Determine whether C. C, both, or neither can be placed in the blank to make the statement true.
(T. R. C) (T. R. C. V)
Choose the correct answer below.
OOnly C
O Only S
O Both C & C
O None of the above
As
2
CICCERR

The requried, factored form of 6x²+7x-10 is (6x - 5)(x + 2).

To factor 6x²+7x-10, we need to find two numbers whose product is -60 (the product of the coefficient of x² and the constant term) and whose sum is 7 (the coefficient of x).

Now, we can factor by grouping:

(6x² + 12x) - (5x + 10)

6x(x + 2) - 5(x + 2)

(6x - 5)(x + 2)

Therefore, the factored form of 6x²+7x-10 is (6x - 5)(x + 2).

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The solution is, the value of the variables are x = 40 and, y = 160.

Notice that "x" and "3x+20" are supplementary angles so their sum is 180°

(x) + (3x + 20) = 180

4x + 20 = 180

4x = 160

x = 40

To solve for "y", you have 2 options: either notice that "x" and "y-20" are supplementary angles so their sum is 180° or notice that "3x + 20" and "y - 20" are vertical angles so are equal to each other. I am going to solve using the first option because it is less work.

(x) + (y - 20) = 180°

40 + y - 20 = 180

y + 20 = 180

y = 160

Answer: x=40, y=160

The solution is, the value of the variables are x = 40 and, y = 160.

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complete question:

Find the value of each variable

The area of the parallelogram is 35 square millimeters.

To find the area of a parallelogram, we multiply the base by the height. Given that the base of the parallelogram is 10 mm and the height is 3.5 mm, we can calculate the area as follows:

Area = base * height

Area = 10 mm * 3.5 mm

Area = 35 mm²

Therefore, the area of the parallelogram is 35 square millimeters.

It is also important to remember to include the units when giving the answer, which in this case is square millimeters (mm²).

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The exponential function in the form y= ab^x is y = 16(2)^7

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

Function that goes through points (0,16) and (7,2048)

An exponential function is represented as

y = ab^x

Where

a = y when x = 0

This means that

a = 16

So, we have

y = 16b^x

Using the other point, we have

16b^7 = 2048

Divide

b^7 = 128

So, we have

b = 7

So, the function is y = 16(2)^7

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The coordinates of each points are:

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

We have,

The coordinates of each point are in an ordered form.

i.e

(x, y)

x is the x-axis value.

y is the y-axis value.

Thus,

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

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The best answer is It is not possible to save any money this month without having a negative actual net income.

This is because saving money means spending less than you earn.

If the actual net income is already zero or positive, there is no room to save without spending more than the income, which would result in a negative actual net income.

Therefore, option B, C, and D are incorrect as they all suggest that it is possible to save money without having a negative actual net income, which is not possible.

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Answer:

56

Step-by-step explanation:

Kaden has 7 bags of animal toys.

Each bag has these animal toys in it.

• 1 whale toy

• 5 dolphin toys

• 2 turtle toys

Total number of toys in each bag: 1 + 5 + 2 = 8

Number of bags: 7

Total number of animals: 7 × 8 = 56

Answer: 7x 8=t and 7x(1+5+2)=t

Step-by-step explanation:

7x8=t. There are 7 bags with 8 (1+5+2) toys in each.

7x (1+5+2).  There are 7 bags with 1+5+2 (8) toys in each.

a. The range of data is 37 (max: 83, min: 46).

b. The box-and-whisker plot:

Min: 46  Q1: 53  Median: 61  Q3: 68  Max: 83

---|----|----|----|----|----|----|----|----|---

46  53  61  68  83

c. The five-number summary:

Minimum (46): Lowest speed recorded.

First Quartile (Q1 - 53): 25% of the cars were traveling at 53 mph or below.

Median (61): The middle value in the dataset, meaning 50% of cars were traveling at or below 61 mph.

Third Quartile (Q3 - 68): 75% of the cars were traveling at 68 mph or below.

Maximum (83): Highest speed recorded.

d. The IQR (Q3-Q1 = 68-53 = 15) tells you the spread of the middle 50% of the speeds. It gives an idea of how varied the speeds are in the dataset.

e. Since the majority of recorded speeds (more than 50% - based on the median) are above the 50 mph speed limit, the residents should be concerned about speeding.

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A catfish with a length of 45 inches would weigh 50 pounds.

From the attached scatter plot, the line of best fit passes through the points (25, 14) and (30, 23)

Using the two point form, the equation of line passing through points (25, 14) and (30, 23) would be,

(y - y₁)/(y₂ - y₁) = (x - x₁)/(x₂ - x₁)

(y - 14)/(23 - 14) = (x - 25)/(30 - 25)

(y - 14)/(9) = (x - 25)/(5)

y - 14 = (9/5)x - (9 × 5)

y - 14 = (9/5)x - 45

y = (9/5)x - 45 + 14

y = (9/5)x - 31

For a length of 45 inches, the weight would be,

y = (9/5)(45) - 31

y = (9 × 9) - 31

y = 81 - 31

y = 50

Thus, the weight of the catfish = 50 pounds

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Find the complete question below.

