solve x - 3 = 7

3 - 3 = 7
x - 3 ___ = 7 ____
x ___ = ___
x = ___

Answer:

Step-by-step explanation:

Rewrite X^2+22x=31, leaving space after the "22x:"

X^2+22x                          = 31

The coefficient of x is 22.  Take half of that, obtaining 11.  

Square this result:  11^2 = 121.

Write in "+121      -121" after the x term:

X^2+22x  + 121 - 121 = 31

Rewrite X^2+22x + 121 as

          (x + 11)^2  -121 =  31

Add 121 to both sides:

           (x + 11)^2 = 152

Take the square root of both sides:

            x + 11 = ±√152 = ±2√38

Finally, x = -11 ±2√38.

This is "solution by completing the square"

Answer: OPTION A

Step-by-step explanation:

We have this quadratic equation: [tex]x^2+22x=31[/tex]

In order to complete the square the first step is to pick the coefficient of the x term, divide it by 2 and square it. Then:

[tex](\frac{22}{2})^2=11^2[/tex]

Now we must add 11² to both sides of the equation:

[tex]x^2+22x+11^2=31+11^2[/tex]

Therefore, after complete the square and factor, we get:

[tex](x+11)^2=152[/tex]

This matches with the option A.

Answer:

3BC

Step-by-step explanation:

8BC - 9BC + 10BC - 6BC = BC(8 - 9 + 10 - 6) = BC(3) = 3BC

There you go in the attached.

Answer:

40 students play all three games .

Step-by-step explanation:

You have universal and it says everyone likes all three games so your union is same as universal and there is no complement or any one who didn't like any games so use formule of universal = n A + n B + n C - n only interaction or who likes any two .Solve it and you will get your answer

Answer:

see explanation

Step-by-step explanation:

The perimeter (P) is the length of all 3 sides of the triangle

The triangle is isosceles with 2 equal sides 20 - 7xy

P = 20 - 7xy + 20 - 7xy + 12 = 52 - 14xy

When x = 2, y = 1, then

P = 52 - 14(2)(1) = 52 - 28 = 24

Answer:

3

Step-by-step explanation:

The digit in the tenths place of 25.391 is 3.

Answer: [tex]3[/tex]

Step-by-step explanation:

It is important to know that, in order to find the digit in the tenth place of a decimal number, you need to indentify the first digit located to the right of the decimal point.

Therefore, knowing this and having the decimal number provided in the exercise:

 [tex]25.391[/tex]

You can observe that the  first digit to the right of the decimal point is 3.

Therefore, the digit in the tenths place of ths decimal number is: [tex]3[/tex]

Answer:

Step-by-step explanation:

get rid of the denominator by multiplying by x

Hello There!

The number of adult tickets sold in the school play = 225

Total Number Of Tickets = 505

Number Of Student Tickets = x + 55

Number of adult tickets sold can be represented by X

Number of student tickets = X + 55

X+X+55=505

2x+55=505

2x=505-55

2x=450

X=225

Answer:

225

Step-by-step explanation:

x+x+55 = 505

2x + 55 = 505

2x = 505-55

2x = 450

x = 225

GOOD LUCK ! ;)

Answer:

$17.10

Step-by-step explanation:

Bracelet cost  $15

4% sales tax:  0.04($15) = $0.60

10% Fed tax:  0.10($15) = $1.50

Summing these three amounts, we get a total cost of $17.10.

Answer:

Rule is (x, y+k)

New point is (-3,9)

Step-by-step explanation:

A point translated vertically k units up means the x coordinate remains the same in the translation but the y coordinate is increased by k units

This can be represented mathematically as;

Let;s assume the point to be A with coordinates (x,y) then to get the image of the point under  a vertical translation k units up you add k to the y coordinate value.

Given ;

[tex]A=(\frac{x}{y} )\\\\T=(0,k)\\\\A'=(\frac{x}{y} )+(\frac{0}{k} )=(\frac{0+x}{y+k} )\\\\A'=\frac{x}{y+k} =(x,y+k)[/tex]

where T is the translation

In the question

Given (-3,-6) and T is (0,5) the new coordinate will be

[tex]=(\frac{-3}{4}) +(\frac{0}{5} )=\frac{-3}{9} =(-3,9)[/tex]

Answer:

Step-by-step explanation:

You use latex very well. Nice work.

sqrt(17) = 4.123

sqrt(5) = 2.236

==============

pi + 7

=====

5

3.14 + 7

======

5

10.14/5 = 2.028

Answer

B. \frac{\pi +7 }{5}   2.028

C. \sqrt{5}               2.236

A. \sqrt{17}              4.123

Answer:

4,444097208657794

Step-by-step explanation:

c = 20ft

b = 19.5ft

just use the pythagorean theeorem

Answer:

the first option

a = -2

b = 3

Step-by-step explanation:

See photo attached. (:

Answer with explanation:

→Draw a Line segment of any length on a piece of paper.Measure the length of segment with the help of Straightedge.

