2 What operation should be done first to solve 6x + 5 = 35?
o
Subtract 5
O Add 5
Multiply by 6
O Divide by 6

Answer:

y=ax+b

y=5(-6)+28=-2

a

Answer:

11.5 cm²

Step-by-step explanation:

We know that the triangle has a base of 3 + 4 = 7 and a height of 3 + 2 = 5. Therefore, the area of the triangle is 7 * 5 / 2 = 17.5. The area of the 3 by 2 rectangle is 3 * 2 = 6 so the shaded area is 17.5 - 6 = 11.5 square cm.

Answer:

EA, or s

Step-by-step explanation:

The line AE could also be named any of the following:

AC, EC, CE, CA, EA

If you’re only looking at the line segment AE, the only option is:

EA

Since I don’t know whether you need the line or line segment, you might want go with EA since it’s on both lists. It could also be line s.

Problem 6, part c)

The tickmarks indicate the sides are the same length. This triangle is isosceles.

The two base angles are always opposite the congruent sides. One base angle is 25, so the other base angle must be 25 as well (base angles are congruent for isosceles triangles).

The three angles of this triangle are

25, 25 and 4x+2

Add those three angles up, set the result equal to 180, and solve for x

4x+2+25+25 = 180

4x+52 = 180

4x = 180-52

4x = 128

x = 128/4

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

Problem 7, part a)

We use the same idea as with the last problem above. This works because this triangle is also isosceles (due to the tickmarks).

The three angles of this triangle are

(4x+1), (4x+1) and (5x-4)

note how (4x+1) shows up twice because it is a base angle

Add up those angles and set it equal to 180 to solve for x

(4x+1) + (4x+1) + (5x-4) = 180

13x - 2 = 180

13x = 180+2

13x = 182

x = 182/13

x = 14

Using this x value, we can find angle F

angle F = 5x-4

angle F = 5*14-4

angle F = 70-4

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

Problem 7, part b)

We'll use the x value found back in part a) above.

angle D = 4x+1

angle D = 4*14+1

angle D = 56+1

Angle E is also 57, since D and E are congruent base angles

note how D+E+F = 57+57+66 = 180 to help confirm our answers

Answer:

The equation that best represents the relationship is [tex]y=\frac{1}{2}x+2[/tex].

Step-by-step explanation:

We are given the following table representing the two quantities below;

x        y

2       3

4       4

6       5

8       6

Firstly, we will find the two-point slope here, that is;

Consider two points; ([tex]x_1,y_1[/tex]) = (2, 3) and ([tex]x_2,y_2[/tex]) = (4,4)

Now, the formula for finding slope is;

Slope =  [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

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

Similarly, finding the slope for the points (6,5) and (8,6);

Slope =  [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

          =  [tex]\frac{6-5}{8-6}[/tex]  =  [tex]\frac{1}{2}[/tex]

Now, the linear equation of the line having slope is given by;

[tex]y-y_1=m\times (x-x_1)[/tex]  ; where m = slope and consider ([tex]x_1,y_1[/tex]) = (2, 3)

So, the equation of the line is;

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

[tex]y-3=\frac{1}{2}x-1[/tex]

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

Hence, the equation that best represents the relationship is [tex]y=\frac{1}{2}x+2[/tex].

Answer:

y = -1/2x + 11

The value of x will be 50 degrees. The correct option is B.

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The opposite angles of the parallelogram are equal and the sum of the adjacent angles of the parallelogram is 180 degrees.

Angle A is 130 degrees then angle F will also be 130 degrees. The angle E will be calculated as below:-

∠F + ∠ E = 180

130 + ∠E = 180

∠E = 180 - 130

∠E = 50

Therefore, the value of x will be 50 degrees. The correct option is B.

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Answer:

value of the variable: 3/2

perimeter: 84 feet

Step-by-step explanation:

Let's find the value of the variable first:

It is a square, so all 4 sides are the same (have the same length)

This means, 3(2f + 4) = 12f + 3

Simplify it,

6f + 12 = 12f + 3

6f = 9

f = 3/2

So, the variable f = 3/2!

Let's find the perimeter:

First, we find the value of one side of the square

12f + 3 is a side

because f = 3/2, we know that the one side of a square is 18 + 3 ft, which is 21 ft

Like I said, all 4 sides are the same in a square, so we can just calculate the length of 1 side, and multiply it by 4!

so 21 * 4 = 84!

The perimeter of this square is 84 feet!

I hope this helps! Please tell me if I did anything wrong, thank you and have a great day =D

Answer: There will be 12 engineers remaining in the product development department.

Step-by-step explanation:

So the givens are:

60 employees and 1/3 are engineers and if 40% of engineers are moved to another division and how many engineers will remain in the product development department?

So what we need to do:

60 * 1/3 = 60 / 3 = 20

There are 20 engineers.

20 * 40% = 8

There are 8 engineers that are going to be moved to another division.

20 - 8 = 12

12 engineers will remain in the development department.

Hence, your answer.

By calculations, 12 engineers will remain in the development department.

A companys product development division has 60 employees. Of these, [tex]\frac{1}{3}[/tex] are engineers.

The third part of a number is obtained by dividing a number by three, or what is the same, multiplying by a third ([tex]\frac{1}{3}[/tex]), thus dividing the number into a total of three equal parts.

In this case:

[tex]\frac{1}{3}[/tex]×60= 20

So, a companys product development division has 20 engineers.

40% of engineers are moved to another division.

The percentage is a way of referring to a proportion taking the number 100 as a reference. To calculate the percentage of a quantity, the quantity is multiplied by the percentage and divided by 100.

In this case:

40% of engineers= 40%×20=[tex]\frac{40x20}{100}[/tex]= 8

8 engineers are moved to another division.

The number of engineers who remain in the department is calculated by subtracting the total number of engineers in the department and the number of engineers who move to another division:

20 - 8= 12

12 engineers will remain in the development department.

Learn more about percentage with this examples:

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Answer:

Step 2

Step-by-step explanation:

In step 2 the expression was 40+20 which would have been 60 but he might have thought addition sign was subtraction so he did 40-20 which is 20 so he is wrong made mistake in step 2

Answer:

YES

Step-by-step explanation:

For example, in the figure displayed in the attachment, the length of [tex] YM = MS + SY [/tex]

[tex] MS = 3 [/tex]

[tex] SY = 10 [/tex]

Therefore, [tex] YM = 3 + 10 = 13 [/tex].

The lengths of segments MS and SY sums up to give you the length of YM.

Answer:

(b

Step-by-step explanation:

the line graph is showing this: x<10

Answer:

Option H (the third option)

Step-by-step explanation:

A person must be at least 10 years old.

Let the person's age be x years

therefore, he has to be x≥ 10 (the person's age has to be equal or more than 10 )

a = 85 10cent coins

b = 117 20cent coins

a = 10c coins

b = 20c coins

$31.90 = c3190

a + b = 202 => a = 202 - b

10a + 20b = 3190

10(202 - b) + 20b = 3190

2020 - 10b + 20b = 3190

10b = 3190 - 2020

10b = 1170

b = 117 (20cent coins)

a = 202 - 117

= 85 (10cent coins)

Answer:

99,595

Step-by-step explanation:

We are looking at division and remainders. What do you do when a remainder is present? You usually add it when multiplying to get the final number, but since we are doing this backwards, we have to subtract the numbers divided by the remainder.

25 - 20 = 5

30 - 25 = 5

40 - 35 = 5

Look for the LCM (Least Common Multiple) for 20, 30, and 40 :

600

Now for the equation :

n + 5 = Multiple of all numbers and LCM =

n + 5 = 166 * 600 = 99,600

n = 99,600 - 5 = 99,595

The greatest 5 digit number which when divided by 25, 30 and 40 has a remainder of 20, 25, and 35 is 99,595

The reason why the above value arrived at is correct is as follows:

The required parameter;

To find a 5 digit number that with remainder of 20, remainder of 25 and a remainder of 35, when divided by 25, 30, and 40 respectively

Strategy;

Find the LCM of the divisor, then find the highest common multiple of the

LCM that is a 5 digit number, equate the expression for the required 5 digit

number to the highest common multiple of LCM of the divisors by adding

a value that will give a factor of the divisor as follows;

Let x represent the 5 digit number, from the question, we get;

x = 25·a + 20

x = 30·b + 25

x = 40·c + 35

x < 99,999

The 5 digit number is not a multiple of 25, 30, and 40, therefore, the number is not a multiple of the LCM of 25, 30, and 40 which is 600

The highest multiple of 600 which is a 5 digit number = 99,600

Therefore, we can write;

25·a + 20 + 5 = 30·b + 25 + 5 = 40·c + 35 + 5 = 99,600

However;

25·a + 20 + 5 = x + 5

By transitive property, we get

x + 5 = 99,600

∴ x = 99,600 - 5 = 99,595

The 5 digit number, x = 99,595

Learn more about LCM here:

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

Work Shown:

Multiply the first coefficient (6) and the last term (-7) to get -42. We need to find factors of -42 that add to -19

Turns out that those two numbers are -21 and 2, which you find by trial and error.

-21 * 2 = -42

-21 + 2 = -19

Break up -19x as -21x+2x and use the factor by grouping method

6x^2 - 19x - 7

6x^2 - 21x + 2x - 7

(6x^2 - 21x) + (2x - 7)

3x(2x - 7) + 1(2x - 7)

(3x+1)(2x-7)

The factorization represents the length*width, since this product is equal to the rectangle's area.

----------------------

Plug x = 15 into each factor

3x+1 = 3*15+1 = 46

2x-7 = 2*15-7 = 23

The length and width are 46 and 23

Answer:

12

Step-by-step explanation:

144 chairs in total.

the room is square, this means that the number must be multiplied by the same number

12x12= 144

there are 12 chairs on the first row.

Hello, please consider the following.

[tex]\displaystyle \lim_{x\rightarrow3}~\dfrac{2x^2-18}{x^2-3x} \\ \\ \\ =\lim_{x\rightarrow3}~\dfrac{2(x^2-3^2)}{x(x-3)} \\ \\ \\ =\lim_{x\rightarrow3}~\dfrac{2(x-3)(x+3)}{x(x-3)} \\ \\ \\ =\lim_{x\rightarrow3}~\dfrac{2(x+3)}{x} \\ \\ \\=\dfrac{2(3+3)}{3}\\ \\ \\=\dfrac{2*3*2}{3} =\Large \boxed{\sf \bf \ 4 \ }[/tex]

Thank you

[tex]\\ \tt\longmapsto {\displaystyle{\lim_{x\to 3}}}\dfrac{2x^2-18}{x^2-3x}[/tex]

[tex]\\ \tt\longmapsto {\displaystyle{\lim_{x\to 3}}}\dfrac{2(x^2-9)}{x^2-3x}[/tex]

[tex]\\ \tt\longmapsto {\displaystyle{\lim_{x\to 3}}}\dfrac{2(x^2-3^2)}{x^2-3x}[/tex]

[tex]\\ \tt\longmapsto {\displaystyle{\lim_{x\to 3}}}\dfrac{2(x+3)\cancel{(x-3)}}{x\cancel{(x-3)}}[/tex]

[tex]\\ \tt\longmapsto {\displaystyle{\lim_{x\to 3}}}\dfrac{2x+6}{x}[/tex]

[tex]\\ \tt\longmapsto \dfrac{2(3)+6}{3}[/tex]

[tex]\\ \tt\longmapsto \dfrac{6+6}{3}[/tex]

[tex]\\ \tt\longmapsto \dfrac{12}{3}=4[/tex]

Answer:

[tex](x+8)^2 = 86[/tex]

Step-by-step explanation:

Given

[tex]x^2 + 16x = 22[/tex]

Required

Determine an equivalent equation

[tex]x^2 + 16x = 22[/tex]

Get the coefficient of x

[tex]Coefficient = 16[/tex]

Divide this by 2

[tex]Result = \frac{16}{2}[/tex]

[tex]Result = 8[/tex]

Take its square

[tex]Result = 8^2[/tex]

[tex]Result = 64[/tex]

Add this to both sides of the equation

[tex]x^2 + 16x + 64 = 22 + 64[/tex]

[tex]x^2 + 16x + 64 = 86[/tex]

Expand the expression on the right hand side

[tex]x^2 + 8x + 8x + 64 = 86[/tex]

Factorize

[tex]x(x+8)+8(x+8) = 86[/tex]

[tex](x+8)(x+8) = 86[/tex]

[tex](x+8)^2 = 86[/tex]

Hence, the equivalent equation is [tex](x+8)^2 = 86[/tex]

Answer:

135°

Step-by-step explanation:

Because the lines are parallel, <1 and <3 are the same.

Answer:

5 miles.

Step-by-step explanation:

We would be using the Pythagoras Theorem to solve for this.

I have attached a diagram to better help you to better understand my explanation this.

The shortest distance from her playground to her house = Hypotenuse

Pythagoras Theorem for a triangle =

c² = a² + b²

Where c = Hypotenuse

a = 3 miles due west

b = 4 miles north

c² = 3² + 4²

c² = 9 + 16

c² = 25

c = √25

c = 5 miles

Therefore, the shortest distance to Alicia's home from the playground is 5 miles.

Answer:

Step-by-step explanation:

Hello, please consider the following.

We will multiply the numerator and denominator by

[tex]3-\sqrt{3}[/tex] to get rid of the root in the denominator.

Let's do it!

[tex]\begin{aligned}\dfrac{\sqrt{12}}{\sqrt{3}+3}&=\dfrac{\sqrt{2^2*3}*(3-\sqrt{3})}{(3+\sqrt{3})*(3-\sqrt{3})}\\\\&=\dfrac{2\sqrt{3}*(3-\sqrt{3})}{3^2-\sqrt{3}^2}\\\\&=\dfrac{2\sqrt{3}*(3-\sqrt{3})}{9-3}\\\\&=\dfrac{2\sqrt{3}*(3-\sqrt{3})}{6}\\\\&=\dfrac{6\sqrt{3}}{6}-\dfrac{2*3}{6}\\\\&=\sqrt{3}-1\\\\\large &\boxed{=-1+\sqrt{3}}\\\end{aligned}[/tex]

Thank you

Step-by-step explanation:

Here,

[tex] = \frac{ \sqrt{12} }{ \sqrt{3} + 3} [/tex]

is given.

Now, rationalizing it,

[tex] = \frac{ \sqrt{12} }{ \sqrt{3} + 3} \times \frac{ \sqrt{3} - 3 }{ \sqrt{3} - 3} [/tex]

now, simplifying it,

[tex] = \frac{ \sqrt{12 } \times \sqrt{3 } - 3 }{( { \sqrt{3} )}^{2} - 9} [/tex]

or, simplifying it we get,

[tex] = \frac{3}{ - 6} [/tex]

= 1/ -2

Hope it helps...

The correct answer is A. Mean

Explanation:

In the analysis of numerical data, means refers to the average value. This is found by adding all the values, in this case, all the salaries and then dividing the total by the total of values, in this case, 235. This sample statistic is affected by each of the values that are added, due to this, if a value changes or was corrected, the mean needs to be revised. Also, this does not occur in the case of the minimum (lowest value), the median (value in the middle), or in the mode (most frequent value.)

Answer:

8

Step-by-step explanation:

Jason = 22

Taylor = x

Taylor is 8

Answer:

Step-by-step explanation:

[tex]a_n=\frac{1}{3} a_{n-1}[/tex]

Answer:

hello your question is incomplete attached is the complete question

answer : 25/2 ( A )

Step-by-step explanation:

using Stokes' Theorem to calculate

F = 5yi + 7xj  + [tex]z^3 k[/tex]

line y = 5 - 2x

attached below is the remaining part of the solution to the question

Answer:

ray

Step-by-step explanation:

ray is the answer because it starts with a startline but has no endpoint so it goes on for infinity.

Answer:

The values of r = -3/2 ,7

Step-by-step explanation:

2r2 - 11r - 21 = 0.

The is a quadratic equation in the form

2r²-11r -21= 0

Let's determine the value of r using factorization method

2r² -14r +3r -21= 0.

2r(r-7)+3(r-7)= 0

(2r+3)(r-7)= 0

2r+3= 0

2r= -3

r= -3/2

And

r-7= 0

r= 7

The values of r = -3/2 ,7

Answer:

y=3/2x-2

Step-by-step explanation:

Find the slope first:

[tex]m=\frac{y_{2-y_{1} } }{x_{2}-x_{1} } =\frac{1-(-2)}{2-0}=\frac{3}{2}[/tex]

Then solve for y-intercept:

[tex]y=\frac{3}{2}x+b\\-2=\frac{3}{2}(0)+b\\-2=b[/tex]

Now, write out your complete equation:

y=3/2x-2

Answer:

49 and 118

Step-by-step explanation:

Let the two numbers be x and y

x+y = 167

y = 3x-29

Substitute into the first equation

x+ 3x-29 = 167

Combine like terms

4x - 29 = 167

add 29 to each side

4x = 167+29

4x = 196

Divide by 4

4x/4 = 196/4

x = 49

x+y = 167

49+y = 167

y = 167-49

y =118

Answer:

[tex]\Huge \boxed{\mathrm{49 \ and \ 118}}[/tex]

Step-by-step explanation:

Let the first number be [tex]x[/tex]

Let the second number be [tex]y[/tex]

[tex]x+y=167[/tex]

[tex]y=3x-29[/tex]

Applying substitution method.

[tex]x+3x-29=167[/tex]

Combining like terms.

[tex]4x-29=167[/tex]

Adding 29 to both sides.

[tex]4x=196[/tex]

Dividing both sides by 4.

[tex]x=49[/tex]

Substituting x = 49 for the second equation.

[tex]y=3(49)-29[/tex]

Multiplying the numbers.

[tex]y=147-29[/tex]

Subtracting.

[tex]y=118[/tex]

The two required numbers are 49 and 118.

Answer:

$87,461

Step-by-step explanation:

Given that the dimensions or sides of lengths of the triangle are 119, 147, and 190 ft

where S is the semi perimeter of the triangle, that is, s = (a + b + c)/2.

S = (119 + 147 + 190) / 2 = 456/ 2 = 228

Using Heron's formula which gives the area in terms of the three sides of the triangle

= √s(s – a)(s – b)(s – c)

Therefore we have = √228 (228 - 119)(228 - 147)(228 - 190)

=> √228 (109)(81)(38)

= √228(335502)

=√76494456

= 8746.1109071 * $10

= 87461.109071

≈$87,461

Hence, the value of a triangular lot with sides of lengths 119, 147, and 190 ft is $87,461.

Answer:

310%

Step-by-step explanation:

310% can be expressed as a mixed number because 150% would be 1 1/2.

310% would be 3 1/10.