The adjacent angles ∠1 and ∠2 have measures of

Answer:

y-7=x-4

Step-by-step explanation:

If you change the equation to y=mx+b yout would get Y=x+3 plug in the point (4,7) and you would get 7=4+3

7=7 so that is correct.

Answer:

C. 16 days

Step-by-step explanation:

Let´s say each worker does 1 ¨work¨, for each day, in order to complete the job in 15 days. That´s a total of 150 work.

If only 6 workers worked for the first 5 days, then we only do 30 by Day 5.

2 more workers join, so they do 8 work each day, 24 work in 3 days, 54 work by Day 8.

4 more workers join to complete the job, so we now do 12 work each day.

150 - 54 = 96

96 work is left to do, which would be done in 8 days by 12 workers.

8 days + 8 days = 16 days

Answer:

\(y = 6\\\\x = 6\sqrt{2}\\x=8.485\)

Step-by-step explanation:

The base-angles converse theorem states that in a triangle where two angles are congruent, the sides opposite the congruent angles are congruent. One can apply this theorem to the given triangle, and thus, y = 6, because of the base angles converse theorem.

It is also given that the given triangle is a right triangle, therefore, the isosceles triangle with a right angle theorem is applicable. This theorem states that in a right triangle (a triangle with a right angle), that is isosceles (two sides are congruent), the third side (non-congruent side) is equal to the length of the two congruent sides times the square root of (2). Hence, x = \(6\sqrt{2}\), in the decimal form that is 8.485.

Answer:F + S = 124

Step-by-step explanation:

Also, you want the total mixture to contain 8% vinegar so: .06F + .11S = .08(310)

Now, we can solve the system of equations using substitution.

F + S = 310

.06F + .11S = .08(310)

F = 310 - S      [solve 1st equation for F]

.06(310 - S) + .11S = .08(310)     [substitute into 2nd equation]

18.6 -.06S +.11S = 24.8

.05S = 6.2

S = 124

Answer:

The mean is 16

Step-by-step explanation:

15+17+20+15+13 =80

80÷5=16

Answer:

\( - 2 \sqrt{5} \)

Step-by-step explanation:

\( \sqrt{20} - \sqrt{80} \)

\(2 \sqrt{5} - 4 \sqrt{5} \)

\((2 - 4) \sqrt{5} \)

\( - 2 \sqrt{5} \)

Answer:

1/2 - 4, 1/2 2, 2 1/4,

Step-by-step explanation:

1/2, - 4 1/2 2,2,1/4

The table when completed looks like this:

x   -2   -1   0   1   2

f(x) 4   2   1    2   4.

We plot these points on the graph: (-2, 4), (-1, 2), (0, 1), (1, 2), (2, 4).

A function exists as a relation between a dependent variable (f(x)) and an expression of an independent variable (x), utilized to define the value of a dependent variable from a provided value of an independent variable.

We have been given a function,

\($f(x)=\left \{ {{(1/2)^{x},x\leq 0 } \atop {2^x > 0}} \right.\)

We have to estimate the value of f(x) when x = {-2, -1, 0, 1, 2}

If the values of x ≤ 0, take f(x) = (1/2)ˣ then

f(-2) = (1/2)⁻² = 2² = 4

f(-1) = (1/2)⁻¹ = 2¹ = 2

f(0) = (1/2)⁰ = 1

If the values of x > 0,  take f(x) = 2ˣ then

f(1) = 2¹ = 2

f(2) = 2² = 4

The table exists as follows

x   -2   -1   0   1   2

f(x) 4   2   1    2   4.

We plot these points on the graph: (-2, 4), (-1, 2), (0, 1), (1, 2), (2, 4).

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-18/35 is the answer to (-3/5) divided by (7/6)

The answer is 1.C 2.$500

Answer:

✔️∆ACD is a scalene triangle

✔️∆ABC is an isosceles triangle

✔️∆ABD is a scalene triangle

Step-by-step explanation:

✔️All three sides of ∆ACD are of different lengths, therefore, judging by side lengths, ∆ACD is a scalene triangle.

✔️∆ABC has two equal side lengths, AC and BC. ∆ABC is an isosceles triangle because isosceles triangles have two equal sides.

✔️BC = AC

AC² = 5² - 3² (pythagorean theorem)

AC² = 25 - 9 = 16

AC = √16 = 4

Therefore, BC = 4

In ∆ABD,

BD = 4 + 3 = 7

AD = 5

AB = 5.7

All three sides are unequal, therefore ∆ABD is a scalene triangle.

\(\bf Step-by-step~explanation:\)

Let's look at (a) first. Since -5 is in parenthesis, we have to replace x with -5. You do the same thing on (b): replace x with 2.

\(\bf Step~1~(a):\)

We have to replace x with -5.

\(\bf f(x)=x^2-2x\\f(-5)=(-5)^2-2(-5)\\f(-5)=25-2(-5)\\f(-5)=25+10\\f(-5)=35\)

\(\bf Step~2~(b):\)

We have to replace x with 2 now.

\(\bf f(x)=x^2-2x\\f(2)=2^2-2(2)\\f(2)=4-2(2)\\f(2)=4-4\\f(2)=0\)

\(\large\boxed {\bf Our~final~answer:~f(-5)=35; ~f(2)=0}\)

The survey would also ask the respondent to provide an estimate of their total credit card spending in the past 12 months.

The survey would ask questions about the respondent's credit card usage, such as how often they use credit cards, what types of purchases they make with credit cards, how much they spend on average each month, and any other related questions.

The survey would also ask the respondent to provide an estimate of their total credit card spending in the past 12 months. The survey should also include a margin of error of +/- $3500 to ensure the accuracy of the results.

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Answer:

Step-by-step explanation:

As we know that from a theorem,

A greater angle of a triangle is opposite a greater side. Let ABC be a triangle in which angle ABC is greater than angle BCA; then side AC is also greater than side AB. For if it is not greater, then AC is either equal to AB or less.

As we have  angle A =120 so it means the other 2 angles will be less than angle A , hence the opposite side to angle A is BC ,

Hence BC line is the longest line in triangle ABC

Case : BC is the longest side

#Remember that the total degree of triangle is 180°

#If A° = 120° so B° + C° = 180°-120°

B° + C° = 60°

#From here, you already know that even the total of both of B and C is less than 120° which is the degree of A.

#If you are gonna find the length of BC, then you need to use trigonometry which will be

BC/sinA = AB/sinB = AC/sinC

#so, from here you can know that BC will be the longest one, because bigger the value, in sin, will be smaller the value

x < -2 is the solution for the given inequality.

To solve the inequality:

-3(x - 3) > 5 - 5x

We can start by using the distributive property and simplifying both sides of the inequality:

-3x + 9 > 5 - 5x

Next, we can add 5x to both sides of the inequality to get the x terms on one side:

2x + 9 > 5

Then, we can subtract 9 from both sides of the inequality to isolate the variable:

2x > -4

Finally, we divide both sides by 2, remembering to reverse the inequality because we are dividing by a negative number (-3):

x < -2

Therefore, the solution to the inequality is x < -2.

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Answer:

Your answer will be B. A town's population grows at a rate of 7.2% every year.

Step-by-step explanation:

Pls give me brainliest thx

Answer:

If f(-5) = 7, then the point P(-5, 7) will be on the graph of f

where -5 is the x-coordinate and 7 is the y-coordinate

Step-by-step explanation:

The plot of the residuals to the area indicates that the graph that corresponds to the residuals is the second option.

Please find attached the graph of the residual plot for the data created with MS Excel

A residual plot is a tool used for assessment of statistical models, to determine how fit the model is to the data. A residual plot is a plot of the residuals to the input or x-values of the data.

The trend line for the data in the question obtained using MS Excel indicates that we get; y = 0.1128·x + 3.6158

The residuals, which is the difference between the actual values and the calculated value obtained using MS Excel are;

Area (in²)    \({}\)              Residuals

x-value

5 \({}\)                             -1.0178

10 \({}\)                           -0.2718

24 \({}\)                           0.605

46 \({}\)                           0.7874

53 \({}\)                           0.7018

78 \({}\)                           0.0758

84 \({}\)                           -0.129

100 \({}\)                         -0.7538

The above values for the areas and the residuals indicates that the residual plot is n shaped, with the first two values being below the x-axis, which corresponds to the second option

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Recall: SOHCAHTOA

Sin M = Opp/Hyp

Reference angle = M

Opp = 3√/21

Hyp = 15

Sin M = (3-√21)/15

Sin M = √21/5

Cos M = Adj/Hyp

Reference angle = M

Adj = 6

Hyp = 15

Cos M = 6/15

Cos M = 2/5

Tan M = Opp/Adj

Reference angle = M

Opp = 3√21

Adj = 6

Tan M = (3√21)/6

Tan M = √21/2

:Therefore: Sin M = √21/5

Cos M = 2/5

Tan M = √21/2

Answer:

\(\sf \sin M=\boxed{\dfrac{\sqrt{21}}{5}}\)

Step-by-step explanation:

Trigonometric ratios

\(\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}\)

where:

Given:

\(\sf \sin M=\dfrac{3\sqrt{21}}{15}\quad\cos M=\dfrac{6}{15}\quad\tan M=\dfrac{3\sqrt{21}}{6}\)

\(\implies \sf \sin M=\dfrac{3\sqrt{21}}{15}=\dfrac{\sqrt{21}}{5}\)

The statements supported by the data in the table are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

To determine which statements are supported by the data in the table, let's analyze the given information:

The mean number of cars sold in a month is the same at both dealerships.

To calculate the mean, we need to find the average number of cars sold each month at each dealership.

For Admiral Autos:

(4 + 19 + 15 + 10 + 17) / 5 = 65 / 5 = 13

For Countywide Cars:

(9 + 17 + 14 + 10 + 15) / 5 = 65 / 5 = 13

Since both dealerships have an average of 13 cars sold per month, the statement is supported.

The median number of cars sold in a month is the same at both dealerships.

To find the median, we arrange the numbers in ascending order and select the middle value.

For Admiral Autos: 4, 10, 15, 17, 19

Median = 15

For Countywide Cars: 9, 10, 14, 15, 17

Median = 14

Since the medians are different (15 for Admiral Autos and 14 for Countywide Cars), the statement is not supported.

The total number of cars sold is the same at both dealerships.

To find the total number of cars sold, we sum up the values for each dealership.

For Admiral Autos: 4 + 19 + 15 + 10 + 17 = 65

For Countywide Cars: 9 + 17 + 14 + 10 + 15 = 65

Since both dealerships sold a total of 65 cars, the statement is supported.

The range of the number of cars sold is the same for both dealerships.

The range is determined by subtracting the lowest value from the highest value.

For Admiral Autos: 19 - 4 = 15

For Countywide Cars: 17 - 9 = 8

Since the ranges are different (15 for Admiral Autos and 8 for Countywide Cars), the statement is not supported.

The data for Admiral Autos shows greater variability.

To determine the variability, we can look at the range or consider the differences between each data point and the mean.

As we saw earlier, the range for Admiral Autos is 15, while for Countywide Cars, it is 8. Additionally, the data points for Admiral Autos are more spread out, with larger differences from the mean compared to Countywide Cars. Therefore, the statement is supported.

Based on the analysis, the statements supported by the data are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

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The Present value is $6,139.132.

We have,

FV=100000, pmt = 4000, I =5%, n=10

So, The present value formula is

PV=FV / (1 + \(i)^n\)

So, PV =  100, 000 / (1+ 5/100\()^{10\\\)

PV = 100,000 / (1+ 0.05\()^{10\\\)

PV = 100, 000/ (1.05\()^{10\\\)

PV = 100,000 / 1.6288946

PV= $6,139.132

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Answer:

Step-by-step explanation:

Answer:

111.22

\(A = \pi r^2 = \pi * r^2 = 111.22\)

It should be noted that the number of sample size based on the information will be 300.

In order to calculate the sample size, we can use the following formula:

n = z² * p * (1-p) / E²

n = 1.96² * 0.5 * (1-0.5) / 0.05²

= 300

A questionnaire is a method of gathering data that makes use of written questions to be answered by the respondents. It is a popular method of data collection because it is relatively easy to administer and can be used to collect a wide variety of information.

In the first column, the population is the entire National Capital Region (NCR). The sample is the city of Manila. In the second column, the population is all STEM students. The sample is all academic track students. In the third column, the population is all the tablespoons of sugar in the jar. The sample is one tablespoon of sugar. In the fourth column, the population is all the vowels in the word "juice". The sample is the vowel "i".

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Answer:

  b.  $154,810

Step-by-step explanation:

You want to know the price of a home that can be purchased for a monthly payment of $879.32 on a 30-year loan at 5.5%.

The given table tells you the multiplier m used to find the monthly payment p from the loan amount P for different time periods and interest rates.

  p = (P/1000)×m

The table value for a 30-year loan at 5.5% is m = 5.68. Solving the equation for P, we have ...

  1000p/m = P

  1000(879.32/5.68) = P ≈ 154,809.86 ≈ 154810

You qualify for a loan of $154,810.

__

Additional comment

The multiplier 5.68 is found on row 2 (5.5%) of column 4 (30 years).

By answering the presented question, we may conclude that As a result, equation the answer is (b) $154,810.

A mathematical equation is a formula that connects two statements and denotes equivalence with the equals symbol (=). An equation is a mathematical statement that shows the equality of two mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the variables 3x + 5 and 14. A mathematical formula describes the connection between the two sentences that occur on opposite sides of a letter. The symbol and the single variable are frequently the same. As in 2x - 4 Equals 2, for instance.

To establish the purchase price of a property, we must use the monthly payment and the table supplied to determine the mortgage amount that corresponds to the monthly payment.

According to the data, the monthly payment per $1000 of mortgage for a 30-year fixed mortgage at a 5.5% interest rate is $5.68.

Hence, to calculate the mortgage amount for a $879.32 monthly payment, we may apply the following formula:

Mortgage amount = monthly payment / mortgage payment per $1000

$879.32 mortgage amount / $5.68 per $1000

Loan amount = $154,810

As a result, the purchasing price of a house is $154,810.

As a result, the answer is (b) $154,810.

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The amount that I spent by using the equation y = 1/2x , according to my friend's expense is $7.5.

In its simplest form in algebra, the definition of an equation is a mathematical statement that two mathematical expressions are equal. For example, 3x + 5 = 14 is an equation where 3x + 5 and 14 are two terms separated by an equal sign. 

There are two types of equations:

Identities and conditionals. The identity applies to all values ​​of the variable. Constraint expressions apply only to specific values ​​of variables. Equations are written as two expressions separated by an equal sign ("="). 

Solution:

Given, amount spent by friend = $15

           Equation: y = 1/2x

So, amount spent by me is as follows

y = (1/2)×15

  =15/2

y  = $7.5

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The amount of money you are spending is $7.50 according to the given equation.

A mathematical equation is a statement that expresses the relationship between two values using mathematical symbols. An equation typically involves a variable, which is a symbol that stands for a number that can change, and an equals sign. Equations can be used to solve a variety of problems in mathematics.

The equation y = 1/2x states that 'y' is equal to one half of 'x'. This equation can be used in many different ways to solve real-life problems. In this case, 'x' represents the amount of money your friend spent at the carnival. 'y' represents the amount of money you spent. To solve for 'y', we divide the value of 'x' by 2.

In the question, your friend spent $15 at the carnival. Therefore, 'x' is equal to 15. We then divide 15 by 2, which gives us 7.5. This means that you spent $7.50 at the carnival.

The equation y = 1/2x is a simple but powerful tool for solving problems. It can be used for a variety of tasks, including finding out how much money you spent at the carnival if you spent half as much as your friend. All you have to do is plug in the value of 'x' and divide it by two.

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Answer:

We will split the trapezoid into right angle triangle and rectangle

Traingle with base 3cm and height 10 - 6 = 4cm

Area of traingle

       = \(\frac{1}{2}*base *height = \frac{1}{2} * 3 * 4 = 6cm^{2}\)

Area of rectangle with sides 6cm and 3cm

       =\(6 * 3 = 18cm^{2}\)

Therefore, area of the trapezoid

       = \(6+18 = 24cm^{2}\)

Area of the semi circle with radius 3/2 = 1.5cm

        = \(\frac{1}{2}\pi r^{2} = \frac{1*\pi *1.5*1.5}{2} = 1.125\pi cm^{2}\)

\(Total area = 24 + 1.125\pi =27.53cm^{2}\)

Answer:

0.167

Step-by-step explanation:

if you divide 30/180 it will get you a decimal of 0.166666667 but if you were to divide 180 by 30 you will get 6

technecaly your answer would be 0.166666667 but you only take the first number in the decimal which is 0.1 then take six 0.16 then add the 7 0.167

that should end up being your answer if i did the math right

Answer:

Step-by-step explanation:

5/12 * 6/15 =30/180

1/6=1/6

which is true, Right-hand side is equal to left-hand side