Which values are possible rational roots of 4x3+9x2−x+10=0 according to the rational root theorem? Select each correct answer. ±12 ±2 ±52 ±25

We have been given that a rectangle has a height to width ratio of 3:4.5.

Let h be height and w be width of rectangle.

We can set our given information in an equation as:

[tex]\frac{h}{w} =\frac{3}{4.5}[/tex]

[tex]h=\frac{3}{4.5} *w[/tex]

Now we will substitute h=1 in this equation.

[tex]1=\frac{3}{4.5} *w[/tex]

[tex]3w=4.5[/tex]

[tex]w=\frac{4.5}{3} =1.5[/tex]

We can see that width of rectangle is 1.5 times height of rectangle.

Our one set of dimensions of rectangle will be: height=1 and width=1.5.

We can get many set of dimensions for our rectangle by multiplying both height and width of rectangle by same number.

Multiplying by 5 we will get our dimensions as: height 5 and width 7.5.  

Therefore, (1 and 1.5) and (5 and 7.5) dimensions for rectangle will be scaled version of our rectangle.

Two examples of dimesions for rectangles that could be scaled versions of this rectangle are (2,3) and (4,6).

Rectangle has a height and width.

[tex]\dfrac{height}{width}=\dfrac{3}{4.5}\\\\\dfrac{height}{width}=\dfrac{30}{45}\\\\\dfrac{height}{width}=\dfrac{2}{3}[/tex]

[tex]height = 2x\\width=3x[/tex]

Now let [tex]x=1[/tex]

So dimensions of height and width is [tex]2\times1 \; and\; 3\times1[/tex]

So it is [tex](2,3)[/tex]

Now let [tex]x=2[/tex]

So dimensions of height and width is [tex]2\times2 \; and\; 3\times2[/tex]

So it is [tex](4,6)[/tex]

Hence many dimesions of rectangles are possible.

Learn more about rectangle here;

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Everything looks good until the final step. The answer is not c = 26. It should be more like c = 25.495 which is approximate. You would use your calculator to find this value. If you round to the nearest whole number, then c = 25; however, this is a bad idea because it implies that the hypotenuse is the same length as the longer leg, which is not the case here. Recall that the hypotenuse is always the longest side.

The final answer is 25.49 or 25.5

which of the following???

Answer:

B. A loan

Step-by-step explanation:

hope this helps

Answer:

The coefficient of determination is used to measure how well a model fits the real data, or how well it can replicate them. The closer to 1 the value of R ^ 2 the more accurate the model is.

In this case, that R ^ 2 = 0.661 means that the model fits moderately to the variable to be studied.

For a linear regression model, the coefficient of determination is the square of the correlation coefficient r of Pearson. So:

[tex]r =\sqrt{R^2}[/tex]

r = 0.813

This value of r close to 1 means that the length of the essays sent to a teacher (x) and the score that the teacher gave to the essay (and) are highly related.

3 pounds of sunflower seeds.

The repeating decimal 1.6 falls under the categorization of Rational numbers. It can be expressed as a fraction, specifically 5/3, but it does not qualify as an integer or a whole number as those contain no fractions or decimals.

The number 1.6 (1.666...) is a repeating decimal and belongs to the set of numbers known as Rational numbers, but not integers or whole numbers.

By definition, Rational numbers are any numbers that can be expressed as the fraction of two integers. In other words, a number is rational if it can be written in the form a/b where a and b are integers and b is not zero. Here, 1.6 repeating can be written as 5/3 (a/b form), indicating it's a rational number.

Integers and Whole numbers are always without fractions or decimals. Hence, the number doesn't fall in these categories.

Therefore, the correct answer is D: 1.6 (1.666...) is a rational number, but it is not an integer or a whole number.

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The mode of the first data set is 19, and the IQR of the second data set is 4, but 4 is not a provided option in your question.

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Hey there!

When you multiply two exponents, you "add" the numbers on the exponents.

3+3=6

Therefore, m³·m³=[tex]m^{6}[/tex]

Therefore, your answer is A

I hope this helps! I hope your day is as grand as 10[tex]^{6}[/tex]!

The answer to your question is m^{6} or A

Opposite angles have the same measures. This allows you to set and solve the following equations:

[tex] \begin{cases} 26-6x = 20-8x \\ 5y = 9y-76 \end{cases} [/tex]

To solve both equations, let's move all the terms involving the variables on the left hand side, and all constant terms on the right hand side:

[tex] \begin{cases} -6x+8x = 20-26 \\ 5y-9y = -76 \end{cases} [/tex]

Sum like terms:

[tex] \begin{cases} 2x = -6 \\ -4y = -76 \end{cases} [/tex]

Divide the first equation by 2 and the second by -4:

[tex] \begin{cases} x = -3 \\ y = 19 \end{cases} [/tex]

Answer:

4 pounds of ingredients are used in each batch.

Step-by-step explanation:

Amount of flour = [tex]21\frac{1}{2}pounds = \frac{43}{2}pounds[/tex]

Amount of butter = 8 pounds

Amount of sugar = [tex]18\frac{1}{2}pounds= \frac{37}{2} pounds[/tex]

So, the total amount of all ingredients will be:   [tex](\frac{43}{2}+\frac{37}{2}+8)pounds = (\frac{43+37+16}{2}) pounds= \frac{96}{2} pounds = 48 pounds[/tex]

Given that, she makes 12 batches of cookies using all the ingredients.

Thus, the amount of ingredients used in each batch [tex]=\frac{48}{12} pounds = 4 pounds[/tex]

y = 2x -5

y= -3x + 1

Here both the equations are in y = mx + b

where m is the slope and b is the y intercept

y =2x -5, the slope = 2  and b intercept = -5

y= -3x + 1, the slope = -3  and b intercept = +1

Both the equations have different slope. So there should be a single solution

Yes, the system of equations have a solution

To find out how many cases of Caesar dressing are used, divide the ranch cases used by the ranch ratio (72/8=9) and then multiply by the Caesar ratio (9*3=27). Therefore, the buffet uses 27 cases of Caesar dressing.

The question involves finding out how many cases of Caesar dressing the buffet uses if they use 72 cases of ranch dressing and the ratio of ranch to Caesar dressing is 8:3.

First, we determine the unitary ratio by dividing the number of ranch cases used by the corresponding ratio number for ranch. In this case, 72 cases divided by 8 gives us 9 cases per unit ratio.

Since the ratio for Caesar dressing is 3, we then multiply the unit ratio by 3 to find the number of Caesar cases used.

72 cases of ranch ÷ 8 (ranch ratio) = 9 cases per unit

9 cases per unit × 3 (Caesar ratio) = 27 cases of Caesar dressing

Answer:

Option B is correct.

Step-by-step explanation:

Polyhedron is a solid figure which is entirely made up of polygons.

Means faces of the polyhedron are the polygons.

Minimum number of polygons required to for a polyhedron is 4 triangles.

Polyhedron made up of 4 triangles is known as Tetrahedron.

Tetrahedron has 6 edges.

Therefore, Option B is correct.

We need to construct an equilateral triangle inscribed in a circle, two congruent circles are created such that the center of each circle is also a point on the other circle.

Following would be correct directions:

A. Using a straightedge draw a line segment between the endpoint of the diameter of the circle that is not also the radius of the second circle and the bottom point of intersection of the two circles.

B. Using a straightedge draw a line segment between the endpoint of the diameter of the circle that is not also the radius of the second circle and the upper point of intersection of the two circles.

D. Using a straightedge draw a line segment between the top intersection point of the two circles and the radius of the first circle.

Therefore, incorrect direction would be

C. Using a straightedge draw a line segment between the two intersection points of the two circles.

Option D is incorrect because drawing a line segment between the top intersection point of the two circles and the radius of the first circle does not necessarily form the side of an equilateral triangle inscribed in a circle.

To determine which of the given directions for constructing an equilateral triangle inscribed in a circle does not work, we need to visualize the basic properties of such a triangle and its relationship to the circles. An equilateral triangle inscribed in a circle has all its vertices on the circumference of the circle, and the sides of the triangle are equal in length.

Option A suggests drawing a line segment from the endpoint of the diameter of the first circle that is not also the radius of the second circle to the bottom point of intersection of the two circles. This is one correct method to form the side of an equilateral triangle. Similarly, option B, which involves drawing a line segment between the endpoint of the diameter and the upper intersection point of the two circles, also forms a side of the equilateral triangle correctly.

Option C suggests drawing a line between the intersection points of the two circles. This will correctly create the base of the equilateral triangle. However, option D is incorrect because it states to draw a line segment between the top intersection point of the two circles and the radius of the first circle. This would not generally create the side of an equilateral triangle unless the radius mentioned coincidentally falls on another vertex of the triangle, which typically is not the case. Therefore, option D would not represent directions to construct the sides of the equilateral triangle.

The cost would be:

46,640 Points.

11x + y = 4

x  |   y

0  |   4

[tex]\frac{4}{11}[/tex] |   0

plot the y-intercept (0, 4) and the x-intercept ([tex]\frac{4}{11}[/tex], 0)

or

11x + y = 4

-11x        -11x

      y = -11x + 4      ⇒ m = [tex]\frac{-11}{1}[/tex], b = 4

plot at point the y-intercept "b = 4" (0,4).  plot the next point using the slope "m = [tex]\frac{-11}{1}[/tex]" from point (0,4), count down 11 and to the right 1 (1,-7).

Using intercepts would not provide an accurate graph because you have to estimte where ([tex]\frac{4}{11}[/tex], 0) is, so it is best to use slope-intercept form.

***********************************************************************************************************

x + y = -2

x  |   y

0  |  -2

-2 |   0

plot the y-intercept (0, -2) and the x-intercept (-2, 0)

or

x + y = -2

-x         -x

     y = -x - 2     ⇒ m = [tex]\frac{-1}{1}[/tex], b = -2

plot at point the y-intercept "b = -2" (0,-2).  plot the next point using the slope "m = [tex]\frac{-1}{1}[/tex]" from point (0,-2), count down 1 and to the right 1 (1,-3).

Both methods are easy to use so either can be used.

**********************************************************************************************************

x - 2y = 18

x  |   y

0  |  -9

18 |   0

plot the y-intercept (0, -9) and the x-intercept (18, 0)

or

x - 2y = 18

-x           -x

   -2y = -x + 18

    [tex]\frac{-2y}{-2} = \frac{-1}{-2}x + \frac{18}{-9}[/tex]

       y = [tex]\frac{1}{2}x[/tex] - 9

plot at point the y-intercept "b = -9" (0,-9).  plot the next point using the slope "m = [tex]\frac{1}{2}[/tex]" from point (0,-9), count up 1 and to the right 2 (2,-8).

Using intercepts will make a large graph since you have to plot (18,0) so it is best to use the slope-intercept form.

answer is equal to 2X3/3X4 which is equal to1/2

[tex]\frac{3}{4}[/tex] of [tex]\frac{2}{3}[/tex]

[tex]\frac{3}{4} * \frac{2}{3} = \frac{3(2)}{4(3)} = \frac{1}{2}[/tex]

Answer: [tex]\frac{1}{2}[/tex] cup of butter

Because the equation is in slope-intercept form, we know the first point will be -4, as that is the y-intercept.

We can input a value of x into the equation to find the y value that goes along with that value of x.

y = (-5/6)x - 4

We'll use x = 6 for this.

y = (-5/6)6 - 4

y = -5 - 4

y = -9

to draw the graph we only require 2 points

choose any value of x, substitute into the equation and solve for y

x = 0 : y = 0 - 4 = - 4 ⇒ (0, - 4 )

x = 6 : y = - 5 - 4 = - 9 ⇒ (- 6, - 9 )

Plot these 2 points and draw a straight line through them for graph

Answer : A

A. 3 × (2 × 6) = 36

we have 3 times 2 times 6.  All the numbers have multiplication in between . so it comes under Associative property of multiplication.

B. (3 + 2) × 6 = 30

we have 3+2 . there is a + sign in between.  so it does not comes under Associative property of multiplication

C. 6 + (5 × 6) = 36

we have 6 +  . there is a + sign in between.  so it does not comes under Associative property of multiplication

D. 3 × (2 + 6) = 24

we have 2 + 6 . there is a + sign in between.  so it does not comes under Associative property of multiplication

Answer:

The graph at the bottom.

Step-by-step explanation:

We have been given equation of an absolute value function [tex]y+7=|x+5|[/tex]. We are asked to choose the graph of the given function.

We know that standard absolute function is in form [tex]y=|x-h|+k[/tex], where, (h,k) represents vertex of function.

Let us convert our given function in standard form.

[tex]y+7-7=|x+5|-7[/tex]

[tex]y=|x+5|-7[/tex]

[tex]y=|x-(-5)|-7[/tex]

Since the vertex of our given function would be at point [tex](-5,-7)[/tex], therefore, the graph at the bottom is the correct choice.

[tex]\frac{(new) - (original)}{original} = \frac{110 - 125}{125} = \frac{-15}{125} = -0.12[/tex] The negative means it is a decrease.

0.12 x 100 = 12%  

Her weight decreased 12%

Answer: B

Answer:

Option A is the correct answer.

Explanation:

 Let A be the base area and h be the height of prism.

 Volume of prism =  Base area x Height = a x h =ah

 Now we have base area of pyramid = Base area of prism = a ( both have same type of base)

Height of pyramid = 3 x height of prism = 3h

Volume of pyramid = 1/3 x Base area x Height = 1/3 x a x 3h = ah

Comparing both volumes, we will get Volume of prism = Volume of pyramid

So their ratio is 1.

Option A is the correct answer.

The volume of a pyramid with a height three times that of a prism's, but with the same base area, is equal to the volume of the prism, making the ratio 1.

To find the ratio of the volume of the pyramid to the volume of the prism with the same base area, we use the formula for the volume of a pyramid, which is Vpyramid = (1/3)Ah, where A is the area of the base and h is the height. The volume of a prism is given by Vprism = Ah.

Since we know the height of the pyramid is three times the height of the prism (3h), we can substitute in the formula: Vpyramid = (1/3)A(3h) = Ah, which simplifies to the same formula for the volume of the prism. This means that the volume of the pyramid is equal to the volume of the prism. Therefore, the correct ratio is Option A: 1.

Answer: Option B. 96 ft^3

Solution:

Volume of the prism: V=?

V= A * H

Height of the prism: H=4 ft

Area of the base (triangle) : A=b*h/2

Base of the triangle: b=6 ft

Height of the triangle: h=8 ft

A=(6 ft)*(8 ft)/2

A=48 ft^2/2

A=24 ft^2

V=A*H

V=(24 ft^2)*(4 ft)

V=96 ft^3

Answer:

The model that best fits the data is the one with the highest value of [tex]R ^ 2[/tex]. In this case it is the quadratic, with a coefficient of determination [tex]R ^ 2 = 0.9675[/tex].

Step-by-step explanation:

To find the different regression models, the Excel software was used.

