Jeremy rides his bike at a rate of 12 miles per hour. The table below
represents the number of hours and miles Kevin rides. Assume both bikers
ride at a constant rate.

the solution of a system of linear equations is (4,36) with the help of the substitution method.

The algebraic approach to solving simultaneous linear equations is known as the substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve.

The given system of equations is

[tex]y=9x\\y=8x+4[/tex]

We shall solve it with the help of the substitution method

Substitute the value of y in Equation 2

[tex]9x=8x+4\\9x-8x=4\\x=4[/tex]

Put the value of x in Equation 1

[tex]y=9*4=36[/tex]

Hence the solution of a system of linear equations is (4,36) with the help of the substitution method.

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Answer:

Step-by-step explanation:

(1,-2) (-3,1)

1.     y--1=  -- 3/4 (x+3)

2.    y=  --3/4x--5/4

The hypotenuse of the triangle is x = 10.

We can see that we have a right triangle, then we can use the trigonometric relation:

cos(a) = (adjacent cathetus)/hypotenuse

Replacing the known values:

cos(60°) =5/x

Solving for x we will get:

x = 5/cos(60°) = 10

That is the value of x.

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There were approximately 1131 blueberries in the box at first.

To find the total number of blueberries in the box at first, follow these

First, we need to add up the percentages of blueberries Gerry ate on Monday and Tuesday. On Monday, he ate 0.5 (or 50%) of the blueberries and on Tuesday, he ate 25% of the blueberries.

So, he ate a total of 50% + 25% = 75% of the blueberries.

Since Gerry ate 848 blueberries altogether, which is 75% of the total number of blueberries in the box, we can now set up a proportion to find the total number of blueberries:

(75% of the total number of blueberries) = 848]

We can express 75% as a decimal (0.75) and set up an equation:

0.75 × (total number of blueberries) = 848

Now, to find the total number of blueberries, divide both sides of the equation by 0.75:

(total number of blueberries) = 848 / 0.75

5. Solve for the total number of blueberries:

(total number of blueberries) = 1130.67

Since there can't be a fraction of a blueberry, we can round up to the nearest whole number:

There were approximately 1131 blueberries in the box at first.

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Question

Gerry picked 0.5 of the blueberries in a box on Monday and 25% of the blueberries on Tuesday. If he picked a total of 848 blueberries altogether, how many blueberries were in the box at first?

Thus, 5/7 path of the second mosaic Trent will complete in 1 hours.

A mixed number is a representation of both a whole number and a improper fraction. In most cases, it denotes a number that falls either between two whole numbers.

Divide the numerator and denominator to create a mixed number from an incorrect fraction. The solution here becomes the numerator, the remainder the denominator, and the denominator stays the same.

Given:

Time to complete simple mosaic = 2/5 hours.

Now, Time to complete second mosaic = (3 1/2)*2/5 hours.

Convert the 3 1/2 (given in mixed fraction into proper fraction).

= (3*2 + 1)/2

= 7/2

So, to complete second mosaic Trent took = (7/2)*(2/5) = 7/5 hours.

In 7/5  hours ---> 1 complete part.

In 1 hour --> 5/7 part complete

Thus, 5/7 path of the second mosaic Trent will complete in 1 hours.

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Answer:

y = (-1/4)x - 1

Step-by-step explanation:

We can write an equation for this line in slope-intercept form:

[tex]y=mx+b[/tex],

where [tex]m[/tex] is the slope of the line and [tex]b[/tex] is the y-coordinate of the y-intercept.

First, to solve for the slope:

slope = rise / run

slope = -1 / 4

slope = -1/4

Next, to find the y-intercept, we can see that the line crosses the y-axis (vertical axis) when y = -1.

Finally, we can form an equation using these two pieces of information.

y = (-1/4)x - 1

[tex] \: [/tex]

To determine which bus is the most consistent, we need to compare the interquartile ranges (IQR) and ranges of the two data sets.

Bus 47 has an IQR of 8 and a range of 8.

Bus 14 has an IQR of 6 and a range of 6.

The IQR is a better measure of variability than the range because it is less sensitive to outliers. In this case, we can see that Bus 14 has a smaller IQR, indicating that the travel times for Bus 14 are more consistent.

Therefore, Bus 14 is the most consistent bus in terms of travel times.

The volume of the solid obtained by rotating the region about the y-axis is 3036π cubic units.

How to find the volume by rotating the region?

To find the volume of the solid obtained by rotating the region enclosed by the graphs of y=27-x, y=3x-9, and x=0 about the y-axis, we need to use the method of cylindrical shells.

Here the region is bounded by the graphs of y=27-x, y=3x-9, and x=0. We can see that the region is a trapezoid with vertices at (0, -9), (6, 9), (18, 9), and (27, 0).

Next, we need to determine the height and radius of each cylindrical shell. The height of each shell is the difference between the y-coordinates of the top and bottom of the shell. The radius of each shell is the x-coordinate of the shell.Let's consider a shell with x-coordinate x. The height of the shell is given by (27 - x) - (3x - 9) = 36 - 4x. The radius of the shell is x. The volume of the shell is given by 2πrhΔx, where Δx is the thickness of the shell.

Therefore, the total volume of the solid is given by:

[tex]V = \int0^6 2πx(36 - 4x)dx + \int6^18 2πx(9)dx + \int18^27 2πx(27 - x - 9)dx[/tex]

Simplifying and evaluating the integral, we get:

V = 2π(216) + 2π(243) + 2π(243/2) = 3036π

Therefore, the volume of the solid obtained by rotating the region about the y-axis is 3036π cubic units.

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Rotating the area about the y-axis yields a solid with a volume of 3036 cubic units.

The cylindrical shell method must be used to determine the solid's volume after rotating the region enclosed by the graphs of

y=27-x, y=3x-9, and x=0 about the y-axis.

In this case, the graphs of y=27-x, y=3x-9, and x=0 define the region's boundaries. The region is a trapezium, as can be seen, with vertices at (0, -9), (6, 9), (18, 9), and (27, 0).

The height and radius of each cylindrical shell must then be determined. Each shell's height is determined by the difference between its top and bottom y-coordinates.

Each shell's x-coordinate corresponds to its radius.Consider a shell with the coordinates x and y. (27 - x) - (3x - 9) = 36 - 4x gives the height of the shell. The shell has a radius of x. 2rhx, where x is the shell's thickness, gives the volume of the shell.

As a result, the solid's entire volume can be calculated using:

When we simplify and assess the integral, we obtain:

V = 2π(216) + 2π(243) + 2π(243/2)

  = 3036π

As a result, the region's volume after being rotated about the y-axis is 3036 cubic units.

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The volume of the prism is 0.343 cubic inches.

What is Volume ?

Volume is a measure of the amount of space occupied by a three-dimensional object. It is the quantity of space that a solid object occupies in three dimensions. Volume is often expressed in cubic units, such as cubic meters, cubic centimeters, or cubic inches , depending on the system of measurement used.

To find the volume of a rectangular prism, we multiply its length, width, and height.

In this case, the length, width, and height of the prism are all 0.7 inch. Therefore, the volume of the prism is:

Volume = (length) x (width) x (height)

= (0.7 x (0.7) x (0.7)

= 0.343 cubic inches

Therefore, the volume of the prism is 0.343 cubic inches.

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Mega Movies hosted a film premiere on Friday night. They charged $9 for adults and $5 for children. Therefore, the equation is written as 11 children; 120 adults  went to the premier.

Let children be x and adult be y

As the cost of the entry fee is in the ratio of 9 to 6

so, 9x+5y= 1135 ----------------- (1)

and x +y = 131  ------------------- (2)

Multiplying equation (2) by 9, we get:

9x + 9y = 1179

Now, subtracting equation (2) and (1), we get:

9x + 9y = 1179

9x+5y= 1135

⇒ 4y = 44

⇒ y = 11

Now putting y = 11 in equation  (1) , we get:

   9x+5y = 1135  

⇒ 9x + 5× 11 = 1135

⇒ 9x = 1080

⇒ x = 120

Therefore, 11 children; 120 adults  went to the premier.

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A′(2, 1), B′(6, 1), and C′(2, 5) are the image's positions as a result of moving the triangular 6 units to the right.

The order of the numbers is always latitude first, semicolon after which is followed by longitude. For instance, New York City is located approximately at 40°N and 74°W in terms of latitude and longitude. The approximate coordinates for Sydney are 34°S and 150°E. When using a chart or globe, your longitude as well as latitude won't be precisely accurate.

To translate a point (x, y) to the right by 6 units, we add 6 to the x-coordinate.

So, the image of vertex A(-8, 1) would be A'(-8 + 6, 1) = A'(-2, 1).

Similarly, the image of vertex B(0, 1) would be B'(0 + 6, 1) = B'(6, 1).

And, the image of vertex C(-4, 5) would be C'(-4 + 6, 5) = C'(2, 5).

