Determine the missing number in the equation.

The equation 4 times 7 equals 4 times 10 in parentheses minus 4 times blank

Answer:

8x - 4 = 60 (alternate angles, parallel lines a and b)

8x = 64

x = 8

Triangle ABC and the triangle EFG are congruent by the first and third statement.

What is the congruent diagram?

Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.

In the given example triangle ABC and triangle EFG having one same side of length 2.

By the ASA (Angle side angle) criteria, we want two angles are same then the triangles are congruent.

When "m ∠ B and m ∠ F"  and "m ∠ A and m ∠ E" are same then the triangles are congruent.

Therefore, the first option is correct.

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Given,

The statement is "The height of a person and his weight".

Required/

Identify the statement is inverse or direct variation.

As the height of the person increase then its their weight is also increased.

Similarly,

The height of the person decrease then its their weight is also decreased.

Hence, it is direct variation.

we get that:

so the answer is x=-6

We can convert that 30% into a decimal, as: 0.3 (That's 30/100)

Now, we can multiply this 0.3 by any quantity that we want to calculate 30% from.

For example, let's take Justin's commission:

Adding this to his base salary,

We can conclude that Justin's paycheck for the week would be $1,117.5

Similarly, the expression for Justin's paycheck in a week were he made x dollars in sales is:

Answer:

Use the information from parts a

Step-by-step explanation:

Answer:

3.16

Step-by-step explanation:

The perimeter of the triangle is 46.4 and the length of a triangle's boundary taken as a whole is referred to as its perimeter.

Calculate the perimeter of a triangle:

Perimeter of a triangle = a +b + c

Therefore, the triangle's perimeter is 46.4, and the whole length of a triangle's boundary is referred to as the triangle's perimeter.

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It will take 1.62 seconds for an acron to fall on the branch of 7 feet high.

For the given question,

An acorn fell from a branch 20 feet high.

An acorn landed on a branch 7 feet high.

The total distance travelled by and acron is 20 - 7 = 13 feet.

Let the final velocity of an acron is 'v'.

The initial velocity of an acron 'u' is zero.

Using third equation of straight line.

Put the values.

v² = 2×9.8×13

v = 15.96 ft/sec

Put the value in first equation of straight line.

v = u + gt

15.96 = 0 + 9.8×t

t = 15.96/9.8

t = 1.62 seconds.

Thus, it will take 1.62 seconds for an acron to fall on the branch of 7 feet high.

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EXPLANATION:

We are given the original price of a laptop computer at $1,700.

Now the price has been increased to $1,800.

Note that there is a $100 increase over the original price.

For us to calculate the percent increase we shall use the ratio of the increase over the original price and calculate as a percentage.

We can now set up the following equation;

We now cross multiply;

Rounded to one decimal place, the percent increase is;

ANSWER:

The equation to describe different possible combinations of roast beef and shrimp that he can buy for $96 is 4b + 10s = 96.

A mathematical 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.

Let roast beef = b

Let shrimp = s

Total cost = 96

Therefore the equation will be:

(4 × b) + (10 × s) = 96

4b + 10s = 96

This illustrates the equation.

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To answer this question we need to remember that:

then:

now we need to remember that:

hence:

Therefore:

and the asnwer is A.

The probability it fails to detect an underfilled can for the first time when it encounters the 10th underfilled is [tex]0.01667496[/tex].

What is probability?

Probability is defined as the possibility of an event to occur.

An automated weight monitor can detect underfilled cans of beverages with probability [tex]0.98[/tex]

Thus probability of success will be [tex]p=0.98[/tex]

So probability of failure [tex]q=1-p=1-0.98=0.02[/tex]

To find the first wrong detection happening on the tenth trial the first nine trials must be success followed by failure in the tenth trial.

Thus, required probability [tex]=p^9q^1=(0.98)^9(0.02)=0.01667496[/tex]

Hence the probability it fails to detect an underfilled can for the first time when it encounters the 10th underfilled is [tex]0.01667496[/tex].

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11. The amount he pays in annual state income tax is $1,497.

13. The amount that will be paid for tax will be $2000.

14. The amount he pays in annual state income tax is $707.50.

11. Given;

Annual earnings = $57,900

State tax rate = 3%

Amount earned in exemption = $8,000

Taxable Income = Annual Income - Exemptions

Igor's taxable income = $57,900 - $8,000 = $49,900

Taxable Income × Tax rate = Amount paid as tax

The amount he pays is therefore; $49,900 × 3% = $1,497

13. The amount that will be paid as tax will be:

= 4.6% × $43500

= $2000

Therefore, the amount is $2000.