For the linear regression model, the following equation was obtained:

[tex]y = 2.0809x + 1.291 [/tex]

with a coefficient of determination [tex]R ^ 2 = 0.8911 [/tex]

For the quadratic regression model, the following equation was obtained:

[tex]y = 0.1663x ^ 2-0.0498x + 4.8229[/tex]

with a coefficient of determination [tex]R ^ 2 = 0.9675[/tex]

Finally, for the exponential regression model, the following equation was obtained:

[tex]y = 4.4281e ^ {0.1513x}[/tex]

with a coefficient of determination [tex]R ^ 2 = 0.9635 [/tex]

The coefficient of determination [tex]R ^ 2[/tex] measures how well a predictive mathematical model fits reality. The value of [tex]R ^ 2[/tex] is always between 0 and 1. The closer you get to 1, the more accurate is the built model.

Therefore, the model that best fits the data is the one with the highest value of [tex]R ^ 2[/tex]. In this case it is the quadratic, with a coefficient of determination [tex]R ^ 2 = 0.9675[/tex]

The results obtained are summarized in the attached table.

To find the best fitting regression model and coefficient of determination, we conduct a regression analysis using the number of practice passes as the input variable and competition passes as the output. Different models fit the data differently, and by comparing the R2 values, we can determine which model is the best fit. This requires either software or a graphing calculator.

The student's question pertains to regression modeling in mathematics, specifically finding the best fit model and coefficient of determination (R2) which quantifies how well the regression model fits the observed data. To determine which model most represents the data between the number of practice passes and competitive passes in question, we must first perform a regression analysis, using the practice passes as the input (x) and the competition passes as output (y).

There are various types of regression models, including linear, exponential, logarithmic, and quadratic, each fitting the data differently. Linear involves a straight line representing the data, while exponential and logarithmic models exhibit curves, and quadratic involves a parabola. Identification of the most suitable model is through comparing R2 values for each model where higher values indicate better fits.

It is important to note that this process generally requires software or a graphing calculator such as Excel, SPSS, R, or a TI calculator. Specific steps may vary depending on the tool used.

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75 : 100 = x : 400

x = 75 * 400 : 100

x = 300

no of lots to be created=4/2/3=12/2=6

To find the answer of this question, you would take 4 acres and divide it by 2/3. This is because the development is 4 acres and is being divided  into a certain number (that we are going to find) of 2/3 acre lots.

So by dividing the area of the neighborhood development lot (4 acres) by 2/3, you would find the total number of 2/3 acre lots that are going to be created.

4 acres / 2/3 acre lots

To divide fractions, you would multiply the fraction by its reciprocal. So your new expression, instead of 4 ÷ 2/3, would be 4 × 3/2.

Multiply straight across.

4 × 3/2 = 12/2 = 6

6 neighborhood development lots can be created by dividing the 4 acre lot into 2/3 acre lots.

22x + 11 = 4x - 7

-4x   -11    -4x -11

18x = -18

X=-1

Hello there!

Solve for x.

[tex]22x+11=4x-7[/tex]

Explanation

↓↓↓↓↓↓↓↓↓↓

First you had to subtract by 11 from both sides of the equations.

[tex]22x+11-11=4x-7-11[/tex]

Simplify

[tex]22x=4x-18[/tex]

Then you subtract by 4x from both sides of the equations.

[tex]22x-4x=4x-18-4x[/tex]

Simplify

[tex]18x=-18[/tex]

Divide by 18 from both sides of the equations.

[tex]\frac{18x}{18}=\frac{-18}{18}[/tex]

Simplify it should be the correct answer.

[tex]x=-1[/tex]

Answer⇒⇒⇒⇒⇒⇒x=-1

Hope this helps!

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Have a great day!

-Charlie

Hey there!!

Given equation :-

... [tex]\frac{2x}{7} + 2 = 5[/tex]

Subtracting 2 on both sides :

... [tex]\frac{2x}{7} = 3[/tex]

Multiplying 7 on both sides :

... [tex]2x = 21[/tex]

Dividing by 2 on both sides :

... [tex]x = \frac{21}{2}[/tex]

Hope my answer helps!!