Line R: 2x + 2y = 18 Line M: x + y = 9 Which statement is true about the solution to the set of equations?

Answer:

See Explanation

Step-by-step explanation:

Given

Students = 24

Musical Instrument and Sport = 6

Neither = 3

Sport = 14

Required

Complete the two-way frequency table

-------------------------------------------------------- Plays sport || Does not play sport

Plays a musical instrument ---------------------6--------------------------------------

Does not play a musical instrument -------------------------------------3-----------

Total ---------------------------------------------------- 14 ---------------------------------------

To solve this, we'll make use of the following naming rules

A represent students that plays musical instrument; A = 6

B represent students that do not play musical instrument

C represent students that plays sport

D represent students that do not play sport; D = 3

Considering the first column [Plays a sport] and taking note of the naming rules;

[tex]A + B = 14[/tex]

Substitute 6 for A

[tex]6 + B = 14[/tex]

Solve for B

[tex]B = 14 - 6[/tex]

[tex]B = 8[/tex]

Also, given that there are 24 students in the class and 14 of them play sport; this implies that 10 do not play sport

Considering the second column [Does not play a sport]

[tex]C + D = 10[/tex]

Substitute 3 for D

[tex]C + 3 = 10[/tex]

Solve for C

[tex]C = 10 - 3[/tex]

[tex]C = 7[/tex]

Hence, the complete table is:

-------------------------------------------------------- Plays sport || Does not play sport

Plays a musical instrument ---------------------6--------------------------7----------

Does not play a musical instrument ---------8--------------------------3---------

Total ---------------------------------------------------- 14 -----------------------10---------

Step-by-step explanation:

We need to say that [tex]9^{3/4}[/tex] is equivalent to what.

We know that, (3)² = 9

So,

[tex]9^{3/4}=((3)^2)^{3/4}\\\\=3^{3/2}[/tex]

We can write [tex]3^{3/2} =3\times 3^{1/2}[/tex]

And [tex]3^{1/2}=\sqrt{3}[/tex]

So,

[tex]3\times 3^{1/2}=3\sqrt{3}[/tex]

So, [tex]9^{3/4}[/tex] is equivalent to [tex]3\sqrt{3}[/tex].

Hence, this is the required solution.

Answer:

43

Step-by-step explanation:

Using Thales theorem:

● SP/LN = RP /RN

Notice that RN = 2×RP

● SP/LN = RP/2RP

● SP /LN = 1/2

● SP / (5x-14) = 0.5

● (2x+3)/(5x-14) = 0.5

● 2x+3 = 0.5(5x-14)

● 2x+3 = 2.5x -7

Add 7 to both sides

● 2x+3+7 = 2.5x-7+7

● 2x+10 = 2.5x

Sustract 2x brom both sides

● 2x+10-2x = 2.5x-2x

● 10 = 0.5x

Multiply both sides by 2

● 10×2 = 0.5x×2

● 20 = x

Replace x with 20 in Sp expression:

● SP = 2x+3

● SP = 2×20+3

● SP = 43

Answer:

5.2/0.052 is 100, and 100 is 10^2, so the missing divisor is 10^2

Answer:

100

Step-by-step explanation:

5.2/x = 0.052

Since the decimal place moves 2 places to the left from 5.2 to 0.052, the divisor is 100.

5.2/100 = 0.052

Answer:

243 as a power of 3

= 3^5

=243

Answer:

(-4,7)

Step-by-step explanation:

solved by graphing

Answer:

[tex]\large\boxed{z}[/tex]

Step-by-step explanation:

What is square root of the product of the number z and itself?

Break down into smaller parts

What is the product of the number z and itself?

Product = multiply

Write an equation multiplying z by itself

z * z

Bring back the full question: What is the square root of the product of the number z and itself?

Now we can just add a [tex]\sqrt{}[/tex] to the front of our equation to solve the problem.

[tex]\sqrt{z * z}[/tex]

Simplify

z * z = [tex]z^{2}[/tex]

[tex]\sqrt{z^{2} }[/tex]

In this case, the square root cancels out the exponent ([tex]z^{2}[/tex]), so [tex]\sqrt{z^{2} }[/tex] can simplify to z.

Hope this helps :)

Answer:

The maximum number of boxes that will fit on the shelf = 189 boxes

Step-by-step explanation:

First, to harmonize the units of the dimensions given, let us convert the unit of the Pick-Me-Up teabags to cm.

1 cm = 10mm

1mm = 0.1cm

∴ 120mm = 0.1 × 120 = 12cm

Therefore, the base of each box is 12cm²

Next, let us calculate the area of the shelf.

Dimension of shelf = 65cm × 35cm

∴ Area of shelf = 65 × 35 = 2275cm²

Therefore, to calculate how many boxes will fit into the shelf, we will divide the area of the shelf by the area of the boxes of Pick-Me-Up teabag. This is shown below.

Area of shelf = 2275cm²

Area of boxes = 12cm²

Number of boxes that will fit on the shelf = Area of shelf ÷ Area of boxes

= 2275 ÷ 12 = 189.58 boxes

since there are no fractional boxes, we will round down to the nearest whole number of boxes.

Hence, the maximum number of boxes that will fit on the shelf = 189 boxes

Answer:

x = 16

Step-by-step explanation:

The figure shown shows an inscribed angle F and central angle E. Both angles intercept the same arc.

Therefore, angle E is twice the measure of angle F, according to the central angle theorem of a circle.

Thus,

m<E = 2 * m<F

(x + 94)° = 2(55)

We can find the value of x with this equation.

x + 94 = 110

Subtract 94 from both sides

x = 110 - 94

x = 16

Answer:

2x²-32 ⇒ x²=16⇒ (-4,4)

4x²-100 ⇒x²=25 ⇒(-5,5)

x²-55=9 ⇒x²=64 ⇒(-8,8)

x²-140=-19 ⇒x²=121 ⇒(-11,11)

2x²-18=0 ⇒x²=9 ⇒(-3,3)

Answer:

Step-by-step explanation: Further explanation

[tex]2x^2-32=0\\\\\mathrm{Add\:}32\mathrm{\:to\:both\:sides}\\\\2x^2-32+32=0+32\\\\2x^2=32\\\\\frac{2x^2}{2}=\frac{32}{2}\\\\\mathrm{For\:}x^2=f\left(a\right)\\\\\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{16},\:x=-\sqrt{16}\\\\x=\sqrt{16},\:x=-\sqrt{16}\\x=4,\:x=-4[/tex]

[tex]4x^2-100=0\\\mathrm{Add\:}100\mathrm{\:to\:both\:sides}\\4x^2-100+100=0+100\\4x^2=100\\\frac{4x^2}{4}=\frac{100}{4}\\x^2=25\\\mathrm{For\:}x^2=f\left(a\right)\\\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\x=\sqrt{25},\:x=-\sqrt{25}\\\\x=5,\:x=-5[/tex]

[tex]x^2-140=-19\\x^2-140+140=-19+140\\x^2=121\\\mathrm{For\:}x^2=f\left(a\right)\\\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\x=\sqrt{121},\:x=-\sqrt{121}\\x=11,\:x=-11[/tex]

[tex]x^2-55=9\\x^2-55+55=9+55\\x^2=64\\\mathrm{For\:}x^2=f\left(a\right)\\\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\x=\sqrt{64},\:x=-\sqrt{64}\\x=8,\:x=-8\\[/tex]

[tex]2x^2-18=0\\2x^2-18+18=0+18\\2x^2=18\\\frac{2x^2}{2}=\frac{18}{2}\\x^2=9\\\mathrm{For\:}x^2=f\left(a\right)\\\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\x=\sqrt{9},\:x=-\sqrt{9}\\x=3,\:x=-3[/tex]

Answer:

5.2 inches

Step-by-step explanation:

Let a be the side of the square poster.

The area of it is:

● A = a^2

● 27 = a^2

● a = √27

● a = √(9×3)

● a = 3√3

● a = 5.19

Round it to the nearest tenth

● a = 5.2 inches

The length of one side of the poster is approximately 5 inches rounded to nearest tenth.

We round numbers because they are easy to deal with and they also retain their value to that place they have been rounded.

According to the given question the area of a square poster is 27inch².

We have to determine the length of one side of the poster.

We know area of a square is (side)².

∴ (side)² = 27.

side = [tex]\sqrt{27}[/tex].

We know [tex]\sqrt{25}[/tex] is 5 and [tex]\sqrt{36}[/tex] is 6 so [tex]\sqrt{27}[/tex] will lie between 5 and 8 and much closer to 5.

learn more about rounding of numbers here :

https://brainly.com/question/15235224

#SPJ2

Answer:

=x(x-1) +3x

= x^2-x+3x

=x^2 +2x

=x(x+2)

Step-by-step explanation:

Answer:

18y^3 + 24y^5.

Step-by-step explanation:

6y^3(3 + 4y^2)

= 6*3 y^3 + 6*4 y^(3+2)

= 18y^3 + 24y^5.

Answer:

7³

Step-by-step explanation:

Using PEMDAS, we see that E (which stands for exponents) comes before M (which stands for multiplication) and A (which stands for addition) so the first operation you should do is 7³.

Answer:

-.26

Step-by-step explanation:

If you take the absolute value (indicates how far a number-negative/positive- is from 0) of each number u listed you will find that .26 is the smallest number,thus smallest number.

Answer:

-.26 is closest to 0 on the number line.

Step-by-step explanation:

To find distance we use absolute value to find the smallest absolute value.

The absolute value of each number is as follows

-0.26 (0.26)

0.3 (0.3)

0.275 (0.275)

-0.51 (0.51)

In order from least to greatest we have

.26, .275, .3, .51

Therefore -.26 is closest to 0 on the number line.

Good luck!!

Answer:

slope = 2 : 8 or 1:4

Step-by-step explanation:

a(-3, 4)

b(5, 6)

slope = rise / run

slope (6-4, 3+5))

slope = 2 : 8 or 1:4

Answer:

Slope =¼

Step-by-step explanation:

[tex](-3, 4) \: (5, 6) \\ x _{1} = - 3 , y_1 = 4 \\ x_2 = 5 \\ y_2 = 6[/tex]

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\ m = \frac{6 - 4}{5 - ( - 3)} \\ m = \frac{2}{8} = \frac{1}{4} [/tex]

Answer:

145.8

Step-by-step explanation:

l.s.f for the two is 3:5

volume scale factor will be 3³:5³ which us 27:125

so 27×675 / 125

= 145.8

Answer:

Step-by-step explanation:

Given the  ratio of  the profit, cost of  materials and labour  in the production of

an article to be 5:7:13 respectively, total ratio = 5+7+13 = 25

If the cost of labour is x, the cost of material will be 840+x (since the  cost of materials is Le  840 more than that of  labour)  .

Let the total cost of producing the article be y.

Cost of labour = 13/25 * y = x

Cost of labour  = 13y/25 = x.................... 1

Cost of material = 7/25*y = 840+x

Cost of material = 7y/25 = 840+x ..................... 2

From 1, 13y = 25x

x = 13y/25 ................... 3

Substituting equation 3 into 2:

7y/25 = 840+x

7y/25 = 840+13y/25

collect the like terms:

7y/25 - 13y/25 = 840

-6y/25 = 840

-6y = 25*840

y = 25*840/6

y = 3,500

Hence the total cost of producing the article is 3500

Answer:

32 adulta

Step-by-step explanation:

96÷6 = 16 number of families

now we need to see how many adults there are in 16 families.

and the number is 32 adults.

Answer:

32 adults.

Step-by-step explanation:

At the very least, there are 4 children for every 2 adults. That means that, at the very least, there are 6 people in one group to get into the fun fair.

96 / 6 = 16

So, there are 16 groups trying to get into the fun fair, with 2 adults in each group. 2 * 16 = 32 adults are in the queue.

Hope this helps!

Answer:

The x-intercept is (-2,0)

The y-intercept is (0,3)

Step-by-step explanation:

An x-intercept is the point when the graph crosses the x-axis. In other words, the y-coordinate of the x-intercept is 0 (since it lays on the x-axis). In other words, to solve for the x-intercept(s), plug in 0 for y and solve for x:

[tex]-3x+2y=6\\-3x+2(0)=6\\-3x=6\\x=-2[/tex]

So, the x-intercept is (-2,0).

Likewise, the y-intercept is the point when the graph crosses the y-axis. Because it's on the y-axis, the x-coordinate value would be 0. Thus, to find the y-intercept, plug in 0 for x and solve for y:

[tex]-3x+2y=6\\-3(0)+2y=6\\2y=6\\y=3[/tex]

Thus, the y-intercept is (0,3).

Answer:

2n+7

Step-by-step explanation:

First lets find the common difference which is 2, now we can use this formula to find the nth term.

an = a1 + (n - 1 ) d

an= 9+(n-1)2

=9+2n-2

=2n+7

To check let's insert n=5, 2(5)=10+7=17.

15+2=17!

Answer:

5.08 cm

Step-by-step explanation: You dont have the choices for answers.

2inches is also 1/6 of a foot, etc

Answer:

U B = 100.5

Step-by-step explanation:

the upper bound of the size of the television screen= 95.5 since it is corrected to the nearest 5 then the U B =100.5 cm

The upper bound of the size of the television screen is 100.5 cm

The conversion of the size of the television screen to the nearest 5cm from the initial size of 95 cm is = 100 cm.

Now, the upper bound of the size of the television screen which is 100 is can be determined by the addition of a half value to 100 cm:

i.e.

= (1/2) + 100 cm

= 0.5 + 100 cm

= 100.5 cm

Therefore, we can conclude that the upper bound of the size of the television screen is 100.5 cm

Learn more about nearest value here:

https://brainly.com/question/16382026?referrer=searchResults

Answer:

First, an asymptote means that the function "tends to go" to a value, bt actually never reaches it.

The functions here are:

A.f(x) = 2 + 1

B.f(x) = x^2 + 1

c.f(x) = x^2 - 1

D.f(x) == +1

The functions are really poorly written, but i will try to answer this.

first:

"a root at x = -1"

Means that f(-1) = 0,

The only function that is zero when x = -1, is the option c.

f(-1) = (-1)^2 - 1 = 1 - 1 = 0.

Now, if we want to have a vertical asymptote at x = 2, then we should have a function like:

[tex]f(x) = \frac{something}{x - 2}[/tex]

So we want to have a quotient, where the denominator is equal to zero when x = 2, this will lead to a vertical asymptote.

I can not see this in the options provided, so i guess that the functions are just not well written.

For a horizontal asymptote, we have something like:

[tex]f(x) = \frac{something}{x} + 1[/tex]

So as x starts to grow, the first term in the function will start to decrease, until it becomes really close to zero (but is never equal to zero) so in that case we have an horizontal asymptote to f(x) = 1.

Answer:

Step-by-step explanation:

25x(4x -10y + 3)

the solution is C. 25x

Answer:

It would be y = -x + 9

Step-by-step explanation:

Answer:

Y=-x+9

Step-by-step explanation:

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope / gradient

c is the y intercept

y = 3x + 7

Comparing this equation with the general form above

Gradient of the line = 3

2y - 6x = 8

Divide both sides by 2

We have

y - 3x = 8

To make y the subject move 3x to the right side of the equation

That's

y = 3x + 8

Comparing with the general form above that's y = mx + c

The gradient = 3

y = 3x + 7

A(2 , y ) , B( x , 4)

Since they lie on the line we can substitute their values into the equation to find the missing points

For A(2 ,y)

We have

y = 3(2) + 7

y = 6 + 7

For B( x , 4)

4 = 3x + 7

3x = 4 - 7

3x = - 3

Divide both sides by 3

Hope this helps you

Answer: Choice B)

The relation is a function because there are no vertical lines that can be drawn on the graph that pass through more than one point.

This graph passes the vertical line test. Any input (x) leads to one and only one output (y). An example of a graph failing the vertical line test would be a graph that is a sideways parabola.

the graph will shift 3 units to the right