please answer all the questions

Answer:

If two linear functions have the same coefficients of x, then the graphs of the two linear functions do not intersect at exactly one point.

Step-by-step explanation:

The statement that is logically equivalent to q→ p is:

If two linear functions have the same coefficients of x, then the graphs of the two linear functions do not intersect at exactly one point.

This is because the contrapositive of an implication is logically equivalent to the original implication. The contrapositive of q→ p is ¬p→ ¬q, which means:

If two linear functions do not have different coefficients of x, then the graphs of the two functions do not intersect at exactly one point.

Simplifying this statement, we get:

If two linear functions have the same coefficients of x, then the graphs of the two linear functions do not intersect at exactly one point.

Another way to write the mixed number 2 4/12 is 2 1/3.

Another way to represent the shaded portions that model the mixed number 2 4/12 is by simplifying the fraction to its simplest form.

In this case, 4/12 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 4. By simplifying, we get 1/3. Thus, the mixed number 2 4/12 can be expressed as 2 1/3.

This representation implies that there are two whole units (2) and an additional fractional part equivalent to one-third (1/3) of a unit. It provides a clearer and more concise representation of the same quantity, avoiding unnecessary complexity.

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Answer:

C. (-2,0)  **See diagram**

Step-by-step explanation:

For a coordinate system, the origin is the point located at (0,0).

Any coordinate ordered pair (x,y) is given with the x-coordinate (the "left-right" distance from the origin) first, and the y-coordinate (the "up-down" distance from the origin) second.

With the given starting point (-6,3), the original point is to the left (in the negative "x" direction) 6 units, and up (in the positive "y" direction) 3 units.

the y-coordinate

To translate (slide or move) the point down 3 units would affect the y-value by subtracting 3.  The original y-value is 3, so subtracting 3 will give a new y-value result of 0.

the x-coordinate

To translate the point right 4 units would affect the x-value by adding 4.  The original x-value is -6, and we need to add 4.

Adding positive and negative numbers

When adding two numbers where one is positive and one is negative, we'll want to look at the magnitude ("size," or distance from zero) of the two numbers.  Negative six is 6 units from zero, and positive four is 4 units from zero.

When adding one positive and one negative number, the result has a sign matching the number with the larger magnitude, and a value that is the difference of their two magnitudes.

The negative six is the larger number, so the result will be negative.

The difference between 4 and 6 is 2 (counting from 4 up to 6 takes two steps... or differently, six minus four is two).

So adding 4 to -6 will give a new x-value result of -2.

Hence, the final point (as illustrated in the diagram), is (-2,0), which is answer choice C.

The area of a triangle is given by the formula 1/2 * base * height. Substituting the given values for the base and height into this formula, we get:

1/2 * √63 * √28 = 1/2 * 7√9 * 2√7 = 7 * √9 * √7 = 21√7 cm^2

So the area of the triangle is 21√7 cm^2.

Answer:

x = 12, y = -1

Step-by-step explanation:

x - 2y = 14            (call this equation '1.')

x + 3y = 9             (call this '2')

'2' - '1' :

0x  + (3 - -2)y = 9 -14

(3 + 2)y = -5

5y = -5

y = -1.

substitute than into '1':

x - 2(-1) = 14

x + 2 = 14

x = 12.

check we are correct by subbing into '2'.

x + 3y = 9

12 + 3(-1) = 12 - 3 =9

so, x= 12 and y = -1

Answer:

X=14+2y

14+2y+3y=9

14+5y=9

5y=9-14

5y=–5

Y=–1

It should be noted that triangle ABC is an isosceles triangle.

An isosceles triangle has two sides of equal length, and the third side is longer than the other two sides. In triangle ABC, AB = DCE, which means that sides AB and DCE are equal in length. The third side, AC, is longer than AB and DCE, because ABC = 80, which is greater than 50.

The two angles opposite the equal sides are also equal. In triangle ABC, angles A and C are equal because sides AB and AC are equal.

The altitude (a line drawn from a vertex perpendicular to the opposite side) bisects the opposite side. In triangle ABC, the altitude from vertex A bisects side BC.

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Answer:

C, 3:7

Step-by-step explanation:

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The surface area of the prism is 62 in²

The formula for surface area of a right triangular prism is expressed as;

Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)

Such that the parameters are;

Substitute the values

Perimeter= 2(12 + 4) = 2(16) = 32 in

Base area = 1/2 base ×height

Base area = 1/2 × 12 × 5

Multiply the values, we get;

Base area = 30 in

Surface area = 30 + 32

Add the values

Surface area = 62 in²

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The rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.

The volume of the liquid in the bowl is given by the following integral:

[tex]V = \int\limitsx_{0}^{h} \, \pi r^{2}(y) dy[/tex]

where r = radius of the bowl and y = height of the liquid.

