is y=10 a solution to the inequality y + 6 < 14

Answer:

35 degrees.

Explanation:

The figure shown is an isosceles triangle. An isosceles triangle has two of its sides and base angles to be equal.

Since the sum of the angles in a triangle is 180 degrees, hence:

110 + (base angles) = 180

110 + (<1 + <1) = 180 (since base angles are the same)

110 + 2<1 = 180

2<1 = 180-110

2<1 = 70

Divide both sides by 2

2<1/2 = 70/2

<1 = 35 degrees

Hence the angle between an eave and the horizontal support beam is 35 degrees.

A Nickel is 5 cents = 5/100 = $0.05

A dime is 10 cents = 10/100 = $0.1

A quarter is 25 cents = 25/100 = $0.25

Let N represent the number of nickels

Let D represent the number of dimes

Let Q represent the number of quarters

Jacob opened his piggy bank and found Nickels, Dimes, and Quarters totaling 81 coins. It means that

N + D + Q = 81

The total value of the coins was $7.90. It means that

0.05N + 0.1D + 0.25Q = 7.9

The number of Dimes was 7 less than triple the number of Quarters. It means that

D = 3Q - 7

The system of equations is

N + D + Q = 81

0.05N + 0.1D + 0.25Q = 7.9

D = 3Q - 7

For solving this question, you should apply the equation:

The question gives

Next step - replace the values in the equation

Solution

Why can the Vertical Angle Theorem NEVER be used to prove two triangles are congruent?

The Vertical angle theorem states that vertical angles are always congruent.

We can't use this to proof congruence between two triangles because this theorem not provide enough evidence to obtain the SSS, ASA, SAS, AAS, HHL. For this reason is not appropiate to use it for this case.

Answer:

The equation of the line k is

Explanation:

Given that k is perpendicular to line m, defined as:

y = 3x - 1

the slope of k is the negative reciprocal of the slope of line m.

The slope of m is 3

The negative reciprocal of m is -1/3 (this is the slope of k)

Therefore, k is in the form

Since this line passes through the point (x, y) = (-4, 3), we can use this to obtain the value for the y-intercept, b

Solving for b by subtracting 4/3 from both sides

The equation is therefore,

Answer

Option B is correct.

Angle ABC > Angle DBC

Explanation

Since it's been proven that

Angle ABC = Angle ABD + Angle DBC

Since Angle ABD > 0,

Angle ABC > Angle DBC is the part that completes the proof that

Angle ABC > Angle RST

Hope this Helps!!!

Given

Wholesale price for a pair of shoes = $3.50.

Wholesale price by 60%.

Find

price of the pair of shoes in the department store

Explanation

Price in deparrtmental store is 60% more than wholesale

so ,

Final Answer

Therefore , the price of the pair of shoes in the department store is $5.60.

To find the other factor of the polynomial

We need to find two integers which multiplication gives 36 and addition is -13.

This integers would be -9 and -4, then we have

now we factor the right term using common factors:

Hence:

Therefore, the other binomial we are looking for is (p-4).

The Solution:

Given that a coat costs $99.99 and the sales tax is $75.

We are required to find the actual sales tax and the total cost of the coat.

Step 1:

We shall find the sales tax.

Thus, the sales tax is $7.00 or 700 cents.

Step 2:

We shall find the total cost of the coat.

The total cost of the coat is the sum of the coat's cost and the sales tax.

Therefore, the correct answers are:

Sales tax =$7.00 or 700 cents.

Total cost = $106.99 or 10699 cents..99 or 10699 cents.

The percent error of the house of the pizza would be 2.

Suppose the actual value and the estimated values after the measurement are obtained. Then we have:

Error = Actual value - Estimated value

To determine the percent error, we will measure how much percent of the actual value, the error is, in the estimated value.

We have been given that House of Pizza says that their pizzas are 14 inches wide, but when measured, the pizza was 12 inches.

WE know that Error = Actual value - Estimated value

Then Error = 14 - 12 = 2

Therefore, the percent error would be 2.

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SOLUTION:

We want to know the scale factor of the transformation from;

We do this by taking ratios of corresponding sides, they should be the same in either case;

Thus , the scale factor is;

Thus, the scale factor is 2.

Verify each option

A ---> 1/sinx=cscx -----> is not the answer

C ---> cosx/tanx=cosx/(sinx/cosx)=cos^2x/sinx -----> is not the answer

E ---> cotxsinx=(cos/sinx)sinx=cosx ----> is not the answer

therefore

The answer is

Answer:

B, D, E.

Step-by-step explanation:

B:  [tex]\frac{1}{cos(x)}[/tex]

D: [tex]\frac{tan(x)}{sin(x)}[/tex]

E: [tex]tan(x) csc (x)[/tex]

In this problem, we want to determine tangent of 62 degrees.

Recall the identity of tangent:

We are given the triangle:

Since we are referencing 62 degrees, the arrow pointing away from the 62 degrees is headed toward the opposite side. Therefore, the opposite side is 15, and the adjacent side is 8.

Tangent of 62 degrees is 15/8.

Given

Data from graph

Procedure

It is more likely to rain on the first 15 days of the month

Step-by-step explanation:

there are 3 x-intercepts (the x- values when y = 0). because y is only 0, when one of the 3 factors is 0.

and that is the case for

x = -7

x = -1

x = 2

so, formally, the x- intercepts are

(-7, 0), (-1, 0), (2, 0)

the y intercept is the y- value when x = 0.

(0 + 7)(0 + 1)(0 - 2) = 7×1×-2 = -14

the y-intercept is formally

(0, -14)

To find:

The piecewise function for the graph.

Solution:

From the graph, it is clear that when x is less than -1, the graph passes through (-1, -3) and (-2, -5).

It is known that the equation of a line passes through two points is given by:

So, the equation of line passing through (-1, -3) and (-2, -5) is:

So, the first drop down is "2x - 1", and second drop down is "x is less than or equal to -1".

Now, the graph passes through (1, 5) and (2, 6). So, the equation of the line is:

So, the third drop down menu is "x + 4" and the fourth drop down menu is "x is greater than or equal to 1".

To solve the quadratic equation, factor the expression and then clear x from each of the factors obtained.

This equation has 2 solutions which are -5 and -1.

Solution

For this case we can select the following two points:

(0,0) and (4,6)

We can find the slope using this formula:

then the answer after simplify would be:

3/2

Given:

The length of the rectangular garden, l=50 feet.

The breadth of the rectangular garden, b=35 feet.

The width of the path around the garden, w=3 feet.

The figure can be drawn as,

So, the length of the fence, L=l+2w.

The breadth of the fence, B=b+2w

The perimeter of the fence can be calculated as,

Therefore, the perimeter of the fence is 194 ft.

Option B is correct.

According to the question, both polygons are similar. It means you can use proportions to find the value of x.

Replace for the given values in the picture

x has a value of 2.

Given that:

To prove that:

We know that congruent parts of congruent triangles are congruent

Given that E is the midpoint of AC, therefore,

By the SAS congruency theorem as illustrated above, it is sufficient to prove that the triangles are congruent

Given:

z = 1.40 and z = 2.13

Let's find the area under the standard normal curve.

Let's find the score using the standard normal distribution table:

NORMSDIST(1.40) = 0.9192

NORMSDIST(2.13) = 0.9834

To find the area between them, we have:

P(1.40 < Z < 2.13) = P(Z<2.13) - P(Z<1.40) = 0.9834 - 0.9192 = 0.0642

Therefore, the area under the curve between z=1.40 and z=2.13 is 0.0642

ANSWER:

0.0642

To verify that something is a function, we use the horizontal line rule. That is, if the horizontal line passes through two points, then the graph is not a function, like this:

Then the circles and the ellipses are not functions. Then the functions in the problem would be:

1, 3 and 6.

The expression that simplify to rational number are as follows:

A rational number is a number that is in the form of p/q, where p and q are integers, and q is not equal to 0.

In a simpler terms,  If a number can be expressed as a fraction where both the numerator and the denominator are integers, the number is a rational number.

Rational numbers can also be expressed in decimal form.

Rational numbers have terminating decimals.

Therefore, let's find the rational simplification in the options.

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The classification of each cost item as a differential cost, a sunk cost, an opportunity cost, or None, is as follows:

1. Cost of the old X-ray machine                                  Sunk cost

2. The salary of the head of the Radiology Dept.      None

3. The salary of the head of the Laboratory Dept.     None

4. Cost of the new color laser printer                          Differential cost

5. Rent on the space occupied by Radiology             None

6. The cost of maintaining the old machine               Differential cost

7. Benefits from a new DNA analyzer                         Opportunity cost

8. Cost of electricity to run the X-ray machines         Differential cost

9. Cost of X-ray film used in the old machine            Sunk cost

A differential cost is a cost that arises as the cost difference between two alternatives.

A sunk cost is an irrelevant cost in managerial decisions because it has been incurred already and future decisions cannot overturn it.

An opportunity cost is a benefit that is lost when an alternative is not chosen.

Thus, the above cost classifications depend on the decision to replace the old X-ray machine with a new machine (new X-ray or new DNA analyzer).

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Required Classify each item as a differential cost, a sunk cost, or an opportunity cost in the decision to replace the old X-ray machine with a new machine. If none of the categories apply for a particular item, select "None".

1. Cost of the old X-ray machine

2. The salary of the head of the Radiology Department

3. The salary of the head of the Laboratory Department

4. Cost of the new color laser printer

5. Rent on the space occupied by Radiology

6. The cost of maintaining the old machine

7. Benefits from a new DNA analyzer

8. Cost of electricity to run the X-ray machines

9. Cost of X-ray film used in the old machine

Factoring

Factor the expression:

Divide the expression into two halves:

Factor b^2 from the first group and xb from the second group:

Now find the greatest common multiple of 72 and 96:

72= 2*2*2*3*3

96=2*2*2*2*2*2*3

Now we take the common factors with their least number of repetitions:

GCF=2*2*2*3=24

Now we find the GCF of 90 and 120:

90=2*3*3*5

120=2*2*2*3*5

GCF=2*3*5=30

Taking the GCF of each group:

Now we finally take out 3z+4h from both groups:

This last expression can be further factored by taking out 6b from both terms:

This is the final expression factored as much as possible

From the given expression

a) The linear system of a matrix form is

The linear system of the given matrix will be

b) The entries in A of the matrix is

c) The dimensions of A, X and B are

So, y is a system two distinct exponential functions.

The function on the bottom is a cubic function with a y-intercept of -3, and the full dot means that point is included in the domain.

y = x^3 - 3, x ≤ 2

The other function is a quadratic function with a currently unknown y-intercept. The hollow dot on point 2 means that the point is not included in the domain of the function.

y = x^2 + b, x > 2

So, given that there is only one option that matches this, even with the unknown b value, we know:

[tex]y = \left \{ {{x^3 - 3, x\leq 2} \atop {x^2 + 6, x > 2}} \right.[/tex]

So the answer is C.

Four points that are contained in the inverse function include the following:

An inverse function refers to a type of function that is obtained by reversing a mathematical operation in a given function (f(x)).

In order to determine the inverse of the given function, we would interchange both the input value (x) and output value (y) as follows:

y = 2x - 4

x = 2y - 4

Subtracting 4 from both sides, we have:

x + 4 = 2y - 4 + 4

2y = x + 4

Dividing both sides by 2, we have:

y = (x + 4)/2

y = x/2 + 4

When x = 0, we have:

y = x/2 + 4

y = 0/2 + 4

y = 4

Point = (0, 4).

When x = 1, we have:

y = x/2 + 4

y = 1/2 + 4

y = 4.5

Point = (1, 4.5).

When x = 2, we have:

y = x/2 + 4

y = 2/2 + 4

y = 5

Point = (2, 5).

When x = 4, we have:

y = 4/2 + 4

y = 0/2 + 4

y = 6

Point = (4, 6).

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For 6 sandwiches and 3 dozen cookies, the total time taken by Brenda would be 33 minutes.

Given is Brenda who must make at least 6 sandwiches and at least 3 dozen cookies. It takes her 4 minutes to make a sandwich, and 45 minutes to make a dozen cookies.

If she makes [x] sandwiches and [y] dozen cookies, then the total time she would take to make them can be written as -

t = 4x + 3y

For 6 sandwiches and 3 dozen cookies, we can write -

t(6, 3) = 4 x 6 + 3 x 3 = 24 + 9 = 33 minutes

t(6, 3) = 33 minutes

Therefore, for 6 sandwiches and 3 dozen cookies, the total time taken by Brenda would be 33 minutes.

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{Complete question is given below -

She must make at least 6 sandwiches and at least 3 dozen cookies. It takes her 4 minutes to make a sandwich, x, and 45 minutes to make a dozen cookies, y.}