Answers
Answer:
x = 4, 1/4
solving steps
\(\sf \rightarrow x + \dfrac{1}{x}=4\dfrac{1}{4}\)
make the denominators same
\(\sf \rightarrow \dfrac{x(x)}{x} + \dfrac{1}{x}=4\dfrac{1}{4}\)
simplify the following
\(\sf \rightarrow \dfrac{x^2}{x} + \dfrac{1}{x}=\dfrac{17}{4}\)
join both fractions together
\(\sf \rightarrow \dfrac{x^2+1}{x}=\dfrac{17}{4}\)
cross multiply
\(\sf \rightarrow 4(x^2+1)=17(x)\)
simplify
\(\sf \rightarrow 4x^2-17(x)+4=0\)
completing square
\(\sf \rightarrow 4x^2-16(x)-x+4=0\)
factor
\(\sf \rightarrow 4x(x-4)-1(x-4)=0\)
group the variables
\(\sf \rightarrow (4x-1)(x-4)=0\)
simplify
\(\sf \rightarrow (x-4)=0, \ (4x-1) =0\)
final answer
\(\sf \rightarrow x=4, \ x =\dfrac{1}{4}\)
Answer:
\(\boxed{x = \dfrac{1}{4}}\) and \(\boxed{x = 4}\)
Step-by-step explanation:
Given equation:
\(x + \dfrac{1}{x} = 4\dfrac{1}{4}\)
Step-1: Convert the mixed fraction on the R.H.S into improper fraction
\(x + \dfrac{1}{x} = 4\dfrac{1}{4}\)
\(x + \dfrac{1}{x} = \dfrac{4 \times4 + 1}{4}\)
\(x + \dfrac{1}{x} = \dfrac{16 + 1}{4}\)
\(x + \dfrac{1}{x} = \dfrac{17}{4}\)
Step-2: Make common denominators on the L.H.S:
\(x + \dfrac{1}{x} = \dfrac{17}{4}\)
\(\dfrac{x^{2} }{x} + \dfrac{1}{x} = \dfrac{17}{4}\)
Step-3: Combine the denominators on the L.H.S
\(\dfrac{x^{2} }{x} + \dfrac{1}{x} = \dfrac{17}{4}\)
\(\dfrac{x^{2} +1}{x} = \dfrac{17}{4}\)
Step-4: Use cross multiplication
\(\dfrac{x^{2} +1}{x} = \dfrac{17}{4}\)
\(x^{2} +1} = \dfrac{17x}{4}\)
\(4(x^{2} +1}) = {17x}\)
Step-5: Simplify the distributive property
\(4(x^{2} +1}) = {17x}\)
\(4x^{2} +4} = {17x}\)
\(-17x + 4x^{2} +4} = 0\)
Step-6: Change "-17x" to "-16x - x" as it is equivalent
\(-17x + 4x^{2} +4} = 0\)
\((-16x - x) + 4x^{2} +4} = 0\)
Step-7: Factor the common terms
\((-16x - x) + 4x^{2} +4} = 0\)
\(-16x - x + 4x^{2} +4} = 0\)
\(4x(-4 + x) - 1(x - 4) = 0\)
Step-8: Group the terms
\(4x(-4 + x) - 1(x - 4) = 0\)
\((x - 4)(4x - 1) = 0\)
Step-9i: Use cross multiplication for (x - 4)
\((x - 4)(4x - 1) = 0\)
\(x - 4 = \dfrac{0}{4x - 1 } = 0\)
Step-9ii: Use cross multiplication for (4x - 1)
\((x - 4)(4x - 1) = 0\)
\(4x - 1 = \dfrac{0}{x - 4} = 0\)
Thus \(x - 4 = 0\) and \(4x - 1 = 0\).
Step-10: Simplify both equations
\(4x - 1 = 0\) \(x - 4 = 0\)
\(4x = 0 + 1\) \(x = 0 + 4\)
\(4x = 1\) \(\boxed{x = 4}\)
\(\boxed{x = \dfrac{1}{4}}\)
Related Questions
f(x)= int 0 ^ x (t^ 3 +7t^ 2 +4) dt then
Answers
Since the given function is
\(f(x)=\int_0^x(t^3+7t^2+4)dt\)That means
\(f^{\prime}(x)=(t^3+7t^2+4)\)Then to find f''(x) we will differentiate f'(x) with respect to t
\(\begin{gathered} f“(x)=3t^{3-1}+7(2)t^{2-1}+0 \\ \\ f“(x)=3t^2+14t \end{gathered}\)The answer is
\(f“(x)=3t^2+14t\)I need help with this question
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Using word problems and equations, Sarah worked for 10 hours and Penelope worked for 5 hours
What is the number of hours Sarah and Penelope worked?This is a word problem and in order to solve this, we need to translate mathematical statements in form of word problems into mathematical equations.
Let's assume that Sarah worked x hours.
Given that Sarah can iron 30 shirts per hour, the total number of shirts she ironed is 30x.
Since Penelope worked half the hours of Sarah, Penelope worked x/2 hours.
Given that Penelope can iron 35 shirts per hour, the total number of shirts she ironed is 35 * (x/2) = (35/2)x.
The total number of shirts ironed by both Sarah and Penelope is 475 shirts.
So, we can write the equation: 30x + (35/2)x = 475.
To solve this equation, we can simplify it: (60/2)x + (35/2)x = 475, which becomes (95/2)x = 475.
Now, we can solve for x: x = (475 * 2) / 95 = 10.
Therefore, Sarah worked 10 hours and Penelope worked half of that, which is 5 hours.
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Select the correct answer.
Which statement correctly compares the graph of function g with the graph of function ??
FE) = e²-
g(x) = ² - 4
O A.
OB.
O C.
O D.
The graph of function g is a horizontal shift of the graph of function to the right.
The graph of function g is a vertical stretch of the graph of function f.
The graph of function g is a vertical compression of the graph of function f.
The graph of function g is a horizontal shift of the graph of function f to the left.
Reset
Next
Answers
A statement that correctly compares the graph of function g with the graph of function f include the following: C. The graph of function g is a vertical compression of the graph of function f.
What is a dilation?In Mathematics and Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.
Therefore, the dimension or side lengths of the dilated geometric object would be stretched or compressed (shrunk) depending on the scale factor that is applied.
When the parent function \(f(x) = e^x -4\) is vertically compressed by a scale factor of 1/2, the transformed function g(x) is given by the following equation;
g(x) = kf(x)
g(x) = 1/2f(x)
\(g(x) = \frac{1}{2} e^x -4\)
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I need help with question 3 in a Pre algebra homework I gotta place numbers to biggest and smallest.
Answers
In meter, centimeter and millimeter largest unit is meter, then centimeter and then milimeter. For conversion 1 m=100 cm, 1 m=1000 cm.
Convert all the number to same unit for compare with each other.
First option is 7560 m.
Second option is,
\(7.56\times10\text{ cm}\times\frac{1\text{ m}}{100\text{ cm}}=0.756\text{ m}\)Third option 7.56 m is already in meter.
Consider the fourth option,
\(7.56\times10^4\text{ m=75600 m}\)Consider option fifth,
\(7.56\times10^4\text{ cm}\times\frac{1\text{ m}}{100\text{ cm}}=756\text{ m}\)Now check which digit is largest.
Largest is 75600 so first blank digit is ,
\(7.56\times10^4\text{ m}\)Second larget is 7560. So second blank digit is 7560 m.
Third largest is 756 m, So third blank digit is,
\(7.56\times10^4\text{ cm}\)Fourth largest is 7.56 m so in fourth blank digit is,
7.56 m
Fifth largest or smallest digit is 0.756 m. So in last blank digit is,
\(7.56\times10\text{ cm}\)4. A bag of cat food has 16 1/2 cups of food. Cupcake (the cat) eats 1 1/2 cups a day. How many days will the bag of cat food last? *
Answers
Answer:
11
Step-by-step explanation:
Since the cat is eating 1.5 a day and there is 16.5 cups of food. You will just need to divide 16.5 by the 1.5
i dont understand this
Answers
We can Add 7 black beads to make ratio 3 : 1.
Since we can only change the number of black beads, decide how many black beads you will add based on how many white beads there are.
There are three white beads in the picture.
Total beads we will have (b meaning black)b : 3
Ratio black : white beads 3 : 1
Use the common ratio, which is a number that both sides of the original ratio multiply by to get to the new ratio.
Find common ratio by dividing total by ratio white beads: 3/1 = 3
Multiply ratio black beads by common ratio. 3 X 3 = 9
We need 9 black beads in total.
Check answer
9 : 3
Both sides divisible by 3; reduce ratio
= 3 : 1
Which is Correct ratio
Hence, There will be a total of 9 black beads, but we already have 2 black beads:
(9 total) - (2 original) = (7 to add)
Therefore , we need to add 7 black beads.
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Which equation represents the parabola with focus (8, 4) and vertex (8, 2)
Answers
Answer:
Step-by-step explanation:
The focus lies above the vertex, so the parabola opens upwards.
Herbert was given a pocket watch bass grandfather. The value of the watch, for any given year, t, from the time Herbert received it is modeled by the function f(t) = 150(1.35)^t. He was also given a classic guitar. It's value for any given year is modeled by the function represents in the table:
t: 0, 1, 2, 3, 4
g(t): 175 210, 252, 302.40, 362.88
What is the positive difference in values of the items in the sixth year?
A.) $385.57
B.) $472.66
C.) $835.54
D.) 893.60
Answers
Answer:
the answer is A
Step-by-step explanation:
I took the test
A teacher is organizing binders for her students. She has 54 pieces of lined paper, 36 pieces of grid paper, and 72 dividers. What is the greatest number of identical binders that she can make? Please help!
Answers
Using the highest common factor, the greatest number of identical binders that the teacher can make is 18.
What is the highest common factor?The highest common factor or multiple of the given numbers is the highest number that can divide them without a remainder.
We know that 2, 9, and 18 can divide 54, 36, and 72 without leaving a remainder.
We can see that the highest common factor is 18.
When we divide 54 by 18, the quotient is 3. If you divide 36 by 18, the quotient is 2. When you divide 72 by 18, the result is 4.
The number of lined paper = 54 pieces
The number of grid paper = 36 pieces
The number of dividers = 72 dividers
The common factors of 54, 36, and 72 are 2, 9, and 18.
The highest common factor of 54, 36, and 72 is 18.
Thus, 18 binders containing 3 pieces of lined paper, 2 pieces of grid paper, and 4 dividers can be made from the collection, using their HCF.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answers
Inequalities help us to compare two unequal expressions. The correct representations of the inequality –3(2x – 5) < 5(2 – x) are A and C.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
The given inequality can be written as,
-3(2x - 5) < 5(2 - x)
-6x + 15 < 10 - 5x (It is the third option)
-6x + 5x < 10 - 15
-x < -5
x > 5 (First option)
Hence, the correct representations of the inequality –3(2x – 5) < 5(2 – x) are A and C.
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Which expression is equivalent to StartRoot 8 x Superscript 7 Baseline y Superscript 8 Baseline EndRoot? Assume x greater-than-or-equal-to 0.
x y squared StartRoot 8 x cubed EndRoot
2 x cubed y cubed StartRoot x y squared EndRoot
2 x cubed y Superscript 4 Baseline StartRoot 2 x EndRoot
4 x cubed y Superscript 4 Baseline StartRoot x EndRoot
Answers
The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.
To understand why this is the case, let's break down each expression and simplify them step by step:
StartRoot \(8 x^7 y^8\) EndRoot:
We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.
Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.
(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:
Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.
Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.
Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.
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Use the graph to solve the equation.
f(x) = 0
The solutions are x =
Answers
Answer: ok so: the graph of a function intersects the x-axis will be the roots of f(x) = 0. Because the coordinates of the point where it intersects the xaxis will be (x, 0). y will be 0. What you need to do is add 0 wherever x is for eample: when multiplying 3 and 0 you get 0 then subtract 2 and y would equal negative 2. I hope this helps you
Step-by-step explanation:
From the graph, the x values are -1 and 3, as the line cuts the x-axis at that coordinates: (-1,0), (3,0)
i need help with 7th grade math please 40 points need help ASAP + brainleist
Answers
Answer:
Area = 92 m^2
Step-by-step explanation:
Area of Trapezoid: Area = 1/2 * (Top_Base + Bottom_Base) * Height.
Area = 1/2 * (16m + 7m) * 8m
Area = 1/2 * (23m) * 8m
Area = 23m * 4m = 92 m^2
Answer:
92 m²
Step-by-step explanation:
Formula for area of trapezoid :
A = 1/2 x (a + b) x ha and b = parallel sides of the trapezoidh = height of the trapezoidSolving with the given values :
A = 1/2 x (16 + 7) x 8A = 4 x 23A = 92 m²Joanna's vegetable garden covers an area of 16 of a square mile. If the garden is 14 mile wide, how long does the garden stretch?
112 mile
1 over 12 mile
512 mile
5 over 12 mile
23 mile
2 thirds mile
34 mile
Answers
The length of the rectangular garden given the area and width is 8/7 miles
Area of rectangleA rectangle is a form of quadrilateral having opposing sides parallel and four right angles. The area of a rectangle can be calculated by multiplying the length by width.
Width of the rectangular garden = 14 mileLength of the rectangular garden = x mileArea of the garden = 16 square milesArea of a rectangular garden = length × width
16 = x × 14
16 = 14x
divide both sides by 14x = 16 / 14
x = 8/7 miles
Therefore, the length of the rectangular garden given the area and width is 8/7 miles.
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Assume the random variable X is normally distributed with mean = 50 and standard deviation = 7. Compute the probability, P(X > 35). Be sure to draw a normal curve with the area corresponding to the probability shaded.
Answers
Answer:
P [ X > 35 ] = 0,983 or P [ X > 35 ] = 98,3 %
Step-by-step explanation: See Annex valid region for 98,3 in red lines
P [ X > 35 ] = 1 - P [ X ≤ 35 ]
P[ X ≤ z ] = ( X - μ₀ ) / σ
P [ X ≤ 35 ] = ( 35 - 50 ) / 7
P [ X ≤ 35 ] = - 15 / 7
P [ X ≤ 35 ] = - 2,1428
We find for z(score) = - 2,14 in z-table the value of 0,01618
P [ X ≤ 35 ] = 0,01618 or P [ X ≤ 35 ] ≈ 1,62 %
And
P [ X > 35 ] = 1 - 0,01618
P [ X > 35 ] = 0,983 or P [ X > 35 ] = 98,3 %
What are the coordinates of the terminal point determined by t = 1177?
○ A (-4)
○ B. (-.-)
OC (1)
OD. (1.)
Answers
The Coordinates of the terminal point determined by `t = 1177` are approximately `(-0.17101, -0.98526)`.Thus, the correct option is B (-0.17101, -0.98526).
The following trigonometric function represents a point P on the unit circle as a function of the angle θ in standard position: `(cos θ, sin θ)`.
Here, we have to determine the coordinates of the terminal point determined by `t = 1177`.Terminal Point on a unit circle:The terminal point is a point on a circle that lies on the terminal side of an angle. The angles that end on the same terminal side of the x-axis are called coterminal angles. The angle between the positive x-axis and the line segment connecting the origin of the circle and the point on the circle is called the angle in the standard position.
So, the angle measure `t = 1177` may be too large or too small to locate the corresponding point P on the unit circle. To find an equivalent angle between 0 and 360 degrees, we may subtract or add an integral number of revolutions: `1177 - 360 × 3 = 97`.That is, an angle of `t = 1177` degrees is coterminal with an angle of `t = 97` degrees. The terminal point determined by `t = 1177` is the same as the terminal point determined by `t = 97`.
The point on the unit circle with `t = 97` degrees lies in the fourth quadrant because the standard angle of 97 degrees is obtained by rotating a ray 97 degrees counterclockwise from the positive x-axis.So, `P = (cos 97°, sin 97°)`.We can approximate the values of `cos 97°` and `sin 97°` using a calculator or computer software as: `cos 97° ≈ -0.17101` and `sin 97° ≈ -0.98526`.
Therefore, the coordinates of the terminal point determined by `t = 1177` are approximately `(-0.17101, -0.98526)`.Thus, the correct option is B (-0.17101, -0.98526).
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Find the equation of the parabola in vertex form that has a vertex of (4,-2) and a y intercept of (0,-66)
Answers
The equation of the Parabola in vertex form that has a vertex of (4, -2) and a y-intercept of (0, -66) is:y = -4(x - 4)^2 - 2
The vertex form of a parabola is given by:y = a(x - h)^2 + k
where (h, k) is the vertex of the parabola.
We are given that the vertex is (4, -2), so we can substitute these values in the equation to get:y = a(x - 4)^2 - 2
Now, we need to find the value of "a". To do this, we can use the fact that the y-intercept is (0, -66). Since the point (0, -66) lies on the parabola, we can substitute x = 0 and y = -66 in the equation above to get:-66 = a(0 - 4)^2 - 2
Simplifying this, we get:-66 = 16a - 2
Adding 2 to both sides, we get:-64 = 16a
Dividing both sides by 16, we get:a = -4
Substituting this value of "a" in the equation above, we get the equation of the parabola in vertex form:y = -4(x - 4)^2 - 2
Therefore, the equation of the parabola in vertex form that has a vertex of (4, -2) and a y-intercept of (0, -66) is:y = -4(x - 4)^2 - 2
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19. Annie registra cuánto dinero encuentra en una semana. Encuentra $0.19 el lunes, 0.22 el miércoles y $0.35 el jueves. El resto de los días no encontró dinero.
Answers
The amount of money found on Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday is $0.19, $0, $0.22, $0.35, $0, $0, and $0, respectively.
Annie finds money on certain days of the week and records the amount. The amount of money she found on Monday is $0.19. The amount of money she found on Wednesday is $0.22. The amount of money she found on Thursday is $0.35.
We know that she does not find any money on rest of the days. There are seven days in a week. So, she found $0 on Tuesday, Friday, Saturday, and Sunday.
Hence, the amount of money found on Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday is $0.19, $0, $0.22, $0.35, $0, $0, and $0, respectively.
The complete question is given below.
Annie records how much money she finds in a week. She finds $0.19 on Monday, $0.22 on Wednesday, and $0.35 on Thursday. The rest of the days he found no money. Write the amount of money found on all the days of the week.
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Despite the large number of questions Allison missed on her final exam in Organic Chemistry, her score was listed as being in the 72nd percentile of scores for all students. Her score falls
a. between the first quartile and the median.
b. between the minimum and the first quartile.
c. between the third quartile and the maximum
d. between the median and the third quartile.
Answers
Answer:
A
Step-by-step explanation:
The product of 0.4 and a number is 8.
(a) Represent the statement as an equation. Use n for the variable.
(b) Determine the solution set using the replacement set .
Answer:
Answers
20 is a solution to the equation by using the replacement set.
Let the unknown variable be n.Given the following data:
Output = 8a. To represent the statement as an algebraic equation:
In this exercise, you're required to write a mathematical expression (algebraic equation) that represents the word sentence given.
Translating the word sentence into an algebraic expression, we have;
The product of 0.4 and a number is 8:
\(0.4n = 8\)
b. To determine the solution set using the replacement set:
Let's use the following set of numbers (0, 1, 10, 20)When n = 0:
\(0.4(0)=8\\\\0\neq 8\)
When n = 1:
\(0.4(1)=8\\\\0.4\neq 8\)
When n = 10:
\(0.4(10)=8\\\\4\neq 8\)
When n = 20:
\(0.4(20)=8\\\\8= 8\)
Therefore, 20 is a solution to the equation by using the replacement set.
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Answer:
20 is the answer.
Step-by-step explanation:
what is 7 times 4/5 ???
Answers
7 times 4/5 is the same as:
\(7\cdot\frac{4}{5}=\frac{7\cdot4}{5}\)So now we operate so:
\(\frac{28}{5}=5.6\)Evaluate the expression shown below and write your answer as a fraction in simplest form.
\frac{1}{10}+\frac{11}{20}
10
1
+
20
11
Answers
The addition of the fraction 1/10 + 11/20 based on the computation will be 13/20.
What is a fraction?In mathematics, a fraction is defined as a portion of the whole. If a pizza is cut into four equal pieces, each slice is represented by ¼.
It should be noted that a fraction simply means a part of a whole number. It should be noted that it's usually expressed as a/b where a is the numerator and b is the denominator.
In this case, we want to add 1/10 + 11/20. This will be illustrated thus:
= 1/10 + 11/20
= 2/20 + 11/20
= 13/20
Therefore the addition is 13/20.
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Re-write the quadratic function below in Standard Form
y = -9(x - 2)2 – 3
Answers
Answer:
Step-by-step explanation:
y = -9(x-2)2-3
multiply 9 by 2
y = -18(x-2)-3
multiply -18 by x and -2
y = -18x + 36 - 3
subtract 36 and 3
y = -18x + 33
add 18x to both sides
y + 18x = 33
the student government claims that 70% of all students favor an increase in student fees to buy indoor potted plants for the classrooms. a random sample of 12 students produced 2 in favor of the project.
(a) What is the probability that 2 or fewer in the sample will favor the project, assuming the student government's claim is correct? (Use 3 decimal places.) (b) Do the the data support the student government's claim, or does it seem that the percentage favoring the increase in fees is less than 70%? The data do not give us any indication that the percent favoring the increase in fees differs from 70%. The data seem to indicate that the percent favoring the increase in fees is greater than 70%. The data seem to indicate that the percent favoring the increase in fees is less than 70%. The data seem to indicate that the percent favoring the increase in fees is equal to 70%.
Answers
The probability that 2 or fewer in the sample will favor the project is 4.368 × 10⁻⁶ and Also The data seem to indicate that the percent favoring the increase in fees is less than 70%
According to the question,
It is given that according to the student's government
The probability that number of students in favor of increment in fees : p = 0.70
The probability that number of students against the increment : q = 0.30
Sample Size : n = 12
Number of students follows Binomial distribution
(a) We have to find the probability that 2 or fewer in the sample will favor the project
P( x ≤ 2) = P(0) + P(1) + P(2)
As we know ,
P(x) = ⁿCₓpˣq⁽ⁿ⁻ˣ⁾
=> P( x ≤ 2) = ¹²C₀p⁰q¹² + ¹²C₁p¹q¹¹ + ¹²C₂p²q¹⁰
=> P( x ≤ 2) = 1×(0.30)¹² + 12×(0.70)(0.30)¹¹ + 12×11/2 × (0.70)²(0.30)¹⁰
=> P( x ≤ 2) = (0.30)¹⁰ [ 0.09 + 0.21 + 0.48]
=> P( x ≤ 2) = 5.9×10⁻⁶[0.78]
=> P( x ≤ 2) = 4.368 × 10⁻⁶
Which is very close to zero
(b) The data doesn't support the student government claim.
The data seem to indicate that the percent favoring the increase in fees is less than 70%.
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What is the value of x?
Answers
Answer: Value of x is 16
Step-by-step explanation:
Triangle ABC and ADE are Similar Triangles using Angle-Angle-Angle similarity,
therefore,
\(\frac{AB}{BC}=\frac{AD}{DE}\)
AB=x
BC=8
AD=x+6
DE=11
on substituting value,
\(\frac{x}{8}=\frac{x+6}{11}\)
on cross multiplying,
11x = 8x+48,
subtracting 8x on both sides,
3x = 48,
dividing both sides by 3,
x=16
Therefore, value of x is 16
3 6 9 12 15 18 21 24 27 30 is odd or even numbers?
Answers
Answer: Half of them are even and half of them are odd.
Step-by-step explanation:
The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.
The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.
Therefore, out of the given numbers, half of them are even and half of them are odd.
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Select whether the pair of lines is parallel, perpendicular, or neither. y−4=3(x+5), y+3=−13(x+1)
Answers
Answer:
neither
Step-by-step explanation:
parallel lines will have the same number next to the x
perpendicular lines will have the negative reciprocal number next to the x
(for example 2 and -1/2 are negative reciprocals)
y−4=3(x+5)
parenthesis first
y−4=3x+15
y=3x+19
y+3= −13(x+1)
y+3= −13x−13
y= −13x−16
3x and −13x are neither the same nor negative reciprocals of each other so
the answer is neither
True or False: The range of sine is...
True
False
Answers
It is false that the range of the sine function is 0 ≤ ∅ ≤ π
How to determine the true statement?From the question, we have the following parameters that can be used in our computation:
Function: sine function
Also from the question, we have
Range: 0 ≤ ∅ ≤ π
As a general rule, we have:
The minimum value of a sine function is -1The maximum value of a sine function is 1This means that the range of the sine function is from [-1, 1].
This can also be represented as -1 ≤ ∅ ≤ 1
Hence. the given statement about the sine function is false
Read more about sine functions at
https://brainly.com/question/21902442
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Answer:
The answer is false.
Step-by-step explanation:
The range of the sine function is NOT 0 ≤ ∅ ≤ π
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find out the time at which the rocket will reach its max, to the nearest 100th of a second.
Answers
Answer:
x=5.09 seconds (times at max)
Step-by-step explanation:
Use the Remainder Theorem to determine which of the roots are roots of F(x). Show your work.
Polynomial: F(x)=x^3-x^2-4x+4
Roots: 1, -2, and 2.
Answers
Answer: x1=1 x2=-2 and x3=2
Step-by-step explanation:
1st x1=1 is 1 of the roots , so
F(1)=1-1-4+4=0 - true
So lets divide x^3-x^2-4x+4 by (x-x1), i.e (x^3-x^2-4x+4) /(x-1)=(x^2-4)
x^2-4 can be factorized as (x-2)*(x+2)
So x^3-x^2-4x+4=(x-1)*(x^2-4)=(x-1)(x-2)*(x+2)
So there are 3 dofferent roots:
x1=1 x2=-2 and x3=2