12. a) We can see that the exemptions for a married person are $4000 and $2000 per dependent. Since there are 2 dependents, therefore:

Amount for exemptions = $4000 + (2 dependents × $2000 per dependent)

Amount for exemptions = $4000 + $4000 = $8000

Amount for exemptions = $8000

b) Taxable wages = Annual gross pay - Exemptions

Taxable wages = $63840 - $8000 = $55840

Annual state income taxes = Taxable wages × State tax rate

Annual state income taxes = $55840 × 4% = $2233.6

14. The amount he pays in annual state income tax is $707.50.

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The irrational number on a number line is 13.1. All real numbers that are not rational are considered irrational numbers. In other words, it is impossible to describe an irrational number as the ratio of two integers.

All real numbers that are not rational numbers are referred to be irrational numbers in mathematics. In other words, it is impossible to describe an irrational number as the ratio of two integers.There is no length, no matter how short, that could be used to express the lengths of both of the two supplied segments as integer multiples of itself.

Square Root of 172 to the nearest tenth, means to calculate the square root of 172 where the answer should only have one number after the decimal point.

We calculate the square root of 172 to be:

√172 = 13.11487704860400

Reduce the tail of the answer above to two numbers after the decimal point: 13.11

Round 13.11 so you only have one digit after the decimal point to get the answer: 13.1

To check that the answer is correct, use your calculator to confirm that 13.1² is about 172.

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Answer:

52:56 and 39:42

Step-by-step explanation:

The ratios equivalent to 13:14 are:

52:56

39:42

3:4 is not equivalent to 13:14 because 3 is not a multiple of 13.

Answer:

[tex]\frac{17}{4}[/tex]

Step-by-step explanation:

Replace y with 3/2 and solve for x

2x + 3(3/2) = 13

2x + 9/2 = 13  Subtract 9/2 from both sides

2x = [tex]\frac{13}{1}[/tex] - [tex]\frac{9}{2}[/tex]

2x = [tex]\frac{26}{2}[/tex] - [tex]\frac{9}{2}[/tex]

2x = [tex]\frac{17}{2}[/tex]  Divide both sides by 2

x = [tex]\frac{17}{2}[/tex] ÷ [tex]\frac{2}{1}[/tex]

x = [tex]\frac{17}{2}[/tex] x [tex]\frac{1}{2}[/tex]

x = [tex]\frac{17}{4}[/tex] o r4 [tex]\frac{1}{4}[/tex] or 4.25

Graph 1 contains the two angles in the domain 0 ≤ θ ≤ 360º that have cosine given by cos(θ)  = -3/5.

The sine and the cosine of an angle are represented in the unit circle, in which:

Hence the cosine of the angle is negative when the x-axis is negative, which happens in these following quadrants:

The only equation that can be solved in the context of this problem is:

cos(θ)  = -3/5.

The solution is composed by two angles, one in the second quadrant and one in the third quadrant, hence Graph 1 shows the correct solution.

The exact angles are found applying the inverse cosine function as follows:

θ = arccos(-3/5) = 126.9º = 233.1º.

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The correct option regarding the discounts is given as follows:

Store Z has the best sale price of $28.

The discount can be a percentage or an amount off, and the calculations are explained as follows:

Considering the discount plans and the original price of $35, the discounted prices in this problem are as follows:

Hence the correct statement is given as follows:

Store Z has the best sale price of $28.

The complete problem is:

Leo wants to buy some shoes. He found the shoes at three different stores for a price of $35. The stores are each having a sale:

Which statement about the sale price of these shoes is true?

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Answer:

x = -11

Step-by-step explanation:

Hello!

This is a one-step equation. To solve for x, you simply have to isolate it.

Since -16 is being added to x, we can add 16 to both sides to cancel out the negative 16.

The value of x is -11.

Answer:

1 answer

Step-by-step explanation:

when the terms are collected

[tex]4k = 0[/tex]

[tex]k = 0[/tex]

Answer:

%25 of customers ordered ice tea.

Step-by-step explanation:

To find percentage = Part/Whole x 100

35/140 x 100 = 0.25 x 100 = %25

a. the distribution of X ~ N(15,5)

b.  the probability that it lasted at least 12 days = 0·72575

c.  the probability that it lasted between 17 and 22 days  = 0.30567

d. 72% of all of these types of trials are completed within  13 days

(a)

The x follow normal distribution with mean standard deviation

X ~ N(15,5)

(b)

probability at least 12 days.

P(X≥12) = 1 - P(X ≤12)

            = 1 - P((X - μ)/б ≤ (12-15)/5 ]]

            = 1 - P[Z  < -0.6]

            = 1 - 0·27425

            = 0·72575

(c)

Probability at least between 16 & 21 days

P(16 < x < 21) = p( (16-15)/5 <  (X - μ)/б - (21-15)/5]

                     = p (0.2 < Z < 1.2 )

                     = p[Z < 1.2] - P[Z < 0.2]

                     = 0.8849 - 0.5792

                     = 0.30567

(d)

standard normal table z is 0.65

p (Z < 0.65) = 0.74215

using Z score formula

X = Z x  б + μ

X = 0.65 x 5 + 15

X = 13

This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Before we can determine the probability that a certain event will occur, we must first know the total number of outcomes.

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The point in the feasible region maximizes the objective function is (5, 0)

The given parameters are

Objective function: C = 7x - 3y

Subject to (i.e. the constraints)

    x ≥  0, y ≥ 0

    y ≤ 1/5x + 2, 5 ≥ y + x

Next, we plot the graph of the constraints (see attachment)

This is done by entering the inequalities in a graphing calculator

From the graphing calculator, we have the feasible regions to be

(5, 0), (2.5, 2.5) and (0, 5)

Substitute (5, 0), (2.5, 2.5) and (0, 5) in the objective function: C = 7x - 3y

So, we have

(5, 0): C = 7(5) - 3(0)

C = 35

(2.5, 2.5): C = 7(2.5) - 3(2.5)

C = 10

(0, 5): C = 7(0) - 3(5)

C = -15

The value 35 is greater than 10 and -15

The coordinates at this value are (5, 0)

Hence, the coordinates is (5, 0)

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Answer:

nothing but B2. 0 hours

The bus will take 1.5 hours to cover 90 kilometers at an average speed of 60 km/hr.

Speed can be thought of as the rate at which an object covers distance.

i.e.

Speed = distance traveled/time taken

After arranging the equation we get,

Time taken = Distance traveled/Average speed

Here distance traveled by bus = 90 km

The average speed of the bus = 60 km/hr

So total time taken = 90/60 = 1.5 hours

So the bus will take 1.5 hours to cover 90 kilometers at an average speed of 60 km/hr.

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The hypotenuse of a right triangle = 19.31cm

What is Hypotenuse?

The longest side of a right-angled triangle, or the side across from the right angle, is called the hypotenuse. The Pythagorean theorem, which asserts that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.

Let the measure be,

Perpendicular = 18cm

Base = 7cm

Hypotenuse = ?

To find the Hypotenuse we can Pythagoras Theorem:

Hypotenuse² = Perpendicular²+ Base²

H² = (18)² + (7)²

H² = 324 + 49

H² = 373

H = [tex]\sqrt{373}[/tex]

H = 19.31cm

Hence, The measure of the other leg is²

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Answer:

============================

The total deposit over 12 weeks:

Equation in general form:

Answer:

It has reflectional symmetry with four lines of symmetry.

Step-by-step explanation:

======================================================

Explanation:

Choice A is false since it does have rotational symmetry. See choice B.

Choice B is close, but the "90 degrees" needs to be "45 degrees". Each 45 degree rotation of the figure has the "before" and "after" be the same.

Choice C is one of the answers. There's a vertical line of symmetry, and a horizontal one as well.  Then there are two diagonal lines of symmetry. Each goes through the center. A line of symmetry is a mirror line to allow us to reflect one half over this line to get the other half.

Choice D is another answer. It has point symmetry since we can pick any point on the figure and reflect it over the center point, to land on a corresponding image point on the opposite side of the figure. For example, the northern most point reflects over the center to land on the southern most point.

The solutions to the quadratic equation using completing the square method are  x = -(√109)/2 - 5/2 and x = (√109)/2 -5/2.

Given the quadratic equation in the question;

To solve using  completing the square method, first add 21 to both sides

x² + 5x - 21 = 0

x² + 5x - 21 + 21 = 0 + 21

x² + 5x = 21

Next, create a trinomial square on the left side of the equation, determine the value that is equal to the square of half of b which is 5.

( b/2 )² = ( 5/2 )²

Now, add ( 5/2 )²  to both sides of the equation

x² + 5x + ( 5/2 )² = 21 + ( 5/2 )²

Simplify

x² + 5x + 25/4 = 21 + 25/4

Add 21 and 25/4

x² + 5x + 25/4 = 109/4

Factor the perfect trinomial.

x² + 5x + 25/4 = 109/4

( x + 5/2 )² = 109/4

Solve for x by taking the square root of both sides.

x + 5/2 = ±√( 109/4 )

x = -5/2 ±√( 109/4 )

x = ±(√109)/2 -5/2

x = -(√109)/2 - 5/2, (√109)/2 -5/2

Therefore, the solutions to are x = -(√109)/2 - 5/2 and x = (√109)/2 -5/2.

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