We have
tan(2x) = sin(2x) / cos(2x)
tan(2x) = (2 sin(x) cos(x)) / (2 cos²(x) - 1)
Recall that
sin²(x) + cos²(x) = 1
and since sin(x) is negative, it follows that
sin(x) = - √(1 - (2/3)²) = -√5/3
Then
tan(2x) = (2 (-√5/3) (2/3)) / (2 (2/3)² - 1) = 4√5
Use the given information to determine which lines if any are parallel state The postulate or theorem that justifies
Answer: 13 and 14
Step-by-step explanation: algbra
P(q) = 1/4
P(R) = 2/3
If Q and Rare independent events, find the P(Q and R).
Answer:
P(Q ∩ R) = 1/6
Step-by-step explanation:
Given:
P(Q) = 1/4P(R) = 2/3For independent events Q and R,
P(Q ∩ R) = P(Q)P(R)
Therefore,
P(Q ∩ R) = (1/4)(2/3)
= 2/12
= 1/6
Hello Please Find The Answer To This Question (easy)
The equation of the line that is perpendicular to y = -5/2 x + 1 and passing through (10, 3) will be y = 2/5 x + 1.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The equation of the perpendicular line will be given as
y = mx + c
The given equation is y = -5/2 x + 1.
The slope of the line is -5/2.
Then the product of the slope of the perpendicular lines is a negative one.
-5/2 × m = - 1
m = 2/5
Then the equation will be
y = 2/5 x + c
Then the equation is passing through (10, 3). Then we have
3 = 2/5 × 10 + c
3 = 2 + c
c = 1
Then the equation is y = 2/5 x + 1.
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[70 POINTS!] What is the volume of the pyramid? Explain your reasoning.
Volume of cuboid=abc
Volume of prism :-
Area of base×Heightab ×cabcSame volume i.e 39 units²
If a,b,c=a,b,c
HELP FOR BRAINLIESTTT WITH THE RIGHT ANSWERRR
Causation and Correlation
Answer:
the answer is the 3rd option!
Answer
The answer is definitely 3 :)
Suppose you invest $7500 at an annual interest rate of 4.2% compounded continuously. How much will you have in the account after 2 years? Round the solution to the nearest dollar.
$17,373
$8158
$8157
$17,372
Answer:
$ 8157
Step-by-step explanation:
7500 e^.042(2) = 8157.22 ~ 8157
PLEASE HELP!!!!! IMA DESPRATE!!!!!! ach side of a telescope lens can be described by the equation f(x) = x2/58, where x is the width of the lens and f(x) is half its thickness.
If the lens is 2.9 inches wide, what is the total thickness (rounded to the nearest hundredth)?
Since the lens is 2.9 inches wide, the total thickness of the lens is 0.29 in
To answer the question, we need to know what equations are.
What are equations?Equations are mathematical expressions which show the relationship between two variables.
The total thickness of the lensSince f(x) = x²/58 describes half the thickness of the lens where x = width of lens.
So, the total thickness of the lens is y = 2f(x)
= 2 × x²/58
= x²/29
Since x = 2.9 in, substituting x into the equation, y, we have
y = x²/29
y = (2.9)²/2
y = 8.41/29
y 0.29 in
So, the total thickness of the lens is 0.29 in
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Please explain what I got wrong and how it's supposed to be written
Answer:
x is greater than or equal to 16.
Step-by-step explanation:
Hi! It says atleast 80 points, so your sign should be flipped over to show that x+64 needs to be ATLEAST 80. Then they asked you to solve for x. To solve for x, you subtract 64 from each side to get x is greater than or equal to 80-64, otherwise known as 16.
The inequality is [tex]x +64 \ge 80[/tex]
It solves to [tex]x \ge 16[/tex]
She needs at least 16 more points.
=========================================================
Further Explanation:
"At least 80" means "80 or more"
In other words, the lowest grade she can get is 80
x = number of points she needs
x+64 = number of points she has, after adding on the earlier 64 points
The x+64 must be 80 or larger. So the inequality to set up is [tex]x+64 \ge 80[/tex]
You had the right idea, but need to flip the inequality sign.
To solve this inequality, you subtract 64 from both sides and you should end up with [tex]x \ge 16[/tex]
This says she needs at least more 16 points to go with the 64 points she already has.
