Length of room, l = 3x + 1 ft.
Breadth of room, b = x² -1 ft.
Now, it is given that university wants each room to have 195 ft² of living space.
So,
[tex]lb = A\\\\(x^2-1)(3x+1)=195\\\\3x^3+x^2-6x-1=195\\\\3x^3+x^2-6x-196=0[/tex]
So, above equation has two complex root and one real root i.e x = 4.08 ft .
Therefore, Length of room is 13.24 ft and breadth is 15.65 ft.
Hence, this is the required solution.
Jack works after school. Each day he is paid a set amount, plus an hourly wage. Look at the table. Choose the linear function f Jack can use to find his pay.
Hours 1 1.5 2 2.5 3
Pay 18 23 28 33 38
A. f(x) = 10x + 8
B. f(x) = 15x + 3
C. f(x) = 0.5x + 1
D. f(x) = x + 18
Answer:
A: f(x)=10x+8
PLEASE ANSWER QUICK A team is ordering sweatshirts and sweatpants for its players. Each sweatshirt costs $25 and each pair of sweatpants costs $21. Write an algebraic expression to represent the total cost if x players want sweatshirts and y players want sweatpants.
Answer:
25x+ 21y
You multiply x by sweatshirts and y by sweatpants
Step-by-step explanation:
I don't know what sport your talking about or how many people are on the team so im not really sure but hete
Heidi uses 5 grams of tea leaves to make 25 fluid ounces of tea. Last week she made 75 fluid ounces of tea. How many grams of tea leaves did Heidi use to make tea last week?
Given :
Heidi uses 5 grams of tea leaves to make 25 fluid ounces of tea.
Last week she made 75 fluid ounces of tea.
To Find :
How many grams of tea leaves did Heidi use to make tea last week.
Solution :
Let, x gram of leaves are required last week.
So,
[tex]\dfrac{x}{5}=\dfrac{75}{25}\\\\x = 5\times\dfrac{75}{25}\\\\x = 5\times 3\\\\x = 15 \ grams[/tex]
Therefore, 15 grams of tea leaves is used last week.
Hence, this is the required solution.
Determine the x- and y-intercepts of the graph of x+2y=−4 . Then plot the intercepts to graph the equation.
Answer:
To determine the y-intercept, convert the equation into slope-intercept form.
x + 2y = -4
Subtract x from both sides
2y = -x-4
divide by 2 on both sides
y = -1/2(x) - 2 (this is the formula, with a slope of -1/2 and y-intercept of -2
This gives you a y-intercept of -2, which can be plotted at (0, -2)
For the x-intercept, plug in 0 for y into the formula.
x + 2y = -4
x + 2(0) = -4
x + 0 = -4
x=-4
This gives you an x-intercept of -4, which can be plotted at (-4, 0). Put those two numbers on the line and graph it, remembering that your slope is -1/2
Hope this helps!
please help i will give you brainliest!
Answer:
[tex]y=-\frac{2}{5} x+3[/tex]
Step-by-step explanation:
Slope, line, form.
y=mx+b
Points: 0,3 and -5,5
Find slope: 5-3/-5-0 or -2/5
y=-2/5x+b
5=-2/5(-5)+b
5=2+b
b=3
y=-2/5x+3
Hope this helps ;D
Sandra has $60 in a savings account. The interest rate is 5%, compounded annually.
To the nearest cent, how much interest will she earn in 1 year?
Answer:
$3 or 300 cents.
Step-by-step explanation:
She has 60 dollars in the savings account, and the interest rate is 5%, so you do 60*1.05 and get 63.
Before beginning voice lessons, Aubrey already knew how to sing 357 pieces, and she expects to learn 2 new pieces during each week of lessons. After 78 weeks of voice lessons, how many pieces will Aubrey be able to sing, in total? Write and solve an equation to find the answer. pieces
What are the correct answers?
Answer:
A function is a relation between sets where for each input, there is exactly one output.
1) Yes
2) Yes
3) Yes
4) No
Answer:
1) Yes
2) Yes
3) Yes
4) No
Jason buys three shirts with a listed price of $20 each. Jason uses a coupon that provides "Buy Two, Get One Free". What is the total final price Jason pays?
Given:
Jason buys three shirts with a listed price of $20 each.
He uses a coupon that provides "Buy Two, Get One Free".
To find:
The total final price Jason pays.
Solution:
Total number of shirts he buys = 3
Since he uses a coupon that provides "Buy Two, Get One Free", therefore he need to pay for 2 shirts and 1 he will get free.
Cost of 1 shirt = $20
Cost of 2 shirts = 2 × $20
= $40
Therefore, total final price Jason pays is $40.
On Olga's 16th birthday, her uncle invested $2,000 in an account that was locked into a 1.75% interest rate, compounded monthly. How much will Olga have in the account when she turns 18? Round to the nearest cent.
