Tony believes that x = -9 is a root of the polynomial x^2 + 13x + 36. Erika, however, believes that x = 4 is a root of the same polynomial. Who is correct?

Answer:

x=7 is the answer

3x+6=27 is the equation

x=7 is the correct answer for the equation.

To solve the equation 3x + 6 = 27, subtract 6 from both sides and then divide by 3 to get x = 7. Verify by substituting x = 7 back into the original equation. This confirms the solution is correct by making a true statement.

Step by Step Solution:

When solving an algebraic equation, the goal is to find the value of the variable that makes the equation true. For example, consider the equation 3x + 6 = 27. To solve for x, follow these steps:

Subtract 6 from both sides of the equation: 3x + 6 - 6 = 27 - 6, which simplifies to 3x = 21.

Next, divide both sides by 3: 3x / 3 = 21 / 3, which gives x = 7.

To verify the solution, substitute x = 7 back into the original equation: 3(7) + 6 = 27. Simplifying this, we get 21 + 6 = 27, which is a true statement, verifying our solution.

Note that an identity in algebra is an equation that is true for all values of the variable, such as 6 = 6. In our example, the solution x = 7 makes both sides of the original equation equal, thus satisfying the equation.

Answer:

  3 cm

Step-by-step explanation:

The formula for the area of a rectangle is ...

  A = LW . . . . . . area is the product of length and width

Fill in the given values and solve for the width (W).

  18 cm² = (6 cm)W

  (18 cm²)/(6 cm) = W = (18/6) cm²/cm . . . . . . divide by the coefficient of W

  W = 3 cm

The width of the rectangle is 3 cm.

The width of a rectangle, with a length of 6 cm and an area of 18 cm squared, is 3 cm.

The question is asking for the width of a rectangle which we can find using the formula for the area of a rectangle. The formula is: Area = Length x Width. From the given question, we know that the area is 18 cm2 and the length is 6 cm. So, we can set up the equation: 18 = 6 x Width. To solve for width, we divide both sides of the equation by 6. This gives us Width = 18 ÷ 6 which equals 3 cm.

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Answer:

(351.04, 368.96)

Step-by-step explanation:

Given that population mean= 360

Std devitaion = 4

margin of error = 2.5%= 0.025

Since population std deviation is known we can use Z critical value

For two tailed critical value for 2.5% would be

2.24

Margin of error = ±Critical value*std deviation

= ±2.24(4)

= ±8.96

Confidence interval =(Mean - margin of error, mean + margin of error)

=[tex](360-8.96, 360+8,.96)\\= (351.04, 368.96)[/tex]

Answer:

368 is the answer

Answer:

Same side interior angles

They are also supplementary (add up to 180 deg)

Step-by-step explanation:

see attached

Answer: 591

Step-by-step explanation:

1773/3= 591

Answer:

-1.6

Step-by-step explanation:

Ⓗⓘ ⓣⓗⓔⓡⓔ!

Your equation will be 2x*6=(11*x)-(8/5)

12x=11x-1.6

-11x -11x

x=-1.6

(っ◔◡◔)っ ♥ Hope this helped! Have a great day! :) ♥

The number that satisfies the given condition the product of twice a number and six is the same as the difference of eleven times the number and 8/5 is -1.6.

Let's assume the number we are looking for is "x."

The problem states that the product of twice the number and six is the same as the difference of eleven times the number and 8/5.

Step 1: Express the given statement as an equation.

The product of twice the number and six is 2x * 6 = 12x.

The difference of eleven times the number and 8/5 is 11x - 8/5.

Now, we can set up the equation:

12x = 11x - 8/5

Step 2: Solve for x.

To solve for x, we need to isolate x on one side of the equation. Subtract 11x from both sides of the equation:

12x - 11x = 11x - 11x - 8/5

x = -8/5

The number we are looking for is x = -8/5 or -1.6.

To learn more about number click on,

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Answer:

18:24

18:24

15:20

15:20

Step-by-step explanation:

Because 18/3:24/3 = 3:4

Also, 15/5:20/5 = 3:4

Answer:

7

Step-by-step explanation:

To solve this equation you have to use PEMDAS

Because of PEMDAS, we start with parenthesis.

4+27 ÷(4+5)= ?     4+5 = 9     4+27 ÷ 9 = ?

There are no exponents or multiplication so we skip to division.

4+27 ÷ 9 = ?   27 ÷ 9 = 3    4+3=?

Then we do addition

4+3 =7

Answer:

An equation of a line perpendicular to ja and passing through k is:

y = -x + 10

Answer:

Solid / plane

Step-by-step explanation:

A cross-section is a geometric concept, representing the intersection of a solid and a plane. The shape of the cross-section depends on how the plane intersects with the solid. A related physics concept is the continuity equation which states that the amount of incompressible liquid entering a cross-sectional area must equal the amount leaving it.

In mathematical terms, a cross-section is usually the intersection of a 3-dimensional solid with a plane. This concept is often used in Geometry. For instance, if we intersect a cylinder with a plane perpendicular to the base of the cylinder, the cross-section will be a circle which is the same size as the base of the cylinder. On the other hand, if the plane is parallel to the axis of the cylinder, the cross-section would be a rectangle.

A related concept, from the field of Physics, as described in Figure 14.28, is the continuity equation, usually applied when analyzing fluid dynamics. The equation posits that the volume of fluid entering a cross-sectional area of a duct or pipe must equal the volume of fluid leaving it, assuming the fluid is incompressible. This is because the mass of liquid cannot change within a closed system.

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Answer:

OPTION D: (-1, 10)

Step-by-step explanation:

The equation of a line in standard form is given by: [tex]$ \textbf{y} \textbf{-} \textbf{y}_\textbf{1} \hspace{1mm} \tetxbf{=} \hspace{1mm} \tetxtbf{m}(\textbf{x - x}_{\textbf{1}}) $[/tex]

Here, m is the slope of the line.

[tex]$ (x_1, y_1) $[/tex] is the point on the line.

Therefore, comparing it with the given data:

[tex]$ y - 2= -\frac{2}{3}(x - (-1)) $[/tex]

[tex]$ \implies y_1 = -2 $[/tex]

[tex]$ \& \hspace{2mm} x_1 = -1 $[/tex]

Hence, the point on the line is: (-1, 2).

Hence, the answer.

Term life insurance is insurance that insures you for a certain time period like 5 years for example.

Usually in months and years is how its done.

Term life insurance is for a specific time period and is the cheapest way to buy life insurance.

Unlike permanent life insurance policies, which cover an individual for their entire life, term life insurance offers protection for a predetermined period, such as 10, 20, or 30 years. Because it does not accumulate cash value and only pays out a death benefit if the insured passes away during the specified term, premiums for term life insurance tend to be lower compared to permanent policies.

The affordability of term life insurance makes it an attractive choice for individuals seeking to secure financial protection for their loved ones during specific critical periods, such as the years when children are growing up or when a mortgage is being paid off.

It's a straightforward and efficient way to provide a death benefit for beneficiaries in case the insured passes away within the chosen term, offering financial security without the long-term commitment and higher premiums associated with permanent life insurance options.

Answer:the tip itself will be $6.20 but in total it will all cost $68.20

Step-by-step explanation:

Answer:

42/72

Step-by-step explanation:

42/7=6

12*6=72

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Theres no tables but y=67x would be the equation

since 67 is the constant which =m in y=mx+b

The equation 2.1 plus 2 x equals 7.5 can be used to find the value of x ⇒ 4th answer

Step-by-step explanation:

In an isosceles triangle:

∵ The triangle is isosceles

- That means it has two equal sides

∵ The shortest side is y

∵ The length of the other two sides is x

∴ The perimeter of the triangle = y + 2 x

∵ The perimeter of the triangle = 7.5 m

- Equate the expression of the perimeter by 7.5

∴ y + 2 x = 7.5

∵ The shortest side measures 2.1 m

∴ y = 2.1

- Substitute y by 2.1 in the equation above

∴ 2.1 + 2 x = 7.5

The equation 2.1 plus 2 x equals 7.5 can be used to find the value of x

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Answer:

D

Step-by-step explanation:

The correct answer is 1/24

Fruit: apple, mango, orange, lime

Cup size: small, regular, large

Ice: cubed, crushed

If you count every variation you'll get to 24.

The chances are 1 in 24.

Answer: x = 2y + 4

Step-by-step explanation:

y=1/2x-4

multiply both sides by 2

2y=x-4

substract from both sides 2y

0=x+–2y-4

substract from both sides x

-x=-2y-4

multiply both sides by -1 to get positive x

x=2y+4

Answer:B. (3,4)

Step-by-step explanation:

because looking at the x-axis we see that the 3 is pointing to that point, and looking at the y-axis we can see that the 4 is pointing to the same point as the 3. Therefore the answer is B (3,4)

Answer:

(3,4)

Step-by-step explanation:

when looking at the x and y axis on the graph you see where the lines intersect. when on the x-axis at 3 you go up 4 times and on the y-axis 4 you go to the right 3 times showing both lines intersecting each other.  

took the quiz on edg :)

The correct answer is $71.

Mariah's monthly property insurance premium, given that her $75,000 wood house and $10,000 contents are situated in a rural area, would be approximately $71.67.

To calculate Mariah's monthly property insurance premium, we need to note that her house is made of wood and that she lives in a rural area. In the table, the annual premium per $100 coverage for a wood building in a rural area is 1.0 and for the contents, it is 1.1.

Following the steps below, we can calculate Mariah's monthly property insurance premium:

So, Mariah's monthly property insurance premium would be approximately $71.67.

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Answer:

64.94% or as a decimal .65

Step-by-step explanation:

7.7 billion (x)=15 million

7.7x /7.7 and 15/7.7

is about .... 64.94% which is about .65

x- represents the unknown percentage.

Sorry if incorrect :(

Final answer:

The correct system of linear inequalities that models Kim's work situation is option B, which includes the inequalities x + y ≤ 15 and 5x + 7y ≥ 65. These inequalities account for the maximum hours she can work and the minimum income she wants to earn. The correct option is B.

Explanation:

The student is asking for the system of linear inequalities that models Kim's work situation based on the hours she can work at two different jobs with different hourly rates. To model this situation, we have two variables: x for the number of hours worked at the first job and y for the hours at the second job. The first inequality comes from the maximum hours she can work, which is 15. Therefore, the combined hours worked at both jobs cannot exceed 15, which gives us:

x + y ≤ 15

The second inequality is derived from Kim's target earnings, which is at least $65. So, the income from both jobs combined must be at least $65, which gives us:

5x + 7y ≥ 65

Taking into account the given options, the correct system of linear inequalities is represented by option B:

x + y ≤ 15

5x + 7y ≥ 65

Answer:

Step-by-step explanation:

y = 5x + 2.....so we will sub in 5x + 2 for y, back into the other equation

3x = -y + 10

3x = - (5x + 2) + 10

3x = -5x - 2 + 10

3x + 5x = 8

8x = 8

x = 8/8

x = 1

y = 5x + 2

y = 5(1) + 2

y = 5 + 2

y = 7

check it... (1,7)

3x = -y + 10                           y = 5x + 2

3(1) = -7 + 10                          7 = 5(1) + 2

3 = 3 (correct)                       7 = 7 (correct)

so ur solution is : x = 1 and y = 7...or (1,7) <=====

Answer:

(1,7)

Step-by-step explanation:

Since we know that y=5x+2, we replace y in the bottom equation with 5x+2.

3x=-(5x+2)+10

Then distribute the - into both of the parentheses (multiply both terms by -1):

3x=-5x-2+10

Then add like terms:

3x=-5x+8

Add 5x to both sides:

8x=8

Divide both sides by 8:

x=1

Plug the known x value into y=5x+2:

y=5(1)+2

Multiply:

y=5+2

Add:

y=7

Put values into (x,y) form:

(1,7)

Final answer:

To find the probability of having 2, 3, or 4 successes in five trials where the probability of success is 40%, we calculate each scenario's probability using the binomial probability formula and sum them. The total probability is 65.3%, rounded to the nearest tenth of a percent.

Explanation:

To calculate the probability of having 2, 3, or 4 successes in five trials of a binomial experiment where the probability of success is 40%, we use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

Where:

P(X = k) is the probability of k successes in n trials

C(n, k) is the combination of n trials taken k at a time

p is the probability of success on an individual trial

(1-p) is the probability of failure on an individual trial

Let's calculate each probability:

P(X = 2) = C(5, 2) * 0.4² * 0.6³

P(X = 3) = C(5, 3) * 0.4³ * 0.6²

P(X = 4) = C(5, 4) * 0.4⁴ * 0.6¹

To find the total probability of having either 2, 3, or 4 successes (P(X = 2 or 3 or 4)), we add up these probabilities:

P(X = 2 or 3 or 4) = P(X = 2) + P(X = 3) + P(X = 4)

Let's use the combination formula to calculate these probabilities:

P(X = 2) = 10 * 0.4² * 0.6³ = 0.2304

P(X = 3) = 10 * 0.4³ * 0.6² = 0.3456

P(X = 4) = 5 * 0.4⁴ * 0.6 = 0.0768

Therefore:

P(X = 2 or 3 or 4) = 0.2304 + 0.3456 + 0.0768 = 0.6528 or 65.3% (rounded to the nearest tenth of a percent)

Answer:

Step-by-step explanation:

3/2x - 14 - 2 = 0

3/2x - 12 = 0

3/2x = 12

2x = 36

x = 18

The seventh term is 23.

Step-by-step explanation:

Given, First term, a = 11

= 11 + (6*2)

= 11 + 12 = 23

Answer:

Step-by-step explanation:

sorry

no graph paper to graph

Answer:

D

Step-by-step explanation:

side HG is 3

side FG is 5 hypotenuse

sin F = 3/5 = opposite/hypotenuse

cos G is adjacent/hypotenuse

adjacent side is HG which = 3

hypotenuse is 5

Without additional context, we cannot give a direct answer for cos G based only on sin F = 3/5. If F and G are complementary angles in a right triangle, cos G would also be 3/5. Otherwise, more information about the relationship between F and G is needed.

To solve this question, we need a bit more context because there is not enough information provided to directly determine the value of cos G. However, typically, if sin F is given as 3/5 for a right triangle, then by the Pythagorean theorem, we know cos F = √(1 - sin^2 F), which calculates to 4/5, assuming F is an angle in a right triangle in standard position with F between 0 and 90 degrees.

This doesn't directly give us cos G, but if we assume G is the complementary angle to F in a right triangle (F + G = 90 degrees), then cos G = sin F and we could say cos G is also 3/5. If sine and cosine relate to different triangles or different contexts, we would need the relationship between angles F and G or additional information to solve for cos G.