Ask question

Ask question

All categories

3241004551 [841]

3 years ago

12

Find the length of x. Assume the triangles are similar.

1 answer:

Veronika [31]3 years ago

6 0

Answer:

x = 32

Step-by-step explanation:

The longest side is double the length of the shortest side, so x is 2·16 = 32.

You might be interested in

You decide to enter in a rowing competition. To train, you go to the boat house and begin rolling down stream. You row for the s

fredd [130]

Answer:

Time spent rowing down stream $=100\ seconds$

Speed of boat in still water $=14\ ms^{-1}$

Step-by-step explanation:

Let speed of boat in still water be $= x\ ms^{-1}$

Speed of current $= 10\ ms^{-1}$

Speed of boat down stream = $\textrm{Speed of boat in still water +Speed of current}= (x+10)\ ms^{-1}$

Distance rowed down stream = 2400 m

Time spent rowing down stream = $\frac{Distance}{Speed}=\frac{2400}{x+10}\ s$ = $\frac{Distance}{Speed}=\frac{2400}{x+10}\ s$

Speed of boat up stream = $\textrm{Speed of boat in still water -Speed of current}= (x-10)\ ms^{-1}$

Distance rowed up stream = $\frac{1}{6} \textrm{ of distance rowed downstream}=\frac{1}{6}\times 2400 = 400\ m$

Time spent rowing up stream = $\frac{Distance}{Speed}=\frac{400}{x-10}\ s$

We know that,

$\textrm{Time spent rowing down stream =Time spent rowing up stream}$

So,

$\frac{2400}{x+10}=\frac{400}{x-10}$

Cross multiplying

$2400(x-10)=400(x+10)$

Dividing both sides by $400$

$\frac{2400(x-10)}{400}=\frac{400(x+10)}{400}$

$6(x-10)=x+10$

$6x-60=x+10$

Adding 60 to both sides.

$6x-60+60=x+10+60$

$6x=x+70$

Subtracting both sides by $x$

$6x-x=x+70-x$

$5x=70$

Dividing both sides by 5.

$\frac{5x}{5}=\frac{70}{5}$

∴ $x=14$

Speed of boat in still water $=14\ ms^-1$

Time spent rowing down stream = $\frac{2400}{14+10}=\frac{2400}{24}=100\ s$

3 0

3 years ago

The fitted regression is Sales = 832 − 28.2 Price. (a-1) If Price = 1, what is the prediction for Sales? (Round your answer to 1

almond37 [142]

Answer:

Part (a-1): The prediction for Sales is 803.8.

Part (a-2): The correct option is: An increase in price decreases sales.

Part (B): The prediction for sales is 211.66

Part (C): The intercept is meaningful as sales will be maximized when price is zero.

Step-by-step explanation:

Consider the provided regression:

Sales = 832 − 28.2 Price

(a-1) If Price = 1, what is the prediction for Sales?

Substitute Price = 1 in above regression.

Sales = 832 − 28.2 (1) = 803.8

Hence, the prediction for Sales is 803.8.

Sales (a-2) Choose the correct statement.

Here we can observe that as we increase the price, sales decrease.

Thus, the correct option is: An increase in price decreases sales.

(b) If Price = 22, what is the prediction for Sales?

Substitute Price = 22 in above regression.

Sales = 832 − 28.2 (22)

Sales = 832 − 620.4

Sales = 211.66

Hence, the prediction for sales is 211.66

Sales (c) Choose the right option.

As we increase the price, sales decrease that means the sales will be maximum if the price is 0.

The intercept is meaningful as sales will be maximized when price is zero.

3 0

3 years ago

.Bryan was given the equation y= -5x+3. He says the rate of change is 3 and the initial value is -5. Is Bryan correct? If not, c

Mekhanik [1.2K]

Answer:

Correct rate of change is -5; correct initial value is 3.

Step-by-step explanation:

The rate of change is the coefficient of the x term, which here is -5. So Bryan has the rate of change wrong.

The initial value of the function is found by letting x = 0. Here, we get

y = -5(0) + 3, or y = b = 3. The initial value is 3, not -5.

8 0

3 years ago

Find the area and the circumference of the circle. Round your answers to the nearest hundredth.

Alik [6]

Answer:

$area = 200.96 \: {units}^{2} \\ circumfrence = 50.24 \: units$

Step-by-step explanation:

The formula to find the area and circumference of a circle is:

$area = \pi {r}^{2} \\ circumfrence = 2\pi \: r$

<em>*</em><em>no</em><em>te that pi is 3.14*</em><em> </em>Therefore the area is:

$formula = \pi {r}^{2} \\ 3.14 \times {8}^{2} = \\ 3.14 \times 64 = 200.96$

Therefore the circumference is:

$formula = \: 2\pi \: r \\ (2)(3.14)(8) = \\ 3.14 \times 16 = 50.24$

3 0

2 years ago

Showing algebraic support, find the value of x.

Travka [436]

Answer:

x = 52.5

Step-by-step explanation:

The triangle on the left has 2 congruent sides, thus is isosceles

The base angles of an isosceles triangle are also congruent, thus

x = $\frac{180-75}{2}$ = $\frac{105}{2}$ = 52.5

3 0

3 years ago