21. You place a mat around a 25 in by 21 inch painting as shown. The mat
is twice as wide at the left and right of the painting as it is at the top an
bottom of the painting. The area of the mat is 714 square iinches (note:
the area of the border). How wide is the mat at the left and right of the
painting? At the top and bottom of the painting? (P.264 #66)
Answers
Using a quadratic equation according to the area of the rectangular mat, it is found that:
At the top and bottom of the painting, the width is 0.654 inches.At the left and right of the painting, the width is of 1.308 inches.The area of a rectangle of length l and width w is given by:
[tex]A = lw[/tex]
In this problem:
The length of the figure is of [tex]l = 25 + 4x[/tex].The width of the figure is of [tex]w = 21 + 2x[/tex].Area of 714 square inches, thus:[tex]lw = 714[/tex]
[tex](25 + 4x)(21 + 2x) = 714[/tex]
[tex]8x^2 + 134x + 525 = 714[/tex]
[tex]8x^2 + 134x - 189 = 0[/tex]
Which is a quadratic equation with [tex]a = 8, b = 134, c = -189[/tex].
The, to find the widths of the mat, we have to first find the value of x, solving the quadratic equation.
[tex]\Delta = 134^2 - 4(8)(-189) = 24004 [/tex]
[tex]x_{1} = \frac{-134 + \sqrt{24004}}{2(8)} = 0.654[/tex]
[tex]x_{2} = \frac{-134 - \sqrt{24004}}{2(8)} = -9.03[/tex]
We are interest in the positive value of x, so x = 0.654.
At the top and bottom of the painting, the width is of 0.654 inches.[tex]2(0.654) = 1.308[/tex]
At the left and right of the painting, the width is of 1.308 inches.A similar problem is given at https://brainly.com/question/14099239
Related Questions
toni had 5 1/2 kilograms of sugar.how many cakes can he bake if he ise 1/4 hilogram of sugar per cake?
pls i need the answer
Answers
Answer:
22 cakes
Step-by-step explanation:
5 1/2kg = 11/2 = 22/4
22/4 is what you have in sugar while you only need 1/4 per cake, so you can make 22 cakes
Answer:
He can makec 22 cakes
Step-by-step explanation:
He use,
[tex] \frac{1}{4} kg = 1 \: \: cake \\ [/tex]
Let's find how many caked will he make from 5 1/2kg
Let the unknown number of cakes be x
[tex] \frac{1}{4} = 1 \\ 5 \frac{1}{2} = x[/tex]
[tex] \frac{1x}{4} = 5 \frac{1}{2} \\ \frac{1}{4} x = \frac{11}{2} [/tex]
Use cross multiplication
[tex]2 \times 1x = 11 \times 4 \\ 2 x= 44 \\ \frac{2x}{2} = \frac{44}{2} \\ x = 22[/tex]
Hope this helps you
Let me know if you have any other questions :-):-)
Formule una propiedad algebraica basica del sistema de numeros reales para justificar cada uno de los siguientes enunciados, donde Y y Z representan numeros reales. a) (y + 2)z+3=(yz+2z)+3 b) (4+7)y=y(4+7) C) (1+4)+3=4+(1+3)
Answers
Answer:
Nose :>
Step-by-step explanation:
.
The algebraic properties that can be applied in this case are: distributive property, commutative property, associative property.
