Answer:
(-3, -5)
Step-by-step explanation:
(i) 3 (a + 5b) + a (a + 4) (ii) y (10 - y) + 3 (y - 2) (iii) 2 (8a - 5b) + 3 (5a - 12) (iv) 3 (y - 3) + ( 8 - 6y + x) (v) a (a - 2b) + b (b + 2a - c) (vi) 5 (x - y + z) + (4x + 3y) plzz solve
Answer:
[tex]3 (a + 5b) + a (a + 4) = a^2 + 7a + 15b[/tex]
[tex]y (10 - y) + 3 (y - 2) = - y^2+13y - 6[/tex]
[tex]2 (8a - 5b) + 3 (5a - 12) = 31a -10b - 36[/tex]
[tex]3 (y - 3) + ( 8 - 6y + x) = -3y + x-1[/tex]
[tex]a (a - 2b) + b (b + 2a - c) =a^2 + b^2 - bc[/tex]
[tex]5 (x - y + z) + (4x + 3y) =9x - 2y +5z[/tex]
Step-by-step explanation:
Solving (i):
[tex]3 (a + 5b) + a (a + 4)[/tex]
Open brackets
[tex]3 (a + 5b) + a (a + 4) = 3a + 15b + a^2 + 4a[/tex]
Collect like terms
[tex]3 (a + 5b) + a (a + 4) = a^2 + 4a+3a + 15b[/tex]
[tex]3 (a + 5b) + a (a + 4) = a^2 + 7a + 15b[/tex]
Solving (ii)
[tex]y (10 - y) + 3 (y - 2)[/tex]
Open bracket
[tex]y (10 - y) + 3 (y - 2) = 10y - y^2 + 3y - 6[/tex]
Collect like terms
[tex]y (10 - y) + 3 (y - 2) = - y^2+10y + 3y - 6[/tex]
[tex]y (10 - y) + 3 (y - 2) = - y^2+13y - 6[/tex]
Solving (iii)
[tex]2 (8a - 5b) + 3 (5a - 12)[/tex]
Open bracket
[tex]2 (8a - 5b) + 3 (5a - 12) = 16a -10b + 15a - 36[/tex]
Collect like terms
[tex]2 (8a - 5b) + 3 (5a - 12) = 16a+ 15a -10b - 36[/tex]
[tex]2 (8a - 5b) + 3 (5a - 12) = 31a -10b - 36[/tex]
Solving (iv)
[tex]3 (y - 3) + ( 8 - 6y + x)[/tex]
Open bracket
[tex]3 (y - 3) + ( 8 - 6y + x) = 3y - 9 + 8 - 6y + x[/tex]
Collect like terms
[tex]3 (y - 3) + ( 8 - 6y + x) = 3y - 6y + x- 9 + 8[/tex]
[tex]3 (y - 3) + ( 8 - 6y + x) = -3y + x-1[/tex]
Solving (v):
[tex]a (a - 2b) + b (b + 2a - c)[/tex]
Open bracket
[tex]a (a - 2b) + b (b + 2a - c) =a^2 - 2ab + b^2 + 2ab - bc[/tex]
Collect like terms
[tex]a (a - 2b) + b (b + 2a - c) =a^2 + 2ab- 2ab + b^2 - bc[/tex]
[tex]a (a - 2b) + b (b + 2a - c) =a^2 + b^2 - bc[/tex]
Solving (vi)
[tex]5 (x - y + z) + (4x + 3y)[/tex]
Open brackets
[tex]5 (x - y + z) + (4x + 3y) =5x - 5y +5z+4x +3y[/tex]
Collect like terms
[tex]5 (x - y + z) + (4x + 3y) =5x +4x +3y- 5y +5z[/tex]
[tex]5 (x - y + z) + (4x + 3y) =9x - 2y +5z[/tex]
Get as many people to answer this question will give brainiest for free!!!!
Answer:
huh?
Step-by-step explanation:
Write an equation in slope intercept form for the given line (-7,2) and (5,8)
PLEASE HELP ASP 10 MINUTES LEFT TILL THE DEADLINE
Answer: y= 0.5x + 5.5
Step-by-step explanation: Y = mx + C
SLOPE INTERCEPT FORM:
First we need to find the slope of the two points. Which is y2-y1 / x2-x1.
8 is Y2 and 2 is Y1. 5 is Y2 and -7 is Y1. Plug those numbers into a calculator and solve. The slope (m) is 1/2 or 0.5
Then we have to find C as the slope intercept form is Y = mx + C. To find C we replace x and y with one of the points, and solve as an algebric equation. C will be 5.5
Jerry plans on saving money for a trip by putting $1 in a savings account the first month and then adding
enough to double the amount in the account each following month. Write a function to show how much money Jerry will have in his savings account s (t) after t months
9514 1404 393
Answer:
s(t) = 2^(t-1)
Step-by-step explanation:
The amount in the account is the sum of the series ...
1 + 1 +2 +4 +8 +16 +...
We note that terms after the first are a geometric sequence with a first term 1 and a common ratio 2. The sum of such a sequence is ...
Sn = a1×(r^n -1)/(r -1) . . . . where n is the number of terms being summed
For our values, this simplifies to ...
Sn = 1×(2^n -1)/(2 -1) = 2^n -1
We notice here that the account balance is 1 more than this sum, and that n = t-1, so the balance a(t) is ...
s(t) = 1 +(2^(t -1) -1)
s(t) = 2^(t -1) . . . . . . the function showing how much Jerry has
What is the factored form?
Answer:
(2x-7)(4x+2)
Step-by-step explanation:
HELP HELP PLEASE!! D:
Determine the missing side length:
Please don't give cap!
Answer:
c = 35
Step-by-step explanation:
[tex]c^{2} = a^{2} + b^{2}[/tex]
[tex]c^{2} = 21^{2} + 28^{2}[/tex]
[tex]c^{2} = 1225[/tex]
[tex]\sqrt{c^{2} } = \sqrt{1225}[/tex]
[tex]c = 35[/tex]
3(x+2)^2+7 in standard form
Answer:-2x^2+3x-7=0
Step-by-step explanation:
Factories:
[tex] {6x}^{2} + 4xy - 3x - 2y[/tex]
answer plzz with formula plzz
Answer:
[tex][tex] {6x}^{2} + 4xy - 3x - 2y[/tex][/tex]
6x²+4xy-3x-2y
2x(3x+2y)-1(3x+2y)
(3x+2y)(2x-1) is your answer
Please help me with the question I asked I’m doing a text please.
Answer:
Wait, what question?? I can try to do it.
I need help with these questions (see image). Please show workings.
Answer:
Q1. 37.3 cmQ2. (a) 8.66 cm (b) 17.3 cmStep-by-step explanation:
Question 1
GivenChord 1 c1 = 36 cmChord 2 c2 = 30 cmRadius r = d/2 = 50/2 = 25 cmChords are parallelTo find The distance between the chordsSolutionThe distance between the chords is sum of the distances between the center and the midpoint of the chords
The segments between the center to the midpoints of the chords for right triangles with one side being the radius.
The distance is:
h = h1 + h2 h1 = [tex]\sqrt{r^2 - (c1/2)^2} = \sqrt{25^2 - 18^2} = \sqrt{301}[/tex] ≈ 17.3 cm (rounded)h2 = [tex]\sqrt{r^2 - (c2/2)^2} = \sqrt{25^2 - 15^2} = \sqrt{400}[/tex] = 20 cmh = 17.3 + 20 = 37.3 cm------------------------------------------
Question 2
GivenEquilateral triangle inscribed into circleSide of the triangle is 30 cmTo findDistance between the center and the sideRadiusSolutionMidpoint of the side, the center and the vertex form a right triangle with 30° angle at the vertex.
Let the radius be r, the distance from the center to the side be h
Then we have:
r² = h² + (30/2)²As per property of 30°-60°=90° triangle, the side opposite to 30° is half of the hypotenuse. In this case, h = r/2 or r = 2h
Substitute r into equation above and solve for h:
(2h)² = h² + 2253h² = 225h² = 75h = √75 = 8.66 cm (rounded)Find the value of r:
r = 2*8.66 = 17.3 cm (rounded)Your portfolio must include a minimum of the following five types of equations and solutions:
Two one-step equations
Two equations that contains fractions
One equation with distributive property
One equation with decimals
One real-world problem that is solved by an equation
Once you have created each equation, you will solve it and show your work. Pretend that you are teaching the equations to a new pre-algebra student. Or you can actually teach them to a sibling or friend!
This is a total of 7 equations and solutions.
i had gotten a 70 on the 1st try i want a better grade
Answer: 2 step equations: x-12=4 and 3x=6. Equations that contain fractions: Equations with distributive property: 4x+2=2(x+6). One equation with decimals: 0.75X+25=50. Real world problem that is solved by an equation: Kelly intakes up to 2,000 calories per day. Today she ate breakfast which had 300 calories. For lunch she had 2 pb&j sandwiches with some chocolate milk on the side. That in total had 1,050 calories. When she had dinner she Intakes another 250 calories. For snack she had ice cream which was 150 calories with cookies. If each cookie had 50 calories how many cookies did she have?
Step-by-step explanation:
The images is where I showed all the work
The solution is given below.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
here, we have,
One-Step Equations:
Number one: x + 6 = 8
Solve: To begin, you must subtract 6 on both sides to get x by itself.
x = 8 When you subtract 6 on both sides, you get x = 8 which is your answer.
This is a one-step equation, meaning it only took us a single step in order to solve this equation.
Number two: x - 5 = 15
Solve: To solve this one-step equation, first, start off by adding 5 on both sides.
Since it's only one step, your answer will be x = 20. All we had to do was add 5 to isolate the variable.
Two equations that contain fractions:
Number one: x - 1/2 = 2/4
Solve: x - 1/2 = 2/4
To begin, we have to add 1/2 to get x by itself. Since 2/4 and 1/2 don't have common denominators, all we have to do is multiply 1/2 by 2/2 to get a common denominator of 4. 1/2 x 2/2 is equal to 2/4. 2/4 + 2/4 is 4/4 which is equal to 1. Your answer is x = 1.
Number two: x + 3/4 = 2/4
Solve: To begin, we have to subtract 3/4 on both sides. Since 2/4 and 3/4 have a common denominator of 4, we can go ahead and subtract right away. 2/4 - 3/4 is equal to -1/4. x = -1/4.
One equation using distributive property:
Number one: 3(x + 2) = 18
Solve: To begin, we have to distribute the 3 to x and 2 (multiply). We get 3x + 6 = 18. To get x by itself, we have to first subtract 6 on both sides. We then get 3x = 12. Now, divide by 3 on both sides so that x is completely isolated, and we get x = 4.
One equation with decimals:
Number one: x + 0.25 = 0.75
Solve: To begin, we have to subtract 0.25 on both sides. When we do this, 0.75 - 0.25, we get x = .50 We can also write this as a fraction .50 is the same thing as 1/2. x = 1/2 or .50
One real-world problem:
Number one: Maria went to the store and she had 20 dollars to spend. She got a notebook for 5 dollars, and she wanted to buy pens with the rest. Each ben cost 5 dollars, how many pens can she buy in total?
Solve: We know that Maria had a total of 20 dollars in total and she already spent 5 dollars. We also know that each pen cost 5 dollars. When knowing this we can write this equation: 5x + 5 = 20. Since we don't know how many pens she's going to buy, we can just write a variable, in this case, x. Now we solve. Just like always, we need to isolate the variable. To do this, we have to first subtract 5. We then get, 5x = 15. Now, divide by 5 on both sides and we get x = 3. That means that Maria can buy a total of 3 pens.
To learn more on equation click:
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Veronica and Chad are walking down the street. Veronica walks at a speed of 5 miles per hour, and Chad walks at a speed of 4 miles per hour. Write an equation for the distance(d), in miles, each person walks over time(t), in hours. Do the equations represent linear functions?
Answer:
Veronica:
d=5t
Chad:
d=4t
Step-by-step explanation
yes they do represent linear equations
An ice cream shop offers a choice of three types of cones and 31 flavors of ice cream. A
customer gets to choose a cone and a type of ice cream. How many different 1-scoop ice
cream cones can a customer order?
HELPPP PLEASE !!!!!!!!
Answer:
20
Step-by-step explanation:
1. First simplify 8a + 4 then substitute a=2 so 8(2) + 4 = 16+4=20
Now you try the rest
Which of the following qualities does not describe a line? Select all that apply.
imaginary
endless
curved
has no width
has two endpoints
short answers plz
Answer:
the words that I would use are endless, has no width and is curved. I wouldn't use imaginary (you could) and a line never has two end points.
Step-by-step explanation:
(feel free to correct me if I'm wrong or you disagree)
LeBron James made 19 out of 32 shots on Tuesday. What percent of his shots did he make? Round to the nearest whole percent.
Answer:
59%
Step-by-step explanation:
19/32= 59.375 so rounded would be 59 :)
Answer:
59%
Step-by-step explanation:
32 shots is the total, so it's 100%
100% = 32 shots
1% = 32 ÷ 100 = 0.32
19 ÷ 0.32 = 59.375
59.375 estimated to 59
Hugo cut 15 short strips of paper then he cut 14 long strips how many strips of paper did he go cut in all
A.1 strip of paper
B.28 strip of paper
C.2 strip of paper
D.29 strips of paper
Answer:
D.) 29
Step-by-step explanation:
Add 15 and 14
18. When an article is sold for $100 a profit of 25% is made on the cost price. What is the cost price?
Answer:
$80
Step-by-step explanation:
100/1.25 = 80
The cost price of the article that makes a profit of $100 will be $400.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
When an article is sold for $100 a profit of 25% is made on the cost price.
Let 'x' be the cost price of the article. Then the equation is given as,
25% of x = $100
Simplify the expression, then we have
0.25x = $100
x = $100 / 0.25
x = $400
The cost price of the article that makes a profit of $100 will be $400.
More about the percentage link is given below.
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The sum of two numbers is 55. The larger number is five less than twice the smaller number.
Write a system of equations and find the two numbers.
Answer:
x=20
y=35
Step-by-step explanation:
lets say:
x+y=55
2x=y+5
y being the bigger number
dexcribe y in terms of x:
55-x=y
now replace y in the second equation
2x=55-x+5
2x=60-x
3x=60
x=20
so y=35
Answer:
the nr are 20 and 35
Step-by-step explanation:
55=x+(2x-5)
PLEASE HELP
What two numbers that add each other give you -7 but times it give you -120
HELP PLEASE
I WILL GIVE YOU BRAINLIEST
Answer:
x = - 4, x = 1
Step-by-step explanation:
The solutions to the quadratic are the values of x where the graph crosses the x- axis.
The graph crosses the x- axis at x = - 4, x = 1
Thus the solutions are x = - 4 , x = 1
Does the set of numbers form a Pythagorean triple? Explain.
2, 3, 4
Choose the correct answer below.
o
No, because the given numbers do not satisfy the equation a? + b2 = c?.
Yes, because the given numbers satisfy the equation a? + b2 = c?
No, because the given numbers satisfy the equation a² + b2 = c?.
Yes, the given numbers do not satisfy the equation a? + b2 = ca.
O
Answer:
No because the given numbers do not satisfy the equation a² + b² = c²
Answer:
No, because the given numbers satisfy the equation a^2+b^2=c^2.
Step-by-step explanation:
The Pythagorean triple 2, 3, 4. We can put it in our formula, a^2+b^2=c^2. So, that will equal:
2^2+3^2=4^2
(4+9.....16)?
And 4+9=13, which does not equal 16. So No, because the given numbers satisfy the equation a^2+b^2=c^2 is correct.
If you liked this solution, be sure to hand out a Brainliest. Thank you so much.
DUBS, Signing off.
Write the number below as a fraction in its simplest form
0.569
Answer:
[tex] \binom{569}{1000} [/tex]
Step-by-step explanation:
Step 1:
[tex] \binom{0.569}{1} [/tex]
Step 2:
Then multiply both by 1000
[tex] \binom{569}{1000} [/tex]
It cant be simplifyed further so its in simplest form
A landscape plan includes a rectangular flower bed that is surrounded the wood planks. In the drawing, the rectangular flower bed is 6 in. by 8 in. The length and width of the actual flower bed will be 24 times larger than the length and width in the drawing.
(a) What is the perimeter of the drawing? Show your work.
(b) What is the perimeter of the actual flower bed? Show your work.
(c) What is the effect on the perimeter of the flower bed with the dimensions are multiplied by 24? Show your work.
(a). Perimeter of the drawing = 28 in.
(b). Perimeter of the actual flower bed = 672 in.
(c). Perimeter of the actual flower bed is 24 times the perimeter of the
drawing.
Perimeter of a rectangle: Perimeter of a rectangle is given by the expression,
Perimeter = 2(Length + Width)
Given in the question,
Length of the flower bed in the drawing = 6 in. Width of the flower bed in the drawing = 8 in. Actual length and width of the flower bed is 24 times longer thanthe length and width in the drawing.
a). Perimeter of the drawing = 2(length + width)
= 2(6 + 8)
= 28 in.
b). Length of actual flower bed = 24(Length of the flower bed in drawing)
= 24(6)
= 144 in
Width of the actual flower bed = 24(width of the flower bed in drawing)
= 24(8)
= 192 in
Perimeter of the actual bed = 2(144 + 192)
= 672 in.
c). [tex]\frac{\text{Perimeter of the flower bed in drawing}}{\text{Perimeter of the actual flower bed}}[/tex] = [tex]\frac{28}{672}[/tex]
[tex]\frac{\text{Perimeter of the flower bed in drawing}}{\text{Perimeter of the actual flower bed}}=\frac{1}{24}[/tex]
Perimeter of the actual flower bed = 24(perimeter of the flower bed in drawing)
Therefore, (a) Perimeter of the the drawing = 28 in.
(b) Perimeter of the actual flower bed = 672 in.
(c) Perimeter of the actual flower bed is 24 times the
perimeter of the drawing.
Learn more about the perimeter here,
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How will the graph of the function f(x) = 3x translate when the function is changed to f(x) = 3(x-2)
Answer:
Step-by-step explanation:
Subtracting from the x value shifts the graph to the right that many units. In this case the graph is shifted to the right by 2 units.
Answer:
It moves to the right 2
Step-by-step explanation:
:)
b.
Convert each rational number in the table to its decimal equivalent.
0
0
20
99
= 0.20
30
99
0.30
45
= 0.45
99
99
10
= 0.10
99
62
= 0.62
99
58
0.58
77
99
0.7
81
= 0.81
99
98
99
0.98
99
Do you see a pattern? Explain.
Can you find other rational numbers that follow similar patterns?
Answer:
0.39
Step-by-step explanation:
each one is below zero i guess
6a+5=5 what is a in the equation?
Answer:
a = 0
Step-by-step explanation:
Given
6a + 5 = 5 ( subtract 5 from both sides )
6a = 0 , then
a = 0
Jose bought 9 movie tickets for a total of $54. Adult tickets cost $8 each and child tickets cost $3.50. How many adult tickets did he buy?
Answer:
5
Step-by-step explanation:
5 x 8 = 40
3.50 x 4 = 14
3. A line contains the points P (1,1) and Q (7,10) what is the slop of the line
Answer:
9/6 is the slope but that simplifies to 3/2
Step-by-step explanation:
y2-y1
x2-x1
10-1=9
7-1=6
7a+5=61 what is a in the equation
Answer:
a=8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
7 * 8 = 56
56 + 5 = 61