$Write the following phrase as an algebraic expression. Use y for theunknown."A number times 9"

8.5 bags will actually be needed if B=x(2x+7)+3(2x+7)+(x+4)(2x+7), where the quantity (2x + 7) equals 4

Expression: An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.) Expressions can be thought of as similar to phrases. In language, a phrase on its own may include an action, but it doesn't make a complete sentence.

Number of bags needed B=x(2x+7)+3(2x+7)+(x+4)

where the quantity (2x+7)=4

2x+7=4

2x=4-7

2x=-3

x=-3/2

now we are given the no. of bags needed

B=x(2x+7)+3(2x+7)+(x+4)

substitute the value of x which is found above x=-3/2

B=(-3/2)(2(-3/2)+7)+3(2(-3/2)+7)+((-3/2)+4)

B=8.5

hence 8.5 bags are needed

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Proportionately, in 30 seconds, James can type A, 60 words since he can type 40 words in 20 seconds.

Proportions set two ratios as equal to each other.

Proportions are the portions of a variable in another variable.

Proportions, like ratios, are stated in fractions, decimals, or percentages.

The number of words James can type in 20 seconds = 40 words

In 30 seconds, based on the above unit rate, James can type = 60 words (40/20 x 30)

Thus, based on the ratio of James' typing speed, in 30 seconds he can type 60 words.

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The missing reasons in the proof that shows that the triangles are congruent by SSS are:

3. Definition or parallelogram

4. Alternate interior angles theorem

5. Reflexive property of congruency

6. SSS Congruence Theorem

The SSS congruence theorem is applicable when two triangles have three pair of corresponding side lengths that are congruent to each other. The SSS congruence theorem states that they are congruent to each other. This theorem can be used in proof where it is established that the three sides of two triangles are equal to each other.

A side is congruent to itself according to the reflexive property of congruency. This means that if two triangles share a common side, the two angles therefore have a pair of corresponding congruent sides in a proof.

Therefore, the missing reasons for the proof are explained below:

Statements                  Reasons                                          

1. AD║BC                    1. Definition or parallelogram

2. ∠ADB ≅ ∠CBD      2. Alternate interior angles theorem

3. AB║CD                   3. Definition or parallelogram

4. ∠ABD ≅ ∠CDB       4. Alternate interior angles theorem

5. DB ≅ DB                 5. Reflexive property of congruency

6. ΔABD ≅ ΔCDB       6. SSS Congruence Theorem

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Answer:

Step-by-step explanation:

A.

35 dollars represents the cost of renting the coolers (I think it's a constant since it does not say it is the cost per cooler).

B.

0.50 cent represents the cost per water bottle in the function (the coefficient in front of b, the amount of water bottles being purchased).

C.

C is the total cost.

C = 0.50b + 35

D.

I'm not sure what this is asking. Y = 0.50x + 35's domain is all real numbers but I'm not sure what it means by "appropriate domain for the function" unless the problem is using the average statistics from actual high school football games based on how many water bottles are purchased or something else.

E.

The graph would be all real numbers unless I'm wrong. Which is very possible on d and e but I think I provided the correct info on the others.

We need 30 ml of the 15 percent solution to complete the order.

Here, we are given that we need to prepare 180 mL of a 2.5% solution by diluting a 15% solution with water.

the 180 ml 2.5% solution will contain-

2.5% pf 180 ml acid

= 2.5/100 × 180

= 25/1000 × 180

= 1/40 × 180

= 18/4

= 9/2

= 4.5 ml

Water in the 180 ml solution will be = 180 - 4.5 = 175.5

Now, we have say x ml of 15% solution

It must contain 4.5 ml of acid

Thus-

15% of x = 4.5

15/100 × x = 4.5

x = 4.5 × 100/15

x = 450/15

x = 30

Thus, we need 30 ml of the 15 percent solution, hence, option C.

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Step1

we can factor the numerator and denominator because we have a square subtract

step 2

restricted values of X are when the denominator is 0

then

factor this

and find the value of x what make each parenthesis 0

first restricted value is x=1

and the other restricted value is x=-1

SOLUTION

Given the question, the following are the solution steps to answer the question.

STEP 1: Write the given system of equation

STEP 2: Solve the given equation

Subtract equation 2 from equation 1

STEP 3: Solve for x

The values of x and y are 5 and -1 respectively meaning that the system has one solution, hence the type of system of equation given is a CONSISTENT system of linear equation.

If an individual borrowed 84000 the Starting loan principal is $84,000; Interest rate is 3%; Number of payment per year is 12 payments per year; Loan term is 23 years; Payment amount is $422.

a. Identifying  the starting loan principal, the interest rate, the number of payments per year, the loan term, and the payment amount.

Starting loan principal = $84,000

Interest rate =3%

Number of payment per year = 12 payments per year

Loan term = 23 years

Payment amount = $422

b. Total payment

There are 12 payments every year for 23 years, so

12 × 23 = 276

c. Total amount

Total amount 276× $422

Total amount = $116,472

d. Toward principal and interest

Toward Principal = $84,000

Toward Interest = $116,472 - $84,000

Toward Interest = $32,472

Therefore the starting loan principal is $84,000.

