A system of equations is shown:
4x = -3y + 17
3x - 4y = -6
What is the solution to this system of equations? (5 points)
(3,2)
(-3,-2)
(-2,-3)
(2,3)

Answer:

x = 7; y = 4 1/3

Step-by-step explanation:

The solution is the point of intersection of the lines.

Read the point of intersection.

You can also solve the system using algebra.

y = 1/3 x + 2

y = 4/3 x - 5

1/3 x + 2 = 4/3 x - 5

x + 6 = 4x - 15

-3x = -21

x = 7

y = 1/3 x + 2

y = 1/3 × 7 + 2

y = 2 1/3 + 2

y = 4 1/3

Answer: x = 7; y = 4 1/3

The surface area of this pyramid with a regular pentagon as its base is equal to 851.09 square units.

In Mathematics, a complete circle has a magnitude of 360° and when it is divided by the 10 triangles, the angle formed at the center of the pentagon would always be equal to 36°.

Also, the length of the apothem of a pentagon can be calculated by using this formula:

a = s/2tan(36)

Where:

Substituting the given parameters into the formula, we have;

a = 10/2tan(36)

a = 10/1.45

a = 6.90 units.

Next, we would determine the slant height of this pyramid by applying Pythagorean theorem:

c² = a² + b²

c² = 6.9² + 13²

c² = 47.61 + 169

c² = 216.1

c = √216.1

c = 14.72 units.

For the surface area, we have:

Mathematically, the surface area of a pyramid with a regular pentagon as its base can be calculated by using this formula:

SA = 1.72l² × (5/2 × l × h)

SA = 1.72(14.72)² × (5/2 × 14.72 × 13)

SA = 372.69 + 478.4

SA = 851.09 square units.

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Answer:

Step-by-step explanation:

A square is made up of 4 sides that are equal in length. They can all be called "x" or "s" or whatever variable you want. The formula for the area of a square (and also the area of a rectangle) is Area = side × side.

If you called your sides "x", then the formula is A = x × x or A = x². Another way to note the area of either a square or a rectangle is to call the "bottom" the base and one of the sides the height and then the area formula looks like this:

A = b × h

or

A = length × width

They are all the same thing.

Answer: A: y= 3x + 3

Step-by-step explanation:

The y intercept has to be 3 which is found when x = 0 that eliminates B and C. Then just plug in -1 or 1 into A or D and you will find that plugging in either with get you the y value provided on A.

#43

So

200/2=100 pairs of 201

Sum

#44

400/2=200 pairs of 401

Sum

#45

800/2=400 pairs of 801

Sum

#46

2000/2=1000 pairs of 2001

Sum

Answer:

43.  20,100

44.  80,200

45.  320,400

46.  2,001,000

Step-by-step explanation:

Gauss's method

General formula for the sum of the first n integers:

[tex]1+2+3+ \dots +n=\dfrac{1}{2}n(n+1)[/tex]

Question 43

Given sum:  

Therefore, n = 200.

Substitute the value of n into the formula:

[tex]\implies \dfrac{1}{2}(200)(200+1)=100 \cdot 201=20100[/tex]

Question 44

Given sum:  

Therefore, n = 400.

Substitute the value of n into the formula:

[tex]\implies \dfrac{1}{2}(400)(400+1)=200 \cdot 401=80200[/tex]

Question 45

Given sum:  

Therefore, n = 800.

Substitute the value of n into the formula:

[tex]\implies \dfrac{1}{2}(800)(800+1)=400 \cdot 801 =320400[/tex]

Question 46

Given sum:  

Therefore, n = 2000.

Substitute the value of n into the formula:

[tex]\implies \dfrac{1}{2}(2000)(2000+1)=1000 \cdot 2001=2001000[/tex]

Answer:

[tex]\Large\boxed{1)~6x+7}[/tex]

[tex]\Large\boxed{2)~-7x+5y+8}[/tex]

Step-by-step explanation:

Given expression

4x + 7 + 2x

Move like terms together

= 4x + 2x + 7

= (4x + 2x) + 7

Combine like terms

[tex]\Large\boxed{=6x+7}[/tex]

Given expression

-4x + 3y - 3x + 8 + 2y

Move like terms together

= -4x - 3x + 3y + 2y + 8

= (-4x - 3x) + (3y + 2y) + 8

Combine like terms

[tex]\Large\boxed{=-7x+5y+8}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The differential equation [tex]cos(x)dx+\frac{y}{x} dy=0[/tex] is not exact.

