Answer:
B) 55 cm
Step-by-step explanation:
it’s correct from EDGE
Question
2. Determine
the
acute
angle
between the planes
x - 2y + 5z = 3
2x + y - 3z = 15.
Distance of a plane from the origin:
Answer:
Acute angle between the two planes: approximately [tex]43^\circ[/tex].
Step-by-step explanation:
Find the normal vector of each plane:
The normal vector of the plane [tex]x - 2\, y + 5\, z = 3[/tex] is [tex]\displaystyle \begin{bmatrix}1 \\ -2 \\ 5\end{bmatrix}[/tex].The normal vector of the plane [tex]2\, x + y - 3\, z = 15[/tex] is [tex]\displaystyle \begin{bmatrix}2 \\ 1\\ -3\end{bmatrix}[/tex].As the name suggests, there is a [tex]90^\circ[/tex] angle between a plane and its normal vector. The following four angles will correspond to the vertices of a quadrilateral:
The [tex]90^\circ[/tex] angle between the first plane and its normal vector.The angle between the normal vector of each plane.The [tex]90^\circ[/tex] angle between the second plane and its normal vector.The smallest angle between these two planes.The sum of these four angles should be [tex]360^\circ[/tex]. Two of these four angles were known to be [tex]90^\circ[/tex]. Once the third angle (the angle between the two normal vectors) is found, subtractions would give the measure of the other angle (the smallest angle between these two planes.)
Make use of the dot product to find the angle between these two normal vectors. Let [tex]\theta[/tex] denote the angle between these two vectors.
[tex]\displaystyle \cos \theta = \frac{\begin{bmatrix}1 \\ -2 \\ 5\end{bmatrix} \cdot \begin{bmatrix}2 \\ 1 \\ -3\end{bmatrix}}{\sqrt{1^2 + (-2)^2 + 5^2} \cdot \sqrt{2^2 + 1^2 + (-3)^2}} \approx -0.73193[/tex].
Before continuing, notice that the smallest angle between the two planes would be [tex]360^\circ - 90^\circ - 90^\circ - \theta = 180^\circ - \theta[/tex].
Consider the identity: [tex]\cos\left(180^\circ - \theta\right) = -\cos \theta[/tex].
In other words, [tex]\cos\left(180^\circ - \theta\right)[/tex], the cosine of the smallest angle between the two planes (which the question is asking for) will be the opposite of [tex]\cos \theta[/tex], the cosine of the angle between the two normal vectors.
Therefore, the cosine of the smallest angle between the two planes will be [tex]-(-0.73193) = 0.73193[/tex].
Apply the inverse cosine function to find the size of that angle:
[tex]\arccos(0.73193) \approx 43^\circ[/tex].
Simplify fully 56:16
Answer:
7/2
Step-by-step explanation:
help........plsplav j h
2r + 1+(4R)+7 as an equivalent expression
Answer
6r+8
Step-by-step explanation:
2r+1+r+r+r+r+7
= 6r+8
Lita's softball team wone 8 games last month and 10 this month. What was the percent change in games the team won?
A banana contains 105 calories. Last week, brendan and lea ate a total of 14 bananas. How many calories does this represent?
Answer:
1470
Step-by-step explanation:
Multiply
Will mark as brainliest if correct!
Answer:
14
Step-by-step explanation:
it's a simple matter of percentage on top of basic subtraction.
I will mark brainliest pls answer ASAP and pls don’t answer if your not sure
james is stocking shelves with notebooks. if he has 5 different notebooks, in how many ways can he arrange them on a shelf?
Answer: 120
Step-by-step explanation: I got it right, hope this helps ✨
Answer:
he has I20 different ways to put the books
Step-by-step explanation:
to solve this you would multiply 5x4x3x2 this is how many different combinations he can but the note book on the shelf. 5x4x3x2 is equal to 120
Help!!!!!!!!!!!!!!!!!!!!!!
Answer:
-1:-15
-7:-69
6:48
1:3
2:12
Step-by-step explanation:
On my Ti-84 calculator I went into y=. Next, in y1=, I would put in the function and the next step is to press 2nd and graph. Now there's a table with all the answers you're looking for.
if 1 yard of ribbon cost 83 cents how much does 1 foot cost
Answer:
27.7 cents or round to 28 cents
Step-by-step explanation:
3 feet in one yard. 83÷3=27.6666666
Helppppppppopp asappppppppp
Answer:
10 = 74°
7 is alternate to 12 so 12 is 74°
Given the binomials (x − 3), (x − 1), (x + 2), and (x + 3), which one is a factor of f(x) = 2x3 + 3x2 − 2x − 3?
Answer:
nswer:
(x-1) is factor of our function.
Step-by-step explanation:
We are given a function and we are asked to find the correct factor from the given options.
Let us factor out our polynomial.
Therefore, (x-1) is correct choice for factor of our polynomial.
Step-by-step explanation:
Answer: B. (x-1)
Step-by-step explanation: I just took the test and got it right <3
An investor invested a total of $2,100 in two mutual funds. One fund earned a 5% profit while the other earned a 3% profit. If the investor’s total profit was $83, how much was invested in each mutual fund?
The amount invested in the mutual fund that earned 5% was $___.
The amount invested in the mutual fund that earned 3% was $___.
Answer:
The amount invested in the mutual fund that earned 5% was $1000.
The amount invested in the mutual fund that earned 3% was $1100.
Step-by-step explanation:
Let the amount invested in the mutual fund that was earned 5% be x and the amount invested in the mutual fund that earned 3% be y.
Statement 1: [tex]\frac{5}{100}[/tex]X+[tex]\frac{3}{100}[/tex]y = 83
Statement 2: x+y = 2100
I'll use the elimination method:
Statement 1 × 20: x+[tex]\frac{60}{100}[/tex]y = 1660
Minus Statement 1 × 20 from Statement 2: x+y-x-[tex]\frac{60}{100}[/tex]y = 2100-1660
[tex]\frac{40}{100}[/tex]y = 440
y = [tex]\frac{100}{40}[/tex]×440
= 1100
x = 2100-1100
= 1000
I’m terrible at percents so ...... if anybody can help that would be nice :))
Answer:
There are 625 trees in the park.
Step-by-step explanation:
Assume that there are x trees in the park
∵ The number of trees in the park = x
∵ 27% of them are oaks
∵ 16% are pins
∵ 33% of them are banyans
∵ The remaining are willows
→ The percentage of the total number of trees is 100%
∴ The percent of the remaining = 100% - (27 + 16 + 33)%
∴ The percent of the remaining = 100% - 76%
∴ The percent of the remaining = 24%
∵ The number of willows trees = 150
∴ 24% of x = 150
∴ 24% × x = 150
→ Change the percent to a decimal by divide it by 100
∵ 24% = [tex]\frac{24}{100}[/tex] = 0.24
∴ 0.24 × x = 150
∴ 0.24x = 150
→ Divide both sides by 0.24
∴ x = 625
∴ There are 625 trees at the park.
Michael buys pants from a clothing company for $70 dollars. He then sells each pair of pants in his clothing shop at a 40% markup. How much is the markup on the pants?
Answer:
$98
Step-by-step explanation:
70 is the original price, but the mark up is 40%. So, 40% of 70 is 28
$70 + $28 = $98
A friend tells you that her savings account doubled in 9 years. Use the Rule of 72 to estimate what the APR of her account was.
answer:The rule of 72 says that an amount will double when the product of the percentage and the number of years equals 72...so for 8 years, you would need to earn 9%
A used bookstore sells hardback books and paperback books. A hardback book costs $11, including tax. A paperback book costs $5, including tax. Jamal bought 3 more paperback books than hardback books. Jamal spent $47. How many paperback books did Jamal buy?
Answer:
5 paperback books
Step-by-step explanation:
From the question:
A used bookstore sells hardback books and paperback books. A hardback book costs $11, including tax. A paperback book costs $5, including tax. Jamal spent $47.
Let the number of paper backs = p
Let the number rod hardbacks = h
Hence:
$11 × h + $5 × p = $47
11h + 5p = 47
Jamal bought 3 more paperback books than hardback books.
h + 3 = p
h = p - 3
How many paperback books did Jamal buy?
Hence:
11h + 5p = 47
11(p - 3) + 5p = 47
11p - 33 + 5p = 47
16p = 47 + 33
16p = 80
p = 80/16
p = 5
Hence, he bought 5 paper back books
hi everyone,can someone help me find what -1+(-3)?
Answer: -4 is the answer
Step-by-step explanation: google caculator
Answer:
-4
Step-by-step explanation:
if you add 2 negatives it will be a negative
what is 1\10 in semplis form
Answer:
1/10 is the simplest form of the fraction
Will mark brainliest!
Answer:
3/2 then 1 then 0.65 then 6/10 and lastly 0.06
Step-by-step explanation:
[FIRST TO ANSWER GETS BRAINLIEST] Here is a rectangle ABCD. The length of the rectangle is increased by 10%. The width of the rectangle is increased by 5%. Find the percentage increased in the perimeter of tge rectangle.
On a blueprint, the diagram of a building has a height of 23 cm.
The height of the building is x times the height of the diagram.
Which equation represents the height, h, of the building?
A h = 23+x
B X = 23=h
C h = 23x
D
X = 23h
Answer:
C h = 23x
Step-by-step explanation:
The height is h, so we want h = something.
The blueprint height is 23 cm.
The real height is x times 23 cm, so it is 23x.
h = 23x
Answer: C h = 23x
Sum of 5 and 9 less than 17
Answer:
15?
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
5+9=14
14-17=-3
please answer the image below
Answer:
Rectangle = l * b = 14 *10
Semi Circle = ( pi * r^2 ) /2
here, diameter of circle is 10 so radius = 5
so area of semicircle = ( pi * 5^2)/2 = 39.26991
so total area = 140 + 36.26991 = 176.26991 or 176.3
Step-by-step explanation:
Step-by-step explanation:
area of the shape = area of rectangle + area of semicircle
area of rectangle = l×b
10×14 =140
area of semicircle
r =d/2
r=10/2=5
[tex] \frac{\pi \times {r}^{2} }{2} [/tex]
[tex] (\frac{22}{7 } \times {5}^{2}) \div 2[/tex]
[tex]78.5 \div 2[/tex]
=32.29
total area = 140+32.29
170.29
170.3
Find the perimeter of the similar figure 48cm 60cm
Answer:
make me brainlist pls! 240 is permimeter
Step-by-step explanation:
Plz help it would mean a lot
Answer:
643663
Step-by-step explanation:
b = d
What survival rate in the 10th year would make the average of loss over the 10 year period equal to 38.0%
Answer: 63%
Step-by-step explanation:
First step
Find the 10th year rate of loss that will make the average of loss over the 10 years to equal 38.0%.
Assume this rate is x;
[tex]\frac{(36.2 + 29.0 + 46.2 + 37.5 + 40.9 + 40.0 + 32.6 + 40.5 + 40.1 + x)}{10} = 38.0\\\\\frac{343 + x}{10} = 38\\\\x = 380 - 343\\\\x = 37[/tex]
x = 37%
Second step - Survival rate
The survival rate is calculated by;
= 1 - rate of loss
= 1 - 37%
= 63%
An artist mixes yellow and blue paint to make the perfect shade of green. She uses 2 ounces of blue paint for every 7 ounces of yellow.If the mixing container only holds 40 ounces of paint, what is the most green paint the artist can make, and what recipe should she use? 20 points please help me
Answer:
she could only make 4 of green paint
The sum of twice a number, m, and 7 is equal to 15 less than the number,
m. What is the value of m?
Answer:
2m+7 = m-15
2m-m+7 = -15
1m = -15-7
1m = -22
m = -22