The sum of two numbers is 402. The difference between the two numbers is 148. Find the two numbers

[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]

yes

yes

yes

yes

yes

yes

no

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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Answer:

consistent system with equation [tex]y=6x+5[/tex]

Step-by-step explanation:

[tex]18x-3y=-15[/tex],   [tex]-6x+y=5[/tex]

To solve by substitution, we have to isolate a variable in one of the equations. I will isolate y in the second equation.

[tex]-6x+y=5[/tex]

+6x           +6x

[tex]y=6x+5[/tex]

Next, substitute this y value for y in the first equation:

[tex]18x-3y=-15[/tex]

[tex]18x-3(6x+5)=-15[/tex]

and distribute.

[tex]18x-18x-15=-15[/tex]

[tex]-15=-15[/tex]

We are left with an equality of constants. This means that the system of equations is actually just one equation, meaning it has an infinite number of solvable points (this is sometimes called consistent). And, its equation is just what we solved for in the first step:

[tex]y=6x+5[/tex]

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

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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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°.

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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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°

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

The cost is given as

Where x is the number of hours

The y-intercept is obtained from the graph as shown below

The value of the y-intercept is obtained to be 10

The y-intercept represents the value represents the fixed cost.

The slope of the cost is obtained from the cost function to be 0.5.

The slope represents the change in cost with respresent to time (hour).

Hence,

lank 1: 10

Blank 2: The fixed cost

Blank 3: 0.5

Blank 4: Change in cost or charge with respect to time used in hours

Blank 5:

Answer:

donde están lo calisado los continentes

In the equation [tex](2x^{9} y^{n})(4x^{2}y^{10}) = (8x^{11}y^{20})[/tex] value of n = 10

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6 is multiplied by itself four times, yielding 6 6 6 6. You can write this as 64. In this case, the exponent is 4 and the base is 6.

[tex](2x^{9} y^{n})(4x^{2}y^{10}) = (8x^{11}y^{20})[/tex]

exponents multiplied with the same base: am * an = a{m + n}

On the powers of x, use the Rule of Multiplying Exponents.

⇒ x⁹ * x²  = x⁹⁺² = x¹¹

The powers of y operate similarly.

⇒ [tex]y^{n} * y^{10} = y^{n + 10} = y^{20}[/tex]

Since y¹⁰⁺¹⁰ = y²⁰

Therefore in the given equation, the value of n = 10

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For x = 2

Since:

The function is discontinuous at x = 2. Besides since the function has a vertical asymptote on one of the sides, we can conclude it is a infinite discontinuity.

For x = 6:

Since:

The function is discontinuous at x = 6, at this point the function has a jump discontinuity

Solution

From the given graph,

The maxima is

The minima isThe inetrev

aterval inwh which the function is increasing is

dec

The correct options are,

A. Rectangle ABCD is similar to rectangle EFGH.

D. The dilation is an enlargement.

F. The scale factor of the dilation is 2.5.

The similarity criteria of rectangles are that their corresponding sides should be proportional to each other. The ratio of their corresponding length is equal to L = 25÷10, which gives L=2.5, and the ratio of their corresponding width is equal to W = 15÷6, which gives w = 2.5. Hence, both rectangles are similar.

The dilation is an enlargement because the size of the rectangle is increased by a scale factor of 2.5.

The scale factor of the dilation is the ratio of the sides, which is equal to 2.5.

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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)

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 :

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.

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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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!

The number of wallets does Julian need to make in order to break even are 35.

X 1, ldots, and x n are the variables, and display style b, a 1, ldots, and a n are the coefficients. In mathematics, a linear equation is an equation that can be written as x 1, ldots, and x n + a n + b = 0. Ax + By = C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5. Finding both intercepts of an equation in this format is rather simple (x and y). frequently actual numbers. The first-degree equations are linear equations. The following is the equation for a straight line. Ax+by+c = 0, where a and b are both zeros, is the conventional form of a linear equation.

In order to "break even," his earnings and expenses have to be equal. The number of wallets (x) is represented in both equations. Simply put, you have to work out the equations in the system.

Both the given equation are equal to y

So,

16x - 130 = 8x + 150

16x - 8x = 150 + 130

x = 280/8

x = 35

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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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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

__________________________________________

Answer:

23

Step-by-step explanation:

12 * 2= 24

24-1= 23

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

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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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 slope of the equation, represented by the value of y/x for the given values of x and y, is 3/1, 3/1, 3.

The slope of a line can be used to gauge how steep it is. Slope is theoretically determined as "rise over run" (change in y divided by change in x).

The slope is the ratio of the rise in height between two points to the fall in elevation between those same two points.

The x and y values are provided.

The equation's slope is shown by the ratio y/x.

if y = -3 and x = -1,

y/x = 3/1

if y = 3 and x = 1

y/x = 3/1

if y = 6 and x = 2

y/x = 6/2 = 3

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To find the answer you substitute in the expression the g by -4 and the m by 3, as follow:

To evaluate:

1. Make operations in parenthesis:

2. Multiplication

3. Addition: