Finding Angle measures between intersecting lines​

Answer:

D

Step-by-step explanation:

Given the 2 equations

2x - 3y = 14 → (1)

5x + 3y = 21 → (2)

Adding the 2 equations term by term will eliminate the y - term

(5x + 2x) + (- 3y + 3y) = (14 + 21)

7x = 35 ( divide both sides by 7 )

x = 5 → D

Answer:

  B)  one solution

Step-by-step explanation:

The ratio of x-coefficient to y-coefficient is different in the two equations, so the lines have different slopes. Two lines with different slopes will always have exactly one point of intersection. You don't need to graph the equations to know there is ...

  one solution

__

A graph is attached. As it happens, the two lines are perpendicular. The solution is (2, 0).

Hello There!

In an experiment, The independent variable is the variable that the person doing the experiment changes on purpose so they can see if it affects another variable in the experiment. Independent variables are also called "The Manipulated Variables"

I Hope This Helped You!

Have Great Day!

Be Safe,

TheBlueFox

Answer:

5.25 miles - 3 miles = 2.25 miles

2.25 miles is the extra miles.

2.25 miles x $1.20 = $2.7

Total:

$2.7 + ($1.5 x 3 miles)

=$2.7 + $4.5

=$7.2

5.5 miles will cost $2.7.

If we want to find when the population of species A will be equal to the population of species B, we need to see when the two equations for the population of each species are equal, ie. equate them and solve for t. Thus:

2000e^(0.05t) = 5000e^(0.02t)

(2/5)e^(0.05t) = e^(0.02t) (Divide each side by 5000)

2/5 = e^(0.02t) / e^(0.05t) (Divide each side by e^(0.05t))

2/5 = e^(-0.03t) (use: e^a / e^b = e^(a - b))

ln(2/5) = -0.03t (use: if b = a^c, then loga(b) = c )

t = ln(2/5) / -0.03 (Divide each side by -0.03)

= 30.54 (to two decimal places)

Therefor, the population of species A will be equal to the population of species B after 30.54 years.

I wasn't entirely sure about the rounding requirements so I've left it rounded to two decimal places.

Answer:

None.

Step-by-step explanation:

5/a - 2 / (1 - a) = 2 (a - 1)

Multiply each term by  a(1 - a)(a - 1):

5 (1 - a)(a - 1) - 2a(a - 1)  = 2a(1 - a)

5( a - 1 - a^2 + a)  - 2a^2 + 2a = 2a - 2a^2

5(-a^2 +  2a  - 1) - 2a^2 + 2a = 2a - 2a^2

-5a^2 + 10a - 5 - 2a^2 + 2a - 2a + 2a^2 = 0

-5a^2 + 10a - 5 = 0

-5(a^2 - 2a + 1) = 0

= -5(a - 1)^2 = 0

So a = 1.

But a = 1 cannot be a root because 2/ 1 - a would be 2/0 which is undefined.

Also 2 / (a - 1) is undefined.

Answer:

93%

Step-by-step explanation:

1 + 3 + 21 + 35 = 60 = 100%

21 + 35 = 56 = x%

60 = 100%

56 = x%

60x = 56 * 100

x = 56* 100 / 60

x = 2*23*2*2*5*5 / 2*2*3*5

x = 23*2*5/3

x = 93%

To find the percent of soldiers in the new army unit, you divide the number of soldiers in the unit by the total number of soldiers in the army and multiply by 100. However, the question doesn't provide the total number of soldiers in the army, making it impossible to calculate this percentage.

The question is asking what percent of the soldiers in the newly formed army unit consists of the total personnels. The total number of soldiers in the unit is the sum of staff sergeants, sergeants, PFCs, and PVTs which is 1 + 3 + 21 + 35 = 60 soldiers. The percent of soldiers in the army is the number of soldiers in the unit divided by the total number of soldiers in the army multiplied by 100. However, without the context of the total number of soldiers in the army, it is impossible to calculate this percentage. For example, if the total army size is 600, then the percent of soldiers in this unit would be (60/600)*100 = 10%. The keywords here are

percent

,

total soldiers

, and

army unit

.

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The three-dimensional figure that is formed by the rotation is (a) an hemisphere

From the figure, we can see that the line is rotated along the y-axis.

And the length of rotation reduces as the rotation moves downward

This rotation would create an hemisphere

The option (a) represents an hemisphere

Hence, the three-dimensional figure that is formed by the rotation is (a) an hemisphere

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Answer:

Length: 13 feet,

Width: 4 feet.

Step-by-step explanation:

Let w represent width of bulletin board.

We have been given that the length is 3 feet less than 4 times the width. So the length of the bulletin board would be [tex]4w-3[/tex].

We have been given the area of a bulletin board is 52 square feet. We know that a bulletin board is in form of rectangle, so its area would be length times width.

We can represent this information in an equation as:

[tex]w(4w-3)=52[/tex]

Let us solve for w.

[tex]w(4w-3)=52[/tex]

[tex]4w^2-3w=52[/tex]  

Use quadratic formula:

[tex]w=\frac{-(-3)\pm\sqrt{(-3)^3-4\cdot 4\cdot (-52)}}{2\cdot 4}[/tex]

[tex]w=\frac{3\pm\sqrt{9+832}}{8}[/tex]

[tex]w=\frac{3\pm\sqrt{841}}{8}[/tex]

[tex]w=\frac{3\pm29}{8}[/tex]

[tex]w=\frac{3-29}{8}\text{ (or) }w=\frac{3+29}{8}[/tex]

[tex]w=\frac{-26}{8}\text{ (or) }w=\frac{32}{8}[/tex]

[tex]w=\frac{-13}{4}\text{ (or) }w=4[/tex]

Since width cannot be negative, therefore, width of the bulletin board is 4 feet.

Substitute [tex]w=4[/tex] in expression [tex]4w-3[/tex] to find length of bulletin board.

[tex]4w-3\Rightarrow 4(4)-3=16-3=13[/tex]

Therefore, length of the bulletin board is 13 feet.

Answer:

[tex]14\ miles[/tex]

Step-by-step explanation:

Let

[tex]A(-2, 2), B(1, 2), C(1, -2),D(-2, -2)[/tex]

Plot the coordinates

see the attached figure

we know that

The perimeter is equal to

[tex]P=2(AB+AD)[/tex]

we have

[tex]AB=(1-(-2))=3\ units[/tex]

[tex]AD=(2-(-2))=4\ units[/tex]

substitute

[tex]P=2(3+4)=14\ units[/tex]

Convert to miles

If each unit represents 1 mile

then

[tex]14\ units=14\ miles[/tex]

Answer:

15 units sq

Step-by-step explanation:

Good job

Answer:

Its B ''In Step 2, she divided 8 by 100 instead of 100 by 8, so she cannot multiply the numerator by the factor.''

Hence, in step [tex]2[/tex] she did the mistake.

What is the multiplication?

Multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Here given that,

Step 1: [tex]\frac{1}{8}=\frac{?}{100}[/tex]

Step 2: [tex]8[/tex] divided by [tex]100 = 0.08[/tex]

Step 3: [tex]0.08[/tex] multiplied by [tex]1 = 0.08[/tex]

Step 4: [tex]0.08[/tex]

She did the mistake in step [tex]2[/tex] it would be,

[tex]\frac{100}{8}=12.5[/tex]

Hence, in step [tex]2[/tex] she did the mistake.

To know more about the multiplication

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For this case we have that the area of the kite is given by the area of two triangles, the triangles share the same base of 2 + 2 = 4. One of the triangles has height of 6 and the other has height of 7.

So, the total area is given by:

[tex]A = \frac {1} {2} * 4 * 6 + \frac {1} {2} * 4 * 7\\A = \frac {1} {2} 24+ \frac {1} {2} 28\\A = 12 + 14\\A = 26[/tex]

So, the kite area is 26

ANswer:

Option D

Answer:

To better understand the data you're working with

Step-by-step explanation:

Note that, the sample is a subset of your whole population (population here is a general definition, it could be a population of cars for example), which means that if you want to understand your population your best "bet" would be using a sample to try to estimate some unknown characteristics of your population. Let's suppose you want to estimate the true mean of your population, then you would need a sample, and if this sample is big enough you could approximate the estimative to the true mean.

It's hard to say exactly what this survey could mean, but the general idea is to understand your data a little more, see if there is any pattern, if a certain value occurs more than others, to calculate the sample mean, median and standard deviation, and so on...

Hope it helped!

Answer:

For b, the answer is that your trying to find out what the type of funtion may be. It could be either exponential, linear, or quadratic.

Step-by-step explanation:

That's what the lesson in edg is all about.

Answer:

  40 ft by 70 ft

Step-by-step explanation:

The 50 ft side of the house can add to the total perimeter of the play area, allowing it to be 170+50 = 220 feet. Then the sum of length and width will be half that, or 110 feet.

Factors of 2800 that have a sum of 110 are 40 and 70.

The play area fence can extend 10 ft either side of the house, out 40 ft, then 70 ft across the back, for a total length of 170 ft. Dimensions of the play area are 40 ft by 70 ft.

[tex]{_{15}C_{11}}\cdot {_{11}C_2}=\dfrac{15!}{11!4!}\cdot\dfrac{11!}{2!9!}=\dfrac{12\cdot13\cdot14\cdot15}{2\cdot3\cdot4}\cdot\dfrac{10\cdot11}{2}=75,075[/tex]

Answer: There are 715 ways to choose his starting lineup which includes designating the two captions.

Step-by-step explanation:

Since we have given that

Number of members = 15

Number of players = 11

Number of captions must be included = 2

So, Number of remaining members = 15-2 = 13

Number of remaining players = 11 - 2 = 9

So, Number of ways to choose starting line up is given by

[tex]^{13}C_9\\\\=715[/tex]

Hence, there are 715 ways to choose his starting lineup which includes designating the two captions.

Answer:

Revenue , Cost and Profit Function

Step-by-step explanation:

Here we are given the Price/Demand Function as

P(x) = 253-2x

which means when the demand of Cat food is x units , the price will be fixed as 253-2x per unit.

Now let us revenue generated from this demand i.e. x units

Revenue = Demand * Price per unit

R(x) = x * (253-2x)

      = [tex]253x-2x^2[/tex]

Now let us Evaluate the Cost Function

Cost = Variable cost + Fixed Cost

Variable cost = cost per unit * number of units

                      = 3*x

                      = 3x

Fixed Cost = 6972 as given in the problem.

Hence

Cost Function C(x) = 3x+6972

Let us now find the Profit Function

Profit = Revenue - Cost

P(x) = R(x) - C(x)

      = [tex]253x-2x^2 - (3x+6972)\\253x-2x^2-3x-6972\\253x-3x-2x^2-6972\\250x-2x^2-6972\\-2x^2+250x-6972\\[/tex]

Now we have to find the quantity at which we attain break even point.

We know that at break even point

Profit = 0

Hence P(x) = 0

[tex]-2x^2+250x-6972[/tex]=0

now we have to solve the above equation for x

[tex]-2x^2+250x-6972 = 0[/tex]

Dividing both sides by -2 we get

[tex]x^2-125x+3486 = 0\\[/tex]

Now we have to find the factors of 3486 whose sum is 125. Which comes out to be 42 and 83

Hence we now solve the above quadratic equation using splitting the middle term method .

[tex]x^2-42x-83x+3486 = 0\\x(x-42)-83(x-43)=0\\(x-42)(x-83)=0\\[/tex]

Hence

Either (x-42) = 0 or (x-83) = 0 therefore

if x-42= 0 ; x=42

if x-83=0 ; x=83

Smallest of which is 42. Hence the number of units at which it attains the break even point is 42.

