Answer:
It's a right angle triangle with 90° at C
Step-by-step explanation:
sin A = cosB when
A + B = 90
The condition that sin A equals cosine B, with A and B being acute angles, indicates that both angles are complementary and add up to 90 degrees, suggesting a right-angled triangle.
Explanation:When given the condition that sin A equals cosine B in a triangle, and both angles A and B are acute, we can determine that triangle A and B are complementary, which means they add up to 90 degrees.
This is due to the co-function identity, where sin(90° - θ) = cos(θ) and cos(90° - θ) = sin(θ) for acute angles in right-angled triangles.
If A and B are in the same triangle, and given it is a right triangle (since they are acute and the sine of one equals the cosine of the other), we can conclude that A + B = 90°, and thus, the third angle will also be 90 degrees, making the triangle a right-angled one.
if f(x)+5x-4/2 find f(10)
Answer:
f(x) = 48
Step-by-step explanation:
If you substitute 10 for x, you get:
5*10-4/2
Simplify:
50-2
f(x) = 48
0.076952 to 3 significant figure
Answer:0.0770
Step-by-step explanation:
0.076952 the five makes 9 round up.
Since you can't have ten the six increases by 1 so it is
0.077
Then you could add a zero on the end to 0.0770 so it is to 3 sig fig
Answer:
0.0770.
Step-by-step explanation:
That would be rounded to the next 3 digits after the second 0.
So it is 0.0770.
(The 7695 is rounded to 770 because the digit after the 9 is 5, so the 69 is rounded up to 70).
Find the volume of a solid generated by revolving the region bounded by the graphs of the equations about the y-axis. Y= 4(3-x), Y= 0, and X= 0.
Answer:
[tex]\displaystyle V = 36 \pi[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
GraphingCoordinates (x, y)FunctionsFunction NotationIntersection PointsExpand by FOILCalculus
Integrals
Area under the curveIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Volume of Revolution Formula [y-axis]: [tex]\displaystyle V = \pi \int\limits^b_a {r^2} \, dy[/tex]
Step-by-step explanation:
Step 1: Define
Identify
y = 4(3 - x)
y = 0
x = 0
Step 2: Redefine
Rewrite (Revolving around y-axis)
[Division Property of Equality] Divide 4 on both sides: [tex]\displaystyle \frac{y}{4} = 3 - x[/tex][Subtraction Property of Equality] Subtract 3 on both sides: [tex]\displaystyle \frac{y}{4} - 3 = -x[/tex][Division Property of Equality] Divide -1 on both sides: [tex]\displaystyle 3 - \frac{y}{4} = x[/tex]Rewrite: [tex]\displaystyle x = 3 - \frac{y}{4}[/tex]Step 2: Find Bounds of Integration
See attachment
Look at y-values, right to left.
Bounds: [0, 12]
Step 3: Find Volume
Substitute in variables [Volume of Revolution Formula]: [tex]\displaystyle V = \pi \int\limits^{12}_0 {(3 - \frac{y}{4})^2} \, dy[/tex][Integrand] Expand [FOIL]: [tex]\displaystyle V = \pi \int\limits^{12}_0 {(\frac{y^2}{16} - \frac{3y}{2} + 9)} \, dy[/tex][Integral] Rewrite [Integration Property - Addition/Subtraction]: [tex]\displaystyle V = \pi \bigg[ \int\limits^{12}_0 {\frac{y^2}{16}} \, dy - \int\limits^{12}_0 {\frac{3y}{2}} \, dy + \int\limits^{12}_0 {9} \, dy \bigg][/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle V = \pi \bigg[ \frac{1}{16} \int\limits^{12}_0 {y^2} \, dy - \frac{3}{2} \int\limits^{12}_0 {y} \, dy + 9 \int\limits^{12}_0 {} \, dy \bigg][/tex][Integrals] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle V = \pi \bigg[ \frac{1}{16}(\frac{y^3}{3}) \bigg| \limits^{12}_0 - \frac{3}{2}(\frac{y^2}{2}) \bigg| \limits^{12}_0 + 9(y) \bigg| \limits^{12}_0 \bigg][/tex][Integrals] Evaluate [Integration Rule - FTC 1]: [tex]\displaystyle V = \pi \bigg[ \frac{1}{16}(576) - \frac{3}{2}(72) + 9(12) \bigg][/tex][Brackets] Multiply: [tex]\displaystyle V = \pi [36 - 108 + 108][/tex][Brackets] Add: [tex]\displaystyle V = \pi [36][/tex]Multiply: [tex]\displaystyle V = 36 \pi[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Applications of Integration
Book: College Calculus 10e
Given the function, f(x)= square root 3x+3+3, choose the correct transformation(s).
