An_ is the set of numbers that include negative numbers
and the subset of_ numbers (...-3, -2, -1, 0, 1, 2, 3...). Also
described as positive numbers and their opposites and zero.
Blank 1:
Blank 2:​

Answer:

Correct option is

b. If two sides and one included angle are equal in triangles PQS and PRS, then their corresponding sides are also equal.

Step-by-step explanation:

Here, we are given the line RQ, which is divided in two equal parts by a line PS which is perpendicular to RQ.

The foot S of PS is on the line RQ.

First of all, let us do a construction here.

Join the point R with P and P with Q.

Please refer to the attached image.

Now, let us consider the triangles  PQS and PRS:

Now, Two sides and the angle included between the two triangles are equal.

So by SAS congruence we can say that [tex]\triangle PRS \cong \triangle PQS[/tex]

Therefore, the corresponding sides will also be equal.

RP = QP

RP is the distance between R and P.

QP is the distance between Q and P.

Hence, to prove that P is equidistant from R and Q, we have proved that:

b. If two sides and one included angle are equal in triangles PQS and PRS, then their corresponding sides are also equal.

Answer:

[tex]81+144i[/tex]

Step-by-step explanation:

We want to simplify:
[tex]\displaystyle (-3\sqrt{-81})(-5+\sqrt{-9}) + 9i[/tex]

Recall that:

[tex]\displaystyle \sqrt{-a} = i\sqrt{a}[/tex]

Therefore:
[tex]\displaystyle \begin{aligned} (-3\sqrt{-81})(-5+\sqrt{-9}) + 9i & = (-3i\sqrt{81})(-5+i\sqrt{9})+9i \\ \\ &= -(3i(9))(-5+i(3))+9i \\ \\ & = -27i(-5+3i)+9i \\ \\ & = 135i -81i^2 + 9i \\ \\ & = 144i - 81i^2 \\ \\ & = 81+144i\end{aligned}[/tex]

Note that i² = -1.

In conclusion:

[tex]\displaystyle (-3\sqrt{-81})(-5+\sqrt{-9})+9i = 81 + 144i[/tex]

Answer:

B

Step-by-step explanation:

The domain of a function is all of the x values of a function. Since there seem to be no constraints on the values of x (we know this because the function is continuous and it goes on forever in both sides), the answer is B.

Answer:

B. All real numbers

Step-by-step explanation:

Hey there!

Well the domain is all the x-values in the graph and by looking at where the lines are going we can tell that the graph domain is all real numbers.

Hope this helps :)

Answer:

Yes it will occur

Step-by-step explanation:

The lobby measures 45 feet by 45 feet

Area of the lobby = 45 * 45

=2025 ft^2

So, the lobby has 2025 tiles

subtract 1 black tile in the center

2025 tiles - 1 black tile =2024 tiles

The number of blue tiles and black tiles is 2024 tiles

He wants the outer edge to be the same color as the center tile so, divide by 2

2024/2 = 1012 tiles

The number of tiles in the outer edge is 1012 tiles and the number of tiles in the center is 1012 tiles

Answer:

[tex]\large \boxed{\mathrm{7800 \ brownies}}[/tex]

Step-by-step explanation:

975 brownies are produced per 1 hour.

To find how many brownies are produced in 8 hours, multiply the brownies amount by the hours.

975 × 8 = 7800

7800 brownies will be produced in an 8 hour shift.

Answer:

the answer is 7800

Step-by-step explanation:

975 brownies are created per 60 minutes.

To discover what number of brownies are created in 8 hours, duplicate the brownies sum continuously.

975 × 8 = 7800

7800 brownies will be created in a 8 hour move.

Answer:

36 lbs

Step-by-step explanation:

let the weight of each boy's backpack be B and the weight of each girl's backpack be G.

Given that the total weight of all (i.e 10 boys' and 10 girls') backpacks equals 600 lbs,  i.e.

10B + 10G = 600   (simplifying by dividing both sides by 10)

B + G = 60 ------- eq 1

Also given that a girl's backpack is 1.5 times LESS than a boy's backpack.

written another way, we can say that a boy's backpack is 1.5 times MORE than a girl's backpack, or:

B = 1.5G   (rearranging)

B - 1.5G = 0     ------ eq 2

We can solve eq 1 and eq 2 by elimination,

(eq 1) - (eq 2)

(B + G) - (B - 1.5G) = 60 - 0

B + G - B + 1.5G = 60

G  + 1.5G = 60

2.5G = 60   (divide both sides by 2.5)

G = 60 / 2.5

G = 24 lbs   (substitute this into equation 1)

B + G = 60

B + 24 = 60

B = 60 - 24

B = 36 lbs

Answer:

Step-by-step explanation:

The given trigonometric expression is :

11 cos^2 x +3 sin^2 x+6sinx cosx +5

or, we can write it as,

(9 cos^2 x + 2 cos^2 x) + (2 sin^2 x + sin^2 x) + 6sinx cosx +5

Again, after rearranging the terms, we can write the whole expression as,

(9 cos^2 x + sin^2 x + 6sinx cosx) + (2 cos^2 x + 2 sin^2 x) + 5

Then if you factor the following underlined section as you would with a polynomial:

(9 cos^2 x + sin^2 x + 6sinx cosx) + (2 cos^2 x + 2 sin^2 x) + 5

You get:

(3 cos x + sin x)^2 + 2 (cos^2 x + sin ^2 x) + 5

Now, the term inside the second bracket (cos^2 x + sin ^2 x) is a very popular trigonometric identity and it's value is equal to one.

So, now the whole expression becomes,

(3 cos x + sin x)^2 +7

Now, the maximum and the minimum value of the whole expression depends upon the maximum and the minimum value of the term (3 cos x + sin x), which is of the form (a cosx + b sinx),

The maximum and minimum value of (a cosx + b sinx) is relatively easy to find.

So, I've attached a screenshot from a relevant document below:

Here, a=3 and b=1,

So, R= √10

As the value of cosine of any angle lies between -1 to 1, so the value of the value of expression cos(x − α) will lie between -1 to 1.

Hence, the maximum and the minimum value of (a cosx + b sinx) will be -R and R and all the values of the expression will lie between them.

i.e., in our case between (-√10) to √10.

Again, coming back to our original expression,

(3 cos x + sin x)^2 +7

The value of the term in bracket will lie between (-√10) and √10.

But, there is a catch here, as the squares of negative terms come out be positive, hence we can't take the negative term to find the minimum value of our expression. the minimum value of the expression will be at the minimum non-negative value in the range, which is zero.

So, the minimum value will be,

(0)^2 + 7=7

and the maximum value will be,

(√10)^2 +7 = 17

Answer:

[tex]\large \boxed{\mathrm{Option \ C}}[/tex]

Step-by-step explanation:

[tex]{\mathrm{view \ attachment}}[/tex]

Answer:

 y = -1/2x + 4

Step-by-step explanation:

We have two points ( 8,0) and ( 0,4)

We can find the slope

m =(y2-y1)/(x2-x1)

    = (4-0)/(0-8)

    4/-8

   -1/2

We can use the slope intercept form

 y = mx+b where m is the slope and b is the y intercept

 y = -1/2x + 4

Answer:

Step-by-step explanation:

eq. of line with intercepts a and b is

[tex]\frac{x}{a} +\frac{y}{b} =1\\here ~eq. ~of ~line~ is ~ \frac{x}{8} +\frac{y}{4} =1\\or x+2y=8\\[/tex]

Answer:

is -5,-3

Step-by-step explanation:

set up the tablet and done

Answer:

D, 9^4 * 8^4

Step-by-step explanation:

The rule is whenever you have multiplication inside arentheses and it is raised to a power, you distribute the power to both the number s and solve.

I confirmed D is right on a calculator also.

Answer:

D

Step-by-step explanation:

Answer:

7x + 2

Step-by-step explanation:

Answer:

All real numbers

Step-by-step explanation:

Adding f(x) and g(x) together gets you, (4x-5) + (3x-7) = 7x - 12

If you graph this function you get a slanted line, which extends forever so the domain will be all real numbers.

Answer:

The fraction filled with water is 7/40

Step-by-step explanation:

Okay.

Here we start by calculating the volume of the cylindrical tank.

Mathematically, that would be;

V = π * r^2 * h

From the question

r = 80 cm = 80/100 = 0.8 meters

h = 1.4 meters

π = 22/7

Plugging these values into the volume equation, we have;

V = 22/7 * 0.8 * 0.8 * 1.4 = 2.816 m^3

But mathematically;

1 m^3 = 1000 liters

So 2.816 m^3 = 2.816 * 1000 = 2816 liters

So the fraction filled with water will be;

492.8/2816 = 0.175 = 175/1000 = 7/40

Answer:

Increase in profit = 531.52

Step-by-step explanation:

I'll take your word for it.

What you'd need to do for each kind of pizza and price, multiply the number sold and profit/loss for each, and add them up.

Calculations have been tabulated and shown in the attached diagram.

Answer

Increase in profit

= 2221.88 - 1690.36

= 531.52

Answer:

0

Step-by-step explanation:

Answer:

83 adult tickets and 217 student tickets.

Step-by-step explanation:

Let number of adult tickets sold = [tex]x[/tex]

Given that total number of tickets = 300

So, number of student tickets = 300 - [tex]x[/tex]

Cost of adult ticket = $15

Cost of student ticket = $11

Total collection from adult tickets = $[tex]15x[/tex]

Total collection from student tickets =  [tex](300-x)\times 11 = 3300-11x[/tex]

Given that overall collection = $3630

[tex]15x+(3300-11x) = 3630\\\Rightarrow 15x-11x=3630-3300\\\Rightarrow 4x = 330\\\Rightarrow x = 82.5[/tex]

So, for atleast $3630 collection, there should be 83 adult tickets and (300-83 = 217 student tickets.

Now , collection = $3632

Answer:

Step-by-step explanation:

x^2 - 17 x + 60

we should find two numbers such that their sum is equal to -17 and product is equal to 60

The two numbers are -12 and -5

now, x^2 - 12 x - 5 x + 60 { splitting the middle term }

x ( x- 12 ) - 5 ( x - 12 )

= ( x - 5 ) ( x - 12 )

hope this helps

plz mark as brainliest !!!!!!                        

Answer:

Step-by-step explanation:

[tex]x^2-17x+60\quad \implies\quad a=1\,,\quad b=-17\,,\quad c=60\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\dfrac{-(-17)\pm\sqrt{(-17)^2-4\cdot1\cdot60}}{2\cdot1}=\dfrac{17\pm\sqrt{289-240}}{2}=\dfrac{17\pm\sqrt{49}}{2}\\\\x_1=\dfrac{17-7}{2}=5\quad,\qquad x_2=\dfrac{17+7}{2}=12\\\\\\x^2-17x+60=(x-5)(x-12)[/tex]

or:

    x² - 17x + 60 =

= x² - 12x - 5x +60 =

= x(x - 12) - 5(x - 12) =

= (x - 12)(x - 5)

Answer:

Below

Step-by-step explanation:

● 2x(7a+8a) -5+56×2÷3

● 14ax + 8a -5 +56×2÷3

When you have multiplication and division go from left to right

● 14ax + 8a -5 +112÷3

● 14ax + 8a -5 +112/3

● 14ax + 8a - 15/3 + 112/3

● 14ax + 8a + 97/3

Answer:

1-lettuce 4ab x 12ab = 48a²b²

2-beets 3ab x 3ab = 9a²b²

3-tomato 4ab x 5ab = 20a²b²

4-corn 2ab x 3ab = 6a²b²

5-carrot 12ab x 3ab = 36a²b²

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

I had this question and got it right the user above explains it in detail

Answer:

6x-21

Step-by-step explanation:

Area of a rectangle is length times width.

3*(2x-7)-

6x-21

Answer:

6x - 21

Step-by-step explanation:

Since area = L x W (Length x Width)

--> 3(2x - 7)

6x - 21

Answer:

see attachment

Step-by-step explanation:

Hey there! I'm happy to help!

Like terms are numbers with the same variable and same power. 5 and 7 are like terms because they have no variable. 6x and 6y are not because they have different variables. 7x² and 6y² are also not like terms because they have different variables. 7x and 5x are like terms, and 5y³ and 9y³ are like terms.

We see that 2x and -x have the same variables. We can then combine them.

2x-x=x

Now we have x+3=7.

We subtract 3 from both sides, giving us x=4.

Have a wonderful day! :D

Answer:

40 degrees.

Step-by-step explanation:

Rotations are a rigid transformation and therefore preserve size and angles.

Answer:

[tex]\boxed{125}[/tex]

Step-by-step explanation:

Hey there!

Well 5 raised to the 3 can be written as,

[tex]5^3[/tex]

This is 5*5*5

= 125

Hope this helps :)

Answer:

2x  5

Step-by-step explanation:

1/2(6x - 10) - x =

= 3x - 5 - x

= 2x - 5

The other side of the given equation so it's true for all values of x is 2x-5.

Given that, 1/2(6x-10)-x.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now, 6x/2 - 10/2 -x

= 3x-5-2

= 2x-5

Therefore, the other side of the given equation so it's true for all values of x is 2x-5.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ2

Answer:

Domain:  

( − ∞ , 0 ) ∪ ( 0 , ∞ ) , { x | x ≠ 0 }

Step-by-step explanation:

i used math. way for help

Answer:

Step-by-step explanation:

3) G

Step-by-step explanation:

Q(-1,-1) R(3,1) S(2,-4)

x+2 y+3 translation then rotation 180 (x,y) be (-x,-y)

Q -1+2 -1+3 (1,2) (-1,-2)

R 3+2 1+3 (5,4) (-5,-4)

S 2+2 -4+3 (4,-1)

Answer:

Stationery section will be 4 feet wide.

Step-by-step explanation:

Total area of bookstore = 288 sq ft

Area to be devoted to stationery = [tex]\frac{1}6[/tex] of total area = [tex]\frac{1}{6} \times 288 = 48\ sq\ ft[/tex]

Length of stationery section = 12 ft

To find:

Width of stationery section = ?

Solution:

First of all, let us have a look at the area of rectangle:

[tex]A = Length \times Width[/tex]

Here, we are given the length for stationery section and area of stationery section has been calculated above.

And we have to find the Width of stationery section.

So, let us put the two values to find the third value.

[tex]\Rightarrow 48 = 12 \times Width\\\Rightarrow Width = \dfrac{48}{12}\\\Rightarrow \bold{Width = 4\ ft}[/tex]

So, the answer is:

Stationery section will be 4 feet wide.