If f(x) = x2 + 1 and g(x) = 3x+1, find [f (2) - g(1)]2
9
2
1

Answer:

26 i think

Step-by-step explanation:

39=13 x 3 SOOOOOOOOOO....

13 x 2 = 26

i hope this helps

Answer:

y = - 3x + 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 7) and (x₂, y₂ ) = (2, 1) ← 2 points on the line

m = \(\frac{1-7}{2-0}\) = \(\frac{-6}{2}\) = - 3

the line crosses the y- axis at (0, 7 ) ⇒ c = 7

y = - 3x + 7 ← equation of line

The equation of the line in fully simplified slope-intercept form is y = -2.8x + 7

The linear graph represents the given parameter

For the graph, we have the points

(0, 7) and (25, 0)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 7

Using the point (2.5, 0) on y = mx + 7, we have

m(2.5) + 7 = 0

2.5m + 7 = 0

Evaluate

m = -2.8

So, we have

y = -2.8x + 7

Hence, the equation of the line in fully simplified slope-intercept form is y = -2.8x + 7

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Answer:

7.002

Step-by-step explanation:

thousandths place is the 3rd from the decimal

as a decimal? I cant see the full thing

Answer:

  -2-√3

Step-by-step explanation:

The sum of angles formula for tangent is ...

  tan(A+B) = (tan(A) +tan(B))/(1 -tan(A)tan(B))

For the desired angle, we can use A=45°, B=60°. Then we have ...

  tan(105°) = (tan(45°) +tan(60°))/(1 -tan(45°)tan(60°))

The tangent values we need are ...

  tan(45°) = 1

  tan(60°) = √3

Then our tangent is ...

  tan(105°) = (1 +√3)/(1 -1·√3) = (1 +√3)²/((1 -√3)(1 +√3)) = (4+2√3)/(-2)

  tan(105°) = -(2+√3)

the y intercept is the value of the y coordinate when the x-coordinate is 0, in this case, we have the point (0,-5)

the y-intercept is -5

The equations that represent the circle having a with radius 8 and center (10,−7) are; (x - 10)² + (y + 7)² = 8²

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle, and r is its radius.

We have given that circle having radius of 8 units. Thus, r = 8.

Since we know that circle having the center (10,−7).

Thus, the equation of the circle, with a radius of 8 units is;

(x - h)² + (y - k)² = r²

(x - 10)² + (y + 7)² = 8²

Thus, the equations that represent the circle having a with radius 8 and center (10,−7) are; (x - 10)² + (y + 7)² = 8²

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Given:

Point A is located at \(-\dfrac{6}{8}\).

Point B is located at \(-\dfrac{1}{8}\).

To find:

The distance between points A and B.

Solution:

We know that,

Distance between points A and B = Location of A - Location of B

Using this given values, we get

Distance between points A and B \(=-\dfrac{6}{8}-\left(-\dfrac{1}{8}\right)\)

                                                        \(=-\dfrac{6}{8}+\dfrac{1}{8}\)

                                                        \(=\dfrac{-6+1}{8}\)

                                                        \(=-\dfrac{5}{8}\)

Distance cannot be negative. So, we need to find the absolute value of \(-\dfrac{5}{8}\).

\(|-\dfrac{5}{8}|=\dfrac{5}{8}\)

The distance between A and B is \(\dfrac{5}{8}\).

Therefore, the correct option is D.

Answer:

the relation ship is that for every week she gets 10 dollars plus the original 150 dollars from her birthday.

Hope This Helps!!!

Regarding probability, the option with the correct statement is presented as follows;

When two events A and B are independent, the joint probability of the events can be found by multiplying the probability of the individual events.

The probability of an event is the ratio of the number of times the event occurs to the number of all possible events.

The probability of the union of mutually exclusive events is zero, therefore, we get;

P(A ∩ B) = 0

The union of two events consists of the possible outcomes that are in A or in set B or in set A ∩ B

The union of events A and B consists of all outcomes in the sample space that are contained in both event A and event B is incorrect

The joint probability of independent events A and B can be obtained from the product of the probability of event A and event B as follows;

P(A and B) = P(A) × P(B)

The correct option is therefore;

The probability of the union of two events is found from the sum of the probabilities of the two events minus the probability of the intersection of the two events, which can be presented as follows;

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

P(A) + P(B) ≤ 2

P(A ∩ B) ≤ 1

The larger the value of P(A) and P(B) the larger the value of P(A ∩ B), such that we get; P(A ∪ B) ≤ 1

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Answer:

x = 0

General Formulas and Concepts:

Pre-Algebra

Step-by-step explanation:

Step 1: Define equation

5x - 8(1 + 7x) = -8

Step 2: Solve for x

Step 3: Check

Plug in x into the original equation to verify it is a solution.

Here we see that -8 does indeed equal -8.

∴ x = 0 is a solution of the equation.

hello,

Omar: 84

Maryam: 12

In total, they have 84 + 12 = 96 dollars

First, lets analyze the alternatives.

a. Omar has $32; maryam has $96

It can be, because the amount of her is exactly three times his amount.

however the total exceeds the value they have, so it is false.

b. Omar has $48; maryam had $48

False, because they have the same value.

c. Omar has $24; maryam has $72

24 x 3 = 72

24 + 72 = 96

So, this is true.

d. Omar has $72; maryam has $24

False, because he has three times of her amount.

Right answer: C.

Answer:

0.3939

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

100°

Step-by-step explanation:

tThe sum of all arc measures that make up that circle is 360 degrees.

QS + RQ + RS = 360

QS = 360 - 120 - 140 = 100

An arc angle is the degree measurement of that angle inside the circle, opposite the arc

m∠R = arc QS = 100°

Answer:

∠ R = 50°

Step-by-step explanation:

the inscribed angle R is half the measure of its intercepted arc QS

the sum of the arcs on a circle is 360° , that is

RQ + QS + SR = 360°

120° + QS + 140° = 360°

QS + 260° = 360° ( subtract 260° from both sides )

QS = 100°

Then

∠ R = \(\frac{1}{2}\) × 100° = 50°

If two figures can be mapped onto one another or if all pairings of angles and side lengths are congruent, the figures are said to be congruent.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

If two triangles are the same size and shape, they are said to be congruent. To establish that two triangles are congruent, not all six matching elements of either triangle must be located. There are five requirements for two triangles to be congruent, according to studies and trials. The congruence properties are SSS, SAS, ASA, AAS, and RHS.

here, we have,

Both triangles are said to be congruent if the three angles and three sides of one triangle match the corresponding angles and sides of the other triangle.

In Δ PQR and ΔXYZ, as shown in figure,

we can identify that PQ = XY, PR = XZ,

and QR = YZ

and ∠P = ∠X,

∠Q = ∠Y and ∠R = ∠Z.

Then we can say that Δ PQR ≅ ΔXYZ.

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Answer:

25

Step-by-step explanation:

Divide: 5 : 1/5 = 5/1 · 5/1 = 5 · 5/1 · 1 = 25/1 = 25 Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 1/5 is 5/1) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators.In other words - five divided by one fifth is twenty-five.

I hope this helps! Thanks!

Answer:

Choose (D)

y-y1=m(x-x1)

y-2=1/2(x+6)

Answer:

The solution:

X = 16 and Y = -6

Step-by-step explanation:

The equations to be solved are:

x+y = 10 ------- equation 1

x+2y = 4 ----------- equation 2

we can multiply equation 1 by -1 to make the value of x and y negative.

This will give us

-x- y = - 10 ------- equation 3

x+2y = 4 ----------- equation 2

We will now add equations 3 and 2 together so that x will cancel itself out.

this will give us

y = -10 +4 = -6

hence, we have the value of y as -6.

To get the value of x, we can put this value of y into any of the equations above.  (I will use equation 1)

x - 6 = 10

from this, we have that x = 4

Therefore, we have our answer as

X = 16 and Y = -6

Answer:

D

Step-by-step explanation:

Sum of Inner angles of a triangle = 180

59 + 48 + a = 180

107 + a = 180

a = 73

y = 73 * 2 = 146 degrees

Dolma received a total amount of Rs 1,29,260 at the beginning of BS 2080.

Given:

Principal amount (P) = Rs 1,20,000

Interest rate (R) = 9% per annum

Income tax rate (T) = 5% of the interest earned

First, we calculate the interest earned

Interest (I) = P x R/100

= 1,20,000 * 9/100

= 10,800

Next, we calculate the income tax

Income Tax = I x T/100

= 10,800 x 5/100

= 540

Now, Total amount = P + I - Income Tax

= 1,20,000 + 10,800 - 540

= Rs 1,29,260

Therefore, Dolma received a total amount of Rs 1,29,260 at the beginning of BS 2080.

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Answer:

Step-by-step explanation:

208

Hannah needs 150.71 gallons of soda and 17.29 gallons of fruit drink to make 168 gallons of punch that costs $1.66 per gallon.

What is meant by budget?

Let's assume that Hannah needs to use x gallons of soda and y gallons of fruit drink to make 168 gallons of punch.

We know that the cost of soda is $1.57 per gallon and the cost of fruit drink is $2.41 per gallon, and Hannah's budget requires that the punch cost $1.66 per gallon.

So we can set up the following system of equations:

x + y = 168 (total amount of punch)

1.57x + 2.41y = 1.66(168) (total cost of punch)

Simplifying the second equation:

1.57x + 2.41y = 278.88

Now we can use substitution or elimination method to solve for x and y.

Using substitution:

x = 168 - y

1.57(168 - y) + 2.41y = 278.88

264.36 - 1.57y + 2.41y = 278.88

0.84y = 14.52

y = 17.29

So Hannah needs 17.29 gallons of fruit drink.

Using x + y = 168, we can find that she needs 150.71 gallons of soda.

Therefore, Hannah needs 150.71 gallons of soda and 17.29 gallons of fruit drink to make 168 gallons of punch that costs $1.66 per gallon.

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When comparing loans with different terms, it is important to consider not just the APR in order to get a more accurate picture of the total cost of borrowing and help you make a more informed decision about which loan is right for you

The annual percentage rate (APR) is a measure of the annual cost of borrowing, expressed as a percentage of the loan amount. It takes into account the interest rate, any fees or other charges associated with the loan, and the length of the loan.

However, because the APR takes into account the length of the loan, it is not an accurate way to compare loans with different loan terms. For example, a loan with a lower APR but a longer term will generally have a higher overall cost than a loan with a higher APR but a shorter term, even though the APR is lower.

Therefore, when comparing loans with different terms, it is important to consider not just the APR, but also the loan term and any fees or charges associated with the loan.

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The assertion is true. Both 7√5 and √2 + 21 are irrational numbers because they cannot be expressed as fractions.

The assertion is true. Both 7√5 and √2 + 21 are irrational numbers.

An irrational number is defined as a number that cannot be expressed as a fraction of two integers and has an infinite non-repeating decimal representation.

In the case of 7√5, the square root of 5 is an irrational number because it cannot be expressed as a fraction. Multiplying it by 7 does not change its irrational nature.

Similarly, √2 is also an irrational number because the square root of 2 cannot be expressed as a fraction. Adding 21 to √2 does not alter its irrationality.

The reason provided, that every integer is a rational number, is not relevant to the given assertion. While it is true that every integer is a rational number because it can be expressed as a fraction (e.g., 3 can be written as 3/1), it does not contradict the fact that 7√5 and √2 + 21 are irrational numbers.

In conclusion, the assertion is valid, and both 7√5 and √2 + 21 are irrational numbers.

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The percentage of drivers who are at least 45 is 62%

From the question, we have the following parameters that can be used in our computation:

The table of values

From the table, we have

Age 45 = 62 percentile

When represented properly

So, we have

Age 45 = 62%

This means that the percentage of drivers who are at least 45 is 62%

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Based on the information we can infer that 5/8 between 6 people is equal to 15/24.

To calculate the part that corresponds to each person, divide the fraction 5/8 by the number of people, which in this case is 6. To simplify the fraction, you can reduce the numerator and denominator by dividing both by their maximum common factor, which is 3.

5 ÷ 3 = 1 and 2 remainder8 ÷ 3 = 2 and 2 remainder

So the fraction can be simplified to 1 2/8, which can also be expressed as 1 1/4 or 5/4 in its most simplified form. This means that each person would receive 5/4 of the original share, and since there are 6 people in total, you can multiply 5/4 by 6 to get the total share that corresponds to all 6 people:

(5/4) x 6 = 30/4 = 15/2 = 15/24

So each person would receive 15/24 of the original amount.

Note: Here is the question in English:

5/8 divided in 6 people

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Step-by-step explanation:

\(1meter = 39.37inches \\ 8.104meters = (39.37 \times 8.104)inches \\ = 319.05448inches\)

There are \(3.1496\cdot 10^6\) inches in \(8\cdot 10^4\) meter.

Important information:

Using the given information,

1 meter = 39.37 inches

Using this conversion, we get

\(8\cdot 10^4\) meter = \(39.37\times (8\cdot 10^4)\) inches

\(8\cdot 10^4\) meter = \(39.37\times 80000\) inches

\(8\cdot 10^4\) meter = \(3149600\) inches

\(8\cdot 10^4\) meter = \(3.1496\cdot 10^6\) inches

Therefore, there are \(3.1496\cdot 10^6\) inches in \(8\cdot 10^4\) meter.

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