Simplify the expression .
A.
B.
C.
D.

Answer:

-20j+ 6j=-14j

-14j + 18j=4j

4j-9j=-5j

-5j=-3-17

-5j =-20

j =-20÷-5

j =4

To transform A to A', B to B' and C to C' rotate the triangle ABC clock- wise 90° about the A.

Simple polygons with three sides and three internal angles make up triangles.

It is one of the fundamental geometric shapes in which the three vertices are connected to one another.

Triangles come in 4 different varieties.

1. Equilateral: Equilateral triangles have three equal sides and three identical 60-degree angles.

2. Isosceles: Isosceles triangles have equal sides and angles on both of their two sides.

3. Right-angled: In right-angled triangles, one of the angles is a right angle (90°).

4. Scalene: Triangles with this property do not have equal sides or angles.

To transform A to A', B to B' and C to C' rotate the Triangle ABC 90° clock- wise about the A.

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The greatest number of equations are available in all the types specified in option A), option B) and option C). So 'all of the above' is the correct choice.

As given in the question,

Let us discuss

option A) Equations with no solutions

examples are:

x+ y = 0

x+ y = 1

Many such pairs of simultaneous linear equations can be formulated and number of such equations possible is infinite.

Let us discuss

option B) Equations with infinitely many solutions

example:

x+ y = 0

Number of such equations possible is infinite.

Let us discuss

option C) Equations with exactly one solution

example:

x=4

Number of such equations possible is infinite.

Therefore, the greatest number of equations are available in all the types specified in option A), option B) and option C). So 'all of the above' is the correct choice.

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By using subtraction, we get that, the total yardage for the drive was that they gained 7 yards.

We are given that:

On a drive,

A football team first gains = 3 yards.

Then it lost = 11 yards.

Then it again gained = 15 yards.

We need to find its total yardage.

For this, we will subtract the yards lost from the yards gained by the team.

So, we get that:

total yardage = 3 + 15 - 11

total yardage = 18 - 11

total yardage = 7 yards.

Therefore, by using subtraction, we get that, the total yardage for the drive was that they gained 7 yards.

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Answer:

M∠2 = 37°

M∠3 = 143°

M∠4 = 37°

Step-by-step explanation:

∠3 is the complete opposite of ∠1

143° + 143° = 286°

there is 360° in a full circle or a repeating angle (aka the scissors)

360°-286°=74°

since ∠2 and ∠4 is opposite of each other

74°÷2=37°

Answer:

[tex]m \angle 2= \boxed{37}\;^{\circ}\\\\m \angle 3= \boxed{143}\;^{\circ}\\\\m \angle 4= \boxed{37}\;^{\circ}[/tex]

Step-by-step explanation:

Angles on a straight line sum to 180°.

⇒ m∠1 + m∠2 = 180°

⇒ 143° + m∠2 = 180°

⇒ m∠2 = 37°

Vertical Angle Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Applying the Vertical Angle Theorem:

The issue price (present value) of the bonds issued by Frontier World is $42,223,423.81.

The present value refers to the discounted future cash flows of the bonds (including interests and the repayment of the bonds).

The present value represents the current price of the bonds, at which they are issued.

The present value can be computed using the online finance calculator.

N (# of periods) = 20 (10 x 2)

I/Y (Interest per year) = 6% (Market Rate)

PMT (Periodic Payment) = $1,375,500

FV (Future Value) = $39,300,000

Bond Interest Rate = 7%

June 30 = $1,375,500 ($39,300,000 x 3.5%)

Dec. 31 = $1,375,500 ($39,300,000 x 3.5%)

Results:

Present Value (PV) = $42,223,423.81

Sum of all periodic payments = $27,510,000 ($1,375,500 x 20)

Total Interest = $24,586,576.19

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Required: 1-a. If the market rate is 6%, calculate the issue price. (FV of $1, PV of $1, FVA of $1, and PVA of $1)

The expression can be rewritten as:

2*(n - 3)

This is twice an integer number, so this is an even number

Here we know that n is an integer larger than 1, and we have the expression:

n² - (n - 2)² - 2

Now, remember that for any integer m, 2m is always an even number.

Expanding the term in the middle of the expression we get:

n² - (n - 2)² - 2

n² - (n² - 4n + 4) - 2

4n - 4 - 2 = 4n - 6 = 2*(n - 3)

Integer numbers are closed under addition, then n - 3 is an integer, so we have:

2*(n - 3)

This is twice an integer, so this is an even number.

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Answer:

57

Step-by-step explanation:

75/100 *76

5700/100 =57

The features of a binomial experiment are

From the question, we understand that the experiment is a binomial experiment

As a general rule, a binomial experiment is any experiment that has only two possible outcomes

These outcomes are represented as

These outcomes can also be represented as

The representation of the outcomes are:

There are other features of a binomial experiment.

One of these features is:

The binomial experiment has a number of n identical or unique trials

Another features of a binomial experiment is

The probability of success on one trial is the same for all other trials

Hence, the two other features of a binomial experiment are

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Answer:

x = 11°

Step-by-step explanation:

Hello!

These angles are called vertical angles or angles opposite to each other during the intersection of two lines.

Vertical angles are equal to each other, so we can set the expressions equal to each other and solve for x.

The value of x is 11°.

Answer:

[tex]x=\boxed{11}[/tex]

Step-by-step explanation:

Vertical Angle Theorem

The opposite vertical angles of two straight intersecting lines are congruent.

Therefore, equate the expressions and solve for x:

[tex]\boxed{\begin{aligned}(9x-4)^{\circ}&=(8x+7)^{\circ}\\9x-4&=8x+7\\9x-4-8x&=8x+7-8x\\x-4&=7\\x-4+4&=7+4\\x&=11\end{aligned}}[/tex]

Therefore:

[tex]x=\boxed{11}[/tex]

Answer:

9  57/ 100

Step-by-step explanation:o convert the decimal 9.57 to a fraction, just follow these steps:

Step 1: Write down the number as a fraction of one:

9.57 = 9.57/ 1

Step 2: Multiply both top and bottom by 10 for every number after the decimal point:

As we have 2 numbers after the decimal point, we multiply both numerator and denominator by 100. So,

9.57 / 1

= (9.57 × 100)

(1 × 100)

= 9 57/ 100

.

(This fraction is alread reduced, We can't reduce it any further).

As the numerator is greater than the denominator, we have an IMPROPER fraction, so we can also express it as a MIXED NUMBER, thus 9 57/ 100

is also equal to 9 57/ 100

when expressed as a mixed numbeR

Answer:

9 3/4

Step-by-step explanation:

Convert to a mixed number by placing the numbers to the right of the decimal over 100. Reduce the fraction.

Answer:

Step-by-step explanation:

it can be simplified to [tex]\frac{sec \theta}{cot\theta+tan\theta} =sin\theta[/tex]  . if you multiply each side by the denominator, it becomes [tex]sec\theta=\frac{sin^2\theta}{cos\theta} + cos\theta[/tex] since [tex]tan\theta=\frac{sin\theta}{cos\theta}[/tex] and cotan is the reciprocal of that. Because [tex]sec\theta=\frac{1}{cos\theta}[/tex] so multiplying each side gives [tex]1=sin^2\theta+cos^2\theta[/tex], and [tex]sin^2\theta+cos^2\theta[/tex] is equal to 1.

Considering the definition of an equation and the way to solve it, the number of monthly movies watched that would make the two plans have an equal monthly cost is 26.

An equation is an algebraic equality in which there are unknowns with unknown value. The unknown represents the number, if any, that makes the equality true. This unknown number is the solution of the equation.

This is, the solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:

Being "x" the number of monthly movies watched, you know that:

If the two plans have an equal monthly cost, the equation in this case is:

A= B

34 + 2x= 8 + 3x

Solving:

34 - 8= 3x - 2x

26= x

Finally, 26 monthly movies watched would make the two plans have an equal monthly cost.

