Find constant proprotionality

Answer:

         [tex]\large\boxed{\large\boxed{8.06units}}[/tex]

Explanation:

The figure is a right triangle with:

Hence, you must use Pythagora's theorem, which is valid for all right triangles:

             [tex]hypotenuse^2=(leg_1)^2+(leg_2)^2[/tex]

Substituting the data:

        [tex]hypotenuse^2=(7unit)^2+(4unit)^2=49unit^2+16unit^2=65unit^2[/tex]

Square root both sides:

         [tex]hypotenuse=\sqrt{65unit^2}=8.06unit[/tex]

Answer:

8.06

Step-by-step explanation:

Answer:

0.35

Step-by-step explanation:

a randomly chosen person's chance of being an athlete is 100%, or 1.00

Therefore: if the probability of a randomly chosen athlete is a swimmer is 0.65 or 65%, The probability of a randomly chosen athlete to NOT be a swimmer is:

1.00 - 0.65 = 0.35 or 35%

Final answer:

The probability that a randomly chosen athlete is not a swimmer is 0.35, calculated by subtracting the probability of being a swimmer (0.65) from 1.

Explanation:

If the probability that a randomly chosen athlete is a swimmer is 0.65, this means that there is a 65% chance of selecting a swimmer from a group of athletes. Since the total probability for any event is always equal to 1 (or 100%), we subtract the swimmer probability from 1 to find the probability that an athlete is not a swimmer.

To calculate: 1 - 0.65 = 0.35. Therefore, the probability that a randomly chosen athlete is not a swimmer is 0.35, or 35%.

The polynomial 4x5 – 16x2 + 13x8, when rearranged in standard form by ordering the terms in descending degree, becomes 13x8 + 4x5 – 16x2.

The question asks to express the given polynomial 4x5 – 16x2 + 13x8 in standard form. In mathematics, a polynomial is generally expressed in standard form when its terms are written in decreasing order by degree.

Here, the degrees from highest to lowest of the terms in our polynomial are 8, 5, and 2. So the polynomial in standard form would be: 13x8 + 4x5 – 16x2

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Answer:

The answer is x = 8.

Step-by-step explanation:

LCD is the least common denominator of fractions. LCD represents the smallest number that can be used as a common denominator for a particular set of fractions.

The given equation is [tex]\frac{5}{2x} + \frac{1}{4} = \frac{9}{2x}[/tex]

Here we can take LCD as 4x because 4x is divisible by 2x as [tex]\frac{4x}{2x} = 2[/tex],  4x is divisible by 4 as [tex]\frac{4x}{4} = 1[/tex]

therefore we can write

[tex]\frac{5}{2x} + \frac{1}{4} = \frac{9}{2x} \hspace{0.2cm} \Rightarrow \hspace{0.2cm} \frac{10}{4x} + \frac{x}{4x} = \frac{18}{4x} \hspace{0.2cm} \Rightarrow \hspace{0.2cm} \frac{x + 10}{4x} = \frac{18}{4x}[/tex]

now we can eliminate the LCD from both sides of the equation and we get

x + 10 = 18    [tex]\therefore[/tex]      x  = 18 - 10       [tex]\therefore[/tex]    x = 8.

well, we know the tree is growing at a rate of 36 feet every 3 years, how many feet is that in 1 year alone?   well, simply 36/3 = 12.

so the tree is growing 12 feet per year.

when it was first planted, it was 5 feet tall, and then after every year, we have to add 12 feet subsequently, let's do that

year 1 .......... 5 + 12(1)

year 2 .......... 5 + 12(2)

year 3 .......... 5 + 12(3)

year 4 .......... 5 + 12(4)

year 5 .......... 5 + 12(5)

year 6 .......... 5 + 12(6)

year 7 .......... 5 + 12(7)

year y .......... 5 + 12(y)

[tex]\bf \stackrel{\textit{height}}{h}~~=~~\stackrel{\textit{initial height}}{5}~~+~~\stackrel{\textit{yearly rate}}{12y} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{tree is now}}{77} = 5 + 12y\implies 72=12y\implies \cfrac{72}{12}=y\implies \boxed{6=y}[/tex]

Answer:

-1.25

Step-by-step explanation:

The slope of the line that passes through the points (-10, -4) and (10, -29) is calculated using the formula for slope and simplifying the resulting expression to yield a slope of -1.25.

In mathematics, the slope of a line that passes through two points (x1, y1) and (x2, y2) can be calculated using the formula: slope = (y2 - y1) / (x2 - x1). So, let's input the coordinates of our two points into this formula:

slope = (-29 - (-4)) / (10 - (-10))

This simplifies to: slope = (-29 + 4) / (10 + 10)

So we end up with: slope = -25 / 20

Finally, simplifying further gives us: slope = -1.25

Therefore, the slope of the line that passes through the points (-10, -4) and (10, -29) is -1.25.

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The surface area of the box if it is scaled up by a factor of 10 is 10425 square inches

Solution:

Given that, surface area of a box is 104.25 square inches

The area of a scaled object will be equal to the scale factor squared multiplied by area of original box

If the scale factor is three, the area of the new object will be nine times, or three squared, the area of the original object.

Therefore, by above definition,

Let "z" be the scale factor

x =  the surface area of the scaled box

y = the surface area of the original box

Here,

z = 10

y = 104.25

Then we get,

[tex]x = z^2 \times y\\\\x = 10^2 \times 104.25\\\\x = 100 \times 104.25\\\\x = 10425[/tex]

Thus the surface area of the box if it is scaled up by a factor of 10 is 10425 square inches

Final answer:

To find the total number of seats in the stadium section, we determine there are 14 rows and 10 seats per row, resulting in a total of 140 seats.

Explanation:

To determine the total number of seats in this section of the basketball stadium, we'll first find out how many rows and columns are present, based on the provided information. Kyleigh is seated in the 7th row from the back and the 8th row from the front of the section. This implies that there are a total of 14 rows (7+8-1 because the row Kyleigh is seated in counts for both the front and the back).

Similarly, Kyleigh's seat is the 4th row from the right and 7th from the left. This means there are a total of 10 seats in each row (4+7-1, as Kyleigh's seat counts for both the right and the left).

To find the total number of seats in this section, we multiply the number of rows by the number of seats per row: 14 rows × 10 seats per row = 140 seats.

Answer:

20 km

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

We can disregard the length of the line from the Library and the House, as Davina does not use that path at all.

We know that 1 unit on the grid represents 1 km. We define the lengths of the route from the graph:

Davina's House to School = 4 units = 4 km

School to Library = 6 units = 6 km

The entire trip Davina takes from House to Library would be 4 km + 6 km = 10 km total.

We also know that Davina takes the same route back from the Library to House. It would be the same exact route and length. Therefore:

2(10 km) = 20 km total

Answer:19.200

Step-by-step explanation:

19.200x1=19.200

Answer:

6.71

Step-by-step explanation:

From Pythagoras theorem, we know that;

x^2 = 6^2 + 3^2

x^2 = 36 + 9

x^2 = 45

x = sqrt(45)

x = 6.71

Answer:

12.56 units

Step-by-step explanation:

C=pid

C = 3.14(4)

C = 12.56

[tex]\text{Hey there!}[/tex]

[tex]{\bf{Which\ expression\ is\ equivalent\ to \ 9^5?}[/tex]

[tex]\bf{Note: 9^5=59,049}[/tex]

[tex]\bf{Well, \ it\ is\ telling\ us\ that\ 9\ is\ expanded/expressed\ 5\ times}[/tex]

[tex]\bf{It\ CAN'T\ be\ option\ A. \ because\ 9\times 5\ because\ it\ equals \ 45}\\\\\bf{It\ CAN'T\ be\ option\ B.\ because\ the\ question\ is\ NOT\ asking\ 5^9}\\\\\bf{It\ CAN\ be\ option\ C.\ because\ it\ expressed\ the\ equation\ out }\\\\\bf{It\ CAN'T\ be\ Option\ D.\ because\ that\ equals\ 4,613,203,125\ and\ that\ is\ way\ too}\\\bf{big}[/tex]

[tex]\boxed{\boxed{\bf{Your \ answer:C. 9\times9\times9\times9\times9}}}\checkark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Final answer:

None of the given expressions are equivalent to g^5, as they all include the number 9. For a proper understanding, g^5 means multiplying g by itself five times (g x g x g x g x g). In exponentiation, such as (10²)³, exponents are multiplied to get the result (10&sup6;).

