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3 years ago

Points H, G and F are collinear. Point G is between Hand G. Solve for x. HG = x, GF = 1, HF = 10 *

Mathematics

1 answer:

aliina [53]3 years ago

8 0

Answer:

x = 11

Step-by-step explanation:

It is given that,

Points H, G and F are collinear. Point G is between H and G.

It means,

HG = GH + HG

We have, HG = x, GH = 1, HG = 10

Putting all the values, we get:

x = 1 +10

x = 11

It is very clear that the value of x is 11.

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Given that the measure of angle GHJ = 154 degrees find the angle of HIJ

vichka [17]

Answer:

the correct answer is 77°

Step-by-step explanation:

Angle GHJ and IHJ form supplementary angles which add up to 180°

therefore angle IHJ=180-154

angle IHJ=26°

Triangle IHJ is an isosceles triangle whose base angles HIJand IJH are equal. Lets assign them the same value, x° each

since the sum of all interior angles of a triangle add up to 180°, then x°+x°+26°=180°

2x+26=180

2x=154°

x=77°

Therefore both HIJ and IJH measure 77°

6 0

2 years ago

The average heights of x number of girls and 15 boys is 123. if the average heights of boys is 125 and that of girls is 120.find

mamaluj [8]

Answer:

$x = 10$ . In other words, there number of girls is $10$ .

Step-by-step explanation:

The average of a number of measurements is equal to the sum of these measurements over the number of measurements.

$\displaystyle \text{Average} = \frac{\text{Sum of measurements}}{\text{Number of measurements}}$ .

Rewrite to obtain:

$\begin{aligned}& \text{Sum of measurements}= (\text{Number of measurements}) \times (\text{Average}) \end{aligned}$ .

For this question:

$\begin{aligned}& \text{Sum of heights of boys} \\ &= (\text{Number of boys}) \times (\text{Average height of boys}) \\ &= 15 \times 125 = 1875\end{aligned}$ .

$\begin{aligned}& \text{Sum of heights of girls} \\ &= (\text{Number of girls}) \times (\text{Average height of girls}) \\ &= x \times 120 = 120\, x\end{aligned}$ .

Therefore:

$\begin{aligned}& \text{Sum of boys and girls} \\ &= \text{Sum of heights of boys} + \text{Sum of heights of girls}\\ &= 1875 + 120\, x\end{aligned}$ .

On the other hand, there are $(15 + x)$ boys and girls in total. Using the formula for average:

$\begin{aligned}& \text{Average height of boys and girls} \\ &= \frac{\text{Sum of heights of boys and girls}}{\text{Number of boys and girls}} \\ &= \frac{1875 + 120\, x}{15 + x}\end{aligned}$ .

From the question, this average should be equal to $123$ . In other words:

$\displaystyle \frac{1875 + 120\, x}{15 + x} = 123$ .

Solve this equation for $x$ to obtain:

$1875 + 120\, x= 123\, (15 + x)$ .

$(123 - 120)\, x = 1875 - 123 \times 15$ .

$x = 10$ .

In other words, the number of girls here is $10$ .

5 0

3 years ago

A plane flying horizontally at an altitude of 1 mile and a speed of 510 mi/h passes directly over a radar station. Find the rate

sdas [7]

Answer:

442 miles

Step-by-step explanation:

Given

To properly solve this question, I illustrate some given parameters using attached image

From the image, apply Pythagoras theorem

$x^2 + 1^2 = y^2$

Differentiate w.r.t time (t)

$2x\frac{dx}{dt} + 0 = 2y\frac{dy}{dt}$

$2x\frac{dx}{dt} = 2y\frac{dy}{dt}$

Divide both sides by 2

$x\frac{dx}{dt} = y\frac{dy}{dt}$

From the question, we have that the plan travels are 510mi/h.

This implies that:

$\frac{dx}{dt} = 510mi/h$

So, we then calculate the value of x when the distance (y) is 2mi i.e.:

$y = 2mi$

Apply Pythagoras theorem

$x^2 + 1^2 = y^2$

$x^2 + 1^2 = 2^2$

$x^2 + 1 = 4$

$x^2 = 4-1$

$x^2 = 3$

$x = \sqrt 3$

So, the expression becomes:

$x\frac{dx}{dt} = y\frac{dy}{dt}$

$\sqrt 3 * 510 = 2* \frac{dy}{dt}$

$\frac{\sqrt 3 * 510}{2} = \frac{dy}{dt}$

$\sqrt 3 * 255 = \frac{dy}{dt}$

$\frac{dy}{dt} = 255\sqrt 3$

$\frac{dy}{dt} = 255 * 1.7321$

$\frac{dy}{dt} = 441.655$

$\frac{dy}{dt} = 442$

<em>Hence, the distance is 442 miles</em>

7 0

2 years ago

247÷10^2 and 247 ×10^2

Shalnov [3]

PEMDAS:
247/100 = 2.47
247* 100 = 24700
*You must ALWAYS apply the exponents first, THEN divide the equation.

7 0

3 years ago

How does drawing a rectangle support the idea of composing a larger unit from smaller units

pav-90 [236]

Answer:

When you think rectangles, you think areas. Small areas aggregate to form bigger ones.

If you drew a rectangle, it's easy to divide it into smaller units by simply taking a line through its midsection from one length to the other and one width to the other. One can either form smaller squares or rectangles from a larger one.

When that is one, you'd have taken the larger area of a rectangle which is simply the product of the value of its length and it's the breadth, and divided it into smaller units.

Cheers!

4 0

2 years ago

Points H, G and F are collinear. Point G is between Hand G. Solve for x. HG = x, GF = 1, HF = 10 *​

Points H, G and F are collinear. Point G is between Hand G. Solve for x. HG = x, GF = 1, HF = 10 *