For given question,

we have been given  a differential equation [tex]cos(x)dx+\frac{y}{x} dy=0[/tex]

We have to determine given differential equation is exact or not.

Compare it with M dx + N dy = 0

⇒ M = cos(x) and N = y/x

Find the derivative of M with respect to y.

[tex]\Rightarrow M_y=-sin(x)[/tex]

Now, find the derivative of N with respect to x.

[tex]\Rightarrow N_x=\frac{-y}{x^{2} }[/tex]

Since [tex]M_y \neq N_x[/tex], given differential equation is not exact.

Therefore, the differential equation [tex]cos(x)dx+\frac{y}{x} dy=0[/tex] is not exact.

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Answer:

m∠6 = 54°

Step-by-step explanation:

Given the diagram, we know that line b is a straight line and angles 1 (the angle measuring 13x + 9°) and 2 are supplementary angles and thus add up to 180.  

We also know angles 2 and 7 (the angles measuring 5x + 9°) are alternate exterior angles and are therefore congruent.

So since angle 2 = 5x + 9, we can do:

13x + 9 + 5x + 9 = 180

18x + 18 = 180

18x = 162

x = 9

Angles 7 and 6 are also congruent plugging x into angle 7 also gives us the measure of angle 6:

5(9) + 9 = 45 + 9 = 54°

Check the picture below.

well, let's take a peek at the distances of each side.

[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{3}) ~\hfill AB=\sqrt{[ 4- 0]^2 + [ 3- 0]^2} \\\\\\ ~\hfill AB=\sqrt{25}\implies \boxed{AB=5} \\\\\\ B(\stackrel{x_1}{4}~,~\stackrel{y_1}{3})\qquad C(\stackrel{x_2}{4}~,~\stackrel{y_2}{-3}) ~\hfill BC=\sqrt{[ 4- 4]^2 + [ -3- 3]^2} \\\\\\ ~\hfill BC=\sqrt{36}\implies \boxed{BC=6}[/tex]

[tex]C(\stackrel{x_1}{4}~,~\stackrel{y_1}{-3})\qquad A(\stackrel{x_2}{0}~,~\stackrel{y_2}{0}) ~\hfill CA=\sqrt{[ 0- 4]^2 + [ 0- (-3)]^2} \\\\\\ ~\hfill CA=\sqrt{25}\implies \boxed{CA=5} \\\\\\ \textit{so it's an \underline{isosceles triangle}}[/tex]

Answer:

[tex]z=\frac{t^{2}(m-3) }{4}[/tex]    or    [tex]z=\frac{1}{4}t^{2} (m-3)[/tex]

Step-by-step explanation:

[tex]t=\sqrt{\frac{4z}{m-3} }[/tex]

[tex]t^{2} =\frac{4z}{m-3}[/tex]

[tex]4z=t^{2} (m-3)[/tex]

[tex]z=\frac{t^{2}(m-3) }{4}[/tex]

Hope this helps

Using it's concept, the probability that two red marbles are chosen from the vase is of 0%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that there are no red marbles, hence the number of desired outcomes is of 0, and there is a 0% probability that two red marbles are chosen from the vase.

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The vertex of the function is a minimum and the coordinate of the vertex of the function is (0.2, -2.4)

The function is given as:

f(x) = 5x^2 + 2x - 3

Expand the function

f(x) = 5x^2 + 5x - 3x - 3

Factorize the function

f(x) = (5x - 3)(x + 1)

Set the function to 0

(5x - 3)(x + 1) = 0

Solve for x

x = 3/5 and x =-1

Hence, the x-intercept is 3/5 and -1

The vertex of the function is a minimum.

This is so because the leading coefficient of the function is positive

Here, we have:

f(x) = 5x^2 + 2x - 3

Differentiate and set to 0

10x + 2 = 0

Solve for x

x = -0.2

Substitute x = -0.2 in f(x) = 5x^2 + 2x - 3

f(0.2) = 5(0.2)^2 + 2(0.2) - 3

Evaluate

f(0.2) = -2.4

Hence, the vertex of the function is (0.2, -2.4)

To do this, we simply plot the x-intercept and the vertex.

And then connect the points

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Given the equation written by Fiona and Henry, If both linear equations have the same solutions, Henry's equation is x - 5/2y = 25/2.

Hence, option D is the correct answer.

This question is incomplete, the missing answer choices are;

A. x- 5/4y =25/4

B. x-5/2y=25/4

C. x-5/4y =25/4

D. x- 5/2y=25/2

Given the linear equation written by Fiona; y = 2/5x - 5.

From the answer choices provided, they are in the form of x - (m)y = b.

We will transform Fiona's equation into that form.

y = 2/5x - 5

Divide each term by the coefficient of x.

y(5/2) = (5/2)2/5x - (5/2)5

5/2y = x - 25/2

25/2 = x - 5/2y

x - 5/2y = 25/2

Given the equation written by Fiona and Henry, If both linear equations have the same solutions, Henry's equation is x - 5/2y = 25/2.

Hence, option D is the correct answer.

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[tex]\frac{-2x^{2} +25 }{(x-2) (x-5)} ,x\neq 2,x\neq 5[/tex]  is the difference.

What is an expression?

⇒ An expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.)

Calculation :

⇒   [tex]\frac{3x^{2} }{(x^{2} -7x+10)}- \frac{5x} {x-2}[/tex]

⇒   [tex]\frac{3x^{2} }{(x-2)(x-5)}- \frac{5x} {x-2}[/tex]

⇒1/(x-2) [(3x²-5x{x-5})/(x-5)]

⇒1/(x-2) [(3x²-5x²+25x)/(x-5)]

⇒1/(x-2) [ (-2x²+25x)/(x-5)]

⇒[tex]\frac{-2x^{2} +25x }{(x-2)(x-5)}[/tex]

at x=2 and x=5 the denominator becomes zero If the denominator of a fraction is zero, the expression is not a legal fraction because its overall value is undefined.

⇒   [tex]\frac{-2x^{2} +25 }{(x-2) (x-5)} ,x\neq 2,x\neq 5[/tex] is the difference

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Answer:

[tex]\textsf{19.} \quad S_{20}=1490[/tex]

33.  None of these are correct.

Step-by-step explanation:

General form of an arithmetic sequence:

[tex]a_n=a+(n-1)d[/tex]

where:

Given values:

Substitute the given values into the formula and solve for a:

[tex]\implies 27=a+(20-1)(-5)[/tex]

[tex]\implies 27=a+(19)(-5)[/tex]

[tex]\implies 27=a-95[/tex]

[tex]\implies a=27+95[/tex]

[tex]\implies a=122[/tex]

Sum of the first n terms of an arithmetic series:

[tex]S_n=\dfrac12n[2a+(n-1)d][/tex]

where:

Given values:

Substitute the given values into the formula and solve:

[tex]\implies S_{20}=\dfrac{1}{2}(20)[2(122)+(20-1)(-5)][/tex]

[tex]\implies S_{20}=10[244-95][/tex]

[tex]\implies S_{20}=10[149][/tex]

[tex]\implies S_{20}=1490[/tex]

Sum of the first n terms of a geometric series:

[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]

where:

Given values:

Substitute the given values into the formula and solve:

[tex]\implies S_6=\dfrac{1458\left(1-\frac{1}{3}^6\right)}{1-\frac{1}{3}}[/tex]

[tex]\implies S_6=\dfrac{1456}{\frac{2}{3}}[/tex]

[tex]\implies S_6=\dfrac{1456 \cdot 3}{2}[/tex]

[tex]\implies S_6=2184[/tex]

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a. 1/ 15

b. 76/ 15

c. 1/12

a. 2/5 divided by 6

= 2/ 5 ÷ 6

= 2/ 5 ÷ 6/ 1

Take the inverse of the dividing fraction, we have

= 2/ 5 × 1/ 6

Multiply through

= 2/30

= 1/ 15

b.  3 and 1/3 times 5 and 2/5

= 3 + 1/ 3 × 5 + 2/ 5

From the knowledge of BODMAS, we multiply first

= 3 + 5/3 + 2/ 5

Find the LCM

= 45 + 25 + 6/ 15

= 76/15

c. 1/4 + 1/3 -1/2

Let's find the LCM

= 3 + 4 - 6 / 12

Add first

=  7 - 6/ 12

= 1/ 12

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Answer: In a right triangle, the square of the Hypotenuse equals the sun of the squares of the other two sides.

Step-by-step explanation: a^2+b^2=c^2

Answer: the Pythagoras theorem states that in a right angled triangle, the square of THE HYPOTENUSE is equal to the sum of the squares of the OTHER TWO SIDES.

Step-by-step explanation: :)

Answer: 4

Step-by-step explanation:

[tex]7+(-3)\\=7-3\\=\boxed{4}[/tex]

If a diameter intersects a chord of a circle at a perpendicular then the chord is bisected.

The solution to the problem:

A circle's chord is intersected perpendicularly by its diameter, which also passes through the center of the circle. The chord and diameter are perpendicular. Any line that is perpendicular to a chord on the circle and passes through its center divides it. The chord is divided equally by the diameter.

Therefore, the chord is bisected.

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Answer:

93.32 %

Step-by-step explanation:

33.2   is    1.2   away from 32     this is  1.2 / .8 = 1.5 standard deviations ABOVE the mean     z -score = + 1.5

from z-score table this corresponds to .9332     this is  93.32 %

The probability that a randomly selected passenger car gets more than 33.2 mpg is 0.14.

The p-value, used in null-hypothesis significance testing, represents the likelihood that the test findings will be at least as extreme as the result actually observed, assuming that the null hypothesis is true.

Let the random variable X represent the miles-per-gallon rating of passenger cars. Compute the probability that a randomly selected passenger car gets more than 33.2 mpg as follows:

The probability will be calculated as below;-

[tex]P(x > 33.2) = p(\dfrac{x-\mu}{\sigma} > \dfrac{33.2 - 32}{0.8})[/tex]

P( x > 33.2) = 1 - P ( z < 1 )

P( x > 33.2) = 1 - 0.86

P( x > 33.2) = 0.14

Thus, the probability that a randomly selected passenger car gets more than 33.2 mpg is 0.14.

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x=-2

Step-by-step explanation:

Solution Given:

3(x-3) = 5(2x + 1)

Opening bracket we get

3x-9=10x+5

keeping common value in same side

-9-5=10x-3x

-14=7x

x=-14/7

x= -2

Answer:

-2 =x

Step-by-step explanation:

3(x-3) = 5(2x + 1)

To solve for x

Distribute

3x -9 = 10x +5

Subtract 3x from each side

3x-9-3x = 10x -3x+5

-9 = 7x+5

Subtract 5 from each side

-9-5 = 7x+5-5

-14 = 7x

Divide by 7

-14/7 = 7x/7

-2 =x

Using it's concept, there is a 0.2344 = 23.44% probability that you will choose a block labeled with a T or a block labeled with a 6.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For each block, there are 8 outcomes, since there are 2 blocks, there are 8² = 64 total outcomes. For the desired outcomes, we have that:

Hence there are 8 + 7 = 15 desired outcomes, and the probability is given by:

p = 15/64 = 0.2344.

0.2344 = 23.44% probability that you will choose a block labeled with a T or a block labeled with a 6.

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There will be a vertical stretch with a factor of 3.

If the equation is y=15x+100 then the coordinate (0,100) of the equation shows that Jared had $100 when he started his saving.

Given an equation y=15x+100 that shows the amount of money saved by Jared for his bike based on the number of months that have passed.

We are required to find what the coordinate (0,100) mean in the context of the equation.

Equation is like relationship between two or more variables that are expressed in equal to form. Equations of two variables look like ax+by=c.It may be linear equation, quadratic equation, cubic equation or many more dependng on the power of variable present in that equation.

When we put x=0 in the equation we get the following:

y=15*0+100

y=100

It means that he had $100 in the beginning when he just started doing his savings.

Hence if the equation is y=15x+100 then the coordinate (0,100) of the equation shows that Jared had $100 when he started his saving.

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The surface area of the sphere is 108.16π in². So, option b is correct.

The surface area of the sphere is calculated by the formula,

A = 4πr²

In terms of diameter - d;

A = 4π × (d/2)²

  = 4π × d²/4

  = πd² sq. inches

The given sphere has a diameter d = 10.4 inches

So, the surface area of the sphere is calculated by

A = πd²

  = π × (10.4)²

  = 108.16 π sq. inches

So, option b is correct.

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Disclaimer: The given question on the portal is incomplete. Here is the complete question.

Question: Select the correct answer. the diameter of a sphere measures 10.4 inches. What is the surface area of the sphere?

a. 432.64π in²

b. 108.16π in²

c. 54.08π in²

d. 216.32π in²

Answer:

Step-by-step explanation:

The surface area of the sphere is 108.16π in². So, option b is correct.

What is the surface area of a sphere?

The surface area of the sphere is calculated by the formula,

A = 4πr²

In terms of diameter - d;

A = 4π × (d/2)²

 = 4π × d²/4

 = πd² sq. inches

Calculation:

The given sphere has a diameter d = 10.4 inches

So, the surface area of the sphere is calculated by

A = πd²

 = π × (10.4)²

 = 108.16 π sq. inches

So, option b is correct.

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Disclaimer: The given question on the portal is incomplete. Here is the complete question.

Question: Select the correct answer. the diameter of a sphere measures 10.4 inches. What is the surface area of the sphere?

a. 432.64π in²

b. 108.16π in²

c. 54.08π in²

d. 216.32π in²

The volume of the cylinder that has same height and radius with the given cone is 5,346 cm³

Pyramids and prisms are examples of three-dimensional shapes, as are shapes with curved surfaces. The three-dimensional prism shape has two bases that are parallel and congruent. Any polygon is acceptable for the bases, which are two of the faces. Rectangles make up the remaining faces.

Given that the cylinder and the cone have the same radius and height, the volume of a cylinder equals 3 times the volume of a cone.

According to the given figure:

Given, a cone that has a volume of 1,782 cubic cm, has the same radius and height with a cylinder,

therefore,

Volume of the cylinder = 3 x (1,782)

Volume of the cylinder = 5,346 cubic centimeters

Hence,  the volume of the cylinder is 5,346 cubic centimeter.

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The age of the oldest person that leaves the room is 36 years

The average of a data is defined as the ratio of the sum of the data to the sample size. Mathematically;

Average = sum/sample size

If the average age of a group of 8 people is 22. then;

22 = Xn/8

Xn = 22 * 8

Xn = 176

If after the oldest person leaves the room the average age decreases to 20, hence;

20 = H/7

H = 140

Xn  = H + x

176 = 140 + x

x = 176 - 140

x = 36

Hence the age of the oldest person that leaves the room is 36 years

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Based on the calculations, the sum of this geometric series is equal to 9,990.

Mathematically, the standard form of a geometric series can be represented by the following expression:

[tex]\sum^{n-1}_{k=0}a_1(r)^k[/tex]

Where:

Also, the sum of a geometric series is given by this mathematical expression:

[tex]S=\frac{a_1(1-r^n)}{1-r}[/tex]

Given the following data:

Substituting the given parameters into the formula, we have;

[tex]S=\frac{9000(1-0.1^3)}{1-0.1}\\\\S=\frac{9000(1-0.001)}{1-0.1}[/tex]

S = 9000(0.999)/0.9

S = 8,991/0.9

S = 9,990.

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