If-9(y-13) = 16, then y=​

Answer:

(1,10) is not a solution to the inequality.

Step-by-step explanation:

First, you want to insert the values of x and y in the inequality.

So, [tex]10\leq 4(1) +1[/tex]

[tex]10\leq 5[/tex]

That inequality is not true, so we know that (1,10) is not a valid solution.

The two consecutive whole numbers that it lies between are 28 and 29.

The consecutive numbers are those number which follow each other continuously in the order from smallest to largest numbers.

Let the two consecutive numbers be x and x + 1

x + x + 1 = 57

Combine like terms;

2x + 1 = 57

Now Subtract 1 from both sides;

2x = 57- 1

2x = 56

Divide both sides by 2

x = 56/2

x = 28

Thus, x + 1 = 28 + 1 = 29

The two consecutive whole numbers that it lies between are 28 and 29.

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The number of squirrels that the biologists predict there will be 2 years after they started counting will be 43 squirrels.

It should be noted that a function is used to show the relationship between the variables.

It should be noted that the function that's given is illustrated as:

n = 40 + 1.5t

In this case, it should be noted that t = 2 years.

Therefore, the number of squirrels that the biologists predict there will be 3 years after they started counting will be:

n = 40 + 1.5t

n = 40 + 1.5(2)

n = 40 + 4

n = 43

Therefore, the number of squirrels that the biologists predict there will be 2 years after they started counting will be 43 squirrels.

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The interest rate 2% per year

The time period is 7 years

The initial investment is $600

The current investment is $84

The interest rate can be calculated as follows

84/600 × 7

= 84/4200

= 0.02

The interest rate is

= 0.02 × 100

= 2%

Hence the interest rate is 2%

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The expression acquired is h(x) = 3.5 sin(1/3x ₊ 4π/3)₊2.5

Given h(x) = a sin(bx ₊ c) ₊ d

The h(x) function intersects its mid line at (₋4π , 2.5)

and has its maximum points at (₋5π/2 , 6)

therefore, x₂ ₋ x₁  = ₋5π/2 ₋ (₋4π)

= ₋5π/2 ₊ 4π

= 3π/2

⇒ 2π/b = 3π/2  4

⇒ 2π/b = 6π

⇒b = 1/3

hence, a = b ₋ 2.5

a = 3.5

now h(x) = 3.5 sin(1/3x ₊ c) ₊ 2.5

x = ₋4π

h(₋4π) = 3.5 sin( ₋4π/3 ₊ c) ₊ 2.5

₋4π/3 ₊ c = 0

c = 4π/3

therefore, h(x) = 3.5 sin(1/3x ₊ 4π/3)₊2.5

hence after solving the equation we get the expression for h(x) as

h(x) = 3.5 sin(1/3x ₊ 4π/3)₊2.5

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Answer:

8

Step-by-step explanation:

Order of Operations:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Parentheses First:

(9 + 3) = 12 and (6 - 7) = -1

12 + 4(-1) = 12 + (-4) = 8

Hey there!

(9 + 3) + 4(6 - 7)

= 9 + 3 + 4(6) + 4(-7)

= 9 + 3 + 24 - 28

= 12 + 24 - 28

= 36 - 28

= 8

Therefore, your answer should be:

8

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

2 associate property

Step-by-step explanation:

(3 + 4) + 5 3 + (4 + 5)  On the left side, the 4 is "associating" with the 3", but on the left side the 4 is "associating;" with the 5.

The ratio of the height to the perimeter of this mural 57 : 152.

We are given that:

Length = 135 feet

height = 285 feet

Mural is of a rectangular shape

We will first find the perimeter.

Perimeter = 2(l + w)

Perimeter = 2(95 + 285)

Perimeter = 2(380)

Perimeter = 760 feet

We will now find the ratio of the height to the perimeter of this mural.

