Solve the following equation for x.
10 = 2 – 4(ar – 3)
OA. -
a
OB.
Oc.
OD.
5
a

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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Answer:

a-25

b-243

5^3 = 125/3 = 25

3^6 = 729/3 = 243

The pattern is empty the second pail, leaving the first and third pail full and the fourth and sixth pails empty.

Given that, there are 6 pails in a row. The first 3 pails are filled with water.

The easiest way to solve this problem is to empty the second pail, leaving the first and third pail full and the fourth and sixth pails empty. This will create the desired pattern of full, empty, full, empty, full, empty.

Therefore, empty the second pail, leaving the first and third pail full and the fourth and sixth pails empty.

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The three vertices will give us the dilated figure.

First we find the slope of the line that would pass through the point of dilation, (-3, 0), and each vertex.

From (-3, 0) to (5, 4), the slope would be

m = (4-0)/(5--3) = 4/8

Since the scale factor is 1/2, this means each part of the slope would be multiplied by this scale factor:

(4(1/2))/(8(1/2)) = 2/4

This means from our point of dilation we count up 2 and over 4; this puts the new point at (-3+4, 0+2) = (1, 2).

From (-3, 0) to (3, 8) the slope is

m = (8-0)/(3--3) = 8/6

Multiplying the rise and run by 1/2, we have

(8(1/2))/(6(1/2)) = 4/3

This means the dilated point would be up 4 and over 3 from (-3, 0), putting it at (-3+3, 0+4) = (0, 4).

From (-3, 0) to (-5, 4), the slope is

m = (4-0)/(-5--3) = 4/-2.

Multiplying the rise and run by 1/2, we have

(4(1/2))/(-2(1/2)) = 2/-1

This means the dilated point would be up 2 and over -1 from (-3, 0), putting it at (-3+-1, 0+2) = (-4, 2).

These three vertices give us the dilated figure.

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Answer: 1.   1/15

              2.    3/10

               3.    1/6

             4.   3/10

Step-by-step explanation:

Hope this helps!

The quadratic equation that fits each set of points (0.-8), (2, 0), and (-3, -5) is -3x² + 10x - 8 = 0

Quadratic equation:

Quadratic equation refers algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

Given,

Here we have the set of points (0.-8), (2, 0), and (-3, -5).

Now, we have to find the quadratic equation for this points.

We know that the standard form of the quadratic equation is,

y = ax² +  bx + c

Here we have to use each point value in order to find the value of a, b and c to find the quadratic equation of the points,

First we have to take the point (0, -8) and apply it on the formula, then we get,

-8 = a(0)² +  b(0) + c

-8 = c

Now, use the point (2,0), then we get,

0 = a(2)² +  b(2) + c

0 = 4a + 2b + c --------------------(1)

Finally, take the point (-3, -5), then we get the equations,

-5 = a(-3)² +  b(-3) + c

-5 = 9a - 3b + c --------------------(2)

Now, apply the value of c as -8, then we get,

4a + 2b = 8 ----------------(3)

9a -3b = 3 -----------------(4)

Divide equation (4) by 3 and equation (3) by 2 on both sides then we get,

2a + b = 4

3a - b = 1

When we subtract these equation then we get the value of

a = -3

Then the value of b is

2(-3) + b = 4

b = 4 + 6

b = 10

Therefore, the quadratic equation is -3x² + 10x -8 = 0

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Step-by-step explanation:

tan0=opp/adj

where opposite =3,adjacent =x,=70

tan 70=3/x

2.7474=3/x

2.7474x=3

divide both sides by 2.7474

x=3/2.7474

x=1.0919

x=1.10 to 1 d.p

Solution

For this case we can use the following operation to solve the problem

C= 24 + 0.70 x (Represent the cost function with x the number of DVD duplicated)

R= 150 represent the revenue

Then we can do this:

R= C

150= 24 +0.7x

And solving for x we got:

0.7x= 126

x = 126/0.7= 180

and then the solution for this case would be 180 units for the brak even point

Given:

Five points P, Q, R, S ,T on a coordinate plane.

To find:

The coordinates of (i) P, (ii) Q, (iii) T, (iv) (Ordinate of T) – (Abscissa of R) and (v) (Abscissa of Q) – (Ordinate of S).

Solution:

From the given graph it is clear that the coordinates of given points are

P = (1,1)

Q = (-3,0)

R = (-2,-3)

S = (2,1)

T = (4,-2)

(i)

Coordinates of point P are (1,1).

Therefore, the correct option is (a).

(ii)

Coordinates of point Q are (-3,0).

Therefore, the correct option is (b).

(iii)

Coordinates of point T are (4,-2).

Therefore, the correct option is (c).

(iv)

Ordinate is y-coordinate and abscissa is x-coordinate.

