[tex]10 ^{k - 2} = 100[/tex]
find the value of k​

Answer: x

Step-by-step explanation:

    For this equation, the variable y is dependent on the value of x. The value of y changes depending on the value of x. This means that x is the independent variable for this equation.

Answer:

The diver's position in feet (depth) when she swims with dolphins is -83 feet.

Step-by-step explanation:

First highlight the important information from the question.

A diver sits on a boat at the surface of the ocean preparing to dive. She dives in and descends to -128 feet. After a few minutes, she ascends 45 feet to swim with a pod of dolphins that has appeared. What integer represents the diver's position in feet (depth) when she swims with the dolphins?

So, first she descends -128 feet, then she ascends 45 feet to swim with dolphins. So, now that we have the important information highlighted we can solve the problem.

-128+45=-83.

The diver's position in feet (depth) when she swims with dolphins is -83 feet.

Hope this helps!

If not, I am sorry.

The range of the function given the domain x > -2 is; Range; y < -8.

The range of a function is the set of all possible outcomes of the function. In this scenario, since the domain of the function is given as X > -2. It follows from the function that at all times, the range of the function is given by; y < -8 from; y < 5(-2) +2; y< -8.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: E.\:\: \overline{DC}[/tex]

or

[tex]\qquad \tt \rightarrow \: F.\:\:\overline{CD}[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

A line with two dots at ends (two ends) represents a line segment.

And it can be represented as :

[tex]\qquad \tt \rightarrow \: \overline{DC}[/tex]

or

[tex]\qquad \tt \rightarrow \: \overline{CD}[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Using an exponential function, it is found that the substance is 7,535 years old.

The function is given by:

[tex]A(t) = A(0)e^{-kt}[/tex]

In which:

Carbon-14 has a half life of 5700 years, that is, A(5700) = 0.5A(0), hence we use this to find k.

[tex]A(t) = A(0)e^{-kt}[/tex]

[tex]0.5A(0) = A(0)e^{-5700k}[/tex]

[tex]e^{-5700k} = 0.5[/tex]

[tex]\ln{e^{-5700k}} = \ln{0.5}[/tex]

[tex]k = -\frac{\ln{0.5}}{5700}[/tex]

k = 0.00012160476

Hence:

[tex]A(t) = A(0)e^{-0.00012160476t}[/tex]

It was 40% of the amount when A(t) = 0.4A(0), hence we solve for t.

[tex]A(t) = A(0)e^{-0.00012160476t}[/tex]

[tex]0.4A(0) = A(0)e^{-0.00012160476t}[/tex]

[tex]\ln{e^{-0.00012160476t}} = \ln{0.4}[/tex]

[tex]t = -\frac{\ln{0.4}}{0.00012160476}[/tex]

t = 7535.

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Answer:

4 is my answer:))))) maybe this will help

Answer:

1

Step-by-step explanation:

it depends on how many choices there are

If there is 1 choice for an appetizer, 1 choice for an entrée, and 1 choice for a dessert

(1 * 1 * 1 = 1)

then there is 1 meal choice

If there are 7 choices of appetizers, 12 choices of entrée, and 6 choices of dessert.

(7 * 12 * 6 = 504)

then there are 504 different options

If there are 5 choices for an appetizer, 12 choices for an entrée, and 3 choices for a dessert

(5 * 12 * 3 = 180)

then there are 180 options

12 choices for entrées, 10 choices for side dishes, and 6 choices for dessert

(12 * 10 * 6 = 3240)

then there are 3240 meal options

you have to multiply the number of entrées (e), meals (m), and desserts (d)

e * m * d = x

you are solving for x, which is the different meals available aka your answer.

so plug in the numbers and that should give you the answer!

hope this helps:)

Answer:

432 mm²

Step-by-step explanation:

We need to cut out 3x3 squares from corners and make an open box. It's height will be 3mm(see the plan). So volume will be:
V = 12 * 12 * 3 = 432mm²

The cost of 1 liter for the small and medium cans is 4.4 and 2.4.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

As,  

Small can: A 200 ml can costs £0.88.

Medium can: A 500 ml can costs £1.32.

Large can: A 1 litre can costs £3.60.

Now, 200 ml = 0.2 l

500 ml = 0.5 l

For 0.2 l = 0.88

For 1 l= 0.88/0.2

For 1 liter = 4.4

For 0.5l medium can = 1.32

For 1 l medium can= 1.32/0.5

For 1 l medium can = 2.4

Hence, cost of 1 liter for the small can is £ 0.88 the cost of 1 liter for the medium can is £ 2.4.

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It has been proved that point A is equidistant from the sides of angle PQR.

Any line or point that divides an angle or a side in equal parts is called a Bisector.

It is given that

Point A is the bisector of Angle PQR

Referring to the image

1. QA is the bisector of angle PQR : Given

2.Angle PQA = Angle RQA : Definition of Bisector

3.Angle QXA = Angle QYA : Definitions of Perpendicular

4. Angle QXA = Angle QYA : All right angles are congruent.

5. QA ≅QA :  Reflexive Property of Congruence

6. ΔPQA ≅ΔRQA : AAS Congruence Postulate

7. AX ≅AY  Corresponding parts of Congruent Triangles

8. Point A is equidistant from the sides of Angle PQR : Definition of equidistant.

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Answer:

The Father is currently 47 and the Son is 7

Step-by-step explanation:

Let F and S be the present ages of Father and Son, respectively.

We are told that (F-2) = 9(S-2) [2 years ago, father age was nine times the son age]

We also learn that (F+3) = 5(S+3)  [3 years later it will be 5 times only]

Take the first expression and isolate one of the variables (S or F).  I'll isolate F:

(F-2) = 9(S-2)

F = 9S - 16

Now use this in the second expression:

(F+3) = 5(S+3)

((9S-16)+3) = 5(S+3)

9S-13 = 5S+15

4S = 28

S = 7

Since F = 9S-16,

F = 9*(7)-16

F = 47

Father is 47 and Son is 7

CHECK:

Was the father 9 times the age of his son 2 years ago?

Father would have been 45 and son 5.  Yes, 9*5 = 45

In 3 years will he be 5 times older than his son?  Yes, Father would be 50 and son would be 10.  5*(10) = 50

Answer:

x=46

Step-by-step explanation:

4(x+1)-3x=50

first you gotta take care of the () so multiple by 4

(4x+4) -3x=50

combine like terms, subtract 4-3 to get 1 so you have 1x left

4 + x = 50

and then solve for x

x=46

( i checked it to make sure it was right so dw)

Answer:

1/16 is the answers for the question

Step-by-step explanation:

please mark me as brainlest

Answer:

Step-by-step explanation:

Answer:

96Km

Step-by-step explanation:

l wrote 90/60 because the speed is given in hours.

so I had to deal with hours only not hours and minutes.

that's why I wrote 90/60 .

you can also choose to divide.

I mean to change the minutes to hours so that the formula can work.

good day.

Answer:

48

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

edge 2023

Answer:

A = 80g B = 200g

Step-by-step explanation for A:

First, you would find what the serving size is divided by to get the number of people needed to feed 6/3 = 2. Then take that number (3) and divided it by the fish (240g) to get 240/3 = 80.

Step-by-step explanation for B:

You will first need to find how much butter goes into ONE pie by dividing 80 by 6 which is 1.33333333333333. Then do 1.333333333333333 times the number of people to feed (15) to get 200.

Answer: 4 blue chips (brochure), 6 yellow chips (news article), and 10 red chips (computer presentation).

Step-by-step explanation: If you have 20 colored chips, then 20% of the people that chose the brochure will be 20% of 20 of the chips. That is 20 * 0.2 = 4. Now, to find how to model the people who chose the news article, it will be 30% of the 20 chips. That is 20 * 0.3 = 6. Thus, 6 chips can be modeled for the news articles. Lastly, we add 6 + 4 and that is 10. The rest is another ten out of the 20. Thus, we can use 10 red chips to model the computer presentation.

The teacher should use 4 blue chips for the making a brochure option, 6 yellow chips for the writing a news article option, and 10 red chips for the designing a computer presentation option.

A division is a process of splitting a specific amount into equal parts.

To model this situation using colored chips, we can use the following approach:

Divide the total number of chips (20) into five equal parts, each representing 20% of the total number of students.

For the making a brochure option, use four blue chips to represent the 20% of students who choose this option.

For the writing a news article option, use six yellow chips to represent the 30% of students who choose this option.

For the designing a computer presentation option, use ten red chips to represent the remaining 50% of students who choose this option.

So, the teacher should use 4 blue chips for the making a brochure option, 6 yellow chips for the writing a news article option, and 10 red chips for the designing a computer presentation option.

Hence,  the teacher should use 4 blue chips for the making a brochure option, 6 yellow chips for the writing a news article option, and 10 red chips for the designing a computer presentation option.

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Answer:

B. Never

Step-by-step explanation:

that's just what my math teacher told us...

