Tina raised the number 3 to a power and then added 19 to the result .She obtained the sum 100. To what power did she raise 3 ?​

Answer:

The width is 7 inches and the length is 9 inches

Step-by-step explanation:

So we can divide 32 by 2 because we know perimeter is 2(l*w)

So it becomes 16, and it is now (l*w)

We know that the length is 2 inches longer so we subtract 2 from 16.

It then becomes 14 inches so therefore we can then divide it by 2.

14 divided by 2 is 7 and therefore we add 2 because we subtracted the two from earlier temporarily.

Therefore the width is 7 and the length is 9.

Final answer:

To find the dimensions of the picture frame with a perimeter of 32 inches and length 2 inches more than its width, equations based on the rectangle's perimeter formula are used. The width is found to be 7 inches, leading to a length of 9 inches.

Explanation:

To determine the dimensions of a rectangular picture frame where the perimeter is 32 inches and the length is 2 inches longer than the width, we can set up two equations based on the properties of a rectangle's perimeter. The perimeter (P) of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width. Let's denote the width of the frame as w inches; thus, the length will be w + 2 inches since the length is 2 inches longer than the width.

Now, since the perimeter is 32 inches, we plug in our expressions for length and width into the perimeter formula: 2(w + 2) + 2w = 32. Simplifying this, we get 2w + 4 + 2w = 32. Combining like terms, we have 4w + 4 = 32. Subtracting 4 from both sides, we get 4w = 28. Dividing both sides by 4, we find w = 7 inches.

Therefore, the width of the frame is 7 inches, and the length, being 2 inches longer, is 7 + 2 = 9 inches. So the dimensions of the frame are 7 inches by 9 inches.

For this case we must factor the following quadratic expression:

[tex]x ^ 2-6x + 9[/tex]

To factor, we must find two numbers that when multiplied give as result +9 and when added or subtracted give as result -6.

These numbers are:

-3 and -3

[tex]-3-3 = -6\\-3 * (- 3) = + 9[/tex]

So, we have:

[tex](x-3) (x-3)[/tex]

ANswer:

Option D

Answer:

D. (x - 3)(x - 3)

Step-by-step explanation:

We are given the following expression and we are to factorize it:

[tex]x^2-6x+9[/tex]

Finding factors of positive 9 such that when added they give a result of -6.

[tex] x ^ 2 - 6 x + 9 [/tex]

[tex] x ^ 2 - 3 x - 3 x + 9 [/tex]

Factorizing them to get:

[tex] x ( x - 3 ) - 3 ( x - 3 ) [/tex]

[tex] ( x - 3 ) ( x - 3 ) [/tex]

16x 2.5x 5= 200 that’s the volume I think it’s saying there is 19.3 grams for every centimeter of volume soo 200x 19.3 =3,860 mass ..... I would double check me

Answer:

Gold bar volume = 16 * 2.5 * 5 = 200

Density * Volume = Mass

19.3 * 200 = 3,860 grams of gold

Step-by-step explanation:

Solve for x in x + 2y = 65

x = 65 - 2y

Substitute x = 65 - 2y into 2x + 3y = 105

130 - y = 105

Solve for y in 130 - y = 105

y = 25

Substitute y = 25 into x = 65 - 2y

x = 15

Therefore;

x = 15

y = 25

Answer:

see explanation

Step-by-step explanation:

The diagonals of a parallelogram bisect each other, hence

AE = EC, that is

x² - 6 = 5x ( subtract 5x from both sides )

x² - 5x - 6 = 0 ← in standard form

(x - 6)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 1 = 0 ⇒ x = - 5

However x > 0 ⇒ x = 6

AC = x² - 6 + 5x = 6² - 6 + 5(6) = 36 - 6 + 30 = 60

To find the value of x in parallelogram ABCD, set up an equation using the given information and solve for x. Use the fact that the diagonals of a parallelogram bisect each other to find AC.

To find the value of x in parallelogram ABCD, we can set up an equation using the given information:

AE = x2-6

CE = 5x

By solving this equation, we can find the value of x.

To find the value of AC, we can use the fact that in a parallelogram, the diagonals bisect each other. So, AC = CD/2. By substituting the value of CD from the earlier equation, we can find AC.

Answer:

30 degrees

Step-by-step explanation:

A right angle is 90 degrees. Subtract 30 and you get 60. Then divide it by two because the leftover is 2x.

Answer:

x=30

Step-by-step explanation:

90-30=60

60/2=30

I got the 90* from the right angle

Answer:

- 3108

Step-by-step explanation:

The sum to n terms of an arithmetic series is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2[tex]a_{1}[/tex] + (n - 1)d ]

Substitute the given values into the formula

[tex]S_{24}[/tex] = [tex]\frac{24}{2}[/tex] [ (2 × - 26) + (23 × - 9) ]

                          = 12 ( - 52 - 207 )

                         = 12 × - 259 = - 3108

Answer:

Step-by-step explanation:

I believe you do, 4 times each number in the absolute value symbol. 4 times n, 4 times positive 8.  4n+32=56

You minus 32 on both sides and you get 24. Then you take 24 and divide it by 4, and there is your answer 6.

You can check it by plugging 6 into the equation.

If we reduce the expression by cancelling common factors, your answer would be 840.

Answer:

True

Step-by-step explanation:

Any point on the x- axis has a y- coordinate of zero, hence

(2, 0) lies on the x- axis

Answer:

4/3

Step-by-step explanation:

If 1/3 quart of paint covers 1/4 of a basketball field, multiply 1/3 by 4 (since the denominator of 1/4 is 4 and the denominators represents the amount of peices that you're dividing the court into.)

(Remember that 4 is the same as 4/1)

Now, multiply the numerators and denominators.

1 x 4 = 4

3 x 1 = 3

= 4/3

So, 4/3 quart of paint would cover the enitre basketball court. I hope this helps!

It takes 1 and 1/3 quart of paint to paint the entire basketball court.

To find out how much paint it takes to paint the entire basketball court, we need to find the total amount of paint that covers 1 basketball court. We know that 1/3 of a quart of paint covers 1/4 of a basketball court. So to find the amount of paint that covers the entire basketball court, we can multiply the amount that covers 1/4 of a court by 4.

1/3 quart * 4 = 4/3 quart.

Therefore, it takes 4/3 quart or 1 and 1/3 quart of paint to paint the entire basketball court.

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The formula for the volume of a cylinder is V = π r^2 h

We know what the volume (V) and PI is so:

536.94 = 3.14 r^2 h

But since we don't know the height, it is not possible to find the radius as we cannot find the value of a variable if there are still more than 1 variable in an equation in which we don't know the value of

I would suggest to delete this question and add the height or tell us the height of the cylinder in the comments

Answer:

66 yards

Step-by-step explanation:

it eaquls that because it is PerfEctIng liveS

Answer:

The sum is

[tex]7.92\times 10^3[/tex]

Step-by-step explanation:

We want to add

[tex]4.9\times 10^2 and 6.8\times 10^3[/tex]

The sum of these two numbers is:

[tex]4.9\times 10^2 +6.8\times 10^3[/tex]

This is the same as:

[tex]4.9\times 100 +6.8\times 1000[/tex]

[tex]490 +6800=7290[/tex]

We rewrite 7290 in standard form to get;

[tex]7.92\times 10^3[/tex]

Answer:

The answer is B.

Step-by-step explanation:

Please mark brainliest!

x = 90 - 28

x = 62°

The answer is choice B.

Answer:

The answer is B; 62 degrees

Step-by-step explanation:

A straight line has an angle measure of 180 degrees

So our equation to solve for x is: 180 - 90 - 28 = x

Therefore, x = 62

Answer:

The correct option is the fourth one.

Step-by-step explanation:

FIRST QUESTION:

To solve this problems we need to know the following things:

1. Given f(x) = k*g(x). We know that the graph of f(x) will be identical to the graph of g(x) but enlarged or compressed depending on the value of k.

2. Given f(x) = g(x) + k. We know that the graph of f(x) will be identical to the graph of g(x) but shift downwards if k<0 or shift upwards if k>0.

Having said this, we have that:

f(x) = 1/2 * log_2 (x) - 8

In this case, there are two transformations: The function is supressed by 1/2 and also shifted downwards by 8 units.

SECOND QUESTION

We need to find the portion of domain where f(x) = x^2 + a is one-to-one.

A function f is one-to-one if each x in the domain has exactly one image in the range. And, no y in the range is the image of more than one x in the domain.

So if we want a one-to-one function we need to restrict the domain starting from x=0. So it would be: [0, inf)

Now to find the inverse function, we need to solve the equation for "x"

y = x^2 + a

y - a = x^2

x = sqrt(y-a)

Then, the inverse function would be:

y = sqrt(x-a)

The correct option is the fourth one.

Answer:

see explanation

Step-by-step explanation:

When constructing the ratio to solve, let x be the quantity to be found.

In this case the total number of employees

The 1 part of the ratio represents employees laid off, that is 22

The 5 part of the ratio represents total employees

The x and 5 go together, either on the numerator or denominator

[tex]\frac{5}{1}[/tex] = [tex]\frac{x}{22}[/tex]

5 and x both on numerator

OR

[tex]\frac{1}{5}[/tex] = [tex]\frac{22}{x}[/tex]

5 and x both on denominator

Both will lead to the same answer

[tex]\frac{5}{1}[/tex] = [tex]\frac{x}{22}[/tex] ( cross- multiply )

x = 5 × 22 = 110 ← total number of employees

[tex]\frac{1}{5}[/tex] = [tex]\frac{22}{x}[/tex] ( cross- multiply )

x = 5 × 22 = 110 ← total number of employees

To solve the equation -3 + 1 + 10x = x + 4, the like terms are combined, variables are moved to one side, and the resulting linear equation is simplified to find x = 2 / 3.

To solve the equation -3 + 1 + 10x = x + 4, you first need to simplify and rearrange the equation to isolate the variable x on one side. Start by combining like terms on the left side:

-3 + 1 = -2, so the equation simplifies to -2 + 10x = x + 4.

Next, move the x terms to one side by subtracting x from both sides of the equation:

10x - x = 4 + 2

This simplifies to 9x = 6. Finally, divide both sides by 9 to solve for x:

x = 6 / 9 or x = 2 / 3.

The solution to the equation is x = 2 / 3.

Answer:

x = - 3, x = 0, x = 2

Step-by-step explanation:

To find the zeros equate f(x) to zero, that is

x³ + x² - 6x = 0 ← factor out x from each term

x(x² + x - 6) = 0

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

Equate each factor to zero and solve for x

x = 0

x + 3 = 0 ⇒ x = - 3

x - 2 = 0 ⇒ x = 2

Answer:  The zeroes of the given function are -3, 0 and 2.

Step-by-step explanation:  We are given to find the zeroes of the following function :

[tex]f(x)=x^3+x^2-6x~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

zeroes of a function y = f(x) are found by solving the following equation :

f(x) = 0.

Therefore, from equation (i), we have

[tex]x^3+x^2-6x=0\\\\\Rightarrow x(x^2+x-6)=0\\\\\Rightarrow x(x^2+3x-2x-6)=0\\\\\Rightarrow x(x(x+3)-2(x+3))=0\\\\\Rightarrow x(x-2)(x+3)=0\\\\\Rightarrow x=0,~~x-2=0,~~x+3=0\\\\\Rightarrow x=0,~2,~-3.[/tex]

Thus, the zeroes of the given function are -3, 0 and 2.

Answer:

-4/5

Step-by-step explanation:

Please use a symbol such as x or Ф to represent an angle; your 0 is too easily confused with zero.

If Angle Ф lies in the second quadrant, and sin Ф=3/5, find cos Ф.

The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse:  sin Ф = opp / hyp = 3 / 5.  Thus the opp side has length 3 and the hyp has length 5.  By the Pythagorean Theorem,

the adj side has length √(5² - 3²), or √(25-9), or √16, or ±4.  Because the angle is in the 2nd quadrant, choose adj = -4.

Then the cosine of this angle is  cos Ф = adj / hyp = -4 / 5  

Final answer:

To find cos 0, use the Pythagorean identity and evaluate.

Explanation:

To find cos 0, use the Pythagorean identity and evaluate. The given information states that angle 0 lies in the second quadrant and sin 0 = 3/5. We need to find cos 0. Since angle 0 is in the second quadrant, cosine is negative in that quadrant. We can use the Pythagorean identity to find cos 0 = √(1 - sin² 0), which becomes cos 0 = √(1 - (3/5)²). Evaluating this gives us cos 0 = √(1 - 9/25) = √(16/25) = 4/5.

Answer:

25

Step-by-step explanation:

15x12=180

8x25=200

The expression is [tex]\(15 \times 12 + 8 = 188\)[/tex].

To represent "8 more than the product of 15 and 12", you would first calculate the the product of 15 and 12, and then add 8 to to the result.

1. Calculate the product of of 15 and 12:

 [tex]\(15 \times 12 = 180\)[/tex]

2. Add 8 to to the result:

 [tex]\(180 + 8 = 188\)[/tex]

So, the expression representing "8 more than the product of of 15 and 12" is [tex]\(15 \times 12 + 8\)[/tex], which simplifies to to [tex]\(188\)[/tex].

Answer:

56

Step-by-step explanation:

To calculate the quotient of the sum of 1/2 and 1/3 divided by the product of 1/2 and 1/3, we need to perform two separate calculations first: one for the sum and one for the product.
1. Calculate the Sum:
First, we find the sum of the fractions 1/2 and 1/3. To add two fractions, we need a common denominator. The least common multiple of 2 and 3 is 6, so we convert both fractions to have a denominator of 6:
\[
\frac{1}{2} = \frac{3}{6}, \quad \text{ and }\quad \frac{1}{3} = \frac{2}{6}.
\]
Then, we add the two fractions:
\[
\frac{3}{6} + \frac{2}{6} = \frac{3+2}{6} = \frac{5}{6}.
\
The sum of 1/2 and 1/3, therefore, is 5/6.
2. Calculate the Product:
Next, we find the product of the two fractions by multiplying them directly:
\[
\frac{1}{2} \times \frac{1}{3} = \frac{1 \times 1}{2 \times 3} = \frac{1}{6}.
\]
The product of 1/2 and 1/3 is 1/6.
3. Divide the Sum by the Product:
Finally, we divide the sum by the product:
\[
\frac{5/6}{1/6} = \frac{5}{6} \times \frac{6}{1} = \frac{5 \times 6}{6 \times 1} = \frac{30}{6} = 5.
\
The quotient of the sum of 1/2 and 1/3 divided by the product of 1/2 and 1/3 is 5.
Thus, the final answer to the question is 5.

Answer:

$1456.25

Step-by-step explanation:

$12.25 multiplied by 25 = $306.25

now you have  $306.25 + $1150 = $1456.25

which is your answer $1456.25

Answer:

revenue

Step-by-step explanation:

It is another name for funds or money received from a sale of goods or services.

Answer:

it is revenue

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

12 1/2 -(-4 1/2) = 12 1/2 + 4 1/2

                       =25/2 + 9/2

                       = 34 /2

                       = 17

The value of the given expression is 17

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is an expression, 12 1/2-(-4 1/2), we need to simplify it,

12 1/2 -(-4 1/2)

= 12 1/2 + 4 1/2

=25/2 + 9/2

= 34 /2

= 17

Hence, the value of the given expression is 17

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Answer:

24

Step-by-step explanation:

Just plug it into the calculator.

Answer: D.  L1 is parallel to L4 because L1 is parallel to L3 and L3 is parallel to L4.

Step-by-step explanation: Since L1 and L3 are both perpendicular to L2, L4 is parallel to L1 if L1 is parallel to L3

Answer:

The correct option is D.

Step-by-step explanation:

It is given that L1 is perpendicular to L2, L2 is perpendicular to L3, and L3 is parallel to L4.

L1 ⊥L2, L2 ⊥ L3, L3║L4.

If one line perpendicular to second line and second line perpendicular to third line, then first and third line are parallel.

[tex]L_1\perp L_2,L_2\perp L_3\Rightarrow L_1\parallel L_3[/tex]

Using transitive property of parallel lines.

[tex]L_1\parallel L_3,L_3\parallel L_4\Rightarrow L_1\parallel L_4[/tex]

L1 is parallel to L4 because L1 is parallel to L3 and L3 is parallel to L4.

Therefore the correct option is D.

Answer:

16. 270/3630

17.240/ 3630

18. 1550/ 3630

19. 560/3630

Step-by-step explanation:

Selected at random means all the books combined which is 3630 the it asks for which ever specific thing which is just the number of those books over the total.

Hope this helps!

Answer:

With fractions: [tex]y=-\frac{7}{5} x+\frac{48}{5}[/tex]

With decimals: [tex]y=-1.4x+9.6[/tex]

Step-by-step explanation:

First we are finding the slope of line AB using the slope formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

where

[tex]m[/tex] is the slope

[tex](x_1,y_1)[/tex] are the coordinates of the first point

[tex](x_2,y_2)[/tex] are the coordinates of the second point

The first point is A= (-3, -1) and the second one is B = (4, 4), so [tex]x_1=-3[/tex], [tex]y_1=-1[/tex], [tex]x_2=4[/tex] and [tex]y_2=4[/tex].

Replacing values

[tex]m=\frac{4-(-1)}{4-(-3)}[/tex]

[tex]m=\frac{4+1}{4+3}[/tex]

[tex]m=\frac{5}{7}[/tex]

Now, since AB and BC form a right angle, BC is perpendicular to AB. The slope of a perpendicular line is the negative reciprocal of the other line; in other words, the slope of BC is the negative reciprocal of the slope of AB. To find the negative reciprocal of the slope of AB we just need to multiply its slope by -1 and invert the fraction:

[tex]m_{AB}=\frac{5}{7}[/tex]

[tex]m_{BC}=-\frac{7}{5}[/tex]

Finally, to complete the equation of BC, we are using the point-slope formula:

[tex]y-y_1=m(x-x_1)[/tex]

where

[tex]m[/tex] is the slope

[tex](x_1,y_1)[/tex] are the coordinates of the point

We know that [tex]m_{BC}=-\frac{7}{5}[/tex], so [tex]m=-\frac{7}{5}[/tex]. Since the line passes throughout point B = (4, 4), [tex]x_1=4[/tex] and [tex]y_1=4[/tex].

Replacing values

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-4=-\frac{7}{5} (x-4)[/tex]

[tex]y-4=-\frac{7}{5} x+\frac{28}{5}[/tex]

[tex]y=-\frac{7}{5} x+\frac{28}{5}+4[/tex]

[tex]y=-\frac{7}{5} x+\frac{48}{5}[/tex]

[tex]y=-1.4x+9.6[/tex]

Answer:

-7x − 5y = -48

Step-by-step explanation:

This was correct on plato :D