Estimate the solution to the following system of equations by graphing.

Answer: Option (1)

Step-by-step explanation:

The domain is the set of input values, also known as the set of x-values.

Answer:

-32/21

Step-by-step explanation:

First, we can convert -0.35 into a fraction: -35/100, which could be further simplified to -7/20.
Dividing a fraction by another is the same thing as multiplying a fraction by the reciprocal (denominator over numerator) of the fraction. Therefore, we can rewrite this expression as: 8/15 * -20/7
To find the answer to that, you simply multiply the numerators together and the denominators together separately. The final answer is -32/21.

Answer:

-1 11/21

First step:

First, you change the decimal into a fraction. To do that you look at the decimal place at the end of -0.35. The decimal place is hundredths. That means the fraction form of -0.35 is -35/100.

Now to simplify it just find out what both the numbers can be divided by. In this case, 35 and 100 can be divided by 5. If you divide them both by 5 you get -7/20

Fraction form: -7/20

Second step:

Now you just plug it in to the equation.

8/15÷(-7/20)

To solve this you need to change it to multiplication and flip the second fraction.

8/15×(-20/7)

Final step:

Now you multiply the fractions.

8/15×(-20/7)= -32/21 or -1 11/21

Final answer: -1 11/21

Answer:

$200

Step-by-step explanation:

Consider the original price be x

As per the question

Solving the equation yields:

In conclusion

the original price of the jacket was $200

Answer:

1) X² + 1 - 2X

2).x² + 4 - 4x

3) 9 + x² - 6x

4) y² + 16 - 8y

5) 4x² + 1 - 4x

6) 9 + 4y² - 6y

7) 4x² + y²- 8y

8) 1 + 16a² - 8a

9) 9x²+ 4y² - 12xy

10) -x²- 16y² + 8y

11) -x²- 25y + 10xy

The statement is given as the distance between points (x₁, y₁) and (4, 8) is the square root of (x₁ - 8)² + (₁-4)². Hence, the given statement is false, it is  √[(x₁-4)² + (y₁-8)²].

The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

D = √[(x-p)² + (y-q)²]  

WE have been given two points.

So,

The distance between points (x₁, y₁) and (4, 8)

D = √[(x-p)² + (y-q)²]  

D = √[(x₁-4)² + (y₁-8)²]  

But the statement is given as the distance between points (x₁, y₁) and (4, 8) is the square root of (x₁ - 8)² + (₁-4)².

Hence, the given statement is false, it is  √[(x₁-4)² + (y₁-8)²].

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The change is decay and the percentage rate of decrease will be 95%.

An exponential function is a function where a number is raised to the variable i.e. base is raised to the exponent times.

Here given the exponential function is y= 4300(0.042)ˣ

Now we have to identify if the change in exponential function represents growth or decay, and have to determine the percentage rate of increase or decrease.

Here in the exponential function, the base is less than 1 so the change is decay.

The equation represents exponential decay because the decay factor is lesser than 1.

The general form of the exponential equation is:

y(x)= a(1-r)ˣ such that r is the decay.

equating with the equation

y= 4300(0.042)ˣ

a= 4300

and 1-r=0.042

⇒r= 1-0.042

⇒r= 0.958

the perecentage of decay will be r*100= 0.958*100= 95%

Therefore the change is decay and the percentage rate of decrease will be 95%.

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Answer:

[tex]3x^3 + 4x^2 -3x + 2[/tex]

Step-by-step explanation:

The area of the swimming pool will be equal to [tex]length * width[/tex].

We know that the length is [tex]3x^2-2x+1[/tex] and the width is [tex]x+2[/tex].

Therefore we can substitute those into the equation:

[tex](3x^2-2x+1)(x+2)\\[/tex]

Then, we expand the brackets using a grid (attached).

After this, we collect like terms to find the final answer:

[tex]3x^3+6x^2-2x^2-4x+x+2\\3x^3 + 4x^2 -3x + 2[/tex]

Our final answer is: [tex]3x^3 + 4x^2 -3x + 2[/tex]

Answer:

They are parallel because their slopes are equal.

Step-by-step explanation:

See attached image.

The smallest 4-digit number which is exactly divisible by 72 and 108 is 1080.

The least common multiple that is divisible by both a and b is the smallest positive integer, lowest common multiple, or smallest common multiple of two numbers a and b, generally indicated by LCM.

The Least common multiple of both the numbers 72 and 108 is 216. Since 216 is the least common multiple of both the numbers. Therefore, the four-digit number needs to be a multiple of 216 to be divisible by both the numbers. Thus, when 216 is multiplied by 5 the result is 1080, which is divisible by both 72 and 108. Hence, the smallest 4-digit number which is exactly divisible by 72 and 108 is 1080.

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Answer:

I will assume that the term "x+2/2" is meant to be "(x + 2)/2)."  Otherwise the equation would read (x/3) = x + 1

Step-by-step explanation:

(x/3) = (x + 2)/2

x = 3*(x+2)/2   [Multiply both sides by 3]

x = (3x + 6)/2

x = (3/2)x + 6/2

x - (3/2)x = 3

-0.5x = 3

x = -6

====================

Check:

Does (x/3) = (x + 2)/2 for x = -6?

(-6/3) = (-6 + 2)/2

-2 = -4/2

-2 = -2  YES

Answer: No

Step-by-step explanation:

A proportional relationship can be represented by y = kx, for some constant k. This means the graph should be a line, which is not shown. Thus, the graph does not represent a proportional relationship.

Answer:

no

Step-by-step explanation:

because it does not represent any propotional relationship.

6 (x - 5) = 4x + 20

6x - 30 = 4x + 20

6x - 4x = 20 + 30

2x = 50

[tex]x = \frac{50}{2} [/tex]

x = 25

Answer: The value of x = 25 ✅

Step-by-step explanation:

Hii! Do you need to know the solution to the equation [tex]\boldsymbol{6(x-5)=4x+20}[/tex]? No problem! (:

     In any equation, there's a variable that we need to solve for. Here the variable is "x".

So now let's solve for x...

[tex]\twoheadrightarrow\sf 6(x-5)=4x+20[/tex]

[tex]\bullet[/tex] "distribute" 6

[tex]\twoheadrightarrow\sf 6x-30=4x+20[/tex]

[tex]\bullet[/tex] subtract "4x" from both sides

[tex]\twoheadrightarrow\sf 2x-30=20[/tex]

[tex]\bullet[/tex] add "30" to both sides

[tex]\twoheadrightarrow\sf 2x=50[/tex]

[tex]\bullet[/tex] divide both sides by "2"

[tex]\twoheadrightarrow\sf x=25\;\;\;[/tex] ✅

--

Hope that this helped! Best wishes.

[tex]\it Reach\;far.\;Aim\;high.\;Dream\;big.[/tex]

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[tex]\bigstar\underbrace[/tex]

The transformation is nonrigid because the segment lengths are not preserved.

The image related to the question cannot be found. However, the question can still be solved

The given parameters are:

From the question, we understand that the side lengths are not equal.

This means that the triangles are dilated.

And the scale factor of dilation is

Scale factor = 6/3 = 10/5 = 8/4

Scale factor = 2

The scale factor of dilation is 2

Dilation is a non rigid transformation.

Hence, the transformation is nonrigid because the segment lengths are not preserved.

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Answer:

The transformation is nonrigid because the segment lengths are not preserved.

Using a calculator, we have that:

To find the equation, we need to insert the points (x,y) in the calculator.

In this problem, we have that:

Hence the regression equation is:

y = -4.75x + 88.57143.

Also using a calculator, the correlation coefficient is of -0.906.

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Answer:

LKO = NMO

Step-by-step explanation:

This is because both of the angles lie on the same "vertical angle", the line segment that connects M to K. The segment MN is also parallel to segment LK. If you have two congruent line segments, then the measure of the angles are congruent.

The y coordinates doesn't change under a horizontal stretch while the x coordinates do not change under a vertical stretch.

It should be noted that coordinates are vital in determine the position of an object or points.

In this case, the y coordinates doesn't change under a horizontal stretch while the x coordinates do not change under a vertical stretch.

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Answer:

The y-coordinates do not change under a horizontal stretch. The x-coordinates do not change under a vertical stretch.

Step-by-step explanation:

The answers to the following question is

1) KL = 10

2) TE= 15 cm

3) angle PUT= 13

4) angle SQP = 21

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.

1) Using similarity property in given triangle

SR/ KI= SJ / JK

AS, JK= 2 SJ

SR/ KI= SJ / 2 SJ

5/ KI =  1/2

KL= 10

2) As, the diagonal of parallelogram bisect equally each other then

VE = TE

AS, VE = 15

So, TE= 15 cm

3) As, PU is the bisector of angle SUT

angle PUT= 1/2 (angle SUT)

PUT = 1/2 (26)

angle PUT= 13

4) As PQ is the bisector SQR

angle PQR= angle SQP = 21

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The number of passwords that would be allowed if users were allowed to reuse the letters and numbers is 30891577600

The given parameters are:

Password length = 8

Letters = 6

Numbers = 2

There are 26 letters and 10 digits.

Since the letters and the numbers can be repeated, then the number of passwords is:

Count = 26^6 * 10^2

Evaluate

Count = 30891577600

Hence, the number of passwords is 30891577600

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Answer:

The difference between the Ranges in the dot plots is 2.

I've included a figure with the two-dot plots explained for easier comprehension.

The value on the far left of the numbered line that contains at least one point is the minimum value for students in Class A, and the maximum value is three (the value to the extreme right of the numbered line that contains, at least, one point).

Range = 3 - 0 = 3

The value to the far left of the numbered line that has at least one point is the minimum value for students in Class B, and the maximum value is 5. (the value to the extreme right of the numbered line that contains, at least, one point).

Range = 5 - 0 = 5

The dot plots' range differences are 5 - 3 = 2, which is a difference of two.

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The coordinates of the vertices of the reflected image are (-3,4)  (0,4) (-3, 2) (0,2).

Reflection is a mathematical transformation of a shape by moving the vertices of the shape across a line of reflection.

Analysis:

coordinates of the shape before transformation are: (-3, 0) (0,0) (-3, -2) 0, -2)

Across the line of transformation, the corresponding vertices(old and new) must be equal distance from the line of reflection.

Also for reflection on y-axis only y-coordinates are affected.

so for point(-3, 0) 0 is 1 unit away from y = 1 so the other coordinate 1 unit away from y = 1 is y = 2 making the new point (-3, 2) same as others .

Find the image in the attached file below.

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Answer:

5. y = 2/3x + 1

8. y = 4/7x - 4

Step-by-step explanation:

5. (-6, -3) and (6, 5)

You can use the slope formula which is (y2-y1)/(x2-x1) to find the slope and plug it back into the slope-intercept form to find the y-intercept

(5-(-3)) / (6-(-6)) = 8 / 12 = 2/3

slope-intercept form: y=mx+b where m is the slope and b is the y-intercept

to find b you can plug in one of the coordinates and the slope

5 = 6(2/3) + b

5 = 4 + b

1 = b

y = 2/3x + 1

8. (-7, -8), (21, 8)

m = (8 -  (-8)) / (21 - (-7)) = 16 / 28 = 4/7

plug in one of the coordinates and the slope to find b or the y-intercept

8 = 21(4/7) + b

8 = 12 + b

-4 = b

y = 4/7x - 4

Answer:

Step-by-step explanation:

The attached graph represents the graph of f(x) = (x - 1)^2 - 2

The equation is given as:

f(x) = (x - 1)^2 - 2

Next, we set x to -2, -1, 0, 1 and 2.

So, we have:

f(-2) = (-2 - 1)^2 - 2 = 7

f(-1) = (-1 - 1)^2 - 2 = 2

f(0) = (0 - 1)^2 - 2 = -1

f(1) = (1 - 1)^2 - 2 = -2

f(2) = (2 - 1)^2 - 2 = -1

This means that the table of values is

x      f(x)

-2    7

-1    2

0    -1

1     -2

2    -1

Next, we plot the above points and connect them.

See attachment for the graph of f(x) = (x - 1)^2 - 2

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The coordinates of a point located on the grid is (64.65, 12.4).

We need to find the coordinates of the point given on the grid.

In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

Now, from the given grid we can see that the point is located at (64.65, 12.4)

Therefore, the coordinates of a point located on the grid is (64.65, 12.4).

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First let's define bisected

To bisect an angle means to split an angle exactly in half. Both sides of a bisected angle are equal to each other

The original angle (48 degrees) is bisected so we must divide 48 by 2 to find a degree of each angle

48 ÷ 2 = 24

The measure of each new angle is 24 degrees

Answer:

(1) 85×9=765 (2) 127×3=381

The value of FY in the triangle will be 30.11

From the information given, the value of BE will be:

= [tex]\sqrt{64.2}[/tex]² - [tex]\sqrt{51.2}[/tex]²

= 38.7

From the triangle, DY will be

= [tex]\sqrt{64.22}[/tex]² - [tex]\sqrt{61.7}[/tex]²

= 17.7

AY will be:

= [tex]\sqrt{61.7}[/tex]² + [tex]\sqrt{17.7}[/tex]²

= 64.2

FY will now be:

= [tex]\sqrt{64.2 - 56.7}[/tex]²

= 30.11

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Answer:

I believe the terms would be 31, 35, 39.

Step-by-step explanation:

We know this because 43-27 is 16. since there are 3 terms missing, we divide the answer by 4, and you get 4. The number you get there is how many you add to each term to get the missing ones. For example, 27+4=31. The pattern is adding 4 to each term. Hope I helped!