Select the term that describes the quadratic portion in this quadratic equation. 7x^2 - 12x + 16 = 0

The length of rectangle is 19 cm and width is 31cm

What are the rectangle's perimeter and area?

The region that a rectangle occupies in a two-dimensional space is referred to as the area of a rectangle. The quantity of square units required to entirely fill a rectangle is another way to describe its area. The whole distance encircling a rectangle's edge is referred to as its perimeter.

Given that:

Let the length of the given rectangle be x cm

Then the width = x+12

now area = 589cm^2

Length x breath = 589 = x(x+12)

x^2 + 12x = 589

x^2 + 12x - 589 = 0

(x-19)(x+31) = 0

x = 19 , -31

But x cant be negative so x = 19

Length = 19 cm

Width = 31 cm

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Answer:

x = 60°, y = 100°, z = 120°, w = 80°

Step-by-step explanation:

x and 120° are adjacent angles on a straight line and sum to 180°

x + 120° = 180° ( subtract 120° from both sides )

x = 60°

Similarly

y + 80° = 180° ( subtract 80° from both sides )

y = 100°

and

z + 60° = 180° ( subtract 60° from both sides )

z = 120°

--------------------------------------------------------------------

The sum of the interior angles in a quadrilateral = 360°

sum the interior angles of the quadrilateral and equate to 360°

60° + 80° + 120° + 4th angle = 360°

260° + 4th angle = 360° ( subtract 260° from both sides )

4th angle = 100°

w and 100° are adjacent angles on a straight line and sum to 180° , so

w + 100° = 180° ( subtract 100° from both sides )

w = 80°

11011₂ = 2⁴ + 2³ + 2¹ + 2⁰ = 27

15 + x₂ = 27

x₂ = 12 = 8 + 4 = 2³ + 2² = 1100₂

Answer:

Step-by-step explanation:

the answer is A-Triangle A. They both have the same angle degrees when you find all of them

Derek will need approximately $15,631,115.49 in his retirement account on his 65th birthday.

Let A be the amount Derek needs to have in his retirement account on his 65th birthday.Assuming the interest rate of 10%, A will grow to A * 1.1 dollars on his 66th birthday.

On his 66th birthday, Derek will withdraw $161,349.00 and the amount remaining in his account will grow to (A - 161,349.00) * 1.1 dollars. This will be his new amount, which will grow to (A - 161,349.00) * 1.1^2 dollars on his 67th birthday.

Derek will continue this pattern until his 89th birthday. At this point, the amount remaining in his account will be exactly zero since he will have withdrawn all of his money on his 89th birthday.

We can therefore set up the following equation to solve for A:

A * 1.1^21 + (A - 161,349.00) * 1.1^20 + (A - 161,349.00 * 2) * 1.1^19 + ... + (A - 161,349.00 * 23) * 1.1 = 0

Simplifying this equation by factoring out A and solving for it yields:

A * (1.1^21 + 1.1^20 + 1.1^19 + ... + 1.1 - 23) = 161,349.00 * (1 + 1.1 + 1.1^2 + ... + 1.1^23)

A = (161,349.00 * (1 + 1.1 + 1.1^2 + ... + 1.1^23)) / (1.1^21 + 1.1^20 + 1.1^19 + ... + 1.1 - 23)

A ≈ $15,631,115.49

Therefore, Derek will need approximately $15,631,115.49 in his retirement account on his 65th birthday.

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The number of dots that should be place above the 3 in the dot plot is: 4 dots

A dot plot is one that is used to represent any data in the form of dots or small circles. It is similar to a simplified histogram or a bar graph as the height of the bar formed with dots represents the numerical value of each variable. Dot plots are thus used to represent small amounts of data. For example, a dot plot can be used to collect the vaccination report of newborns in an area, which is represented in the following table.

Now, from the given table, we see the pea pods and the number of peas they have.

Now, from the table, only one Pea pod has 2 peas and that's why we have one dot above 2.

However, we can see that 4 pea pods have 4 number of peas and as such we will have 4 dots above 3.

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The approximate probability that at most 19 out of 100 randomly chosen American women have a height shorter than 61 inches is 0.2420

To solve this problem, we can use the normal distribution and the properties of the mean and standard deviation provided.

Let's denote X as the random variable representing the height of an American woman. We are interested in finding the probability that at most 19 out of 100 women chosen at random have a height shorter than 61 inches.

First, we need to standardize the values using the Z-score formula:

Z = (X - μ) / σ

Where:

X is the value we want to standardize (in this case, 61 inches),

μ is the mean of the distribution (63.8 inches),

σ is the standard deviation of the distribution (4 inches).

Standardizing 61 inches, we get:

Z = (61 - 63.8) / 4

= -0.7

Next, we need to find the probability corresponding to Z = -0.7. Since we want to find the probability of at most 19 women being shorter than 61 inches, we need to find the cumulative probability up to Z = -0.7.

Using a standard normal distribution table or a statistical software, we can find that the cumulative probability corresponding to Z = -0.7 is approximately 0.2420.

Therefore, the approximate probability that at most 19 out of 100 randomly chosen American women have a height shorter than 61 inches is 0.2420 (or 24.20% when rounded to the nearest second decimal place).

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Answer: The exponential format of  algebraic expressions is an expression that includes an exponent. All expressions containing exponents are written in exponential format.

Step-by-step explanation:
• How to represent the same number of iterative multiplications

By writing a number as the basis for the number of repetitions

It is written as a small number in the upper right corner.

• Small numbers are called exponents, exponents, powers, or orders.

e.g. 10 x 10 x 10 x 10 = 10^4

Answer:

a shortcut way of writing repeated multiplication involving base and exponents  

Step-by-step explanation:

i think this is the answer

The solution to the given initial value problem, obtained using Laplace transforms, is y(x) = 0. This means that the function y(x) is identically zero for all values of x.

To find the solution of the initial value problem using Laplace transforms for the equation d²y/dx² + 9y = 9sin(t)u(t - 3), where y(0) = y'(0) = 0, we can follow these steps:

Take the Laplace transform of the given differential equation.

Applying the Laplace transform to the equation d²y/dx² + 9y = 9sin(t)u(t - 3), we get:

s²Y(s) - sy(0) - y'(0) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Since y(0) = 0 and y'(0) = 0, the Laplace transform simplifies to:

s²Y(s) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Solve for Y(s).

Combining like terms, we have:

Y(s) * (s² + 9) = 9 * (1/s² + 1/(s² + 1))

Multiply through by (s² + 1)(s² + 9) to get rid of the denominators:

Y(s) * (s⁴ + 10s² + 9) = 9 * (s² + 1)

Simplifying further, we have:

Y(s) * (s⁴ + 10s² + 9) = 9s² + 9

Divide both sides by (s⁴ + 10s² + 9) to solve for Y(s):

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9)

Partial fraction decomposition.

To proceed, we need to decompose the right side of the equation using partial fraction decomposition:

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9) = A/(s² + 1) + B/(s² + 9)

Multiplying through by (s⁴ + 10s² + 9), we have:

9s² + 9 = A(s² + 9) + B(s² + 1)

Equating the coefficients of like powers of s, we get:

9 = 9A + B

0 = A + B

Solving these equations, we find:

A = 0

B = 0

Therefore, the decomposition becomes:

Y(s) = 0/(s² + 1) + 0/(s² + 9)

Inverse Laplace transform.

Taking the inverse Laplace transform of the decomposed terms, we find:

L^(-1){Y(s)} = L^(-1){0/(s² + 1)} + L^(-1){0/(s² + 9)}

The inverse Laplace transform of 0/(s² + 1) is 0.

The inverse Laplace transform of 0/(s² + 9) is 0.

Combining these terms, we have:

Y(x) = 0 + 0

Therefore, the solution to the initial value problem is:

y(x) = 0

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Answer:

OOOOOOOOHHH SHUTE BROTHER SORRY WISHED I COULD HELP but im blonde so sowwy

X has a normal distribution, X that will give it a mean of zero and a variance , then the mean of Y = E(10+5X) = 1020

The variance is a measure of variability. It is calculated by taking the average of squared deviations from the mean. Variance tells you the degree of spread in your data set. The more spread the data, the larger the variance is in relation to the mean.

Given that,

E(x) = 30

Var(x) = 144

E(y) = ?

Var(y) = 144

Then,

E(10+5X)

To do this, we make use of the following equation

E(ax + by) = a E(x) + b E(y)

E(10+5X) = 10 E(x) + 5 E(y)

E(10+5X) = 10*30 + 5*144

E(10+5X) = 300 + 720

E(10+5X) = 1020

Therefore,

X has a normal distribution, X that will give it a mean of zero and a variance , then the mean of Y = E(10+5X) = 1020

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Answer:

4h+1.5

Step-by-step explanation:

Answer:

2x squared + 25

Step-by-step explanation:

Step-by-step explanation:

area of rectangle

height×base

(2x-5)(2x-2)=

=4x^2-4x-10x+10

=4x^2-14x+10

(we get quadratic equation)

a=4 b=-14 c=10

firat find discriminant with formula:

D=b^2-4ac(-14)^2-(4×4×10)=196-160=36

now find x1 and x2 with formula:

X=(-b±√D)/2a

x1=(14+√36)/8=20/8=2.5

x2=(14-√36)/8=8/8=1

lets put values :

if we put x2 value as a base, which is 1 in given height and base, we will get 2(1)-2=0. measure of amy side can't be 0.

and if we put x2 in height, it will give us zero.

so no matter which one we put as value. we will get 0cm^2. so i think it cant be detected. im sorry if im wrong

The margin of error will be E = ± 4.04 %

The margin of error is defined as the error in the sample data of the statistics.

Given that:-

sample data = ( p ).

success p^ = success percentage = 40 %

confidence interval CI = 98%

sample size n = 800

margin of error E:

E=z-critical \(\dfrac{\sqrt{P(P-1)}}{n}\)

The margin of error "E" for estimation of population proportion ( p ) is given by:

P ( Z < Z-critical ) = a/ 2

a = 1 - CI  

P ( Z < Z-critical ) = (1 - 0.98) / 2  

P ( Z < Z-critical ) = 0.01    

Z-critical = 2.33  

The error E = ± 4.04 %

Thus, the correct answer is E=± 4.04 %

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The exponent property which must be applied first to simplify the expression as given in the task content is; The power of a power property.

It follows from the task content that the exponent property which must be applied first in a bid to simplify the expression be determined.

Since the expression given is;

(4y)³ • (2g)² • y • g

Consequently, to solve the parentheses, the power of a power property must be used first so that we have;

4³•y³ • 2²•g² • y • g

The expression can then be further simplified by using the the product of a power property on like terms so that the simplified form is therefore;

256g³y⁴.

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Answer:A linear model is appropriate because the scatterplot shows a strong, positive linear relationship.

Step-by-step explanation:

Answer:

y = -½x + 7

Step-by-step explanation:

To write the equation of the line in slope-intercept form, y = mx + b, find the slope value (m) and the y-intercept value (b).

Using any two points on the line, say (0, 7) and (2, 6):

\( slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 7}{2 - 0} = \frac{-1}{2} \)

Slope (m) = -½

y-intercept (b) = 7 (this is where the y-axis is cut across by the line)

To write the equation, substitute m = -½, and b = 7 into y = mx + b.

Thus:

y = -½x + 7

Answer:

x + 600 ≥ 2400

Step-by-step explanation:

Given:

Amount needed = $2,400

Amount they had = $600

Find:

Amount they need

Computation:

Assume;

Amount they need = x

x + 600 ≥ 2400

We need to find the area of a rectangle. The area of a rectangle is given by:

The rectangular tiles that measure 1.5 feet by 0.8 feet. So the area of each tile is:

Therefore, the number of tiles will be the total area of the floor divided by the area of each tile:

The cubic polynomial with zeros (3,0), (-6,0) and (1,0) is given as follows:

D. x³ + 2x² - 21x + 18.

We are given the zeros of the polynomial, which then can be obtained using the Factor Theorem.

The zeros of the polynomial are given as follows:

x = 3, x = -6, x = 1.

Then, applying the Factor Theorem, considering a leading coefficient of 1, the polynomial is given as the product of it's linear factors as follows:

(x - 3)(x + 6)(x - 1)

(x² + 3x - 18)(x - 1)

x³ + 2x² - 21x + 18.

