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3 years ago

Need to show a 5 step problem on how to get the answer. Using x and y

Mathematics

1 answer:

ZanzabumX [31]3 years ago

4 0

Answer: $5.64

Step-by-step explanation:

Let x represent 1 box of batteries

Let y represent 1 case of batteries

Given: 14x = 3y

Given: 158 = 14x + 3y

Use substitution: 158 = 14x + 14x

Simplify: 158 = 28x

Divide by 28: 5.64 = x

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Solve the right triangle, ΔABC, for the missing sides and angle to the nearest tenth given angle B = 39° and side c = 13.

hram777 [196]

Answer:

Part 1) $b=8.2\ units$

Part 2) $a=10.1\ units$

Part 3) $A=51\°$ and $C=90\°$

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

Find the side b

we know that

In the right triangle ABC

The function sine of angle B is equal to divide the opposite side angle B (AC) by the hypotenuse (AB)

$sin(B)=AC/AB$

we have

$AB=c=13\ units$

$AC=b$

$B=39\°$

substitute

$sin(39\°)=b/13$

solve for b

$b=(13)sin(39\°)$

$b=8.2\ units$

step 2

Find the side a

we know that

In the right triangle ABC

The function cosine of angle B is equal to divide the adjacent side angle B (BC) by the hypotenuse (AB)

$cos(B)=BC/AB$

we have

$AB=c=13\ units$

$BC=a$

$B=39\°$

substitute

$cos(39\°)=a/13$

solve for a

$a=(13)cos(39\°)$

$a=10.1\ units$

step 3

Find the measure of angle A

we know that

In the right triangle ABC

$C=90\°$ ----> is a right angle

$B=39\°$

∠A+∠B=90° ------> by complementary angles

substitute the given value

$A+39\°=90\°$

$A=90\°-39\°$

$A=51\°$

5 0

3 years ago

A line that includes the point (7,0) has a slope of 1. What is its equation in slope-intercept form?

LiRa [457]

Answer:

$y = x-7$

Step-by-step explanation:

To write the equation of the line in slope-intercept form, use the slope-intercept formula, $y = mx +b$ . Find real values for the $m$ and $b$ and substitute them into the formula.

1) We know that $m$ represents the slope, so substitute 1 in its place. However, we still need to find $b$ , or the y-intercept. So, along with substituting that 1 in for $m$ , substitute the x and y values for (7,0) for the x and y in the formula as well. Then, isolate $b$ to find its value:

$y = mx + b\\0 = (1)(7)+b\\0 = 7 + b\\-7 = b$

So, $b$ = -7.

2) Now, just substitute the found values for $m$ and $b$ into the slope-intercept formula. Remember that the slope is $m$ , so substitute 1 in, and $b$ is -7, so substitute -7 in its place as well. This gives the following equation in slope-intercept form:

$y = 1x -7$ or $y = x-7$

3 0

3 years ago

A laptop computer is purchased for $1850 . After each year, the resale value decreases by 35% . What will the resale value be af

Natali [406]

Answer:

1850 * 0.7^3 = 634.55

Step-by-step explanation:

7 0

3 years ago

If the volume of a cube is 12,167 cubic inches, what is the length of a side of the square?

Grace [21]

Answer:

23 in

Step-by-step explanation:

Volume of a Cube: V = a³

Step 1: Define

V = 12,167 in³

a = ?

Step 2: Solve for side length a

Substitute: 12,167 = a³
Cube root both sides: 23 = a
Rewrite: a = 23

Step 3: Check

Plug in a to verify it's a solution.

Substitute: V = (23 in)³
Evaluate: V = 12,167 in³

3 0

3 years ago

A solid shape is made by joining two cones.

dlinn [17]

The surface area of the solid shape is the amount of space on it

The radius of the two cones is 2.93 cm

<h3>How to determine the radius?</h3>

The given parameters are:

Cone 1: slant height, l = 2r
Cone 2: slant height, L = 3r
Surface area = 135. 21 cm²

The surface area of the shape is calculated using:

T = πr(L + l)

So, we have:

135.21 = πr(2r + 3r)

Evaluate

135.21 = 5πr²

Divide both sides by 5π

r² = 135.21/5π

Evaluate the quotient

r² = 8.61

Take the square root of both sides

r = 2.93

Hence, the radius of the cones is 2.93 cm