Answer:
Largest possible mural that can be painted on the wall is 24 feet wide and 13.5 feet high.
Step-by-step explanation:
Design of a mural is 16 in. wide and 9 in. high.
Dimensions of the wall are 24 ft by 14 ft.
If we enlarge the size of the design along the width the wall, scale factor to be used,
Scale factor = [tex]\frac{\text{Width of the wall}}{\text{Width of the design}}[/tex]
= [tex]\frac{24}{16}[/tex]
= [tex]\frac{3}{2}[/tex]
With the same scale factor, height of the design will be,
[tex]\frac{3}{2}=\frac{\text{Height of the wall used}}{\text{Height of the design}}[/tex]
[tex]\frac{3}{2}=\frac{\text{Height of the wall used}}{9}[/tex]
Width of the wall used = [tex]\frac{3\times 9}{2}[/tex]
= 13.5 ft
Therefore, largest possible mural that can be painted on the wall is 24 feet wide and 13.5 feet high.
WILL GIVE BRAINLIEST, PLEASE HELP! Given the foci and vertices of an ellipse, complete the following steps.
Answer:
a) The location of the center of the ellipse is [tex](4,-6)[/tex]. It is determine by knowing the location of foci and Midpoint formula.
b) The standard equation of the ellipse is [tex]\frac{(x-4)^{2}}{31}+\frac{(y+6)^{2}}{81} = 1[/tex].
c) Major semiaxis ([tex]a[/tex]): [tex]a = 9[/tex], Minor semiaxis ([tex]b[/tex]): [tex]b = \sqrt{31}[/tex]
Step-by-step explanation:
a) Foci are located in the major axis of the ellipse, given the locations of ends of the major axis and locations of the foci. We can determine the location of the center of the ellipse by Midpoint formula:
[tex](h,k) = \frac{1}{2}\cdot F_{1}(x,y) + \frac{1}{2}\cdot F_{2} (x,y)[/tex] (1)
Where [tex]F_{1} (x,y)[/tex] and [tex]F_{2} (x,y)[/tex] are the locations of the foci.
If we know that [tex]F_{1}(x,y) = (4, -6-5\sqrt{2})[/tex] and [tex]F_{2} (x,y) = (4,-6+5\sqrt{2})[/tex], then the location of the center of the ellipse is:
[tex](h,k) = (4, -6)[/tex]
The location of the center of the ellipse is [tex](4,-6)[/tex]. It is determine by knowing the location of foci and Midpoint formula.
b) Now we need to determine the length of each semiaxis:
Major semiaxis ([tex]a[/tex])
[tex]a = \sqrt{[V_{2}(x,y)-(h,k)]\,\bullet\,[V_{2}(x,y)-(h,k)]}[/tex] (2)
[tex]V_{2}(x,y)-(h,k) = (4,3)-(4,-6)[/tex]
[tex]V_{2}(x,y) - (h,k) = (0, 9)[/tex]
[tex]a = 9[/tex]
Please notice that [tex]V_{2}(x,y)[/tex] is one of the vertices of the ellipse in the major axis.
Distance between focus and center ([tex]c[/tex])
[tex]c = \sqrt{[F_{2}(x,y)-(h,k)]\,\bullet\,[F_{2}(x,y)-(h,k)]}[/tex]
[tex]F_{2}(x,y) -(h,k) = (4-4,-6+5\sqrt{2}+6)[/tex]
[tex]F_{2}(x,y) - (h,k) = (0, 5\sqrt{2})[/tex]
[tex]c = 5\sqrt{2}[/tex]
Minor semiaxis ([tex]b[/tex])
[tex]c^{2} = a^{2}-b^{2}[/tex] (3)
[tex]b = \sqrt{a^{2}-c^{2}}[/tex]
If we know that [tex]a = 9[/tex] and [tex]c = 5\sqrt{2}[/tex], then the length of the minor semiaxis is:
[tex]b = \sqrt{31}[/tex]
In this case, the standard equation of the ellipse is defined by this formula:
[tex]\frac{(x-h)^{2}}{b^{2}}+\frac{(y-k)^{2}}{a^{2}} = 1[/tex]
If we know that [tex]a = 9[/tex], [tex]b = \sqrt{31}[/tex] and [tex](h,k) = (4, -6)[/tex], then the standard equation of the ellipse is:
[tex]\frac{(x-4)^{2}}{31}+\frac{(y+6)^{2}}{81} = 1[/tex]
The standard equation of the ellipse is [tex]\frac{(x-4)^{2}}{31}+\frac{(y+6)^{2}}{81} = 1[/tex].
c) The lengths of the axes are, respectively:
Major semiaxis ([tex]a[/tex]): [tex]a = 9[/tex]
Minor semiaxis ([tex]b[/tex]): [tex]b = \sqrt{31}[/tex]
Answer:
a) The location of the center of the ellipse is . It is determine by knowing the location of foci and Midpoint formula.
b) The standard equation of the ellipse is .
c) Major semiaxis (): , Minor semiaxis ():
Step-by-step explanation:
7 ( 2x - 3 ) = 7
Show work and you will get Brainliest
Answer:
x=2
Step-by-step explanation:
Distribute the 7 across the 2x and 3:
[tex](7)(2x)-3(7)=7[/tex]
[tex]14x-21=7[/tex]
Isolate the x term by adding 21 on both sides:
[tex]14x=28[/tex]
Isolate x by dividing by 14 on both sides:
[tex]\frac{14x}{14}=\frac{28}{14}[/tex]
[tex]x=2[/tex]
If this helped, brainliest answer would be greatly appreciated!
Simplify (-2/3 square root 6)(9 square root 3)
Answer:
Exact Form:
-18√2
Decimal Form:
-25.45584412
3 tons 400 ounces=ounces
Answer:1 ton is 32,000 ounces so 3 tons is 96000 ounces + 400 = 96,400 ounces total
Hope this helps :)
first to answer correct will be the baranist .the ratio of students who wear spectacles is 2:5.
1.what is the ratio of students who wear speactacles and those who dont.
2.if there are 15 students who dont wear speactacles ,how many students wear speactacles in the class.
3.how many students are there in class
Answer:
1) Who wear: 2:5
Whi don't wear: 3:5
2) 10 don't wear spectacles
3) 25
Hope it helps!!!
Someone please help me
Answer:
Step-by-step explanation:
cone: attached picture below
composite shape: To calculate the area of a composite shape you must divide the shape into rectangles, triangles or other shapes you can find the area of and then add the areas back together. You may have to calculate missing lengths before finding the area of some of the shapes.
ratio: not sure about that question sorry
last question: i have no idea what it is about because my device won't open the picture sorry
though i have answered 2 question of yours
have a great evening
Answer:
ConeSurface area:
A = πr(r + l) r = √(10² - 8²) = √36 = 6A = 3.14(6)(6 + 10) = 301.44#1A = 25π, C = ?A = πr² ⇒ 25π = πr² ⇒ r² = 25 ⇒ r = 5C = 2πr = 2*3.14*5 = 31.4#2A = 5*7 + (5 - 2)*4 + 1/2*4*(6 - (5 - 2)) = 35 + 12 + 6 = 53#10Scale factor
k = 3/4Area is a function of two dimensions, each has k applied
The ratio of areas is the k² = (3/4)² = 9/16Option C
#6Volume of prism:
V = Bh = 1/2(8*5)*6 = 120Volume of pyramid:
V = 1/3Bh = 1/3(8*5)*9 = 120Option A, same volume
#7Ratio of areas:
20/45 = 4/9Scale factor is:
k² = 4/9k = √4/9k = 2/3Make r the subject - picture underneath
Answer:
The answer is r = 6a / (5m² - 1).
Step-by-step explanation:
The steps are :
[tex]m = \sqrt{ \frac{6a + r}{5r} } [/tex]
[tex] {m}^{2} = \frac{6a + r}{5r} [/tex]
[tex]5r {m}^{2} = 6a + r[/tex]
[tex]5r {m}^{2} - r = 6a[/tex]
[tex]r(5 {m}^{2} - 1) = 6a[/tex]
[tex]r = \frac{6a}{5 {m}^{2} - 1 } [/tex]
Answer:
r = [tex]\frac{6a}{5m^2-1}[/tex]
Step-by-step explanation:
Given
m = [tex]\sqrt{\frac{6a+r}{5r} }[/tex] ( square both sides )
m² = [tex]\frac{6a+r}{5r}[/tex] ( multiply both sides by 5r )
5rm² = 6a + r ( subtract r from both sides )
5rm² - r = 6a ← factor out r from each term on the left side
r(5m² - 1) = 6a ← divide both sides by (5m² - 1)
r = [tex]\frac{6a}{5m^2-1}[/tex]
Omar is painting a 24-square-foot wall. The wall is divided into squares that each measure 14 square foot. How many squares is the wall divided into? Enter your answer in the box.
Complete question :
Omar is painting a 24-square-foot wall. The wall is divided into squares that each measure 1/4 square foot. How many squares is the wall divided into?
Answer:
96
Step-by-step explanation:
Given that:
Total area of wall = 24 ft²
Area of each division =. 1/4 ft²
Number of division = x
The number of divisions * area of each division = total area of wall
x * 1/4ft² = 24ft²
Divide both sides by 1/4 ft²
x = 24ft² ÷ 1/4 ft²
x = 24 * 4 /1
x = 96
Hence, wall is divided into 96 squares
45 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!! If △EFG (purple triangle) is the image of △ABC (blue triangle), how could △EFG have been created? Graph A. △ABC was reflected over the x-axis to create △EFG. B. △ABC was reflected over the y-axis to create △EFG. C. △ABC was rotated 360∘ about the origin to create △EFG. D. △ABC was rotated 180∘ about the origin to create △EFG.
can i get some help pls i don't know how to write this equation
Answer: x = (log(y) /(400 log1.0065) or x = log(initial cost)/1.126
Step-by-step explanation: Take the log of both sides of your equation:
log(y) = log(400)(1.0065)^x
log (y) = log 400 + log(1.0065)^x
Subtract log(400) from both sides:
log(y) - log 400 = xlog(1.0065)
Divide both sides by log(1.0065)
[log(y) - log(400)]/log(1.0065) = x
Now, if you want to know how many years it will take for the guitar to be worth $200, replace y with 200 and solve.
A mechanical device makes a clicking sound every 3 seconds. If the device was plugged on for 15 hours, calculate the number of times the device made the clicking sound.
4
The formula for the volume of a sphere is
V= 3 #rº. What is the formula solved for r?
Answer:
B. r = 3√(3V - 4π)
Step-by-step explanation:
volume of a sphere,V = 4/3πr³
Solve for r
V = 4/3πr³
V - 4/3π = r³
r³ = V - 4π/3
Cross product
r³ = V*3 - 4π
r³ = 3V - 4π
Find the cube root of both sides
3√r³ = 3√(3V - 4π)
r = 3√(3V - 4π)
after spending 2/5 of her pocket money,Joyce realised she has spent $18.00. find her pocket money.
Answer:
1235674895
Step-by-step explanation8
how do I solve use elimination
x+3y=13
5x+6y=38
Answer:
(4, 3 )
Step-by-step explanation:
Given the 2 equations
x + 3y = 13 → (1)
5x + 6y = 38 → (2)
Multiplying (1) by - 2 and adding to (2) will eliminate the y- term
- 2x - 6y = - 26 → (3)
Add (2) and (3) term by term to eliminate y
3x + 0 = 12
3x = 12 ( divide both sides by 3 )
x = 4
Substitute x = 4 into either of the 2 equations and solve for y
Substituting into (1)
4 + 3y = 13 ( subtract 4 from both sides )
3y = 9 ( divide both sides by 3 )
y = 3
solution is (4, 3 )
Factorise by grouping: x² - 5x + 2x - 10
Answer:
[tex]\boxed {\boxed {\sf (x+2)(x-5)}}[/tex]
Step-by-step explanation:
To factor by grouping, first divide the polynomial into 2 groups with parentheses.
[tex]x^2-5x+2x-10[/tex]
[tex](x^2-5x)+ (2x-10)[/tex]
Factor the greatest common factor (GCF) out of both binomials.
For the first binomial, the GCF is x.
[tex]x(x-5) +(2x-10)[/tex]
For the second binomial, the GCF is 2.
[tex]x(x-5)+2(x-5)[/tex]
Factor out the common binomial which is (x-5).
[tex](x+2)(x-5)[/tex]
The factorized form of x²-5x+2x-10 is (x+2)(x-5)
what is the H.C.F of 48,30 and 18?
Answer:
G.C.F is 6
Step-by-step explanation:
Hope this helps.
Answer:
6
Step-by-step explanation:
Pls help me
Determine X
Answer:
x=8
Step-by-step explanation:
180-148=32
12=32-x/2
32-x=24
x=8
Mr. and Mrs. Doran have a genetic history such that the probability that a child being born to them with a certain trait is 37%. If they have six children, what is the probability that at most one of their six children will have that trait? Round your answer to the nearest thousandth.
Answer:
Yes
Step-by-step explanation:
Answer:
Sum: 0.78619≈0.786
Step-by-step explanation:
n=4
r=1, 2, 3, 4
r=1,2,3,4
"At least" counts up.
p=32\%=0.32
p=32%=0.32
q=1-0.32=0.68
q=1−0.32=0.68
The chance a success does NOT occur.
_{n}C_{r}p^rq^{n-r}
The probability that at most one of their six children will have that trait is 0.68
How to determine the probability?From the question, the given parameters are
Number of children, n = 6
Probability of a child with the trait, p = 37%
The required probability that at most one will have that trait is represented as P(x ≤ 1)
This probability is calculated ;
P(x ≤ 1) = P(0) + P(1)
Where
P(x) = ⁿCₓ * pˣ (1 - p)ⁿ⁻ˣ
So, we have
P(x ≤ 1) = ⁷C₀ (37%)⁰ (1 - 37%)⁷⁻⁰ + ⁷C₁ (37%)¹ (1 - 37%)⁷⁻¹
Evaluate;
P(x ≤ 1) = ⁷C₀ * 1 * (63%)⁷ + ⁷C₁ * (37%) * (63%)⁶
So, we have;
P(x ≤ 1) = 1-0.32= 0.68
Hence, the probability is 0.68
Read more about probability at
brainly.com/question/251701
#SPJ2
solve for x
(11x + 5)°
9x - 7i < 3 (3x - 7u)
Answer:
Step-by-step explanation:
9x - 7i < 3(3x - 7i)
9x - 7i < 9x - 21i
-7i < -21i
14i < 0i < 0
I need quick help pls!!!!!!
Answer: i don,t know sorry but i wish you the best of luck
Step-by-step explanation:
Answer:
do the math
Step-by-step explanation:
please help me,
11x13 = _ x 13+5 x 13
what is the number that goes in the blank
Answer:
14508 if I'm wrong I'm sorry
OMG HELP MEEEEEEEE PLZZZZZZZZZZZZZZ ALL BELOW
Answer:
-2w-1 ???
Step-by-step explanation:
i dont fully understand whats happening here hope this can help
Answer:
1) -2w - 1
2) 8(4k+3)
Step-by-step explanation:
attached below!!
I hope im right!!
Melody spent 16 days traveling in South America. How many weeks and days did Melody travel in South America?
Answer: 2 week and 2 days
Step-by-step explanation:
Given
Melody spent 16 days in South America
A week consists of 7 days
In 2 weeks it is, 14 days
So, 16 days is equivalent to 2 weeks and 2 days
Melody spent 2 weeks and 2 days in South America
Please help me,
11x13 = _ x 13+5 x 13
what is the number that goes in the blank
Answer:
6
Step-by-step explanation:
11x13=143
5x13 = 65
143 - 65 = 78
78/13= 6
Carter has 37 coins, all nickels and dimes in his piggy bank. The value of the coins is $3.10. How
many dimes does Carter have?
What is the area of a rectangle with vertices (2, 3), (9, 3), (9, Negative 2), and (2, Negative 2)?
---square units
Answer:
35 units
Step-by-step explanation:
edg
Rationalise the denominator.
Simplify your answer fully.
1/r6+r5
Please answer ASAP no links please and thanks u
Step-by-step explanation:
the answer is b
Answer:
C. 120 ft^2
Step-by-step explanation:
The area of the triangles= (1/2*3*4)2=12
The area of the larger parallelogram=5*9=45
The area of the bottom rectangle=4*9=36
The area of the vertical rectangle=3*9=27
Totale Surface Area=12+45+36+27=120
If I have 20 shares of a stock worth a total value of 440.80 what is the price per share of the stock?
If my total value dcreases by 6% what is it now?
Answer:
The price per share of the stock is 22.04. If the total value decreases by 6% the price becomes 20.71.
Step-by-step explanation:
440.80/20= 22.04
100-6= 94%
0.94 x 440.80= 414.35
414.35/20= 20.71
