the x-intercepts of the parabola are -2 and 4, and the y-intercept is 8.
The x-intercepts of a quadratic function are defined as the points where the graph crosses the x-axis, which implies that y=0 for those points. The y-intercept of a function is defined as the point where the graph crosses the y-axis, which implies that x=0 for those points.
Given that Amie and Taylor have written two different functions that represent the same parabola:
f(x) =-(x+2)(x-4) and g(x) =-1 (x-1)^2 +9.We have to find the x-intercepts of the parabola and the y-intercept.
The standard form of the quadratic equation is
ax^2+ bx + c = 0.
The discriminant of the quadratic equation is b^2 - 4ac which helps in determining the nature of roots for the quadratic equation. The quadratic equation of the form
f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola with axis of symmetry x = h.
For the given quadratic functions:
f(x) =-(x+2)(x-4)andf(x) =-1 (x-1)^2 +9.
In order to find the x-intercepts of the parabola, we will equate the function value to zero and solve for x:
f(x) =-(x+2)(x-4)0 =-(x+2)(x-4)x + 2 = 0 or x - 4 = 0x = -2 or x = 4
Therefore, the x-intercepts of the parabola are -2 and 4.
Similarly, to find the y-intercept, we set x = 0:f(x) =-(x+2)(x-4)f(0) =-(0+2)(0-4)f(0) = 8
Therefore, the y-intercept of the parabola is 8.
Hence, the x-intercepts of the parabola are -2 and 4, and the y-intercept is 8.
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0.04 less than 1.38
First, you need to understand the vocabulary.
Saying x less than y means that you are subtracting from y. Your x here is 0.04, and your y is 1.38
y-x = 1.38-0.04 = 1.34
According to a secret government report, 1/3 of
all the jelly beans in the world are red. If that
1/3 amounts to 38,567,942 red jelly beans, how
many jelly beans are there in total?
Proportionately, the total jelly beans in the world will be 115,703,826.
What is a proportion?A proportion refers to a fraction of a whole.
A proportion is a ratio or a number relationship between two or more values or variables.
The proportion of a whole value can be represented as a fraction, decimal, or percent.
Data and Calculations:Red jelly beans in the world = 1/3
And 1/3 = 38,567,942
1/1 = 115,703,826 (38,567,942/1/3)
Thus, if 1/3 of the jelly beans in the world is 38,567,942, then the whole jelly beans will be 115,703,826.
Thus, proportionately, the total jelly beans in the world will be 115,703,826 because 1/3 of 115,703,826 is 38,567,942.
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A linen napkin, in the shape of a square, has sides that are 10 inches long.
If the napkin is folded along the diagonal, whats the length of the diagonal?
round to the nearest tenth.
Answer: A=187.5,2
Step-by-step explanation:
please helppp I really don't understand this lol
Answer:
Khan Academy.
Step-by-step explanation:
You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.
just this please helppp
The height of the water depth is h = 14 + 6 · sin (π · t/6 + π/2), where t is in hours, and the height of the Ferris wheel is h = 21 + 19 · sin (π · t/20 - π/2), where t is in seconds. Please see the image to see the figures.
How to derive equations for periodical changes in time
According to the two cases described in the statement, we have clear example of sinusoidal model for the height as a function of time. In this case, we can make use of the following equation:
h = a + A · sin (2π · t/T + B) (1)
Where:
a - Initial position, in meters.A - Amplitude, in meters.t - Time, in hours or seconds.T - Period, in hours or seconds. B - Phase, in radians.Now we proceed to derive the equations for each case:
Water depth (u = 20 m, l = 8 m, a = 14 m, T = 12 h):
A = (20 m - 8 m)/2
A = 6 m
a = 14 m
Phase
20 = 14 + 6 · sin B
6 = 6 · sin B
sin B = 1
B = π/2
h = 14 + 6 · sin (π · t/6 + π/2), where t is in hours.
Ferris wheel (u = 40 m, l = 2 m, a = 21 m, T = 40 s):
A = (40 m - 2 m)/2
A = 19 m
a = 21 m
Phase
2 = 21 + 19 · sin B
- 19 = 19 · sin B
sin B = - 1
B = - π/2
h = 21 + 19 · sin (π · t/20 - π/2), where t is in seconds.
Lastly, we proceed to graph each case in the figures attached below.
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Use facts about tangents and sextants to find new angles and arcs. PLS HELP!! GEOMETRY!! WILL MATK BRAINLIST!!
Applying the angle of intersecting secants theorem, the measure of angle B is: 35°.
What is the Angle of Intersecting Secants Theorem?The measure of the angle formed outside a circle by two intersecting secants is equal to half the positive difference of the measures of the arcs they intercept based on the angle of intersecting secants theorem.
Applying the angle of intersecting secants theorem, we have the following:
Let the missing measure of the arc for angle A be x. Therefore:
6 = 1/2(x - 17)
2(6) = x - 17
12 = x - 17
12 + 17 = x
x = 29°
m∠B = 1/2(99 - x)
Plug in the value of x
m∠B = 1/2(99 - 29)
m∠B = 35°
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Order the following expressions from least to greatest
(Quick Please)
Q.estimate the area of each polygon in square units.
i cant understand the question can someone help me and provide detailed explanation with the solution. please provide reasons so i can grasp the concept.
The area of the polygon is 12 square units. In mathematics and everyday life, an estimate is an approximate calculation or guess that is close to the actual value but may not be exact.
To make an estimate or guess, you can square off the parallelogram and create a rectangle and add your squares (or multiply 3x4) to = 12": This part explains a method for estimating the area of a parallelogram. It suggests that if you take a parallelogram and "square it off" (convert it into a rectangle by drawing a perpendicular line), you can then find the area of the rectangle, which is easier to calculate. In this case, the dimensions of the rectangle are given as 3 units for the base and 4 units for the height, and the estimated area is 12 square units.
You can use the formula for the exact area using base x height (3x4) you get the same answer of 12 square units": This part emphasizes that the estimation method used in step 2 (multiplying 3 by 4) produces the same result as the exact formula for finding the area of a parallelogram, which is base times height. In this case, both the estimation and the formula give an area of 12 square units.
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. the percentage error if 625.483 is approximated to 3 significant digits is
a. 0.0662
b. 0.0772
c. 0.0552
d. 0.0882
Percentage error is the difference between an actual value and its expected value per the actual value which is expressed in percentage. In the given question, the percentage error is option b. 0.0772
Percentage error is the difference between an actual value and its expected value per the actual value which is expressed in percentage.
This can be expressed as;
percentage error = [tex]\frac{actual value - expected value}{actual value}[/tex] x 100%
Where the actual value is the accurate value, and the expected value is derived from the actual value.
Thus in the given question, it can be deduced that,
actual value = 625.483
expected value = 625.000
The difference between the two values = (625.483 - 625.000)
= 0.483
So that,
percentage error = [tex]\frac{0.483}{625.483}[/tex] x 100%
= 0.07722
percentage error = 0.0772
Therefore, the required percentage error is 0.0772 i.e option b.
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A linear function contains the following points. x 0 2 4 6 y 3 -1 -5 -9
What are the slope and y-intercept of this function?
A. The slope is -2. The y-intercept is (3,0).
B. The slope is -1/2 The y-intercept is (0,3)
C. The slope is 2. The y-intercept is (0,3)
D. The slope is -2. The y-intercept is (0,3)
Answer:
D. The slope is -2. The y-intercept is (0,3)
Step-by-step explanation:
You can use any two points.
Let's use the first two points: (0, 3), (2, -1)
slope = (y_2 - y_1)/(x_2 - x_1)
slope = (-1 - 3)/(2 - 0)
slope = -4/2
slope = -2
The y-intercept occurs when x = 0. For x = 0, y = 3, so the y-intercept is 3 which means the point (0, 3).
Answer: D. The slope is -2. The y-intercept is (0,3)
If a person stands 40 ft from a tree and the angle of elevation made from their eyes (5 ft above the ground) to the top of the tree is 47°, how tall is the tree? Round your answer to the nearest foot.
Using the given information, the height of the tree is 48 ft
TrigonometryFrom the question, we are to determine the height of the tree
In the given diagram, the height of the tree is (x + 5) feet
First, we will determine the value of x
tan 47° = x / 40
x = 40 × tan47°
x = 42.89 ft
∴ The height of the tree = (42.89 + 5) ft
Height of the tree = 47.89 ft
Height of the tree ≈ 48 ft
Hence, the height of the tree is 48 ft.
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Answer 1/4 + 3/5-3/10 =
Answer:
11/20
Step-by-step explanation:
1/4= 10/40
3/5=24/40
3/10=12/40
10/40+24/40= 34/40
34/40 - 12/40= 22/40
simplifies to 11/20
If p(a) = 2/3, p(b) = 4/5, and p(anb) = 3/5, what is P( AuB) ( the n is the arc shape direction, so is the u)
By the inclusion/exclusion principle,
[tex]P(A\cup B) = P(A) + P(B) - P(A\cap B)[/tex]
[tex]P(A\cup B) = \dfrac23 + \dfrac45 - \dfrac35[/tex]
[tex]P(A\cup B) = \dfrac{10}{15} + \dfrac{12}{15} - \dfrac9{15}[/tex]
[tex]P(A\cup B) = \boxed{\dfrac{11}{15}}[/tex]
In the triangle below, what is the measure (in degrees) of angle X?
66°
55°
X
Answer:
59
Step-by-step explanation:
Angle degrees in a triangle add up to 180
66+55+x=180
121+x=180
x=59
Answer
59°
Step-by-step explanation:
A triangle's angles add up to 180°.
So to find the last angle of the shape, you need to add the given angles and then subtract the answer from 180° looking like this:
66° + 55° = 121°
180° - 121° = 59°
WILL GIVE BRAINLIEST
The number of lattes sold daily by two coffee shops is shown in the table.
Shop A Shop B
55 36
52 40
50 34
47 39
51 44
48 41
53 40
53 38
Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain.
Mean for both coffee shops because the data distribution is symmetric
Median for both coffee shops because the data distribution is not symmetric
Mean for shop B because the data distribution is symmetric; median for shop A because the data distribution is not symmetric
Mean for shop A because the data distribution is symmetric; median for shop B because the data distribution is not symmetric
Answer:
It will be a more accurate thing to put it into the mean.
Step-by-step explanation:
Mainly, there is a lot of numbers in the data. So the reason Mean for shop A because the data distribution is symmetric; median for shop B because the data distribution is not symmetric.
Hoped this helped. Please mark me brainliest!
HELP IM BEING TIMED I NEED THE ANSWER QUICKLY AS POSSIBLE!!
What is the range of the absolute value function below?
According to the graph
It's a Translated modulus functionIt has vertex at (4,1)Maximum value is 1
So
Range is
f(x)≤1Option C
What is the area of this triangle?
_units²
The area of the triangle is 4 units²
What is the area of a triangle?The area of a triangle is the half the base multiplied with the height of that triangle
Area = 1/ 2 × b × h
From the figure given,
base = 7 - 3 = 4 units
height = 4 - 2 = 2 units
Area = 1/ 2 × 4 × 2
Area = 1/ 2 × 8
Area = 4 units²
Thus, the area of the triangle is 4 units²
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Explain why the triangles are similar, and then find the values of x and y.
The values of x and y from the figure is 9 and 5 respectively
Similarity theorem of triangleTwo triangles are similar if the ratio of the similar sides is equal to a constant. From the given diagrams;
x/(8+4) = 6/8
x/12 =6/8
8x = 6 * 12
8x = 72
Divide both sides by8 to have:
8x/8 = 72/8
x = 9
Similarly;
10+y/x = 10/6
10+y/9 = 10/6
10+y/9 = 5/3
Cross multiply
3(10+y) = 5(9)
30 + 3y = 45
3y = 45-30
3y = 15
y = 5
Hence the values of x and y from the figure is 9 and 5 respectively
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Mediciones recientes del fondo del mar que se extiende a lo largo de las crestas a medio océano muestran que la deriva continental es del orden de 4 cm. Suponga que este valor ha sido constante a través del tiempo y considere la distancia actual entre Sudamérica y África como 5000 millas. ¿Cuánto tarda Aproximadamente pangea en fragmentarse?
Usando proporciones, hay que la pangea tardra aproximademente 20,116,750 años para fragmentar-se.
¿Qué es una proporción?Una proporción es una fracción de la cantidad total, e puede ser encontrada aplicando una regla de três.
La deriva continental es del orden de 4 cm al año. La distancia actual entre Sudamérica y África es de 5000 millas. En cm, esta distancia es la seguiente:
5000 millas = 5000 x 160934 cm = 80,467,000 cm.
Asi, el tiempo que levará para la pangea fragmentar-se es:
t = 80,467,000/4 = 20,116,750 años
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The Random Variable is normally distributed with mean = 98 and standard deviation =
20.41.
On the sampling distribution with n = 81, for what value of the sample mean (X) would have
10% of the possible sample means less than it? Round your answer to 2 decimal places.
If mean is 98, standard deviation is 20.41, n=81 then sample mean will be 131.57445 which would have 10% of the possible mean less than it.
Given that mean is 98,standard deviation is 20.41,n=81 and significance level be 10%.
We are required to find the value of sample mean.
Because the value of n is greater than 30 so we will use z statistics in the problem.
We know that,
Z=(X-μ)/σ in which μ is population mean, σ is standard deviation.
Confidence level=1-0.01=0.09 means 90%.
Z value for 90% confidence level be 1.645.
we have to put the value of Z=1.645 , μ=98,σ=20.41 to get the value of X.
1.645=(X-98)/20.41
1.645*20.41=X-98
33.57445=X-98
X=98+33.57445
X=131.57445
Hence if mean is 98, standard deviation is 20.41, n=81 then sample mean will be 131.57445 which would have 10% of the possible mean less than it.
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rationalize the denominator
PLS HELP
Answer:
x = 5, y = sqrt6, z = 3
Step-by-step explanation:
[tex]\frac{10}{\sqrt{6} } \\\\\frac{(10)(\sqrt{6} )}{(\sqrt{6} )(\sqrt{6}) } \\\\\frac{10\sqrt{6} }{6} \\\\or\\\\\frac{5\sqrt{6} }{3}[/tex]
❄ Hi there,
let us revise the way we rationalize the denominator before we get down to the actual process.
__________
Suppose you had a problem, and you did all the steps, and you arrived at the following answer: [tex]\sf{\dfrac{10}{\sqrt6}}[/tex].
Well, this answer is not in its simplest form, because it has an irrational number in its denominator.
So what we do is we get rid of that irrational number in the denominator by multiplying the fraction's top & bottom by [tex]\sqrt6[/tex]:
[tex]\sf{\dfrac{10\sqrt6}{\sqrt6\times \sqrt6}}[/tex]
Now we simplify
[tex]\sf{\dfrac{10\sqrt6}{6}}[/tex]
Reduce
[tex]\sf{\dfrac{5\sqrt6}{3}}[/tex]
- - - - - - - -
Which set of numbers can represent the side lengths, in millimeters, of an obtuse triangle?
8, 10, 14
9, 12, 15
10, 14, 17
12, 15, 19
Answer:
8, 10, 14
Step-by-step explanation:
1. 8² + 10² = 164 and 14² = 196, so this works.
2. 9² + 12² = 15² = 225, so this is a right triangle.
3. 10² + 14² = 296 and 17² = 289, so this is an acute triangle.
4. 12² + 15² = 369 and 19² = 361, so this is an acute triangle.
Answer:
a
Step-by-step explanation:
Sofa co is selling sofas with a 33% discount off the original price to reduce its stock. Calculate the discounted price of a sofa originally selling for £999.00. Please show your working.
which number produces a rational number when multiplied by 1/3
A. 2
B. -√17
C. 0.166
D. 2/3
Please could you answer this one decently quick for me? thanks!
The number which produces a rational number when multiplied by 1/3 is; Choice A; 2.
What is a rational number?It follows from the definition of rational number that they can be represented as the quotient a/b of two integers such that b ≠ 0.
On this note, it follows that when 1/3 is multiplied by 2; the result is 2/3 which is a rational number.
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Laurel appears at Comedy Cafe at a random time between 1:00 and 2:00. Hardy turns up at a random time between 2:00 and 2:30. The probability that Laurel waits for no more than 40 minutes for Hardy can be expressed in the form $m/n$, where $m$ and $n$ are relatively prime positive integers. Find $m n$.
Answer:
i need more info please
Step-by-step explanation:
x/4 ÷ 2/3 = 1/5
solve for x
The value of x from the equation x/4 ÷ 2/3 = 1/5 is 8/15
Fractionx/4 ÷ 2/3 = 1/5
x/4 × 3/2 = 1/5
(x × 3) / (4 × 2) = 1/5
3x / 8 = 1/5
cross product3x × 5 = 8 × 1
15x = 8
x = 8/15
Therefore, value of x from the equation x/4 ÷ 2/3 = 1/5 is 8/15
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Which of the following is a geometric sequence?
A. 7, 4, 1, -2, …
B. 2, 4, 6, 8, …
C. 1, 1/2, 1/4, 1/8, …
D. 1, 1, 2, 3, 5, …
Answer: C
Step-by-step explanation:
Each term is half the previous term.
Which equation gives the lines show on Graph y= 2x+4
y= -1/2x-4
y=1/2x+4
y=2x-4
Alex has 84 quarters and nickels worth a total of $17.80.
Which equation can be used to find q, the number of quarters Alex has?
The equation which can be used to find the number of quarters and nickels is; n + q = 84, 0.05n + 0.25q = 17.80.
Quarters and nickelsTotal coins = 84Total value = $17.80let
Number of quarters = qNumber of nickels = nn + q = 84
0.05n + 0.25q = 17.80
From equation (1)
n = 84 - q
Substitute into (2)
0.05n + 0.25q = 17.80
0.05(84 - q) + 0.25q = 17.80
4.2 - 0.05q + 0.25q = 17.80
- 0.05q + 0.25q = 17.80 - 4.2
0.20q = 13.60
q = 13.60 / 0.20
q = 68
Substitute q = 68 into
n + q = 84
n + 68 = 84
n = 84 - 68
n = 16
Therefore, the number of quarters and nickels are 68 and 16 respectively.
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At the movie theatre, child admission is and adult admission is . On Wednesday, tickets were sold for a total sales of . How many child tickets were sold that day
The child tickets were sold that day is 82.
Given the cost of child admission $6.30 and the cost of adult admission $9.80 and on Wednesday 144 tickets were sold for a total sales of $1124.20.
Let the child tickets are x and adult tickets are y.
On Monday, 144 tickets were sold for a total sales.
x+y=144 ........(1)
Total sales = $1124.20
Need to find the child tickets sold on Wednesday.
Total sales = 6.30x+9.80y
Total sales = $1124.20
So,6.30x+9.80y=1124.20 .......(2)
Find the value of y from equation (1), we get
x+y-x=144-x
y=144-x
Now, we will substitute the value of y in equation (2) to find the value of x, we get
6.30x+9.80(144-x)=1124.20
Apply the distributive property that is a(b+c)=ab+ac, we get
6.30x+9.80×144-9.80x=1124.20
6.30x+1411.2-9.80x=1124.20
Combine the variable terms on left side, we get
1411.2-3.5x=1124.20
subtract 1411.2 from both sides, we get
1411.2-3.5x-1411.2=1124.20-1411.2
-3.5x=-287
Divide both sides with -3.5x, we get
-3.5x/(-3.5)=-287/(-3.5)
x=82
Therefore, 82 child tickets were sold on Wednesday when cost of child admission $6.30 and the cost of adult admission $9.80.
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