Afreen says, "I am thinking of 3 consecutive numbers. The first is a multiple of 4, the second is a multiple of 5 and the third is a multiple of 6." What could the numbers be? Can you find 3 possible sets of numbers?

Answer:

Step-by-step explanation:

taking the inverse is essentially saying

x = (f(x) + 3)^2

root(x) - 3 = f(x) and -root(x) -3 = f(x)

(you have to take both the positive and negative roots)

plug in 49 for x and get 4 and -10.

The value of the inverse function, to the function f(x) = (x + 3)², at f(x) = 49, is; f⁻¹(49) = 4

The notation f⁻¹(x) represents the inverse of the function f(x). The inverse function, f⁻¹(x) undoes the the effect of the function f(x), meaning, that if y = f(x), then x = f⁻¹(y)

The value of f⁻¹(49) for the function, f(x) = (x + 3)² is the x-value, such that f(x) = 49, which can be obtained by solving the equation f(x) = (x + 3)², for x as follows;

Taking the square root of both sides of the equation, we get;

√(f(x)) = √((x + 3)²)

√(f(x)) = (x + 3)

Subtracting 3 from both sides, we get;

√(f(x)) - 3 = x + 3 - 3 = x

√(f(x)) - 3 = x

The above function is the inverse function, f⁻¹(x) that takes an output value, f(x), to produce the corresponding input value, x of the original function;

The inverse function, f⁻¹(x) = √(f(x)) - 3, takes the original output, f(x) to produce the original input x

When the output value is f(x) = 49 we get;

f⁻¹(49) = √(49) - 3 = ±7 - 3

Restricting the domain of the original function, f(x) to (x + 3) ≥ 0, or x ≥ -3, so that its inverse is also a function and produces only one value, we get;

f⁻¹(49) = 7 - 3 = 4

f⁻¹(49) = 4

Learn more on the inverse of a function here: https://brainly.com/question/1559611

#SPJ2

Answer:

160m

Step-by-step explanation:

Since the rectangles are similar and we have their proportion of coefficient, the larger rectangle is twice the smaller rectangle.

Furthermore, the ratio of two longer sides should equal the ratio of the two shorter sides.

Therefore, for our case, we multiply the smaller rectangle by 2.

Hence;

(80 × 2)m

= 160 m

NB:

The ratio of the areas of two similar shapes or figures is equivalent to the square of the corresponding sides.

Answer:

Corina can make 3 friendship bracelets.

Step-by-step explanation:

Solve for how much string is needed for one friendship bracelet:

4 pieces × 1 foot

4 feet

Convert feet into inches (1 foot = 12 inches):

4 feet × 12 inches

48 inches

Divide the total string by each bracelet's string:

144 inches ÷ 48 inches

3 friendship bracelets

Answer:лаксдкннйд

Step-by-step explanation:

Answer:

2x+3x=90

or ,5x=90

or,x=90/5

X=18

Answer:

90/5=18 degrees

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The statement of congruency shows which vertices are corresponding.

Answer: D  

Answer:

35.2

Step-by-step explanation:

tan(58) = x/22

or, x = 22×tan(58)

or, x = 35.2 (rounded to the nearest tenth)

Answered by GAUTHMATH

Solution given:

Cos[tex]\theta_{1}=\frac{10}{17}[/tex]

[tex]\frac{adjacent}{hypotenuse}=\frac{10}{17}[/tex]

equating corresponding value

we get

adjacent=10

hypotenuse=17

perpendicular=x

now

by using Pythagoras law

Hypotenuse ²=perpendicular²+adjacent ²

substituting value

17²=x²+10²

17²-10²=x²

x²=17²-10²

x²=189

doing square root

[tex]\sqrt{x²}=\sqrt{189}[/tex]

x=[tex]3\sqrt{21}[/tex]

now

In I Quadrant sin angle is positive

Sin[tex]\theta_{1}=\frac{perpendicular}{hypotenuse}[/tex]

Answer:

sin theta = 3 sqrt(21)/17

Step-by-step explanation:

cos theta = adj / hyp

We can find the opp by using the Pythagorean theorem

adj^2 + opp ^2 = hyp^2

10^2 +opp^2 = 17^2

100 + opp^2 = 289

opp^2 = 289-100

opp^2 = 189

Taking the square root

opp = sqrt(189)

opp = 3 sqrt(21)

Since we are in the first quad, opp is positive

sin theta = opp /hyp

sin theta = 3 sqrt(21)/17

The ratio 4:3 means for every 4 girls there are 3 boys.

Divide total girls by 4, multiply that by 3 to get total boys:

180/4 = 45 x 3 = 135

There are 135 boys

For total students add boys and girls:

180 + 135 = 315 total students

3 rolls would cost $1.17.

There exists a direct proportion between two values when one exists as a multiple of the other.

In direct proportion, if one quantity exists increased or decreased then the other quantity increases or declines, respectively. But in indirect or inverse proportion, if one quantity increases then the different quantity decreases and vice-versa.

If 7 rolls of tape cost $2.73,

Then 1 roll of tape would cost $2.73/7 = $0.39

Now, the cost of 3 roll of tapes would be 0.39*3 = $1.17

Therefore, at same rate the 3 rolls of tape would cost $1.17.

To learn more about Direct Proportion refer to:

https://brainly.com/question/1266676

#SPJ2

Answer:

4.5, - 27, 162, - 972, 5832

Step-by-step explanation:

Using the recursive rule and a₁ = 4.5 , then

a₂ = - 6a₁ = - 6 × 4.5 = - 27

a₃ = - 6a₂ = - 6 × - 27 = 162

a₄ = - 6a₃ = - 6 × 162 = - 972

a₅ = - 6a₄ = - 6 × - 972 = 5832

The first 5 terms are 4.5, - 27, 162, - 972, 5832

Answer:

The 2nd one is 3x+1

The 3rd answer is x+3

Step-by-step explanation:

Given g(x)=4x-1 and f(x)=x-2

Subtracting both

4x-1-(x-2)=4x-1-x+2=x(4-1)+(2-1)=3x+1

The next one is 3x+1-(2x-2)=3x+1-2x+2=x+3

i think its b Step-by-step explanation:

[tex] \frac{5x}{ \frac{5x}{3} } = \frac{15x}{5x} = 3[/tex]

Answer:

m,4+ a+b

Step-by-step explanation:

an exterior angle equals the sum of the 2 opposite interior angles

Answer:

bro the co ordinates are in the picture itself

Answer:

A'(-3,0) ; B'(0,0); C'(3,6) ; D'(-3,6)

Step-by-step explanation:

O(-6,-6)

A( -5 , -4)  = A( -6+1 , -6 + 2)

A'(-6+3 ,-6+6) = A'(-3,0)

B(-4,-4) = B(-6+2 , -6+2)

B'(-6+6,-6+6)= B'(0,0)

C(-3,-2) = C(-6+3, -6+4)

C'(-6+9 , -6+12) = C'(3,6)

D(-5 , -2) = D(-6+1 , -6 +4)

D'(-6+3, -6+12)=D'(-3,6)

Answer:

Smaller factor/larger figure = 3/6 = ½

Step-by-step explanation:

Scale factor of similar figures is usually the ratio of one to the other.

In the diagram given, the scale factor is the length of any side of the smaller figure divided by the length of the corresponding side length of the bigger figure.

Length of smaller figure = 3

Corresponding length of larger figure = 6

Scale factor = smaller figure/larger figure = 3/6

Simplify

Scale factor = ½

Answer:

-7/5

Step-by-step explanation:

I think let me know

Answer:

7/-5  or -7/5

Step-by-step explanation:

This shall be quite an easy problem, I shall be doubting that this is high school, however, I am happy to aid :)

We shall begin by labeling the points given to us to prepare for inputting the values in the slope formula

(3,4).     (8,-3)

x1,y1     x2,y2

Slope Formula:

y1 - y2

x1 - x2

Inputting the values:

4 - (-3)

3 - 8

Solve:

7

-5

The slope of the line passing through the points (3,4) and (8,-3) shall be 7/-5 or -7/5 negatives shall go both ways of fractions

Answer:

∠4 = ∠8

Step-by-step explanation:

the lines are parallel if a pair of corresponding angles are congruent

Answer:

12 miles

Step-by-step explanation:

1/3 of an hour = 20 minutes = 4 miles

1 minute = 4/20 miles

60 minutes = 4/20 x 60 miles

                   = 4 x 3 miles

                   = 12 miles

60 minutes = 1 hour

=> 1 hour = 12 miles

Jacks unit rate is 12 miles/hr

Answer:

12

Step-by-step explanation:

There are two ways of doing this problem. I think the easiest way is to use a decimal in the denominator and round

4/0.333333333 = 12.000000001

The answer is obviously meant to be 12.

The other way is more sophisticated, but more accurate.

4/1 // 1/3               This is a 4 tier fraction. The rule is to invert the denominator (turn the bottom fraction upside down) and multiply.

4/1 * 3/1 = 12

The first method is easier to understand. The second is more accurate and more useful for physics.

Answer:

If u add the number it will show u te answer which is 7

Step-by-step explanation:

Answer:

profit is 25%

Step-by-step explanation:

profit%=sp-cp/cp×100%

=350-280/280×100%

=0.25×100

=25%

Answer:

TE = 7

Step-by-step explanation:

The centroid divides a median in this ratios 1/3 and 2/3. In particular

XT = 2/3 XE

XT = 2/3 * 21

XT = 14

TE = 7

Answer:

The set [tex]S[/tex] of non-negative integers in the inequality [tex]2x < 4[/tex] is

[tex]S = \{0, 1\}[/tex]

Step-by-step explanation:

The non-negative integers are given as [tex]\mathbb{Z}_{\ge 0} = \{ 0, 1, 2, \ldots \}[/tex]

For the inequality [tex]2x < 4[/tex], we have

[tex]2x < 4 \implies x < \dfrac{4}{2} \implies x < 2[/tex]

Therefore,

[tex]x\in \mathbb{R}:x\in(\infty, 2)[/tex]

Note: 2 is not included

The integers are

[tex]\ldots -2, -1, 0, 1[/tex]

And the non-negative integers are

[tex]0, 1[/tex]

Answer:

no solution

Step-by-step explanation:

Answer:

Step-by-step explanation:

I get no solution also (the answer is imaginary).

Answer:

Step-by-step explanation:

This is most easily solved with calculus, believe it or not. It is way more direct and to the point, with a whole lot less math!

The position function is given. The velocity function is the first derivative of the position, so if we find the velocity function and set it equal to 0, we can solve for the amount of time it takes for the rocket to reach its max height. Remember from physics that at the top of a parabolic path, the velocity is 0.

If:

[tex]s(t)=-16t^2+112t+360[/tex], then the velocity function, the first derivative is:

v(t) = -32t + 112 and solve for t:

-112 = -32t so

t = 3.5 seconds. Now we know how long it takes to get to the max height, we just need to find out what the max height is.

Go back to the position function and sub in 3.5 for t to tell us that position of the rocket at 3.5 seconds, which translates to the max height:

[tex]s(3.5)=-16(3.5)^2+112(3.5)+360[/tex] and

s(3.5) = 206 feet. I imagine that your answer, if you had to choose one from the list, would be 200 feet, rounded a lot.

Answer:

Pam: $181

Amanda: $362

Julie: $452

Step-by-step explanation:

(What does Mike have to do with this problem?)

Let a = Amanda's pay

Let p = Pam's pay

Let j = Julie's pay

"Amanda made twice what Pam earned"

a = 2p

"Julie made $90 more than Amanda"

j = a + 90

j = 2p + 90

Pam earned p

Total salary

a + p + j = 2p + p + 2p + 90

Total salary

$995

2p + p + 2p + 90 = 995

5p = 905

p = 181

a = 2p = 2(181) = 362

j = 2p + 90 = 362 + 90 = 452

Answer:

Pam: $181

Amanda: $362

Julie: $452

Answers:

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

Explanation:

In this context, a zero is another term for x intercept or root. This is where the graph either touches or crosses the x axis. This occurs in three locations: x = -3, x = 2, and x = 0. So those are the three roots. That makes the first three statements true, while the remaining two others are false.

Side note: x = 0 doesn't always have to be involved. Its quite possible to have x = 0 not be an x intercept. The term "zero" is a bit misleading in that regard. I prefer either "root" or "x intercept" instead.

Answer:

The time it takes to make rag dolls for a mission in Africa.

The time taken.

The cost of an end year party.

Step-by-step explanation:

The dependent variable refers to the variable which is predicted or measured in an experiment , the value of the dependent variable relies on the variation in the independent or predictor variable.

The time it takes to make rag dolls for a mission in Africa and the number of people working on the dolls ;

DEPENDENT VARIABLE = The time it takes to make rag dolls for a mission in AFRICA. This is because time taken will depend on the number of people working.

The distance travelled while walking and the time taken ;

DEPENDENT VARIABLE = THE time taken

The time taken will depend on distance traveled.

The cost of an end of year grade 9 party and the number of people attending ;

DEPENDENT VARIABLE = The cost of an end year party.

Cost of partybwill depend on the number of people attending.