a) Work out the value of 19 + 7 divided by 2-5

Answer:

x=7

Step-by-step explanation:

Hope this helps!

The solutions to the equations are

1. x = 4

2. x = -12

3. x = 0 and x = 4

The solutions to the inequalities are

4. -5 < x < 1

5. x ≤ -3 and x ≥ 4

From the question, we have the following equations

1. 4x + 6 = 8x - 10

2. -3/4x - 2 = -1/2x + 1

3. |4 - 2x| + 5 = 9

Next, we split the equations to 2

So, we have

1. y = 4x + 6 and y = 8x - 10

2. y = -3/4x - 2 and y = -1/2x + 1

3. y = |4 - 2x| + 5 and y = 9

Next, we plot the system of equations (see attachment) and write out the solutions

The solutions are

1. x = 4

2. x = -12

3. x = 0 and x = 4

From the question, we have the following inequalities

4. x² + 4x - 5 < 0

5. x² - x - 12 ≥ 0

Next, we plot the system of inequalities (see attachment) and write out the solutions

The solutions are

4. -5 < x < 1

5. x ≤ -3 and x ≥ 4

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Using alternating and corresponding angle theorems, the values of x are 11, 4, -4 and 10 respectively

Alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.

1)

9x + 8 = 107 (alternating angles are equal)

9x + 8 = 107

9x = 107 - 8

9x = 99

x = 11

2)

20x = 80 (alternating angles are equal)

20x = 80

x = 4

3)

x + 84 = 80 (corresponding angles are equal)

x = 80 - 84

x = -4

4) 120 + 6x = 180

This is gotten from applying alternating angle theorem and angle on a straight line theorem

120 + 6x = 180

6x = 180 - 120

6x = 60

x = 10

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Answer:

201

Step-by-step explanation:

177 times 2=354

354-153=201

Answer:

130 times

Step-by-step explanation:

If you convert the time to minutes, 120 seconds is 2 minutes. Since Ran's heart beats 65 times a minute, you multiply 65 by 2 and get 130

The equation of a circle having endpoints of diameter as (4,9) and (4,-3) is (x - 4)² + (y - 3)² = 36.

The "center" of circle is called as midpoint of diameter.

The "x-coordinate" of "mid-point" is = (4+4)/2 = 4, and

The "y-coordinate" of "mid-point" is = (9+(-3))/2 = 3.

So, center of circle is (4,3),

The radius of circle is half the length of the diameter, which is distance between two endpoints of diameter. We find distance using distance formula:

⇒ distance = √((x₂ - x₁)² + (y₂ - y₁)²), where (x₁,y₁) and (x₂,y₂) are "end-points" of diameter.

⇒ distance = √((4 - 4)² + (9 - (-3))²)

⇒ √(144) = 12.

So, radius is 6.

The equation of circle with center (h,k) and radius "r" is : ⇒ (x - h)² + (y - k)² = r²,

Substituting the values

We get,

⇒ (x - 4)² + (y - 3)² = 6²,

⇒ (x - 4)² + (y - 3)² = 36,

Therefore, the equation of the circle is (x - 4)² + (y - 3)² = 36.

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Answer:

AAS

Step-by-step explanation:

As we can see, they tell us that both of the angles on the bottom are congruent. Since they share a side, that means that one side is congruent too. So it must be two angles and one side. It can't be ASA, because the congruent side is not in between the two congruent angles, so it must be AAS

Hey There!!

Your correct choice will be AAS Theorem.

Step-by-step explanation:

Because, two angles and any side of one triangle are congruent to two angles and any side of another triangle, then these triangles are congruent Thus, given a triangle ADB and CDB. ∠BAD = ∠BCD = 90°. (Angle), Then, BD = BD (The common side) As given AAS Theorem. Therefore, ∆ADB ≅ ∆CDB by the AAS theorem.

Hope This Explaining was not confusing . . .

