factor x^4+2x^2-10x^2=0

The solution of the given system of equations is (20/17, 19/17)

We can solve a system of equations using:

- graphical method

- elimination method

- substitution method

The given system of equations:

2x - 3y = -1  ...... (1)

3x + 4y = 8  ...... (2)

To be able to use the elimination method, multiply equation (1) by 3 and equation (2) by 2.

    2x - 3y = -1   (⨉3)

⇔ 6x - 9y =  -3   .........(3)

   3x + 4y = 8  (⨉2)

⇔ 6x + 8y = 16   .........(4)

Substract equation (3) from (4)

6x + 8y = 16

6x - 9y  =  -3   –

      17y = 19

          y = 19/17

Substitute  y = 19/17 into equation (1)

2x - 3y = -1

2x - 3(19/17) = -1

2x - 57/17 = -17/17

2x = (-17 + 57) / 17

2x = 40/17

x = 20/17

Thus, the solution is (20/17, 19/17)

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We came to the conclusion that ΔQRT ≅ ΔSRT is under the side-side-side (SSS) condition.

So,

Given: ΔQRS/SRT is isosceles with QR ≅ SR; RT bisects QS at point T.

To prove: ΔQRT ≅ ΔSRT

So, we can say that ΔQRT ≅ ΔSRT under SSS condition.

Therefore, ΔQRT ≅ ΔSRT is congruent under SSS condition.

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Answer:

1

Step-by-step explanation:

We have to convert the whole number into an improper fraction :

4  = 4/1

Now we multiply the numerators together and the denominators together :

4 × 1 = 4

1 × 4 = 4

Our new fraction is 4/4 = 1

Hope this helped and have a good day

Answer:

4

Step-by-step explanation:

let the number be n then four times the number is 4n and

4n + 3 = 19 ( subtract 3 from both sides )

4n = 16 ( divide both sides by 4 )

n = 4

then the number n is 4

The probability of selecting that both chips are purple is 3/40

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

It is Given that A bag contains 3 red chips, 5 green chips, 2 yellow chips, 4 brown chips, and 6 purple chips. One chip is chosen at random, the color noted, and the chip returned to the bag.

The probability of selecting that both chips are purple

= 6/20 x 5/20

= 30/400

= 3/40

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The volume of the candle is 36.9 cubic inches.

Given that the candle is in a circular pillar shape. That is it is in cylindrical shape.

Height of the candle, h = 6 inches

Width of the candle = Diameter of the base circle = 2.8 inches

Radius of the circle, r = 2.8/2 = 1.4 inches

We need to calculate the volume of the cylindrical candle.

Volume of a cylinder = Area of the base circle x height of the cylinder

Therefore, volume of the candle, V = [tex]\pi r^2 h[/tex]

                                                           = 3.14 x 1.4 x 1.4 x 6

                                                           = 36.9264

                                                           = 36.9 cubic inches

The question is incomplete. Find the complete question below:

A circular pillar candle is 2.8 inches wide and 6 inches tall. Find the volume of the candle. Round to the nearest tenth if necessary.

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Using algebra, The product of two consecutive numbers is 18 more then 8 times a number

Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics

The two consecutive numbers are :

x and x+1

x(x+1) = 8(x+1) + 18

x^2 + x = 8x + 8 + 18

x^2 + x = 8x + 26

x^2 + x - 8x - 26 = 0

x^2 - 7x - 26 = 0

Substitute a=1,b=−7 and c=−26 into the quadratic formula

       - B  ±  √ B2-4AC

 x =   ————————

                     2A

Accordingly,  B^2  -  4AC   = 49 - (-104) =    153

Applying the quadratic formula :

             7 ± √ 153

  x  =    —————

                  2

x  =  ( 7 ± 3 ×  4.123 ) / 2

​

Two real solutions:

x =(7+√153)/2=(7+3√ 17 )/2= 9.685

or:

x =(7-√153)/2=(7-3√ 17 )/2= -2.685

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The first five terms of the sequence. an=n2 +2​ are 3, 6, 11, 18 and 27.

The sequence is given as n² + 2.

The first term will be:

= n² + 2 = 1² + 2 = 1 + 2 = 3

The second term will be:

= n² + 2 = 2² + 2 = 4 + 2 = 6

The third term will be:

= n² + 2 = 3² + 2 = 9 + 2 = 11

The fourth term will be:

= n² + 2 = 4² + 2 = 16 + 2 = 18

The fifth term will be:

= n² + 2 = 5² + 2 = 25 + 2 = 27

Therefore, the first five terms of the sequence. an=n2 +2​ are 3, 6, 11, 18 and 27.

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The number of new jobs gained is 2,842.

A graph can be described as a pictorial representation of data. A graph is made up of a x-axis and a y-axis.

Percentage can be described as a fraction of an amount expressed as a number out of hundred. The sign used to represent percentage is %.

Percentage increase from 2009 to 2016 = percentage increase x number of employees in 2009

14.8% x 19,200

0.148 x 19,200 = 2,842

Here is the complete question:

A professor expects the education and health service industries to increase total employees by 14.8% from 2009 to 2016. Based on the employment graph below, approximately how many new jobs will the education and health service industries gain between 1/2009 and 1/2016?

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Answer:

c. 16,273,200

Step-by-step explanation:

Edge 2022

Suppose f(x)=2 x-5 and g(x)=|-3 x-1| Find the value. g(2)-f(0)

g(2)- f(0) = 12

Given:

f(x)=2 x- 5

g(x)=|-3 x-1|

To find g(2), substitute x=2 in g(x).

g(x)=|-3 x-1|

g(2)=|-3 (2)-1|

     =|-6-1|

     =|-7|

g(2) = 7

To find f(0), substitute x=0 in f(x).

f(x)=2 x- 5

f(0)=2(0)- 5

f(0) = -5

Now,  g(2)-f(0)  =7-(-5)

                        =7+5

                        =12

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Solution :

Yes, the conveyors are in a proportional relationship.

Given,

A conveyor belt moves at a constant rate of 12 feet in 3 seconds.

A second conveyor belt moves 16 feet in 4 seconds.

There is a proportional relationship if the ratios of each pair of values are the same.

- First conveyor belt

12 feet in 3 seconds.

Ratio = 12 / 3 = 4

- Second conveyor belt

16 feet in 4 seconds.

Ratio = 16 / 4 = 4

Ratios are the same.

4 = 4

Thus the conveyors are in a proportional relationship.

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Answer:

Step-by-step explanation:

So it gives us the equation y=2x+3

Thinking process

1. What you want to do is remove the 3 from the equation so you just get y=2x

How to solve(example)

For the first row to find x first minus 3 from 9 which is 6

9-3=6

Then six divided by two so you can find x.

2x=6

x=3

Answer:

365/83

Step-by-step explanation:

Distribute where we can

106x - 318 + 18 =23x + 69 - 4

Get variables on one side and constants on the other

106x - 23x = 65 + 300

Do the math

83x = 365

Divide both sides by 83

365/83

Answer:

x = 365/83

Step-by-step explanation:

53(2x−6)+18=23(x+3)−4

106x-318+18=23x+69-4

106x-23x=69-4+318-18

83x = 365

x = 365/83

The answer is an decimal form is 2.75

In the given Statement is:

What is the value of 4x² + 2x - 1 when x = 3/4 ?

Express the answer as a decimal.

Let's Come to the solution:

4x² + 2x - 1 __(1)

Now put the value of x = 3/4 in above equation:

4 (3/4)² + 2 (3/4) - 1

Solve the equation, and get the answer

4 x (9/16) + 3/2 - 1

9/4 + 3/2 - 1

Taking the L.C.M

= [tex]\frac{9+6-4}{4}[/tex]

= 11/4

= 2.75 is the answer

Hence, The answer is an decimal form is 2.75

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Answer:

- 1 [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

substitute x = - 5 into f(x)

f(- 5) = [tex]\frac{1}{4}[/tex] × - 5 = - [tex]\frac{5}{4}[/tex] = - 1 [tex]\frac{1}{4}[/tex]

Solving for the rate, you make $15 per hour as a tutor.

Rate is defined as the ratio between two quantities of different units.

Let x = rate

n = total amount you've earned = $195.00

t = time you've worked = 8 hours

If in one week, you earned $75.00 at your afterschool tutoring job, and after working 8 more hours the following week, you had a total of $195.00, then we can express this as

n = xt + $75.00

Substitute the values to solve the rate, x.

n = xt + $75.00

$195.00 = x(8 hours) + $75.00

8hours (x) = $195.00 - $75.00

8hours (x) = $120.00

x = $15/hr

rate = $15 per hour

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The equation of the line in point-slope form, which passes through the pair of points located at (-10 , 3) and (-2 , -5), is y - 3 = -(x + 10).

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Getting the slope of the two points: (-10 , 3) and (-2 , -5).

m = (y2 - y1)/(x2 - x1)

m = (-5 - 3)/(-2 - -10)

m = -8/8

m = -1

Using the point slope form, plug in the values of the slope and one point to set up the equation.

(y - y1) = m(x - x1)

where m = -1 and (x1 , y1) =  (-10 , 3)

(y - 3) = -1(x - -10)

y - 3 = -(x + 10)

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If 37 kids stayed home, the daycare normally has 143 kids.

We can use algebra to solve the problem.

Let's call the total number of kids in the daycare "x".

We know that 74% of the kids were absent, which means that 26% (100% - 74%) of the kids came to the daycare.

Note:  37 kids stayed home.

Set up the following equation:

0.26x = 37

To solve for x,  divide both sides by 0.26:

x = 37 / 0.26

x ≈ 142.31

Therefore, the daycare normally has approximately 143 kids.

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The slope of a line can be positive, negative, zero, or undefined. The horizontal line does not rise vertically (y1 − y2 = 0), so the slope is zero, but the vertical line does not extend horizontally (that is, x1 − x2 = 0), so the slope is undefined. As mentioned above, the horizontal line has zero slopes. This does not mean that the horizon has no slope. Since the horizontal line is m=0, it is represented symbolically by the expression y=b. Functions defined by horizontal lines are often called constant functions. The slope of the vertical line is undefined. Any two points on the vertical line have the same x-coordinate, so the gradient cannot be computed as a finite number according to the equation

M=(y2-y1)/(x2-x1)

This is because division by zero is an undefined operation.

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CN and DN are radii of the same circle. So, they are equal in length then the value of DN = 8 cm.

A circle is defined as the collection of all points in the plane that are a fixed distance (the radius) from a fixed point (the center). A radius is any interval that connects a point on a circle to its center. Any two radii have the same length according to the definition of a circle.

A circle is a two-dimensional closed figure in which the set of all points in the plane is equidistant from a given point known as the "center."

A circle is a shape formed by all points in a plane that are at a given distance from the center. It is the curve traced out by a point moving in a plane so that its distance from a given point remains constant.

Here, CN and DN are radii of the same circle. So, they are equal in length then the value of DN = 8 cm.

The complete question is:

If CN = 8 centimeters, find DN.

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Answer:

Step-by-step explanation:

Hey there!

(3^2)^4

= (3 * 3)^4

= (9)^4

= 9^4

= 9 * 9 * 9 * 9

= 81 * 81

= 6,561

Therefore, your answer should be:

6,561

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

x=100

Step-by-step explanation:

√x-6+2=6

√x -4 =6

√x =6+4

√x = 10

squere both sides of the equation

x =100

Answer:

3 hours i believe

Step-by-step explanation:

i did 11.25 (11 1/4) divided by 3.75 (3 3/4)

The total number of hours in a single shift is 3 hours

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total number of hours in a single shift be = A

Now , The total length of equal shifts Skylar worked last week = 3 3/4 shifts

The total length of equal shifts Skylar worked last week = 15 / 4 shifts

The total number of hours Skylar worked in the week = 11 1/4 hours

The total number of hours Skylar worked in the week = 45 / 4

Now , the equation will be

Total length of equal shifts Skylar worked last week = total number of hours Skylar worked in the week

So ,

Total length of one shift of Skylar = total number of hours Skylar worked in the week / Total length of equal shifts Skylar worked last week

On substituting the values in the equation , we get

Total length of one shift of Skylar A = ( 45/4 ) / ( 15/4 )

On simplifying the equation , we get

A = ( 45/4 ) / ( 15/4 )

A = 45 / 15

A = 3 hours

Therefore , the value of A is 3 hours

Hence , The total number of hours in a single shift is 3 hours

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Answer:

w = 3,−5

Step-by-step explanation:

If ur solving for w then that i presume.

Answer: 76

Step-by-step explanation:

4 * 22 = 88

88-12 = 76

In mathematics, the logarithm is the reciprocal of a power. This means that the logarithm of a given number x is the exponent by which another fixed number (the base b) must be increased to get that number x. The simplest logarithm counts the number of times the same element occurs when multiplying repeatedly. The logarithm of x to base b is denoted by log b (x), or log b x without parentheses. Also, if confusion is impossible or the base doesn't matter, log x shows that even without an explicit base: B. In big O notation.

Solution:

Your problem → log (3,1/27)

log (3, (127)) =-3

Solution steps:

=log (3,127)

=log (3,0.037037)

=log3(0.037037)

=-3

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The expression for 7(2+9) IS A(B+C) which is distributive property of addition over multiplication.

Only two arithmetic procedures are subject to the commutative property: Multiplication and Addition

 A + B = B + A Which is Commutative property of addition

A.B = B.A, which is a commutative property of multiplication.

Distributive property is A(B+C) =AB+AC

The operation on numbers that are available in brackets can be distributed for each number outside the bracket, according to the distributive property. It is one of the mathematical properties that is used the most. Commutative and associative qualities are the other two important features.

from the given data 7(2+9) =7*2+7*9

                                                =14+63

                                                =77

Now, we can clear that 7(2+9) =7(9+2)

Hence, the expression for commutative property of addition is A(B+C) = AB+AC.

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The equation of line parallel to the given equation and goes through the given point is y = 7x - 26.

Given the data in the question;

First, we determine the slope by comparing the equation with the slope intercept formula ( y = mx + b )

y = 7x + 3

Hence,

Slope m = 7

Next, we use the point-slope formula y-y₁ = m( x-x₁ ) to determine the equation of the line parallel.

Note that, the slopes must equal.

Given that; slope m = 7, Point: (-4,-2)

Plug into the point-slope formula and simplify.

y-y₁ = m( x-x₁ )

y - (-2) = 7( x - (-4) )

y + 2 = 7( x + 4 )

y + 2 = 7x + 28

y = 7x + 28 - 2

y = 7x - 26

Therefore, the equation of line parallel to the given equation and goes through the given point is y = 7x - 26.

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Compare the two numbers 12,-√150

[tex]-\sqrt{150} =-12.24[/tex]

So,12  >  -√150

What is a square root?

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