Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.

Answer:

[tex]f(x) = 7x + 30[/tex]

Step-by-step explanation:

We need at least two points to write the equation of a straight line.

The recursive formula that Elijah wrote is:

[tex]f(0) = 30[/tex]

[tex]f(n + 1) = f(n) + 7[/tex]

When we substitute n=0, we get:

[tex]f(0 + 1) = f(0) + 7[/tex]

[tex]f(1) = 30 + 7[/tex]

[tex]f(1) = 37[/tex]

The points (0,30) and (1,37) lies on this line.

The equation of this line is of the form:

[tex]f(x) = mx + b[/tex]

where b =30 is the y-intercept and m=7 is the slope.

We plug in these values to get:

[tex]f(x) = 7x + 30[/tex]

Note that the slope of the line is equal to the common difference of the Arithmetic Sequence.

You could also use the two points to find the slope:

[tex]m = \frac{37 - 30}{1 - 0} = 7[/tex]

Answer:

[tex]-6y^2+5y+2[/tex]

Step-by-step explanation:

I'm assuming you want to simplify:

[tex]3y^2+5y-(4y^2+5)-8y^2-(-7-3y^2)[/tex]

Distribute to get rid of the ( ):

[tex]3y^2+5y-4y^2-5-8y^2+7+3y^2[/tex]

Put like terms together:

[tex]3y^2-4y^2-8y^2+3y^2+5y-5+7[/tex]

Combine the like terms:

[tex]-6y^2+5y+2[/tex]

Answer:

4 19/32

Step-by-step explanation:

convert into improper fractions

6 1/8= 49/8

1 x 3/4= 3/4

49/8 x 3/4 = 147/32

reduce into mixed number

4 19/32

To convert the mixed numbers 6 1/8 and 1 3/4 to improper fractions, resulting in 49/8 and 7/4, respectively. Then, perform the division as multiplication with the reciprocal of the second fraction, which yields 3 1/2.

Firstly, it's essential to convert the mixed numbers into improper fractions. The given mixed numbers are 6 1/8 and 1 3/4. We can convert 6 1/8 to an improper fraction by multiplying 6 (the whole number) by 8 (the denominator) and then adding 1 (the numerator) to get 49/8. With 1 3/4, we multiply 1 (the whole number) by 4 (the denominator), then add 3 (the numerator), which gives us 7/4.

Now, the division 49/8 ÷ 7/4 can be performed. To divide fractions, we multiply the first fraction by the reciprocal of the second. Therefore, we will multiply 49/8 by 4/7. The result is 196/56. This simplifies to 3 1/2 when converted back to a mixed number.

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Answer:

it is not possible that Brayden made it back to his starting point.

Step-by-step explanation:

Part 1: Step 1: Define the map scale

REAL:MAP

1 km : 1 cm

5 km : 5 cm

14 km : 14 cm

8 km : 8 cm

Step 2: Sketch the map according to the scale.

Shown on the map in the picture attached.

Part 2: As shown on the map, it is not possible that Brayden made it back to his starting point.

!!

Answer: 3 losses

Step-by-step explanation: The win to loss ratio is 4:1. Their losses are 1/4 of their wins. Multiply 12, their number of wins, by 1/4.

12 x 1/4 = 3

They have lost 3 games.

Given the ratio of 4:3:1 for wins, ties, and losses, and the information that the team has won 12 games, you calculate that '1 part' of the ratio equals 3 games by dividing 12 by 4. As losses are represented by '1 part' in the ratio, the team has lost 3 games.

In this baseball team scenario, the ratio of wins to ties to losses is 4:3:1 respectively. You know that the team has won 12 games. In a ratio, every part represents something equivalent, so we need to find what '1 part' is. Since '4 parts' represents 12 wins, you divide 12 by 4 to get '1 part', which is 3 games. Therefore, since losses represent '1 part' of your ratio, the team has lost 3 games.

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Answer:

They must mix

_44_ pounds of the Organic Free Trade Blend

_36__ pounds of the Rift Valley Blend.

Round your answers to the nearest whole number of pounds.

Step-by-step explanation:

The formula you are using is:

Total price * total amount= Organic price * amount organic + Rift price * amount rift

First we will simplify it by calculating it for each pound of final mix.

So this is 10.82 * 1 = 8.30 * x + 13.90 * y.

Since the total amount should be 1 pound, you could say that x+y = 1, or that y = 1-x.

If you fill this in you get

10.82 * 1 = 8.30 * x + 13.90 * (1-x)

Which you can solve as follows.

10.82 * 1 = 8.30 * x + 13.90 - 13.90x

10.82 = 13.90 - 5.6x

-5.6x = -3.08

x = -3.08/-5.6 = 0.55

So you will need 0.55 of Organic coffee for each pound of the final mix.

So in total you will need 0.55 * 80 = 44 pounds of Organic coffee.

So you need 80 - 44 = 36 pounds of Rift Valley Coffee.

To produce the desired coffee blend, the coffee distributor needs to mix approximately 51 pounds of Organic Free Trade Blend with 29 pounds of Rift Valley Blend.

This problem falls under a category of Mathematics known as Algebra. We'll start by defining two variables: x, representing the weight of the Organic Free Trade Blend, and y, representing the weight of the Rift Valley Blend.

From the total weight of the mix, we get our first equation: x + y = 80

Then, by weighing the cost of each part against the total, we get our second equation: 8.3x + 13.9y = 10.82 * 80.

Solving these two equations simultaneously, we find that approximately 51 pounds of Organic Free Trade and 29 pounds of Rift Valley blend are needed to create the desired mixture.

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[tex]\bf \underset{\textit{\Large 18 + 8 = 26 units}}{\stackrel{\textit{18 units}}{\boxed{-18}\rule[0.35em]{10em}{0.25pt}}0\stackrel{\textit{8 units}}{\rule[0.35em]{5em}{0.25pt}\boxed{8}}}[/tex]

Answer:

Step-by-step explanation:

The ruler Postulate:

the distance between number A and number B

AB = |B - A|

We have A = -18 and B = 8. Substitute:

|8 - (-18)| = |8 + 18| = |26| = 26

Step-by-step explanation:

[tex]\dfrac{a^m}{a^n}=a^{m-n}\to\dfrac{h^\frac{3}{2}}{h^\frac{4}{3}}=h^{\frac{3}{2}-\frac{4}{3}}=h^{\frac{(3)(3)}{(2)(3)}-\frac{(2)(4)}{(2)(3)}}=h^{\frac{9}{6}-\frac{8}{6}}=h^{\frac{1}{6}}\\\\(a^m)^n=a^{mn}\to\bigg(p^\frac{1}{4}\bigg)^\frac{2}{3}=p^{\left(\frac{1}{4}\right)\left(\frac{2}{3}\right)}=p^\frac{2}{12}=p^\frac{1}{6}\\\\a^m\cdot a^n=a^{m+n}\to z^\frac{3}{4}\times z^\frac{5}{6}=z^{\frac{3}{4}+\frac{5}{6}}=z^{\frac{(3)(3)}{(4)(3)}+\frac{(5)(2)}{(6)(2)}}=z^{\frac{9}{12}+\frac{10}{12}}=z^\frac{19}{12}[/tex]

[tex]\left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\to\bigg(\dfrac{x^2}{y}\bigg)^\frac{1}{3}=\dfrac{\left(x^2\right)^\frac{1}{3}}{y^\frac{1}{3}}=\dfrac{x^{(2)\left(\frac{1}{3}\right)}}{y^\frac{1}{3}}=\dfrac{x^\frac{2}{3}}{y^\frac{1}{3}}[/tex]

When simplifying exponential expressions, the first property to use depends on the specific operation being performed, such as squaring, dividing, or cubing. By utilizing the appropriate property, you can simplify the expression more efficiently.

When simplifying an expression involving exponents, the first property to use depends on the specific operation being performed. Here are the properties:

By applying these properties in the appropriate situations, you can simplify exponential expressions efficiently.

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Answer:

y=-3(x-1)^2+5

Step-by-step explanation:

The vertex form of a parabola is y=a(x-h)^2+k where (h,k) is the vertex.

We are given the vertex (h,k) is (1,5) so that makes the equation we have

y=a(x-1)^2+5.

We still need to find a.

We do have the point (0,2) on our parabola.

