x+3+7(x-5) show work

Answer:

Total amount of water = 5,200,000

Step-by-step explanation:

Given:

water produced = 50,000 quarts of water per week

Production drop = 5% = 0.05 per year

Number of week in year = 52 week

Find:

Total amount of water

Computation:

Sum = a / r

a = 50,000 x 52

a = 2,600,000

Sum = a / [1-r]

Sum = 2,600,000 / 5%

Sum = 2,600,000 / 0.05

Total amount of water = 5,200,000

Answer:

The equation of the line is y = 3x - 7

Step-by-step explanation:

Parallel lines have the same gradient: the equation of the line would have a gradient of 3 (the gradient is the number in front of x).

y = 3x + c

If the line goes through the point (3, 2) then (3, 2) would satisfy the equation of the line. This means we can substitute 3 for x and 2 for y:

2 = 3(3) + c

2 = 9 + c

c = 2 - 9

c = -7

The equation of the line is y = 3x - 7

Hope this helps!

18. The statement (A∩B)⊆B is True,

19. The cardinality of the power set of C, denoted as ∣P(C)∣, is 4,

20. The statement P(C)={{∅},{{c}},{∅,{c}}} is True.

18. To determine if (A∩B)⊆B is True or False, we need to check if every element in the intersection of A and B is also an element of B. The intersection of A and B is {b}, and {b} is an element of B, so the statement is True.

19. The power set of a set C, denoted as P(C), is the set of all subsets of C, including the empty set and C itself. In this case, C={∅,{c}}. The power set of C, P(C), is {{∅},{{c}},{∅,{c}},C}. Therefore, the cardinality of P(C), denoted as ∣P(C)∣, is 4.

20. The statement P(C)={{∅},{{c}},{∅,{c}}} is True. It correctly represents the power set of C, which includes the subsets {{∅}} (which represents the empty set), {{c}} (which represents the set containing the element c), and {{∅,{c}}}, as well as the set C itself.

In summary, the given statements are as follows:

1. (A∩B)⊆B is True.

2. ∣P(C)∣ = 4.

3. P(C)={{∅},{{c}},{∅,{c}}} is True.

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Let A,B, and C be sets where A={a,b,c,d,e},B={b,{c,d},∅}, and C={∅,{c}}. Evaluate the following: (A∩B)⊆B. True or False?

Let A,B, and C be sets where A={a,b,c,d,e},B={b,{c,d},∅}, and C={∅,{c}}. Evaluate the following : ∣P(C)∣= ?

Let A,B, and C be sets where A={a,b,c,d,e},B={b,{c,d},∅}, and C={∅,{c}} P(C)={{∅},{{c}},{∅,{c}} True or False

Answer:

b is correct.

Step-by-step explanation:

Starting at (-2, -3), go 4 units up and then 5 units to the right. You will end up at (3, 1).

We will have the following:

We can see that the function follows a path of exponential decay, so the expression that models it is:

Answer: B, D, and E

Step-by-step explanation:

All of the values I've given you are greater than -1/4.

By using a number line, for example, you'd see that 0, 1, and 1 1/4 are all towards the right of -1/4. This means that they're greater than -1/4.

So, the values that are greater than -1/4 are 0, 1, and 1 1/4

The area of triangle TUV with vertices T(-8,2), U(-2,8), and V(-9,9) are 13.4 units.

A triangle is a closed two-dimensional plane figure that has three sides, three angles, and three vertices. The sum of the angles of a triangle is always 180 degrees. Triangles can be classified based on the length of their sides and the size of their angles. Some common types of triangles include equilateral, isosceles, scalene, acute, obtuse, and right triangles. Triangles are a fundamental concept in geometry and are used in many areas of mathematics and science.

Here,

To find the area of triangle TUV, we can use the formula:

Area = 1/2 * base * height

We can choose any two sides of the triangle as the base and the corresponding height. Let's choose TU as the base and the perpendicular distance from V to TU as the height.

First, let's find the length of TU:

TU = √[(8 - 2)² + (-2 - (-8))²]

= √[6² + 6²]

= 6√(2)

Next, let's find the slope of TU:

mTU = (8 - 2) / (-2 - (-8))

= -3/2

The line perpendicular to TU passing through V has a slope equal to the negative reciprocal of mTU:

mVQ = 2/3

The equation of the line passing through V and perpendicular to TU is:

y - 9 = (2/3)(x + 9)

Solving for x and y at the point where this line intersects TU, we get:

y = (2/3)x + 19

(2/3)x + 19 = -3x/2 + 7

x = -8/7

y = 94/21

The perpendicular distance from V to TU is the absolute value of y - 8:

|94/21 - 8| = 2/21

So, the area of triangle TUV is:

Area = 1/2 * TU * (2/21)

= (1/21)√(2)

To find the area of rectangle QRS, we need to find the length and width. We can use the distance formula to find the length QR and the width QS:

QR = √[(9 - (-8))² + (9 - 2)²]

= √[289]

= 17

QS = √[(9 - (-9))² + (2 - 2)²]

= √[324]

= 18

So, the area of rectangle QRS is:

Area = QR * QS

= 17 * 18

= 306

Area of triangle QRS = Area of rectangle QRS - Area of triangle TUV

= 306 - (1/21)√(2)

≈ 13.4 units

So, the answer is (C) 13.

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Complete question:

Triangle TUV, with vertices T(-8,2), U(-2,8), and V(-9,9), is drawn inside a rectangle. What is the area, in square units, of the triangle TUV?

A. 7

B. 10

C. 13

D. 18

Answer:

a = 2

Step-by-step explanation:

the constant terms inside the factors will multiply to give the constant term of the expansion, that is

a × 9 × - 4 = - 72

- 36a = - 72 ( divide both sides by - 36 )

a = 2

The slope (m) and y-intercepts are:

2. (m) is -1 and m = 4;       3. m = 2 and the b = 1.     5. m = 1 and m = -2;

6. m = -3 and b = -5.       8. m = 3 and b = -1.          9. m = -1 and b = 3.

The value of the slope in an equation is represented as m while the y-intercept is represented as b, where the equation is in the form of y = mx + b, in slope-intercept form.

In the equation y = -x + 4, the slope (m) is -1 and the y-intercept is 4.

In the equation y = 2x + 1, m = 2 and the b = 1.

In y = x - 2, the m = 1 and the y-intercept is -2.

In y = -3x - 5, m = -3 and b = -5.

In y = 3x - 1, m = 3 and b = -1.

In y = -x + 3, m = -1 and b = 3.

The graph of y = -x + 4 is in figure 1, while that of y = 2x + 1 is in figure 2.

The graph of y = x - 2 is in figure 3, while that of y = -3x - 5 is in figure 4.

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Answer:

B. \( y = 160x + 2400 \)

Step-by-step explanation:

The linear equation for that represents the above data is given in slope-intercept form as \( y = mx + b \), where:

m = slope = \( \frac{y_2 - y_1}{x_2 - x_1} \)

b = starting value = y-intercept = 2,400

Slope of the linear equation using (0, 2400) and (10, 4000):

\( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4000 - 2400}{10 - 0} = \frac{1600}{10} = 160 \)

Substitute m = 160, and b = 2,400 in \( y = mx + b \).

Thus, the linear equation in slope-intercept form would be:

✅\( y = 160x + 2400 \)

To dilate a point at a point, you start by selecting a center of dilation and a scale factor.

Then, for each point that you want to dilate, you do the following:

For example, if you wanted to dilate point P by a scale factor of 2, with the center of dilation at O, you would draw a line segment from O to P, double its length, and then draw a new line segment from O to the new point, using the new length that you calculated. The new point would be the point that you arrive at when you complete this line segment.

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The blanks to complete the proof are filled as follows

17. Reflexive property

18. Angle-Angle-Side Congruence

19. Corresponding Parts of Congruent Triangles are Congruent

The AAS Congruence Theorem, also known as the Angle-Angle-Side Congruence Theorem, is a criterion for proving that two triangles are congruent. "AAS" stands for "Angle-Angle-Side."

According to the AAS Congruence Theorem, if two angles of one triangle are congruent to two angles of another triangle, and the included sides between those angles are also congruent, then the two triangles are congruent.

Hence using AAS theorem we have that line BA is equal to line BC (CPCTC - Corresponding Parts of Congruent Triangles are Congruent)

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Now

Equation in slope intercept form

If each GB be x

Here

Option A is correct

Answer:

0.3425

multiply the 13.7 by 2 1/2%.

now, we have 34.25.

Divide the 34.25 by 100, and that's your answer.

In this case, the standard deviation is 3.7, so the variance is 3.7², or 13.69. This means that the data points in the data set are, on average, 13.69 units away from the mean.

The variance of a data set is a measure of how the data points are distributed around the mean. It is calculated by squaring the standard deviation, which is the average distance of the data points from the mean.

Variance is a useful measure for quantifying the spread and variability of the data points in a data set. By knowing the variance, it is possible to make predictions about how likely it is that a given data point will fall within a certain range from the mean.

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Answer:

$175

Step-by-step explanation:

you need to specify if harriet got the 7 portion or the 5 portion. I'll answer as if she got the 7 portion.

They split it into 12 portions because the ratio is 7:5 and 7+5=12. So do $300/12=25

Assuming Maya got the 5 portion, do $25 x 5 = $125, so Maya got $125.

Assuming Harriet got the 7 portion, do $25 x 7 = $175, so Harriet got $175.

The equation that can be used to find x, the number of yards that Aj walks and runs each week is 2x = 400 + 90.

Let's assume that Aj runs x yards each week. Then, the number of yards that Aj walks each week would be (x + 90) yards, since he walks 90 more yards than he runs.

The total distance that Aj covers each week would be the sum of the distance that he runs and the distance that he walks, which is given as 400 yards.

So, we can write an equation as:

Distance covered by Aj = Distance that he runs + Distance that he walks

or,

Simplifying this equation gives:

Therefore, the equation that can be used to find x, the number of yards that Aj walks and runs each week is 2x = 400 + 90.

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Answer:

x=9

Let's solve your equation step-by-step

12(x−2)+3x=x+12+10x

Step 1: Simplify both sides of the equation.

12(x−2)+3x=x+12+10x

(12)(x)+(12)(−2)+3x=x+12+10x(Distribute)

12x+−24+3x=x+12+10x

(12x+3x)+(−24)=(x+10x)+(12)(Combine Like Terms)

15x+−24=11x+12

15x−24=11x+12

Step 2: Subtract 11x from both sides.

15x−24−11x=11x+12−11x

4x−24=12

Step 3: Add 24 to both sides.

4x−24+24=12+24

4x=36

Step 4: Divide both sides by 4.

4x/4=36/4

x=9

Answer:

x=9

Answer: x = 9

Step-by-step explanation:

12(x − 2) + 3x = x + 12 + 10x

12(x - 2) + 3x = 11x + 12

12x - 24 + 3x = 11x + 12

15x - 24 = 11x + 12

15x = 11x + 12 + 24

15x = 11x + 36

15x - 11x = 36

4x = 36

x = 36/4

x = 9

We divide both sides by 8, which yields -2 = x. This means that x is equal to -2, the correct answer is B) x = -2.

To solve the equation -9x + 1 = -x + 17, we can simplify and isolate the variable x.

First, let's combine like terms by adding 9x to both sides:

-9x + 9x + 1 = -x + 9x + 17

Simplifying further:

1 = 8x + 17

Next, let's isolate the variable x by subtracting 17 from both sides:

1 - 17 = 8x + 17 - 17

Simplifying again:

-16 = 8x

To solve for x, we divide both sides by 8:

-16/8 = 8x/8

-2 = x

Therefore, the solution to the equation -9x + 1 = -x + 17 is x = -2.

To solve the equation, we want to isolate the variable x on one side of the equation. We start by combining like terms. By adding 9x to both sides, we eliminate the variable terms on the left side, resulting in 1 = 8x + 17.

Next, we isolate the variable x by subtracting 17 from both sides. This simplifies the equation to -16 = 8x.

To solve for x, we divide both sides by 8, which yields -2 = x. This means that x is equal to -2. Therefore, the correct answer is B) x = -2.

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Rule for even

\(\\ \sf\longmapsto \boxed{\sf f(-x)=f(x),x\in D_f}\)

Rule for odd

\(\\ \sf\longmapsto \boxed{\sf f(-x)=-f(x),D_f}\)

#1

\(\\ \sf\longmapsto f(x)=\sqrt{x^2}-9\)

\(\\ \sf\longmapsto f(4)=\sqrt{4^2}-9=4-9=-5\)

\(\\ \sf\longmapsto f(-4)=\sqrt{(-4)^2}=4-9=-5\)

#2

\(\\ \sf\longmapsto g(x)=|x-3|\)

\(\\ \sf\longmapsto g(2)=|2-3|=|-1|=1\)

\(\\ \sf\longmapsto g(-2)=|-2-3|=|-5|=5\)

\(\\ \sf\longmapsto -g(2)=-1\)

#3

\(\\ \sf\longmapsto f(x)=\dfrac{x}{x^2-1}\)

\(\\ \sf\longmapsto f(3)=\dfrac{3}{3^2-1}=\dfrac{3}{9-1}=\dfrac{3}{8}\)

\(\\ \sf\longmapsto f(-3)=\dfrac{-3}{(-3)^2-1}=\dfrac{-3}{8}\)

\(\\ \sf\longmapsto -f(3)=\dfrac{-3}{8}\)

#4

\(\\ \sf\longmapsto g(x)=x+x^2\)

\(\\ \sf\longmapsto g(1)=1+(1)^2=2\)

\(\\ \sf\longmapsto g(-1)=-1+(-1)^2=0\)

\(\\ \sf\longmapsto -g(1)=-2\)

Step-by-step explanation:

c

Consumption of Bananas per year = 5, 250, 000 metric tons

We know 1000 kg = 1 metric ton, so

Consumption of Bananas per year (in kg) = 5, 250, 000 x 1000 = 5, 250, 000, 000 kgs

Cost of Banana = $2.10 per kg

So,

Cost of all bananas = 5, 250, 000, 000 x 2.10 = $ 11,025,000,000 (per year)

Taking a year to be 365 days, let's find the cost for a day:

Since there are 317 million [317,000,000] people in the US, the cost per person every day is:

Rounding to the nearest cent,

Charlotte and her sister enjoyed a special dinner in a restaurant, and the bill was $53.86. 11.99%  tip did she leave.

Percent tip she give:

\(\frac{6.46}{53.86}\) × 100

= 11.99 %

A percentage, or percent, is a number smaller than or equal to 100. The term "per 100" refers to a percentage of a total amount. 45 percent, for instance, is 45 out of 100. Finding the share of a whole in terms of 100 is what percentage means. You can use online calculators or manually calculate it.

Percentages are utilized extensively and in numerous contexts. Discounts in stores, interest rates at banks, inflation rates, and numerous media statistics are all expressed as percentages. Understanding the financial aspects of everyday life requires knowledge of percentages.

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Step-by-step explanation:

you have one rectangle "at the base"

S = b × h = 2ft × 6ft = 12 ft²

one rectangle "at the back"

S = b × h = 2ft × 10ft = 20 ft²

one rectangle "along the length of the hypotenuse"

S = b × h = 2ft × 8ft = 16 ft²

and two triangles

S = (b × h) / 2 = (6ft × 8ft)/2 = 24 ft²

total S = 12ft²+20ft²+16ft²+24ft²+24ft² = 96 ft²

Answer:   76 ft²

Step-by-step explanation:

Surface area for the prism = all the area's from the net added up.

Area triangle = 1/2 bh      b=base, we need to find    h, height=C=8

Use pythagorean to find base

c²=a²+b2

D² = C² + b²

10² = 8² + b²

b² = 100-64

b² = 36

b = 6

Area triangle = 1/2 (6)(8)

Area triangle = 24

Area of top rectangle = LW

L, length = A = 2

W, width = C = 8

Area of top rectangle = (2)(8)

Area of top rectangle = 16

Area of bottom rectangle =  LW

L, length = A = 2

W, width = B = 6

Area of bottom rectangle = (2)(6)

Area of bottom rectangle = 12

Surface Area = 2(triangle) + (top rectangle) + (bottom rectangle)

Surface Area = 2(24) +16 +12

Surface Area = 48 +28

Surface Area = 76 ft²

the antiderivative of the function f(x) = 2 csc(x) cot(x) sec(x) tan(x) is F(x) = 2x + C.

