Concept is trigonometry. The tangent of 30° is √3.
Explanation:To find the tangent of 30°, we can use a special right triangle. One type of special right triangle is a 30-60-90 triangle. In this triangle, the ratio of the lengths of the sides opposite the angles are 1:√3:2.
Since we want to find the tangent of 30°, which is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle, we can set up the equation:
tan 30° = opposite/adjacent = (√3)/1 = √3
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Simplify completely 6x-12/10
Answer: =6x+ −6/5
Step-by-step explanation:
Let's simplify step-by-step.
6x−12/10 =?
= 6x + −6/5
* Hopefully this helps:) Mark me the brainliest:) For a better a understanding I included the picture of what I exactly mean incase you didn't understand the work that I showed you :)
For this case we must simplify the following expression:
[tex]6x- \frac {12} {10}[/tex]
If we divide the numerator and denominator between "2", then we can rewrite the fraction as:
[tex]\frac {12} {10} = \frac {6} {5}[/tex]
So, we have:
[tex]6x- \frac {6} {5}[/tex]
Answer:
[tex]6x- \frac {6} {5}[/tex]
Solve the system of equations. y = -5x - 8 y = 4x + 1 a. ( 1, -3) c. ( 3, 1) b. ( -1, -3) d. No solution
Answer:
(-1,-3)
Step-by-step explanation:
The given system of equations is;
[tex]y=-5x-8...(1)[/tex]
and
[tex]y=4x+1...(2)[/tex]
Let us equate the two equations to get;
[tex]4x+1=-5x-8[/tex]
Group similar terms;
[tex]4x+5x=-8-1[/tex]
Simplify;
[tex]9x=-9[/tex]
Divide both sides by 9.
[tex]x=-1[/tex]
Put x=-1, into any of the equations, say (2);
[tex]y=4(-1)+1[/tex]
[tex]y=-4+1[/tex]
[tex]y=-3[/tex]
The solution is;
(-1,-3)
The house shown is a composite of more than one shape. Which of these methods would you use to find the volume of the house?
Answer:
find the area on one shape and the area of the other and add the shapes areas to get your answer
Step-by-step explanation:
Answer: Add the volume of a rectangular prism to the volume of a triangular prism.
Step-by-step explanation:
A. Find the volume of a pyramid.
Neither of the shapes shown are a pyramid and there should be two shapes added together.
B. Find the volume of a rectangular prism.
There should be two shapes being added together, however this is one of the shapes shown.
C. Add the volume of a rectangular prism to the volume of a triangular prism.
This is the answer because the bottom shape of the house is a rectangular prism since there are six faces all with four sides. The top shape is a triangular prism because two of the faces are triangles and the other three are rectangles. This shape would not be a pyramid because in order for it to be categorized that way it would need at least four triangular faces that connect at a point.
D. Add the volume of a rectangular prism and a pyramid.
The triangular prism is shown, however the shape used to represent the roof of the house would be classified as a rectangular prism.
Solve for x. Use the completing square method. x^2+8x=7
Answer:
√23 - 4 , -√23 - 4
Step-by-step explanation:
By completing the square
half of 8 is 4
7+4^2= 23
(x+4)^2=23
Answer:
√23 - 4 , -√23 - 4
Step-by-step explanation:
William is drafting his fantasy basketball team. He needs to select one player for each position. The following table shows how many players are available for each position.
Position Number of players
Point guard 101010
Shooting guard 121212
Small forward 777
Power forward 222
Center 999
How many different teams could William draft?
Answer: 15120
Step-by-step explanation:
10×12×7×2×9=15120
Answer: 15120
Step-by-step explanation:
Given: The number of players at point guard = 10
The number of players at shooting guard = 12
The number of players at small forward = 7
The number of players at power forward = 2
The number of players at center = 9
Then, the number of different teams William could draft is given by :-
[tex]10*12*7*2*9=15120[/tex]
Hence, William could draft 15120 different teams.
If sin A = 0.31, cos A = 0.95, sin B = 0.47, and cos B 0.88, what is sin(A+B)?
Answer:
option B
0.72
Step-by-step explanation:
Given in the question,
sin A = 0.31
cos A = 0.95
sin B = 0.47
cos B = 0.88
To solve sin(A+B) we will use trigonometry identities
Compound-angle formulae
sin(A + B) = sin A cos B + cos A sin BPlug values in above formula
(0.31) (0.88)+ (0.95) (0.47)
0.2728 + 0.4465
0.7193
≈ 0.72
Answer:
0.72
Step-by-step explanation:
Use the sum formula for the sine function:
sin (A + B) = sin A cos B + cos A sin B
Insert the givens into the above formula:
sin (A + B) = (0.31)(0.88) + (0.95)(0.47)
= 0.7193, or approx 0.72
a circle with radius of 2cm sits inside a 7cm x 11cm rectangle. what is the area of the shaded region ?
Answer:
The area of the shaded region is [tex](77-4\pi)\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of the shaded region is equal to the area of the rectangle minus the area of the circle
step 1
Find the area of the rectangle
[tex]A=(7)(11)=77\ cm^{2}[/tex]
step 2
Fin the area of the circle
[tex]A=\pi (2)^{2}=4\pi \ cm^{2}[/tex]
step 3
Find the area of the shaded region
[tex]77\ cm^{2}-4\pi \ cm^{2}=(77-4\pi)\ cm^{2}[/tex] -----> exact value
To find the approximate value use [tex]\pi=3.14[/tex]
[tex](77-4(3.14))=64.44\ cm^{2}[/tex] -----> approximate value
A car is traveling at a rate of 99 kilometers per hour. What is the car's rate in meters per second? How many meters will the car travel in 10 seconds?
Answer:
The answer is 16.5 meters in 10 seconds
Step-by-step explanation:
First you divide 99 by 60 seconds
When you get 1.65 you multiply it by 10 second.
When you multiply 1.65 by 10 second you get 16.5 meters in 10 seconds
Find all the zeros of the function f(x) = x^3 -2x^2 +16x -32
Answer:
Real zeros: x = 2All zeros: x = 2, x = -4i and x = 4iStep-by-step explanation:
[tex]f(x)=x^3-2x^2+16x-32\\\\\text{The zeros:}\\\\f(x)=0\Rightarrow x^3-2x^2+16x-32=0\\\\x^2(x-2)+16(x-2)=0\\\\(x-2)(x^2+16)=0\iff x-2=0\ \vee\ x^2+16=0\\\\x-2=0\qquad\text{add 2 to both sides}\\\boxed{x=2}\\\\x^2+16=0\qquad\text{subtract 16 from both sides}\\x^2=-16<0\qquad\text{no real solutions}\\\\\text{In the set of the complex numbers}\\x^2=-16\to x=\pm\sqrt{-16}\\\boxed{x=-4i\ \vee\ x=4i}[/tex]
17. Solve the equation. Show your work. 3x – 10 = 5x + 32
3x - 10 = 5x + 32
3x - 10 + (-5x + 10) = 5x + 32 + (-5x + 10)
-2x = 42
-0.5(-2x) = -0.5(42)
x = -21
Answer:
x = -21Step-by-step explanation:
[tex]3x-10=5x+32\qquad\text{add 10 to both sides}\\\\3x-10+10=5x+32+10\\\\3x=5x+42\qquad\text{subtract 5x from both sides}\\\\3x-5x=5x-5x+42\\\\-2x=42\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2x}{-2}=\dfrac{42}{-2}\\\\\boxed{x=-21}[/tex]
The set of ordered pairs shown represents a function, f,
{(–5, 3), (4, 9), (3, –2), (0, 6)}
Select THREE ordered pairs that could be added to the set that would allow f to remain a function.
Question 10 options:
A)
(-3, -2)
B)
(4, 0)
C)
(0, -1)
D)
(1, 6)
E)
(2, 3)
F)
(-5, 9)
Answer:
B) (4, 0)
C) (0, -1)
E) (2, 3)
Step-by-step explanation:
If we see the rule of function then it says that,
a function is a special relationship where each input, x, has a single output, y.
It means that for every value of x there SHOULD be a different value of y.
A)
(-3,-2) Rejected
because when x = 3, y = -2
D)
(1, 6) Rejected
because when x = 0, y = 6
F)
(-5, 9) Rejected
because when x = 4, y = 9
Answer:
The correct options are A, D and E.
Step-by-step explanation:
The given set of ordered pairs represents a function
[tex]f=\{(-5, 3), (4, 9), (3, -2), (0, 6)\}[/tex]
We need to find THREE ordered pairs that could be added to the set that would allow f to remain a function.
A relation is a function if there exist unique value of y for each value of x.
The x values for given function are -5, 4, 3 and 0.
If we add (-3,-2) in the given set, then we unique value of y for each value of x. So, option A is correct.
If we add (4,0) in the given set, then we have y=0 and y=9 at x=4. Since the set have more than one value of y for same x-value, therefore option B is incorrect.
If we add (0,-1) in the given set, then we have y=-1 and y=6 at x=0. Since the set have more than one value of y for same x-value, therefore option C is incorrect.
If we add (1,6) in the given set, then we unique value of y for each value of x. So, option D is correct.
If we add (2,3) in the given set, then we unique value of y for each value of x. So, option E is correct.
If we add (-5,9) in the given set, then we have y=9 and y=3 at x=-5. Since the set have more than one value of y for same x-value, therefore option F is incorrect.
Therefore the correct options are A, D and E.
The number of eggs in the refrigerator e decreased by 2 equals 18. What’s the equation?
E-2=18 should be your answer
✧･ﾟ: *✧･ﾟ:* *:･ﾟ✧*:･ﾟ✧
Hello!
✧･ﾟ: *✧･ﾟ:* *:･ﾟ✧*:･ﾟ✧
❖ The correct answer is e - 2 = 18.
e is being decreased by 2 so we represent this as, -2. The problem says it equals 18 so therefore, the equation will be written as e - 2 = 18
~ ʜᴏᴘᴇ ᴛʜɪꜱ ʜᴇʟᴘꜱ! :) ♡
~ ᴄʟᴏᴜᴛᴀɴꜱᴡᴇʀꜱ
A video merchant sold 24 cases of tapes, which was 20% of what he had left. What percent of tapes did he sell?
PLEASE I NEED THIS VERY SOON AND IT'S NOT 20%
Answer:
16.7%
Step-by-step explanation:
Total number of cases sold = 24
In order to find what percentage of cases were sold we first need to know the total number of cases that the merchant had.
Let the total number of cases the merchant initially had was x. After selling 24 cases, the number of cases he is left with is x - 24
According to the statement, the number of cases sold (i.e. 24) is 20% of the number of cases the merchant originally had (i.e. x - 24)
This can be written as:
24 is 20% of x - 24
In equation form this becomes:
24 = 20% of ( x - 24)
24 = 0.20(x - 24)
24 = 0.20x - 4.8
24 + 4.8 = 0.20x
28.8 = 0.20x
x = 144
This means the merchant initially had 144 cases of tapes. He sold 24 of them. So the percentage of cases he sold will be:
[tex]\frac{24}{144} \times 100\%\\\\ = 16.7%[/tex]
Therefore, the merchant sold 16.7% of the cases of tapes.
Kevin will take 4 math tests this term. All of tests are worth the same number of points. After taking the first 3 tests, his mean test score is 88 points. How many points does he need on his last test to raise his mean test score to 90 points?
Answer:
360 points in total, Kevin needs 96 more.
Step-by-step explanation:
88 x 3 is 264
To get a mean of 90, Kevin needs 360 points in total because 90 x the 4 tests is 360.
360 - 264 is 96
so he needs 96 more points.
Find The angle of CBD
Answer:
Angle CBD is 125°.
Step-by-step explanation:
Remember that the sum of all the interior angles of a triangle is 180°. We know two of these angles from the diagram for problem #3: 67° amd 58°. Thus, angle ABC is 180° less the sum of 67° and 58°, or 180° - (67° + 58°), which comes out to 180° - 125°, or 55°.
This 55° and angle CBD are supplementary angles. In other words, 55° + <CBD must sum up to 180°. Subtracting 55° from 180° yields 125°.
Angle CBD is 125°.
Answer:
125°Step-by-step explanation:
We know that ∠CBD = ∠ACB + ∠CAB [ External Angle of a Triangle theorem]
∠CBD = 58° + 67° = 125°
18-5w+7w-4=28 does any one knows that answer
Answer: w=7
All work is shown in the attached sheet! :)
If the original price of a pair of shoes is $80 but a sign above the shoes reads “Sale - 20% discount”, then what price would a costumer pay for the shoes (excluding tax)?
A.) 64
B.) 6
C.) 16
D.) 80
E.) 60
Answer:
A.) 64
Step-by-step explanation:
The first step is identifiying the original price of the shoes and the discount
Next you will decide what type of equation you will need. For this situation, you would need a subraction equation.
80 - 20% = ?
If you choose to slove with a calculator, don't put 0.2 in the place of 20%. We dont do this because it will result in a different answer. 80 - 0.2 = 79.8.
Now we solve the problem
80 - 20% = 64
Last Labor Day, I weighed 135 pounds. I have gained x pounds. Write an expression for my current weight
Answer:
135+x
Step-by-step explanation:
thi is because yoou gained x so you add that to your weight
Hello there!
An equation you could use is: 135 + x = y
This is because you gained x pounds, and you are adding that on to you original weight of 135 pounds, giving you a total of y ponds.
I hope this helps and have a great day!
Mila reads at a rate of 2 paragraphs per minute.
After reading for 3 minutes, she had read a total of 6 paragraphs.
Yes this is true because if she can read 2 paragraphs every minute you would multiply 2 by 3 since that’s how many minutes she read for.
2 paragraphs x 3 minutes = 6 paragraphs
Hope this helps.
Answer:
Yes this is true because if she can read 2 paragraphs every minute you would multiply 2 by 3 since that’s how many minutes she read for.
2 paragraphs x 3 minutes = 6 paragraphs
Hope this helps.
Step-by-step explanation:
Is he correct? Explain your reasoning.
Answer:
Yes
Step-by-step explanation:
The equation is y=2x+4
Andy's assertion is incorrect because the correct equation for the given data must include a y-intercept term. Hence, the equation would be of the form y = mx + b, with the slope m being 2 and the y-intercept b being 4. For this dataset, the equation would be y = 2x + 4.
Explanation:Andy's statement that he can write an equation of the form y=mx for the given values is incorrect. If we look at the table, we see that as x increases by 1 unit, y increases by 2 units. This indicates that the slope of the line (m) is 2. However, the y-intercept is 4, not 0, hence our equation should have a form y = mx + b, where b ≠ 0. So, for this data, a correct equation would be y = 2x + 4.
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The complete question is here:
Andy uses the table below to write a linear equation.
x : -1, 0, 1, 2
y : 2, 4, 6, 8
He says he can write an equation of the form y=mx for the given values. Is he correct? Explain your reasoning.
Help me please guys
For 7A)
The sum of -4 can not be both positive as from the set of rules (+)(+) can only make postive and -4 is decleared as negative
For 7B)
The sum of -4 can not be both negative as both negative (-)(-) is equivalent to a positive and the integer is -4 meaning it can not be negative
The reasonable answer to this would be two different numbers
It could be negative and positive
Or positive and negative
Nothing else
Need help!
Need help with my pre cal, not sure what to do with this question
Answer:
y = 3x - 1
Step-by-step explanation:
We can manipulate the scatter plot feature in Ms. Excel then we simply add the linear trend line displaying the equation on the chart.
The excel output is attached below.
The relation exhibited by the data set is y = 3x - 1; given the value of x, the value of y is obtained by multiplying x by 3 and subtracting 1 from the result.
Write the fraction as a decimal. Round to the nearest hundredth, if necessary.
7/8
Answer:
0.875
Step-by-step explanation:
We know that
7/8
is the same as
7÷8
Then using
Long Division for 7 divided by 8
and rounding to a Max of 3 Decimal Places gives us
=0.875
hope this helps:)sorry if it doesnt
plz give brainliest
Answer:
0.875
Step-by-step explanation:
7/8 IS 0.875
you can round to hundredth
so 0.88
what is more 500 mL of water or 0.75 L of water
it is 0.75 L because the L are more than a mL
Answer:
Step-by-step explanation:
0.75
The slope of the line passing through the points (-2,6) and (6,4) is
Answer:
[tex]-\frac{1}{4}[/tex]
Step-by-step explanation:
[tex]rule of slope = \frac{y^2-y^1}{x^2-x^1}[/tex]
4 - 6 = -2
6 - -2 = 8
-2 ÷ 8 = -0.25 (-1/4)
Answer:
The slope is [tex]-\frac{1}{4}[/tex]
Step-by-step explanation:
Let [tex](x_1,y_1)=(-2,6)[/tex] and [tex](x_2,y_2)=(6,4)[/tex].
The slope of the line passing through these two points is given by;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We substitute the values to obtain;
[tex]m=\frac{4-6}{6--2}[/tex]
[tex]m=\frac{-2}{8}[/tex]
[tex]m=-\frac{1}{4}[/tex]
solve for v 42=7/6v
Answer:
[tex]\boxed{\bold{v=36}}[/tex]
Step-By-Step Explanation:
Switch Sides
[tex]\bold{\frac{7}{6}v=42}[/tex]
Multiply Both Sides By 6
[tex]\bold{6\cdot \frac{7}{6}v=42\cdot \:6}[/tex]
Simplify
[tex]\bold{7v=252}[/tex]
Divide Both Sides By 7
[tex]\bold{\frac{7v}{7}=\frac{252}{7}}[/tex]
Simplify
[tex]\bold{v=36}[/tex]
A rectangular prism has a length of 11 centimeters, a width of 9 centimeters, and a height of 3 centimeters. Its volume is _______ cubic centimeters.
Answer:
297
Step-by-step explanation:
To find V or Volume to multiply all of the number so 11 time 9 times 3 equals 297. So V = 297
Plz help!!!!!!!!!!!!
Answer:
-8
Step-by-step explanation:
(-32)^(3/5) is equivalent to (-2^5)^(3/5) and applying exponent rules then simplifying you can get your answer.
Answer:
Step-by-step explanation:
Let's just see what happens if we do
(-32)^(1/5)
That means what number do you start with that when multiplied 5 times gives you - 32?
The answer is - 2
-2 * - 2 * -2 * -2 * -2 = -32
Now when you have a root sign that goes to the 1/5 power, you can take out 1 of the factors and throw the other 4 away.
[tex]\sqrt[5]{-2 * - 2 * - 2 * -2 * -2} = - 2[/tex] take one - 2 from under the root sign and throw the other 4 away
That's not the answer. We have one more step.
What is -2 to the 3rd power.
(-2)^3 = - 8
So the answer is -8
[tex]\sqrt[5]{- 32}^3 = -8[/tex]
Triangle ABC is similar to triangle DEF. The length of
AC is 12 cm. The length of
BC is 18 cm. The length of
DF is 10 cm.
What is the length of
EF?
Answer: [tex]EF=15cm[/tex]
Step-by-step explanation:
You know that the triangle ABC and the triangle DEF are similar.
Therefore, if the lenght of AC is 12 centimeters and the lenght of DF is 10 centimeters, then you can find the ratio as following:
[tex]ratio=\frac{DF}{AC}\\\\ratio=\frac{10cm}{12cm}\\\\ratio=0.8333[/tex]
Then, the calculte the length of EF, you must multiply the lenght BC of the triangle ABC by the ratio obtained above.
Therefore, the lenght EF is the following:
[tex]EF=0.8333(18cm)\\EF=15cm[/tex]
Answer:
The length of EF = 15 cm.
Step-by-step explanation:
We are given that the two triangles, ABC and DEF, are similar to each other,
Given that the length of AC = 12 cm, BC = 18 cm and DF = 10 cm, we are to find the length of EF.
For this, we can simply use the ratio method.
[tex] \frac { EF } { BC } = \frac { DF } { AC } [/tex]
[tex] \frac { EF } { 18 } = \frac { 10 } { 12 } [/tex]
[tex] E F = \frac { 10 } { 12 } \times 18 [/tex]
EF = 15 cm
State a true conclusion.
1) All rabbits like lettuce.
2) My pet is a rabbit. Conclusion:
I think it would be: "My pet rabbit likes lettuce."
I believe it would be 2) my pet is a rabbit.