Write a function for the tranformations described below:
"The cubic function shifts 7 units right and 5 units up."

The point at which this cable would pass through the road shown is at the y-intercept of (0, -17/2).

Mathematically, the slope of a straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

By critically observing the road shown in the graph above, the points on the line include the following:

Points (x, y) = (0, -2)

Points (x, y) = (-3, 0)

Substituting the given points into the formula, we have;

Slope, m = (0 + 2)/(-3 - 0)

Slope, m = 2/-3

Slope, m = -2/3.

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

-2/3 × m₂ = -1

-2m₂ = -3

m₂ = 3/2

At point (7, 2), a linear equation for the line can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

Where:

Substituting the given points into the formula, we have;

y - 2 = 3/2(x - 7)

y - 2 = 3x/2 - 21/2

y = 3x/2 - 21/2 + 2

y = 3x/2 - 17/2

At the y-intercept of (0, -17/2), the cable pass through the road.

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As per given information about change in uplift it occurs at the rate of 0.1 m per 1,000 years then change in uplift over 1,000,000 years is equal to 100m.

As given in the question,

Rate of occurring of uplift is equal to 0.1m per 1000 years

Represent the given relation in equality form we get,

Change of uplift in 1000 years  = 0.1 m

⇒ 1 year = 0.1 m / 1000

⇒ 1,000, 000 years = ( 0.1 m / 1,000 ) × 1,000, 000

⇒ 1,000, 000 years =  ( 1 m / 10,000 ) × 1,000, 000

⇒  1,000, 000 years =  100 m

Therefore, for given information about change in uplift it occurs at the rate of 0.1 m per 1,000 years then change in uplift over 1,000,000 years is equal to 100m.

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Answer: 2

Step-by-step explanation:

if you plug in -6 into x, we get

36 - 36 + 2

the 36s will cancel each other out, leaving us with only 2 as our final answer.

Answer: -70

Step-by-step explanation:

-[tex]6^{2}[/tex] + 6(-6)+2

= -36 - 36 + 2

= - 70

The value of x on the frequency density axis is 200.

What is frequency?

The frequency of a repeated event is its number of instances per unit of time. In some cases, it is also referred to as temporal frequency or ordinary frequency to underline differences with spatial and angular frequencies, respectively.

What is density?

The mass of a substance per unit of volume is its density. Density is most frequently represented by the symbol, however, the Latin letter D may also be used.

Here, we have

x is about half of the number of beehives producing 16 to 18 kg of honey, for the middle blue bar.

x = half of 400

x = 200

Hence, The value of x on the frequency density axis is 200.

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Answer:

8 bagels

Step-by-step explanation:

This is a remainder division problem. We need to divide 719 by 9 and find the remainder.

First off, 9 is bigger than 7, so we need to move to the next digit. How many times does 9 go into 71? 9 times 7 is 63! That's the closest smaller number we can get, so I will write a 7 in the long division problem above the 1. I will subtract 63 from 71 to get 8.

      7

9 | 719

   -63

       8

Now, the 9 can be brought down, making our 8 into an 89. How many times does 9 go into 89? 9 times 9 is 81! That's the closest we can get! I will write a 9 by the 7 above the 9 in 719, and write 81 below the 89. Subtracting these leaves us with a remainder of 8.

      79

9 | 719

  -63 ↓

      89

      -81

         8

This means that the bagels were sent in 9 equal shipments of 79 bagels each, and the baker was left with 8 bagels!

The person has about 20 yellow beads.

The percentage is a ratio that can be expressed as a fraction of 100.

Given that, the person received 45 beads out of which 45% are yellow.

Therefore, the number of yellow beads is,

45% of 45

= (45×45)/100

= 2025/100

= 20.25

≈ 20

Hence, the person has about 20 yellow beads.

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Answer:

11/48

Step-by-step explanation:

x-2/5=2/3-3x-2/6

collect like terms

x-2/5 + 3x = 2/3 - 2/6

taking LCM on both sides

[(x-2) + 5(3x)]/5 = [2(2) -2]/6

(16x - 2)/5 = 2/6

cross multiply

6(16x - 2) = 5(2)

96x - 12 = 10

96x = 22

therefore; X = 22/96

= 11/48

CHECK:

(11/48 - 2)/5 = 2/3 - 3(11/48) - 2/6

(-85/48)/5 = 2/3 - 11/16 - 2/6

-85/48 × ⅕ = -17/48

-17/48 = -17/48

Answer:

[tex]x=\frac{11}{60}[/tex]

Step-by-step explanation:

Given the equation

[tex]x-\frac{2}{5}=\frac{2}{3}-3x-\frac{2}{6}[/tex]

Lets solve for x.

Simplify the right side of the equation.

Cancel the common factor of 2 and 6 .

Factor 2 out of 2 .

[tex]x-\frac{2}{5}=\frac{2}{3}-3x-\frac{2(1)}{2(3)}[/tex]

[tex]x-\frac{2}{5}=\frac{2}{3}-3x-\frac{1}{3}[/tex]

Combine the numerators over the common denominator.

[tex]x-\frac{2}{5}=-3x-\frac{2-1}{3}[/tex]

[tex]x-\frac{2}{5}=-3x-\frac{1}{3}[/tex]

Move all terms containing x to the left side of the equation.

Add [tex]3x[/tex] to both sides of the equation.

[tex]x-\frac{2}{5}+3x=\frac{1}{3}[/tex]

Add [tex]x[/tex] and [tex]3x[/tex].

[tex]4x-\frac{2}{5}=\frac{1}{3}[/tex]

Move all terms not containing x to the right side of the equation.

Add [tex]\frac{2}{5}[/tex] to both sides of the equation.

[tex]4x=\frac{1}{3}+\frac{2}{5}[/tex]

To write [tex]\frac{1}{3}[/tex] as a fraction with a common denominator, multiply by [tex]\frac{5}{5}[/tex] .

[tex]4x=\frac{1}{3}*\frac{5}{5} +\frac{2}{5}[/tex]

To write [tex]\frac{2}{5}[/tex] as a fraction with a common denominator, multiply by [tex]\frac{3}{3}[/tex]

[tex]4x=\frac{1}{3}*\frac{5}{5} +\frac{2}{5}*\frac{3}{3}[/tex]

Simplify.

Write each expression with a common denominator of 15 , by multiplying each by an appropriate factor of 1 .

[tex]4x=\frac{11}{15}[/tex]

Divide each term in [tex]4x=\frac{11}{15}[/tex] by 4 and simplify.

[tex]x=\frac{11}{60}[/tex]

The expression y = 660(0.902)ˣ represents a decay , the rate of decrease is 9.8% .

In the question ,

it is given that ,

the the exponential function is y = 660(0.902)ˣ

we need to determine that , the equation represents a growth or decay .

0.902 is the variable that will determine a growth or decay .

Since, 0.902 is less than 1 , so it represents a decay function .

To find the rate we subtract 0.902 from 1

= 1 - 0.902

= 0.098

= 9.8% decrease rate

Therefore , The expression y = 660(0.902)ˣ represents a decay , the rate of decrease is 9.8% .

The given question is incomplete , the complete question is

Identify if it's Growth or Decay , and determine the percentage rate of increase or decrease , the function is y = 660(0.902)ˣ ?

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Answer:

  about 21.3 cm²

Step-by-step explanation:

Given a triangle with three sides 6 cm, 8 cm, and 12 cm, and smallest angle 26.4°, you want the area.

  A = 1/2ab·sin(C)

  A = 1/2(12 cm)(8 cm)·sin(26.4°) ≈ 21.34 . . . . square units

The semiperimeter is ...

  s = (6 +8 +12)/2 = 13

The area is ...

  A = √(s(s -a)(s -b)(s -c))

  A = √(13·(13 -12)(13 -8)(13 -6)) = √(13·1·5·7) = √455

  A ≈ 21.33 . . . . square centimeters

The area of the triangle is about 21.3 cm².

__

Additional comment

The problem with over specifying the dimensions of a geometry problem is that it is often difficult to make them consistent. Here, the area values agree to three significant figures. That is about all we can expect, given the angle precision is 3 significant figures.

Your answer depends on the set of dimensions you choose to use. It will be different yet if you use the Law of Sines to find angle A or B for the Sine Formula, especially if you round the angle value to tenths.

The attachment shows the solution using side lengths only.

The answer is a) 0 height, b) 25 seconds c) 10,600 feet d) 3 times e) (x+1)(x-3)(x+5).

A projectile is fired vertically upward, and its height s(t) in feet after t seconds is given by the function defined by

s(t) = -16t² + 800t + 600.

To find out

(a) From what height was the projectile fired

Given height functions: s(t) = -16t² + 800t + 600

Now,

[tex]s^{'}(t)[/tex] - -32t+800

(b) Now, to find the time it will attain maximum height,

[tex]s^{'}(t)[/tex] = 0

-32t = -800

t = 25 seconds

(c) The maximum height it will reach

= [tex]-16*(25)^{2} + 800*25+600[/tex]

= -10000+20000+600

= 10,600 feet

(d) Between what two times (in seconds, to the nearest tenth) will it be more than 5000 ft above the ground

By putting x = 3

[tex]P(3) = 4*(3)^{3}-50 * (3)^{2}-8*3+6[/tex]

= 108-90-24+6

= 114-114

= 0

Therefore x = 3 is a zero of P(x)

