The sum of 8 and three times a number is 41

Answer:

[tex]2x^{4} - 3x^{2} + 7x[/tex]

Step-by-step explanation:

Simplifying the given polynomial expression is; -(1/4)x³ - (7/2)x² + (214/16)x + (7/2)

We want to simplify the polynomial expression;

((1/2)x + 2)((1/2) - 2x) + ((1/4)x + (7/2))

Let us expand the first bracket to get;

((1/2)x * (1/2) + (2 * (1/2)) - ((1/2)x * 2x) - (2 * 2x))

⇒ (1/4)x + 1 - x² - 4x

⇒ 1 + (15/4)x - x²

Thus, our expression is now;

(1 + (15/4)x - x²)((1/4)x + (7/2))

This can be multiplied out to give;

(1/4)x + (15/16)x - (1/4)x³ + (7/2) + (105/8)x - (7/2)x²

= -(1/4)x³ - (7/2)x² + (107/8)x + (15/16)x + (7/2)

= -(1/4)x³ - (7/2)x² + (214/16)x + (7/2)

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The number of cabinets that can be placed along the wall is 15.

It should be noted that in this scenario, we simply have to calculate the perimeter.

This will be:

= 2(length + width)

= 2(1 1/2 + 6)

= 2(7 1/2)

= 15

Therefore, the number of cabinets that can be placed along the wall is 15.

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The equation for the sentence 10 more than p is -3" will be B. p + 10 = -3.

It should be noted that an equation illustrates the relationship between the variables that are given.

In this case, the equation for the sentence 10 more than p is -3" will be:

p + 10 = -3

p = - 3 - 10

p = -13

The value of P is -13.

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Answer:

to extend over or past and cover a part of The roof shingles overlap each other. 2 : to have something in common with Baseball season overlaps the football season in September. 1 : to occupy the same area in part The two towns overlap.

Step-by-step explanation:

i would need a photo of the lines to find the values of other angles

The direction of the resultant vector is 58 degrees east-north if the mouse walks 15 m east, makes a 90° left turn, walks 8 m, makes another 90° left turn, and walks 10 m.

It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.

It is given that:

A mouse is trapped in a maze.

He walks 15 m east, makes a 90° left turn, walks 8 m, makes another 90° left turn, and walks 10 m.

Based on the data given:

tanA = 8/(-10+15) = 8/5

A = tan⁻(8/5)

A = 58 degrees

The direction will be 58 degrees east-north

Thus, the direction of the resultant vector is 58 degrees east-north if the mouse walks 15 m east, makes a 90° left turn, walks 8 m, makes another 90° left turn, and walks 10 m.

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Answer:

[tex](1, -1)[/tex] and [tex](-\frac{1}{5}, \frac{7}{5})[/tex]

In decimal form this would be (1, -1) and (-0.2, 1.4)

Step-by-step explanation:

Basically here we are trying to solve a system of 2 equations. The first one is a straight line and the second is a circle. This can be done graphically and graph is attached. There will be two points where the line cuts the circle so two solution sets

The equations are

Line Equation [tex]y = 1 - 2x[/tex]    (1) and

Circle Equation [tex]x^2+ y^2 = 2[/tex]   (2)

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

Plug this value of y into the second equation for the circle
[tex]x^2 + (1-2x)^2= 2[/tex]

Apply the perfect squares formula [tex]\left(a-b\right)^2=a^2-2ab+b^2[/tex]

[tex](1-2x)^2 = 1^2-2\cdot \:1\cdot \:2x+\left(2x\right)^2\\= 1-4x+4x^2\\\\[/tex]

So equation (2) becomes
[tex]1-4x+4x^2 +x^2 = 2 \\\\\\5x^2 -4x - 1 = 0[/tex]

Solve using the quadratic formula
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Here a is the coefficient of x ², b is the coefficient of x and  c is the constant

So
[tex]x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:5\left(-1\right)}}{2\cdot \:5}[/tex]

Now,

[tex]\sqrt{\left(-4\right)^2-4\cdot \:5\left(-1\right)} = \sqrt{\left(-4\right)^2+4\cdot \:5\cdot \:1}[/tex]

= [tex]\sqrt{16+20} = \sqrt{36} = 6[/tex]

Therefore
[tex]x_{1,\:2}=\frac{-\left(-4\right)\pm \:6}{2\cdot \:5}[/tex]

[tex]x_1=\frac{-\left(-4\right)+6}{2\cdot \:5}[/tex] = [tex]\frac{-\left(-4\right)+6}{2\cdot \:5} =[/tex]  [tex]\frac{10}{2\cdot \:5}[/tex] [tex]= 1[/tex]

[tex]x_2 = \frac{-\left(-4\right)-6}{2\cdot \:5}[/tex] [tex]= \frac{4-6}{2\cdot \:5}[/tex] = [tex]-\frac{1}{5}[/tex]

To find corresponding values for [tex]y_1 y_2[/tex] plug these values of [tex]x_1, x_2[/tex] into the line equation

[tex]y_1 = 1- 2(1) = -1[/tex]
[tex]y_2 = 1 - 2(-\frac{1}{5}) = 1 + \frac{2}{5} = \frac{7}{5}[/tex]

So the two points of intersection are

[tex](1, -1)[/tex] and ([tex](-\frac{1}{5}, \frac{7}{5})[/tex].

In decimal form this would be (1, -1) and (-0.2, 1.4)

See attached graph

Using it's concept, the average rate of change of the function on the interval [0,2] is of -1.5.

Before going into the average rate of change, the other items are correct.

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

For the interval [0,2], we have that:

Hence the rate is:

r = (0 - 3)/(2 - 0) = -1.5.

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first of all let's recall that on the negative side of the number line, the closer to 0, the greater, so -1 is much greater than -1,000,000.

well, let's simply try to convert both fractions to the same denominator by multiplying top and bottom by 1 or namely the same value, hmmm let's multiply -2/3 by 2/2 = 1, and -1/2 by 3/3 = 1

[tex]-\cfrac{2}{3}\cdot \cfrac{2}{2}\implies -\cfrac{4}{6}\hspace{5em}-\cfrac{1}{2}\cdot \cfrac{3}{3}\implies -\cfrac{3}{6}[/tex]

well, rats, no much wiggling room there, well, let's simply multiply them again by 1, in this case hmmmm 2/2 for both

[tex]-\cfrac{4}{6}\cdot \cfrac{2}{2}\implies \boxed{-\cfrac{8}{12}}\hspace{5em}-\cfrac{3}{6}\cdot \cfrac{2}{2}\implies \boxed{-\cfrac{6}{12}} \\\\\\ \underset{-\cfrac{2}{3}}{\boxed{-\cfrac{8}{12}}}\hspace{5em} < \qquad -\cfrac{7}{12}\qquad < \hspace{5em} \underset{-\cfrac{1}{2}}{\boxed{-\cfrac{6}{12}}}[/tex]

Answer: 1/2 * n

1 hour of practice in 2 days

2 hours of practice in 4 days

5 hours of practice in 10 days

Step-by-step explanation:

60 minutes=1 hour

30 minutes * 1 hour/60 minutes=

30*1/60=

30/60=1/2 hour.

1/2 * n

1/2 * 2 = 1 hour of practice in 2 days

1/2 * 4 =

4/2 = 2 hours of practice in 4 days

1/2 * 10=

10/2 = 5 hours of practice in 10 days

Answer:

Step-by-step explanation:try using quizlet

Based on the numbers given, we can say that 51 is a multiple of 3.

51 is not a prime number which means that it has factors and it is a multiple of several numbers.

The factors of 51 include:

1, 3, 17, and 51

Out of the numbers given of 2,3,5,6,9,10, it therefore means that 51 is a multiple of only one number which is 3. When 3 is multiplied by 17, it gives 51.

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Answer:

[tex]p ≤6[/tex]

Step-by-step explanation:

Inequality: [tex] - 4p +36 ≥2p[/tex]

Collect like terms

→ [tex] - 4p - 2p≥ - 36[/tex]

→ [tex] - 6p≥ - 36[/tex]

Divide both sides by -6

→ [tex] \frac{ - 6p}{ - 6}≤\frac{ - 36}{ - 6} [/tex]

Therefore: [tex]p ≤6[/tex]

Answer:

Evan could be thinking of 200,000.

Step-by-step explanation:

The digit 2 in 328,907 has values 20,000 so in Evan's number it has the values 200,000.

Answer:

30

Step-by-step explanation:

150/5 = 30

Answer: 30

Step-by-step explanation:

Based on the fact that the model has a scale of 1/12, solving the equation of 12x = 86 to determine the tons of the completed sculpture gives 7 tons.

The model is said to have a scale of 1/12 of the original stone landmark which means that if the original famous landmark weighs 86 tons, the tons of the model can be found by the formula:

12x = 86

When solving for x which is the tons of the completed sculpture, the weight would be:

12x = 86

x = 86 / 12

x = 7 tons

In conclusion, the completed sculpture would weigh 7 tons.

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The slope of the line having points (3,135), (5,225), and (7,315) is 45

Slope:

The ratio of how much y grows as x grows by a certain amount is known as a line's slope. The slope of a line indicates how steep it is, or how much y rises as x rises. Anywhere along the line, the slope remains constant (the same).

The formula of slope for a line(m)=[tex]\frac{y2-y1}{x2-x1}[/tex]

Given the points  (3,135) , (5,225) and (7,315)

Consider any two points, Let's say  (3,135) and (5,225).

Slope=[tex]\frac{225-135}{5-3}[/tex]

Slope=45

Therefore, The slope of the line having points (3,135), (5,225), and (7,315) is 45

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In linear equation, S = x2 + 36/x  the surface area S of the box as a function of the length x of one of the sides.

What in mathematics is a linear equation?

Let x = length of the sides of the base, and h = the height.  The volume is given as 9 m3

Volume = area of base * height

9 = x2*h

So 9/x2 = h

The surface area, S, of the box is:

S = (Area of Base) + 4*(Area of a Vertical Side)

S = x2 + 4 * (xh)

Substitute 5/x2 in place of h:

S = x2 + 4 * x * (9/x2)

S = x2 + 36/x

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Answer:

One pen is $4.25 and one pencil is $1.85.

Step-by-step explanation:

Let cost of pens be x and cost of pencils be y.

1. 4x+3y=22.55

2. 3x+2y=16.45

Sub. 1.-2.,

x+y=22.55-16.45

x=6.1-y

Sub. x=6.1-y into 1.,

y=1.85

x=4.25

Answer:

Cost of a box of pens = $4.25

Cost of a box of pencils = $1.85

Step-by-step explanation:

Given information:

Define the variables:

Create two equations from the given information:

[tex]\textsf{Equation 1}: \quad 4x + 3y = 22.55[/tex]

[tex]\textsf{Equation 2}: \quad 3x + 2y = 16.45[/tex]

Multiply Equation 1 by 3:

[tex]\implies 3 \cdot 4x + 3 \cdot 3y = 3 \cdot 22.55[/tex]

[tex]\implies 12x + 9y = 67.65[/tex]

Multiply Equation 2 by 4:

[tex]\implies 4 \cdot 3x + 4 \cdot 2y = 4 \cdot 16.45[/tex]

[tex]\implies 12x + 8y = 65.80[/tex]

Subtract the equations to eliminate the term in x:

[tex]\begin{array}{r rr}& 12x+9y = &67.65\\- & 12x+8y = &65.80\\\cline{2-3} & y = & 1.85\end{array}[/tex]

Substitute the found value of y into one of the equations and solve for x:

[tex]\implies 3x + 2y = 16.45[/tex]

[tex]\implies 3x + 2(1.85) = 16.45[/tex]

[tex]\implies 3x + 3.7 = 16.45[/tex]

[tex]\implies 3x =12.75[/tex]

[tex]\implies x=4.25[/tex]

Solution

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Answer:

Step-by-step explanation:

6.92

Answer:

a) The probability that Jim wins is 0.56.

b) The probability that Henry wins is 0.44.