Question 3. Gene and Dixie, husband and wife (ages 35 and 32), both work. They have an adjusted gross income of $95,000 in 2017, and they are filing a joint income tax return. Both have an employer-provided retirement plan at work. What is the maximum IRA contribution they can make? How much of that contribution is tax deductible?
The maximum IRA contribution for 2017 and 2018 was $5,500 and the amount is fully tax-deductible.
What is an IRA contribution?An individual retirement account (IRA) contribution is a tax-advantaged contribution that allows the taxpayer to save money for retirement.
Given the couple's adjusted gross income of $95,000 in 2017, the maximum IRA contribution is $5,500 fully tax-deductible.
IRA contributions fall into:
Traditional IRA (tax on withdrawals)Roth IRA (after-tax contributions).Thus, the maximum IRA contribution for 2017 and 2018 was $5,500 and the amount is fully tax-deductible.
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A number between 1 and O is multiplied by 1,000.
The answer has to be:
Answer:
1,000
Step-by-step explanation:
uhhhh haha
how many ml of curry powder are needed
Answer:
How many grams of curry powder are in 1 teaspoons? 2.13 grams of curry powder fit into one teaspoon. 2 teaspoons of curry = 4.26 grams of curry.
Hope this helps...
-6(-3 + x) = 6
solve for x please
-6(-3+x) = 6
-3+x = 6+6
-3+x=12
-3x=12
x=12^3
x=2
Which equation can be used to determine the value of x?
(3x + 18) = 93
All of these
(3x + 18) + 93 = 90
(3x + 18) + 93 = 180
None of these
Answer:
(3x + 18) + 93 = 180
23 + X
Step-by-step explanation:
(3x + 18) + 93 = 180, its supplymentery
180 - 93 = 87
87 - 18 = 69
3x = 69
69/3 = 23
23 = X
Answer:
Step-by-step explanation:
Remark
You have to assume nothing you should have to assume. You have to assume that 93 degrees on 3x + 18 sit on the same straight line. If it just looks that way, you are on shaky ground. You must be told. It's a good thing to keep in mind. Likely you'll get more questions like this. Just be aware you should not have to assume anything to make the problem work.
If the two angles both have one leg on what is marked as a straight line, then the sum of the two angles must = 180
Solution
The first one is not true. 3x + 18 is smaller than 90 degrees because 93 is more than 90 degrees. If A is true then the line is bent a bit.
B is not true. We just found one equation that doesn't work.
C is not true either. The result of trying to solve C will make x minus because 93>90 and 18 when subtracted makes 3x even more minus.
D is true
(3x + 18) + 93 = 180 Subtract 93 from both sides.
(3x + 18) + 93-93 = 180 - 93 Combine
(3x + 18) = 87 Remove the brackets
3x + 18 = 87 Subtract 18
3x+18-18 = 87-18
3x = 69 Divide by 3
3x/3 = 69/3
Answerx = 23
E is not true because D is true.
What is the general form of the equation of the line shown?
Y-2=0
y+2=0
X-2 = 0
Answer:Option A is correct.
y-2=0
Step-by-step explanation:
Option A is correct.
General form of the equation of the line: y-2 = 0
Step-by-step explanation:
The general form of the equation is given by:
y = mx +b where m is the slope and b is the y-intercept.
y-intercepts of the line is the value of y at the point where the line crosses the y-axis(i.e x= 0)
From the given figure;
we can see that the line crosses the y-axis at y =2 and also here the slope is , m= 0
therefore, by definition of y-intercepts
y-intercept (b) = 2
Therefore, the equation of line as shoen in figure is:
y = (0)x + 2
or
y = 2
y-2 = 0
Therefore, the general form of the equation line as shown in the figure is:
y-2 =0
What is the ratio for the volumes of two similar spheres, given that the ratio of their radii is 5:6?
Answer:
125 : 216
Step-by-step explanation:
Let the volumes of the spheres be V₁ and V₂ respectively.
Volume (Sphere radius = 5) :
V₁ = 4/3π(5)³V₁ = 4/3π x 125V₁ = 500/3πVolume (Sphere radius = 6) :
V₂ = 4/3π(6)³V₂ = 4/3π x 216V₂ = 864/3πTaking the ratio of V₁ and V₂ :
V₁/V₂500/3π x 3π/864500/864125 : 216Given ratio: [tex](\text{Radius of Sphere}_1 : \text{Radius of Sphere}_2) = (5 :6)[/tex]
Step-1) Multiply both sides of the ratio by x:
[tex]\implies (\text{Radius of Sphere}_1 : \text{Radius of Sphere}_2) = (5x :6x)[/tex]
[tex]\implies \text{Radius of Sphere}_1 = 5x;\ \text{Radius of Sphere}_2 = 6x[/tex]
Step-2) Substitute the radiuses of each sphere into the "Volume formula"
Volume of sphere₁ Volume of sphere₂
[tex]\implies \ \ \ \ \ \ \ \ \dfrac{4}{3} \pi r^{3} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \dfrac{4}{3} \pi r^{3}[/tex]
[tex]\implies \ \ \ \ \ \ \ \ \dfrac{4}{3} \pi (5x)^{3} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \dfrac{4}{3} \pi (6x)^{3}[/tex]
[tex]\implies \ \ \ \ \ \ \ \ \dfrac{4}{3} \pi (5x)(5x)(5x) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \dfrac{4}{3} \pi (6x)(6x)(6x)[/tex]
[tex]\implies \ \ \ \ \ \ \ \ \dfrac{4}{3} \pi (125x^{3} ) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4 \pi (2x)(6x)(6x)[/tex]
[tex]\implies \ \ \ \ \ \ \ \ \dfrac{500x^{3} }{3} \pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 288x^{3} \pi[/tex]
Step-3) Plug the volume of both spheres in ratio form:
The ratio for the volumes of the two spheres must be in the respective place of the ratio for the radiuses of the two similar spheres. Therefore,
Ratio form: [tex]\underline{(\small\text{Volume of sphere}_1 : \text{Volume of sphere}_2)}[/tex]
[tex]\implies \dfrac{500x^{3} }{3} \pi: 288x^{3} \pi[/tex]
Step-4) Simplify both sides of the ratio:
[tex]\implies \dfrac{500x^{3} }{3}: 288x^{3}[/tex]
[tex]\implies \dfrac{500 }{3}: 288[/tex]
[tex]\implies \dfrac{500 }{3}} \div{\dfrac{288}{1} } \implies \dfrac{500}{3} \times \dfrac{1}{288} \implies \dfrac{500}{864} \implies \boxed{\dfrac{125}{216}}[/tex]
Therefore, the ratio for the volumes of two similar spheres is 125 : 216.
Find the area of the parking space shown to the right
-18ft and 9 1/4 ft-
Answer:
166 1/2 or 166.5
Step-by-step explanation:
The formula for finding area is length*width. This can also just be written as A=l*w. Our area is still unknown, so it'll stay as A in this equation. Here, our length and width don't matter all that much, so we can input them where we please.
Now, we have the equation A=18*9 1/4
So, let's solve! 18*9 1/4 is equal to 166 1/2 or 166.5
With this, the area is equal to 166 1/2 or 166.5
At Sam's Club, a case of 16 boxes of macaroni and cheese can be purchased for $24.00. Which equation could be used to describe this situation?
A. x+16=24
B. x-16= 24
C. x/16=24
D. 16x=24
Thanks
Answer:
D
Step-by-step explanation:
16 times the # of boxes = $24.
You can solve this equation by doing 24/16=$1.5 per box
If one 1+1 to 2+2 is 8....... Then what the hell is this?
Answer:
it’s cross multiplication.
Step-by-step explanation:
I’m wondering if you had a teacher that was trying to explain this and even online I had a teacher who would explain something when nobody understood the topic.
1. 2 * 13 = 26
2. 10 * x = 10x
26 = 10x
Answer:
X=2.6
Step-by-step explanation:
This shows 'cross multiplying'
This is a 'short cut' method of finding the common denominator of two fractions in order to 'work' with them :
2/x = 10/13 <==== common denominator is 13x
so multiply the L side by 13/13 and the right side by x/x to get
26/13x = 10x / 13x Now with common denominator, you can solve.
Equate the numerators :
26 = 10x <====== there is your 'short cut' found by cross multiplying
x = 26/10 = 2.6
List all of the factors of the number 30
Look at circle B below. The circumference of the circle is approximately 157 units. Which best represents the area of circle B?
Answer:
area of circle B=1964 square unit
What is the area of a circle with a radius of 35 inches?
in²
(Use 3.14 for Pi.)
Answer:
[tex] \boxed{ \tt{Area \: \: of \: a \: circle = \pi \: {r}^{2} }}[/tex]
Plug the values and then solve :[tex] \longrightarrow \tt \: 3.14 \times 35^{2} [/tex]
[tex] \longrightarrow \tt \: 3846.5\: in ^{2} [/tex]
Our final answer is 3846.5 in ^2--------- HappY LearninG <3 --------
[tex]\rule{50}{1}\large\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]
What is the area of a circle with a radius of 35 inches?
[tex]\rule{50}{1}\large\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]
We're asked to find the area of a circle, which we can find using the following formula:-
[tex]\Large\textsf{$A=\pi r^2$}[/tex]
Where:-
A=area[tex]\pi[/tex] = pi [3.14...]r = radius (we're given that it's equal to 35 inches)Replace r with 35 and π with 3.14:-
[tex]\Large\text{$A=3.14\times35^2$}[/tex]
[tex]\bigstar[/tex] On simplification,
[tex]\Large\text{$A=3.14\times1,225$}[/tex]
[tex]\bigstar[/tex] On further simplification,
[tex]\Large\text{$A=3846,5 in^2$}[/tex]
Good luck with your studies! :-)[tex]\rule{50}{1}\smile\smile\smile\smile\smile\rule{50}{1}[/tex]
Giving brainliest please help
Answer:
[tex](x, \: y) --->\: (x - 3, \: \: y - 5)[/tex]
NEED HELP URGENTLY
Which equation would you use to find the distance between the two points? A. |2 - 4| B. |2 - (-4)| C. |-5 - 5| D. |2 + (-4)|
picture below.
Answer:
B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
I believe that's right
Use the coordinate grid below to draw a square the has one vertex in each quadrant, and has an area of 16 square units. Prove that your figure has the correct area using distance and area calculations.
PLEASE HELP AND NO LINKS!
The area of the cube using the distance formula is 16 square units and each side measure is 4 units.
What is a cube?It is defined as three-dimensional geometry that has six square faces and eight vertices.
We have a cube shown in the picture.
Area of the cube = 16 square units
Area of cube = side²
Side = √16 = 4 units
Each side of the cube = 4 units.
From the attached figure, we can see each side lies on each quadrant.
Using the distance formula, we can calculate the distance between two
points:
[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The area of the cube = 4×4 = 16 square units
Thus, the area of the cube using the distance formula is 16 square units and each side measure is 4 units.
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divide (6x^3 + 26x^2 + 16x - 24) / (x + 3)
Answer:
2(x+2)(3x-2)
Step-by-step explanation:
Hope I helped you
keith has a debt of $145.50 at the beginning of the summer. he wants to have at least 200 in the account at the end on the summer if he plans to save 75.50 each week what is the minimum number of weeks he’ll have to work in order to meet his goal?
Total amount he needs to save = 200 + 145.50 = 345.50
Number of weeks = total needed / weekly savings
345.50 / 75.50 = 4.57
He will need to work 5 weeks.
Translate the triangle.
Then enter the new coordinates.
Answer:
B'(-1,6)
C'(2,6)
Step-by-step explanation:
You just have to change the x by -2 and the y by +4 because we know that (3,4) turned to (1,8)
Hope this helped!
And 18 ounce box of raisins cause $2.88 a 24 ounce box of raisins cost $3.60 which one is the better deal
Answer:
the 24-ounce box
Step-by-step explanation:
18/2.88 = 6.25$
24/3.6 = 6.67$
GEOMETRY
I'm working on a project and im not quite sure what bullet points 1 & 2 are asking. Help would be appreciated by telling me what I have to do.
Answer:
Its like how much you multiply the original shape by, to the new one.
For example, if your new shape is double the size of the original shape, then the scale factor is 2, because you would multiply the original by 2, to get the size of the new.
However, if your new shape is half the size, then the scale factor is 1/2, as you multiply the original by half to get the new shape.
Hope this cleared things up, lmk down below if you any further questions.
Diego was trying to write (5^2)^4 with a single exponent and wrote (5^2)^4=5^2+^4=5^6. What should the answer be? Explain Diego's error in complete sentences and thoughts.
Answer:
5^8
Step-by-step explanation:
Diego added the exponents. This was an error. If he was simplifying
5^2 × 5^4, then he could add the exponents and get a correct answer. But his problem had a power raised to a power. In this case, you multiply the exponents to simplify.
(5^2)^4 means
5^2×5^2×5^2×5^2
which is
5×5×5×5×5×5×5×5
which is 5^8.