The radius of the bowl is equal to the distance from the curve y = (4/(8-x)) - 1 to the y-axis. This can be found using the following equation:

r = √{(4/(8-x)) - 1}² + 1²

The height of the liquid is equal to the distance from the curve y = (4/(8-x)) - 1 to the x-axis. This can be found using the following equation:

h = (4/(8-x)) - 1

Substituting these equations into the volume integral:

[tex]V = \int\limitsx_{0}^{h } \, \pi {\sqrt{(4/(8-x)) - 1)^{2} + 1^{2} (4/(8-x))} - 1 dy[/tex]

Evaluate this integral using the following steps:

Expand the parentheses in the integrand.

Separate the integral into two parts, one for the integral of the square root term and one for the integral of the linear term.

Integrate each part separately.

The integral of the square root term can be evaluated using the following formula:

[tex]\int\limits^{b} _{a} \, dx \sqrt{x} dx = 2/3 (x^{3/2}) |^{b}_{a}[/tex]

The integral of the linear term can be evaluated using the following formula:

[tex]\int\limits^{b} _{a} \, {x} dx = (x^{2/2}) |^{b}_{a}[/tex]

Substituting these formulas into the integral:

V = π { 2/3 (4/(8-x))³ - 1/2 (4/(8-x))² } |_0^h

Evaluating this integral:

V = π { 16/27 (8-h)³ - 16/18 (8-h)² }

The rate of change of the volume of the liquid is given by:

dV/dt = π { 48/27 (8-h)² - 32/9 (8-h) }

The rate of change of the volume of the liquid is 7π cm³ s⁻¹. Also the depth of the liquid is one-third of the height of the bowl. This means that h = 2/3.

Substituting these values into the equation for dV/dt:

dV/dt = π { 48/27 (8-2/3)² - 32/9 (8-2/3) } = 7π

Solving this equation for the rate of change of the depth of the liquid:

dh/dt = 7/(48/27 (8 - 2/3)² - 32/9 (8 - 2/3)) = 1.25 cm s⁻¹

Therefore, the rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.

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The speed of the butterfly travelling is 30 miles per hour as given on the graph G.

For F, the slope is 150/25 = 6 so this is false

For G, the slope is 150/5 = 30, this is true.

For H, the slope is 25/150 = 1/6, This is false

For J, th slope is 5/150 = 1/30, this is also false.

Thus, the correct answer is option G.

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Full Question:

See attached image

The value of each variable is:

x = 11 units

y = 11√2 units

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

We can find the value of each variable using trigonometric ratios:

tan 45° = x/11 (tan = opposite/adjacent)

1 = x/11

x = 11 units

sin 45° =  9/y (sine = opposite/hypotenuse)

(√2)/2 = 11/y

y = 11/ (√2)/2

y = 11√2 units

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The exponential function [tex]y = 2 + 3^x[/tex] is a exponential growth function with these following features:

An exponential function has the definition presented as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

The function for this problem is given as follows:

[tex]y = 2 + 3^x[/tex]

The addition by 2 means that the asymptote of the function is given as follows:

y = 2.

Hence the y-coordinate of the y-intercept is given as follows:

[tex]y = 2 + 3^0[/tex]

y = 3.

The parameter b is given as follows:

b = 3.

As |b| > 1, we have an exponential growth function.

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The area of each slice from the circle is 18π square units. Option C

The area of a circle is an enclosed region within a confined boundary. The area of a circle is measured as the product of π multiplied by the square of a radius.

From the information given:

The radius of the circle (r) = 12 units

The area of the circle = πr²

The area of the circle = π(12)²

The area of the circle = 144π

However, if the area is divided into 8 congruent(similar and equal) slices, the slice of each area will be:

=  144π/8

= 18π

The circumference of a circle = 2πr

If the radius = 12

The circumference of a circle = 2π(12)

The circumference of a circle = 24π

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Answer:

Blue

Step-by-step explanation:

The answer is blue because there is more blue marble than red.

Answer:

Step-by-step explanation:

The area of a circle is calculated using the formula A = πr², where A is the area, π is approximately 3.14 and r is the radius of the circle.

For the first circle with a radius of 3 ft, the area would be A = 3.14 * 3² = 28.3 ft². So the correct answer is C. 28.3 ft².

For the second circle with a radius of 7 cm, the area would be A = 3.14 * 7² = 153.9 cm². So the correct answer is H. 153.9 cm².

The surface area of the cylinder is 905 square centimeters

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

Diameter, d = 12 cm

Height, h = 18 m

This means that

Radius, r = 12/2 = 6 cm

Using the above as a guide, we have the following:

Surface area = 2πr(r + h)

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

Surface area = 2π * 6 * (6 + 18)

Evaluate

Surface area = 905

Hence, the surface area is 905 square centimeters

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Based on the dot plots, it appears that students generally did more push-ups this year than last year.

The range of the push-ups completed this year is 12, while the range of the push-ups completed last year is only 10.

This means that there is a greater spread of values in the data set for this year, with some students completing many more push-ups than others. In the data set for last year, the values are more evenly distributed, with most students completing between 5 and 10 push-ups.

The range of a data set affects the shape of the dot plot by determining how spread out the values are. A wide range will result in a dot plot that is more spread out, while a narrow range will result in a dot plot that is more compact. In the case of the push-up data, the wider range of values for this year results in a dot plot that is more spread out than the dot plot for last year.