Final answer:

The cost function is C(x) = $6972 + ($3 × x). The revenue function is R(x) = 253x - 2x². The profit function is P(x) = (253x - 2x²) - ($6972 + $3x). The smallest break-even point is where P(x) = 0.

Explanation:

To answer the student's series of questions involving cost, revenue, and profit functions, as well as the break-even quantity, we need to derive these functions from the given information and perform the necessary calculations. The unit cost to produce bins of cat food is $3, and the fixed cost is $6972. Meanwhile, the price-demand function is given by p(x) = 253 - 2x.

The cost function, C(x), which represents the total cost of producing x units, can be expressed as:

C(x) = Fixed Costs + (Variable Cost per Unit × x)
Thus, C(x) = $6972 + ($3 × x).

The revenue function, R(x), is the total income from selling x units, defined by:

R(x) = Price per Unit × x
So, using the price-demand function, R(x) = (253 - 2x)x = 253x - 2x².

The profit function, P(x), is found by subtracting the cost function from the revenue function:

P(x) = R(x) - C(x)
Therefore, P(x) = (253x - 2x²) - ($6972 + $3x).

To calculate the break-even point, where profit is zero, you need to solve the equation P(x) = 0 for x.

Answer:1 out of 13

Step-by-step explanation:

because you take both of them and add them together and if one gets a banana and the other one gets an orange that will be one out of thirteen

Answer:

  $28

Step-by-step explanation:

Put the given value into the formula and do the arithmetic.

  p(15) = -2(15 -9)^2 +100

  = -2(6^2) +100

  = -72 +100

  = 28

The profit on T-shirts selling for $15 would be $28.

Answer:

B -$28

Step-by-step explanation:

1. This kite has a 90 degree angle, which is equivalent to angle B.

2. Distance RB is 2.

3. Distance SB is 1.

4. The kite forms a right triangle.

5. Distance RS is the hypotenuse which has not been given. We can call RS by any variable of choice.

Answer:

Option C) [tex]0 \leq x \leq 9[/tex]

Step-by-step explanation:

We are given the following information in the question:

The number of users of a cell tower  increased by a factor of 1.5 every year from 2010 to 2019.

[tex]f(x) = 5000(1.5)^x[/tex]

where f(x) is the number of cell tower users and x is the years from the year 2010.

We have to find the domain for the given function.

Domain of a function is defined as the possible values of x the function can take, so that the function is defined.

Since this function gives the number of cell users from 2010 to 2019, thus, it is applicable from year 2010 to 2019.

x takes the value of years after 2010.

Thus  for year 2010, x = 0 and for year 2019, x = 9

Thus, the domain of the given function is given by:

[tex]0 \leq x \leq 9[/tex]

Mean means average.

To find the average, add the data then divide it by the amount of individual data you have.

(6.5 + 5 + 3 + 2 + 2 + 3.5 + 5)/2 = mean

27/2 = mean

13.5 = mean

13.5 miles is the mean distance that Jim jogged.

Answer:

120*pi in^3

Step-by-step explanation:

We are given

Radius of cone=r=6 in

Height of cone=h=10 in

We know that the formula for finding the volume of cone is:

[tex]V=\frac{1}{3}\pi *(r)^{2}*h[/tex]

Putting the values of radius and height:

[tex]V=\frac{1}{3}\pi *(6)^{2}*10\\=\frac{1}{3}\pi *36*10\\=\frac{360}{3}\pi\\=120\pi[/tex]

So, the volume of cone in terms of pi is 120pi cubic in^3 ..

Answer:

The volume of cone = 120π cubic inches

Step-by-step explanation:

Points to remember

Volume of cone = (πr²h)/3

Where r - Radius of cone and

h - Height of cone

To find the volume of cone

Here r = 6 in and h = 10 in

Volume = (πr²h)/3

 = (π * 6² * 10)/3

 = (π * 36 * 10)/3

 = 360π/3

 = 120π cubic inches

Therefore volume of cone = 120π cubic inches

Answer:

√3 + 12 = x

Step-by-step explanation:

Simplify both sides of the equation, isolating the variable.