Answer: horizontal stretch, left 3,up 3
Step-by-step explanation: you guys are welcome! And be blessed
Is the square root of 72 rational or irrational? Explain.
Answer:
No, it is not rational.
Step-by-step explanation:
A rational number is a number that can be in the form p/q. where p and q are integers and q is not equal to zero.
A triangle has sides of length 7, 10, and s. Write an equation representing the perimeter p of the triangle
Answer:
7(2+10)
14+10
=26 is the perimeter
S=7
Hope this helped
Step-by-step explanation:
Answer:
P=7+10+s
The perimeter is the length of all sides, so add 7, 10, and s to get p!
Hope this comes to help someone!
Write an equation of the line that passes through point (-1, 5) and has the slope
m = 4.
Answer: 4x - y + 9 = 0
Step-by-step explanation:
A bale of hay in the shape of a rectangular prism has a length of 4 feet, a width of 2 feet, and a height of 2 feet. A cylindrical bale of hay has a diameter of 4 feet and a height of 6 feet. How many rectangular bales contain the same amount of hay as one cylindrical bale? Round your answer to the nearest tenth.
Answer:
2
Step-by-step explanation:
Answer:
About 4.7
Step-by-step explanation:
First Find the volume of the cylindrical bale.
V= π(r)^2*6
V=π(2)^2*6
V=π*4*6
V=π24
The answer is about 75.4
Now find the volume of the Rectangular Prism
V= w*h*l
V= 2*2*4
The answer is 16
Finally divide 75.4÷16 Which to the nearest tenth is 4.7.
p.s please correct me if I am wrong.
Aimee has four 100-point projects for her class. Her scores
on the first three projects are shown below. What score
does she need on Project 4 so that her average score for
the four projects is 80?
She needs a 94.
72+ 75 + 79 + 94 = 320
320 ÷ 4 = 80
Answer:
94%
Step-by-step explanation:
I NEED HELP IMMEDIATELY!!! Allen has four times as many cards as Bob, and Jane has twice as many cards as Allen. Together, Allen and Jane have 468 cards. How many cards do Allen, Jane, and Bob each have?
Answer:
Allen- 144 cards
Jane- 288 cards
Bob- 36 cards
Step-by-step explanation:
Here's what we know:
a = 4b (Allen has 4 times Bob's cards)
j = 2a (Jane has twice Allen's)
a + j = 432 (Allen and Jane have 432 cards all together)
Start with substituting:
4b + 2a = 432
4b + 2(4b) = 432
Distribute:
4b + 8b = 432
Simplify:
12b = 432
Divide both sides by 12:
b = 36
To find how much Allen has just multiply 36 times 4.
a= 144 cards
To find how much Jane has multiply 144 times 2.
j= 288 cards
Answer:
156
312 and
39
Step-by-step explanation:
Let Allen be A , Jane be J and Bob be B
Allen has 4 times as Bob
So
A = 4B
Jane has twice as Allen
So
J = 2A
Together, Allen and Jane has 468 cards
A + J = 468
Substitute 2A for J in the third equation.
We have
A + J = 468
A + 2A = 468
3A = 468
Divide both sides by 3
3A/3 = 468/3
A = 156
Recall
A = 4B
Therefore
156 = 4B
Divide both sides by 4
156/4 = 4B/4
39 = B
B = 39
Also,
J = 2A
J =2 x 156
J = 312
Allen has 156 cards
Jane has 312 cards and
Bob has 39 cards
Evaluate the expression c=-2.7
c+18 =?
Answer:
15.3
Step-by-step explanation:
-2.7+18=15.3
Answer:
Step-by-step explanation:
When c=-2.7, we substitute the value of c into the expression so we can add
c+18=-2.7+18=18-2.7=15.3
6 divided by 2 ( 1+2=)=
Answer:
9
Step-by-step explanation:
6 divided by 2 equals 3 (1 plus 2 ) equals 3, 3 times 3 equal 9
WILL MARK U AS BRAINLIEST PLZ HELP
Answer:
112 if you don't include the triangle sides as they are not necessary, but 124 if you include one triangle and 136 if you include both triangle sides
Which of the following is equal to the expression 6(11 + 3)?
(A) 6x14
(B) 33+3
( 66+3
D
6(11x3)
Answer: A. 6x14
Step-by-step explanation:
6(11+3)
6x11 = 66
6x3= 18
66+18= 84
6x14= 84
Use distributive property: a(b + c) = ab + ac
Steps to solve:
6(11 + 3)
~Use distributive property
(6 * 11) + (6 * 3)
~Simplify
66 + 18
~Add
84
Lets check each option to see which one equals 84.
Option A:
6 * 14
84
We don't need to check anymore options since Option A is correct.
Best of Luck!
HELP ASAP PLEASEEEE
im kinda begging
Answer:
x = -1
-1 + 6 = 5
Since its a negative, you're actually subtracting it from 6.
4(2x - 5) = 5x -20 +3x
Answer:
All real numbers
Step-by-step explanation:
Distribute the 4 on the left side
4(2x-5)=5x-20+3x
8x-20=5x-20+3x
Combine like terms on the right side
8x-20=8x-20
All real numbers are solutions, because both sides are equal
Hope this helps! :)
Simplify the following expression(1/5)(-5/7)(2/4)
Answer:
-1/14
Step-by-step explanation:
To simplify the expression, you should first divide up the parts to make it easier. Multiply 1/5 by -5/7 first. When you multiply the two fractions, the fives cancel out since there is a five in both the numerator and the denominator. This leaves us with just -1/7.
[tex]\frac{1}{5} *\frac{-5}{7} =\frac{-1}{7}[/tex]
Now, multiply -1/7 by 2/4. Notice that you can simplify 2/4 to 1/2. You can't cancel out anything in this expression so simply multiply the two fractions.
[tex]\frac{-1}{7} *\frac{1}{2} =-\frac{1}{14}[/tex]
I moved the negative sign from the numerator out front, but you don't have to do that.
Write this equation in slope intercept form 3x+2y=4
To write the equation 3x + 2y = 4 in slope-intercept form, subtract 3x from both sides, then divide each term by 2. The slope-intercept form of the equation is y = (-3/2)x + 2.
Explanation:
To write the equation 3x + 2y = 4 in slope-intercept form, we need to isolate y on one side of the equation.
Step 1: Subtract 3x from both sides to get 2y = -3x + 4.
Step 2: Divide each term by 2 to get y = (-3/2)x + 2.
Therefore, the equation 3x + 2y = 4 in slope-intercept form is y = (-3/2)x + 2.
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Answer:
Step-by-step explanation:
If 3/4 pound of broccoli is priced at $2.09 per pound, what is the price?
Answer:
$1.57
Step-by-step explanation:
2.09 × 3/4 = 1.5675, rounded to 1.57
Answer:
I believe the answer is $1.57 about. The answer is longer but that is rounded.
Step-by-step explanation:
I just did 3/4 times 2.09 and got 1.57 because if a whole pound is 2.09 then 3/4 times the whole pound would give you 3/4 of the price.
Plot the given parabola on the axes. Plot the roots, the vertex and two other points.
y=−x2+2x+48
To plot the parabola y = -x² + 2x + 48, find the vertex at (1, 49), the roots at -6 and 8, and two additional points at (0, 48) and (2, 48). Then, plot these points on a graph and sketch the parabola.
Explanation:To plot the given parabola y = -x² + 2x + 48, we must follow several steps:
Find the vertex. The formula for the x-coordinate of the vertex is -b/2a. In this equation, a = -1 and b = 2, so the x-coordinate is -2/-2 = 1. Substituting x = 1 into the equation gives us y = -12 + 2 * 1 + 48 = 49. So, the vertex is (1, 49). Find the roots. The roots are the x-values when y = 0. We solve -x2 + 2x + 48 = 0. Factoring the quadratic can give us the roots, but this equation doesn't factor nicely. We use the quadratic formula instead: x = [-b ± sqrt(b2 - 4ac)] / 2a = [-2 ± sqrt((2)2 - 4*(-1)*48)] / 2*(-1). This gives us two roots, -6 and 8. Choose two other points. Let's choose x = 0 and x = 2. When x = 0, y = 48. When x = 2, y = -22 + 2 * 2 + 48 = 48. So, the two other points are (0, 48) and (2, 48). Plot these points on a coordinate grid and draw the parabola.Learn more about Plotting Parabola here:
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Square root of -3
find the square root of -3
Answer:
i times the square root of 3
Step-by-step explanation:
Whenever you take a square root of a number, look for anything that you could take out! Like if you have the square root of 40, that’s 4 * 10, so you could take out a 2 from the square root and leave the 10.
In this, we see that it’s the square root of 3 times the square root of -1, which we can simplify to the square root of 3 times “i.” We use i to represent the square root of -1.
the volume of an ice cream cone is 12 pi cubic cm. if the height is 9 cm, what is the diameter of the cone ?
The diameter of the cone is 4√3 cm, which is approximately 6.93 cm when rounded to two decimal places.
Explanation:To find the diameter of the cone, we first need to identify the formula for the volume of a cone, which is V = (1/3)πr^2h. Given that the volume (V) of the ice cream cone is 12π cubic cm and the height (h) is 9 cm, we can set up the equation to solve for the radius (r):
12π = (1/3)πr^2(9)
We can simplify this equation by dividing both sides by π and multiplying both sides by 3/9 (which is the reciprocal of 1/3 times 9):
12 = r^2
Therefore, r = √12 cm. To find the diameter, which is twice the radius, we calculate:
Diameter = 2r = 2(√12) cm = 2(√4√3) cm = 4√3 cm
The diameter of the cone is 4√3 cm or approximately 6.93 cm when rounded to two decimal places.
Elsa saving money to buy a game so far she had saved $36 which is 3/4 of the total cost of the game how much does the game cost
Answer:
48
Step-by-step explanation:
36 = 3/4x
Divide by three then multiply by four to get x instead of 3/4x
36/3 = 12 x 4 = 48
Answer:
$48
Step-by-step explanation:
She has saved 36 which is 3/4
3/4=36/x
36/3=12
12*4=48
Geometry end of year review escape room: room H
Answer:
1) D
2) A
3) C
4) B
5) B
6) C
Step-by-step explanation:
1) V = Bh
V = πr² (h)
V = π (7²)(5)
V = 49π (5)
V = 245π
V ≈ 769.3
2) V = 1/3 Bh
V = 1/3 (12*12)(9)
V = 1/3 (144)(9)
V = 1/3 (1296)
V = 432
3) V = 4/3πr³
V = 4/3 π (4.5³)
V = 4/3 π (91.125)
V = 121.5π
V ≈ 381.51
4) 3 pairs of rectangles
2(16)(5) = 2(80) = 160
2(16)(11) = 2(176) = 352
2(11)(5) = 2(55) = 110
Add together 160 + 352 + 110
622
5) Two triangles 3 rectangles
Triangle
2(1/2)(18)(5) = 18*5 = 90
Rectangles
18*7 = 126
5*7 = 35
18.7*7 = 130.9
Add together 90 + 126 + 35 + 130.9 = 381.9
C) SA = πr² + πrl --> l is the slant height
SA = π (8²) + π (8)(17)
SA = 64π + 136π
SA = 200π
SA ≈ 628
DACBBC
Starting with 60, divide by 5 --> 12
add by 13 --> 25
multiply by 3 --> 75
subtract by 11 --> 64
cube root 64 --> 4
Multiply 60 --> 240
CODE: 240
The amount of three-dimensional space enclosed by a closed surface is known as volume. The code is 240.
What is volume?The amount of three-dimensional space enclosed by a closed surface is expressed as a scalar quantity called volume.
1. The volume of a cylinder with a radius of 7 ft and a height of 5 ft is,
[tex]\rm \text{Volume of Cylinder} = \pi r^2 h = \pi \times 49 \times 5=769.7\ ft^3[/tex]
2. The Volume of the Pyramid with a side 12m, while the height is 9m is,
[tex]\rm \text{Volume of Pyramid} = \dfrac13 \times (\text{Area of square}) \times height = \dfrac13 \times 12^2 \times 9 = 432\ m^3[/tex]
3. The volume of the sphere with a diameter of 9 yds, can be written as,
[tex]\rm \text{Volume of sphere}=\dfrac{4}{3} \pi r^3=\dfrac43 \times \pi \times (\dfrac{9}{2})^3=381.7\ yd^3[/tex]
4. The surface area of the cuboid with a length of 16 cm, width of 5 cm, and height of 11 cm can be written as,
[tex]\rm \text{Surface area of Cuboid} = 2[(L\times W)+(W\times H)+(L\times H)][/tex]
[tex]\rm \text{Surface area of Cuboid} = 2[(16\times 5)+(5\times 11)+(16\times 11)] = 622\ cm^2[/tex]
5. The surface area of the given figure can be written as,
Surface Area of figure = 2(Area of the triangle) + Area of slant side + Area of rectangle + Area of base
[tex]\rm \text{Surface Area of figure} = (\dfrac{2 \times 5 \times 18}{2}) + (18.7 \times 7)+(18 \times 7) + (5 \times 7) = 381.9\ in^2[/tex]
6. The surface area of a cone is given as,
[tex]\text{Surface Area of Cone}=\pi r(\sqrt{h^2+r^2})+\pi r^2[/tex]
The radius of the cylinder is 8 mm while the height is 15 mm, therefore, the surface area can be written as,
[tex]\rm\text{Surface Area of Cone}=\pi \times 8(\sqrt{15^2+8^2})+\pi \times 8^2 = 628.3\ mm^2[/tex]
Now, if we fill the results accordingly in fill in the blanks we will get,
Starting with 60, divide by 5
then add by 13
then multiply by 3
and subtract by 11
Now, cube root your result 64
Multiply the starting number60.
Thus, the code is 240.
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What is the solution for the equation
5/3b^3-2b^2-5=2/b^3-2?
b= -4 and b=0
b= -4
b= 0 and b=4
b= 4
Answer:
b=0.46005 approx
Step-by-step explanation:
ugh its to messy just solve it like a quadratic
Calculate the reciprocal of -0.07,correct to one decimal place
The reciprocal of the given decimal number -0.07 is decimal number -14.3.
The given decimal number is -0.07.
The reciprocal of any quantity is, one divided by that quantity. For any number ‘a’, the reciprocal will be [tex]\frac{1}{a}[/tex]. If the given number is multiplied by its reciprocal, we get the value 1.
The given decimal written in fraction as [tex]-\frac{7}{100}[/tex].
Reciprocal of [tex]-\frac{7}{100}[/tex] is [tex]-\frac{100}{7}[/tex]
[tex]-\frac{100}{7}=-14.285[/tex]
[tex]\approx-14.3[/tex]
Therefore, the reciprocal of the given decimal number -0.07 is decimal number -14.3.
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Final answer:
The reciprocal of -0.07, when rounded to one decimal place, is -14.3.
Explanation:
To calculate the reciprocal of any number, you simply divide 1 by that number.
The reciprocal of a number is the multiplicative inverse of that number.
In this case, for the number -0.07:
The reciprocal of -0.07 is calculated as follows:
Divide 1 by -0.07:
1/-0.07
= -100/7
= - 14.2857 which equals approximately -14.2857.
To round the result to one decimal place, we consider the first decimal digit after the point, which is 2. Since 2 is less than 5, we don't round up the preceding digit.
Round this number to one decimal place, giving us -14.3.
Therefore, the reciprocal of -0.07, correct to one decimal place, is -14.3.
Ten less than 40% of a number is -4. Please just write out equation >~
Answer:
Number is "n"
(.40 * n) -10 = -4
Step-by-step explanation:
The phrase 'ten less than 40% of a number is -4' can be translated into a mathematical equation as 0.4x - 10 = -4. By using the rules of algebra, we can simplify this equation to find that the unknown number x equals 15.
Explanation:The question deals with an equation involving the term 'ten less than 40% of a number'. This phrase can be translated into a mathematical equation as follows: 0.4x - 10 = -4, where x is the unknown number we're trying to find.
Following the rules of algebra, you would want to simplify this equation as much as possible. Let's add 10 to both sides of the equation, which gives us 0.4x = 6. To isolate 'x', we divide both sides of the equation by 0.4, which gives us x = 6 / 0.4. When you perform this division, you find that x = 15.
Thus, the number that 'ten less than 40% of' equals -4 is 15.
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There is an 8% tax in the town where the store is located. What is miguel’s total cost after sales tax has been added?
Final answer:
To determine Miguel's total cost including the 8% sales tax, add the pre-tax total of $20.98 to the sales tax amount, which is calculated as $20.98 multiplied by 0.08, totaling $22.66.
Explanation:
To calculate Miguel’s total cost including an 8% sales tax on his purchases, follow these steps:
First, find the total cost before tax by adding the prices of the items. If Miguel bought items totaling $20.98, this is the pre-tax total.
Next, convert the tax percentage to a decimal form. For an 8% sales tax, this is done by dividing by 100, which gives us 0.08.
Then, calculate the amount of sales tax by multiplying the pre-tax total by the decimal tax rate: $20.98 × 0.08 = $1.6784.
Round the sales tax to the nearest cent, which gives us $1.68.
Finally, add the sales tax to the pre-tax total to find the total cost: $20.98 + $1.68 = $22.66.
The total cost for Miguel after adding the 8% sales tax is $22.66.
An element with a mass of 550 grams decays by 18.8% per minute. To the nearest minute, how long will it be until there are 60 grams of the element remaining
Answer: 11
Step-by-step explanation:
Exponential Functions:
y=ab^x
y=ab
x
a=\text{starting value = }550
a=starting value = 550
r=\text{rate = }18.8\% = 0.188
r=rate = 18.8%=0.188
\text{Exponential Decay:}
Exponential Decay:
b=1-r=1-0.188=0.812
b=1−r=1−0.188=0.812
\text{Write Exponential Function:}
Write Exponential Function:
y=550(0.812)^x
y=550(0.812)
x
Put it all together
\text{Plug in y-value:}
Plug in y-value:
60=550(0.812)^x
60=550(0.812)
x
\frac{60}{550}=\frac{550(0.812)^x}{550}
550
60
=
550
550(0.812)
x
Divide both sides by 550
0.109091=0.812^x
0.109091=0.812
x
\log 0.109091=\log 0.812^x
log0.109091=log0.812
x
Take the log of both sides
\log 0.109091=x\log 0.812
log0.109091=xlog0.812
use power rule to bring x to the front
\frac{\log 0.109091}{\log 0.812}=\frac{x\log 0.812}{\log 0.812}
log0.812
log0.109091
=
log0.812
xlog0.812
Divide both sides by log(0.812)
10.638757=x
10.638757=x
x\approx 11
x≈11
Answer:
x\approx 11
x≈11
e^x=59 round to the nearest ten-thousandth