Meaning that option D is correct.

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Events A and C as well as events B and D are independent.

Two events A and B are independent if the occurrence or non-occurrence of one event does not affect the probability of the other event.

In the given events, it is not explicitly mentioned how the events are related. However, based on typical assumptions about burrito ingredients and customer preferences, we can make some assumptions:

Assuming that the choice of meat (chicken or carne asada) and the choice of beans (black beans or pinto beans) are independent of each other, we can conclude that events A (The burrito is a chicken burrito) and C (The customer requested black beans) are independent. The choice of chicken meat in the burrito does not affect the probability of the customer requesting black beans.

Similarly, events B (The burrito is a carne asada burrito) and D (The customer requested pinto beans) are independent. The choice of carne asada meat in the burrito does not affect the probability of the customer requesting pinto beans.

So, based on these assumptions, events A and C as well as events B and D are independent.

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The way to break an irregular figure into shapes that you have area formulas for is by using 1 parallelogram and 1 rectangle.

To find the area of an irregular figure, you can divide it into simpler shapes that you know the area formulas for. In this case, using 1 parallelogram and 1 rectangle can be a good way to break the irregular figure into shapes that you have area formulas for.

A parallelogram has an area formula of base times height, while a rectangle has an area formula of length times width. By dividing the irregular figure into these shapes, you can calculate their areas separately and then add them together to find the total area of the figure.

Using other combinations of shapes such as 1 parallelogram and 1 triangle, 1 rectangle and 1 triangle, or 1 square and 1 triangle may not be as effective in breaking down the irregular figure into simpler shapes.

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Answer:

12.5

Step-by-step explanation:

for people who don't get another  quizzez assignment about ratios from their teachers, this question showed & the correct answer was 12.5 Hope this answer somehow helps.

Ounces of yogurt need for 10 ounces of blueberries is 8 ounce

Ratio of ounces of blueberries to ounces of yogurt = 4:5

Ounces of yogurt need for 10 ounces of blueberries

Ounces of yogurt need for 10 ounces of blueberries = 10[4 / 5]

Ounces of yogurt need for 10 ounces of blueberries = 2[4]

Ounces of yogurt need for 10 ounces of blueberries = 8 ounce

So, Option "A" is the correct answer to the following question.

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Answer:

40.00 percent probability

Step-by-step explanation:

odds are that 15 will be a particular event and 10 will be another event. 15 to 10 probability. There is a 60.00 percent probability that you will choose the cheese bunnes and 40.00 percent probability that you will choose pretzels

Answer:

You get paid $9 per hour

Step-by-step explanation:

Answer:

5280 miles

Step-by-step explanation:

So, you are one third of the way to the mid point.

One-third can be represented as a fraction - \(\frac{1}{3}\).

The mid point will be half the race, so \(\frac{1}{2}\).

If you are a third of the way to the halfway point, you are \(\frac{1}{3} \cdot \frac{1}{2} = \frac{1}{6}\)  done with the race.

If 880 miles is \(\frac{1}{6}\) of the race, then the total amount of the race will be 6 times 880 (as \(\frac{1}{6} \cdot \frac{6}{1} = 1\)).

\(880\cdot 6 = 5280\)

So the race in total is 5280 miles long.

Hope this helped!

Answer:

y= -6x+3

Step-by-step explanation:

0- -1 = 1

3 - 9 = -6

distance = 6.08

Answer:

49.17

Step-by-step explanation:

A scaled copy of polygon with the scaled factor of 2 is Scale factor is defined as

It is a growing organism that falls between (0, infinity). According to the scale factor, an original figure might be either raised or decreased.

Consider two circles that appear to be the same. The word "identical" does not guarantee that both circles are of similar size. They could have various radii. One figure would be the other figure scaled down.

The ideas of ratio and proportion are intimately related to scale considerations. A given amount is multiplied or divided in ratio and proportions to create a new quantity.

A Scaled copy involves multiplying the lengths in the original figure by scale factor.

Here scale factor = 2,

Since the scale factor > 1, so there is an enlargement.

So, the scale copy's sides are 2 times of the sides of figure A.

Take the reference of grid:

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