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2 years ago

What should be done to both sides of the equation in order to solve y + 8.5 = 17.2?

Mathematics

2 answers:

yan [13]2 years ago

8 0

Answer:

subtract 8.5

Step-by-step explanation:

this will isolate y

LenKa [72]2 years ago

5 0

Answer:

subtract 8.5

Step-by-step explanation:

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Which equation does the graph of the systems of equations solve?

mihalych1998 [28]

Answer:

$\text{B. }\frac{1}{3}x-3=-x+1$

Step-by-step explanation:

Let's start by taking a look at the blue line. The slope of any line that passes through two points is equal to the change in y-values over the change in x-values. We can see that the line passes through points (0, 1) and (1, 0). Assign these points to $(x_1,y_1)$ and $(x_2, y_2)$ (doesn't matter which you assign) and use the slope formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Let:

$(x_1,y_1)\implies (0,1)\\(x_2,y_2)\implies (1, 0)$

The slope is equal to:

$m=\frac{0-1}{1-0}=\frac{-1}{1}=-1$

Therefore, the slope of this line is -1. In slope-intercept form $y=mx+b$ , $m$ represents slope, so one of the lines must have a term with $-x$ in it, which eliminates answer choices A and D.

For the second line, do the same thing. The red line clearly passes through (0, -3) and (3, -2). Therefore, let:

$(x_1,y_1)\implies (0,-3)\\(x_2,y_2)\implies (3, -2)$

Using the slope formula:

$m=\frac{-2-(-3)}{3-0}=\frac{1}{3}$

Thus, the slope of the line is 1/3 and the other line must have a term with $\frac{1}{3}x$ in it, eliminating answer choice C and leaving the answer $\boxed{\text{B. }\frac{1}{3}x-3=-x+1}$

*You can find the exact equation of each line by using the slope formula as shown and plugging in any point the line passes through into $y=mx+b$

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2 years ago

What are the major goals of America's foreign policy?

mafiozo [28]

Answer:

The State Department has four main foreign policy goals: Protect the United States and Americans; Advance democracy, human rights, and other global interests; Promote international understanding of American values and policies

Step-by-step explanation:

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1 year ago

-HELPPP!

suter [353]

Answer:

p(x) = A(x - 4i)(x + 4i)(x - 3)(x + 3), with A = 1.

it matches

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1 year ago

First, he needs to run to the store. To get to the store from his apartment, he can walk 1.2 miles North and 0.5 miles East alon

Pachacha [2.7K]

Answer:

If Henry walks along the sidewalks, he will walk 1.7 miles in total. It will take him 17 minutes to reach the store and another 17 minutes to come back.

If Henry cuts through the city, he will walk √(1.2² + 0.5²) = 1.3 miles in total. It will take him 22.3 minutes to reach the store and another 22.3 minutes to come back.

Even though Henry will need to walk a longer distance if he walks along the sidewalks, he will be able to reach the store and back back in a shorter time than if he cuts through the city.

6 0

2 years ago

Use the figure below to answer the questions.

Archy [21]

Answer:

a. What is the name of the 3D shape?

The name of the 3D shape is Prism

b. What is the formula for total surface area for this shape?

Total surface area:

$S=2A_{b}+P_{b}h$

c. What is the surface area of the figure?

The surface area of the figure is 144 cm²

Step-by-step explanation:

a. What is the name of the 3D shape?

The 3D shape has two congruent and parallel faces (triangles) and the other faces are parallelograms, then the 3D shape is a prism

b. What is the formula for total surface area for this shape?

Total Surface area:

$S=2A_{b}+P_{b}h$

where:

Area of the base of the prism: Ab

Perimeter of the base: Pb

Height of the prism: h

c. What is the surface area of the figure?

The base of the prism is a triangle. Then to calculate the area of the base, we must use the formula to calculate the area of a triangle:

$A_{b}=\frac{bh}{2}\\ A_{b}=\frac{(4 cm)(3 cm)}{2}\\ A_{b}=\frac{12cm^{2} }{2}\\ A_{b}=6cm^{2}$

The perimeter of the base is the perimeter of the triangle, equal to the sum of the sides of the triangle:

$P_{b}=4cm+3cm+5cm\\ P_{b}=12cm$

h: Height of the prism is the distance between the bases of the prism (the triangle), then h=11 cm

Then, replacing in the formula the known values:

$S=2(6 cm^{2})+(12 cm)(11 cm)\\ S=12 cm^{2}+132 cm^{2}\\ S=144 cm^{2}$

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2 years ago