It takes b minutes for Sylvia's bathtub to fill with water.
How many minutes will it take to fill 3 same-size bathtubs?
Write your answer as an expression.

if a line is perpendicular to another line with slope m, the perpendicular line's slope is always -1/m. Since the slope of the given line is -4, the perpendicular slope would be 1/4 (-1/-4 = 1/4). Our line right now is y = (1/4)x + b. Now substitute the given point in for x and y to solve b. In this case b = -1, so your line would be  y = (1/4)x + -1.

Answer: 11

Step-by-step explanation:

plug in 4 any instance you see "x"

f(x) = 3x - 1​

f(4) = 3(4) - 1 = 11

Functions are mappings who map inputs to at max one corresponding outputs. The value of function at x=4 is: [tex]f(4) = 11[/tex]

You can simply replace those variables with the value you know of them and then operate on those values to get a final value. This is the result of that expression at those values of the considered variables.

For given case, we have:

[tex]f(x) = 3x - 1[/tex]

Taking x = 4, we get:

[tex]f(4) = 3(4) - 1 = 3 \times 4 - 1 = 12 - 1\\f(4) = 11[/tex]

Thus, The value of function at x=4 is: f(4) = 11

Learn more about evaluating functions here:

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Part A

h(d) = (-1/5)d^2 + 2d is the same as h(d) = -0.2d^2 + 2d because -1/5 = -0.2

I'll use x in place of d, and y in place of h(d) to get this equivalent equation: y = -0.2x^2 + 2x

Let's find the vertex of y = -0.2x^2 + 2x

Note how y = -0.2x^2 + 2x is in the form y = ax^2+bx+c with

a = -0.2

b = 2

c = 0

So the x coordinate of the vertex is

h = -b/(2a)

h = -2/(2(-0.2))

h = 5

Plug this value into the h(d) function to compute the corresponding y coordinate

h(d) = -0.2d^2 + 2d

h(5) = -0.2(5)^2 + 2(5)

h(5) = 5

Coincidentally, the x and y coordinates of the vertex are both the same. This wont be the case in general.

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Answers:

The vertex is located at (5,5)

The interpretation is that the highest the dolphin can get is 5 feet off the surface of the water and this occurs 5 horizontal feet away from the starting point. Imagine a parabola that opens downward to have a highest point at the vertex mentioned.

====================================

Part B

From part A above, we found x = 5 to be the x coordinate of the vertex. Simply double this value to get 10 as the answer. The reason why this works is because x = 0 is the starting x intercept, or the starting point which the dolphin jumps from. Also, its because of the hint given how the vertex is between each x intercept.

If the dolphin started from any other point on the x axis, then this trick of "double the result from part A" wouldn't apply.

Part C below shows that x = 0 and x = 10 are the two x intercepts. This helps confirm the proper range.

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Answer: 10 feet

====================================

Part C

h(d) = y = height of dolphin

we want to find the two x values that make y = 0, which help us figure out when the dolphin jumps out of the water and when it lands back in the water

--------

Plug y = 0 into the equation y = -0.2x^2 + 2x and solve for x

y = -0.2x^2 + 2x

-0.2x^2 + 2x = y

-0.2x^2 + 2x = 0

x(-0.2x + 2) = 0 .... factor out x

x = 0 or -0.2x + 2 = 0 .... zero product property

x = 0 or -0.2x = -2

x = 0 or x = -2/(-0.2)

x = 0 or x = 10

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Answer:

The two x intercepts are x = 0 and x = 10

This means the parabola crosses the x axis at the locations (0,0) and (10,0).

Answer:

x=15

Step-by-step explanation:

Answer:

x=15

Step-by-step explanation:

4x+10=x+5+50

4x+10=x+55

4x-x+10=55

3x+10=55

3x=55-10

3x=45

x=45/3

x=15

Answer:

x=-3, y=5. (-3, 5).

Step-by-step explanation:

y=x+8

x+y=2

----------

x+x+8=2

2x+8=2

2x=2-8

2x=-6

x=-6/2

x=-3

y=-3+8=5

Answer:

(-3,5)

Step-by-step explanation:

Answer:

S₈ = 296

Step-by-step explanation:

Given: 2 + 12 + 22 + 32 + .... + (10n - 8) = [tex]$5n^2 - 3n $[/tex]

To prove [tex]$ S_8 $[/tex] is true, substitute [tex]$ n = 8 $[/tex] and compare LHS and RHS

n = 8:

[tex]10n - 8 = 10(8) - 8[/tex]

[tex]$ \implies 72 $[/tex]

[tex]$ \therefore LHS = 2 + 12 + 22 + 32 + 42 + 52 + 62 + 72 $[/tex]

[tex]$ = 296 $[/tex]

Now, Substituting n = 8 in RHS, we get:

[tex]$ 5n^2 - 3n = 5(8)^2 - 3(8) = 5(64) - 24 $[/tex]

[tex]$ = 296 $[/tex]

Therefore, RHS  = 296

We see, LHS = RHS

Hence, we can conclude that [tex]$ S_8 $[/tex] is correct.

