C and D are vertical angles with mC = -x+26 and m D = 2x - 10
What is m D?

Answer:

1.57 is approximately equal to π/2.

Answer:

D, X^2 -18 + 81 = -45 + 81

Step-by-step explanation:

it is complating squer method that used for solving x in a quadratic equetion . in this step you will add

(y/2)^2 if y is the cofitient of x .

Answer:

432

Step-by-step explanation:

The multiplication of number 24 times 18 gives the result 432.

To multiply 24 by 18, you can follow the standard multiplication algorithm:

   24

x  18

-----

192  (24 multiplied by 8)

240 (24 multiplied by 10)

-----

432    (The final product)

Therefore, 24 multiplied by 18 equals 432.

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1) There is a vertical asymptote since the function grows infinitely as it approaches x = 1 from both sides.

2) The value of c that makes the function continuous on the interval (-∞,∞) is c = 3/8.

3) The function f(x) = 4x²-3x³ + 2x²+x-1 has at least one real root on the interval [-0.6,-0.5].

Question 1

We are asked to draw a function that has three different discontinuities at x = -2, x = 1, and z = 3 where the discontinuities are caused by a jump, a vertical asymptote, and a hole in the graph respectively.

Below is the graph we have for the function:

Note that at x = -2, there is a jump discontinuity since the limit of the function as x approaches -2 from the left (-2-) is not equal to the limit as x approaches -2 from the right (-2+) while at x = 1, there is a vertical asymptote since the function grows infinitely as it approaches x = 1 from both sides.

On the other hand, at x = 3, there is a hole in the graph since the function is not defined there but there exists a point on the curve, which is extremely close to the hole, that is defined (in other words, it exists) and that point lies on the limit of the function as x approaches 3 from either side.

Question 2

We are given that:

f(x) = [cr¹ +7cx³+2, x < -1 |4c-x²-cr, x ≥ 1

We are also asked to find the values of the constant c which makes the function continuous on the interval (-[infinity], [infinity]).

Let us evaluate the limit of the function as x approaches -1.

This will help us find the value of c.

We know that when x < -1, the function takes the form cr¹ +7cx³+2.

Thus,lim f(x) as

x → -1 = lim cr¹ +7cx³+2

= c(1) + 7c(-1) + 2

= -5c + 2

We also know that when x ≥ 1, the function takes the form 4c-x²-cr.

Thus,

lim f(x) as x → -1

= lim 4c-x²-cr

= 4c - 1 - c

= 3c - 1

We know that the function will be continuous when the limits from both sides are equal.

Hence,

-5c + 2

= 3c - 1<=>

8c = 3<=>

c = 3/8

Therefore, the value of c that makes the function continuous on the interval (-[infinity], [infinity]) is c = 3/8.

Question 3

We are given that:

f(x) = 4x²-3x³ + 2x²+x-1

We are also asked to show that the following equation has at least one real root on the interval [-0.6,-0.5].

To show that the equation has at least one real root on the interval, we need to find the values of the function at the two endpoints of the interval.

If the values at the two endpoints have opposite signs, then the function must have a real root in the interval [by the Intermediate Value Theorem].

Thus, we evaluate f(-0.6) and f(-0.5)

f(-0.6) = 4(-0.6)²-3(-0.6)³ + 2(-0.6)²+(-0.6)-1

= -1.5636f(-0.5)

= 4(-0.5)²-3(-0.5)³ + 2(-0.5)²+(-0.5)-1

= -1.375

If we compare the values at the endpoints of the interval, we can see that:

f(-0.6) < 0 < f(-0.5)

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Answer:

The new volume is 81.2% of the prior, this is true for any for any values of radius and height, as long as they are changed as stated.

Step-by-step explanation:

The volume of a cylinder is given by:

\(V = \pi*r^2*h\)

If we increase the diameter by 15%, then the radius is increased by 7.5% and the new radius is:

\(r_{new} = 1.075*r\)

If we decrease the height by 30%, then the new height is 70% of the prior and is given by:

\(h_{new} = 0.7*h\)

Applying to the volume formula we have:

\(V_{new} = pi*(r_{new})^2*h_{new}\)

\(V_{new} = \pi*(1.075*r)^2*0.7*h\\V_{new} = 1.16*0.7*\pi*r^2*h\\V_{new} = 0.812*\pi*r^2*h\\V_{new} = 0.812*V\)

The new volume is 81.2% of the prior, this is true for any for any values of radius and height, as long as they are changed as stated.

The amount of time required for the person to reach using compound interest 22600 dollar is 13 years

What is compound interest?