Answer:

it's definitely a positive nonlinear graph

Step-by-step explanation:

Answer:its a. 5,000,000

Step-by-step explanation:

Final answer:

Option a, 5,000,000 nanometers, is the correct choice as it does not equate to 50 millimeters; it equates to 5 millimeters instead, making it not equal to the other options listed.

Explanation:

The question asks which of the provided options is not equal to 50 millimeters. We can convert each option to see which one does not equal 50 mm:

a. 5,000,000 nanometers (nm) - This equates to 5,000,000 nm × 1 m / 1,000,000,000 nm = 0.005 m or 5 mm, which is not equal to 50 mm.

b. 0.05 meters (m) - This is equal to 0.05 m × 1000 mm / 1 m = 50 mm, which is equal to 50 mm.

c. 5 centimeters (cm) - This is equal to 5 cm × 10 mm / 1 cm = 50 mm, which is equal to 50 mm.

d. 50,000 micrometers (µm) - As 1 µm is 1/1000 mm, this is equal to 50,000 µm × 1 mm / 1000 µm = 50 mm, which is equal to 50 mm.

Therefore, the correct answer is a. 5,000,000 nanometers, as it is the only option that does not equate to 50 mm.

Answer:

139 ft

Step-by-step explanation:

So the zip line forms a right triangle.  The height of the triangle is 150 ft, and the opposite angle is 40°.  The horizontal distance covered by the zip liner can be found with trigonometry, specifically with tangent.

tan 40° = 150 / x

x = 150 / tan 40°

x ≈ 179 feet

But this includes the 40 ft long body of water, so the amount of ground covered is:

179 ft - 40 ft = 139 ft

Answer:

29; 30

Step-by-step explanation:

1. To the nearest whole number.

Whole numbers are numbers like 27, 28, 29, and 30.

A is between 28 and 29, but it is closer to 29.

To the nearest whole number, A = 29.

2. To the nearest 10

The tens are numbers like 10, 20, 30, and 40.

A is between 20 and 30, but it is closer to 30.

To the nearest ten, A = 30.

Answer:

Step-by-step explanation:

Let [tex]u^2=x^4\\u = x^2[/tex]

Subbing in:

[tex]9u^2-2u-7=0[/tex]

a = 9, b = -2, c = -7

The product of a and c is the aboslute value of -63, so a*c = 63.  We need 2 factors of 63 that will add to give us -2.  The factors of 63 are {1, 63}, (3, 21}, {7, 9}.  It looks like the combination of -9 and +7 will work because -9 + 7 = -2.  Plug in accordingly:

[tex]9u^2-9u+7u-7=0[/tex]

Group together in groups of 2:

[tex](9u^2-9u)+(7u-7)=0[/tex]

Now factor out what's common within each set of parenthesis:

[tex]9u(u-1)+7(u-1)=0[/tex]

We know this combination "works" because the terms inside the parenthesis are identical.  We can now factor those out and what's left goes together in another set of parenthesis:

[tex](u-1)(9u+7)=0[/tex]

Remember that [tex]u=x^2[/tex]

so we sub back in and continue to factor.  This was originally a fourth degree polynomial; that means we have 4 solutions.

[tex](x^2-1)(9x^2+7)=0[/tex]

The first two solutions are found withing the first set of parenthesis and the second two are found in other set of parenthesis.  Factoring [tex](x^2-1)[/tex] gives us that x = 1 and -1.  The other set is a bit more tricky.  If

[tex]9x^2+7=0[/tex] then

[tex]9x^2=-7[/tex] and

[tex]x^2=-\frac{7}{9}[/tex]

You cannot take the square root of a negative number without allowing for the imaginary component, i, so we do that:

[tex]x=[/tex]±[tex]\sqrt{-\frac{7}{9} }[/tex]

which will simplify down to

[tex]x=[/tex]±[tex]\frac{\sqrt{7} }{3}i[/tex]

Those are the 4 solutions to the quartic equation.