Using f(x), what is the equation that represents g(x)?
Og(x) = log5 (x) - 3
O
g(x) = log5 (x) +3
Og(x) = log5 (x-3)
Og(x) = logs(x + 3)

-5x - 5 = 3x + 19

---Move the x's to one side

-5x - 3x - 5 = 3x - 3x + 19

-8x - 5 = 19

---Isolate the -8x by removing the -5 from the left side

-8x - 5 + 5 = 19 + 5

-8x = 24

---Divide both sides by -8 to get x by itself

x = -3

Hope this helps!

-5x-5= 3x+19

= > -5x-3x= 19+5

= > -8x= 24

= >-x=24/8

= >x= -3

x[x²-25] - [x³+8] = 17

x³- 25x - x³- 8 = 17

-25x = 17 + 8

-25x = 25

x = -1

Answer: [tex]\Large\boxed{y-1=\frac{4}{5} (x+2)}[/tex]

Step-by-step explanation:

Given the requirement for function

Point-slope form : y - y₁ = m (x - x₁)

Given information

m = 4/5

Point = (x₁, y₁) = (-2, 1)

Substitute values into the function form

y - y₁ = m (x - x₁)

y - (1) = (4/5) (x - (-2))

Simplify the function

[tex]\Large\boxed{y-1=\frac{4}{5} (x+2)}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

D) 4 8/12

Step-by-step explanation:

To first start this, let's make 2 5/6 an in-proper fraction by adding 12 and removing the whole 2. =17/6. Then let's get a common denominator by multiplying both the denominators by each other...6x4 and 4x6, but we also multiply the numerators by the same thing that the denominators are getting multiplied by... 17x4 and 7x6. We will then get 68/24 and 42/24. And then we can add both numerators with eachother and keep the denominator to get, 110/24... and making this into a propor fraction would equal 4 16/24... and dividing by 2 would equal 4 8/12

The reverse number of the three-digit number is 732

Let the three-digit number be xyz.

So, the reverse is zyx

This means that

Number = 100x + 10y + z

Reverse = 100z + 10y + x

From the question, we have the following parameters:

y = x + 1

z = 1 + 2y

The sum is represented as:

100x + 10y + z + 100z + 10y + x = 10^3 - 31

100x + 10y + z + 100z + 10y + x = 969

Evaluate the like terms

101x + 101z + 20y = 969

Substitute y = x + 1

101x + 101z + 20(x + 1) = 969

101x + 101z + 20x + 20 = 969

Evaluate the like terms

101x + 101z + 20x = 949

121x + 101z = 949

Substitute y = x + 1 in z = 1 + 2y

z = 1 + 2(x + 1)

This gives

z = 2x + 3

So, we have:

121x + 101z = 949

121x + 101* (2x + 3) = 949

This gives

121x + 202x + 303 = 949

Evaluate the sum

323x = 646

Divide by 323

x = 2

Substitute x = 2 in z = 2x + 3 and y = x + 1

z = 2*2 + 3 = 7

y = 2 + 1 = 3

So, we have

x = 2

y = 3

z = 7

Recall that

Reverse = 100z + 10y + x

This gives

Reverse = 100*7 + 10*3 + 2

Evaluate

Reverse = 732

Hence, the reverse number of the three-digit number is 732

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Given :-

Solution :-

>> 2x + 5 < x + 1 / 4

>> 4 (2x + 5) < x + 1

>> 4 × (2x + 5) < x + 1

>> 8x + 20 < x + 1

>> 8x - x < 1 - 20

>> 7x < 1 - 20

>> 7x < -19

>> x = -19 / 7

[tex]\boldsymbol{\sf{2x+5 < \dfrac{x+1}{4} }}[/tex]

Multiply the two sides of the equation by 4. Since 4 is > 0, the direction of inequality remains the same.

          [tex]\boldsymbol{\sf{8x+20 < x+1 }}[/tex]

Resta x en los dos lados.

              [tex]\boldsymbol{\sf{8x+20-x < 1 }}[/tex]

Combine 8x and −x to get 7x.

                [tex]\boldsymbol{\sf{7x+20 < 1 }}[/tex]

Subtract 20 on both sides.

                 [tex]\boldsymbol{\sf{7x < 1-20 \ \ \longmapsto \ \ [To \ subtract] }}[/tex]

                  [tex]\boldsymbol{\sf{7x < -19 }}[/tex]

Divide the two sides by 7. Since 7 is >0, the direction of inequality remains the same.

                     [tex]\boldsymbol{\sf{x < -\dfrac{19}{7} } }[/tex]

As the end result, it is not simplified or divided, then

                               [tex]\blue{\boxed{\boldsymbol{\sf{Answer \ \ \longmapsto \ \ x < -\frac{19}{7} }}}}[/tex]

ヘ( ^o^)ノ＼(^_^ )If you want to learn more about mathematics, I share this link to complement your learning:

Answer:

QP = | a - d |

Step-by-step explanation:

since the y- coordinates of P and Q are equal , both b

then PQ is the absolute value of the difference of the x- coordinates, that is

QP = | a - d | = | d - a |

A simultaneous equation refers to two or more equations that are solved at the same time.

A simultaneous equation refers to two or more equations that are solved at the same time. Now we shall solve each of the equations;

a. 2x + y = 3 ------(1)

   x - y = 4 ------ (2)

x = 4 + y  ----- (3)

Substituting (3) into (1)

2(4 + y) + y = 3

8 + 2y + y = 3

8 + 3y = 3

3y = 3 - 8

3y = -5

y = -5/3

Hence;

 x - y = 4

x - (-5/3) = 4

x = 4 + 5/3

x = 17/3

b. 2x + 6y =9 -----(1)

x + 3y = 2 ------ (2)

x = 2 - 3y ------ (3)

Substitute (3) into (1)

2( 2 - 3y)  + 6y =9

4 - 6y + 6y = 9 (From this stage we can see that it is not possible to solve the quadratic)

c. 6x - 3y = 12 -----(1)

4x + 2y = 10 ---- (2)

12x - 6y = 24 ---- (3)

12x + 6y = 30 --- (4)

Add (3) to (4)

24x = 54

x= 54/24 = 9/4

Hence;

4(9/4) + 2y = 10

9 + 2y = 10

2y = 10 - 9

y = 1/2

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The age of Tommy is currently 40-years old

According to the statement

we have given that the tommy is five times as old as bianca and in eight years, tommy will only be three times as old as bianca.

And we have to find the present age of the tommy.

So, This is a question involving the ratio of ages.

Let the ages of Tommy and Bianca in the present be T and B respectively.

STEP 1: Let:

T = 5B

T + 8 = 3 (B+8)

Then

STEP 2: We can substitute T with 5B since the two variables are equal, to create:

5B + 8 = 3 (B + 8)

Then

STEP 3: Finally, we can expand and solve:

5B + 8 = 3B + 24

2B = 16

B = 8

T = 5B = 5 x 8 = 40

T = 40

Therefore, The age of Tommy is currently 40-years old

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Answer: 5 cm

Step-by-step explanation:

B = [tex]\sqrt{13^{2} -12^{2} } = 5[/tex]

Answer:

OPTION C, 5

Step-by-step explanation:

Using the formula, substitute the hypotenuse and the other leg of the right triangle.

13²=12²+b²

Rearrange appropriately.

13²-12²=c²

Convert.

13²=169

12²=144

Apply and work out.

169-144= 25

c²=25

c=√25

c=5

OPTION C is therefore the answer.

Please comment below if you need more help! :)

Answer:

a) -6/2

b) -9/2

Step-by-step explanation:

a) rearrange by making y the subject as y = mx+c

y = -6/2x-9/2

the gradient = -6/2

b) c is the y-intercept as it touch the y-axis, therefore -9/2 is where the line crosses the y-axis

The critical values for a 2-tailed sign test for 13-coin flips (alpha of. 05) is: ± 1.96

For given question,

We need to find the critical values for a 2-tailed sign test for 13-coin flips.

