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-4x+3x = 2

Answer:

Step-by-step explanation:

a)

[tex]x^2+10x+16=\\x^2+2x+8x+16=\\x(x+2)+8(x+2)=\\(x+2)(x+8)[/tex]

b)

[tex]x^2+7x+12=\\x^2+3x+4x+12=\\x(x+3)+4(x+3)=\\(x+3)(x+4)\\[/tex]

c)

[tex]x^2+13x+12=\\x^2+x+12x+12=\\x(x+1)+12(x+1)=\\(x+1)(x+12)[/tex]

Answer:

[tex]\textsf{(a)} \quad (x+8)(x+2)[/tex]

[tex]\textsf{(b)} \quad (x+4)(x+3)[/tex]

[tex]\textsf{(c)} \quad (x+12)(x+1)[/tex]

Step-by-step explanation:

Factoring quadratics

[tex]\textsf{Given}: \quad x^2+10x+16[/tex]

Two numbers that multiply to 16 and sum to 10 are: 2 and 8.

[tex]\implies x^2+2x+8x+16[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(x+2)+8(x+2)[/tex]

Factor out the common term (x + 2):

[tex]\implies (x+8)(x+2)[/tex]

[tex]\textsf{Given}: \quad x^2+7x+12[/tex]

Two numbers that multiply to 12 and sum to 7 are: 3 and 4.

[tex]\implies x^2+3x+4x+12[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(x+3)+4(x+3)[/tex]

Factor out the common term (x + 3):

[tex]\implies (x+4)(x+3)[/tex]

[tex]\textsf{Given}: \quad x^2+13x+12[/tex]

Two numbers that multiply to 12 and sum to 13 are: 1 and 12.

[tex]\implies x^2+x+12x+12[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(x+1)+12(x+1)[/tex]

Factor out the common term (x + 1):

[tex]\implies (x+12)(x+1)[/tex]

Answer:

j = 2

Step-by-step explanation:

Slope of a line is given by:
[tex]\medium \text{$\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$}[/tex]

where (x₁, y₁) and (x₂, y₂) are two points on the line

This is commonly referred to as rise/run

Given the two points (6, 1) corresponding to (x₁, y₁) and (9, j) corresponding to (x₂, y₂)

[tex]\text{Slope = }\dfrac{\ensuremath{j}-1}{9-6}=\dfrac{j-1}{3}[/tex]

But we are given the slope as 1/3

So we get
[tex]\dfrac{j-1}{3} = \dfrac{1}{3}[/tex]

Multiplying by 2 on both sides gives us:

j - 1 = 1

Adding 1 to both sides gives us

j - 1 + 1 = 1 + 1

j = 2

Answer:

Step-by-step explanation:

Answer:

find prime numbers between 1-20:

= 2,3,5,7,11,13,17,19

=8 prime numbers

probability of winning = 8/20=2/5

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From the inequality concept ( -7 / 10) > ( -5 / 6).

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.

Given fractional numbers are -5/6 and -7/10. The numbers in the form of inequality will be calculated as:-

-7 / 10 = -0.7

-5 / 6 = -0.84

-0.7 > -0.84

-7 / 10 > -5 / 6

Therefore, from the inequality concept ( -7 / 10) > ( -5 / 6).

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The inches of ribbon that Anais use to trim the curtains is 12 inches.

From the information, Anais bought 2 1/2 yards of ribbon and then he had 1 feet 6 inches of ribbon left after trimming some curtains.

It should be noted that 12 inches = 1 feet

Therefore, the inches that will be left will be:

= 2 1/2 - 1 6/12

= 2 1/2 - 1 1/2

= 1 feet

It should be noted that 1 feet = 12 inches.

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The equation of the line parallel to the given line that contains C is obtained as y = x + 6.

For the given question;

The equation of the line is given as;

y = x + 4

The standard form of the equation of line in slope intercept form is;

y = m x + c

where, m is the slope and c is the y intercept.

On comparing;

m₁ = 1

Now, the other lien is parallel to the given line.

Thus, slopes of both lines will be equal.

m₁ = m₂ = 1

The passing points of the line are;

(x₁, y₁) = C(1, 7)

Now, the equation of lien will be;

y - y₁ = m₂(x - x₁)

Put the values;

y - 7 = 1(x - 1)

Simplifying.

y = x + 6

Thus, the equation of the line parallel to the given line that contains C is obtained as y = x + 6.

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the formula for a function of the form y= a е⁻ˣ +b x with global minimum at (1,10)  is  y= 5е¹ ⁻ ˣ +5 x

We can use first and second derivative tests to determine all coefficients of the function described in statement so that the point given is an absolute minimum. The expressions for such tests are introduced below:

First Derivative Test

-a .е⁻ˣ +b = 0   (1)

b=a .е⁻ˣ

Second Derivative Test

y''= a . .е⁻ˣ  (2)

Where y'' >0

If we know that ( x,y) = 9 1,10) , then we have the following system:

10 = a е⁻¹ +b (3)

b= a е⁻¹  (4)

y'' = a е⁻¹  (5)

By (4) in (3):

10= 2aе⁻¹

a=10/2е⁻¹

a= 5е

By (5) we prove that y''>0, and we get the value of  by (4):

b=5

Thus, the formula for a function of the form y= a е⁻ˣ +b x with global minimum at (1,10)  is . y= 5е¹ ⁻ ˣ +5 x

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The percent increase in her salary resulted from her promotion is 6.67%.

The annual salary of Marisol as an engineer = $75000.

After, the promotion salary of Marisol as an engineer = $80000.

We have to find the increment in her salary after promotion in percentage.

Before finding the increment in percentage we find the total increment in dollar in her salary after promotion.

Total increment in dollar = Salary after Promotion − Salary before Promotion

Total increment in dollar = $80,000 − $75,000

Total increment in dollar = $5000

As we know that we can find the percentage by multiplying the required number by 100 because percentage is the ratio with 100.

So, the increment in salary after promotion in percentage.

% increment = (Total increment/Salary before) * 100

% increment [tex]= (\frac{5000}{75000})*100[/tex]

% increment = 0.0667 * 100

% increment = 6.67%

Now we see that percent increase in her salary resulted from her promotion is 6.67%.

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the provided graph is not a function .

s

mixed expression as a rational expression will be  [tex]\frac{2g+9}{g}[/tex]

In mathematics, a fraction is a number that is expressed as a quotient in which the numerator and denominator are divided. In a simple fraction, both are integers. A complicated fraction contains a fraction in either the numerator or denominator. Any fraction that is right has a numerator that is less than its denominator.

to convert mixed fraction into rational fraction

we multiply denominator with whole number and add it with numerator and the result of this gives numerator . and the denominator is same as mixed fraction .

so for the given expression ,

2 * g + 9 is numerator

and g is denominator .

= [tex]\frac{2g+9}{g}[/tex]

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The correct answer is that y does not vary directly with x.

If y and x are directly related, then the equation y=kx would be true for each point in the set.

What is the explanation:

If y is directly related to x, then every point in the set would fit the equation y=kx.

For the first point, we would have 11=7k, which would imply that k=11/7.

For the second point, we would have 13=8k, which would imply that k=13/8.

By utilizing proportions to check, we can see that 11/7 does not equal 13/8.

Cross multiplying yields 11*8=7*13, or 88=91

Since this is untrue, k is not a constant and y does not change in accordance with x.

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Answer: -3 and -4

Step-by-step explanation:

The sum of -3 + -4 = -7

The product of -3 x -4 = 12 (a negative times a negative equals a positive)

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

Explanation:

The given translation rule is (x, y) → (x+8, y - 3) which says "shift 8 units right and 3 units down".

The inverse transformation will undo each to get "8 units left and 3 units up"

So the inverse is (x, y) → (x-8, y + 3)

Use this inverse to determine the preimage of point T'(2,-6)

[tex](\text{x},\text{y})\to(\text{x}-8,\text{y}+3)\\\\(2,-6)\to(2-8,-6+3)\\\\(2,-6)\to(-6,-3)\\\\[/tex]

Therefore, preimage point T is located at (-6,-3) which points us to answer choice B

If we were to apply the rule of "shift 8 units right and 3 units down" to T(-6,-3), you should arrive at T'(2,-6)

Answer:

x=4

Step-by-step explanation:

15-9=6

10-6=4

Answer:

x = 6 cm

Step-by-step explanation:

The two shapes are similar. That means one figure is exactly a multiple of the other figure

We can see that the ration of the length of the bigger rectangle  to the length of the smaller rectangle is 15/9 = 5/3  

Therefore the ratio of the width of the bigger rectangle  to the width of the smaller rectangle must also be 5/3

Given width of big rectangle = 10 and that of small rectangle is x

We get

10/x = 5/3

Multiply by x both sides:
x ×   10/x   =   x × 5/3

10 = 5x/3

Multiply by 3 both sides

30 = 5x

5x = 30

Dividing by 5 both sides
5x/x = 30/5
x = 6 cm

The number line that correctly compares √24 and 4.256 is number line C.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.

This ultimately implies that, a number line can be used for the comparison of two or more numbers such as √24 and 4.256. Also, a number line typically decreases in numerical value towards the left and increases in numerical value towards the right.

Taking the square root of √24, we have:

√24 = 4.899

In this context, we can reasonably and logically deduce that 4.899 is greater than 4.256 (4.899 > 4.256) and would be placed at the right hand side of the number line and further from 4.899 as shown in number line C in the image attached below.

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Answer:

34.98is the answer ............ .............

Answer: 34.98

Step-by-step explanation:

'Percent (%)' means 'out of one hundred':

6% = 6 'out of one hundred',

p% is read p 'percent',

6% = 6/100 = 6 ÷ 100

What does it mean to calculate the percentage of a number?

6% of 583 = ?

... is equivalent to multiplying them:

6% × 583 = ?
6% of 583 =

6% × 583 =

6/100 × 583 =

(6 ÷ 100) × 583 =

6 × 583 ÷ 100 =

3,498 ÷ 100 =

34.98

For f(x) = 2x + 3 and g(x) = -x^2 + 1, The composite function defined by (f o g)(x) is equal to (f o g)(x) = - 2 x^2 + 5

As per the question statement, We are given f(x) = 2x + 3 and g(x)=x^2+1

and we are supposed to find the composite function defined by (f o g)(x)

(f o g)(x) = f(g(x))

(f o g)(x) = 2 (g(x)) + 3

(f o g)(x) = 2( -x^2 + 1 ) + 3

(f o g)(x) = - 2 x^2 + 5

Hence, For f(x) = 2x + 3 and g(x) = -x^2 + 1, The composite function defined by (f o g)(x) is equal to (f o g)(x) = - 2 x^2 + 5

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:The \:\: angles \:\: are \:\: 60° \:\: and \:\:30° [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Sum of two complementary angles is 90°

Let's assume one of them to be x, the other one will be x/2 as one of the angles is complementary to other one.

[tex]\qquad \tt \rightarrow \: x + \dfrac{x}{2} = 90[/tex]

[tex]\qquad \tt \rightarrow \: \dfrac{2x + x}{2} = 90[/tex]

[tex]\qquad \tt \rightarrow \: 3x = 90 \times 2[/tex]

[tex]\qquad \tt \rightarrow \: x = 180 \div 3[/tex]

[tex]\qquad \tt \rightarrow \: x = 60 \degree[/tex]

and

[tex]\qquad \tt \rightarrow \: \dfrac{x}{2} = 60 \div 2 = 30 \degree[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

Yes, 7 x [tex]10^{-3}[/tex] in standard form is 0.007mm

8 x [tex]10^{-5}[/tex] in standard form is 0.00008 mm.  The mask will catch particles that are much smaller than 0.007 in diameter.

Step-by-step explanation:

Answer:

80 degrees

Step-by-step explanation:

Sunday-56 fluid ounces of water require to reach your goal.

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Answer:

2*2*2

That's the prime product of their common factors

The function which has a graph with the largest positive x-intercept is C. f(x) = 2(x-8) +1

The value of the x coordinate at the point where the graph crosses the x-axis is known as the x-intercept for any curve. Alternatively, we can say that the x-intercept is the value of the x coordinate at the point where the value of the y coordinate equals zero.

Let y be 0, so lets find the x-intercept of

A. 2(x+5)-1 = 0                                    

⇒ 2(x+5) = 1

⇒ 2x + 10  = 1

⇒ 2x  = -9

⇒ x = -9/2

B. 8(x+8) = 0

⇒ x+8 = 0

⇒ x = 0 −8

⇒ x = −8

C.  2(x-8) +1 = 0

⇒ 2x − 15 = 0

⇒ 2x = 15

⇒ x = 15/2

⇒ x = 7.5

D. 13(x-3) = 0

⇒ x − 3 = 0/13

⇒ x − 3 = 0

⇒ x = 0 + 3

⇒ x = 3

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a. The complete table for the ordered pairs that are solutions to y = x³ - 4 is

x             y

-1            -5

0            -4

1             -3

2            4

b. The graph of the equation is shown below

From the question, we are to complete the given table of ordered pairs that are solutions to the given equation.

The given equation is

y = x³ - 4

Now, we will determine the values of y for the given values of x

When x = -1

y = x³ - 4

y = (-1)³ - 4

y = -1 - 4

y = -5

(-1, -5)

When x = 0

y = x³ - 4

y = (0)³ - 4

y = 0 - 4

y = -4

(0, -4)

When x = 1

y = x³ - 4

y = (1)³ - 4

y = 1 - 4

y = -3

(1, -3)

When x = 2

y = x³ - 4

y = (2)³ - 4

y = 8 - 4

y = 4

(2, 4)

Thus,

The table is

x             y

-1            -5

0            -4

1             -3

2            4

The graph is shown below

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Subtracting 1 from the parent function will transform the function in the following way: b Subtracting 1 from the parent function shifts the function down one unit

This refers to as movement of object in an organized way such that the movement can always be calculated from the initial position.

The movement involved in transformation on images is ordered and there are some terms used to classify such movements. some of the terms are:

The movement done in the question is a translation. This is a linear movement towards a particular direction.  the movement is translation is usually:

Subtracting 1 from the parent function. the parent function as used refers to the y direction hence option b is the correct answer

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Answer: No, this is not a function.

Functions exist when there are a unique set of x-values and each can match with a y-value. There cannot be a repeating x-value because this creates a discontinuity in the graph. You can have as many repeating y-values as you’d like as long as they each have a unique x-value and are not duplicate plot points.

Since x = 7 repeats in the domain of x-values, this cannot be a function.

The area of the triangle in the image is 10 square units, thus, option C is the correct one.

For a triangle of height H and a base B, the area is given by:

A = H*B/2.

In the image we can see that the base of the triangle goes from (0, 0) to (5, 0), then the length of the base is 5 units.

While the height goes from (0, 0) to (0, 4), so the height is 4 units.

Then the area will be:

A = (4 units)*(5 units)/2 = (20 square units)/2 = 10 square units.

The area is 10 square units.

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The depth of the bottom of the hole after the second day is 36 feet using addition operation.

In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the sum refers to the outcome of the operation.

Given the depth on the first day is 26 ½ feet.

Depth on the second day = 9½ feet more than on the first day i.e. 9½ feet + depth on the first day

This implies, depth on the second day = 9½ + 26 ½

= 36 feet

Therefore, the depth of the bottom of the hole after the second day is 36 feet.

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