Answer: 83 degrees
Step-by-step explanation:
In order to find theta, you must take the arccosine of both sides. The arccosine eliminates the cosine, and extracts the argument. Therefore:
[tex]cos(x)=\frac{2}{16} =\frac{1}{8}[/tex]
[tex]arccos(cos(x))=arccos(\frac{1}{8} )=x[/tex]
Use a calculator the find the arccosine of 1/8. Its nearly impossible to find the exact answer without one:
[tex]x=arccos(\frac{1}{8} )[/tex]
[tex]x=83[/tex]
Evaluate each expression.
The temperature during a winter day was less than –3 degrees Fahrenheit. Yuri wants to write an inequality for the temperature during the winter day. Yuri uses the variable t to represent the temperature. Which expression should Yuri write?
t greater-than negative 3
t greater-than 3
t less-than negative 3
t less-than 3
Answer:
The answer is t < -3
Step-by-step explanation:
t < -3 is the answer, because since the temperature is less than -3 degrees Fahrenheit it has to be t < -3
Complete the square to transform the expression x2 6x 5 into the form a(x − h)2 k. (x 6)2 4 (x 6)2 − 4 (x 3)2 − 4 (x 3)2 4
An equation is formed of two equal expressions. The equation x²+6x+5 into the form a(x − h)²+k is written as (x+3)²-4.
What is an equation?
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The transformation of the equation from x²+6x+5 into the form a(x − h)²+k can be done in the following steps as shown below,
1. Taking +5 on the right-hand side of the equation,
[tex]x^2+6x+5 = 0\\\\x^2+6x = -5[/tex]
2. Now if we add +9 on both sides of the equation, we will get,
[tex]x^2+6x = -5\\\\x^2+6x+9 = -5+9[/tex]
3. Now we look at the left side of the equation as the square of the binomial expression (x+3).
[tex]x^2+6x+9 = -5+9\\\\(x+3)^2 =4[/tex]
4. Taking +4 from the right side of the equation to the left side of the equation,
[tex](x+3)^2 =4\\\\(x+3)^2 -4=0[/tex]
Thus, the equation is in the form of a(x − h)²+k, where the value of a is 1, h is -3 and the value of k is -4.
Hence, the equation x²+6x+5 into the form a(x − h)²+k is written as (x+3)²-4.
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Find the area. Please help me with this problem:)
Answer:
132 square feet
Step-by-step explanation:
If you need an explanation, just ask.
Hope this helps! Pls give brainliest!
what is the height of the prism?
Answer:
option 1
Step-by-step explanation:
[tex]x - 3 + \frac{7 x- 9}{ {x}^{2} - 2 } [/tex]
your required answer
Help?? It's for calc.
Answer:
the answer is 1.258
Answer:
1.258
Step-by-step explanation:
The population of a town decreased by 2.5% each year. The variable y gives the population
after x years.
Answer: I assume you want an equation so thats what ill do.
y = x(0.975)
Chloe is installing new windows in her house and needs to determine the amount of sealant she will need around the outside edge of each rectangular window. Each of the windows has an area of 2,160 Inches squared with a length of 60 inches. What is the perimeter of each window?
To find the width of each window, use the formula w = StartFraction A Over l EndFraction, where w represents the width, A represents the area, and l represents the length. To find the perimeter, use the formula P = 2 l + 2 w, where P represents the perimeter, l represents the length, and w represents the width.
Answer:
240
Step-by-step explanation:
because each side is 60 inches so do 60x4 and you get 240
Answer:
Option D!
Step-by-step explanation:
Hope this helps.
The volume of a cone is 400π cm3. The height of the cone is 12 cm.
What is the length of the radius of the cone?
Answer:
10 cmStep-by-step explanation:
The volume of cone formula:
V = 1/3πr²hSubstitute te given values into the formula and solve for r:
400π = 1/3πr²(12)100 = r²r = √100r = 10Answer:
10 cm
Step-by-step explanation:
Volume of a cone
[tex]\sf V= \dfrac{1}{3} \pi r^2 h[/tex]
where:
V = volumer = radiush = heightGiven information:
V = 400π cm³h = 12 cmTo find the length of the radius, substitute the given values into the formula and solve for r:
[tex]\begin{aligned}\sf V& = \sf \dfrac{1}{3} \pi r^2 h\\\\\implies \sf 400 \pi & = \sf \dfrac{1}{3} \pi r^2(12)\\\\ \sf 400 \pi & = \sf \dfrac{12}{3} \pi r^2\\\\ \sf 400 \pi & = \sf 4\pi r^2\\\\ \sf \dfrac{400 \pi}{4 \pi} & = \sf r^2\\\\ \sf r^2 & = \sf 100 \\\\ \sf \sqrt{r^2} & = \sf \sqrt{100}\\\\ \sf r & = \sf 10\end{aligned}[/tex]
Therefore, the length of the radius of the cone is 10 cm.
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robert gets a loan from his bank.
he agrees to borrow £6000 at a fixed annual simple interest rate of 7%
he also agrees to pay the loan back over a 10-year-period.
how much money in total will ha have paid back at the end of the 10 years?
Answer:
£10200
Step-by-step explanation:
Amount borrowed (P) = £6000
Rate of interest (R) = 7%
Time (T) = 10 years
First, let us calculate the simple interest (SI) for 10 years.
Formula for simple interest is given as:
[tex]S.I.=\frac{PRT}{100}[/tex]
Plugging the values of P, R and T in the above formula, we find:
[tex]S.I.=\frac{6000(7)(10)}{100}[/tex]
S.I.= £4200
Total money paid back at the end of the 10 years
= £6000 + £4200
= £10200
Find the missing value to the nearest hundredth.
Answer:
24.62°
Step-by-step explanation:
sin^-1 (5/12)
=24.62
Answer:
24.62°
Step-by-step explanation:
sin^-1(5÷12) = 24.62°
(if you are allowed to use calculator)
Select TRUE or FALSE for each of the statements below.
In hanger A, 2x + 5 = 16
In hanger B, y = 2400
In hanger C, 4z = 20.8 -4.4
in hanger D, w + 2/3 = 20/3 ÷ 2
Answer:
1 true
2 false
3 true
4 false
Step-by-step explanation:
Two negative integers are 8 units apart on the number line and have a product of 308.
Which equation could be used to determine x, the smaller negative integer?
x2 + 8x – 308 = 0
x2 – 8x + 308 = 0
x2 + 8x + 308 = 0
x2 − 8x − 308 = 0
Answer:
X²-8x+308
Step-by-step explanation:
two negative integers -x and -x= +x²
8units apart=-8x
all equals 308
X²-8x=308
bring everything to the LHS
X²-8x-308=0
Given the function f(x) = 0. 5|x – 4| – 3, for what values of x is f(x) = 7? x = –24, x = 16 x = –16, x = 24 x = –1, x = 9 x = 1, x = –9.
If the value of the function f(x) is 7, then the value of x is –16, and 24. Then the correct option is B.
What is a function?The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
The given function is f(x) = 0.5 |x – 4| – 3
If the value of the function f(x) is 7, then the value of x will be
0.5 |x – 4| – 3 = 7
0.5 |x – 4| = 10
|x – 4| = 20
x – 4 = ±20
For positive signs, we have
x – 4 = 20
x = 24
For negative signs, we have
x – 4 = –20
x = –16
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Which of the following statements about check-cashing companies is FALSE?
Answer:
there are no statements...
What causes a quadratic formula to have negative roots?
Answer:
When a, b, and c are real numbers, a ≠ 0 and the discriminant is negative, then the roots α and β of the quadratic equation ax2 + bx + c = 0 are unequal and not real. In this case, we say that the roots are imaginary.
If a ≠ 0 and the discriminant is negative, then the roots α and β of the quadratic equation ax² + bx + c = 0 are unequal and not real.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Discriminant is √[tex]\sqrt{b^2- 4ac }[/tex]
a ≠ 0 and the discriminant is negative, then the roots α and β of the quadratic equation ax² + bx + c = 0 are unequal and not real.
In this case, we say that the roots are imaginary.
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Amira decides to estimate the volume of an apple by modeling it as a sphere. She measures its circumference as 43.4 cm. Find the apples's volume in cubic centimeters. Round your answer to the nearest tenth if necessary.
The formula for the circumference of a circle (or a sphere) is [tex]2\pi r\\[/tex].
The formula the volume of a sphere is [tex]\frac{4}{3}\pi r^3[/tex].
Assuming 43.4 includes the pi, we can do the equation [tex]43.4=2\pi r[/tex]
Solving the equation, we get [tex]\frac{43.4}{2\pi } =r[/tex]
Substituting r into the formua for the volume of a sphere, we get [tex]\frac{4}{3} *\pi *(\frac{43.4}{2\pi } )^3[/tex]
Solving the cube (probably with a calculator), we get [tex]\frac{4}{3} *\pi *\frac{81746.504}{8\pi ^3}[/tex]
It is a bit messy, but we can simplify further by cancelling out the pi's, which leaves us with [tex]\frac{4}{3} *\frac{81746.504}{8\pi ^2}[/tex].
With the butterfly method (or whatever you may call it), we can cancel out the 4 in the numerator and the 8 in the denominator, and multiply the 3 in the denominators.
Which gets us this: [tex]\frac{81746.504}{6\pi ^2}[/tex]
Using a calculator, we get our final answer of (about) 1380.44cm^3
This was very messy, I apologize if I did make any mistakes.
When moving. it can often be a questionable matter to decide among moving luck companies. u haut currently charges $19.95 per day for a 10' moving truck and $0.59 per mie. imagine that another company you- haul, moves into the market anchoffes the same 10 truck for $70 per day. assume a one-day rental takes place. using systems of linear equations, anden what mileage conditions would it make make sense to choose one company over the other? o a mileage = 50.05 o b. mileage = 50 oc. mileage = 84.83 ос o d. mileage = 70 o e. mileage = 84.03 = .
Answer:
Try to multiple 0.59x to $70, divide $19,95 to whatever answer u got from 0.59 to $70 then add 84.83334 and then there's your answer
Step-by-step explanation:
Done this and got right
How many times more sunscreen is in Bottle B than in Bottle A? Provide
your answer using a decimal.
Using the volume of the rectangular prisms, it is found that there is 1.5 times more sunscreen in Bottle B than in Bottle A.
What is the volume of a rectangular prism?The volume of a rectangular prism of dimensions l, w and h is given by:
V = lwh.
For bottle A, we have that, in inches, l = 1, w = 2, h = 6, hence the volume in cubic inches is given by:
Va = 1 x 2 x 6 = 12 in³.
For bottle B, we have that, in inches, l = 1.5, w = 3, h = 4, hence the volume in cubic inches is given by:
Vb = 1.5 x 3 x 4 = 18 in³.
The ratio between the volumes is given by:
r = Vb/Va = 18/12 = 1.5.
Hence, there is 1.5 times more sunscreen in Bottle B than in Bottle A.
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Ramer and knox began a partnership by investing $64,000 and $94,000, respectively. the partners agreed to share net income and loss by giving annual salary allowances of $52,000 to ramer and $41,600 to knox, 10% interest allowances on their investments, and any remaining balance shared equally. (enter all allowances as positive values. enter losses as negative values.) required: 1. determine each partner's share given a first-year net income of $102,800. 2. determine each partner's share given a first-year net loss of $20,800.
Each partner's share given a first-year net income of $102,800 is $-3,300.
Each partner's share given a first-year net loss of $20,800 is $-44,300.
What is each partner's share?Partner' share = net income / loss - interest - salary salary allowance
Interest = ($64000 x 10%) + ($94000x 10%) = $15,800
Salary = $52,000 + $41,600 = $93,600
Share of net income = [$102,800 - (15,800 + 93600)] / 2 = $-3,300
Share of net loss = [-20,800 - (15,800 + 93600)] / 2 = $-44,300
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A cylinder is a radius of 10 inches and a height of 6 inches. About what is it's volume in cubic inches? Use 3.14 for pie
Answer:
1884
Step-by-step explanation:
square the 10 which is 100 and multiply 6 which is 600 and then multiply 600*3.14 which is 1884
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The mass of an ant is 5 x 10-3 grams. The mass of a bee is 1 x 10-¹ grams. Based on this information, how many ants equal the mass of a bee?
20 ants equals to mass of the bee if the mass of an ant is 5 x 10-3 grams and the mass of a bee is 1 x 10-¹ grams.
Ratio and proportionGIven the following parameters from the question
Mass of an ant = 5 x 10⁻³ grams
Mass of the bee = 1 * 10⁻¹ grams
Find the ratio of both masses
Ratio = 1 x10⁻¹ /5 x 10⁻³/
Ratin = 0.1/0.005
Ratio = 20
This shows that 20 ants equals to mass of the bee
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I need helppppppppppppppppppp
Answer:
See explanation
Step-by-step explanation:
look at the photo
I hope it will help you <3
Answer:
Step-by-step explanation:
*The other person that answered may be correct, but this was my way of solving the functions.
A and B are complementary. If B = 26°, what is the measure of A?
26°
154°
64°
74°
Answer:
64°
Step-by-step explanation:
When angles are complementary, they can be added together to equal 90°.
90° - 26° = 64°
The measure of angle A is 64°.
what is the surface area and volume of this figure? urgent!
Answer:
V=4960in^3
S.A=2116in^2
Step-by-step explanation:
36x2
1- 72in^2
5-2=3in
8x3
2- =24in^2
5-2=3in
5+3=8in
8x10
3- =80in^2
36-(10+8)=
0.5×18×8
4-=72in^2
72+24+80+721
C.S.A=248in^2
V= 248×20
=4960in^3
248x2
1- =496in^2
36x20
2- =720in^2
20×2
3- =40in^2
20×5
4- =100in^2
20×8
5- =160in^2
20×20
6- =400in^2
20×10
7- =200in^2
=496+720+40+100+160+400+200
=2116in^2
bob rented a truck for one day.there was a base fee of $14.75, and there was an additional charge of 25 cents for each mile driven. the total cost, C (in dollars), for driving x miles is given by the following function. C(x)=0.25x+14.75 what is the total rental cost if bob drove 40 miles
C(x)=0.25x+14.75
=C(40)=0.25x+14.75
=40c=0.25(40) + 14.75
=40c=10+14.75
=40c=24.75
how to solve 3x - y = -1 and -3x - y= 5
I use 1/12 of my salary to pay for rates and taxes,1/16 to pay for insurance and 5/6 to meet other expenses. if i have r320 left of my monthly salary, calculate my yearly salary.
The yearly salary after paying for taxes, insurances and other expenses is r808.42.
What is the yearly salary?The first step is to determine the total fraction used to pay for taxes, insurances and other expenses:
1/2 + 1/16 + 5/6
(48 + 6 + 80) / 96 = 134 / 96= 1 19/48
Now subtract 1 19/48 from 1
1 19/48 - 1 = 19/48
Finally, divide 19/48 by 320
320 x 48/19 = r808.42
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What is the coordinate of the midpoint of AB?
Answer:
(5,4)
Step-by-step explanation:
that is directly between the two points
Shana spends $18 on some almonds. She pays for the almonds with two $10 bills. How much change does Shana get back? Enter your answer in the box. $
Answer:
$2
Step-by-step explanation:
2($10)=$20
$20-$18=$2