Use the x-intercept method to find all real solutions of the equation.
x^3-8x^2+17-10=0

Answer:

The width of the rectangle is [tex]5xy^3[/tex].

Step-by-step explanation:

The area of a rectangle is the product of length and width of the rectangle.

[tex]A=length\times width[/tex]

It is given that the area of the rectangle is [tex]15x^3y^4[/tex] square meters and the length of the rectangle is [tex]3x^2y[/tex].

[tex]15x^3y^4=3x^2y\times width[/tex]

[tex]width=\frac{15x^3y^4}{3x^2y}[/tex]

[tex]width=\frac{3\times 5\times x^2\times xy^3\times y}{3x^2y}[/tex]

Cancel out common factors 3x²y.

[tex]width=5xy^3[/tex]

Therefore the width of the rectangle is [tex]5xy^3[/tex].

Answer: Option 'c' is correct.

Step-by-step explanation:

Since we have given that

Number of students who are interested in being on the team = 9

Number of positions to fill on his basket ball team = 3

So, the combinations of the three positions he can choose for the team is given by

[tex]3\times 9=27[/tex]

Hence, Option 'c' is correct.

The coach can choose 84 different combinations of the three positions from 9 interested students for the basketball team.

The coach needs to choose 3 out of 9 students to fill the positions on his basketball team. This is a combination problem, and the number of ways to choose [tex]\( r \)[/tex] items from [tex]\( n \)[/tex] items is given by the combination formula:

[tex]\[ C(n, r) = \frac{n!}{r!(n-r)!} \][/tex]

Here, [tex]\( n = 9 \) (number of students) and \( r = 3 \)[/tex] (number of positions to fill).

[tex]\[ C(9, 3) = \frac{9!}{3!(9-3)!} \][/tex]

[tex]\[ C(9, 3) = \frac{9!}{3!6!} \][/tex]

[tex]\[ C(9, 3) = \frac{9 \times 8 \times 7}{3 \times 2 \times 1} \][/tex]

[tex]\[ C(9, 3) = \frac{504}{6} \][/tex]

[tex]\[ C(9, 3) = 84 \][/tex]

So, the coach can choose from 84 different combinations for the team positions.

The correct answer is:

B: 84

Answer:

Greece had a larger difference ($7.07)

Step-by-step explanation:

Brazil -

18.33 - 12.25 = 6.08

Greece-

16.55 - 9.48 = 7.07

Answer:

Greece has the larger difference between categories

Step-by-step explanation:

Difference in categories of Brazil

[tex]= 18.33 - 12.25\\= 6.08\\[/tex]

Difference in categories of Greece

[tex]= 16.55 - 9.48\\= 7.07\\[/tex]

Thus, Greece has the larger difference between categories

Answer:

PLEASE GIVE BRAINLIEST

Step-by-step explanation:

30% + 25% =55%

55/100 = 11/20

Answer:

12.=0.06

13. =-5.12

14. =0.5

Step-by-step explanation:

12. .1 + .2 -.3 x.4/.5

.1+.2 -.12/.5

.1+.2-.24

.3-.24=.06

13. 3.2^2

10.24-15.36=-5.12

14. 4.2 x5/6 /10 +3/20

3.5 / 10 + 3/20

0.35+3/20

7/20+3/20=10/20

0.5

Answer:

(a)

let m represents renting movie and c represents the total cost of buying a rental card.

As per the given statement: A video store charges $10 for a rental card plus $2 per movie.

⇒ c(m) = 2m + 10                      ......[1]

which implies that this equation represents the slope intercept form(i.e y = ax+b) where 2 is the slope and a y-intercepts of 10.

(b)

Graph of the given equation:

c(m) = 2m + 10

you can see in the figure given below.

(c)

now, to find the cost of buying a rental card and renting 6 movies.

⇒ m = 6 [ as m represents renting movie]

Substitute this m =6 in equation [1];

c(6) = 2(6) + 10

c(6) = 12 + 10

c(6) = 22.

Therefore, the total cost of buying a rental card and renting 6 movies is, $22.

Answer:

[tex]\frac{C}{2\pi } =r[/tex]

Step-by-step explanation:

Recall to find the circumference of a circle the formula is [tex]C=\pi d[/tex] or [tex]C=2\pi r[/tex]. Since we need r, we will use the second formula for circumference.

We start by solving for r in the Circumference formula. using inverse operations. We divide both sides (as the inverse of multiply) by 2pi.

[tex]C=2\pi r\\\frac{C}{2\pi } =r[/tex].

Answer: C

Step-by-step explanation:

Answer:

976 421; 124 679

Step-by-step explanation:

Part A. Largest number

Leslie's number was 976 421.

This is because the largest numbers are in the positions of largest value.

For example, 9 in the hundred thousands place, the next largest number in the ten thousands place, and so on.

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

Part B. Smallest number

The smallest possible number is 124 679.

The value of the 4 is greater than the value of the 6 because the 4 is in the thousands place and the 6 is only in the hundreds place.

4000 > 600.

Answer:

Estimate is 150 and actual product is 138.

Step-by-step explanation:

To estimate products, we round the numbers to nearest unit place, 10th, 100th, 1000th, and so on.

Given are the numbers 3 and 46.

We can round 46 ≈ 50.

So Estimation would be 3 x 46 ≈ 3 x 50

3 times 5 is 15 and we can add zeros after it.

So estimation is 3 x 46 ≈ 150.

Now actual product would be...

3 times 6 is 18, so we note down 8 and 1 goes to carry over 4.

3 times 4 is 12 and carry 1 will be added in it, so 12 + 1 = 13.

It means the actual product is 3 x 48 = 138.

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have the points (3, 5) and (4, 6). Substitute:

[tex]d=\sqrt{(4-3)^2+(6-5)^2}=\sqrt{1^2+1^2}=\sqrt{1+1}=\sqrt2\approx1.4[/tex]

The distance between the two points is 1.4.

Option D is the correct answer.

The distance between two points of a line is given as:

Distance =  √(c - a)² + (d - b)²

We have,

To find the distance between the two points (3, 5) and (4, 6)

We can use the distance formula:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Substituting the given values, we get:

d = √((4 - 3)² + (6 - 5)²)

d = √(1² + 1²)

d = √2

To the nearest tenth, the distance is approximately 1.4.

Therefore,

The distance between the two points is 1.4.

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Answer: Two sides are 7in, and the two other sides are 9.5 in.

Step-by-step explanation:

Since there are two sides that will be longer than the other two, 2.5 will be subtracted twice:

33in -2.5in -2.5in = 28in

Since there are 4 sides, 28in is divided by 4:

28in/4 = 7in

To find the 2 larger sides, add 2.5 back to the side length:

7in +2.5in = 9.5in

Parallelogram is a closed shaped quadrilateral in which the opposite sides are equal and parallel. The length of the parallelogram tile of the shorter side is 7 in and the length of the longer side is 9.5 in.

A store sells tiles in the shape of a parallelogram.

The perimeter of each tile is 33 inches.

One side of each tile is 2.5 inches longer than another side.

Parallelogram is a closed shaped quadrilateral in which the opposite sides are equal and parallel. As the opposite sides are equal in parallelogram thus the perimeter of the parallelogram is twice the sum of the two different sides.

Let l be the length of the shorter side. Thus longer side will be (2.5+l ).

Now the perimeter [tex]P[/tex] of the parallelogram tile can be given as,

[tex]P=2[l+(2.5+l)}[/tex]

[tex]33=4l+5[/tex]

[tex]4l=33-5[/tex]

[tex]l=\dfrac{28}{4}[/tex]

[tex]l=7[/tex]

Thus the length of the parallelogram tile of the shorter side is 7 in and the length of the longer side is 9.5 in.

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Answer:

Linear

Step-by-step explanation:

This can be written in slope intercept form (y=-5x+7) and there are no exponents.

[tex]\dfrac{o+4m+p}{6}=e\qquad\text{multiply both sides by 6}\\\\o+4m+p=6e\qquad\text{subtract o and 4m from both sides}\\\\\boxed{p=6e-o-4m}[/tex]

Answer:

X^2 y

Step-by-step explanation:

So now you can make this x^2 y because the ^3 cancels it out

Answer:

x^6/27y

Step-by-step explanation:

(x^2/3y^1/3)^3

x^2 ^3/  (3^3 y^1/3 ^3)

Using the power of power rule, when a power is raised to a power, we multiply the powers.

x^ (2*3)/ (3^3 y^(1/3*3))

x^6/(27 y^1)

x^6/27y

To find the perimeter of a rectangle in terms of x, add up the length and width and multiply by 2.

The perimeter of a rectangle can be found by adding up all four sides. In this case, the length and width of the rectangle are represented by the factors of the area measure:

10x² + 13x - 3 = (2x - 1)(5x + 3)

So the length is (2x - 1) and the width is (5x + 3). The perimeter can be calculated using the formula:

Perimeter = 2(length + width)

Substituting the values, the perimeter in terms of x is:

Perimeter = 2((2x - 1) + (5x + 3))

Simplifying further:

Perimeter = 2(7x + 2)

Perimeter = 14x + 4

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Answer:

6-y

Step-by-step explanation:

Six less than y means you take away y from six.

Hope this helps

Answer:

The cost of soft pretzel is $1.25

Step-by-step explanation:

Let $x be the price of one slice of pizza and $y be the price of one soft pretzel.

1. 9 slices of pizza cost $9x and 5 soft pretzels cost $5y. Together they cost $33.25, then

9x+5y=33.25.

2. 4 slices of pizza cost $4x and 6 soft pretzels cost $6y. Together they cost $19.50, then

4x+6y=19.50.

3. Solve the system of two equations:

[tex]\left\{\begin{array}{l}9x+5y=33.25\\4x+6y=19.50\end{array}\right..[/tex]

Multiplythe first equation by 4, the second equation by 9 and subtract them:

[tex]4(9x+5y)-9(4x+6y)=4\cdot 33.25-9\cdot 19.50,\\ \\36x+20y-35x-54y=133-175.5,\\ \\-34y=-42.5,\\ \\y=\$1.25.[/tex]

Then

[tex]4x+6\cdot 1.25=19.50,\\ \\4x=19.50-7.50,\\ \\4x=12,\\ \\x=\$3.[/tex]

Answer: Each soft pretzel cost $1.25

Step-by-step explanation:

Hi, we have to write an equation for each case:

9 x + 5 y = 33.25

4x +6 y = 19.50

Where x is the price of 1 slice of pizza, and y is the price of each soft pretzel.

Multiplying the first equation by 4, and the second equation by 9

36x +20y =133

36x +54y =175.5

And subtracting the first equation to the second equation

36x +54y =175.5

-

36x +20y =133

____________

34 y = 42.5

Solving for y  

y =42.5/34

y = $1.25

Each soft pretzel cost $1.25

Answer:

a ≠ 2b

Step-by-step explanation:

The given expression is

[tex]\frac{8ab^{2}x}{4a^{2}b-8ab^{2}}[/tex]

[tex]=\frac{8ab^{2}x}{4ab(a-2b)}[/tex]

Simplifying it, we have

[tex]\frac{8ab^{2}x}{4a^{2}b-8ab^{2}} = \frac{bx}{a-2b}[/tex]

For the above fraction to exist, the denominator must not be equal to zero.

i.e, a-2b ≠ 0

=> a≠2b

∴ The algebraic fraction exists when a≠2b.

Answer:

A valid exclusion for the algebraic fraction is when a=2b

Step-by-step explanation:

You have:

[tex]8ab^2x/4a^2b-8ab^2[/tex]

First you must to simplify:

Taking out common factor 4ab

[tex]4ab(2bx)/4ab(a-2b)[/tex]

[tex]2bx/a-2b[/tex]

The fraction can be written only if  the denominator is different to zero, then

a-2b[tex]\neq[/tex]0

the excluded values are where  

a-2b=0

this expression is equal to 0 when a=2b

Answer:

Option B - {(-3, 16), (0, 15), (3, 14)}

Step-by-step explanation:

Given : Equation [tex]\frac{1}{3}x+y=15[/tex].

To find : Which if the following are ordered pairs of this equation?

Solution :

Re-write the equation in linear equation format,

[tex]y=-\frac{1}{3}x+15[/tex]

Taking point, (-3,16)

We substitute x=-3,

[tex]y=-\frac{1}{3}(-3)+15[/tex]

[tex]y=1+15[/tex]

[tex]y=16[/tex]

It is true.

Taking point, (0,15)

We substitute x=0,

[tex]y=-\frac{1}{3}(0)+15[/tex]

[tex]y=0+15[/tex]

[tex]y=15[/tex]

It is true.

Taking point, (3,14)

We substitute x=3,

[tex]y=-\frac{1}{3}(3)+15[/tex]

[tex]y=-1+15[/tex]

[tex]y=14[/tex]

It is true.

Therefore, the ordered pairs are {(-3, 16), (0, 15), (3, 14)}.

So, option B is correct.

The completed table would look like this:

Snack Type                Number Sold                 Percentage

Fruit Cup                          6                        18.75%

Veggie Sticks                         6                        18.75%

Chips                                 14                        43.75%

Water                                 4                          12.5%

Veggie Sticks:

Look at the "number of items sold" column for veggie sticks. It shows 6.

Divide the number of veggie sticks sold by the total number of snacks sold (32) and multiply by 100% to find the percentage.

(Number of veggie sticks) / (Total number of snacks) * 100%

= 6 / 32 * 100%

= 0.1875 * 100%

= 18.75% (round to two decimal places)

Chips:

Look at the "number of items sold" column for chips. It shows 14.

