Graph a right triangle with the points (-6, 4) and (-9,8) forming the hypotenuse. Using the sides, find the
distance between the two points in simplest radient form.

The original value for the first angle so that the angle measures form a triangle is 39.5°

For any triangle to be formed, its three interior angles must sum up to 180°. Thus the sum of the interior angles of a triangle is 180°

Considering, the angles: 115.1°, 47.5° and 93°, their sum which is 255.6° is not equal to 180° so they cannot form a triangle.

but a new value represented by x for the first angle 115.1° can be derived as follows;

x + 47.5° + 93° = 180°

x + 140.5 = 180° {subtract 140.5° from both sides}

x = 180° - 140.5°

x = 39.5°

Therefore, the new value for the first angle 115.1° that will make the angle measures form a triangle is 39.5°

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The answers to each part of the labelled graph is given below.

A function describes a relationship between a dependent and independent variable. Example -

y = f(x) = 5x + 9

Given are the distance - time (x{t}) and the velocity - time, (v{t}) graphs as shown in the image.

We can conclude for each part of the graph as -

The object is moving in the forward direction at a constant velocity.

The object is not moving.

The object is slowing down in the backward direction.

The object is changing directions.

The object is speeding up in the forward direction.

Therefore, the answers to each part of the labelled graph is given above.

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Answer:

Step-by-step explanation:

y=4x + (7/2)

when x=5

y=4(5)+ (7/2)

 =20+3.5             or         20+ (7/2)

 =23.5                 or          (40+7)/2 =47/2 =23.5

An Experimental study is used. As subjects were randomly assigned to two groups, and one group was given an herb and the other group a placebo. after months, the numbers of respiratory tract infections each group had were compared.

Experimental investigations or study involve introducing an intervention and observing its results. Typically, volunteers in experimental research are grouped randomly, or by chance.

During a randomized controlled trial (RCT), participants are divided into two or more groups at random. While the control group is given nothing or a placebo, the intervention group is given the new drug, for example. The outcome of each group is then investigated by the researchers. The intervention can thus be blamed for any variations in the results.

Whereas, Observational study is the Studies in which researchers look at how a risk factor, diagnostic test, treatment, or other intervention affects a population without attempting to alter who is or is not exposed to it.

Hence, it is experimental study.

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By comparing the population range to the mean of the sample ranges, the answer will be D) The population range equal the youngest official at the time of death and the mean of the sample ranges is equal to the oldest official at the time of death.

Creating a tonne of random numbers between 40 and 70 points so that we can see that the population range is equal to 70. That is presumably the oldest value that is still valid. The population range is the sum of the data generated at the highest level and the lowest level. The population range is now 30 points. by taking a handful of random samples.

We want a sample table containing random samples of the data so we don't have to worry about this. Going through the samples with the new table that will be generated here and want to find this range by taking the max of each sample. Subtracting the mean from each sample from the range samples from 1 to 10. The range for the initial data was 30 points because the entire range was 40 to 70 points; nevertheless, we can observe that this range varies from 64 to 70 points.

We made the table because we wanted the mean of the average of our separate ranges to be 21.7. The mean value of the ranges in 100 samples will be discovered if the sample size is increased. A sample's range is not representative of the population. We can infer that we do it since the samples' range and average range are greatly dissimilar.

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The angles of the rhombus are

             m∠ADC = 58°

             m∠BCD = 122°

What is a rhombus?

An example of a quadrilateral is a rhombus. It is a unique instance of a parallelogram in which the diagonals bisect each other at a 90° angle and all sides are equal.

The properties of a rhombus are:

From the figure,

In ΔDOC.

∠ODC = 180° - ( 90+61) = 29°

The diagonal bisects ∠ADC

So ∠ADC = 2∠ODC = 2 × 29° = 58°

Since the diagonal bisects the angle, ∠BCD = 2∠ACD

                                                                           = 2×61° = 122°

Therefore the angles of the rhombus are

             m∠ADC = 58°

             m∠BCD = 122°

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The histogram for the stickers from the small package is distributed as follows:

Normally.

To obtain the distribution of the histogram, we must correctly identify the mean and the median of the distribution.

Hence the distribution is defined as follows:

The ordered distribution is given as follows:

13, 15, 18, 19, 22, 24.

Hence the median is of:

(18 + 19)/2 = 18.5.

The mean is of:

(13 + 15 + 18 + 19 + 22 + 24)/6 = 18.5.

They are equal, hence the histogram is normal = symmetric;

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Answer:

A) 10

Step-by-step explanation:

3(8)(5) / 6(2) = 120/12 which equals 10

Answer: A = 10

Step-by-step explanation:

substitute the value of the variable into the equation and simplify

Hope this helps !

Answer:

most appropriate is y=3x - 13 but it is not the correct one.comparing y=3x-13 with y=mx+c the we get,m(slope)=3 whereas comparing y=X+4 with y=mx +c,we get m(slope)=1.But the slopes of parallel lines are always equal.

The correct equation for the line is y=X -1.

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Answer:

125 days

Step-by-step explanation:

1.) First, you need to make the number equivalent!

1.5L=1500mL

2.) Then you need to divide 1500mL by how much she drinks every day!

1500mL divide by 12mL = 125 days

So the carton will last 125 days

:) Hope you have a good day!

Answer:

the carton will last for 125 days

Step-by-step explanation:

carton contain 1.5L

1.5L= 1.5×1000ml

= 1500ml

1day=12ml

1/12 ×1500 days = 1500ml

125 days = 1500ml

If Ellis drink 12ml of yoghurt everyday then the carton with 1.5L will last for 125 days.

On solving the provided question, we can say that  the given function, f(6)=26.

 where a, b, and c are numbers and an is not equal to zero, is  quadratic function. A parabola is the shape of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they all share the same fundamental "U" shape.

f(n^2) = f(n) + 6

On putting n=2,

we get,

f(4) = f(2^2)  = f(2) + 6 = 8 + 6 = 14

On putting n=4, we get

f(16) = f(4^2) = f(4) + 6 = 14 + 6 = 20

On putting n=16, we get

f(256) = f(16^2) = f(16) + 6 = 20 + 6 = 26

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Answer:

The "solution" is the intersection point of the two lines when drawn on a graph plot.

Explanation:

If a graphical plot is made with sufficient resolution linear equations may be solved by observing the solution point(s) on the graph coordinates.

Question 20

The quadrilateral is a rhombus because there are four congruent sides. The quadrilateral cannot be more specifically classified as a square because one of the interior angles is not a right angle.

Question 21

The quadrilateral is a parallelogram because the diagonals bisect each other.

Question 22

The quadrilateral is a square because it is a rhombus (four congruent sides) with a right angle.

Answer: The monthly payment on a bank loan would be $480, which is lower than the monthly credit card payment.

To calculate the monthly payment on the bank loan, we can use the formula:

monthly payment = P * (r / (1 - (1 + r)^(-n)))

where P is the total loan amount, r is the annual interest rate as a decimal, and n is the number of months of the loan.

For a loan of $16,000 at 8% interest for 3 years (36 months)

r = 0.08/12 = 0.0067

n = 36

P = 16000

So, the monthly payment = 16000 * (0.0067 / (1 - (1 + 0.0067)^(-36))) = 480

To calculate the monthly credit card payment, we can use the formula:

M = P * r * (1 + r)^n / [(1 + r)^n - 1]

where P is the total loan amount, r is the monthly interest rate, and n is the number of months of the loan.

For a credit card with an annual rate of 15% for 7 years (84 months)

r = 0.15/12 = 0.0125

n = 84

P = 16000

So, the monthly payment = 16000 * 0.0125 * (1 + 0.0125)^84 / [(1 + 0.0125)^84 - 1] = 511.11

As we can see the monthly payment on the bank loan is lower than the monthly credit card payment. So, the correct answer is "The monthly payment on a bank loan would be $480, which is lower than the monthly credit card payment."

Answer:

How many couples bought tickets?

50

Step-by-step explanation:

s + 2c  = 196              Eq. 1

6s + 10c = 1076          Eq, 2

s = single tickets

c = couple tickets

From Eq. 1:

s = 196 - 2c                 Eq. 3

Replacing Eq. 3 in Eq. 2:

6(196-2c) + 10c = 1076

(6*196 + 6*-2c) + 10c = 1076

(1176 - 12c) + 10c = 1076

1176 - 2c = 1076

1176 - 1076 = 2c

100 = 2c

c = 100/2

c = 50

From Eq. 3:

s = 196 - 2c

s = 196 - 2*50

s = 196 - 100

s = 96

Check:

From Eq. 2:

6s + 10c = 1076

6*96 + 10*50 = 1076

576 + 500 = 1076

Suzanne pays $21.03 in sales tax for the computer upgrades.

Tax in math is a type of mathematical problem that involves the distribution of a certain amount of money among several parties. The problem is solved by calculating the amount of money each party needs to pay in order to make the distribution fair and equitable. This type of math problem is often used to determine the amount of taxes that need to be paid by individuals or businesses. Tax problems can also be used to analyze the effects of different tax policies on the economy.

This amount is rounded to the nearest cent and is calculated by multiplying the pre-tax cost of the upgrades ($311.60) by the sales tax rate (6.75%). Thus, the equation would be: $311.60 x 6.75% = $21.03.

Suzanne must pay an additional $21.03 for the sales tax on her purchase, making the total cost of the upgrades $331.60.

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The inequalities that represent the situation can be presented as follows;

x + y ≤ 13

16·x + 6·y ≥ 120

Please find attached the graph of the inequality created with MS Excel

An inequality is a non equal comparison between expressions, quantities, or numbers.

The specified information are;

The amount Gabriella makes lifeguarding = $16 per hour

The amount she makes walking dogs = $6 per hour

The maximum number of hours Gabriella can work in a week = 13 hours

The minimum amount Gabriella must earn in a week = $120

Let x represent the number of hours Gabriella spends lifeguarding, and let y represent the number of hours Gabriella spends walking dogs.

The system of inequalities that can be obtained based on the above details are;

The graph of the above inequalities can be obtained by making y the subject of the inequalities as follows;

y ≤ 13 - x

y ≥ (120 - 16·x)/6 = 20 - (8/3)·x

y ≥ 20 - (8/3)·x

The feasible region is in the triangle with vertices (13, 0), (7.5, 0), (4.2, 8.8)

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∠1and∠2 form a linear pair, so by the Supplement Postulate, they are supplementary. That is, m∠1+m∠2=180°. m∠2+m∠3=180°.

We must determine the dimensions of angles 1 and 2. The geometric property can be used to: When two chords collide inside of a circle, the angle that is created is half the total of the intercepted arcs of the chords. In light of this, m1 = 50° and m2 = 130°.

According to the diagram, the angles 1 and 3 are vertical, and m1 = 90. Since their measurements are equivalent, m3 = 90 and 1 and 2 are additional. Angles 1 and 2 compliment one another. Two additional angles, the total of whose measurements equals 180 degrees.

The angles 1 and 2 complement one another. Because they have a similar side, angles 1 and 2 are neighbouring angles. Adjacent angles are two angles in a plane that do not share interior points but do share a vertex and a side.

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Based on whether the function is increasing or decreasing, the slope values are calculated. Then, the required slope values of A, B, C, D, E, and F are 1/2, 0, 1, 3, -3, and -1.

We match the slopes with the points in the given graph. For this, we must know that,

We may determine the rate at which the function is increasing or decreasing by measuring the slope's magnitude. Here, in this graph, first, the slope is zero at B. Therefore, the value of the slope in B is zero (0).

We can determine from the graph that the slope is descending at points E and F. Additionally, the slope is ascending at points A, C, and D.

Therefore, slope D> slope C> slope A> slope B. So, the slope values for D, C, and A are 3, 1, and 1/2 respectively.

Also, slope F> slope E. So, the slope values for F and E are -1 and -3.

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The value of sum of squared deviations is 12.

The given population is 1,1,1,5

First find the mean:

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Mean = (Sum of all the observations/Total number of observations)

Mean=[tex]\frac{1+1+15}{4}=\frac{8}{4}=2[/tex]

The Mean is 2.

The symbol of mean is usually given by the symbol [tex]\bar x[/tex]. The bar above the letter x, represents the mean of x number of values.

[tex]\bar X[/tex] = (Sum of values ÷ Number of values)

Subtract the mean from each observation and square the resulting difference. Then add the differences to get SS:

SS=[tex](1-2)^{2}+ (1-2)^{2}+ (1-2)^{2}+ (5-2)^{2}[/tex]

[tex]=1+1+1+(3)^{2} \\=3+9\\=12[/tex]

Therefore, the value of SS is 12.

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The solution is

a) The ratio of x values to the y values from the table is 2 : 3

b) The ratio of x values to the y values from the graph is 2 : 3

c) The ratio of x values to the y values from the table and graph is equivalent

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion be represented as A

Now , the equation will be

Let the x values from the table be x = { 8 , 10 , 12 }

Let the y values from the table be y = { 12 , 15 , 18 }

Now , y = kx , where k is the proportionality constant

Substituting the values in the equation , we get

12 = k ( 8 )

Divide by 8 on both sides of the equation , we get

k = 12/8

k = 3/2

So , the ratio of x values to the y values is 1/k = 2 : 3

Now ,

15 = k ( 10 )

Divide by 10 on both sides of the equation , we get

k = 15 / 10

k = 3/2

So , the ratio of x values to the y values is 1/k = 2 : 3

And ,

18 = k ( 12 )

Divide by 12 on both sides of the equation , we get

k = 18/12

k = 3/2

So , the ratio of x values to the y values is 1/k = 2 : 3

From the graph , the ratio is also 2 : 3

Hence , the ratio of x to y is given by 2 : 3

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The scale factor that would be applied to Figure A to produce Figure B is 10/3 = 3 (1/3).