Explanation:

The expression g^5 represents g multiplied by itself 5 times. Looking at the given options, it is clear that none of them are equivalent to g^5 since they all involve the number 9, not the variable g. However, to understand the concept, if you were to express g^5 in a long form similar to the options, it would be g x g x g x g x g.

When discussing raising a number to an exponent, such as in (10²)³, you multiply the exponents, resulting in 10&sup6;. This comes from the law of exponents, which tells us that (a²)³ = a²×³. In this case, you would multiply 2 and 3 to get 6 as the new exponent for a.

This concept also applies to expressions inside parentheses raised to a power, affecting everything inside the parentheses. In the case of (27x³)(4x²), each term within the parentheses must be raised to the indicated power.

Answer:

$0.01455

Step-by-step explanation:

(2.25 in^3)/(2304 in^3) = 0.0009765625

2.25 is 0.0009765625 part of 2304. Therefore, 2.25 in^3 is worth 0.0009765625 of $14.90

0.0009765625 * $14.90 = $0.01455

Answer:

- 1

Step-by-step explanation:

m = (y-y') / (x - x')

m = (6 - 8) / (4 - 2) = -2 / 2 = - 1

Answer:

slope = -1

Step-by-step explanation:

Final answer:

The probability that all 3 marbles rolled out are white is found by calculating the combinations of drawing 3 white from 6 white marbles over the total combinations of drawing 3 marbles from all 20 marbles, resulting in an answer of 1/57.

Explanation:

The student asks about the probability that all 3 marbles rolled out are white given the total numbers of red, white, and blue marbles in the bag. To find this probability, you apply the principles of combinatorics to calculate the likelihood of drawing 3 white marbles one after another without replacement from a set of 12 red, 6 white, and 2 blue marbles.

To solve this, you first determine the total number of ways 3 marbles could be drawn from the bag, which would be combinations of 20 marbles taken 3 at a time, noted as C(20,3). Then calculate the combinations of 6 white marbles taken 3 at a time, C(6,3). The probability is the ratio of these two combinations, so:

Probability = White marble combinations / Total possible combinations = 20 / 1140 = 1 / 57

The correct answer is B. 1/57.

Answer:

4c < 28

divide by 4 both sides

x < 7

x = -0.6y + 5.6 is the answer

Answer:

False

Step-by-step explanation:

The angle above 111 degrees must be 69 degrees because of supplementary angles (111+69=180)

And since the triangles are congruent, angle 2 must be 69 degrees as well.

Hope this helped.

Answer:

I'm assuming you're learning how to simplify and solve algebraic expressions. This is a word problem? In any case, in 6+t=20 you're trying to isolate the variable, t. It makes more sense to subtract 6 from both sides of the equation. On the left side, subtracting 6-6 = 0, leaving us with t, and if we subtract 6 from 20 (remember you have to do the same thing on both sides), you get 14. Therefore, t = 14.

I'm trying to make of it what the word problem is trying to say. You could subtract 20 from both sides, but it's not going to leave you with an isolated variable, and then you'll get negative numbers involved unnecessarily. Colins reasoning (if it means that he came up with that equation simply based on Marge's "subtracting 20 from both sides of the equation to solve it), doesn't make sense to me at all. I would say his reasoning does not make sense, because of all I explained above. I hope that helps even just a little. I feel like something else is missing from the question.

Step-by-step explanation:

Final answer:

Colin's reasoning about subtracting 20 from both sides of the equation 6+t=20 is incorrect because it does not logically solve for 't'. The correct method is to subtract 6 from both sides to isolate 't', leading to the solution t=14.

Explanation:

Colin's reasoning does not make sense because if Marge subtracted 20 from both sides of the equation 6+t=20, she would have been solving the equation improperly. When solving for 't', you would want to isolate the variable on one side, which means subtracting or adding the opposite of whatever value is with 't'. If we start with Colin's proposed equation:

And we subtract 6 from both sides to isolate 't', we get:

Which simplifies to:

Therefore, subtracting 20 from both sides wouldn't make sense in this context since that operation would not help to solve for 't' in the equation 6+t=20.

Measures of angles are X = 102° and Y = 78°

Step-by-step explanation:

⇒ 24 + Y + Y = 180

⇒ 2Y = 180 - 24 = 156

⇒ Y = 156/2 = 78°

⇒ X = 24 + Y = 24 + 78 = 102°

Answer:

The effect of doubling all the dimensions of a triangular pyramid will have on the volume of the pyramid is to increase it by 8 times.

Step-by-step explanation:

i) volume of triangular pyramid  = [tex]\frac{1}{3}[/tex] [tex]\times[/tex] Area [tex]\times[/tex] height

     = [tex]\frac{1}{3}[/tex] [tex]\times[/tex] (Base of triangle [tex]\times[/tex] perpendicular height of triangle) [tex]\times[/tex] height

ii) if we double all the dimensions then the three variables((Base of triangle, perpendicular height of triangle, height of pyramid) will be doubled

  and the volume of the new pyramid will be 8 times that of the original one.

The answer is 34.

Because you do 90-56=34

x=34

Answer:

x= 34

Step-by-step explanation:

Answer:

A value that satisfies this equation is called a root, zero or solution of the equation!! We have three ... Solve each by factoring. 1) x2 + 4x -5 = 0 ... Follow the explanation and sample problem to review completing the square.

Step-by-step explanation:

x^2 - 4x = 80

x^2 - 4x + 4 = 80 + 4 (Divide b, which is 4, by 2 and square it.)

x^2 - 4x + 4 = 84

sqrt(x + 2)^2 = sqrt(84)

x + 2 = plus or minus sqrt(84)

Subtract 2 from both sides

x = -2 plus or minus sqrt(84)

Answer:

I think that the answer is c

To solve the system of equations, subtract one equation from another to eliminate a variable, then substitute back to find the values of x, y, and z. The correct solution is (x = 0, y = 1, z = 0).

To solve this system of equations, we can use various methods such as substitution, elimination, or matrices. Let's solve it using elimination:

Given the system of equations:

1. ( 4x + 3y + 6z = 3 )

2. ( 5x + 5y + 6z = 5 )

3. ( 6x + 3y + 6z = 3 )

We'll eliminate one variable at a time. Let's start by eliminating ( z ):

From equations 1 and 3, we see that (4x + 3y + 6z) and (6x + 3y + 6z) have the same coefficients for ( z ) but different constants. Subtracting equation 3 from equation 1, we get:

[ (4x + 3y + 6z) - (6x + 3y + 6z) = 3 - 3 ]

[ 4x - 6x = 3 - 3 ]

[ -2x = 0 ]

[ x = 0 ]

Now, substitute ( x = 0 ) into one of the original equations. Let's use equation 1:

[ 4(0) + 3y + 6z = 3 ]

[ 3y + 6z = 3 ]

[ 3y = 3 - 6z ]

[ y = 1 - 2z ]

Now, we have expressions for ( x ) and ( y ). Let's substitute ( x = 0 ) and ( y = 1 - 2z ) into equation 2:

[ 5(0) + 5(1 - 2z) + 6z = 5 ]

[ 5 - 10z + 6z = 5 ]

[ -4z = 0 ]

[ z = 0 ]

So, we found ( x = 0 ), ( y = 1 - 2z = 1 - 2(0) = 1 ), and ( z = 0 ).

Therefore, the solution to the system of equations is ( (x = 0, y = 1, z = 0) ), which corresponds to option c.

Answer: incomplete question

Complete question:A group sold 150 flowers and trees. They sold the flowers for $3.00 each and the trees for $2.00 each. They made $300.00 from this sale.

Which equation will help to determine the number of flowers and the number of trees sold?

A. 2F + 3T = 150

B. F + T = 300

C. 3F + 2T = 300

D. F + T = 150 + 300

Answer: C. 3F + 2T = 300

Step-by-step explanation:

Let F stand for flower and T for trees

Flowers sold for $3 and trees sold for $2

Therefore, F + T = 150. . .1

3F + 2T = $300. . .2

Equation 2 would help determine the cost of selling tree.

3F+2T=$300