find the original price of a pair of shoes that was discounted 20% and now sell for $54

➷ Add 24 to both sides:

x^2 + 10x + 24

Find two values that multiply to make 24 but add to make 10

As you will notice, this is 6 and 4

Now factorize it:

(x + 4)(x + 6)

The values of x would be the opposite of what is in the parenthesis

Therefore x = -4 or x = -6

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

x= -6                    x=-4

Step-by-step explanation:

x2 + 10x = −24

Add 24 to each side

x2 + 10x+24 = −24+24

x2 + 10x +24=0

Factor

(x+6) (x+4) = 0

Using the zero product property

x+6 = 0             x+4 = 0

x+6-6 = 0-6      x+4-4 =0-4

x= -6                    x=-4

we know the blue and white paints are on a 1.5 : 5 ratio, thus, if we have a total of 16.25 gallons of paint to be split along that ratio, we can simply divide 16.25 by (1.5+5) and distribute accordingly.

[tex]\bf \cfrac{blue}{white}\qquad \stackrel{ratio}{1.5:5}\qquad \cfrac{1.5}{5}~\hspace{5em}\cfrac{1.5\cdot \frac{16.25}{1.5+5}}{5\cdot \frac{16.25}{1.5+5}}\implies \cfrac{1.5\cdot \frac{16.25}{6.5}}{5\cdot \frac{16.25}{6.5}} \\\\\\ \cfrac{1.5\cdot 2.5}{5\cdot 2.5}\implies \cfrac{3.75}{12.5}\qquad \qquad \boxed{\stackrel{blue}{3.75}~:~\stackrel{white}{12.5}}[/tex]

To find out how much of each color to mix, set up a proportion and solve for x. You will need 3.75 gallons of blue paint and 12.5 gallons of white paint.

To find out how much of each color to mix, we can set up a proportion.

Let's say x represents the amount of blue paint needed, and y represents the amount of white paint needed.

We can set up the following equation:

1.5 quarts / 5 quarts = x gallons / (16.25 - x) gallons

Cross multiplying gives us:

5x = 1.5(16.25 - x)

Simplifying the equation gives us:

5x = 24.375 - 1.5x

Combining like terms gives us:

6.5x = 24.375

Dividing both sides by 6.5 gives us:

x = 3.75

So, you will need 3.75 gallons of blue paint and 16.25 - 3.75 = 12.5 gallons of white paint.

QUESTION 1

The given expression is

2+8

The greatest common factor of 2 and 8 is 2.

We can rewrite as: [tex]2+8=2\times1+2\times4[/tex]

Factor to get: [tex]2+8=2(1+4)[/tex]

QUESTION 2

Given: 9-3

Greatest common factor of 9 and 3 is 3.

Rewrite as: [tex]9-3=3\times3-3\times1[/tex]

Factor: [tex]9-3=3(3-1)[/tex]

QUESTION 3

Given: 30+25

Greatest common factor of 30 and 25 is 5.

Rewrite as: [tex]30+25=5\times6+5\times4[/tex]

Factor: [tex]30+25=5(6+4))[/tex]

QUESTION 4.

Given: 35-14

The greatest common factor of 35 and 14 is 7.

Rewrite as:  [tex]35-14=5\times7-2\times7[/tex]

Factor:  [tex]35-14=7(5-2)[/tex]

QUESTION 5

The given expression is 81-18.

The greatest common factor of 81 and 18 is 9.

Rewrite as: [tex]81-18=9\times9-9\times2[/tex]

Factor: [tex]81-18=9(9-2)[/tex]

QUESTION 6

Given: 60+100

The greatest common factor of 60 and 100 is 20.

Rewrite as : [tex]60+100=20\times3+20\times5[/tex]

Factor: [tex]60+100=20(3+5)[/tex]

QUESTION 7

Given: 28-20

The greatest common factor of 28 and 20 is 4.

Rewrite as: [tex]28-20=4\times7-4\times5[/tex]

Factor: [tex]28-20=4(7-5)[/tex]

QUESTION 8

Given: 72+48

The greatest common factor of 72 and 48 is 24.

Rewrite as: [tex]72+48=24\times3+24\times2[/tex]

Factor: [tex]72+48=24(3+2)[/tex]

QUESTION 9

The given expression is [tex]12x+18[/tex].

The greatest common factor of [tex]12x[/tex] and 18 is 6.

Rewrite as; [tex]12x+18=6\times2x+6\times3[/tex]

Factor; [tex]12x+18=6(2x+3)[/tex]

QUESTION 10

Given: [tex]4y+10[/tex]

The greatest common factor of [tex]4y[/tex] and 10 is 2.

Rewrite the expression as; [tex]4y+10=2\times2y+2\times5[/tex]

Factor:  [tex]4y+10=2(2y+5)[/tex]

Answer:

20 + 8 + 0.1 + 0.09

Step-by-step explanation:

Answer:

20 + 8 + 0.1 + 0.09

20 wholes +8 wholes =28 then...