Therefore, the coordinates of the image after translating the triangle 6 units to the right are:

A′(−2, 1), B′(6, 1), C′(2, 5).

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Given equation represents a circle with center at (1, 1) and vertex form [tex](x - 1)^2 + (y - 1)^2 = 2.[/tex]

A circle is a closed shape in geometry that consists of all points that are equidistant from a central point called the center. A circle is defined by its radius, which is the distance from the center to any point on the circumference (outer boundary) of the circle. The diameter of a circle is twice the radius, and the circumference is the total distance around the circle.

The given equation [tex]x^2 + y^2 - 2x - 2y = 1[/tex]represents a conic section known as a circle.

To rewrite the given equation in vertex form for a circle, we need to complete the square for both x and y terms separately. The vertex form of a circle is given by:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

where (h, k) is the center of the circle and r is the radius.

Let's complete the square for x and y terms:

[tex]x^2 - 2x + y^2 - 2y = 1[/tex]

Adding and subtracting the necessary terms to complete the square:

[tex]x^2 - 2x + 1 + y^2 - 2y + 1 = 1 + 1[/tex]

Rewriting the equation in vertex form:

[tex](x - 1)^2 + (y - 1)^2 = 2[/tex]

So, the conic section represented by the given equation is a circle with its center at (1, 1) and a radius of √2, and the vertex form of the circle is [tex](x - 1)^2 + (y - 1)^2 = 2.[/tex]

Therefore, Given equation represents a circle with center at (1, 1) and vertex form [tex](x - 1)^2 + (y - 1)^2 = 2.[/tex]

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Answer:

223

Step-by-step explanation:

i am in 6th grade

The equation of the line in slope-intercept form is y = -11x + 29.

To find the slope of given points we are using the slope-intercept formulae

The line passing through the point are (x1, y1) and (x2, y2) is given by:

m = (y2 - y1) / (x2 - x1)

m is the slope of the line.

Putting all values in the above equation, we get:

m = (-15 - (-4)) / (4 - 3) = -11

So the slope of the line is -11

To write the equation of line the point-slope form of the equation we can use

y - y1 = m(x - x1)

Put all values into the equation

y - (-4) = -11(x - 3)

Simplifying, we get:

y + 4 = -11x + 33

Subtracting 4 from both sides, we get:

y = -11x + 29

So the equation of the line in slope-intercept form is y = -11x + 29.

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Answer:

To estimate the number of pentagons in the tub, we can use the proportion of pentagons in the sample of geometric shapes that Mrs. Chen selected and apply it to the total number of geometric shapes in the tub.

The proportion of pentagons in the sample is:

4 / (3 + 2 + 2 + 4 + 2) = 4 / 13 ≈ 0.31

We can assume that this proportion is representative of the entire tub of geometric shapes, and we can apply it to the total number of geometric shapes in the tub:

0.31 x 250 ≈ 77.5

Rounding to the nearest whole number, we can estimate that there are approximately 78 pentagons in the tub.

Therefore, the estimated number of pentagons in the tub is 78.

The t-distribution becomes flatter as the sample size increases.

The t distribution, compared to the z distribution, is more peaked for small samples but increasingly like the z distribution as n increases.

The t-distribution :

A t-distribution is a symmetric distribution that is similar to the standard normal distribution, also known as the z-distribution.

It is a continuous probability distribution that is used to estimate population parameters when the sample size is small (less than 30) or when the population standard deviation is unknown.

The t-distribution has more variability than the standard normal distribution due to the smaller sample size.

For a given number of degrees of freedom, the t-distribution has more density in the tails than the standard normal distribution.

The z-distribution :

The standard normal distribution is also known as the z-distribution. It is a continuous probability distribution that has a mean of zero and a standard deviation of one.

The z-distribution is bell-shaped, with a median of zero, a mode of zero, and a mean of zero.

In conclusion, the t-distribution has a peakier curve than the z-distribution, especially for small sample sizes.

However, as the sample size increases, the t-distribution approaches the z-distribution.

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All tests of hypothesis are based on the assumption that the null hypothesis is true. C. the null hypothesis is true is the correct option.

In hypothesis testing, two hypotheses are compared:

The null hypothesis (H0) and the alternative hypothesis (Ha).The null hypothesis is the statement that is assumed to be true, while the alternative hypothesis is the statement that the researcher is trying to prove.

For example, if the researcher wants to test whether a new drug is effective in treating a certain disease, the null hypothesis would be that the drug has no effect, while the alternative hypothesis would be that the drug is effective.

Therefore, all tests of hypothesis are based on the assumption that the null hypothesis is true option c is correct..

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A word sentence that represents this inequality is "A number x is more than 1."

What is Inequality ?

In mathematics, an inequality is a statement that compares two values, expressing that one value is greater than, less than, greater than or equal to, or less than or equal to the other value. Inequalities are represented using symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">

Inequality: x > 3

Word sentence: The value of x is greater than 3.

Explanation: Based on the graph, we can see that the shaded area represents all the values of x that are greater than 3. Therefore, the inequality that represents this graph is x > 3, which means that x is any number greater than 3.

Question 2:

Word sentence: A number x is more than 1.

Explanation: The inequality represented by the given graph is x > 1, which means that x is any number greater than 1.

Therefore, a word sentence that represents this inequality is "A number x is more than 1."

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Thus, the surface area with the dimensions of a rectangular prism as 6m by 4 m by 15 m is found as: S = 348 sq. m.

A rectangular prism is a 3 solid that is surrounded by 6 rectangular faces, 2 of which are the bases (the top face and bottom face), and the remaining 4 are lateral faces. It likewise has 12 edges and 8 vertices.

A rectangular prism is sometimes known as a cuboid because of its shape. A shoe box, an ice cream bar, or a matchbox are some instances of rectangular prisms in everyday objects.

Dimensions of rectangular prism :

surface area of a rectangular prism:

S = 2(lw + wh + hl)

S = 2(6*4 + 4*15 + 15*6)

S = 348 sq. m.

Thus, the surface area with the dimensions of a rectangular prism as 6m by 4 m by 15 m is found as: S = 348 sq. m.

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Answer: 50

Step-by-step explanation:

2*6+2*4+2*15=12+8+30=50

Answer:

It would be the last one.

Step-by-step explanation:

hope this is correct

Answer:

6/7x

Step-by-step explanation:

g/7 x 6 = 6/7 x

Answer: g / 7 x 6

Explanation:

The measures are: [tex]MK = 30[/tex]

[tex]NL = 13[/tex]

[tex]m/MKL = 41^\circ[/tex]

[tex]m/NLK = 41^\circ[/tex]

[tex]y \approx 17.79^\circ[/tex]

In a rhombus, all sides are equal in length and opposite angles are congruent. Let's denote the measures as follows:

MK = 30 (Given)

NL = 13 (Given)

m/MKL = 41° (Given)

m/NLK = x (To be determined)

m/MKL = y (To be determined)

Since JKLM is a rhombus, we know that JM = KL and JK = ML. We can use the properties of a rhombus to find the values of x and y.

First, we can use the fact that opposite angles in a rhombus are congruent. Since   [tex]m/MKL = 41^\circ[/tex] , then m/NLK (opposite angle) is also 41°.

Next, we can use the fact that diagonals of a rhombus bisect each other at a 90° angle. Since MK = 30 and NL = 13, the diagonals JL and KM intersect at their midpoint, which we can denote as O.

Using the properties of right triangles, we can form a right triangle JOM with JO = JK/2 = ML/2 (since JL is the diagonal and KM is its midpoint), OM = MK/2 = 30/2 = 15, and JM = JK = ML (since JK = ML in a rhombus).

Now we can use trigonometry to find the value of y. In right triangle JOM, we have:

[tex]sin(y) = OM/JM = 15/JM[/tex]

Since JM = KL (by the properties of a rhombus), and KL is a diagonal bisecting NL, we can use Pythagoras' theorem to find KL:

[tex]KL^2 = NL^2 + LK^2 = 13^2 + (MK/2)^2 = 13^2 + 15^2 = 169 + 225 = 394[/tex]

[tex]KL = \sqrt394[/tex]

So, we can substitute JM = KL = √394 in the equation for sin(y):

[tex]sin(y) = 15/\sqrt394[/tex]

Taking the inverse sine of both sides:

[tex]y = sin^(-1)(15/\sqrt394)[/tex]

Using a calculator, we can find the approximate value of y to be  [tex]y ≈ 17.79^\circ.[/tex]

Therefore, the measures are: [tex]MK = 30[/tex]

[tex]NL = 13[/tex]

[tex]m/MKL = 41^\circ[/tex]

[tex]m/NLK = 41^\circ[/tex]

[tex]y \approx 17.79^\circ[/tex]

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Answer: 8

Step-by-step explanation: a triangle has a total of 180 adding all the angles

Answer:

8°

Step-by-step explanation:

The sum of the three interior angles in a triangle is always 180°.

Third angle = 180 - (88 + 84) = 8

Answer:

This rectangle is shifted 1 unit to the left and then 4 units down. So the algebraic rule is (x - 1, y - 4).

Answer:

A

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

99° is an exterior angle of the triangle , then

2x + 43 = 99 ( subtract 43 from both sides )

2x = 56 ( divide both sides by 2 )

x = 28

Answer:

Therefore, 2 + 2 with a square root of 9 is equal to 8.

Step-by-step explanation:

We can simplify the expression "square root of 9" to just 3. Then, we have:

2 + 2(3) = 2 + 6 = 8

Therefore, 2 + 2 with a square root of 9 is equal to 8.

Tnx   :)  :)  ;)

The following equation is given using the PEMDAS order of operations and we get the solved expression as -1.

BODMAS, also known as PEMDAS, is an acronym used to remember the order of operations in mathematics. The letters in the acronym stand for:

B - Brackets

O - Order (exponents and roots)

D - Division

M - Multiplication

A - Addition

S - Subtraction

BODMAS tells us about the order in which to perform mathematical operations in an expression. This is important because performing the operations in the wrong order can give us a different answer than what is intended.

We start by evaluating 6(6), which is 36. Next, we combine 36 and 18 to get 54.

Finally, we subtract 55 from 54 to get -1.

Therefore, the answer to the expression 6(6) + 18 - 55 is -1, not 118.

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The coordinates of R' when rotated 90° about their center of rotation is (-6, -3).

Geometry is a branch of mathematics that deals with the study of shapes, sizes, relative positions of objects, and the properties of space.

The point R(3, -6) is located in the fourth quadrant as both the x-coordinate and y-coordinate are positive.

When the sails rotate 90 degrees clockwise, the point R will move to a new location R' in the third quadrant where both the x-coordinate and y-coordinate are negative.

To find the coordinates of R', we need to swap the x-coordinate and y-coordinate of point R and then negate the new x-coordinate.

That is, if R' has coordinates (x, y), then x = -6 and y = -3.

Hence, the coordinates of R' are (-6, -3).

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The center and radius of a circle given by the equation x² - 10x + y² + 6y - 30 = 0  is (5,-3) and√64 = 8 units.

When finding the center and radius of a circle given by the equation x² - 10x + y² + 6y - 30 = 0, one can use the following steps:

The first step is to rearrange the equation into the standard form, (x - a)² + (y - b)² = r². This is done by completing the square for both the x and y terms in the equation.

x² - 10x + y² + 6y - 30 = 0x² - 10x + 25 + y² + 6y + 9 - 30 = 25 + 9(x - 5)² + (y + 3)² = 64 Therefore, the center of the circle is (5,-3), and the radius is √64 = 8 units.

Explanation:  Given the equation x² - 10x + y² + 6y - 30 = 0, we want to find the center and radius of the circle. The standard form of the equation of a circle with center (a,b) and radius r is (x - a)² + (y - b)² = r². We will begin by completing the square for the x terms and the y terms separately: For the x terms: x² - 10x= x² - 10x + 25 - 25= (x - 5)² - 25 For the y terms: y² + 6y= y² + 6y + 9 - 9= (y + 3)² - 9 Now we can substitute these expressions back into the original equation and simplify: x² - 10x + y² + 6y - 30 = 0(x - 5)² - 25 + (y + 3)² - 9 - 30 = 0(x - 5)² + (y + 3)² = 64 The equation is now in standard form,

which means that the center of the circle is (5,-3) and the radius is √64 = 8 units.

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Step-by-step explanation:

To find the width of the border, we first need to calculate the area of the picture.

Area of the picture = length x width = 8 in x 11 in = 88 in²

Let the width of the border be "x".

The new length of the picture will be 11+2x, and the new width will be 8+2x.

The total area of the new picture with the border will be:

total area = (11+2x) x (8+2x) = 108 in²

Expanding this equation gives:

88 + 22x + 16x + 4x² = 108

Simplifying and rearranging the terms, we get:

4x² + 38x - 20 = 0

We can solve for x using the quadratic formula:

x = (-b ± sqrt(b² - 4ac)) / 2a

where a = 4, b = 38, and c = -20.

Plugging in these values, we get:

x = (-38 ± sqrt(38² - 4(4)(-20))) / 2(4)

x = (-38 ± sqrt(1936)) / 8

x = (-38 ± 44) / 8

The two possible solutions are:

x = 1.5 or x = -5

Since a negative width for the border does not make sense, the width of the border should be 1.5 inches.