1Use the Zero Product Property to solve for x.
a. (x +13)(x - 7) = 0
b. (2x+ 3)(3x - 7) = 0
C. x(x-3) = 0
d. x^2 – 5x = 0
e. x^2 – 2x – 35 = 0
f. 3x^2 + 14x - 5 = 0​

Answer:

The expression 75ℎ represents the total charge for Elegance Home Architects.

If the Johnson family hires the design firm for 15 hours, then Elegance Home Architects will be cheaper.

If the Johnson family hires the design firm for 40 hours, then Rock the House Digital Designs will be cheaper.

Step-by-step explanation:

Given the following :

Rock the house digital designs :

Initial consultation charge = $500

Additional hour of work for house plan = $50 /hr

Elegant Home Architect:

Charge = $75 / hr

h = number of hours fro which Johnson's family hires the design firm

Total amount charged by Elegant home Architect = 75 × h = 75h

Total amount charged by Rock the house digital design = (500 + 50h)

If h = 15 hours :

Total amount charged by Elegant home Architect = 75 × 15 = $1,125

Total amount charged by Rock the house digital design = (500 + 50(15)) = 500 + 750 = $1,250

Hence, Elegant home Architect is cheaper.

If h = 40 hours :

Total amount charged by Elegant home Architect = 75 × 40 = $3,000

Total amount charged by Rock the house digital design = (500 + 50(40)) = 500 + 2000 = $2,500

Hence, Rock the house digital design is cheaper.

Answer:

I don't think this is right since it is a negative number but i tried ;-; -10.2

Step-by-step explanation:

First do the area of the rectangle(bookmark) ((L x W)) = 40 ... Then do the area of the semicircle(holes) 50.27 ((extra- next cut that in half, = 25.135(optional- round to 25.1?) x2)), And subtract that number from 40. = -10.2

The equation d=65t models the distance, d, that Malcolm's family travels after t hours. Malcolm's family travels 65 miles per hour faster than Theo's family.

The equation d=65t models the distance, d, that Malcolm's family travels after t hours. To calculate how much faster Malcolm's family travels than Theo's family, we must first know the speed of Theo's family. Let's say Theo's family travels at 25 miles per hour. To calculate the difference in speed between the two families, we must subtract 25 mph from 65 mph. The difference is then 40 mph, meaning Malcolm's family travels 40 mph faster than Theo's family.

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The value of the given integral after the calculation is 54π/5.

here,

we consider the given data and try to simplify the integral

The integral is ∭Ey2 dV that is over the solid hemisphere x2+y2+z2≤9, y≥0x2+y2+z2≤9, y≥0.

The evaluation of the given integral can be possible using spherical coordinates. Furthermore, the solid hemisphere can also be described as 0≤θ≤π/2 and 0≤Ф≤2π.

therefore,

spherical coordinates are Ey² = (ρsinΦ)²= ρ²sin²φ

now, the Jacobian for the given spherical coordinate is r²sinθ

now,

∭Ey2 dV =∭ρ²sin³φr²sinθdρdθdφ

=∫\(0^{(\pi /2)}\) ∫\(0^{(\pi /2)}\) ∫\(0^{3}\)ρ⁴sin³φ sinθdρdθdφ

=(3⁵/5) x (1/2) x (2/3)

=54π/5

The value of the given integral after the calculation is 54π/5.

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Answer:

3. The equivalent fractions are presented as follows;

\(\dfrac{2}{3} = \dfrac{2 \times 2}{3 \times 2} =\dfrac{4}{6}\)

4.  The equivalent fractions are presented as follows;

\(\dfrac{2}{3} = \dfrac{4 \times 2}{4 \times 3} =\dfrac{8}{12}\)

5. The reason why it works is because \(\dfrac{1}{8} + \dfrac{1}{8} = \dfrac{1}{4}\)

Step-by-step explanation:

3. Based on the shaded region of the given figures, the two fractions are equivalent

Mathematically, we can show the equivalency of the two fractions as follows;

\(\dfrac{2}{3} =\dfrac{2}{3} \times 1 = \dfrac{2}{3} \times \dfrac{2}{2} = \dfrac{2 \times 2}{3 \times 2} =\dfrac{4}{6}\)

Therefore;

\(\dfrac{2}{3} = \dfrac{2 \times 2}{3 \times 2} =\dfrac{4}{6}\)

4. From the shaded region of the given figure, the fractions are equivalent

Mathematically, we have;

\(\dfrac{2}{3} =\dfrac{2}{3} \times 1 = \dfrac{4}{4} \times \dfrac{2}{3} = \dfrac{4 \times 2}{4 \times 3} =\dfrac{8}{12}\)

Therefore;

\(\dfrac{2}{3} = \dfrac{4 \times 2}{4 \times 3} =\dfrac{8}{12}\)

5. The amount of salt required by the recipe = 1/4 teaspoon of salt

The measure of the spoon Jonas has = 1/8 teaspoon

When Jonas adds two 1/8 teaspoons, he gets;

\(\dfrac{1}{8} + \dfrac{1}{8} = \dfrac{1 + 1}{8} = \dfrac{2}{8} = \dfrac{2 \times 1}{2 \times 4} = \dfrac{2}{2} \times \dfrac{1}{4} = 1 \times \dfrac{1}{4} = \dfrac{1}{4}\)

Therefore;

\(\dfrac{1}{8} + \dfrac{1}{8} = \dfrac{1}{4}\)

Two 1/8 measuring teaspoons are equivalent to one 1/4 teaspoons and therefore Jonas is able to get the 1/4 teaspoons of salt the recipe asks for b combining two 1/8 measuring teaspoons of salt he has because 1/8 + 1/8 = 1/4.

Answer:

y = 3x - 5

Step-by-step explanation:

y - y1 = m (x - x1)

y - (-2) = 3 (x - 1)

y + 2 =  3x - 3

- 2  on both sides

y = 3x - 5

Answer: 6m+4n=32

Step-by-step explanation:

m=4

n=2

From this, we can deduce that m+n=32.

6*4=24 and 4*2=8. 24+8=32

So, 6m+4n=32. Hope this was what you were looking for!

T is a point in the line segment SU

SU = ST + TU

SU = 4x

ST = 2x + 6

TU = 4

\(4x =( 2x + 6 )+ 4 \\ 4x = 2x + 10 \\ 4x - 2x = 10 \\ 2x = 10 \\ x = \frac{10}{2} \\ \\ x = 5\)

x = 5

ST = 2x + 6 = (5×2) + 6

HOPE THIS WILL HELP....

Miranna is offered a 75% raise of her hourly rate to reach a private lesson, which would make her hourly pay $21.88.

This is calculated by taking the original hourly rate of $12.50 and multiplying it by 1.75 (the percent raise she is getting).

The relationship between the percent raise and Miranna's new pay is the same as the relationship between her original pay and her new pay. The percent raise (75%) is equal to the scale factor (1.75) between her original and new pay. In other words, the percent raise is a measure of the degree of increase between her original pay and her new pay.

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The point that creates a right triangle with the points (3, 6) and (8, -2), which Christopher could place on the graph to create a right triangle is the point (8, 7.25)

A right triangle is a triangle with one ninety degrees (90°) interior angle.

The points on the right triangle Christopher already graphed (3, 6), and (8, -2)

The property of a right triangle is one of the interior angles is 90°, therefore, the legs or two of the sides of a right triangle are perpendicular.

The slope of the line joining the specified two points is found as follows;

Slope = (-2 - 6)/(8 - 3) = -8/5

The slope of the line perpendicular to the line segment Christopher used to join the points (3, 6), and (8, -6) is 5/8

The equation of the perpendicular line is therefore;

y - 6 = (5/8)·(x - 6)

y = (5/8)·(x - 6) + 6 = 5·x/8 + 18/8

y = 5·x/8 + 18/8

When x = 8, we get; y = 5 × 8/8 + 18/8 = 7.25

Therefore, the point (8, 7.25), forms a right triangle with the points (3, 6) and (8, -2)

A point Christopher can place on the graph to create a right triangle is (8, 7.25)

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Answer:

4x^2 + 3x - 6

Answer:

4x^2+3x-6

Step-by-step explanation:

Answer:

I use to know this

Step-by-step explanation:

there a app the can help you do it

Answer:

1:3

Step-by-step explanation:

If 1/4 contains nut then the number without nuts will be 1-1/4 =3/4

Hance the ratio of nuts chocolate to chocolate without nuts is 1/4:3/4

by multiplying both by the LCD of 4

we will have 1:3 as the ratio

The package weighs approximately 10.9 pounds.

Let's assume the weight of the package in pounds is "x". We can break down the cost of sending the package by media mail into three parts:

1. The cost for the first pound: $2.41.

2. The cost for the additional pounds up to six pounds: $0.41 per pound.

3. The cost for the additional pounds beyond six pounds: $0.39 per pound.

To determine the weight of the package, we need to solve the equation based on the given information:

Cost = $2.41 + $0.41 * (x - 1) + $0.39 * (x - 7)

We know that the cost of sending the package is $7.99, so we can set up the equation as follows:

$7.99 = $2.41 + $0.41 * (x - 1) + $0.39 * (x - 7)

Now, we can solve this equation to find the value of "x," which represents the weight of the package.

$7.99 - $2.41 = $0.41 * (x - 1) + $0.39 * (x - 7)

$5.58 = $0.41x - $0.41 + $0.39x - $2.73

$5.58 = $0.8x - $3.14

$0.8x = $8.72

x ≈ 10.9

Therefore, there are around 10.9 pounds in the bundle.