Answer:
$2070.6Step-by-step explanation:
Step one:
given data
principal p= $2000
Rate r= 1.75% = 0.0175
time t= 18-16= 2years
Required
The final amount of the compounded principal
The compound interest formula is
A=P(1+r)^t
A=2000(1+0.0175)^2
A=2000(1.0175)^2
A=2000*1.0353
A=2070.6
The account when she turns 18 will be $2070.6
contractor needs to pour a concrete floor in the shape of a rectangle. The figure shows the design for the concrete floor.
40 ft
30 ft
30 ft
40 ft
The contractor uses the converse of the Pythagorean theorem to prove that the floor is rectangular. How can he do this?
А
He can show that 30 + 40 equals the square of the length of each diagonal.
B
He can show that 40 - 30 equals the square of the length of each diagonal.
С
He can show that 302 + 402 equals the square of the length of each diagonal
D
He can show that 402-302 equals the square of the length of each diagonal
Answer:
A
Step-by-step explanation:
I would go with A. If this is wrong I'm so so so sorry, Although this is still what I think is correct.
How can you solve standard form and intercept form?
Answer:
The standard form of such an equation is Ax + By + C = 0 or Ax + By = C. When you rearrange this equation to get y by itself on the left side, it takes the form y = mx +b. This is called slope intercept form because m is equal to the slope of the line, and b is the value of y when x = 0, which makes it the y-intercept.
Step-by-step explanation:
Find the value of:
a) x2 when x = 6
b) y2 when y= -9
c) z2 when z = 0.7
Step-by-step explanation:
(a)= 6×2= 12
(b)= -9×2=-18
(c)= 0.7×2=1.4
What is the slope of y=x+5?
Answer:
1
Step-by-step explanation:
since the formula is
y=x+5 and x is the slope
1 is the slope
Answer:
the slope is 1 and the y intercept is 5
find x if 2^(3x-1)=128√5
Answer:
i think its x=6
Step-by-step explanation:
At the museum, there were 4,050 students in attendance from a total
of 15 different school districts. What was the average attendance from
each school district?
First to Answer:
270
Step by step
4050/15 = 270
Im not certain its 270 So i'd wait for another answer to confirm! Let me know if its correct or not!
Marcia works 11 hours per day, 6 days a week. How many hours does she work in a 5-week period? Plz plz plzzzz help.
Answer:
330
Step-by-step explanation:
11*6=. 66
66*5= 330
Please a need the answer and the solution please
Answer:
Step-by-step explanation:
To find the first table y = 4x + 2, to find each y value we have to substitute each x value into the equation.
4(-2) + 2 = -6 so -2 is going to have the y as -6
4(-1) + 2 = -2 so -1 is going to have the y as -2
4(0) + 2 = 2 so 0 is going to have the y as 2
4(1) + 2 = 6 so 1 is going to have the y as 6
4(2) + 2 = 10 so 2 is going to have the y as 10
So these are the points you would graph (-2, -6), (-1, -2), (0, 2), (1,6), and (2, 10)
For the next talbe y = 3x + 1 we do the same thing
3(-2) + 1 = -5 so -2 is going to have the y as -5
3(-1) + 1 = -2 so -1 is going to have the y as -2
3(0) + 1 = 1 so 0 is going to have the y as 1
3(1) + 1 = 4 so 1 is going to have the y as 4
3(2) + 1 = 7 so 2 is going to have the y as 7
The ooints to graph are (-2, -5), (-1, -2),(0,1), (1, 4) and (2,7)
For the next table y = 6x - 5
6(-2) - 5 = -17 so -2 is going to have the y as -17
6(-1) - 5 = -11 so -1 is going to have the y as -11
6(0) - 5 = -5 so 0 is going to have the y as -5
6(1) - 5 = 1 so 1 is going to have the y as 1
6(2) - 5 = 7 so 2 is going to have the y as 7
The points to graph (-2, -17), (-1, -11), (0, -5), (1, 1) and (2, 7)
For the next table y = 5 + 2x
5 + 2(-4) = -3 so -4 is going to have the y as -3
5 + 2(-2) = 1 so -2 is going to have the y as 1
5 + 2(0) = 5 so 0 is going to have the y as 5
5 + 2(3) = 11 so 3 is going to have the y as 11
5 + 2(5) = 15 so 5 is going to have the y as 15
(-4, -3), (-2, 1), (0, 5), (3, 11) and (5, 15)
For the next table y = 8x - 10
8(-4) - 10 = -42 so -4 is going to have the y as -42
8(-2) - 10 = -26 so -2 is going to have the y as -26
8(0) - 10 = -10 so 0 is going to have the y as -10
8(2) - 10 = 6 so 2 is going to have the y as 6
8(4) - 10 = 22 so 4 is going to have the y as 22
(-4, -42), (-2, -26), (0, -10), (2, 6) and (4, 22)
For the last table
2(-2) = -4 so -2 is going to have the y as -4
2(-1) = -2 so -1 is going to have the y as -2
2(0) = 0 so 0 is going to have the y as 0
2(-1) = -2 so -1 is going to have the y as -2
2(-2) = -4 so -2 is going to have the y as -4
(-2, -4), (-1, -2), (0, 0), (-1, -2) and (-2, -4)
Can someone help with this question?
What is the solution to the equation 3/5(y-5) = - (y+3) +2
Answer:
[tex]\frac{5}{4}[/tex]
Step-by-step explanation:
Given expression:
[tex]\frac{3}{5}[/tex](y - 5) = - (y + 3) + 2
To solve this problem, multiply both sides by 5;
5 x [tex]\frac{3}{5}[/tex](y - 5) = 5[-(y + 3) + 2}
3(y - 5) = 5(-y - 3 + 2)
expand,
3y - 15 = 5(-y -1)
3y -15 = -5y - 5
Collect like terms;
3y + 5y = -5 + 15
8y = 10
y = [tex]\frac{10}{8}[/tex] = [tex]\frac{5}{4}[/tex]
my head is HURTINGG and I cannot do this
put these decimals in order
3.5
14.2
4.37
10.4
17.86
8.93
Answer:
I think you didn't specify what order this decimals you want to be so:
If you want these to be in ascending order (lowest to highest), then:3.5, 4.37, 8.93, 10.4, 14.2 and 17.86.If you want these to be in descending order (highest to lowest), then:17.86, 14.2, 10.4, 8.93, 4.37 and 3.5.Hope this helps and if you could mark me as brainliest. Thanks!
What is the measure of angle A'B'C?
All Angles Added: 180
Measures of Idiviudual Angles
A=70 C=70 B=40
-------------------------------------------------------------------------------
Step-by-step explanation:
All angles of a triangle when combined must equal 180 degrees.
Since the triangle is an isosceles triangle, at least 2 sides must be congruent meaning that A=C since the triangle is not equilateral.
Customers at an ice-cream shop took a survey. The results showed that 144 customers rated the shop as being very satisfactory" This number represented 45% of the total number of customers who took
the survey
What was the total number of customers who took the survey?
A 189
B 65
C 99
D 320
Answer:
D
Step-by-step explanation:
Brian has reduced his cholesterol level by 8% after his last check up. If his original level was 260, what is his approximate cholesterol level now?
Help!! It should be easy it’s 7th grade math
Answer:
The watermelon candies taste $0.13 more.
Step-by-step explanation:
First, in order to find out how much each candy costs per ounce, you have to take the cost and divide it by the number of ounces. 3.48 divided by 12 is 0.29, so the watermelon candies cost $0.29 per ounce. 1.38 divided by 8 is 0.16, so the chewy chocolates cost $0.16 per ounce. In order to find how much more the watermelon candies cost, we have to subtract the cost of the watermelon candies by the cost of the chocolate candies. 0.29-0.16=0.13, so the watermelon candies cost $0.13 more than the chocolate candies.
What is the slope of the graph?
Answer:
The slope of the graph is 3/4
Step-by-step explanation:
Answer:
If the line goes through 20,10, and 60, 40, then the slope is 3/4.
what is k in 1/4k = 3 (-1/4k + 3)?
Answer:
k = 9
Step-by-step explanation:
1/4k = 3(-1/4k + 3) distribute
1/4k = -3/4k + 9
+3/4k +3/4k Add
k = 9 Answer
-3(x + 5) = 6 - 3(2x + 4) solve for x and show work
Answer:
-3
Step-by-step explanation:
-3(x + 5) = 6 - 3(2x + 4)
-3x - 15 = 3(2x + 4)
-3x - 15 = 6x + 12
+3x +3x
-15 = 9x + 12
-12 -12
-27 = 9x
-------------
9
x = -3
If 3 < 1 - x, what is value for x
Answer:
x < -2
Step-by-step explanation:
if a polygon is translated, which of the following characteristics of the polygon are the same?
A side length
B area
C the coordinates of the vertices.
the following characteristic of the polygon that are the same are A SIDE LENGTH AND B AREA
Translation is a rigid transformation.
The characteristics that will remain the same are: (a) side length and (b) area
When a polygon is translated, the polygon undergoes a rigid transformation.
A rigid transformation does not change the side length and angle of a shape.
The side lengths of the polygon would remain unchanged.Since the side lengths are not altered, then the area of the polygon will also remain unchanged.However, the coordinates would change; because the polygon would change its position after translation.
Hence, the correct options are:
(a) and (b)
Read more about translations at:
https://brainly.com/question/12463306
Hi. I need help with this questions.
See image for question
Answer:
NoneStep-by-step explanation:
Given expression
9x² - 2(k + 7)x + kIf this is a perfect square then it should be in the form of:
(3x)² - 2(3x)(√k) + (√k)²Comparing the two expressions, we see that:
(k + 7) = 3√k(k + 7)² = 9kk² + 14k + 49 - 9k = 0k² + 5k + 49 = 0D = √(5² -4*49) = √-171Since the discriminant is negative, there is no solution