Answer: The vertex form of a parabola is:
y = a(x - h)^2 + k
Where (h, k) is the vertex of the parabola.
In this case, we are given that the vertex is (1, -2), so the equation of the parabola will be:
y = a(x - 1)^2 - 2
We know that the parabola passes through (0, -5), and it is given by the equation.
-5 = a(0 - 1)^2 - 2
so,
a = 1/3
The final equation of the parabola is :
y = 1/3(x-1)^2 - 2
so, the points that are on the parabola are:
A. (2,-3)
B. (-1,-14) is not true,
y = 1/3 (-1 -1)^2 - 2 = -1/3 + 2 = 1/3 ≠ -14
C. (3,2)
D. (2,-5)
E. (3,-14) is not true
y = 1/3 (3-1)^2 - 2 = -4/3 ≠ -14
F. (-2,7) is not true
y = 1/3 (-2-1)^2 - 2 = -7/3 + 2 = -1/3 ≠ 7
Therefore A, C and D are the correct answers.
Step-by-step explanation:
What is the multiplicative inverse of 3?
A) -3. B) -1/3. C) 1/3 D) 3
Answer:
C) 1/3
Step-by-step explanation:
When a number is multiplied by its multiplicative inverse, it should be equal to 13 = 3/1
3/1 x 1/3 = 3/3 = 1
cos(-0)=3, sin 0 <0
What is the value of sin ?
2√3/ 3
√6/3
-2 √3/3
-√6/3
On solving the provided question we can say that - here in trigonometry [tex]sinx(2cosx - 1) = 0\\[/tex] => sinx = 0 and 2 cosx -1 =0
what is trigonometry?The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.
[tex]sin 2x - sinx = 0\\-sinx + 2cosx sinx=0\\sinx(2cosx - 1) = 0\\[/tex]
sinx = 0 and 2 cosx -1 =0
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I ned help i do not understand
Answer:
x=78
Step-by-step explanation:
x+x+24=180
2x+24=180
2x=156
x=78
From nose to tail your first dog is 5 feet long. Your first dog is the length of your second dog. How many feet long f is your second dog
According to fraction and ratio, second dog is 3/2 feet long.
In math, what is a fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
First dog is 5 feet long.
then,
5 feet is equal to 4/5 of the second dog's length.
multiply both sides by 5/4.
5/4 x 5 feet is the second dog's length.
The second dog is 25/4 feet long.
The second dog is 6(1/4) feet long.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
The correct representations of the inequality expression are (a) 6x – 15 > -10 + 5x and (c) 3(2x – 5) > -5(2 – x)
How to determine the correct representationsFrom the question, we have the following expression that can be used in our computation:
–3(2x – 5) < 5(2 – x)
Divide bot sides of the inequality by -1
So, we have the following representation
3(2x – 5) > -5(2 – x)
Next, we open the brackets
This gives
6x – 15 > -10 + 5x
Hence, the representation is 6x – 15 > -10 + 5x
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Complete question
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
(a) 6x – 15 > -10 + 5x
(b) 6x – 15 < -10 + 5x
(c) 3(2x – 5) > -5(2 – x)
(d) 3(2x – 5) < -5(2 – x)
Abc and def are complementary angles what is the measure of x?
Complementary angles add to 90 degrees. This means that 65 + x = 90, so x = 90 - 65 = 25.
Which of the following r-values represents the strongest correlation?
A. 0.55
B. 0.65
C. 0.35
D. 0.45
Answer:
0.65
Step-by-step explanation:
The r-value option (B) 0.65 represents the strongest correlation.
What is the correlation coefficient?The correlation coefficient is a quantitative method of calculating correlation. It is a statistical concept, which helps in establishing a relation between predicted and actual values obtained in a statistical experiment.
For the given situation,
We need to determine the r-value that represents the strongest correlation.
The relationship between two variables is generally considered strong when their r value is larger than 0.7.
Among the options, 0.65 is near to 0.7, so it has strongest correlation.
Hence we can conclude that the r-value option (B) 0.65 represents the strongest correlation.
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puts $700.00 into an account to use for school expenses. The account earns 4% interest,
compounded continuously. How much will be in the account after 7 years?
Answer:
$926.19Step-by-step explanation:
Use formula:
A = Pe^(rt)Given
P = $700r = 4% = 0.04t = 7 yearsFind the amount:
A = 700*e^(0.04*7) = 926.19give me a numerical expression that represents the product of four squared and sixty-three.
please !!
Answer:
Step-by-step explanation:Step 1: Remove parentheses by multiplying factors.
= (x * x) + (1 * x) + (2 * x) + (2 * 1)
Step 2: Combine like terms by adding coefficients.
(x * x) = x2
(1 * x) = 1x
(2* x) = 2x
Step 3: Combine the constants.
(2 * 1) = 2
Step 4: Therefore, Simplifying Algebraic Expression is solved as
= x2 + 3x + 2.
Select the correct answer. Solve the quadratic equation by factoring.
9x -16 = 0
Answer:
x = 16/9
Step-by-step explanation:
9x -16 = 0
9x = 16
x = 16/9
Let's check
9(16/9) -16 = 0
144/9 - 16 = 0
16 - 16 = 0
0 = 0
So, x = 16/9 is correct!
Answer:
Step-by-step explanation:
9x = 16
x = 16/9
Please hurry it's timed i need help
The solution of the given function cosx - √(3 - 3cos³x) = 0 is C. 30° + 360° n, 330° + 360°n
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
We are given the function as;
cosx - √(3 - 3cos³x) = 0
cosx = √(3 - 3cos³x)
Taking square root on both sides.
cos ²x = √(3 - 3cos³x) ²
cos ²x = (3 - 3cos³x)
For solving for x in
cos ²x = (3 - 3cos³x)
cos ²x = 3 (1 - cos³x)
(1 - cos³x) = cos ²x/3
x= π/6 + 2πn
or
x=11π/6 + 2πn
where n is an integer.
30° + 360° n, 330° + 360°n
The correct answer is C.
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A wall has a tiled mosaic consisting of 25 triangular tiles. Each tile has a base of 6 cm and a height of 8 cm. Find the area of the mosaic.
Answer:
1200
Step-by-step explanation:
Please help! Due today! :(
The answer is 1.57! I hope this helps you!
please help you don't have to show work
Answer:
1. a
2. 422
3. 156.06
Step-by-step explanation:
Graph the systems of equations.
{2x+y=8
−x+2y=6
Need help really fast thank you so much!
Use the Line tool to graph the lines.
Answer:
x = 2
y = 4
Step-by-step explanation:
what value of x would prove that the following triangle is a right angle? Answers x=7 x=2 x= 14 x= 10
Step-by-step explanation:
Pythagoras' TheoremFor Pythagoras' Theorem to be valid, the triangle must be a right-angled one.
The formula is:
c^2 = a^2 + b^2
Where c is the longest side. While a,b are the side lengths.
SolutionUsing the above formula and the measurements given in the question, we can find the value of x.
By Pythagoras' Theorem,
26^2 = (5x)^2 + (12x)^2
676 = 25x^2 + 144x^2
169x^2 = 676
x^2 = 676 ÷ 169
x^2 = 4
x = 2
The cost of 1 cup is $10. IF the cups come in sets of 5 and I have $170, how many cups I buy?
Answer:
15
Step-by-step explanation:
5 X 10 = 50
170 / 50 = 3 sets = 15
unit 8 right triangle and trigonometry homework 5 trigonometry: finding sides and angles solve for x round to the nearest tenth.
plllls I will make brainlesst
Answer:
5. x = 25.6
6. x = 11.0
7. x = 41.8°
8. x = 64.2°
9. x = 12.8°
10. x = 51.3°
Step-by-step explanation:
Let's find the x value for each triangle.
For point 5
We have:
x: is the opposite cathetus to 52°
20: is the adjacent cathetus to 52°
52°: is the angle
We can find "x" with the following trigonometric function:
[tex] tan(52) = \frac{x}{20} [/tex]
[tex] x = tan(52)*20 = 25.6 [/tex]
For point 6
We have:
x: is the hypotenuse
5: is the opposite cathetus to the given angle
27°: is the angle
To find "x" we need to use the trigonometric function:
[tex] sin(27) = \frac{5}{x} [/tex]
[tex]x = \frac{5}{sin(27)} = 11.0[/tex]
For point 7
We know:
x°: is the angle
6: is the hypotenuse
4: is the opposite cathetus to x°
Hence, x is:
[tex] sin(x) = \frac{4}{6} [/tex]
[tex] x = sin^{-1}(\frac{4}{6}) = 41.8 [/tex]
For point 8
We have:
x°: is the angle
14: is the adjacent cathetus to x°
29: is the opposite cathetus to x°
To calculate "x" we need to use the trigonometric function tan(x):
[tex] tan(x) = \frac{29}{14} [/tex]
[tex] x = tan^{-1}(\frac{29}{14}) = 64.2 [/tex]
For point 9
We have:
x°: is the angle
54: is the hypotenuse
12: is the opposite cathetus to x°
We can use sin(x) to solve for x:
[tex] sin(x) = \frac{12}{54} [/tex]
[tex] x = sin^{-1}(\frac{12}{54}) = 12.8 [/tex]
For point 10
We have:
x°: is the angle
40: is the hypotenuse
25: is the adjacent cathetus to x°
We need to use cos(x) to solve for x:
[tex] cos(x) = \frac{25}{40} [/tex]
[tex] x = cos^{-1}(\frac{25}{40}) = 51.3 [/tex]
I hope it helps you!
To solve the given questions, either of the trigonometric functions; sine, cosine and tangent of an angle has to be applied appropriately to either of the questions. The answers to the questions are:
5. x = 25.60
6. x = 11.00
7. x = [tex]41.8^{o}[/tex]
8. x = [tex]64.2^{o}[/tex]
9. x = [tex]12.8^{o}[/tex]
10. x = [tex]51.3^{o}[/tex]
The questions given are right angled triangles which requires the application of trigonometric functions appropriately. A right angle triangle is one that has one of its angles to be [tex]90^{o}[/tex].
So, each of the questions can be solved as follows:
5. Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
Tan 52 = [tex]\frac{x}{20}[/tex]
⇒ x = Tan 52 * 20
= 25.5988
x = 25.60
6. Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]
Sin 27 = [tex]\frac{5}{x}[/tex]
⇒ x = [tex]\frac{5}{Sin 27}[/tex]
= 11.0134
x = 11.00
7. Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]
Sin x = [tex]\frac{4}{6}[/tex]
= 0.66667
x = [tex]Sin^{-1}[/tex] 0.66667
= [tex]41.8^{o}[/tex]
x = [tex]41.8^{o}[/tex]
8. Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
Tan x = [tex]\frac{29}{14}[/tex]
= 2.0714
x = [tex]Tan^{-1}[/tex] 2.0714
= [tex]64.2^{o}[/tex]
x = [tex]64.2^{o}[/tex]
9. Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]
Sin x = [tex]\frac{12}{54}[/tex]
= 0.22222
x = [tex]Sin^{-1}[/tex] 0.22222
= [tex]12.8^{o}[/tex]
x = [tex]12.8^{o}[/tex]
10. Cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]
Cos x = [tex]\frac{25}{40}[/tex]
= 0.625
x = [tex]Cos^{-1}[/tex] 0.625
= [tex]51.3^{o}[/tex]
x = [tex]51.3^{o}[/tex]
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9514 1404 393
Answer:
x ≈ 4.2
Step-by-step explanation:
The relevant trig relation is ...
Tan = Opposite/Adjacent
tan(72°) = b/x = 13/x
x = 13/tan(72°) ≈ 4.223956
Rounded to the nearest tenth, x ≈ 4.2.
please help me if you can!!
( links = report )
Answer: 3150
Step-by-step explanation:
V = lwh
V = 25 x 7 x 18
V = 3150
Find the Values of x and y
The values of x and y could be 25 and 113
What are parallel lines ?
parallel lines can be stated as , they both are equi distant from each other and which never intersect.
From the given figure,
y+12 = 3x + 50
as both are parallel to each other.
y-3x = 38
and 5x = y + 12
as vertically opposites are always equal .
y = 3x + 38
y = 5x - 12
hence,
5x - 12 = 3x +38
2x = 50
x = 25
put x = 25 in y = 3x + 38
y = 3 * 25 + 38
y = 113
hence the values of x and y are 25 and 113 respectively.
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How do you draw a line segment equal to a given segment?
draw a line from the starting point of the segment to the endpoint using the same angle and length.
1. Place a ruler or straightedge on the given segment and draw a line along the length of the ruler.
2. Use a compass to create a line segment equal to the given segment. Set the compass to the length of the given segment, place the point of the compass on one end of the segment, and draw an arc to the other end of the segment.
3. Use a protractor to measure the angle and length of the given segment. Then, draw a line from the starting point of the segment to the endpoint using the same angle and length.
The answer explains three methods for drawing a line segment equal to a given segment: using a ruler or straightedge, using a compass, and using a protractor.
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Which function has zeros of -8,1 and,3
Answer:
Step-by-step explanation:
(x+8)(x-1)(x-3)
Gina is cleaning the tile floor in her kitchen. It takes her 20 minutes to clean 50 tiles.
How many tiles can she clean in 1 minute?
Answer:
2.5
Step-by-step explanation:
just divide 50 by 20
Select the three statements that correctly describe the coordinate system.
Answer:
I think no 3
if wrong correct me please
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Find the volume of this square based pyramid. 5 ft 6 ft
Answer:
Volume of pyramid =1/3× Area of base × height
Since the base is a square
Area of base = l²
l = length
= 6²
= 36ft²
Height of pyramid = 5ft from the diagram above
Volume = 1/3× 36ft² × 5ft
= 60ft³
Can somebody teach my how to find the length of the third side of a triangle?
Answer:
Step-by-step explanation:
formula 0.5 x base x height
Answer:
Remember the formula a^2+b^2=c^2
Step-by-step explanation:
This can be used on right triangles. Now your a and b represent the legs of a triangle and the c represents the hypotenuse(the longest side). If you had a leg that was 2 inches and a second leg that was 4 inches you would plug it into the equation so...
2^2+4^2=c^2
Now evaluate
2^2=4
4^4=16
so
4+16=c
20=c
Now take the square root of 20 which is approximately 4.47 or leave it as square root of 20
If you had one leg and a hypotenuse then plug in and solve like any other equation.
Hope this helps!
What would a 44% decrease of 13 be?
a taxi charges $2.35 fee plus $0.55 per mile. melissa has no more than $15 to spend on her taxi ride how many miles can she go?
Answer:
2.35 + 0.55 × 15 = 10.6
Therefore, she can go 10.6 miles.
Answer:
10.6
Step-by-step explanation:
2.35 + 0.55 x 15 = 10.6
Your teacher has disabled instant marking. Your marks will appear after the due date.
35%
Patryk has 7 cards.
There is a number on each card.
|2||3||4||5|| 6 ||7|| 8
Patryk takes two of the cards at random.
He works out the product of the numbers on the two cards.
Work out the probability that the product is an odd number.
EH
Type here to search
O
1/7 is the probability that the product is an odd number.
What is the simple definition of probability?
A probability is a number that expresses the possibility or likelihood that a specific event will take place.
Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
Total Cards are 7
2 cards out of 7 cards can be selected in ⁷C₂ = 21 ways
Product would be odd if both cards are odd
3 , 5 , 7 are odd cards
2 cards out of 3 Can be selected in ³C₂ = 3 ways
( 3 , 5) , ( 3 , 7) , ( 5 , 7)
Hence probability the product of the numbers on the 2 cards is odd number
= 3/21
= 1/7
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