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The complete question is:

An individual borrowed 84000 at an APR of 3% which will be paid off with monthly payments of $422 for 23 years

a. Identify the amount​ borrowed, the annual interest​ rate, the number of payments per​ year, the loan​ term, and the payment amount.

A. The amount borrowed is

 The annual interest rate is

 The number of payments per year is

  The loan term is

  The payment amount is

B. How many total payments does the loan​ require? What is the total amount paid over the full term of the​ loan?

C. Of the total amount​ paid, what percentage is paid toward the principal and what percentage is paid for​ interest?

The percentage paid toward the principal is

and the percentage paid for interest is:

I prefer the two-column proof since it is the most common format in high school textbooks. One can easily find each of the steps of the proof, and one can correct any step so you can continue the next one step by step in a chronological list of them.

It is easy to audit this type of proof, and I am very comfortable using it.

△ABD is congruent to △CDB (△ABD ≅ △CDB) under the SAS congruency condition.

So, △ABD ≅ △CDB:

Therefore, △ABD is congruent to △CDB (△ABD ≅ △CDB) under the SAS congruency condition.

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Arc Length

Given a circle of radius r, the length of the arc formed by a central angle θ is given by:

We are given the central angle ∠JKL = 144° and the radius r = JK = 6 units.

The angle must be converted to radians by using the equivalence π = 180°

Thus:

Calculating the arc length:

The length of the arc JL is 15.08 units

Answer:       456 Miles

Step-by-step explanation:

The solution to the function expression, (f - g)(x) is: D. 2x³ + 6x² - 8x + 1.

To evaluate or subtract functions that has polynomials, all we simply need to do is to pair like terms together and combine them.

Given the following:

f(x) = 2x³ + 6x² – 5x – 3 and g(x) = 3x – 4

Therefore:

(f - g)(x) = f(x) - g(x)

Substitute

(2x³ + 6x² – 5x – 3) – (3x – 4)

2x³ + 6x² - 5x - 3 - 3x + 4

Combine like terms

2x³ + 6x² - 5x - 3x - 3 + 4

2x³ + 6x² - 8x + 1

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Complete Question:

f(x) = 2x³ + 6x² – 5x – 3

g(x) = 3x – 4

Find (f - g)(x).

O A. (f - g)(x) = 2x³ + 6x² – 2x – 7

O B. (f - g)(x) = 2x³ + 6x² – 2x + 1

O c. (f - g)(x) = 2x³ + 6x² – 8x – 7

O D. (f - g)(x) = 2x³ + 6x² – 8x + 1

The given function is

f(x) = x^3

Recall, if a function, f(x) is shifted c units upwards, the new function would be f(x) + c. This means that if we translate the given function 3 units upwards, the new function would be x^3 + 3

Also, if a function, f(x) is shifted d units to the left, the new function would be

f(x + d). This means that if we translate x^3 + 3 7 units to the left, the new function would be (x + 7)^3 + 3

The function is

f(x) = (x + 7)^3 + 3

Lysosomes are important to the health of cells of the following reason:

Lysosomes can be defined as protective organelles that contain enzymes that can be used to break down negative microorganisms that invade the body. The Lysosomes are very important to the health of cells because they protect the cells from being damaged by viruses and bacteria that can limit the growth of the body.

So, the option that explains why lysosomes are important to the health of cells is that they break down worn-out cell parts that are no longer needed. Option A is accurate.

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Explanation

Step 1

when you have 2 points of a line P1 and P2, you can easily find the slope using:

Let

P1=A=(-1,5)

P2=B=(3,-1)

Step 2

replace

I hope this helps you

We have functions f and g defined as:

f(x) = 5x - 2

g(x) = 4x - 2

We can subtract both functions:

f(x) - g(x) = (5x - 2) - (4x - 2) = 5x - 2 - 4x + 2

Then:

f(x) - g(x) = x

But, by definition, we know that:

(f - g)(x) = f(x) - g(x)

Putting these together:

(f - g)(x) = x

Now, if x = -3:

(f - g)(-3) = -3

EXPLANATION

The area of a semicircle is given by the following relationship:

The radius of the semicircle is diameter/2=14/2 = 7 feet

Replacing terms:

Computing the power:

Simplifying numbers:

In conclusion, the answer is the option D.

Let the coordinates of points be,

The distance between the two points using distance formula is,

Therefore, distance between the two points is 15.7.

The exact values of the sine of the addition and subtraction of two angles are 576 / 1105 and 264 / 1105, respectively.

Since angle A is in the fourth quadrant and B is in the second quadrant, then we find the following inequalities:

cos A > 0, sin A < 0

cos B < 0, sin B > 0

If we know that cos A = 13 / 85 and sin B = 12 / 13, then the missing trigonometric functions according to the fundamental trigonometric formula are:

sin A = - √(1 - cos² A)

sin A = - √[1 - (13 / 85)²]

sin A = - 84 / 85

cos B = - √(1 - sin² B)

cos B = - √[1 - (12 / 13)²]

cos B = - 5 / 13

And the exact value of the sine of the addition and subtraction of two angles is found by the following formula:

sin (A + B) = sin A · cos B + cos A · sin B

sin (A + B) = (- 84 / 85) · (- 5 / 13) + (13 / 85) · (12 / 13)

sin (A + B) = 576 / 1105

sin (A - B) = sin A · cos B - cos A · sin B

sin (A - B) = (- 84 / 85) · (- 5 / 13) - (13 / 85) · (12 / 13)

sin (A - B) = 264 / 1105

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Given that;

Note that cosine is positive on the fourth angle quadrant while tangent is negative.

From;

Thus, the tangent is;

We have to find the zeros of the polynomial f(x) = 2x^3-23x^2-28x-8.

The independent coefficient is -8, that has factors ±1,±2,±4 and ±8.

The leading coefficient is 2, and has factors ±1 and ±2.

The possible rational zeros (p/q) are: ±1/2, ±2/2=±1, ±4/2=±2 and ±8/2=±4.

The possible rational zeros are: ±1/2, ±1, ±2 and ±4.

Answer:

Two of the sides are 25cm and the other two sides are 35cm.

Step-by-step explanation:

The perimeter is the distance all the way around the shape.

The shape is a parallelogram, so two sides across from each other are the same length. And the other two sides are also the same as each other. See image.

The shorter sides can be labelled x and the longer sides can be labelled x + 10. This is because the question said the long side is 10cm more than the short side.

see image.

Add up all the sides to make them equal to the perimeter. Set it equal to 120. See image.

Solve for x.

x + x+10 + x + x+10 = 120

4x + 20 = 120

Subtract 20.

4x = 100

Divide by 4.

x = 25

The short sides are 25cm and the long sides are 35cm.

Check:

25+35+25+35=

120 Check!

Median:

To find the median, we first need to sort the values from smallest to highest.

The median separates the bottom 50% from the top 50%.

In a sorted set of n elements, which n is odd, the median is the element at the position: ((n+1)/2).

If n is even, the median is given by the mean of the elements at those following positions: (n/2, (n/2)+1).

Example:

Sorted: {1,2,3}

n = 3, element at the position (3+1)/2 = 2.

So the median is 2.

Sorted: {1,2,3,4}:

n = 4, so the mean between the elements at these following positions:

n/2 = 4/2 = 2, the element at the position 2 is 2.

(n/2)+1 = (4/2)+1 = 2 + 1 = 3, the element at the position 3 is 3.

The median is 2+3/2 = 5/2 = 2.5

In this question:

We have 20 elements.

The median will be the mean between the 10th and the 11th elements of the sorted set.

Sorted set:

In an ascending way.

{0.275, 0.277, 0.278, 0.279, 0.281, 0.282, 0.283, 0.289, 0.29, 0.296, 0.296, ...}

The 10th element is 0.296

The 11th element is also 0.296

(0.296 + 0.296)/2 = 0.296

The median is 0.296

Harrison Heights Elementary School has 3 fourth grade classrooms. Each classroom has 28 students.

From the given statement;

Number of four grade classrooms = 3

Number of student in each classromm = 28

So,

for total number of students in 3 four grade students = 3 x (number of student in one class)

= 3 x (28)

= 84 students

Answer : 84 students

The water level change after 8 years is 8 inches if it is lowers one inch per year.

Integer representation of 8 = 1000 in binary .

A fixed-point number with the radix point placed after the least-significant bit is an integer. They differ from real numbers or floating-point numbers, where the radix point is always at the same place. You should be aware that computers handle integers and floating-point numbers differently. They are shown differently and processed differently (e.g., floating-point numbers are processed in a so-called floating-point processor). We'll talk about floating-point numbers later.

An integer is represented by a fixed number of bits in computers. Integers can be stored in 8-bit, 16-bit, 32-bit, or 64-bit formats. There are two representation techniques for integers in addition to bit-lengths:

Positive and zero integers can both be represented as unsigned integers.

Positive, negative, and zero are all represented by signed integers.

Hence , If the water level drops one inch per year for eight years, the decrease in water level will be 8 inches.

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We have to find the price of one loaf of bread.

With the information we have, we can construct a system of equations.

Let B be the price of one loaf of bread and R the price of a roll.

Then, if one loaf of bread and six rolls cost $1.80, we can write:

We also know that two loaves of bread and four rolls cost $2.40, so we can write:

We can solve for B with the method of elimination: we can substract the first equation from 1.5 times the second equation.

This can be express in mathematica terms as:

Then, we have just calculated that the loaf of bread costs $0.90.

Answer: the cost of a loaf of bread is $0.90.

We have

we make the next equality

then we sum like terms

Then we substitute the value of x in the first equation

ANSWER

x=-3

y=-11

your answer is
x=-3 or y=-11