Answer:
Simplify:
[tex]\frac{( {x}^{2} + 6x + 9) }{x - 3} [/tex]
Factoring:
[tex] {x}^{2} + 6x + 9[/tex]
The first term is, x2 its coefficient is 1 .
The middle term is, +6x its coefficient is 6 .
The last term, "the constant", is +9
Step-1 : Multiply the coefficient of the first term by the constant 1 • 9 = 9
Step-2 : Find two factors of 9 whose sum equals the coefficient of the middle term, which is 6 .
-9 + -1 = -10
-3 + -3 = -6
-1 + -9 = -10
1 + 9 = 10
3 + 3 = 6 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 3 and 3
[tex] {x}^{2} + 3x + 3x + 9[/tex]
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x+3)
Add up the last 2 terms, pulling out common factors :
3 • (x+3)
Step-5 : Add up the four terms of step 4 :
(x+3) • (x+3)
Which is the desired factorization.
Multiply (x+3) by (x+3)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x+3) and the exponents are :
1 , as (x+3) is the same number as [tex](x+3) {}^{1}[/tex]
and 1 , as (x+3) is the same number as[tex](x + 3) {}^{1} [/tex]
The product is therefore, [tex](x + 3) {}^{(1 + 1)} = (x + 3) {}^{2} [/tex]
Factor the expression x^2+9+8
Answer:
2+17
x^{2}+17
x2+17
Step-by-step explanation:
Answer:
[tex](x+1)(x+8)[/tex]
Step-by-step explanation:
Hi there!
[tex]x^2+9x+8[/tex]
We must ask ourselves: What two factors of 8 add up to 9? That would be 1 and 8.
1 × 8 = 8 and 1 + 8 = 9.
Rewrite the expression accordingly:
[tex](x+1)(x+8)[/tex]
I hope this helps!
a
Blue and green dye are mixed in a 7:4 ratio to make 44 litres
of a teal-coloured dye. A further 8 litres of green dye are added
to the mixture. What is the new ratio of blue to green dye in its
simplest form?
Answer:
7:4 is the new ratio.
Step-by-step explanation:
set a proportion; (8+4 = 12)
7 x
-- = --
4 12
12/4 = 3
3 x 7 = 21
x = 21
new ratio: 21:12
simplifies: 7:4 (division of 3)
The new ratio of blue to green dye in its simplest form is 7/6.
Blue and green dye are mixed in a 7:4 ratio to make 44 litres of a teal-coloured dye. A further 8 litres of green dye are added to the mixture. What is the new ratio of blue to green dye in its simplest form to be determined.
The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
Calculating the fraction of blue and green in the teal dye,
Blue dye = 7/(4+7) * 44
Blue dye = 7/11 * 44
Blue dye = 28 liters
Similarly,
Green dye = 7/12*44
Green dye = 16
Now
Blue dye = green dye = 28+16 = 44
Now gree dye is increase by 8 liters
new volume fraction of green dye = 16+8
= 24
a fraction of blue dye remains the same,
the ratio of blue dye to new green dye in teal colored.
= 28/24
=7/6
Thus, the new ratio of blue to green dye in its simplest form is 7/6.
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A boy is launching a toy rocket he got for his birthday from the top of an 80 ft building. The function representing
the height is f(0) = -16x? +64x + 80 where x represents time in seconds.
How many seconds did it take the rocket to reach it's maximum height?
A
144 sec
B)
2 sec
Eliminate
1.5 sec
D)
128 sec
Answer:
2 seconds, assuming the "?" in the equation is supposed to be ^2 (the exponent of 2): f(h) = -16x^2 +64x + 80
Step-by-step explanation:
You can either graph the functuion or take the first derivative to find the maximum height. The first derivative will give us the slope for a values of x. The slope at the top height of the rocket is zero, since it has stopped and is starting it's way back down.
First Derivative:
f(x) = -16x^2 +64x + 80
f'(x) = -32x + 64
Set this equal to zero and solve for x
0 = -32x + 64
x = 2 seconds.
Use 2 seconds in the original equation to find the height at 2 seconds.
f(2) = -16x^2 +64x + 80
f(2) = -16(2)^2 +64*(2) + 80
f(2) = 144 feet
Graph:
A graph is attached. You can locate the maximum at (2,144)
if f(x)=x/2-2 and g(x)2x^2+z-3, find (f+g)(x)
Answer:
Step-by-step explanation:
f(x)=3x + 4. (6) g(x) = x2 +. 1 x.
Lesson 6 Practice Problems
1. A pink paint mixture uses 4 cups of white paint for every 3 cups of red paint.
The table shows different quantities of red
and white paint for the same shade of pink.
Complete the table.
white paint
(cups)
red paint
(cups)
4
3
1
1
4
5
Answer:
WHITE PAINT PINK PAINT
(CUPS) (CUPS)
4 3
4/3 1
1 3/4
16/3 4
5 15/4
-Lexi
Not very good at math guys I really need to pass my Highschool test pls help
Answer:
5 $3.00
Step-by-step explanation:
For every 5 apples, the cost is $3.00
Six ounces of a nutrition shake provides 2 grams of protein. Will 24 ounces of the drink provide 10 grams of protein? Explain
Answer:
(Hope this helps can I pls have brainlist (crown)☺️)
Step-by-step explanation:
In pic
PLZ HELP ME!!!!!!!!!!!!!!!!!!!!!!
Answer:
i have no idea what this question is asking for but my guest is that you need to reformate the equations
-5x+y=-11 in y+mx+b format is y=5x-11
x-y=7 in y=mx+b formate is y=-x+7
1.) 5/11 = 2.) 6/8 = 3.) 8/13 = 4.) 4/9 = 5.)
p 7/15=
Answer:
1. 5/11 = five elevenths = 5:11
2. 6/8 = six eighths = 6:8
3. 8/13 = eight thirteenths = 8:13
4. 4/9 = four ninths = 4:9
5. 7/15 = seven fifteenths = 7/15
Step-by-step explanation:
1. To convert numerical fractions into word form, here are a few tips:
Write the numerator of the fraction spelled out exactly as it appears as a number (for example, if the numerator is 5, you spell out the word "five") Write the denominator of the fraction like you would write ranking for a contest (for example, if the denominator is 11, you write it as eleventh)2. To convert a fraction into colon form, here are a few tips:
Remember, fractions are ratios. Ratios can be written as x : y.The ratio compares the numerator to the denominator, having the numerator to the left side of the colon and the denominator on the right side. (For example, if the fraction is 6/8, the colon form is 6 : 8).Paul and Kelly are throwing darts at the hexagonal dartboard shown below. Paul told Kelly that if they throw darts at the board 100 times, of them should hit a 5.
If the prediction holds true, approximately how many times would their darts hit a 5?
Shown & Given:
The dartboard holds 5 in the maximum space.
Known:
Out of 100, it is know that they will hit 5 more than 50 times.
Possible Answers:
55, 66, or 77.
The most likely one is:
66
Find the common difference of the arithmetic sequence 13, 21, 29, .
Answer: 8
Step-by-step explanation:
dude these qts are due in 10 mins pls help!
Answer:
I can't see the last answer choice.
9/LM = 6/4.5
Step-by-step explanation:
9cm is to 6cm as LM is to 4.5cm
9/6 = LM/4.5
Rewriting: 9/LM = 6/4.5
GIVING BRAINLIST!! PLS ANSWER
Trina is buying 12 shirts for the drama club.She will choose a style for the blank shirts and then pay additional charge of $2.75 for each shirt to have the club logo. If Trina cannot spend more than $99, how much can she spend on each blank shirt? Write and solve an inequality to find the possible cost of each blank shirt.
Answer:
The most she can spend on each blank shirt is $5.50.
Step-by-step explanation:
In order to set up the inequality, we need to write an expression for the total cost of each shirt wherein the price of each blank shirt is "x". Tina needs to buy 12 shirts and there is an additional charge of $2.75 for each logo. The total cost needs to be less than or equal to $99.
This gives us 12 * (x + 2.75) ≤ 99
We can then distribute:
12x + 12 * 2.75 ≤ 99
12x + 33 ≤ 99
Then subtract 33 from both sides:
12x ≤ 66
And finally divide by 12 on both sides:
x ≤ 5.5
Answer:
Step-by-step explanation:
12x + 2.75*12 < 99 Combine 12 * 2.75
12x + 33 < 99 Subtract 33 from both sides
12x < 99 - 33 Combine
12x <66 Dive by 12
x < 66/12
x < 5.50
The very most she can spend is 5.50 on each shirt. Actually it should be 5.49 which will be less than 99. It will come to 65.88 which is just 12 cents less than 99, but it answers the problem. The problem does not use less than or equal which would mean that 99 is the answer ≤
36 x 1/9, show work please !
Answer:
4 [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
39 × [tex]\frac{1}{9}[/tex]
39 times 1 is 39
39/9 is 4.33333333 Which is also, 4 [tex]\frac{1}{3}[/tex]
Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. (0,0); y = 2/5x + 8
Answer:
(y-0)=2/5(x-0)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!9
Answer:
A. 1/5
Step-by-step explanation:
1. The formula to find the slope of a line given two points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].
y_2 = y-coordinate of point 2y_1 = y-coordinate of point 1x_2 = x-coordinate of point 2x_1 = x-coordinate of point 12. (Solving)
[tex]\frac{(3)-(2)}{(4)-(-1)}[/tex] [tex]\frac{1}{4+1}[/tex] [tex]\frac{1}{5}[/tex]Therefore, the answer is A. 1/5.
[tex]\huge \bf༆ Answer ༄[/tex]
Consider two points (-1 , 2) and (4 , 3)
Slope (m) of the graph is : -
[tex] \sf \dfrac{y2 - y1}{x2 - x1} [/tex][tex] \sf\dfrac{3 - 2}{4 - ( - 1)} [/tex][tex] \sf \dfrac{1}{4 + 1} [/tex][tex] \sf\dfrac{1}{5} [/tex][tex]꧁ \: \large \frak{Eternal \: Being } \: ꧂[/tex]
A pool with a square bottom is to have a volume of 2000 cubic feet. The owners plan to use a fancy tile to complete the pool. The sides of the pool will cost $80 per square foot and the bottom of the pool will cost $40 per square foot. Find the pool dimensions that will minimize the cost of construction.
Considering the given conditions in the question, the dimensions that will minimize the cost of construction of the pool are:
base length = 10 feet
base width = 10 feet
pool depth = 20 feet
Volume of a material implies the maximum amount of substance that it can contain.
From the given question, it is expected that the pool would have the shape of a cuboid, thus its volume can be determined by:
volume of the pool = length x width x height
= base area x height
Thus, given that the volume of the pool is 2000 cubic feet, then;
2000 = base area x height
i. Let the dimensions of the square base be 10 feet, and its height 20 feet, so that;
volume = 10 x 10 x 20
= 2000 cubic feet
The cost of constructing the pool of the assumed dimensions would be:
Total area of its sides = 4 x 200
= 800 square feet
The cost of tiling the sides of the pool = $80 x 800
= $ 6400.0
Area of the base of the pool = 10 x 10
= 100 square feet
The cost of tiling the base of the pool = $40 x 100
= $4000
Total cost = $6400 + $4000
= $10400
Total cost of constructing the pool with the assumed dimensions is $10400.
ii. Let the dimensions of the square base be 20 feet, and its height 5 feet, so that;
volume = 20 x 20 x 5
= 2000 cubic feet
The cost of constructing the pool of the assumed dimensions would be:
Total area of its sides = 4 x 100
= 400 square feet
The cost of tiling the sides of the pool = $80 x 400
= $ 32000
Area of the base of the pool = 20 x 20
= 400 square feet
The cost of tiling the base of the pool = $40 x 400
= $16000
Total cost = $16000 + $32000
= $48000
Total cost of constructing the pool with the assumed dimensions is $48000.
Therefore, the dimensions that will minimize the cost of construction of the pool are:
base length = 10 feet
base width = 10 feet
pool depth = 20 feet
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Given 2x² = -8, x is
A) -2
B) 2
C) 2i or -2i
B) 4i or -4i
NO LINKS!!!
Answer:
2x^2=-8
2x^2/2=-8/2
x^2=-4
x=2
Step-by-step explanation:
HOPE THAT THIS IS HELPFUL.
HAVE AN AWESOME DAY.
20% tip on a bill of $22.41
Answer:
5 people - Tip per person = $0.90
Total per person = $5.39
10 people - Tip per person = Tip per person $0.45
Total per person = $2.70
Answer: the answer is $4.49 because if your bill is 22.41 and you divide that by 20 its 4.482 so then you add the 2 to the 8 which is 9 so 4.49
Find the measure of the missing angle.
30°
a=
Answer:
the measurement of a is 60°............
Answer:
A=60
Step-by-step explanation:
it adds up to 180 so subtract 30 and 90 for the right angle and you got 60
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!8
Answer:
B
Step-by-step explanation:
X menas time, so we posisionate this in the axis, you begin with 2 dollars, and increase the cost with the time, hope this hlps :)
What does the y-intercept represent in this situation? The weight of oats, in pounds, in the final mixture. The weight of hay, in pounds in the final mixture. The amount of protein the feed has if no oats are added. The amount of protein the feed has if no hay is added.
Your welcome!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The y-intercept in the situation given represents: C. The amount of protein the feed has if no oats are added.
What is the Y-intercept of a Linear Function?The y-intercept of a linear function is the initial value or the value of y when x equals 0.
The initial value in this situation is the amount of protein in the feed when the amount of oats added is 0.
Therefore, the y-intercept represents: C. The amount of protein the feed has if no oats are added.
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David is a salesman for a local Ford dealership. He is paid a percent of the profit the dealership makes on each car. If the profit is under $800, the commission is 25%. If the profit is at least $800 and less than $1,000, the commission rate is 27.5% of the profit. If the profit is $1,000 or more, the rate is 30% of the profit. Find the difference between the commission paid if David sells a car for a $1,000 profit and the commission paid if he sells a car for a $799 profit?
Answer:
At the city museum, child admission is $5.90 and adult admission is $9.20. on sunday, 144 tickets were sold for a total sales of $1136.70 . how many adult tickets were sold that day?
Step-by-step explanation:
The required difference between the commission paid is $100.25 when David sells a car for a $1,000 profit and for a $799 profit.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
We have to determine the difference between the commission paid if David sells a car for a $1,000 profit and the commission paid if he sells a car for a $799 profit
The profit = $1,000
The profit is $1,000 or more, the rate is 30% of the profit.
So, the commission paid :
⇒ 30% of $1,000 = $300
The profit = $799
The profit is under $800, the commission is 25%.
So, the commission paid :
⇒ 25% of $799= $199.75
The required difference between the commission paid :
⇒ $300 - $199.75 = $100.25
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Can I get steps to solve this?
Answer:
8 and 1/2 pints
Step-by-step explanation:
4.25 cups/ 1 × 2 pints/ 1 cups
= 4.25 × 2 pints
= 8.5 pints
8 and 1/2 pints
What is the symbol for a square root
Answer:
The symbol for a square root is [tex]\sqrt{}[/tex].
:)
Answer:
√
Step-by-step explanation:
Math=Explanitory
Here is a scale drawing of a garden.
Tom wants to plant a tree in the garden according to the following rules:
it must be 4 m from A and 2 m from CD.
Place a cross where Tom can plant the tree.
The location of the tree can be found by taking point A as the origin of
coordinate plane, represented by the drawing area.
Response:
The the graph showing the location where Tom can plant the tree is attached.Method used to find the location for planting the treeThe area Tom wants to plant the tree in the garden is given by the following rule;
Distance of the tree from A = 4 m
Distance of the tree from CD = 2 m
1 cm in the scale drawing = 2 m
Solution:
Taking point A as the origin, we have;
The location of the tree from point A is given by the radial length, r = 2 cm.
The distance of the tree from the line CD is given by the line, y = 1.5 cm,
given that 1 cm from CD = 1.5 cm from point A
Therefore, we have;
The y-coordinate of the location of the tree is; y = 1.5Equation of the circular distance from A is; x² + y² = r²Where;
r = 2
y = 1.5
We have;
x² + 1.5² = 2²
x² = 2² - 1.5² = 1.75
x = √(1.75)The coordinate of the location of the tree from A is; (√(1.75), 1.5) Please find attached, the graph showing the location where Tom can plant the tree in relation to point A.
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Paul wanted to bring his family to the Children’s Museum. There was an exhibit with carnival rides. The tickets for each ride were $1.35 per ticket. Paul purchased 30 tickets for the rides and spent a total of $46.85 at the museum. Paul spent his money only on ride tickets and admission. The price of the museum admission is the same for everyone. (a) Define your variables. (b) Write a linear equation that can be used to determine the cost for anyone who only pays for tickets and museum admission. Use y to represent the total cost and x to represent the number of ride tickets. (c) Explain your answer to Part 1b.
Do NOT say you don't know, include files, or anything else. I need real answers not people faking answers to get points.
We want to define and solve a linear equation to model the given case.
The answers are:
a) x = number of tickets, y = total cost.
b) y = $1.35*x + $6.35
We know that:
The tickets for each ride were $1.35 per ticket.
Paul purchased 30 tickets
He spent a total of $46.85 (on tickets and admission)
The cost for the 30 tickets is:
30*$1.35 = $40.50
a) Now we can define two variables:
y = total cost
x = number of tickets
b) the linear equation would be:
y = $1.35*x + P
Where P is the price of admission.
And we know that the total cost for 30 tickets is $46.85, then we have:
$46.85 = $40.50 + P
$46.85 - $40.50 = P = $6.35
So the admission price is $6.35
This means that the linear equation is:
y = $1.35*x + $6.35
c) Brief explanation, we have the variable y that represents the total cost, it is equal to the admission price (which we found) plus $1.35 times the number of tickets bought (x).
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identify the steeper line y = 3x + 4 or y = 6x + 11
Answer:
y=6x+11
Step-by-step explanation:
The slope of y=3x+4 is 3 and the slope of y=6x+11 is 6.
Hope this helps :)
y = 3x + 4 is the steeper line with the slope 3
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The given two lines are y = 3x + 4 and y = 6x + 11
In the given line y = 3x + 4
The slope of the line is 3
In the given line y = 6x + 11
The slope of the line is 6
Among the two lines the line y = 3x + 4 has less slope. So the the steeper line y = 3x + 4
Hence, y = 3x + 4 is the steeper line with the slope 3
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what is the value of
r t s 100°
Catalog # Size Package Content Price* Qty
BR1400106 6 reactions of 50 µl Reagents for coupled transcription/translation reactions
€196.00
0
BR1400101 24 reactions of 50 µl Reagents for coupled transcription/translation reactions
€591.00
0
BR1400102 96 reactions of 50 µl Reagents for coupled transcription/translation reactions
€1,864.00
HELP GIVING BRAINLIEST (NO LINKS) 50 POINTS
Expression A: 2(x + 1)
Expression B: 2x + 2
which statement does not show that these expressions are equivalent
A.subsitiuting any value of x makes the expressions equivalent
B. Both expressions involve addition
C. The expressions name the same number regardless of the value of x
D. 2(x +1) can be rewritten as 2x + 2 using the distributive property
Answer:
B. Both expressions involve additionStep-by-step explanation:
A. Substituting any value of x makes the expressions equivalent
FalseB. Both expressions involve addition
True. Both expressions involve multiplication tooC. The expressions name the same number regardless of the value of x
FalseD. 2(x +1) can be rewritten as 2x + 2 using the distributive property
False