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Answer:

A. 7:10

B. 10:17

Explanation: The ratio of A. would be 14:20, simplified would be 7:10. The ratio of B. would be 20:34, simplified being half of both numbers. Giving you 10:17.

Answer:

x < -4 or x > -2

Step-by-step explanation:

[tex]2 |x + 3| + 1 > 3[/tex]

[tex]2 |x + 3| > 2[/tex]

[tex] |x + 3| > 1[/tex]

x + 3 > 1 or x + 3 < -1

x > -2 or x < -4

Answer:

Step-by-step explanation:

Answer: The graph that matches the equation:

The line on the graph is a function

The given parameter is the graph

From the graph, we can see that the curve or the line is a quadratic function

As a general rule, all lines represented by a quadratic function are functions

This implies that the line is a function

It should be noted that:

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

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The function modeling given situation, where y represents the total weight of the crates in pounds, has a range described by the inequality 0 ≤ y ≤ 2000. The correct answer would be an option (C).

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The set that includes all the output values that the function expects is the range of a function.

The following information is provided regarding the input and output for this problem

The number of containers placed inside the vehicle as input.

Total weight of the crates loaded into the truck or output.

The range of this problem is represented by the following inequality:

0 ≤ y ≤ 2000.

The weight of an amount will never assume a negative value, and the maximum weight is 2,000 pounds, as stated in the problem.

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The exponential function which shows the exponential growth rate of graduating women is: A(t) = A₀e∧(0.037t).

The following equation can be used to calculate an exponential function again for number of women graduating from four-year colleges in t years after 1930:

A(t) = A₀e∧(rt)

In which A₀ is the starting point and r is the exponential growth rate expressed as a decimal.

In 1930, 48780 women received a bachelor's degree.

This implies that;

A₀ = 48780

In 2004, approximately 756000  people

The year 2003 is 73 years after 1930, that also means

Using the equation as an example:

A(t) = A₀e∧(rt)

Put the values;

756000 = 48780 e∧(73r)

e∧(73r) = 756000/ 48780

e∧(73r) = 15.49

Taking log both side;

73r = ㏑ 15.49

r = 2.7/7

r = 0.037

The function becomes;

A(t) = A₀e∧(0.037t)

Thus, the exponential function which shows the exponential growth rate of graduating women is: A(t) = A₀e∧(0.037t).

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Notice that

Then, the answer is c=25.

Answer:

To one decimal place, x = 7.7 cm

Step-by-step explanation:

Let y equal BD.

Since AD is a bisector of angle BAC, angle DAB is 17°.

tan(17°) = y/21, so y = 21 tan(17°)

tan(34°) = (x + 21 tan(17°))/21

21 tan(34°) = x + 21 tan(17°)

x = 21(tan(34°) - tan(17°)) = 7.7 cm

The equation of the line is y = -400x + 800

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

The given parameters are

Initial number of gallon, c = 800

Constant rate, m = -400 gallons per hour

This means that

Slope = -400

y-intercept = 800

A linear equation is represented as

y = slope * x + y-intercept

i.e.

y = mx + c

So, we have

y = -400x + 800

Hence. the equation of the amount of grain is y = -400x + 800

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Step-by-step explanation:

we can find the number of students passed in both subject by following method.

Solution;

EXPLANATION

The perimeter Perimeter is given by the sum of the sides as follows:

P = z + 5 + z + 5 + z + z

Substituting P=26 and adding like terms,

26 = 10 + 4z

Subtracting -10 to both sides:

26 - 10 = 10 - 10 + 4z

Simplifying:

16 = 4z

Dividing both sides by 4:

16/4 = z

Switching and simplifying:

z = 4

So,

Equation: 26 = 10 + 4z

z = 4

If you want to make an annual salary of $31,836, then your sales must be $25,280

Ok, so you want to earn a total of $31,836, and he has a fixed salary of $30,572, so the missing amount is:

$31,836 - $30,572 = $1,264

Now, we know that you make a commission of the 5% of what you sell, so if X is what you sell, then to make the desired salary X must be:

X*0.05 = $1,264

Solving that linear equation for X we get:

X = $1,264/0.05 = $25,280

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