Follow the same steps as for veggie sticks:

(Number of chips) / (Total number of snacks) * 100%

= 14 / 32 * 100%

= 0.4375 * 100%

= 43.75% (round to two decimal places)

Water:

Look at the "number of items sold" column for water. It shows 4.

Follow the same steps as for veggie sticks and chips:

(Number of water bottles) / (Total number of snacks) * 100%

= 4 / 32 * 100%

= 0.125 * 100%

= 12.5% (round to two decimal places)

Therefore, the completed table would look like this:

Snack Type Number Sold Percentage

Fruit Cup 6 18.75%

Veggie Sticks 6 18.75%

Chips 14 43.75%

Water 4 12.5%

For complete question refer to image:

Answer:$5.1

Step-by-step explanation: so since theres the 1 in 1.2 we know we have $3.40 right?, yeah so, half of $3.40 is 1.7 so jus add $1.7 to $3.40 wich is $5.1

Answer: (B) a=3, b=3

Step-by-step explanation:

   [tex]\dfrac{(2xy)^4}{4xy}[/tex]

[tex]=\dfrac{2^4x^4y^4}{4xy}[/tex]

[tex]=\dfrac{16x^4y^4}{4xy}[/tex]

[tex]=4x^{4-1}y^{4-1}[/tex]

[tex]=4x^3y^3[/tex]

Answer:

b

Step-by-step explanation:

Answer:

10.8

Step-by-step explanation:

7.2 X 1.5 = 10.8

Assuming  two houses are 1.5 inches apart on the map. The actual distance between the houses is 10.8 miles.

Let x represent the actual distance

Given:

1 inch = 7.2 miles

1.5 inch =? miles

Hence:

1/ 7.2 = 1.5/ x

x= 7.2×1.5

x=10.8 miles

Inconclusion assuming  two houses are 1.5 inches apart on the map. The actual distance between the houses is 10.8 miles.

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Answer: 3(7+q)

Step-by-step explanation:

Answer:

The simplified form of [tex]3(2+q) + 15[/tex] is 3(7+q)

Step-by-step explanation:

Given: 3(2+q) + 15

Step 1: Multiply bracket with 3

[tex]=3\times (2+q)+15[/tex]

Step 2: Now combine like terms

[tex]=6+15+3q[/tex]

Step 3: Add the combined terms

[tex]=21+3q[/tex]

Step 4: taking 3 common :

[tex]=3(7+q)[/tex]

The simplified form of [tex]3(2+q) + 15[/tex] is 3(7+q)

Answer:

Before cooling begins, the temperature of the water is 22°C.

Step-by-step explanation:

I think this is right

Answer:

Before cooling begins, the temperature of the water is 22°

22

°

C

.

Step-by-step explanation:

Answer:

she has a 70 percent chance of getting a yellow one

Step-by-step explanation:

Answer:

7/10 is your answer.

Answer:

slope =4

Step-by-step explanation:

The slope intercept equation of a line is written in the form

y= mx+b

where m is the slope and b is the y intercept.

Since y =4x+5 is written is this form, we can see that 4 is the slope and 5 is the y intercept

Answer:

D: y=2|x|-1

Step-by-step explanation:

We need to find the equation which describes the graph

The general form of equation for this graph is y=|x|

The graph opens upwards so its positive

We cannot choose option (a) and option (d) because it has -2

Lets check with option b  and d

In the graph, the y values starts at -1. (0,-1) is the vertex.

Lets plug in (0,-1)  and check with option b

y=2|x|+1

-1= 2|0|+1

-1=+1, its false.

Lets check with option (d)

y=2|x|-1

-1= 2|0|-1

-1=-1, its true

Option D is the answer

Answer: If the rate of change is $1 = 78p, then if you have 160p, how much dollars you will get?

(if p are penys)

100p = 1 pound

if $1 = 78p = 0.78 pound

→ 1  pound = $1/0.78 = $1.28

→ 160*1 pound = $160/0.78 = $205.13

So if you change 160 pounds, you will get 205 dollars and 13 cents.

The number of dollars when 160 pounds is exchanged will be 205.13.

You may multiply the pounds by the exchange rate to get how many dollars you will receive for 160 pounds if the exchange rate is $1 = 78p.

160 pounds multiplied by the 78p to the dollar conversion rate results in:

160 pounds multiplied by 100 pence equals 16,000 pence.

Since there are 100 pence in a pound, we divide the amount in pence by 100 to get dollars:

16,000 p divided by 78p is $205.13

Consequently, if you convert 160 pounds to dollars at the current exchange rate of $1 = 78p, you will get around 124.80 dollars in return.

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20 cents per apple

1/5=.20