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Answer:

Step-by-step explanation:

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The probability of a family with 4 people will be 0.244.

Here, we have,

A survey found the distribution of some families by size and is as follows:

Family Size 2 3 4 5 6 7 8

Frequency 87 50 61 31 16 3 2

The probability is given as,

P = (Favorable event) / (Total event)

The probability of a family with 4 people is calculated as,

P = (61) / (87 + 50 + 61 + 31 + 16 + 3 + 2)

P = 61 / 250

P = 0.244

Hence, The probability of a family with 4 people will be 0.244.

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Answer:

To find the angle of elevation, we can use the inverse tangent function (arctan). The angle of elevation is the angle between the ground and the line of sight from the ground to the top of the ladder.

Let's calculate it:

Angle of elevation = arctan(opposite/adjacent)

Angle of elevation = arctan(15 feet / 18 feet)

Using a calculator or table of trigonometric functions, we can find the arctan of (15/18) to be approximately 41.19 degrees.

Rounded to the nearest degree, the angle of elevation from the ground to the top of the ladder is 41 degrees.

Step-by-step explanation:

The length of each side of the wood is 5 centimetres.

Doug has 8 square pieces of wood. Each piece of wood have a side length of s cm. The total area of all 8 pieces of wood is 200 cm².

Hence, using quadratic equation let's find the length of each side of the wood.

Therefore,

8s² = 200

Hence,

8s² = 200

divide both sides of the equation by 8

s² = 200 / 8

s² = 25

s = √25

s = 5 centimetres

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The speed of the radius changing at the instance the radius is 4 feet is 0. 72 ft per second.

Given that the balloon is inflating at the rate of 144 cubic feet per second :

dV  / dt = 144 cubic feet/second.

The volume equation of a sphere would need to be differentiated as a result to find the rate at which the radius of the balloon is changing:

dV/ dt = d / dt [4/3 x π x r ³ ]

dV/ dt = 4π x r²  x dr / dt

144 = 4 π x (4)² x dr / dt

144 = 64 π x dr / dt

dr / dt = 144 / ( 64 π )

dr / dt = 9/( 4 π ) feet /second.

dr / dt = 0. 72 ft per second

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Answer:

A

Step-by-step explanation:

With function transformation, added/subtracted numbers outside of the x always mean the function is being translated up/down. In this case, since the 2 is being replaced with a 4, the new function is 2 units higher than the previous function.

Charlotte's reading rate per month is 2/3 books per month

To find the rate we use the principle of division to evaluate the amount of books read over a certain period of time .

Here ;

Number of books read = 8

Number of months over which book was read = 12

Reading rate = Number of books read / Number of months

Reading rate = 8 / 12

Reading rate = 2/3

Here, Charlotte's reading rate is 2/3 books per month

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The table of values for the function rule y = √(x + 6) is

x | f(x)

-15 | Not a real number

6 | 0

19 |  5

75 | 9

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

y = √(x + 6)

To fill in a table using a function rule, we apply the function rule to each input to calculate the corresponding output, and write these values in the right-hand column of the table

We have the x values to be

x = -15, -6, 19 and 75

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

y = √(-15 + 6) = Not a real number

y = √(-6 + 6) = 0

y = √(19 + 6) = 5

y = √(75 + 6) = 9

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The missing statement is the quadratic formula and the correct option therefore is the third option;

The quadratic formula is used to find the solution of a quadratic equation. The quadratic formula is; [tex]x = \frac{-b\pm\sqrt{b^2-4\cdot a\cdot c} }{2\cdot a}[/tex]

The statements and reasons can be presented algebraically as follows;

Statements [tex]{}[/tex]                                          Reasons

[tex]x^2+\frac{b}{a}\cdot x+(\frac{b}{2\cdot a} )^2 = -\frac{4\cdot a\cdot c}{4\cdot a^2}+ \frac{b^2}{4\cdot a^2}[/tex]        Find a common denominator on the

                                                            right side of the equation

[tex]x^2 + \frac{b}{a} \cdot x+(\frac{b}{2\cdot a} )^2 = \frac{b^2-4\cdot a \cdot c}{4\cdot a^2}[/tex]                 Add the fractions together on the

                                                     [tex]{}[/tex]        right side of the equation

[tex](x +\frac{b}{2\cdot a} )^2 = \frac{b^2 - 4\cdot a \cdot c}{4\cdot a^2}[/tex]                             Rewrite the perfect squared equation

                                                      [tex]{}[/tex]      to the left side of the equation as a

                                                        [tex]{}[/tex]    binomial squared

[tex]x + \frac{b}{2\cdot a} = \pm\sqrt{\frac{b^2 - 4\cdot a \cdot c}{4\cdot a^2} }[/tex]                   Take the square root of both sides of  the

                                                    [tex]{}[/tex] equation

[tex]\underline{x = \frac{-b\pm\sqrt{b^2 - 4\cdot a \cdot c} }{2\cdot a}}[/tex]                                 Simplify the right side of the equation    

The correct option is therefore;

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Answer:

A

Step-by-step explanation:

i took the test

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