→Now if it is a number divisible by 3,with the help of compass divide the length of segment by 3 and by placing the compass on the straightedge open the compass starting from 0 up to that length.

→If the number is not divisible by 3, round the number to nearest rational number.

→And then Mark arc with the help of Compass from starting of line segment the length being equal to the number obtained after dividing by 3,and after obtaining the first point taking the same width mark second arc from the point obtained.

This is required trisected line segment.

⇒The Statement is True which is we can trisect a line segment using only a straightedge and a compass.

Answer:

True

Step-by-step explanation:

Just did the test :)

Answer: The y-intercept would be 10

Step-by-step explanation:

(-2, 15), (1, 6), (2, 3), (4, -3), (7, -12) are the coordinate points, you can graph it to find the intercept. I used the graphing calculator desmos.

Answer:its 9

Step-by-step explanation:

Answer:

y = 5x - 4

see attached for graph

Answer: $17.80

Step-by-step explanation:

2.80 + 3(5) = x

2.80 + 15 = x

17.80 = x

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The total amount paid by Jacob is $17.8.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

Jacob bought a magazine for $2.80. Also, three candy bars for $5 each. Therefore, the amount paid by Jacob is,

Amount paid by Jacob = $2.80 + (3 × $5)

                                      = $17.8

Hence, the total amount paid by Jacob is $17.8.

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Answer:

c = -2

Step-by-step explanation:

The two functions are given as:

f(x) =  x^2 - 2x

g(x) = 6x + 4

To find:

(f+g)(x) = 0

We can evaluate (f+g)(x) using the given functions.

We know that:

(f+g)(x) = f(x) + g(x)

= x²- 2x + 6x + 4

= x² + 4x + 4

Now, we have for x = c:

c² + 4c + 4 = 0

x² + 2c + 2c + 4 = 0

c(c+2) + 2(c+2) = 0

(c+2)² = 0

c+2 = 0

c = -2

Answer:

‭1.267650600228229401496703205376e+130‬

Step-by-step explanation:

√400 =20

20¹⁰⁰ = ‭1.267650600228229401496703205376e+130‬

Hope this helps!

For this case we have that from 2:16 am until 2:16 pm exactly 12 hours have passed. On the other hand, from 2:16 p.m. until 8:16 p.m., exactly 6 hours have elapsed.

If we add, we have that from 2:16 am to 8:16 pm have elapsed: 12 + 6 = 18 hours.

As we ask for the time elapsed between 2:16 am until 8:10 pm we must subtract 6 minutes. So, we have:

18 hours with 54 minutes

Answer:

18 hours with 54 minutes

Answer:

(a) 15/3 = 100/x

(b) There are 20 toddlers in the class.

Step-by-step explanation:

(a)

The total number of students is 100% of the students.

Let the total number of students be x.

15% of students is to 3 as 100% of students is to x.

15/3 = 100/x

(b)

15/3 = 100/x

Cross multiply the equation.

15x = 3 * 100

15x = 300

Divide both sides by 15.

x = 20

Answer: There are 20 toddlers in the class.

Answer:

6/7

Step-by-step explanation:

One way of doing this problem is to find the square root of numerator separately (it is 6) and the square root of the denominator likewise (it is 7).  Then the value of the given expression is 6/7.

The value of the given expression is [tex]\frac{6}{7}[/tex].

What is a mathematical expression?

"A mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context."

The given mathematical expression is

[tex](\frac{36}{49})^{\frac{1}{2}} \\= (\frac{6^{2} }{7^{2} })^{\frac{1}{2}}\\= [(\frac{6}{7})^{2}]^{\frac{1}{2}}\\= \frac{6}{7}[/tex]

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Answer:

72 campers.

Step-by-step explanation:

You can do this with a simple equation. 180% = 1.8 as a decimal fraction. Let x be this  year's attendance. Then:

x = 1.8* 40

x = 72 campers.

Answer:

72 Campers

Step-by-step explanation:

Hope this helps:)

Answer:

x^2 +8x+12

Step-by-step explanation:

(X+2)(x+6)

Foil

first: x*x = x^2

outer: x*6 = 6x

inner : 2*x = 2x

last: 2*6 = 12

Add them together:  x^2 +6x+2x+12 = x^2 +8x+12

Answer: X^4 you just subtract or add with exponents

Step-by-step explanation:

In mathematics, when you multiply variables that have the same base, you add their exponents. The solution to the problem X^-3•x^7 is x^4.

To multiply the variables with the same base, you need to add their exponents. In this case, x-3 multiplied by x7 would be equal to x-3+7 or x4. Therefore, the answer is x4.

The problem given is X^-3•x^7. This problem involves the multiplication of two variables with exponents. In mathematics, when you multiply variables with the same base, you keep the base and add the exponents. This is called the 'Laws of Exponents'. Therefore, for X^-3•x^7, our base is X, so we add the exponents -3 and 7 to get 4. Hence, the result is x^4.

