Julie is solving the equation 3x² + 5x + 15 = 0 and notices that the discriminant b^2 - 4ac has a value of -155. This
tells her that the equation has

A one real roots.
B one imaginary root.
C two real roots.
D two imaginary roots

Answer:

x=1/3k-y-z

Step-by-step explanation:

3x+3y+3z=k

Move the variables to the right

3x= -3y-3z+k

Divide both sides of the equation by 3

x=1/3k-y+z

Answer:

Step-by-step explanation:

x = -A x 2/7 + 10

Answer:

-3.5 (or -3.50); each cup of coffee is $3.50

Step-by-step explanation:

the slope of the function is what is in front of the x

that is

-3.50 or just -3.5

this means that each cup of coffee is $3.50

Solution

From the given graph,

The maxima is

The minima isThe inetrev

aterval inwh which the function is increasing is

dec

Answer:

d ≈ 11.40

Step-by-step explanation:

K: (-4, -6); L: (5, 1)

    (x₁, y₁)     (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(5 - (-4))² + (1 - (-6))²

d = √(5 + 4)² + (1 + 6)²

d = √(9)² + (7)²

d = √81 + 49

d = √130 ≈ 11.40

I hope this helps!

The statement is true. This is an example of Factorization being correct as it takes the factors of the quadratic equation set them equal to 0 and then calculates the value of x.

In the given question, an example of factorization is taken for the equation x²+4x-21 which is factorized using the Middle-Term split rule. We have to find out if the example is conducted correctly.

Factorization is the rule to factorize an equation such that its factors if multiplied together form the equation itself.

We will verify the factorization, for equation x²+4x-21

=> x² + 4x - 21

=> x² + 7x -3x -21

=> x(x + 7) -3(x + 7)

=> (x + 7)(x - 3) = 0

=> x = -7, x = 3

Hence, the statement is True.

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10

Step-by-step explanation:

f(2)=

3(2)+4

3x2+4

using PEMDAS multiplication comes first

6+4

=10

Answer:

f(2) = 10 and f(3) = 13

Step-by-step explanation:

In this context f(2) means "what is y when x equals 2?"  How about when x = 3?  So we plug the values into the equation and solve for f(x) - which is basically what we called "y" in algebra.

Answer:

x = 7

y = 5

(7, 5)

Step-by-step explanation:

From the way, this question looks I'm going to assume substitution.

x + y = 12

x - y = 2

------------------

2x = 14

÷2   ÷2

-------------

x = 7

x + y = 12

7 + y = 12

-7          -7

-------------------

y = 5

I hope this helps!

yes

yes

yes

yes

yes

yes

no

The value of f(x+​h) is x² + 2xh + h² - 9, the value of f(x+​h)−​f(x) is 2xh + h², and the value of (f(x+h)−f(x))/h is 2x + h.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The function:

f(x) = x² - 9

(a) f(x + h)

f(x + h) = (x + h)² - 9

f(x + h) = x² + 2xh + h² - 9

​(​b)​ f(x+​h)−​f(x)

= x² + 2xh + h² - 9 - (x² - 9)

f(x+​h)−​f(x)  = 2xh + h²

​(​c) (f(x+h)−f(x))/h

= (2xh + h²)/h

= 2x + h

Thus, the value of f(x+​h) is x² + 2xh + h² - 9, the value of f(x+​h)−​f(x) is 2xh + h², and the value of (f(x+h)−f(x))/h is 2x + h.

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The point lie in Quadrant IV (8 , -9).

Quadrant in coordinate geometry is divided into four parts which is called Quadrants.

And, To find the in which quadrant does point (8, -9) lie ?

Now According to the above explanation is that:

We have, Point is (8, -9)

Thus, we can clearly see that

This point is lie in Quadrant IV (8 , -9).

Hence, The point lie in Quadrant IV (8 , -9).

