Solve the system of equations.

The given equation  m<2 = 28⁰ so here in this case option A is correct .

Simplification:

       <1 = <3

<1 = 5x + 8              ………………equation 1.

<3 = 12x – 20         ………………equation 2.

By angle property <1 = <3  [ given ]

and

<1 = <2   [ vertically opposite angles ]

We have some options so we can use it to get answer more quickly:

Put <1=28 and <3=28

And solve it for X.

28 = 5x + 8                     Eq1

20=5x => x=4

28 = 12x - 20                 Eq2

28 + 20 = 12x

48 = 12x

4 = x

X = 4

As <1 = <2 ( vertically opposite angles )

From the first equation  <1 = <2  = 5x + 8 ......( equation 3)

Putting the value of x = 4 in (equation 3)

<2 = 5* 4+ 8

<2=28

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An inequality to find the number of batches of rolls Liz can make is 13n/4 ≤ 26 and she cannot make more than 8 batches of rolls.

In order to solve this word problem, we would assign a variable to the number of batches, and then translate the word problem into an algebraic inequality as follows:

Let the variable n represent the number of batches.

Since Liz has 26 tablespoons of yeast left in the jar and each batch of biscuits takes 3 1/4 -tablespoons, we have:

3 1/4 (n) ≤ 26

13n/4 ≤ 26

Cross-multiplying, we have:

13n ≤ 26 × 4

13n ≤ 104

n ≤ 104/13

n ≤ 8.

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Complete Question:

Liz wants to make several batches of biscuits. She has 26 tablespoons of yeast left in the jar and each batch of biscuits takes 3 1/4 -tablespoons. Write and solve an inequality to find the number of batches of rolls Liz can make.

The factored form of f(x) = x³ + 8x² - 23x - 30 is (x - 3)(x + 10)(x + 1).

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given a polynomial f(x) = x³ + 8x² - 23x - 30.

If f(3) = 0 then x - 3 is one of the factors of the polynomial f(x).

∴ f(x) = f₁(x)(x - 3), where f₁(x) is a quadratic equation we obtain it by long division or synthetic division.

f₁(x) = x² + 11x + 10.

Now, x² + 11x + 10 = 0.

x² + 10x + x + 10 = 0.

x(x +10) + 1(x + 10) = 0.

(x + 10)(x + 1) = 0.

x + 10 = 0 Or x = 1 = 0.

x = - 10 Or x = - 1.

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a) 90° counterclockwise about the origin

How can a rectangle be rotated?

A shape with rotational symmetry is a rectangle, for instance. When a rectangle is rotated around its center, the shape and placement remain unchanged. The placement of the specified points is the only distinction. Rectangles are of order 2 because they have half-turn symmetry.

When rectangle ABCD is rotated 90° counterclockwise about the origin , the vertex of 'A' in rectangle ABCD is (2,1) becomes (-1,2) in rectangle A'B'C'D'.

Therefore when rectangle ABCD is rotated we get rectangle A'B'C'D'.

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Answer:

  38 units

Step-by-step explanation:

You want the perimeter of pentagon ABCDE with vertices at A(4, -2), B(4, 10), C(7, 10), D(15, 4), E(7, -2).

The perimeter of a plane figure is the sum of the lengths of its sides.

By counting grid squares, or subtracting coordinates, you can find the lengths of the vertical and horizontal segments easily:

  AB = 12, BC = 3, EA = 3

The lengths of the diagonal segments can be found using the distance formula or your knowledge of Pythagorean triples. Counting grid squares (or subtracting coordinates), you see that each diagonal side has a vertical distance of 6 and a horizontal distance of 8. These correspond to twice the lengths of the sides in a 3-4-5 triangle, so you know the diagonal length is twice the hypotenuse: 2·5 = 10.

The Pythagorean theorem, or the distance formula, will tell you the same thing:

  c² = a² +b² . . . . . . Pythagorean theorem for sides a, b, hypotenuse c

  c = √(a² +b²)

  diagonal length = √(6² +8²) = √100 = 10

Then the remaining two sides are ...

  CD = 10, DE = 10

The perimeter is ...

  perimeter = AB +BC +CD +DE +EA

  = 12 +3 +10 +10 +3 = 38 . . . units

The perimeter of pentagon ABCDE is 38 units.

The x-intercepts of the quadratic function g(x) = x² - 10x + 24 are given as follows:

(4, 0) and (6, 0).

A function crosses the x-axis when the numeric value of the function is of y = 0, hence these points are called the x-intercepts of the function.

In this problem, the definition of the function is given as follows:

g(x) = x² - 10x + 24.

This function can be simplified as follows:

g(x) = (x - 6)(x - 4).

Applying the inverse of the Factor Theorem, the x-intercepts are given as follows:

Hence the x-intercepts of the function are given by the third option, which is of (4, 0) and (6, 0).

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Answer: C

Step-by-step explanation: trust me

The relationship in the scatterplot is positive and nonlinear.

We utilize correlation to assess the strength of a linear relationship between two numerical variables. The strength of a linear relationship is gauged by correlation.

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The solution of the expression, [tex]x^{2} -10x+25 = 0[/tex], using completing the square method is [tex](x-5)^{2}[/tex].

According to the question,

We have the following expression:

[tex]x^{2} -10x+25 = 0[/tex]

Now, we will use completing the square method to solve this expression.

We will first try to convert the first and last term into perfect squares and rewrite the expression by splitting the middle term in multiplication of 2 and the squares .

[tex]x^{2}[/tex]-2*x*5+[tex]5^{2}[/tex] = 0

Now, we know that this expression fits in the identity:

[tex](a-b)^{2} = a^{2} +b^{2} -2ab[/tex]

In this case, we have a = x and b = 5

[tex](x-5)^{2}[/tex]

Hence, the solution of the expression, [tex]x^{2} -10x+25 = 0[/tex], using completing the square method is [tex](x-5)^{2}[/tex].

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The value of PC is 40 when C is the circumcenter of triangle PQR.

Given that,

Consider the complete question is

C is the circumcenter of triangle PQR.

PC=3x-7

RC=5x-15 &

QC= 51-x

We have find the side PC.

A triangle's vertices are equidistance spaced from its circumcenter.

PC=RC=QC

RC=QC

5x-15= 51-x

5x+x= 51+15

6x=66

x=11

The value of x is 11.

We must determine PC's worth.

Substitute x=11 in the above equation.

PC= 3x+7

PC= 3(11)+7

PC=33+7

PC= 40

Therefore, The value of PC is 40 when C is the circumcenter of triangle PQR.

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The tuition does not appear to have an association with graduation rate.

A scatter plot is a particular kind of plot or mathematical diagram that displays values for generally two variables for a collection of data. It uses Cartesian coordinates. A dot is used to symbolize each point on the scatter plot. It is used to demonstrate the link between the dots by illustrating how many of them would fall within the path of a straight line.

It is clear that there is no relation between tuition and graduation rate. Some selective colleges may have higher tuition and higher graduation rates but there may be some selective colleges with higher tuition but lower graduation rates.

Hence, the tuition does not appear to have an association with graduation rate. Option 2 is correct.

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Answer:

I think it's A- Higher tuition causes students to graduate at higher rates.

Step-by-step explanation:

tell me if I'm wrong...  forgive me if i am

The line with no slope will be a horizontal line the correct option is line b.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.

Given that on a coordinate plane, line A has a negative slope, line b is horizontal, line c is vertical, and line d has a positive slope.

The line with no slope will be line b because the line is a horizontal line.

Therefore, the line with no slope will be a horizontal line the correct option is line b.

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Answer:

C. Line C

Step-by-step explanation:

Edge 2023

Answer:

6.4 packs (7 as integer)

Step-by-step explanation:

Area of the square: 8^2 = 64 m^2

64 : 10 = 6.4

In 27 minutes, Daquin completed 30% of his schoolwork. He must therefore finish another 70% of her homework.

We must multiply both sides of the equation by 3 to see how long it takes Daquin to finish 10% of the homework. It takes her 9 minutes.

We simply need to multiply our time estimate by seven to determine how long it will take her to complete the remaining 70% of her homework.

9 minutes are required for 10% of the homework.

63 minutes are required to complete 70% of the homework.

% finished equals 30%

Duration: 27 minutes

70% of the homework is still to be done.

Time required for the remaining task is 70/30 divided by 27 is equal to 63 minutes.

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Answer:

D: 12

Step-by-step explanation:

multiples of 4: 4,8,12,16,20

12 is the only number that can be divided by 4 on the list

Hopes this helps please mark brainliest

Answer:

D. 12

Step-by-step explanation:

12 is a multiple of 4 because 4 goes into 12 (evenly, with no remainder).

That's what being a multiple means.

All the "answers" to 4 times table questions are multiples of 4. Here they are:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48...

Can't actually list them all because the list goes on forever.

The option that is a a linear equation is B. 4x - 2 = 20.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign

This is illustrated as 4x - 2 = 20

4x = 20 + 2

4x = 22

x = 22/4 = 5.5

This illustrates an equation.

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The diagrams are shown in the solution.

A rectangle is a quadrilateral with all four interior angles 90°.

(1) The rectangle diagram of 1/2 × 5/6 can be drawn by converting the fractions into integers.

The dimension can be written as:

1/2 : 5/6

Multiply the ratio by 6:

3 : 5

Hence, the rectangle of  1/2 × 5/6 is proportional to 3×5.

The diagram is shown.

Similarly, the diagrams of other rectangles are shown.

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Answer:

6

Step-by-step explanation:

slope = m = [tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]

put values and find answer:

[tex]=\frac{14+4}{-1+4}[/tex]

=  [tex]\frac{18}{3}[/tex]

=  [tex]6[/tex]

The required numerical expression is evaluated as 67.2. Option A is correct.

Given that,
An expression is given 7.5 × 6.6 ÷ 0.6 − 15.3, we have to evaluate the given expression.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
= 7.5 × 6.6 ÷ 0.6 − 15.3
Simplify,
= 7.5 × 11 - 15.3
= 82.2 - 15.3
= 67.2

Thus, the required numerical expression is evaluated as 67.2. Option A is correct.

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The factorization of given polynomial is 4x(-x+3). Therefore, option A is the correct answer.

The given algebraic expression is -4x²+12x.

The factors are the polynomials which are multiplied to produce the original polynomial.

The factorization of the given polynomial is

-4x²+12x

= 4x(-x+3)

The factorization of given polynomial is 4x(-x+3). Therefore, option A is the correct answer.

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The inequality of the change of state of the gas in the driver's truck indicates;

Part A: The inequality  that represents the temperature at which the gas in the truck will be in liquid form is; -40 ≤ T ≤ 140

Part B: The graph is a shaded region bounded by two solid vertical lines at t = -40 and t = 140

Part C: The gas will be frozen because the temperature is below the freezing point temperature of the gas.

An inequality indicates the relationship between two expressions that are not equal

The temperature at which the gas freezes = -40 °F

Temperature at which the gas evaporates = 140 °F

Part A: The inequality that represents the temperature at which the gas in the truck will remain in liquid form, t is; -40 ≤ t ≤ 140

Part B: The description of the graph of the inequality is a region on the coordinate plane bounded by two solid vertical lines at x = -40 and x = 140, the region between the two solid vertical lines is shaded/.

Part C: The temperature of -49 °F obtained in January 1989 in Nome, Alaska is not in the feasible region of the graph of the inequality, therefore, the gas in the driver's truck will not remain in liquid form, and would freeze, such that the driver would not drive on the specified date.

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Answer:

[tex]9x = 3x - 36 \\ 6x = - 36 \\ x = - 6[/tex]

hopefully this will u...^⁠_⁠^

The length of the shortest ladder that will reach from the ground over the fence to the wall of the building is 11.31 feet

Let L stand for the ladder's overall length.

Right angled triangle ΔAGB contains the following:

L² = h² +(x+4)²

( Since by using Pythagorean Theorem)

Triangles AGB and CDB also have similarities.

As a result, the corresponding sides' ratio is equal.

Hence, we have:

h/4 = (x+4)/x

h = 4(x+4)/x

As a result, when we enter the value of h in equation (1), we obtain:

L² = h² +(x+4)²

L² = (4(x+4)/x)² +(x+4)²

L² = (16(x+4)²/x²)+(x+4)²

L² = (x+4)²(16/x² + 1)

We now have to reduce L.

Therefore, we employ the differentiation method.

We distinguish in relation to x as follows:

L² = (x+4)²(16/x² + 1)

2L dL/dx =2(x+4)(16/x² + 1) + (x+4)² (-32/x³)

2L dL/dx =2(x+4){ (16/x² + 1) + (x+4) (-16/x³)

2L dL/dx =2(x+4){ (16/x² + 1 -16/x²-64/x³)

2L dL/dx =2(x+4){ (1-64/x³)

when the derivative is zero we have:

2(x+4){ (1-64/x³) = 0

x= -4 and x³ = 64 and x =∛64 = 4

But x can't be negative.

Hence, we have:

x = 4

After solving equation (2) with this value of x, we get the following result:

L² = (x+4)²(16/x² + 1)

L² = 128

L = 11.313 feet

Hence,

L = 11.313 feet

which on rounding to two decimal places is: 11.31 feet

As a result, the shortest ladder's length, measured from the ground to the building's wall over the fence, is 11.31 feet.

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Answer:

Last option: 31

Step-by-step explanation:

No. of catalogs that can be arranged

= (longest side of shelf ÷ longest side of catalog) × (shortest side of shelf ÷ shortest side of catalog)

= (56 ÷ 5) × (5 ÷ 4)

= 31

No, to construct a confidence interval, the population should be is approximately normal.

The information about distribution of population is important in order to find out the sampling distribution. When we want to construct confidence interval, the accuracy of results depend on three conditions.

1. The data needs to be randomly selected.

2. The sampling distribution needs to be normally distributed

3. The observations must be independent.

So one of the conditions is to ensure that the population is normally distributed.

We know from the central limit theorem, the sampling distribution is approximately normal as long as the expected number of successes and failures are equal or greater than 10

np ≥ 10

n(1 - p) ≥ 10

When the population follows normal distribution then a small number of samples will be adequate, on the other hand, if the population is skewed then we need a greater sample size to ensure normal sampling distribution.  

Therefore, the population is approximately normal before constructing a confidence interval.

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Answer:

Step-by-step explanation:

a find the interpret the slope and the y-intercept of the graph

The probability is 0.1.

acc to our question-

Hence,The probability is 0.1.

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Answer:

9.4

Step-by-step explanation: