A construction crew has just finished building a road. The road is 10 kilometers long. If the crew worked for 4 2/3 days, how many kilometers of road did they build each day? (Assume they built the same amount each day.)

For this case we must find the value of "x" that meets the following equation:

[tex]\frac {4} {3} = x + \frac {10} {15}[/tex]

We subtract [tex]\frac {10} {15}[/tex] on both sides of the equation:

[tex]\frac {4} {3} - \frac {10} {15} = x\\\frac {15 * 4-3 * 10} {3 * 15} = x\\\frac {60-30} {45} = x\\- \frac {30} {45} = x[/tex]

We simplify:

[tex]x =\frac {6} {9}=\frac{2}{3}[/tex]

Finally, [tex]x =\frac {2} {3}[/tex]

Answer:

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

For this case we have the following quadratic equation:

[tex]-2x ^ 2 -6x + 5 = 0[/tex]

Where:

[tex]a = -2\\b = -6\\c = 5[/tex]

The roots will be given by the following formula:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]

Substituting the values we have:

[tex]x = \frac {- (- 6) \pm \sqrt {(- 6) ^ 2-4 (-2) (5)}} {2 (-2)}\\x = \frac {6 \pm \sqrt {36 + 40}} {- 4}\\x = \frac {6 \pm \sqrt {76}} {- 4}\\x = \frac {6 \pm \sqrt {2 ^ 2 * 19}} {- 4}\\x = \frac {6 \pm2 \sqrt {19}} {- 4}\\x = \frac {3 \pm \sqrt {19}} {- 2}[/tex]

We have two roots:

[tex]x_ {1} = \frac {-3- \sqrt {19}} {-2}\\x_ {2} = \frac {-3+ \sqrt {19}} {2}[/tex]

Answer:

[tex]x_ {1} = \frac {-3- \sqrt {19}} {2}\\x_ {2} = \frac {-3+ \sqrt {19}} {2}[/tex]

Answer:

This is just a relation.

Step-by-step explanation:

It is easy to see if a set of ordered pairs is a relation or a relation that is a function.

If all the points are distinct, then you just have to look at the [tex]x[/tex]-coordinates.

If all the [tex]x[/tex]-coordinates are different, then it is a function. Otherwise, it is a just a relation.

So this cannot be a function because there is at least two different points that have [tex]x=0[/tex].

Answer:

f(x) = x³ + x² - 5x + 3

Step-by-step explanation:

The cubic polynomial has zeros at 1, 1, - 3.

Therefore, x = 1, 1, - 3 are the roots of the polynomial and hence, (x - 1), (x - 1) and (x + 3) will be factors of the cubic polynomial.

Hence, we can write the polynomial as a function of x as

f(x) = (x - 1)(x - 1)(x + 3)

⇒ f(x) = (x² - 2x + 1)(x + 3)

⇒ f(x) = x³ - 2x² + 3x² + x - 6x + 3

⇒ f(x) = x³ + x² - 5x + 3

So, this is the cubic polynomial function in standard form. (Answer)

Answer:

[tex]A(x)=7x^2-2x+10[/tex]

Step-by-step explanation:

Long Division

The polynomial long division implies the sequential division of each term of the dividend polynomial by the terms of the divisor polynomial. The procedure is a well-know sequence of steps from which there are two outputs: the quotient and the remainder.

We have two mathematical models, one for the total number of visitors who went to a theme park:

[tex]F(x)=126x^3+279x^2+90x+450[/tex]

The other for the number of shows played at the theme park in the same period

[tex]G(x)=18x+45[/tex]

Where x is the number of days since October 1. We are required to find the expression for the average number of visitors per show. It comes by dividing F(x) by G(x). We must perform a long division as shown  below.

The average number of visitors per show is

[tex]A(x)=7x^2-2x+10[/tex]

For example, day 5

[tex]A(5)=7\ 5^2-2(5)+10=175[/tex]

There were 175 visitors per show (on average)

Explanation:

The equation is already in standard form.

A is 1. The number 1 is often unwritten.

B is -3. The negative or positive sign is included with the equation.

C is -6. (If using this for the quadratic formula, c is actually 6 because the equation should equate to 0).

Multiply the miles per gallon by the total gallons:

32.4 x 12.7 = 411.48 total miles.

Answer:

411.48

Step-by-step explanation:

411.48

Answer:

w=3 9\17

Step-by-step explanation:

Answer:

There is No Solution for the equation.

Step-by-step explanation:

Given:

[tex]-2x+9-3x=-5x+3[/tex]

We need to find number of solutions for above equation.

Now Solving the equation we get;

[tex]-5x+9=-5x+3[/tex]

Now adding both side by 5x we get;

[tex]-5x+9+5x=-5x+3+5x\\\\9=3[/tex]

Which can't be true.

Hence There is No Solution for the equation.

Answer:

6 × 35

2×3×5×7

6 × 15

2×3×3×5

So your least common multiple is 2

Answer: 2

Step-by-step explanation:

Answer:

6 × 35

2×3×5×7

6 × 15

2×3×3×5

So your least common multiple is 2

Answer: The graph is a parabola facing up ,

Step-by-step explanation:

Since the coefficient of [tex]x^{2}[/tex] is positive , then the graph is a parabola facing up.

The minimum point is at x = -2 ( using the formula for calculate vertex , x = [tex]\frac{-b}{2a}[/tex] )

And the y - intercept = 4

The correct mathematical expression for eight times the difference of 4 and a number is 8(4 - n), where 'n' is the variable representing the number.

The expression that represents eight times the difference of 4 and a number can be written as 8(4 - n), where 'n' represents the number in question. In this expression, '4 - n' is the difference between 4 and the number, and by multiplying this difference by eight, we are following the order of operations where the subtraction within the parentheses is performed first before the multiplication.

Answer:

Step-by-step explanation:

p = peaches, m = mangos

1.75p + 1.50m = 22

m = p + 6

1.75p + 1.50(p + 6) = 22

1.75p + 1.50p + 9 = 22

1.75p + 1.50p = 22 - 9

3.25p = 13

p = 13 / 3.25

p = 4 <====== she bought 4 peaches

m = p + 6

m = 4 + 6

m = 10 <===== she bought 10 mangos

check...

1.75p + 1.50m = 22

1.75(4) + 1.50(10) = 22

7 + 15 = 22

22 = 22 (correct)

The number of peaches and the number of mangos that Savannah bought

are 4 and 10 respectively.

The variable use to write the equation is x and it is the number of peaches

Savannah and her children bought

let

the number of peaches Savannah and her children bought = x

Therefore

the number of mangoes Savannah and her children bought = x + 6

The total worth of what they bought = $22

Therefore,

1.75x + 1.50(x + 6) = 22

1.75x + 1.50x + 9 = 22

3.25x + 9 = 22

3.25x = 22 - 9

3.25x = 13

x = 13 / 3.25

x = 4

Therefore,

number of peaches bought = 4

number of mangoes bought = 4 + 6 = 10

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Answer:

46 centimetres tall

Step-by-step explanation:

Since Donte is 138cm tall and his height is three times that of his dog; his dog's height is 138cm/3 = 46cm tall.

Therefore, Donte's dog is 46cm tall.

Answer:

b.) Triangle 7 has a 40 degree angle and a 35 degree angle. Triangle 8 has a 40 degree angle and a 105 degree angle.

Step-by-step explanation:

b.) triangle 7's 3 angles: 40° , 35° and 180° - 40° - 35° = 105°

    triangle 8: 40° , 105° and 180° - 40° - 105° = 35°

they have all 3 corresponding angles congruent, triangle and triangle 8 is similar (AAA)

Answer:

b.) Triangles 7 and 8 are similar.

Step-by-step explanation:

If triangles have the same angle measurements, they are similar

If we have two angles, we can find the third by using the equation 180 (total of all angles in any triangle) - angle 1 -angle 2 = angle 3.

Let's set up this value with values from triangle 7.

180-40-35=angle 3

105=angle 3

Thus, the angle measurements of triangle 7 are 35, 40, anf 105.

Let's set up the same equation with value for triangle 8.

180-40-105=angle 3

35=angle 3

Thus, the angle measurements of triangle 8 are 35, 40, anf 105, the same as those of triangle 7, meaning the two triangles are similar.

Answer:

4,2,0,-1

Step-by-step explanation:

Let

x ----> the independent variable or input value

y ----> the dependent variable or output value

we have the ordered pairs

(-1,2),(-3,-1),(6,0),(-1,4)

The input values are -1,-3,6,-1

The output values are 2,-1,0,4

Orders the output values from greatest to least

4>2>0>-1

therefore

4,2,0,-1

Answer:

4,2,0,-1

hope this helps

In this question, we're trying to find out how much Jamal spent on apples.

We know that he bought 2 pounds of red apples and 3.2 pounds of green apples.

We also know that each pound of apples, no matter what kind it is, are $1.65 a pound.

In order to find the total cost of these apples, we would need to multiply the amount of pounds he has to the cost per pound.

Solve:

2 · 1.65 = 3.3‬0

3.2 · 1.65 = 5.28‬

Add those numbers together:

5.28‬ + 3.30 =  8.58‬

This means that Jamal spent $8.58‬ on apples.

Answer:

$8.58‬

Answer:

$8.58‬

Step-by-step explanation: this ok?

Answer: Jamie is incorrect

Step-by-step explanation:

The same number 10 is subtracted from both numbers 19 and 20. There result will only be the same if both numbers are equal.

We compare both numbers;

19 and 20

On the number line 19 comes before 20, which means 20 is greater than 19. Hence the result of subtracting the same number 10 from both of them cannot be the same.

So Jamie is incorrect.

Answer:

she is wrong 19-10 equals to 9

Step-by-step explanation:

you subtract 19 from 10 and get 9:)

Answer:

C

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

Given

y = 2x² - 8x + 9

The coefficient of the x² term must be 1, so factor out 2 from 2x² - 8x

y = 2(x² - 4x) + 9

To complete the square

add/ subtract ( half the coefficient of the x- term)² to x² - 4x

y = 2(x² + (- 2)x + 4 - 4) + 9

   = 2(x - 2)² - 8 + 9

   = 2(x - 2)² + 1 → C

The given quadratic equation y = 2x^2 - 8x + 9 can be rewritten into vertex form by completing the square, resulting in y = 2(x - 2)^2 + 5.

The given equation y = 2x2 - 8x + 9 can be rewritten in vertex form by completing the square for the -8x term. The vertex form of a quadratic equation is y = a(x - h)2 + k, where (h,k) is the vertex of the parabola.

First, we need to divide the coefficient of the x term, which is -8, by 2 to get -4. Then, we square this result to get 16.

This should be inserted into the equation to complete the square, however, we must also take it out again in order to not change the equation. The new equation will be y = 2(x2 - 4x + 16) - 2*16 + 9 = 2(x - 2)2 + 5.

The correct answer then is B. y = 2(x - 2)2 + 5

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Answer:

The area of the hexagon is 108 cm².

Step-by-step explanation:

Consider the below figure attached with this question.

From the below figure we get

Length of rectangle = 12 cm

width of rectangle = 5 cm

It is given both triangles are identical.

Base of each triangle = 12cm

Height of each triangle = (13-5)/2 = 4 cm

Area of rectangle is

[tex]Area=length\times width=12\times 5=60[/tex]

Area of rectangle is

[tex]Area=\frac{1}{2}\times base\times height[/tex]

[tex]Area=\frac{1}{2}\times 12\times 4=24[/tex]

Area of one triangle 24 cm². So, area of both triangle is

[tex]2\times 24=48[/tex]

Area of hexagon = Area of rectangle + Area of both triangles

                            = [tex]60+48[/tex]

                            = [tex]108[/tex]

Therefore, the area of the hexagon is 108 cm².

By finding the areas of the rectangle and the two triangles separately and adding them together, we determine that the area of the hexagon is 125 cm².

To find out the area of the hexagon, you would need to find the areas of the rectangle and the triangles separately, and then add them together. The rectangle's area can be calculated easily using the formula for the area of a rectangle: Length x Breadth.

Assuming the rectangular part length to be 13cm and breadth to be 5cm, area of rectangle = 13cm x 5cm = 65cm².

The two triangles appear to be right triangles. You can use the formula for the area of a right triangle: 0.5 x Base x Height.

Assuming the base and height of the triangles to be 12cm and 5 cm, therefore the area of one triangle is 0.5 x 12cm x 5cm = 30cm². Since there are two of these triangles, their combined area = 2 x 30cm² = 60cm².

Finally, combining the areas of the rectangle and triangles equals the area of the hexagon: 65cm² + 60 cm² = 125 cm².

The area of the hexagon is

125 cm²

.

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Answer:

Amount of juice left over is 1.5 cups.

Step-by-step explanation:

Given:

Amount of juices Grace has = 6 cups

Number of friends = 8

She divides the juice equally among her friends.

Now we will first find Amount of juice each friend will have.

Amount of juice each friend will get can be calculated by dividing Amount of juices with total number of friends.

Framing in equation form we get;

Amount of juice each friend will have = [tex]\frac{6}{8}= \frac{3}{4}\ cups \ \ \ OR \ \ \ \ 0.75\ cups[/tex]

Number of friends who do not drink = 2

Amount of juice left will be equal to Number of friends who do not drink multiplied by Amount of juice each friend will have.

