A mouse traveled a total distance of StartFraction 3 Over 24 EndFraction of a mile in a maze over the past 3 hours. The mouse traveled the same distance each hour. To determine the distance that the mouse traveled each hour, Matt performed the calculations below.

Answer:

see explanation

Step-by-step explanation:

area of Δ ABC is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

Here b = 4x - 6 and h = 2x - 3 , then

A = [tex]\frac{1}{2}[/tex] (4x - 6)(2x - 3) ← expand using FOIL

   = [tex]\frac{1}{2}[/tex](8x² - 24x + 18) ← distribute

    = 4x² - 12x + 9

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Area of rectangle CBFG is calculated as

A = lb ( l is length, b is breadth )

Here l = 4x - 6 and b = 3x - 2, then

A = (4x - 6)(3x - 2) ← expand using FOIL

   = 12x² - 26x + 12

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Area of trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)

where h is the height and b₁, b₂ the parallel bases

Here h = 2x - 3, b₁ = 4x + 1, b₂ = 2x + 3 , then

A = [tex]\frac{1}{2}[/tex] (2x - 3)(4x + 1 + 2x + 3)

   = [tex]\frac{1}{2}[/tex] (2x - 3)(6x + 4) ← expand using FOIL

   = [tex]\frac{1}{2}[/tex] (12x² - 10x - 12) ← distribute

   = 6x² - 5x - 6

Answer:

12 : 24

Step-by-step explanation:

sum the parts of the ratio, 1 + 2 = 3 parts

Divide 36 by 3 to find the value of one part of the ratio.

36 ÷ 3 = 12 ← value of 1 part of the ratio , thus

2 parts = 2 × 12 = 24

Thus

36 in the ratio 1 : 2 is 12 : 24

Answer: Choice E) Insufficient information to prove congruence.

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Explanation:

We're given that AB = DC and BE = CE. This means we have two pairs of congruent sides and we could use SAS if we know that angle ABE = angle DCE. However, we don't know this information.

While we do know that angle AEB = angle DEC (vertical angle theorem), this is not enough information. Recall that SSA is not a valid congruence theorem. The angles in question are not between the sides mentioned in the previous paragraph.

Therefore, we don't have enough information to prove the triangles congruent.

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Side notes:

Answer:

40squared units!

I hope it will be useful.

Answer: 40 square units

Step-by-step explanation:

I took the assignment

Answer:

a T-shirt costs £5

a hat costs £2

Step-by-step explanation:

Suppose

A T-shirt=x

A Hat=y

So the equation is

8x+y=42

3x+y=17

So

8x+y=42

3x+y=17

------------

5x=25

x=5

So a T-shirt costs £5

3.5+y=17

15+y=17

y=2

So a hat costs £2

Answer:

t-shirt: £5

hat: £2

Step-by-step explanation:

Please see the attached picture for the full solution.

Answer:

54°

Step-by-step explanation:

total angels is 360°

(15*100)/360 = 54°

Answer: 3/14

Step-by-step explanation:

Answer:

[tex]f(x) = \frac{5x^2 + 4x - 1}{x - 2}[/tex]

Step-by-step explanation:

Given

VA; [tex]x = 2[/tex]

SLA: [tex]y = 5x - 1[/tex]

Zero of function: [tex](-1,0)[/tex]

Required

Determine the rational function in expanded form

Analyzing the vertical asymptote

The vertical asymptote is given as:

[tex]x = 2[/tex]

Subtract 2 from both sides

[tex]x - 2 = 2 - 2[/tex]

[tex]x - 2 = 0[/tex]

This means that the denominator must be [tex]x - 2[/tex]

Analyzing the zero of the function

The zero of the function is given as: [tex](-1,0)[/tex]

This means that [tex]x = -1[/tex], when [tex]y = 0[/tex]

Equate [tex]x = -1[/tex] to 0 by add 1 to both sides

[tex]x + 1 =- 1 + 1[/tex]

[tex]x + 1 =0[/tex]

This means that one of the numerators must be [tex]x + 1[/tex]

Analyzing the slant asymptote:

[tex]y = 5x - 1[/tex]

This means that one of the numerators must be [tex]5x - 1[/tex]

Hence, the function is:

[tex]f(x) = \frac{(5x - 1)(x+1)}{x - 2}[/tex]

Expand the numerator

[tex]f(x) = \frac{5x^2 + 5x - x - 1}{x - 2}[/tex]

[tex]f(x) = \frac{5x^2 + 4x - 1}{x - 2}[/tex]

Answer:

0.5

Step-by-step explanation:

Co-ordinate of the mid point of the segment whose co-ordinates are -6 & 7 is =

[tex] \frac{7 + ( - 6)}{2} = \frac{1}{2} = 0.5[/tex]

Answer:

B(2,10)

D'(4,-1)

Step-by-step explanation:

ok to find this we need to know what the translation is

from (2,2) to (-4,-1)

subtract 6 from x and subtract 3 from y

im gonna chak another just in case

3rd one

(10,10) to (4,7)

same rule

so for the second one they give us (-4,7)

to get this we subtracted 6 from x and 3 from y from original so

lets work backwards

add 6 from x and add 3 from y

(-4,7)+(6,3)

answer(2,10)

now D'

subtract 6 from x and 3 from y

(10,2)-(6,3)

(4,-1)

Answer:

He will be able to make 16 pieces of lumber

Step-by-step explanation:

Answer:300

Step-by-step explanation:

Answer:

your answer is that it decreases to 7%

Answer:

28% decrease

Step-by-step explanation:

(18−25)|25|×100

=−725×100

=−0.28×100

=−28%change

=28%decrease

Answer:

$51.67

Step-by-step explanation:

Hope this helps!      :3

plz mark as brainliest!

Answer:

132

Step-by-step explanation:

it is

Simple interest is the interest calculated on the principal at a given rate for a time period.

The formula for simple interest is given as,

SI = (P x R x T) / 100

P = Principal

R = rate

T = time in years

The interest that will be paid after 3 years with 8% interest is $132.

It is the interest calculated on the principal at a given rate for a time period.

The formula for simple interest is given as,

SI = (P x R x T) / 100

P = Principal

R = rate

T = time in years

We have,

P = $550

R = 8%

T = 3 years

SI = (P x R x T) / 100

SI = (550 x 8 x 3) / 100

SI = $132

Thus,

The interest that will be paid after 3 years with 8% interest is $132.

Learn more about simple interests here:

https://brainly.com/question/25845758

#SPJ2

Answer:

The radius of the sphere is 7 units

Step-by-step explanation:

Surface Area

Given a sphere of a radius (r), the surface area is given by the formula:

[tex]\displaystyle A=4\pi r^2[/tex]

If the surface area is given, we can solve for r:

[tex]\displaystyle r=\sqrt{\frac{A }{4\pi }}[/tex]

The surface area of a sphere is given A=196π.

Calculating the radius:

[tex]\displaystyle r=\sqrt{\frac{196\pi}{4\pi }}[/tex]

[tex]\displaystyle r=\sqrt{49}[/tex]

r = 7 units

The radius of the sphere is 7 units

transversal angles

Step-by-step explanation:

When two or more lines are cut by a transversal, the angles which occupy the same relative position are called corresponding angles . When the lines are parallel, the corresponding angles are congruent .

Step-by-step explanation:

log(z) is defined when z > 0.

For log(9 - x²) to be defined, we have 9 - x² > 0.

=> x² < 9, -3 < x < 3.

The domain of y = log(9 - x²) is (-3,3).

Answer:

x              y

2              9

3              7

4              5

5              3

Step-by-step explanation:

Answer:

9

7

5

3

The order is from up to down

The formula is simply this: C = πd. In this equation, "C" represents the circumference of the circle, and "d" represents its diameter. That is to say, you can find the circumference of a circle just by multiplying the diameter by pi.

The formula is C=2πr

Answer:

Step-by-step explanation:

Remark

It's a right triangle so you can use a^2 + b^2 = c^2

a = 3

c = 5

3^2 + b^2 = 5^2         Expand

9 + b^2 = 25              Subtract 9 from both sides

b^2 = 25 - 9

b^2 = 16                     Take the square root of both sides.

√b^2 = √16

b = 4

Answer:

10.60 inches

Step-by-step explanation:

18.45

-7.85

_____

10.60 inches

Answer:

The relationship between the two is that they are equal.

Step-by-step explanation:

Since y = cosx is a even function, that means that cosx = cos(-x). Therefore, cos 90 degrees = cos -90 degrees.

We can also test this out:

cos 90 = 0

cos -90 = cos 270 = 0

Therefore, this came to the same conclusion as our first solution.

I hope this helps! :)

Answer:

1/2

Step-by-step explanation:

Since you are going from the biggest to smallest, it would be 1/2. If you are going from the smallest to biggest it would be 2. So the answer is 1/2. :)

Answer:

x = 10

Step-by-step explanation:

-1/2x + 2 = -x + 7

multiply by 2 so that -1/2x becomes -x

(-1/2x + 2 = -x + 7)2

-x + 4 = -2x + 14

subtract 4 from both sides

-x = -2x + 10

add -2x to both sides

x = 10

Answer:

ones

Step-by-step explanation:

It is given that Jim wants to divide 762 coupons equally among 9 stores.

So dividing 762 by 9, we get

[tex]$=\frac{762}{9}$[/tex]

= 84.66

The position of the digit before the decimal place start with 'ones' and then proceeds to tens, hundreds, thousands, etc.

Therefore, the first digit of the quotient is in the ones place of the position value or place value.