Prove: <1= <3
Complete the proof (reasons A and B).

A. Definition of supplementary angles
And Substitution property

B. Angle addition postulate
And Subtraction property of equality

C. Subtraction property of equality
And Definition of linear pair

D. Addition property of equality
And Angle addition postulate

The graph of the equation p(x) = -3x- 1 has been plotted

The equation is given that

p(x) = -3x - 1

We know the slope intercept form of the line

y = mx + b

Where m is the slope of the line

b is the y intercept

Compare both equation

The slope of the line m = -3

The y intercept b = -1

At x = 1

The value of p(1) = -3(1) -1

= -3 - 1

= -4

At x = 2

The value of P(2) = -3(2) -1

= -6 - 1

= -7

Substitute the value for x and find the value of y.

Draw the graph using the points

Hence, the graph of the equation p(x) = -3x- 1 has been plotted

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Answer:

1700 - 700x

Step-by-step explanation:

assuming x is the number of weeks, the equation is 1700 - 700x equals the amount you are trying to solve for. You can say you are solving for y.

The error occurs in Litas work is in step 3 and step 4.

An exponential function is a mathematical function of the following form:

f ( x ) = aˣ where x is a variable, and a is a constant called the base of the function.

The given expression is

25⁻⁴/(5⁻²)²

The given steps are

Step 1,

25⁻⁴/(5⁻²)²

Step 2,

(5²)⁻⁴/(5⁻²)²

Step 3,

(5²⁻⁴)/(5⁻²⁺²)

The step 3 is wrong because the exponents should be multiplied but not added.

The actual step should be

(5⁻⁸)/(5⁻⁴)

Hence the error occurs in Litas work is in step 3 and step 4.

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The baker needs  [tex]\frac{25}{12}[/tex]  cups of sugar.

Number of batches of cupcakes a baker needs to make = [tex]3 \frac{1}{8}[/tex]

Number of cups of sugar each recipe uses =   [tex]\\\frac{2}{3}[/tex]

Quantity of sugar required to make  [tex]3 \frac{1}{8}[/tex]  batches of cupcakes = [tex]3 \frac{1}{8}[/tex]  × [tex]\\\frac{2}{3}[/tex]

                                                                                            = [tex]\frac{25}{8}[/tex] × [tex]\frac{2}{3}[/tex]

                                                                                            =  [tex]\frac{25}{12}[/tex]

Therefore, the quantity of sugar required to make  [tex]3\frac{1}{8}[/tex]  batches of cupcakes is   [tex]\frac{25}{12}[/tex]  cups.

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The total amount of money spent on pass and lunch for each student is $19.28.

The first step is to determine the amount that was spent on a pass for each student. The cost of one pass can be determined by dividing the total amount spent on passes by the total number of teachers and students.

Cost of one pass = total amount spent on one pass / total number of people

Cost of one pass = 526.26 / (47 + 2)

Cost of one pass = 526.26 / 49

Cost of one pass = $10.74

The second step is to determine the amount spent on lunch for one student. This can be determined by dividing the total amount spent on lunch by the total number of students.

Cost of one lunch = total cost of lunch / total number of students

401.38 / 47 = $8.54

Total amount spent on pass and lunch for each student = cost of lunch for one student + cost of a pass for one student

$8.54 + $10.74 = $19.28

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Answer:

27

Step-by-step explanation:

it's a function with 3 as the slope and x as 9. So it's 27.

Answer:

Line 1:  [tex]y=-x+2[/tex]

Line 2:          [tex]y=2x-1[/tex]

Step-by-step explanation:

Line 1

Staring with line one, let's find the slope!

Between the two known points, the rise, or change in y, is 2, and the run, or change in x, is -2. The slope is the rise over the run, so:

[tex]-\frac{2}{2} =-1[/tex]

The slope is negative 1! The line crosses the y-axis at [tex]y=2[/tex], so 2 is the y-intercept. Using the slope-intercept formula, the equation is:

[tex]y=-x+2[/tex]

Line 2

To find the slope of line 2, find the rise and the run between the two known points! The rise is 4, and the run is 2. Simplified, this is:

[tex]\frac{4}{2} =2[/tex]

The slope is 2! The line crosses the y-axis at [tex]y=-1[/tex], so -1 is the y-intercept. Using the slope-intercept formula, the equation is:

[tex]y=2x-1[/tex]

Answer:

y=2x-1 , y=x+2 , the solution of the system is (1,1)

Step-by-step explanation:

Lines can be expressed in the form y=mx+b where m is the slope and b is the y-intercept.

m= rise/run

Looking at the blue line:

m =2/1 =2

The slope is 2 since you rise 2 squares and run to the right one square.

We see that the line crosses the y-axis at (0,-1) so the y-intercept is -1.

Putting it all together: y=2x-1

Looking at the red line:

m = -1 / 1 = -1

We see that the line crosses the y-axis at (0,2) so the y-intercept is 2.

Putting it all together: y=1x+2 or simply y=x+2

The solution to the system is the point that satisfies both equations. Rather than solving it algebraically, we can simply look at the graph and find a point that is on both lines, aka the intersection. In this case, the intersection is (1,1).

The perimeter of the rectangle is 59.9 m.

The area of the rectangle is = 223.2 m²

the length(L) of the rectangle is = 16 m

we know that the area of the rectangle is given by

Area  = Length x Breadth

A =  LB

therefore ,

LB=  223.2

16 x B = 223.2

B = 223.2/ 16

B = 13.95 m

∴ breadth or the rectangle is 13.95 meter.

Now , we know that the perimeter of the rectangle is given by ,

(P) perimeter = 2( Length + Breadth )

P = 2(L + B)

P = 2( 16 + 13.95)

P = 2( 29.95)

P = 59.9 m

So the perimeter of the rectangle is 59.9 meter.

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The value of m∠5 is 125°. option A is the correct answer

From the question, we have

m∠1=70°

As the sides are equal.

∠2=∠3=(180°-70°)/2

= 55°

∠5 = 180°-55°  (Linear pair)

= 125°

Subtraction:

Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.

The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.

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There are two closed containers and four balls can just fit in each of the containers, then container A has a smaller surface area.

A three-dimensional solid shape's capacity is referred to as its volume. It is difficult to visualize in any shape, yet this can be evaluated among forms.

As per the data in the question,

Radius, r = 30 mm

Height, h = 60 × 4 = 240 mm

Use the equation of the surface area of the cylinder, SA = 2πr² + 2πrh

SA = 2π(30)² + 2π (30)(240)

SA = 50,868.

Now, calculate the area of a rectangular prism,

Area of top and bottom,

= (60 + 60) × (60 + 60) × 2

= 120 × 120 × 2 = 28,800

Area of 2 sides,

= 2 × (60 × 120) = 14,400

Area of front and back,

= 2 × (60 × 120) = 14,400

Total Surface Area = 28,800 + 14,400 + 14,400 = 57,600

Therefore, A has a smaller surface area.

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Answer:

x = 9

Step-by-step explanation:

Start by dividing both sides by the singular number, 3. We divide by 3 and not 21 because 21 is the result of the equation, not the coefficient.

[tex]\frac{3\left(x-2\right)}{3}=\frac{21}{3}[/tex]

We got 21 over 3 because you cannot divide 3 times an unknown number subtracted by 2 by 3. This is because we do not know the number. So that's where 21 comes in.

Next, simplify this equation by dividing whole numbers.

[tex]\frac{3}{3} = 1[/tex]

[tex]1\left(x-2\right) = \left(x-2\right)[/tex]

[tex]\frac{21}{3} = 7\\= x-2 = 7[/tex]

Lastly, add 2.

[tex]x - 2 + 2 = 7 + 2\\2 + 2 = 4\\7 + 2 = 9\\= x - 4 = 9\\x = 9[/tex]

Why x - 4 is 0: We assume x is always equal to 1, since 4 does not go into 1, the result would be 0. x - 0 = 0. Therefore, the problem became x = 9.

Hope this helps!

Answer: The standard form of a linear equation is Ax+By=C. To change an equation written in slope-intercept form (y=mx+b) to standard form, you must get the x and y on the same side of the equal sign and the constant on the other side. Use inverse operations to move terms.

Step-by-step explanation:

the answer would be a= -1

By solving a system of equations we will see that Anna works 2 hours washing cars and 5 hours landscaping.

First, we need to define the variables that we will be using, these are:

We know that she works 7 hours in total and earns $78 in total, so we can write the system of equations:

x + y = 7

x*$9 + y*$12 = $78

Isolating x on the first equation we get:

x = 7 - y

Replacing this on the other equation we get:

(7 - y)*$9 + y*$12 = $78

$63 - $9*y + $12*y = $78

$63 + $3*y = $78

$3*y = $78 - $63

$3*y = $15

y = $15/$3 = 5

Then the value of x is:

x = 7 - y = 7 - 5 = 2

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Answer:

x = 4

Step-by-step explanation:

g (x) = 3x + 5

3x + 5 = 17

subtract 5 from both sides

3x = 12

divide by 3

x = 4

The solution of the mathematical statement is 1440 and uprising is a change in direction of a point in the coordinate plane

From the question, we have the following mathematical statement that can be used in our computation:

"what is 32 times 45"

This means that

32 times 45

Express as numbers

So, we have

32 x 45

Evaluate the product

So, we have

1440

Hence, the result is 1440

There is no direct term for uprising in mathematics.

However, the closest synonyms to uprising is revolution (in this case, it is rotation)

Rotation (uprising) implies that we change the direction of a shape, figure or object.

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The correct choice is (a). The conclusion from the study is causality cannot be inferred because there is no control group.

Treatment in a study involves administering a stimulus, known as a treatment, to a group or portion of the sample while the rest of the sample is excluded from the stimulus. A successful treatment manipulation is one in which members of the treatment group perform better than members of the control group on the measures measured in study.

Given that the investigators collected data from a random sample of drivers and measured several variables, including the study's explanatory variables, it was possible to closely examine the cannot suggest a cause-and-effect relationship. No control group exists.

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Complete question:

A study was conducted on the effect of daytime running lights on cars. Researchers gathered data from a random sample of 3,248 drivers and measured quite a few variables, in addition to the explanatory variable of daytime running lights and the response variable of less accidents. According to a newspaper article summarizing the study, those cars that had daytime running lights were more likely to be operated by drivers who were confident and attentive. Drivers whose cars did not have daytime running lights were about 22% more likely to have an accident. What conclusion can we draw from this study? Explain.

a. We can infer a cause-and-effect relationship because the sample was selected randomly.

b. We cannot infer a cause-and-effect relationship because we do not have a control group.

c. We can infer a cause-and-effect relationship because multiple variables were included.

d. We cannot infer a cause-and-effect relationship because treatments were not assigned randomly.

e. We cannot infer a cause-and-effect relationship because the treatments imposed were not blocked correctly.

Answer:

We cannot infer a cause-and-effect relationship because treatments were not assigned.

Step-by-step explanation:

Got it right on test

Step-by-step explanation:

well that is the really easy one :

the number of produced drills cannot be more than 210 per day.

while the first inequality addressed the work hours, the second simply addresses the number of drills.

therefore,

x + y <= 210

Answer:  A

Step-by-step explanation:

A for 1 gram it is $1.00

B for 1 gram it is $1.25

C for 1 gram it is $1.66

D for 1 gram it is $1.25

The quadratic equation is −x²+10x. Domain for the given equation is (0,10) and the Range is (0,25]. The x-intercept is (0,10) and the area is 10.

Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.

Here,

quadratic function in standard form that models f(x), the total area of the playground in square feet in terms of its width x in feet,

f(x)=−x²+10x

The graph is given below,

Domain=(0,10)

range=(0,25]

To determine the domain that must exist between them, we used the xx-intercepts. We excluded them from the domain because the area at the x-intercepts is 0.

Since an area must be greater than 0, y>0y>0 follows. Remembering that the vertex of the graph of f(x) has the maximum point of (5,25) the maximum value for y is 25.

−x²+10x is the quadratic equation. The domain and range of the given equation are (0,10) and (0,25), respectively. (0, 10) is the x-intercept, and 10 is the area.

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We can easily see that two similar equation of under cube root of x.

So, the graph of cube root of x is identical.

The graph of under root x is positive half of parabola, consist of origin (0, 0). Its symmetric on the positive x-axis.

The graph of the  cube root function f(x) = ∛x.Take the numbers -8, -1, 0, 1, and 8 in the x column calculate the cube root of each of these numbers, and fill them in the column labeled y. Then we have 5. Just plot them and join them by a curve. As this curve is not complete, just extend it on both sides.

We can easily see that two similar equation of under cube root of x.

So, the graph of cube root of x is identical.

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Answer:

D F on edge

next one is A C D

Step-by-step explanation:

trust

Answer: First you have to think about what to multiply 9 by to get a number that ends with 6. The answer to that is 3. So 9*3=36. Then you need to subtract 36 from 86. You get 50. So now you need to divide. 36/9=3 and 50/10=5. So the chef bought 3 bags of red onions and 5 bags of yellow onions.

Step-by-step explanation:

Answer:

3 yellow onion bags, 5 red onion bags

Step-by-step explanation:

hope it helped!

Answer: -2 ==> A

Step-by-step explanation:

-23 - 12 - (-33) =

-23 - 12 + 33 = ==> subtracting by a negative number is basically adding by the positive number

-(23 + 12) + 33 =

-35 + 33 =

-(35 - 33)=-2 ==> A

Answer: -2

Step-by-step explanation:

Answer:

532

Step-by-step explanation:

594 [monkeys]  - 62 [birds] = 532

The possible rational zeros are x = -1 and x = 1/3 for the given function f(x) = 3x² + 2x - 1.

The quadratic function is defined as a function containing the highest power of a variable is two.

The function is given in the question as:

f(x) = 3x² + 2x - 1

To determine possible rational zeros for the given function.

f(x) = 3x² + 2x - 1

For finding rational zeros, f(x) = 0

3x² + 2x - 1 = 0

3x² + 3x - x - 1 = 0

3x(x +1) - 1(x +1) = 0

(x +1)(3x - 1) = 0

(x +1) = 0 and (3x - 1) = 0

x = -1 and 3x = 1

x = -1 and x = 1/3

Thus, the possible rational zeros are x = -1 and x = 1/3 for the given function f(x) = 3x² + 2x - 1.

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Answer:

101

Step-by-step explanation:

Since the total number of cheeseburgers was twice the number of hamburgers, let the number of sold hamburgers be h

Twice of h = 2(h)

Hence,

2(h) + h = 303

2h + h = 303

3h = 303

Divide both sides by the coefficient of h

h = 101

Therefore, the total number of hamburgers sold was 101

The standard form of a quadratic function is y = 3/2x² + 17/2x - 7

From the question, the points on the quadratic equation are given as

(2,4), (3,5) and (4,3)

The standard form of a quadratic equation is represented as

y = ax² + bx + c

So, we have

Point (2,4):

4a + 2b + c = 4

Point (3,5):

9a + 3b + c = 5

Point (4,3):

16a + 4b + c = 3

Solving using an online calculator. we have

a = 3/2, b = 17/2 and c = -7

Substitute a = 3/2, b = 17/2 and c = -7 in y = ax² + bx + c

y = 3/2x² + 17/2x - 7

Hence, the equation is y = 3/2x² + 17/2x - 7

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Answer:

(2a,a)

Step-by-step explanation:

Hope this helps!

Answer: The answer is 56

Step-by-step explanation: bc 14 cookies is for 4 ppl and there are 12 ppl next time 4x3=12 so 14+14+14+14= 56 u would add 3 more 14's bc 14 cookies for 4 ppl and to check it 56 divided by 4 is 14.