Two numbers have a difference of 28. What is the sum of their squares if it is a minimum?

ANSWER

[tex]GCF=5x {y}^{2}

[/tex]

[tex]5x {y}^{2} (4+ 2y + 3{x}^2 )[/tex]

EXPLANATION

The given expression is

[tex]20x {y}^{2} + 10x {y}^{3} + 15 {x}^{3} {y}^{2} [/tex]

This can be rewritten as:

[tex] {2}^{2} \times 5x {y}^{2} + 2 \times 5x {y}^{3} + 3 \times 5{x}^{3} {y}^{2} [/tex]

The greatest common factor is the product of the least powers of the factors common to all the terms;

[tex]GCF=5x {y}^{2}

[/tex]

We factor to obtain;

[tex]5x {y}^{2} (4+ 2y + 3{x}^2 )[/tex]

Jade can buy a maximum of 6 magazines or 2 pies with her $24 weekly budget. The slope of her budget constraint is -2, representing the trade-off between pies and magazines. The opportunity cost of purchasing a pie is 3 magazines.

Jade has a weekly budget of $24, which she allocates between magazines and pies. Let's address the questions one by one:

if you mean 60 × 2 it will be 120

Answer:

12

Step-by-step explanation:

just use google or a calculater or a phone

Answer:

n= -0.7

Step-by-step explanation:

so first subtract 1.8 from 3.2 and then divide by -2

-2n = 1.4

n = -0.7

hope this helps!!

formula for area of circle is

[tex]\pi {r}^{2} [/tex]

the diameter is 2 times the radius.

so if diameter is 11 then radius is 5.5

so then the answer will be 94.985

Answer:

Step-by-step explanation:

Answer: Option B is correct.(1, -5) lies on the graph

Answer:

(1,-5)

Step-by-step explanation:

The slope is found by the change in Y over the change in X.

Slope = (25 - -3) / (-36 - 12)

Slope = 28 / -48

Simplify:

Slope = -7/12

Answer:

[tex]\$4,081.54[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=10\ years\\ P=\$2,250\\ r=0.06\\n=4[/tex]  

substitute in the formula above  

[tex]A=\$2,250(1+\frac{0.06}{4})^{4*10}=\$4,081.54[/tex]  

Answer:

This is a vertical line, that passes through x=-2

Step-by-step explanation:

This is a vertical line, x=-2 means that no matter what value has 'y' the variable 'x' will be -2.

Watch the attached picture

Answer is 70

Angle *2 = 35*2 = 70

The measure of angle EOD, formed by arc ED at the center O, is 70 degrees, given that angle ECD on the same arc is 35 degrees.

let's break down the step-by-step calculation for finding the measure of EOD, given that ECD is 35 degrees:

Recall that for any angle formed by an arc at the center of a circle (EOD in this case), it is twice the measure of the angle formed by the same arc at any point on the circumference (ECD).

Given that ECD is 35 degrees, we will use this information to find the measure of EOD.

Apply the rule that EOD = 2 × ECD.

Substitute the value of ECD into the formula: EOD = 2 × 35.

Calculate the result: EOD = 70 degrees.

Therefore, the measure of EOD, which is the angle made by the arc ED at the center O, is 70 degrees.

To know more about angle:

https://brainly.com/question/30147425

#SPJ2

Answer:

(-5,-8)

Step-by-step explanation:

Given in the question an equation,

x² + 10x = - 17

x² + 10x + 17 = 0

here a = 1

        b = 10

        c = 17

Step 1

Find the value of x using the formula

x = -b/2a

x = -10/2

x = -5

Step 2

Find the value of y by plugging x = -5 in the equation above

(-5)² + 10(-5) + 17 = y

25 - 50 + 17 = y

y = -8

vertex (h,k) = (-5,-8)

Answer: C) y ≥ 3x - 2;  [tex]y\leq \dfrac{1}{2}x+3[/tex]

Step-by-step explanation:

Blue line:

y-intercept (b) = -2

slope (m) is 3 up, 1 right = 3

shading is above

⇒ y ≥ 3x - 2

Yellow line:

y-intercept (b) = 3

slope (m) is 1 up, 2 right = [tex]\dfrac{1}{2}[/tex]

shading is below

[tex]\implies \bold{y\leq \dfrac{1}{2}x+3}[/tex]

Answer: 0.122449

Step-by-step explanation:

If one side is 1/7, first convert that into a decimal, which is 0.14286. Than square that 0.14286 x 0.14286= 0.020408. That’s the area of one square. Now multiply that by 6 (the number of sides in a cube) and you get 0.122449.

Answer: Third option is correct.

Step-by-step explanation:

Since we have given that

6, 6, 6, 7, 8, 8, 29

We will calculate the measures of central tendency:

1) Mode - the most occurring element in the data set.

So, Mode = 6

2) Median - the middle value of organised data set

So, Median = 7

3) Mean - the average of all data set

So, Mean = [tex]\dfrac{6+6+6+7+8+8+29}{7}=\dfrac{70}{7}=10[/tex]

So, we can see that Mode and Median are giving the closest value to each other, whereas Mean is giving the farthest value as compared to rest.

Hence, Mean is the least appropriate for describing the given data set.

Thus, Third option is correct.

Answer:

Step-by-step explanation:

Sum and Difference Formula

cos( U +/- V ) = cosU*cosV -/+ sinU*sinV

cos( U - V ) = cos(70)cos(20) + sin(70)sin(20)

cos( U - V ) = cos (70 - 20)

cos( 50 ) = .642788

Answer:

y = [tex]\frac{x+4}{-2}[/tex] or [tex]\frac{-x}{2}[/tex] -2

Step-by-step explanation:

This question is asking to find the inverse of the equation therefore you will have to interchange x and y

ie : x= -2y-4

THEN solve for y ( perform opposite operation )

x = -2y -4

(take -4 to the other side ) [it will be a +4 ]

x+ 4 = -2y

NOW take -2 to the other side [ you will divide everything on the left by -2]

[tex]\frac{x+4}{-2}[/tex] ( this could be your final answer )

OR

simplify

( NOT complusory)

[tex]\frac{-x}{2} - 2[/tex]

Final answer:

To find the inverse function of f(x) = -2x - 4, switch x and y and solve for the new y to get the inverse function f¹(x) = -0.5x - 2.

Explanation:

The question asks to find the inverse function of f(x) = -2x - 4. To find the inverse, we switch the roles of x and y in the equation and solve for the new y. Here are the steps:

Write the function as y = -2x - 4.

Swap x and y to get x = -2y - 4.

Solve for y to find the inverse function. Add 4 to both sides to get x + 4 = -2y, and then divide by -2 to find y = -0.5x - 2.

Therefore, the inverse function, f⁻¹(x), is y = -0.5x - 2.

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \cfrac{(a^{-3}b^{-1}c^{-5})^{-2}}{(a^5b^4c^2)^5}\implies \stackrel{\textit{distributing the exponent}}{\cfrac{(a^6b^2c^{10})}{(a^{25}b^{20}c^{10})}}\implies \cfrac{c^{10}c^{-10}}{a^{25}a^{-6}b^{20}b^{-2}} \\\\\\ \cfrac{c^{10-10}}{a^{25-6}b^{20-2}}\implies \cfrac{c^0}{a^{19}b^{18}}\implies \cfrac{1}{a^{19}b^{18}}[/tex]

Answer:

A; The integer is 16

B; The integer has an absolute value of 16

D; The integer has an absolute value of 16

Answer:

b and d

Step-by-step explanation:

Pablo amd his mom would take Eight minutes

Final answer:

Pablo and his mom would take 3 minutes to put up the tent working together, as they combine their work rates to determine their joint effectiveness.

Explanation:

To determine how many minutes Pablo and his mom would take to put up the tent working together, we can use the concept of combined work rates. Pablo can put up a tent in 12 minutes and his mom can do it in 4 minutes. We calculate their combined work rate by adding the reciprocal of each person's time because working together means their rates add up.

Pablo's rate is 1 tent per 12 minutes, or 1/12 tents per minute. His mom's rate is 1 tent per 4 minutes, or 1/4 tents per minute. Combined, their rate is (1/12) + (1/4) tents per minute.

First, find a common denominator for the fractions, which would be 12 in this case, so we get:

(1/12) + (3/12) = 4/12

Therefore, their combined rate is 4/12 or 1/3 tents per minute. To find out how long it would take them to set up one tent, we take the reciprocal of the combined rate. Thus, 1 tent would take them 1/(1/3) minutes, or simply 3 minutes.

Working together, Pablo and his mom can put up the tent in 3 minutes.

Answer:

538-8=530

530/10=53

your answer is 53 students

Step-by-step explanation:

Answer:

3 units

Step-by-step explanation:

Answer:

I know I am a little late but the answer is 3

Step-by-step explanation:

I took the test part 1

Answer:

B

Step-by-step explanation:

15*21=315

12*15=180

180/2=90

315+90=405

Answer:

y = 2x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = 2

The line passes through the y- axis at (0, 3) ⇒ c = 3

y = 2x + 3 ← equation of line

Answer: The answer is D) 126in3

Step-by-step explanation:

When you multiply 42 and 9 you get 378, so from there you divide your answer by 3 which gets you

126in

formula for slope y2-y1 over x2-x1 so the answer should be -1.1 over -6.3

Answer:

"Mean = Mode"

Step-by-step explanation:

Let's find the mean, median, and mode of the number set.

-1, -1, 0, 1, 1, 1, 1, 2, 2, 2, 3

Mean:

this is the average. We add up all of the numbers and divide by the number of numbers (11).

Mean = [tex]\frac{-1+-1+0+1+1+1+1+2+2+2+3}{11}\\=\frac{11}{11}\\=1[/tex]

the mean is 1

Median:

this is the "middle" number when arranged from least to greatest. From 11 numbers, the 6th number is the middle one. We can see from the arrangement below, that "1" is the middle number.

the median is 1

Mode:

this is the number that occurs the "most". Looking at the numbers, "1" occurs 4 times, which is the most. So

mode is 1

From the 3 choices, the first choice is right "mean = mode".

Answer:

[tex]\large\boxed{SA=397.5\ in^2}[/tex]

Step-by-step explanation:

The formyla of an area of a triangle:

[tex]A=\dfrac{bh}{2}[/tex]

b - base

h - height

Area of a base:

[tex]B=\dfrac{(15)(13)}{2}=97.5\ in^2[/tex]

Area of one triangle of lateral area:

[tex]L=\dfrac{(15)(10)}{2}=75\ in^2[/tex]

The Surface Area:

[tex]SA=B+4L\to SA=97.5+4(75)=397.5\ in^2[/tex]

Answer:

For direct variation, use the equation y = kx, where k is the constant of proportionality. For inverse variation, use the equation y = k/x, again, with k as the constant of proportionality. These problems might use the word 'proportion' instead of 'variation,' but it means the same thing.

Step-by-step explanation:

Final answer:

Direct and inverse variation equations have distinct relationships between variables: direct variation involves both variables increasing at a constant rate, while inverse variation involves one variable decreasing as the other increases.

Explanation:

Direct variation equations and inverse variation equations are different in their structures and relationships between variables. In direct variation equations, as one variable increases, the other also increases at a constant rate, while in inverse variation equations, as one variable increases, the other decreases at a constant rate.

For example, in a direct variation equation like y = kx, as x increases, y increases at a constant rate determined by k. In contrast, in an inverse variation equation like y = k/x, as x increases, y decreases at a constant rate determined by k.

The result is 332.5 degrees.

To convert an angle from radians to degrees, we use the conversion factor that 1 radian = 180/π degrees. In this case, the angle is 133π/72 radians.

So, to convert 133π/72 radians to degrees, we multiply by the conversion factor:

(133π/72) * (180/π) degrees.

Solving this gives us the angle in degrees:

133 * 180 / 72 = 332.5 degrees.

Answer:

the answer is a

Step-by-step explanation:

5*2 is 10

10*2 is 20

20*2 is 40

5,10,20,40