find the prime factorization of 11250

The lengths of the sides of the rectangles are;

a. (2•x + 3) and (x + 2)

b. (6•x + 2) and (x + 1)

c. (x + (2 + √3)) and (x + (2-√3))

The given functions are presented as follows;

a. 2•x² + 7•x + 6

By factoring of the above function we have;

2•x² + 7•x + 6 = (2•x + 3) × (x + 2)

The lengths of the sides of the rectangle are therefore;

b. 6•x² + 7•x + 2

The above function can be factored as follows;

6•x² + 7•x + 2 = (6•x + 2) × (x + 1)

The rectangle side lengths are;

c. x² + 4•x + 1

Using the quadratic formula, the above function can be factored to give;

x² + 4•x + 1 = (x + (2 + √3)) × (x + (2-√3))

The sides of the rectangle are therefore;

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Answer:

look at attached image for the step-by-step proof. thanks for reposting this lol

Let's try solving the problem using the order of operations method, otherwise known as PEMDAS.

[tex]\begin{tabular}{c | l}Order of Operation & Required Operation \\\cline{1-2}1 & Parentheses () \\2 & Exponents e^{x} \\3 & Multiplication \times \\4 & Division \div \\5 & Addition + \\6 & Subtraction -\end{tabular}[/tex]

We are given this question :

[tex]\mathrm {\frac{7}{4} - 9 \div .08 + \frac{4}{5} - 7 \times .8}[/tex]

Since there are no parentheses or exponents, let's multiply.

[tex]\mathrm {\frac{7}{4} - 9 \div .08 + \frac{4}{5} - 5.6}[/tex]

The next step is to divide.

[tex]\mathrm {\frac{7}{4} - 112.5 + \frac{4}{5} - 5.6}[/tex]

After that, add.

[tex]\mathrm {\frac{7}{4} - 112.5 + 0.8 - 5.6}[/tex]

[tex]\mathrm {\frac{7}{4} - 111.7 - 5.6}[/tex]

Finally, subtract the remaining terms.

[tex]\mathrm {1.75 - 111.7 - 5.6}[/tex]

[tex]\mathrm {-109.95 - 5.6}[/tex]

[tex]\mathrm {-115.55}[/tex]

The final answer is -115.55.

I hope this helped solve the problem.

Good luck on your studies!

Answer:

-115.55

Step-by-step explanation:

7/4 -9÷ .08 + 4/5 -7 * .8

I would change fractions to decimals

1.75 - 9 ÷ .08  +.8 -7 * .8

Now using pemdas, multiply and divide from left to right

1.75 -112.5 +.8 -7 * .8

1.75 -112.5 +.8 -5.6

Now add and subtract from left to right

-110.75+.8 -5.6

-109.95-5.6

-115.55

[tex]CD=14.37cm.[/tex]

Find CD:

Let,

[tex]r_{1}[/tex] be a radius of Circle A

[tex]r_{2}[/tex] be a radius of Circle B

Given:

[tex]r=4cm.[/tex]

Circumference: [tex]2\pi r[/tex]

[tex]2\pi r_{1} =20[/tex]

[tex]r_{1} =\frac{10}{\pi }[/tex]

[tex]CD=D_{1} +D_{2}[/tex]

[tex]=2r_{1} +2rx_{2}[/tex]

[tex]=2*(\frac{10}{\pi } )+2*4[/tex]

[tex]CD=14.37cm.[/tex]

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The slope of a line is -2.

The slope of a line can be described as follows:

The slope of a line is a measure of its steepness

Slope = rise / run

slope = y₂ - y₁ / x₂ - x₁

using (0, -4)(-1, -2)

x₁ = 0

x₂ = -1

y₁ = -4

y₂ = -2

Therefore,

slope = -2 - (-4) / -1 - 0

slope = -2 + 4 / -1

slope = 2 / -1

slope = -2

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Answer:

(2, - 1 )

Step-by-step explanation:

3x - y = 7 → (1)

2x + 3y -= 1 → (2)

multiplying ( 1) by 3 and adding to (2) will eliminate y

9x - 3y = 21 → (30

add (2) and (3) to eliminate y

11x = 22 (divide both sides by 2 )

x = 2

substitute x = 2 into either of the 2 equations and solve for y

substituting into (2)

2(2) + 3y = 1

4 + 3y = 1 (subtract 4 from both sides )

3y = - 3 ( divide both sides by 3 )

y = - 1

solution = (2, - 1 )

The equation that Sean woul have solved using the cross multiplication would be option a.

[tex]\frac{10}{x^2-1} =\frac{15}{3x-3}[/tex]

We have to open the equation by using cross multiplication

10(3x - 3) = 15(x² - 1)

= 30x - 30 = 15x² - 15

we would have to factorize

30(x-1) = 15(x-1)(x+1)

We have to divide by 15(x-1)

2 = x + 1

take the like terms

2 -1 = x

x = 1

Hence the equation that has the extraneous solution is option a because the solution is 1.

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Answer:

m<DCF = 155°

Step-by-step explanation:

m<DCF = m<D + m<E

m<DCF = 72° + 83°

m<DCF = 155°

Answer:

4th option

Step-by-step explanation:

given

sinΘ = [tex]\frac{5}{13}[/tex] and cosΘ = [tex]\frac{12}{13}[/tex] , then

( [tex]\frac{5}{13}[/tex] )² + ( [tex]\frac{12}{13}[/tex] )²

= [tex]\frac{25}{169}[/tex] + [tex]\frac{144}{169}[/tex]

= [tex]\frac{25+144}{169}[/tex]

= [tex]\frac{169}{169}[/tex]

= 1

showing sin²Θ + cos²Θ = 1

Solving a linear equation, we conclude that the book has 276 pages in total.

From pages 1 to 9, each page needs one digit, so at this point we have 9 digits.

From page 10 to 99, each one needs 2 digits. Then in these pages we have:

(99 - 9)*2 = 180 digits.

So at this point we have 180 + 9 = 189 pages.

Now, for each page after this point, we will add 3 digits more.

So if there are x pages after this point, the total number of digits will be:;

N = 189 + x*3

Now we need to solve this linear equation for N = 720 digits, then:

720 = 189+ x*3

720 - 189 = x*3

531 = x*3

531/3 = x = 177

So there are 177 pages after page number 99, this means that the book has:

99 + 177 = 276 pages in total.

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2461,8

hope this helps!! just use the formulas and substitute

The corresponding angles are ∠2 and ∠6 i.e., ∠2≅∠6 according to the corresponding angles theorem. So, option 2 is correct.

The theorem states that,

The lines 'AB' and 'CD' are parallel and cut by a transverse 'EF' if and only if their corresponding angles are congruent.

The corresponding angles are those which lie on the same side of the transverse one is interior and the other is an exterior angle.

From the diagram,

Lines 'AB' and 'CD' are parallel and line 'EF' cuts these parallel lines.

So, the corresponding angles formed are:

(∠1, ∠5), (∠2, ∠6), (∠3, ∠7), and (∠4, ∠8)

According to the theorem, they are congruent. I.e.,

∠1 ≅ ∠5

∠2 ≅ ∠6

∠3 ≅ ∠7

∠4 ≅ ∠8

So, option 2 is correct.

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Disclaimer: The given question is incorrect. Here is the correct question.

Question: Lines 'c' and 'd' are parallel lines cut by the transversal 'p'. Which must be true by the corresponding angles theorem?

1) ∠1 = ∠7

2) ∠2 = ∠6

3) ∠3 = ∠5

4) ∠5 = ∠7

The missing dimension in the figure given in the question is 9 ft

Diameter of small circle / Diameter of big circle = Height of small / Height of Big

24 / d = 8 / 36

Cross multiply

d × 8 = 24 × 36

d × 8 = 864

Divide both sides by 8

d = 864 / 8

d = 108 in

Divide by 12 to express in feet

d = 108 / 12

d = 9 ft

Thus, the missing dimension is 9 ft

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If the solids are similar, then their lengths/dimensions are proportional.

24 inches / 8 inches = d / 3 feet

---Cross Multiply

8d = 72

d = 9 feet

Hope this helps!

Using the normal distribution, it is found that the standard deviation is of 26.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem, we have that the mean is of [tex]\mu = 95[/tex], while X = 110 has a p-value of 0.75, hence X = 110, Z = 0.575, and then we solve for [tex]\sigma[/tex] to find the standard deviation.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.575 = \frac{110 - 95}{\sigma}[/tex]

[tex]0.575\sigma = 15[/tex]

[tex]\sigma = \frac{15}{0.575}[/tex]

[tex]\sigma = 26[/tex]

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An equation to describe the relationship between l and r is, as l = r so

5l + 13r = 108.

To find the equation which represents the relationship between l, the number of lilies, and r, the number of roses:

Therefore, an equation to describe the relationship between l and r is, as l = r so 5l + 13r = 108.

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The correct question is given below:

Flannery used 30 lilies and 78 roses to create six identical flower arrangements. Write an equation to describe the relationship between l, the number of lilies, and r, the number of roses.

Answer:

Step-by-step explanation:

r=13/5L

It is true that the graph represents a function

For a graph to represent a function, the following must be true

Each x value on the graph must point to exactly one

The above means that the function must pass the vertical line test

The given graph would pass the vertical line test

This is so because:

Each x value on the graph points to exactly one

Hence, the graph represents a function

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Answer:

[tex] {x}^{4} [/tex]

Step-by-step explanation:

[tex] { {( - x}^{2} )}^{2} = ( - {x}^{2} )( - {x}^{2} ) = {x}^{4} [/tex]

An expression is defined as a set of numbers, variables, and mathematical operations. The value of the given expression when simplified is equal to x⁴.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression can be simplified as shown below,

(-x²)²

= (-x × -x)²

Since the product of two negatives is always positive, therefore, we can write,

= -x² × -x²

As per the rule of exponents, the expression can be written as,

= x⁴

Hence, the value of the given expression when simplified is equal to x⁴.

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The description of this graph tells us that the equation 2x + 3y ≤ 15 was shaded to the bottom while x + y ≥ 3 was shaded to the top as shown in the diagram.

a. The first equation of the graph when it was drawn was shaded to the bottom, while the upper part of the shading has is that of the equation x + y ≥ 3.

b. (5,1) are the solutions for the equation 2x+3y<15. This is given that when x and y are substituted we would still have less than 15.

C The point in the graph would be 2,3. At this point, Michael would be able to buy 2 sandwiches and 3 hot lunches. This is still within his budget for 3 students.

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Answer:

Step-by-step explanation:

2,3 is the anwser

Answer:

382.19cm²

Step-by-step explanation:

a / sin(A) = b / sin(B)

a / sin(68) = 53 / sin(95)

a = (53 x sin(68)) / sin(95)

a = 49.33

area = ½absin(C)

C = 180 - (95 + 68)

C = 180 - 163

C = 17°

area = ½(53)(49.33)sin(17)

area = 382.19cm²

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate, which are the x-axis and y-axis.

In this exercise, you're required to plot a graph for the data (velocity and time) recorded for an object that is falling from rest.

Based on the graph for the data (see attachment), we can logically deduce the following points:

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Complete Question:

Plot a graph for the following data recorded for an object falling from rest

a. What kind of a curve did you obtain?

b. What is the relationship between the variables?

c. What do you expect the velocity to be after 4.5 s?

d. How much time is required for the object to attain a speed of 100 ft/s?

Answer:

a) horizontal compression with a factor of 0.5 and a horizontal reflection over the y-axis.

b) Pick one the two correct answers:

translation of 2 units right

translation of 2 units down

Step-by-step explanation:

If function f(x) is transformed into f(ax) then it is stretched or compressed horizontally.

If |a| > 1 it is compressed horizontally.

If 0 < |a| < 1, it is stretched horizontally.

If a is negative, then it is reflected over the y-axis.

a) Compare y = -2x with y = x.

The change is in that x became -2x.

Here, a = -2.

Since |-2| = 2, and 2 > 1, it has a compression of a factor of 2 horizontally.

Also, since -2 is a negative number, it is reflected over the y-axis.

Answer: horizontal compression with a factor of 0.5 and a horizontal reflection over the y-axis.

If function f(x) is transformed into f(x) + b then it is translated vertically b units. If b > 0, the translation is b units up. If b < 0, the translation is b units down.

b) y = x - 2

This can be thought of the function f(x) becoming f(x) - 2.

It is a translation of 2 units down.

Interestingly, in this case, this can also be thought of x being replaced by x - 2 which is a translation of 2 units to the right.

Answer:

There are two correct answers (use only one of the two below):

translation of 2 units right

translation of 2 units down

Answer:

-(10/7)

Step-by-step explanation:

See attached graphic. The slope of the Green Line is cut off in the problem photo, but can be calculated from the graph to find the slope of the Red Line. The answer options are on drugs; pick the one that looks closest.

Answer:

-4/3

Step-by-step explanation:

The resultant of subtractions of u = <-8, 4> and v = <2, 7> are

-u-v = <6, -11>,

u-v = <-10, -3>,

and v-u= <10,3>.

What is a vector in simple definition?

The resultant of subtractions of u = <-8, 4> and v = <2, 7> are

-u-v = <6, -11>,

u-v = <-10, -3>,

and v-u= <10,3>.

Given that,

The results of the given vector subtractions for u = <-8, 4> and v = <2, 7>.

We have to determine,

The value of -u-v, u-v, and v-u.

According to the question,

The results of the given vector subtractions for u = <-8, 4> and v = <2, 7>.

The value of -u-v is,

-u -v = - < -8 ,4 > - <2,7>

-u -v = <8, -4> - < 2, 7 >

-u - v = < 8 - 2 , -4 - 7 >

-u -v =  < 6 , - 11 >

The value of u-v is,

u -v = < -8 ,4 > - < 2,7 >

u - v = < - 8  - 2, 4 - 7 >

u - v = < 10 ,3>

The value of v - u is,

v - u = < 2 , 7>  - < - 8,4 >

v - u = <  2 + 8 ,  7 - 4 >

v - 4 = <  10 , 3 >

Hence, The resultant of subtractions of u = <-8, 4> and v = <2, 7> are

-u-v = <6, -11>,

u-v = <-10, -3>,

and v-u= <10,3>.

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Answer:

The frame will be 4 inches in width

Step-by-step explanation:

The length of the outside is 24+2x

The width of the outside is 20+2x

(24+2x)(20+2x) - 20(24) = 416

480 + 40x + 48x + 4x2 - 480 = 416

4x2 + 88x - 416 = 0

x2 + 22x - 104 = 0

(x+26)(x-4) = 0

x = -26 or x=4

The frame will be 4 inches in width

The solution to the system of equations is x = 3 and y = 11

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

y equals x plus 8

y equals 3 x plus 2

Rewrite properly as

y = x + 8

y = 3x + 2

Substitute y = x + 8 in y = 3x + 2

x + 8 = 3x + 2

Evaluate the like terms

2x = 6

Divide by 2

x = 3

Substitute x = 3 in y = x + 8

y = 3 + 8

Evaluate

y = 11

Hence, the solution to the system of equations is x = 3 and y = 11

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The solution to the system of equation is as follows:

x = 3

y = 11

y = x + 8

y = 3x + 2

Using substitution method,

3x + 2 = x + 8

subtract x from both sides

3x - x + 2 = x - x + 8

2x + 2 = 8

subtract 2 from both sides

2x + 2 - 2 = 8 - 2

2x = 6

divide both sides by 2

2x / 2  = 6 / 2

x = 3

y = 3 + 8 = 11

y = 11

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The answer is B.

Since ΔQRS ~ ΔXYZ, the value of tan(Q) is :

The assumptions of a regression model can be evaluated by plotting and analyzing the error terms.

Important assumptions in regression model analysis are

Hence we can conclude that the assumptions of a regression model can be evaluated by plotting and analyzing the error terms.

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Answer:

They are the same

Step-by-step explanation:

LA cyl =

[tex]2\pi \: rh[/tex]

SA sphere =

[tex]4\pi {r}^{2} [/tex]

If the sphere is inscribed in the cylinder, they have the same radius. The height of the cylinder is the diameter (Or 2× radius) of the sphere.

If you substitute 2r for h, then both formulas are

[tex] 4\pi{r}^{2} [/tex]

Answer:

120

Step-by-step explanation:

Lets find the numbers multiples of 6 that are in the range from 104-140:

108, 114, 120, 126, 132, 138

Now out of these lets find which is divisible by 15

[tex]\frac{108}{15}=7.2\\\\\frac{114}{15}=7.6\\\\\frac{120}{15}=8\\\\\frac{126}{15}=8.4\\\\\frac{132}{15}=8.8\\\\\frac{138}{15}=9.2[/tex]

120 Is the only solution in this set which is also equally divisible by 15, making it the answer.

From the attached speed versus time graph, it can be seen that the orange or first or car is speeding up. The third or green car is slowing down, and the blue or second car is maintaining a constant speed.

Speed Analysis from the Graph

The graph in the attachment shows the linear increase in speed of the first car over time. Therefore, we can say that it is accelerating at a certain rate.

The graph shows how the speed of the third car is decreasing with time. This demonstrates that the green vehicle is de-accelerating.

The graph shows a straight line for the second car. It displays that the speed does not alter as seconds or minutes pass. We might infer that the blue car is continuing to travel at its current pace as a result.

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Answer:

A C B

Step-by-step explanation:

Which of the cars is speeding up?  

A

Which of the cars is slowing down?  

C

Which of the cars is maintaining a constant speed?  

B