Select the correct answer.
Which statement is true about the y-intercept of a quadratic function?
ОА.
A quadratic function can only have one y-intercept.
OB.
A quadratic function can have up to two y-intercepts.
O c.
The y-intercept is also called a zero of the function.
OD
The y-intercept is located at the point where the value of y is 0.

Answer:

y = m - 6

Step-by-step explanation:

You can plug in the values and each time the equation comes out true

Answer:

Step-by-step explanation:

You can plug in the values and each time the equation comes out true

4 = 10 - 6

5 = 11 - 6

6 = 12 - 6

Step-by-step explanation:

The probability that Becky's proportion of poses held for over a minute is greater than Carla's is 0.741.

This can be determined by using the z-table, which shows the probability that a random variable is in the range that is a certain distance away from the mean.

In this case, we are looking at the probability that a random variable is greater than C, so we use the z-value for 0.741.

The integral is ln|x + cos(x)| + C, where C represents the constant of integration.

To find the integral of the function 1/(x + cos(x)), we can employ a combination of algebraic manipulation and the use of standard integration techniques. Here's the solution:

First, let's rewrite the integral in a slightly different form to simplify the process:

∫(1/(x + cos(x))) dx

We notice that the denominator, x + cos(x), is not amenable to direct integration. To overcome this, we employ a substitution. Let's set u = x + cos(x). Now, differentiate u with respect to x: du/dx = 1 - sin(x).

Rearranging this equation, we get dx = du/(1 - sin(x)).

Substituting these values, the integral becomes:

∫(1/(u(1 - sin(x)))) du

Next, we simplify further by factoring out 1/(1 - sin(x)) from the integral:

∫(1/(u(1 - sin(x)))) du = ∫(1/u) du = ln|u| + C

Replacing u with its original expression, we have:

ln|x + cos(x)| + C

Therefore, the answer to the integral is ln|x + cos(x)| + C, where C represents the constant of integration.

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2/3 of 35 is 23. Kofi is 23.

Answer:

Step-by-step explanation:

2+6(3)-10/2

2+18-5 NOT 8(3)-10/2: 2+6*3!=8*3=>2(3)+6(3)=8(3)

20-5=15

A rectangle and two semicircles make up this figure. The perimeter of this figure is 423.52m.

The complete length of a shape's boundary is referred to as the perimeter in geometry. The perimeter of a shape is determined by adding the lengths of all of its edges and sides. Linear measurements like centimeters, meters, inches, and feet are used to express its dimensions. The area around a form's edge is known as its perimeter. The perimeter of a shape is always calculated by summing the lengths of its sides.

Perimeter=2*1/2πd+2a

d=68, a=105

Perimeter = 2*1/2*3.14*68+2*105

423.52m

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9514 1404 393

Answer:

  F = 3.84×10^23/R²

Step-by-step explanation:

No units are given for distance, so we cannot give a constant of proportionality that has suitable units.

The general form for inverse square variation is ...

  F = k/R²

Then the value of k can be found from ...

  k = F·R² = (6×10^5)(8×10^8)^2 = 3.84×10^23

The formula relating the given F and R is ...

  F = 3.84×10^23/R²

Answer:

4.5 hours

Step-by-step explanation:

fbdjdbercyTxxivdu

Answer:

Basically You are asking how many hours we need to reach 7:00, if we are at 2:30, so: we need 4hours, to reach 6:30, and and extra 30minutes to reach 7:00pm. The answer is 4hours and 30minutes.

To simplify the expression (2x-3)(5x^2-2x+7), we can use the distributive property.

First, multiply 2x by each term inside the second parentheses:

2x * 5x^2 = 10x^3

2x * -2x = -4x^2

2x * 7 = 14x

Next, multiply -3 by each term inside the second parentheses:

-3 * 5x^2 = -15x^2

-3 * -2x = 6x

-3 * 7 = -21

Combine all the resulting terms:

10x^3 - 4x^2 + 14x - 15x^2 + 6x - 21

Now, combine like terms:

10x^3 - 19x^2 + 20x - 21

So, the simplified expression is 10x^3 - 19x^2 + 20x - 21.

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Answer:

the area of the rectangle is A=L•W

The length is 3m less than twice its width W: L+ 3m=2W...->, L=2W-3m

A=L-W

27m²=(2W-3m)-W

27m2=2w2-3m-W

2w2-3wm-27m2=0

....use quadratic formula -(-3m)+ (-3m)²-4-2-(-27m²)

W=

2-2

w=(3m± √9m²+216m²)

w=(3m+ √225m²)

W=(3m± 15m...you need only positive root because width cannot be negative

W= 3m+15m

4

W=. 4

18m

W=4.5m ......now find the L

L=2.4.5m-3m

L=9m-3m

L=6m

Answer:

W = 4.5cm

L = 6cm

Step-by-step explanation:

The x-intercept of function f(x) is x = 7.

We have,

Since the x-intercept of a function is the value of x at which the function equals zero, we can find it by setting f(x) = 0 and solving for x.

Let's assume that the function f(x) is a linear function of form f(x) = mx + b, where m is the slope and b is the y-intercept.

Since we know that f(-1) = 7 and f(5) = 7/2, we can set up two equations:

-7m + b = 7 (when x = -1)

5m + b = 7/2 (when x = 5)

To solve for m and b, we can subtract the first equation from the second to eliminate b:

5m + b - (-7m + b) = 7/2 - 7

12m = -13/2

m = -13/24

Now we can substitute m into either equation to solve for b:

-7(-13/24) + b = 7

b = 91/24

Therefore,

The function f(x) is f(x) = (-13/24)x + 91/24.

To find the x-intercept, we can set f(x) = 0:

(-13/24)x + 91/24 = 0

x = 7

Thus,

The x-intercept of function f(x) is x = 7.

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Every rational number is of form = P/2

where q=0 & p, q are polynomial functions.

Let f(x)= P(x)/q(x),q(x)=0

where p(x) & q(x) are polynomials

Since p(x) & q(x) are polynomials we know that every polynomial function is continuous.

p(x),q(x) are continuous functions if p, q are continuous then  p/q is continuous. Thus f(x)= p(x)/q(x) is continuous except at q(x)=0.

In calculus, the ε-δ definition of a limit is an algebraically precise formulation of evaluating the limit of a function. Informally, the definition states that a limit L of a function at a point \(x_{0}\) exists if no matter how \(x_{0}\) is approached, the values returned by the function will always approach L. This definition is consistent with methods used to evaluate limits in elementary calculus, but the mathematically rigorous language associated with it appears in higher-level analysis. The ε-δ definition is also useful when trying to show the continuity of a function.

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If a company's sales decreased 1% this year, to $7958 then the sales last year was $8036.36.

To find the sales last year, we need to reverse the 1% decrease and calculate it based on the current sales.

Let's denote the sales last year as X.

1% decrease from X can be represented as: X - (1/100) × X

= X - 0.01X

= 0.99X

According to the given information, the sales this year is $7958, which is equal to 0.99X.

0.99X = $7958

To find X, we divide both sides of the equation by 0.99:

X = $7958 / 0.99

X ≈ $8036.36

Therefore, the sales last year were approximately $8036.36.

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Answer:

When a circle is rotated 360 degrees about a line, it forms a three-dimensional object called a "sphere."

Step-by-step explanation:

Start with a two-dimensional circle. A circle is a flat, round shape with a constant radius, and it lies on a plane.

Choose a line, let's call it line "m," around which you want to rotate the circle. The line "m" can be any line in space.

Imagine taking the circle and rotating it around line "m" while keeping the circle's center fixed. The circle will rotate in a full 360-degree revolution around the line.

As the circle rotates, each point on its circumference traces out a path, forming a three-dimensional shape. This shape is known as a sphere.

The resulting sphere is a perfectly symmetrical object. All points on its surface are equidistant from its center, and it has no edges or faces like other polyhedral shapes.

To summarize, rotating a circle 360 degrees about a line produces a sphere, which is a three-dimensional object with no edges or faces, where all points on its surface are equidistant from its center.

Answer:

  c) BC/tan(20°)

Step-by-step explanation:

The mnemonic SOH CAH TOA can help you remember the relations between trig functions and angles. It tells you ...

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

  Tan = Opposite/Adjacent

In the case of the present triangle, these relations mean ...

  sin(B) = AC/BC   ⇒   AC = BCsin(70°)

  cos(C) = AC/BC   ⇒   AC = BCcos(20°)

  tan(B) = AC/BA   ⇒   AC = BAtan(70°)

  tan(C) = BA/AC   ⇒   AC = BA/tan(20°)

__

The answer choice that is not on this list is ...

  c) BC/tan(20°) . . . . . . not equivalent to AC

_____

Additional comment

The interior angle at C is the supplement of the given angle 160°. These angles form a linear pair.

  C = 180° -160° = 20°

The interior angle at B is the complement of the interior angle at C.

  B = 90° -20° = 70°

Answer:

B. 46.

Step-by-step explanation:

First we set up the equation A(n)=-172 and substitute the given equation for A(n), giving us -172=8+(n-1)(-4). Simplifying, we get -180=(-4n+12), or -4n=-192, or n=48. However, n represents the number of terms in the sequence, and since the sequence starts with n=1, we need to subtract 1 from our answer to get the term number corresponding to A(n)=-172. Therefore, the answer is B) 46.

Answer:

Answer:

\( \huge\mathfrak\pink{S} \huge\mathfrak\purple{o} \huge\mathfrak\blue{l} \huge\mathfrak\red{u} \huge\mathfrak\green{t} \huge\mathfrak\pink{i}\huge\mathfrak\purple{o}\huge\mathfrak\red{n}\huge\mathfrak\orange{➔}\ \)

by using Pythagoras law:

h²=p²+b²

x²=9²+12²

x=√225=15unit

The lack of significant variation "There is no association because the distribution of favorite music is the same among the subject groups.,", hence option 4 is correct.

When comparing the conditional distribution of one categorical variable across many groups identified by another categorical variable, a clustered bar graph, also known as a grouped bar graph, is employed. There will be a change in the shape of the distribution between groups if there is a relationship between the two variables. The distribution across groups should be essentially the same if the variables are substantially independent.

The lack of significant variation in the distribution of favorite music throughout the range of preferred disciplines raises the possibility that there is no correlation between preferred musical genre and preferred academic fields.

If there is a relationship between preferred musical genre and preferred academic topics, then the distribution of preferred music must vary for each subject.

The last choice, which claims that "There is no association because the distribution of favorite music is the same among the subject groups.," is thus the one that is right.

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The length of side x is approximately 24.87, rounded to the nearest hundredth.

how can we find side of the triangle?

To find the length of side x, we can use the sine function, which relates the opposite side to an angle to the hypotenuse:

sin(11°) = opposite side/hypotenuse

Rearranging this equation, we get:

opposite side = sin(11°) * hypotenuse

We know that the hypotenuse has a length of 130, so we can substitute that in:

opposite = sin(11°) * 130

Using a calculator, we can evaluate sin(11°) to be approximately 0.1919, so we can substitute that in as well:

opposite = 0.1919 * 130

Simplifying this expression, we get:

opposite ≈ 24.87

Therefore, the length of side x is approximately 24.87, rounded to the nearest hundredth.

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The number of race times recorded as portrayed by the number of data points is seven(7).

From the task content;

Additionally, it follows from the task content that the times recorded were; 6.8,7.3,7.1 ,7.0,7.2,7.3 and 7.0.

On this note, the number of race times recorded as portrayed by the number of data points is seven(7).

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Answer:

\(\cos y = -\dfrac{\sqrt{3} }{3}\)

\(\tan y = \sqrt{2}\)

Step-by-step explanation:

Recall that

\(\boxed{\csc y := \dfrac{1}{\sin y}}\)

\(\boxed{\cot y := \dfrac{\cos y}{\sin y}}\)

We know that

\(\csc y = \dfrac{-\sqrt{6} }{2}\)

Note that according to the definition of \(\csc y\) it is true that both sine and cosine are negative, once \(\csc y = \dfrac{-\sqrt{6} }{2}\) . Because \(\cot y > 0\), this conclusion is true. We basically have

\(\boxed{(-a)(1/-b)=a/b \text{ such that } a,b\in\mathbb{R}_{\geq 0}}\)

Sure it is true \(\forall y\in\mathbb{R}\) but perhaps this way is better to understand.

In order to find sine, we can use the definition and manipulate the rational expression.

\(\csc y = \dfrac{-\sqrt{6} }{2} = \dfrac{-\sqrt{6} / -\sqrt{6} }{2/-\sqrt{6} } = \dfrac{1 }{-\dfrac{2}{\sqrt{6} } }\)

Therefore,

\(\sin y =-\dfrac{2}{\sqrt{6} }\)

Here I just divided numerator and denominator by \(-\sqrt{6}\).

Now, to find cosine we can use the identity

\(\boxed{\sin^2y +\cos ^2y =1}\)

Thus,

\(\left(-\dfrac{2}{\sqrt{6} }\right)^2 + \cos ^2y =1 \implies \dfrac{4}{6 } +\cos ^2y =1\)

\(\implies \cos ^2y =1 - \dfrac{4}{6 } \implies \cos ^2y =\dfrac{1}{3 } \implies \cos y = \pm \dfrac{\sqrt{1} }{\sqrt{3} } = \pm \dfrac{\sqrt{1} \sqrt{3} }{3} = \pm \dfrac{\sqrt{3} }{3}\)

\(\cos y = \pm\dfrac{\sqrt{3} }{3}\)

Once we have \(\cot y > 0\), we just consider

\(\cos y = -\dfrac{\sqrt{3} }{3}\)

FInally, for tangent, just consider

\(\boxed{\tan y := \dfrac{\sin y}{\cos y}}\)

thus,

\(\tan y = \dfrac{\sin y}{\cos y} = \dfrac{-\frac{2}{\sqrt{6} }}{-\frac{\sqrt{3} }{3}} = \dfrac{6}{\sqrt{18} } =\dfrac{6}{3\sqrt{2} } =\dfrac{2}{\sqrt{2} } = \sqrt{2}\)

Step-by-step explanation:

Taking the provided equation ,

\(\implies \dfrac{3x+4}{5}-\dfrac{2}{x+3} =\dfrac{8}{5} \)

1) Here denominator of two fractions are 5 and x +3 . So their LCM will be 5(x+3)

\(\implies \dfrac{(x+3)(3x+4)-(2)(5)}{5(x+3)}=\dfrac{8}{5} \)

2) Transposing 5(x+3) to Right Hand Side . And 5 to Left Hand Side .

\(\implies 5(3x^2+4x+9x+12 -10) = 40(x+3)\)

3) Multiplying the expressions.

\( \implies 5(3x^2+13x+2) = 40x + 120 \)

4) Opening the brackets .

\(\implies 15x^2+ 65x + 10 = 40x + 120 \)

5) Transposing all terms to Left Hand Side .

\(\implies 15x^2 + 65x - 40x + 10 - 120 = 0 \\\\\implies 15x^2 +25x - 110 = 0\)

6) Solving the quadratic equation .

\(\implies 5(3x^2+5x -22) = 0 \\\\\implies 3x^2+13x-22 = 0 \\\\ \implies x = \dfrac{-b\pm \sqrt{b^2-4ac}}{4ac} \\\\\implies x = \dfrac{-5\pm \sqrt{5^2-4(-22)(3)}}{2(3)} \\\\\implies x = \dfrac{-5\pm \sqrt{289}}{6}\\\\\implies x =\dfrac{-5\pm 17}{6} \\\\\implies x = \dfrac{17-5}{6},\dfrac{-17-5}{6}\\\\\implies x = \dfrac{12}{6},\dfrac{-22}{6} \\\\\underline{\boxed{\red{\bf\implies x = 2 , \dfrac{-11}{3}}}}\)

Answer:

\(x=2\\x=-\frac{11}{3}\)

Step-by-step explanation:

Solve the rational equation:

\(\displaystyle \frac{3x+4}{5}-\frac{2}{x+3}=\frac{8}{5}\)

To eliminate denominators, multiply by 5(x+3) (x cannot have a value of 3):

\(\displaystyle 5(x+3)\frac{3x+4}{5}-5(x+3)\frac{2}{x+3}=5(x+3)\frac{8}{5}\)

Operate and simplify:

\(\displaystyle (x+3)(3x+4)-5(2)=(x+3)(8)\)

\(\displaystyle 3x^2+4x+9x+12-10=8x+24\)

Rearranging:

\(\displaystyle 3x^2+4x+9x+12-10-8x-24=0\)

Simplifying:

\(\displaystyle 3x^2+5x-22=0\)

Rewrite:

\(\displaystyle 3x^2-6x+11x-22=0\)

Factoring:

\(\displaystyle 3x(x-2)+11(x-2)=0\)

\(\displaystyle (x-2)(3x+11)=0\)

Solving:

\(x=2\\x=-\frac{11}{3}\)

Answer:

about 20.5 hours

Step-by-step explanation:

first find out how much money he earned during the week by subtracting the friday balance and the monday balance

375.75 - 83.50 = $292.25 was the amount earned during the week

divide the amount earned by the amount earned per hour

292.25 / 14.25 ≈ 20.5 hours worked that week

hope this helps <3

Answer:

  the solutions cannot include 0

Step-by-step explanation:

When you consider this equation, you see denominators of 5x and 4x. These cannot be zero, because the equation is undefined when they are zero. So, the value x cannot have is 0.

Answer:

Step-by-step explanation:

If the order you select them is important

nmber of ways = 9! / (9-7)!

= (9*8*7*6*5*4*3*2*1) / (2*1)

= 9*8*7*6*5*4*3

= 181,440.

If the order does not matter:

nmber of ways = 9! / ((9-7)! * 7!)

= 9*8 / 2*1

= 36.

Answer:

translate?

Step-by-step explanation

translate it and i can help

Answer:

volume of sphere=4/3πr³=4/3×3.14×6²=164.16cm³

Answer:if you know how to do this your smart and in two years if someone can Answer ill give you a mil in cash swear

Step-by-step explanation:

Answer:

√10/2

Step-by-step explanation:

I took le test