wo runners are saving money to attend a marathon. The first runner has $112 in savings, received a $45 gift from a friend, and will save $25 each month. The second runner has $50 in savings and will save $60 each month.

Which equation can be used to find m, the number of months it will take for both accounts to have the same amount of money?

112 – 25m + 45 = 50 – 60m
112 + 25 + 45m = 50m + 60
112 + 25 – 45m = –50m + 60
112 + 25m + 45 = 50 + 60m

Hello,

[tex]\displaystyle \int {-\dfrac{2}{3} \sqrt{(2-5x)^3}} \, dx \\\\\displaystyle=-\dfrac{2}{3}*\dfrac{-1}{5} \int {-5*(2-5x)^{\frac{3}{2} }} \, dx \\\\\displaystyle=\dfrac{4}{3}*(2-5x)^{\frac{5}{2} }+C[/tex]

Answer:

Doug share the cards with his three other friends.

Step-by-step explanation:

If there were 24 cards and each person was suppose to get 6

24 ÷ 6 = 4

The cards were shared among 4 people including Doug himself.

Have a nice day :)

Answer:

$68.25

Step-by-step explanation:

To get the sales tax, you must notice that the sales tax is 7% of 975.

That is equal to:

975 × 0.07

0.07 is equal to 7%, or [tex]\frac{7}{100}[/tex].

The answer to the equation is 68.25.

Answer:

€3,551.05

Step-by-step explanation:

31*29=899

899*3.65=€3,551.05

the school will get an estimate of €3,551.05

The answer is C or 3 miles per hour

how is it 3?:

there is a point at 6 and another at 3 all we do is 6 - 3 = 3

Answer:

496 in.²

346 mm²

880 in.²

168 cm³

960 m³

420 yd³

Step-by-step explanation:

SA = 2(wl + hl + hw)

SA = 2 · (8 · 16 + 5 · 16 + 5 · 8)

SA = 496

SA = 2(wl + hl + hw)

SA = 2 · (5 · 13 + 6 · 13 + 6 · 5)

SA = 346

SA = 2(wl + hl + hw)

SA = 2 · (4 · 20 + 15 · 20 + 15 · 4)

SA = 880

V = whl

V = 4 · 7 · 6

V = 168

V = whl

V = 10 · 8 · 12

V = 960

V = whl

V = 14 · 3 · 10

V = 420

Step-by-step explanation:

V = πr²h

V = 3 × 14² × 28

v = 16464cm³

Answer:

B

Step-by-step explanation:

[tex]2xy + 3xt - 7yt = 0[/tex]

[tex]3xt - 7yt = - 2xy[/tex]

Factor out t

[tex]t(3x - 7y) = - 2xy[/tex]

Divide by 3x-7y

[tex]t = - \frac{2xy}{3x - 7y} [/tex]

But since x and y are positive, the answer is positive

[tex]t = \frac{2xy}{3x - 7y} [/tex]

Answer:

x = -8 and y = 6

Step-by-step explanation:

3x - 4y = -24

Solve for y - intercept

3x - 4y = -24

To find y intercept , substitute x = 0

3 × 0 - 4y = -24

Any expression multiplied by 0 equals 0.

0 - 4y = -24

-4y = -24

Divide both sides by -4

-4y / -4 = -24/-4

y = 6

Similarly, Solve for x-intercept

3x - 4y = -24

To find x- intercept , susbtitute y = 0

3x - 4 × 0 = -24

Any expression multiplied by 0 equals 0.

3x - 0 = -24

3x = -24

Divide both sides by 3

3x / 3 = -24 / 3

x = -8

Therefore, y = 6 and x = -8

Answer:

Step-by-step explanation:

9.7 = [tex]\frac{97}{10}[/tex]

Count the number of places in the decimal number after the decimal point.

Here , there is only one place.

