If the frame has a 400 square inch surface area, its breadth is 5 inches.
Let's call the width of the frame w.
The total width of the painting and the frame is 24 inches + 2w inches since there is a frame of width w on both sides of the painting.
Similarly, the total height of the painting and the frame is 18 inches + 2w inches, since there is a frame of width w on both the top and bottom of the painting.
The area of the frame is the difference between the area of the rectangular frame and the area of the painting. The area of the rectangular frame is (24 inches + 2w inches) * (18 inches + 2w inches) = 432 inches + 72w inches + 36w inches + 4w^2 inches. The area of the painting is 24 inches * 18 inches = 432 inches.
Therefore, the area of the frame is 432 inches + 72w inches + 36w inches + 4w^2 inches - 432 inches
= 72w inches + 36w inches + [tex]4w^2[/tex] inches = 400 inches.
Combining like terms, we get [tex]4w^2[/tex] inches + 108w inches = 400 inches.
Dividing both sides by 4, we get [tex]4w^2[/tex] inches + 27w inches = 100 inches.
We can use the quadratic formula to solve this equation in the quadratic form:
w = [tex]\frac{(-b +/- sqrt(b^2 - 4ac))}{2a}[/tex]
= [tex]\frac{(-27 +/- sqrt(27^2 - 4 * 1 * 100))}{2*1} \\[/tex]
= [tex]\frac{(-27 +/- sqrt(729 - 400))}{2}[/tex]
= [tex]\frac{(-27 +/- sqrt(329)) }{2}[/tex]
= [tex]\frac{(-27 +/- sqrt(289))}{2}[/tex]
The solutions are w =[tex]\frac{ (-27 + 17)}{2}[/tex] = -5 inches and w = [tex]\frac{(-27 - 17)}{2}[/tex] = -22 inches.
Since the width of the frame must be positive, the correct solution is w = -5 inches. The frame is five inches wide.
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The number of songs Oliver has downloaded this year, divided by 12, is equal to 24. What is an equation that represents this situation, and how many songs has Oliver downloaded?
A. 12d = 12: d = 1 song downloaded
B. 12d = 24: d = 2 songs downloaded
C. d12 = 24: d = 288 songs downloaded
D. b12 = 12: d = 144 songs downloaded
Answer:
c
Step-by-step explanation:
24×12=288 songs downloaded
this is because you have to do opposite operations according to one of the operations of math
An equation that represents the given situation is d/12 =24, and the number of songs Oliver has downloaded is 288. So, option C is the correct answer.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, the number of songs Oliver has downloaded this year, divided by 12, is equal to 24.
Let the number of songs downloaded be d.
So, the equation is d/12 =24
d=288
The equation to represent the scenario is d/12 =24. Therefore, option C is the correct answer.
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Need help plz with this if nobody don’t mind
Answersheeeeeeeeeeeeeeeeeeeeeeeeeesssh
Step-by-step explanation:
Mrs. Thomas and Mrs. Maas were folding report cards to send home to parents. The ratio of the number of report cards Mrs. Thomas folded to the number of report cards Mrs. Maas folded is :. At the end of the day, Mrs. Maas folded a total of 273 report cards. How many did Mrs. Thomas fold?
Answer: 182 report cards
Step-by-step explanation:
The ratio of the number of report cards Mrs. Thomas folded to the number of report cards Mrs. Maas folded is 2:3.
Mrs. Maas folded 273 report cards so the number of report cards folded by Mrs. Johnson can be found using direct proportion. Assume Mrs. Johnson folded x report cards:
2 : 3
x : 273
Cross multiply to get:
3x = 546
x = 546 / 3
x = 182 report cards
Please help me with this homework
A line with a slope of 0 contains the point (3,4) . The point -2,? is also on the line. What is the missing y-coordinate?
The solution is ___________
please don't use files
HELPPPPPPPP!!!!!!!!!!!!
Answer:
A) True
Step-by-step explanation:
The x values, 1 2 3 can go to the y values B L A
However, if there were two lines at 2 1 2 3 going to any of the y values it would not be a function
Here is a picture explaining it.
Answer:
The answer is True or you could say jast A
i will mark branlyest
Jess dug a hole 7.3 inches deep on Tuesday. After he dug on Wednesday, the hole was 9.7 inches deep. What distance did Jess dig on Wednesday? A –17 inches B –2.4 inches C 2.4 inches D 17 inches
Answer:
Jess dug 2.4 inches deep on Wednesday.