By ☆Itsbrazts☆

Answer:

31.4

Step-by-step explanation:

The equation is C=πd

meaning C= π 10

which equals 31.4

Answer:

That means that the roller coaster can be 800 feet or taller

which means greater than or equal to

r≥800

Step-by-step explanation:

Answer:

y is greater than or equal to 800 feet

Step-by-step explanation:

It says it is at least 800 feet, so it has to be higher than 800

Answer:

x - 3

Step-by-step explanation:

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

=  \(-\frac{9-x^{2}}{x+3}\)

=     \(-\frac{3^2-x^2}{x+3}\)

=     \(-\frac{(3-x)(x+3)}{x+3}\)

=     \(-\frac{(3-x)}1}\)

= x - 3

Answer:

A. -4< n<8 B.-4< n< 8

Step-by-step explanation:

Answer:

D.-4<n<8

Step-by-step explanation:

Answer:

65x

Step-by-step explanation:

Observe que estos son terminos similares... por lo que podemos simplemente sumarlos y restarlos. Entonces obtenemos:

25x + 12x + 31x - 8x + 5x

= 37x + 31x - 8x + 5x

= 68x - 8x + 5x

= 60x + 5x

= 65x

Answer: If you look at the x axis 1 is less than $1 so if you follow the x axis to the right until you find a number of minutes that meets the y axis of $1 so x4, y1 that means  $.25 per minute if you divide 1 by 4. So 1 is the correct answer.

Step-by-step explanation:

1. Follow the x axis until the x and y axis meet. This is $1.00 on the y axis.

2. Then you would divide 1 by 4 and you get .25. Each minute would be $.25.

Answer:

\(y=-4x^{2} +7x+6\\\)

Step-by-step explanation:

\(y=ax^{2} +bx+c\\\)

Points are (1,9), (2,4), and (4,-30).

\(\\9=a+b+c\\4=4a+2b+c\\-30=16a+4b+c\\\)

Subtract the first from the second.

-5 = 3a+b

Subtract 4 times the second from the third.

-34=12a+2b

-14=-2b

b=7

a=-4

c=6

Answer: Volume of lid = 29.44 cubic cm and surface area = 40.41 cubic cm.

Step-by-step explanation:

Given: For  lid of the spherical shaped bottle,

Diameter = 5 cm

Height = 4.5 cm

Radius = Half of diameter = 2.5 cm

Volume of cone = \(\dfrac13\pi r^2 h\)

Volume of lid  \(=\dfrac13(3.14)(2.5)^2(4.5)=29.4375\approx29.44\text{ cm}^3\)

Surface area of cone = \(\pi r\sqrt{h^2+r^2}\)  [as lide has no base we don't include area of base.]

Surface area of lid = \((3.14)(2.5)\sqrt{(2.5)^2+(4.5)^2}= 7.85\sqrt{26.5}\approx40.41\text{ cm}^3\)

Hence, volume of lid = 29.44 cubic cm and surface area = 40.41 cubic cm.

Answer:

Step-by-step explanation:

-4x - 8 + 6 = 5 -3x - 3

-4x - 2 = -3x + 2

-x - 2 = 2

-x = 4

x = -4

For the expression 2(-2x - 4) + 6 = 5 – 3(x + 1) the value of x is -4.

Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.

The given expression is,

2(-2x - 4) + 6 = 5 - 3(x + 1)

To find the value of x, simplify the expression,

-4x - 8 + 6 = 5 - 3x - 3

-4x - 2 = 2 - 3x

-4 = 4x - 3x

x = -4

The required value of x is -4.

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Answer:

here is the answer

Step-by-step explanation:

Y-intercept is the point  at which the line intersects the y axis- meaning x = 0

From the table y = -20 when x= 0

y-intercept: -20

To find the slope

m = deltaY/deltaX = -20+10/0-5 = 2

Slope 2

Choice : A

The slope and y-intercept of the line represented by the points shown in the table are (a) slope: 2, y-intercept: –20

The entries on the table can be represented using the following ordered pair:

\((x,y) \to \{(0.-20) \ (5,-10)\ (10,0)\ (15,10)\ (20,20)\}\)

The y-intercept is the y-value when the x-value of the function is 0.

From the ordered pair above,

y = -20, when x = 0

So, the y-intercept is -20

The slope (m) is calculated using:

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

So, we have:

\(m=\frac{-20 --10}{0-5}\)

\(m=\frac{-10}{-5}\)

Divide

\(m = 2\)

So, the slope is 2

Hence, the true statement is (a) slope: 2, y-intercept: –20

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Answer:

0-25=1

25-50=3

50-75=4

Step-by-step explanation:

To create a histogram, we need to group the data into intervals or bins and count the number of data points that fall into each bin. We can then plot the counts as bars on a graph.