Answer:

x = 72

y = 15

Step-by-step explanation:

m and n are parallel lines so we can write the following equation:

108 + x = 180 because these angles are supplementary

if we subtract 108 from both sides

x = 72 we can also write the following equation:

5y - 3 = x because these are alternate angles

5y - 3 = 72 add 3 to both sides

5y = 75 divide both sides by 5

y = 15

Answer:

[tex]\large \boxed{\sf 3x\sqrt[3]{y^5}}[/tex]

Explanation:

[tex]\rightarrow \dfrac{\sqrt[3]{\sf 189x^5y^7}}{\sqrt[3]{\sf 7x^2y^2}}[/tex]

[tex]\rightarrow \sf \sqrt[3]{\dfrac{\sf 189x^5y^7}{\sf 7x^2y^2}}[/tex]

[tex]\rightarrow \sqrt[3]{\sf 27x^3y^5}[/tex]

[tex]\rightarrow \sqrt[3]{\sf 27} \sqrt[3]{\sf {x^3} }\sqrt[3]{\sf y^5}}[/tex]

[tex]\rightarrow \sf 3x\sqrt[3]{y^5}[/tex]

A fourth of a third of two fifths is a thirtieth.

(1 x 1 x 2) / (4 x 3 x 5) = 2 / 60 = 1 / 30

A thirtieth of a number () is fifteen, the number is four hundred and fifty.

= 15 / (1 / 30) = 15 x 30 = 450

forty percent of four hundred and fifty is one hundred and eighty.

(450 / 100) x 40 = 180

Answer:

The number is 450

Step-by-step explanation:

One fourth is 1/4,

One third is 1/3

and two fifths is 2/5

let the number be x.

So,

One fourth of one third of two fifths of x is 15.

that is,

1/4 * 1/3 * 2/5 * x = 15

2/4*3*5* x = 15

2/60 * x = 15

1/30 * x = 15

1 * x = 15*30

x = 450

Therefore the number is 450

Answer:

A key turning point in American politics was the election of 1980. It indicated the new electoral power of the suburbs. The success that Reagan had as a conservative would initiate a group of parties because liberals and conservatives would either leave politics or change party affiliations through the 1980s and 1990s. The research shows this caused the 1980 election to be recalled as one of America's best historical events.

Step-by-step explanation:

The League of Women Voters is pleased to welcome President Jimmy Carter, the Democratic Party's candidate for re-election to the Presidency, and Governor Ronald Reagan of California, the Republican Party's candidate for the Presidency. The candidates will debate questions on domestic, economic, foreign policy, and national security issues.

In the debate between sitting president Jimmy Carter and Republican challenger Ronald Reagan, Reagan's arguments and explanations best match the available evidence. Carter claims his policies had reduced the inflation rate by 10% in less than a year and points to the 9 million jobs he had provided to reduce unemployment rates. Reagan refutes this by mentioning that while Carter may have decreased the inflation rate from the beginning of the year, the inflation rate increased from 4.4% at the start of his presidency to almost 12% now. A graph provided by Ed Genuity proves this to be true, therefore current evidence supports Reagan's claim.

In the final week of the 1980 presidential campaign between Democratic President Jimmy Carter and Republican nominee Ronald Reagan, the two candidates held their only debate. And then, during the debate, Reagan posed what has become one of the most important campaign questions of all time: “Are you better off today than you were four years ago?” Carter’s answer was a resounding “NO,” and in the final, crucial days of the campaign, his numbers tanked.

On Election Day, Reagan won a huge popular vote and electoral victory. The “better off” question has been with us ever since. Its simple common sense makes it a great way to think about elections. And yet the answers are rarely simple.

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D. √48 =√16*3 = 4√3

Simplify the radical by breaking the radicand up into a product of known factors.

16*3 = 48

this means that √48 = √16*3, but this can be simplified.

√16 = 4, √3 = √3 because it cannot be simplified farther

making the most simplified answer 4√3

it is 3 numbers all together and they are 25, 36 and 49.

Answer:

tan theta - cot theta

Step-by-step explanation:

sin/cos = tan

cos/sin = cot

Step-by-step explanation:

[tex] = { ({1}^{3} )}^{4} [/tex]

[tex] = {1}^{3 \times 4} [/tex]

[tex] = {1}^{12} [/tex]

[tex] = 1[/tex]

The height of the tree will be 18.35 feet.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Matt is trying to measure the height of a tree using trigonometry.

He is having trouble because of the terrain around the tree.

The horizontal distance from the tree to Matt's eyes is 120 feet.

The angle of depression from the horizontal is 30°.

Matt's angle of sight to the top of the tree is 23°.

The diagram is given below.

Let x be the height of tree and AM be h.

The value of (h + x) will be

tan 30° = (x + h) / 120

   x + h = 69.288

Then the value of h will be

tan 23° = h / 120

        h = 50.94 feet

Then the height of the tree will be

⇒ h + x – h

⇒ 69.29 - 50.94.

⇒ 18.35 feet

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The equation given is matched with the respective vertex forms.

The standard equation for a circle is given by

(x-h)² + (y-k)² = r²

The equation given in the question are

x² + y²  − 4x + 12y − 20 = 0

(x − 6)²  + (y − 4)²  = 56

x²  + y²  + 6x − 8y − 10 = 0

(x − 2)²  + (y + 6)²  = 60

3x²  + 3y²  + 12x + 18y − 15 = 0

(x + 2)²  + (y + 3)²  = 18

5x²  + 5y²  − 10x + 20y − 30 = 0

(x+3)²  + (y-4)²  = 35

2x²  + 2y²  − 24x − 16y − 8 = 0

(x-1)²  + (y+2)²   = 11

The first equation is

x² + y²  − 4x + 12y − 20 = 0

It can be written ad

x² -4x + 4 - 4 +y²+12y +36-36 -20 = 0

(x-2)² +(y+6)²= 60

The second equation is

x²  + y²  + 6x − 8y − 10 = 0

x² +6x +9-9 +y²  -8y +16-16 -10 = 0

(x+3)²  + (y-4)²  = 35

The third equation is

3x²  + 3y²  + 12x + 18y − 15 = 0

(x + 2)²  + (y + 3)²  = 18

The fourth equation is

5x²  + 5y²  − 10x + 20y − 30 = 0

(x-1)²  + (y+2)²   = 11

The fifth equation is

2x²  + 2y²  − 24x − 16y − 8 = 0

(x − 6)²  + (y − 4)²  = 56

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Answer: y = (x - 1) (7x + 5)

Step-by-step explanation:

y = 7x² - 2x - 5     Use the slip and slide method.

y = x² - 2x - 35    Factor

y = (x - 7) (x + 5)  Slide 7 back in, divide -7 by 7 to get -1. Slip 7 into (x + 5).

y = (x - 1) (7x + 5)

The factorized form of the quadratic equation is  y = (7x+5)(x - 1).

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

To factor the quadratic function, we need to find two binomials whose product is equal to the given quadratic. Here's one way to factor y = 7x² - 2x - 5:

First, we need to find two numbers whose product is 7(-5) = -35 and whose sum is -2. These numbers are -7 and 5, since (-7)(5) = -35 and (-7) + 5 = -2.

Next, we use these two numbers to split the middle term of the quadratic:

y = 7x² - 7x + 5x - 5

Notice that we have a common factor of 7x in the first two terms and a common factor of 5 in the last two terms. We can factor these out to get:

y = 7x(x - 1) + 5(x - 1)

Now, we have a common factor of (x - 1), which we can factor out to get the factored form:

y = (7x + 5)(x - 1)

Therefore, the correct answer is: y = (7x+5)(x - 1).

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Answer:

  (b)  3 terms, degree 10

Step-by-step explanation:

When simplifying polynomials, the first thing you look at is the exponents of the variables in each term. (The terms are separated by + or - signs.) Only terms with the same set of exponents can be combined.

When considering the degree of the polynomial, you look at the sum of exponents of the variables in each term. That sum is the degree of the term. The degree of the polynomial is the highest of the degrees of the terms.

__

The four terms have variables s and t. If we write the exponents of those variables as an ordered pair, we will have one ordered pair for each term:

  5s⁶t²  ⇒  (exponent of s, exponent of t) ⇒ (6, 2); degree = 6+2 = 8

  6st⁹  ⇒  (1, 9); degree = 1+9 = 10

  -8s⁶t²  ⇒  (6, 2); degree 6+2 = 8 (this is a like term to the first term)

  -6t⁷  ⇒  (0, 7); degree 0+7 = 7

The degrees are 8, 10, 8, 7, so the highest degree is 10. This is the degree of the polynomial.

__

We can only combine the terms containing s⁶t². Doing that gives ...

  (5 -8)s⁶t² +6st⁹ -6t⁷ = -3s⁶t² +6st⁹ -6t⁷ . . . . . three terms

In "standard form", the terms are written in order of decreasing degree:

  6st⁹ -3s⁶t² -6t⁷ . . . . . . 3 terms, degree 10