Match the terms to their definition.


1. expression

a branch of mathematics that uses variables

2. opposite numbers

a mathematical statement that shows two expressions are equal using an equal sign

3. equation


a line that graphically represents all numbers

4. arithmetic sequence


a value that is substituted in for the variable in a function in order to generate an output value

5. function


two numbers that are the same distance from zero on the number line, but in opposite directions

6. family of facts


a single term; multiple terms connected by an addition or subtraction sign

7. input


a number belonging to the set made up of the counting numbers: 1, 2, 3, and so on

8. coordinate plane


a set of numbers where the difference is the same between any two consecutive terms

9. integer


all possible combinations for a set of numbers (2 + 3 = 5, 3 + 2 = 5, 5 - 3 = 2, 5 - 2 = 3)

10. negative number


a relation in which for any given input value, there is only one output value

11. natural number


a number that is less than zero

12. number line


a two-dimensional system in which a location is described by its distance from two intersecting, perpendicular axes

13. algebra


a number belonging to the set made up of the whole numbers and their opposites

Answer:

Step-by-step explanation:

(0,2). y=mx+b or 2=-2 × 0+b, or solving for b: b=2-(-2)(0).

Answer:

the required equqtion is x-y=2

Answer:

216

Step-by-step explanation:

outcome of one die is 1 out of 6 and if you roll 3 dices, the outcome is 216 possible outcomes because 6 times 6 times 6 is 6 cubed or 216

Step-by-step explanation:

just try out some values to get a clue

f(0)<= -|0+1|+1 = 0

okay, that value is true for all graphs

let's try another

f(1) <= -|1+1|+1 = -1

for x=1 the inequality only applies for a region less or equal to -1

B and D are clearly out. C covers just to much above

Only A remains as an option

note that |-5| is just 5. this notation is to say "how far away from 0. -5 is just 5 units away from zero.

in terms of calculating it, it makes everything inside it positive (distance from zero is never negative)

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

First we find out the area of circle, and then subtract the area of triangle from it to find the area of the shaded region

Area of Circle

Here, r=radius

area of circle= π×r²

                     = π × 5²     (radius=half of diameter)

                     = 25π

                     = 78.54cm²

Area of Triangle

Here, b=base, h=height

area of triangle = [tex]\frac{1}{2\\}[/tex]×b×h

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

                          = 24cm²

Area of shaded region= area of circle - area of triangle

                                     = 78.54 - 24

                                     = 54.54

                                     ≈ 54.5cm² [Ans]

The area of the shaded segment is 100/3π square centimeter

What is a area?

Area is nothing but the surface bounded by the object in 2D.

What is a segment?

A part of a line or curve between two points In circle we can say segment is nothing but a region or area cutoff from the circle by chord.

What is a segment area?

Area bounded by a segment. Area of segment has a formula (θ/360°)πr²

According to the question

θ=120°

radius =10cm

area of segment = (120°/360°)π(10²)

120°/360° =0.333

10²=100

0.333×π×100

33.3π or (100/3)π

Thus area of the shaded segment is 33.3π or (100/3)π square centimeters

To know more about area here

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Answer:

80%

Step-by-step explanation:

x : 100 = 64 : 80

x = (100 * 64)/80 = 80%

Answer:

80%

Step-by-step explanation:

Is means equals and of means multiply

64 = P * 80

Divide each side by 80

64/80 = P

.8 = P

Change to percent form by multiplying by 100

80% = P

. ( m →(N v Q)) →((M→N) v (M→Q))

2.((T v U) → V) → (T → (U → V)) wut tyhe hell is this

Answer:

1.043

Step-by-step explanation:

Decimal multiplier to increase by x% is computed as:-

100% + x%

The decimal multiplier to increase by 4.3% would be

100% +4.3% = 104.3%

To remove% we divide the number by 100, so the number will become

Hence, The decimal multiplier to increase by 4.3% = 1.043

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Hope this Helps

Answer:

50/50

Step-by-step explanation:

It's random

Answer:

option c is the correct answer

Answer:

c. 1/3

Step-by-step explanation: Substitute the corresponding x and y values into the slope formula, m = y2-y1/x2-x1. Then simplify the equation and you will get 1/3.

Answer:

[tex]Shaded = 212.5cm^2[/tex]

Step-by-step explanation:

Given

See attachment

Required

The shaded region

First, calculate the area of the complete rectangle

[tex]Area =Length * Width[/tex]

[tex]Area = 14cm * 25cm[/tex]

[tex]Area = 350cm^2[/tex]

Next, calculate the area of the triangle

[tex]Area = \frac{1}{2} * Base * Height[/tex]

[tex]Area = \frac{1}{2} *25cm * 11cm[/tex]

[tex]Area = 137.5cm^2[/tex]

Subtract the area to calculate the shaded region area

[tex]Shaded = 350cm^2 - 137.5cm^2[/tex]

[tex]Shaded = 212.5cm^2[/tex]

Find the area of the top, which is a circle.

Area of a circle = pi x r^2

Area = 3.14 x 1.5^2 = 7.065

Now for the volume multiply the area of the top by the height:

7.065 x 12 = 84.78 cubic inches

Round to the nearest tenth: 84.8 cubic inches

Answer:

Volume of cylinder is 84.78 inches.

Step-by-step explanation:

Volume of cylinder = π × r ² × h

Where,

And we have given that

Substitute the values

Volume of cylinder = 3.14 × (1.5 inches) × 12 inches

= 3.14 × 2.25 inches² × 12 inches

multiply the values , we get

Volume of cylinder = 84.78 inches³.

84.8 inches³ is the round nearest to tenth.

9514 1404 393

Answer:

  5196 m

Step-by-step explanation:

The difference in elevation is found by subtracting one elevation from the other. Usually, we're interested in the positive difference, so we subtract the smaller number from the larger.

  5040 -(-156) = 5040 +156 = 5196

The difference in elevation is 5196 meters.

Answer:

z = 2.2

Step-by-step explanation:

[tex]-\frac{z}{0.5} + 1.4 = -3\\\\-\frac{z \times 10}{0.5 \times 10} + 1.4 = -3\\\\-2z + 1.4 = -3\\\\-2z = -3 - 1.4\\\\-2z = -4.4\\\\z = \frac{-4.4}{-2}\\\\z = 2.2[/tex]

Answer:

156

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1; Define

Identify

f(x) = 5ˣ + 1

Interval x [0, 4] →b = 4, a = 0

Step 2: Find Rate of Change

Answer:

4.605170185988091

Step-by-step explanation:

ln 100 = 4.605170185988091

e^4.605170185988091 = 100

Step-by-step explanation:

100=1 log 10(1)=0

I hope this is helpful for you

Answer:

160 chips

Step-by-step explanation:

Given

[tex]n = 8[/tex] --- players

[tex]c = 60[/tex] --- chips per player

First, calculate the total chips

[tex]Total = n * c[/tex]

[tex]Total = 8 * 60[/tex]

[tex]Total = 480[/tex]

After 5 players are out; there are 3 players remaining in the game

So, the average number of chip with each of the remaining player is:

[tex]Average = \frac{Total}{n-5}[/tex]

[tex]Average = \frac{480}{8-5}[/tex]

[tex]Average = \frac{480}{3}[/tex]

[tex]Average = 160[/tex]

Answer:

A.

Null:

H0: u= 5.65

Alternative:

H1: u > 5.65

B.

The test statistic

Xbar = 6.24

u = 5.65

S = 1.24

N = 57

T = 6.24-5.65/(1.24/√57)

= 0.59/(1.24/7.5498)

= 0.59/0.1642

Test statistic = 3.593

C.

With alpha = 0.05

Df = n-1 = 57-1 = 56

T critical = 1.673

D.

If t test > 1.673 reject the null hypothesis

3.593>1.673, reject the null hypothesis

We conclude that there is enough evidence that the technique helped the participants to learn more.

Answer:

Step-by-step explanation:

sorry i don't know how to draw the diagram,then i can explain better.

9/x=x/27

x²=9×27=9×9×3

x=9√3

Answer:

10

Step-by-step explanation:

Triangles AYZ and XYZ are congrunt, therefore AZ = XZ = 10

Answer:

The point of intersection is:

[tex]\displaystyle \left(\frac{6\sqrt{5}}{5}, \frac{3\sqrt{5}}{5}+5\right)\approx \left(2.68, 6.34)[/tex]

Step-by-step explanation:

We want to find the point in QI at which the line with the equation:

[tex]y=0.5x+5[/tex]

Intersect a circle with a radius of 3 and a center of (0, 5).

First, write the equation of a circle. The equation for a circle is given by:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where (h, k) is the center and r is the radius.

Since our center is (0, 5), h = 0 and k = 5. The radius is 3. So, r = 3. Substitute:

[tex](x-0)^2+(y-5)^2=(3)^2[/tex]

Simplify:

[tex]x^2+(y-5)^2=9[/tex]

At the point where the two equations intersect, its x-coordinate and y-coordinate will be the same. Therefore, we can substitute the equation of the line into the equation of the circle and solve for x. So:

[tex]x^2+((0.5x+5)-5)^2=9[/tex]

Simplify:

[tex]x^2+(0.5x)^2=9[/tex]

Square:

[tex]x^2+0.25x^2=9[/tex]

Combine like terms:

[tex]\displaystyle 1.25x^2=\frac{5}{4}x^2=9[/tex]

Solve for x:

[tex]\displaystyle \begin{aligned} x^2&=\frac{36}{5} \\ x&=\pm\sqrt{\frac{36}{5}} \\ x&\Rightarrow \frac{6}{\sqrt{5}}=\frac{6\sqrt{5}}{5}\approx2.68\end{aligned}[/tex]

Note that since we are looking for the point of intersection in QI, x should be positive. So, we can ignore the negative answer.

To find the y-coordinate, substitute the x-value back into either equation. Using the linear equation:

[tex]\displaystyle y=0.5\left(\frac{6\sqrt{5}}{5}\right)+5=\frac{3\sqrt{5}}{5}+5\approx 6.34[/tex]

So, the point of intersection in QI is:

[tex]\displaystyle \left(\frac{6\sqrt{5}}{5}, \frac{3\sqrt{5}}{5}+5\right)\approx \left(2.68, 6.34)[/tex]

Answer:

10/35

Step-by-step explanation:

4*2.5=10

14*2.5=35

4/14=10/35

Answer:

Greg is 28.

Step-by-step explanation:

Greg's age is y.

y - 5 = 23

y - 5 + 5 = 23 + 5

y = 28

Answer:

[tex]90m^2 and 144 m^2[/tex]

Step-by-step explanation:

Given :

Length of the rectangle (l)=15m

Width of the rectangle (w)= 6 m

Area of the rectangle can be calculated as :

[tex]A=l*w\\A=(15)(6)\\A=90 m^2[/tex]

Now,

Side of square (s)=12 m

Area of the square can be find:

[tex]A=s^2\\A=12^2\\A=144 m^2[/tex]