which choice is equivalent to the expression below? heLp!

Answer:

x = - 3[tex]\sqrt{2}[/tex], x = [tex]\sqrt{2}[/tex]

Step-by-step explanation:

Given

x² + 2[tex]\sqrt{2}[/tex] x - 6

To calculate the zeros equate to zero

x² + 2[tex]\sqrt{2}[/tex] x - 6 = 0 ( add 6 to both sides )

x² + 2[tex]\sqrt{2}[/tex] x = 6

One way is to use the completing the square method

add ( half the coefficient of the x- term )² to both sides

x² + 2[tex]\sqrt{2}[/tex] x + ([tex]\sqrt{2}[/tex])² = 6 + ([tex]\sqrt{2}[/tex])²

x² + 2[tex]\sqrt{2}[/tex] x + 2 = 6 + 2

(x + [tex]\sqrt{2}[/tex] )² = 8

Take the square root of both sides

x + [tex]\sqrt{2}[/tex] = ± [tex]\sqrt{8}[/tex] = ± 2[tex]\sqrt{2}[/tex]

subtract [tex]\sqrt{2}[/tex] from both sides

x = - [tex]\sqrt{2}[/tex] ± 2[tex]\sqrt{2}[/tex]

x = - [tex]\sqrt{2}[/tex] - 2[tex]\sqrt{2}[/tex] = - 3[tex]\sqrt{2}[/tex], or

x = - [tex]\sqrt{2}[/tex] + 2[tex]\sqrt{2}[/tex] = [tex]\sqrt{2}[/tex]

Here is your answer

D. 17, 18, 32

REASON:

Sum of any two sides of a triangle is always greater than the third side.

So,

17+18= 35

35>32

In other cases

a. 12+15= 27

27 <30

b. 14+16= 30

30 <34

c. 15+16= 31

31 <33

Hence other three can't be sides of a triangle.

HOPE IT IS USEFUL

The side lengths that could represent a triangle is 17, 18, 32

A triangle is a polygon with three sides and three angles. Type of triangles are isosceles, equilateral, scalene and obtuse.

For a triangle, the sum of any two sides must be greater than the third side. Hence:

For 12, 15 , 30; 12 + 15 < 30

For 14, 16 , 34; 14 + 16 < 34

For 15, 16 , 33; 15 + 16 < 33

For 17, 18 , 33; 17 + 18 > 33

The side lengths that could represent a triangle is 17, 18, 32

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Answer:

13.

Step-by-step explanation:

12.9 is closer to 13.

square root 167 is 12.923, this rounded to the nearest unit is 13

Answer:

about $5,203.02

Step-by-step explanation:

5000(1+(.04/4))^4

The total amount accrued, principal plus interest, with compound interest on a principal of $5,000.00 at a rate of 4% per year compounded 1 times per year over 3 years is $5,624.32.

Given Data

A = P + I where

P (principal) = $5,000.00

I (interest) = $624.32

Calculation Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 4/100

r = 0.04 rate per year,

Then solve the equation for A

A = P(1 + r/n)^nt

A = 5,000.00(1 + 0.04/1)^(1)(3)

A = 5,000.00(1 + 0.04)^(3)

A = $5,624.32

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Answer:

B

Step-by-step explanation:

Using the rule of exponents

[tex]\frac{a^{m} }{a^{n} }[/tex] ⇔ [tex]a^{(m-n)}[/tex]

Hence

[tex]\frac{3^{4} }{3^{2} }[/tex] = [tex]3^{(4-2)}[/tex] = 3² = 9 → B

The answer is 9

because 3 to the power of 4 is 81 and 3 to the power of 2 is 9 so it’s 81 divided by 9 which is 9

Answer:

15' x 20' = 300 square foot

2,275 x 300 = 7.583

17 x 22 = 374

374 x 7.583 = 2,836.042

Which you have to round to the nearest dollar

2,836.042 which will come out to be $2,837.00

Step-by-step explanation:

the answer is since A = l × w

A= 30 × 40

A= 1200 square inches

Answer:

7 units to the left

Step-by-step explanation:

Because if you move to the left you subtract 7 from the x-axis number or in this case 7, so 7-7=0.

Answer:

7 units to the left.

Step-by-step explanation:

QUESTION 5

The side length of the first tra-pezoid and the second tra-pezoid are in the ratio [tex]5:7[/tex].

To find the corresponding ratio of their area, we square each term in the ratio.

The ratio of the area of the first figure, to the ratio of the area of the second is

[tex]5^2:7^2=25:49[/tex]

QUESTION 6

The side length of the first figure and the second figure are in the ratio [tex]12:7[/tex].

To find the corresponding ratio of their area, we square each term in the ratio.

The ratio of the area of the first figure, to the ratio of the area of the second figure is

[tex]12^2:7^2=144:49[/tex]

QUESTION 7

Let [tex]h[/tex] represent the height of this triangle.

[tex]\sin 30\degree=\frac{h}{6}[/tex]

This implies that;

[tex]h=6\sin 30\degree[/tex]

[tex]h=3ft[/tex]

The area of the triangle is [tex]=\frac{1}{2}bh[/tex]

The base is 9 ft and the height is 3 ft.

We substitute these values to obtain;

[tex]A=\frac{1}{2}(9)(3)[/tex]

[tex]A=13.5ft^2[/tex] to the nearest tenth.

QUESTION 8

The area of a parallelogram is [tex]base\times\:height[/tex]

Let h represent the height of this parallelogram.

[tex]\sin60\degree=\frac{h}{6}[/tex]

[tex]h=6\sin60\degree[/tex]

[tex]h=3\sqrt{3}m[/tex]

The area of the parallelogram is [tex]=10\times3\sqrt{3}m^2[/tex]

[tex]=30\sqrt{3}m^2[/tex]

[tex]=52.0m^2[/tex] to the nearest tenth.

Answer:

Option c

[tex]y\geq-3[/tex] or [tex]y \leq 21[/tex]

Step-by-step explanation:

The absolute value is a function that transforms any value x into a positive number.

Therefore, for the function [tex]f(x) = |x|[/tex]  x> 0 for all real numbers.

Then the inequation:

[tex]|y-9| \leq 12[/tex] has two cases

[tex](y-9)[/tex]    if [tex]y \geq 9[/tex]  (i)

[tex]-(y-9)[/tex]    if [tex]y < 9[/tex] (ii)

We solve the case (i)

[tex]y \leq 9 + 12\\y\leq21[/tex]

We solve the case (ii)

[tex]-y +9 \leq 12\\-y \leq 12-9\\y \geq -3[/tex]

Then the solution is:

[tex]y\geq-3[/tex] or [tex]y \leq 21[/tex]

Answer:

its c the answer above me is correct

Step-by-step explanation:

Answer:

10^5

Step-by-step explanation:

100,000

= 10 x 10 x 10 x 10 x 10

= 10^5

Answer:

A

Step-by-step explanation:

The area (A) is calculated using

A = [tex]\frac{1}{2}[/tex] bc sinA ← substitute values

A = 0.5 × 14 × 8 × sin30° = 28 units² → A

Answer:

The area of the plate is 21 inches

Step-by-step explanation:

* Lets revise some rules of a circle

- The circumference of a circle = 2πr , where r is the radius of it

- The area of the circle = πr²

* Lets solve the problem

∵ A circular plate has circumference 16.3 inches

∵ The circumference = 2πr

∵ π = 3.14

- Lets find the radius of the plate

∵ 16.3 = 2(3.14)r

∴ 16.3 = 6.28r

- Divide both sides by 6.28

∴ r = 16.3/6.28 = 2.5955 ≅ 2.6

∴ The radius of the plate is 2.6 inches

* Lets find the area of the plate

∵ The area = πr²

∵ π = 3.14

∵ 4 = 2.6

∴ The area = 3.14(2.6)² = 21.22 ≅ 21

* The area of the plate is 21 inches

To find the area of a circle with a circumference of 16.3 inches using 3.14 for pi, you first calculate the radius and then use the formula A = πr² to get the area, which when rounded to the nearest whole number is approximately 21 inches².

To calculate the area of a circular plate when given its circumference, we first need to find the radius of the circle. We use the formula for the circumference of a circle, C = 2πr, where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius. The student has provided the circumference as 16.3 inches, so we solve for r:

C = 2πr

16.3 inches = 2 × 3.14 × r

16.3 inches / (2 × 3.14) = r

16.3 inches / 6.28 = r

2.597 inches = r

Now that we have the radius, we can use the area formula for a circle, A = πr². Plugging in our radius we get:

A = 3.14 × (2.597 inches)²

A = 3.14 × 6.7473 inches²

A = 21.205 inches²

Rounding to the nearest whole number:

A ≈ 21 inches²

The answer would be 8 inches.

Answer:

W = 8 inches

Step-by-step explanation:

Volume of a rectangular prism is V= LWH,

we are given V = 528, L = 12, and H = 5 1/2.  Plug  them in and find W..

First convert 5 1/2 to an improper fraction

5 1/2 becomes 11/2

   528 = (12)(11/2)W

      528 = (132/2)W

        528 = 66W

            8 = W  (divide both sides by 66)

Answer:

The standard form of the quadratic equation is [tex]f(x)=-2x^{2}+12x-16[/tex]

Step-by-step explanation:

we know that

The standard form of a quadratic equation is

[tex]f(x)=ax^{2}+bx+c[/tex]

we have

[tex]f(x)=-2(x-3)^{2}+2[/tex]

convert to standard form

[tex]f(x)=-2(x-3)^{2}+2\\f(x)=-2(x^{2} -6x+9)+2\\f(x)=-2x^{2}+12x-18+2\\f(x)=-2x^{2}+12x-16[/tex]

Answer:

B

Step-by-step explanation:

did it on edge

ANSWER

No solution

EXPLANATION

The first equation is

[tex]y = {x}^{2} - 2x[/tex]

and the second equation is

[tex]y = - 2x - 1[/tex]

We equate the two equations to obtain;

[tex] {x}^{2} - 2x = - 2x - 1[/tex]

This implies that

[tex] {x}^{2} = - 2x + 2x - 1[/tex]

[tex] {x}^{2} = - 1[/tex]

There is no real number whose square is -1.

Therefore, the equation has no solution.

Answer: no solution

Step-by-step explanation: no cap

only the last one since the others don’t pass the vertical line test

which is when you draw a straight line down your function and if it hits 2 or more points it is not a function

The correct graph should have x values that have no more than one y value.

Depending on the kind of function that is graphed, various graph types exist.

Linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal graphs are the eight most often used types.

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Answer:

10) 40,80,160

11) 64, 256, 1024

12) 5, 2.5, 1.25

Step-by-step explanation:

Hope this helps. :)

Answer:

a=27

b=13.5

c=3.5

Step-by-step explanation:

This answer explains how to calculate the number of different sizes of bags that can be made from a specific amount of nuts, considering whole numbers of bags.

a. To determine how many 1-pound bags can be made from a 27-pound bag of nuts, divide 27 by 1, which gives you 27 bags.

b. For 2-pound bags, divide 27 by 2 to get 13.5 bags. Since you can't have half a bag, you can make only 13 bags.

c. To find the number of 3/4-pound bags from a 2.5-pound bag, divide 2.5 by 0.75, which equals 3.33 bags, but you can make only 3 bags because you can't have a fraction of a bag.

Answer:

-135

Step-by-step explanation:

The summation notation of 10∑n=2 -2n-3.

We can find the values by substituting n into -2n-3.

Let's begin where n = 2

-2(2) - 3 = -7

-2(3) - 3 = -9

-2(4) - 3 = -11

-2(5) - 3 = -13

-2(6) - 3 = -15

-2(7) - 3 = -17

-2(8) - 3 = -19

-2(9) - 3 = -21

-2(10) - 3 = -23

This gives us:

-7 + -9 + -11 + -13 + -15 + -17 + -19 + -21 + -23 = -135

The question is likely related to evaluating a summation sequence using sigma notation, but the specifics are unclear due to possible typos. The correct approach would be to substitute values of n into the given expression and sum the results, but the question needs clarification.

The student's question appears to involve the concept of a summation, indicated by the sigma notation (Σ), which is a common topic in high school mathematics, particularly in algebra, pre-calculus, or AP statistics. However, the question, as written, is incomplete or contains typos that make it unclear. The phrase '10 sigma n=2 -2n-3' is not sufficient to provide a full context for an evaluation. It is likely that the student is asking to evaluate a summation formula that starts at n=2, but the upper limit of the summation (10) and the actual expression to be summed (-2n-3) are not clearly linked.

