Answer:
1. [tex]Perimeter = 10x^2+ 22x - 16[/tex]
2. [tex]Area = 6x^4 +28x^3 + 14x^2 - 48x[/tex]
3. [tex]x = 1[/tex] or [tex]x = -3.2[/tex]
4. [tex]Length = 0[/tex] and [tex]Width = 8[/tex]
5. [tex]Length = 6.72[/tex] and [tex]Width = 1.28[/tex]
6. Second Solution
7. [tex]Area = 8.6016[/tex]
Step-by-step explanation:
Given
[tex]Length = 3x^2 + 5x - 8[/tex]
[tex]Width = 2x^2 + 6x[/tex]
Solving (1): The perimeter
Perimeter is calculated as thus:
[tex]Perimeter = 2 * (Length + Width)[/tex]
Substitute values for Length and Width
[tex]Perimeter = 2 * (3x^2 + 5x - 8 + 2x^2 + 6x)[/tex]
Collect Like Terms
[tex]Perimeter = 2 * (3x^2+ 2x^2 + 6x + 5x - 8 )[/tex]
[tex]Perimeter = 2 * (5x^2+ 11x - 8 )[/tex]
Open Bracket
[tex]Perimeter = 10x^2+ 22x - 16[/tex]
Solving (2): The Area:
Area is calculated as thus:
[tex]Area = Length * Width[/tex]
Substitute values for Length and Width
[tex]Area = (3x^2 + 5x - 8) * (2x^2 + 6x)[/tex]
Expand Bracket
[tex]Area = 2x^2(3x^2 + 5x - 8) + 6x(3x^2 + 5x - 8)[/tex]
Open Bracket
[tex]Area = 6x^4 + 10x^3 - 16x^2 + 18x^3 + 30x^2 - 48x[/tex]
Collect Like Terms
[tex]Area = 6x^4 + 10x^3 + 18x^3 - 16x^2 + 30x^2 - 48x[/tex]
[tex]Area = 6x^4 +28x^3 + 14x^2 - 48x[/tex]
Solving (3): If perimeter is 16, show that x = 1 and x = -3.2
In (a) [tex]Perimeter = 10x^2+ 22x - 16[/tex]
Substitute 16 for Perimeter
[tex]16 = 10x^2+ 22x - 16[/tex]
Equate to 0
[tex]10x^2+ 22x - 16 -16=0[/tex]
[tex]10x^2+ 22x - 32=0[/tex]
Expand
[tex]10x^2+ 32x -10x- 32=0[/tex]
Factorize
[tex]x(10x + 32) - 1(10x + 32) = 0[/tex]
[tex](x - 1)(10x + 32) = 0[/tex]
Split
[tex]x - 1 =0[/tex] or [tex]10x + 32 = 0[/tex]
[tex]x = 1[/tex] or [tex]10x = -32[/tex]
[tex]x = 1[/tex] or [tex]x = -32/10[/tex]
[tex]x = 1[/tex] or [tex]x = -3.2[/tex]
Solving (4): Using x = 1; Solve the dimension of the rectangle
We have that:
[tex]Length = 3x^2 + 5x - 8[/tex]
[tex]Width = 2x^2 + 6x[/tex]
Substitute 1 for x in the given parameters
[tex]Length = 3(1)^2 + 5(1) - 8[/tex]
[tex]Length = 3*1 + 5*1 - 8[/tex]
[tex]Length = 3 + 5 - 8[/tex]
[tex]Length = 0[/tex]
[tex]Width = 2(1)^2 + 6(1)[/tex]
[tex]Width = 2*1 + 6*1[/tex]
[tex]Width = 2 + 6[/tex]
[tex]Width = 8[/tex]
Solving (5): Using x = -3.2; Solve the dimension of the rectangle
We have that:
[tex]Length = 3x^2 + 5x - 8[/tex]
[tex]Width = 2x^2 + 6x[/tex]
Substitute -3.2 for x in the given parameters
[tex]Length = 3(-3.2)^2 + 5(-3.2) - 8[/tex]
[tex]Length = 3*10.24 + 5(-3.2) - 8[/tex]
[tex]Length = 30.72 -16 - 8[/tex]
[tex]Length = 6.72[/tex]
[tex]Width = 2(-3.2)^2 + 6(-3.2)[/tex]
[tex]Width = 2*10.24 + 6(-3.2)[/tex]
[tex]Width = 20.48 -19.2[/tex]
[tex]Width = 1.28[/tex]
[tex]Length = 6.72[/tex] and [tex]Width = 1.28[/tex]
Solving (6):
In the first solution of the dimensions in number 4, we have that
[tex]Length = 0[/tex] and [tex]Width = 8[/tex]
This dimension can not be considered because the length of a rectangle can not be 0
In the second solution of the dimensions in number 5, we have that
[tex]Length = 6.72[/tex] and [tex]Width = 1.28[/tex]
This dimension makes more sense because both dimensions are greater than 0
Solving (7): Using (6), determine the Area
In (6), we conclude that
[tex]Length = 6.72[/tex] and [tex]Width = 1.28[/tex]
So, Area is calculated as thus:
[tex]Area = Length * Width[/tex]
[tex]Area = 6.72 * 1.28[/tex]
[tex]Area = 8.6016[/tex]
Will give Brainliest!!!
Madeline borrowed some money from her friend in order to help buy a new video game system. Madeline agreed to pay back her friend $5 per week, and after 13 weeks, Madeline still owed her friend $5. Write an equation for L,L, in terms of t,t, representing the amount Madeline owes her friend after t weeks.
Answer:
5 x T = L
Step-by-step explanation:
The scatterplot below shows the number of coupons that are used at the grocery store and amount of money that is saved. A graph titled Coupon Use and money saved has number of coupons used on the x-axis, and coupon savings (dollars) on the y-axis. Points are grouped together and increase. Which statement about the scatterplot is true? As coupon use decreases, the amount of savings increases. As coupon use increases, the amount of savings increases. Regardless of high coupon use, the amount of savings remains low. Regardless of high savings, coupons use remains low.
Answer:
b, i did the quiz
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Divya (height 53 cm) and Surjeet ( 58 cm ) are standing in a ground .If distance between their toes is 12 cm ,what is the distance between their heads ?
Answer:
The answer would be 17 cm
Step-by-step explanation:
If the distance between their feet is 12 cm, then the distance between their heads would also be 17 cm, because of their five cm height difference. [ You add that on to their normal distance]. I hope this helped! If I'm wrong, I'm sorry and please let me know... Have a great day!!
1) f(x) = 5x^4+ 49x^2+ 36
Answer:
That's the simplest I could do, sorry
The cost of a telephone call from Wilson to East Meadow is $0.60 for the first three minutes plus $0.17 for each additional minute. What is the greatest number of whole minutes of a telephone call if the cost cannot exceed $2.50?
Answer:
14 minutes
Step-by-step explanation:
divide 2.50$ by 0.17$ and u get 14 minutes if you round it
Use the figure at the right. If JK = 4x + 24 and NO = 26, what is the value of x?
Answer:
X = 1/2
Step-by-step explanation:
JK = NO
4x + 24 = 26
4x = 2
x = 1/2
I need help quickly please
Which of these tables best represents the equation y = 5x – 8
The best and only represents the equation y = 5x – 8 is done in the table C.
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given a linear equation y = 5x - 8
As we can see that this equation has a slope of 5 and a y-intercept of -8
To ease the process we will calculate the value of y at different values of x:
For x = 0 ,
y = 5 * 0 - 8 = -8
For x = 1
Y = 5-8 = -3
For x = 2
Y = 5*2 - 8
y = 2
For x = 3
y = 5*3 -8
y = 7
for x = 4
y = 20 *8
y = 12
Since only table C is satisfying the situation.
therefore, The best and only represents the equation y = 5x – 8 is done in table C.
Learn more about Linear equations here:
https://brainly.com/question/11897796
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Complete Question:
What is the vertex of the standard form quadratic f (x) = x^2+14x+35
Answer:
x=50
Step-by-step explanation:
What is the answer to this?
16 > -f, if f = 15?
Answer:
16>-15
Step-by-step explanation:
16>-f, if f = 15 - given equation
f= 15, so subsitute 15 in -f. This gives us 16>-15 because, f = 15, and there was a minus making is negative.
what is the rate of change?
Jose has $6 and saves $1 a day.
Answer:
The rate of change is 1$
Step-by-step explanation:
Jose is getting one dollar a day (the only thing in the equation that is changing)
An oblique cylinder has a diameter of 14 units. The volume of the cylinder is 1,176 cubic units. what is the height of the cylinder
9514 1404 393
Answer:
about 7.64 units
Step-by-step explanation:
The volume is given by the formula ...
V = πr²h
Then the height is ...
h = V/(πr²) = 1176/(π·7²)
h ≈ 7.64 . . . . units
Answer:
B. 24 units
Step-by-step explanation:
Just took the Pre-Test on Edg (2020-2021)!
Factor the expression x²+9
The sum of two integers is -129, if one of them is 150, find the order
Answer: -279
Step-by-step explanation:
-129-150= -279
to check
-279+150= -129
1. There are 3 boys for every 6 girls at a
movie. If there are 24 girls, how many
boys are at the movie?
