Match the expression with its
name.

9x^4-3x+4

A. Quadratic monomial
B. Not a polynomial
C. Cubic binomial
D. Fourth-degree trinomial

Answer:

c

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The easiest way is to try and proceed. Let's try solving these two.

Start by dividing the top equation by 3

15x/5 - 3y/3 = - 12/3

3x - y = -4

Add 4 to both sides

3x - y + 4 = -4 + 4

3x - y + 4 = 0                 Add y to both sides

3x + 4 = y

===============

Substitute the right side of the second equation into the 4x + 4 = y equation

3x + 4 = 5x + 7

3x - 3x + 4 = 5x - 3x + 7

4 = 2x + 7                

subtract 7 from both sides

-3 = 2x

Divide by 2

-1.5 = x

y = 5x + 7

y = 5(-1.5) + 7

y = -7.5

y = -0.5

=======

By inspection, you can see that the slopes of the lines are not the same.

You can also see that the slope of the first line is not the negative reciprocal of the slope of the second line.

You can also see that the lines intersect at one point (-1.5,-0.5) so they are not the same line.

Answer C

answer: x= -(7+√33)/4 , x=-(7-√33)/4

The roots of the given equation should be  [tex]x= -(7+\sqrt 33)\div 4 , x=-(7-\sqrt 33)\div 4[/tex]

The equation is [tex]2x^2+7x=-2[/tex]

[tex]2x^2 + 7x + 2 = 0\\\\x = [-7 \pm \sqrt (7^2 - 4\times 2\times 2)] \div 2\times 2\\\\x = -7\div 4 \pm \sqrt (33) \div 4\\\\= (-7 \pm \sqrt33) \div 4[/tex]

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To graph the function y = -x^2 + 4, calculate a set of (x, y) values for the function, plot these points on a graph, and connect them to form a downward-opening parabola.

To make a table of values for the function rule y = -x2 + 4 and then graph the function, we need to choose a range of x values, calculate the corresponding y values and plot these points on a graph.

Here's a possible table of values:

After calculating the values, we plot the points (-2, 0), (-1, 3), (0, 4), (1, 3), and (2, 0) on a graph and draw a curve through these points to visualize the parabola represented by the equation y = -x2 + 4. The graph will be a downward-opening parabola with its vertex at (0, 4).

Answer:

59,000

Step-by-step explanation:

180,000 - 68,000 = 112,000

112,000 - 53,000 = 59,000

59,000 attended the show in Minneapolis

To calculate the Minneapolis concert audience size for Maroon 5, we subtracted the combined audience sizes of Chicago and Milwaukee from the total tour audience, finding the Minneapolis audience to be 59,000 people.

The question revolves around calculating the audience size for Maroon 5's concert in Minneapolis, given the total audience size for a 3-city tour and the audience sizes for two of the cities. Maroon 5 played to at least 180,000 people across three cities, with audiences of 68,000 in Chicago and 53,000 in Milwaukee.

To find the Minneapolis audience size, we subtract the known audience sizes from the total audience size:

Therefore, the audience size for the Minneapolis show was 59,000 people.

Answer:

6 book for $32.16

Step-by-step explanation:

Divide 21.80 by 4 and you will get 5.45

5.45 is the price for each book

Divide 32.16 by 6 and you will get 5.36

5.36 is the price for each book

Answer:

The answer would be the 6 books

Step-by-step explanation:

If you do 21.80 divied by 4 you get 5.45.If you go the same with the 6 books and the number of money you get 5.36.

Angela's earnings are calculated by applying her 7% commission rate to the total sales of $26,300, resulting in her earning $1,841 for the month.

Angela earns money purely through a commission system where she makes a 7% commission on her sales. To calculate Angela's earnings for the month, we first need to apply the commission rate to her total sales. Angela sold $26,300 worth of merchandise.

So, Angela earned $1,841 from her commission for the month.

The variable x represents the total number of days in the total fees equation of “pay upfront” y = 33 + 8x, and “drive now pay later” Y = 18 + 11x.

In other terms, an equation is a mathematical statement stating that "this is equivalent to that." It appears to be a mathematical expression on the left, an equal sign in the center, and a mathematical expression on the right.

Given:

The “pay upfront” car rental company charges an insurance and gas fee of $33,

Daily rental fee = $8 per day,

The “drive now pay later” car rental company charges an insurance and gas fee of $18,

Daily rental fee = $11 per day,

Write the equation for the total fees by “pay upfront” as shown below,

y = 33 + 8x

Here, y is the total fees and x is the number of days,

Write the equation for the total fees by “drive now pay later” as shown below,

Y = 18 + 11x

Here, Y is the total fees and x is the number of days,

Thus, x represents the number of days.

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Final answer:

The variable x represents the number of days a car is rented at two different car rental companies. Calculations can be made to compare total costs based on this variable, determining which company offers the better deal for a given rental period.

Explanation:

Comparing Car Rental Company Costs

The question asks us to interpret the role of the variable x in the context of comparing costs between two different car rental companies, one with the option to pay upfront and the other with the option to drive now pay later. The "pay upfront" company charges a flat fee for insurance and gas at $33, with an additional daily rental fee of $8. On the other hand, the "drive now pay later" company has a lower initial fee for insurance and gas at $18, but a higher daily rental fee of $11. The variable x represents the number of days the car is rented.

To determine which option is more cost-effective, one can set up equations for each company's rental costs in terms of x (the number of days) and compare the total costs. For the "pay upfront" company, the cost equation is C = $33 + $8x. For the "drive now pay later" company, it is C = $18 + $11x. By analyzing these equations, one can determine the breakeven point or compare costs for a specific rental period.

Answer:

2:3. Since there are 3 tops for every 2 bottoms (3:2) you would flip the ratio around so there are 2 bottoms for every 3 tops.

The ratio of bottoms to tops is 2:3.

To find the ratio of bottoms to tops, we can use the information given in the question. Ana wants to have three tops for every two bottoms. This means that for every 2 bottoms, she will have 3 tops. The ratio of bottoms to tops is therefore 2:3.

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Answer:

Deon drove the truck 201 miles.

Step-by-step explanation:

Base Fee + (.98* Number of miles)= Cost

19.99 + .98x = 216.97

Subtract 19.99 from both sides.

.98x = 196.98

Divide both sides by .98

x = 201

Answer:

[tex](x-6)^{2}+(y+16)^{2}=6,400[/tex]

Step-by-step explanation:

we know that

The equation of a circle in standard form is equal to

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

In this problem we have

The center of the radio tower (position) is the point [tex](6,-16)[/tex]

The radius of the radio tower (range) is [tex]r=80\ miles[/tex]

substitute

[tex](x-6)^{2}+(y+16)^{2}=80^{2}[/tex]

[tex](x-6)^{2}+(y+16)^{2}=6,400[/tex]

The standard equation for the radio tower's signal range is (x - 6)² + (y + 16)² = 6400, representing a circle with a center at (6, -16) and a radius of 80 miles.

The student is asking for the equation of a circle that represents a radio tower's signal range on a coordinate grid. Since the radio tower is centered at (6, -16) and has a range of 80 miles, the equation of the circle can be written using the standard form of a circle's equation, which is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. Substituting the given values, the equation becomes (x - 6)² + (y + 16)² = 80².

Answer:

B.(-5,-7)

Step-by-step explanation:

According to the rule of rotation if you were to have a 270* clockwise you would first switch the x and y values. Ex: (-7,5) -> (5,-7). next you would make the original y coordinate a negative. (5,-7) -> (-5,-7).

Solve for x (isolate/get x by itself)

[tex]\frac{1}{4}x-7=\frac{3}{8}x-5[/tex]    Add 5 on both sides

[tex]\frac{1}{4}x-7+5=\frac{3}{8}x-5+5[/tex]

[tex]\frac{1}{4}x-2=\frac{3}{8}x[/tex]   Subtract 1/4x on both sides

[tex]\frac{1}{4}x-\frac{1}{4}x-2=\frac{3}{8}x-\frac{1}{4}x[/tex]

[tex]-2=\frac{3}{8}x-\frac{1}{4}x[/tex]   Make the denominators the same of the fractions in order to combine them. Multiply 2 to the top and bottom of 1/4x

[tex]-2=\frac{3}{8}x-\frac{2}{8}x[/tex]

[tex]-2=\frac{1}{8}x[/tex]    Multiply 8 on both sides

[tex]-2(8)=(8)\frac{1}{8}x[/tex]

-16 = x

87.96+30x<200

Subtract 87.96 from both sides

30x= 112.04

X=3.73

She can buy 3 t shirts

Answer:

3 shirts

Step-by-step explanation:

1. Subtract the cost of tickets (87.96) from the total (200)

    200-87.96 = 112.07

2. Divide 112.07 by the cost per shirt (30)

    112.07 / 30 = 3.74

Since you cannot purchase part of a shirt - she can buy 3 shirts.

Answer with explanation:

 y= |x| -1

|x|=x , if x≥0

and = -x , if x<0.

