefore, you get that the area of the larger trapezoid is:

 [tex]x=(771)(\frac{256}{49})\\\\x=4,028m^2[/tex]

To the nearest whole number, the area of the other similar figure is: b. 4,028 m².

The ratio of the areas of two similar figures equals the ratio of the square of their corresponding sides.

Thus:

Let x represent the area of the other figure.

Therefore:

771/x = (28²)/(64²)

771/x = 784/4,096

x = (771 × 4,096)/784

x = 4,028

Therefore, to the nearest whole number, the area of the other similar figure is: b. 4,028 m².

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1. Multiply the amount of iced tea mix by 1/3 to get the amount of water.

Explanation:

As seen in the graph, for every 1 cup of water, 3 tablespoons of the mix are needed.

3 * X = 1

X= 1/3

2. Use the equation y=3x

X=18 , y=cups of water needed

Y= 3*18

Y= 54 cups of water are needed

Answer:

the area is multiplied by 9.

Step by Step Explanation:

Let x be the base

Let y be the height

Since all dimensions were multiplied by the same number, 3,

Original area,

1/2 × x × y = (1/2)xy

New area,

1/2 × 3x × 3y = (1/2)(9)xy

Hence, area is multiplied 9 times.