A number is multiplied by 8, and that product is added to 2. The sum is equal to the product of 2 and 21. Find the number

Answer:

B

Step-by-step explanation:

Let the two numbers be a and b.

The product of the two is 120 and their sum of their squares is 289. In other words:

[tex]\displaystyle ab = 120 \text{ and } a^2 + b^2 = 289[/tex]

And we want to find the sum of the two numbers.

We can use the perfect square trinomial. Recall that:

[tex]a^2 + 2ab + b^2 = (a+b)^2[/tex]

From the first equation, multiply by two:

[tex]2ab = 240[/tex]

Add the two equations together:

[tex](a^2+b^2)+(2ab) = (289)+(240)[/tex]

Simplify and rewrite:

[tex]a^2+2ab+b^2 = 529[/tex]

Factor using the perfect square trinomial pattern:

[tex](a+b)^2 = 529[/tex]

And take the square root of both sides:

[tex]\displaystyle a + b = \pm\sqrt{529} = \pm23[/tex]

Hence, the sum of the two numbers is 23 or -23.

In conclusion, our answer is B.

Answer:

B

Step-by-step explanation:

It just is

Answer:

Step-by-step explanation:

x - first

x + 12 - second

x + (x + 12) = 44

2x=44-12

x=16

first number is 16

second number is 16+12=28

two numbers are 16 and 28

16 and 28 are the required two numbers when one number exceeds another by 12 and their sum is 44

One number exceeds another by 12 and their sum is 44

We need to find the two numbers

Two expressions with equal sign is called equation.

Let x be the first number

x + 12 be the  second number

x + (x + 12) = 44

2x=44-12

x=16

Therefore first number is 16

second number is 16+12=28

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Answer:

Which describes the relationship between the distance and the difference? The distance is always the opposite of the difference. ... The distance is the absolute value of the difference.

Answer:

18.63

Step-by-step explanation:

[tex] \frac{6}{10} = 0.6 \\ \frac{3}{100} = 0.03[/tex]

[tex]10 + 8 + 0.6 + 0.03 = 18.63[/tex]

92.000.070.108

Step-by-step explanation:

Thousand has 3 zeros, a million has 6 and a billion has 9.

So for ninety-two billion, you take 92 and add 9 zeros behind it because a billion has 9 zeros

(92.000.000.000)

Answer:

r = (-4,9]

Step-by-step explanation:

hope this will help

Answer:

-4<y≤2

Step-by-step explanation:

The range of a graph is the range of the y values.

Answer:

5/10, 1, 2/4,

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\sf x = 17}[/tex]

Step-by-step explanation:

Since m is a straight line, its measure is 180 degrees.

So,

2x + 5 + 8x + 5 = 180

2x + 8x + 5 + 5 = 180

10x + 10 = 180

10x = 180 - 10

10x = 170

Divide both sides by 10

x = 17

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

-36

Step-by-step explanation:

-7+1[3-32]

= -7-29

= -36

Answer:

[tex]f=12-\frac{t}{20}[/tex]

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

2x + (14 • 2) = 30

2x + 28 = 30

2x = 30 - 28

2x = 2

x = 2/2

x = 1

Hope this helps you. Do mark me as brainliest.

Step-by-step explanation:

3(2-x)=9

this is the answer to the statement

The expression three times the quantity two decreased by x is nine is - 1

A quantity two decreased by x can be expressed thus :

Multiplying the quantity by 3 :

The expression can be written Mathematically as thus : 3(2 - x) = 9

The expression can be expanded further as :

3(2 - x) = 9

6 - 3x = 9

Collect like terms

-3x = 9 - 6

-3x = 3

x = (3 ÷ -3)

x = - 1

Therefore, the expression equates to - 1

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Answer:

-7/19

Step-by-step explanation:

First simplify the fractions. 18/-57= -6/19.

-6/19x7/6=-42/114

-42/114=-7/19

I hope this helps! I also put it into an online calculator to make sure it is right and it is!

Answer:

is this u want?

Step-by-step explanation:

if no so sorry..

Answer:

join me on no comments yet the story is about to the turf and a bagane and pinni geting step by step explanation friendship is not working properly and the story of a y I have a mantra and sister about your self and the story of the story is a bagane unda and the story and the portion of the story of the story of the story is about the event of a y you know if

Try this option:

only periodical functions have many zeros, that is why y=sinx and y=cosx are the correct answer.

The functions y = x and y = x³ have infinitely many zeros. These functions pass through the origin and have a unique property that allows them to intersect the x-axis an infinite number of times.

The two functions with infinitely many zeros from the given list of twelve basic functions are y = x and y = x³

The function y = x has infinitely many zeros because any value of x that equals zero will result in y also being zero.

In other words, for every x value of 0, the corresponding y value is also 0.

This makes the function pass through the origin (0, 0) and have an infinite number of zeros.

2. The function y = x³ also has infinitely many zeros because the cube of any real number is zero if and only if the number itself is zero.