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Answer:10.9

Step-by-step explanation:

This belief best illustrates the phenomenon known as political polarization, where individuals strongly align with their own political ideology and tend to view those with opposing beliefs as less correct and less trustworthy.

Political polarization refers to the deep divide and strong ideological alignment within a society, leading individuals to firmly adhere to their own political beliefs and view those with opposing views as less valid or trustworthy. Kate and Carmine's belief reflects this polarized mindset, where they both believe that their own political ideology is more correct and reliable compared to the opposing ideology.

Political polarization often leads to a lack of understanding and empathy between individuals with differing political beliefs, as each side tends to dismiss or devalue the perspectives of the other. This can hinder constructive dialogue and compromise, making it difficult to find common ground or reach consensus on important political issues. The phenomenon of political polarization has become increasingly prominent in many societies, shaping political discourse and contributing to social divisions.

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Answer:

Our calculator limits your interest deduction to the interest payment that would be paid on a $1,000,000 mortgage. Interest rate: Annual interest rate for this

Step-by-step explanation:

Answer:

Step-by-step explanation:

español?

no se yo no halo español :v

Answer:

y = x + 7

Step-by-step explanation:

x = number of weeks

y = the total number of quizzes y.

Cole has already taken 7 quizzes = + 7

he expects to have 1 quiz during each week of this quarter = 1x

y = 1x + 7

y = x + 7

2 measurements can be treated as continuous random variables. 1 discrete random variable, and a fourth that cannot be treated as a random variable. (option d)

There are a few ways that a continuous random variable differs from a discrete variable: Due to the fact that it can contain an infinite number of values within a given interval, continuous random variables are typically uncountable. Measurements like height, weight, distance, and a plethora of other decimal values are examples of these variables. On the other hand, discrete random variables have values that can be counted, and the values of successive values are typically whole numbers.

In the above scenario, The number of starfish is a discrete variable, whereas the starfish's weight and percentage of the plot's area are continuous variables.

It is not a random variable whether the plot is in progress or halfway between high tide and low tide.

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Answer:

43

Step-by-step explanation:

If x = 4, then plug in an x in the given equation

7(4) + 15 = 43

Therefore h(4) = 43

I hope this helps! :)

The dimensions that minimize the amount of material needed for the cup are approximate: Height: 2.71 inches and Radius: 14.70 inches.

From the data,

A thin-walled cone-shaped cup is to hold 36π in³ of water when full.

Let the height of the cone-shaped cup be h and the radius of the top of the cone be r.

The volume of the cone is given by:

=> V = (1/3)πr² h

Since V = 36π, we have:

=> (1/3)πr² h = 36π

=> r² h = 108

The surface area of the cone is given by:

=> A = πr² + πr√(r² + h²)

Using the equation r²h = 108, we can solve for h in terms of r:

=> h = 108/r²

Substituting this into the equation for A, we get:

=> A = πr² + πr√(r² + (108/r²)²)

To minimize A, we need to find the critical points by taking the derivative of A with respect to r and setting it equal to zero:

=> dA/dr = 2πr + π(1/2)(r² + (108/r²)²)^(-1/2)(2r(-108/r^³)) = 0

Simplifying this equation, we get:

=> r⁴ - 54 = 0

Solving for r, we get:

r = √54 ≈ 2.71 in

Substituting this value of r into the equation for h, we get:

=> h = 108/7.344 = 14.70 in

Therefore,

The dimensions that minimize the amount of material needed for the cup are approximate: Height: 2.71 inches and Radius: 14.70 inches.

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There are two vertical asymptotes at angles of 0.5π radians and 1.5π radians and it occurs every π radians.

Tangent function is a kind of trigonometric function, that is, a kind of transcendent function. This function has a period of π radians and for f(x) = tan x, the vertical asymptotes are contained in the points:

x = 0.5π + i · 2π, where i is an integer.

Hence, there are two vertical asymptotes at angles of 0.5π radians and 1.5π radians and it occurs every π radians.

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The total surface area of the solid is 496π/3, in terms of π.

To calculate the total surface area of the solid composed of a cone and cylinder, we need to find the surface area of each shape and then add them together.

The surface area of a cone can be calculated using the formula:

πr² + πr√(r² + h²)

where r is the radius of the base and h is the height. In this case, the radius of the cone is 8 cm and the height is 15 cm, so we have:

π(8)² + π(8)√(8² + 15²) = 64π + 120π/3 = 256π/3

The surface area of a cylinder can be calculated using the formula:

2πr² + 2πrh

where r is the radius of the base and h is the height. In this case, the radius of the cylinder is also 8 cm and the height is 20 cm, so we have:

2π(8)² + 2π(8)(20) = 256π + 320π = 576π

Therefore, the total surface area of the solid is:

256π/3 + 576π = (256π + 1728π)/3 = 496π/3

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Thus, the p-value is greater than 0.10 (the significance level α), indicating that there is not enough evidence to support the alternative hypothesis.

To find the p-value, we need to calculate the test statistic and compare it to the critical value.

Given:

Sample 1: sample size (n1) = 22, variance (\(s_{1}^2\))

= 8, mean (x1(bar))

= 51

Sample 2: sample size (n2) = 20, variance (\(s_{2}^2)\)

= 11, mean (x2(bar))

= 50.5

To calculate the test statistic, we can use the formula for the difference in means:

t = (x1(bar) - x2(bar)) / √((\(s_{1}^2\)/n1) + (\(s_{2}^2\)/n2))

Substituting the given values:

t = (51 - 50.5) / √((8/22) + (11/20))

  = 0.5 / √(0.3636 + 0.55)

  = 0.5 / √0.9136

  ≈ 0.53

Now we need to find the degrees of freedom. For independent samples with equal variance, the degrees of freedom (df) can be calculated using the formula:

df = n1 + n2 - 2

Substituting the given values:

df = 22 + 20 - 2

  = 40

With α = 0.10, the critical value for a one-tailed test (upper tail) with 40 degrees of freedom is 1.684.

Now, we can determine the p-value. Since the alternative hypothesis is μ1 - μ2 > 0, we are conducting an upper-tailed test.

The p-value is the probability of obtaining a test statistic as extreme as the one observed (t = 0.53) under the null hypothesis.

By comparing the test statistic to the critical value, we can determine the conclusion:

Since the test statistic (0.53) is less than the critical value (1.684), we fail to reject the null hypothesis.

Therefore, the conclusion is: "We don't have enough evidence to conclude that the difference in means is > 0; therefore, H0 is not rejected."

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Answer:

-5/4 or -1.25 or -1 1/4

Step-by-step explanation:

To estimate the integral √(ln(2)) ln(x) dx within an accuracy of 0.01 using upper and lower sums for a uniform partition of the interval [1, e], we need to divide the interval into at least n subintervals. The answer is obtained by finding the minimum value of n that satisfies the given accuracy condition.

We start by determining the interval [1, e], where e is approximately 2.718. The function ln(x)^2 is increasing, meaning that its values increase as x increases. To estimate the integral, we use upper and lower sums with a uniform partition. In this case, the width of each subinterval is (e - 1)/n, where n is the number of subintervals.

To find the minimum value of n that ensures the accuracy condition S - S < 0.01, we need to evaluate the difference between the upper sum (S) and the lower sum (S) for the given partition. The upper sum is the sum of the maximum values of the function within each subinterval, while the lower sum is the sum of the minimum values.

Since ln(x)^2 is increasing, the maximum value of ln(x)^2 within each subinterval occurs at the right endpoint. Therefore, the upper sum can be calculated as the sum of ln(e)^2, ln(e - (e - 1)/n)^2, ln(e - 2(e - 1)/n)^2, and so on, up to ln(e - (n - 1)(e - 1)/n)^2.

Similarly, the minimum value of ln(x)^2 within each subinterval occurs at the left endpoint. Therefore, the lower sum can be calculated as the sum of ln(1)^2, ln(1 + (e - 1)/n)^2, ln(1 + 2(e - 1)/n)^2, and so on, up to ln(1 + (n - 1)(e - 1)/n)^2.

We need to find the minimum value of n such that the difference between the upper sum and the lower sum is less than 0.01. This can be done by iteratively increasing the value of n until the condition is satisfied. Once the minimum value of n is determined, we have the required number of subintervals for the given accuracy.

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Note: The must be \(0.04v^2\) instead of \(0.04v\).

Given:

The stopping distance, d ( in feet) for a van moving at a velocity (speed) v miles per hour is modeled by the equation:

\(d=0.04v^2+1.1v\)

To find:

The stopping distance for a velocity of 10 miles per hour.

Solution:

We have,

\(d=0.04v^2+1.1v\)

where, d is stopping distance and v is velocity.

Substitute v=10  in the given equation to find the stopping distance for a velocity of 10 miles per hour.

\(d=0.04(10)^2+1.1(10)\)

\(d=0.04(100)+11\)

\(d=4+11\)

\(d=15\)

So, the stopping distance for a velocity of 10 miles per hour is 15 ft.

Therefore, the correct option is c.

Answer:

6 ways

Step-by-step explanation:

William has a sticker album.

We are told in the question that:

Some pages have 1 sticker on them, and other pages have 2 stickers on them. If William has 18 stickers

The many different ways that can he put the stickers in the album is calculated as:

18 stickers ÷ ( 1 stickers + 2 stickers)

= 18 ÷ 3

= 6 ways

Therefore, the different ways that he can put the stickers in the album is 6 ways