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3 years ago

Enter your answer and show all the steps that you use to solve this problem in the space provided.

Mathematics

2 answers:

Masja [62]3 years ago

7 0

Answer:

x² + 23x + 49

Step-by-step explanation:

The shaded area is the difference of areas of the rectangle and the square.

Rectangle:

A₁ = (x + 10)(2x + 5) = 2x² + 5x + 20x + 50 = 2x² + 25x + 50

Square:

A₂ = (x + 1)² = x² + 2x + 1

Shaded region:

A₁ - A₂ =
2x² + 25x + 50 - (x² + 2x + 1) =
2x² + 25x + 50 - x² - 2x - 1 =
x² + 23x + 49

ruslelena [56]3 years ago

5 0

Answer:

area of shaded region: x² + 23x + 49

solve:

Area of full rectangle:

$Length * Width$

$(x + 10 ) *( 2x + 5)$

$2x^2 + 5x + 20x + 50$

$2x^2 + 25x + 50$

Area of un-shaded rectangle:

$Length * Width$

$(x+1)(x+1)$

$x^2 + x+ x+ 1$

$x^2 + 2x + 1$

Area of shaded = Area of full rectangle - Area of un-shaded rectangle

$\hookrightarrow 2x^2 + 25x + 50 - (x^2 + 2x + 1)$

$\hookrightarrow 2x^2 + 25x + 50 - x^2 - 2x - 1$

$\hookrightarrow x^2 + 23x +49$

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The vertices of a right triangle are (0, 0), (1, 0), and (0, 1).

Alchen [17]

Answer:

(3,3)

Step-by-step explanation:

Given

$Vertices: (0,0)\ (1,0)\ (0,1)$

$Scale\ Factor = 3$

Required

Determine which can't be any of the new vertices

First, we need to determine the new vertices:

$New\ Vertex = Scale\ Factor * Old\ Vertex$

For (0,0):

$New\ Vertex = 3 * (0,0)$

$New\ Vertex = (3 * 0,3 * 0)$

$New\ Vertex = (0,0)$

For (1,0):

$New\ Vertex = 3 * (1,0)$

$New\ Vertex = (3 * 1,3 * 0)$

$New\ Vertex = (3,0)$

For (0,1):

$New\ Vertex = 3 * (0,1)$

$New\ Vertex = (3 * 0,3 * 1)$

$New\ Vertex = (0,3)$

Comparing the calculated new vertices to the list of given options; (3,3) can't be any of the new vertices of the new triangle

5 0

4 years ago

Please answer this question fast in 2 minutes

Stolb23 [73]

Answer:

(-20, 19)

Step-by-step explanation:

We need to use the Midpoint Formula, which says that given two points $(x_1,y_1)$ and $(x_2,y_2)$ , the midpoint is $(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )$ .

Here, we are given one of the endpoints and the midpoint:

endpoint S = (5, -8)

midpoint M = (-7.5, 5.5)

Plug these into the formula. In $\frac{x_1+x_2}{2}$ , x1 = 5, and this whole expression is equal to -7.5:

$\frac{x_1+x_2}{2}=\frac{5+x_2}{2} =-7.5$

Solve for x2:

5 + x2 = 2 * (-7.5) = -15

x2 = -15 - 5 = -20

Now, let's find y2. y1 is just -8, and the entire expression for the y-coordinate of the midpoint is equal to 5.5. So:

$\frac{y_1+y_2}{2}=\frac{-8+y_2}{2} =5.5$

Solve for y2:

-8 + y2 = 2 * 5.5

-8 + y2 = 11

y2 = 11 + 8 = 19

The coordinates of T are thus (-20, 19).

~ an aesthetics lover

5 0

3 years ago

Help, I need to know the area of this.

GaryK [48]

Answer:

300ft^2

Step-by-step explanation:

4 0

4 years ago

A chicken salad recipe calls for 1 8

NARA [144]

Answer: $1.0625\ pounds$ or $\frac{17}{16}\ pounds$

Step-by-step explanation:

The complete exercise is: "A chicken salad recipe calls for $\frac{1}{8}$ pound of chicken per serving . How many pounds of chicken are needed to make $8\frac{1}{2}$ serving".

You can convert the Mixed number to a Decimal number. Divide the numerator 1 by the denominator 2 and then add the quotient to the Whole number. Then, you get:

$8+0.5=8.5$

Now divide the numerator 1 by the denominator 8 to write the fraction to a Decimal number. Then:

$\frac{1}{8}= 0.125$

Let be "x" the amount of pounds are needed to make $8\frac{1}{2}$ serving.

Then, you can set up the following proportion:

$\frac{1}{0.125}=\frac{8.5}{x}$

Solving for "x", you get:

$\frac{1}{0.125}=\frac{8.5}{x}\\\\x(\frac{1}{0.125})=8.5\\\\x=8.5*0.125\\\\x=1.0625$

or $\frac{17}{16}\ pounds$

7 0

3 years ago

A red car is driving along the road in the direction of the police car and is 130 feet up the road from the location of the poli

pishuonlain [190]

Complete question:

A police car is located 50 feet to the side of a straight road. A red car is driving along the road in the direction of the police car and is 130 feet up the road from the location of the police car. The police radar reads that the distance between the police car and the red car is decreasing at a rate of 75 feet per second. How fast is the red car actually traveling along the road.

Answer:

The red car is traveling along the road at 80.356 ft/s

Step-by-step explanation:

Given

Police car is 50 feet side off the road

Red car is 130 feet up the road

Distance between them is decreasing at the rate of 75 feet per sec

Let x be how far the police is off the road.

Let y be how far the red car is up the road.

Let h be the distance between the police and the red car.

This forms a right triangle so we can use the Pythagorean theorem, to solve for h

h² = x² + y²

h² = 50² + 130²

h² = 19400

h = √19400

h = 139.284 ft

Again;

Let dx/dt be how fast the police is traveling toward the road.

Let dy/dt be how fast the red car is traveling along the road.

Let dh/dt be how fast the distance between the police and the car is decreasing.

Recall that, h² = x² + y² (now differentiate with respect to time, t)

2h(dh/dt) = 2x(dx/dt) + 2y(dy/dt)

divide through by 2

h(dh/dt) = x(dx/dt) + y(dy/dt)

since the police car is not, dx/dt = 0

and dy/dt is the how fast is the red car actually traveling along the road

139.284(75) = 50(0) + 130(dy/dt)

10446.3 = 0 + 130(dy/dt)

dy/dt = 10446.3 / 130

dy/dt = 80.356 ft/s

Therefore, the red car is traveling along the road at 80.356 ft/s

6 0

4 years ago