So replace (x,y) with (0,2) and solve for a.

2=a(0-1)^2+5

2=a(-1)^2+5

2=a(1)+5

2=a+5

-3=a

So the equation is

y=-3(x-1)^2+5

Answer:

-2

Step-by-step explanation:

[tex]\sqrt{16+9}-(\sqrt{16}+\sqrt{9})[/tex]

We are going to use PE(MD)(AS) to evaluate.

We are going to do the operations in the grouping symbol.

A grouping symbol is anything that operations grouped together in it like that first square root.

[tex]\sqrt{25}-(\sqrt{16}+\sqrt{9})[/tex]

We can also perform the operation inside the other grouping symbols ().

But it has addition and square roots. The square roots come first then the addition.

Now the square roots can be kind of though as exponents and actually you could think of something like [tex]\sqrt{9}[/tex] as [tex]9^{\frac{1}{2}}[/tex].

Anyways, this gives us:

[tex]\sqrt{25}-(4+3)[/tex]  

Now the addition inside the ( ):

[tex]\sqrt{25}-(7)[/tex]

Now we have square root and subtract left.  The square root part will come first and then the subtract:

[tex]5-7[/tex]

[tex]-2[/tex]

Answer:

The value of k is -11.

Step-by-step explanation:

Given equation is 3√(x-k)-2=10

Step 1: Since the value of x = 5, we will substitute value of x in the given equation.

3√(5-k)-2=10

=> 3√(5-k) = 10 + 2

=> 3√(5-k) = 12

Step 2: Dividing both sides by 3

3√(5-k)/3 = 12/3

√(5-k) = 4

Step 3 : Squaring both sides

√(5-k)^2 = 4^2

(5-k) = 16

Step 4 : Separating the value of

=> 5-16 = k

=> -11 = k

=> k = -11

Therefore, the value of k is -11.

!!

Answer:

the correct answer is -11

Step-by-step explanation:

Answer:

A.

5 ^ (5/6)

Step-by-step explanation:

5 ^ (1/2)  * 5 ^ (1/3)

We know that a^b * a^ c = a ^ (b+c)

5 ^ (1/2 + 1/3)

5^ (3/6+2/6)

5^ (5/6)

Answer:

5^(5/6)

Step-by-step explanation:

5^(1/2)*5^(1/3)=5^(1/2+1/3)=5^(5/6)

When multiplying numbers with same base you add the exponents.

[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (\stackrel{x}{-6},\stackrel{y}{5})~~ \begin{cases} x=-6\\ y=5 \end{cases}\implies 5=k(-6)\implies \cfrac{5}{-6}=k~\hfill \boxed{y=-\cfrac{5}{6}x}[/tex]

Answer:

m = 200

Step-by-step explanation:

30 m = 6000 Divide both sides by 30

30 m / 30 = 6000 / 30

m = 200

Hello!

Answer:

Out of all the options, the following apply: B. Equilateral, D. Isosceles, and F. Acute.

Explanation:

An equilateral triangle is one where all sides and angles are equal. All three angles are the same in this triangle, so it is equilateral.

An isosceles triangle is one where at least 2 sides are equal. In this triangle, all three sides are equal, so it's isosceles.

An acute triangle is one where there are 3 angles that are less than 90 degrees. All angles are 60 degrees, so it is acute.

Have a fabulous day! :)

Answer:

25.9

Step-by-step explanation:

12+7x−(1−3) (evaluate parentheses first)

= 12+ 7x - (-2)

= 12+ 7x + 2

= 14+ 7x

When x = 1.7, equation becomes

14+ 7(1.7)

= 14 + 11.9

= 25.9

Answer:

Step-by-step explanation:

f(x) = x3 - 6x2 + 8x

     = x(x²- 6x+8)

f(x) = x (x-2)(x-4)

Answer:

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

Step-by-step explanation:

The point-slope equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the graph we have the points: (0, 3) and (2, -5). Substitute:

[tex]m=\dfrac{-5-3}{2-0}=\dfrac{-8}{2}=-4[/tex]

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

Answer:

640

Step-by-step explanation:

The maximum force required to stretch the spring that distance is 640N. This is calculated by dividing the work done (8J) by the distance (0.025m) to find the force, and then doubling this figure because the maximum force is needed at maximum extension of the spring.

