The table shows ordered pairs of the function y=8 - 2x. What is the value of y when x = 8?

Answer:

\(y=1x-10\)

Step-by-step explanation:

\(y=mx+b\)

m(slope) = 1

b(y-intercept) = -10

\(y=1x-10\)

✨Hope this helps✨

30 gallons of 28% butterfat and 30 gallons of 16% butterfat should be combined to create a 60-gallon mixture that is 22 % butterfat.

Let x gallon of 28% butterfat mixed with the y gallon of 16% butterfat to obtain 60 gallons of 22.5% butterfat,

⇒ x + y = 60 ⇒ x = 60 - y ----(1),

Quantity of butterfat in x gallon + quantity of butterfat in y gallon = total quantity of butterfat,

⇒ 28% of x + 16% of y = 22% of 60

⇒ 0.28x + 0.16y = 0.22 × 60

⇒ 0.28x + 0.16y = 13.2

⇒ 28x + 16y = 1320

⇒ 14x + 8y = 660

From equation (1),

14(60-y) + 8y = 660

840 - 14y + 8y = 660

6y = 180

y = 30

Again from equation (1),

x = 60 - y

= 60 - 30

= 30

Hence, 30 gallons of 28% butterfat and 30 gallons of 16% butterfat are combined to create a 60-gallon mixture that is 22%

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Answer:

the answer is (B) 10.

Step-by-step explanation:

To find the maximum possible number of spools that can be taken from the box without having at least 2 spools of each color, we need to find the maximum number of spools that can be taken without taking 2 spools of any one color.

The worst-case scenario is if we take all but one spool of one color, leaving only one spool of that color in the box. Then we can take all the spools of the other two colors, and one more spool of the first color, without having at least 2 spools of any one color.

So the maximum possible number of spools that can be taken is:

4 (red) + 5 (white) + 1 (green) = 10

Therefore, the answer is (B) 10.

\(y^3 - 6y^2 = 0\\y^2(y-6)=0\\y^2=0 \vee y-6=0\\y=0 \vee y=6\)

Answer:

a=2 b=3 c= 180 d=180 is sns

Translate triangle JKL left 1 unit and downward 10 units; the triangles are congruent

From the question, we have the following parameters that can be used in our computation:

Triangle JKL to triangle MNO

From the figure, we can see that translating the triangle JKL left 1 unit and downward 10 units would give triangle MNO

The above also implies that the triangles are congruent

This is because translation is a rigid transformation

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Option A. The only graph that could represent the function with the zeros of -2 and 4 is the graph is : A parabola declines from (negative 3 point 1, 10) through (negative 3, 8), (negative 2, 0), (negative 1, negative 4), (1, negative) and rises through (2, negative 8), (3, negative 4), (4, 0), (5, negative 6), and (5 point 5, 10).

The zeros of a quadratic function are the x-values where the function equals zero (where it crosses the x-axis). In this case, you mentioned that the zeros of the function are -2 and 4.

Looking at the provided options:

A. This graph crosses the x-axis at (-2, 0) and (4, 0), which are indeed the zeros of the function. Therefore, this could be a possible representation of the function.

B. This graph crosses the x-axis at (-4, 0) and (2, 0). These are not the zeros given for the function (-2 and 4), so this graph is not a possible representation of the function.

C. This graph crosses the x-axis at (-4, 0), but it never crosses at x=4. Instead, it crosses at x=2. Therefore, this is not a possible representation of the function.

D. This graph crosses the x-axis at (2, 0), but does not cross the x-axis at x=-2. Therefore, this is not a possible representation of the function.

So, the only graph that could represent the function with the zeros of -2 and 4 is the graph provided in Option A.

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Answer: 4.3 meters

Step-by-step explanation:

Let the angle opposite the 3-meter side be \(\alpha\).

Using the Law of Sines,

\(\frac{\sin \alpha}{3}=\frac{\sin 25^{\circ}}{2}\\\\\sin \alpha=1.5 \sin 25^{\circ}\\\\\alpha=\arcsin(1.5 \sin 25^{\circ})\)

Using the sum of the angles in a triangle, the angle opposite the side \(\ell\) is \(155^{\circ}-\arcsin(1.5 \sin 25^{\circ})\).

Using the Law of Sines,

\(\frac{\ell}{\sin(155^{\circ}-\arcsin(1.5 \sin 25^{\circ})}=\frac{2}{\sin 25^{\circ}}\\\\\ell =\frac{2\sin(155^{\circ}-\arcsin(1.5 \sin 25^{\circ})}{\sin 25^{\circ}}\\\\\ell \approx 4.3\)

Answer:  The correct answer is 4.3

Step-by-step explanation:

This is an Obtuse Scalene Triangle

Side a = 2

Side b = 3

Side c = 4.26571

Angle ∠A = 25°

Angle ∠B = 39.34°

Angle ∠C = 115.66°

Area = 2.70415

Perimeter p = 9.26571

Semiperimeter s = 4.63285

Calculate c, ∠B, and ∠C based on given a, b, and ∠A.

∠B = arcsin(b·sin(A)/a)

= 0.68662 rad = 39.34°

∠C = 180° - A - B = 2.01864 rad = 115.66°

c = a·sin(C)/sin(A) = 4.26571 = 4.3

Answer:

0.090909

Step-by-step explanation:

I used a calculator

The length of side CB to one decimal place is 89.3.

To find the length of side CB in the given triangle, we can use the sine rule. The sine rule states that in a triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

In this case, we have the angle C as 53° and the side opposite to it, side CB, as the unknown. Let's denote the length of side CB as x.

According to the sine rule:

sin(C) / x = sin(A) / AB

We know that angle A is 37° and AB is 120 units. Plugging in the values:

sin(53°) / x = sin(37°) / 120

To find x, we can rearrange the equation:

x = (120 * sin(53°)) / sin(37°)

Calculating this expression gives us:

x ≈ 89.32

Rounding this value to one decimal place, the length of side CB is approximately 89.3.

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Answer:

\( x = \frac{\sqrt{6}}{2} \)

Step-by-step explanation:

Reference angle = 45°

Opposite side = x

Hypotenuse = √3

Use the following trigonometric ratios formula to find x:

\( sin(\theta) = \frac{opp}{hyp} \)

Plug in the values

\( sin(45) = \frac{x}{\sqrt{3}} \)

Multiply both sides by √3

\( \sqrt{3}*sin(45) = x \)

\( \sqrt{3}*\frac{\sqrt{2}}{2} = x \)

\( \frac{\sqrt{3*2}}{2} = x \)

\( \frac{\sqrt{6}}{2} = x \)

The amount deposited in an account that pays 3% and 7% of interest will be $225 and $775, respectively. Then the correct option is D.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

You have $1000 to put resources into two distinct records. To set aside the cash you really want for school, you really want to average a 6.1 percent premium. Assuming the two records pay a 3% and 7 % premium.

Let 'x' be the amount deposited in an account that pays 3% of interest. Then the amount deposited in another account that pays 7% of interest is (1000 - x). Then the equation is given as,

0.03x + 0.07(1000 - x) = 0.061 × 1000

Simplify the equation, then we have

0.03x + 0.07(1000 - x) = 0.061 × 1000

0.03x + 70 - 0.07x = 61

-0.04x + 70 = 61

0.04x = 70 - 61

0.04x = 9

x = 9 / 0.04

x = $225

Then the amount in the second account will be given as,

⇒ $1000 - $225

⇒ $775

The amount deposited in an account that pays 3% and 7% of interest will be $225 and $775, respectively. Then the correct option is D.

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Answer:

\( {(x + 5)}^{2} - {x}^{2} \\ {x }^{2} + 10x + 25 - {x}^{2} \\ 10x + 25 \\ 5(2x + 5)\)

\( \{ \: \alpha \: , \: \beta , \: a, \: b \}\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{n} \)

where, n denotes to number of elements in set .

Since, given set contains 4 elements .

Thus , 2⁴ {2 raise to power 4} .

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{4} \)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 2 \times 2 \times 2 \times 2\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 4 \times 4\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 16\)

Therefore, Required subsets are 16.

They are , Namely;

\( \sf \longrightarrow \: subsets \: = \phi \: \{ \alpha \} \{ \beta \} \{ a\} \{ b\} \: \{ \alpha \beta \} \{ \alpha a\} \{ \alpha b\} \{ \beta a\} \{ \beta b\} \: .....\)

_____________________________

If n is the number of elements in the set then,

No. of subsets possible for this subset is 2^n that's the (2 raise to the power n).

Let's take another example, {1,2}

Here, n = 2

subsets =2^2 =4

Subsets = ϕ, {1}, {2},{1,2}

Note :- every set is a subset of itself i.e. {1,2} and ϕ is a subset of every set

Answer:

m<2 = 104º

m<3 = 76º

m<4 = 104º

Step-by-step explanation:

given: m<1 = 76º

m<3 = m<1 this is because they are opposite angles which equals each other

A straight line = 180º

so m<1 + m<2 = 180 and m<3 + m<4 = 180

m<2 = 180 - m<1

m<2 = 180 - 76

m<2 = 104º

m<2 = m<4 so m<4 is also 104º

Hope this helps, Let me know if you have any questions !

m∠1 = 76°   Given.

m∠1 ≅ m∠3   Vertical Angle theorem.

m∠3 = 76° CPCTC

m∠1 + m∠2 = 180° (supplementary angles)

m∠3 + m∠2 = 180° (supplementary angles)

m∠1 & m∠3 ∴ Congruent (congruent supplements theorem)

m∠2 + m∠3 = 180° (supplementary angles)

m∠4 + m∠3 = 180° (supplementary angles)

m∠2 & m∠4 ∴ Congruent (congruent supplements theorem)

∴ IF m∠1 = 76° (Given)

THEN:

m∠2 = 104° (Supplementary angles)

m∠3 = 76° (Definition of vertical angles)

m∠4 = 104° (Supplementary angles)

Answer:

b

Step-by-step explanation:

yes

Answer:

i belive the answer is b to

Answer:

thx for giving brainliest

The combined inequality for the conditions is 2x + 3y > 7.

The mathematical expression for inequality states that neither side is equal. In mathematics, inequality occurs when the relationship results in a non-equal comparison between two expressions or numbers. Any of the inequality symbols, such as greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠).

Given inequalities,

-2x + 5 < 2 and 3y - 3 > 1

-2x + 5 < 2

subtract 2 from both sides

-2x + 5 - 2 < 2 - 2

-2x + 3 < 0

multiply by -1 to change the sign,

-1(-2x + 3) > 0

2x - 3 > 0 .......(1)

and 3y - 3 > 1

subtract 1 from both sides

3y - 3 - 1 > 1 - 1

3y - 4 > 0..........(2)

since both equations are greater than zero we can add both equations,

2x - 3 + 3y - 4 > 0

2x + 3y > 7

Hence combined equation is 2x + 3y > 7.

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The complete question is -2x + 5 < 2 and 3y - 3 > 1,

find the combined equations.

Mr. Marshal spent 1/4 of his salary on miscellaneous expenses and $1,680 on rental; therefore, he spent 1/36 of his entire salary on the trip.

To find the fraction of money spent on miscellaneous, we need to calculate the sum of the fractions spent on rental, food, and bank and subtract it from 1.

Rental: 1/5

Food: 1/10

Bank: 1/4

To find the fraction spent on miscellaneous:

Fraction spent on miscellaneous = 1 - (Rental + Food + Bank)

Rental + Food + Bank = 1/5 + 1/10 + 1/4 = (8 + 4 + 5)/40 = 17/40

Fraction spent on miscellaneous = 1 - 17/40 = 23/40

So, Mr. Marshal spent 23/40 of his salary on miscellaneous.

To find the amount spent on rental, we multiply the fraction spent on rental by his salary:

Amount spent on rental = (1/5) \(\times\) $8,400 = $1,680

Therefore, Mr. Marshal spent $1,680 on rental.

If Mr. Marshal spent 4/9 of the miscellaneous amount on a trip, we need to calculate the fraction of his entire salary spent on the trip.

Fraction spent on the trip = (4/9) \(\times\) (23/40) = 92/360 = 23/90

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Answer:

f(3)=2

Step-by-step explanation:

To find f(3), we simply need to find the ordered pair at x=3.

From the graph, we can see that the ordered pair at x=3 is (3,2).

Thus, f(3)=2.

And we're done!

How would you describe the difference between the graphs of f(x) = 2x² and g(x) = -2x²: D. g(x) is a reflection of f(x) over the x-axis.

In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y).

This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative or negative to positive.

In this context, we can reasonably infer and logically deduce that a graph of transformed function g(x) = -2x² would be created by applying a reflection over or across the x-axis to the graph of the parent function f(x) = 2x² as shown in the image attached below.

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Answer:

x=-5

Step-by-step explanation:

3(2x+1)=7x-2

6x+3=7x-2

6x-7x=-2-3

x=-5

3(2x + 1) = 7x-2

3*2x+3*1=7x-2

6x+3=7x-2

6x-7x=-3-2

-1x=-5

x=5

The transformation of f(x) to g(x) is :

From the question, we have the following parameters that can be used in our computation:

The functions f(x) and g(x)

Where, we have

f(x) = x

g(x) = 1/9x - 2

The graph of the functions f(x) and g(x) are added as an attachment

And we have the transformations to be:

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Answer:

6.2

Step-by-step explanation:

For this we use a method called Pythagoras theorem.

to find '?' we will have to use this method

\(A^{2}\) +\(B^{2}\) =\(C^{2}\)

since we don't know what A is we will name it x

\(x^{2}\)+\(5^{2}\)=\(8^{2}\)

x+25=64

64-25=39

\(x^{2}\)=39

x=\(\sqrt{39}\)

x=6.2

A probability tree is a visual representation of the possible outcomes of an event or series of events. In this case, the event takes a marble out of the bag.

The first step in building a probability tree is to create a starting point that represents the first state of the problem. In this case, the starting point is a bag containing 3 green marbles and 5 white marbles.

The next step is to branch from the starting point and show the possible results of the first event. This includes taking out  the marble out of the bag. The probability of getting a green marble is 3/8 and the probability of getting a white marble is 5/8.

After the first event, the issue status changes. In this case, the bag contains 2 green marbles and 4 white marbles.

The next step is to branch out from the state after the first event and show the possible outcomes of his second event involving pulling another marble out of his pocket. The probability of getting a green marble is 2/6 and the probability of getting a white marble is 4/6. The final step is to label the endpoints of the tree with the possible outcomes of the problem and the probabilities of each outcome.

The probability tree starts with an sack of 3 green marbles and 5 white marbles, as shown in the design showing the possible outcomes of selecting a marble, the new state of the sack after each selection, and the probability of each outcome

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a = 24

n= 10

r = 96/24 = 4

Replacing:

s = 8,388,600