We have been given an alpha level of 0.05 that is 5%

⇒ α = 0.05

We know that in hypothesis testing, a critical value is a point on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis.

These are the points on the distribution which have the same probability as your test statistic, equal to the significance level α.

The critical values are assumed to be at least as extreme at those critical values.

Now we find 1 - α

⇒ 1 - α = 1 - 0.05

⇒ 1 - α = 0.95

Because it is a two-tailed test, we are going to divide 0.95 by 2.

⇒ 0.95/2 = 0.475

Now we look in the z-table to find out cutoff points.

For the area of 0.475, the critical values is ± 1.96 .

Therefore, the critical values for a 2-tailed sign test for 13-coin flips (alpha of. 05) is: ± 1.96

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Answer:

10, 8

Step-by-step explanation:

l + w = 18

l*w = 80

8 and 10 works

Answer:

no

Step-by-step explanation:

The answer is x < 1.

Bring the constant to the other side.

Divide by 4 on both sides.

[tex]\Large\texttt{Answer}[/tex]

[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad\space\space\qquad\qquad\qquad}}[/tex]

[tex]\Large\texttt{Process}[/tex]

[tex]\rm{4x-6 < -2}[/tex]

Do you remember that we need to get x by itself to find its value?

We should do this:

⇨ Add 6 to both sides

[tex]\rm{4x-6+6 < -2+6}[/tex]

On the left hand side (lhs), the 6s add up to zero; on the right hand side (rhs), the -2 and 6 result in 4. Hence

[tex]\rm{4x < 4}[/tex]

Now divide both sides by 4

[tex]\rm{\cfrac{4x}{4} < \cfrac{4}{4}}[/tex]

Simplifying fractions gives us

[tex]\rm{x < 1}[/tex]

* what this means is: numbers less than 1 will make the statement true

[tex]\Large\texttt{Verification}[/tex]

Substitute 1 into the original inequality [tex]\boxed{4x-6 < -2}[/tex]

[tex]\rm{4(1)-6 < -2}[/tex]

[tex]\rm{4-6 < -2}[/tex]

Do the arithmetic

[tex]\rm{-2 < -2}[/tex]

Hope that helped

The equation of the parabola given in the graph is:

(x - 5)² = -8(y + 4).

The equation of a quadratic function, of vertex (h,k), is given by:

a(y - k) = (x - h)²

In which a = 4p is the leading coefficient.

In this problem, the vertex is at point (5,-4), hence h = 5, k = -4, and the equation is:

a(y + 4) = (x - 5)²

The focus is at y = -6, which means that p = -6 - (-4) = -2, hence the leading coefficient is:

a = 4p = 4(-2) = -8

Hence the equation is:

(x - 5)² = -8(y + 4).

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Answer:

he didn't mistake step 2

Length of the line

= [tex]\sqrt{((-2)-(-8))^{2}+(10-2)^{2} }[/tex]

= [tex]\sqrt{36+64}[/tex]

=[tex]\sqrt{100}[/tex]

= 10

Solving a system of equations, we conclude that the value of x is 28.

Here we have the quadratic number pattern:

6, 15, x, 45, ...

First, we have that:

15 - 6 = 9

So 9 is the first difference.

Then we will have:

x = 15 + 9 + a

(where a is the second difference, constant of the sequence).

And:

45 = x + 9 + a + a

Then we have a system of equations:

x = 15 + 9 + a

45 = x + 9 + a + a

We can isolate a on the first equation:

a = x - 24

We can replace that in the other equation:

45 = x + 9 + 2a

45 = x + 9 + 2*(x - 24)

Now we can solve that for x:

45 - 9 = x + 2*(x - 24)

36 = 3x - 48

36 + 48 = 3x

84 = 3x

84/3 = x = 28

The value of x is 28.

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The data which is most likely to be normally distributed is total points scored by a basketball team the whole season.

Given five statements:

1)Daily temperature highs for winter in 25 US cities.

2)Daily stock reports from the stock market.

3) Height of flowers.

4) Total points scored by a basketball team the whole season.

We are required to choose a statement whose data is most likely to be normally distributed.

A normal distribution is an arrangement of data set in which most values cluster in the middle of the range and the rest off symmetrically towards either extreme.It is basically a probability distribution that is most likely symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. Its graph is a bell curve.

So,the statement which is likely to be normally distributed is total points scored by a basketball team the whole season.

Hence the data which is most likely to be normally distributed is total points scored by a basketball team the whole season.

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Answer:

  130

Step-by-step explanation:

The number of integers meeting the criteria can be found by counting them using a counting formula.

Integers divisible by 7 will have the form (7n), where n is some positive integer. The number of them less than 1000 can be found from ...

  7n ≤ 1000

  n ≤ 142.857

There are 142 integers less than 1000 that are divisible by 7.

Similarly, integers divisible by 7 and 11 will be of the form (77n), for some positive integer n.

  77n ≤ 1000

  n ≤ 12.987

There are 12 integers less than 1000 that are divisible by both 11 and 7.

The number of integers less than 1000 that are divisible by 7, but not 11, will be the difference of these numbers.

  142 -12 = 130 integers divisible by 7, but not 11.

The amount paid to the man in the first year given the total he received in four years is $3,700.

= (x + 1000)

= (x + 1500)

Total payment = first year + second year + third year + fourth year

x + (x + 500) + (x + 1000) + (x + 1500) = 17,800

x + x + 500 + x + 1000 + x + 1500 = 17800

4x + 3000 = 17,800

4x = 17,800 - 3000

4x = 14,800

x = 14,800/4

x = $3,700

Therefore, $3,700 was paid to the man in the first year.

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∆BOC is equilateral, since both OC and OB are radii of the circle with length 4 cm. Then the angle subtended by the minor arc BC has measure 60°. (Note that OA is also a radius.) AB is a diameter of the circle, so the arc AB subtends an angle measuring 180°. This means the minor arc AC measures 120°.

Since ∆BOC is equilateral, its area is √3/4 (4 cm)² = 4√3 cm². The area of the sector containing ∆BOC is 60/360 = 1/6 the total area of the circle, or π/6 (4 cm)² = 8π/3 cm². Then the area of the shaded segment adjacent to ∆BOC is (8π/3 - 4√3) cm².

∆AOC is isosceles, with vertex angle measuring 120°, so the other two angles measure (180° - 120°)/2 = 30°. Using trigonometry, we find

[tex]\sin(30^\circ) = \dfrac{h}{4\,\rm cm} \implies h= 2\,\rm cm[/tex]

where [tex]h[/tex] is the length of the altitude originating from vertex O, and so

[tex]\left(\dfrac b2\right)^2 + h^2 = (4\,\mathrm{cm})^2 \implies b = 4\sqrt3 \,\rm cm[/tex]

where [tex]b[/tex] is the length of the base AC. Hence the area of ∆AOC is 1/2 (2 cm) (4√3 cm) = 4√3 cm². The area of the sector containing ∆AOC is 120/360 = 1/3 of the total area of the circle, or π/3 (4 cm)² = 16π/3 cm². Then the area of the other shaded segment is (16π/3 - 4√3) cm².

So, the total area of the shaded region is

(8π/3 - 4√3) + (16π/3 - 4√3) = (8π - 8√3) cm²

The missing value in the table is 12.4

From the question, we are to determine the missing value in the table

From the given information,

The chart shows conversion between kilometers and miles

The given table is

Kilometers           Miles

2                            1.2

7                            4.2

20                          ?

30                          18

NOTE: 1 kilometer ≈ 0.62 miles

Then, 20 kilometer ≈ 20×0.62 miles

20 kilometer ≈ 12.4 miles

Hence, the missing value in the table is 12.4

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**Disclaimer** Hi there! I assumed the unit [ mph ] represents miles per hour and [ m/s ] represents meters per second. The following answer will be according to this understanding. If I am wrong, please let me know and I will modify my answer.

Answer: [tex]\Large\boxed{23~m/s}[/tex]

Step-by-step explanation:

Given information

Speed = 52 mph

Given conversion factors

1 mile ≈ 1609 meters

1 hour = 3600 seconds

Convert the unit from mph to m/s using conversion factors

The basic idea is that you utilize the factors and cancel out unnecessary units

[tex]\dfrac{52~miles}{1~hour} \times\dfrac{1~hour}{3600~seconds} \times\dfrac{1609~meters}{1~miles}[/tex]

Simplify by multiplication

[tex]=\dfrac{52~miles}{3600~Seconds} \times\dfrac{1609~meters}{1~miles}[/tex]

[tex]=\dfrac{52\times 1609~meters}{3600~Seconds}[/tex]

Simplify the fraction

[tex]=\dfrac{83668~meters}{3600~Seconds}[/tex]

[tex]\Large\boxed{\approx23~m/s}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The number of terms, 'n' is 8

Let's determine the common ratio;

common ratio, r = 3/1 = 3

The formula for sum of geometric series with 'r' greater than 1 is given as;  Sn = a( r^n - 1) / (r - 1)

n is unknown

Sn = 3280

Substitute the value

3280 = 1 ( 3^n - 1) / 3- 1

3280 = 3^n -1 /2

Cross multiply

3280 × 2 = 3^n - 1

6560 + 1 = 3^n

6561 = 3^n

This could be represented as;

3^8 = 3^n

like coefficient cancels out

n = 8

Thus, the number of terms, 'n' is 8

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Answer:

4

Step-by-step explanation:

18 + 18 = 36

So you got 36 cuz you times by two so you times the same for x

which is

2 x 2 = 4

Answer:

4

Step-by-step explanation:

We can set up a proportion.

18:2 = 36: x

If we multiply 18 by 2, and multiply 2 by 2, we can get 18:2 = 36:4, so x is equal to 4

The value of function f(x) at x = 7 is f(7) = 28

For given question,

we have been given the value of function f(x) at x = 5.

f(5) = 12

We have been given that f'(x) is continuous on 5 and 7

Also, [tex]\int\limits^7_5 {f(x)} \, dx =16[/tex]

We need to find the value of f(7)

Since ∀x, f'(x) = f'(x), f is a primitive function of f' .

And f ' is continuous

[tex]\Rightarrow \int\limits^7_5 {f(x)} \, dx =16\\\\\Rightarrow [f(x)]_5^7=16[/tex]

⇒  [f(7) - f(5)] = 16

⇒ f(7) - 12 = 16

⇒ f(7) = 16 + 12

⇒ f(7) = 28

Therefore, the value of function f(x) at x = 7 is f(7) = 28

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We have enough data to reject our null hypothesis if the value of our test statistics falls below critical values of z at a 1.25% level of significance (critical values are -1.645 and 1.645). This is because the test statistic value will not fall within this region.

Given that the population mean is 650, we do a two-tail hypothesis test with a level of significance of 0.025.

Let, μ = population mean

Thus, Null hypothesis, [tex]H_{0}[/tex]:μ= 650.

Alternate Hypothesis, [tex]H_{A}[/tex]:μ≠650

In this case, the population mean is equal to 650, according to the null hypothesis.

The alternative hypothesis, on the other hand, contends that the population mean is not 650.

First things first: the level of significance to be accepted for the two-tailed test is ([tex]\frac{\alpha }{2}[/tex]= [tex]\frac{0.025}{2}[/tex]) = 0.0125 or 1.25%.

Therefore, the following is the decision rule for rejecting a null hypothesis:

We have enough data to reject our null hypothesis if the value of our test statistics falls in the rejection region and is less than the critical values of z at a 1.25% level of significance (critical values are -1.645 and 1.645). This is because the test statistic value will not fall within this region.

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