The width and length of the rectangle is 7ft and 10 feet respectively.
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
Given, The length of a rectangle is 11 ft less than three times the width has an area of 70ft².
Assuming the width of the rectangle to be x ft, therefore the length of the rectangle is (3x - 11) ft.
We know the Area of a rectangle (A) = length×width.
∴ x.(3x - 11) = 70.
3x² - 11x = 70.
3x² - 11x - 70 = 0.
3x² - 21x + 10x - 70 = 0.
3x(x - 7) + 10(x - 7) = 0.
(x - 7)(3x + 10) = 0.
x - 7 = 0 Or 3x + 10 = 0.
x = 7 Or x = - 10/3.
A negative value of x is inadmissible here as length cannot be negative.
So, the width of the rectangle is 7 ft and the length of the rectangle is
10 ft.
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Jessica plans to purchase a car in one year at a cost of $30,000. how much should be invested in an account paying 10% compounded semiannually to have the funds needed?
How do you graph y^2=x^3?
Write an equation that can be used to find the area A of a rectangular rug whose sides are 5 feet long and x feet long
Mika wrote the table of points below. x y 0 2 3 5 6 8 Which explains whether or not Mika has described a proportional relationship, and why?
Answer:
B
Step-by-step explanation:
Edg 2020
Answer:
Step-by-step explanation: Answer B
Which expression is equivalent to r^9/r^3
Answer:
The correct option is B.
Step-by-step explanation:
The given expression is
[tex]\frac{r^9}{r^3}[/tex]
According to the property of exponent,
[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]
Using this property of exponent, we get
[tex]\frac{r^9}{r^3}=r^{9-3}[/tex]
[tex]\frac{r^9}{r^3}=r^{6}[/tex]
The expression [tex]r^{6}[/tex] is equivalent to the given expression.
Therefore the correct option is B.
A baby wriggled so much that weighing him at the clinic was a problem. So the doctor held the baby and stood on a scale. Then the nurse held the baby and stood on the scale. Then the doctor held the nurse who held the baby and stood on the scale. the three results were 78 kg, 69 kg and 142 kg respectively. What was the weight of the baby.
Long question but help me out ( it was 69 kg I mean)
can someone pls help me
A party rental company has chairs and tables for rent. The total cost to rent 3 chars and 2 tables is $20. The total cost to rent 8 chairs and 4 tables is $45. What is the cost to rent each chair and each table?
Equations:
8c + 4t = 45
3c + 2t = 20
Modify for elimination: ( multiply 2nd eq by -2)
8c + 4t = 45
-6c + -4t = -40
Subtract and solve for "c":
2c = 5
c = $2.50 (cost of one chair)
Solve for "t":
3c + 2t = 20
3(2.50) + 2t = 20
7.50 + 2t =20
2t=12.50
T= 12.50/2 =6.25
t = $ 6.25 (cost of one table)
Table = 6.25 each
Chair = 2.50 each
Check:
3(2.50) + 2(6.25) =
7.50 +12.50 = 20
8(2.50) + 4(6.25) =
20.00 + 25.00 = 45.00
Find the value of x. If necessary, round your answer to the nearest tenth. O is the center of the circle. The figure is not drawn to scale.
A. 13
B. 26
C. 77
D. 38.5
Find the limit of the function algebraically. limit as x approaches negative nine of quantity x squared minus eighty one divided by quantity x plus nine.
What is the solution of the equation 6x - 8 = 4x? X=
no idea. please help:)
Plato-Match each set of conditions with the corresponding relationship between ∆ABC and ∆XYZ and the criterion (if any) that proves the relationship.
Need help with this question! Will attach pic! A satellite is to be put into an elliptical orbit around a moon as shown below.The moon is a sphere with radius of 1000 km. Determine an equation for the ellipse if the distance of the satellite from the surface of the moon varies from 953 km to 466 km
Solve for z: 3z -5 +2z=25 -5z
To answer this question you will have to combine like terms.
3z-5+2z=25-5z
Combine 3z and 2z first because they have z in common and are on the same side: 3z+2z=5z
Now you have -5+5z=25-5z
Now you will go ahead and distribute since you can't combine anymore on certain sides.
You can add 5 to 25 on the other side: 25+5=30
Then add 5z to 5z on the other side: 5z+5z=10z
So now your equation should look like this: 10z=30
From here you will have to divide both sides by 10: 10/10=1(since it came to 1 it will just stay as z instead of 1z) 30/10=3
So your solution should come to: z=3
What is the measure of RST?
Answer:
∠TSR = 93°
Step-by-step explanation:
In the figure attached as we know ∠S = [tex]\frac{mQR+mPT}{2}[/tex] [ By the theorem of angles of the intersecting secants in a circle]
∠S = [tex]\frac{131+43}{2}[/tex]
= [tex]\frac{174}{2}[/tex]
= 87°
Now we have to find the measure of ∠RST
Since ∠QSR + ∠TSR = 180° [ supplementary angles]
87° + ∠TSR = 180°
∠TSR = 180 - 87 = 93°
Therefore, m∠TSR = 93° is the answer.
the questionnnnnnnn issssssssss
Your job pays $8 per hour. (a) Write an algebraic expression for your pay in dollars for working h hours. (b) What is your pay if you work 36 hours?
The following is an incomplete paragraph proving that ∠WRS ≅ ∠VQT, given the information in the figure where segment UV is parallel to segment WZ.:
Segments UV and WZ are parallel with line ST intersecting both at points Q and R respectively
According to the given information, segment UV is parallel to segment WZ while angles SQU and VQT are vertical angles. Angle VQT is congruent to angle SQU by the Vertical Angles Theorem. Because angles SQU and WRS are corresponding angles, they are congruent according to the Corresponding Angles Postulate. Finally, angle VQT is congruent to angle WRS by the _____________________.
Which Property of Equality accurately completes the proof?
Reflexive
Substitution
Subtraction
Transitive
Answer:
Transitive
Step-by-step explanation:
Just took the test
Hope it helps :)
What is the initial value of the function represented by this graph?
A coordinate grid is shown with x and y axes labeled from 0 to 7 at increments of 1. A straight line joins the ordered pair 0, 2 with the ordered pair 7, 5.
0
1
2
5
The initial value of a function is the value of the function when x = 0
o when x = 0, y = 2 so the initial value is 2
Answer:
2
Step-by-step explanation:
The initial value is what you start off with, so it is 2! :)
Find x 58 degrees and adjacent 4.0
Which of the following shows 2 + (x + 3y) rewritten using the Associative Property of Addition
Answer:
[tex](2+x)+3y[/tex]
Step-by-step explanation:
In associative property , when we add the numbers we can group the numbers in any combination.
for example : [tex]a+(b+c)= (a+b)+c[/tex]
[tex]2 + (x + 3y)[/tex] can be written as [tex](2+x)+3y[/tex] using associative property.
The terms can be grouped in any combination
[tex](2+x)+3y[/tex]
What property is illustrated by the equation (8 + 2) + 7 = (2 + 8) + 7? A. Commutative property of addition B. Associative property of Addition C. Distributive property D. Identity Property of Addition
Sam picked a card from a standard deck. What is the probability that Sam picked a heart or a king?
A. 1/13
B. 16/52
C. 17/52
D. 16/53
Answer: Option 'B' is correct.
Step-by-step explanation:
Since we have given that
Number of cards in a deck = 52
Number of heart = 13
Number of king = 4
But we know that heart contains one king too.
So, to avoid double counting we have to subtract 1 from it.
so, Number of king = 3
So, Probability that Sam picked a heart or a king is given by
[tex]\frac{13}{52}+\frac{3}{52}\\\\=\frac{16}{52}\\\\[/tex]
Hence, Option 'B' is correct.
What is the range of this set of heights in centimeters?
{140, 166, 132, 165, 152, 168, 181, 158, 173, 171, 180, 182, 163, 177, 180, 142, 147, 149, 178}
38
41
46
50
(If you can help me with this maybe you can help me with my last posted question? It hasn't been answered and I need help!)
Final answer:
The range of the given set of heights is 50 cm, which is determined by subtracting the smallest height (132 cm) from the largest height (182 cm) in the set.
Explanation:
The range of a set of numbers is the difference between the largest and the smallest numbers in the set. To find the range of the given heights in centimeters, you first identify the largest and smallest numbers in the set {140, 166, 132, 165, 152, 168, 181, 158, 173, 171, 180, 182, 163, 177, 180, 142, 147, 149, 178}. The smallest height is 132 cm, and the largest is 182 cm.
Now, subtract the smallest value from the largest value to determine the range:
Range = Largest value – Smallest value
Range = 182 cm – 132 cm
Range = 50 cm
Therefore, the range of the given set of heights is 50 cm.
How do I solve this? (Geometry)
7x4 = 28
5 x z = 28
z = 28/5 = 5.6
Write | √3 - 2i | in a + bi form.
Evaluate the following expression using the values given:
Find 3x2 − y3 − y3 − z if x = 3, y = −2, and z = −5.
When $n$ is divided by 10, the remainder is $a$. when $n$ is divided by 13, the remainder is $b$. what is $n$ modulo 130, in terms of $a$ and $b$?
If
N = a (mod 10)
N = b (mod 13)
gcd(10,13) = 1
then
N = 10 bx + 13 ay (mod 130)
Where
10x + 13y = 1
-> (10x + 13) (mod 2) = 1 (mod 2)
-> y (mod 2) = 1
y = -3, x = 4
-> N = 40b – 39a (mod 130)
It is given that ra + sb should be non-negative:
N = 40b – 39a (mod 130)
N = 40b + (130 – 39)a (mod 130)
N = 40b + 91a (mod 130)
Therefore, N modulo 130, in terms of a and b is: N = 40b + 91a (mod 130).
Final answer:
To find the value of n modulo 130 in terms of a and b, one must solve two congruences using the Chinese Remainder Theorem. The solution would require computations beyond the scope of this response and would result in n expressed as a linear combination of a and b modulo 130.
Explanation:
To solve for the values of n modulo 130, given that when n is divided by 10, the remainder is a, and when n is divided by 13, the remainder is b, we can express n in the following forms:
n = 10k + a, where k is some integer
n = 13l + b, where l is some integer
Since 10 and 13 are coprime, Chinese Remainder Theorem tells us that there is a unique solution for n modulo 130 that satisfies both of these congruences. To find n in terms of a and b, we must find k and l such that these two equations give the same n for a particular value of n between 0 and 129 inclusive. This can be done through careful calculations or using a method designed for solving simultaneous congruences.
Once the suitable k and l values are found, the value of n modulo 130 can be stated. Since the exact solution requires more context or computational techniques, we can't provide the specific number in this case, but the final answer will be in the form: n ≡ (something involving a and b) (mod 130).
How many cookies will Tanya have if she bakes 6batches more than the maximum number of batches in the table
Answer:
325 cookies
Step-by-step explanation: I just took the test and got it right.