Answer:

82.28 in

Step-by-step explanation:

Answer:

The Proceeds of maturity after 10 years is $1613.4

Step-by-step explanation:

Given as :

The maturity value = $ 6000

The rate applied at 6 % compounded quarterly

The Time period = 4 years

Now,

Amount = Principal × [tex](1+\dfrac{\textrm Rate}{4\times 100})^{\textrm 4\times Time}[/tex]

Or, Amount = 6000  × [tex](1+\dfrac{\textrm 6}{4\times 100})^{\textrm 4\times 4}[/tex]

Or, Amount = 6000 × [tex](1.015)^{16}[/tex]

Or,  Amount = 6000 × 1.2689

∴  Amount = $ 7613.4

So, The proceeds after 10 years = $ 7613.4 - $ 6000 = $ 1613.4

Hence The Proceeds of maturity after 10 years is $1613.4   Answer

Answer:

The answer is C , 5^(1/3)

Answer:

24

Step-by-step explanation:

in this, the blank is 'y'. I filled the x with -8

)(−8)−(−8−40)=(2)(−8)−(y−8)

Step 1: Simplify both sides of the equation.

(10)(−8)−(−8−40)=(2)(−8)−(y−8)

(10)(−8)+−1(−8−40)=(2)(−8)+−1(y−8)(Distribute the Negative Sign)

(10)(−8)+(−1)(−8)+(−1)(−40)=(2)(−8)+−1y+(−1)(−8)

(10)(−8)+8+40=(2)(−8)+−y+8

−80+8+40=−16+−y+8

(−80+8+40)=(−y)+(−16+8)(Combine Like Terms)

−32=−y+−8

−32=−y−8

Step 2: Flip the equation.

−y−8=−32

Step 3: Add 8 to both sides.

−y−8+8=−32+8

−y=−24

Step 4: Divide both sides by -1.

−y

−1

=

−24

−1

y=24

Answer:

y=24

Answer:

234 ÷ g

Step-by-step explanation:

Convert "234 divided by g" into algebraic form, which is:

234 ÷ g

It can also be written as 234/g.

An expression is has no equal sign, as opposed to an equation, which has an answer.

Answer:

$10

Step-by-step explanation:

$45 x 5 = 225

$225 + $10 = $235

Answer:

They will need $10 more dollars

Step-by-step explanation:

So 45 times 5 is 225 so what that means is that for each week they raised 45 dollars multiply that by 5 weeks and they made $224 dollars then subtract that from 235 so (235-225=10)

They will need $10 more dollars

Answer:

Step-by-step explanation:

(y-y)=m(x-x)

(y--3)=2(x-7)

y+3=2x-14

y+3+14=2x

Answer:

(3 + 4x)(9 - 12x + 16x²) = 0

(4m - 1)(16m² + 4m + 1) = 0

Step-by-step explanation:

Here we have to solve the sum of two cubes which is [tex]27 + 64x^{3}[/tex]

Now, the equation is [tex]27 + 64x^{3} = 0[/tex]

⇒ 3³ + (4x)³ = 0

⇒ (3 + 4x)[3² - 3(4x) + (4x)²] = 0

⇒ (3 + 4x)(9 - 12x + 16x²) = 0

So, (3 + 4x) = 0 or (9 - 12x + 16x²) = 0

Therefore, from the above two relation we can solve for x.

One root will be [tex]- \frac{3}{4}[/tex] and the others we will get by applying Sridhar Acharya Formula, which will give a pair of conjugate imaginary roots of the equation.  

Again, we have to solve the difference of two cubes which is [tex]64m^{3} - 1[/tex]

Now, the equation is [tex]64m^{3} - 1 = 0[/tex]

⇒ (4m)³ - 1³ = 0

⇒ (4m - 1)[(4m)² + 4m(1) + 1²] = 0

⇒ (4m - 1)(16m² + 4m + 1) = 0

So, (4m - 1) = 0 or (16m² + 4m + 1) = 0

Therefore, from the above two relation we can solve for m.