Step-by-step explanation:
9.7-7.3=2.4 9 . 7
-
7 . 3
___
2 . 4
Answer:
2.4 inches
Step-by-step explanation:
i did the assignment :)
1. Write a similarity statement if the triangles are similar
2. If the traingles are similar, state the triangle similarity postulate (shortcut) you used to prove similarity.
U
36
73
30
15
D
E
Answer:
The triangles are not similar
Step-by-step explanation:
The sides are not proportional
36/73 does not equal to 15/30
Problem #2 - 8.2B
Which point on the number line best represents the location of 98 ?
F Point M
G Point N
H Point P
J Point O
PLEASE ANSWER WILL GIVE BRAINLIEST
I dont know which one?? please help...
Answer: the first one
Step-by-step explanation: it has nothing to do with the function
Find the area and thank
Answer:
add it
Step-by-step explanation:
Answer:
It’s 40
Step-by-step explanation:
-3/2+2 hi jjjjjjjjjjjjjjj
Answer:
1/2 is the answer
Step-by-step explanation:
1) Make the denominators the same.
[tex] - \frac{3}{2} + 2 \times \frac{2}{2} [/tex]
2) Simplify. Denominators are now the same.
[tex] - \frac{3}{2} + \frac{4}{2} [/tex]
3) Join the denominators.
[tex] \frac{ - 3 + 4}{2} [/tex]
4) Simplify.
[tex] \frac{1}{2} [/tex]
Therefor, the answer is 1/2 and in decimal form the answer will be 0.5.
Why is LMNO=PQRS?? Help
Answer:
They are equal because they’re the same shape with the same lengths, but one is rotated. This is an example of rotation.
Step-by-step explanation:
find the Surface Area of this shape
Answer:
V≈94423.71
Step-by-step explanation:
V=πr2h=π·342·26≈94423.7088
Use the distributive property to solve the equation -2(x+5) =4
Hailey is going to paint a wall in her bedroom. The bottom part of the wall is a rectangle (16ft. x 18ft.), and the top part is a triangle (8 ft. high x 18ft. long). What is the total area of the wall?
Answer:
Area of wall = 360 ft²
Step-by-step explanation:
Given:
One part of wall (Rectangle) = 16ft x 18ft
Another part of wall (Triangle) = 8ft x 18ft
Find:
Area of wall
Computation:
Area of wall = Area of rectangle + Area of triangle
Area of wall = (l x b) + (1/2)(b)(h)
Area of wall = (16 x 18) + (1/2)(8)(18)
Area of wall = 288 ft² + 72 ft²
Area of wall = 360 ft²
A cereal box is 8 1/2
inches long, 2 1/2
inches wide, and 12 inches high. What is the volume of the box?
The volume of the cereal box is blank cubic inches.
Answer:
V = 255
Step-by-step explanation:
Cereal box is a rectangular prism.
Rectangular Prism formula:
V = whl
Given:
w = 2.5
h = 12
l = 8.5
Work:
V = whl
V = (2.5)(12)(8.5)
V = 255
Answer: 1428
Step-by-step explanation: Length of the cereal box = 8 1/2 inches
= 17/2 inches
Width of the cereal box = 3 1/2 inches
= 7/2 inches
Height of the cereal box = 12 inches
Then
Volume of the cereal box = Length * Width * Height
= (17/2) * (7/2) * 12 cubic inches
= 17 * 7 * 12 cubic inches
= 1428 cubic inches
Please help! The question is:
In a marketing survey involving 1,000 randomly chosen people, it is found that 630 use brand P, 420 use brand Q, and 210 use both brands. How many people in the survey use brand P and not brand Q?
By Set theory, 420 many people in the survey use brand P and not brand Q.
What is Set theory?
The mathematical concept of sets, which are well-defined collections of things that are referred to as their members or elements, is known as set theory. As only sets are the subject of pure set theory, the only sets that are taken into account are those whose members are also sets.
The major reason why set theory is significant is because it offers the axioms upon which the rest of mathematics is constructed. We study sets and their characteristics in the area of mathematical logic known as set theory. A collection of items or a group of items is referred to as a set. These items are frequently referred to as elements or members of a set.
P use = 630 people
Q use = 420 people
both P&Q use ie P∩Q = 210 People
use brand P but not brand Q = P/ P∩Q
= 630 - 210
= 420
Learn more about Set theory
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please help im sorry that it's 4 problems
Answer:
the first 1 in standard form is [tex]y=-2x^{2} +8x-8[/tex]
12. [tex]y=2x^{2} +4x-16[/tex]
13. [tex]y=-3x^{2}+6x+9[/tex]
14.[tex]y=2x^{2} +2x-4[/tex]
Step-by-step explanation:
hope this helps have a good rest of your night/day :) ❤
can I get brainliest please I only have 4 plz
Solve the following quadratic equation for all values of xx in simplest form.(Solving Quadratics with Square Roots (Level 1)
(x+10)^2-8=8
Rectangle PQRS is rotated 90° counterclockwise about the origin.
Answer:
Can you please provide more information about the rectangle? Do you have a graph or some points?
Answer:c
Step-by-step explanation:
What is 2 x 3/4?
It must be !!
Answer:
1.5
Step-by-step explanation:
[tex]\frac{2x3}{4}= \frac{6}{4}[/tex]
[tex]\frac{6}{4}[/tex] ÷2=
[tex]\frac{3}{2}[/tex]
Hope this helps :)
Answer:
1 1/2 or 3/2
Step-by-step explanation:
2 x 3/4
6/4
3/2
1 1/2
Write the equation of the line that passes through (-4, 3) and is perpendicular to the line y = 7/5x-2/5
Answer:
y - 3 = (-5/7)(x + 4)
Step-by-step explanation:
The given line, y = 7/5x-2/5, has a slope of 7/5. Any line perpendicular to this one must have a slope tht is the negative reciprocal of 7/5, which is -5/7.
Use the point-slope formula to come up with an equation for this new line:
y - 3 = (-5/7)(x + 4)
What is the slope of the line below?
1. 1/4
2. −1/4
3. 2
4. −2
Answer:
2
Step-by-step explanation:
Answer:
It is number three{ 3) 2 }I hope that is useful for you :)
While drawing a triangle, Michael decided that he wanted to have the longest side to measure 32 cm. Which pair of side lengths could create the other two sides of his triangle? (7TH GRADE MATH)
Answer:
c
Step-by-step explanation:
Which of the following is true about the sequence graphed below?
Answer:
Step-by-step explanation:
The sequence is arithmetic because the terms have a common difference.
Hopes this helps:)
please help!! dont answer if you dont know
Answer:
6/7
Step-by-step explanation:
4/7×3/2=6/7. ( by doing reciprocal and cancelling four by two)
Answer:
[tex]\frac{6}{7}[/tex]
Step-by-step explanation:
[tex]\frac{4}{7}[/tex] ÷ [tex]\frac{2}{3}[/tex] = [tex]\frac{4}{7}[/tex] × [tex]\frac{3}{2}[/tex] = [tex]\frac{12}{14}[/tex] = [tex]\frac{6}{7}[/tex]
Mrs. Patterson but a set of building blocks for her son each cube shaped block measured 4 cm on one side what is the volume of six building blocks
Given:
The shape of all building blocks is a cube of side 4 cm.
To find:
The volume of six building blocks.
Solution:
Volume of a cube is:
[tex]V=a^3[/tex]
Where, a is the side length of the cube.
Putting [tex]a=4[/tex], we get
[tex]V=(4)^3[/tex]
[tex]V=64[/tex]
It means the volume of each building block is 64 cubic cm.
Now, the volume of six building blocks is
[tex]Volume=6\times V[/tex]
[tex]Volume=6\times 64[/tex]
[tex]Volume=384[/tex]
Therefore, the volume of six building blocks is 384 cubic cm.
PLEASE HELP I REALLY NEED IT
Answer:
The answer is 12 bags
Step-by-step explanation:
This is because the first big rectangle is 48 feet while the smaller one is 12 feet. By adding them together you get 60. 60 divided by 5 is 12 so its 12 bags.
Answer:
12 bags
Step-by-step explanation:
12 x 4 = 48
2 x 6 = 12
48 + 12 = 60
60ft² is the area of the garden.
60 ÷ 5 = 12
12 bags are needed
PLS HELP! DONT SKIP PLS.
Elena borrowed some money from her brother. She pays him back by giving him the same amount every week. The graph shows how much she owes after each week. 1. What is the slope of the line?
2. Is the slope positive or negative?
3. How much money did Elena borrow? (Hint: Vertical Intercept)
Answer:
1. -3
2. negative
3. $18
Step-by-step explanation:
1. slope is rise/run so...
-3/1=-3
2. because run was a change of 3 DOWN the y axis we and run is a change of 1 to the right on x axis we have a negative slope. -3
3. she borrowed $18. Vertical intercept means the point where our line crosses the vertical axis. (Vertical axis is Y axis.)