The best descriptions that suits a pyramid is option B.

Pyramids have triangular faces and a polygonal base.

A pyramid is a 3D figure built with a base of a polygon and triangular faces all connected together. A pyramid connects each vertex of the base to a common tip or apex giving it the typical shape.

A pyramid is made by connecting the base to the apex. Sometimes, the triangular sides are also called lateral faces to distinguish them from the base. In a pyramid, each edge of the base is connected to the apex that forms the triangular face.

Hence the correct option is B.

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Our calculation led to a P-value of .516, exceeding the predefined significance level of 0.01 which thereby disproves any evidence indicating individuals whose applications were unsuccessful came from a group whose members had higher mean ages than those who were successful.

We will use a two-sample t-test.

Unsuccessful applicants (Group 1):

n1 = 23

Mean1 (x1) = 41.6

Standard deviation1 (s1) = 14.5

Successful applicants (Group 2):

n2 = 25

Mean2 (x2) = 39.7

Standard deviation2 (s2) = 5.4

Claim: μ1 > μ2

Opposite: μ1 ≤ μ2

In order to compare the means of two independent samples, a two-sample t-test is used.

The initial step involves calculating both the pooled variance (Sp^2) and standard error (SE).

To calculate Sp^2, use the formula ((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2),

As per our specific data set regarding sample one consisting of 22 values with an average age of 41.6 years old, and sample two having 24 values averaging at 39.7 years old, we derived a pooled variance value of 120.569.

After that, employ the equation SE = √((Sp^2/n1) + (Sp^2/n2)), which yields a value of 3.685 via inputting the aforementioned values.

Using these results enables us to take the difference of the two averages divided by SE in a simplified manner giving a t-score equal to .516.

In light of this test possessing a significance level of 0.01 and utilizing only one tail, a comparison of the calculated t-score to the t-distribution table must occur; using a critical t-value of 2.410 wherein the degrees of freedom are required to be 46.

Our calculation led to a P-value of .516, exceeding the predefined significance level of 0.01 which thereby disproves any evidence indicating individuals whose applications were unsuccessful came from a group whose members had higher mean ages than those who were successful.

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Volume is found by multiplying length x width x height

The value of the k is; 1/12

The proportion is given by the expression;

y = kxz

Given the values;

y=6 when x=4 and z=12

To find the constant, k;

6 = k*4*12

6= 48k

k = 4/48

k = 1/12

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96 is the smallest number that is a multiple of 4, 6, and 8 and is between 67 and 113.

Given that, Lena must choose a number between 67 and 113 that is a multiple of 4,6, and 8.

Start listing the multiples of 4 between 67 and 113, which are 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, and 108.

We can then narrow down the list by looking for the multiples of 6, which are 72, 78, 84, 90, 96, and 102, and the multiples of 8, which are 72, 80, 88, 96, 104, and 112.

Since 96 is the smallest number that is a multiple of 4, 6, and 8 and is between 67 and 113.

Therefore, 96 is the smallest number that is a multiple of 4, 6, and 8 and is between 67 and 113.

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The solution to the logarithmic equation log₂(x + 4) + log₂(3) = log₂(8) + log₂(2x − 5) is x = 4

Consider the logarithmic equation,

log₂(x + 4) + log₂(3) = log₂(8) + log₂(2x − 5)

We need to solve this equation for x.

Here, the base of logarithm is 2.

Applying product rule of logarithm to log₂(x + 4) + log₂(3) we get,

log₂(x + 4) + log₂(3) = log₂(3(x + 4))

So, our equation becomes,

log₂(3(x + 4)) = log₂(8) + log₂(2x − 5)

log₂(3x + 12) = log₂(2³) + log₂(2x − 5)             .......(2³ = 8)

log₂(3x + 12) = 3log₂(2) + log₂(2x − 5)

log₂(3x + 12) = (3 × 1) + log₂(2x − 5)

log₂(3x + 12) -  log₂(2x − 5) = 3

Applying power identity of logarithm to  -log₂(2x − 5) we get,

-log₂(2x − 5) = 1 / [log₂(2x − 5)]

So, our equation becomes,

log₂(3x + 12) + [1 / log₂(2x − 5)] = 3

Applying product rule of logarithm to  log₂(3x + 12) + [1 / log₂(2x − 5)] we get,  log₂(3x + 12) + [1 / log₂(2x − 5)] =  log₂[(3x + 12) / (2x − 5)]

So, our equation becomes,

log₂[(3x + 12) / (2x − 5)] = 3

Now, exponentiate both sides.

(3x + 12) / (2x - 5) = 2³

(3x + 12) / (2x - 5) = 8

(3x + 12) = 8(2x - 5)

3x + 12 = 16x - 40

13x = 52

x = 4

This is the required value of x.

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The complete question is:

Solve the logarithmic equation.

log₂(x + 4) + log₂(3) = log₂(8) + log₂(2x − 5)

Answer: 17/5 or 3 2/5

Step-by-step explanation:

You separate the whole numbers from the fractions.

8-5=3 and 4/5-2/5=2/5

Then you combine the fraction with the whole number:

3 2/5 or 17/5 as a mixed fraction.

2 pounds 6 ounces in ounces is equivalent to 38 ounces.

The given measurement is -

2 pounds 6 ounces

In 1 pound, there are 16 ounces.

So, we can write that -

2 pounds 6 ounces = 2 x 16 + 6

2 pounds 6 ounces = 38 ounces

So, 2 pounds 6 ounces in ounces is equivalent to 38 ounces.

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The measure of the angle m∠ZYX of the trapezoid is equal to 139°

A trapezoid is a quadrilateral with two parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs. The adjacent angles of the trapezium are supplementary, so their sum is equal to 180°.

3x + 19 + x + 1 = 180°

4x + 20 = 180°

4x = 180 - 20 {collect like terms}

4x = 160

x = 160/4 {divide through by 4}

x = 40

m∠ZYX = 3(40) + 19 = 139°.

WXYZ is a trapezoid. Equation used to solve for x is (3x + 19) + (x + 1) = 180° because the angles m∠XYZ and m∠WXY are adjacent angles.

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The solutions of the equation are p = -7 + √87 and p = -7 - √87.

We have,

To solve by completing the square, we want to rearrange the equation so that the left side is a perfect square trinomial.

Here are the steps:

- Move the constant term (-38) to the right side:

p² + 14p = 38

- Take half of the coefficient of p (which is 14) and square it:

(14/2)² =  49

- Add and subtract this value to the left side of the equation:

p² + 14p + 49 - 49 = 38

- Simplify the left side by factoring the perfect square trinomial:

(p + 7)² - 49 = 38

- Add 49 to both sides of the equation:

(p + 7)² = 87

- Take the square root of both sides of the equation, remembering to include both positive and negative roots:

p + 7 = ±√87

Solve for p:

p = -7 ± √87

Therefore,

The solutions are p = -7 + √87 and p = -7 - √87.

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The calculated value of x in the right triangle is 8

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

The right triangle

The value of x can be calculated by using the corresponding sides of similar triangles

Using the similarity theorem of triangles, we have the following equation

x/2√6 = 2√6/3

When both sides are cross muliplied, we have the following equation

3x = 4 * 6

Divide both sides by 3, we get

x = 4 * 2

Evaluate the product of 4 and 2

x = 8

Hence, the value of x is 8

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The balloon's vertical distance above the ground is given as follows:

h = 10.7 ft.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the angle of 24º, we have that:

Hence the height is obtained as follows:

tan(24º) = h/24

h = 24 x tangent of 24 degrees

h = 10.7 ft.

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The incorrect statement is the reflection is over x-axis.

Given that an image has been reflected to form another image, we need to find the incorrect statement from the given options,

A reflection is known as a flip.

A reflection is a mirror image of the shape.

An image will reflect through a line, known as the line of reflection.

A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.

So, here the image is reflected over y-axis so the rule (x, y) → (-x, y) can be followed,

Also, the orientation of the image is preserved.

Since, the transformation is reflection, so the image and pre-images are congruent.

Hence, the incorrect statement is the reflection is over x-axis.

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The incorrect statement is the reflection is over x-axis.

Given that,

an image has been reflected to form another image, we need to find the incorrect statement from the given options,

So, here the image is reflected over y-axis so the rule (x, y) → (-x, y) can be followed,

Also, the orientation of the image is preserved.

Since, the transformation is reflection, so the image and pre-images are congruent.

Hence, the incorrect statement is the reflection is over x-axis.

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The value of x is given as follows:

x = 26.

To obtain the value of x, first we must consider that the angle between the two lines, to the left of the transversal line, is congruent to the angle of 5x - 7.

Then the angle stated above is a consecutive interior angle with the angle of (2x + 5)º, meaning that they are supplementary angles, that is, the sum of their measures is of 180º.

Hence the value of x is obtained as follows:

5x - 7 + 2x + 5 = 180

7x = 182

x = 182/7

x = 26.

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The total surface area of the given triangular prism is: 72.5 in²

To get the surface area of this prism, what we will do is to find the area of each of the surfaces and add up to get the total surface area.

The formula for the area of a triangle is:

Area = ¹/₂ * b * h'

where:

b is base length

h is height

Total Surface Area = (¹/₂(5 * 5)) + 3(¹/₂*5*8)

Total Surface Area = (25/2) + 60

Total Surface Area = 72.5 in²

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The required simplified value of x is -377.

To solve for x in the given equation:

7 + √(-36 - 5x) = 250/5

First, simplify the right-hand side:

7 + √(-36 - 5x) = 50

√(-36 - 5x) = 43

Square both sides to eliminate the square root:

-36 - 5x = 1849

Solve for x:

x = (-1849 - 36)/5

x = -377

Therefore, the value of x is -377.

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Answer:

First, we need to isolate the radical term on one side of the equation:

7 + V(-36 - 5x) = 250

V(-36 - 5x) = 243    (subtract 7 from both sides)

-36 - 5x = 243^2     (square both sides)

-36 - 5x = 59049

-5x = 59049 + 36

-5x = 59085

x = -11817

Therefore, x = -11817.