Find the area of the trapezium.

Angle ∠IKJ is 29.5 degrees for triangle IKJ.

A triangle is a three-sided polygon that consists of three edges and three vertices.

The given triangle is IKJ.

The angles are given as follow.

∠JIK = 53°,

∠IKJ = (82-5x), and

∠KJI = (7x+24)°.

We need to find the angle ∠IKJ .

By angle sum property of triangle, the sum of three angles is 180 degrees.

∠JIK+∠IKJ+∠KJI = 180

Fifty three plus eighty two minus five times of x plus seven times of x plus twenty four equal to one hundred and eighty.

53+82-5x+7x+24=180

Add the like terms

159+2x=180

One hundred fifty nine plus two times of x equal to one hundred eighty.

subtract 159 on both sides

2x=21

Divide both sides by 2.

x=10.5

So ∠IKJ is 82-5(10.5)=29.5 degrees.

Hence, the value of angle ∠IKJ is 29.5 degrees.

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Answer: $18.49

Step-by-step explanation:

First, add both the tax rate, 4.315 + 4 = 8.315%

Then take 17.07 divided by 100%, then times 8.315% = $1.42

Then add 17.07 + 1.42 = $18.49

The solution to the linear equation 3(x + 5) = 1/9 is

x = -4 26/27.

The correct answer is option D; None of these choices are correct.

3(x + 5) = 1/9

open parenthesis

3x + 15 = 1/9

Substract 15 from both sides

3x = 1/9 - 15

3x = (1-135)/ 9

3x = -134/9

divide both sides by 3

x = -134/9 ÷ 3

Multiply by the reciprocal of 3

x = -134/9 × 1/3

= -134/27

x = -4 26/27

Therefore, -4 26/27 is the solution that satisfies the equation 3(x + 5) = 1/9

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Answer:

104.5 min

Step-by-step explanation:

47.5:5=x:11

1. Simplify

9.5:1=x:11

2.Solve

x=104.5

Therefore the solution to this question of 2 pulleys is )16 rpm

b)360 rad/min  c)39.6 rad/min d) 7200cm/min

A pseudovector used in physics to express how quickly an object's angular position or orientation changes over time is called an angular velocity, rotational velocity, or angular frequency vector.

For the smaller pulley, it does 48 rpm (revolutions per minute) each revolution is 360 degrees. This indicates that the pulley completes one revolution every second .

radians / π = degrees / 180  

radians = πx 360 / 180 = 2 π radians per second

The distance covered by both pulleys is equivalent for the larger pulley.

then d1 = d2

every second, small pulley covers a distance of 40π (small pulley circumference) = d1

d2 = 40π = 120π (large pulley circumference) x factor (f)

f = 1/3

a) the revolutions per min by larger pulley=16 rpm

b) the speed of smaller pulley = 3*2π=6π=6rad/sec=360rad/min

c) then speed of the large pulley = 1/3 * 2π = 2/3 π = 0.66 rad/sec=39.6rad/min

d)the speed of smaller pulley=7200 cm/min

Therefore the solution to this question of 2 pulleys is )16 rpm

b)360 rad/min  c)39.6 rad/min d) 7200cm/min

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Answer:

[tex]\huge\boxed{\sf k = 3}[/tex]

Step-by-step explanation:

[tex]5+6i+(-2+ki)=3+9i\\\\5 + 6i-2+ki=3+9i\\\\Combine \ like \ terms\\\\5-2+6i+ki=3+9i\\\\3+(6+k)i=3+9i\\\\Comparing \ both \ sides\\\\6 + k = 9\\\\Subtract \ 6 \ both \ sides\\\\k = 9-6\\\\k = 3\\\\\rule[225]{225}{2}[/tex]

Answer:

Step-by-step explanation:

To prove this statement, we can use the contrapositive. The contrapositive of the statement "If a + b > 100, then a, b, or both must be greater than 50" is "If a and b are both less than or equal to 50, then a + b is less than or equal to 100."

To prove the contrapositive, we must show that if a and b are both less than or equal to 50, then a + b is indeed less than or equal to 100. This is easy to do, because if a and b are both less than or equal to 50, then the largest possible value for a is 50 and the largest possible value for b is 50. Therefore, the largest possible value for a + b is 50 + 50, which is equal to 100.

Since the contrapositive is true, it follows that the original statement must also be true. Therefore, we have proven that if a + b > 100, then a, b, or both must be greater than 50.

Answer:

Jordan

Step-by-step explanation:

The composite number was 21.

21 can be divided by 3 and 7.

Answer: Jordan.

Step-by-step explanation:

Prime numbers are special numbers that have no divisors other than itself and [tex]1[/tex]. Prime numbers are observed in the lists created by the students.

Compound numbers are numbers that can be written as the product of at least two prime numbers. When we look at Jordan's list, we will see that the number [tex]21[/tex] breaks this rule. Because the number [tex]21[/tex] is the product of both prime numbers [tex]3[/tex] and [tex]7[/tex]. It is not a prime number. It is a composite number.

Answer:

(x²-2) (5x³-3)

Step-by-step explanation:

rearrange terms

5x⁵-10x³-3x²+6

find one factor

(x²-2) (5x³-3)

Answer:

the answer is 40q

Step-by-step explanation:

8x5 is 40 when using the distributive property

Answer:

Unless these took place in different time periods, Laticia did first.

Step-by-step explanation:

28.7 < 42.7

Answer:

  1180 cm³

Step-by-step explanation:

You want the volume of a prism with an L-shaped base. It is 20 cm between bases. The outside dimensions of the L are 7 cm high by 11 cm wide; the inside dimensions are 3 cm high by 6 cm wide.

The formula for the volume of a prism is ...

  V = Bh

where B is the area of the base, and h is the distance between them. We know h, but we need to find B.

The area of an L-shape is the area of the rectangle with the outside dimensions, less the area of the rectangle with the inside dimensions.

  A = LW -lw

  A = (11 cm)(7 cm) -(6 cm)(3 cm) = 77 cm² -18 cm² = 59 cm²

Using the above formula, the volume is ...

  V = (59 cm²)(20 cm) = 1180 cm³

The volume of the prism is 1180 cubic centimeters.

__

Additional comment

The dimensions of the inside of the L are found by subtracting the given width of the legs from the outside dimensions.

 7 cm -4 cm = 3 cm . . . . inside height

  11 cm -5 cm = 6 cm . . . . inside width

You can also find the area of the base by extending one or the other of the lines to divide it into two rectangles. Extending the vertical line makes the left rectangle 7 cm high by 5 cm wide. The right rectangle is 4 cm high by 6 cm wide. Then the area is 7·5 +4·6 = 35+24 = 59, as above.

The probability of landing on a 5 and then landing on an even number is 8.3%.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

The number of 5 on the dice is one.

Probability is the ratio of the number of favorable outcome to the total number of outcome.

The number of faces of dice is 6.

The probability of getting 5 is 1/6.

The even faces on the dice are 2, 4, 6.

The number of even number faces is 3.

The probability of getting even number is 3/6 = 1/2.

The probability of two independent event is the product of the probability of the events.

Therefore, the probability is (1/6) × (1/2)

                                              = 1/12

                                               = 0.083

                                              = 8.3%

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People in my family ordered 1 chicken dinner and 5 steak dinner.

There are total 6 peoples in a family.

Let's x number of people order chicken dinner

and y number of people order steak dinner.

Here we have to use concept of linear equation.

we have to make 2 linear equation and solve them to get the value.

sum of number of people is 6.

[tex]x + y = 6[/tex] --- i

total bill came to $99.

1 chicken dinner takes $14.

So x chicken dinners takes x*14

1 steak dinner takes $17.

So y steak dinners takes y*17.

Sum of both dinners price

[tex]x*14+y*17 = 99[/tex] -- ii

From equation i x = 6 - y.

put value of x in equation ii.

(6-y)*14+y*17 = 99

84-14*y+17*y = 99

3*y = 99-84

3*y = 15

y = 5

x = 6-5 = 1.

So 1 people ordered chicken dinner and 5 people ordered steak dinner.

Given Question is incomplete Complete Question here

Your family goes to a southern style restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14 and some order the steak dinner for $17. If the total bill was $99 l, how many people ordered each dinner?

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The value of CPI will be 178.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

In 1983, a pair of jeans cost $66.35.

And, A pair of jeans costs $118.10 today.

Now,

Since, In 1983, a pair of jeans cost $66.35.

And, A pair of jeans costs $118.10 today.

Hence, The value of CPI will be;

CPI = 118.10 × 100 / 66.35

      = 11810 / 66.35

       = 178

Thus, The value of CPI will be 178.

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The unknown angle in the triangle is as follows:

∠E = 100 degrees.

The sum of angles in a triangle is 180 degrees.

In the diagram, BCD is cut by transversal ACE , AB and perpendicular to BCD and CE ≅ ED.

Therefore,

∠ACB = 180 - 50 - 90 (sum of angles in a triangle)

∠ACB = 180 - 140

∠ACB = 40 degrees

Therefore,

∠ACB ≅ ∠DCE

Hence,

∠DCE = 40 degrees.

Triangle CDE is an isosceles triangle since CE ≅ DE.

Hence,

∠CDE = 40 degrees

∠E = 180 - 40 - 40

∠E = 180 - 80

∠E = 100 degrees.

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Answer: Yes it does, it is -125x to the power of 3.

Step-by-step explanation:

Answer:MONKEY

Step-by-step explanation:

CAUSE I SAID DO

There are 1024 ways to answer the 5 multiple choice question having 4 options

The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. A permutation is a term that describes the variety of possible arrangements or orders of objects.

We have 5 multiple choice questions.

And we are given four options to solve the question

Repeating is permitted (you can answer "c" on all of the questions if you want to)

So ,

We will use permutation to solve the question

[tex]n^{r}[/tex]

r is number of questions = 5

n is number of choices = 4

[tex]4^{5}[/tex] = 4×4×4×4×4 = 1024

There are 1024 ways to answer the 5 multiple choice question having 4 options

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Using the percentage writing form, we know that Ivan ate 4 pizza slices.

By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage.

The percentage calculation formula is (value/total value)100%.

Add all percentages as numbered values, divide by the total number of sets, and you get the average percentage.

The results by 100.

So, we know that:

Ivan ate 40% of the pizza.

And the pizza was cut into 10 slices.

Rewrite the percentage value as:

4/100 = 0.4

We can calculate how many slices Ivan consumed by multiplying the percentage value by the number of slices:

10 + 0.4 = 4

Hence, Ivan ate 4 slices of pizza.

Therefore, using the percentage writing form, we know that Ivan ate 4 pizza slices.

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Answer: The number is 12

Step-by-step explanation:

Let x= the number that is unknown

The sum of three and a "number"= 3+"x"

Divided by three, means that x+3 is divided by 3

Is five, means that (x+3)/3=5

Algebra:

[tex]\frac{x+3}{3}=5[/tex]

Multiply by 3 to arrive at x+3=15

Subtract both sides by 3, then x=12

Answer:

11

Step-by-step explanation:

-5 + 8 x 2

Do multiplication first because PEMDAS -5 + 16

Then add: 11

Answer:

11

Step-by-step explanation:

8x2 = 16
-5+16 = 11

If you do a question like this always use PEMDAS. Do it in order.

P arenthesis

E exponents

M ultiplcation

D ivision

A ddition

S ubtraction

Answer:

-2 = x 4-2 square units

Step-by-step explanation:

sum = as per as chart

Answer:

x/78 = 55/100

Step-by-step explanation:

There is ONLY ONE __ line parallel to the provided line that passes through a certain point that is not contained in the supplied line.

Parallel lines are any two or more lines that are in the same plane but never cross one another ( never intersect). Both have the same slope and are equally far from one another.

We have a line and a point outside the line;

from that point, we can generate many lines, but only one of those lines will be parallel to the line as it is. From a point, we can make many lines, but that point can only create one line that will be parallel to a given line.

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Answer:

12

Step-by-step explanation:

The measure of each interior angle is [tex]\frac{180(8-2)}{8}=135^{\circ}[/tex].

[tex]\implies 135=9x+27 \\ \\ 15=x+3 \\ \\ x=12[/tex]

Sampling technique is the easiest to use here is systematic sampling.

Given :

if an analyst is studying the wait times at a clinic and the only list of patients available is on hard copy .

The sampling technique in this scenario is used is systematic sampling.

Systematic sampling :

Systematic sampling is a type of probability sampling method in which sample members from a larger population are selected according to a random starting point but with a fixed, periodic interval.

k = N/n

where

k = systematic sampling interval

N = population size

n = sample size.

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Answer:

Step-by-step explanation:

P = F/a

Pa = F

a = F/P

Answer:

a = [tex]\frac{F}{p}[/tex]

Step-by-step explanation:

P =[tex]\frac{F}{a}[/tex]  multiple both sides by a

aP = [tex]\frac{F}{a}[/tex] [tex]\frac{a}{1}[/tex]  On the right side of the equal sign, the a's cancel each other out

aP = F  Divide both sides by P

[tex]\frac{aP}{P}[/tex] = [tex]\frac{F}{P}[/tex]  The P's cancel out on the left side of the equal sign.

a = [tex]\frac{F}{P}[/tex]

Answer:

the percent being discounted is 25% and the flat booking fee is 15

Step-by-step explanation:

t is the cost of the ticket.  -.25t is the 25% coupon being taken off.  The 15 is the booking fee.

An Exponential Function that can depict this situation is [tex]A(t) = 25000(0.94)^{t}[/tex]

What is an Exponential Function?

An exponential function is a mathematical function of the following form: [tex]f(x)=a^{x}[/tex]. where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e , which is equal to approximately 2.71828.

Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula [tex]y=a(1-r)^{x}[/tex] wherein y is the final amount, a is the original amount, r is the decay factor, and x(or t) is the amount of time that has passed.

Given :

The initial amount is 25,000, and the rate of decay is 6%, or 0.06.

Write the exponential Decreasing function.

[tex]A(t) = a(1-r)^{t}[/tex]

Substitute 25,000 for a and 0.06 for r.

[tex]A(t)=25,000(1-0.06)^{t} = 25,000(0.94)^{t}[/tex]

Hence , the Situation can be represented by [tex]A(t) = 25000(0.94)^{t}[/tex]

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[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$ 150\\ P=\textit{original amount deposited}\dotfill & \$600\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years \end{cases} \\\\\\ 150 = (600)(0.05)(t) \implies \cfrac{150}{(600)(0.05)}=t\implies 5=t[/tex]