Given:
Length of a rectangular monitor screen is 5 in more than it's width.
If the length were doubled and if the width were deceased by 1 in the area would be increased by 170 in².
To find:
The length and width of the screen.
Solution:
Let width of the screen be x inches.
Length of a rectangular monitor screen is 5 in more than it's width. So,
Length of screen = (x+5) inches
Area of screen is
[tex]Area=length\times width[/tex]
[tex]A_1=(x+5)\times x[/tex]
[tex]A_1=x^2+5x\text{ in}^2[/tex]
If the length were doubled and if the width were deceased by 1 in the area would be increased by 170 in².
New length = 2(x+5) inches
New width = (x-1) inches
So, new area is
[tex]A_2=2(x+5)(x-1)[/tex]
[tex]A_2=(2x+10)(x-1)[/tex]
[tex]A_2=2x^2+10x-2x-10[/tex]
[tex]A_2=2x^2+8x-10 \text{ in}^2[/tex]
Area increased by 170 in².
[tex]A_2-A_1=170[/tex]
[tex](2x^2+8x-10)-(x^2+5x)=170[/tex]
[tex]2x^2+8x-10-x^2-5x=170[/tex]
[tex]x^2+3x-10=170[/tex]
Subtract 170 from both sides.
[tex]x^2+3x-10-170=0[/tex]
[tex]x^2+3x-180=0[/tex]
Splitting the middle term, we get
[tex]x^2+15x-12x-180=0[/tex]
[tex]x(x+15)-12(x+15)=0[/tex]
[tex](x+15)(x-12)=0[/tex]
[tex]x=-15,12[/tex]
Width cannot be negative. So, x=12.
Width = 12 inches
Length = 12+5 = 17 inches
Therefore, the length of screen is 17 inches and width is 12 inches.
which equation is y=(x+3)^2+(x+4)^2 rewritten in vertex form?
Answer:
[tex]y-1/2=2(x+7/2)^2[/tex]
Step-by-step explanation:
Equation of the Quadratic Function
The vertex form of the quadratic function has the following equation:
[tex]y-k=a(x-h)^2[/tex]
Where (h, k) is the vertex of the parabola that results when plotting the function, and a is a coefficient different from zero.
The given function is:
[tex]y=(x+3)^2+(x+4)^2[/tex]
Expanding the squares:
[tex]y=x^2+6x+9+x^2+8x+16[/tex]
Simplifying:
[tex]y=2x^2+14x+25[/tex]
Factoring 2 from the first two terms:
[tex]y=2(x^2+7x)+25[/tex]
The expression in parentheses must be completed to form the square of a binomial:
[tex]y=2(x^2+7x+49/4-49/4)+25[/tex]
Isolating the square of the binomial:
[tex]y=2(x^2+7x+49/4)-49/2+25[/tex]
Operating and Factoring:
[tex]y=2(x+7/2)^2+1/2[/tex]
Rearranging:
[tex]\boxed{y-1/2=2(x+7/2)^2}[/tex]
Comparing with the vertex form:
a=2, h=-7/2, k=1/2
HELP PLEASE!!!! WHICH SET OF VALUES IS A FUNCTION?
Answer:
The light blue one
Step-by-step explanation:
For a statistics question, I'm given a probability (which is 1/8) of flipping three coins and getting three heads and I'm asked to interpret this probability. What does it mean to interpret a probability?
Answer:
probabilty is the chance for you to get something
Answer:
This is the likelihood of getting 3 heads
In my town, gas prices are always listed to the thousandths place. Since the smallest coin we have is the penny, we have to round them to the hundredths place. If the price of gas is $8.162, what will the price be when we round it to the hundredths place?
Answer:
$8.16Step-by-step explanation:
given the amount $8.162
if we are to round this amount to the nearest hundredth, we would have
$8.16
this is because will have already consider the last value in the given digit and this value is not up to 5 hence we are not able to round the number next to it up, but we have to retain its current value of 6.
therefore the value is
$8.16
Answer:
$8.16
Step-by-step explanation:
given the amount $8.162
if we are to round this amount to the nearest hundredth, we would have
$8.16
this is because will have already consider the last value in the given digit and this value is not up to 5 hence we are not able to round the number next to it up, but we have to retain its current value of 6.
therefore the value is
$8.16
Given that the slope is -4 and the y intercept is -4 what is the equation of the line?
Answer: srry i think it is y = mx + b, where m is the slope and b is the y-intercept. Slope-intercept is the form used most often as the simplified equation of a line.
Step-by-step explanation: where m is the slope and b is the y-intercept. Slope-intercept is the form used most often as the simplified equation of a line.
(-5) - (-48)÷(-16)+(-2)×6
Please help I’ll give brainiest!!
Answer:
c
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
They have you pay a initial amount of $2
Danielle answered 24 out of 30 questions correct on her Math test and
21 out of 25 questions correct on her Science test On which test did she
Score higher?
Answer:
Science
Step-by-step explanation:
To calculate the percentages, divide the amount of correct answers by the amount of questions there are.
Math:
24/30=.8=80%
Science:
21/25=.84=84%
The science score is 4% higher.
A parachute is descending at a rate of 28 feet per minute. Find the total change in altitude of the parachute after 4 minutes.
Answer:
The parachute descended 112 feet
Step-by-step explanation:
Help me plzzzzzzz.thank you
Help me please what is 2+2 please help me.
Answer:
6969694204206969
Step-by-step explanation:
lololololololol
URGENT AND EASY 8TH GRADE MATH
Answer:
x < -8
Step-by-step explanation:
I used a calculator
Answer:
x<-8
Step-by-step explanation:
Let's solve your inequality step-by-step.
122<−2(8x+3)
Step 1: Simplify both sides of the inequality.
122<−16x−6
Step 2: Flip the equation.
−16x−6>122
Step 3: Add 6 to both sides.
−16x−6+6>122+6
−16x>128
Step 4: Divide both sides by -16.
−16x /−16 > 128 /−16
x<−8
Help pleaseeee ASAP
Answer:
The third one I think
Step-by-step explanation:
If you walked 5 miles down a trail and then walked 2 1/4 miles back, how many miles away are you from your starting point?
miles
Answer:
3 3/4
Step-by-step explanation:
5 - 2 1/4 = 3 3/45 - 2 = 3A train leaves the station at 6:00 P.M. traveling west at 80 miles per hour. On the parallel track, a second train leaves the station 3 hours later traveling west at 100 miles per hour. At what time will the second train catch up with the first train?
SHOW YOUR WORK PLZ I WILL GIVE YOU BRINLEY
IF YOU SHOW YOUR WORK WORK
Answer:
9 AM
Step-by-step explanation:
Let t = traveling time of the 1st train, when the 2nd train catches up
Then
(t-3) = traveling time of the the 2nd train.
When this occurs, both trains will have traveled the same distance;
Write a distance equation: Dist. = speed * time
100(t-3) = 80t
100t - 300 = 8t
100t- 80t = +300
20t = 300
t = 300/20
t = 15 hrs.
Time = 6 PM + 15 hrs. = 9 AM the next day
solve the inequality plz i need help asapx/3-2<4
Answer:
here is your answer 1<4
Pls help me I don’t know this :(
Answer:
B 25% I worked this out, tell me if it helped and plz mark Brainliest ^w^
What percent of 80 is 8
Answer:
P = 10%
Step-by-step explanation:
Of means multiply and is means equals
P * 80 = 8
Divide each side by 80
P = 8/80
P = .1
Change to percent form
P = 10%
Answer:
Hi sorry
Step-by-step explanation:
sorry bhai plzzzzxxxxxxzzzzzzzzzzzzzzzztry ur best
Determine the missing angle measures in the parallelogram below:
СІ
120°
IA
B В
How do u find the volume of rectangular brick?
Answer:
the answer is to use the formula lxwxh or length x width x height
The high school decided to buy new unitorms for the girls and boys' basketball teams. They plan to buy 35 uniforms with a total cost of $1,235. The store
offers discounts based on the number of items the school buys, as shown below. What will the discounted price be for the high school?
Answer:
$802.75
Step-by-step explanation:
1235x0.35=432.25
1235-432.25=802.75
Ryan works at the car wash making $5.30 per hour plus tips. Last week Ryan worked 32 hours and earned $403. How much in tips did Ryan make last week? a. $86.40 b. $148.00 c. $169.60 d. $233.40 Please select the best answer from the choices provided A B C D
Ryan earned $233.40 from the tips. Option D is correct
Ryan works at the car wash making $5.30 per hour plus tips.
Last week Ryan worked 32 hours and earned $403
How much in tips did Ryan make last week?
In mathematics, it deals with numbers of operations according to the statements.
Let the tip Ryan get be x,
Ryan earned $5.30 per hour.
Ryan earned $403 for 32 hours of the working,
Ryan worked 32 hours so,
Ryan earned = 32 * 5.30
= 196.4
Total tips that Ryan earned = total earning - Ryan earned
= $403 - $196.4
= $233.40
Thus, Ryan earned $233.40 from the tips. Option D is correct
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ6
On June 6, you buy $1.2 pounds of bananas. The bananas cost $1.17 per pound. On June 7, you spent $3.47 on Takis, a candy bar, and a coke from Circle H convenience store. On June 8, you received $25 tip for helping your neighbor mow their lawn. On June 8, you spend $14.80 on a pair of wireless bluetooth headphones Date Transactions Payment(-) Deposit(+) Balance June 5 June 6 June 7 June 8 June 8
Answer:
We are not given the initial balance, so I will write down $X
Date Particulars Payment Deposit Balance
June 5 Starting balance $X
June 6 Purchased bananas $1.40 $X - $1.40
June 7 Purchased candy & coke $3.47 $X - $4.87
June 8 Tip received $25 $X + $20.13
June 8 Purchased headphones $14.80 $X + $5.33
show that the area of the rectangle ABCD is 3 route 5 cm
Answer:
Please see the attached picture for the full solution.
Which integer is between 30 and 40 ?
A. 5
B.
6
C.
20
D.
35
Answer:
D)35. Hope it hepls
Step-by-step explanation:
because 35 is between 30 and 40
Find the sum or difference of the polynomials. (7x2 + 5x − 3) + (4x2 − 3x + 2)
Answer:
[tex]11x^{2} +2x-1[/tex]
Step-by-step explanation:
Combine Like Terms:
[tex]7x2+5x+-3+4x2+-3x+2[/tex]
[tex](7x^{2} +4x^{2} )+(5x+-3x)+(-3+2)[/tex]
[tex]11x^{2} +2x-1[/tex]
-3x + 4=6x-5 solve for x
Step-by-step explanation:
[tex] -3x + 4=6x-5\\\\6x+3x=4+5\\\\9x=9\\\\x=\sf{\dfrac{9}{9}}\\\\X=1[/tex]
Which number line represents the solution to the inequality
1
+
2
x
<
−
7
?
Answer:
[tex]\boxed {x < -4}[/tex] (Choice D)
Step-by-step explanation:
You first need to solve the following inequality in order to get the actual answer and find the actual graph:
[tex]1 + 2x < -7[/tex]
-Subtract [tex]1[/tex] to both sides:
[tex]1 - 1 + 2x < -7 - 1[/tex]
[tex]2x < -8[/tex]
-Divide both sides by [tex]2[/tex]:
[tex]\frac{2x}{2} < \frac{-8}{2}[/tex]
[tex]\boxed {x < -4}[/tex]
The number line graphed:
What is S? Please and thank you!
9= S+9
Answer: S=0
hope this helps
Step-by-step explanation:
answer s =0
Step-by-step explanation:
because you just have to get rid of the 9 and by doing that you ned yo subtract it by 9
Which equation shows a proportional relationship between x and y?
y=−3x−2
y = 9
y = 4x
y = 3x + 1
ILL MAKE MOST BRAINLIEST!!!
Given:
There exist a proportional relationship between x and y.
To find:
The equation which represents a proportional relationship between x and y.
Solution:
If there exist a proportional relationship between x and y, then
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
where, k is constant of proportionality.
We know that, proportional relationship passes through the origin because (0,0) satisfy [tex]y=kx[/tex].
For x=0, check which equation has y=0.
In option A, [tex]y=-3(0)-2=-2[/tex].
In option B, [tex]y=9[/tex].
In option C, [tex]y=4(0)=0[/tex].
In option D, [tex]y=3(0)+1=1[/tex]
Only in option C, we have a equation of the form [tex]y=kx[/tex] with 4 as constant of proportionality and it passes through (0,0).
Therefore, the correct option is C.
Answer:
answer is c
Step-by-step explanation:
its 7=4x