Height : perimeter = 285 : 760

Reduce to lowest terms

Height : perimeter = 57 : 152

Therefore, we get that, the ratio of the height to the perimeter of this mural 57 : 152.

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The number of students in the 9th grade is 250.

Based on the information, the percentage of those who brought their good from home will be:

= 100 - 24%

= 76%

Therefore, 76% of x = 190

0.76x = 190

x = 190/0.76

x = 250

Therefore, the number of students in the 9th grade is 250.

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Applying addition of integers, the final results of the expressions are given as follows:

a) -6.

b) -6.

c) 35.

d) -1.

To add two integers, we have to keep in mind their signals, if they are the same or different, as follows:

Hence, for item a, we have that:

For item b, the solution is found as follows:

For item c, the solution is found as follows:

For item d, the solution is found as follows:

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Step-by-step explanation:

X=48 becase 42+90=132

180-132= 48

When you subtract two numbers, if you reduce the first number in the subtraction by one, the result is one less. This is true.

It should be noted that in subtraction when you reduce the first number, you will get a value that's lesser by 1.

In this case, if we have 20 - 5 = 15, then 19 - 5 = 14. We can see that 14 and 15 is a difference of 1.

Therefore, when you subtract two numbers, if you reduce the first number in the subtraction by one, the result is one less. This is true.

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the number that makes it correct is 10

let's write it like this

23+5=x+18

28=x+18

you would subtract 18 from each side to get x

28-18=10

18-18=0

x=10

Answer:

It's the first one: 7 to the fourth over 3 to the tenth.

Step-by-step explanation:

Answer:

I think it is the first one

Step-by-step explanation:

For the given figures, both Priya and Tyler's opinions are incorrect.

Scaling is the process of measuring as well as assigning numbers to objects according to predefined rules.

Scaling is the process of locating the measured items on the continuum, an ongoing sequence of numbers with which the objects are assigned.

As, for the given question;

As a result, both Priya as well as Tyler are incorrect. None of them are acceptable to us.

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The complete question is-

Priya and Tyler are discussing the figures shown below. Priya thinks that B, C, and D are scaled copies of A. Tyler says B and D are scaled copies of A. Do you agree with Priya, or do you agree with Tyler? Explain your reasoning.

Answer: width of the garden is 42

Step-by-step explanation:

let's say "x" = the garden's length

and "y" = the garden's width

the length of the garden is 10 feet longer than its width

x-10=y

the garden's perimeter is 188 feet

we can set up a new equation like this:

2x+2y=188

now we have two equations and we can solve using the system of equations.

x-10=y

add 10 on both sides to isolate "x"

x=y+10

2x+2y=188

substitue x for y+10 in the second equation

2(y+10)+2y=188

expand

2y+20+2y=188

combine like terms

4y+20=188

subtract 20 from both sides

4y=168

divide by four on both sides

y=42

the width of the garden is 42 feet

Employee’s total annual contribution is $1513.75

And, Employee’s monthly deduction is $126.15

Here,

Dorsey Williams has a single plan.

And, His PPO annual premium is $4,325.

His employer pays 65%.

We have to find the Employee’s total annual contribution.

And, Employee’s monthly deduction.

What is Annual contribution?

The amount credited to Account balance after the end of each Plan Year for which the Performance Goals are achieved is called Annual contribution.

Now,

His PPO annual premium is $4,325.

And, His employer pays 65%

Hence,

Employee’s total annual contribution = 4,325 (1 - 65%)

                                                        = 4,325 (35%)

                                                        = 4,325 x 35/100

                                                        = 1513.75

And, Employee’s monthly deduction = 1513.75 ÷ 12 = 126.15

Therefore, Employee’s total annual contribution is $1513.75

And, Employee’s monthly deduction is $126.15

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Answer:

13

Step-by-step explanation:

We can think of this as drawing 3 pairs of each color, and then the next pair will guarantee we have 4 of one color.

This is 3(4)+1=13 pairs.

Step-by-step explanation:

let me see, if I understand this right.

7 pairs of green socks = 14 green socks.

6 pairs of white socks = 12 white socks.

5 pairs of red socks = 10 red socks.

4 pairs of blue socks = 8 blue socks.

in total : 44 socks (or 22 pairs).

the person is pulling socks always 2 at a time. but each sock can be any color.

or are the pairs still connected, and each draw pulls a pair of equal socks ?

and then the question also really is, what is meant by 4 pairs have the same color ? that i find 4 groups of 2 socks each with the save color inside the group (making them pairs), or truly 4 pairs with the same color (e.g. 4 red pairs, or 4 green pairs) ?

if the pairs are still connected, only the second question makes sense.

the worst that can happen in that scenario is drawing

3 pairs of blue socks.

3 pairs of red socks.

3 pairs of white socks.

3 pairs of green socks.

this now like in Baseball : the bases are loaded. any additional runner will cause a score.

because any additional draw must complete one of the groups of 4 pairs.

so, latest after the 4×3 = 12 draws, we get a 13th draw. that gives us 4 equally colored pairs of socks for sure.

so, we need 13 draws.

if each sock is in there individually, and we still want to have 4 pairs of socks all with the same color, then it starts similarly :

the socks get pulled 2 by 2 but that means each drawn pair can have different colors of the individual socks.

in the worst case after drawing 24 socks (12 groups of 2 socks), we have the same situation as in the previous case.

but now, pulling 2 more socks does not guarantee a full set of 4 pairs. we could get 2 different socks that add only half a pair to 2 color groups.

the same with the next pulled group of 2. they fill up the other 2 color groups with half-pairs.

but now the base are loaded. by pulling the next (3rd) additional group of 4, we complete at least one color group with 4 full pairs.

so, we need 12 + 3 = 15 draws to make absolutely sure.

now, if we have individual socks, and want to get 4 pairs of socks that have just the same color inside their pair, we need to think a little bit differently.

after 2 draws (4 socks) we have in the worst case 4 individual socks with different colors.

after the next 2 draws we can be already lucky, but in the worst case we are not but have now either 2.5 full pairs of one color and 3 individual socks, or 2 full pairs in one color, 1 full pair in a second color, and 2 individual socks, or 1.5 pairs in one color, 2×1 full pairs in 2 other colors, and 1 individual sock.

with the next draw in the worst case we could only extend the second case and get 2.5 pairs in one color, 1.5 pairs in the second color and still 2 individual socks.

but now the bases are loaded, and the next draw of 2 socks guarantees that we have 4 real pairs of socks (either 3 and 1 and still 2 individual socks, or 3 and 2 pairs and 2 individual socks, or 2 and 2×1 and wherever the second sock goes, it does not matter, or any other combination where at least one of the individual socks have been combined to a pair.

so, we need

2+2+1+1 = 6 draws.

[tex]

\cot(a-b)=\frac{\frac{1}{(x+1)(x-1)}+1}{\frac{1}{x-1}+\frac{1}{x+1}} \\ \\ =\frac{1-1+x^2}{2} \\ \\ =\frac{x^2}{2} \\ \\ \therefore 2\cot(A-B)=x^2[/tex]

Answer:

See below for proof.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5 cm}\underline{Trigonometric Identities}\\\\$\cot \theta=\dfrac{1}{\tan \theta}$\\\\$\tan (A \pm B)=\dfrac{\tan A \pm \tan B}{1 \mp \tan A \tan B}$\\\end{minipage}}[/tex]

[tex]\begin{aligned}\implies 2\cot (\alpha - \beta) & =\dfrac{2}{\tan (\alpha - \beta)}\\\\ & =\dfrac{2}{\dfrac{ \tan \alpha - \tan \beta}{1+\tan \alpha \tan \beta}}\\\\ & =\dfrac{2(1+\tan \alpha \tan \beta)}{ \tan \alpha - \tan \beta}\\\\ & =\dfrac{2(1+(x+1)(x-1))}{ (x+1) - (x-1)}\\\\& = \dfrac{2(1+(x^2-x+x-1))}{x+1-x+1}\\\\& = \dfrac{2(1+(x^2-1))}{2}\\\\& = \dfrac{2x^2}{2}\\\\& = x^2\end{aligned}[/tex]

Hence verifying that 2cot(α - β) = x².

