y<-4x-2 choose the graph that best models the inequality

Answer:

Step-by-step explanation:

In the given figure, the triangle ABC is a right triangle with a right angle at C. We need to find the length of the side AB.

Using the Pythagorean theorem, we know that in a right triangle with sides of length a, b, and c (where c is the hypotenuse), we have c^2 = a^2 + b^2.

In this case, we have AC = 4 and BC = 3. So, applying the Pythagorean theorem, we get:

AB^2 = AC^2 + BC^2

AB^2 = 4^2 + 3^2

AB^2 = 16 + 9

AB^2 = 25

Therefore, AB = 5.

The expansion will be:

a) (x-6) (x+7) = x² + x - 42

b) (2x-3)(5x-4) = 10x² - 23x + 12

c (x+3)(x+5) = x² + 8x + 15

The factorization will be:

a) 2(x+3)

b) 3x(3x-4)

c) 2(12x² + 8x-1)

An equation simply has to do with the statement that illustrates the variables given.

In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

Therefore, the expansion will be:

a) (x-6) (x+7) = x² + x - 42

b) (2x-3)(5x-4) = 10x² - 23x + 12

c (x+3)(x+5) = x² + 8x + 15

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Answer:

[tex] a_{old} = \frac{1}{2} (x)(4x) = 2 {x}^{2} [/tex]

[tex] a_{new} = \frac{1}{2} (x + 9)(4x + 2)[/tex]

[tex] = (x + 9)(2x + 1)[/tex]

[tex] = 2 {x}^{2} + 19x + 9[/tex]

Answer: 2x

Step-by-step explanation: Separate variables from numbers, 4x-2x=2x, and 1-1=0. Therefore, the answer is 2x.

Answer:

2(x+1)

Step-by-step explanation:

Add you 1s together, than take a 2x out and that vies you 2 on the outside 2x/2= x and 2/2= 1 which gives you your answer.

The area of the rhombus by decomposition is

The rhombus is decomposed into simpler elements which are

Area of 2 triangles

= 2 * 1/2 * base * height

= 2 * 1/2 * x * h

= 2 * 1/2 * 3 * 4

= 12 square units

Area of a parallelogram

= base x height

= y * h

= 5 * 4

= 20 square units

Area of the rhombus

= 20 square units + 12 square units

= 32 square units

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Answer:

V = 16155.3 cubic feet

Step-by-step explanation:

The formula for volume (V) of a cone is

[tex]V=1/3\pi r^2h[/tex], where r is the radius and h in the height.

In the diagram, we're shown that the radius is 21 feet and the height is 35 feet.  Thus, we can plug everything into the formula including 3.14 instead of the entire pi number:

[tex]V=1/3(3.14)(21)^2(35)\\V=16155.3[/tex]

The number of parents you have to sample is calculated as: 5918

The formula for the margin of error here is:

E = z(σ/√n)

where:

E is margin of error

σ is standard deviation

n is sample size

We are given:

E = 2

σ = $78.5

At 95% Confidence Level, z = 1.96

Thus:

2 = 1.96(78.5/√n)

Square both sides to get:

4 = 23672.9/n

n = 23672.9/4

n = 5918

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The value of the quotient of 4 1/2 ÷ 2/3 is,

⇒ 27/4

We have to given that;

The expression is,

⇒ 4 1/2 ÷ 2/3

Now, We can simplify as;

⇒ 4 1/2 ÷ 2/3

⇒ 9/2 × 3/2

⇒ 27/4

Thus, The value of the quotient of 4 1/2 ÷ 2/3 is,

⇒ 27/4

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Part A: The Table for the data set above and it's title are attached accordingly.

Part B:

1) The shortest marker in the data set is Marker 1, which has a length of 4.00 inches.

2) The longest marker in the data set is Marker 14, which has a length of 6.75 inches.

3) The range of the data set is 2.75 inches, calculated by subtracting the shortest marker (4.00 inches) from the longest marker (6.75 inches).

4) To find the median, we need to arrange the data set in order from smallest to largest:

4.00, 4.25, 4.75, 5.00, 5.00, 5.25, 5.50, 5.50, 5.625, 6.00, 6.25, 6.25, 6.25, 6.50, 6.75

The median is the middle value, which is 5.50 inches.

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Answer:

i'm pretty sure its c, but if not then sorry

Step-by-step explanation:

Answer:

The equation of the line in the point-slope form is y+3=2/3(x−5)

Step-by-step explanation:

B

Answer:

D. 67 square inches

Step-by-step explanation:

The area of a 16-inch pizza is:

A = πr^2 = π(8)^2 = 64π

Since the pizza was cut into 12 equal slices, each slice has an area of:

64π / 12 = 16π/3

Each boy ate 4 slices, so the total area of pizza each boy ate is:

4(16π/3) = 64π/3

Rounding to the nearest whole square inch, we have:

64π/3 ≈ 67 square inches

Therefore, the answer is D. Each boy ate approximately 67 square inches of pizza.

Hope this helps!

The area of the irregular pentagon is determined using it's coordinates. Its area is: 30.5

First indicate the coordinates:

A (1,4)

B(4, 3)

C(4, -3)

D(-1-2)

E(-1.5, 2)

Using the shoe lace formula:

Area = (1/2) | (x1y2 + x2y3 + ... + xny1) - (y1x2 + y2x3 + ... + ynx1) |

where n is the number of vertices, and

(x1,y1), (x2,y2), ..., (xn,yn) are the coordinates of the vertices in clockwise or counterclockwise order.

Plugging in the values,

Area = Area = (1/2) | (1*3 + 4*(-3) + 4*2 + (-1.5)*(-2) + (-1)*4) - (4*3 + 4*(-1.5) + (-1)*(-3) + 3*2 + (-2)*1) |

Area = 30.5

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The expressions B and C are equivalent to the given expression:

A logarithmic function is the inverse of an exponential function. In other words, if we have an exponential function that takes a base, b, and raises it to a power, x, to get a result, y, then the logarithmic function is the inverse of that process.

Simplify the expression using logarithmic property,

log m + log n = log (m.n)

Expression can be written as,

log₂(2) + log₂(8) = log₂(2x8)

                         = log₂ 16

simplify further,

log₂16 = log₂(2)⁴

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Therefore the 95% confidence interval is,

(219.25, 534.75)

Here sample standard deviation is given but the sample size is large. Therefore we use z table to find the critical value.

Therefore the 90% confidence interval for the mean GPA for students at the University who are employed and who are not employed is,

(0.112, 0.308)

For the next problem,

We follow the same procedure as we have done in the first problem.

And here the data is different and we construct 95% confidence interval.

Therefore the 95% confidence interval is,

(219.25, 534.75)

And we interpret this confidence interval as,

We are 95% confident that the true difference in the mean daily caorie intake for teens who do eat fast food on a typical day and those who do not falls within this interval.

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Start by putting the possible integers your friend can select

[tex]\text{S}=\{1,2,3,4,5,6,7,8,9,10\}[/tex]

Then, call the 2 possible events as A and B, and what are the possible integers in each event:

A = Be more than 6

B = The number is odd

 [tex]\text{A}=\{7,8,9,10\}[/tex]

 [tex]\text{B}=\{1,3,5,7,9\}[/tex]

The probability of the union of two events can be calculated as:

[tex]\text{P}(\text{A}\cup\text{B})=\text{P(A)}+\text{P(B)}-P(\text{A}\cap\text{B})[/tex]

Then,

         [tex]\text{P(A)}=\dfrac{\text{number of elements in A}}{\text{number of elements in S}}[/tex]

                             [tex]\text{P(A)}=\dfrac{4}{10}[/tex]

         [tex]\text{P(B)}=\dfrac{\text{number of elements in B}}{\text{number of elements in S}}[/tex]

                              [tex]\text{P(B)}=\dfrac{5}{10}[/tex]

[tex]\text{P(A}\cap\text{B})=\dfrac{\text{number of elements in A and B}}{\text{number of elements in S}}[/tex]

                        [tex]\text{P(A}\cap\text{B})=\dfrac{2}{10}[/tex]

Finally,

[tex]\text{P(A}\cup\text{B})=\dfrac{4}{10}+\dfrac{5}{10}- \dfrac{2}{10}[/tex]

          [tex]\text{P(A}\cup\text{B})= \dfrac{7}{10}[/tex]

Answer:

the probability that the number will be more than 6 or odd is: 7/10

Start by putting the possible integers your friend can select

[tex]\text{S}=\{1,2,3,4,5,6,7,8,9,10\}[/tex]

Then, call the 2 possible events as A and B, and what are the possible integers in each event:

A = Be more than 6

B = The number is odd

 [tex]\text{A}=\{7,8,9,10\}[/tex]

 [tex]\text{B}=\{1,3,5,7,9\}[/tex]

The probability of the union of two events can be calculated as:

[tex]\text{P}(\text{A}\cup\text{B})=\text{P(A)}+\text{P(B)}-P(\text{A}\cap\text{B})[/tex]

Then,

         [tex]\text{P(A)}=\dfrac{\text{number of elements in A}}{\text{number of elements in S}}[/tex]

                             [tex]\text{P(A)}=\dfrac{4}{10}[/tex]

         [tex]\text{P(B)}=\dfrac{\text{number of elements in B}}{\text{number of elements in S}}[/tex]

                              [tex]\text{P(B)}=\dfrac{5}{10}[/tex]

[tex]\text{P(A}\cap\text{B})=\dfrac{\text{number of elements in A and B}}{\text{number of elements in S}}[/tex]

                        [tex]\text{P(A}\cap\text{B})=\dfrac{2}{10}[/tex]

Finally,

[tex]\text{P(A}\cup\text{B})=\dfrac{4}{10}+\dfrac{5}{10}- \dfrac{2}{10}[/tex]

          [tex]\text{P(A}\cup\text{B})= \dfrac{7}{10}[/tex]

Answer:

the probability that the number will be more than 6 or odd is: 7/10

Answer:

To find the gross profit, we need to subtract the cost of the dolls sold from the gross sales revenue (after returns have been deducted).

First, we need to calculate the net sales revenue, which is the gross sales revenue minus the returns:

Net sales revenue = Gross sales revenue - Returns

Net sales revenue = ₱42,356 - ₱3,479

Net sales revenue = ₱38,877

Next, we can calculate the gross profit:

Gross profit = Net sales revenue - Cost of goods sold

Gross profit = ₱38,877 - ₱27,212

Gross profit = ₱11,665

Therefore, the gross profit from the sale of the dolls is ₱11,665.

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The restrictions on the expression are x = -9/5 and x = -4 and the simplified expression is (2x - 1)/(x + 4)

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

[tex]\frac{10x^2 + 13x - 9}{5x^2 + 29x + 36}[/tex]

When the above expressions are factorized, we have

[tex]\frac{10x^2 + 13x - 9}{5x^2 + 29x + 36} = \frac{(5x + 9)(2x - 1)}{(5x + 9)(x + 4)}[/tex]

To calculate the restrictions, we set the denominator to 0

So, we have

(5x + 9)(x + 4) = 0

Evaluate

x = -9/5 and x = -4

So, the restrictions are x = -9/5 and x = -4

Next, we simplify the expression

[tex]\frac{10x^2 + 13x - 9}{5x^2 + 29x + 36} = \frac{(5x + 9)(2x - 1)}{(5x + 9)(x + 4)}[/tex]

Cancel out the common factors

[tex]\frac{10x^2 + 13x - 9}{5x^2 + 29x + 36} = \frac{2x - 1}{x + 4}[/tex]

Hence, the simplified expression is (2x - 1)/(x + 4)

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Answer: The regular price of the sofa is $705.71.

Step-by-step explanation:

Regular price = Sale price / (1 - Discount rate)

* 65% = 0.65

Regular price = $247 / (1 - 0.65) = $247 / 0.35 = $705.71

Answer:

-1.75

Step-by-step explanation:

12.5 - (31 / 2) + 1 1/4 = -1.75

Answer:

Since the given quadratic function has zeros of -8 and 4, we know that the factors of the quadratic equation are (x + 8) and (x - 4).

The maximum of the function occurs at the midpoint between the zeros, which is (-8 + 4)/2 = -2. So, the x-coordinate of the vertex is -2.

We also know that the y-coordinate of the vertex is 18. So, the vertex of the quadratic function is (-2, 18).

Using the vertex form of the quadratic function, we can write:

F(x) = a(x + 2)^2 + 18

Since the function has zeros of -8 and 4, we can write:

F(x) = a(x + 8)(x - 4)

a(x + 2)^2 + 18 = a(x + 8)(x - 4)

ax^2 + 6ax - 128a - 576 = ax^2 + 16ax - 32a

10ax - 96a - 576 = 0

10a(x - 6) = 0

a = 0 or x = 6.

Since the vertex is a maximum and the coefficient of the x^2 term is positive, we know that a > 0. Therefore, we can conclude that x = 6 and a = 3.

Hence, the value of "a" in the function equation is 3.

Answer:

r/p = 2

Step-by-step explanation:

The proportional relationship between the amount of raisins and the amount of peanuts can be expressed as:

r/p = k

where k is the constant of proportionality.

To find an equation with a constant of proportionality greater than 1, we simply need to choose a value of k that is greater than 1. For example, if we choose k = 2, the equation becomes:

r/p = 2

To check that this equation is correct, we can use the original ratio of 4 cups of raisins for every 6 cups of peanuts:

4/6 = 2/3

This confirms that the constant of proportionality is indeed 2, and that the equation for the relationship with a constant of proportionality greater than 1 is:

r/p = 2

Answer:Let's use the formula for the area of a sector to find the radius of the sector:

Area of sector = (1/2) * radius^2 * angle in radians

We know the area of the sector is 75pi/16 and the angle in radians is 3pi/8, so we can plug those values in and solve for the radius:

75pi/16 = (1/2) * radius^2 * 3pi/8

Simplifying:

75pi/16 = (3/16) * radius^2 * pi

Multiplying both sides by 16/3pi:

25 = radius^2

Taking the square root of both sides:

radius = ±5

Since a radius can't be negative, we have:

radius = 5

Therefore, the radius of the sector is 5 units.

Answer:

D. The data has an outlier, therefore the range will be much greater than it would be without the outlier.

Step-by-step explanation:

The given data consists of six values, ranging from 187 to 1984. The numbers are not listed in order. There is an obvious outlier value, 1984, which is potentially impacting the spread and central tendencies of the data. However, without calculating the range or interquartile range, it is difficult to determine the extent of its impact.

Answer:

d got it right in edge.

Yes, an answer can be incorrect even if it looks reasonable

Yes, an answer can be incorrect even if it looks reasonable. This is because an answer might seem reasonable on the surface but may not be correct due to various reasons such as calculation errors, incorrect assumptions, or misinterpretation of the problem.

For instance, in a math problem that involves converting units of measurement, a student may have calculated the answer and arrived at a number that seems reasonable.

However, if the student used the wrong conversion factor or made an error in calculations, the answer would be incorrect despite appearing reasonable.

Similarly, in a word problem, an answer may seem reasonable but might not take into account all the given information, resulting in an incorrect solution.

Therefore, it is important to double-check answers and verify that they make sense in the context of the problem and that all the given information has been taken into account to ensure accuracy.

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Answer:

Part A: ∠A ≈ 27.7 °

Part B: c ≈ 8.75

Step-by-step explanation:

Part A:

Use the Law of Cosines.

Cosθ =

[ a² + b² - c² ] / [ 2ab ]

Sub in all the information where θ is A.

A = cos⁻¹ { [10² + 7² - 5²] / [2×10×7]

A ≈ 27.7 ° (1 decimal place)

Part B:

Use the Law of Cosines, but instead the unknown is the side c.

Rearrange to isolate c:

c² = a² + b² - 2ab×cosθ

c = √(5² + 6² - 2×5×6×cos(105°))

c ≈ 8.75 (2 decimal places)