(e) How long to the nearest tenth of a second will the projectile be in the air

Now, factoring,

[tex]f(x) = x^{3}+3x^{2} -13x-15\\ \\= x^{3}+x^{2} +2x^{2}+2x-15x-15\\ \\ = (x+1)(x^{2} +5x-3x-15)\\\\= (x+1)(x(x+5)-3(x+5))\\\\=(x+1)(x-3)(x+5)[/tex]

Hence the answer is a) 0 height, b) 25 seconds c) 10,600 feet d) 3 times e) (x+1)(x-3)(x+5)

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Answer:

40 questions

Step-by-step explanation:

100-85=15

15/100=6/x

cross multiply

15x=100(6)

15x=600

x=40

there were 40 questions on the test

hopes this helps please mark brainliest

After f(x) = 2x translated up 5 units, then it reflect in x-axis is g(x) = f(2x)+5.

What does a graphing translation mean?

The rules for transforming a function f(x) into g(x):

g(x) = a·f(b(x-c)) + d

Hence, After f(x) = 2x translated up 5 units, then it reflect in x-axis is g(x) = f(2x) + 5.

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A six sided dice is tossed twice. The probability of getting either a 1 or a 2 on your first toss and a 1 or a 2 on your second toss is 1/9 .

A dice has six faces or sides and it is throws twice . When a dice is toss first time,

Total possible outcomes on toss = 6 ={ 1,2,3,4,5,6}

In our first toss we want to get 1 or 2

So, favourable outcomes of getting 1 or 2 = 2

Probability of getting 1 or 2 on first toss= favourable cases /total outcomes = 2/6 = 1/3

For second toss, we want to get a1 or a2 again.

Total possible outcomes = 6

Probability of getting a1 or a2 on second toss= 2/6= 1/3

Now, Multiply these probsbilites togethers and chance of getting 1 or 2 on first and second which is 1/3× 1/3 = 1/9

Hence , probability of getting either a 1 or a 2 on your first toss and a 1 or a 2 on your second toss is 1/9.

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The equation for the proportional relationship is y = 65x

The animal shelter wants to track its profit for each animal that is

adopted.

The cost of each animal adoption = $65

Consider the number of animal adoption = x

Consider the total profit from animal adoption = y

From the given the details, we can say that the profit from the animal adoption is directly proportional to the number of animal adoption,

Then the relationship will be

y ∝ x

y = kx

Here the cost of each animal adoption is k = 65

Then the equation will be

y = 65x

Hence, the equation for the proportional relationship is y = 65x

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Check the picture below.

The 8 cm² area on a map  represent the actual area = 3200000000 cm² .

Scale factor of a map

S = 1/20000

The scale factor for area is found by squaring the scale factor for length. Thus the scale factor for area is S^2

When applied to the area we consider  S^2 as a scale factor.

The area on the map = 8 cm²

So The actual area = 8 × (20000)^2 = 8× 20000×20000

=3200000000 cm²  = 320000 m² =32 hectare.

So the 8 cm² area on a map  represent the actual area = 3200000000 cm² .

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Answer:y=8x-5

Step-by-step explanation:

you put the problem into slope intercept form y minus y one equals the slope the parentheses x minus x one then use the distributor property so then it’s y=

This is the required final answer  Emily spends $300y/x  and Andy spends $432y/x for wire.

The answer provided below has been developed in a clear step-by-step manner.

1 foot =12 inches

1 yard=36 inches

Emily needs (25×12)=300 inches wire

and Andy needs (12×36)=432inches wire

As the cost for x inches wire is $y

cost for a 1-inch wire is $x/y

So, the cost for 300 inches of wire is $300y/x

cost for 432 inches of wire is $432y/x

so, Emily spends $300y/x

and Andy spends $432y/x for wire.

More than 20 different currencies go by the name dollar. The Australian dollar, Brunei dollar, Canadian dollar, Hong Kong dollar, Hogan dollar, Jamaican dollar, Liberian dollar, Namibian dollar, New Taiwan dollar, New Zealand dollar, Singapore dollar, United States dollar, Trinidad and Tobago dollar, and a number of others are among them. Like many nations that use the peso as their currency, the majority of those currencies are denoted by the dollar sign $.

The word "dollar" is a translation of the German word "thaler," which means "person or thing from the valley" in English. America's monetary unit is called after the "thaler," the name given to the first silver mine-produced coins, which were initially coined in Joachimsthal, Bohemia, in 1519.

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At point 1, the carrying capacity is both the area is around 5, and therefore it can very well be said that growth rate in Area A is at a much higher pace than that of Area B. And that can subsequently be verified from the succeding graph.

What is Carrying Capacity?

The quantity of humans, other living species, or crops that a place can support without negatively impacting the environment is termed as carrying capacity.

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Answer:

a₈ = - 1280

Step-by-step explanation:

the nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 10 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-20}{10}[/tex] = - 2 , then

a₈ = 10 [tex](-2)^{7}[/tex] = 10 × - 128 = - 1280

The 8th term of geometric sequence is -1280

Step of calculate geometric sequence

This is a geometric sequence. The geometric number sequence is characterized by the presence of a ratio (the ratio between the next term and the previous term). The next term is the product of the previous term with the ratio. Another sequence called arithmetic sequence is characterized by the presence of difference (the difference between the next term and the previous term).

10, -20, 40, ...

We will first analyze the things that can be found in the three numbers in the sequence. The thing to look for is the first term (a) and also the ratio (r). The first term can also be written as U1, where the 2nd term is U2, and the n-th term is Un.

[tex]a = 10[/tex]

[tex]r=\frac{U2}{U1}[/tex]

[tex]r=\frac{-20}{10}[/tex]

[tex]r=2[/tex]

When the first term (U1) and ratio (r) have been obtained, then we can find the 8th term by substitute it in the formula.

[tex]Un=ar^{n-1}[/tex]

With that formula, let's find the 8th term.

[tex]U8=10(-2)^{8-1}[/tex]

[tex]U8=10(-2)^{7}\\U8=10(-128)\\U8=-1280[/tex]

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Solving the inequality -6.6 < 1.7 + u for u, the solution is simplified as: u > -8.3 or -8.3 < u.

In maths, an inequality is defined as a statement that is used to compare two quantities that are unequal. For example, we can state that 5 is greater than 3 + 1, or 5x is less than 4x + 3x. We can equally state that a given value of a variable can be equal to or greater than a number, and so on.

Basically, we are comparing two unequal quantities when we state inequalities.

Given the inequality, -6.6 < 1.7 + u, we are asked to solve the inequality for u. That is, we need to find the possible value that u represents in the inequality or that would make the inequality true.

Therefore:

-6.6 < 1.7 + u

Subtract 1.7 from both sides

-6.6 - 1.7 < 1.7 + u - 1.7 [subtraction property of equality]

-8.3 < u

It can be rewritten as:

u > -8.3

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Answer:

x=−286

Step-by-step explanation:

22=(x)/(-13) just follow the order

Answer:

1. 51°

2. 55°

3. 5x + 10

Step-by-step explanation:

1. We know ∠B + 39° = 90°, so ∠B = 90 - 39 = 51

2. We can use an algebraic equation to solve this problem.

    2x + 70 = 180

    2x + 70 (-70) = 180 (-70)

    2x (/2) = 110 (/2)

    x = 55

3. ∠ABD = (3x + 10) + (2x) = 5x + 10

Answer: 3/5

Step-by-step explanation:

              Once such a triangle is chosen, the sine of the angle is equal to the length of the opposite side, divided by the length of the hypotenuse: The other trigonometric functions of the angle can be defined similarly; for example, the tangent is the ratio between the opposite and adjacent sides. As stated, the values and.

Measure of angle M is 76°, angle N is 76° and side LN is 18 in.

According to figure,

LM = 18 in

∠NLM = 28°

In triangle LMN

LN = LM

     = 18 in

Therefore, ∠LMN = ∠LNM = x     (LN = LM)

∠LMN + ∠NLM + ∠LNM = 180°

x + 28 + x = 180

   2x + 28 = 180

           2x = 180 - 28

           2x = 152

             x = 152/2

             x = 76

Hence, ∠M = ∠N = 76°.

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The total flying time for the round trip if there was no wind would be 2 hours 24 minutes. The result is obtained by using the elimination method.

The elimination method is a method for solving system of linear equations where we eliminate one variable so that we can get an equation in one variable. In doing that, we can either add or subtract the equations.

Given the case that an airplane takes 1 hour 30 minutes to fly 600 km against the wind. It takes only 1 hour in the return trip.

What would be the total flying time for the round trip if there was no wind?

Let's say:

When the airplane leaves,

v - w = 600 km / 1.5 hour

v - w = 400 kph ... (equation 1)

When the airplane returns,

v + w = 600 km / 1 hour

v + w = 600 kph ... (equation 2)

We eliminate the equation 2 and 1 to get the speed of the airplane.

v - w = 400 kph

v + w = 600 kph +

2v = 1000 kph

v = 1000 ÷ 2

v = 500 kph

For the round trip, the airplane would fly 600 × 2 = 1200 km.

The total flying time if there was no wind would be

t = s/v

t = 1200/500

t = 2.4 hour

t = 2 hours 24 minutes

Hence, the  total flying time for the round trip if there was no wind is 2 hours 24 minutes.

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Answer:

C: 9

Step-by-step explanation:

3^4/3^2

3*3*3*3/3*3 cancel out 2 threes from the bottom and top.

3*3=9