What properties can we apply in this situation?a) Distributive Property: (y + 2)z + 3 = yz + 2z + 3. The distributive property establishes that multiplication is distributed over addition or subtraction, allowing us to simplify the original expression by adding the product of y and z to 2z and then adding 3.b) Commutative property: 4y + 7y = y(4 + 7). The Commutative Property of Multiplication states that the order of the factors does not affect the result. Here, 4y and 7y can be rearranged as y(4) and y(7) respectively, keeping the same result.c) Associative Property: (1 + 4) + 3 = 4 + (1 + 3). The Associative Property of Addition states that numbers can be grouped in different ways without changing the sum total. Both sides of the equation group the numbers the same way.Note: The question is in Spanish. Here is the question in English:
Formulate a basic algebraic property of the real number system to justify each of the following statements, where Y and Z represent real numbers. a) (y + 2)z + 3 = (yz + 2z) + 3
b) (4 + 7)y = y (4 + 7)
c) (1 + 4) + 3 = 4 + (1 + 3)
Learn more about algebraic properties in: https://brainly.com/question/30237937
#SPJ3
Question is in picture. Please help
Answers
Answer:
Step-by-step explanation:
441 km in 45s does
215 km in 25s doesnt
649 km in 110s doesnt
0.04 kL to g
What is the answer to this
Answers
Answer:
40g
Step-by-step explanation:
The answer is 40 gallons
Convert 34.6 centimeters to inches. Use 1 in=2.54 cm.
Answers
Estimate 25.65 + 13.23 + 6.35 by rounding each number to the nearest tenth.
a. 26 + 13 + 6 = 45
b. 25.7 + 13.2 + 6.4 = 45.3
c. 25.6 + 13.2 + 6.3 = 45.1
d. 25.7 + 13.3 + 6.4 = 45.4
Answers
Answer:
b. 25.7 + 13.2 + 6.4 = 45.3Step-by-step explanation:
25.65 ≈ 25.7, 13.23 ≈ 13.2, 6.35 ≈ 6.4
25.65 + 13.23 + 6.35 =25.7 + 13.2 + 6.4 = 45.3Correct choice is b.
Find the Measure of The missing angles
Answers
Answer:
∆K = 98°
∆M = 82°
∆G = 118°
∆H = 62°
Step-by-step explanation:
∆K & ∆G is by corresponding angle
and
∆M & ∆H is by linear pairs
plz help me I'm about to cry
Answers
Answer:
yyy i will help....... dont cry
First correct answer gets Brainliest
Answers
Answer:
37.6
Step-by-step explanation:
......... . .. .................
A dolphin swims 15 feet below sea level, and then jumps 4 feet above sea level. How far did the dolphin rise?
Answers
Answer:
19 feet
Step-by-step explanation:
The dolphin goes from 15 feet below then he goes above the ocean by 4. So add 15 + 4 to get 19 feet.
Examine the following sequence 1, 4, 9, 16, 25.... Why is 36 the next number in the sequence? Because the pattern
is:
a. Add the next even number
Cube the number of the term, n
b. Square the number of the term, n
d. Add 2 + the number of the term, n
C.
Please select the best answer from the choices provided
А
B
ОООО
Save and Exit
Next
Submit
Mark this and return
Answers
Answer:
b
Step-by-step explanation:
1,4,9,16,25,36,...
we see every number is square of numbers .
every number can be represented by n²
1²=1
2²=4
3²=9
4²=16
5²=25
6²=36
A furniture store purchased a dining room table and marked it up 150% from the original cost
of $456. A week later, the store placed the dining room table on sale for 30% off. What was
the discount price?
Answers
Answer:
Step-by-step explanation:
Identify what you are asked to find. What is the sales tax?
Choose a variable to represent it. Let t = sales tax.
Write a sentence that gives the information to find it. The sales tax is 6.5% of the purchase price.
Translate into an equation. (Remember to change the percent to a decimal).
Simplify. t = 25.48
Check: Is this answer reasonable? Yes, because the sales tax amount is less than 10% of the purchase price.
Write a complete sentence that answers the question. The sales tax is $25.48.
(b)
Identify what you are asked to find. What is the total cost of the bicycle?
Choose a variable to represent it. Let c = total cost of bicycle.
Write a sentence that gives the information to find it. The total cost is the purchase price plus the sales tax.
Translate into an equation. (Remember to change the percent to a decimal).
Simplify. c = 417.48
Check: Is this answer reasonable? Yes, because the total cost is a little more than the purchase price.
Write a complete sentence that answers the question. The total cost of the bicycle is $417.48.
Exercise 6.3.1 :
Find (a) the sales tax and (b) the total cost: Alexandra bought a television set for $724 in Boston, where the sales tax rate was 6.25% of the purchase price.
Answer a
Answer b
Exercise 6.3.2 :
Find (a) the sales tax and (b) the total cost: Kim bought a winter coat for $250 in St. Louis, where the sales tax rate was 8.2% of the purchase price.
Answer a
Answer b
Example 6.3.2 :
Evelyn bought a new smartphone for $499 plus tax. She was surprised when she got the receipt and saw that the tax was $42.42. What was the sales tax rate for this purchase?
Solution
Identify what you are asked to find. What is the sales tax rate?
Choose a variable to represent it. Let r = sales tax.
Write a sentence that gives the information to find it. What percent of the price is the sales tax?
Translate into an equation.
Divide.
499r499=42.42499(6.3.1)
Simplify r = 0.085
Check. Is this answer reasonable? Yes, because 8.5% is close to 10%. 10% of $500 is $50, which is close to $42.42.
Write a complete sentence that answers the question. The sales tax rate is 8.5%.
Exercise 6.3.3 :
Diego bought a new car for $26,525. He was surprised that the dealer then added $2,387.25. What was the sales tax rate for this purchase?
Answer
Exercise 6.3.4 :
What is the sales tax rate if a $7,594 purchase will have $569.55 of sales tax added to it?
You can use the method of calculating the percentage of an amount to find out the discount amount.
The discount price for the given condition was $205.2
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is [tex]\dfrac{a}{100} \times b[/tex]
How to find the discount price?First we will find the marked price since the discount price was calculated on the marked price.
Since marked price was 150% of the cost price $456, thus,
[tex]\text{Marked price} = \dfrac{456}{100} \times 150 = \$684[/tex]
Thus, the marked price of the furniture was $684
Now, since the discount offered on the price was 30%, thus,
[tex]Discount = \dfrac{\text{Marked price}}{100} \times \text{Discount percent} =\dfrac{684}{100} \times 30\\\\Discount = \$205.2[/tex]
Thus,
The discount price for the given condition was $205.2
Learn more about percentage here:
https://brainly.com/question/11549320
Is (3,-10) a solution to the function y = - 4x + 2? Answer "yes" or "no". Then explain why it is or
is not a solution
Need ASAP
Answers
Answer:
Yes
Step-by-step explanation:
( x, y ) = ( 3, - 10 )
Here,
x = 3
y = - 10
y = - 4x + 2
- 10 = - 4 ( 3 ) + 2
- 10 = - 12 + 2
- 10 = - 10
LHS = RHS
Therefore,
( 3, - 10 ) a solution to the function y = - 4x + 2.
standard form of 1.23 * 10 to the 11th power
Answers
1. Convert to decimal notation
The exponent is 11, making it 10 to the power of 11. As the exponent is positive, the solution is a number greater than the origin or base number. To find our answer, we move the decimal to the right 11 time(s):
[tex]1.23 -> 123000000000[/tex]An item is priced at $14.84 if the sales tax is 8% what dose the item cost including sales tax
Answers
Answer:
16.03
Step-by-step explanation:
8% = 0.08
Multiply the price with the percent
0.08 x 14.84 = 1.1872
Add 1.1872 to 14.84
1.1872 + 14.84 = 16.0272
Round to the nearest cent since it's money
help me please!! 50 points
Answers
Answer:
pls mark as brainliest and follow
2.5% of 2 2/5
is what number?
Answers
Answer:
The number is 0.06, or 6 hundredths.
Step-by-step explanation:
If we convert 2 2/5 to a decimal, we get 2.4
Then, we can convert our percentage to a decimal by moving our digits two units down, giving us .025.
Now, we can multiply 2.4 and .025, which gives us 0.06
Please answer as soon as possible HURRY! Please I need help
2. Write a Linear equation for the function represented by the table
Answers
Step-by-step explanation:
I will help you if you follow me please if you really want to get answer please follow me
Simplify the expression shown using Order of Operations. You must show your work to earn full credit. Perform on
operation per line in your response.
30 - [10 + (32 . 4))
Answers
Answer:
30-[10+( 128)]=
30-[138]=
-108
Step-by-step explanation:
Answer:
30-[10+( 128)]=
30-[138]=
-108
Step-by-step explanation:
-11/16*(-4/33) van you please help me answer this question?
Answers
Answer:
1/12
Step-by-step explanation:
[tex] - \frac{11}{16} \times - \frac{4}{33} [/tex]
if you know how to cancel, you can cancel the 4 and 16. The 4 becomes a 1 and 16 becomes a 4. Next cancel the 11 and 33. the 11 becomes a 1 and the 33 becomes a 3.
[tex] - \frac{1}{4} \times - \frac{1}{3} [/tex]
multiply, two negatives make a positive
[tex] \frac{1}{12} [/tex]
One gallon of water weighs approximately 8 1/3lbs. How much does 25 3/4 gallons of water weigh?
Answers
Hope it help
I NEED HELP VERY BADLY
Tracy has a savings account which earns interest at a rate of 8% each year. Let t
represent the amount of interest Tracy earns.
George earns the same amount of interest as Tracy. Let g represent the amount of interest George earns.
Peter does not earn the amount of interest as Tracy. Let p represent the amount of interest Peter earns.
Which statement is true?
A.
g ≠ p
B.
t ≠ g
C.
t = g
D.
p = t
Answers
This is because
A states that George’s interest doesn’t equal peters which is false because if peters isn’t the same as Terry’s it can’t equal georges either
B states that Terry’s interest doesn’t equal georges which we know isn’t true because it says they both have an 8% interest
C state that Terry’s equals George’s which it does because it tells us they have the same interest rate
D state that peters equals Terry’s which it states is false
Answer:
A
Step-by-step explanation:
Someone help its multiple choice im so confused
Answers
B, he was shot in the back
E, the arrow went under his left armpit
This all is correct considering the paragraph i just read!
I wish you luck on the rest of your assessment!
mark this as brainliest if i helped at all!! :)
What is the value of this expression when a = 7 and b = -4
Answers
Answer:
[tex] \longmapsto\frac{ |2a| - b }{3} \\ = \frac{ 2|a| - b }{3} \\ = \frac{2 |7| - ( - 4) }{3} \\ = \frac{2(7) + 4}{3} \\ = \frac{14 + 4}{3} \\ = \frac{18}{3} \\ = \boxed6[/tex]
D. 6 is the right answer.Anya drove 2 hours to get to the train
station. Then she rode the train for 14
hours. She drove about 55 miles per
hour. The train traveled at about 80
miles per hour. How many miles did
Anya travel altogether?
Answers
How many tenths are there in ⅘
Answers
Answer:
8
Step-by-step explanation:
4/5 = ?/10
4/5 * (2/2) = ?/10
8/10 = ?/10
Answer:
8
Step-by-step explanation:
multiply the denominator and numerator, you get 8/10
what is 5+6? Show your work
Answers
Answer:
11
Step-by-step explanation:
2+2+1(5)+3+3(6) =11
Definition of Linear relationship
Answers
Answer:
Résultat de recherche d'images pour "Definition of Linear relationship"
A linear relationship (or linear association) is a statistical term used to describe a straight-line relationship between two variables. Linear relationships can be expressed either in a graphical format or as a mathematical equation of the form y = mx + b
Step-by-step explanation:
HELP !! Look at the photo please
Answers
What is the solution to the system -3×+4y+2z=-3 2×-4y-z=0 y=3x-13
Answers
Answer:
x=5, y=2, z=2
Step-by-step explanation:
y=3x-13
-3x+4y+2z = -3x + 4(3x-13) + 2z = 9x+2z-52 = -3
9x + 2z = 49 ... (1)
2x-4y-z = 2x-4(3x-13)-z = -10x-z+52 = 0
10x + z = 52 ... (2)
(2)*2-(1): 11x = 55 x = 5
y = 3x-13 = 15-13 = 2 y=2
z = (49-9x) / 2 = 2 z = 2