So,the above function can be written as

 [tex]y=\left \{ {{x-1,for, x\geq 0 } \atop {-x-1,for x<0}} \right.[/tex]

First Drawing the graph of

y= x-1 for, x ≥ 0

And , then , y= -x -1 ,for x <0.

and then combining, the two we get.

Answer:

what they said

Step-by-step explanation:

Answer:

33/65

Step-by-step explanation:

We know that there was a # of even numbers drawn = to 6+10+14+3, which equals 33.

This means, in 65 trials, 33 had even outcomes. This means the experimental probability is 33/65 or approximately 51% (the most precise I could get is 33/65= 0.50769230769)

Answer:

166.66 and 166.67 rounded

Step-by-step explanation:

Answer:

The answer is 166.(666)

Step-by-step explanation:

:D

Answer:

[tex]m=\frac{\sqrt{3}}{2}[/tex]

Step-by-step explanation:

we know that

The tangent of angle theta is equal to divide the opposite side angle theta by the adjacent side angle theta

[tex]tan(\theta)=\frac{m}{(1/2)}=2m[/tex]

[tex]tan(\theta)=\sqrt{3}[/tex]

so

[tex]2m=\sqrt{3}[/tex]

[tex]m=\frac{\sqrt{3}}{2}[/tex]

Answer:

Step-by-step explanation:

Six times a number is greater than 2 less than 4 times the same number.​

n - the number

six times a number: 6n

is greater than: >

2 less than 4 times the same number: 4n - 2

6n > 4n - 2             subtract 4n from both sides

6n - 4n > 4n - 4n - 2

2n > -2         divide both sides by 2

2n : 2 > - 2 : 2

n > -1

Check the picture below.

now, let's recall that running a segment from a midpoint across to a midpoint in a triangle, creates a midsegment, and a midsegment which is parallel to the "base" of the triangle, is always half of that base.

now, noticing the picture on the top-left triangle, we know those points are midpoints, so those in red are midsegments and therefore half the base, to make it short

IC = HE/2 = 7

JB = IC/2 = 3.5

now onto the top-right triangle, which is the same thing just basing itself on its other end

CG = AH/2 = 10

DF = CG/2 = 5

now, let's go to the  picture on the bottom-center

we  know that DG = 4, and since D and G are midpoints, DG is the midsegment of CEH thus

CH = 2DG = 8

likewise, on the green triangle ACH, the midsegment IB is half of the base CH, we know CH = 8, so IB = 4.

Answer:

144°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 10, hence

sum = 180° × 8 = 1440°, thus

each angle measure = 1440° ÷ 10 = 144°

Answer:

Part 18) Option D 100 square meters

Part 19) Option A 60 cubic meters

Part 19) Option C. 212 cubic centimeters

Step-by-step explanation:

Part 18) Estimate the surface area of the prism

we know that

The surface area of the prism is equal to

[tex]SA=2B+PH[/tex]            

where

B is the area of the base

P is the perimeter of the base

H is the height of the prism

Find the area of the base B

[tex]B=3.5*7=24.5\ m^{2}[/tex]

Find the perimeter of the base P

[tex]P=2*(3.5+7)=21\ m[/tex]

we have

[tex]H=2.4\ m[/tex]

substitute

[tex]SA=2(24.5)+(21)(2.4)=99.4\ m^{2}[/tex] ----> exact value

Estimate the surface area

we have

[tex]L=3.5=4\ m[/tex] ----> round up

[tex]W=7\ m[/tex]

[tex]H=2.4=2\ m[/tex] ----> round down

Estimate the area of the base B

[tex]B=4*7=28\ m^{2}[/tex]

Estimate the perimeter of the base P

[tex]P=2*(4+7)=22\ m[/tex]

substitute in the formula

[tex]SA=2(28)+(22)(2)=56+44=100\ m^{2}[/tex]

Part 19) Estimate the volume of the prism

The volume of the prism is equal to

[tex]V=BH[/tex]

we have

[tex]B=3.5*7=24.5\ m^{2}[/tex]

[tex]H=2.4\ m[/tex]

substitute

[tex]V=(24.5)(2.4)=58.8\ m^{3}[/tex] ----> exact value

Estimate the volume

we have

[tex]L=3.5=4\ m[/tex] ----> round up

[tex]W=7\ m[/tex]

[tex]H=2.4=2\ m[/tex] ----> round down

Estimate the area of the base B

[tex]B=4*7=28\ m^{2}[/tex]

substitute in the formula

[tex]V=(28)(2)=56\ m^{3}[/tex]    

Part 20) The volume of the prism is equal to

[tex]V=BH[/tex]

we have

[tex]B=6*6.8=40.8\ cm^{2}[/tex]

[tex]H=5.2\ cm[/tex]

substitute

[tex]V=(40.8)(5.2)=212.16\ cm^{3}[/tex] ----> exact value

Estimate the volume

we have

[tex]L=6\ cm[/tex]

[tex]W=6.8=7\ cm[/tex] ----> round up

[tex]H=5.2=5\ cm[/tex] ----> round down

Estimate the area of the base B

[tex]B=6*7=42\ cm^{2}[/tex]

substitute in the formula

[tex]V=(42)(5)=210\ cm^{3}[/tex]    

Answer: y=1/3x+4

You're welcome

Answer: [tex]x-3y+12.5=0[/tex]

Step-by-step explanation:

From the give en graph , the coordinates of the point marked for library =(7,6.5)

The slope of the Hope road passing from points (0,6) and (3,7) is given by :-

[tex]\text{Slope}=\dfrac{\text{Change in y-coordinate}}{\text{Change in x-coordinate}}\\\\\Rightarrow\ \text{Slope}=\dfrac{7-6}{3-0}=\dfrac{1}{3}[/tex]

Since , a street that passes through the building site and is parallel to the Hope road​, then the slope of the street will be :-

[tex]m=\dfrac{1}{3}[/tex]

[ The two parallel sides have same slopes. ]

Now, the equation of line having slope [tex]m=\dfrac{1}{3}[/tex] and passing through (7,6.5) is given by :-

[tex](y-6.5)=\dfrac{1}{3}(x-7)\\\\\Rightarrow3(y-6.5)=x-7\\\\\Rightarrow\ 3y-19.5=x-7\\\\\Rightarrow x-3y+12.5=0[/tex]

Hence, the equation of a street that passes through the building site and is parallel to the Hope road​  : [tex]x-3y+12.5=0[/tex]

Answer:

Step-by-step explanation:

In the absence of a picture, I will have to assume that the two shorter sides of the triangle are given and are 28" and 15" and that the hypotenuse is unknown.

If that's the case, then we use the Pythagorean Theorem to find the length of the hypotenuse:

28² + 15² = hyp², or

784 + 225 = 1009 = hyp²

Taking the square root of both sides, we get

hyp = 31.8 in

Answer:

third side = 31.8 in

Step-by-step explanation:

Given that two sides of the right angle triangle are 28 in and 15 in.

Now we need to find about what is the third side of the right angle triangle.

So apply the formula of Pythagorean theorem.

[tex](Hypotenuse)^2=(Leg_1)^2+(Leg_2)^2[/tex]

[tex](Hypotenuse)^2=(28)^2+(15)^2[/tex]

[tex](Hypotenuse)^2=784+225[/tex]

[tex](Hypotenuse)^2=1009[/tex]

[tex]Hypotenuse=\sqrt{1009}[/tex]

[tex]Hypotenuse=31.7647603485[/tex]

Which is approx 31.8.

Hence Length of the third side = 31.8 in.

choice B is the correct answer

Answer: the second option is correct

Step-by-step explanation:

Answer:

238

Step-by-step explanation:

let the number of marbles Sam has be x, then

Jim has x + 92 ← 92 more than Sam

After swap of 18 marbles

Sam has x - 18 and sam has x + 92 + 18 = x + 110

Jim now has twice as many as Sam, that is

x + 110 = 2(x - 18)

x + 110 = 2x - 36 ( subtract x from both sides )

110 = x - 36 ( add 36 to both sides )

146 = x

At first Jim had 146 + 92 = 238 marbles

Answer is 27.5

= 92+18

=110 divided by 2

=55

Haha this is wrong

ANSWER

[tex]S_4 = \frac{208}{375} [/tex]

EXPLANATION

The given series is:

[tex]\sum_{n=1}^{\infty} \frac{2}{3} ( - { \frac{1}{5} })^{n - 1} [/tex]

When n=1, the first term is

[tex]a = \frac{2}{3} [/tex]

The sum of terms of a geometric sequence is given by the formula;

[tex]S_n = \frac{a {(1 - {r}^{n} )} }{1 - r} [/tex]

The sum of the first 4 terms is:

[tex]S_4= \frac{ \frac{2}{3} {(1 - { ( - \frac{1}{5} )}^{4} )} }{1 - - \frac{1}{5} } [/tex]

[tex]S_4 = \frac{208}{375} [/tex]

The value for S4 is represented by the third option, [tex]\frac{208}{375}[/tex] .

You can define a geometric sequence when you have a common ratio between the numbers of a sequence. This common ratio can be found when you multiply or divide the previous term by the next term of the sequence and you find the same value. The formula for geometric sequences is:

[tex]a_n=a_1*r^{n-1}[/tex], where:

[tex]a_n[/tex]=[tex]n^{th}[/tex] term

[tex]a_1[/tex]= the first term

Example

2, 4,8, 16, ....

Here, you have:

[tex]a_1[/tex]= 2

[tex]r=\frac{a_2}{a_1}=\frac{a_3}{a_2}=2[/tex] ,  then: 2 x 2= 4; 4 x 2=8; 8 x 2=16 - Note that the numbers represent the example sequence.

For solving this exercise also it is necessary to apply the formula for the geometric sequence for finite terms since the question asks [tex]S_4[/tex], in the other words, the sum for n=4. Thus,[tex]S_n=\frac{a_1*(1-r^n)}{1-r}[/tex].

For the given series, when n=4, you have

                              [tex]\frac{2}{3} *(\frac{-1}{5})^{n-4} \\ \\ \frac{2}{3} *(\frac{-1}{5})^{4-4}\\ \\ \frac{2}{3} *(\frac{-1}{5})^{0}\\ \\ \frac{2}{3} *1=\frac{2}{3}[/tex]

Therefore, [tex]a_1=\frac{2}{3}[/tex].

Now, you will find S4 from the formula for the geometric sequence for finite terms

[tex]S_n=\frac{a_1*(1-r^n)}{1-r}\\ \\ =\frac{\frac{2}{3}\cdot \left(1-\left(-\frac{1}{5}\right)^4\right)}{1-\left(-\frac{1}{5}\right)}\\ \\ \frac{\frac{2}{3}\left(1-\left(-\frac{1}{5}\right)^4\right)}{1+\frac{1}{5}}=\frac{\frac{416}{625}}{\frac{6}{5}}=\frac{416\cdot \:5}{625\cdot \:6}=\frac{208}{375}[/tex]

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Answer: It will take 2 hours. 120 minutes. 4 half-hours.

Answer:

9.3 feet

Step-by-step explanation:

See attachment for the picture.

Let f represent how high up the bird is in the tree.

This side length of the right triangle is opposite the given angle which is 25 degrees.

The side length adjacent to the given angle is 20 ft.

We use the tangent ratio to obtain:

[tex]\tan 25\degree=\frac{opposite}{adjacent}[/tex]

We substitute the values to obtain:

[tex]\tan 25\degree=\frac{f}{20}[/tex]

[tex]f=20\tan 25\degree[/tex]

f=9.3 ft

Therefore the bird is 9.3 feet high up in the tree.

Answer:

The equation of the perpendicular line is y = -x - 2

Step-by-step explanation:

* Lets revise the form of the slope intercept for

- The slope intercept form is y = mx + b, where m is the slope of

  the line and b is the y-intercept

* Now lets revise the relation between the slopes of the

 perpendicular lines

- If two lines are perpendicular, then the product of their slopes is -1

# Ex: If line L has slope m1 and line K has slope m2, and L ⊥ K

∴ m1 × m2 = -1

∴ m2 = -1/m1

* Now lets solve the problem

- We need to find the equation of the line which is perpendicular to

 the line whose equation is y = x + 3 and passes through point (2 , -4)

- Find the slope of the given equation

∵ y = x + 3

- In this form the slope is the coefficient of x

∴ m = 1

- Find the slope of the perpendicular line

∵ The slope of the perpendicular line = -1/m

∴ The slope of it = -1/1 = -1

- Write the equation of the line with the value of the slope

∴ y = -x + b

- To find the value of b substitute x , y in the equation by the x and

  y of the given point

∵ The line passes through point (2 , -4)

∵ y = -x + b

∴ -4 = -1(2) + b

∴ -4 = -2 + b ⇒ add 2 for both sides

∴ b = -2

- Write the equation with the value of b

∴ y = -x - 2

Answer:

A) x=4

Step-by-step explanation:

-We know that the triangles are equal by using Angle-Angle-Side theorem.

-Take one of the triangles.

-We know that the base of the triangle will be 3 on both sides because they are both equal.

-By using the Pythagorean theorem, we can now find the answer for x.

5^2=3^2+x^2

25=9+x^2

subtract 9 from both sides.

16=x^2

To 'undo' the squaring of the x, we need to take the square root on both sides.

[tex]\sqrt{16} =x[/tex]

The answer would be 4 because 4^2 equals 16.

x=4

The correct answer would be x=4