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Answer: x = 6, x = -4

Step-by-step explanation:

Find two numbers whose product is the c-value (-24) and sum is the b-value (-2):

0 = x² - 2x - 24

                    ∧

                   1 -24

                   2 -12

                   3  -8

                   4  -6 = -2    This works!

0 = (x + 4)(x - 6)

Apply the Zero-Product Property (set each factor equal to zero and solve)

0 = x + 4      0 = x - 6

-4 = x            6 = x

The solutions are x = 6 and x = -4. Therefore, the zeros of the function are 6 and -4.

Finding the Zeros of the Function p(x) = x^2 – 2x – 24

To find the zeros of the function p(x) = x^2 – 2x – 24, we need to determine the values of x that make the function equal to zero. This means we solve the equation:

x^2 – 2x – 24 = 0

This is a quadratic equation and can be solved using factoring. We look for two numbers that multiply to -24 and add to -2. These numbers are 4 and -6:

(x - 6)(x + 4) = 0

Setting each factor equal to zero gives us the solutions:

So, the zeros of the function p(x) = x^2 – 2x – 24 are 6 and -4.

The number of wheels on a group of buses involves mathematical calculations and can be analyzed using multiplication, probability, and physics, particularly when combined with other factors such as passenger capacities or mechanical variables like angular velocity of a flywheel within the bus.

The question about the number of wheels on a group of buses relates to mathematical calculations, specifically pertaining to multiplication and potentially to probability and combinatorics if one were analyzing how to most efficiently deploy a fleet of buses for transportation or which bus to take based on passenger load and capability.

A practical example of a bus-related math problem would be: if a bus has 6 wheels, then a fleet of 10 buses would have a total of 60 wheels. This is a straightforward multiplication problem (10 buses x 6 wheels per bus = 60 wheels).

In the context of probabilistic analysis, considering a situation where buses have different passenger capacities, we might use the expected value formula E(X) = Σx₁p(x₁) to calculate the best option for transportation based on various factors, including the number of passengers each bus can transport.

Moreover, buses also have a place in physics problems. For instance, calculating the angular velocity a bus's flywheel must have to achieve a certain speed involves understanding the concepts of rotational kinetic energy and its transformation into translational energy. This more complex application lies within the realm of physics but has roots in mathematical computation.

Answer:

The equation is y=-x+6.

Step-by-step explanation:

To find the slope of this equation, we use the equation m=y2-y1/x2-x1, where m is the slope. Take one y coordinate and subtract it from the other and do the same with the x coordinates. Then, divide the difference of the y coordinates by the difference of the x coordinates. For example, 6-2/0-4. This gets us 4/-4. You can also do 2-6/4-0 which gets us -4/4. No matter what, we get -1 for each (we don't include the 1 in front of the x). To find the y-intercept, plug in the coordinates. For example, do 6=0(-1)+b or 2=4(-1)+b. No matter which you use, you get an answer of b=6. This gives you an equation of y=-x+6. Hope this helps :)

The equation of the line that passes through the points (4,2) and (0,6) is y = 6 - x

To determine the equation for the line that passes through the points (4,2) and (0,6),

We will use the formula for the determining the equation of a line with two given points

The formula for the determining the equation of a line with two given points is

[tex]\frac{y-y_{1} }{x-x_{1} }=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

The given points are (4,2) and (0,6)

Therefore,

x₁ = 4

y₁ = 2

x₂ = 0

y₂ = 6

Now, putting these into the formula,

We get

[tex]\frac{y-2}{x-4}=\frac{6-2}{0-4}[/tex]

This becomes

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

[tex]\frac{y-2}{x-4}=-1[/tex]

Then, the equation becomes

[tex]y-2 = -1(x-4)[/tex]

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

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

[tex]y = 6-x[/tex]

Hence, the equation of the line that passes through the points (4,2) and (0,6) is y = 6 - x

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Answer:

slope = [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 2) and (x₂, y₂ ) = (4, 3)

m = [tex]\frac{3-2}{4+1}[/tex] = [tex]\frac{1}{5}[/tex]

Answer:

1/5

Step-by-step explanation:

To cover the distance of 14 miles at a speed of 14 miles per hour Brian will take 1 hour means 60 minutes.

The speed is the rate of distance covered by a person or a vehicle in a particular time.

We have been given the distance=14 miles

Speed=14 miles per hour

We have also been given the formula of distance which is

d=rt

we have to rearrange it to calculate time

t=d/r

so the time will be calculated as t=14/14

t=1 hour because the speed is of per hour.

Hence Brian will take 60 minutes to cover the required distance.

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Answer:

B???

Step-by-step explanation:

Answer:

The correct option is A. Figure B repeats in the tessellation shown below.

Step-by-step explanation:

Tessellation can be defined as the arrangement of geographical patterns that are closely attached together to form a particular pattern.

The given figure is formed by the arrangement off figure B.

This large pattern is formed by the repetition of this smaller pattern,

Figure B repeats in the tessellation shown below. Therefore, the correct option is A.