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

We are given that the initial investment done by a person is $9500

And the interest rate is 6.25% semi annually that is twice

And after how much time he will have 22600 dollars

To find that we use compound interest formula

\(A=p(1+\frac{r}{n}) ^{nt}\)

Substituting the values we get

\(22600= 9500(1+0.03125)^{2t}\\2.37= (1+0.03125)^{2t}\\t= 13 years\)

Hence the time required to reach $22600 is approximately 13 years

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Answer: The sum of two odd numbers is an even number.

Step-by-step explanation:

Some examples:

3(odd)+3(odd)=6(even)

29(odd)+9(odd)=38(even)

Answer:

x + y is an even number. /proved

Step-by-step explanation:

If x and y both are odd numbers, then they can be written as,

x = 2a + 1

y = 2b + 1                                        (where a and b are integers)

The sum of x and y is,

x + y = (2a + 1) + (2b + 1)

        = 2a + 2b + 2

        = 2(a + b + 1)

Since a and b are both integers, the expression (a + b + 1) is also an integer.

Therefore, x + y is an even number.

The quantity of tomatoes in ounces Amanda picks each day as required to be determined on the task content is; 1.5 ounces.

It follows from the task content that Amanda grows tomatoes in pots on the rooftop of her building in which case, after 2 days, she picked a total amount of 3 pounds of tomatoes.

Since the same amount of tomatoes is picked each day;

The unit rate which represents the ounces of tomatoes she picked each day is; 3/2 = 1.5 ounces per day.

Ultimately, the number of ounces of tomatoes she picks each day is; 1.5 ounces.

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The value of h(20) is 46 and the meaning in the context of the situation is that the balloon is at 46 feet after 20 seconds

The equation of the function is given as

h(t) = 2t + 6

For h(20), it means that t = 20

So, we have

h(20) = 2 * 20 + 6

Evaluate

h(20) = 46

Hence, the value of h(20) is 46 and the meaning in the context of the situation is that the balloon is at 46 feet after 20 seconds

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Answer:

multiply by the reciprocal!

so if you have 1/(2/5) it is the same as 1 * (5/2)

The function that represents the balance after t years can be written as:

A(t) = 200(1 + 0.03)^t

To represent the balance after t years for an investment of $200 that earns 3% annual interest, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the balance after t years

P = the principal amount (initial investment)

r = the annual interest rate (in decimal form)

n = the number of times the interest is compounded per year

t = the number of years

In this case, the principal amount P is $200, the annual interest rate r is 3% (or 0.03 as a decimal), and we'll assume the interest is compounded once per year (n = 1).

Therefore, the function that represents the balance after t years can be written as:

A(t) = 200(1 + 0.03)^t

Simplifying further:

A(t) = 200(1.03)^t

This function can be used to calculate the balance after any number of years t.

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Answer:

5.94

Step-by-step explanation:

75 - 69.06 = x

x = 5.94

Answer:

21,704

Step-by-step explanation:

Find the volume of both the top of the silo (hemisphere) and the end bit of the silo (cylinder)

V = \(\frac{2}{3}\) \(\pi\)\(r^{3}\) is the formula for finding the volume of a hemisphere

V = \(\pi\)\(r^{2}\)h is the formula for finding the volume of a cylinder

Let's find the hemisphere first.

We're using 3.14 for pi, so the equation would look like this

V = \(\frac{2}{3}\) x 3.14 x \(12^{3}\)

V = \(\frac{2}{3}\) x 3.14 x 1728

V = 3617.28 \(ft^{3}\)

Now let's find the volume of the cylinder.

V = 3.14 x \(12^{2}\) x 40

V = 3.14 x 144 x 40

V = 18,086.4 \(ft^{3}\)

Last, you add both volumes together.

3617.28 + 18,086.4 = 21,703.68

Round it to make it 21,704.

The total number of cubic feet of grain or volume of the grain that the silo can hold is 28947.41 .

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Given that the top of a silo is a hemisphere

Radius(r) = 12 ft.

Then, the volume of a hemisphere is,

V = 2/3πr³

V = 2/3 x 3.14 x 12³

V = 10851.84 feet³

And, the bottom of the silo is a cylinder with

height (h) = 40ft.

the volume of a cylinder is,

V = πr²h

V = 3.14 x 12² x 40

V = 18095.57

So, the total volume is

V = 10851.84 + 18095.57

V = 28947.41

Then, total volume = total number of cubic feet of grain

Hence, the required answer is, 28947.41 .

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Answer:

11 students study woodwork but not metalwork

Step-by-step explanation:

Since there are 30 students in total and 6 study neither woodwork nor metalwork, there are 30 - 6 = 24 students who study at least one of the two subjects.

Since 15 students study woodwork and 13 study metalwork, there are 15 + 13 = 28 students who study woodwork or metalwork or both.

Subtracting the number of students who study at least one of the two subjects from the number of students who study woodwork or metalwork or both, we get 28 - 24 = 4 students who study both woodwork and metalwork.

