Answer:
A = 78.46
Step-by-step explanation:
55^2 = 50^2 + 35^2 − 2(50)(35)cos(A)
3025 = 2500 + 1225 - 3500 cos A
- 3500 Cos A = -3725 + 3025
-3500 cos A = -700
cos A = -700/-3500
= 0.2
A = cos^-1 0.2
A = 78.46
Answer:
A=78.46° (to 4sf)
Step-by-step explanation:
The only way to approach this problem is to solve the equation.
55²=50²+35²-2(50)(35)cos(A)
3025=2500+1225-3500cosA
3025=3725-3500cosA
Now collecting like terms together:
3025-3725=-3500cosA
-700=-3500cosA
CosA=0.2
A=78.46° (to 4sf)
Which value for x makes the sentence true? 1/50+x=1/10
Answer:
2/25 is the Answer, as a decimal it is 0.08
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
x + 1/50 = 1/10
Step 2: Subtract 1/50 from both sides.
x + 1/50 - 1/50 = 1/10 - 1/50
X = 2/25
Proof that it is the answer
0.02 + 0.08 = 0.1
0.02 is 1/50
0.08 is 2/25
0.1 is 1/10
Hope this helps!
[tex]\bold{Hey\ there!} \\ \bold{\frac{1}{50}+x=\frac{1}{10}}\\ \\ \bold{You\ have\ to\ simplify\ both\ sides\ of\ your\ equation\downarrow}\\ \bold{Like:x+\frac{1}{50}=\frac{1}{10}} \\ \\ \bold{Next,\ you\ have\ to\ \underline{SUBTRACT}\ by\ \frac{1}{50}\ on\ your\ sides} \\ \bold{x+\frac{1}{50}-\frac{1}{50}=\frac{1}{10}-\frac{1}{50}}\\ \\ \bold{Cancel:\frac{1}{50}-\frac{1}{50}because\ it\ equals\ to\0!} \\ \bold{Keep:\frac{1}{10}-\frac{1}{50}\ because\ it\ helps\ us\ solve\ for\ our\ answer!}[/tex]
[tex]\bold{\frac{1}{10}-\frac{1}{50}=\frac{2}{25}} \\ \\ \\ \\ \boxed{\boxed{\bold{Answer:x=\frac{2}{25}}}}\checkmark \\ \\ \\ \bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy\ your\ day!} \\ \\ \\ \frak{LoveYourselfFirst:)}[/tex]
a line passing through the origin intersects the point -8 -5 what is the slope of the line
To find the slope of a line passing through the origin and a point, use the formula slope = (y2 - y1)/(x2 - x1). For a line passing through origin and the point (-8,-5), the slope is 5/8.
Explanation:The topic at hand revolves around the concept of slope and the algebra of straight lines. The slope is calculated by finding the change in y (vertical axis) over the change in x (horizontal axis). To find the slope of a line passing through the origin and the point (-8,-5), use the formula slope = (y2 - y1)/(x2 - x1).
In this case, the origin is point (0,0) and the given point is (-8,-5). So to find the slope, we substitute these values into the slope formula: slope = (-5 - 0)/(-8 - 0) = 5/8. Therefore, the slope of the line passing through the origin and the point (-8,-5) is 5/8.
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The slope of the line is 5/8.
Explanation:The slope of a line, denoted by m, represents the rate of change between the vertical and horizontal components of two points on the line.
To find the slope of a line passing through the origin and intersecting the point (-8, -5), we can use the slope formula. The slope formula is given by: m = (y2 - y1) / (x2 - x1).
Plugging in the values from the given point gives: m = (-5 - 0) / (-8 - 0)
= -5 / -8
= 5/8.
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Find the volume of the figure: an oblique cylinder next to a cube.
Answer:
[tex](2,200\pi +8,000)\ ft^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the figure is equal to the volume of cube plus the volume of the cylinder
step 1
Find the volume of the cube
The volume of the cube is equal to
[tex]V=b^{3}[/tex]
we have
[tex]b=2(10)=20\ ft[/tex] ----> the length side of the cube is equal to the diameter of the cylinder
so
[tex]V=20^{3}=8,000\ ft^{3}[/tex]
step 2
Find the volume of the cylinder
The volume of the cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]r=10\ ft[/tex]
[tex]h=42-20=22\ ft[/tex]
substitute
[tex]V=\pi (10)^{2} (22)[/tex]
[tex]V=2,200\pi\ ft^{3}[/tex]
step 3
The volume of the figure is equal to
[tex](2,200\pi +8,000)\ ft^{3}[/tex]
The volume of the figure = volume of oblique cylinder + volume of cube = 2,200π + 8,000 cubic feet.
What is the Volume of an Oblique Cylinder?Volume of oblique cylinder = πr²h [radius of cylinder = r].
The volume of the figure = volume of oblique cylinder + volume of cube = πr²h + s³
Given the following:
s = 2(10) = 20 ftr = 10 fth = 42 - 20 = 22 ftPlug in the values into πr²h + s³:
The volume of the figure = π(10²)(22) + 20³
The volume of the figure = 2,200π + 8,000 cubic feet.
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HELP PLEASE SOMEONE PLEASE HELP ME?!!!!!!!!!!!!!!!!!!!!!!!!!!!1
Answer:false
Step-by-step explanation: divide each side by 7 you get b ≤ -7. The red line needs to go the other way since it is less than
Answer:
False, it is incorrect
Step-by-step explanation:
7b≤ -49
Divide by 7
7b/7 ≤-49/7
b ≤-7
We have a closed circle at -7 (closed because of the equals)
b is less than so the lines goes to the left
One month jenny rented 3 movies and 5 video games for a total of $40. The next month she rented 12 movies and 2 video games for a total of $43. Find the rental cost for each movie and each video game.
movies is 2.59 and videos is 5.944
//Hope this helps
The correct answer is $6.50 for each video game and $2.50 for each movie. My work:
3 x 2.50 = $7.50 and 5 x 6.50 = $32.50
32.50 + 7.50 = $40.00
12 x 2.50 = $30.00 and 2 x 6.50 = $13.00
30.00 + 13.00 = $43.00
Hope this helps.
A home appliance salesperson wants to earn a total of 3,600 next month including his base salary and commissions. He earns a base salary of $800 per month and earns 20% commission for all sales in that month. What is the value of the merchandise that the salesperson must sell to reach his goal?
Answer:
He must sell $14000 of merchandise
Step-by-step explanation:
The salesperson earns a base salary of $800
This means that he must make
$3600 - $800 = $2800 worth of commisions
Let x, be the value of the mechandise that he needs to sell.
This means that
x*0.20 = $2800
x = $2800/0.20
x = $14000
He must sell $14000 of merchandise
Is the point (-10, -34 ) on the line y=3x-4 Show how you know
Answer:
yes
Step-by-step explanation:
Substitute x = - 10 into the equation and if the value obtained equals - 34 then the point satisfies the equation and lies on the line
x = - 10 : y = (3 × - 10) - 4 = - 30 - 4 = - 34 ← agrees
Hence (- 10, - 34) lies on the line y = 3x - 4
I need the answer to this please
Answer:
~
Step-by-step explanation:
There isn't enough context information to solve the following problem.
59.4 scientific notation
Answer:
5.94x10^1
Step-by-step explanation:
In scientific notation all numbers are written in the form of m×10n (m times ten raised to the power of n), where the exponent n is an integer, and the coefficient m is any real number, called the significand or mantissa. If the number is negative then a minus sign precedes m (as in ordinary decimal notation).
(x^(2))/(9)+(y^(2))/(49)=1 The distance from the center to the major intercept is
Answer:
7
Step-by-step explanation:
This is an equation of an ellipse of the form:
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]
Where a and b are the minor and major intercepts, given a<b
In this question, a<b and a = 3 and b = 7
The distance from the center to the major intercept is b, thus the distance we are seeking for is 7
Answer:
b = 7 units.
Step-by-step explanation:
The given equation of the ellipse is
[tex]\frac{x^{2} }{9} +\frac{y^{2} }{49}=1[/tex]
As we know in an ellipse [tex]\frac{x^{2} }{a^{2} }+ \frac{y^{2} }{b^{2}}=1[/tex]
a will be major axis and b is the minor axis when ( a > b )
In the given equation 49 > 9 ⇒ b² > a²
so major axis will be = √49
= 7
Therefore, distance from center to the major intercept is b = 7 units.
Estimate 31,969 divided by 488. Round the numbers and the divide.
32,000 divided by 500 = 64
Answer: 32000/500= 64 approximately
Step-by-step explanation:
64 is the answer because 31969/488= 65.51
The amount of time t (in hours) that it takes to fill a swimming pool varies inversely with the pumping rate r(in kiloliters per hour). The constant of variation is 4. Find how long it will take to fill the pool when the pumping rate is 3.2 kL/hr
A.) 12.8 hrs
B.) 1.25 hrs - APEX
C.) 7.2 hrs
D.) 0.8 hrs
the answer to the problem is c
The answer is actually B) 1.25
Will mark BRAINLIEST!!!!
I think it's d but not sure
What are the real zeroes
You have to plug the values in the expression and see if it returns zero.
The only points where the function evaluates to zero are [tex] x=\pm 3[/tex] and [tex]x=6[/tex]
What exponential function represents the data in the table?
x f(x)
3 64
4 256
5 1024
Answer: [tex]f(x)=4^x[/tex]
Step-by-step explanation:
The general exponential function is given by :-
[tex]f(x)=Ab^x[/tex], where A is initial amount , b is multiplicative growth rate and x is time period.
Also, the multiplicative growth rate is the common ratio of the consecutive terms.
From the given table , [tex]b=\dfrac{256}{64}=4[/tex]
Substitute, x = 3 , f(x)=64 and b=4 , we get
[tex]64=A(4)^3\\\\\Rightarrow\ 64=A(64)\\\\\Rightarrow\ A=1[/tex]
Hence, the exponential function represents the data in the table is
[tex]f(x)=(1)(4)^x\\\\\Rightarrow\ f(x)=4^x[/tex]
The number a is smaller than the number b by 1/5 of b . By what part of a is b bigger than a?
Answer:
it is bigger by 1/5
Step-by-step explanation:
What is the value of x so that the line segment with endpoints W(x, −2) and X(5, −4) is parallel to the line segment with endpoints Y(2, 2) and Z(5, 6)?
x equals six start fraction one over two end fraction
x = 6
x equals three start fraction one over two end fraction
x = 7
Answer:
x equals six start fraction one over two end fraction
Step-by-step explanation:
Segments which are parallel have the same slope. Find the slope of of YZ. Then using that value, find the slope WX and solve for the value of x.
Slope of YZ is:
[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{6-2}{5-2} =\frac{4}{3}[/tex]
Since they are parallel, then WX has a slope of 4/3 too.
Slope of WX is:
[tex]m = \frac{y_2-y_1}{x_2-x_1}\\\\\frac{4}{3} = \frac{-4--2}{5-x}\\\\\frac{4}{3} =\frac{-2}{5-x}\\\\ (5-x)\frac{4}{3} = -2\\\\ 20 - 4x = -6\\\\-4x = -26 \\\\ x = 6 \frac{1}{2}[/tex]
What is the value of y in the product of powers below?
Answer:
y =0
Step-by-step explanation:
From the equation;
8³ × 8⁻⁵×8^y = 8⁻²= 1/8²
From the laws of indices;
aⁿ×aⁿ = a^2n
Therefore;
8³ × 8⁻⁵×8^y = 8^(3+-5+y)
8^(-2+y) = 8^-2 ; but the bases are the same and thus the exponents are the same;
-2 + y = -2
y = 0
Answer:
The value of y is 0
Step-by-step explanation:
8³ * 8^-5*8^y = 8^-2 or 1/8²
Taking indices of both sides
From first law of indices;
Multiplication sign change to addition; i.e. x^a * x^b = x^(a + b).
So,
8³ * 8^-5*8^y = 8^-2
Becomes
8^(3 + (-5) + y) = 8^-2
Same base of 8 can cancel one another. So, we're left with
3 + (-5) + y = -2
Open the bracket
3 - 5 + y = -2
-2 + y = -2
Make y the subject of formula
y = 2 - 2
y = 0
Hence, the value of y in the equation is 0
the sum of two numbers is 17. one number is 3 less than 2/3 of the other number. what is the lesser number?
the lesser number is 5.
steps:Let the first number = x
Let the second number = y
set up two equations
x + y = 17
2/3 x -3 = y
sub the second equation into the first one
x + 2/3 x - 3 = 17
collect like terms (1x = 3/3 x)
5/3 x - 3 = 17
add 3 to both sides
5/3 x = 20
multiply by 3 on both sides
5x = 60
divide by 5 on both sides
x = 12
sub back in one of the equations and solve to find the other number:
x + y = 17
12 + y = 17
y= 5
the lesser number is 5•have a good day• :) ~ ♡lipika♡
The lesser number is 5.
Let us consider that first number is x .
Since, second number is 3 less than 2/3 of the other number.
So that, second number [tex]=\frac{2}{3}x-3[/tex]
The sum of both number is 17.
[tex]x+\frac{2}{3}x-3=17\\\\\frac{5}{3}x=17+3\\\\\frac{5}{3}x=20\\\\x=20*\frac{3}{5}=12[/tex]
Lesser number is. [tex]=\frac{2}{3}x-3=\frac{2}{3}*12-3=5[/tex]
Hence, the lesser number is 5.
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Need help please !!!
Answer:
option C is the correct answer
Step-by-step explanation:
The trigonometric equation you are using has a general form
y = A* tan w*(x - r)
Where
A is the amplitude of the function
w is the frequency rad/s
r is the phase shift
In your case
A = -2
The frequency is
w = (2*pi)/period
period = pi/4
w = 8
r = -pi/2
y = -2* cos 8*(x + pi/2)
The graph shows the function f(x)=−12x+26 and g(x)=−(15)−x+2+3 .
What are the solutions of the equation −12x+26=−(15)−x+2+3 ?
Answer:
Step-by-step explanation:
-12x+x+26+15-2-3=0
-11x+36=0
-11x=-36
x=36/11
or x=3.2̅7̅
What is the value of -6.5 + (-2.5)-(-18)?
Answer:
9
Step-by-step explanation:
what is the height of a triangle with area 67.5 square meters and base 9 meters?
Answer:15
Step-by-step explanation:h=2 A/b meaning h=2 67.5/9
Answer:
h = 15 meters
Step-by-step explanation:
The area of a triangle is determined by its height multiplied by its base.
The equation is A = 1/2*bh.
Plugging in the numbers gives us 67.5 = 1/2*9h.
Dividing by 4.5 in both sides gives us that h = 67.5/4.5 = 15 meters.
Express the area of a rectangle with length 4x^34x
3
4, x, start superscript, 3, end superscript and width 555 as a monomial.
The awnser is 20 x 3
Hope this helps!
The area of a rectangle with length 4x^3 and width 5 is expressed as the monomial 20x^3 by multiplying the length and width.
To express the area of a rectangle as a monomial when given the length and width, we simply need to multiply these two dimensions together. In this case, the rectangle has a length of 4x^3 and a width of 5. The area (A) of a rectangle is given by the formula A = length * width.
So, the area of this rectangle can be calculated as:
A = 4x^3 * 5
Now, we multiply the numerical coefficients (4 and 5) and then combine them with the variable part:
A = (4 * 5) x^3
A = 20x^3
This expression, 20x^3, represents the area of the rectangle as a monomial
Order from greatest to least : 2/3,66%,0.67
2/3 is 0.6 repeating
66% is just 66%
same with 0.67
order is 0..67, 2/3, then 66%. i am the stupid.
% = decimal number
Answer:
0.67, 2/3, 66%
Step-by-step explanation:
2/3 decimal is 0.66666666667
66% decimal is 0.66
and 0.67 is 0.67
Hope this helped! Please mark as brainliest! Thanks!
Help in this question please, please
Answer:
28 and a=lenth times width
Step-by-step
mutiply 7 time 4 and it is 28
the volume of a cylinder is 1,356.48^ feet. If the diameter is 12 feet, calculate the height of the cylinder.
Answer:
11.99 ft
Step-by-step explanation:
The formula for the volume of a cyl. of radius r and height h is V = πr²h.
Solving this immediately for h yields:
V
h = ----------
πr²
Inserting the known quantities results in:
V 1356.48 ft³
h = ---------- = ---------------------- Note that r = (1/2)d, so r = (1/2)(12 ft) = 6 ft
πr² 3.14159 (6 ft)²
= 11.994 ft
The height of the cyl. is 11.99 ft (to the nearest hundredth foot)
Final answer:
To find the height of the cylinder with a volume of 1,356.48 cubic feet and a diameter of 12 feet, divide the volume by the area of the base (calculated with a radius of 6 feet) to get approximately 11.99 feet.
Explanation:
To calculate the height of a cylinder when the volume and diameter are given, we use the formula for the volume of a cylinder, V = πr²h, where V is the volume, r is the radius, and h is the height. In this case, we have a volume of 1,356.48 cubic feet and a diameter of 12 feet, meaning the radius is 6 feet (half of the diameter). So we can plug these values into our formula to solve for h.
First, calculate the area of the base (πr²): 3.14159 × (6 feet)² = 3.14159 × 36 = 113.0976 square feet. Then we divide the given volume by this area to find the height: 1,356.48 cubic feet / 113.0976 square feet = 11.99 feet. Therefore, the final answer for the height of the cylinder is approximately 11.99 feet.
At an elementary school there are two fenced in areas on the playground. The small play area is
1
4
the area of the large play area. The total square footage of the two areas is 2000 ft2. What is the size of the small play area?
A) 200 ft2
B) 400 ft2
C) 800 ft2
D) 1600 ft2
Well, this is just a big guess, but probably the most sense-able, B) 400 ft²
Sarah Wood and her husband have agreed to purchase a house for $87,500.00. Washington Savings and Loan is willing to finance the purchase but requires a $5,000.00 down payment and closing costs of 3 percent of the amount of the mortgage loan. What are the total closing costs?
The mortgage loan amount is $82,500. The closing costs are 3 percent of the loan amount. Therefore, the total closing costs are $2,475.
Explanation:Sarah Wood and her husband are purchasing a house for $87,500.00, but they are making a down payment of $5,000.00. Therefore, the mortgage loan amount is $87,500 - $5,000 = $82,500. The closing cost for this mortgage loan is 3 percent of the loan amount. Thus, to calculate the total closing costs, we multiply the loan amount by 3%. Therefore, total closing costs are $82,500 * 0.03 = $2,475.00.
So, total closing costs are $2,475.00.
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The total closing costs are $2,475.00.
Explanation:To calculate the total closing costs, we need to find 3 percent of the mortgage loan amount.
First, calculate the mortgage loan amount by subtracting the down payment from the house price: $87,500.00 - $5,000.00 = $82,500.00.
Then, find 3 percent of $82,500.00 by multiplying it by -
0.03: $82,500.00 * 0.03
= $2,475.00.
So, the total closing costs are $2,475.00.
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8 If f(x) = x3, which of the following describes the graph of f(x + 2)? A. The graph of f(x + 2) is a horizontal shift of f(x) = x3 two units to the right. B. The graph of f(x + 2) is a vertical shift of f(x) = x3 two units up. C. The graph of f(x + 2) is a horizontal shift of f(x) = x3 two units to the left. D. The graph of f(x + 2) is a vertical shift of f(x) = x3 two units down.
Answer:
C
Step-by-step explanation:
In translating graphs of functions, we can follow 2 rules:
1. The graph of [tex]f(x)+a[/tex] is the graph of [tex]f(x)[/tex] shifted a units UP VERTICALLY and the graph of [tex]f(x)-a[/tex] is the graph of [tex]f(x)[/tex] shifted a units DOWN VERTICALLY.
2. The graph of [tex]f(x+a)[/tex] is the graph of [tex]f(x)[/tex] shifted a units to the LEFT HORIZONTALLY and the graph of [tex]f(x-a)[/tex] is the graph of [tex]f(x)[/tex] shifted a units RIGHT HORIZONTALLY.
If we understand the 2 rules above, we clearly know that f(x+2) will be a horizontal shift to the LEFT, of course, with respect to the function [tex]f(x)=x^3[/tex]. Looking at the answer choices, C is right.