In the diagram below, isosceles triangle ABC is drawn with AB is congruent AC and side BC extended through point D. If
m/ACB=2x+16 and m angle ACD=5x+24, find the measure of angle A.

The ratios, 1 : 4 and 2 :6 are not equivalent.

Ratio shows the relationship that exist between two or more numbers. Ratio is used to compare two or more numbers. It shows the number of times that one value is contained within other value(s).

In order to determine if the ratios are equivalent, express 2 : 6 in its simplest form. To do this, divide 2 and 6 by 2, a common  multiple of both numbers.

2 :6 in its simplest form is 1 : 3

Since, 1 : 3 is different from 1 : 4, the ratios are not equivalent.

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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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An ordered stem-and-leaf plot has the following results:

0=4 counts

1=7 counts

2=6 counts

3=4 counts

4=1 count

The shape of the distribution is skewed to the right

Part 1

An ordered stem-and-leaf plot:

                              Total Counts          

0 | 3 4 5 7             | 4

1 | 2 2 4 4 5 7 7    | 7

2 | 0 3 4 4 5 8      | 6

3 | 3 4 7 9             | 4

4 | 1                       | 1

Part 2

Shape of distribution

When the data in the stem-and-leaf plot given above is plotted in graph, the tail of the plot will be on the right. Hence, the shape of the distribution is skewed to the right

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Step-by-step explanation:

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

Solution;

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 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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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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a)The expression for the total cost for all four classes can be given as 32s + 200. b) the rational expression for the cost per student is 2(4s+25)/s c) if each class has 20 students then the cost per student is equal to $10.50.

a) Total cost expression can be determined as follows:

total fees of admission + fees of bus = total cost

total cost = (4s × 8) + 200

total cost = 32s + 200

b) A rational expression to determine the cost per student can be calculated as follows:

cost per student = total cost ÷ the total number of students

cost per student = 32s + 200 ÷ 4s

We now factor the numerator by using its GCF;

cost per student = 4 × 2 (4s + 25) / 4×s

cost per student =2 (4s + 25) / s

c) Now using this expression we can find the cost per student if each class has 20 students;

cost per student = 2 (4s + 25) / s

cost per student = 2 ( 4×20 + 25)/ 20

cost per student = 2 ( 80 + 25) / 20

cost per student = 2 (105) / 20

cost per student = 210 / 20 = $10.50

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Notice that

Then, the answer is c=25.

Answer:

-20j+ 6j=-14j

-14j + 18j=4j

4j-9j=-5j

-5j=-3-17

-5j =-20

j =-20÷-5

j =4

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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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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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:

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

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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Answer:

57

Step-by-step explanation:

75/100 *76

5700/100 =57

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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Answer: The graph that matches the equation:

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.

This polynomial have 5 degree , 4 terms and one connstant

Algebraic expressions called polynomials only have non-negative integer powers for their variables. A polynomial is, for instance, Expressions with one or more terms that have a non-zero coefficient are called polynomials. The terminology include constants, exponents, and variables. The "leading term" refers to the first term of the polynomial in standard form. A standard polynomial is one in which the first term, which has the highest degree, is followed by succeeding terms that are organized in descending order of the exponents or powers of the variables, then by constant values. A "coefficient" is a number that has been multiplied by a variable.

Given that : [tex]9m^{5}+3n^{2} +2q^{2} +1[/tex]

[tex]9m^{5}+3n^{2} +2q^{2} +1[/tex]

This polynomial have 5 degree , 4 terms and one connstant

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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]

The most appropriate choice for fraction will be given by

Fraction of banana bread will be donated to the homeless is [tex]\frac{1}{4}[/tex]

What is a fraction?

Suppose there is a collection of objects and some part of the objects are taken from the collection. The part which has been taken is called fraction. In other words, part of a whole is called fraction.

The upper part of the fraction is called numerator and the lower part of the fraction is called denominator.

Here,

Total number of banana breads 16

Number of adults who got banana bread = 6

Number of Children who got banana bread = 6

Total number of children and adult who got banana bread = 6 + 6 = 12

Number of banana breads given to the homeless = 16 - 12 = 4

Fraction of banana bread given to the homeless = [tex]\frac{4}{16}[/tex]

                                                                                 = [tex]\frac{1}{4}[/tex]

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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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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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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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