Write an equation to describe the variation. Use k for the constant of proportionality.
y varies directly as u and inversely as p^4

Answer:

This polynomial can be simplified to a difference of squares

[tex]16a^2 - 4a + 4a - 1=(4a-1)(4a+1)[/tex]

Step-by-step explanation:

Simplify the expression

[tex]16a^2 - 4a + 4a - 1\\\\16a^2- 1[/tex]

remember that 4 ^ 2 = 16

Therefore

[tex]16a^2- 1= 4^2a^2 -1[/tex]

Remember that

[tex](4a) ^ 2 = 4 ^ 2a ^ 2[/tex]

[tex]4^2a^2 -1=(4a)^2 -1[/tex]

As [tex]1 ^ 2 = 1[/tex] then

[tex](4a)^2 -1= (4a)^2 -1^2[/tex]

Remember that [tex]c ^ 2 -b ^ 2 = (c + b) (c-b)[/tex]

In this case [tex]c = 4a[/tex] and [tex]b = 1[/tex]

Finally

[tex](4a)^2 -1^2 = (4a-1)(4a+1)[/tex]

Answer:

your answer is {-2,-3}

Answer: 16/25

4/10 divided by 5/8 = ?

Dividing two fractions is the same as multiplying the first fraction by the reciprocal or inverse of the second fraction.

Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes -

4/10 x 8/5 = ?

For fraction multiplication, multiply the numerators and then multiply the denominators to get -

Numerators: 4 x 8 = 32

Denominators: 10 x 5 = 50

Fraction: 32/50

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 32 and 50. The GCF (Greatest Common Factor) would be 2.

Numerator: 32 / 2 = 16

Denominator: 50 / 2 = 25

Fraction: 16/25

4/10 divided by 5/8 = ?

Cross multiply -

Numerator x Denominator: 4 x 8 = 32

Denominator x Numerator: 10 x 5 = 50

Fraction: 32/50

Reduce by dividing both the numerator and denominator by the Greatest Common Factor, which is 2.

Numerator: 32 / 2 = 16

Denominator: 50 / 2 = 25

Fraction: 16/25

Answer:

C

Step-by-step explanation:

g(x) - f(x)

= x - 3 - (3x + 2)

= x - 3 - 3x - 2 ← collect like terms

= - 2x - 5

This is defined for all real numbers → C

In 1 pack there is 6 pencils cause you need to divide 36 by 6. In 3 packs there are 18 pencils because 6 pencils times 3 packs is 18 pencils!

Hope this helped!

Answer with step-by-step explanation:

We are given that there are 36 pencils in 6 packs and we are to find out how many pencils are there in one pack and three packs.

To find the number of pencils in one pack, we need to divide the number of pencils by the number of packs.

Number of pencils on 1 pack = 36/6 = 6 pencils

To find the number of pencils in 3 packs, we will multiply the number of pencils in one pack by 3.

Number of pencils in 3 packs = 6 * 3 = 18 pencils

Let P be a point outside the circle such that triangle LMP has legs coincident with chords MW and LK (i.e. M, W, and P are colinear, and L, K, and P are colinear). By the intersecting secants theorem,

[tex]m\angle LPM=\dfrac{m\widehat{LM}-m\widehat{WK}}2\impliesm\angle LPM=48^\circ[/tex]

The angles in any triangle add to 180 degrees in measure, and [tex]\angle MLK\congruent\angle MLP[/tex] and [tex]m\angle LMW=m\angle LMP[/tex], so that

[tex]m\angle MLK+m\angle LPM+m\angle LMP=180^\circ[/tex]

[tex]\implies\boxed{m\angle LMW=67^\circ}[/tex]

Answer: OPTION B.

Step-by-step explanation:

Given the equation [tex]48=-8(\frac{3b}{4}+2)[/tex] you can find an equivalent equation by simplifying it.

You need to remember the multiplication of signs:

[tex](-)(-)=+\\(+)(+)=+\\(+)(-)=-[/tex]

Now you can apply the Distributive property:

[tex]48=\frac{(-8)(3b)}{4}+(-8)(2)\\\\48=\frac{-24b}{4}-16[/tex]

Simplifying the equation, you get:

[tex]48=-6b-16[/tex]

You can observe that this equivalent equation matches with the equation provided in option B.

Answer:

sw=t

Step-by-step explanation:

300 times the number of weeks,equals the total income

Answer:

[tex]g(x)=0.8x+1.6[/tex]

Step-by-step explanation:

we have

[tex]-4x-6=-5y+2[/tex]

Solve for y

That means-----> isolate the variable y

Subtract both sides -2

[tex]-4x-6-2=-5y+2-2[/tex]

[tex]-4x-8=-5y[/tex]

Divide by -5 both sides

[tex](-4x-8)/(-5)=y[/tex]

Rewrite

[tex]y=(-4x-8)/(-5)[/tex]

[tex]y=\frac{4}{5}x+\frac{8}{5}[/tex]

[tex]y=0.8x+1.6[/tex]

Convert to function notation

Let

g(x)=y

[tex]g(x)=0.8x+1.6[/tex]

ANSWER

B.

[tex](f+g)(x) ={3}^{x} + 2x + 6[/tex]

EXPLANATION

The given functions are:

[tex]f(x) = {3}^{x} + 10[/tex]

and

[tex]g(x) = 2x - 4[/tex]

We want to find (f+g)(x).

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

[tex](f+g)(x) ={3}^{x} + 10 + 2x - 4[/tex]

Combine similar terms,

[tex](f+g)(x) ={3}^{x} + 2x + 10- 4[/tex]

Simplify:

[tex](f+g)(x) ={3}^{x} + 2x + 6[/tex]

The correct answer is B

The answer is B. Hope this helped

Answer:

I would say that it is all of them besides the 35% of the participants do not like to surf.

The correct statements are:

A)

The total number of students who were studied= 160

Number of boys= 105

Hence, Percentage of boys is calculated as:

[tex]Percent\ Boys=\dfrac{105}{160}\times 100\\\\i.e.\\\\Percent\ Boys=\dfrac{1050}{16}\\\\\\Percent\ Boys=65.625\\\\which\ is\ approximately\ equal\ to:\\\\Percent\ Boys=66\%[/tex]

B)

Number of students who like to surf=125

Hence,

Percent who like to surf is calculated as:

[tex]=\dfrac{125}{160}\times 100\\\\\\=\dfrac{1250}{16}\\\\=78.125\%[/tex]

C)

Number of boys=105

and number of boys who like to surf=80

Hence, the proportion of boys who like to surf is:

80/105

D)

Number of people who do not like to surf=35

Number of girls who do not like to surf=10

Hence,the proportion of girls who do not like to surf is:

              10/35

E)

Proportion of boys who like to surf=80/105=0.76190

and proportion of boys who like to surf= 45/55=0.8181

Hence, the proportion of girls who like to surf are more than those of boys who like to surf.

(  Since,   0.8181 < 0.76190 )

Answer:

aroma.

bouquet.

fragrance.

perfume.

savor

Step-by-step explanation:

Answer:

ambrosial, aromatic odoriferous, balmy, blend of floral scents

Step-by-step explanation:

brainiest please

Answer:

[tex]m=-2[/tex]

Step-by-step explanation:

we know that

The ratio of rise to run is equal to the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

[tex](-1,7)\ (4,-3)[/tex]

Substitute the values

[tex]m=\frac{-3-7}{4+1}[/tex]

[tex]m=\frac{-10}{5}=-2[/tex]

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

[tex]\text{a will automatically equal one because it is unknown}[/tex]

[tex]\text{First you have to distribute your negative sign}\downarrow[/tex]

[tex]\text{Like: 2a - 5+ (-1)(3a+1)}[/tex]

[tex]\text{We get: 2a+(-5)+(-1)(3a)+(-1)(1)}[/tex]

[tex]\text{-1(3a)= -3a}[/tex]

[tex]\text{-1(1)= -1}[/tex]

[tex]\text{Our new equation becomes: 2a + (-5) + (-3a) + -1}[/tex]

[tex]\text{After solving that COMBINE YOUR LIKE TERMS}[/tex]

[tex]\text{\underline{2a}+ -5 + \underline{-3a} + -1 }[/tex]

[tex]\text{(2a + -3a)+ (-5 + -1)}[/tex]

[tex]\text{2a + -3a = -1a}[/tex]

[tex]\text{-5 + -1 = -6}[/tex]

[tex]\text{Now we can replace -1 with the value of -a}[/tex]

[tex]\boxed{\boxed{\text{Thus, your answer is: D. -a - 6}}}}\checkmark[/tex]

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

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

I believe 5 marbles on the 6th line.

Line 1: 10

2: 10-1=9

3: 9-1=8

4; 8-1=7

5: 7-1=6

6: 6-1=5

For the pattern given, the number of marbles in the sixth line is 5.

Given that:

"Starting with 10, every consecutive line has a number one less than the previous line."

This is the pattern of the positions of the marbles.

The first line has 10 marbles.

The second line has 10 - 1 = 9 marbles.

The third line has 9 - 1 = 8 marbles.

The fourth line has 8 - 1 = 7 marbles

The fifth line has 7 - 1 = 6 marbles

The sixth line has 6 - 1 = 5 marbles.

The number of marbles in any line will be 10 - (n - 1) marbles for any nth line.

Hence the number of marbles is 5.

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Answer:

B. infinitely many solutions

Step-by-step explanation:

–2(–x + 9) = 2(x – 9)

Distribute the -2 on the left side. Distribute the 2 on the right side.

2x - 18 = 2x - 18

Add 18 to both sides.

2x = 2x

The equation means two times a number x is equal to two times the same number x. This is true for all numbers x. Every number is a solution of this equation.

Answer: B. infinitely many solutions

The answer is B.

Hope this helps :)

QUESTION 1

We want to solve the linear equation,

–12 + 3b – 1 = –5 – b

Group similar terms:

3b+b=-5+1+12

Combine similar terms,

4b=8

Divide both sides by 4

b=2.

QUESTION 2

We want to find the equation of the given line that passes through

(-3,2) and (2,-1)

The slope of this line is

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

The equation is given by the formula:

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

We plug in the known values to obtain;

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

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

[tex]5y + 5 = - 3x + 6[/tex]

[tex]3x + 5y = 1[/tex]

See attachment for solution steps and answer.

Answer:

37ft³

Step-by-step explanation:

Volume of the fish tank = length × width × height = 5ft × 3ft × 3ft = 45ft³

Volume of the cubic stone = length × length × length = (2ft)³ = 8ft³

Volume of the water = volume of the fish tank - volume of the cubic stone

i.e Volume of the water = 45ft³ - 8ft³ = 37ft³

Answer:

A

Step-by-step explanation:

This one is best done by doing a pre factor.

140 = 14 * 10 Now all you need do is factor those two numbers.

140 = 7*2 * 5 * 2

Rearranging this you get 2 * 2 * 5 *7

A

Final answer:

The prime factorization of 140 is found by dividing it by the prime numbers 2, 2, 5, and 7 in sequence, resulting in 2 x 2 x 5 x 7, which corresponds to option A.

Explanation:

The prime factorization of a number is the expression of the number as a product of its prime factors. To find the prime factorization of 140, we can use a factor tree or continuously divide by prime numbers. Beginning with the smallest prime number, 2, we divide 140 by 2 to get 70. Then, we divide 70 by 2 again to get 35. After that, we divide 35 by its smallest prime factor, which is 5, to get 7. Since 7 is already a prime number, we have completed the factorization. So, the prime factorization of 140 is:

2 x 2 x 5 x 7

Therefore, the correct answer is A.2 x 2 x 5 x 7.

Answer:64

Step-by-step explanation:

The graph of the inequality equation 3y-5x>-6 will have a dotted line and shaded left wards (Option D).

How to graph the inequality equation?

The graph of the inequality equation given is sketched by simplifying the equation as shown below;

The given inequality equation;

3y - 5x > - 6

3y > 5x - 6

y > 5x/3 - 2

when x = 0, the value of y becomes;

3y - 5x > - 6

3y - 0 > - 6

y > - 2

when y = 0, the value of x is calculated as;

3y - 5x > - 6

0 - 5x > - 6

x < 6/5

The graph of the inequality equation 3y - 5x > - 6 is shown in the image attached.

i do not speak spanish

Answer:

you can see the solution in the photo i have uploaded

Answer:

Step-by-step explanation:

If all we need to do is to evaluate this expression, a calculator is one way to go.

Here's what I'd type in for the first expression:

(2*4^(2/3))^1/3 = 1.7145

... and for the second expression:

128^(1/3) = 5.0397

Therefore, the first expression, divided by the second, is 0.3402.

Answer:

[tex] a = \frac { \sqrt { 5 } } { 1 5 } ,\:a = -\frac {\sqrt{5}}{15}[/tex]

Step-by-step explanation:

We are given the following expression which are to solve for a and give the answer in radical form:

[tex]\frac{2}{3a^2} =30[/tex]

To solve this, we will multiply both the sides by [tex]3a^2[/tex] to get:

[tex]\frac{2}{3a^2}\cdot \:3a^2=30\cdot \:3a^2[/tex]

Simplify it to get:

[tex]2=90a^2[/tex]

[tex] a = \frac { \sqrt { 5 } } { 1 5 } ,\:a = -\frac {\sqrt{5}}{15}[/tex]

Answer: A; Linear, Strong

Step-by-step explanation: A linear scatterplot is normally when most of the dots on the scatterplot board are quite close to each other in a line. When it is strong it when most of the dots seem to form an actual line.

I hope this info helps!

A scatterplot categorized as "A: Linear, Strong" indicates a distinct and well-defined linear relationship, with closely clustered data points along the trend line, highlighting a robust association between the variables.

The correct answer is option A.

The scatterplot's visual characteristics provide insights into the nature of the relationship between two variables. In this case, when the answer is categorized as "A: Linear, Strong," it implies that the scatterplot predominantly exhibits a linear trend, suggesting a consistent and directional association between the variables. In a linear scatterplot, most data points align closely along a straight line, indicating a systematic relationship.

The term "strong" further emphasizes the degree of correlation or association between the variables. A strong linear scatterplot implies that the points are tightly clustered around the line, indicating a robust and noticeable relationship. The strength of the association is a reflection of how well the data points conform to the linear pattern, emphasizing the reliability of the trend observed.

In summary, when a scatterplot is described as "A: Linear, Strong," it signifies a clear and well-defined linear relationship between the variables, with data points forming a closely packed arrangement along the trend line.

Answer:

21

Step-by-step explanation:

207-18=189..then divide by 9

The problem involves subtracting Sara's remaining money from her initial amount to find the total spent on books, then dividing by the number of books, giving us that each book cost 21 dollars.

This is a basic algebra problem where we need to find the cost of each book. Sara initially has 207 dollars and after buying 9 books, she has 18 dollars left. Therefore, we can calculate the total spent on books by subtracting the final amount from the initial.

The calculation is: 207 dollars - 18 dollars = 189 dollars.

Now, to find the cost of each book, divide the total spent by the number of books. So, 189 dollars divided by 9 books results in 21 dollars per book.

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Answer:

I dont have idea what I need to the to help you

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Mean is the Average of all the observations.

Here there are 10 observations.

And The total sum of these observations is: 1+2+2+3+3+4+7+7+7+9=45

So mean = Total sum/ Total no: of observations

-> Mean =45/10= 4.5

Hope it helps...

Regards;

Leukonov/Olegion.

Answer:

To find the area of a rectangle multiply its height by its width. For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area.

The area of a square is length times width:

Area = length x width

^^^This is the same for a rectangle too

The only difference is that the length of all the sides of a square are equal to each other, so to find the area of a square you are essentially multiplying on side with it self

Look at the example below

Hope this helped!!!