Step-by-step explanation:

Hope this helps!

Answer:

22 and 23

Step-by-step explanation:

The first step is to make an equation that models this problem. Since the two numbers are consecutive, make them [tex]x[/tex] and [tex]x+1[/tex].

Since it says three times the larger number is 47 more than the smaller number, that means

[tex]3 (x+1) = x+47[/tex]

[tex]3x+3 = x+47[/tex]

[tex]2x+3=47[/tex]

[tex]2x=44[/tex]

[tex]x=22[/tex]

The smaller number is 22, and the larger number is 23.

Answer:

1 cm : 12.5 m

Step-by-step explanation:

Answer: 1250000:1

Step-by-step explanation:

Scale factor: 50 km/4 cm=25 km/2 cm

25 km/2 cm=

(25 * 1000 m)/(2 * 1/100 m)=   ==> convert to common measurement which is meters.

(25000 m)/(2/100 m)=

(25000*100 m)/(2*100/100 m)=

2500000 m/2 m=1250000/1

The sum of the expression in simplest form is 8( x + 2y)

Algebraic expressions are expressions made up of variables, terms, factors, constants and coefficients.

They are also made up of mathematical operations such as addition, subtraction, multiplication, division, etc

Given the expressions;

(3x+9y) and (5x+7y)

Let's find the sum

3x + 9y + 5x + 7y

collect like terms

3x + 5x + 9y + 7y

8x + 16y

Find common factor

8( x + 2y)

Thus, the sum of the expression in simplest form is 8( x + 2y)

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Answer:

x - intercept; (80, 0)

y - intercept; (0, ∞)

Step-by-step explanation:

Let Week be w and Amount be A;

We see an inverse proportionality;

[tex]{ \rm{w \: \alpha \: \frac{1}{A } }} \\ \\ { \rm{w = \frac{m}{A} }}[/tex]

m is a constant of proportionality;

When w is 1, A = 68

[tex]{ \rm{ 1 = \frac{m}{68} }} \\ \\ { \rm{m = 68}}[/tex]

Therefore;

[tex]{ \tt{w = \frac{68}{A} + c }} \\ [/tex]

c is a constant;

When w is 0, A is 80

[tex]{ \rm{0 = \frac{68}{80} + c}} \\ \\ { \rm{c = - \frac{17}{20} }}[/tex]

Overall equation:

[tex]{ \rm{y = \frac{68}{x} + \frac{17}{20} }} \\ [/tex]

For x-intercept, y = 0

[tex]{ \rm{ \frac{17}{20} = \frac{68}{x} }} \\ \\ { \rm{x = 80}}[/tex]

For y-intercept, x = 0

y = ∞

The length and width of the rectangle is 23 and 11 cm.

Given, perimeter = 68 cm

A rectangle's perimeter P is determined by the equation P=2l+2w, where l is the rectangle's length and w is its width. In the formula A=lw, where l is the length and w is the width, the area A of a rectangle is determined.

let the width of the rectangle be x.

and length of the rectangle be 12 ₊ x

Formula of the perimeter = 2l ₊ 2w

68 = 2(12 ₊ x) ₊  2x

68 = 2x ₊ 24 ₊ 2x

68 ₋ 24 = 4x

44 = 4x

x = 44/4

x = 11

Hence the width of the rectangle is 11 cm and length:

12 ₊ x

= 12 ₊ 11

= 23 cm

Hence we get the length and width of the rectangle as 23 and 11 cm.

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