6. Choose the correct answer.
Which theorem or postulate could be used to prove the congruence of the pair of triangles?

Sketch a graph that shows the relationship between grams of honey and cups of flour needed for a bakery recipe. To know how much honey is needed for 17 cups of flour

Given data:

Let flour x grams plotted on x-axis

honey y grams plotted on y-axis

We have 2 points to find the slope of linear equation

[tex]m = \frac{y_{2}- y_{1} }{x_{2}- x_{1} } = \frac{35-14}{25-10} = \frac{21}{15} = \frac{7}{5} = 1.4[/tex]

[tex](x_{1}, y_{1}) = (10,14)\\ \\(x_{2}, y_{2}) = (25,35)[/tex]

Linear equation is

y = mx+c

[tex]y = \frac{7}{5}x+c = 1.4x+c[/tex]

Adding points (10,14) in above equation

[tex]y = \frac{7}{5}x+c \\\\14 = \frac{7}{5}*10+c\\ \\[/tex]

c = 0

So, the relation between x grams of flour requires y grams of honey is

[tex]y = \frac{7}{5}x[/tex]

or

y = 1.4x

When x = 17

[tex]y = \frac{7}{5}*17 = 23.8[/tex]

Hence the answer is, y = 23.8 g of honey is needed for 17 cups of flour.

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The vectors combined sum is equal to (-1, 1)

Given data;

Let 'w' be the vector with an initial point (2,0) and terminal point (3,2).

Let 'v' be the vector with the initial point (2,2) and terminal point (0,1).

To find the sum of two vectors, firstly;

For 'w';

w = (3 - 2)i + (2 - 0)j

w = i + 2j → (I)

For 'v';

v = (0 - 2)i + (1 - 2)j

v = -2i + j → (II)

Now,

From (I) & (II);

w + v = (i + 2j) + (-2i + j)

        = -1, 1

Hence, the sum of the vectors w + v = (-1, 1)

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Answer:

No

Step-by-step explanation:

According to the first triangle inequality theorem, the lengths of any two sides of a triangle must add up to more than the length of the third ...

18 + 21   = 38   are not more than 39  

Answer:No,the side of lengths 18m,21m and 39m could not form a

Step-by-step explanation:

To form a triangle, the sum of any two sides must be greater than the third side.

here,

18m + 21m = 39m

the sum to two side is equal to third side that is 39m

that's why these three sides cannot form any triangle

The distance between two points of a line is given as:

Distance =  [tex]\sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2 }[/tex]

The distance from Maria's desk to Monique's desk is √85.

Option B is the correct answer.

The distance between two points of a line is given as:

Distance =  [tex]\sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2 }[/tex]

We have,

Maria's desk.

We will write the coordinates in the form of (x, y).

(6, -1) = [tex](x_1, y_1)[/tex]

Monique's desk.

We will write the coordinates in the form of (x, y).

(-3, 1) = [tex](x_2, y_2)[/tex]

The distance between Maria's desk and Monique's desk.

= [tex]\sqrt{(-3 - 6)^2 + (1+1)^2 }[/tex]

= √(81 + 4)

= √85

Thus,

The distance from Maria's desk to Monique's desk is √85.

Option B is the correct answer.

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Answer: 2050

Step-by-step explanation:

The equation that represents the proportional relationship between cups and ounces is n = 0.125c

The 4 ounce = 0.5 cup

Here we have to use the unitary method

Unitary method is the method of finding the value of the single unit

One ounce = 0.5 / 4

= 0.125

Where c represents the cups and n represents the ounce

Then,

n = 0.125c

Similarly

1.5 cups = 12 ounce

1 cup = 12 / 1.5

= 8 ounce

Then,

c = 8n

Then the the correct equation is n = 0.125c

Hence, the equation that represents the proportional relationship between cups and ounces is n = 0.125c

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Answer:

n = 0.125

Step-by-step explanation:

do not listen to the other answer I don't fell like explaining but I got it correct.

The [tex]A^{-1}[/tex] for the matrix is

[tex]A^{-1} = \left[\begin{array}{ccc}-1&-1&8\\1&0&-5\\0&1&-4\end{array}\right][/tex]

How to find inverse of a matrix ?

Only square matrices with an equal number of rows and columns, such as 2 *2, 3*  3, etc., allow us to find the inverse of the matrix. The adjoint of the provided matrix is divided by the determinant of the given matrix to produce the inverse matrix, to put it simply.

[tex]A^{-1} = \frac{1}{|A|} Adj A[/tex]

|A|=-5(4-3)+4(4-3)-5(4-4)

|A|=-5+4

|A|=-1

[tex]Adj A = \left[\begin{array}{ccc}1&1&-8\\-1&0&5\\0&-1&4\end{array}\right][/tex]

[tex]A^{-1} = \frac{1}{-1}\left[\begin{array}{ccc}1&1&-8\\-1&0&5\\0&-1&4\end{array}\right][/tex]

[tex]A^{-1} = \left[\begin{array}{ccc}-1&-1&8\\-1&0&-5\\0&1&-4\end{array}\right][/tex]

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In the simplified expression, the coefficient of the term b² is -1.

When you solve any Math Operations, it is necessary to be attentive to the order of the operations.

First, you should solve the operation insides of Parentheses. After that priority is given to Exponents. Thereon,  you can solve multiplication or division operations from left to right. Finally, addition or subtraction  from left to right

See the order below

The question gives the expression (4a² +2ab) - (2a² -ab + b²). Therefore, for solving the expression you should follow the order of the math operations.

       4a² +2ab -2a² +ab - b²

       2a²+3ab-b²

Like, there are no more similar terms. Therefore, you can represent the expression (4a² +2ab) - (2a² -ab + b²) by  the expression  2a²+3ab-b².

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Answer:

[tex]\frac{\sqrt{170} }{7}[/tex]

Step-by-step explanation:

Length = x

Width = 7x

Therefore 7x into x = 170, Rectangle area formula

7x^2=170

7x=root over 170

x = root over 170/ 7

Answer:

(0,0) o girls make 0 bracelets.

(1,4)  1 girl makes 4 braclets

Step-by-step explanation:

The answer  r = 7, and the missing terms are -2, -14, -98, -686, -4802. in the Geometric progression.

What is Geometric progression?

A geometric progression, sometimes termed a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio. A geometric progression with the common ratio 3 is, for instance, the sequence 2, 6, 18, 54,... A geometric series having a common ratio of 1/2 is also 10, 5, 2.5, 1.25, etc.

By calculating the product of the values of a set of numbers, the Geometric Mean (GM) is the average value or mean that denotes the central tendency of the data. The average of the data set's numbers is defined by the mean. There are several distinct forms of means, including arithmetic mean (AM), geometric mean (GM), and harmonic mean (HM).

Here 1st term a = -2

4th term given is ar³= -686

r³= -686/-2

r=∛343

a) r=7

2nd term will be  -14

3rd term will be -98

5th term will be -4802

b) -2, -14, -98, -686, -4802.

Hence, r = 7, and the missing terms are -2, -14, -98, -686, -4802.

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Answer:

18/25 chapters / hour

Step-by-step explanation:

Answer:

i believe its 1.2

Step-by-step explanation:

hopethishelpsya:)

The answer is 6/5.

When the numerator is always higher than or equal to the denominator, the fraction is said to be an improper fraction.  When a fraction contains a whole number and a proper fraction is said to be a mixed fraction.

Write the given equation with mixed fraction to an improper fraction,

[tex]2\frac{1}{4}+\frac{2}{5}\div \left(\frac{-1}{2}\right)-\frac{1}{4}=\frac{9}{4}+\frac{2}{5}\div \left(\frac{-1}{2}\right)-\frac{1}{4}[/tex]

When we divide a fraction, we convert division into multiplication by turning the fraction upside down. Here, we convert the division sign before (-1/2) into multiplication by changing this fraction upside down as (-2/1).

Therefore,

[tex]2\frac{1}{4}+\frac{2}{5}\div \left(\frac{-1}{2}\right)-\frac{1}{4}=\frac{9}{4}+\left(\frac{2}{5}\times\left(\frac{-2}{1}\right)\right)-\frac{1}{4}[/tex]

Now using the BODMAS rule, solve the bracket first. Followed by multiplication, addition, and subtraction.

[tex]\begin{aligned}2\frac{1}{4}+\frac{2}{5}\div \left(\frac{-1}{2}\right)-\frac{1}{4}&=\frac{9}{4}-{\frac{4}{5}-\frac{1}{4}\\&=\frac{8}{4}-\frac{4}{5}\\&=\frac{40-16}{20}\\&=\frac{24}{20}\\&=\frac{6}{5}\end{aligned}[/tex]

Therefore, the answer is 6/5.

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The complete question is -

Simply the given expression 2 1/4+2/5÷(−1/2)−1/4

Answer:a polygon cannot have 7.2 sides

Step-by-step explanation:

each exterior angle of a regular polygon with n sides is equal and these angles add up to 360∘ . a polygon cannot have 7.2 sides. since , the exterior angle of a regular polygon cannot be 50∘

Answer:

72

Step-by-step explanation:

- reason why it's 72

tens            ones

(2+5)=7             2

A/Q:

Answer: The answer would be B, The number of movies purchased by an individual subscriber for a particular month.

Step-by-step explanation:

Looking at the problem and graph it can be determined there is a day and date purchased. But there isn't a time frame over the course of a few months.

Using only the information in the database, we can conclude that the answer will be B, The number of movies purchased by an individual subscriber for a particular month.

There is a day and date purchased, it can be seen by looking at the problem and graph. But there isn't a timeline that spans several months. A graph is a diagram or visual representation that organizes the presentation of facts or values. The points on a graph are typically used to depict the relationships between two or more things. A straightforward two-dimensional graph is created when a vertical and horizontal line join at the origin. The y axis is vertical and the x axis is horizontal. In simple line graphs, the x and y axes are divided into evenly spaced subdivisions and assigned integer values.

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x=-1

Step-by-step explanation:

3(-2x+1)-2(x+13)=7x-4(1-x)

-6x+3-2x-26=7x-4+4x

-8x+3=7x-4+4x+26

-8x+3=7x+4x+22

-8x+3=11x+22

-8x-11x=22-3

-19x=19

-19/19x = 19/-19

x = -1

The minimum unit cost of the car is $12232.1

Given: cost function C(x)=0.9x² - 414x + 59,366

In order to find the minimum point, take the derivative of the cost function:

dC/dx = 2x - 414          (equate to zero and solve for x)

2x - 414 = 0                

2x = 414

x = 414/2 = 207

Thus, the minimum point is at x =207

The minimum unit cost can be obtained by substituting x = 207 into the cost equation:

C(x) = 0.9x² - 414x + 59,366

C(207) = 0.9(207)² - 414(207) +  59,366

          = 38564.1 - 85698 + 59,366

           = $12232.1

Therefore, the minimum unit cost is $12232.1

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Using the concepts of unitary method, we got that 4 cups of  pancake mix will be required to yield 60 pancakes.

The unitary method is the method for solving the problem by the first value of a single unit and then finding the value by multiplying the single value.

We are given that one cup of pancake mix will yield 15 pancakes, and we are asked to yield 60 pancakes.

So,15 pancakes will be yielded by as many as pancake mix=1

therefore, 60  pancakes will be yielded by as many as pancake mix=(60/15)=4.

Hence, if one cup of pancake mix will yield 15 pancakes, then  4 cups of pancake mix will be required to yield 60 pancakes.

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Answer:

11

Step-by-step explanation:

1x2x3x5 = 30  Product means the answer in a mulitplication problem.

Sum is the answer to an addition problem

1+2+3+5 = 11

Force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity.

Forces it to accelerate in the direction of the force , this is a vector quantity that is represented in newtons.

net force = total pulling force = weight of the hanging mass.

Force will remain constant.

acceleration = constant pulling force / total mass to be pulled.

acceleration also remain constant.

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Answer: 4.4

Step-by-step explanation:

First, know that 10% is equal to 0.1. Calculate 10% of 4 and add that to 4 to find the final value:

[tex]4+4*0.1=4+0.4=4.4[/tex]

Answer: 14

Step-by-step explanation:

What is 10 more than 4 We are looking for a new number which is 10 more than 4 We will get the new number by adding 10 to 4 We write it down as: 4+10=14

The relative humidity is a measure the average amount of vapor in the air and the random sample of 100 days refers the distribution displays a gap with a potential outlier located between 40% and 45%.

Average:

Basically, the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set is known as an average.

Given

Relative humidity is a measure, expressed as a percentage, of the amount of water vapor present in air. the following histogram summarizes the relative humidity, at noon, for a random sample of 100 days for a certain city.

Here we need to find the best description of the distribution

Basically, the relative humidity is a variable expressed as a percentage that represents the amount of water vapor present in air. It can be  is used to monitor and predict weather conditions, and it is calculated based on the temperature of the air.

And it is also independent of temperature because a high temperature can have low relative humidity and vice-versa.

While we looking into the given question, there are no observed data values between 45% relative humidity and 55% relative humidity, so there is a gap displayed in the distribution.

Therefore, the value located between 40% and 45% is unusually small when compared with the other data values. And this point are known as outliers that are used to test that it is an outlier would require using the 1.5×IQR rule or using the two standard deviations rule.

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The factorization of the expression is -3(1+3z+7y+0.8)

Factorisation of an algebraic expression means writing the given expression as a product of its factors. These factors can be numbers, variables, or an algebraic expression.

To the factor a number means to break it up into numbers that can be multiplied to get the original number.

in the expression, -3 −9z−21y−2.4, it is discovered that -3 is a common factor in all the terms.

Therefore dividing all the terms by -3 and bring -3 out of parentheses we have -3(1+3z+7y+0.8)

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The correct statement of the inequality representation is d On a number line, −5 is located to the right of –6.

A number line is a horizontal representation of parts with equal intervals

The numbers in a number line is arranged to be increasing from left to right , hence drawing a number line will have the smaller values to the left of the bigger values

-5 > -6

this is read as -5 is greater than -6 therefore

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The effect that sample size on the mean of the sampling distribution has is that it effects the variations .

In the question ,

If the sample size is increased ,

which means if the number of sample is increased then the errors in the sampling distribution becomes very less .

and if the sample size is decreased then it leads to the increase in the error  of the distribution .

The formula for the relationship between variation and sample size is given by ,

σx = σ / sqrt (n)

we can see that the variation and sample size are inversely proportional .

Which means that increase in the sample size results in a reduction of variation.

Therefore , The effect that sample size on the mean of the sampling distribution has is that it effects the variations .

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Answer:

10.49

Step-by-step explanation:

We should solve this by subtracting the total amount of fuel minus the gallons left to find the gallons used.

In other words:

Subtract the total amount of fuel minus the gallons left

[tex]15.04 -4.9[/tex]

Answer:

[tex]10.49[/tex]

I hope this answers your question :)

Note: Make sure you line up the decimal places!!

experimental probability = 0.6

What is experimental probability ?

Actual experiments and sufficient documentation of the occurrence of occurrences serve as the foundation for experimental probability, sometimes referred to as empirical probability. A number of real experiments are carried out in order to ascertain the likelihood of any event. Random experiments are studies that don't have a predetermined outcome. The results of such experiments are unpredictable. The likelihood of random experiments is calculated repeatedly. A trial is a repeating of an experiment that is performed a certain number of times. The experimental probability's mathematical formula is denoted by;

Probability of an Event P(E) = Number of Trials / Total Number of Occurrences of an Event

15 times were used in the experiment by Kendra.

According to the table, out of the 15 instances, we receive a blonde class leader 9 times.

Therefore, the experimental likelihood that the class leader for this week has blonde hair is = [tex]\frac{n(blonde)}{n(all trails)} =\frac{9}{15} =\frac{3}{5} = 0.6[/tex]

0.6 will be the experimental probability that this week's class leader will

have blonde hair

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