Answer:

3x^2

Step-by-step explanation:

Explained in image.

< TSU = 4y + 11 = 23 degrees

What does angle relationship mean?

We talk of angle relationships because we are comparing position, measurement, and congruence between two or more angles. For example, when two lines or line segments intersect, they form two pairs of vertical angles

we have to find m < TSU if SU bisects < TSV, m < TSU = 4y + 11, m < USV = 6y + 5

SU bisects < TSV

=>    < TSU = < USV

4y + 11 = 6y + 5

-2y = -6

y = 3

< TSU = 4y + 11 = 23 degrees   ( put the value of y=3)

∠USV = 6y + 5 = 23 degrees      ( put the value of y=3)

Hence ,< TSU = 4y + 11 = 23 degrees

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Answer: 3.69

Step-by-step explanation:

Answer:

3.69

Step-by-step explanation:

If the last digit in the fractional part of 3.691 is less than 5, then simply remove the last the digit of the fractional part.

By using subtraction method we get 55.157.8987

What is subtraction method?

In mathematics, subtraction refers to the act of removing something from a set of related objects or numbers. What is left in the group decreases as a result of subtraction.

Let cost of each cow=x

cost of each goat =y

Given 2x+9y=98200------------(equation 1)

9y=98200-2×Y=98200-2x/9-----------(equation 2)

Also 3x+4y= 9800+2200

          3x+4y=1004004y=100,

400-3xY=100400-3x/4---------(equation 3)

From equation 2 and 3 we get

Y=Y98200-2x/9

 =100400-3x/4

 =196,400-8x

 =301200-27x

 =19x

 =104,800

 =x=55.157.8987

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Using proportions, it is found that the total job cost for Randi is of $6,674.24.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

The total amount of square yards that she needs is given by:

111.02 + 31.82 + 161.92 = 304.76.

The cost per square yard is given by:

15.01 + 3.12 + 3.77 = $21.9.

Hence the total cost is given by:

304.76 x 21.9 = $6,674.24.

The total job cost for Randi is of $6,674.24.

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The converse of the conditional statement "If it is sunny, then it is 80° Fahrenheit." is "If it is 80° Fahrenheit, then it is sunny".

Given the conditional statement "If it is sunny, then it is 80° Fahrenheit."

and asked for the converse statement if it exists

converse:

A statement's converse is formed by switching the hypothesis and conclusion. "If two lines do not intersect, they are parallel," is the converse of "If two lines intersect, they are parallel." "If p, then q" is the converse of "if q, then p."

Therefore, the converse of conditional statement is  "If it is sunny, then it is 80° Fahrenheit."

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Answer: A:  If it is sunny, then it is 80° Fahrenheit. The converse is valid.

Step-by-step explanation: Hope that helped!

The expression -4x² + 2x - 5(1 + x) is equivalent to the expression - (4x² + 3x + 5).

The equivalent is the expression that is in different forms but is equal to the same value.

The quadratic expression is given below.

⇒ -4x² + 2x - 5(1 + x)

Simplify the expression, then the expression will be given as,

⇒ -4x² + 2x - 5(1 + x)

⇒ -4x² + 2x - 5 - 5x

⇒ -4x² - 3x - 5

⇒ - (4x² + 3x + 5)

The expression -4x² + 2x - 5(1 + x) is equivalent to the expression - (4x² + 3x + 5).

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Answer: The answer is C

Step-by-step explanation: