Mae Ling earns a weekly salary of $315 plus a 7.5% commission on sales at a gift shop. How much would

colleen decided to ride her bike from her home to visit her friend gabe. Four miles away from home, her bike got a flat tire and

disa [49]

4 more

If it takes 6 miles to get there,(4+2) And then 6+2 is how much she walked. And 4 is how much she rode. 8-4=4

6 0

3 years ago

Susie has planned a trip to a city 60 miles away. She wishes to have an average speed of 60 miles/hour for the trip. Due to a tr

Nutka1998 [239]

Answer:

90 mi/h

Step-by-step explanation:

Given,

For first 30 miles, her speed is 30 miles per hour,

Let x be her speed in miles per hour for another 30 miles,

Since, here the distance are equal in each interval,

So, the average speed of the entire journey

$=\frac{\text{Average speed for first 30 miles + Average speed for another 30 miles}}{2}$

$=\frac{30+x}{2}$

According to the question,

$\frac{30+x}{2}=60$

$30+x=120$

$\implies x = 90$

Hence, she needs to go 90 miles per hour for remaining 30 miles.

7 0

3 years ago

Area of DEF = 6 sq ft

Anna11 [10]

Answer:

54 ft^2

(54 in green box; 2 in grey box)

Step-by-step explanation:

We have 2 similar triangles, ABC and DEF.

The area of triangle DEF is given as 6 sq ft.

Side BC of triangle ABC measures 12 ft.

The corresponding side to BC in triangle DEF is EF. It measures 4 ft.

That gives us a scale factor from triangle DEF to triangle ABC.

<em>To find the scale factor between two similar polygons, divide the length of a side of the second polygon by the length of the corresponding side of the first polygon.</em>

scale factor = BC/EF = (12 ft)/(4 ft) = 3

The scale factor of side lengths is 3.

The ratio of the areas is the square of the scale factor.

ratio of areas = 3^2 = 9

Now multiply the area of the first triangle (DEF) by the ratio of areas to get the area of the second triangle (ABC).

area of triangle ABC = 9 * (area of triangle DEF)

area of triangle ABC = 9 * (6 sq ft)

area of triangle ABC = 54 sq ft

Answer: 54 ft^2

(54 in green box; 2 in grey box)

6 0

4 years ago

PLease answer !!! Find constants $A$ and $B$ such that \[\frac{x + 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}\] for all

Xelga [282]

Answer:

1. $(A,B) = (3,-2)$

2. The values of t are: -3, -1

Step-by-step explanation:

Given

$\frac{x + 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}$

$|t| = 2t + 3$

Required

Solve for the unknown

Solving $\frac{x + 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}$

Take LCM

$\frac{x + 7}{x^2 - x - 2} = \frac{A(x+1) + B(x-2)}{(x - 2)(x-1)}$

Expand the denominator

$\frac{x + 7}{x^2 - x - 2} = \frac{A(x+1) + B(x-2)}{x^2 - 2x + x -2}$

$\frac{x + 7}{x^2 - x - 2} = \frac{A(x+1) + B(x-2)}{x^2 - x -2}$

Both denominators are equal; So, they can cancel out

$x + 7 = A(x+1) + B(x-2)$

Expand the expression on the right hand side

$x + 7 = Ax + A + Bx - 2B$

Collect and Group Like Terms

$x + 7 = (Ax + Bx) + (A - 2B)$

$x + 7 = (A + B)x + (A - 2B)$

By Direct comparison of the left hand side with the right hand side

$(A + B)x = x$

$A - 2B = 7$

Divide both sides by x in $(A + B)x = x$

$A + B = 1$

Make A the subject of formula

$A = 1 - B$

Substitute 1 - B for A in $A - 2B = 7$

$1 - B - 2B = 7$

$1 - 3B = 7$

Subtract 1 from both sides

$1 - 1 - 3B = 7 - 1$

$-3B = 6$

Divide both sides by -3

$B = -2$

Substitute -2 for B in $A = 1 - B$

$A = 1 - (-2)$

$A = 1 + 2$

$A = 3$

Hence;

$(A,B) = (3,-2)$

Solving $|t| = 2t + 3$

Because we're dealing with an absolute function; the possible expressions that can be derived from the above expression are;

$t = 2t + 3$ and $-t = 2t + 3$

Solving $t = 2t + 3$

Make t the subject of formula

$t - 2t = 3$

$-t = 3$

Multiply both sides by -1

$t = -3$

Solving $-t = 2t + 3$

Make t the subject of formula

$-t - 2t = 3$

$-3t = 3$

Divide both sides by -3

$t = -1$

<em>Hence, the values of t are: -3, -1</em>

7 0

3 years ago

Read 2 more answers

Solve for x given the equation x-5+7=11

Alexeev081 [22]

Answer:

9

Step-by-step explanation:

x-5+7=11

First think of what +7 = 11 then subtract by 5

check :)

7 0

4 years ago