By scaling, we can create a drawing of an object that corresponds to the object's true size. In geometry, scaling refers to either growing or reducing figures in order to preserve their fundamental shape. Similar figures are those that have been scaled.

Given two pentagons in Figure A and figure B.

We are asked the scale factor from figure A to figure B.

Hence the final figure is figure B and the initial figure is Figure A.

The scale factor of any figure is defined as formulated as:

Scale factor = Dimensions of final figure ÷ Dimensions of original figure

According to the given figures we can observe that:

Length of the base of the pentagon in figure A is 5 inches, and that of figure B is 1 (1/2) = 3/2 inches.

Substituting the dimensions in the formula of the scale factor we have:

Scale factor = 5 ÷ (3/2)

Scale factor = 10/3

Converting into mixed fraction:

10/3 = 3 (1/3)

Hence, the scale factor that would be applied to Figure A to produce Figure B is 10/3 = 3 (1/3).

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If A=(4,-5) and 8 (7,-9), 7 units is the length of AB

distance = √( (7−4)^2 + (−9−(−5))^2 )

Plugging in the numbers and solving, we get:

distance = √( (3)^2 + (−4)^2 )

distance = √( 9 + 16 )

distance = √49

distance = 7 units

Therefore, the length of AB is 7 units.

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The onto functions (surjective functions) are:

c. f(m, n) = m + n + 1.

At first we have to identify onto (surjective) functions from Z x Z to Z, we need to check if each element in the codomain (Z) has at least one preimage in the domain (Z x Z).

a. f(m, n) = 2m - n

This function is not onto because for odd numbers in the codomain (Z), there is no pair of integers (m, n) in the domain that will map to them.

b. [tex]f(m, n) = m^2 - n^2[/tex]

This function is not onto because for negative numbers in the codomain (Z), there is no pair of integers (m, n) in the domain that will map to them.

c. f(m, n) = m + n + 1

This function is onto. For any integer 'z' in the codomain (Z), we can find a pair of integers (m, n) in the domain such that m + n + 1 = z.

For example, if z = 0, we can choose m = 0 and n = -1, and then m + n + 1 = 0.

d. f(m, n) = |m| - |n|

This function is not onto because negative numbers in the codomain (Z) cannot be obtained from the domain (Z x Z).

For example, there is no pair of integers (m, n) in the domain that maps to -1.

Hence, The onto functions (surjective functions) are:

c. f(m, n) = m + n + 1.

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263,187.70 rad / hour is the angular velocity of the nail in radians per hour.

The equation relating angular velocity and linear velocity is:

w = v / r

where,

w = angular velocity, v = linear velocity, and r = radius

Since r is in inches, convert v to inches:

v = (54 miles per hour) * (63360 inches / mile)

v = 3,421,440 inches / hour

Solving for w:

w = (3,421,440 inches / hour) / 13 inches

w = 263,187.70 rad / hour

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Answer:

First tank = 13 fish

Second tank = 13 fish + 8 more fish

13 + 8 = 21 fish in the second tank.

These types of questions are categorized under exponential equations which involve addition, subtraction, multiplication, and division of exponents.

Exponents is the term used to describe a way to represent huge numbers using powers. In other words, the exponential describes how many times a number has been multiplied by itself. Various rules of exponents are presented according to the capacities they possess.

The following rule governs multiplication: Add the exponents while maintaining the base's consistency.

When bases are raised by a power of two or more, multiply the exponents while maintaining the original base.

Division Rule: When dividing like bases, take the exponent of the denominator and divide it by the exponent of the numerator, keeping the exponential base constant.

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division

john stops at toy store a to buy 16 toy cars. Toy store A sells 6 toy cars for $4.20. John stops at toy store b and sees that they sell 4 toy cars for $3.80. How much money did John save by buying toy cars at toy store A?

The amount in sale tax, Suzanne paid for the computer upgrades is 21.03 dollars.

Suzanne buys upgrades for her computer . The upgrades cost $311.60 before taxes. The sales tax rate is 6.75%.

Therefore, the amount of sales tax Suzanne paid for the computer upgrades can be calculated as follows;

A sales tax is a tax paid to a governing body for the sales of certain goods and services.

amount of the sale tax = 6.75% of 311.60

amount of the sale tax = 6.75 / 100 × 311.60

amount of the sale tax = 2103.3 / 100

Therefore,

amount of the sale tax = 21.033

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