One root will be [tex] \frac{1}{4}[/tex] and the others we will get by applying Sridhar Acharya Formula, which will give a pair of conjugate imaginary roots of the equation.  (Answer)

Answer:take 193 and subtract 35. you should get 158 then divide 158 bby 2 you should get 79 add 35 to 79 you should get 114. therefore kelly will have 114 and rachel will have 79

Step-by-step explanation:

Answer:

Kelly collected 114 pounds of newspaper. Rachel collected 79 pounds of newspaper.

Step-by-step explanation:

Write an expression for each girl to figure out how many pounds of newspapers they each collected:

(x represents pounds of newspapers)   Rachel = x     Kelly = x + 35

To solve, combine the two expressions into one equation: 2x + 35 = 193

Then, subtract 35 from both sides of the equation. Make sure you subtract from both sides of the equation to keep it equal: 2x + 35 - 35 = 193  - 35

The equation left is: 2x = 158

Divide both sides by two in order to get the x by itself: 2x ÷ 2 = 158 ÷ 2

The answer will be: x = 79

Then, substitute 79 for x in the first equations:

Rachel = 79    Kelly = 79 + 35

Solve for the final answer: Rachel = 79    Kelly = 114

In the equation y=40+6x, 40 represents the initial number of comic books in Joylin's collection, given to her by her uncle. Over time, she gains additional comic books from monthly subscriptions.

In the provided equation, y=40+6x, the number 40 represents the initial amount of comic books Joylin has before the monthly subscriptions start. This is essentially the number of comic books Joylin's uncle gave her to start her collection. The number 6 represents the number of books she receives monthly from the subscriptions. Therefore, 'x' months after receiving the initial batch of comic books, Joylin has 40 + 6x comic books in her collection.

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Answer:

2x^3 + 3x^2 - 11x - 6.

Step-by-step explanation:

(2x+1) (x-2) (x+3)

= (2x + 1)[x(x + 3)-2(x + 3)]

= (2x + 1)(x^2 + x - 6)

= 2x(x^2 + x - 6) + 1(x^2 + x - 6)

= 2x^3 + 2x^2 - 12x + x^2 + x - 6

= 2x^3 + 3x^2 - 11x - 6.

Good morning,

Answer:

Step-by-step explanation:

(2x+1) (x-2) (x+3)

= (2x+1) [(x-2) (x+3)]

= (2x+1) [x²+3x-2x-6]

= (2x+1) [x²+x—6]

= 2x³+2x²-12x+x²+x-6

=2x³+3x²-11x-6.

:)

Answer:

40 games

Step-by-step explanation:

Here we need to find a number, x, such as 32 is the 80% of x. In this case x is our 100%.

So, if our x number is the correct it must be that the following ratios are equivalent:

100%/80% = x/32 if 32 is the 80% of x

Lets drop the % sign for simplicity:

100/80 = x/32

Now, multiply both sides by 32 to eliminate the 32 on the right side:

(100/80)*32 = (x/32)*32

100*32/80 = x

3200/80 =x

320/8 = x

40 = x

So 32 is the 80% of 40.

32 games is the 80% of 40 games.

Answer: 40

Step-by-step explanation:

Answer:

Below.

Step-by-step explanation:

No - because the length of any one side must not be equal or greater than the sum of the other 2 sides.

Here 7 = 3 + 4 so they can't form a triangle.

Answer:

no

Step-by-step explanation:

as 3+4 = 7 and the sum of the first 2 sides is supposed to be greater than the third side and 7 is the sum of the first 2 side and the third side is also 7

Ms. Mundo can fill 5 full glasses with 40 ounces of tropical punch, with 5 ounces remaining. This remaining amount fills 2/3 of the last glass.

Ms. Mundo made 40 ounces of tropical punch to pour into glasses that each holds 7 1/2 ounces. To find out what fraction of the last glass is full of punch, we first need to determine how many full glasses can be poured from the 40 ounces.

Since each glass holds 7.5 ounces (which is the same as 7 1/2 ounces), we divide 40 by 7.5 to find the number of full glasses:

 40 ÷ 7.5 = 5 remainder 5

This means that 5 full glasses can be filled, with 5 ounces of punch remaining. Now, to find out what fraction of the last glass the remaining punch fills, we divide the leftover ounces by the capacity of one glass:

 5 ÷ 7.5 = 2/3

The fraction of the last glass that is full of punch is 2/3.

