Like terms can be added or subtracted true or false

Answer:

y=8x+13

Step-by-step explanation:

Perpendicular Lines are those with the following condition:

y=a*x+b (1)

y=c*x+d (2)

Where 'a' and 'c' are the respective slope

If These two lines are perpendicular, then

a=- 1/c

Equation (1) for our case is written as y=-(1/8)x-2, meaning that a=-1/8 and b = 2

Using those principles we have that the slope for our needed line ('c') has to be 8.

Now we most use the given point to find the remaining term of the equation (d)

Evaluate it in eq (2) to have this:

-3=8*(-2)+d

resulting that d=13

Answer:  The required value of y is 22.

Step-by-step explanation:  We are given the following function of a and b :

[tex]y=3ab+2b^3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We are to find the value of y when a = 1 and b = 2.

To find the required value of y, we need to substitute the values of a and b in equation (i).

From (i), we get

[tex]y=3\times1\times2+2\times2^3=6+16=22.[/tex]

Thus, the required value of y is 22.

The solution to the given algebraic Expression is; y = 22

We are given the algebraic expression;

y = 3ab + 2b³

We want to find y when a = 1 and b = 2.

Plugging in the relevant values gives;

y = 3(1*2) + 2(2³)

y = 6 + 16

y = 22

In conclusion, the solution to the expression is y = 22

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Answer:

330:1

Step-by-step explanation:

least common multiple of 180 and 594

180: 2×2×3×3×5

594: 2×3×3×11

LCM: 594×2×5 = 5940

GCF: 2×3×3 = 18

ratio:

5940:18

330:1

The ratio of the Least Common Multiple (LCM) of 180 and 594 to the Greatest Common Factor (GCF) of 180 and 594 is 330. This is found by first determining the LCM (5940) and GCF (18), then dividing the LCM by the GCF.

To find the ratio of the Least Common Multiple (LCM) of 180 and 594 to the Greatest Common Factor (GCF) of 180 and 594, first, we find the LCM and GCF separately.

Finally, we divide the LCM by the GCF:

5940 ÷ 18 = 330.

So, the ratio of the LCM of 180 and 594 to the GCF of 180 and 594 is 330. Therefore, the correct answer is (C) 330.

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[tex]3(2x-7)+2+ 2(x+y)=6x-21+2+2x+2y=8x+2y-19[/tex]

Answer:

c. 21/32 inches

C. 1.992

b. 0.3125

Step-by-step explanation:

Given

The inside diameter = 1/2 inches

Wall thickness = 1/16 inches

clearance = 1/32 inches

As it is given that the outside diameter is twice the thickness and diameter.

So,

Outside diameter = 1/2 + 2(1/32)

= 1/2+2/16

= 1/2+1/8

=(4+1)/8

=5/8

We also have to give clearance of 1/32 inches so,

Diameter of hole = 5/8+1/32

=(20+1)/32

=21/32 inches

So the correct answer for question 1 is:

c. 21/32 inches

Rounding off 1.99235 to three decimal places:

1.992

C. 1.992

Expressing 5/16 as a decimal fraction:

0.3125

b. 0.3125

16 completely divides 5 so the answer is already 4 decimal places ..

Answer: 6,050,000

Step-by-step explanation:

5%=0.05

302500/0.05=6,050,000

Answer:

x = 6050000

Step-by-step explanation:

Set up a proportion

5%  = 302500 people

100%  = x

5/100 = 302500

100/100 = x            Cross multiply

5x / 100 = 302500 * 100/100                        Multiply both sides by 100

5x / 100 * 100 = 302500 * 100 / 100 *100    Do the multiplication

5x = 302500 * 100                                         Combine the right.

5x = 30250000                                              Divide by 5

5x/5 = 30250000/5

x = 6050000

1/100 of a million is the 5. It is already rounded to what it should be. So the answer is what we have.

Answer:

  82

Step-by-step explanation:

Alternate exterior angles where the transversal "e" crosses parallel lines "a" and "b" are congruent. x° ≅ 82°

Answer: second option.

Step-by-step explanation:

It is important to remember that  Vertical angles are defined as two non-adjacent angles formed by intersecting lines. These angles share the same vertex and they are congruent.

Observe the figure attached. Since lines "a" and "b" are parallel, you can notice that the angle 82° angle x° are Vertical angles. Therefore, they are congruent.

Then, the value of "x" is:

[tex]x=82\°[/tex]

Answer:

the length is 40 ft

Step-by-step explanation:

perimeter is length+length+height+height.

If the height is 19 ft then the first equation would be 118-(19+19)=80

Then you would do 80/2= 40

The length is 40 ft.

The length of the billboard with a perimeter of 118 feet and a height of 19 feet is 40 feet.

To find the length of the billboard when the perimeter is 118 feet and the height is 19 feet, you can use the formula for the perimeter of a rectangle: Perimeter = 2(length + height). Given that the height is 19 feet, you set up the equation 118 = 2(l + 19) and solve for the length (l).

First, divide both sides of the equation by 2:

59 = l + 19

Next, subtract 19 from both sides:

l = 59 - 19

l = 40

[tex]\huge{\boxed{y+5=2(x-4)}}[/tex]

Point-slope form is [tex]y-y_1=m(x-x_1)[/tex], where [tex]m[/tex] is the slope of the line and [tex](x_1, y_1)[/tex] is a known point on the line.

Substitute the values. [tex]y-(-5)=2(x-4)[/tex]

Simplify the negative subtraction. [tex]\boxed{y+5=2(x-4)}[/tex]

Note: This equation is in point-slope form. If you require or prefer another form, please let me know in a comment below.

Answer:

y = 2x - 13

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, hence

y = 2x + c ← is the partial equation

To find c substitute (4, - 5) into the partial equation

- 5 = 8 + c ⇒ c = - 5 - 8 = - 13

y = 2x - 13 ← equation of line

Answer:

5 to 13

Step-by-step explanation:

There are 5 girls in the class

To find the amount of kids in the class you have to add the girls and boys together.

There are 5 girls and 8 boys.

So 8 + 5 = 13

So there are 5 girls out of 13 students.

Answer:

5 to 13

Step-by-step explanation:

The ratio of girls to all the students in the class is 5 to 13.

8 + 5 = 13

5 girls out of 13 students

The solution to the inequality represented in set-builder notation can also be expressed in interval notation. In this case, the solution set is x > 2/3, indicating that x can take any value greater than 2/3.

The solution to the given inequality, {x | x > 2/3}, can also be represented as x > 2/3 in interval notation. In interval notation, 2/3 is excluded from the solution set, so the inequality becomes x > 2/3. This means that x can take any value greater than 2/3, such as 1, 1.5, 2, 2.5, and so on.

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Another way to represent the solution set {x | x > 2/3} is (2/3, ∞) in interval notation.

Another way to represent the solution set {x | x > 2/3} is by using interval notation.

Interval notation represents a range of values between two endpoints using parentheses or brackets.

In this case, the solution set would be represented as (2/3, ∞) because the values of x are greater than 2/3. This means that x can take any value greater than 2/3, such as 1, 1.5, 2, 2.5, and so on.

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ANSWER

[tex] \sum _{n = 1} ^{18} (6n - 15)[/tex]

EXPLANATION

The given series

[tex] - 9 - 3 + 3 + 9 + ... + 81[/tex]

This is an arithmetic series with a common difference of

[tex]d = - 3 - - 9 = 6[/tex]

The first term of the series is:

[tex]a_1 = - 9[/tex]

The general term is given by:

[tex]a_n =a_1 + d(n - 1)[/tex]

[tex]a_n = - 9+ 6(n - 1)[/tex]

[tex]a_n = - 9+ 6n - 6[/tex]

[tex]a_n =6n - 15[/tex]

The last term is 81

We can use this to determine the number of terms in the series.

[tex]81=6n - 15[/tex]

[tex]81 + 15=6n [/tex]

[tex]6n = 96[/tex]

[tex]n = \frac{96}{6} = 16[/tex]

The summation notation is:

[tex] \sum _{n = 1} ^{18} (6n - 15)[/tex]

Answer:

[tex](x^2+5)*(x-3)[/tex]

Step-by-step explanation:

In grouping method factoring, you must have to split the middle term in a way that the product of two terms in middle must be equal to the product of two terms at the edges of equation. Remember you have to consider the resultant signs as well as the magnitude of both products.

Now in the case given above,

[tex]x^3-3x^2+5x-15[/tex]

the result is [tex]-15x^3[/tex]

Note that the magnitude is 15x^3 and sign is '-' for both products.

Now taking out the common terms, equation becomes;

[tex]x^2(x-3)+5(x-3)[/tex]

Taking out (x-3) as common, now the factorized version we have is:

[tex](x-3)(x^2+5)[/tex]

We understand a linear inequality as an inequality involving a linear function. It's important to know that a linear inequality contains one of the symbols of inequality:

< less than

> greater than

≤ less than or equal to

≥ greater than or equal to

In this problem, we have:

[tex]2x-3y<12[/tex]

In this case, we use the symbol <, so this indicates that [tex]2x-3y[/tex] is less than 12. To solve this, let's write the linear equation in slope-intercept form:

Step 1: Write the expression as an equation:

[tex]2x-3y=12[/tex]

Step 2: Subtract -2x from both sides:

[tex]2x-3y-2x=12-2x \\ \\ -3y=12-2x[/tex]

Step 3: Multiply the entire equation by -1/3

[tex]-\frac{1}{3}(-3y)=-\frac{1}{3}(12-2x) \\ \\ y=\frac{2}{3}x-4[/tex]

The graph of this equation is shown in the firs figure below. To know what's the shaded region let's take point (0, 0) and test it in the inequality:

[tex]2(0)-3(0)<12 \\ \\ 0<12 \ TRUE![/tex]

Since this is true, the shaded region includes point (0, 0) and this is above the graph. We have to draw a dotted line since equality is not included in the solution and this is shown in the second figure below.

Answer:

5y^2−4y−14

Step-by-step explanation:

Equation:2(3y−7)−5y(2−y)

First Distribute:

(2)(3y)+(2)(−7)+5y2+−10y

6y+−14+5y2+−10y

Then Combine Like Terms:

6y+−14+5y2+−10y

(5y2)+(6y+−10y)+(−14)

5y2+−4y+−14

Answer:

5y^2 -4y -14

Step-by-step explanation:

2(3y-7)-5y(2-y)

Distribute

2*3y -2*7  -5y *2 -5y*(-y)

6y -14 -10y +5y^2

Combine like terms and put in decreasing order

5y^2 -4y -14

Answer:

2

Step-by-step explanation:

Varies directly means we multiply to the constant, where as inversely means we divide the constant.

So we have

"y varies directly with the square of x and inversely with z".

This means x^2 will be on top and z will be on bottom.

Like this:

[tex]y=k\frac{x^2}{z}[/tex]

We are given x=9,z=27, and y=6.  This will allow us to find k.

k is constant no matter what (x,y,z) we have.

[tex]6=k\frac{9^2}{27}[/tex]

[tex]6=k\frac{81}{27}[/tex]

[tex]6=k(3)[/tex]

Divide both sides by 3:

[tex]2=k[/tex]

So the constant of variation is 2.

Answer:

The constant of variation is 2.

Step-by-step explanation:

If y is directly influenced by x², it means that the function of y will be multiplied with x². with y being inversely influenced by z, it means that the function will be divided by z. The entire function can be written as being multiplied by an unknown factor, a:

[tex]y=a\frac{x^{2} }{z}[/tex]

Replacing the known values of x, y and z, the unknown factor, a can be calculated:

[tex]6=a*\frac{9^{2}}{27}\\6=a*\frac{81}{27}\\6=a*3\\a=2[/tex]

The constant of variation is 2.

Answer:

2xy is the greatest common factor of the three monomials.

Step-by-step explanation:

There are three monomials such that greatest common factor of first and third monomial is 2xy and greatest common factor of second and third monomial is 2x²y.

As we know greatest common factor means, common prime factors of two numbers or expressions.

Greatest common factors of 1st and second and greatest common factors of 2nd and third monomials have been given.

So, common prime factors of these two greatest common factors will be greatest common factor of all three monomials.

Prime factors of 2xy = (2)(x)(y)

Prime factors of 2x²y = (2)(x)(x)(y)

So common factors are (2)(x)(y) which is the greatest common factors of all three monomials.

Answer:

m∠A = 45.86°

Step-by-step explanation:

A rough sketch of the triangle is shown in the attached pic.

When 3 sides are given and we want to solve for an angle, we use the Cosine Rule. Which is:

[tex]p^2=a^2 +b^2 -2abCosP[/tex]

Where a, b, p are the lengths of 3 sides (with p being the side opposite of the angle we are solving for) and P is the angel we want to solve for

Thus, we have:

[tex]p^2=a^2 +b^2 -2abCosP\\13^2=14^2 +18^2-2(14)(18)CosA\\169=520-504CosA\\504CosA=351\\CosA=\frac{351}{504}\\CosA=0.6964\\A=Cos^{-1}(0.6964)=45.86[/tex]

In △ABC,a=13, b=14, and c=18. Then angle, m∠A is is 46.654°

[tex]\frac{a}{sinA}=\frac{b}{sinB} =\frac{c}{sinC}[/tex]

[tex]a^{2} =b^{2} +c^{2} -2bcCosA[/tex] or

[tex]b^{2} =a^{2} +c^{2} -2acCosB[/tex] or

[tex]c^{2} =a^{2} +b^{2} -2abCosC[/tex]

In our case;

we are going to use Cosine rule to find m∠A

We are given;

a=13, b=14, and c=18

Therefore;

[tex]a^{2} =b^{2} +c^{2} -2bcCosA[/tex]

Replacing the variables;

[tex]13^{2} =14^{2} +18^{2} -2(14)(18)CosA[/tex]

Making CosA the subject;

[tex]CosA = \frac{(13^{2} -14^{2} -18^{2})}{-2(14)(18)}[/tex]

[tex]Cos A = \frac{-351}{-504}[/tex]

[tex]CosA = 0.6964[/tex]

[tex]A = Cos^{-1} (0.6864)[/tex]

[tex]A = 46.654[/tex]

Therefore; In △ABC,a=13, b=14, and c=18, m∠A is 46.654°

Keywords: Sine rule, Cosine rule

Level; High school

Subject: Mathematics

Topic: Triangles

Sub-topic: Cosine and sine rule

Answer:

-9/8

Step-by-step explanation:

We simplify the fraction, then we isolate the variable

Answer:

Step-by-step explanation:

42) 9/4 = 2/x

You can solve it by cross multiplication:

In cross multiplication the numerator of first expression will be multiplied by th denominator of 2nd expression and the numerator of second expression will be multiplied by the   denominator of 1st expression.

So,

9/4 = 2/x

9*x = 2*4

9x=8

Divide both the sides by 9

9x/9 = 8/9

x= 8/9

44) -3/8 = r/3

Perform cross multiplication:

-3 *3 = 8* r

-9=8r

Divide both the sides by 8

-9/8 = 8r/8

-9/8 = r

46) -9/2n = -5/7

Perform cross multiplication:

-9 * 7 = 2n* -5

-63= -10n

negative signs will be cancelled out by each other.

63= 10n

Divide both the sides by 10

63/10 = 10n/10

63/10 = n ....

Answer:

The Symmetric Property of Congruence lets you say that if ∠H ≅ ∠K, then ∠K ≅ ∠H.

Step-by-step explanation:

The Symmetric Property of Congruence lets you say that if ∠H ≅ ∠K, then ∠K ≅ ∠H.

We know that Symmetric property of Congruence states that if:

∠A≅∠B,then ∠B≅∠A

Therefore according to the property,the missing angle in the statement is ∠K....

[tex]\large\boxed{\text{About}\,4.836\,\,\text{meters}}[/tex]

In this question, we're trying to find the radius of the circle.

In this case, we would use the formula:

[tex]r=\sqrt\frac{A}{\pi}\,\,\text{or}\,\,r=\sqrt\frac{A}{3.14}[/tex]

"A" would represent the area, so you would plug in 73.48 in "A."

Your equation should look like this:

[tex]r=\sqrt\frac{73.48}{\pi}[/tex]

Now, you will solve:

[tex]r=\sqrt\frac{73.48}{\pi}\\\\\text{Divide the fraction}\\\\r=\sqrt23.3894104367849385445951\\\\\text{Square it by finding the square root}\\\\r= 4.836259963730\\\\\text{Lets make it shorter}\\\\r=4.836[/tex]

When you're done solving, you should get 4.836

This means that the radius is about 4.836 meters.

Answer:

r=4.84m

Step-by-step explanation:

If the area of a circle is 73.48 square meters, the radius is 4.84m.

Formula: A=πr^2

r = A/π = 73.48/π ≈ 4.83626m

I think the answer is 1/10.

The probability that the brother and sister are both selected is 0.5052.

Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.

For the givens situation,

Total number of boys and a brother = 12

Total number of girls and a sister = 8

A brother is included among boys. So among 12 boys anyone can be a brother.

Similarly, a sister is included among girls. So among 8 girls anyone can be a sister.

The probability that the brother and sister are both selected is

⇒ [tex]P(e)=\frac{(12C_{1} )(8C_{1})}{(20C_{2})}[/tex]    

we know that [tex]nC_{r} =\frac{n! }{r!(n-r)!}[/tex]      

⇒ [tex]12C_{1}=12, 8C_{1} = 8[/tex] and [tex]20C_{2}=190[/tex]

⇒ [tex]P(e)=\frac{(12 )(8)}{190}[/tex]        

⇒ [tex]P(e)=\frac{48}{95}[/tex]

⇒ [tex]P(e)=0.5052[/tex]

Hence we can conclude that the probability that the brother and sister are both selected is 0.5052.

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Answer:

(b-1)(b-1)

Step-by-step explanation:

If you don't see a perfect square here, then your objective since the coefficient of b^2 is 1 and this is a quadratic, is to find two numbers that multiply to be 1 and add up to be -2.

-1(-1)=1 and -1+(-1)=-2.

So the factored form is (b-1)(b-1) or (b-1)^2.

Finding the slope using two points, (5, -1) and (-8, -4)

The formula for slope is

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

In this case...

[tex]y_{2} =-4\\y_{1} =-1\\x_{2} =-8\\x_{1} =-5[/tex]

^^^Plug these numbers into the formula for slope...

[tex]\frac{-4-(-1)}{-8-5}[/tex]

[tex]\frac{-3}{-13}[/tex]

[tex]\frac{3}{13}[/tex]

^^^This is your slope

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Step-by-step explanation:

The formula to find a slope using two points is:

[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\m = ((-4)-(-1))/((-8)-(5))\\m = -3 / -13\\m = 3/13[/tex]

Answer:

Perimeter = 6t - 4

Area = 2t² - 7t - 3

Step-by-step explanation:

Given length = 2t + 1

Width = t - 3

So perimeter = 2t +1 + t - 3 + 2t + 1 + t - 3

= 2t + t + 2t + t + 1 - 3 + 1 - 3

= 6t - 4

Area = (2t + 1)(t - 7)

= 2t² - 6t + t - 3

= 2t² - 7t - 3

Sorry if im wrong but i think thats the answer

For this case we have that by definition:

The area of a rectangle is given by:

[tex]A = a * b[/tex]

Where:

a and b are the sides of the rectangle.

For its part, the perimeter will be given by:

[tex]P = 2a + 2b[/tex]

If we have as data:

[tex]a = 2t + 1\\b = t-3[/tex]

So, the area is given by:

[tex]A = (2t + 1) (t-3)[/tex]

We apply distributive property:

[tex]A=2t^2-6t+t-3\\A=2t^2-5t-3[/tex]

For its part, the perimeter is:

[tex]P = 2 (2t + 1) +2 (t-3)\\P = 4t + 2 + 2t-6\\P = 6t-4[/tex]

ANswer:

[tex]A = 2t ^ 2-5t-3\\P = 6t-4[/tex]

Answer:

D:  one-to-many

Step-by-step explanation:

D:  one-to-many.  This is because there is more than one output associated with a single input.  For input 2, the output could be either 9 or 8.  Similar situation with input -3:  output could be 7 or 6.  This relation is NOT a function.

Option A, One to many

A set of collected ordered pairs is known as a relation. In each ordered pair the left-hand side is mapped with the right-hand side

As you can see the left-hand side of the ordered pair 2 is mapped to both 9,8 and -3 is mapped to 9 and 6 we can safely say that it is a one-to-many relation as the same left-hand side mapping has 2 different right-hand side mapping and there is no similar right-hand side mapping.

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For this case we have that by definition, two magnitudes are directly proportional when there is a constant such that:

[tex]y = kx[/tex]

Where:

k: It is the constant of proportionality

We must find the value of "k" when [tex](x, y): (- 3,2)[/tex]

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

Answer:

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

Answer:

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

Step-by-step explanation:

We are to find the constant of variation, [tex] k [/tex], of the direct variation, [tex] y = k x [/tex] given the coordinates of the point [tex] ( - 3 , 2 ) [/tex].

Direct variation is represented by:

[tex] y = k x [/tex]

where  [tex] k [/tex] is the constant of variation.

Substituting the coordinates of the given point to find the value of [tex] k [/tex].

[tex] 2 = k (-3) [/tex]

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

Answer:

[tex]\large\boxed{y\geq3x+21}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

[tex]-6x+2y\geq42\qquad\text{add}\ 6x\ \text{to both sides}\\\\2y\geq6x+42\qquad\text{divide both sides by 2}\\\\y\geq3x+21[/tex]

Answer:

x = 8

Step-by-step explanation:

Since m and n are parallel lines, then

6x - 2 = 46 ← alternate angles

Add 2 to both sides

6x = 48 ( divide both sides by 6 )

x = 8

Answer:

x=8

Step-by-step explanation:

The value of the angles are the same due to them being alternate interior angles and opposite angles. This means we can set 6x-2=46. Add 2 to each side to isolate the 6x. This leaves you with 6x=48. Divide by 6 to isolate x. 48/6= 8. X=8. Hope this helps :).

Answer:

of what? i know how to do these but tell me the equation

Step-by-step explanation:

you asked a very not telling question. need more info to give an answer