Explanation:
The distributive property tells you that multiplication distributes over addition. In equation form, it looks like ...
a(b +c) = ab +ac
__
Groups and Multiples of GroupsThe parentheses are a grouping symbol. In the above equation, they indicate that the sum (b+c) is to be treated as a group. When it is multiplied by 'a', everything in the group is multiplied by 'a'.
In the real world, there are many ways things are grouped. Baseball cards are packaged together with bubble gum; Cracker Jacks® are packaged together with a prize; left gloves are packaged together with right gloves; a bicycle is a package that has a frame, 2 wheels, a seat, handlebars. If you purchase a number of any of these packages, each of the items in the package is part of your purchase that number of times.
For example, 3 bicycles will have 3 frames, 3×2 = 6 wheels, 3 seats, 3 sets of handlebars. In algebraic form, this might look like ...
3(f +2w + s + h) = 3f +6w +3s +3h
__
Eliminating ParenthesesUsing the distributive property to eliminate parentheses is like regrouping the contents of the packages so like items are grouped together. In our above example, the 3 frames were grouped together when we considered that part of the group of 3 bicycles. The multiplier multiplies every member of the group.
__
Adding ParenthesesThe reverse of the distributive property tells us we can regroup items into sets. It tells us we can take 3 frames, 6 wheels, 3 seats, and 3 handlebars and group them together in a way that makes 3 bicycles, each having a frame, 2 wheels, a seat, and handlebars.
3f +6w +3s +3h = 3(f +2w + s + h)
Often, we're asked to choose the multiplier to be the greatest common factor (GCF) of the numbers of things in the group. That makes each group as small as possible. The multiplier only needs to be a common factor, not necessarily the greatest common factor.
What is the equation of a circle with center (−5, −8) and radius 2?
(x − 5)2 + (y − 8)2 = 4
(x + 5)2 + (y + 8)2 = 4
(x + 5)2 + (y + 8)2 = 2
(x − 5)2 + (y − 8)2 = 2
[tex]\qquad\qquad\huge\underline{{\sf Answer}}☂[/tex]
Standard equation of circle ~
[tex]\qquad \sf \dashrightarrow \:(x - h) {}^{2} + (y - k) {}^{2} = r {}^{2} [/tex]
where,
h = x - coordinate of centre k = y - coordinate of centrer = radius of the circle
Now, let's plug in the values ~
[tex]\qquad \sf \dashrightarrow \:(x - (5)) {}^{2} + (y - ( - 8)) {}^{2} = {2}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:(x + 5) {}^{2} + (y + 8) {}^{2} = {4}^{} [/tex]
Therefore, the correct choice is B
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
The equation of the circle with a center of (4,5) and a radius of 2 units is (x + 5)² +(y + 8)² = 4
How to determine the circle equation?The center of the circle is given as:
Center (a,b) = (-5, -8)
The radius is given as:
Radius, r = 2
The equation of the circle is calculated using:
(x - a)² + (y - b)² = r²
Substitute values for r and (a,b)
(x + 5)² +(y + 8)² = 2²
Evaluate the square of 2
(x + 5)² +(y + 8)² = 4
Hence, the equation of the circle is (x + 5)² +(y + 8)² = 4
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Solve and verify your answer.
A sludge pool is filled by two inlet pipes. One pipe can fill the pool in 11 days and the other pipe can fill it in 24 days. However, if no
sewage is added, waste removal will empty the pool in 32 days. How long (in days) will it take the two inlet pipes to fill an empty pool
Answer:
' =9 93/107 days
Step-by-step explanation:
1/11+1/24
one day =35/264
35/264 -1/32
=107/ 1056- fraction of rem in a day
1 day= 107/1056
x = 1
=107/1056x=1
x=1÷107/1056
1056÷107
=9 93/107 days
A garden table and a bench cost $668 combined. The garden table costs $82 less than the bench. What is the cost of the bench?
Step-by-step explanation:
let the cost of the bench = x
the cost of the garden table = x + 82
x + (x + 82) = 668
2x + 82 = 668
2x = 586
x = 293
The bench costs $293 and the garden table costs 293 + 82 = $375
can you mark me as brainliest, it will help me a lot. thank you in advance
Let R be the shaded region bounded by the graphs of y = e^x, y = -1, x = 1, and the y-axis. R is the base of a solid with cross sections perpendicular to the x-axis as squares. Find the volume of the solid.
Answer:
get a graphing caculator and type the numbers in the rectangle and see what you get
Step-by-step explanation:
When asked to factor the trinomial 4x^2 + 12x + 9, a student gives the answer (2x - 3)(2x - 3). What is one thing wrong with this answer?
A. There is nothing wrong with the answer
B. The minus signs should be plus signs
C. 4 is also a factor of this trinomial
D. The factors are not simplified
The one thing wrong with the answer is option B. The minus signs should be plus signs.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Given quadratic is 4x²+12x+9
Taking common 4
4(x²+3x) + 9
=4(x² + 3x + 9/4) + 9 - 9
=4(x + 3/2)²
=(2x+3)²
=(2x+3)(2x+3)
So, the minus sign must be a plus sign. option B is correct.
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Allie and Roman are now trying to graph the red line shown here.
Allie entered this equation: y=-2
Roman entered this equation: x=-2
Who is right, and how do you know?
Use the given parent function f(x)=|x| to graph g(x)=|x+2|−4. Use the ray tool and select two points to graph each ray.
Answer:
g(x) is the translation of f(x) 2 units to the left and 4 units down
Answer: the largest angle has a measure of _____ degrees.
Answer:
the largest Angle has a measure of 360 degrees
Find all the common factors of 9 and 15.
A) 1, 3
B) 1, 3, 9
C) 1, 3, 5, 9
Answer:
A common factor is a whole number which is a factor of two or more numbers.
[tex]factors \: of \: 9 = 1 \times 3 \times 3[/tex]
[tex]factors \: of \: 15 = 1 \times 3 \times 5[/tex]
since both of the numbers have only 1 and 3 in common.
therefore ,
Option A is correct.
______________________________________
______________________________________
Additional information
★ The highest common factor (HCF) is the greatest factor that will divide into two or more numbers.
★ The lowest common multiple (LCM) is the smallest multiple that is common to two or more numbers.
hope helpful :D
There are 150 boys and girls playing in the soccer tournament.50 of the students are wearing red.what percent of the of players are wearing red.
Answer:
1/3 or 33%
Step-by-step explanation:
You can first do: 50/150
Which is 5/15 simplified
And do the quick math:
1/3 or 33%
Find the equation of the line passing through the given point and
PARALLEL to the given equation. Write your answer in slope intercep
form. (xX_PARALLEL_Xx) *
(5,3) and y = x + 4
Answer:
y= x -2
Step-by-step explanation:
Slope-intercept form:
y= mx +c, where m is the slope and c is the y-intercept
Given equation: y= x +4
This equation is already in the slope-intercept form, thus its slope can be found from the coefficient of x.
Slope= 1
[tex]\textcolor{steelblue}{\text{Parallel lines have the same slope.}}[/tex]
Slope of unknown line= 1
Substitute the m= 1 into y= mx +c:
y= x +c
To find the value of c, substitute a pair of coordinates the line passes through into the equation.
When x= 5, y= 3,
3= 5 +c
c +5= 3
c= 3 -5
c= -2
Thus, the equation of the line is y= x -2.
At the movie theatre , child admission is $ 6.40 and adult admission is $ 9.60 . On Monday , 153 tickets were sold for a total sales of $ 1270.40 . How many adult tickets were sold that day ?
Answer:
91 adult tickets
Step-by-step explanation:
Algebra is really useful here:
Let a = number of adult tickets sold and c = number of child tickets sold.
Thus, we can say that
a + c = 153 (number of tickets)
6.40c + 9.60a = 1270.4. (cost of all of the tickets)
Solving,
c = 153 - a
6.40(153 - a) + 9.60a = 1270.4
979.2 - 6.40a + 9.60a = 1270.4
3.20a = 291.2
a = 91
Kala drove 603 miles in 9 hours at the same rate how many miles would she drive in 12 hours
Answer:
804
Step-by-step explanation:
603/9 x 12
67 x 12
804
Answer:
804 miles in 12 hours
Step-by-step explanation:
603/9 which = 67
67*12 which equal 804
don't forget the unit (mph)
You have four $20 bills, ten $5 bills, and twelve $1 bills in your wallet. If you reach into your wallet twice, what is the probability that you will pull out a $1 bill the first time and a $5 bill the second time?
Answer:
2/28 ?
Step-by-step explanation:
if I'm wrong so sorry
In this figure, the coordinates of the vertices of quadrilateral PARK are (5, 5), (5, 1), (-2, 1), and (0, 5) respectively. The corresponding coordinates of the vertices in the image are (-10, -10), (-10, -2), (4, -2), and (0,-10). Which of the following statements is true? A. Quadrilateral P’A’R’K’ is the image of quadrilateral PARK after a rotation and a dilation. B. Quadrilateral P’A’R’K’ is the image of quadrilateral PARK after a reflection and a dilation. C. Quadrilateral P’A’R’K’ is the image of quadrilateral PARK after a translation and a reflection. D. Quadrilateral P’A’R’K’ is the image of quadrilateral PARK after a rotation and a translation.
Answer:
B
Step-by-step explanation:
Answer:
The other personis wrong its answer A: a rotation and a dilation.
Step-by-step explanation:
I mean its kind of self explanatory but i hope it helps.
i got a 100% on my quiz with this question btw.
7 3/5 - 6 3/5
Pls help i can't do dis math
Step-by-step explanation:
[tex] = 7 \times \frac{3}{5} - 6 \times \frac{3}{5} \\ = \frac{7 \times 5 + 3}{5} - \frac{6 \times 5 + 3}{5} \\ = \frac{38}{5} - \frac{33}{5} \\ = \frac{38 - 33}{5} \\ = \frac{5}{5} [/tex]
Now convert into lowest term
[tex] \frac{1}{1} [/tex]
1/1 is the answer ....
Consider the polynomial function g(x) = 8x5 + ax4 + 5x + 20, where a is an unknown real number. If (x+4) is a factor of g(x), what is the value of a?
[tex]g(x) =8x^5 + ax^4 +5x +20 \\\\\text{If}~ x +4 ~ \text{is a factor of g(x) then,}~ \\\\g(-4)=0\\\\\implies 8(-4)^5 +a(-4)^4+5(-4) +20 = 0\\\\\implies 256a -8192 = 0\\\\\implies a = \dfrac{8192}{256} = 32[/tex]
When a system contains the equations of two parabolas, there can only be one solution.
True or False
candy that costs 31 cents per pound is mixed with candy that costs 46 cents per pound to obtain 50 pounds of candy that costs 40 cents per pound. How many pounds of each of the two types of candy are in the mix?
Answer:
20 lb of 31 cent candy, 30 lb of 46 cent candy
Step-by-step explanation:
sorry don't have one
here is a smiley face for you
:D
The amount of each type of candy (in pounds) that are mixed for the considered condition is: 20 pounds of first type of candy and 30 pounds of second type of candy.
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
For this case, we can assume the separate weights of each type of candies to be represented by variables.
Let we have:
x = weight (in pounds) of first type of candy whose cost is 31 cents per pound.y = weight (in pounds) of second type of candy whose cost is 46 cents per pound.x pounds of first type of candy is mixed with y pounds of second candy.
The weight of the mixture = x + y = 50 pounds
The cost of the mixture = 40 cents per pound = [tex]40 \times 50 = 2000[/tex] cents
Cost of the mixture = cost of x pounds of first candy+ cost of y pounds of second candy = [tex]31x + 46y[/tex]
Thus, we get [tex]31x + 46y =2000[/tex]
Therefore, we got a system of two linear equations as:
[tex]x +y = 50\\31x + 46y =2000[/tex]
From first equation, we get:
[tex]x = 50 -y[/tex]
Substituting this value in second equation, we get:
[tex]31(50-y) + 46y =2000\\1550 + 15y = 2000\\15y = 450\\\\y = 450/15 = 30[/tex]
Putting this value of y in equation for x, we get:
[tex]x = 50-y = 50-30 = 20[/tex]
Thus, the amount of each type of candy (in pounds) that are mixed for the considered condition is: 20 pounds of first type of candy and 30 pounds of second type of candy.
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I took the Integrity Pledge.
Do I put True or False ?
True or False
What does integrity mean?
Answer:
a little confusing, but i think its a fake quiz that asks for your pledge so you put true, and integrity: the quality of being honest and having strong moral principles; moral uprightness
Step-by-step explanation:
Simply the expression 3(2y - 8) - 2y(5-y)
Answer:
-4y - 24 + 2y²
Step-by-step explanation:
1. Simplify the distributive properties
⇒ 3(2y - 8) - 2y(5 - y)
⇒ 6y - 24 - 10y + 2y²
2. Combine like terms
⇒ 6y - 24 - 10y + 2y²
⇒ y(6 - 10) - 24 + 2y²
3. Simplify the expression
⇒ y(6 - 10) - 24 + 2y²
⇒ -4y - 24 + 2y²
what is the area of the regular hexagon
Answer:
720
Step-by-step explanation:
n*180
n
the answer is 720
250 lottery tickets were sold and there are 5 prizes on these ticket if Kunal has purchased one lottery ticket what is the probability that he wins a prize
Total number of tickets sold = 250
Number of prizes = 5
Number of favorable outcomes = 5
[tex]P(A)= \frac{no. of possible outcomes}{No. of total outcomes} [/tex]
[tex]P (getting \: a \: prize) = \frac{5}{250} =\frac{1}{150}[/tex]
help is super appreciated this should probably be fast
2. Determine the y – intercept, zeros, the equation of the axis of symmetry and vertex of each quadratic
relation.
y = (x − 3)(x+3)
[tex]\\ \rm\rightarrowtail y=(x-3)(x+3)=x^2-9[/tex]
Zeros are x intercepts
(3,0) U(-3,0)#2
Y intercept=-9#3
Axis of symmetry=x=0
#4
Vertex=(0,-9)Answer:
Given quadratic equation: y = (x - 3)(x + 3)
Zeros (x-intercepts)
The zeros of a quadratic equation are the points where the graph of the quadratic equation crosses the x-axis. So the x-intercepts (zeros) are when y = 0
⇒ (x - 3)(x + 3) = 0
⇒ (x - 3) = 0 so x = 3
⇒ (x + 3) = 0 so x = -3
Therefore, the x-intercepts are at (3, 0) and (-3, 0).
y-intercept
The y-intercept is the point where the graph crosses the y-axis. So the y-intercept is when x = 0
⇒ (0 - 3)(0 + 3) = -9
Therefore, the y-intercept is at (0, -9)
Vertex
Expand the equation so that it is in standard form y = ax² + bx + c:
⇒ y = x² - 9
x-value of vertex is -b / 2a ⇒ -0 / 2 = 0
substitute the found value of x into the equation to find y:
⇒ y = (0)² - 9 = -9
Therefore, the vertex is (0, -9)
Axis of symmetry
Axis symmetry of a quadratic equation is x = a where a is the x-value of the vertex.
Therefore, the axis of symmetry is x = 0
If you roll a dice 500 times how many times do you expect to get a 5?
Answer:
20
Step-by-step explanation:
60%
Approximate the temperature of the water after 6 intervals
What is the equation of the line in slope-intercept form -8 and 8 ?
Answer:
y = x - 8
Step-by-step explanation:
y = x - 8
Check your answer using (0, -8):
y = x - 8
-8 = 0 - 8
-8 = -8
This statement is true
Also, view the attached graph.
Hope this helps!
If 24% of the Skittles in the bag are red, what percentage of the Skittles are not red?
Answer:
76%
Step-by-step explanation:
Given:
If 24% of the Skittles in the bag are red, what percentage of the Skittles are not red?
Solve:
Percent - Out of 100
100 - 24 = 76
Hence, 76% of the skittles are not red.
~~Lenvy~~
Answer:
76% are not red
Formula:
(Total Skittle %)-(Red Skittle %)=(Non-Red Skittle %)
Work:
100%-24%=76%
Choose the correct graph of the function y=2√x.
Answer:
[D]
Step-by-step explanation:
Graph using the end point and a few selected points.
x y
0 0
1 2
2 2.83
Graph also below:
[RevyBreeze]
Find the midpoint of AB A(-1,2) B(0,-14)
Answer:
given ,
two points A ( -1 , 2 ) and B ( 0 , -14 )
to find - coordinates of midpoint of A and B______________________________________
[tex]\fbox\pink{Solution -}[/tex]
let the midpoint be P ( x , y )
using midpoint formula ,
[tex]P(x,y) = ( \frac{ x_{1} + x_{2} }{2} , \frac{ y_{1} + y_{2} }{2} ) \\ \\ P(x,y) = ( \frac{ - 1 + 0}{2} , \frac{2 + ( - 14)}{2} ) \\ \\ (x,y) = ( \frac{ - 1}{2} , \frac{ - 12}{2} ) \\ \\ x = \frac{ - 1}{2} \\ \\ y = \frac{ - 12}{2} => - 6[/tex]
thus ,
the coordinates of the midpoint are
[tex]\red{P( \frac{ - 1}{2} , - 6)} \\ \\ or \\ \\ \red{P( -0.5 , - 6 )} [/tex]
hope helpful :D
Answer:
Step-by-step explanation:
A(-1,2) x₁ = -1 & y₁ = 2
B(0 ,-14) x₂ = 0 & y₂ = -14
[tex]\text{ \sf Midpoint = $\left(\dfrac{x_{1}+x_{2}}{2} ,\dfrac{y_{1}+y_{2}}{2}\right)$ }[/tex]
[tex]= \left (\dfrac{-1+0}{2} ,\dfrac{2+[-14]}{2} \right) \\\\\\=\left(\dfrac{-1}{2}, \dfrac{-12}{2}\right)\\\\\\=\left( -0.5 , -6 \right)[/tex]