A histogram is a graphical representation of the distribution of a dataset. It consists of a set of contiguous rectangles, where the width of each rectangle represents a range of the values, and the height of each rectangle represents the frequency or count of the number of data points that fall within that range.

One way to choose the bin size is to divide the range of the data (the difference between the maximum and minimum values) by the desired number of bins. For this example, we'll choose a bin size of 10 and create bins from 20 to 70.

Using this bin size, we can group the data into the following bins:

20-29: 2

30-39: 0

40-49: 3

50-59: 3

60-69: 1

To create the histogram, we can plot these counts as bars on a graph, with the bins on the x-axis and the counts on the y-axis.

The histogram shows that the most common diagonal length for televisions at Electronic Emporium is between 40 and 59 centimeters, with fewer televisions having diagonal lengths outside of this range.

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The volume of the pyramid is approximately 5.9 cm³.

To find the volume of a pyramid with a square base, you can use the formula:

Volume = (1/3) * base area * height

First, let's find the area of the square base. The perimeter of the base is given as 5.7 cm, which means each side of the square has a length of 5.7 cm / 4 = 1.425 cm.

The area of a square is given by the formula:

Area = side length * side length

Substituting the side length, we have:

Area = 1.425 cm * 1.425 cm = 2.030625 cm²

Now, we can calculate the volume of the pyramid:

Volume = (1/3) * base area * height

= (1/3) * 2.030625 cm² * 8.6 cm

= 5.91834375 cm³

Rounding to the nearest tenth of a cubic centimeter, the volume of the pyramid is approximately 5.9 cm³.

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The population of Medway, Ohio, is expected to be approximately 3728 in the year 2020.

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

Initial, a = 4007

Rate = 0.36% per year

The decay function is represented as

y = a(1 - rate)^x

So, we have

y = 4007 * (1 - 0.36%)^x

This gives

y = 4007 * (0.9964)^x

The year 2020 is 20 years from 2000

So, we have

x = 20

Substitute the known values in the above equation, so, we have the following representation

y = 4007 * (0.9964)^20

Evaluate

y = 3728

Hence, the approximate solution is 3728

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The transformation rule that describes the rotation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

The rule that describes the transformation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

To understand this, let's apply the transformation rule to each vertex of the original parallelogram ABCD:

Point A (2, 5) becomes A' (-5, 2).

Point B (5, 4) becomes B' (-4, 5).

Point C (5, 2) becomes C' (-2, 5).

Point D (2, 3) becomes D' (-3, 2).

By applying the transformation rule, we observe that the x-coordinate of each point becomes the negative of the original y-coordinate, and the y-coordinate becomes the original x-coordinate.

This transformation is a 90-degree counterclockwise rotation about the origin (0, 0) on the coordinate plane. The image parallelogram A'B'C'D' is obtained by rotating the original parallelogram ABCD by 90 degrees counterclockwise.

Visually, this transformation can be seen as the original parallelogram being rotated around the origin, where the x-axis becomes the y-axis, and the y-axis becomes the negative x-axis.

Therefore, the transformation rule that describes the rotation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

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A ratio displays the multiplicity of two numbers, the total number of employees is 187.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared.

Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were going to compare one data point (A) to another data point (B). This indicates that you are multiplying data A by data B.

So the ratios are-

men : women

4:7

x:119

Now, relationship between 7and 119 is -

men : women

4:7

7*17

x:119

Now,

men : women

4:7

4*17 :7*17

68:119

Total number

68+119= 187

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The correct statement for the given relation being a function is -

B: No, because for each output there is not exactly one input.

What is a relation?

In mathematics, a relation describes the connection between two distinct collections of data. If more than two non-empty sets are taken into consideration, the relationship between them will be determined if there is a connection between their components.

To determine if the relation is a function, we need to check if there is exactly one output (y-value) for each input (x-value).

Looking at the mapping diagram, we see that the input value of 1 and -3 has arrows pointing to one output value which is 0.

Similarly, the input value -1 and 3 has arrows pointing to one output value which is 2.

Therefore, there is not exactly one input for the output value of 0 and 2.

Thus, the relation is not a function because for at least one output there is not exactly one input.

Therefore, this relation cannot be considered a function.

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In a right-angle triangle, a sine function of an angle θ is equal to the opposite side to θ divided by hypotenuse.

Sin θ = Opposite side/Hypotenuse

y = f(x) → x in the domain of f. Trigonometric functions are periodic, therefore each range value is within the limitless domain values (no breaks in between). Since trigonometric functions have no restrictions, there is no inverse.

The inverse sine function (also called arcsine) is the inverse of sine function. Since sine of an angle (sine function) is equal to ratio of opposite side and hypotenuse, thus sine inverse of same ratio will give the measure of the angle. Let’s say θ is the angle, then:

sin θ = (Opposite side to θ/Hypotenuse)

Or θ = Sin-1 (Opposite side to θ/Hypotenuse)

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Answer:

4

Step-by-step explanation:

18 + 18 = 36

So you got 36 cuz you times by two so you times the same for x

which is

2 x 2 = 4

Answer:

4

Step-by-step explanation:

We can set up a proportion.

18:2 = 36: x

If we multiply 18 by 2, and multiply 2 by 2, we can get 18:2 = 36:4, so x is equal to 4

By comparing PIZ > 7 | Z > 4 and P[Z > 3], we can see that they are not equal. The probabilities involve different terms and are calculated based on different conditions. Therefore, the statement "PIZ > 7 | Z > 4 = P[Z > 3]" is not true.

Let's calculate the probabilities involved in the question.

PIZ > 7 | Z > 4 is the probability that Z is greater than 7, given that Z is greater than 4.

P[Z > 3] is the probability that Z is greater than 3.

To calculate these probabilities, we need to understand the distribution of Z. Z represents the number of coffee shops Alexis must visit until she likes 3 coffee shops. Each visit to a coffee shop is an independent event with a probability of 0.4 of liking the shop.

To calculate the probabilities, we can use the geometric distribution, which models the number of trials needed to achieve the first success. In this case, the first success is Alexis liking a coffee shop.

The probability mass function (PMF) of the geometric distribution is given by:

P(X = k) = (1 - p)^(k-1) * p

Where:

- X is the random variable representing the number of trials needed until the first success.

- k is the number of trials needed.

- p is the probability of success.

In our case, we want to find the probabilities PIZ > 7 | Z > 4 and P[Z > 3]. Let's calculate these probabilities using the geometric distribution.

P[Z > 3] = P(Z = 4) + P(Z = 5) + P(Z = 6) + ...

We can calculate the individual probabilities:

P(Z = 4) = (1 - 0.4)^(4-1) * 0.4 = 0.144

P(Z = 5) = (1 - 0.4)^(5-1) * 0.4 = 0.0864

P(Z = 6) = (1 - 0.4)^(6-1) * 0.4 = 0.05184

...

Summing up these probabilities, we find:

P[Z > 3] = 0.144 + 0.0864 + 0.05184 + ...

To calculate PIZ > 7 | Z > 4, we need to consider the conditional probability. Given that Z > 4, we only consider the probabilities starting from Z = 5:

PIZ > 7 | Z > 4 = P(Z = 5) + P(Z = 6) + P(Z = 7) + ...

To find these probabilities, we can use the same formula as before:

P(Z = 5) = (1 - 0.4)^(5-1) * 0.4 = 0.0864

P(Z = 6) = (1 - 0.4)^(6-1) * 0.4 = 0.05184

P(Z = 7) = (1 - 0.4)^(7-1) * 0.4 = 0.031104

...

Summing up these probabilities, we find:

PIZ > 7 | Z > 4 = 0.0864 + 0.05184 + 0.031104 + ...

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This format had 144 possible telephone area codes in the United States and Canada.

We can calculate the number of possible area codes based on the given information by multiplying the number of options for each digit.

There are 8 options for the first digit (2 through 9), 2 options for the second digit (0 or 1), and 9 options for the third digit (1 through 9).

So, the total number of possible area codes is:

8 x 2 x 9 = 144

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