This means that for every x value of 0, the corresponding y value is also 0. Hence, the function y = x³ passes through the origin (0, 0) and has an infinite number of zeros.

In summary, the functions y = x and y = x³ have infinitely many zeros. These functions pass through the origin and have a unique property that allows them to intersect the x-axis an infinite number of times.

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Here we want to see which type of set is a band's setlist.

We will see that it is a discrete set.

We can define two types of sets

Continue sets are those, like the name implies, continuous (or dense). Examples can be the set of real numbers.

Discrete sets are those that have "gaps" between consecutive elements. For example, the integer set is a discrete set. Particularly, discrete sets can be quantized (counted).

Now, we have a list of songs, that can be written as:

L  = {song 1, song 2, song 3, ...}

Here we can see that we have separated elements. Thus, this is a discrete set. This happens because we clearly can separate the element "song 1" from "song 2" (there may be a lapse of time between them, defining the end of the first one), so we have the "gaps" mentioned above.

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We need to find the equation which is equidistant to the given points.

[tex]A(-2,6,3)[/tex] and [tex]B(5,3,-3)[/tex]

This can be done using the distance formula.

Let us take a point [tex]P(x,y,z)[/tex] which is equidistant from both points so

[tex]\sqrt{(x+2)^2+(y-6)^2+(z-3)^2}=\sqrt{(x-5)^2+(y-3)^2+(z+3)^2}\\\Rightarrow y^2-12y+x^2+4x+z^2+49-6z=y^2-6y+x^2+z^2+6z+43-10x\\\Rightarrow 7x-3y-2z+1=0[/tex]

The required equation is [tex]7x-3y-2z+1=0[/tex]

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Answer:

One pound of jelly beans costs $3.75.

One pound of trail mix costs $1.75.

Step-by-step explanation:

Let [tex]x[/tex] be equal to one pound of jelly beans.

Let [tex]y[/tex] be equal to one pound of trail mix.

1) Form equations

We're given:

7 pounds of jelly beans + 9 pounds of trail mix = $42

⇒ [tex]7x+9y=42[/tex]

5 pounds of jelly beans + 3 pounds of trail mix = $24

⇒ [tex]5x+3y=24[/tex]

Now, we have our two equations:

[tex]\displaystyle\left \{ {{7x+9y=42} \atop {5x+3y=24}} \right.[/tex]

2) Solve for x using elimination

[tex]\displaystyle\left \{ {{7x+9y=42} \atop {5x+3y=24}} \right.[/tex]

Multiply the second equation by 3 to change 3y to 9y:

[tex]5x+3y=24\\3(5x+3y)=3(24)\\15x+9y=72[/tex]

Subtract the first equation from the second to eliminate y:

[tex]15x+9y=72\\- 7x+9y=42\\\rule{2.5cm}{0.4pt}\\8x=30[/tex]

Divide both sides by 8 to isolate x:

[tex]\displaystyle x=\frac{30}{8} \\\\x=3.75[/tex]

Therefore, one pound of jelly beans costs $3.75.

2) Solve for y using substitution

[tex]\displaystyle\left \{ {{7x+9y=42} \atop {5x+3y=24}} \right.[/tex]

Now, we know that x=3.75. Plug this value into one of the equations and solve for y:

[tex]5x+3y=24\\5(3.75)+3y=24\\18.75+3y=24\\3y=24-18.75\\3y=5.25\\\\\displaystyley=\frac{5.25}{3} \\\\y=1.75[/tex]

Therefore, one pound of trail mix costs $1.75.

I hope this helps!

[tex]3\cdot[(2\cdot6-5)+(8:4)]-1=\\\\=3\cdot[(12-5)+2]-1=3\cdot(7+2)-1=\\\\=3\cdot9-1=27-1=\boxed{26}[/tex]

Answer:

Area of a triangle

Step-by-step explanation:

1/2bh is used to find the area for a triangle

Answer:

0.063

Step-by-step explanation:

Answer:

(-9/2,-1)

Step-by-step explanation:

Use the midpoint formula to find the midpoint of the line segment.

Answer:

83°

.......................

Answer:

83

Step-by-step explanation:

The inverse of the function y = 9x -4 is obtained by a reflection in the line at ( y = x ). Hence Option D is correct.

Each point of the original figure (the pre-image) has an image that is the same distance from the reflection line as the original point but is on the other side of the line. This transformation is known as a reflection over the line.

The inverse relation for y= 9x -4 will be calculated by putting the value of x equal to y or replacing x by y and y by x in the equation.

Hence Option D is correct.

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Answer:

90°

Step-by-step explanation:

diagonals of a kite intersect each other at 90°

:)

ANSWER :

third option 90 degrees

Step-by-step explanation:

the opossite adjasent angle is 1 that is 90 so angle 3 is opposite adjacent angle of angle 1

*The opposite adjacent angles will always be same