Therefore, the number of students who study woodwork but not metalwork is 15 - 4 = 11

--------------------------------------------------------------------------------------------------------

Step 1:  Determine the number of students who study at least one of the two subjects:

Since there are:

we can determine the number of students who study at least one of the two subjects by subtracting 6 from 30:

30 - 6

24

Thus, 24 students study at least one of the two subjects.

Step 2:  Determine the number of students who study either woodwork or metalwork or both:

Since:

we can determine the number of students who study either woodwork or metalwork or both by adding 15 and 13:

15 + 13

28

Thus, 28 students either woodwork or metalwork or both.

Step 3:  Determine the number of students who study both subjects:

We can determine the number of students who study both subjects by:

28 - 24

4

Thus, 4 students study both subjects.

Step 4:  Determine the number of students who study woodwork but not metal work

Now we can find the number of students who study woodwork by:

15 - 4

11

Thus, 11 students study woodwork but not metalwork.

The inequality that is true is option D. Negative 1 greater-than three-fourths

An inequality is a statement in which two expressions or values are not equal to each other, but have a certain relationship, such as 3 + 4 > 7 or x + y < z. Inequalities can be represented by different symbols, such as <, >, ≤, ≥, ≠ which denotes "less than", "greater than", "less than or equal to", "greater than or equal to", and "not equal to" respectively

An equality, on the other hand, is a statement in which two expressions or values are equal to each other, such as 3 + 4 = 7 or x + y = z. It is represented by the symbol "=".

Therefore, the correct answer is as given above

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Answer:

SSS could be used for equilateral triangles, AAA is impossible, Cannot be determined is easily not an option.

This leaves ASA and SAS

An isoscoles triangle is a triangle that has two equal sides. SAS is an abreviation that says two triangles have 2 equal sides. Therefore, number 4 SAS is correct

Step-by-step explanation:

The median of the legs of a triangle joins the vertex to the midpoint of the opposite side of the triangle.

The correct postulate is (d) SAS

An isosceles triangle has two congruent sides and angles.

This means that, postulates AAA and SSS are not possible.

This is so, because both postulates imply that the sides and angles of the triangles are congruent.

See attachment for illustration of the median of the isosceles triangles.

From the attachment, we have the following observations.

These mean that:

The triangles are congruent by SAS postulate.

Hence, the correct postulate is (d) SAS

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Answer:

your answer is 14.4 ft

Step-by-step explanation:

have a nice day

Answer:

2/36 (5.556%)

I believe so correct me if I am wrong

By applying the Kuhn-Tucker theorem, the maximum value of xy is: 18/25

The constraints are:-4x² - 2xy - 4y²x + 2y ≤ 22x - y ≤ -1

Let us solve this problem by applying the Kuhn-Tucker theorem.

Let us first write down the Lagrangian function:

L = xy + λ₁(-4x² - 2xy - 4y²x + 2y - 2) + λ₂(2x - y + 1)

Then, we find the first order conditions for a maximum:

Lx = y - 8λ₁x - 2λ₁y + 2λ₂ = 0

Ly = x - 8λ₁y - 2λ₁x = 0

Lλ₁ = -4x² - 2xy - 4y²x + 2y - 2 = 0

Lλ₂ = 2x - y + 1 = 0

The complementary slackness conditions are:

λ₁(-4x² - 2xy - 4y²x + 2y - 2) = 0

λ₂(2x - y + 1) = 0

Now, we solve for the above equations one by one:

From equation (3), we can write 2x - y + 1 = 0, which implies:y = 2x + 1

Substitute this in equation (1), we get:

8λ₁x + 2λ₁(2x + 1) - 2λ₂ - x = 0

Simplifying, we get:

10λ₁x + 2λ₁ - 2λ₂ = 0 ... (4)

From equation (2), we can write x = 8λ₁y + 2λ₁x

Substitute this in equation (1), we get:

8λ₁(8λ₁y + 2λ₁x)y + 2λ₁y - 2λ₂ - 8λ₁y - 2λ₁x = 0

Simplifying, we get:

-64λ₁²y² + (16λ₁² - 10λ₁)y - 2λ₂ = 0 ... (5)

Solving equations (4) and (5) for λ₁ and λ₂, we get:

λ₁ = 1/20 and λ₂ = 9/100

Then, substituting these values in the first order conditions, we get:

x = 2/5 and y = 9/5

Therefore, the maximum value of xy is:

2/5 x 9/5 = 18/25

Hence, the required answer is 18/25.

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Answer:

After 3 hours there is left 22.5 grams of radioactive material.

Step-by-step explanation:

We can calculate the mass of radioactive material remaining after 3 hours, by using the decay equation:           

\(N_{t} = N_{0}*e^{-\lambda t}\)     (1)

Where:

\(N_{0}\): is the initial mass = 180 g

\(N_{t}\): is the remaining mass after time t

λ: is the decay constant

The decay constant is given by:

\( \lambda = \frac{ln(2)}{t_{1/2}} \)

Where \(t_{1/2}\) = 1 h.

