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The calculated value of x in the equation (x + 1) (x - 5) = 16 is 7

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

(x + 1) (x - 5) = 16

The above expression is the product of two factors

(x + 1) and (x - 5)

And the result is 16

Express 16 as 8 * 2

So, we have

(x + 1) (x - 5) = 8 * 2

By comparison, we have

x + 1 = 8 and x - 5 = 2

When evaluated, we have

x = 7 and x = 7

This means that the value of x in the equation is 7

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Answer:

The model represents the equation "0 + x² = 1/2", which is not directly related to multiplying with fractions.

Answer:

(0,8)

Step-by-step explanation:

What is needed in order to be a function?

A value of x cannot have more than one value of y. In this question, we have that for x = 0, there are 2 values of y: -2 and 8. So one of those can be removed.

Among the options, we have: (0,8), which is the correct answer

Using relations in a right triangle, the secant of angle θ is given by:

D. 5/4.

The relations in a right triangle are given as follows:

Using the Pythagorean Theorem, the hypotenuse of the triangle is given as follows:

h² = 9² + 12²

h = sqrt(9² + 12²)

h = 15.

The secant of an angle is 1 divided by the cosine, hence:

Which means that option D is correct.

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Answer:

Step completed incorrectly:  2

Correct Answer: y = -4x + 22

Step-by-step explanation:

The graph is a straight line through points M(4, -1) and N(8, 0).  Point Q is located at (6, -2).

To calculate the slope of the line, substitute the points into the slope formula:

\(\textsf{Slope $(m)$}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-(-1)}{8-4}=\dfrac{1}{4}\)

Therefore, the slope of MN is 1/4, so step 1 of Francisco's calculations is correct.

If two lines are perpendicular to each other, the slopes of these lines are negative reciprocals. The negative reciprocal of a number is its negative inverse.

The negative reciprocal of 1/4 is -4.

Therefore, the slope of the perpendicular line is -4.

So Francisco has made an error in his calculation in step 2 by not making the perpendicular slope negative.

Corrected work

\(\textsf{Step 1:} \quad \sf slope\;of\;MN:\; \dfrac{1}{4}\)

\(\textsf{Step 2:} \quad \sf slope\;of\;the\;line\;perpendicular:\; -4\)

\(\begin{aligned}\textsf{Step 3:} \quad y-y_1&=m(x-x_1)\;\; \sf Q(6,-2)\\y-(-2)&=-4(x-6)\end{aligned}\)

\(\textsf{Step 4:} \quad y+2=-4x+24\)

\(\textsf{Step 5:} \quad y+2-2=-4x+24-2\)

\(\textsf{Step 6:} \quad y=-4x+22\)

Therefore, step 2 has been completed incorrectly.

The correct answer is y = -4x + 22.

A cluster sample is a type of sampling technique wherein clusters of subjects that are similar in certain characteristics are selected for the study. In this case, the sample includes 3 owners, 6 players, and 20 fans, all of whom have something in common - an interest in basketball. Therefore, the sample described is a cluster sample.

A cluster sample is a type of sampling technique wherein clusters of subjects that are similar in certain characteristics are selected for the study. In this case, the sample includes 3 owners, 6 players, and 20 fans, all of whom have something in common - an interest in basketball. Therefore, the sample described is a cluster sample. This type of sample is helpful when the researcher is interested in specifically examining a certain group of people and their opinions. A cluster sample is relatively easy to implement and can be used to quickly obtain a large amount of data in a short period of time. It also eliminates the need to identify and select individuals from a population. By using a cluster sample, the sports columnist was able to quickly get feedback from a variety of individuals who may have different opinions on the potential basketball lockout.

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Answer:

3

Step-by-step explanation:

6 divided by 2

The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

To solve this problem, we can use the concept of radioactive decay and the decay factor. Here's how we can calculate the required volume to correct the dose:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = Initial activity * Decay factor

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = Initial activity - 20 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = Remaining activity * Decay factor

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = Desired activity at 9:30 / Remaining activity at 9:30 * Volume at 9:30

Calculate the remaining volume at 9:30:

Remaining volume = Volume at 8 am - Volume withdrawn - Volume accidentally discharged

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume

Let's perform the calculations step by step:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = 180 mCi * 0.841 = 151.38 mCi

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = 180 mCi - 20 mCi = 160 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = 160 mCi * 0.841 = 134.56 mCi

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = (Desired activity at 9:30 / Remaining activity at 9:30) * Volume at 9:30

Volume at 9:30 = Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Volume needed = (20 mCi / 134.56 mCi) * 15 ml = 2.236 ml

Calculate the remaining volume at 9:30:

Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume = 2.236 ml - 15 ml = -12.764 ml

Since the calculated volume to be added is negative, it means that no additional volume is required. The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

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The area of the shaded region, with a frame of 3 units wide, is 264 square units. The inner rectangle is 6x4 units, and the outer rectangle is 18x16 units.

To solve the given problem, we have to find the area of the shaded region if the frame is 3 units wide. If the frame is 3 units wide, then the dimensions of the inner rectangle (the shaded region) will be (12 - 6) × (10 - 6) which simplifies to 6 × 4.

Therefore, we can say that the inner rectangle has a length of 6 units and a width of 4 units.The dimensions of the outer rectangle are (12 + 3 + 3) × (10 + 3 + 3) which simplifies to 18 × 16. Therefore, we can say that the outer rectangle has a length of 18 units and a width of 16 units.

The area of the shaded region can be obtained by subtracting the area of the inner rectangle from the area of the outer rectangle. Therefore, the Area of the outer rectangle = length × width= 18 × 16 = 288 square units

Area of the inner rectangle = length × width= 6 × 4 = 24 square units

Area of the shaded region = Area of the outer rectangle - Area of the inner rectangle = 288 - 24= 264 square units

Therefore, the area of the shaded region is 264 square units.

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Answer:

It will take 43.15 minutes for the lake and the tank to contain the same amount of water.

Step-by-step explanation:

Given that:

Water tank contains 12.3 gallons of water.

1.6 gallons per minute are being added by Mark.

Let,

m be the minutes in which water tank is filling.

T(m) = 1.6m + 12.3

The lake has 98.6 gallons of water.

Water is drained at a rate of 0.4 gallons per minute.

L(m) = -0.4m + 98.6

For same amount of water,

T(m) = L(m)

1.6m+12.3 = -0.4m+98.6

1.6m+0.4m = 98.6 -12.3

2.0m = 86.3

Dividing both sides by 2

\(\frac{2.0m}{2}=\frac{86.3}{2}\\m=43.15\)

Hence,

It will take 43.15 minutes for the lake and the tank to contain the same amount of water.

Definition of a Parallelogram

1) Let's fill in the 2nd row of that table since we know that

Statement Reason

1. ABCD is a parallelogram Given

2. AB ≅ CE Given

3. CD ≅ AB Definition of a Parallelogram

Note that a parallelogram has 2 pairs of congruent and parallel line segments.

2) Thus, the answer is:

"Definition of a Parallelogram".

Answer:

C = 24/25

Step-by-step explanation:

Recall, CAH.

Thus:

Cos T = adjacent/hypotenuse

Reference angle = T

Adjacent = 24

Hypotenuse = 25

Therefore,

Cos T = 24/25

Step-by-step explanation:

If journal prices increased by 15% each year, after 15 years the total price increase would be calculated as follows:

(1 + 0.15)^15 = 2.25

So the total price increase over 15 years would be 225%. This matches the increase reported in the library's report, which concluded that the price increase was 15% per year

Answer:

71 is 10% of 710

52 is 97% of 5200/97

Step-by-step explanation:

Let’s start with 71 is 10% of what number.

basically, what this is saying, is that 71 = 10% times and unknown valu. We can set this as x.

so, 71=0.1x

divide on both sides,

710=x

now the second one.

repeat the same process.

52=0.97x

divide

5200/97 =x

Answer:

if you are asking for decimal its, 0.625.

otherwise 5/8 is also equal to 10/16, 15/24, etc

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

Expand all terms

-9+3k = 3k+9

Bring all like terms to one side

-9-9=3k-3k

Simplify

-18=0

no solution for k because -18 cannot be equal to 0

Answer:

y - 8 = 2 (x - 6)

Step-by-step explanation:

The point-slope equation is ...

y - y1  = m ( x - x1 )

In the coordinate (6,8)

x = 6 and y = 8

m = 2

Plug in values to find the point-slope form

y - 8 = 2 (x - 6)

We are done!

The monomials with a GCF of 7x³y with degree 5 are 7x⁴y and 14x³y².

The Highest Common Factor (HCF) of two numbers is the highest possible number that is divisible by both numbers.

In other words, the highest common factor is the common factor between the two numbers but it should be the highest among all common factors.

As per the given GCF as 7x³y,

The GCF of 14 and 7 is 7.

The GCF of x⁴y and x³y² will be x³y.

Thus,

GCF of 7x⁴y and 14x³y² = 7x³y

So monomials are 7x⁴y and 14x³y².

Hence "The monomials are 7x⁴y and 14x³y²".

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The area of the composite figure is 122.24 units².

The composite figure consist of a rectangle and two semi circles. Therefore, the area of the composite figure is the sum of the area of the individua shapes.

Hence,

area of the composite figure = area of the rectangle + 2(area of semi circle)

Therefore,

area of the composite figure = 9 × 8 + 2(1 / 2 πr²)

area of the composite figure = 72 + πr²

where

r = 8 / 2 = 4 units

Therefore,

area of the composite figure = 72 + 3.14 × 4²

area of the composite figure = 72 + 3.14 × 16

area of the composite figure = 72 + 50.24

area of the composite figure = 122.24 units²

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Answer:

-21

-29-(-8)=-21

Answer:

C

Step-by-step explanation:

Each slope down in the graph represents a drink. so the first drink ended at 30 sec and the second one started at 60 sec so he waited 30 sec inbetween.

Answer: 2

Step-by-step explanation:

Answer:

I think it's 2kg

Step-by-step explanation:

13/5 ÷ 13/10

Reciprocate

13/5 × 10/13

= 26/13

=2kg

Answer:

E.

Step-by-step explanation:

2x+4>10

Subtract 4 from both sides

2x>6

Divide both sides by 2

x>3

So, E represents this inequality as x is greater than 3 and it does not include 3 in it which is represented by an empty bubble.

Answer:

E

Step-by-step explanation:

Answer:

The ranges of g(x) and f(x) are the same and their domains are also the same.

Step-by-step explanation:

The function g(x) is the function f(x) multiplied by 35 and later translated twice, first 6 units up and later 8 units down. Since, both expressions are linear functions, both are continuous and both have the same domains and range due to constant slope.

Hence, the ranges of g(x) and f(x) are the same and their domains are also the same.

For given function function f(x)=-x+3-2, the domain is x > -3 and the range is y ≤ 2. So, correct option is D.

The function f(x)=-x+3-2 is a linear function in the form y=mx+b, where m is the slope and b is the y-intercept. In this case, the slope is -1 and the y-intercept is 1. Therefore, the graph of the function is a straight line that intersects the y-axis at (0,1) and has a slope of -1, meaning that it decreases by 1 for every 1 unit increase in x.

The domain of the function is the set of all possible values of x for which the function is defined. Since there are no restrictions on the value of x in the equation f(x)=-x+3-2, the domain is all real numbers, or (-∞, ∞).

The range of the function is the set of all possible values of y that the function can output. In this case, the lowest possible value of y occurs when x approaches positive infinity, and the highest possible value of y occurs when x approaches negative infinity. Therefore, the range is all real numbers less than or equal to 2, or y ≤ 2.

So, the domain is x ∈ (-∞, ∞) and the range is y ≤ 2. Alternatively, the domain can also be expressed as x > -3, since that is the minimum value of x at which the function is defined.

Correct option is D.

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Complete question is:

What are the domain and range of the function f(x)=-x+3-2?

A) domain: -3 -2

B) domain: -3 -3 range: y<-2

C) domain: x>-3 range:y>-2

D) domain : x>-3 range: y ≤ 2

The radical form of the given expression would be; \(x^{ \frac{5}{8} } = \sqrt[8]{x^{5}}\)

Factor the radicand: If the radicand isn't already in the form of a perfect square, we can factor it into its prime factors and pull out any perfect squares from the radicand.

We are given that

\(x^{ \frac{m}{n} } = \sqrt[n]{x^{m}} \\ x^{ \frac{5}{8} } = \sqrt[8]{x^{5}} \\\)

When the radical has an exponent (such as cube root), divide the exponent by the index of the radical.

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Answer:

\(3 {x}^{2} - 5x + 4x = 3 {x}^{2} - 5 {x}^{2} + 9x \\ 3 {x}^{2} - x = - 2 {x}^{2} + 9x \\ 3 {x}^{2} + 2{x}^{2} = 9x + x \\5 {x}^{2} = 10x \\ 5x = 10 \\ x = \frac{10}{5} = 2 \\ x = 2 \\ thank \: you\)

Answer:

\( \rm x = 2\)

Step-by-step explanation:

\( \rm 3x ^ { 2 } -5x+4x=3x ^ { 2 } -5x ^ { 2 } +9x\)

\( \rm 3x^{2}-x=3x^{2}-5x^{2}+9x \)

\( \rm 3x^{2}-x=-2x^{2}+9x \)

\( \rm 3x^{2}-x+2x^{2}=9x \)

\( \rm 5x^{2}-x=9x \)

\( \rm 5x^{2}-x-9x=0 \)

\( \rm 5x^{2}-10x=0 \)

\( \rm 5x -10 =0 \)

\( \rm x = 10 \div 5 \)

\( \bold{x = 2}\)

Answer:

0.7493 or 74.93%

Step-by-step explanation:

We are given;

Population mean; μ = 100

Population standard deviation; σ = 12

Sample mean 1; x1¯ = 90

Sample mean 2; x2¯ = 120

Z-score formula of the data given is;

z = (x¯ - μ)/σ

z1 = (90 - 100)/12

z1 = -0.83

z2 = (120 - 100)/12

z2 = 1.67

Since we wan to Find the probability that a randomly selected bill is between $90 to $120.

Thus;

P(90 < x¯ < 120) = P(−0.83 < Z < 1.67)

Probability will be gotten from online probability with 2 z-scores calculator to get;

P = 0.7493

The correct option is C

Kenneth's average speed is 58 mph

Average speed is the ratio of distance traveled to the time take

Given that Kenneth drove 194.3 miles in 3 7/20 hours,

3 7/20 is the same as 3.35

his average speed is: 194.3/3.35 = 58

The average speed is 58 mph

The highest point of the quadratic equation that opens down can be (-5, 8)

We have a quadratic equation whose graph opens downwards, and we know that it also passes through the points (-2,5) and (-8, 5).

The highest point will be of the form (x, y).

Such that y is larger than 5, and the value of x is right between the two values above:

x = (-2 - 8)/2

x = -5

So the point is of the form (-5, y) where again y  > 5.

From the given options the only of this form is (-5, 8)

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