Answer:
b = 4.4 feet
Step-by-step explanation:
To find the value of "b", all you need to do is plug the values for "a" and "c" into the pythagorean Theorem and isolate "b".
a² + b² = c² <------ Phythagorean Theorem
9² + b² = 10² <------- Plug in a = 9 and c = 10
81 + b² = 100 <-------- Square both values
b² = 19 <-------- Subtract 81 from both sides
[tex]\sqrt{b^{2} } = \sqrt{19}[/tex] <-------- Square root both sides to remove exponent
b = 4.358...
b = 4.4 feet
Simplify (3^-2)^4
O A. 1 /3^2
O B. 3^2
O c. 3^8
OD.1/3^8
[tex](3^{-2})^4 = 3^{-2 \times 4} = 3^{-8} = \dfrac 1{3^8}\\\\\text{Hence the answer is D.}[/tex]
Answer:
1/3^8
Step-by-step explanation:
[tex]\hookrightarrow (3^{-2} )^{4} \\[/tex]
As,
x⁻²=1/x²
Then,
[tex]\hookrightarrow (\frac{1}{3^{2} } )^{4} \\\\\hookrightarrow (\frac{1}{9} )^{4} \\\\\hookrightarrow ((\frac{1}{3} )^{2})^{4} \\\\\hookrightarrow (\frac{1}{3})^{8}[/tex]
Which of the following functions matches this graph?
The equation that match the graph is
b. y = 3x^2
What is vertical stretch?In mathematics, a vertical stretch is a transformation of a function that changes the distance between the function's graph and the x-axis without changing its shape.
A vertical stretch multiplies all the y-coordinates of a function's graph by a constant factor greater than 1. This causes the graph to be stretched vertically and move further away from the x-axis.
For example, if we have a function f(x) = x^2, a vertical stretch by a factor of 3 would result in the function g(x) = 3x^2.
The graph of g(x) would be the same as that of f(x), but stretched vertically by a factor of 3.
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What is the area of this shape?
The area of the composite shape in the image given is calculated as: 316 yd²
How to Find the Area of a Composite Shape?To find the area of a composite shape, find the area of each of the shape that makes up the figure, then add their areas together.
The area of the composite shape = area of big rectangle + area of small rectangle + area of big triangle + area of small triangle
Area of big rectangle = (length)(width) = (5 + 4)(8) = 72 yd²
Area of small rectangle = (length)(width) = (5)(4) = 20 yd²
Area of big triangle = 1/2(base)(height) = 1/2(12)(4+5+4+7) = 120 yd²
Area of small triangle = 1/2(base)(height) = 1/2(8+5)(16) = 104 yd²
The area of the composite shape = 72 + 20 + 120 + 104 = 316 yd²
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Give the degree of the polynomial. 10yx^5w^4-w^3v^5-5x^11-6
10yx⁵w⁴ - w³v⁵ - 5x¹¹ - 6
Degree = biggest exponent = 11
find the greatest common factor of 21 35 70
Answer:
7
Step-by-step explanation:
21 = 3 x 7
35 = 7 x 5
70 = 2 x 5 x 7
The greatest common factor of 21, 35 and 70 is 7.
Note : -
The greatest common factor ( GCF ) of a set of numbers is the largest factor that all the numbers share.
Miguel is flying a kite, holding his hands a distance of 3.5 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 25
∘
∘
. If the string from the kite to his hand is 150 feet long, how many feet is the kite above the ground? Round your answer to the nearest tenth of a foot if necessary.
Answer:
66.9 ft
Step-by-step explanation:
Kite string forms a right triangle with the horizontal 3.5 feet off of the ground
sin 25 = opp / hyp = height / 150
sin 25 = height / 150
150 sin25 = height but it is 3.5 feet off of the ground...add that in
3.5 + 150 sin25 = true height = ~ 66.9 ft
how much is 27.99$ with 25% extra
Answer:
34.98
Simply add the 27.99 with 25%
= 34.98
Directions:Solve this equation
[tex]5 + 5x= 12x - \frac{12}{5} \times 7\div 5[/tex]
Thanks to whoever answers! <3
Answer:
-3.21538461538
Step-by-step explanation:
[tex]\mathrm{Equation\;Given:}\; 5+5x=\frac{12x-\frac{12}{5}\cdot \:7}{5}[/tex]
[tex]\mathrm{Multiply\;both\;sides\;by\;5}:[/tex] [tex]5\cdot \:5+5x\cdot \:5=\frac{12x-\frac{12}{5}\cdot \:7}{5}\cdot \:5[/tex]
[tex]\mathrm{Now\;we\;have\;}:[/tex] [tex]25+25x=12x-\frac{84}{5}[/tex]
[tex]\mathrm{Subtract\;by\;sides\;by\;25}:[/tex] [tex]25+25x-25=12x-\frac{84}{5}-25[/tex]
[tex]\mathrm{Thus\;we\;have}:[/tex] [tex]25x=12x-\frac{209}{5}[/tex]
[tex]\mathrm{Subtracting\;12x\;from\;both\;sides}:[/tex] [tex]25x-12x=12x-\frac{209}{5}-12x[/tex]
[tex]\mathrm{So\;then\;we\;have:}[/tex] [tex]13x=-\frac{209}{5}[/tex]
[tex]\mathrm{Now\;divide\;both\;sides\;by\;13}:[/tex] [tex]\frac{13x}{13}=\frac{-\frac{209}{5}}{13}[/tex]
[tex]\mathrm{Hence\;we\;have}:\;\;x=-\frac{209}{65}[/tex]
[tex]\mathrm{Decimal\;form}:-3.21538461538[/tex]
Kavinsky
There are 24 students in a class and a decrease of 15%. How many students would you have?
Answer:
20
Step-by-step explanation:
85% of 24 is 20
For which values of m is the equation always true.
Answer:
m∈(-∞;-2]∪[6;+∞).
Step-by-step explanation:
1) Δ=b²-4ac, then
m²-4(m+3)≥0; ⇔m²-4m-12≥0; ⇔ (m-6)(m+2)≥0;
2) m∈(-∝;-2]∪[6;+∝).
The perimeter of a rectangular painting is 304 centimeters. If the width of the painting is 61 centimeters, what is its length?
Answer:
The width of the rectangle is 91 cm
Step-by-step explanation:
61 × 2 = 122
304 - 122 = 182
182 ÷ 2 = 91
Answer:
91 cm
Step-by-step explanation:
61 x 2 (because there are 2 sides with length 61) = 122
304 - 122 = 182
182 / 2 = 91
One number is ten more than twice another. Their sum is one. Find the numbers.
answer:
x = 4
y = -3
steps :
x = 10 + 2y
x + y = 1
2y = x - 10 -> y = 1/2x - 5
x + y = 1 -> y = 1 - x
since theyre both equal to y they are equal to each other
1/2x - 5 = 1 - x
3/2x = 6
x = 4
plug 4 back where x is
y = 1 - 4
y = -3
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The graphs below have the same shape. What is the equation of the graph of g(x)?
A. g(x)=x²-2
B. g(x) = (x + 2)²
C. g(x)=(x-2)^2
D. g(x)=x^2+2
Answer:
B. g(x) = (x + 2)²
Step-by-step explanation:
We got the graph of g by translating the graph of the parent function
f(x) = x² two units to the left
Therefore the equation of the graph of g is (x + 2)²
The sum of Two numbers is 9. The
sum of the squares of the numbers is
41. Find the numbers.
Answer:
4 and 5
Step-by-step explanation:
Assuming your 2nd sentence should be: "The sum of the squares of the two numbers is 41"
X + Y = 9 {equation 1}
X² + Y² = 41 {equation 2}
from equation 1: y = 9-x
Substitute that into equation 2
x² + (9-x)² = 41
x² + 81 - 18x + x²= 41
2x² - 18x + 40 = 0
We can factor out a 2
x² - 9x + 20 = 0
(x-5)(x-4) = 0
x = 5 or 4
checking
Your two numbers are 4 and 5
4² + 5²
= 16 + 25
= 41
Suppose the lengths of 3-year-old cats are normally distributed with a mean of 30 inches and a
standard deviation of 2.92 inches. Find each of the following:
1. The percent of cats between 24.16 and 35.84
2. The percent of cats who are longer than 35.84
3. The percent of cats shorter than 24.16 inches
1. The percent of cats between 24.16 and 35.84 is 95%
2. The percent of cats who are longer than 35.84 is 2.28 %
3. The percent of cats shorter than 24.16 inches is 2.28%
What is the empirical rule formula in statistics?The empirical rule - formula
95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .
Mean, u = 30 inches
Standard Deviation, s = 2.92 inches
Formula for z-score = (x-u)/s
1. We have to find the percent of cats between 24.16 and 35.84 inches.
24.16, z-score = -2
35.84, z-score = 2
According to the empirical rule,
95% of the data values are within 2 standard deviations of the mean.
So, 95% of the cats are between 24.16 and 35.84 inches.
2. Here, x = 35.84
z=(35.84-30)/2.92
z= 2
According to the Empirical Rule,
95% of the values lie within 2 standard deviations of the mean.
So, the percent of cats who are longer than 35.84
100 - 97.72 = 2.28%
3. Now, x = 36.22
Using the formula mentioned above, we get:
z= 24.16-30/2.92
z=-2
According to empirical rule,
68% of the values lie within 1 standard deviation of the mean.
i.e., remaining 32% are outside the 1 standard deviation and half of the values i.e. 16% are below 1 standard deviation.
The percent of cats shorter than 24.16 inches is 2.28%
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Given
μ = 30 inσ = 2.92 inFind z-scores for x = 24.16 and x = 35.84
Use formula
z = (x - μ)/σ 1) z = (24.16 - 30)/2.92 = - 22) z = (35.84 - 30)/2.92 = 2Find the corresponding percentage from z-score table
z = - 2 ⇒ 2.28%z = 2 ⇒ 97.72%Now find the answers#1The percent of cats between 24.16 and 35.84
97.72 - 2.28 = 95.44%#2The percent of cats who are longer than 35.84
100 - 97.72 = 2.28%#3The percent of cats shorter than 24.16 inches
2.28%please help need asap
brainly.com/question/27661391 yo im begging some one to help
Step-by-step explanation:
Find the volume of the candle:
3^2 x 3.14 x 4= 113.04cubic inches.
now divide total wax used by volume of a candle.
3278.16 / 113.04 = 29 candles.
Write a sequence of dilations and translations that maps circle D onto circle C and that shows the two circles you created are similar.
Answer: Circle d
Step-by-step explanation:
Calculus, factor the given polynomial.
Answer:
x² + 10x + 21 = (x + 3)(x + 7)Step-by-step explanation:
x² + 10x + 21 = x² + (3x + 7x) + 21
= (x² + 3x) + (7x + 21)
= x(x + 3) + 7(x + 3)
= (x + 3)(x + 7)
HELPPPPPPPPP!!!!!!!!!!!!!!!!
if the area of a triangle is 64 and the height is 10 what is the base
A frame around a rectangular family portrait has a perimeter of 96 inches. The length of the frame is 6 inches less than
twice the width. Find the length and width of the frame.
Width of the frame is
inches
Length of the frame is
inches
The length is 30 inches.
How to get the length of the frame?
For a frame of length L and width W, the perimeter is:
P = 2*(L + W).
Here we know that:
P = 96 in
L = 2*W - 6in
Replacing that we get:
96in = 2*( (2*W - 6 in) + W)
Now we can solve that equation for W:
96in = 2*(3W - 6in)
96in/2 + 6in = 3W = 54in
W = (54in)/3 = 18in
The width is 18 inches, then:
L = 2*W - 6in = 2*(18 in) - 6in = 30in
The length is 30 inches.
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find the value of x. Cos(67°) = x/1
Answer:
The value of cos 67° is equal to the x- cordinate ( 0.3907 ). therefore, cos 67° = 0.3907
Work out 3 1/2 x 1 3/7, giving your answer in its simplest form?
let's firstly convert the mixed fractions to improper fractions and then get their product.
[tex]\stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}} ~\hfill \stackrel{mixed}{1\frac{3}{7}}\implies \cfrac{1\cdot 7+3}{7}\implies \stackrel{improper}{\cfrac{10}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{2}\cdot \cfrac{10}{7}\implies \cfrac{7}{7}\cdot \cfrac{10}{2}\implies 1\cdot 5\implies 5[/tex]
A square has a perimeter of 40 feet. Find the length of the
diagonal of the square.
Answer:
14.14
Step-by-step explanation:
Answer:
The length of the diagonal of the square is about 14.142 feet
Step-by-step explanation:
Step 1: Determine the length
[tex]P = 4(l)[/tex]
[tex]40\ ft = 4(l)[/tex]
[tex]\frac{40\ ft}{4}=\frac{4(l)}{4}[/tex]
[tex]10\ ft = l[/tex]
Step 2: Determine the diagonal length
Pythagorean theorem → [tex]a^2 + b^2 = c^2[/tex]
a and b are going to be the sides of the square which are both 10 ft so we just plug those in and solve for c
[tex](10)^2 +(10)^2 =c^2[/tex]
[tex]100+100=c^2[/tex]
[tex]\sqrt{200}=\sqrt{c^2}[/tex]
[tex]14.142=c[/tex]
Answer: The length of the diagonal of the square is about 14.142 feet
If ( x - y ) = 2 and xy = 3 find the value of...
[tex] {x}^{3} + {y}^{3} [/tex]........
Answer: 4:7
Step-by-step explanation:
Answer:
28
Step-by-step explanation:
Given :
x - y = 2xy = 3Solving :
2 values which satisfy the given conditions are x = 3 and y = 1Evaluating the expression :
x³ + y³(3)³ + (1)³27 + 128GIVING BRAINLIEST AND 5 STARS TO BEST ANSWER!!! I HAVE 1 HOUR LEFT!!!!!!
Answer:
The origin is where x,y lines meet. I put a cirlce there with no label there. Sorry it's messy
Step-by-step explanation:
I'm only a 6th grader. No hate, please. I only did what I learned from my teacher.
Use the substitution method to determine the solution to the system of equations below. y-2x+2=1 6x - 3y = 3
Answer:
y = 2x - 1
Step-by-step explanation:
y - 2x + 2 = 1
6x - 3y = 3
[tex]y - 2x + 2 = 1 \\ +2x - 2 +2x - 2\\y = 2x - 1[/tex]
Plug in for y:
6x - 3(2x - 1) = 3
6x - 6x + 3 = 3
Simplified, 3 = 3
Answer: this solution has infinite solutions
Step-by-step explanation:
original system:
y-2x+2 = 1
6x-3y = 3
Move 2 to right side of equation
y -2x = -1
-3y+6x = 3
solve for y in first equation
⇒ y = 2x - 1
insert y into second equation
⇒ -3(2x-1) + 6x = 3
simplify
⇒ -6x+3+6x = 3
simplify once more
⇒ 3 = 3
this solution has infinite solutions
i need this answer fast and as soon as possible
Find the volume of the podium in the shape of a prism.
Answer:
8640
Step-by-step explanation:
1) Volume of the lower prism:
V1 = 27*20*12 = 6480
2) Volume of the higher prism:
V2 = 9*20*12 = 2160
3) Volume of the podium: V1 + V2 = 8640
Someone please check my answers for 5 & 6, correct me if they are incorrect. May someone also please help me with 7 & 8? Thank you!
For part 5 the total value is $1845, for part 6 the total net worth is $3200, and for part 7 the debt to assets value is 0.433.
What is debt?It is defined as the amount one party needs to pay to another party as the first party borrowed an amount that will be credited by the second party. Debt occurs when one party cannot be able to purchase something under normal circumstances.
5)
Total value = 20×30 + 18×40 + 35×15 = $1845
6)
Net worth = (3500 + 300 + 600) - (1000+200) = $3200
7)
Total debt value = 2000+3200 = $5200
Total assets value = 10000+1300+700 = $12000
Debt to assets value = 5200/12000 = 0.433
Similarly, we can find any debt to assets value by using the formula:
Debt to assets value = Total debt/Total assets
Thus, for part 5 the total value is $1845, for part 6 the total net worth is $3200, and for part 7 the debt to assets value is 0.433.
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What is the probability that a person with an iron deficiency is 20 years or older?
A.
0.23
B.
0.34
C.
0.60
D.
0.78
The answer to this is:
0.34
The probability that a person with an iron deficiency is 20 years or older will be 0.34. Then the correct option is B.
What is probability?Its simple notion is that something will most likely occur. The favorable event's proportion to the overall number of occurrences.
The table is given below.
Then the probability that a person with an iron deficiency is 20 years or older will be
P = 102 / 300
P = 0.34
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