To find the antiderivative F(x) of the function f(x) = 2 csc(x) cot(x) sec(x) tan(x), we can simplify the expression and integrate each term individually.

We know that csc(x) = 1/sin(x), cot(x) = 1/tan(x), sec(x) = 1/cos(x), and tan(x) = sin(x)/cos(x).

Substituting these values into the expression:

f(x) = 2 * (1/sin(x)) * (1/tan(x)) * (1/cos(x)) * (sin(x)/cos(x))

= 2 * (1/sin(x)) * (1/(sin(x)/cos(x))) * (sin(x)/cos(x)) * (sin(x)/cos(x))

= 2 * (1/sin(x)) * (cos(x)/sin(x)) * (sin(x)/cos(x)) * (sin(x)/cos(x))

= 2 * 1

= 2

The antiderivative of a constant function is simply the constant multiplied by x. Therefore:

F(x) = 2x + C

where C represents the constant of the antiderivative.

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Answer:

the answer is B.

Step-by-step explanation:

the answer is b because both sides increase

Answer:

3 - 21m

Step-by-step explanation:

-4 + 7(1-3m)

-4 + 7 - 21m

3 - 21m

a. This is an experiment. The reason why this is an experiment is that the subjects were divided into low fitness and high fitness groups, which means that they have been manipulated. The exercise program can be considered the independent variable, while the physical fitness level is the dependent variable.

b. No, we cannot conclude with certainty that higher fitness causes higher self-confidence.

Although the study has shown that the high fitness-group has a higher average score for "self-confidence," correlation does not equal causation. There may be other factors that have influenced the relationship between fitness and self-confidence.

Furthermore, the study did not establish a cause-and-effect relationship between physical fitness and self-confidence. It only showed a correlation between the two. A more comprehensive study that controls for other variables and includes a larger and more diverse sample size would be necessary to establish causation.

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a) An example of a polynomial of degree 5 for which x=1 is a critical number but not a local minimum nor a local maximum is:

P(x) = (x-1)^2(x-2)(x+1)(x+3)

To see why x=1 is a critical point but not a local minimum nor a local maximum, we can compute the first and second derivatives of P(x):

P'(x) = 2(x-1)(x-2)(x+1)(x+3) + (x-1)^2(x+1)(x+3) + (x-1)^2(x-2)(x+3) + (x-1)^2(x-2)(x+1)

P''(x) = 2(x-2)(x+1)(x+3) + 2(x-1)(x+1)(x+3) + 2(x-1)(x-2)(x+3) + 2(x-1)(x-2)(x+1) + 4(x-1)(x-2)(x+1)(x+3)

We can see that P'(1) = 0, so x=1 is a critical point. To determine whether it's a local minimum or maximum, we need to look at the sign of P''(1). However, computing P''(1) gives us:

P''(1) = 2(1-2)(1+1)(1+3) + 2(1-1)(1+1)(1+3) + 2(1-1)(1-2)(1+3) + 2(1-1)(1-2)(1+1) + 4(1-1)(1-2)(1+1)(1+3) = 16

Since P''(1) is positive, we know that x=1 is not a local maximum or a local minimum, but rather an inflection point.

b) To determine the intervals on which f(x) = (x-2)(x+3) is decreasing and increasing and find local minima and maxima, we can compute the first and second derivatives of f(x):

f'(x) = 2x+1

f''(x) = 2

We can see that f''(x) is always positive, so f(x) is always concave up. Therefore, any critical points of f(x) will be local minima. To find the critical points, we set f'(x) = 0:

2x+1 = 0

x = -1/2

So x=-1/2 is the only critical point of f(x). To determine whether it's a local minimum or not, we can look at the sign of f'(x) on either side of x=-1/2:

When x < -1/2: f'(x) < 0, so f(x) is decreasing.

When x > -1/2: f'(x) > 0, so f(x) is increasing.

Therefore, we know that x=-1/2 is a local minimum of f(x).

c) To determine the intervals on which f(x) = (x+1)(x-2)(x+3) is decreasing and increasing and find local minima and maxima, we can compute the first and second derivatives of f(x):

f'(x) = 3x^2-2x-7

f''(x) = 6x-2

To find the critical points of f(x), we set f'(x) = 0:

3x^2-2

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