.1 tenth+.09 hundereths=.19 add..

28+.19=.  28.19

Answer:

20cm

Step-by-step explanation:

Answer:

The correct answer is option 2

45 cm

Step-by-step explanation:

It is given a circle with circumference C = 180 cm

To find the length of arc ABC

From the figure we can see that the central angle of arc ABC = 90°

Therefore the arc length = (90/360) * Circumference

Arc ABC  = (90/360) * 180 = (1/4) * 180 = 45

Therefore arc length = 45 cm

The correct answer is option 2

store a single drink cost $3/12 =25c

store b single drink cost $5.50/ 22 = 25c

store c single drink cost $4.75/18 = 26c

store d single drink cost $8/36 = 22c

hence store d offers the best buy

To determine the best buy among four stores selling soft drinks, compare the price per can or pack for each store. Store D offers the best buy with a cost of approximately $0.22 per can.

To determine which store offers the best buy, we need to compare the prices per can or pack of each store.

Therefore, Store D offers the best buy with a cost of approximately $0.22 per can.

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4 · x^4 · x^4 · y

4 x^8 y

In words: four times x to the eighth times y

Answer:

x^3 - 7x^2 + 4x + 30

Step-by-step explanation:

The equation is already simplified to its fullest if we're looking at factored form.

Otherwise, just multiply everything out using a punnett square.

Answer:

x^3 - 7x^2 + 4x + 30

Step-by-step explanation:

I just did this one hope this helps

Answer:

x = -6   x=4

Step-by-step explanation:

x^ 2 + 2 x = 24

Subtract 24 from each side

x ^2 + 2 x-24 = 24-24

x^2 +2x -24 = 0

Factor

What 2 numbers multiply to -24 and add to 2

6*-4 = -24

6+-4 = -2

(x+6) (x-4) =0

Using the zero product property

x+6 =0           x -4=0

x+6-6=0-6     x-4+4=0+4

x = -6   x=4

Answer:

20 kg

Step-by-step explanation:

If we want any value in grams to be in kilograms, we divide it by 1000

in this example: 20000/1000

=20 kg

Answer:

The answer is D. 4r^6.

<3

-Callie

Step-by-step explanation:

Answer:

D. 4r^6.

Step-by-step explanation:

Bonsoir,

Combien fait 87$ augmenté de 200% ?

87 $ x 200/100 = 174 $ d'augmentation,  

174 + 87 = 261 $

Put the answer into a calculator;

-√17 = -4.123105626

√17 = 4.123105626

Round to the nearest tenth by looking at the 2nd digit after the decimal point. If it is 5 or greater, round up, otherwise round down.

-√17 = 4.123105626

2 is less than 5, so we leave it as it is.

-√17  ≈ -4.12

√17 = 4.123105626

2 is less than 5, so we leave it as it is.

√17 = 4.12

v ≈ -4.12, 4.12

Answer:

X + Y     and    x+0+(y+0)    are both correct

Step-by-step explanation:

Explanation is on the image  

Option A, x + y and B. x + 0 + (y + 0)

(x + 0) + y + 0 is equivalent to.

equation is the relationship between variable and represented as    is example of polynomial equation.

(x + 0) + y + 0
= x + 0 + (y + 0 )
= x + y

Thus both the option A. and B. is correct.

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Answer:

A) 4

Work is shown in attached sheet! :)

Answer:

Option A is correct

Common ratio = 4

Step-by-step explanation:

Common ratio(r) : In a geometric series, the common ratio is the ratio of a term to the previous term.

[tex]r = \frac{a_2}{a_1}=\frac{a_3}{a_2}= \frac{a_4}{a_3}=.....[/tex]

As per the statement:

The values in the table represent a exponential function.

Since, Geometric sequences and exponential functions are very closely related to each other.

At x= 1;

y = 9

At x = 2;

y = 36 and so on....

By definition we have;

[tex]r = \frac{36}{9} =\frac{144}{36}=......[/tex]

After solving we get;

r  =4

Therefore, the common ratio of the associated geometric is, 4

[tex]\bf ~\hspace{10em}\textit{function transformations} \\\\\\ \begin{array}{llll} f(x)= A( Bx+ C)^2+ D \\\\ f(x)= A\sqrt{ Bx+ C}+ D \\\\ f(x)= A(\mathbb{R})^{ Bx+ C}+ D \end{array}\qquad \qquad \begin{array}{llll} f(x)=\cfrac{1}{A(Bx+C)}+D \\\\\\ f(x)= A sin\left( B x+ C \right)+ D \end{array} \\\\[-0.35em] ~\dotfill\\\\ \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\ \bullet \textit{ flips it upside-down if } A\textit{ is negative}[/tex]

[tex]\bf ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if } B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{ C}{ B}\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\[/tex]

[tex]\bf \bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{ B}[/tex]

now, with that template in mind, let's take a look

[tex]\bf \begin{cases} f(x)=&2^x\\ g(x)=&f(x+k)\\ & f(x-5)\\ &2^{x-5} \end{cases}~\hspace{10em}g(x)=2^{\stackrel{A}{1}(\stackrel{B}{1}x\stackrel{C}{-5})}+\stackrel{D}{0} \\\\\\ \textit{horizontal shift by }\cfrac{C}{B}\implies \cfrac{-5}{1}\implies -5\qquad \qquad \textit{ of 5 units to the right}[/tex]

The graph of g(x) is shifted horizontally 5 units to the right of the graph of f(x).

The correct option is (b).

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).

As per the given data:

We are given 2 functions, and we have to find out the shift in the graph.

f(x) = 2^x

g(x) = f(x+k)

When the value of k = -5 we have to find out the shift in the graph of g(x).

For finding out the shift in the graph of g(x):

g(x) = f(x+k)

By substituting the given value of f(x) = 2^x and k = -5:

g(x) = 2^(x-5)

When y = f(x) is changed to y = f(x - 5) the graph of f(x) shifts 5 units to the right horizontally.

Similarly, for g(x) = 2^(x-5) the graph will shift by 5 units to the right.

Hence, The graph of g(x) is shifted horizontally 5 units to the right of the graph of f(x).

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Answer:

Each side is 25cm long.

Step-by-step explanation:

75/3=25 (This is because each side of an equilateral triangle is equal to each other.) (The perimeter is all sides added together.)

Answer:

equilateral traingle mean all sides are equal..so 75÷3

=25cm

Step-by-step explanation:

its equal....so we just simply just divide..

Answer:

Its the third choice.

Step-by-step explanation:

V = 1/3  pi r^2 h

= 1/3 pi 4^2 * 10

= (160/3) pi cm^3.

Answer:

third one:)

Step-by-step explanation:

i took the k12 test

Answer:

The unit rate is 0.11 $/ounce

Step-by-step explanation:

we know that

To find the unit rates divide the total cost by the total volume

so

(6/54)=0.11 $/ounce

Answer:

100 $

Step-by-step explanation:

Hello

If

300 $ ----> 3 days

X -----------> 1 day

X = [300*1] / (3)

X = 100 $

Best regards

Answer:

D.

Your doing it for a week..5 days, his cases are 12, but how many cases(c) does he need to sell minus his rent vs what his goal is.

Small cooler can hold= 6 gallons

and big cooler can hold= 30 gallons

Let the numbers of gallons hold by a small cooler is: x gallons

and the number of gallons hold by a bigger cooler is: 5x gallons.

( Since it was given that:

The bigger cooler is 5 times as large as the smaller cooler  )

Also the total number of gallons of punch for a party is: 36 gallons

Hence, we get:

   x+5x=36

i.e.  6x=36

On dividing both side by 6 we get:

   x=6

Hence, the number of gallons hold by small cooler is: 6 gallons

and number of gallons hold by big cooler is: 5×6=30 gallons

Answer: 5 cents less

Step-by-step explanation:

The unit price for the 24 pack would be $1.10 and the unit price for the 12 pack would be $1.15.

Answer:

0.05

Step-by-step explanation:

Answer:

Step-by-step explanation:

Factor all the factors making up the square root.

108: 2*2*3*3*3

a^7: a*a*a*a*a*a*a

b^5:b * b * b * b * b

The rule for taking a square root of this is

For every pair, you get to take one number outside the root sign and throw the other one away.

2*3*a * a * a* b * b√(3*a * b)

6a^3b^2 * √(3*a*b)

Answer: 113.1

Step-by-step explanation:

first you have to multiply 4/3*pie or 3.14 times 3

4/3 x 3.14 x 3 = 113.1

Answer:

Step-by-step explanation:

[tex]f(v)=v^2+5v+6\\\\\text{The x-intercept is for y = 0.}\\\\v^2+5v+6=0\\\\v^2+2v+3v+6=0\\\\v(v+2)+3(v+2)=0\\\\(v+2)(v+3)=0\iff v+2=0\ \vee\ v+3=0\\\\v+2=0\qquad\text{subtract 2 from both sides}\\v=-2\\\\v+3=0\qquad\text{subtract 3 from both sides}\\v=-3[/tex]

Answer:

jk(x) = -16x^2 -12x+10

Step-by-step explanation:

j(x) = -4x+2

k(x) = 5+4x

jk(x) = (-4x+2) (5+4x)

FOIL

-4x*5 +-4x*4x +2*5 +2*4x

Combine like terms

-20x-16x^2 +10+8x

-16x^2 -12x+10

jk(x) = -16x^2 -12x+10

Answer:

Step-by-step explanation:

12/5 is the answer.

Answer: 9 or -9 it can be both

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

the square root is fundamentally just what two numbers multiply together to make the number within the square root

9 x 9 = 81

so 9 is the square root

also think of the root of the square

9^2 the root in this case is the nine and te answer is 81