Ordinate of T = -2

Abscissa of R = -2

(Ordinate of T) – (Abscissa of R) = -2 - (-2)

                                                     = -2 + 2

                                                     = 0

Therefore, the correct option is (c).

(v)

Abscissa of Q = -3

Ordinate of S = 1

(Abscissa of Q) – (Ordinate of S) = -3 - 1

                                                      = -4

Therefore, the correct option is (a).

Answer:

x=19

HOPE THIS HELPS

-Todo <3

Step-by-step explanation:

6x+3x-5+14=180

9x+9=180

   -9    -9

9x=171

/9   /9

x=19

Answer:

Step-by-step explanation:

Given functions:

Fill in the table by calculating each value of f(x) and g(x)

Answer:

412.92

Step-by-step explanation:

\(A = P(1+\frac{r}{n} )^{nt}\)

A: Amount, P: Principal, r: interest, n: no.of times compounded yearly and t: time in years

We have P = 300

r = 4% = 0.04

n = 12 (compounded monthly)

t = 8

\(A = 300(1+\frac{0.04}{12} )^{12*8}\\\\300(\frac{12.04}{12} )^{96}\\\\= 412.92\)

Answer:

111.548

-------------------------------

Subtract 201 from 89.

\(201 - 89 = 112\)

we can estimate the answer will be close to 112

Next, work with the decimals. Note that the more you subtract, the bigger the decimal places get.

\(0.768 - 0.316 = 0.452\)

Round 0.452 up from the hundredths place to nearest tenths place.

\(0.452 = 0.5\)

Since the decimal place is bigger, estimate 0.55 instead.

Subtract 0.22

\(0.55 - 0.2 = 0.548\)

Add this number to 112

\(112 + 0.548 = 112.548\)

Subtract 1 because of the estimate.

\(112 - 1 = 111\)

Therefore, we have 111.548 based off of subtracting and estimating in a specific method.

The best estimate for the pigeon population is 540.

Finding an estimate or approximation—a value that may be used for a purpose despite the possibility of incomplete, ambiguous, or unstable input data—is the process of estimation. Despite this, the value is still useful because it was created using the most up-to-date data.

Counting a small sample of something and extrapolating that number to a wider population is how estimation is frequently done. Calculating how many sweets of a certain size are contained in a glass jar is an example of estimation.

380 x 27/19

= 540

So the answer is

540

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Answer: C

Step-by-step explanation:

For box and whiskers plot the box is where the majority of the data is.  the whiskers(the lines on both sides will tell you where the range of numbers lie)

The middle line in the box is the median number.

The question is worded oddly where they want least likely to be more than 30 which means which one will have less than 30. (Double negative question)

You want the majority of the data to be less than 30, which is subway.  C

Answer:

The equation of the line, in slope-intercept form, that passes through (3,-1) and has a slope = -2/3 is:

\(\mathbf{y=-\frac{2}{3}x+1}\)

Step-by-step explanation:

We need to write equation of the line, in slope-intercept form, that passes through (3,-1) and has a slope = -2/3.

The equation for slope-intercept form is: \(y=mx+b\)

where m is slope and b is y-intercept.

We are given slope m = -2/3 and we need to find y-intercept i.e b to write equation of line.

Using point (3,-1) and slope m=-2/3 we can find y-intercept i.e b

\(y=mx+b\\-1=-\frac{2}{3}(3)+b\\-1=-2+b\\b=-1+2\\b=1\)

So, y-intercept b = 1

The equation of the line, in slope-intercept form, that passes through (3,-1) and has a slope = -2/3 is:

\(y=mx+b\\\mathbf{y=-\frac{2}{3}x+1}\)

The tank having shape of a rectangular prism, the volume of tank will be

4,500 inches³.

What exactly is a prism?

A prism is a three-dimensional geometric object that has a pair of identical, parallel polygonal bases and flat, parallelogram-shaped sides connecting them. The most common type of prism is a rectangular prism, which has two rectangular bases and four rectangular sides.

Prisms are classified based on the shape of their bases. For example, if the bases of a prism are triangles, it is called a triangular prism, if the bases are pentagons, it is called a pentagonal prism, and so on.

Now,

To calculate the volume of water that the tank can hold, we need to use the formula for the volume of a rectangular prism:

Volume = Length x Width x Height

Plugging in the values given:

Volume = 25 inches x 12 inches x 15 inches

Volume = 4,500 cubic inches

Therefore,

              the tank can hold 4,500 inches³ of water.

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Step-by-step explanation:

Since equivalent fractions do not always have the same numerator and denominator, one way to determine if two fractions are equivalent is to find a common denominator and rewrite each fraction with that denominator. Once the two fractions have the same denominator, you can check to see if the numerators are equal.

The two fractions with the same numerator and different denominators can not be equal.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

A division number is a number that addresses the piece of the entire, where the entire can be any number. It is a numerator and a denominator.

The fraction is in the form of a numerator and denominator. The two fractions can be equal if and only if their numerator and denominator are equal.

The two divisions with similar numerators and various denominators can not be equivalent.

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Answer:

-3x-7

Step-by-step explanation:

Answer:

AC = 13.3

Make proportional relationship:

\(\dfrac{\text{AB}}{\text{AC}} =\dfrac{\text{AM}}{\text{AN}}\)

Insert values

\(\rightarrow\dfrac{10}{\text{AC}} =\dfrac{6}{8}\)

Cross multiply

\(\rightarrow \text{AC}=\dfrac{10(8)}{6}\)

Simplify

\(\rightarrow \text{AC}=13.3\)

The mode is 1.

It was repeated 4 times whereas 6 was only repeated 3 times, 4 twice, and 0 once.

Answer: 1

The mode is the number that occurs the most within the set of numbers. If the set of numbers is as follows: 1, 4, 4, 1, 1, 0, 6, 6, 6, 1, then the answer is one(1).

However, if the set of numbers appear as follows: 14, 41, 10, 66, 61, then there is no mode.

Answer and Step-by-step explanation:

So, lets write down the information that we have.

Tina:

Box Jumps: 500

Pushups: 350

Sit-ups: 700

Ben:

Box Jumps and Sit-ups: \(\frac{3}{4}\) × (500 + 700)

Pushups: 1.5 × 350

Let's calculate Ben's exercises.

Pushups = 525

Box Jumps + Sit-ups = 900

Look back, and you can see that we can distribute the 3/4 to the numbers, instead of adding the multiplying.

(\(\frac{3}{4}\) × 500)  = 375

(\(\frac{3}{4}\) × 700) = 525

So, Ben did:

Box Jumps = 375

Pushups = 525

Sit-ups = 525

#teamtrees #WAP (Water And Plant)

The  x and y-intercept of the equation [8x - 9y = 15] are ( 15/8, 0 ) and ( 0, -5/3 ) respectively.

Given the equation;

8x - 9y = 15

First, we find the x-intercepts by simply substituting 0 for y and solve for x.

8x - 9y = 15

8x - 9(0) = 15

8x = 15

Divide both sides by 8

8x/8 = 15/8

x = 15/8

Next, we find the y-intercept by substituting 0 for x and solve for y.

8x - 9y = 15

8(0) - 9y = 15

- 9y = 15

Divide both sides by -9

- 9y/(-9) = 15/(-9)

y = -15/9

y = -5/3

We list the intercepts;

x-intercept: ( 15/8, 0 )

y-intercept: ( 0, -5/3 )

Therefore, the  x and y-intercept of the equation [8x - 9y = 15] are ( 15/8, 0 ) and ( 0, -5/3 ) respectively.

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Answer:

X = 97.45 - 42

Step-by-step explanation:

If 42 + X = 97.45, X needs to be 97.45 - 42

you can do the same thing with smaller numbers, for example:

5 + X = 7

7 - 5= 2 and you can check for sure that this is the answer by adding them together 5 + 2= 7 so it's definitely the right answer

so for this question, 97.45- 42 = 55.45 so that's X

you can check that by 55.45 + 42 and if the answer is 97.45 that's the right answer!

I hope that makes sense

Answer: 9

Step-by-step explanation: To divide we need to flip the second fraction we are dividing by. For example:

10/1 divided by 1/4 = 10/1 times 4/1. So in this case, the answer is 40.

Now lets try it with 1/9.

X divided by 1/9 = X times 9/1.

So dividing by 1/9 is equal to multiplying by 9.

The given function for peanuts is continuous function.

A continuous function, as the name implies, refers to one for whom the graph is continuous without a breaks or jumps.

For the given expression in the question;

The relation between the cost 'c' and wight 'p' in pounds for the peanuts is given as;

c = 1.5p

As, you can see that the expression is a polynomial having two variables with the highest degree 1.

And, as we know that the every polynomial is a continuous function.

The given function forms a straight line on as for every different real value of p there s single value of c, which varies linearly.

Therefore, the function c = 1.5p is a continuous function forming a straight line.

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This table shows the frequency of each number obtained after throwing the die 35 times

To prepare a frequency table based on the numbers obtained from throwing a die 35 times, we can list the numbers from 1 to 6 and count the frequency of each number.

Numbers: 1, 2, 3, 4, 5, 6

Frequency: 5, 14, 6, 4, 5, 1

Based on the given numbers, the frequency table would look like this:

Number   | Frequency

1                      5

2                     14

3                      6

4                      4

5                      5

6                       1

This table shows the frequency of each number obtained after throwing the die 35 times.

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