The sum of two numbers is 21. Three times the larger is equal to four times the smaller.
Find them.

Answer:

Number sets are closed under an operation when you perform the operation and the result is another member of the same number set

The expression can be simplified to a polynomial of degree 2.

[tex]x^2 - 10x + 2[/tex]

Here we have the expression:

[tex](3x^2 -11x - 4) - (2x^2 - x - 6)[/tex]

We can directly simplify this by taking the variable as common factor:

[tex](3 - 2)*x^2 + (-11 + 1)*x + (-4 + 6)\\\\x^2 - 10x + 2[/tex]

This is a polynomial, as you can see, the maximum exponent is 2, so the degree of the polynomial is 2.

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Answer: y=7.5

Step-by-step explanation:

Given

y∝(1/√x)

this implies that

y=k/√x    eq(*)

when y=5 and x=36 then

5=k/√36

5=k/6

30=k        eq(1)

to find y when x is 16

put values in eq(*)

y=30/√16

y=30/4

y=7.5

The equation has 2 real roots

The equation is given as:

[tex]y = 3x^2 + 12x - 12[/tex]

Calculate the determinant using

d = b^2 - 4ac

So, we have:

d = 12^2 - 4 * 3 * (-12)

Evaluate

d = 288

Because d > 0

i.e. 288 is greater than 0

Then it means that the equation has 2 real roots

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Answer:

it is A

Step-by-step explanation:

The volatile acid/alkalinity relationship in a digester is volatile acid/alkalinity = 3/80

An equation is an expression that shows the relationship between two or more variables and numbers.

Ratio of volatile acid to alkalinity = 90 mg/L ÷ 2400 mg/L = 3/80

The volatile acid/alkalinity relationship in a digester is volatile acid/alkalinity = 3/80

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Answer:

$9450

Step-by-step explanation:

Answer:

A = $9,450.00

A = P + I where

P (principal) = $9,000.00

I (interest) = $450.00

Calculation Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 5/100

r = 0.05 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 9,000.00(1 + 0.05/1)(1)(1)

A = 9,000.00(1 + 0.05)(1)

A = $9,450.00

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $9,000.00 at a rate of 5% per year compounded 1 times per year over 1 years is $9,450.00.

Work is attached. Hope it helped!

Answer:

x = 1

Step-by-step explanation:

Simplifying

7(x + 1) + -2 = 5(x + 1) + 2

Reorder the terms:

7(1 + x) + -2 = 5(x + 1) + 2

(1 * 7 + x * 7) + -2 = 5(x + 1) + 2

(7 + 7x) + -2 = 5(x + 1) + 2

Reorder the terms:

7 + -2 + 7x = 5(x + 1) + 2

Combine like terms: 7 + -2 = 5

5 + 7x = 5(x + 1) + 2

Reorder the terms:

5 + 7x = 5(1 + x) + 2

5 + 7x = (1 * 5 + x * 5) + 2

5 + 7x = (5 + 5x) + 2

Reorder the terms:

5 + 7x = 5 + 2 + 5x

Combine like terms: 5 + 2 = 7

5 + 7x = 7 + 5x

Solving

5 + 7x = 7 + 5x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5x' to each side of the equation.

5 + 7x + -5x = 7 + 5x + -5x

Combine like terms: 7x + -5x = 2x

5 + 2x = 7 + 5x + -5x

Combine like terms: 5x + -5x = 0

5 + 2x = 7 + 0

5 + 2x = 7

Add '-5' to each side of the equation.

5 + -5 + 2x = 7 + -5

Combine like terms: 5 + -5 = 0

0 + 2x = 7 + -5

2x = 7 + -5

Combine like terms: 7 + -5 = 2

2x = 2

Divide each side by '2'.

x = 1

Simplifying

x = 1

Answer:

Hello! The answer is x = 1.

Step-by-step explanation:

To solve this equation, we need to find x.

The first step in approaching this problem would be to use the distributive property:

7(x + 1) - 2 = 5(x + 1) + 2 will turn into:

7x + 7 - 2 = 5x + 5 + 2

Now, you can combine like terms on each side of the equation:

7x + 5 = 5x + 7

Now, you want to get the x's on one side and the whole numbers on the other side. In order to do this, we will subtract 5 from both sides and subtract 5x from both sides:

7x + 5 = 5x + 7

-5x -5   -5x  -5

This will leave us with:

2x = 2

We will have to now divide both sides by 2 to get x by itself:

2x = 2

--     --

2     2

This leaves us with the result: x = 1

Answer:

B)  0.5

Step-by-step explanation:

The given formula is:

          Height = Constant * Width

You may now choose any point on the graph (the horizontal line represents a point for width, and the vertical line represents a point for height) and put it into the specified formula. Let's test the two supplied points (2, 1):

Now, 2 is on the horizontal line, so we put it in for width, and 1 is on the vertical line, so we plug that in for height. When we do it, we get:

1 = C * 2

(In the expression above we need to solve for C, and we can do that by dividing both sides by 2)

C= 1/2 = 0.5

So, the answer is 0.5 or option B.

The values of x that makes the inequality true are all values less than -5

Given the inequalities below expressed as;

4x-1 < 6x+9

Collect the like terms

4x-6x < 9+1

-2x < 10

x <-10/2

Hence the values of x that makes the inequality true are all values less than -5

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Answer:

D.

Step-by-step explanation:

D. is the binomial since it has 2 terms.

Answer:

3 2/3

Step-by-step explanation:

10 rpms - 6 1/3 rpms = 3 2/3

Answer:

13/40

Step-by-step explanation:

Rewrite a percentage as a decimal: [tex]\frac{32.5}{100}[/tex]

Convert decimals to integers: [tex]\frac{325}{100}[/tex]

Reduce the fraction: [tex]\frac{13}{40}[/tex]

Answer: [tex]\frac{13}{40}[/tex]

32.5% as a fraction in simplest form is 13/40.

Here we have to find fractional form of 35 percent

Since we knw that,

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

To convert a percentage to a fraction,

we can simply write it as a fraction with a denominator of 100.

Then,

we simplify the resulting fraction to its simplest form.

For 32.5%,

we can write this as,

⇒ 32.5/100

Now, we can simplify this fraction by dividing both the numerator and denominator by their greatest common factor (GCF).

The GCF of 32.5 and 100 is 12.5,

so we can divide both by 12.5,

⇒ 32.5/100 = (32.5 ÷ 12.5) / (100 ÷ 12.5)

                   = 13/40

Therefore, 32.5% as a fraction in simplest form is 13/40.

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Answer:

46.67 %

Step-by-step explanation:

Total thickness = 30  

  14 of this is concrete      14/30 x 100% = 46.67 %

Answers:

(a) x = 0.5

(b) Given Below.

Explanation:

(a)

[tex]4^x = 2[/tex]

apply ln both sides

[tex]ln(4^x) = ln(2)[/tex]

simplify

[tex]xln(4) = ln(2)[/tex]

divide both sides by ln(4)

[tex]x = 0.5[/tex]

(b)

Recall that rational numbers can be expressed in fractions a/b

[tex]4^x = 5[/tex]

apply ln on both sides

[tex]ln( 4^x) = ln(5)[/tex]

simplify

[tex]xln( 4) = ln(5)[/tex]

divide both sides by ln(4)

[tex]x =\frac{ ln(5)}{ln(4)}[/tex]

simplify

[tex]x =1.160964047...[/tex]  The value is endless and continues.

The following cannot be expressed as a fraction or whole number.

Hence, the following value of x is irrational.

Answer:

A) Yes, because the sum of any two side lengths is greater than the third side length.

Step-by-step explanation:

All triangles have a property that the sum of two side lengths is greater than the remaining side length.

4 + 8 = 12 > 10, making it a triangle

Considering the given graph, it is found that f(-3) = 1.

First we identity x on the horizontal axis, then we look at the value of y on the vertical axis for which the function is marked at this point.

At this graph, when the horizontal axis is of -3, the vertical axis is of 1, hence f(-3) = 1.

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The number which could be added to both sides of the equation to complete the square is; -2.25.

The quadratic equations give in the task content is; 1=x²-3x. Hence, to express the equation by completing the square method; we have;

1 - 2.25 = (x -3/2)² - 2.25

Hence, the number which should be added to both sides of the equation is; -2.25.

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Answer:

d is correct answer

Step-by-step explanation:

location

of the distribution.

By performing two experiments a lot of times, your brother will see that catching the coin mid-air does not affect the probability.

We assume that the probability of each outcome of the coin is equal, so the probability of getting tails is 0.5 and the probability of getting heads is 0.5

Then, you can say to your brother to perform his experiment a lot of times. In two ways.

First, he lets the coin came down to his hand around 100 times.

Then, he catches the coin in mid-air another 100 times.

He will see that the probability of getting heads (or tails) is (almost) the same in both cases, this will mean that his theory is false.

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Domain: All real numbers

Range: All real numbers

Since the function is linear it is a continuous straight line meaning that the domain and range are all real numbers.

Final answer:

The required distance is 3728.372 miles.

Step-by-step explanation:

Step 1

The distance flown is t hours given by:

2193.16t

Step 2

Let distance be represented by d, thus:

d = 2193.16t

Step 3

d = 2193.16t

Substitute t = 1.7 in the relation:

d = 2193.16 x 1.7

Step 4

Solve for d:

d = 2193.16 x 1.7

d = 3728,372

Answer:

(2) / ((x + 5)(x - 1))

           &

(3x) / ((x - 6)(x - 1))

Step-by-step explanation:

The question is asking you to factor the denominator. In this case, you cannot simplify either of the numerators. You can factor the denominator by asking yourself the question: which two numbers multiply to equal the final number in the quadratic and add to equal the middle number in the quadratic?

1.) 2 / (x² + 4x - 5)

-----> Which two numbers multiply to -5 and add to 4? These numbers are 5 and -1. This makes the factors (x + 5) and (x - 1). The fully simplified answer: (2) / ((x + 5)(x - 1))

2.) 3x / (x² - 7x + 6)

------> Which two numbers multiply to 6 and add to -7? These numbers are -6 and -1. This makes the factors (x - 6) and (x - 1). The fully simplified answer: (3x) / ((x - 6)(x - 1))

*Please let me know if I misinterpreted the question or you need further clarification <3

The polygon formed was convex polygon.

A polygon that has at least one interior angle greater than 180 degree is called concave polygon . It usually has an irregular shape.

A convex polygon has all angles less than 180 degree.

It is given to follow some steps

1. A rectangular sheet of paper is taken .

2. It if folded and unfolded in random directions

3. Lines are drawn on the creases

4. The intersection points are marked A,B,C,D,E,F,G

5. The figure formed is a convex polygon as all the angles measure were less than 180 degree.

Therefore the polygon formed was convex polygon.

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Option A is accurate. The points were plotted with the coordinates (x, log) y), and they are (3, 2.097), (4, 2.796), and (5, 3.495).

Exponents can also be written as logarithms. The other number is equal to a logarithm with a number base. It's the exact inverse of the exponent function.

Identity used;

[tex]\rm log_x (y) = z \\\\ z^x=y[/tex]

From the data we obtained;

[tex]\rm log_3(125) = 5 \\\\ 5^3 = 125[/tex]

[tex]\rm log_5 625 = 4 \\\\ 5^4 = 625[/tex]

[tex]\rm log_5 (3125) = 5 \\\\ 5^5 = 3125[/tex]

The points with the coordinates (x, log) y)) were plotted, the points are (3, 2.097), (4, 2.796), (5, 3.495)

Hence, option A is correct.

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Step-by-step explanation:

x = 11

is a vertical line going through x = 11.

a parallel line going through (9,5) has to be a vertical line too and use x = 9.

so, that is the equation :

x = 9.

Answer:

no solution

Step-by-step explanation:

2x²+ x + 6 = 0

Use quadratic formula

x = (-b±√(b²-4ac))/2a

x = (-1±√(1²-4(2)(6)))/2(2)

x = (-1±√(-47))/2(2)

Step-by-step explanation:

1) the difference betwee the terms given is 3-8=-2-3= -5, then

2) for n-th term: aₙ=8-5(n-1);

3) for the 9-th term: a₉=8-5*8=-32.