What is the solution set for the open sentence, using the given replacement set ? 5x−7=8 ; {1, 2, 3, 4} ? x = 1 x = 2 x = 3 x = 4

Answer:

x = 8

Step-by-step explanation:

Using the rule of logarithms

log x = log y ⇔ x = y

Given

log(3x + 2) = log(4x - 6), then

4x - 6 = 3x + 2 ( subtract 3x from both sides )

x - 6 = 2 ( add 6 to both sides )

x = 8

Answer:

B

Step-by-step explanation:

Noting the following rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] = [tex]\sqrt{ab}[/tex]

Given

([tex]\sqrt{2}[/tex] + [tex]\sqrt{3}[/tex])( [tex]\sqrt{5}[/tex] - [tex]\sqrt{7}[/tex] )

Each term in the second factor is multiplied by each term in the first factor

= [tex]\sqrt{2}[/tex]([tex]\sqrt{5}[/tex] - [tex]\sqrt{7}[/tex]) + [tex]\sqrt{3}[/tex]([tex]\sqrt{5}[/tex] - [tex]\sqrt{7}[/tex]) ← distribute parenthesis

= [tex]\sqrt{10}[/tex] - [tex]\sqrt{14}[/tex] + [tex]\sqrt{15}[/tex] - [tex]\sqrt{21}[/tex]

Answer:

A. The answer is our unit prices when our profit is 0

Step-by-step explanation:

The zeros are the x-intercepts, when the curve passes through the x-axis.

I'm going to call our function P

P(x)=-0.5x^2+221x-224 is equal to 0 (our profit is equal to 0) when x (the unit price is such and such)

The answer is our unit prices when our profit is 0

The expression represents the monthly profit from sales of a product at a given unit price. The zero(s) of the expression represent the unit price(s) when the profit is equal to 0.

The expression -0.5x^2 + 221x - 224 represents the monthly profit, in thousands of dollars, from sales of a product when it is sold at a unit price of x dollars.

The zero(s) of the expression are the unit price(s) when the profit is equal to 0. To find the zero(s), we need to set the expression equal to 0 and solve for x.

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Answer:

It is (2, 2).

Step-by-step explanation:

Answer:

The complete factorization is 3x² (x - 5)² ⇒ 2nd answer

Step-by-step explanation:

* Lets revise how to factorize a trinomial

- Find the greatest common factor of the coefficients of the three terms

∵ The trinomial is 3x^4 - 30x³ + 75x²

- The greatest common factor of 3 , 30 , 75 is 3

∵ 3 ÷ 3 = 1

∵ 30 ÷ 3 = 10

∵ 75 ÷ 3 = 25

∴ 3x^4 - 30x³ + 75x² = 3(x^4 - 10x³ + 25x²)

- Now lets find the greatest common factor of the variable x

∵ x² is the greatest common factor of the three terms

∵ x^4 ÷ x² = x²

∵ 10x³ ÷ x² = 10x

∵ 25x² ÷ x² = 25

∴ 3(x^4 - 10x³ + 25x²) = 3x² (x² - 10x + 25)

- Lets factorize (x² - 10x + 25)

∵ √x² = x

∵ √25 = 5

∵ 2 × 5 × x = 10x

∴ x² - 10x + 25 is a completing square

∴ (x² - 10x + 25) = (x - 5)²

∴ 3x² (x² - 10x + 25) = 3x² (x - 5)²

* The complete factorization is 3x² (x - 5)²

Answer:

3x^2 (x-5)^2

Step-by-step explanation:

3x^4 − 30x^3 + 75x^2

We can factor out a 3x^2 from each term

3x^2 (x^2 -10x +25)

The term inside the parentheses can be factored

What 2 numbers multiply to 25 and add to -10

-5*-5 = 25

-5+-5 = -10

3x^2 (x-5) (x-5)

3x^2 (x-5)^2

Answer:

336

Step-by-step explanation:

Using the definition of n[tex]P_{r}[/tex] = n ! / (n- r) !

where n ! = n(n - 1)(n - 2).... × 3 × 2 × 1

8[tex]P_{3}[/tex]

= 8 ! / (8 - 3) !

= 8 ! / 5 !

= [tex]\frac{8(7)(6)(5)(4)(3)(2)(1)}{5(4)(3)(2)(1)}[/tex]

[ cancel 5(4)(3)(2)(1) on numerator/denominator

= 8 × 7 × 6 = 336

ANSWER

[tex]^8P_3 = 336[/tex]

EXPLANATION

Recall that;

[tex]^nP_r = \frac{n!}{(n - r)!} [/tex]

The given expression is:

[tex]^8P_3[/tex]

We substitute n=8 and r=3

[tex]^8P_3 =\frac{8!}{(8- 3)!} [/tex]

[tex]^8P_3 =\frac{8!}{(5)!} [/tex]

This simplifies to :

[tex]^8P_3 =\frac{8 \times 7 \times 6 \times 5!}{5!} [/tex]

We cancel out the common factors to get:

[tex]^8P_3 = 8 \times 7 \times 6[/tex]

[tex]^8P_3 = 336[/tex]

Hello There!

The answer would be the first one.

This is saying that Tom can not save exactly 50.25 but he must save more than that

Answer:

A

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

f(x) - g(x)

= 3x² - 2x + 4 - (5x² + 6x - 8) ← distribute parenthesis by - 1

= 3x² - 2x + 4 - 5x² - 6x + 8 ← collect like terms

= - 2x² - 8x + 12 → A

Answer:

27

Step-by-step explanation:

Answer:

Step-by-step explanation: I believe you would just take 147 + 224 + 175 + 273 = 819pi cm2

So your answer would be 819pi cm2

The answer is 224 pi

.....................................

Answer:

x = -2 or x = -3/2 thus B. & D. are the answer  

Step-by-step explanation:

Solve for x:

2 x^2 + 7 x + 6 = 0

Hint: | Factor the left hand side.

The left hand side factors into a product with two terms:

(x + 2) (2 x + 3) = 0

Hint: | Find the roots of each term in the product separately.

Split into two equations:

x + 2 = 0 or 2 x + 3 = 0

Hint: | Look at the first equation: Solve for x.

Subtract 2 from both sides:

x = -2 or 2 x + 3 = 0

Hint: | Look at the second equation: Isolate terms with x to the left hand side.

Subtract 3 from both sides:

x = -2 or 2 x = -3

Hint: | Solve for x.

Divide both sides by 2:

Answer:  x = -2 or x = -3/2

Answer:

B and D

Step-by-step explanation:

Given

2x² + 7x + 6 = 0

To factorise the quadratic

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × 6 = 12 and sum = + 7

The factors are + 4 and + 3

Use these factors to split the x- term

2x² + 4x + 3x + 6 = 0 ( factor the first/second and third/fourth terms )

2x(x + 2) + 3(x + 2) = 0 ← factor out (x + 2) from each term

(x + 2)(2x + 3) = 0

Equate each factor to zero and solve for x

x + 2 = 0 → x = - 2 → D

2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - [tex]\frac{3}{2}[/tex] → B

Answer:

[tex]4\pi[/tex] or 12.56

Step-by-step explanation:

[tex]\pi r^{2}[/tex] is the formula to find the area of a circle.

if we plug '2' in... [tex]\pi2^{2}[/tex]

which equals to [tex]4\pi[/tex]

if we multiply 4 with pi, it equals to 12.56

Answer:

Area of circle = 12.56 sq. units

Step-by-step explanation:

radius =  2

Area of circle = π r² sq. units

                       = 3.14 * 2 * 2 = 12.56 sq. units

Answer:

Option B is correct.

Step-by-step explanation:

A proportional relationship is a relationship between two variables where the ratio between the two variables is always the same.

Divide b/a for each option, the option having same ratio for the complete tables have proportional relationship

a)

9/3 = 3

12/4 = 3

20/5 = 4

b)

25/20 = 5/4

30/24 = 5/4

40/32 = 5/4

c)

12/4 = 3

15/5 = 3

24/6 = 4

d)

4/3 = 4/3

9/6 = 3/2

12/16 = 3/4

So, Option B is correct.

Answer: Second Option

Step-by-step explanation:

It is said that two variables a and b are propocionales if when b increases then a increases in a constant rate.

That is, a and b are proportional if the quotient between b and a is always equal to a constant k.

[tex]\frac{b}{a}=k[/tex]

To know which of the tables shows a proportional relationship identify in which of the tables the division of b between a always is constant

You can verify that the table where the quotient of b enters a is always constant is in the second table

[tex]\frac{b}{a}=\frac{5}{4}[/tex]

Answer:

(2.4 , -1)

Step-by-step explanation:

Too many commas in second ordered pair but this is how I will interpret the question:

Find the midpoint of (3.2,2.5) and (1.6,-4.5)

So just average x's  : (3.2+1.6)/2 =4.8/2=2.4

And

    just average y's : (2.5+-4.5)/2=-2/2=-1

The midpoint is (average x's , average y's)

Your midpoint is (2.4             ,     -1             )

answer (2.4 , -1)

Answer:

16

Step-by-step explanation:

4 groups of 4 is 16:

[tex]\left\begin{array}{cccc}*&*&*&*\*&*&*&*&*\*&*&*&*&*\*&*&*&*&*\end{array}\right[/tex]

Answer:

The length of the shorter piece is  13 inches

Step-by-step explanation:

Let's represent the longer piece of pipe with the variable L and the shorter piece of pipe with variable S.

Since the pipe is going to be the length of  L and S together, we can make this equation:

L+S=52

Also we know that the longer piece is three times the shorter piece or

L=3S

Substitute the second equation into the first equation.

L+S=52

3S+S=52

4S=52

Divide both sides by 4

4S/4=52/4

S=13 inches

The length of the shorter piece is 13 inches....

To find the length of longer piece, put the value S=13 in L=3S

L=3S

L=3(13)

L=39 inches

The length of the longer piece is 39 inches....

For this case we have the following equation:

[tex]3 (b + 4) + 8 = -3[/tex]

If we apply distributive property to the terms within the parenthesis we have:

[tex]3b + 12 + 8 = -3[/tex]

We add similar terms to the left side of the equation:

[tex]3b + 20 = -3[/tex]

Subtracting 20 from both sides of the equation:

[tex]3b = -3-20\\3b = -23[/tex]

Dividing between 3 on both sides of the equation:

[tex]b = - \frac {23} {3}[/tex]

In mixed number we have:

[tex]b = -7 \frac {2} {3}[/tex]

Answer:

[tex]b = -7 \frac {2} {3}[/tex]

Answer:

$6240

Step-by-step explanation:

Find the rate by dividing property tax by the appraisal value.

[tex]\frac{3840}{160000}=0.024[/tex]

Now multiply the appraised value by this rate to find the property tax.

[tex]260000*0.024=6240[/tex]

The property tax on a home appraised at $260,000 is $6,240.

To find the property tax on a home appraised at $260,000, we can set up a proportion using the given information. The property tax on a $160,000 home is $3,840, so we have:

$160,000 : $3,840 = $260,000 : x

Using cross-multiplication, we can solve for x:

x = ($260,000 * $3,840) / $160,000

Calculating this, we find that the property tax on a home appraised at $260,000 is $6,240.

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[tex]\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)= x^2+3x-12\qquad \begin{cases} x_1=3\\ x_2=5 \end{cases}\implies \cfrac{f(5)-f(3)}{5-3} \\\\\\ \cfrac{[(5)^2+3(5)-12]~~-~~[(3)^2+3(3)-12]}{2}\implies \cfrac{[25+3]~~-~~[9-3]}{2} \\\\\\ \cfrac{28-6}{2}\implies \cfrac{22}{2}\implies 11[/tex]

Answer:

−27x2

Step-by-step explanation:

It's -27x to the second power so the small 2 at the end

Answer:

[tex]\frac{\sqrt[3]{100x}}{5}[/tex]

Step-by-step explanation:

we have

[tex]\sqrt[3]{\frac{4x}{5}}[/tex]

Multiply inside by [tex]\frac{25}{25}[/tex]

so

[tex]\sqrt[3]{\frac{4x*25}{5*25}}[/tex]

[tex]\sqrt[3]{\frac{100x}{125}}[/tex]

Remember that

[tex]\sqrt[3]{125}=5[/tex]

substitute

[tex]\sqrt[3]{\frac{100x}{125}}=\frac{\sqrt[3]{100x}}{\sqrt[3]{125}}=\frac{\sqrt[3]{100x}}{5}[/tex]

Answer:

consistent  

Solution at (3,2)

Step-by-step explanation:

A consistent and independent solution to a system of linear equations is one point

A consistent and dependent solution to a system of linear equations is where they are the same line ( they could also be called equivalent)

An inconsistent solution is where there is no solution, the lines do not cross

Since the lines cross at exactly one point, this is a consistent and dependent solution

The solution is at x = 3  ( 3 units to the right of the origin)

and y = 2 ( 2 units up from the origin)

(3,2)

Answer:

Consistent :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

−7−4p+5

−4p+(−7+5)

Ans  

−4p−2

your answer is: -4p - 2

Explanation:

first, ignore the -4p for now. do the small equation without the variable. SO, we would do 7 - 5 = 2.

there aren't any addition symbols being used in the equation and there aren't any other numbers with the p variable. this means that the -4p will stay the same. so we would end up with -4p - 2

(this isn't the normal way of solving this, but I did my own way and got the same answer)

Answer:

150(.40)^n is your equation

Step-by-step explanation:

Answer:

[tex]=150\cdot{0.4^n}[/tex]

Step-by-step explanation:

Let n be the number of rounds. Lets look at n=1 which is round one. Therefore if 40% of the contestants are eliminated then we can write an expression of the number of contestants eliminated:

[tex]=150\cdot{0.4}[/tex]

For round two, n=2:

[tex]=150\cdot{0.4)\cdot{0.4}=150\cdot{0.4^2}[/tex]

Therefore for the n number of rounds:

[tex]=150\cdot{0.4^n}[/tex]

Answer: Option D

D. 41​

Step-by-step explanation:

A value [tex]x_i[/tex] is considered an outlier if

[tex]x_i> Q_3 + 1.5IQR[/tex]

or

[tex]x_i <Q_1 - 1.5IQR[/tex]

Where

[tex]Q_3[/tex] is the third quartile

[tex]Q_1[/tex] is the first quartile

IQR is the interquartile range.

[tex]IQR = Q_3-Q_1[/tex]

In this case:

[tex]Q_3=92\\Q_1=72[/tex]

So

[tex]IQR = 92-72 =20[/tex]

[tex]Q_3 + 1.5IQR = 92 + 1.5*20 = 122[/tex]

[tex]Q_1 - 1.5IQR=72-1.5*20=42[/tex]

Then the outlier values will be all those greater than 122 or less than 42

Therefore the answer is the option D.

Answer:

f(1) = 24

Step-by-step explanation:

f(1) is the value of f(x) when x = 1, that is from the table

f(1) = 24

Answer:

√113

or

10.6301458127

Step-by-step explanation:

Plug the coordinated into this equation and make sure you match up the corrdinates in the correct order

d = √(x2 - x1)^2 + (y2 - y1)^2

The number next to the number does NOT mean multiply it mean like this

(x2, y2)  and (x1, y1) so you would plug them in like this:

d = √(-6 - 2)^2 + (4 - (-3))^2

d = √(-8)^2 + (7)^2

d = √(64 + 49

d = √113

or 10.6301458127

Answer with Step-by-step explanation:

The distance(d) between the points (a,b) and (c,d) is given by:

[tex]d=\sqrt{(c-a)^2+(d-b)^2}[/tex]

Here, we have to find distance between (2,-3) and (-6,4)

(a,b)=(2,-3) and (c,d)=(-6,4)

[tex]d=\sqrt{(-6-2)^2+(4-(-3))^2}[/tex]

[tex]d=\sqrt{8^2+7^2}[/tex]

[tex]d=\sqrt{64+49}[/tex]

[tex]d=\sqrt{113}[/tex]

Hence, the distance between the points (2 -3) and (-6 4) on the coordinate plane is:

[tex]\sqrt{113}[/tex]

Answer:

[tex]\large\boxed{x=-\dfrac{2}{3}\ or\ x=1}[/tex]

Step-by-step explanation:

[tex]3x^2-x-2=0\\\\3x^2+2x-3x-2=0\\\\x(3x+2)-1(3x+2)=0\\\\(3x+2)(x-1)=0\iff3x+2=0\ \vee\ x-1=0\\\\3x+2=0\qquad\text{subtract 2 from both sides}\\3x=-2\qquad\text{divide both sides by 3}\\x=-\dfrac{2}{3}\\\\x-1=0\qquad\text{add 1 to both sides}\\x=1[/tex]

Answer:

Step-by-step explanation:

it's -2

The percentage change of 134 to 106 will be -20.89% .

Given ,

Number changed from 134 to 106 .

Now,

Here initially the number was = 134

After reduction the number was = 106

Percentage change = final - initial / initial * 100

Final number = 106

Initial number = 134

so,

Percentage change = 106 -134/134 * 100

Percentage change = -28/134 *100

Percentage change = -20.89%

Thus the percentage change is -20 .89% and the negative sign shows the declining nature of number .

Know more about percentages,

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