which number is a solution of the inequality 8 - 1/4 b > 27

Answer: 43 texts

Step-by-step explanation: first you see your total amount used on texts, so you would do 37-29.99 to give you 7.01. then using that 7.01 you divide it by 0.16, to give you 43.8125, and because you can't go over the 37$ you would round down to 43 texts.

The plot that represents

Is the one in Option A.

Now, in comparison to the graph of

The graph of

Is horizontally compressed by a factor of 4/7

A⁻¹ =  [1/19]   [tex]\left[\begin{array}{ccc}7&-8\\5&-3\end{array}\right][/tex]

x =  [1/19] [tex]\left[\begin{array}{ccc}18\\2\end{array}\right][/tex]

Given matrix A is:

[tex]\left[\begin{array}{ccc}-3&8\\-5&7\end{array}\right][/tex]

The inverse of a matrix is given by A⁻¹ = (1/|A|) × Adj A.

The formula gives the inverse of a 2×2 matrix  [tex]\left[\begin{array}{ccc}a&b\\c&d\end{array}\right][/tex] ,

A⁻¹ =  [1/(ad - bc)]   [tex]\left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right][/tex]

If ad -  bc is not equal to 0 then only the inverse of the matrix exists.

So, in the given matrix A the determinant (ad -bc) is calculated as,

= (-3)×7 - 8×(-5) = -21 + 40 = 19 ≠ 0

Hence, the inverse of the given matrix exists, which is

A⁻¹ =  [1/19]   [tex]\left[\begin{array}{ccc}7&-8\\5&-3\end{array}\right][/tex]

Given [tex]b = \left[\begin{array}{ccc}-2\\-4\end{array}\right][/tex]  we have to solve Ax = b

The equation can be written for x as, x = A⁻¹ b

Substituting A⁻¹ and b matrix in the equation,we have

x =  [1/19]  [tex]\left[\begin{array}{ccc}7&-8\\5&-3\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}-2\\-4\end{array}\right][/tex]

The matrix x is,

x =  [1/19] [tex]\left[\begin{array}{ccc}18\\2\end{array}\right][/tex]

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In the graph y will always be smaller than 1/5(x) - 4 in the inequality x−5y<20.

Mathematical expressions with inequalities on both sides are known as inequalities. In an inequality, we compare two values as opposed to equations. In between, the equal sign is changed to a less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Olivia is chosen for the 12U softball team. What age is Olivia? Because it doesn't say "equals," you are unaware of Olivia's age. But since you already know Olivia's age should be below or equal to 12, you can write it as Olivia's Age 12. This scenario relates to inequalities in the real world.

First we will write the equation in the y-intercept form

y = mx + b

So,

⇒ x−5y<20    

⇒ x -5y - 20 < 20 - 20

⇒  x -5y - 20 < 0

⇒ x -5y - 20 - x +20 < - x +20

⇒ -5y < - x +20

⇒ 5y < x - 20

⇒ y < 1/5(x) - 4

Here slope is 1/5

So the graph is give below ↓↓↓

Thus, In the graph y will always be smaller than 1/5(x) - 4 in the inequality x−5y<20.

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Given:

We are given this figure.

To find:

The area of the given figure.

Step-by-step solution:

As per the question, It is a trapezoid:

Area of trapezoid = 1/2 × (a + b) × h

Here a and b are lengths of parallel sides.

Area = 1/2 × (a + b) × h

Area = 1/2 × (8 + 27) × 6

Area = 1/2 × 35 × 6

Area = 35 × 3

Area = 105 cm²

Final answer:

The final area of the trapezoid = 105 cm²

Distance Between Two Points

The length of a segment that connects two points can be calculated as the distance between those points (x1,y1) (x2,y2) with the formula:

The endpoints of segment AB are A(-5, 2) and B(4, -3). Calculating the distance:

Calculate:

Calculating and rounding to one decimal place:

d = 10.3

The length of segment AB is 10.3 units

given the system of equations:

We will solve the system by substitution as follows:

From equation (2)

substitute with (y) from equation (4) into equation (1)

From the equation (4) and (5) substitute with (x) and (y) into equation (3):

solve the equation to find the value of (z):

substitute into the equations (4) and (5) to find the values of (x, y)

So, the answer will be:

The system has only one solution

x = 5

y = 1

z = 1

We are given the following expression:

To solve the expression we will add the numbers inside the parenthesis:

Now we solve the squares:

Now we solve the product:

Now we solve the operation:

Therefore, the expression is equivalent to 184.

The length of the hypotenuse x is 36 units.

So, let us assume that side x is the hypotenuse of the triangle:

Now, substitute values in the formula as follows:

Rounding off: 36

Therefore, the length of the hypotenuse x is 36 units.

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Answer:

36 units  

Step-by-step explanation:

Vertical angles are always congruent - they always have the same angle measure. If one angle is 40 degrees, the vertical angle across from it will also be 40 degrees.

The angles that occupy the same relative location when a transversal cuts two or more lines are known as corresponding angles.

The figure's matching angle pairings are:

∠1 and ∠5 and ∠2 and ∠6 and ∠7 and ∠8

The matching angles are equivalent when the lines are parallel.

The pairs of angles on one side of the transversal and inside the two lines that make up a transversal that cuts two lines are known as the successive internal angles.

The further internal angles in the illustration above are:

∠3, ∠6, ∠4, and ∠5.

When a transversal cuts two parallel lines, supplemental pairs of subsequent interior angles result.

Pairs of angles on one line are generated when two parallel lines are sliced by a transversal, and these alternate internal angles are congruent.

The pairs of angles outside the two lines and on either side of a transversal that cuts two lines are referred to as the alternate external angles

∠1 and ∠7; ∠2 and ∠8;

When a transversal divides two parallel lines, the resulting alternate exterior angles are congruent.

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First, let's calculate the total price without discount or taxes:

Now, to apply a discount of 8%, we can multiply the cost by 92%, that is, 0.92:

And then, to apply a tax of 7%, we can multiply the cost by 107%, that is, 1.07:

Therefore the correct option is A.

Using the properties of parallel lines, The value of Y is 6.

In a given three-dimensional space, any parallel planes are those that never cross. A line that crosses two or more other lines is said to be transversal. Two distinct angles are created when a line crosses two parallel lines.

According to the listed characteristics of parallel lines, these various forms of angles are used to demonstrate if two lines are parallel to one another.

Given,

Lines l and m must be parallel for the assertion to be true.

4x =(11x-8) - 90 (linear angle

11x - 4x = 98

7x = 98

x = 14

4x = 9y+2

4(14) = 9y + 2

56 - 2 = 9y

y = 6

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After solving for x, we get the value of n as an improper fraction:

(-3).(-1)/2

Given, the expression is:

1/8÷√2=2ⁿ

convert the expression to exponential form.

1/8 ÷ 2¹/² = 2ⁿ

1/2³ ÷ 2¹/² = 2ⁿ

convert both sides of the equation into terms with same base.

2⁻³ ÷ 2¹/² = 2ⁿ

Simplify using exponent rule with same base.

aⁿ.aˣ=aⁿ⁺ˣ

2⁻³⁻¹/²=2ⁿ

Based on the given conditions, corresponding exponents are equal.

n=-3-1/2

Rewrite the fraction using the least common denominator.

n = -6-1/2

calculate the difference.

n = -7/2

improper fraction is : (-3).(-1)/2

Hence we get the value for n as (-3).(-1)/2

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Solution

We draw a venn diagram to illustrate the information

Without the loss of generality

From the question we have that

Therefore, the probability that a chosen customer carries both cash and checks is

The answer is

We have that the empirical rule to construct a 68% confidence interval can be expressed with the following general rule:

in this case, we have the following information:

then, the confidence interval with 68% of confidence is:

therefore, the confidence interval with 68% of confidence is (282,342)

Answer: (307,317)

Step-by-step explanation:

The population standard deviation is known (and is assumed to be normally distributed). Using the Empirical Rule, we know that approximately 68% of the data lies within one standard deviation of the mean. So, the confidence coefficient is zα2=1, approximately.The point estimate for the population mean, μ, is the sample mean, x¯=312.  The standard error for the sampling distribution is σx¯=σn√, where σ is the population standard deviation and n is the sample size. So, the standard error is σx¯=30n√. We did not list a decimal approximation because the instructions stated that only the final answer should be rounded. The error bound for the mean (EBM) is given by the formula EBM=zα2(σn√)=1(3030√). Again, we did not list a decimal approximation because the instructions stated that only the final answer should be rounded. Finally, we can calculate the confidence interval at the desired level of significance using the formula (point estimate−EBM , point estimate+EBM)(312−1(3030‾‾‾√),312+1(3030‾‾‾√))(307,317)

Each equation 3x + 5 and 4x + 8 which is equivalent to each other is matched giving the value 4.

Equations with identical solutions or answers are said to be equivalent. It's common to compare linear equations to one another. When graphed, linear equations result in lines that are straight, have a slope, and have a y-intercept.

The characteristics that make linear equations linear are crucial in determining whether or not the equations will be equivalent when comparing linear equations. There are mathematical ways to determine whether the solutions to the equivalent equations are the same even though it may not initially appear that way.

To match the equation we need to find x first

3x + 5 = 4x + 8

⇒ 5 - 8= 4x - 3x

⇒ x = -3

Putting the value of x in respective equations

⇒ 3(-3) + 5 = 4(-3) + 8

⇒ -9 + 5 = -12 + 8

⇒ 4 = 4

Thus, each equation 3x + 5 and 4x + 8 which is equivalent to each other is matched giving the value 4.

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The function h is defined, for all real numbers , answer is as follows -

h(1) = - 2

h(2) = 3

h(4) = 3.

function, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable

We have been given that

h(x) = 1/4(x) - 1       if x < -2

h(x) = -(x + 1)² + 2  if -2 ≤ x < 2

h(x) = 3                  if x ≥ 2

Find h (1), h (2), and h (4)

For h (1) -

Value of h(1) for h(x) = -(x + 1)² + 2 as if -2 ≤ x < 2

So put x = 1

h(x) = -(x + 1)² + 2

h(1) = -(1 + 1)² + 2

h(1) = -4 + 2

h(1) = - 2

For h (2) -

Value of h(2) for h(x) = 3 as  if x ≥ 2

h(x) = 3

h(2) = 3

For h (4) -

Value of h(4) for h(x) = 3 as  if x ≥ 2

h(x) = 3

h(4) = 3

Hence , the value for given functions - h(1) = - 2 , h(2) = 3 and h(4) = 3.

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The LCM of 3, 16, and 24 = 48

The LCM of 3, 16, and 24 is found below

The LCM = 3 x 2 x 2 x 2 x 2

The LCM = 48

Therefore, the LCM of 3, 16, and 24 = 48

SOLUTION

From

The quotient is the answer gotten after a division is made. Therefore, the answer above is the quotient. Option C is the correct answer

The missing measurement for z would be 6 yds.

The volume of the rectangular prism is the product of the base area and the height.

Given the volume of a rectangular prism is 24 yds cubed

Length of prism = z

Width of prism = 1 yds

Height of prism = 4 yds

The volume of the rectangular prism would be :

volume of the rectangular prism = Base Area × Height

volume of the rectangular prism = Length × Width × Height

Substitute the values in the above formula,

24 yds cubed = z × 1 × 4

Apply the multiplication operation, and we get

24 = 4 z

z = 24/4

z = 6 yds

Therefore, the missing measurement for z would be 6 yds.

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Given: The equation below

To Determine: The value of x

Solution

Let us apply the exponent rule

Hence, the approximate value of x is 2.77, OPTION A

If the ordered pair (x,y) is in the relation and the object x is from the first set and the object y is from the second set, the objects are said to be related. A relation is a type of function.

For The Realation { X | X < -4}
The Graph a is correct solution

In interval notation ( - ∞ , -4 ).

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Solution

Step 1:

Write the expression

Step 2

Answer

6.8 ( 2 significant figure)

True

1) There are three steps, to using mathematical induction.

2) The first one is to check for n=1

3) Secondly, let's prove it for n=k:

4) And finally, for n=k+1

As all of those 3 steps were true. Then we can tell, that this is true.

Answer:

40 years old

Step-by-step explanation:

Define the variables:

Given Ryan is 93 years younger than Stacy:

⇒ r = s - 93

Given 9 years ago, Stacy's age was 4 times Ryan's age:

⇒ 4(r - 9) = (s - 9)

Substitute the first equation into the second equation and solve for s:

⇒ 4(s - 93 - 9) = (s - 9)

⇒ 4(s - 102) = s - 9

⇒ 4s - 408 = s - 9

⇒ 3s = 399

⇒ s = 133

Substitute the found value of s into the second equation and solve for r:

⇒ r = 133 - 93

⇒ r = 40

Therefore, Ryan is 40 years old now.

B

1) Since it is a reflection across the y-axis we can write the following rule:

Pre-image Image

(x, y) (-x,y)

2) Plugging the vertices of ABC we have

Pre-image Image

(x, y) (-x,y)

A(-3,4) A' (3,4)

B(0,2) B' (0, 2)

C(-2,1) C' (2,1)

3) Examining the options, the answer is B

Let the lines BD || AE

So, the triangle ACE is similar to triangle BCD

Then from the properties of similar triangle

The ratio of corresponding sides are always equal:

Substitute the value :

So, the triangles are not similar thus, the lines BD is not parallel to AE

Answer : D

[tex]m < 4 = m < 2[/tex]

(The angles mentioned above are alternative angles since AB || CD)

[tex]m < 2 = m < 4 \\ m < 2 = 35[/tex]

OPTION D IS THE ANSWER.

Answer:

D is correct

Step-by-step explanation:

Angles 2 and 4 are alternate interior angles. Because angle 2 is 35 degrees, a line travels through two parallel lines to form that angle, likewise for angle 2, except for that it is alternate interior. Hope this helps.

step 1

Find the slope

we need two points

so

we take (0,3) and (2,2)

m=(2-3)/(2-0)

m=-1/2

step 2

Find the equation of the line in slope intercept form

y=mx+b

we have

m=-1/2

b=3

substitute

y=-(1/2)x+3

therefore

the rule is