By entering λ into equation (1) we hve:

\( N_{t} = N_{0}*e^{-\frac{ln(2)}{t_{1/2}} t} \)

\( N_{t} = 180 g*e^{-\frac{ln(2)}{1 h} 3 h} = 22.5 g \)

Therefore, after 3 hours there is left 22.5 grams of radioactive material.

I hope it helps you!          

Answer:

Step-by-step explanation:

3x + 8 = 4x + 4

-x + 8 = 4

x = 4

answer is A

Answer:

Step-by-step explanation:

The number of the correct spellings is 28.

The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.

Given that:-

The number of the spellings are:-

N = 40 x 70% = 28

N = 40 x  (70/100)  =  28

Therefore the number of the correct spellings is 28.

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On a blueprint, the length of the hallway is 4.2 units. However, it is important to take into consideration the scale factor, which is 1:2. To find the actual length, we need to multiply the length on the blueprint by the scale factor. So, 4.2 x 2 = 8.4 units. Therefore, the actual length of the hallway is 8.4 units.

On the blueprint with a scale factor of 1:2, the hallway measures 4.2 inches in length. To find the actual length of the hallway in real life, you can use the scale factor. For every 1 inch on the blueprint, there are 2 inches in real life. Therefore, to calculate the actual length, you can multiply the blueprint length by the scale factor:

Blueprint length: 4.2 inches
Scale factor: 1:2 (or 2/1)

Actual length = Blueprint length × Scale factor
Actual length = 4.2 inches × (2/1)
Actual length = 8.4 inches

The actual length of the hallway in real life is 8.4 inches.

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the probability distribution for Michael consistently making two free throw attempts: P (X = 0, 1, 2) = 0.3025, 0.495, and 0.2025, respectively.

The probability distribution displays the likelihood that various conceivable experiment results will occur.

When there are numerous attempts at an event with varying probabilities of success and failure, such as two attempts at free throws with a success probability of 0.45

Then it is appropriate to utilize the Binomial probability formula, where Prob =NcR.Pr.Q(n-r): N = Number of trials, R = Number of successes, P = Success probability, and Q = Failure probability.

Specifically, P (success = 0) = 0.3025, P (success = 1) = 0.495, and P (success = 2) = 0.2025

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The normal curve with a mean of 0 and standard deviation of 1 is called (D)  the z-value.

Therefore, the normal curve with a mean of 0 and standard deviation of 1 is called (D)  the z-value.

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Answer:

c. 25

Step-by-step explanation:

According to the intersecting chords theorem, the product of the segments of a chord equals the product of the segments of the other chord it intercepts.

Thus:

3*x = 5*15

3x = 75

x = 75/3

x = 25

Hence, combine all the solutions we get,

\(x=\frac{\pi}{2} +2n\pi,x=\frac{3\pi}{2} +2\pi n ,\)\(x= sin^{-1} (\frac{1}{3} )+ 2\pi n ,x= sin^{-1 }(\frac{1}{3})+2\pi n\).

Trigonometric identities are equalities which involves trigonometric functions which are true for every value of variables that occur on both sides of the identities.

Given,\(3\sin \left(2x\right) = 2\cos \left(x\right)\)

\(3\sin \left(2x\right)-2\cos \left(x\right)=0\)

Using trigonometric identities, \(sin2x= 2sinx cosx\)

we get,\(-2\cos \left(x\right)+6\cos \left(x\right)\sin \left(x\right)=0\)

Taking \(2cos(x)\) as factor, we get,

⇒\(2cos(x)(3sin(x) -1)\)

⇒\(2cos(x) = 0 , (3sin(x) -1)=0\)

⇒\(cos (x)= 0\) for x= \(x=\frac{\pi}{2} +2n\pi,\frac{3\pi}{2} +2\pi n\) and

\((3sin(x) -1)=0 for x= sin^{-1} (\frac{1}{3} )+ 2\pi n , sin^{-1 }(\frac{1}{3})+2\pi n\)

Hence, combine all the solutions we get,

\(x=\frac{\pi}{2} +2n\pi,x=\frac{3\pi}{2} +2\pi n ,\)\(x= sin^{-1} (\frac{1}{3} )+ 2\pi n ,x= sin^{-1 }(\frac{1}{3})+2\pi n\).

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Answer:

x = 3a- 7/2

Step-by-step explanation:

Multiply 3 by both sides

2x+7=6a

Divide both sides by 2

x = 3a- 7/2

Answer:

~ 1.9 gal

Step-by-step explanation:

80 miles  /  42 miles/gal = 1.9 gal