In this question, we are asked to find the maximum force required to stretch a spring by a certain amount. The work done on an object, in this case, the spring, is equal to the force applied times the distance over which the force is applied. This is expressed in the formula Work = Force x Distance. We are given that the work done is 8 Joules and the distance is 2.5 cm (or 0.025 m, converting centimeters to meters).

So, to find the force, we re-arrange the formula to be Force = Work/Distance. Plugging in the given values, we find Force = 8J/0.025m = 320N. However, the maximum force required to stretch it that distance happens at the maximum extension of the spring, so we have to double that force (because for a spring, force is linear with displacement until it reaches maximum extension). Hence, the maximum force is 2 x 320N = 640N, thus making the correct option the second one.

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Answer:

[tex]1000(.95)^h[/tex]

Step-by-step explanation:

[tex]h(t)=A \cdot B^t[/tex] is an exponential equation where A is the beginning amount and B is the rate that the population grows or dies.

So we start with 1000 bacteria, they are giving us A.

The bacteria population is decreasing because they are dying 5% each hour.

So that is after the first hour we have 1000-.05(1000) or 1000(1)-1000(.05)=1000(1-.05)=1000(.95).

We will keep multiplying by .95 per hour. 0.95 is the repeated factor.

That is the function is [tex]1000(.95)^h[/tex].

If you let h=0 which means 0 hours has happened, you will see the bacteria is 1000 as desired. 1000(.95)^0=1000(1)=1000.

The bacteria population can be determined using the formula (ℎ)=1,000·0.95^ℎ, which represents exponential decay at a rate of 5% each hour. therefore, option D is correct

To determine the bacteria population after a number of hours, we need to use the formula (ℎ)=1,000·0.95^ℎ. This formula represents the exponential decay of the bacteria population at a rate of 5% per hour. The initial population is 1,000, and each hour the population decreases by 5% (or 0.95).

For example, after 1 hour, the population can be calculated as (1,000)·(0.95)^1 = 950 bacteria. After 2 hours, the population would be (1,000)·(0.95)^2 = 902.5 bacteria, and so on.

Therefore, the correct answer is (d) (ℎ)=1,000·0.95^ℎ.

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Answer:

[tex]\large\boxed{-mn+10m+5n}[/tex]

Step-by-step explanation:

[tex](14mn - 12m +7n)-(15mn - 22m +2n)\\\\=14mn-12m+7n-15mn-(-22m)-2n\\\\=14mn-12m+7n-15mn+22m-2n\qquad\text{combine like terms}\\\\=(14mn-15mn)+(-12m+22m)+(7n-2n)\\\\=-mn+10m+5n[/tex]

A (x=y)

By vertical angles, the angle opposite y is equal to y, and x = y because it would transform isometrically onto x (as can be seen by the parallel lines because the transversal can be treated as parallel to itself)

Answer: vertical angles are congruent.

Step-by-step explanation:

Answer: Vertical angles are congruent.

Step-by-step explanation:

Given : Line A and line Bare parallel.

To prove : ∠1≅∠2

We know that when two lines crosses each other, they make vertically opposite angles.

In picture , we have ∠2 and ∠3 are vertical angles.

And it is known that the vertical angles are congruent.

Therefore, ∠2 ≅ ∠3

So the correct reason to the statement "∠2 ≅ ∠3" is "Vertical angles are congruent."

The equation 15x-5+x=-47 simplifies to x=-2.625.

The student has provided the equation 15x - 5 + x = -47 and is looking to simplify it. To simplify this equation, we can combine like terms by adding 15x and x together, resulting in 16x - 5 = -47. The next step is to isolate the variable x by adding 5 to both sides of the equation, which gives us 16x = -42. Finally, we divide both sides by 16 to solve for x: x = -42 / 16.

It seems that there might be confusion with the typos and irrelevant parts in the question; the solution presented does not result in x = 3 or x = -7, as suggested by the incorrect context provided. The proper solution using the equation given leads to x = -42 / 16, which simplifies to x = -2.625. This is the correct solution for the presented equation.

As a check, we can substitute the value of x back into the original equation and confirm that the left side equals the right side, thus verifying our solution.

Answer:

f (x) = (x+5) is linear

Step-by-step explanation:

We are given the following function and we are to determine if it is a linear function or not:

[tex] f ( x ) = ( x + 5 ) [/tex]

For a function to be linear, it must be written in the standard form [tex]y=mx+c[/tex] and its graph gives a straight line.

Whereas, when an equation is squared, its graph becomes a curved one which is not linear.

Therefore, the given function f (x) = (x+5) is linear.

Answer: Yes, it is a linear function.

Step-by-step explanation:

The linear function in Slope-Intercept form is:

[tex]f(x)=mx+b[/tex]

Where m is the slope and b the y-intercept.

In this case, given the following function:

 [tex]f(x)=(x+5)[/tex]

You can observe that it has the form  [tex]f(x)=mx+b[/tex]

You can identify that:

[tex]m=1\\b=5[/tex]

Therefore, you can conclude that it is a linear function.

[tex]\bf \left( y^{\frac{4}{3}}xy^{\frac{2}{3}} \right)^{-\frac{1}{2}}\implies \left( y^{\frac{4}{3}}y^{\frac{2}{3}}x \right)^{-\frac{1}{2}}\implies \left( y^{\frac{4}{3}+\frac{2}{3}}x \right)^{-\frac{1}{2}}\implies \left( y^{\frac{6}{3}}x \right)^{-\frac{1}{2}} \\\\\\ (y^2x^1)^{-\frac{1}{2}}\implies \left( y^{-\frac{1}{2}\cdot 2}x^{-\frac{1}{2}\cdot 1} \right)\implies y^{-1}x^{-\frac{1}{2}}\implies \cfrac{1}{y}\cdot \cfrac{1}{x^{\frac{1}{2}}}\implies \cfrac{1}{y\sqrt{x}}[/tex]

Step-by-step explanation:

[tex]\text{Use}\\\\a^n\cdot a^m=a^{n+m}\\\\(a^n)^m=a^{nm}\\\\a^{-1}=\dfrac{1}{a}\\============================\\\\\bigg(y^\frac{4}{3}\cdot y^\frac{2}{3}\bigg)^{-\frac{1}{2}}=\bigg(y^{\frac{4}{3}+\frac{2}{3}}\bigg)^{-\frac{1}{2}}=\bigg(y^{\frac{4+2}{3}}\bigg)^{-\frac{1}{2}}\\\\=\bigg(y^{\frac{6}{3}}\bigg)^{-\frac{1}{2}}=\bigg(y^2\bigg)^{-\frac{1}{2}}=y^{(2)\left(-\frac{1}{2}\right)}=y^{-1}=\dfrac{1}{y}[/tex]

Step-by-step explanation:

First, use a z-score table or calculator to find the z-score that corresponds to the percentile.  Using a calculator, z = -1.3408 is the bottom 9%, and z = 1.3408 is the top 9%.

Now calculate the length that corresponds to these z scores.

z = (x − μ) / σ

-1.3408 = (x − 6.02) / 0.05

x = 5.95

1.3408 = (x − 6.02) / 0.05

x = 6.09

So the bottom 9% and the top 9% are between 5.95 cm and 6.09 cm.

To separate the top and bottom 9% of nail lengths, we can use the z-score formula. The top 9% length is approximately 6.088 cm and the bottom 9% length is approximately 5.952 cm.

To find the lengths that separate the top and bottom 9%, we can use the z-score formula. The z-score is calculated by subtracting the mean from the data value and dividing it by the standard deviation. For the top 9%, we need to find the z-score that corresponds to an area of 0.91. Now calculate the length that corresponds to these z scores.

z = (x − μ) / σ

-1.3408 = (x − 6.02) / 0.05

x = 5.95

1.3408 = (x − 6.02) / 0.05

x = 6.09

So the bottom 9% and the top 9% are between 5.95 cm and 6.09 cm.

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Answer:

Step-by-step explanation:

Add all 8/20 marbles multiply Times 5 40/100 = 40%

Answer =40%

The price for 200 items is $40,000.

Calculation:-

The whole batch cost $28,000

Number of items=140

Cost of one items= $28000/140

∴cost of 200 items= 200*200  

                                ⇒$40000

Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.

Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.

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