Answer:
y = x - 9 + 3 +3.
Step-by-step explanation:
.
A cube shaped box has a side of length 10mm.What is the volume of the box?
Answer:
formula= l³
Step-by-step explanation:
length of the cube =10mm
volume = l³
= 10³
=10×10×10
ans =1000mm
Write as an algebraic expression five times the sum of a number and 4
Answer:
5(x+4)
Step-by-step explanation:
It's basically asking for the sum of a number and four to be multiplied by 5. Since the sum is made up of the unknown number and four, you'd put four and the unknown number in parenthesis while putting five on the outside, making it 5(x+4).
The angle,2Θ, lies in the third quadrant such that cos2Θ=-2/5. Determine an exact value for tanΘ . Show your work including any diagrams if you plan to use them. (3 marks)
Answer:
[tex]tan(\theta)=\frac{\sqrt{21}}{3}[/tex]
Step-by-step explanation:
1. Approach
One is given the following information:
[tex]cos(2\theta)=-\frac{2}{5}[/tex]
One can rewrite this as:
[tex]cos(2\theta)=-0.4[/tex]
Also note, the problem says that the angle ([tex]2\theta[/tex]) is found in the third quadrant.
Using the trigonometric identities ([tex]cos(2\theta)=2(cos^2(\theta))-1[/tex]) and ([tex]cos(2\theta)=1-2(sin^2(\theta))[/tex]) one can solve for the values of ([tex]cos(\theta)[/tex]) and ([tex]sin(\theta)[/tex]). After doing so one can use another trigonometric identity ([tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]). Substitute the given information into the ratio and simplify.
2. Solve for [tex](cos(\theta))[/tex]
Use the following identity to solve for ([tex]cos(\theta)[/tex]) when given the value ([tex]cos(2\theta)[/tex]).
[tex]cos(2\theta)=2(cos^2(\theta))-1[/tex]
Substitute the given information in and solve for ([tex]cos(\theta)[/tex]).
[tex]cos(2\theta)=2(cos^2(\theta))-1[/tex]
[tex]-0.4=2(cos^2(\theta))-1[/tex]
Inverse operations,
[tex]-0.4=2(cos^2(\theta))-1[/tex]
[tex]0.6=2(cos^2(\theta))[/tex]
[tex]0.3=cos^2(\theta)[/tex]
[tex]\sqrt{0.3}=cos(\theta)[/tex]
Since this angle is found in the third quadrant its value is actually:
[tex]cos(\theta)=-\sqrt{0.3}[/tex]
3. Solve for [tex](sin(\theta))[/tex]
Use the other identity to solve for the value of ([tex]sin(\theta)[/tex]) when given the value of ([tex]cos(2\theta)[/tex]).
[tex]cos(2\theta)=1-2(sin^2(\theta))[/tex]
Substitute the given information in and solve for ([tex]sin(\theta)[/tex]).
[tex]cos(2\theta)=1-2(sin^2(\theta))[/tex]
[tex]-0.4=1-2(sin^2(\theta))[/tex]
Inverse operations,
[tex]-0.4=1-2(sin^2(\theta))[/tex]
[tex]-1.4=-2(sin^2(\theta))[/tex]
[tex]0.7=sin^2(\theta)[/tex]
[tex]\sqrt{0.7}=sin(\theta)[/tex]
Since this angle is found in the third quadrant, its value is actually:
[tex]sin(\theta)=-\sqrt{0.7}[/tex]
4. Solve for [tex](tan(\theta))[/tex]
One can use the following identity to solve for [tex](tan(\theta))[/tex];
[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]
Substitute the values on just solved for and simplify,
[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]
[tex]tan(\theta)=\frac{-\sqrt{0.7}}{-\sqrt{0.3}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{0.7}}{\sqrt{0.3}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}}}{\sqrt{\frac{3}{10}}}[/tex]
Rationalize the denominator,
[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}}}{\sqrt{\frac{3}{10}}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}}}{\sqrt{\frac{3}{10}}}*\frac{\sqrt{\frac{3}{`0}}}{\sqrt{\frac{3}{10}}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}*\frac{3}{10}}}{\sqrt{\frac{3}{10}*\frac{3}{10}}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{\frac{21}{100}}}{\frac{3}{10}}[/tex]
[tex]tan(\theta)=\frac{\frac{\sqrt{21}}{10}}{\frac{3}{10}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{21}}{10}*\frac{10}{3}[/tex]
[tex]tan(\theta)=\frac{\sqrt{21}}{3}[/tex]
whats the simplest form of expression
Step-by-step explanation:
[tex] \frac{2b}{ \sqrt{ {b}^{20} } } \\ = \frac{2b}{ {b}^{10} } \\ = \frac{2}{ {b}^{9} } \\ thank \: you[/tex]
2/b^9
here's the answer to the question
If Caleb bought 1.2 pounds of cheese that was selling for 5.95 per pound. How much did Caleb pay for the cheese.
Answer:
$7.14
Step-by-step explanation:
If each pound of cheese is $5.95. You just have to find out how much 1.2 pounds is worth. So, you multiply 5.95 times 1.2 pounds and you'll get $7.14
Multiplication is the process of multiplying. The total amount that Caleb needs to make for 1.2 pounds of cheese at a rate of $5.95 per pound is $7.14.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
Given that the rate of cheese per pound is $5.95 per pound. Therefore, the amount that Caleb needs to make for 1.2 pounds of cheese is,
Total Amount = $5.95/pound × 1.2 pounds
= $7.14
hence, the total amount that Caleb needs to make for 1.2 pounds of cheese at a rate of $5.95 per pound is $7.14.
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I kinda need help with this
Answer:
x = 1
Step-by-step explanation:
f(x) = 3 or y = 3
Locate y = 3 on the y- axis , go horizontally across to meet the line at (1, 3 )
Then
When f(x) = 3 , x = 1
The sum of two integers with different signs is 8. Give two possible integers that fit this discretion
Answer:
Step-by-step explanation:
16 - 8 which will give 8. The 16 is plus, the 8 is minus. They do have different signs.
15 - 7 which gives 8. Same explanation.
108 - 100 = 8 Same method.
number 39 show work pls tysm
Answer:
42.25/6.5=6.5 per hour
Step-by-step explanation:
Hi! I'm happy to help!
To solve this, we need to divide the amount of money by the number of hours.
You earned $42.25, over the course of 6.5 hours.
42.25/6.5
6.5
So, you earned $6.50 per hour cleaning a community park.
I hope this was helpful, keep learning! :D
PLEASE HELPP MEEE I NEED THE ANDWER QUICKKK
20.00$ - a=8.45$
Answer:
a= 11.55
Step-by-step explanation:
If the answer is 8.45, then the variable equals the difference of 20 minus the answer, 8.45
Hope this helps!
If the divisor is 60, what is the least four-digit dividend that would not have a remainder?
Answer:
2400
which is not having any remainder as 2400÷60=40
Step-by-step explanation:
Answer for-159=-5(1-4n)+6
[tex]- 159 = - 5(1 - 4n) + 6 \\ - 159 = - 5 + 20n + 6 \\ - 159 = 1 + 20n \\ 20n = - 159 - 1 \\ 20n = - 160 \\ \\ n = \frac{ - 160}{20} = - \frac{16}{2} = - 8 \\ \\ n = - 8[/tex]
I hope I helped you^_^
If the mine winch drum diameter is 4,5m, calculate how far the counterweight will lift each single rotation of the drum, use formula C=2πr
Answer:
i have no idea that's why I need ur help
helpppp i don’t remember how to do algebra it’s been two years hahaha
barbara and jeff ate out for dinner the total came to &15.00. they left a 15% tip how much was the tip and the meal together?
Answer:
$17.25
Step-by-step explanation:
The tip is 15% of $15.00, or 0.15 * 15 = $2.25
We add that to the meal's cost, which is $15.00
15.00 + 2.25 = 17.25
what is the value of x in the equation 11+7x=-17
[tex]\\ \rm\Rrightarrow 11+7x=-17[/tex]
[tex]\\ \rm\Rrightarrow 7x=-7-11[/tex]
[tex]\\ \rm\Rrightarrow 7x=-28[/tex]
[tex]\\ \rm\Rrightarrow x=\dfrac{-28}{7}[/tex]
[tex]\\ \rm\Rrightarrow x=-4[/tex]
Answer: x = -4
Step-by-step explanation:
Given equation
11 + 7x = -17
Subtract 11 on both sides
11 + 7x - 11 = -17 - 11
7x = -28
Divide 7 on both sides
7x / 7 = -28 / 7
[tex]\boxed{x=-4}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
59 is 60% of what number
Answer:
duh. 98.33 yeah yeah yeah yeah yeah yeah
Joy drinks 4 bottles of water per day. Each bottle contains
16.5 fluid ounces. How many fluid ounces of water does
she drink per day?
a) 66 fluid ounces
b) 68 fluid ounces
c) 660 fluid ounces
d) 680 fluid ounces
Answer:
A) 66
Step-by-step explanation:
I have no explanation to this but hope it's help
Answer:
a) 66 fluid ounces
Step-by-step explanation:
it's easy
all you have to do is multiply the amount of bottles Joy drinks in a day (in this case 4) with the amount of fluid ounces contained in each bottle she's drinking (in this case 16.5)
so in other words
4 x 16.5 = 66
Write a variable expression for each of following situations. Use b to represent "a full box of pencils.
a. A full box of pencils with 3 extra pencils.
b. Three full boxs of pencils.
Answer:
a. b + 3 extra pencils
b. 3b
Hope that's correct
Six times a number increased by five is fifty-three. What is the number?
Answer:
8
Step-by-step explanation:
6x+5=53
6x=48
6x/6=48/6
x=8
HELP PLZ!Substitute the given values into the formula, and solve for the unknown variable.
A=bh; A = 60, h = 10 what is B
What is the greatest integer that satisfies $6 - x > -9$ ?
Hi :)
6 - x > -9
6 - 16 > -9
-10 > -9
What I did was substitued an integer for x that would just break even and then be more than -9.
What is the interest rate when you borrow $600 for 1 year and pay $45.00 interest?
Answer:
Im not certain but I think 7.5% If you get another answer which is different trust them not me if u get one which is the same it should be correct
The interest rate was 7.5% when borrowing $600 for one year and paying $45.00 interest.
What is the simple interest?Simple interest is defined as interest paid on the original principal and calculated with the following formula:
S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100.
We have been given data as:
Principal (P) = $600
Time (T) = 1 year
Simple interest = $45.00
⇒ Simple interest = P × R × T
Substitute the value of P, and T in the above formula, and solve for R
⇒ 45.00 = 600 × R × 1
⇒ 45.00 = 600R
⇒ R = 45.00/600
⇒ R = 0.075
⇒ R = 7.5/100
⇒ R = 7.5%
Therefore, the interest rate was 7.5%.
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Help help help help me pls !,!,!,
Answer:
96
Step-by-step explanation:
First, you find the area of RPQ using 1/2×base×height. That is, 1/2×6×8. And the answer is 24. Then you multiply 24 by 4 to get the area of all the sides excluding the base to get 96.
There are 8 cupcakes on a plate. Five children will share them equally. How many cupcakes will each child receive? Represent the scenario three ways:
With math vocabulary, as an expression, and as a fraction.
Answer:
Each child will receive eight fifths of the cupcakes.
5x=8 ; x represents how many cupcakes each child receives.
[tex]\frac{8}{5}[/tex]
Step-by-step explanation:
There are 8 cupcakes in total.
5 children.
Divide 8 by 5. [tex]\frac{8}{5}[/tex]
I hope this helps!
pls ❤ and mark brainliest pls!
what are the measures of other angles of parallelograms 56
[tex]\\ \rm\longmapsto A+D=180[/tex]
[tex]\\ \rm\longmapsto D=180-56=124[/tex]
<D=<B=124°[/tex]Write 81 in exponential form
Answer:
3 exponent 4
Step-by-step explanation:
[tex]\huge\text{Hey there!}[/tex]
[tex]\bullet\rm{\ Exponential\ form \ is \ basically \ a \ number \ that \ is \ expressed \ within \ the \ exponent.}[/tex]
[tex]\star\rm{\ Example: a^b, whereas\ \underline{a} \ is \ the \ \bold{base} \ \& \ \underline{b} \ is \ the \ \bf exponent}[/tex]
[tex]\huge\boxed{\square }\huge\textsf{ Answering your question }\huge\boxed{\square{}}[/tex]
[tex]\large\boxed{= 81}[/tex]
[tex]\large\boxed{= 3 \times3 \times 3 \times3}[/tex]
[tex]\large\boxed{= 9\times9}[/tex]
[tex]\large\boxed{= \bf 3^4}[/tex]
[tex]\huge\boxed{\mathsf{\rm Answer: \mathsf{3^4}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
factorize 6(a+1)²+4(a+1)
Answer:
[tex]2(a + 1) \times (3a + 5)[/tex]
Step-by-step explanation:
[tex]6(a + 1 {)}^{2} + 4(a + 1)[/tex]
➡️ [tex]2(a + 1) \times (3(a + 1) + 2)[/tex]
➡️ [tex]2(a + 1) \times (3a + 3 + 2)[/tex]
➡️ [tex]2(a + 1) \times (3a + 5)[/tex]
solve for variable (image attached)
Answer:
x = 2
Step-by-step explanation:
Given
[tex]\frac{3(6x+8)}{4}[/tex] = 15 ( multiply both sides by 4 to clear the fraction )
3(6x + 8) = 60 ( divide both sides by 3 )
6x + 8 = 20 ( subtract 8 from both sides )
6x = 12 ( divide both sides by 6 )
x = 2
The value of x in the equation is 2
The equation given :
3(6x + 8) / 4 = 15
Multiply both sides by 4
3(6x + 8) = 15 × 4
3(6x + 8) = 60
Open the bracket
18x + 24 = 60
18x = 60 - 24
18x = 36
x = 36/18
x = 2
The value of x in the equation is 2
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An article is sold for Rs 500 at 25% gain. If an article is sold for Rs.250. What is loss percentage?
Answer:
The loss percentage is 37.5%
Step-by-step explanation:
Cost Price = 500 × 100/125 = 400
New selling price = Rs. 250 ⇒ Loss = 400 – 250 = 150
Loss percentage = 100 × 150/400 = 37.5%.
Kim is making cookies. She is using a recipe that calls for 1/4 cup of lemon juice. She has a 6 fl oz. bottle of lemon juice. There are 8 fl oz. of lemon juice in 1 cup. How many batches of cookies can she make?
Answer:
3
Step-by-step explanation:
Answer:
Step-by-step explanation:
1 cup = 8 fl oz
x cup = 6 fl oz Cross multiply
6 oz * 1 cup = 8 oz x divide by 8
x = 6 oz /8 oz = 3/4 cup
If kim needs 1/4 cup per batch then she will have enough for 3 batches of 1/4 cup each.
