Work out the following, giving your answers in their simplest form:
a) 2/3 divided by 1/4
b) 7 divided by 2/3

Answer:

The two column proof is presented as follows;

Statement                   [tex]{}[/tex]                  Reason

1. Parallelogram SUPN [tex]\overline {SR}[/tex]⊥ [tex]\overline {UN}[/tex] [tex]{}[/tex]   1. Given

and [tex]\overline {MP}[/tex]⊥ [tex]\overline {UN}[/tex]

2. ∠SRU = ∠PMN = 90°   [tex]{}[/tex]                 2. Definition of perpendicular lines

3. ∠SRU ≅ ∠PMN            [tex]{}[/tex]                 2. Definition of congruency

4. [tex]\overline {UP}[/tex] ║ [tex]\overline {SN}[/tex]                      [tex]{}[/tex]                4. Opposite sides of a parallelogram are                                            [tex]{}[/tex]                                                               congruent

5. ∠SNR ≅ ∠PUM             [tex]{}[/tex]               5. Alternate interior angles are congruent

6. [tex]\overline {UP}[/tex] ≅ [tex]\overline {SN}[/tex]                      [tex]{}[/tex]               6. Opposite sides of a parallelogram are                                            [tex]{}[/tex]                                                              congruent

7. ΔPMU ≅ ΔSRN                 [tex]{}[/tex]           7. By AAS rule of congruency

By the Angle-Angle-Side (AAS) rule of congruency, we have that, if two angles and a corresponding adjacent side (∠SRU ≅ ∠PMN, ∠SNR ≅ ∠PUM, [tex]\overline {UP}[/tex] ≅ [tex]\overline {SN}[/tex])  of two triangles (ΔPMU and ΔSRN) are congruent, then the the two triangles are also congruent (ΔPMU ≅ ΔSRN)

Step-by-step explanation:

Answer:

              11x+23

y=    -    --------------

                  10

Step-by-step explanation:

Answer:

a) how many stamps are worth $0.10 and how many are worth $0.20

b) x + y = 15

   .10x + .20y = 2.40

Step-by-step explanation:

Answer:

10 cans of paint

Step-by-step explanation:

Find the total area of the room

Divide the answer by 10meter squared.

Answer: Divide each term in 3 a ≥ − 6 by 3 . 3 a 3 ≥ − 6 3 Cancel the common factor of 3 . Tap for more steps... a ≥ − 6 3 Divide − 6 by 3 . a ≥ − 2 The result can be shown in multiple forms. Inequality Form: a ≥ − 2 Interval Notation: [ − 2 , ∞ )

Using translation concepts, it is found that graph A is equivalent to the graph of g(x)=-f(x).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The transformation g(x)=-f(x) is a reflection over the x-axis of function f(x), which is given by graph A.

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Answer:

use distance formula

Step-by-step explanation:

enter each set of points into distance formula, find distance then sum all sides

Answer:

x = 3

Step-by-step explanation:

12x = 36

simply 12 will go to the other side and switches to the opposite sign for example + will be -

× will br ÷

so 36 ÷ 12 =3

x = 3

Answer:

1) [tex]3\cdot x^{2}+2\cdot x[/tex] - The polynomial expression is a second-grade binomial, with a coefficient of 3 on the second-grade monomial component and a coefficient of 2 on the first-grade monomial component.

2) [tex]2\cdot x^{2}-5\cdot x + 3[/tex] - The polynomial expression is a third-grade trinomial, with a coefficient of 2 on the second-grade monomial component, a coefficient of -5 on the first-grade monomial component and a coeffcient of 3 on the zero-grade monomial component.

3) [tex]6\cdot x[/tex] - The polynomial expression is a first-grade monomial, with a coefficient  of 6 on the first grade monomial component.

Step-by-step explanation:

1) [tex]3\cdot x^{2}+2\cdot x[/tex] - The polynomial expression is a second-grade binomial, with a coefficient of 3 on the second-grade monomial component and a coefficient of 2 on the first-grade monomial component.

2) [tex]2\cdot x^{2}-5\cdot x + 3[/tex] - The polynomial expression is a third-grade trinomial, with a coefficient of 2 on the second-grade monomial component, a coefficient of -5 on the first-grade monomial component and a coeffcient of 3 on the zero-grade monomial component.

3) [tex]6\cdot x[/tex] - The polynomial expression is a first-grade monomial, with a coefficient  of 6 on the first grade monomial component.

Answer:

3x2 + 2x

This polynomial expression is a quadratic binomial, with a coefficient of 3 on the quadratic term, a linear term with coefficient 2, and no constant.

2x2 − 5x + 3

This polynomial expression is a quadratic trinomial, with a coefficient of 2 on the quadratic term, a linear term with coefficient -5, and constant 3.

6x

This polynomial expression is a linear monomial with a coefficient of 6 on the linear term and no constant.

Step-by-step explanation:

plato answer

Answer:

The answer is 2.89 in 2dp

3 cube is 27

27 minus 6.8 is 20. 2

20. 2 decide by 7 is 2.89

Answer:

  the answer would be 3

Step-by-step explanation:

Because 3 to the third power is 27 and 6 times 8 is 48 so you subtract 27 and 48 and you get 21 so you divided 21 and 7 and you get 3. sorry if that's confusing but I hope it helped.

Answer:

1

Step-by-step explanation:

Find the rise over run

Rise = 3

Run = 3

3/3 = 1

Slope = 1

Answer:

1

Step-by-step explanation:

First, you take any two points from the line, I put (2,1) and (0,-1). You plug it into the formula y2-y1/x2-x1 which would be -1-1/0-2 which is equal to -2/-2=1

Hope this helps

Answer:

[tex]y=3x-15[/tex]

Step-by-step explanation:

Slope intercept form: [tex]y=mx+b[/tex] where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept (the value of y when the line crosses the y-axis)

1) Find the slope of the line ([tex]m[/tex])

When it comes to parallel lines, they will always have the same slope but different y-intercepts. The given equation is [tex]y=3x-5[/tex]. Because 3 is in the place of m, we know that the slope of the line is 3. Therefore, the slope of the line parallel to it will also be 3. So far, this is what our equation looks like:

[tex]y=3x+b[/tex]

2) Find the y-intercept ([tex]b[/tex])

To find the y-intercept, we plug the given point (4,-3) into the equation we currently have and solve for b.

[tex]y=3x+b\\-3=3(4)+b\\-3=12+b[/tex]

Subtract both sides by 12

[tex]-3-12=12+b-12\\-15=b[/tex]

Therefore the y-intercept of our line is -15. Plug -15 back into the original equation as b.

[tex]y=3x+(-15)\\y=3x-15[/tex]

I hope this helps!

Answer:

-16

Step-by-step explanation:

Answer:

The cause is the independent variable. In your study, its value is independent of other variables. The affect is the dependent variable. Its value depends on the independent variable being changed.

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Whenever you are multiplying any numbers or dividing you count them as terms. Since you are multiplying two numbers there will be 2 terms you don't count them if you add.

Tell me if I'm wrong and please explain.

Answer:

this will be the correct answer

Answer:

(x,y) => (x, -y)

Step-by-step explanation:

[tex]y = 7x + 3[/tex]

[tex] - y = 7x + 3[/tex]

[tex]y = - 7x - 3[/tex]

so

[tex]g(x) = - 7x - 3[/tex]

Hence, [tex]g(x) = - 7x - 3[/tex].

What is the function?

Functions are often defined by a formula that describes a combination of arithmetic operations and previously defined functions; such a formula allows computing the value of the function from the value of any element of the domain.

Here given that,

Let [tex]g(x)[/tex] be the reflection across the x-axis of the function [tex]f(x) = 7x + 3[/tex]. Identify the rule for [tex]g(x)[/tex].

So,

[tex]y = 7x + 3\\-y= 7x + 3\\y = - 7x - 3\\g(x)=- 7x - 3[/tex]

Hence, [tex]g(x) = - 7x - 3[/tex].

To know more about the function

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Answer:

[tex]\boxed{\textsf{ Hence the solution set is$ \bf{\bigg( \dfrac{33}{4},\infty \bigg) }$}}.[/tex]

Step-by-step explanation:

A inequality is given to us and we need to find the solution set. So the given inequality to us is ,

[tex]\bf\implies -4x + 35 > 2 \\\\\bf\implies -4x > 2-35 \\\\\bf \implies -4x > -33 \\\\\bf \implies x >\dfrac{-33}{-4}\\\\\bf \implies x > \dfrac{33}{4} \\\\\bf\implies \boxed{\pink{\bf x \in \bigg(\dfrac{33}{4}, \infty \bigg) }}[/tex]

Answer:

Step-by-step explanation:

5

Answer:

2S + 0.065(2S)

Step-by-step explanation:

Since S is the price of a shirt, the price of two shirts would be 2 x S = 2S

a tax is a compulsory sum levied on goods and services. tax increases the price of a good

The price of the 2 shirts would increase by the amount of tax ; 0.065(2S)

This gives = 2S + 0.065(2S)

Alternatively, since two shirts were purchased, the amount of tax would be twice 0.065 - 0.13 - S + S + 0.13S

We want to write two expressions that represent the total cost of the shirts, the expressions are:

Cost = P*(1.065) +  P*(1.065)

cost = P*2.13

We know that Benita buys two shirts for the same price, P.

Then at this moment. the total cost is just:

cost = 2*P

Now we apply a 6.5% tax, then the price increases by 6.5%, this is written as:

P' = P*(1 + 6.5%/100%) = P*(1.065)

Then the total cost is twice that amount, written as:

Cost = P*(1.065) +  P*(1.065)

This can be one of the two expressions.

Now to get the other expression, we just simplify the above one:

cost = 2*P*(1.065) = P*2.13

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Answer:

x < 11

Step-by-step explanation:

Taking the problem piece by piece;

five is greater than

5 >

the result of taking six away from x

x - 6

Solve for x;

5 > x - 6

5 + 6 > x

11 > x

x < 11

Answer:

7.2

Step-by-step explanation:

24/2 = 12

19.2/2 = 9.6

[tex]12^{2}[/tex] - [tex]9.6^{2}[/tex] = 51.84

[tex]\sqrt{51.84}[/tex] = 7.2

Answer:

Y=3/5x-3

Step-by-step explanation:

Answer:

y=5/3x+5

Step-by-step explanation:

1)3y-5x=15

2)3y=15+5x

3)y=5+5/3x

4)y=5/3x+5    

1) Write the equation out

2) Add 5x to both sides of the equation

3) Divide both sides of the equation by 3

4) Reorder the terms  

9514 1404 393

Answer:

  x = 2 m

  y = 30°

Step-by-step explanation:

The side lengths of ΔDEF are 3/9 = 1/3 of those of ΔABC.

  x = DF = 1/3(AB) = (1/3)(6 m)

  x = 2 m

__

Angle measures of ΔDEF are the same as those of the corresponding angles of ΔABC.

  y = ∠B = ∠E = 30°

  y = 30°

Answer:

E = 80 degrees

Step-by-step explanation:

7x + 3 + x + 15 + 74degrees = 180

8x + 92 = 180

8x = 180 - 92

8x = 88

x=11

m<E = 7x + 3

7(11) + 3

77 + 3

= 80

Answer:

your y intercept is 90 and the equation would be y= 90 and x is unknown

Answer:

B.) 42.9

Step-by-step explanation:

The percent that we are trying to find out is 12/28

I know this because if you add the 12 and 16 which is the total amount of people given then it leaves us with an amount of 28 people. Since we are trying to find the percent of the number of people who like fish we have to divide the total by 12 (the number of people who like fish)

Anyways 12 divided by 28 = 42.857etc.

If we simplify this then that gives us our answer of B.) 42.9

Write down the factors for the numerator and the denominator.

Determine the largest factor that is common between the two.

Divide the numerator and denominator by the greatest common factor.

Write down the reduced fraction.

Answer:

4. 21

5. 45

6. 22

Step-by-step explanation:

4. 6 + (2^4) - 1

   6 + (16) - 1

   22 - 1 = 21

5. (4 * 3²) + (18 - 9)

   (4 × 9) + (9)

   (36) + (9) = 45

6. 16 + (5² - 7) ÷ 3

PEMDAS tells us to do what's in Parentheses first

16 + ( 25 - 7) ÷ 3

16 + (18/3)

16 + 6 = 22

Answer:

a.

Step-by-step explanation:

girls 60/50

boys 40/50

40/50 is 10