If the student intended to ask for the evaluation of the summation of the expression -2n-3 from n=2 to n=10, then we would calculate the sum as follows:

However, without clarification from the student, we cannot proceed with certainty. It is important to understand the exact parameters of the summation when dealing with sigma notation and summation formulas.

Answer:

196

Step-by-step explanation:

Divide 140 by 5 to find out how many miles she can drive with one gallon:

140/5 = 28

Multiply by 7:

28 x 7 = 196

hope this helps

Answer:

2

Step-by-step explanation:

2 is actually a prime number because composite numbers have more than 2 factors but prime numbers don't.

Answer:

-5/7 x 1/5 = -5/35 = -7

The answers is -1/7

Hope it helped!!

Answer:

[tex]x=-7[/tex]

Step-by-step explanation:

We can write them both like functions like this

[tex]A=5x-4[/tex]

[tex]B=3x+8[/tex]

Where

x=input

A=Output A

B=Output B

We want the output of A 3 times the output of B this can be written like this:

[tex]A=3B[/tex]

we replace with the functions

[tex]5x-4=3(3x+8)[/tex]

we solve for x

[tex]5x-4=9x+24\\5x-9x=24+4\\-4x=28\\x=\frac{28}{-4}\\x=-7[/tex]

The output that makes the out put of A 3 times teh output of B is [tex]-7[/tex]

To find the input that makes the output of A three times the output of B, solve the equation 3(B's output) = A's output by plugging in the values for each machine. The input that satisfies this equation is X = -7.

To find the input that makes the output of A three times the output of B, we need to solve the equation 3(B's output) = A's output. Let's plug in the given values into the machines to solve for X:

Now we can set up the equation and solve for X:

3(3X + 8) = 5X - 4

9X + 24 = 5X - 4

9X - 5X = -4 - 24

4X = -28

X = -7

Therefore, the input that makes the output of A three times the output of B is X = -7.

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Let the two numbers be 3x and 4x

sum =3x + 4x = 7x

7x = 133

x= 19

the numbers are :

3(19) = 57

4(19) = 76

Answer:

57 and 76

Step-by-step explanation:

Given the ratios are 3 : 4 = 3x : 4x, then

3x + 4x = 133

7x = 133 ( divide both sides by 7 )

x = 19

The numbers are

3 × 19 = 57 and 4 × 19 = 76

Answer:

-5

Step-by-step explanation:

We can just see what x has to be smaller than (or plug in the numbers, but that is more time-consuming).

-3x + 7 < 11 -> -3x < 4 -> x > -4/3

-5 is the only number that is less than or equal to -4/3.

-5 Is not a solution to the inequality

Answer:

1 and 8 are the ones you should choose.

Step-by-step explanation:

Answer: ∠1 and ∠8

Step-by-step explanation:

Given : Line b is parallel to line c .

In the given figure , a traversal line is passing through line b and c.

∠2=120°

Then , ∠1 +∠2=180°   [linear pair]

⇒ ∠1=180°-120°=60°

Now, ∠4 and ∠1 are vertical angles.

Since vertical angles are congruent.

∴ we have , ∠4 ≅ ∠1 =60°

Also, ∠4 and ∠8 are corresponding angles and corresponding angles are congruent.

∴ we have , ∠4 ≅ 8 =60°

∠2 cannot be congruent to ∠4, since both have different measures

∠7 cannot be congruent to ∠4, since ∠7 is congruent to ∠2 (Alternate exterior angles)

Answer:

2x^2-4x-6

Step-by-step explanation:

I don't know what kind of math this is, but simply add up all of the like-terms.

There are 2 +x^2 --> 2x^2

There are 4 -x --> -4x

There are 6 - --> -6

The answer is A

There are two x squared tiles, there are four negative x tiles and there are six single negative tiles

Answer:

Step-by-step explanation:

60 - 55 = 5, car B catches up to Car A 5 miles per hour, they are 5 miles closer every hour

10 / 5 = 2, 2 hours

car b would have driven 60 * 2 = 120