So, multiply and divide by 10. 9.7 *10/1*10 = 97/10

Answer:

Solution given:

Volume of cuboid=975cm³

length[l]=15cm

width[w]=130mm=13cm

height [h]=?

we have:

Volume of cuboid=l*w*h

975=15*13*h

h=[tex]\frac{975}{195}=5cm[/tex]

The height of the cuboid is 5cm.

Answer:

Simplify the expression.

Exact Form:

1 /2

Decimal Form:

0.5

Answer:

The Answer is

Fraction Form: 1/2

Decimal Form: 0.5

Percentage form: 50%

Step-by-step explanation:

I got the answer 1/2 by Adding 1 by 2/3, And then after that I got the answer 2/3 and with that I multiplyied it with 3/4 and I got 1/2

Answer:

the first graph

Answer:

1st option

Step-by-step explanation:

If the rate of change is constant, then it's always a straight line, so the 1st option, and if you see the graph, you'll see the line is going down at a rate of 1/4, so the slope is 1/4. So the answer to your question will be the 1st option.

Answered by GAUTHMATH

Answer:

Angle A is F Angle A = 57. 52+71=123. 180-123=57

Answer:

[tex]s =\frac{25 + 26 + 17}{2} = 34[/tex]

[tex] = \sqrt{34 \times 9 \times 8 \times 17} [/tex]

[tex]17 \times 3 \times 2 \times 2 = 204cm ^{2} [/tex]

area ∆ BEC

[tex] = \frac{1}{2} \times 17 \times h = 204[/tex]

[tex]h = \: \frac{204 \times 2}{17} = 24[/tex]

[tex]area \: trap \: \: abcd \\ = \frac{1}{2}(60 + 77) \times 24 \\ = 137 \times 12 = 1644cm ^{2} [/tex]

Step-by-step explanation:

#keep learning!!

Answer:

Bremen's age is 28 years

Step-by-step explanation:

Bremen's age= x

Omane's age= x+4

x+x+4=60

2x+4=60

2x=60-4

2x=56

2x = 56

2 2

x=28

Answer:

(0,-6)

Step-by-step explanation:

9x + 3y = -18

Solve for y to get equation in slope intercept form

( y = mx + b )

9x + 3y = -18

Subtract 9x from both sides

9x - 9x + 3y = -18 - 9x

3y = -9x - 18

Divide both sides by 3

3y/3 = y

-9x - 18 / 3 = -3x - 6

We're left with y = -3x - 6

The equation is now in y intercept form

y = mx + b where b = y intercept

-6 takes the spot of b therefore the y intercept would be at (0,-6)

Answer:

-1 Not in domain

0 In domain

1 In domain

Step-by-step explanation:

The domain for the square root function is all positive numbers including (0). The domain is the set of real numbers which when substituted into the function will produce a real result. While one can substitute a negative number into the square root function and get a result, however, the result will be imaginary. Therefore, the domain for the square root function is all positive numbers. It can simply be expressed with the following inequality:

[tex]x\geq0[/tex]

Therefore, one can state the following about the given numbers. Evaluate if the number is greater than or equal to zero, if it is, then it is a part of the domain;

-1 => less than zero; Not in domain

0 => equal to zero; In domain

1  => greater than zero: In domain

Answer:

The answer is x = -3.

Step-by-step explanation:

To solve for (x), start by realizing that line segment IJ and line segment JK sum up to line segment IK, which equals 5. These line segments can then be turned into an equation, and the equation will look like [tex]7+x+2x+7=5[/tex].

Next, begin to solve the equation by combining like terms, which will look like [tex]3x+14=5[/tex]. Then, subtract 14 from both sides of the equation, which will look like [tex]3x=-9[/tex], and divide both sides by 3 and simplify, which will look like [tex]x=-3[/tex]. The final answer is x = -3.

Answer:

x=60

Step-by-step explanation:

solve, 180-(90+x) = 180-(30+2x)

Answer:

144[tex]\pi[/tex]

Step-by-step explanation:

Volume of a Sphere :

V = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]

V = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]6^{3}[/tex]

V = [tex]\frac{4}{3}[/tex](216)[tex]\pi[/tex] (216 times 4, divided by 3)

V  = 288[tex]\pi[/tex]

Now divide by 2, it's only half of a sphere.

Note: There must be -4 instead of 4 otherwise all options are incorrect.

Given:

A polynomial function has a leading coefficient of 3 and roots -4, 1, and 2, all with multiplicity 1.

To find:

The polynomial function.

Solution:

The general polynomial function is defined as:

[tex]P(x)=a(x-c_1)^{m_1}(x-c_2)^{m_2}...(x-c_n)^{m_n}[/tex]

Where, a is the leading coefficient, [tex]c_1,c_2,...,c_n[/tex] are the zeros  with multiplicity [tex]m_1,m_2,...,m_n[/tex] respectively.

It is given that a polynomial function has a leading coefficient of 3 and roots 4, 1, and 2, all with multiplicity 1. So, the polynomial function is defined as:

[tex]P(x)=3(x-(-4))^1(x-1)^1(x-2)^1[/tex]

[tex]P(x)=3(x+4)(x-1)(x-2)[/tex]

Therefore, the correct option is A.

Answer:

1)  [tex]T_{(a, \, b)}[/tex] = f(x - a) + b

Coordinate change

(x, y) → (x + a, y + b)

2) RFy(x, y) = f(-x)

Coordinate change

(x, y) → (-x, y)

3) RFx(x, y) = -f(x)

Coordinate change

(x, y) → (-y, x)

4) RCCW90(x, y) = f⁻¹(-x)

Coordinate change

(x, y) → (-y, x)

5) RCCW180(x, y) = -(f(-x))

Coordinate change

(x, y) → (-x, -y)

6) A 270 degrees counterclockwise rotation gives;

RCCW270(x, y) = -(f⁻¹(x))

Coordinate change

(x, y) → (y, -x)

Step-by-step explanation:

1) Horizontal translation a units right = f(x - a)

The vertical translation b units up = f(x) + b

Therefore, we get; [tex]T_{(a, \, b)}[/tex] = f(x - a) + b

The coordinate change

(x, y) → (x + a, y + b)

2) A reflection across the y-axis = RFy(x, y) = f(-x)

The coordinate change

(x, y) → (-x, y)

3) A reflection across the x-axis gives RFx(x, y) → (x, -y)

Therefore, in function notation, we get;

RFx(x, y) = -f(x)

4) A 90 degrees rotation counterclockwise, we get RotCCW90(x, y) → (-y, x)

In function notation RotCCW90(x, y) = INVf(-x) = f⁻¹(-x)

5) A 180 degrees counterclockwise rotation about the origin gives;

(x, y) → (-x, -y)

Therefore, we get;

In function notation RotCCW180(x, y)  = -(f(-x))

6) A 270 degrees counterclockwise rotation gives RotCCW270(x, y) → (y, -x)

In function notation RotCCW270(x, y) = -(f⁻¹(x))

Answer:

2

Step-by-step explanation:

a prime factor is a factor that is a prime number

a prime number is a number that will have a fraction in the quotient if it's divided by any number other than itself

2 is the only prime factor shared between 8 and 12

Answer:

5/6

Step-by-step explanation:

first form numerator you will multiply by π it means 3.14 multiply 11

the answer equals 34.54 ..and then you will use √ it means square root....so the answer is 5

the annwer is

5/6

Answer:

Step-by-step explanation:

[tex]\frac{11\pi }{6}[/tex] =  11 × [tex]\frac{\pi }{6}[/tex] = (12 - 1) × [tex]\frac{\pi }{6}[/tex]

The terminal point located in IV quarter ⇒ x-coordinate is positive and y-coordinate is negative.

(x, y) = ( [tex]\frac{\sqrt{3} }{2}[/tex] , - [tex]\frac{1}{2}[/tex] )