Answer:
The simplified expression of (4-5r+8s)(5r-9) is
40r s-25r^2-72s+65r-36
(hope this helped)
The simplified expression of (4-5r+8s)(5r-9) is [tex]65r - 25r^2 + 9r + 40rs - 72s.[/tex]
The simplified expression of (4-5r+8s)(5r-9) step by step.
Understanding how to simplify expressions can be incredibly useful in algebra and will make solving equations much easier. By using the distributive property, we can multiply the terms inside the parentheses and then combine like terms to get the simplified expression.
To simplify the expression (4-5r+8s)(5r-9), we'll use the distributive property, also known as the FOIL method (First, Outer, Inner, Last). This property allows us to multiply each term in the first parentheses by each term in the second parentheses.
1. First, we multiply the term "4" in the first parentheses by each term in the second parentheses:
4 * 5r = 20r
4 * (-9) = -36
2. Next, we move to the second term in the first parentheses, "-5r," and multiply it by each term in the second parentheses:
-5r * 5r = -25r²
-5r * (-9) = 45r
3. Lastly, we move to the third term in the first parentheses, "8s," and multiply it by each term in the second parentheses:
8s * 5r = 40rs
8s * (-9) = -72s
Now, we have all the resulting terms:
20r - 36 - 25r² + 45r + 40rs - 72s.
To simplify further, we combine like terms. Like terms have the same variable(s) raised to the same power:
20r + 45r = 65r
-36 + 45r = 9r
So, the simplified expression is:
65r - 25r² + 9r + 40rs - 72s.
In mathematical terms, we applied the distributive property to multiply each term in the first parentheses by each term in the second parentheses. Then, we combined like terms to obtain the final simplified expression, 65r - 25r² + 9r + 40rs - 72s.
To know more about Algebra here
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If a1= 7 and an = -4an-1 + n then find the value of a5
Answer:
a₅ = 1701
Step-by-step explanation:
[tex]a_1=7\\\\a_n=-4a_{n-1} + n\\\\a_2 = -4*a_1 + 2\\\\[/tex]
= -4*7 + 2
= -28 + 2
= -26
a₃ = -4a₂ + 3
= -4*(-26) + 3
= 104 + 3
= 107
a₄ = -4a₃ + 4
= -4*107 + 4
= -428 + 4
= -424
a₅ = -4a₄ + 5
= -4*(-424) + 5
= 1696 + 5
= 1701
Which equation best models the data shown on the scatter-plot below?
The scatterplot is an illustration of a linear regression.
The equation that best models the scatter plot is y = 4x+ 35
How to determine the equation of the scatterplot?The equation of a linear regression is represented as:
y = mx + b
Where:
m represents the slope
b represents the y-intercept
From the graph, we have the following points on the line of best fit (see attachment)
(x,y) = (10,75) and (20,105)
The equation is then calculated as:
[tex]y = (\frac{y_2 - y_1}{x_2 - x_1})(x -x_1) + y_1[/tex]
This gives
[tex]y = (\frac{105 - 75}{20- 10})(x -10) + 75[/tex]
Evaluate
[tex]y = 4(x -10) + 75[/tex]
Open the bracket
[tex]y = 4x -40 + 75[/tex]
Simplify
[tex]y = 4x+ 35[/tex]
Hence, the equation that best models the scatter plot is y = 4x+ 35
Read more about scatter plots at:
https://brainly.com/question/6592115
HELPP 30 POINTS A bag of marbles has a mass of 45 grams. What is the mass of 250 bags of marbles in kilograms?
show your work below
Answer:
11.25 kg
Explanation:
1 bag of marbles → 45 grams
250 bags → (45 *250) = 11250 grams
Conversion:
1 kg ↔ 1000 grams
So,
11250 g → (11250/1000) kg = 11.25 kg
Answer:
11.25 kg
Step-by-step explanation:
One bag of marbles = 45 g
⇒ Weight of 250 bags of marbles = 250 × 45 = 11250 g
1000 g = 1 kg
⇒ 11250 g ÷ 1000 = 11.25 kg
Un triángulo rectángulo ABC recto en B , en la region relativa al lado AB se ubica el punto P, tal que la m
this queation is tricky give me a sec
Step-by-step explanation:
Find the surface area of the prism.
13 m
5 m
11 m
12 m
The surface area is
(Type a whole number or a decimal.)
Hint: There are 3 feet in 1 yard.....Math 100pts
Answer:
$0.22/foot
Step-by-step explanation:
Setting up the equation:
⇒ 6 yards of aluminum wire costs $3.96
⇒ 6 yards = $3.96
Simplifying the equation in cost/foot:
⇒ 6 yards = 6(3) feet = 18 feet = $3.96 (1 yard = 3 feet)
⇒ 18 feet = $3.96
⇒ 1 foot = $3.96/18 = $0.22
Answer:
$0.22
Step-by-step explanation:
6 yards costs $3.96
Therefore, to find the cost of 1 yard, divide the cost of 6 yards by 6:
⇒ 1 yard = $3.96 ÷ 6
= $0.66
1 yard = 3 feet
Therefore, to find the cost of 1 foot, divide the cost of 1 yards by 3:
⇒ Price per foot = $0.66 ÷ 3
= $0.22
WILL GIVE BRAINLIEST.
Part A: The area of a square is (16x^2 + 24x + 9) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (5 points)
Part B: The area of a rectangle is (4x^2 − 49y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)
Answer:
Part A: (4x+3) (4x+3)
Part B: 4 (x+y) (x-y)
(If this is not the answer you are looking for, sorry)
Step-by-step explanation:
Part A: (16x²+24x+9)
FOIL
(4x + 3) (4x +3) = 16x²+24x+9
(4x) (4x) = 16x²
(4x) (3) = 12x
(4x) (3) = 12x
12x + 12x = 24x
(3) (3) = 9
Part B: (4x²-4y²)
4 (x² - y²)
You have to factor it completely
4 (x + y) (x - y)
(Make sure to use FOIL to double check)
What is the measure of space inside a suitcase?
Answer:
Linear inches
Step-by-step explanation:
or really, any linear dimension – simply refer to the sum total of your bag's length, width and depth.
Answer:
These are based on the main compartment inside the suitcase and are measured in liters with an average capacity of 20 liters, whilst most large cases have an average capacity of 100 liters.
Step-by-step explanation:Brainliest
A cupcake shop makes 25 dozen cupcakes in 2 days, how many cupcakes are made in 5 days at this rate
A 600
B 650
D 750
D 900
Answer:
D. 750
Step-by-step explanation:
if the shop makes 25 dozen in 2 days that means it makes 300 cupcakes in 2 days because 1 dozen is 12 cupcakes, so you will see that they make 50 dozen in 4 days which is 600 then you know she is only going to be making half of that 25 dozen on the 5th day so you just take half of 300 which is 150 and add it all up: 300+300+150=750
Please help i am confused
Answer: (1)
Step-by-step explanation:
The parts listed in the congruence statement aren't corresponding, meaning they don't have to be congruent.
Complete the table below: Show all your work.
Answer:
Step-by-step explanation:
(-2, 8)
(-1, 6)
(0, 4)
(1, 2)
(2,0)
to "show work" just plug in each x value into that equation. you will never learn if all you do is copy down answers. i have given you all of the correct answers, and all you need to do is plug in the values for each x value into the equation, multiply then add. good luck man.
Write a slope intercept form that contains the points(3,4) and (-6,2)
Answer:
[tex]y=0x+2[/tex]
Step-by-step explanation:
Given the following question:
Point A = (3, 2) = (x1, y1)
Point B = (-6, 2) = (x2, y2)
To write the following points in slope intercept form we first need to calculate the slope by using the formula for slope or rise over run.
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
[tex]m=\frac{2-2}{-6-3} =\frac{0}{-9}[/tex]
[tex]0\div-9=0[/tex]
[tex]m=0[/tex]
Now that we have to slope, we can now write the points in slope intercept form by using the formula y = mx + b and solve for b.
[tex]y=mx+b[/tex]
[tex]y=2[/tex]
[tex]m=0[/tex]
[tex]x=3[/tex]
[tex]2=0(3)+b[/tex]
[tex]0\times3=0[/tex]
[tex]2=0+b[/tex]
[tex]2+0=2[/tex]
[tex]2=b[/tex]
[tex]b=2[/tex]
[tex]y=0x+2[/tex]
Your answer in slope intercept form is "y = 0x + 2."
Hope this helps.
for every 1/2 cup portion of baby cereal you will need 4 oz of milk. how many ounces of milk will you need to prepare 20 portions
Answer:
80 oz
Step-by-step explanation:
20 portions times 4 oz is 80 oz
30 divided (3x5)divided 2 + 1?
Answer
2
Explain
3 x 5 = 15 so 30 divided by 15 equals 2. Now 2 divided by 2 equals 1. Now 1 + 1 = 2
Answer:
2
Step-by-step explanation:
30÷(3×5)÷2+1
30÷15÷2+1
2÷2+1
1+1
2
Hope dis helps
i need help please 100 points
Divide. 8 from 1/3
20
24
12
4
Answer: B. 24
Step-by-step explanation:
8 / 1/3 =
8 * 3 +
24
Answer:
24
Step-by-step explanation:
8 divided by 1/3=24
1/3x4=1 1/3
1/3x12=4
1/3x24=8
1/3x20=7 1/3
students were grouped into 4 classrooms with an average of 33.5 students per classroom. if the students were regrouped into 5 classrooms, what would be the average number of students in each room?
Answer:
26.8
Step-by-step explanation:
Because 33.5 was the average of how many students were in a classroom (if there were 4 classrooms), then 33.5 is can somewhat be the average of how many students were in one classroom; 1/4 of the classrooms can hold an average of 33.5.
Total students that were divided into 4 classrooms :
33.5 × 4 = 134
So if there is 134 students that will be grouped into 5 different classrooms, divide 134 by 5 to find the average amount of students that will be grouped.
134 ÷ 5 = 26.8
So, the average amount of students that will be grouped if they were divided into 5 classrooms would be 26.8 .
Hope this helped !
Number 13. Multiply please.
[tex](x-y)^2 \\\\\\= (x-y)(x-y)\\\\= x * x + (x)(-y)+(-y)(x) +(-y)(-y)\\\\ = x^2 -xy-xy + y^2\\\\=x^2-2xy + y^2[/tex]
Hope that helps!
-4x+y=1
2y-2=8x
How many solutions does this have?
a. no solution
b. one solution
c. infinitely many solutions
Answer:
c. infinotely msny solutions
Answer:
Step-by-step explanation:
y = 4x + 1
2y - 2 = 8x
2(4x + 1) - 2 = 8x
2x + 2 - 2 = 8x
2x + 0 = 8x
6x = 0
x = 0
y = 0 + 1
y = 1
(0, 1)
answer is b. one solution
can you please help me?
Answer:
102 dollars
Step-by-step explanation:
1. a) Solve the following quadratic-quadratic system of equations graphically.
y– 3x² +12x = 16
y + 4x²– 16x = -12
b.) GRAPH
c.) verify your solution (s) algebraically.
Answer:
see explanation
Step-by-step explanation:
look at the photo
[tex]y+2=(x^2/2)-2sin(y)[/tex]
the assumption being that "y" is encapsulating a function in "x" terms.
[tex]y+2=\cfrac{x^2}{2}-2sin(y)\implies \stackrel{\textit{taking the derivative to both sides}}{\cfrac{dy}{dx}+0=\cfrac{1}{2}(2x)\underset{chain~rule}{-2cos(y)\cdot \cfrac{dy}{dx}}} \\\\\\ \cfrac{dy}{dx}=x-2cos(y)\cfrac{dy}{dx}\implies \cfrac{dy}{dx}+2cos(y)\cfrac{dy}{dx}=x \\\\\\ \cfrac{dy}{dx}\left[ 1+2cos(y) \right]=x\implies \cfrac{dy}{dx}=\cfrac{x}{1+2cos(y)}[/tex]
Help me please !!!!!!!
Answer:
25ft/s
Step-by-step explanation:
500ft/20s = 25ft/s
The moon forms a right triangle with the Earth and the Sun during one of its phases, as shown below:
A right angle triangle is shown with the Earth at the right angle. The acute angle between the line joining the Earth and the m
A scientist measures the angle x and the distance y between the Earth and the Sun. Using complete sentences, explain how the scientist can use only these two measurements to calculate the distance between the moon and the Sun.
(It is an answer you have to type)
Answer:
distance between moon and sun= y/sin x
Step-by-step explanation:
by use of trigonometric ratios SOHCAHTOA
dat stuff only works on right angled triangles so that is what gave it away
you will use
Sin x= y/distance between moon and Sun
distance between moon and sun= y/sin x
based on my the sketch in my mind hope am right
MATH MIDDLE SCHOOL ASAP due in 10 mins no explaining to do just answer thank you giving brainlist :)
Answer:
y-9=8
Step-by-step explanation:
A teenager puts $50 into an investment account in January. If by December the balance in the account increases by 17%, what is the amount of money in the account in December?
A.$67.00
B.$58.50
C.$41.50
D.$33.00
Answer:
58.50
Step-by-step explanation:
C.$58.50
|| ▼ Answer ▼ ||
|| ✪ Solution ✪ ||
Step 1:
In this question, we are given the following:
A teenager puts $50 into an investment account in January.
If by December the balance in the account increases by 17%,
what is the amount of money in the account in December?
Step 2:
In this case, we are going to use:
[tex]Amount=Principal~(~1+\frac{Rate}{100})^{n}[/tex]
Here, Principal = $ [tex]50[/tex]
Rate = 17%
[tex]^{n}(Time)=~From~January~to~December=12=months=1~year[/tex]
Then, we have that:
[tex]Amount=50~(~1+\frac{17}{100})^{1}[/tex]
[tex]Amount=50~(~1+0.17~)^{1}[/tex]
[tex]Amount=50~(~1.17)[/tex]
[tex]Amount=[/tex] $ 58.50 (Option B)
CONCLUSION:
The amount of money in the account in December = $ 58. 50 ( OPTION B )
Hope this helps!
If you have any queries please ask.
Thank you to who ever answers this
Answer:
The answer is G.
Step-by-step explanation:
Trust me.
Answer:
J is the answer
Step-by-step explanation:
I had given the explanation but brainly deleted it for having a link.
Just use this:
"What is a box and whisker plot?
A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum.
In a box plot, we draw a box from the first quartile to the third quartile. A vertical line goes through the box at the median. The whiskers go from each quartile to the minimum or maximum.
Example: Finding the five-number summary
A sample of 101010 boxes of raisins has these weights (in grams):
252525, 282828, 292929, 292929, 303030, 343434, 353535, 353535, 373737, 383838
Make a box plot of the data.
Step 1: Order the data from smallest to largest.
Our data is already in order.
252525, 282828, 292929, 292929, 303030, 343434, 353535, 353535, 373737, 383838
Step 2: Find the median.
The median is the mean of the middle two numbers:
252525, 282828, 292929, 292929, \large{30}3030, \large{34}3434, 353535, 353535, 373737, 383838
\dfrac{30+34}{2}=32
2
30+34
=32start fraction, 30, plus, 34, divided by, 2, end fraction, equals, 32
The median is 323232.
Step 3: Find the quartiles.
The first quartile is the median of the data points to the left of the median.
252525, 282828, \large{29}2929, 292929, 303030
Q_1=29Q
1
=29Q, start subscript, 1, end subscript, equals, 29
The third quartile is the median of the data points to the right of the median.
343434, 353535, \large{35}3535, 373737, 383838
Q_3=35Q
3
=35Q, start subscript, 3, end subscript, equals, 35
Step 4: Complete the five-number summary by finding the min and the max.
The min is the smallest data point, which is 252525.
The max is the largest data point, which is 383838.
The five-number summary is 252525, 292929, 323232, 353535, 383838.
Example (continued): Making a box plot
Let's make a box plot for the same dataset from above.
Step 1: Scale and label an axis that fits the five-number summary.
Step 2: Draw a box from Q_1Q
1
Q, start subscript, 1, end subscript to Q_3Q
3
Q, start subscript, 3, end subscript with a vertical line through the median.
Recall that Q_1=29Q
1
=29Q, start subscript, 1, end subscript, equals, 29, the median is 323232, and Q_3=35.Q
3
=35.Q, start subscript, 3, end subscript, equals, 35, point
Step 3: Draw a whisker from Q_1Q
1
Q, start subscript, 1, end subscript to the min and from Q_3Q
3
Q, start subscript, 3, end subscript to the max.
Recall that the min is 252525 and the max is 383838.
We don't need the labels on the final product:
Want to learn more about making box and whisker plots? Check out this video.
Want to practice making box plots? Check out this exercise."
A tree is broken at a height of 5 m from the ground and its top touches the ground at a
distance of 12 m from the base of the tree. Find the original height of the tree.
Answers:
Answer:
AB = 18 m . Thus, the original height of the tree = 18 m.
Step-by-step explanation:
Write down the first 4 terms of a sequence that starts at 0 and decreases by 6 in each term.
Answer:
0, -6, -12, -18
Step-by-step explanation:
start at 0, then subtract by 6 to get -6. then subtract 6 again to get -12. then subtract 6 again to get -18.
please give brainliest!!!!
100 points!!! please help me with this math.
f=72°
d=153°
b=27°
a=64°
be careful i started with f
Answer:
a=64
b=27
d=153
f=72
Step-by-step explanation:
a+72+134+90=360(sum of the angles around a point is 360)
a+296=360
a=360-296
a=64
b=27(vertically opposite angles are equal in magnitude)
27+b+d+e=360(sum of the angles around a point is 360)
d=e (vertically opposite angles are equal in magnitude)
Therefore,
27+27+2d=360
54+2d=360
2d=360-54
2d= 306
d= 306÷2
d= 153
108+f=180(sum of the adjacent angles on a straight line is 180)
f=180-108
f=72
explain whether each equation is a linear equation.
Answer:
3. Not linear
4. Linear
Step-by-step explanation:
3. The equation has an exponent on the x. Since x is squared the graph is a parabola. The graph is a curve, not a line, so it is not linear.
4. Both the x and y have no exponent (which is an exponent of 1) The graph will be a line. This is a linear function.