I need help as soon as possible please??

Answer:

a) Two real solutions.

b) Solutions:  y = -6, y = 12

Step-by-step explanation:

The discriminant is defined as the expression b² - 4ac, which appears under the square root sign in the quadratic formula.

The value of the discriminant determines the nature of the solutions to the quadratic equation:

[tex]\boxed{\begin{minipage}{12 cm}\underline{Discriminant}\\\\$b^2-4ac$ \quad when $ax^2+bx+c=0$\\\\when $b^2-4ac > 0 \implies$ two real solutions.\\when $b^2-4ac=0 \implies$ one real solution.\\when $b^2-4ac < 0 \implies$ no real solutions (two complex conjugate solutions).\\\end{minipage}}[/tex]

To find the number and type of solutions of the given quadratic equation, first rewrite the equation in the form ax² + bx + c = 0.

[tex]\begin{aligned}(y-3)^2-10&=71\\y^2-6y+9-10&=71\\y^2-6y-1&=71\\y^2-6y-72&=0\end{aligned}[/tex]

Compare the coefficients:

Substitute the values of a, b and c into the discriminant formula:

[tex]\begin{aligned}b^2-4ac&=(-6)^2-4(1)(-72)\\&=36-4(-72)\\&=36+288\\&=324\end{aligned}[/tex]

As the discriminant of the given equation is greater than zero, there are 2 real solutions.

To solve the equation, we can use the quadratic formula:

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when}\;\;ax^2+bx+c=0[/tex]

As we have already calculated that the discriminant is 324, we can substitute this, along with the values of a and b, into the formula:

[tex]\implies y=\dfrac{-(-6) \pm \sqrt{324}}{2(1)}[/tex]

[tex]\implies y=\dfrac{6 \pm \sqrt{324}}{2}[/tex]

Solve for y:

[tex]\implies y=\dfrac{6 \pm 18}{2}[/tex]

[tex]\implies y=3 \pm 9[/tex]

[tex]\implies y=-6, 12[/tex]

Therefore, the solutions of the given equation are:

The solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

Given the inequality,

    f(x²-2) < f(7x-8) over D₁ = (-∞, 2)

We need to find the values of x that satisfy this inequality.

Since we know that f is increasing over its domain, we can compare the values inside the function to determine the values of x that satisfy the inequality.

First, we can find the values of x that make the expressions inside the function equal:

x² - 2 = 7x - 8

Simplifying, we get:

x² - 7x + 6 = 0

Factoring, we get:

(x - 6)(x - 1) = 0

So the values of x that make the expressions inside the function equal are x = 6 and x = 1.

We can use these values to divide the domain (-∞, 2) into three intervals:

-∞ < x < 1, 1 < x < 6, and 6 < x < 2.

We can choose a test point in each interval and evaluate

f(x² - 2) and f(7x - 8) at that point. If f(x² - 2) < f(7x - 8) for that test point, then the inequality holds for that interval. Otherwise, it does not.

Let's choose -1, 3, and 7 as our test points.

When x = -1, we have:

f((-1)² - 2) = f(-1) < f(7(-1) - 8) = f(-15)

Since f is increasing, we know that f(-1) < f(-15), so the inequality holds for -∞ < x < 1.

When x = 3, we have:

f((3)² - 2) = f(7) < f(7(3) - 8) = f(13)

Since f is increasing, we know that f(7) < f(13), so the inequality holds for 1 < x < 6.

When x = 7, we have:

f((7)² - 2) = f(47) < f(7(7) - 8) = f(41)

Since f is increasing, we know that f(47) < f(41), so the inequality holds for 6 < x < 2.

Therefore, the solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

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The missing exponent of the expression is determined as 4.

The value of the missing exponent is calculated as follows;

The given function is;

81/256 = (3/4)ˣ

To determine the value of the missing exponent, we will apply the power law of indicial equation as follows;

From base of the exponential function, we will determine the value of x;

3⁴/4⁴ = (3/4)x

(3/4)⁴ = (3/4)ˣ

4 = x

Thus, the missing value of the exponential function is determined by applying rules of exponent.

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The complete question is below:

Find the missing exponent 81/256 =  (3/4)ˣ

The graph in this problem is not a function, as it contains vertically aligned points.

The domain and the range are given as follows:

A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y. Vertically aligned points mean that a value of x is mapped to multiple values of y, that is, a single input is mapped to multiple outputs which disqualify the relation as a function.

When we trace a vertical line through the circle, it would cross the circle at two points, meaning that the graph contains vertically aligned points, and thus, is not a function.

The domain and the range are defined as follows:

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Answer: 1) 66 2)

Step-by-step explanation:

1) 22x3=66

2) C

Hope this helps! :)

The sum of the series converges absolutely by alternate series test

Given data ,

Let the sequence be represented as A

Now , the value of A is

A = ∑n=1 to ∝ ( 1/6n³ )

On simplifying , we get

Taking the common factor out , we get

A = ( 1/6 ) ∑n=1 to ∝ ( 1/n³ )

Now , from the alternate series test ,

A = ( 1/6 ) ( converges )

Hence , the series A converges

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The calculated value of the prime fractorization of the number 130 is 2 * 3 * 5

From the question, we have the following parameters that can be used in our computation:

Number = 130

When the above number is expanded, we have

Number = 2 * 5 * 13

The above product of numbers cannot be further simplified

This means that 2 * 5 * 13 is the prime fractorization of the number 130

Hence, the prime fractorization of the number 130 is 2 * 3 * 5

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Answer:

[tex]28 + y + 36 = 180[/tex]

[tex]64 + y = 180[/tex]

[tex]y = 116[/tex]

Answer:80°

Step-by-step explanation:

We can use the given angle, 50, to determine the other angles of the triangle opposite to the arc that we need to find the measure of.

Because the entire inscribed figure is rectangular, we can use our given angle to determine the other angles of the triangle represented by the given angle, which are 50 and 80.

Now we can use the 80° angle <DPA, which is also equal to <CPB.
This means that the center angle <CPB is also 80°, and it means that the corresponding arc X is also 80°.

The radius of the circular mouse is 3.7 inches.

The area of the circular mouse pad 45 square inches. Therefore, the radius of the circle can be found as follows:

area of the circle = πr²

where

Therefore,

area of the circular mouse = 3.14 × r²

45 = 3.14r²

divide both sides by 3.14

r² = 45 / 3.14

r² = 14.3312101911

square root both sides

r = √14.331210911

r = 3.78565714243

r = 3.7 inches

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The simplest form of the expression (2x-3)(3x²+2x-1) is 6x³ - 5x² - 8x + 3.

Given the expression in the question:

( 2x - 3 )( 3x² + 2x - 1 )

To simplify the expression (2x-3)(3x²+2x-1), we need to use the distributive property of multiplication,

which states that: a(b+c) = ab + ac

Using this property, we can expand the expression as follows:

(2x-3)(3x²+2x-1)

2x(3x²+2x-1) - 3(3x²+2x-1)

6x³ + 4x² - 2x - 9x² - 6x + 3

Add like terms

= 6x³ - 5x² - 8x + 3

Therefore, the simplest form is 6x³ - 5x² - 8x + 3.

Option A) 6x³ - 5x² - 8x + 3 is the correct answer.

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To convert 5.4 square meters to square centimeters is 54,000 cm²

To convert 5.4 square meters (m²) to square centimeters (cm²),

We need to multiply it by 10,000 (since 1 meter = 100 centimeters).

5.4 m² = 5.4 x 10,000 cm² = 54,000 cm²

Therefore, 5.4 square meters is equal to 54,000 square centimeters.

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Compare the data by observing the shape, center, and spread of the data in both representations.

1. Understand the data: Before comparing two representations of data, it is important to understand what the data represents and its context.

2. Identify the type of data: Identify the type of data represented in each representation to ensure the data is comparable.

3. Plot the data: Plot the data in each representation, such as a line plot, box plot, or histogram.

4. Compare the data: Compare the data by looking at the shape, center, and spread of the data in both representations.

Example: To compare data in two-line plots, plot the data as two lines on the same graph. Observe the difference in the shape of the two lines, the difference in center (the average value of the data), and the difference in spread (the range of the data).

Example: To compare data displayed in a box plot, plot the data as two box plots side by side. Observe the difference in the shape of the two box plots, the difference in center (the median value of the data), and the difference in spread (the interquartile range of the data).

Example: To compare data displayed in histograms, plot the data as two histograms side by side. Observe the difference in the shape of the two histograms, the difference in center (the mean value of the data), and the difference in spread (the standard deviation of the data).

List the steps to create a back-to-back stem-and-leaf plot:

1. Organize the data: Organize the data into two sets of numerical data.

2. Create stems: Create a stem for each set of data by dividing the values by a common multiple.

3. Create leaves: Create leaves for each set of data by recording the remainder of the original values after dividing them by the common multiple.

4. Plot the data: Arrange the stems and leaves into a back-to-back stem-and-leaf plot.

5. Compare the data: Compare the data by observing the shape, center, and spread of the data in both representations.

Therefore, compare the data by observing the shape, center, and spread of the data in both representations.

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Answer:

13

Step-by-step explanation:

210+50 is the total number of miles that can be driven. This adds up to 260. 260 divided by 20 is miles per gallon, which equals 13.

The percent increase from 2013 to 2014 is given as follows:

39%.

The percent increase from 2013 to 2014 is obtained applying the proportions in the context of the problem.

The amounts were of 631 in 2013 and 877 in 2014, hence the percentage of 2014's amount relative to 2013's amount is given as follows:

877/631 x 100% = 139%.

The initial amount has a percentage of 100%, hence the percent increase from 2013 to 2014 is given as follows:

139% - 100% = 39%.

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The percentage of the questions she got wrong is 15%

What is a Percentage?

Percentage is a number or ratio by dividing the value by the total value and then multiplying the result by 100.

How to determine this

Out of 20 questions, Claire got 17 questions

i.e the questions she got right = 17

The questions she got wrong = 20 - 17 = 3

To get the percentage she got wrong

= 3/20 *100%

= 300/20%

= 15%

Therefore, the percentage she got wrong is 15%

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The volume of the given figure is 1176 cubic cm.

The value of the figure is calculated by multiplying all three side areas. Volume is a measure of the amount of space that an object or a substance occupies. It is typically expressed in cubic units such as cubic meters (m³), cubic centimetres (cm³), or cubic feet (ft³).

The volume of the figure is calculated as,

Volume = 2 ( 15 x 6 + 20 x 6 + 20 x 18 )

Volume = 1176 Cubic cm

Hence, the volume of the figure will be equal to 1176 Cubic cm.

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The surface area of the figure is  174.7 sq. ft.

Consider the bottom rectangular surface of the figure.

The dimensions of the bottom rectangular surface are: length = 10 ft and width = 3 ft

Using the formula for the area of rectangle, the area of bottom surface of the figure would be,

A₁ = length × width

A₁ = 10 × 3

A₁ = 30 sq. ft.

The dimensions of the right rectangular surface are length = 9 ft and width = 3 ft

Using the formula for the area of rectangle, the area of bottom surface of the figure would be,

A₂ = length × width

A₂ = 9 × 3

A₂ = 27 sq. ft.

The dimensions of the left rectangular surface are length = 11 ft and width = 3 ft

Using the formula for the area of rectangle, the area of bottom surface of the figure would be,

A₃ = length × width

A₃ = 11 × 3

A₃ = 33 sq. ft.

There area two parallel triangular suface with dimensions: base = 11 ft and height = 7.7 ft

Using the formula of the area of triangle the surface area of these two triamgular surfaces would be,

A₄ = 2 × 1/2 × base × height

A₄ = base × height

A₄ = 11 × 7.7

A₄ = 84.7 sq. ft.

So, the total surface area of the figure would be,

A = A₁ + A₂ + A₃ + A₄

A = 30 + 27 + 33 + 84.7

A = 174.7 sq. ft.

This is the required surface area of the figure.

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Answer:

π(5^2)(8) + (1/2)(4/3)π(5^3)

= 200π + 250π/3 = 850π/3 cubic meters

= about 889.67 cubic meters

Answer: 6

Step-by-step explanation:

There are six possible ways that the three boys can initially choose shirts: ABC, ACB, BAC, BCA, CAB, CBA.

The predicted amount of debt for a financial education time of 34 hours is $26,350.

The predicted amount of debt for a financial education time of 24 hours is $31,550.

For the given information, we need to know the regression equation that relates financial education time and amount of debt to predict the amount of debt for different time durations.

Assuming a linear relationship between financial education time and amount of debt, we can estimate the regression equation as:

where a and b are the intercept and slope of the regression line, respectively, and Error is the random error term.

Using the given data points, we can estimate the regression line as:

(a) For a financial education time of 34 hours:

Therefore, the predicted amount of debt for a financial education time of 34 hours is $26,350.

(b) For a financial education time of 24 hours:

Therefore, the predicted amount of debt for a financial education time of 24 hours is $31,550.

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Step-by-step explanation:

Each of the six sides is 7 mm  x 7 mm  =  49 mm^2

  times six sides :  6  * 49 mm^2  = 294 mm^2

Answer:Area = Side2 = a2

Therefore, the total surface area of a cube = 6 × (area of each side)

= 6 × a2 = 6a2 Square Unit

soooooooooo

Answer:

100

Step-by-step explanation:

the room is square this means each wall equal 25 .4 walls *25 =100 square feet

Answer:120

Step-by-step explanation:

The value of the test statistic used in this test is t = -2.168 and the P-value of this test is P-value is 0.034

To test whether the mean time for Dr. McCoy is different from the mean time for Dr. Turk, we can use a two-sample t-test with unequal variances. The test statistic for this test is given by:

t = (X₁ - X₂) / √(s₁²/n₁ + s₂²/n₂)

where X₁ and X₂ are the sample means, s₁ and s₂ are the sample standard deviations, and n₁ and n₂ are the sample sizes.

Plugging in the given values, we get:

t = (78 - 78.7) / √(2.3²/38 + 4.1²/33)

= -2.168

Therefore, the value of the test statistic used in this test is t = -2.168.

b) To find the P-value of this test, we need to use a t-distribution with degrees of freedom given by:

df = (s₁²/n₁+ s₂²/n₂)² / [ (s₁²/n₁)²/(n₁-1) + (s₂²/n₂)²/(n₂-1) ]

Plugging in the given values, we get:

df = (2.3²/38 + 4.1²/33)² / [ (2.3²/38)²/37 + (4.1²/33)²/32 ] ≈ 65.385

Using a t-distribution table or a calculator with t-distribution function, we find that the P-value for a two-tailed test with t = -2.168 and df = 65.385 is approximately 0.034.

Therefore, the P-value of this test is P-value = 0.034

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The length of the third side of the triangle is 10.7 feet.

Patricia is building a garden in her backyard that is shaped like a triangle. She has already built two sides of the garden  and they have length of 6 feet and 7 feet.

She wants to find the length of the third side. The angles between the the built sides is 110 degrees.

Therefore, let's find the third sides using the included angle and the two known sides.

using cosine rules,

c² = a² + b² - 2ab cos C

c² = 6² + 7² - 2(6)(7) cos 110

c² = 36 + 49 - 84 cos 110°

c² = 85 - 84(-0.34202014332)

c² = 85 + 28.7296920394

c = √113.729

c = 10.6643799632

c = 10.7 feet

Therefore,

third side of the triangle = 10.7 feet

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Answer: x = -5

Step-by-step explanation:

Answer:

x=-5

7 - 4 * (-5)

Negative times a negative equals a positive

-4*-5=20

7+20=27

Answer:

MY OPINION IS (REALLLLLL)

Step-by-step explanation:

The minimum number of people over age 30 they must include in their sample is: 829 people

The formula for calculating the standard error is:

SE = μ ± Z(σ/√N)

Where:

σ = the standard deviation,

N = the sample size,

Z = the Z value for the percent confidence level desired.

We must find the Z value, at the 85% confidence level from a Cumulative Standardized Normal table for the 99% confidence level. This gives us the value of Z = 1.44

σ = 1.4 liters

N = 0.07

Thus:

0.07 = 1.44(1.4/√N)

0.07/1.44 = 1.4/√N

1.4/√N = 0.04861

√N = 1.4/0.04861

N = (1.4/0.04861)²

N = 829 people

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