Evaluate the following expression when c = -3 and d= 2: 6/d -10c - c to the fourth  power

Answer:

120 and 90

Step-by-step explanation:

let one number be x and the other y

x + y = 210 (sum = 210)

x - y = 30 (difference = 30)

add the two equations together

2x = 240

divide both sides by 2 to isolate x

x = 120

plug into 1st equation

120 + y = 210

subtract 120 from both sides

y = 90

We take the 2 numbers as 'x' and 'x-30' in order to find those numbers

We plug the values into the given equation

[tex]x + x - 30 = 210\\2x - 30 = 210\\\\2x = 240\\x = \frac{240}{2} \\x = 120\\x - 30 = 120 - 30 = 90\\[/tex]

[tex]120 - 90 = 30[/tex]

Hence , the two numbers are 120 and 90

The amount of syrup she needs is 3/4 cups of syrup. Option A

A fraction can be described as the part of a whole variable, element or number.

The several types of fractions are;

Also, proportion can be defined as a mathematical comparison between two numbers

From the information given, we have that;

6 cups of soap = 1 /4 cup of syrup

Then 18 cups of soap = x cups of syrup

cross multiply, we get;

6x = 18(1/4)

multiply the values

6x = 18/ 4

Divide both sides by the coefficient of x , we get;

x = 18/ 4 × 1/6

x = 3/ 4 cup of syrup

Hence, the value is 3/4

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The 95% confidence interval for the proportion of people who prefer Candidate A is given as follows:

(0.438, 0.522).

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The parameters for this problem are given as follows:

[tex]n = 550, \pi = \frac{264}{550} = 0.48[/tex]

Hence the lower bound of the interval is obtained as follows:

[tex]0.48 - 1.96\sqrt{\frac{0.48(0.52)}{550}} = 0.438[/tex]

The upper bound of the interval is obtained as follows:

[tex]0.48 + 1.96\sqrt{\frac{0.48(0.52)}{550}} = 0.522[/tex]

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Answer:

-4

Sorry if this is wrong.

After evaluating the given expressions the results could be 245 / 89 , 43/6, 33/4 .

What is expression ?

expression can be defined as with the minimum of two variables or numbers and at least one math operation.

Given that ,

7/ 8  * 14  / (3/8 * 6 ) + 2  1/5

= (7/8 * 14 )/ ((18 / 8) + 11/5)

= (98/ 8 ) / (90 + 88) / 40

= (98/ 8 ) /  (178/ 40)

= (98 * 40) / (8* 78)

= 245/89

Hence the final value could be 245/53.

7/ 8  + (6*7/8 - 4 * 3/16 ) / (3/4 )

(7/8 + (21/4 - 3/4 ) )  / (3/4)

(7/8 + 18/4)  / (3/4)

(43/8) / (3/4)

43/6

Hence the final value could be 43/6.

3  1/7  * (3 1/3 * (2/3 + 1/6 ) - 5/18 ) / 2 (3/7)

11/7 * (10/6 - 5/18) / (17/7)

(11/7 )* (27/ 18) /( 17/7)

(11* 27/18 )/ (17)

33/34.

Hence the final value could be 33/34.

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Answer:

what's the question?

Step-by-step explanation:

Step-by-step explanation:

system 1 :

3x + 2y = 7

4x + 7y = 17

system 2 :

12x + 2y = 28

4x + 7y = 17

the first equation in the second system is not a multiple of either equation in the first system, and the second equation in the second system is the same as the second equation in the first system.

thus, the systems are not equivalent.

"12x" gives us the idea what the factor would have to be (4 or 3), if the second equation of the second system would be a multiple of any of the equations in the first system.

as we would have to multiply 3x by 4 to get 12x, and 4x by 3 to get 12x.

but then 2y×4 = 8y, or 2y×3 = 6y, and that is not the same as 2y (part of the first equation of the second system).

that is why this first equation of the second system is not a multiple of either equation in the first system.

and that makes it impossible for both systems to be equivalent. that the second equations are identical, is then not relevant anymore.

Answer: 3/4 is right

Step-by-step explanation:

Answer:

A) Technically he/she can, but they shouldn't really.

B) Yes

C) Yes

D) Yes he/she can but is not necessary to solve the equation

E) Yes

Answer: 800 more hours is required to fly an aircraft

Step-by-step explanation:

Answer:

The objective of the PACER is to run as long as possible while keeping a specified pace. Students run back and forth across a 20-meter space at a pace that gets faster each minute. A point is scored for each 20-meter distance covered. The test is easier in the beginning but progressively gets more difficult.

Step-by-step explanation:

Step-by-step explanation:

the area of a trapezoid is

(a + b)/2 × x

a and b being the 2 bases. and x, as requested, is the height.

A

it does not matter which base is which, as long as we keep using them consistently.

so, let's assume a is the first base :

a = x + 5

and then for the second base

b = 2x - 1

now we use that in the main formula :

(x + 5 + 2x - 1)/2 × x = (3x + 4)/2 × x = (3x² + 4x)/2

A = (3/2)x² + (4/2)x = (3/2)x² + 2x ft²

B

now the height is increased by 4 ft.

that means we need to replace x by x + 4.

(3/2)(x+4)² + 2(x+4) = (3/2)(x² + 8x + 16) + 2x + 8 =

= (3/2)x² + (24/2)x + (48/2) + 2x + 8 =

= (3/2)x² + 12x + 24 + 2x + 8 =

= (3/2)x² + 14x + 32 ft²

with x being the original height, of course.

[tex]8-2z+3(x+y)[/tex] when x is 4, y is 9, and z is 3

Substitute:

[tex]8-2(3)+3(4+9)[/tex]

[tex]8-6+39[/tex]

Solve:

[tex]8-6+39\\=\fbox{23}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{8 - 2z + 3(x + y)}[/tex]

[tex]\mathsf{= 8 - 2(3) + 3(4 + 9)}[/tex]

[tex]\mathsf{= 8 - 6 + 3(4) + 3(9)}[/tex]

[tex]\mathsf{= 8 - 6 + 12 + 27}[/tex]

[tex]\mathsf{= 2 + 12 + 27}[/tex]

[tex]\mathsf{= 14 + 27}[/tex]

[tex]\mathsf{= 41}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{41}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

On solving the provided question we cans ay that -  equation of ellipse is given by (x2/a2) + (y2/b2) = 1.

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

distance of the focus from the centre of the ellipse is given by the equation c = √(a2 – b2).

equation of ellipse is given by (x2/a2) + (y2/b2) = 1.

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The distance between points E(-8, 7) and L(-1, 4) on the coordinate plane is √58 units

An equation shows how two or more numbers and variables are related to each other.

The distance between two points in the coordinate plane is given as:

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

The distance between points E(-8, 7) and L(-1, 4) is:

[tex]EL = \sqrt{(4-7)^2+(-1-(-8))^2}=\sqrt{58}[/tex]

The distance is √58 units

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Answer: 1000 times less

Step-by-step explanation: multiply 0.054x1000

Answer:

1000 times

Step-by-step explanation:

To find how many times less 0.054 is than 54,

we can divide 54 by 0.054.

This gives us 54/0.054 = 1000

This means that 0.054 is 1000 times less than 54.

Solving the provided question, we can say that the quadratic equation is [tex]-16t^2 +vt +s[/tex] so answer is -16+48+3 = 35

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

the quadratic equation is

[tex]-16t^2 +vt +s[/tex]

v = 16

s =3

t =

so answer is -16+48+3 = 35

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The perimeter of the new octagon be 24 feet.

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter.

There are numerous uses in real life for perimeter calculations. The measurement of the fence needed to completely enclose yard or garden is called the perimeter. How far a wheel or circle will roll in one revolution is determined by its circumference, or perimeter.

The length of each side of an octagon is the same. In order to calculate the perimeter of an octagon, multiply 8 by the length of its sides.

Given that the perimeter of an octagon is 27 feet

so the length of its side is 27/8 feet

if the side of the octagon shrink by a scale factor of 8/9

The side of new octagon is (27/8) * (8/9)

The side of new octagon is 3 feet.

So the perimeter of new octagon is 8 * side

⇒ the perimeter of new octagon = 8 * 3 feet

⇒ the perimeter of new octagon = 24 feet

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Answer:

8 hours and 45 minutes.

Step-by-step explanation:

After constructing the frame of the sides 5.25 and sandbox, there is 10 inches of wood left over.

A square is a closed, two-dimensional shape that has four equal sides and four vertices. Parallel to one another are its opposing sides. A square is also equivalent to an equal-length and-width rectangle. A square is a regular quadrilateral with four equal-length sides and four equal-length angles. The square's angles are 90 degrees or at right angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle. A square is a two-dimensional shape with four equal-length sides. A square's opposing sides are parallel to one another, and its four internal angles are all right angles.

given,

The total amount of wood.

= 4 x 65.5

= 262 inches.

Frame:

Side = 5.25 inches

The perimeter of the frame.

= 4 x 5.25

= 21 inches

Now,

Sandbox:

The wood used for the sandbox.

= 11 x 21

= 231 inches

The remaining wood.

= 262 - (21 + 231)

= 262 - 252

= 10 inches

The wood left over after making the frame of sides 5 .25 inches and the sandbox is 10 inches.

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So the person talked for 6 minutes.

The unitary approach involves calculating the value of a single unit, from which we may calculate the values of the necessary number of units.

Two quantities are compared to form a ratio. An equality of two ratios is a percentage. How to format a ratio Analyze the ratio to see whether it is part to part or part to whole. Calculate the whole and the pieces as necessary.

To solve this problem, we can use the following equation:

Cost = (Number of minutes x $0.31) + $0.89 + $1.23

We know that cost is $6.15 and the call lasted 6 hours. Since there are 60 minutes in an hour, we can convert the time in hours to minutes by multiplying 6 hours by 60 minutes/hour

So the number of minutes is 6 hours * 60 minutes/hour = 360 minutes

Now we can substitute the values into the equation:

Cost = (360 minutes x $0.31) + $0.89 + $1.23

Cost = $111.6 + $0.89 + $1.23

Cost = $113.72

The equation does not match the $6.15 cost, which means that the person talked for 6 minutes

So the person talked for 6 minutes.

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Answer:

112.5 miles

Step-by-step explanation:

scale: 1 inch= 35 miles

this means that for every inch on a map, that is 35 miles in real life.

if the distance on a map is 3.5 inches, and you want to find out how much the distant would be in real life, all you have to do is:

3.5 x 35 = 112.5

Answer:

3.945

Step-by-step explanation:

Answer:

226a³b² - 824ab³ + 984b⁴

Step-by-step explanation:

We can factorize the given expression by expanding the two binomials and then combining like terms.

First, expand the two binomials:

10ab (a − 2b)³ +24ab² (3a − 6b)² = 10ab(a³ - 6a²b + 12ab² - 8b³) + 24ab²(9a² - 36ab + 36b²)

Then, combine like terms:

= 10ab(a³ - 6a²b + 12ab² - 8b³) + 24ab²(9a² - 36ab + 36b²)

= (10a³b - 60a²b² + 120ab³ - 80b⁴) + (216a³b² - 864ab³ + 864b⁴)

= (10a³b + 216a³b² - 60a²b² - 864ab³ + 120ab³ + 864b⁴ - 80b⁴)

= (10a³b + 216a³b² - 60a²b² - 864ab³ + 120ab³ + 864b⁴ - 80b⁴)

= (10a³b - 60a²b² + 120ab³ - 80b⁴) + (216a³b² - 864ab³ + 864b⁴)

= (10a³b + 216a³b² - 60a²b² - 864ab³ + 120ab³ + 864b⁴ - 80b⁴)

= (10a³b - 60a²b² + 120ab³ - 80b⁴) + (216a³b² - 864ab³ + 864b⁴)

= 226a³b² - 824ab³ + 984b⁴

The difference between the expansions of (A + B)^2 and (A - B)^2 is the sign of the middle term. In the second case it is negative, due to the negative sign on B.

Here we have two perfect square trinomials, these are:

(A + B)^2

(A - B)^2

Notice that the only difference between these is the sign of the second element.

Now we can expand these two expressions as:

(A + B)^2 = (A + B)*(A + B) = A^2 + 2AB + B^2

The second expression gives:

(A - B)^2 = (A - B)*(A - B) = A^2 + 2*A*(-B) + (-B)^2

                                       = A^2 - 2AB + B^2

There we can see that the only difference between these two expansions is the sign of the middle term. Where in the second case it is negative, due to the negative sign on B.

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Given ,

To Find : The Circumference of a circle

Radius can be the determined by the formula

[tex]r = \frac{d}{2} \\r = \frac{18}{2} \\r = 9yd[/tex]

Now we can apply the formula of the circumference of a circle which is,

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

[tex]Circumference = 2X3.14X9[/tex]

[tex]Circumference = 56.52[/tex]

Hence , the Circumference of a circle is 56.52yd

The time to build the fence will be 10 hours.

The fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since construction company is building a fence that is 1 1/3 miles long and they can building the fence 1/6 Mile every hr.

The time to build the fence will be:

= 1 1/3 ÷ 1/6

= 5/3 × 6/1

= 30 / 3

= 10 hours.

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