Boys
Girls
3
24
There are
boys at the movie.
Answer:
I think its 12
good luck
50 POINTS!!! Urgent, Extremely Confused!
So far, Marta has correctly predicted the winner of 6 out of 13 football games. She wants to know how many consecutive games she would have to predict correctly to raise the percent of correct predictions to 65%.
a. Write an equation to represent this situation.
b. Solve the equation. !Show all steps!
c. Answer the question. How many consecutive games must she predict correctly to raise her percent to 65%?
Answer:
Required Answer:-Marta predicted correctly 6 out of 13 football games .
We need to find first Her's Current percentage[tex]\longrightarrow[/tex][tex]\sf {\dfrac {6}{13}}\times 100 [/tex]
[tex]\longrightarrow[/tex][tex]\sf {\dfrac {600}{13}}[/tex]
[tex]\longrightarrow[/tex][tex]\sf 46.15\% [/tex]
Now We need to add x in both denominator and numerator[tex]\longrightarrow[/tex][tex]\sf {\dfrac {6+x}{13+x}}={\dfrac {65}{100}} [/tex]
Simplify use cross multiplication method[tex]\longrightarrow[/tex][tex]\sf 100 (6+x)=65 (13+x)[/tex]
[tex]\longrightarrow[/tex][tex]\sf 600+100x=845+65x [/tex]
[tex]\longrightarrow[/tex][tex]\sf 100x-65x=845-600 [/tex]
[tex]\longrightarrow[/tex][tex]\sf 35x=245 [/tex]
[tex]\longrightarrow[/tex][tex]\sf x={\dfrac{245}{35}}[/tex]
[tex]\longrightarrow[/tex][tex]\sf x=7 [/tex]
So the new rational number[tex]\longrightarrow[/tex][tex]\sf {\dfrac {6+x}{13+x}}[/tex]
[tex]\longrightarrow[/tex][tex]\sf {\dfrac {6+7}{13+7}}[/tex]
[tex]\longrightarrow[/tex][tex]\sf {\dfrac {13}{20}}[/tex]
[tex]\therefore [/tex] Marti needs to predict more 13 games out of 20 to raise her percentage to 65%.
Which problem is not represented by the
equation 20 + x = 35?
a) A cake needs 35 min in the oven. It has
been in the oven for 20 min.
bI earned 20 000 Dinars. I will get more
money so that the total amount will be
35 000 Dinars.
You are in the 20th floor. You pressed the
35th floor button.
d I bought a shirt for 20 000 Dinars and a
pair of pants for 35 000 Dinars.
Answer:
d the other equations the total is 35. this one the total would be 55
Janice's insurance costs $1,245 a year. How much should she budget for insurance each month? *
ASAP !!
Answer:
$103.75
Step-by-step explanation:
$1,245 devide by 12
A man runs the London marathon at an average speed of 8mph the route is 26 miles what was his time in hours and minutes
Answer:
the only thing you need to do is to divide the speed with the distance
What is the value of z?
Answer:
value of z is39°.
Step-by-step explanation:
64+68+z+9=180°(sum of triangle)
141+z=180
z=180-141
z=39°
Answer:
22
Step-by-step explanation:
Write this statement as a conditional statement in the form “if p, then q.”
Two lines are not on the same plane. So, the lines are skew.
Answer:
if two lines are not on the same plane, then the lines are skew.
Step-by-step explanation:
if p statement is called the hypothesis of the conditional statement.
then q statement is called the conclusion of the conditional statement.
A boat leaves Astoria and travels upstream on the Columbia river for 5 hours. The return trip only takes 3.6 hours because the boat travels 4 miles per hour faster downstream due to the current. How far does the boat travel up the Columbia? Suppossed to solve as an in equality?
Answer:
10.285 miles
Step-by-step explanation:
Given that:
Upstream travel time = 5 hours
Return trip travel time = 3.6 hours
Let upstream travel speed = x mph
Downstream travel speed = x + 4 mph
Distance = speed * time
Upstream distance = x * 5 = 5x
Downstream distance = (x + 4) * 3.6
5x = (x + 4) * 3.6
5x = 3.6x + 14.4
5x - 3.6x = 14.4
1.4x = 14.4
x = 10.285714
x = 10.285 miles
Supplies for last year cause 1477 which was 177 over the budget rounded to the nearest one percent by what percent did it cost to see the budget cost
Answer:
About 12%
Step-by-step explanation:
Answer:
The cost exceeded the budgeted cost by 14%
Step-by-step explanation:
Supplies for last year cost 1,477, which was 177 over budget. So, the budgeted cost was: 1477 - 177 = 1300
Suppose, the cost of supplies exceeded the budgeted cost by
So, the amount of exceeded cost dollar.
Thus, the equation will be......
13x = 177
x= 177/13 = 13.615 = 14
(Rounded to the nearest 1%)
So, the cost exceeded the budgeted cost by 14%
9x+12=24 i feel like i know the answer but im just a bit confused
Answer: x = 4/3 or x = 1.3 or x = 1 1/3
Step-by-step explanation: you have to move everything that does Not have A Variable to the right and solve the equation
9x + 12 = 24
9x = 24 - 12
= 12
x = 12/9
I am confused too. This is the best I can do :(
Clare wants to make an open-top box by cutting out corners of a 30 inch by 25 inch piece of poster board and then folding up the sides. The volume, `V\left(x\right),` in cubic inches of the open-top box is a function of the side length, `x,`in inches, of the square cutouts.
Answer:
V(x) = 4x³ - 110x² + 750x
Step-by-step explanation:
For each side of the base of the open-top box, since x inches is cut out from each side, we have 2x inches removed from each sides dimension.
Since the dimensions of the poster are 30 inches by 25 inches, the area of the base of the open-top box is thus
A(x) = (30 - 2x)(25 - 2x) since we remove 2x inches from each dimension.
Now, the height of the open-top box is x. So, its volume is V(x) = Ax
V(x) = (30 - 2x)(25 - 2x)x
V(x) = (750 - 60x - 50x + 4x²)x
V(x) = (750 - 110x + 4x²)x
Expanding the bracket, we have
V(x) = 750x - 110x² + 4x³
Re-arranging, we have
V(x) = 4x³ - 110x² + 750x
Patrice is a star player for the unc women’s basketball team she has injured her ankle and is doubtful that she will be able to play. If she can play, the coach estimates the will score 78 points. If she is not able to play, the coach estimates they will score 62 points. The team doctor estimates there is a 60-40 chance she will play. Determine the number of points the team can expect to score
Answer:
3
Step-by-step explanation:
PLS HELP MEEEEEEEEEEEEEEEEEE!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
c
Step-by-step explanation:
a is not enough information because the measure of angle 2 could be another random value
b is not correct for the same reason as a
d is not correct because those two angles do not equal 90
c is correct because of a theorem, so basically if you have two angles, and they have segments at 90 angles placed in the specified spots, they are on the bisector
solve the equation. Check the solution. 11-6x-7-8x=6
X= (Type an integer or a simplified fraction.).
Answer:
The answer is x=-1/7
Step-by-step explanation:
11-6x-7-8x=6
Combine like terms
11-7-6x-8x=6
4-14x=6
4-4-14x=6-4
-14x=2
To find x divide both sides by -14
-14x/-14=2/-14
x=-1/7
Mr. Dyer is studying a map. The map has a scale that says 1.5 inches is equivalent to 125 miles. Mr. Dyer measures and sees that two cities are half a foot apart. He has enough gas in his truck to travel 580 miles. Can he make it from one city to the other on the gas in his truck?
Answer: Yes he can make the trip without having to refuel.
The distance between the two cities is 500 miles.
================================================
Work Shown:
half a foot = 1/2 ft = (1/2)*(12 inches) = 6 inches
Based on the scale given, we can say,
(map length)/(real length) = (map length)/(real length)
(1.5 inches)/(125 miles) = (6 inches)/(x miles)
1.5/125 = 6/x
1.5x = 125*6 ............. cross multiply
1.5x = 750
x = 750/1.5 .......... divide both sides by 1.5
x = 500
The two cities are 500 miles apart. Since this is less than 580, he can make the trip without having to refuel.
This is assuming he drives directly from the first city to the second, without any additional pitstops or detours. Though in reality, straight line distance on a map doesn't always necessarily correspond to the road distance traveled (since the road tends to wind or curve often). However, for the sake of this problem, we'll just assume the road is a straight line to keep things simple.
----------------------------------------
Another approach:
1.5 inches = 125 miles
3 inches = 250 miles ..... multiply both sides by 2
6 inches = 500 miles .... multiply both sides by 2
half a foot = 500 miles
So half a foot on paper corresponds to 500 miles in real life.
Tyler painted 9/2 square yards of wall area with 3 gallons of paint.
How many gallons of paint does it take to paint each square yard of wall?
Write multiplication and division equations to represent the situation.
Answer:
you flip 9/2 into 2/9 and then 3/0 multiply across and you get 6/9.
Step-by-step explanation: