What are the coordinates grapging x=3 and y=-2x+1

That's a question about quadratic function.

Any quadratic function can be represented by the following form:

[tex]\boxed{f(x)=ax^2+bx+c}[/tex]

Example:

[tex]f(x)= -3x^2-9x+57[/tex] is a function where [tex]a=-3[/tex], [tex]b=-9[/tex] and [tex]c=57[/tex].

Okay, in our problem, we need to find the value of x when [tex]f(x)=0[/tex]. That's mean that the result of our function is equal to zero. Therefore, we have the quadratic equation below:

[tex]x^2+4x-5=0[/tex]

To solve a quadratic equation, we use the Bhaskara's formula. Do you remember the value of a, b and c? They going to be important right now. This is the Bhaskara's formula:

[tex]\boxed{x=\frac{-b\pm \sqrt{b^2-4ac} }{2a} }[/tex]

So, let's see the values of a, b and c in our equation and apply them in the Bhaskara's formula:

In [tex]x^2+4x-5=0[/tex] equation, [tex]a=1[/tex], [tex]b=4[/tex] and [tex]c=-5[/tex]. Let's replace those values:

[tex]x=\frac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]

[tex]x=\frac{-4\pm \sqrt{4^2-4\times1\times(-5)} }{2\cdot1}[/tex]

[tex]x=\frac{-4\pm \sqrt{16-(-20)} }{2}[/tex]

[tex]x=\frac{-4\pm \sqrt{16 + 20)} }{2}[/tex]

[tex]x=\frac{-4\pm \sqrt{36} }{2}[/tex]

[tex]x=\frac{-4\pm 6 }{2}[/tex]

From now, we have two possibilities:

To add:

[tex]x_1 = \frac{-4+6}{2} \\x_1=\frac{2}{2} \\x_1=1[/tex]

To subtract:

[tex]x_2=\frac{-4-6}{2} \\x_2=\frac{-10}{2} \\x_2=-5[/tex]

Therefore, the result of our problem is: [tex]x_1 = 1[/tex] and [tex]x_2=-5[/tex].

I hope I've helped. ^^

Enjoy your studies.  \o/

Answer:

x = 4[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Pytago:

x[tex]x^{2} +7^{2} = 9^{2} \\\\x = \sqrt{9^{2} - 7^{2} } x = 4\sqrt{2}[/tex]

Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.

Remember: SOH-CAH-TOA

Looking from the given angle, we know the opposite side and want to know the adjacent side. Therefore, we should use the tangent function.

tan(54) = 16/BC

BC = 16/tan(54)

BC = 11.62 units

Hope this helps!

Answer:

72 degrees

Step-by-step explanation:

Area of a sector=(pi*r^2)*(Theta/360)

125*pi=pi*(625)*(theta/360)

(125*360)/625=theta

Theta=72 degrees

The angle theta of the sector of the given circle is 72 degrees.

We have given that,

In the diagram below, the circle has a radius of 25 inches.

The area of the shaded sector is 125π in^2.

[tex]Area \ of \ a \ sector=(pi*r^2)*(\Theta/360)[/tex]

Therefore we get,

[tex]125*pi=pi*(625)*(\theta/360)[/tex]

[tex](125*360)/625=\theta[/tex]

[tex]\theta=72 degrees[/tex]

Therefore we get the angle of the sector of the given circle is 72 degrees.

To learn more about the area of sector visit:

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Answer:

x= (2+ √ 34) /5 , (2- √ 34) /5

decimal form= 1.566

Step-by-step explanation:

Answer:

Option C. √280

Step-by-step explanation:

From the question given above, the following data were obtained

MN = 19

ML = 9

LN =?

We can obtain the value of LN by using the pythagoras theory as illustrated:

M ² = ML² + LN²

19² = 9² + LN²

361 = 81 + LN²

Collect like terms

361 – 81 = LN²

280 = LN²

Take the square root of both side

LN = √280

Therefore, the length of LN is √280

Answer:

√11 cm

Step-by-step explanation:

Pythagorean Thereom

a^2 + b^2= c^2

x^2 +5^2=6^2

x^2 + 25 = 36

subtract 25 from both sides

x^2=11

do the square root

x = √11

Let a, b, and c be vectors each starting at the origin and terminating at the points (x, x + 1), (x + 2, x + 3), and (x + 3, 2x + 4), respectively.

Then the vectors a - b, a - c, and b - c are vectors that point in directions parallel to each of the legs formed by the triangle with these points as its vertices.

If this triangle is to contain a right angle, then exactly one of these pairs of vectors must be orthogonal. In other words, one of the following must be true:

(a - b) • (a - c) = 0

or

(a - b) • (b - c) = 0

or

(a - c) • (b - c) = 0

We have

a - b = (x, x + 1) - (x + 2, x + 3) = (-2, -2)

a - c = (x, x + 1) - (x + 3, 2x + 4) = (-3, -x - 3)

b - c = (x + 2, x + 3) - (x + 3, 2x + 4) = (-1, -x - 1)

Case 1: If (a - b) • (a - c) = 0, then

(-2, -2) • (-3, -x - 3) = (-2)×(-3) + (-2)×(-x - 3) = 2x + 12 = 0   ==>   x = -6

which would make a - c = (-3, 3) and b - c = (-1, 5), and their dot product is not zero. Then the triangles vertices are at the points (-6, -5), (-4, -3), and (-3, -8).

Case 2: If (a - b) • (b - c) = 0, then

(-2, -2) • (-1, -x - 1) = (-2)×(-1) + (-2)×(-x - 1) = 2x + 4 = 0   ==>   x = -2

which would make a - c = (-3, -1) and b = (-1, 1), and their dot product is also not zero. The vertices are the points (-2, -1), (0, 1), and (1, 0).

Case 3: If (a - c) • (b - c) = 0, then

(-3, -x - 3) • (-1, -x - 1) = (-3)×(-1) + (-x - 3)×(-x - 1) = x ² + 4x + 6 = 0

but the solutions to x here are non-real, so we throw out this case.

So there are two possible values of x that make a right triangle, x = -6 and x = -2.

Answer: Distance = √145

Concept:

Here, we need to know the concept of the distance formula.    

The distance formula is the formula, which is used to find the distance between any two points.

If you are still confused, please refer to the attachment below for a clear version of the formula.

Solve:

Given information

(x₁, y₁) = (4, -9)

(x₂, y₂) = (5, 3)

Given formula

[tex]Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substitute values into the formula

[tex]Distance = \sqrt{(5-4)^2+(3+9)^2}[/tex]

Simplify values in the parentheses

[tex]Distance = \sqrt{(1)^2+(12)^2}[/tex]

Simplify exponents

[tex]Distance = \sqrt{1+144}[/tex]

Simplify by addition

[tex]Distance = \sqrt{145}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

[tex]\boxed {\boxed {\sf \sqrt {145} \ or \ 12.04}}[/tex]

Step-by-step explanation:

The distance between 2 points is calculated using the following formula.

[tex]d= \sqrt {(x_2-x_1)^2+(y_2-y_1)^2)[/tex]

In this formula, (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

We know the two points are (4, -9) and (5,3). If we match the values of the points and the coordinating variable, we see that:

Substitute the values into the formula.

[tex]d= \sqrt { ( 5 -4)^2 + ( 3 --9)^2[/tex]

Solve inside the parentheses.

[tex]d= \sqrt {(1)^2 + (12)^2}[/tex]

Solve the exponents.

[tex]d= \sqrt{ 1+144}[/tex]

Add.

[tex]d= \sqrt{145[/tex]

Take the square root.

[tex]d=12.04159458[/tex]

Let's round to the nearest hundredth. The 1 in the thousandth place tells us to leave the 4 in the hundredth place.

[tex]d \approx 12.04[/tex]

The distance between the 2 points is √145 or approximately 12.04.

Answer:

0.0733364

Step-by-step explanation:

Given :

Number of vegans = x ;

Sample size, n = 150

Zα/2 ; Zcritical at 95% = 1.96

p = x / n = 45 / 150 = 0.3

Margin of Error :

Zcritical * √(p(1 - p) / n)

1.96 * √(0.3(1 - 0.3) / 150)

Margin of Error :

1.96 * √(0.3 * 0.7) / 150)

1.96 * √0.0014

Margin of Error = 0.0733364

9514 1404 393

Answer:

  is a polynomial

Step-by-step explanation:

The expression is a sum of products.

Each product involves a numerical value and a product of variables to positive integer powers.

These meet the requirements for an expression to be a polynomial, so ...

  the given expression is a polynomial

Answer:

El capital que prestado al 10% bimestral durante 6 meses y 10 días produce un interés de $1140 es $3,600.

Step-by-step explanation:

Para determinar cuál es el capital que prestado al 10% bimestral durante 6 meses y 10 días produce un interés de $1140 se debe realizar el siguiente cálculo:

6 / 2 = 3

10/60 = 0.16666

10 x 3.1666 = 31.666

31.666 = 1140

100 = x

100 x 1140 / 31.666 = X

114,000 / 31.666 = X

3,600 = X

Por lo tanto, el capital que prestado al 10% bimestral durante 6 meses y 10 días produce un interés de $1140 es $3,600.

This requires finding the number of small sweaters the company made last week

Number of small sweaters the company produced last week is 372

Total sweaters made = 1,612

Let

Small sweaters = 3x

Medium sweaters = x

Large sweaters = 3(3x) = 9x

Total = small + medium + large

1,612 = 3x + x + 9x

1612 = 13x

Divide by 13

x = 1612/13

Medium sweaters = x = 124

Small sweaters = 3x

= 3(124)

= 372

Read more:

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Answer:

the second option #2

one fourth x (26-10) x 3

Step-by-step explanation:

Two of the options (#1 and #4) can be ruled out immediately since they don't involve the difference of 26 and 10.

#3 can be ruled out because the difference needs to be multiplied by one fourth, but this option gives the wrong answer since the multiplication is done before subtraction (BODMAS)

Answer:

c

Step-by-step explanation:

I got it correct on a quiz

Answer:

There are four ways to represent an inequality: Equation notation, set notation, interval notation, and solution graph.

Answer:

You'd think its 34% but apparently it's 16%.

I hope this is right. If its not then it must be 34%.

(A) -- or maybe (B). 80% confident it is A.

ED2021

Answer:

[tex]x ^{m - 3} \div x^{m - 4} \\ \frac{ {x}^{m - 3} }{ {x}^{m - 4} } \\ \frac{ {x}^{m - 3 - m + 4} }{x} \\ \frac{ {x}^{1} }{x} \\ x \: and \: x \: will \: cancel \: each \: other \: hence \: answer \: will \: be \: 1[/tex]

Answer:

a negative integer

Step-by-step explanation:

Answer:

Reflection

Step-by-step explanation:

It is the opposite of the first,...

Answer:

please write this question in English then I give answer

Let missing one be x

If both are similar

[tex]\\ \sf\longmapsto \dfrac{20}{25}=\dfrac{16}{x}[/tex]

[tex]\\ \sf\longmapsto \dfrac{4}{5}=\dfrac{16}{x}[/tex]

[tex]\\ \sf\longmapsto 4x=16(5)[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{16(5)}{4}[/tex]

[tex]\\ \sf\longmapsto x=20[/tex]

Answer:

It's a decimal, so it's around 6.771cm

Step-by-step explanation:

First, divide 144cm² by pi, or 3.14. Then find the square root of the answer, giving you the radius. The formula for the area of a circle is pi x radius squared, so to find out the radius you just use this formula in reverse.

If I messed up or didn't make my explanation clear, please comment.

Answer:

radius is [tex]\frac{12}{\sqrt{\pi } }[/tex] = 6.77 cm

Step-by-step explanation:

we know,

[tex]\pi[/tex] × r² = Area

⇒ [tex]\pi[/tex] × r² = 144

⇒ r² =[tex]\frac{144}{\pi}[/tex]

⇒ r= [tex]\frac{12}{\sqrt{\pi } }[/tex]

∴ r= [tex]\frac{12}{\sqrt{\pi } }[/tex]

pls mark this as the braniliest

Step-by-step explanation:

yo

so sorry I can't

really answer it

Answer:

A: The distribution is skewed to the left.

Step-by-step explanation:

Skewness:

If the distribution has a long left tail, it is skewed to the left.

If it has a long right tail, it is skewed to the right.

Otherwise, it is approximately symmetrical.

In this question:

Lots of values on the start(left), few on the end(right), so it is skewed to the left, and the correct answer is given by option a.

Answer:

113.1

Step-by-step explanation:

use the formula to solve for volume

Answer:

The 99% confidence interval for the difference in two proportions is (0.0456, 0.1944).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Western residents:

39% out of 640, so:

[tex]p_1 = 0.39[/tex]

[tex]s_1 = \sqrt{\frac{0.39*0.61}{640}} = 0.0193[/tex]

Eastern residents:

51% out of 540, so:

[tex]p_2 = 0.51[/tex]

[tex]s_2 = \sqrt{\frac{0.51*0.49}{540}} = 0.0215[/tex]

Distribution of the difference:

[tex]p = p_2 - p_1 = 0.51 - 0.39 = 0.12[/tex]

[tex]s = \sqrt{s_2^2+s_1^2} = \sqrt{0.0215^2+0.0193^2} = 0.0289[/tex]

Confidence interval:

[tex]p \pm zs[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].

The lower bound of the interval is:

[tex]p - zs = 0.12 - 2.575*0.0289 = 0.0456[/tex]

The upper bound of the interval is:

[tex]p + zs = 0.12 + 2.575*0.0289 = 0.1944[/tex]

The 99% confidence interval for the difference in two proportions is (0.0456, 0.1944).

Answer:

the answer is 240 degrees