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The equation of a circle with center (a, b) and radius r is

We are given the center as

To find the radius, we can use the formula to find the distance between two points, that is, the point on the circle and the center.

where (x₁, y₁) = (-14, 9)

(x₂, y₂) = (-11, 12)

Thus, we have

Therefore, inputting all the values into the equation for a circle, we have

A figure is dilated by a scale factor of 3 if the origin is the center of dilation, What is the new vertex, a', if the old vertex was located. at A(3,4)?​

_______________________________________

Please, give me some minutes to take over your question

__________________________________________

The value of (f+g)(x) is c(x) = 2x² + (-2)x + 1.

How can we add linear functions?
Addition of two individual functions, a(x) and b(x); linearly, results in the formation of the functional addition, c(x) of the two functions, such as
c(x) = a(x) + b(x) = (a+b)(x) – (i)
Domain of a quadratic equation:
The domain of a quadratic function f(x) is the set of x-values for which the function is defined, and the range is the set of all the output values, as is the case with any function (values of f). Any x is a valid input for quadratic functions because their domain is typically the entire real line. Generally, for a quadratic equation the domain goes from (-∞ ,∞ ).

Given, f(x)= 2x² - 3x + 5 and  g(x)= x - 4
Let, y = c(x) denote the value of the function (f+g)(x).
Here, following available literature,
c(x) = (f+g)(x) = f(x) + g(x)   [Using (i)]
c(x) = (2x² - 3x + 5)+(x - 4) = 2x² - 3x + 5 + x - 4  = 2x² + (-2)x + 1
Therefore, y = c(x) = 2x² + (-2)x + 1 is the value of (f+g)(x).

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Given the normal distribution, the following can be illustrated:

1. The number of people who have an IQ between 70 and 130 is 1024.

2. The number of people who have an IQ between 85 and 115 is 1024.

The number of people who have an IQ over 145 is 3.

1. The The number of people who have an IQ between 70 and 130 will be:

z(115) = (130-100)/15 = 2

z(85) = (70-100)/15 = -2

P(-2< z < 2) = 0.6827

The number of 1500 that have IQ between 70 and 130 will be:

= 0.6827 × 1500

= 1024

2. The number of people who have an IQ between 85 and 115 will be:

z(115) = (115-100)/15 = 1

z(85) = (85-100)/15 = -1

We need to consult Z-table to find P value with this Z value

P(85< x < 115) = P(-1< z < 1) = 0.6827

Number of people of 1500 that have IQ between 85 and 115:

= 0.6827 × 1500

= 1024

3. The number of people who have IQ over 145?

Z(>145)

=( 145-100)/15

=3

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Step-by-step explanation:

the range is the interval or set of all valid y (functional result) values.

we see that y goes continuously through every value between +5 (we see no y values bigger than that) and -5 (we see no y values lower than that).

the filled dots also tell us that the end points would be included (if this would be a necessary information - it is not, because the curve reaches +5 and -5 also in between).

so, the range is

-5 <= y <= +5

Answer: K= -9

Step-by-step explanation:

5k−3(2k)−9=0

Multiply 3 and 2 to get 6.

5k−6k−9=0

Combine 5k and −6k to get −k.

−k−9=0

Add 9 to both sides. Anything plus zero gives itself.

−k=9

Multiply both sides by −1.

k=−9

(Hope this helps)

Recall that a whole circle is equal to 360°.

Espresso accounts for 5 out of 100 people surveyed.

Therefore,

The proportion of the circle that is represented by the espresso segment is 18°.

If a street that is 270 ft long is covered in snow. City workers are using a snowplow to clear the street. The diameter of the tire is: 3.2 meters.

First step is to determine the circumference of the tire

Circumference of the tire =  (270 m / 27)

Circumference of the tire = 10 meters

Second step is to make use of  3.14 for π to determine the diameter of the tire using this formula

Diameter of the tire = Circumference of the tire /  π

Let plug in the formula

Diameter of the tire = 10 / 3.14

Diameter of the tire = 3.18 meters

Diameter of the tire = 3.2 meters (Approximately)

Therefore 3.2 meters is the diameter.

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Answer:

[tex]{ \tt{ \frac{dy}{dx} + 2x + 1 = 2 }} \\ \\ { \tt{ \frac{dy}{dx} = - 2x + 1 }} \\ \\ { \tt{dy = ( - 2x + 1) \: dx}} \\ \\ { \tt{ \int dy = \int( - 2x + 1) \: dx}} \\ \\ { \tt{y = - {x}^{2} + x + c}} \\ \\ { \tt{y = - x(x + 1) + c}}[/tex]

Answer:

[tex]y=-x^2+x+\text{C}[/tex]

Step-by-step explanation:

Given equation:

[tex]\dfrac{\text{d}y}{\text{d}x}+2x+1=2[/tex]

[tex]\text{Isolate $\dfrac{\text{d}y}{\text{d}x}$}:[/tex]

[tex]\implies \dfrac{\text{d}y}{\text{d}x}+2x+1-2x-1=2-2x-1[/tex]

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=-2x+1[/tex]

Multiply both sides by dx to get all the terms containing y on the left side, and all the terms containing x on the right side:

[tex]\implies \text{d}y=(-2x+1)\;\text{d}x[/tex]

Integrate both sides:

[tex]\implies \displaystyle \int 1\;\text{d}y=\int(-2x+1)\;\text{d}x[/tex]

Fundamental Theorem of Calculus

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Integrate each term separately:

[tex]\implies \displaystyle \int 1\;\text{d}y=\int -2x\;\text{d}x+\int 1\;\text{d}x[/tex]

Take the constant outside the integral:

[tex]\implies \displaystyle \int 1\;\text{d}y=-2\int x\;\text{d}x+\int 1\;\text{d}x[/tex]

Integrate, using the rules given below:

[tex]\implies y=-2 \cdot \dfrac{1}{1+1}x^{(1+1)}+x+\text{C}[/tex]

[tex]\implies y=-x^2+x+\text{C}[/tex]

Integration rules:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Integrating a constant}\\\\$\displaystyle \int n\:\text{d}x=nx+\text{C}$\\(where $n$ is any constant value)\end{minipage}}[/tex]

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We will label the base angles of the triangle as "x".

Since the vertex angle is 3 times the measure of the base angle, the vertex angle will be equal to 3x:

The following image represent the angles in the isosceles triangle:

Now we use the following property of triangles:

The sum of all of the internal angles in a triangle must be equal to 180°.

Thus, we add the angles and equal them to 180°

We combine the terms on the left:

And divide both sides by 5:

And since x=36, the vertex angle will be:

answer: 108°

For the given 14 digit credit card, the value of first letter A is found as 4.

For the given question;

The formula for finding the sun of nth terms of the AP are-

Sn = n/2(a + l)

From the given 14 digits credit card, consider initial 3 letters.

A,_, 8

The sum of three consecutive numbers is 18.

Thus, applying Sum formula of AP

Sn = n/2(a + l)

Put the values;

18 = 3/2(A + 8)

Simplifying;

3A + 24 = 36

A = 12/3

A = 4

Thus, the value of the first digit of the credit card is found as 4.

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Step-by-step explanation:

You will want to divide the cost of $4.99 by 100, this will give you the cost per yard.

Answer:

$4.99 / 100 = $0.0499

About 5 cents per yard.

Please give thanks, 5 stars, and brainliest answer :)

Answer:

23

Step-by-step explanation:

12 * 2= 24

24-1= 23

In finding a number between 9/8 and 10/8, we can use the average of these two.

We can ensure that this number lies between this two.

where a and b are the two numbers

So we have :

Therefore, one number that lies between 9/8 and 10/8 is :

[tex]{\Large \begin{array}{llll} y = ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=-1\\ y=\frac{5}{4} \end{cases}\implies \cfrac{5}{4}=ab^{-1}\implies \cfrac{5}{4}=\cfrac{a}{b} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} x=3\\ y = 320 \end{cases}\implies 320=ab^3\implies 320=ab^{4-1}\implies 320=ab^4 b^{-1} \\\\\\ 320=ab^4\cdot \cfrac{1}{b}\implies \stackrel{\textit{substituting from the previous equation}}{320=\cfrac{a}{b}b^4\implies 320=\cfrac{5}{4}b^4}\implies 320\cdot \cfrac{4}{5}=b^4 \\\\\\ 256=b^4\implies \sqrt[4]{256}=b\implies \boxed{4=b} \\\\\\ \cfrac{5}{4}=\cfrac{a}{b}\implies \cfrac{5}{4}=\cfrac{a}{4}\implies \boxed{5=a}~\hfill {\Large \begin{array}{llll} y =5(4)^x \end{array}}[/tex]

It is found that the displacement between t= 0  and t = 1 second is of 0.536 m.

The equation of motion is given by:

x(t) = 4 sin(πt + π/2)

The displacement between t= 0  and t = 1 second is given by:

d = x(1) - x(0)

Hence,

position of the object when t = 1

x(1) = 4sin(π(1) + 1 (π/2))

= 4 sin (π + π/2)

= 4 sin (3π/2)

= 4 x √3/2

= 2√3

= 3.464

position of the object when t = 0

x(0) = 4sin(π(0) + (π/2))

= 4 sin (0 + π/2)

= 4 x 1

= 4

Then,

d = x(1) - x(0)

= 4 - 3.464

= 0.536(approx)

Therefore, the displacement of the object between t = 0 and t = 1 is 0.536.

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FOR EQUATION INVERSES IT MEANS ... x and y swap positions.

[tex]x = (f(x))^{2} - 9 \\ (f(x))^{2} = x + 9 \\ \sqrt{(f(x))^{2} } = \sqrt{x + 9} \\ f(x) = \sqrt{x + 9} [/tex]

ATTACHED IS THE SOLUTION.

The weight of the elephant on planet B given the ratio of the weights on planet A an B is 72 pounds.

Ratio is used to compare two or more quantities together. It shows the number of times that one quantity is contained in another quantity. In this question, the weight of the elephant on Planet B is 100/3 times that of Planet A.

In order to determine the weight of the elephant on Planet B, multiply the ratio of the weight in planet B by the weight in Planet A and divide by the ratio of weight in planet A.

Weight in Planet B = (3 x 2400) / 100 = 72 pounds

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The non-real solutions of the polynomial expression are x = (1 + 2√-5)/3 and x = (1 - 2√-5)/3

The equation of the polynomial expression is given as:

3x5 + 25x4 + 26x3 – 82x2 + 76x = 48

Rewrite the equation as

3x^5 + 25x^4 + 26x^3 – 82x^2 + 76x - 48 = 0

The points on the graph are given as

(-6, 0), (-5, 500), (-2.5, -450), (0, - 50), (1, 0), (2, 400).

Write out the x-intercepts

(-6, 0) and (1, 0)

This means that

Real solution = -6

Real solution = 1

Rewrite the above as

x = -6 and x = 1

So, we have

x + 6 = 0 and x - 1 = 0

Multiply

(x + 6)(x - 1) = 0

The next step is to divide the polynomial equation 3x^5 + 25x^4 + 26x^3 – 82x^2 + 76x - 48 = 0 by (x + 6)(x - 1) = 0

This is represented as

3x^5 + 25x^4 + 26x^3 – 82x^2 + 76x - 48/(x + 6)(x - 1)

Using a graphing calculator, we have

3x^5 + 25x^4 + 26x^3 – 82x^2 + 76x - 48/(x + 6)(x - 1) = 3x^3 + 10x^2 - 6x + 8

So, we have

3x^3 + 10x^2 - 6x + 8

Factorize

(x + 4)(3x^2 - 2x + 2)

Next, we determine the solution of the quadratic expression 3x^2 - 2x + 2 using a quadratic formula

So, we have

x = (-b ± √(b² - 4ac))/2a

This gives

x = (2 ± √((-2)² - 4 * 3 * 2))/2 * 3

So, we have

x = (2 ± √-20)/6

This gives

x = (2 ± 4√-5)/6

Divide

x = (1 ± 2√-5)/3

Split

x = (1 + 2√-5)/3 and x = (1 - 2√-5)/3

So, the conclusion is that

Using the polynomial expression, the non-real solutions are x = (1 + 2√-5)/3 and x = (1 - 2√-5)/3

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First we need to find the slope by using two points

(15,190)=(t1,y1)

(25,170)=(t2,y2)

Then we calculate the y-intercept

we isolate the b

The equation is