Framing in equation form we get;

Amount of juice left = [tex]2\times \frac{3}{4} = \frac{3}{2} \ cups \ \ \ \ OR \ \ \ \ 1.5\ cups[/tex]

Hence Amount of juice left over is 1.5 cups.

Answer:

Option D. x=-2.5

Step-by-step explanation:

we have

[tex]-2x-3=3^x+2[/tex]

I can divide the expression above in a system of two equations

[tex]y=-2x-3[/tex] ----> equation A

[tex]y=3^x+2[/tex] ----> equation B

Solve by graphing

The solution is equal to the x-coordinate of the intersection point both graphs

using a graphing tool

The intersection point is ( -2.5,2.1)

see the attached figure

therefore

The solution is x=-2.5

Answer:

D) -2.5

Step-by-step explanation:

Answer:

5 more of the sum would be + 5 to the final answer you are adding

Step-by-step explanation:

Answer: 1/9

Step-by-step explanation:

Total number of cards = 6

Probability = required outcome/ all possible outcome

number of kings=4

number of jack=1

Probability of drawing a king = 4/6

probability of drawing a jack = 1/6

Probability of drawing a king and then a jack is p(king and jack) = p(king) × p(jack) = 4/6 × 1/6 = 4/36

= 1/9

Answer:

1/9

thats all

Step-by-step explanation:

Answer:

[tex]\therefore \textrm{Area of Trapezoid }= 70x^{3}y^{2}\ cm^{2}[/tex]

Step-by-step explanation:

Given:

Shape is of Trapezoid

Height = 14xy² cm

Length 1 = 3x² cm ( one Parallel side)

Length 2 = 7x² cm ( other Parallel side)

To Find:

Area of Trapezoid = ?

Solution:

We know that

[tex]\textrm{Area of Trapezoid }= 0.5(length\ 1+length\ 2)Height[/tex]

substituting the given values we get

[tex]\textrm{Area of Trapezoid }= 0.5\times(3x^{2}+7x^{2})\times 14xy^{2}[/tex]

[tex]\textrm{Area of Trapezoid }= (10x^{2})7xy^{2}[/tex]..((x^{a}x^{b}=x^{(a+b)})

[tex]\therefore \textrm{Area of Trapezoid }= 70x^{3}y^{2}\ cm^{2}[/tex]

Answer:

32=2(10+x)

32=20+2x

2x=12

x=6

therefore breadth is 6 cm

area=l×b

10×6=60

Step-by-step explanation:

Answer:

  9

Step-by-step explanation:

The first simplification we can make is to replace 6^0 with 1.

The first rules of exponents we can apply are ...

  (a·b)^c = a^c·b^c . . . . . . similar to the distributive property

  (a^b)^c = a^(b·c)

This reduces your expression to ...

  [tex](2^8\cdot 3^{-5})^{-2}\cdot\left(\dfrac{3^{-2}}{2^3}\right)^4\cdot 2^{28}=2^{8(-2)}\cdot 3^{-5(-2)}\cdot\dfrac{3^{-2(4)}}{2^{3(4)}}\cdot 2^{28}\\\\=2^{-16}\cdot 3^{10}\cdot\dfrac{3^{-8}}{2^{12}}\cdot 2^{28}[/tex]

Now we can apply another two rules of exponents:

  (a^b)(a^c) = a^(b+c)

  1/a^b = a^-b

Using these, we have ...

  [tex]=2^{-16-12+28}\cdot 3^{10-8}\\\\=2^0\cdot 3^2\\\\=1\cdot 9=9[/tex]

The value of the expression is 9.

Answer:

y = -2/3 x + 1/3

Step-by-step explanation:

Use the slope-intercept linear formula: y = mx + b

x and y represent point on the line

m is the slope

b is the y-intercept

The equation of the line requires "m" and "b". We already have "m".

Substitute point (-4, 3) and slope -2/3 into the formula. x=-4; y=3; m=-2/3. Find b by isolating the variable.

y = mx + b

3 = (-2/3)(-4) + b   Simplify

3 = 8/3 + b     Subtract 8/3 from both sides

b = 1/3

Put b = 1/3 into the formula.

y = -2/3 x + 1/3

Answer:

6.39

Step-by-step explanation:

6.39

Answer:

6.39

Step-by-step explanation:

When dividing by 10 you can always just move the decimal place once to the left.

Glad I was able to help!!