Answer:

675 ft 2

Step-by-step explanation:

just did it in a test

Answer:

d)  Mr.Wallace can use the following equations:

    a + b = 9

   2 a + 3 b = 23

Step-by-step explanation:

Here, the total number of students = 23

Number of groups = 9

Each group can have 2 or 3 students.

a is the number of  groups of 2.

⇒ Total students in a groups  = a x (Number of  student in each group)

= a x 2 = 2 a

b is the number of groups of 3

⇒ Total students in b groups  = b x (Number of  student in each group)

= b x 3 = 3 b

So, according to the question:

Total number of groups formed = 9

⇒ a + b = 9

Total number of students  = 23

or Number of students in  ( a  group + b group ) = 23

⇒ 2 a + 3 b = 23

Hence, Mr.Wallace can use the following equations:

a + b = 9

2 a + 3 b = 23

Answer:

The equation is [tex]0.3x\leq 180[/tex] and  consuela can drive maximum  600 miles.

Step-by-step explanation:

Given:

Consuela Budget= [tex]\$250[/tex]

Rental Company Charges = [tex]\$10 \ per\ day[/tex]

Additional Cost = 30 cents per mile = $0.3 per miles.

Number of days for vacation = 7

We need to find the number of miles Consuela can drive and still be in budget.

Let number of miles she can drive be [tex]x[/tex]

Rental Company Charges for per day [tex]\times[/tex] number of days + Additional Cost per mile [tex]\times[/tex] Number of miles she can drive sholud be less than or equal to Consuela Budget

Now the equation will be.

[tex]10\times 70 +0.3x \leq 250\\70 +0.3 x\leq 250\\0.3x\leq 250-70\\0.3x\leq 180\\x\leq \frac{180}{0.3}\\\\x\leq 600 \ miles[/tex]

Hence Consuela can drive maximum of 600 miles to stay within her budget.

Answer:

Law of cosines

Step-by-step explanation:

In this problem i need to use the law of cosines, because the angles are unknown.

we know that

The formula of the law of cosines is equal to

[tex]c^2=a^2+b^2-2(a)(b)cos(C)[/tex]

where

[tex]a=7\ units\\b=8\ units\\c=10\ units\\C=\theta[/tex]

substitute in the formula

[tex]10^2=7^2+8^2-2(7)(8)cos(\theta)[/tex]

[tex]100=49+64-112cos(\theta)[/tex]

[tex]100=113-112cos(\theta)[/tex]

[tex]112cos(\theta)=113-100[/tex]

[tex]112cos(\theta)=13[/tex]

[tex]cos(\theta)=\frac{13}{112}[/tex]

using a calculator

[tex]\theta=cos^-1(\frac{13}{112})[/tex]

[tex]\theta=83.33\°[/tex]

Answer:

A = 10⁰

Step-by-step explanation:

We have 2.247 and this to represented as [tex]$ 2 \times A + 2 \times B + 4 \times C + 7 \times D $[/tex]

[tex]$ 2.247 = \frac{2247}{1000} $[/tex]

[tex]$ 2.247 = 2 \times 10^0 + 2 \times \frac{1}{10} + 4 \times \frac{1}{10^2} + 7 \times \frac{1}{10^3} $[/tex]

Comparing with the given data, we have:

A = 10⁰

B = [tex]$ \frac{1}{10} $[/tex]

C = [tex]$ \frac{1}{10^2} $[/tex]

D = [tex]$ \frac{1}{10^3} $[/tex]

Hence the answer A = 10⁰.

If c is the longest side, then c must be equal to 10 in order to have a right triangle. This is due to the pythagorean theorem

a^2+b^2 = c^2

6^2+8^2 = c^2

36+64 = c^2

100 = c^2

c^2 = 100

sqrt(c^2) = sqrt(100) ... apply square root to both sides

c = sqrt(100)

c = 10

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

So if we know that c = 10, then the side lengths 6,8,c form a right triangle.

Answer:

A'(-16,4), B'(16,-12), C'(8,12), D'(-4,16)

Step-by-step explanation:

The dilation with a center of dilation at (0,0) and scale factor of [tex]\frac{1}{4}[/tex] has the rule

[tex](x,y)\rightarrow \left(4x,4y\right)[/tex]

Quadrilateral ABCD has vertices at points A(-4,1), B(4,-3), C(2,3) and (-1,4).

Therefore, the image vertices are

Answer:

(8, -2)

Step-by-step explanation:

(8, 2) becomes (8. -2)

Answer:

(8 -2)

Step-by-step explanation: