Aiden has some $1 bills and $5 bills. He has 6 bills worth $22 total in his wallet. How many $1 bills does he have?

Solve and check the equation.<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B10%7D%3D%5Cfrac%7B5x%7D%7B7%7D%20-43" id="TexFor

Y_Kistochka [10]

Answer:

x = 70

Step-by-step explanation:

Step 1: Simplify both sides of the equations.

$\frac{x}{10} = \frac{5x}{7}-43$
$\frac{1}{10}x=\frac{5}{7}x-43$

Step 2: Subtract 5/7x from both sides.

$\frac{1}{10}x- \frac{5}{7}x = \frac{5}{7}x - 43 - \frac{5}{7}x$
$\frac{-43}{70}x = -43$

Step 3: Multiply both sides by 70/(-43).

$\frac{-43}{70}x * \frac{70}{-43} = -43*\frac{70}{-43}$
$x = 70$

Step 4: Check if solution is correct.

$\frac{(70)}{10}=\frac{5(70)}{7} -43$
$7 = \frac{350}{7} - 43$
$7 = 50 - 43$
$7 = 7$

Therefore, x = 70.

5 0

2 years ago

Aubrey is making cone-shaped hats for a birthday party. She mistakenly thinks that she will need about 104 square inches of pape

jenyasd209 [6]

Answer:

C. About 75 in²; Aubrey found the surface area of the cone and included the base.

Step-by-step explanation:

In the questions above we were given the following:

Cone with

Diameter(D) = 6 inches

Slant height (l) = 8 inches.

Aubrey made an error in her calculation.

She found the Total Surface area of the cone using the formula:

Total Surface Area of a cone = πrl + πr²

= πr(l + r)

The Total surface area of a cone is the calculated as Sum of the curved surface area of a cone and the base of the cone.

Where:

Curved surface area of the cone is calculated as = πrl

Base of a cone is calculated as = πr²

Where r = radius of the cone

l = slant height of the cone

In the question, we were given

slant height(l) = 8 inches.

radius = Diameter ÷ 2 = 6÷2 = 3 inches.

Using π = 3.14

Surface area = 3.14 × 3(8+3)

= 9.42 × 11

Surface area = 103.62 in²

Approximately to the nearest inch = 104 in² or 104 square inches.

But this answer is WRONG.

The RIGHT FORMULA Aubrey should have used is

Curved Surface Area or the Lateral Area of a Cone = πrL

slant height(l) = 8 inches.

radius = Diameter ÷ 2 = 6÷2 = 3 inches.

Using π = 3.14

Curved Surface Area of a Cone = πrL

= 3.14 × 3 inches × 8 inches

= 75.36 square inches or 75.36in²

Approximately to the nearest inch = 75 square inches or 75 in².

This is the correct answer.

The error Aubrey made was she calculated the Total surface area of the cone which includes the base of the cone instead of calculating the curved surface area of the cone only.

Hence, from the above calculation , we can see that Option C "About 75 in²; Aubrey found the surface area of the cone and included the base" is the correct option.

5 0

3 years ago

Which of the following equations is of a parabola with a vertex at (1, -2)?

arlik [135]

The general eaquation of a parabola in terms of its vertex is:

y = a(x - h)^2 + k

where the vertex point is (h, k)

therefore, an equation of a parabola with vertex (1, -2) is:

y = 5(x - 1)^2 - 2

8 0

3 years ago

Pleaseeeee helpppppp

lakkis [162]

Answer:

Okay so I’m gonna do a few and list a few examples

In slope intercept form its

y=mx+b

Y= Random Y coordinate (Not that important for now while writing)

m= Slope

X= random x coordinate (not that important for now while writing)

b= Y intercept

SO basically plug it in like that so for the first one

the slope is 1/3 and y-intercept is -1

so

y=1/3x-1

And thats how you do it

leave the y and x

Graphing

So for graphing or fining the equation, first identify the y-intercept

The y-intercept is on the y axis (obviously), and its the number where the line first hits, so for the first one, the y intercept is 3 becuase thats where the first line meets on the Y axis. When identified start doing rise over run, lik just go up and right, if there is no space, dot he opposite, go down and go left or right (depends if the line is rising or falling, you can tell if rising (positive) if the line goes from down to up form left to right , if falling (negative) vice versa, up to down from left to right). And just write the equation after identifying the slope And y-intercept, the x and y don’t matter.

4) y= -1/3x+3 (watch your signs, if falling the slope is automatically negative)

5) y=1/2x+1

6) y=4x-5 (negative y-intercept due to the part where the y meets up with the line, its in the negative side)

(remember to write these equations on the top side of the line

4 0

3 years ago

3/4 x 5/6 equals what

SVETLANKA909090 [29]

Answer:

5/8

You just have to multiply the bottom and the top then simplify

7 0

3 years ago