Answer:
x = 3; y = 6
Step-by-step explanation:
x + 2x = 9
3x = 9
x = 3
H varies directly as L. If H=20 when L=50, determine H when L=30
The correct answer is 12
Set up a ratio and then solve. See paper attached. (:
Final answer:
H varies directly as L, and using the constant of direct variation from the given values (H=20 when L=50), we calculated the value of H to be 12 when L is 30.
Explanation:
The concept we are dealing with here is direct variation, which means we can set up a proportion based on the relationship that H varies directly as L. Given that H=20 when L=50, we can determine the constant of variation k by dividing H by L (H = k*L), which gives us k = 20/50 or k = 0.4. With the constant of variation, we can then find the value of H when L=30.
To do this, we use the formula for direct variation again with our constant k and the new value of L:
H = k * L = 0.4 * 30 = 12
Therefore, when L is 30, H is 12.
Idk what end behavior for this?
Answer:
It is b.
Step-by-step explanation:
When x is negative x^5 will also be negative.
f(x) = x^5 - 3x^3 + 2x + 4
As x --> -∞ x^5 will be the main factor for f(x) ---> -∞ .
Similarly x^5 will have the greatest influence when x ---> ∞, so f(x) ---> ∞.
Answer:
b
Step-by-step explanation:
The end behaviour is what happens when x gets larger and positive ( right hand end ) or larger and negative ( left hand end ) Tis is called the end behaviour as x → + ∞ and x → - ∞ respectively
For a polynomial the end behaviour is determined by the term of greatest degree.
For the given function
f(x) = [tex]x^{5}[/tex] - 3x³ + 2x + 4 ← degree 5 polynomial
The leading coefficient is positive
• Odd degree, positive leading coefficient, then
as x → - ∞, f(x) → - ∞
as x → + ∞, f(x) → + ∞
----------------------------------------------------------------------
• Odd degree, negative leading coefficient, then
as x → - ∞, f(x) → f(x) → + ∞
as x → + ∞, f(x) → - ∞
solve sin (x)(sin(x)-1) =0
Answer:
[tex]x=n \pi[/tex] or [tex]x=2\pi n+\frac{\pi}{2}[/tex]
Step-by-step explanation:
The given trigonometric equation is;
[tex]\sin x(\sin x-1)=0[/tex]
By the zero product property;
[tex]\sin x=0[/tex] or [tex]\sin x-1=0[/tex]
For [tex]\sin x=0[/tex], the general solution is [tex]x=n \pi[/tex]
[tex]\sin x-1=0[/tex], [tex]\sin x=1[/tex], the general solution is [tex]x=2\pi n+\frac{\pi}{2}[/tex]
Therefore the general solution is:
[tex]x=n \pi[/tex] or [tex]x=2\pi n+\frac{\pi}{2}[/tex]
The solutions to the equation sin(x)(sin(x)-1) = 0 are:
x = 0, π, 2π, 3π, π/2, 3π/2, 5π/2, and so on.
We have,
To solve the equation sin(x)(sin(x)-1) = 0, we can apply the zero-product property, which states that if a product of factors is equal to zero, then at least one of the factors must be equal to zero.
So, we set each factor equal to zero and solve for x:
sin(x) = 0
To find the solutions for this equation, we look for x values where the sine function equals zero.
The solutions are x = 0, π, 2π, 3π, and so on.
sin(x) - 1 = 0
Adding 1 to both sides:
sin(x) = 1
The solutions for this equation occur when the sine function equals 1, which happens at x = π/2, 3π/2, 5π/2, and so on.
Therefore,
The solutions to the equation sin(x)(sin(x)-1) = 0 are:
x = 0, π, 2π, 3π, π/2, 3π/2, 5π/2, and so on.
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Find the surface area of the sphere. Leave your answers in terms of pi.
Radius = 100
Surface Area = [ ? ] pi
The formula for surface area of a sphere is: A = 4 x PI x r^2
Replace r with the given radius and calculate the area:
Area = 4 x PI x 100^2
Area = 4 x PI x 10,000
Area = 40,000PI
Dianne purchased a ham for $45.15. How many pounds is the ham if it sells for $6.45 per pound?
Find the quotient: –3.5 and –0.875
Answer:
4
Step-by-step explanation:
-3.5/-0.875 = 4
Answer:
The answer is 4 or C
Step-by-step explanation:
Since its a negative-negative equation, the result is a positive number. So take this equation as 3.5/0.875. Your result will be four or C. Hope this helps!
A ship leaving port sails for 75 miles
in a direct 35° north of due east: Find
the magnitude of the vertical and
horizontal components.
Answer:
Vertical= 61.43 miles
Horizontal=43.02 miles
Step-by-step explanation:
We use the trigonometric ratios for a right angled triangle to calculate the components.
The vertical is the adjacent while the horizontal is the opposite.
The vertical is calculated as follows:
V= 75 Cos 35° =61.43 Miles
The magnitude of the horizontal H is calculated as follows:
H= 75 Sin 35° = 43.02 miles
Final answer:
Using trigonometric functions, the horizontal component of the ship's journey is found to be 61.44 miles to the east, and the vertical component is 43.02 miles to the north.
Explanation:
A ship leaving port sails for 75 miles in a direct 35° north of due east. To find the magnitude of the vertical and horizontal components, one can use trigonometric functions based on the angle provided. The horizontal (east) component can be found using the cosine function, and the vertical (north) component can be calculated using the sine function.
To calculate the horizontal (east) component: Horizontal Component = 75 miles * cos(35°) = 75 * 0.8192 = 61.44 miles.
To calculate the vertical (north) component: Vertical Component = 75 miles * sin(35°) = 75 * 0.5736 = 43.02 miles.
Therefore, the ship’s vertical component of movement is 43.02 miles to the north, and the horizontal component is 61.44 miles to the east.
I don't understand how to prove that this is an isosceles triangle.
Check the picture below.
so, two tangents to the same circle, whenever they meet outside the circle, they'll be congruent, namely, AB = AX and CB = CY and DX = DY.
well, we know AB = BC, and we know that AB = AX and CB = CY, therefore
AB = BC = AX = CY = 10.
an isosceles needs twin sides, well, we know DX = DY, and we know that AX = 10 then the triangle's side AD = AX + DX = 10 + DX.
the triangle's side of CD = CY + DY = 10 + DY.
but but but, we know DX and DY are tangents to a common circle meeting outside, so they're equal, so whatever length DX and DY are, is the same, so
10 + DY = 10 + DX
meaning the triangle's sides AX = CD, and for an isosceles, is all you need, twin sides.
Combine these radicals. –23 –11
Answer:
-23
Step-by-step explanation:
what is 2 plus 2 times 489829
Your answer is going to be: 979,660
Answer:
If your equation is (2+2)x489829 then the answer is 1959316
hiwever if your equation is 2+2*489829 then your answer is 979,660
Step-by-step explanation:
Simplify: 2(8 - 2x4).
Answer:
2(8-8x)
Step-by-step explanation:
Distrubutive Property:
↓
A(B+C)=AB+AC
Multiply by the numbers from left to right.
4*2=8
Therefore the correct answer is 2(8-8x).
Answer:
16 - 4x^4
Step-by-step explanation:
Assuming x4 means x^4 or x to the 4th power
2(8 - 2x^4)
Distribute the 2
2*8 - 2 * 2x^4
16 - 4x^4
Subtract 7x - 9 from 2x2 - 11.
Answer:
2x^2 - 7x - 2
Step-by-step explanation:
Write 2x2 - 11 first. Please use " ^ " to indicate exponentiation:
2x^2 - 11
Now change both signs of 7x - 9 and combine the result with 2x^2 - 11:
2x^2 - 11
-7x + 9
-------------------
2x^2 - 7x - 2 (answer)
Answer:
b on edge 2021
Step-by-step explanation:
If 3t -7 =5t, then 6t=
Find the Volume and surface area of the following solid. Take Pi to be 22/7.
Answer:
V= 32340cm^3
A= 5082cm^2
Step-by-step explanation:
Solution is in the picture. The area of the base of cone is not counted
The formulas for volume and surface area largely depend on the type of solid. For a cylinder, the volume is computed by πR²h and the surface area is 2πr(h + r) where Pi (π) is 22/7. Apply these formulas using consistent units such as meters.
Explanation:To compute the volume of a particular solid shape, you would first need to know the specific formula that applies to that shape. For example, the volume of a cylinder can be calculated using πR²h (where R is the radius, and h is the height), and the calculation would use the value 22/7 for Pi (π). The volume of a pillar segment where the cross-sectional area A is given and height h is known could be calculated by multiplying A by h.
Surface area calculations would also depend on the specific shape. The surface area of a cylinder, for example, is 2πr(h + r), with r as radius, h as height, and Pi as 22/7.
Without knowledge of the specific type of solid in question, more detailed steps cannot be provided. However, once the shape is identified, application of the right formulas with consistent units (such as meters) will yield both the volume and surface area of the solid.
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Which of the following properties is necessary to simplify the expression given below?
(–2) + 5(x – 3) – 4x(6 + 1)
Answer:
C. Distributive property
Step-by-step explanation:
The options to your question can be found in the image below.
the correct option is C. Distributive property
(to clear the parenthesis)
(–2) + 5(x – 3) – 4x(6 + 1)
= -2 + 5x -15 -24x -4x
= -17 +5x -28x
= -23x -17
subtract (-2x^2+9x-3)-(7x^2-4x+2)
For this case we must subtract the following expression:
[tex](-2x ^ 2 + 9x-3) - (7x ^ 2-4x + 2) =[/tex]
We must bear in mind that:
[tex]- * + = -\\- * - = +[/tex]
We rewrite the expression:
[tex]-2x ^ 2 + 9x-3-7x ^ 2 + 4x-2 =[/tex]
We add similar terms taking into account that equal signs are added and the same sign is placed, while different signs are subtracted and the sign of major is placed:
[tex]-2x ^ 2-7x ^ 2 + 9x + 4x-3-2 =\\-9x ^ 2 + 13x-5[/tex]
Answer:
[tex]-9x ^ 2 + 13x-5[/tex]
Answer: [tex]=-9x^2+13x-5[/tex]
Step-by-step explanation:
First, you need to remember the multiplication of signs:
[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-[/tex]
Then, to subtract the polynomials given, the first step is to distribute the negative sign:
[tex](-2x^2+9x-3)-(7x^2-4x+2)=-2x^2+9x-3-7x^2+4x-2[/tex]
And finally, you need to add the like terms.
With this procedure, you get the following result:
[tex]=-9x^2+13x-5[/tex]
cheryl bought 3.4 pounds of coffee thay cost $6.95 per pound. How much did she spend on coffee?
Answer:
2,085
Step-by-step explanation:
multiply 3 by 600 then 90 then 5 and then u add them all and u get ur answer
the population of one part of the city is recorded. in 2010 there was a population of 6500 people. from 2010 to 2014 our population increased by 10%. from 2014 to 2017, the population decreased by 6%. what was the population in 2017?
Your question asks to find what was the size of the population in 2017
Answer: 6,721In order to solve this problem, we're going to need to use the given information in the question in order to find the population in 2017.
Key information:
In 2010, population was 6500
In 2014, population increased by 10% from 2010
In 2017, population decreased by 6% from 2014.
With the information above, we can solve the problem.
We're going to start with 6500 as our starting population.
We know that the population increased by 10% in 2014, so we would multiply 6500 by 1.10.
[tex]6500*1.10=7,150[/tex]
The population in 2014 was 7,150.
We know that in 2017, the population decreased by 6% from the population in 2014. So we would find how much 6% is from 7,150 and then subtract that number.
[tex]7,150*.06=429\\\\7,150-429=6,721[/tex]
When you're done solving, you sohuld get 6,721.
The population in 2017 would be 6,721.
I hope this helps!Best regards, MasterInvestorAnswer:
6721
Step-by-step explanation:
the answer is 6721
There are 24,000 square miles of forest in a western state. Forest fires decrease this area by 9.2% each year. The state needs to have
more than 15,000 square miles of forest to keep their funding from a nonprofit wildlife organization.
Which inequality represents this situation, and if the fires continue to decrease the area of the forests at the same rate, will the state be
able to keep their funding from the nonprofit wildlife organization in 5 years?
O
24,000(1.092) > 15,000; no
0
24,000(0.092) > 15,000; yes
0
24,000(0.908) > 15,000; no
0
24,000(1.098) > 15,000; yes
Answer:
Part 1) [tex]24,000(0.908)^{5}> 15,000[/tex]
Part 2) No
Step-by-step explanation:
step 1
Let
x ----> the time in years
y ----> the area of the forests is square miles
we know that
The equation that represent this situation is a exponential function of the form
[tex]y=a(b)^{x}[/tex]
where
a is the initial value
b is the base
we have
[tex]a=24,000\ mi^{2}[/tex]
[tex]b=100\%-9.2\%=90.8\%=90.8/100=0.908[/tex]
substitute
[tex]y=24,000(0.908)^{x}[/tex]
The inequality that represent the situation is
[tex]24,000(0.908)^{x}> 15,000[/tex]
step 2
Verify if the state will be able to keep their funding from the nonprofit wildlife organization in 5 years
For x=5 years
[tex]24,000(0.908)^{5}> 15,000[/tex]
[tex]14,813> 15,000[/tex] ----> is not true
therefore
The state will be not able to keep their funding from the nonprofit wildlife organization in 5 years
Answer:
24,000(0.908) > 15,000; no
Step-by-step explanation:
Given f(x)= 3x-5 find f (x-2)
[tex]f(x-2)=3(x-2)-5=3x-6-5=3x-11[/tex]
Answer:
[tex] f ( x - 2 ) = 3 x - 1 1 [/tex]
Step-by-step explanation:
We are given the following function [tex] f ( x ) [/tex] and we are to find [tex] f ( x - 2 ) [/tex]:
To find [tex] f ( x - 2 ) [/tex], we would consider [tex] f ( x - 2 ) [/tex] as [tex] x [/tex] and substitute [tex] x - 2 [/tex] in place of [tex] x [/tex] so it would be:
[tex] f ( x - 2 ) = 3 ( x - 2 ) - 5 = 3 x - 6 - 5 = 3 x - 1 1 [/tex]
What is the solution to this equation?
5x + 9 - 3x = 18 + 15
Answer:x=12
Step-by-step explanation:
5x+9-3x=18+15
First of all, in the case of a equation that has one vatiable having one power ,you need to bring all the variable together in one side.
5x-3x=18+15-9
0r,2x=18+6
Or,2x=24
Or,x=24/2
Or,x=12
So it's the solution..
To solve the equation 5x + 9 - 3x = 18 + 15, you simplify both sides of the equation to get 2x + 9 = 33. Then, you isolate x by subtracting 9 from both sides to get 2x = 24, and further divide by 2 to get x = 12. Therefore, x = 12 is the solution.
Explanation:The question requires the solution for the equation 5x + 9 - 3x = 18 + 15. To start solving this, first simplify both sides of the equation. The left side simplifies to 5x - 3x + 9, which equals 2x + 9. The right side simplifies to 18 + 15, which equals 33.
So, 2x + 9 = 33. To isolate x, subtract 9 from both sides of the equation, and you'll get 2x = 24. Then divide both sides by 2, and you'll get x = 12.
This means that the solution to the equation 5x + 9 - 3x = 18 + 15 is x = 12.
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Match each pair of angle measures of a triangle with the remaining angle measure
119 degrees and 23 degrees
33 degrees
16 degrees and 10 degrees
BOOOO
65 degrees
20 degrees and 87 degrees
35 degrees
36 degrees and 51 degrees
62 degrees
Answer:
119, 23 - 38
16, 102 - 62
96, 51 - 33
28, 87 - 65
After matching each pair of angle with the remaining angle 1st pair - 38 degree-3rd option, 2nd pair - 62 degree -4th option,3rd pair - 65 degree- 2nd option,4th pair - 33 degree- 1st option
What is the angle sum property of a triangle ?According to Angle sum property of a triangle, the sum of all the interior angles is equal to 180 degree.
It is given the question that
Four pairs of Angles are given , these pairs belong to a triangle and it is been asked to determine the third angle
Let the third angle is x for all the options
1. 119 degrees and 23 degrees
119+23+ x = 180
x = 38 degrees
2. 16 degrees and 102 degrees
16+102+x = 180
x = 62 degree
3. 28 degrees and 87 degrees
28+87 +x = 180
x = 65 degree
4. 96 degrees and 51 degrees
96 + 51+x = 180
x = 33 degree
Therefore the match is as follows
1st pair - 38 degree-3rd option
2nd pair - 62 degree -4th option
3rd pair - 65 degree- 2nd option
4th pair - 33 degree- 1st option
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Find the greatest possible error for each measurement 4 1/2 oz
Answer:
0.05 oz
Step-by-step explanation:
Usually, the greatest number that is allowed for approximation, assuming that the number itself is obtained by approximation, is the greatest possible error of it.
It is usually half the place value of the last digit of the number.
Here we are given [tex]4\frac{1}{2}[/tex] oz which is equal to [tex]4.5[/tex] oz. The last digit is 5 which is at the tenth place (0.1) so the greatest possible error for this would be its half.
[tex]\frac{0.1}{2}[/tex] = 0.05 oz
What value of c makes x2 − 12x + c a perfect square trinomial?
Answer:
for value 36
c makes the perfect square
x2 - 12x +36
= x2 - 2*6x +6^2
= (x-6)^2 #
Answer: The required value of c is 36.
Step-by-step explanation: We are given to find the value of c so that the following expression becomes a perfect square trinomial :
[tex]E=x^2-12x+c~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the value of c, we proceed as follows :
[tex]E\\\\=x^2-12x+c\\\\=(x^2-2\times x\times6+6^2)+c-6^2\\\\=(x-6)^2+c-36.[/tex]
So, for E to be a perfect square trinomial, we must have
[tex]c-36=0\\\\\Righatrrow c=36.[/tex]
Thus, the required value of c is 36.
which of the following describes a simple event
A.spinning a 2 on a spinner
B.spinning a 3 on a spinner and rolling a 1 on a dice
C.getting heads on a coin toss and rolling a 5 on a die
D.drawing a queen from a deck of cards and getting a tail on a coin toss
Answer: c. getting heads on a coin toss and rolling a 5 on a die
Step-by-step explanation:
Given f(x) = 17-xwhat is the average rate of change in f(x) over the interval [1, 5]?
The average rate of change in f(x) over the interval [1, 5] is -1
Step-by-step explanation:Hi! Let me help you to understand this problem. Here we have the following function:
[tex]f(x) = 17-x[/tex]
We need to compute the Average Rate of Change (ARC) in [tex]f(x)[/tex] over the interval [tex][1, 5][/tex]. So what is the average rate of change of a function? In general, for a nonlinear graph whose slope changes at each point, the average rate of change between any two points [tex](x_{1},f(x_{1}) \ and \ (x_{2},f(x_{2})[/tex] is defined as the slope of that line through that two points. Here we have a linear function, so the average rate of change will be the slope of the line:
So:
[tex]ARC=m=-1[/tex]
This can also be calculated as:
[tex]ARC=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}} \\ \\ ARC=\frac{17-5-(17-1)}{5-1} \\ \\ ARC=-1[/tex]
Find the solution(s) to 7x - 42x = 0. Check all that apply.
Answer:
x=0
Step-by-step explanation:
7x - 42x = 0
Combine like terms
-35x = 0
Divide each side by -35
-35x/-35 = 0/-35
x = 0
Answer:
X=6
X=0
Step-by-step explanation:
On aP Ex
Which linear inequality is represented by the graph?
We must find the slope of the graph first, we can do this by finding two perfect points and inputting those points into the formula y2 - y1/x2 - x1
Perfect point #1: (0,1)
Perfect point #2: (2,5)
As mentioned above, input these numbers into our formula.
5-1 = 4
2 - 0 = 2
4/2 = 2
So, the slope of the graph is 2.
Now, we must find the y-intercept which can be found based on where the line intersects with the y-axis. As we can see, the line intersects at (0,1) therefore the y-intercept of the graph is 1.
We now form a linear equation:
y = 2x + 1
However, since this is linear equality graph we will replace the equal sign with an inequality symbol. The inequality symbol we can use is based on the direction of the shaded area. If shaded up, we use the "greater than symbol", if down then we use the "less than symbol".
The line also matters, if the line is dotted we use the normal inequality symbol, but if it is straight then we use one of the "equal to" inequality symbols.
As for our graph, we have a dotted line with the shaded area upwards. Therefore, we will be using the greater than symbol and not a "equal to" symbol.
So, our answer would be y > 2x + 1
The perimeter of a rectangular field is 26 yards. The length is 4 more yards than twice the width. Find the length and width of the field.
A. Length = 8 yards; Width = 4 yards
B. Length = 10 yards; Width = 3 yards
C. Length = 13 yards; Width = 9 yards
D. Length = 8.5 yards; Width = 4.5 yards
The formula for perimeter is P = 2length + 2width (P = 2L + 2W)
You know that the length is 4 more yards then twice the width. In equation form this would be:
length = 4 + 2w
Plug what you know into the perimeter formula:
26 = 2(4 + 2w) + 2w
First you must distribute the 2 to the numbers inside the parentheses, which would be 4 and 2w...
26 = (2 * 4) + (2 * 2w) + 2w
26 = 8 + 4w + 2w
Now you must combine like terms. This means that first numbers with the same variables (w) must be combined...
26 = 8 + 4w + 2w
4w + 2w = 6w
26 = 8 + 6w
Now bring 8 to the left side by subtracting 8 to both sides (what you do on one side you must do to the other). Since 8 is being added on the right side, subtraction (the opposite of addition) will cancel it out (make it zero) from the right side and bring it over to the left side.
26 - 8 = 8 - 8 + 6w
18 = 0 + 6w
18 = 6w
To isolate w divide 6 to both sides
18 / 6 = 6w / 6
w = 3
We know that the width is 3 ft
Now you must find the length. To do this plug 3 where you see w in the equation:
length = 4 + 2w
l = 4 + 2(3)
l = 4 + 6
l = 10
We know that length is 10 ft
Letter B. is the correct answer
Hope this helped!
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Rectangle with length labeled 24 feet and width labeled 14 feet.
What is the area of the rectangle?
76 ft2
168 ft2
38 ft2
336 ft2
Answer:
336 ft^2
Step-by-step explanation:
We are given the dimensions of a rectangle, length 24 feet and width 14 feet, and we are to find the area of this rectangle.
We know that the formula of area of rectangle is given by:
Area of a rectangle = l × w
Substituting the given values in the above formula to get:
Area of rectangle = 24 × 14 = 336 ft^2
Answer:
Area = 336 ft^2
Step-by-step explanation:
Given
Width of rectangle = w = 14 ft
Length of rectangle = l = 24 feet
The formula for finding the area of rectangle is:
Area = Length * width
It can also be denoted as:
A = l*w
Putting the given values of length and width, the area of given rectangle will be:
A = 24 ft * 14 ft
A = 336 ft^2
So, the area of given rectangle is 336 ft^2 ..