An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 100 grams of an alloy containing 35% copper with 60 grams of an alloy containing 55% copper.
Answer the questions below. Do not do any rounding.
(a) How many grams of copper are in the resulting mixture?
(b) What percentage of the resulting mixture is copper?

The lines which are skewed in the rectangular prisms shown are Line QT (↔QT) and Line WX(↔WX).

What is skew in geometry?

This refers to two lines that do not cut across (intersect)  each other and are not parallel to each other. the pair of lines must also be opposite edges of the shape. The lines are not also lying or acting in the same plane. i.e non-coplanar.

How to identify skew lines?

a) Locate lines that do not intersect each other.

b)Find out if these pairs of lines are also not parallel to each other.

c) Examine if these non-intersecting and non-parallel lines are non-coplanar.

If yes then the chosen pair of lines are skew lines.

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Step-by-step explanation:

1. if to rewrite the given equation, then

y= -3(x+5)²+1;

2. the vertex of the parabola is (-5;1) and it is the highest point. Then

3. domain: x is any value, x∈(-∞;+∞);

range: y not greater than 1, y∈(-∞;1].

For the parabola f(x) = -3x² - 30x - 74, the domain is all real numbers (-∞, ∞), and the range is also all real numbers (-∞, ∞).

To determine the domain and range of the given parabola f(x) = -3x² - 30x - 74, we need to understand the behavior of parabolas.

The domain of a function represents all the possible x-values for which the function is defined. In this case, there are no restrictions on the x-values for the given quadratic function. Therefore, the domain is all real numbers, expressed as (-∞, ∞).

The range of a function represents all the possible y-values that the function can produce. For a parabola, if the coefficient of the squared term (in this case, -3) is negative, the parabola opens downward. Since the coefficient is negative, the parabola will have a maximum value. In this example, there is no minimum or maximum specified; thus, the range will also be all real numbers.

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The set of side measurements that could be used to form a triangle are 8, 14, 20.

The concept that will be used is the concept of triangle inequality theorem.

To know if the given 3 side lengths are a triangle, then the use of the  triangle inequality theorem comes into play.

This rule tells us that when we sum 2 sides of a triangle  the value must be greater than the third side.

Then this rule can be applied as

The first option; 8, 14, 20

a+b>c  = 8+14>20

a+c>b  =  8+20>14

b+c>a   = 20+14>8

Therefore, first option is correct.

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Answer:

38.88in²

Step-by-step explanation:

Area of shaded region = Area of square - Area of semi circle

First lets find the area of the square and semi circle

Area of square = s²

Where s = side length

Here we have a given side length of 8in

So s = 8

This means area = 8² = 64in²

Area of semicircle = (πr²)/2

Where r = radius

Here, the side length of the square and the diameter of the semicircle is shared meaning they are congruent. This means the diameter of the semicircle = 8in

To convert from diameter to radius we simply divide by 2

So radius = 8 / 2 = 4

Now we have Area = (πr²)/2

==> plug in r = 4 and π = 3.14

Area = (3.14(4)²))/2

==> simplify exponent

Area = (3.14(16))/2

==> multiply 3.14 and 16

Area = 50.24/2

==> simplify division

Area = 25.12in²

Area of shaded region

We now subtract the two areas

Area of shaded region = Area of square - Area of semi circle

Area of square = 64in² and Area of semicircle = 25.12in²

Area of shaded region = 64in² - 25.12in² = 38.88in²

Answer:

130 in standard form
100+30 in expanded form

Step-by-step explanation:

standard from is writing the sentence in a number fro example
three hundred seventy two is writen as 372 in standard for
expanded form is 300+70+2

Answer:

130 in standard form

In expanded form is100+30=1300

Step-by-step explanation:

For further example 4236

In standard form is 4236

In expanded form is 4000+200+30+6=4236

Answer:

x would be 3 by 2

I am 90% sure but I hope this helps!

Answer:

540 cm₂

Step-by-step explanation:

       [tex]\sf \boxed{Area = (b_1+b_2+b_3)*l + bh}\\\\[/tex]

[tex]\sf \text{where $b_1$, $b_2$ and $b_3$ are the sides of the triangle l is the length of the rectangle}\\\\ \text{and b is the base of the triangle and h is the altitude of the triangle}[/tex]

    b₁ = 12 cm ; b₂ = 5 cm ; b₃ = 13 cm

   l = 16 cm  ;  b = 12 cm and h = 5 cm

Area  = (12 + 5 + 13)*16 + (12*5)

          = 30*16 + 60

          = 480 + 60

          = 540 cm²

Answer:

dd

Step-by-step explanation:d

Answer:

Step-by-step explanation:

a0 - x-y=3

The area of the hula hoop is equal to 450π square inches.

A hula hoop is a toy with the form of a circle, whose area (A), in square inches, has to be found. The area of a circle is described by the following formula:

A = 2π · R²

Where R is the radius of the hula hoop, in inches.

If we know that R = 15 inches, then the area covered by the hula hoop is:

A = 2π · (15 in)²

A = 450π in²

The area is equal to 450π square inches.

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Answers:

1 yard by 72 yards

4 yards by 18 yards

6 yards by 12 yards

8 yards by 9 yards

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

Explanation:

Let's list out all the ways to multiply to 72 using two values

1*72

2*36

3*24

4*18

6*12

8*9

Then cross off something like 2*36 since 2 is prime. We also cross off 3*24 since 3 is prime.

We're left with this list

1*72

4*18

6*12

8*9

which represent the possible dimensions of this rectangle.

Keep in mind that 1 is not prime.

The error in the volume of the cube is gotten as; ±120 in³

In this type of situation, there could be maximum error, relative error and percentage error.

The maximum error is gotten by differentiating the volume equation.

The relative error is gotten by dividing the change in volume by the volume likewise change in length.

The percentage error is just converting the relative error to percentage. Thus;

Thus;

Volume of a cube is given by the formula;

V = x³

dV/dx = 3x²

dV = 3x²(dx)

We are given dx = 1/10

Thus;

dV = ±(3 * 20² × (1/10))

dV = ±120 in³

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Suban need to leave $10000 investment in the bank at 5% per year simple interest for 10 years so that it grows to $15000

According to question,

Principal (P) = 10,000

Rate of interest (I) = 5%

Interest = Amount - Principal

= 15000 - 10000

= 5000

We need to find the number of years

T = ?

Interest = P * R * T / 100

5000 = 10000 * 5 * T / 100

T = 10 years

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Answer:

y=3x+1

y=-17

Step-by-step explanation:

y=3x+1

7=3(2)+1

7=6+1

7=7

y=3(-6)+1

y=-18+1

y=-17

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Part a

The equation for the way Michelle is paid is

Total weekly payment y = 495.50 + 0.105x

Part b

The total payment in a  month = $4021.625

She makes a 10.5% commission on every kayak she sells

Consider the total value of kayaks she sold = x

The rate of commission = 10.5%

The amount of commission = x × (10.5/100)

= 0.105x

The weekly fixed payment = $495.50

Total weekly payment y = 495.50 + 0.105x

Part b

The total value of the kayaks she sold = $19425

Total number of weeks in a month = 4

Then the total payment in a month = (4 × 495.50) + (0.105×19425)

= 1982 + 2039.625

= $4021.625

Hence,

part a

The equation for the way Michelle is paid is

Total weekly payment y = 495.50 + 0.105x

Part b

The total payment in a  month = $4021.625

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Answer:

5/16

Step-by-step explanation:

This is a geometric sequence

aₙ=a₁*rⁿ⁻¹

a₆=10*.5⁶⁻¹

a₆=10*.5⁵

a₆=10*(1/2)⁻⁵

a₆=10*1/32

a₆=10/32=5/16

Answer:

Step-by-step explanation:

Instead you do 45 divided by 8

And you will get 5.625

The time taken by Ashley and Laura to meet each other is 3 hrs

The speed of an object tells us how slow or fast an object moves. The formula for speed is given below

The speed of an object is directly proportional to Distance and Inversely proportional to Time. Hence,

Here we have,

Ashley and Laura are 60 miles apart, traveling toward each other

This means the distance between Ashley and Laura is 60 miles

Speed of Laura = 12 mph

Speed of Ashley = 8 mph

Let us assume that Both Ashley and Laura meet after t hours

Then

The distance traveled by Laura in t hours = 12 mph × t hrs = 12t m

The distance traveled by Ashley in t hours = 8 mph × t hrs = 8t m

As we know the distance between Laura and Ashley is 60 miles

=>  12t m + 8t m = 60 miles

=>  20t miles = 60 miles

=> t = 60/20

=> t = 3hrs

Therefore,

The time taken by Ashley and Laura to meet each other is 3 hrs

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Cost for each pound of chocolate chips is equal to $3.5.

Cost for each pound of walnuts is equal to $1.75

In order to solve this word problem, we would assign variables to the cost for each pound of chocolate chips and each pound of walnuts respectively, and then translate the word problem into algebraic equation as follows:

For 3 pounds of chocolate chips and 2 pounds of walnuts, we have:

3c + 2w = 14              .....equation 1.

For 5 pounds of chocolate chips and 6 pounds of walnuts, we have:

5c + 6w = 28      .....equation 2.

Solving the system of equations by using the elimination method, we have:

3 × (3c + 2w = 14) = 9c + 6w = 42

                                5c + 6w = 28_

4c = 14

c = 14/4

c = $3.5

For the cost for each pound of walnuts, we have:

3c + 2w = 14

3(3.5) + 2w = 14

10.5 + 2w = 14

2w = 14 - 10.5

2w = 3.5

w = 3.5/2

w = $1.75.

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The formula for y in terms of x is a cubic equation:

y = 0.25*x³

We know that y is directly proportional to x³, then we can write the equation:

y = k*x³

Where k is the constant of proportionality.

In this case, we know that when x = 10, the value of y is 250, then we can replace these values in the above equation to find the value of x:

250 = k*10³

250 = k*1,000

Dividing both sides by 1,000 we get:

250/1,000 = k

0.25 = k

Then the equation is:

y = 0.25*10³

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Answer:

I think its 108 each Box is going to cost 108

The absolute value function is represented by f(x) = |x+3| and the

x-intercept of the function is -3.

The function is represented as absolute value of 3 more than x.

hence the function 3 more than x is given by

f(x)=x+3

Now for absolute function:

f(x)=|x+3|

The graph of the function will have no negative value for f(x).

The graph will pass through the point (0,3) which is the y-intercept.

The x-intercept is at (-3,0) .

The domain of the function is all real vales of x.

The range of the function is (0,∞)

The parent function is given by y=|x| .

An procedure that establishes the absolute value of a number or variable is known as a modulus function. It produces the variable count's size.

It is also known as an absolute value function. No matter what input was given to this function, a positive result is always the result.

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The price of each bag of apples is $3.5 and price of  each bag of potatoes is $2.

Given:

a person can buy two bags of apples and two bags of potatoes for $11 at a farmers market the same person by two bags of apples and three bags of potatoes for $13.

Let x be the apples and y be the potatoes.

2x + 2y = 11

2x + 3y = 13

on solving:

2x + 2y - 2x - 3y = 11 - 13

2y - 3y = -2

-y = -2

y = 2

2x + 2y = 11

2x + 2*2 = 11

2x + 4 = 11

2x = 7

x = 7/2

x = 3.5

Therefore The price of each bag of apples is $3.5 and price of  each bag of potatoes is $2.

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Answer:

Apples cost $3.50, potatoes cost $2.

Step-by-step explanation:

If you only add one bag of potatoes and the price jumps two dollars, then the potatoes cost two dollars each. We can substitute this into the equation, which can be solved to find apple price.

Answer:

The answer to this problem is 0.0013.

                  The volume of cone will be [tex]\frac{88r^{3} }{21}[/tex]

Cone:

        A cone is a three-dimensional geometric shape that tapers smoothly from a flat base.

Given,

        The height of a cone is two times its base diameter.

         we have to find the volume of cone in terms of base radius.

let us assume the base radius of cone is equal to r units

                    so diameter(d) of cone will be, d= 2r units

so,

     height(h) of cone will be equal to, h = 2d units

                                                           h = 2x2r units

                                                           h = 4r  units

We know,

              Volume of the cone(V) = [tex]\pi r^{2} h/3[/tex]

                Where,

                             r = radius of base

                            h = height of cone

                            π = 22/7

Thus by using formula,

                                   Volume of cone(V) = [tex]\pi r^{2} h/3[/tex]

                                                                 = 22/7 * [tex]r^{2}[/tex] * 4r/3

                                                                 = 88[tex]r^{3}[/tex]/21

                                                                 = [tex]\frac{88r^{3} }{21}[/tex]

  Hence,

              The volume of cone will be [tex]\frac{88r^{3} }{21}[/tex]

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Answer:

Step-by-step explanation:

Ok:

1. Anything times zero always equals zero.

So: 55555555555555555555555555555555555555555555555555555555555555555555555555x0=

Answer:0

Answer:

3

Step-by-step explanation:

When you substitute 0 in for x in the equation. You are left with f(0) = 3.

Answer:

13

Step-by-step explanation:

if b = 5, then 3(5) - 2 = 15 - 2 = 13

The equation of a circle with a center at (-4, 0) that passes through the point (-2, 1) is (x + 4)² + y² = 5. Option C is correct.

The standard equation of a circle is given by:

(x – h)² + (y – k)² = r²

Where (h, k) is the center of the circle and r is the radius.

We are given:

The circle has a center at (–4, 0) and passes through the point (–2, 1).

Substitute (h, k) with (–4, 0) in the above equation, we will get;

(x – (-4))² + (y – 0)² = r²

(x + 4)² + y² =  r²

Substitute (x, y) with (–2, 1) in the above equation to get the value of r:

(-2 + 4)² + 1² =  r²

(2)² + 1² =  r²

r² = 5

Put the value r² = 5 in (x + 4)² + y² =  r², we will get;

(x + 4)² + y² =  5

So, the equation of the circle is (x + 4)² + y² =  5.

Thus, the equation of a circle with a center at (-4, 0) that passes through the point (-2, 1) is (x + 4)² + y² = 5. Option C is correct.

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Angle BCD is the same as angle FGH which is 122

Step-by-step explanation:

congruent means that they have the same angles.

so, the angle BCD = 122