What is the range of function g?

Answer:

Let a be the smaller of the two primes.

Now the middle of 2 primes is always even. So the middle number a+1 is divisible by 2.

Next the smaller of the primes when divided by 3 can have remainders 1,2.

1 is ruled out as possible remainder because then the remainder of a+2, the bigger of the primes would be (a+2) mod 3=(1+2) mod 3=3 mod 3=0,a contradiction since a prime number(except 3) when divided by 3 cannot have 0 as remainder.

So 2 is the only possible remainder of a. So the remainder of the bigger of the two primes when divided by 3 is (a+2) mod 3= (2+2) mod 3=4 mod 3=1.

This implies the middle number must have remainder (a+1)mod 3=(2+1)mod 3=3 mod 3=0. So the middle number is divisible by 3 also.

Hence a+1 is divisible by both 3 and 2 and since 2 and 3 have no common factors, so the middle number is divisible by 6

Step-by-step explanation:

[tex] \sqrt{ - 81} = 9i \\ \sqrt{ - 11} = i \sqrt{11} \\ \sqrt{ - 20} = i \sqrt{20} [/tex]

Answer:

18

Step-by-step explanation:

X^2 - 7 =

Since we need to evaluate the expression when X = 5, we replace X with 5.

= 5^2 - 7

Now, according to the correct order of operations, we need to do the exponent first. 5^2 = 5 * 5 = 25

= 25 - 7

Finally, we subtract.

= 18

Answer: 18

Answer:

The choose (D)

D. Translate y = |x| up 4 units and shade inside the V.

Answer:

Step-by-step explanation:

you are being asked to "Solve a quadratic"

There are various METHODS to do this.

You will learn a few of them

-graphing

-substation

-complete the square

-quadratic formula

in this case the question wants you to solve it using the

Quadratic formula...

Ax^2 + Bx + C  = 0 is the quadratic.

your A=-1 B=14, and C=61

you just have to plug in those numbers into:

[tex]-B[/tex]   ±  [tex]\sqrt{\frac{B^{2}-4AC}{2A}}[/tex]

-14 ± [tex]\sqrt{\frac{14^{2}-4(-1)(61)}{2(-1)}}[/tex]

you should end up with 7+[tex]\sqrt{110}[/tex] & 7-[tex]\sqrt{110}[/tex]

which is -3.49 or 17.49

-3.49 does not make any sense, the 17.49 distance only makes sense for this problem  

Answer:

10.75

11

Step-by-step explanation:

the mean is the average, so add up all of the values and divide by 8 because there are 8 values :

(11 + 17 + 14 + 11 + 4 + 7 + 11 + 11)/8 = 10.75

the median is the middle value when the numbers are written in ascending or descending order :

4, 7, 11, 11, 11, 11, 14, 17

we can cross out the values on the ends, to get to the middle. if we do this, we are left with 11, 11

find the average of these numbers :

which is 11.

Answer:

16

Step-by-step explanation:

First you calculate the value

(2)÷2^-2

Then you simplify

2^4

=16

Answer:

263.25

Step-by-step explanation:

250 x .053 (5.3%) = 13.25 tax

250 + 13.25 = 263.25 price plus sales tax

Answer:

263.25

Step-by-step explanation:

Answer:

65.1 decibels

Step-by-step explanation:

Given

[tex]I = 3.2 * 10^{-6}[/tex] --- intensity

Required

Determine the sound level

This is calculated using:

[tex]B = 10\log(\frac{I}{I_o})[/tex]

Where:

[tex]I_o = 1 * 10^{-12}[/tex]

So, we have:

[tex]B = 10\log(\frac{3.2 * 10^{-6}}{1 * 10^{-12}})[/tex]

Apply law of indices

[tex]B = 10\log(\frac{3.2 * 10^{-6+12}}{1})[/tex]

[tex]B = 10\log(3.2 * 10^{6})[/tex]

Using a calculator, we have:

[tex]B = 10*6.51[/tex]

[tex]B = 65.1[/tex]

Answer:

Area of sector is 6pi cm^2

Step-by-step explanation:

Mathematically pi radians is 180 degrees

thus pi/6 radians is 180/6 = 30 degrees

The formula for the length of an arc is;

theta/360 * 2 * pi * r

where theta in this case is 30 degrees

And the arc length is pi

so we have

30/360 * 2 * pi * r = pi

30/360 * 2 * r = 1

60r = 360

r = 360/60

r = 6 cm

Now the area of a sector is;

theta/360 * pi * r^2

30/360 * pi * 36

= 6pi cm^2

Answer:

D. y= 0.3x2

Step-by-step explanation:

In quadratic functions, the value of a affects the wideness of the graph. The smaller the absolute value of a, the wider the graph. In these choices, 1/3 and 0.3 are the smallest. To understand which is smaller convert both to decimals; 1/3 is 0.3333 repeating. Therefore, 0.3 is slightly smaller and wider.

Answer:

please see the answer in the picture.

Answer:

3(f - 9)(f + 4)

Step-by-step explanation:

Assuming you require to factorise the expression

3f² - 15f - 108 ← factor out 3 from each term

= 3(f² - 5f - 36) ← factor the quadratic

Consider the factors 0f the constant term (- 36) which sum to give the coefficient of the f- term (- 5)

The factors are - 9 and + 4 , since

- 9 × 4 = - 36 and - 9 + 4 = - 5 , then

f² - 5f - 36 = (f- 9)(f + 4)

Then

3f² - 15f - 108 = 3(f - 9)(f + 4)

Answer:

B

Step-by-step explanation:

For the lines to be parallel.

The 2 given angles are corresponding and congruent, that is

4x - 12 = 3x + 17 ( subtract 3x from both sides )

x - 12 = 17 ( add 12 to both sides )

x = 29 → B

The value of x will be 29°. Then the correct option is B.

If two lines are parallel, then the third line. The corresponding angles are equal angles.

We know that the angle (3x + 17) and (4x – 12) are corresponding angle.

(3x + 17) = (4x – 12)

4x – 3x = 17 + 12

          x = 29°

The value of x will be 29°.

Then the correct option is B.

More about the corresponding angle link is given below.

https://brainly.com/question/1597341

#SPJ5

Answer:

[tex]EF=6[/tex]

Step-by-step explanation:

In this problem, one is given a circle with two secants (that is a line that intersects a circle at two points). One is given certain measurements, the problem asks one to find the unknown measurements.

The product of the lengths theorem gives a ratio between the lengths in the secants. Call the part of the secant that is inside the circle (inside), and the part of the secant between the exterior of the circle and the point of intersection of the secants (outside). The sum of (inside) and (outside) make up the entire secant, call this measurement (total). Remember, there are two secants, ([tex]secant_1[/tex]) and ([tex]secant_2[/tex]) in this situation. With these naming in mind, one can state the product of the length ratio as the following:

[tex]\frac{total_1}{outside_2}=\frac{total_2}{outside_1}[/tex]

Alternatively, one can state it like the following ratio:

[tex]\frac{inside_1+ouside_1}{outside_2}=\frac{inside_2+outside_2}{outside_1}[/tex]

Apply this ratio to the given problem, substitute the lengths of the sides of the secants in and solve for the unknown.

[tex]\frac{EF+FG}{HG}=\frac{SH+HG}{FG}[/tex]

[tex]\frac{2x+4}{5}=\frac{x+5}{4}[/tex]

Cross products, multiply the numerator and denominators of opposite sides of the fraction together,

[tex]\frac{2x+4}{5}=\frac{x+5}{4}[/tex]

[tex]4(2x+4)=5(x+5)[/tex]

Simplify,

[tex]4(2x+4)=5(x+5)[/tex]

[tex]8x+16=5x+25[/tex]

Inverse operations,

[tex]8x+16=5x+25[/tex]

[tex]3x+16=25\\3x=9\\x=3[/tex]

Substitute this value into the equation given for the measure of (EF),

[tex]EF=2x\\x=3\\\\EF=2x\\=2(3)\\=6[/tex]

First, recall that

cos(A - B) = cos(A) cos(B) + sin(A) sin(B)

so you just need to find cos(A) and sin(B).

Since both A and B end in the second quadrant, you know that

• cos(A) and cos(B) are both negative

• sin(A) and sin(B) are both positive

Then from the Pythagorean identity, you get

cos²(A) + sin²(A) = 1   ==>   cos(A) = -√(1 - sin²(A)) = -2√10/7

cos²(B) + sin²(B) = 1   ==>   sin(B) = +√(1 - cos²(B)) = √21/5

You'll end up with

cos(A - B) = (-2√10/7) (-2/5) + (3/7) (√21/5)

… = (4√10 + 3√21)/35

(which makes the last sentence in the question kind of confusing, because this expression doesn't get much simpler and it's certainly not a rational number)

The value of cos(A - B) is approximately 23/25

Given that A and B are in the second quadrant, we have

To find cos(A - B), we have to use trigonometric functions

cos(A - B) = cosAcosB + sinAsinB ...equation(i)

but

[tex]cos^2A + sin^2A =1 \\cos^2A = 1 - sin^2A\\cos^2A = 1 - (\frac{3}{7})^2 = 1 - \frac{9}{49}= cosA= -\frac{2\sqrt{5} }{7}[/tex]

Having the value of cos A, let's solve for cosB

cos B = -2/5

[tex]sin^2B = 1-cos^2B\\sin^2B = 1-(-\frac{2}{5})^2= 1-\frac{4}{25}\\sinB = \sqrt{\frac{21}{25} }=\frac{\sqrt{21} }{5}[/tex]

substituting the values if sinA, cosA, sinB, cosB into equation(i) above;

[tex]cos(A-B)=cosAcosB+sinAsinB\\cos(A-B)=(-\frac{2\sqrt{5} }{7})(-\frac{2}{5})+(\frac{3}{7})(\frac{\sqrt{21} }{5})\\cos(A-B)=\frac{3\sqrt{21}+4\sqrt{5} }{35} \\cos(A-B) = 23/35[/tex]

The value of cos(A-B) is given above

Learn more on trigonometric functions here;

https://brainly.com/question/4326804

Frequency is the number of incidences of an occasion or value. A frequency table that displays the number of incidences of the goods and the number of times, and the further discussion can be defined as follows:

Calculation:

[tex]lower\ \ \ \ \ \ \ \ \ upper \ \ \ \ \ \ \ \ \ frequency\\\\809\ \ \ \ \ \ \ \ \ 921 \ \ \ \ \ \ \ \ \ 3\\\\922 \ \ \ \ \ \ \ \ \ 1034 \ \ \ \ \ \ \ \ \ 3\\\\1035 \ \ \ \ \ \ \ \ \ 1147\ \ \ \ \ \ \ \ \ 2\\\\1148 \ \ \ \ \ \ \ \ \ 1260\ \ \ \ \ \ \ \ \ 4\\\\1261 \ \ \ \ \ \ \ \ \ 1373 \ \ \ \ \ \ \ \ \ 4\\\\1374 \ \ \ \ \ \ \ \ \ 1486\ \ \ \ \ \ \ \ \ 4[/tex]

Learn more:

brainly.com/question/18359774

Answer:

firstable give c+b a polynomial value like x

so its will be x^2+11x+30

after the we have to factor it

30=6×5

and 11=6+5

so its will become

(x+6)×(x+5)=x^2+11x+30

x=c+d

(c+d+6)×(c+d+5)=(c+d)^2+11(c+d)+30

have a great day

[tex] \sf \: \frac{5}{21 } \: rounded \: to \: 3 \: decimal \: places \: is \: \boxed{ \underline{ \bf0.238}}. \\ \longrightarrow \sf \: Just \: divide \: 5 \: by \: 21 \: upto \: 3 \: decimal \: places \\ \sf \: to \: get \: the \: answer.[/tex]

Answer:

x = 3

Step-by-step explanation:

In this piece-wise function, there are three defined sections, each for a different range of x. To find an x where y is -9, we have to set all parts of it equal to -9.

-x,  x < -3

So, we can start by setting -x equal to -9 and solve for x:

-x = -9

x = 9

Our domain for this piece of the function is supposed to be x < -3. x = 9 does not fit into this range, meaning, in this range, there is no x for y = -9.

2x,   -3 ≤ x ≤ -2

We can set the value 2x equal to -9 and, again, solve for x:

2x = -9

x = -4.5

The solution x = -4.5 does not fit into the defined domain of -3 ≤ x ≤ -2, therefore it is not a solution.

-x^2,  x > -2

One last time, we can set -x^2 equal to -9 and solve for x:

-x^2 = -9

x^2 = 9

x = 3, x = -3

We are looking for a solution that fits into the domain, x > -2, x = -3 does not work, but x = 3 does.

In conclusion, the only solution where it fit the domain was x = 3

Answer:

x = 3

Step-by-step explanation:

x = - 3 in interval - 3 ≤ x ≤ - 2 then f(x) = 2x , so

f(- 3) = 2(- 3) = - 6 ≠ - 9

x = 9 in interval x > - 2 then f(x) = - x² , so

f(9) = - 9² = - 81 ≠ - 9

x = 3 in interval x > - 2 then f(x) = - x²

f(3) = - 3² = - 9

x = - 4.5 in the interval x < - 3 then f(x) = - x , so

f(- 4.5) = - (- 4.5) = 4.5

Thus

y = - 9 when x = 3

Answer:

D should be the anwser if im not mistaken!

Step-by-step explanation:

rp= 6 cm and as u can tell the side where q,s lies is a little bit longer so itll be 1 cm longer the r,p!!

Answer:

7

Step-by-step explanation:

Triangle Proportionality Theorem : If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

[tex]\frac{RP}{PT}[/tex] = [tex]\frac{SQ}{QT}[/tex]     Set up proportions

[tex]\frac{6}{18}[/tex] = [tex]\frac{x}{21}[/tex]        Cross multiply

18x = 126   Divide to isolate x

x = 7

Answer:

x = 6 and x = 9

Step-by-step explanation:

16

MN is half the length of KL

MN = [tex]\frac{1}{2}[/tex] × 12 = 6

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

17

Δ LMN and Δ LJK are similar triangles, so the ratios of corresponding sides are equal, that is

[tex]\frac{LM}{LJ}[/tex] = [tex]\frac{MN}{JK}[/tex] , substitute values

[tex]\frac{x}{x+9}[/tex] = [tex]\frac{8.5}{17}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2x = x + 9 ( subtract x from both sides )

x = 9

Answer:

(x+2y)(x+2y)

x²+2xy+2xy+2y²

x²+4xy+2y²

(2x+3y)(2x+3y)

4x²+6xy+6xy+9y²

4x²+12xy+9y²

Answer:

Plotting the points on graph and joining them gives a right angle triangle

Answer:

right angle triangle

Step-by-step explanation:

Slope = (Y1-Y2)/(X1-X2)

The slope of AC is 1/3. The slope of BC is -3. Therefore AC is perpendicular to BC (right angle).

Sheeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeesh

Answer:

leg = 18

hypotenuse = 18 sqrt(2)

Step-by-step explanation:

We know that sin theta = opp side / hypotenuse

sin 45 = 18 / hyp

hyp sin 45 = 18

hyp = 18 / sin 45

hyp = 18 sqrt(2)

Since this is an isosceles triangle ( the two angles are the same measure), the two legs have to be the same length

leg = 18

the lengths of the other leg and the hypotenuse

is 18 units and 18[tex]\sqrt{2}[/tex]units respectively.

Answer:

Solution given:

Let <C=<B=45°

AB=18 units

BC=?

AC=?

again

By using

By usingspecial right triangle ratios

sin C=opposite/hypotenuse=AB/AC=18/AC

Sin 45=18/AC

AC=18/sin45

AC=hypotenuse=18[tex]\sqrt{2}[/tex]units

again

Tan A=opposite/adjacent=BC/AB=BC/18

Tan45=BC/18

BC=Tan45*18

BC=length of another leg=18 units.

Answer:

Step-by-step explanation:

5.1, please this is just a guess from using my head to calculate

Answer:

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