Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0

125° is the  angle of CBD

An angle pair that forms a straight line is referred to as a straight angle pair. This pair's sum of any two or more angles is always equal to 180°.

A straight angle has a 180° angle.

The two angles are from a straight line, and they sum to 180 degrees.

A + B + C = 180

8x -41+ 9x+17 = 180

Conjoin similar terms

17x -24 = 180

24 more on each side

17x -24+24 = 180 +24

17x = 204

multiply by 17

17x/17 = 204/17

x =12

We desire CBD angled.

CBD = 9x+17

= 9*12+17=108+17

= 125

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Answer:

[tex]\frac{4+\sqrt{11} }{5}[/tex]

Step-by-step explanation:

to rationalise the denominator, multiply the numerator and denominator by the conjugate of the denominator.

the conjugate of 4 - [tex]\sqrt{11}[/tex] is 4 + [tex]\sqrt{11}[/tex] , then

[tex]\frac{1(4+\sqrt{11}) }{(4-\sqrt{11})(4+\sqrt{11}) }[/tex] ← expand denominator using FOIL

= [tex]\frac{4+\sqrt{11} }{16-11}[/tex]

= [tex]\frac{4+\sqrt{11} }{5}[/tex]

Answer:

As addition: -13+(-7)=-20

What is the correct standard form for 400+3+0.07+0.001

403.071

Answer:

=4.03071×10²

Step-by-step explanation:

400+3=403

=403+0.07=403.07

=403.07+0.001=403.071

so 403.071 to standard form is 403.071 divide by 100 is 4.03071 and 10 and and also change to 2 zeros and Chang it to powers so =4.03071×10²

The value of b of the equation is -9/5

Given that: line JK passes through points J(-4,-5) and K(-6,3) and if the equation of the line is written in slope-intercept form, y=mx+b

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system

Using the y-y₁/y₂-y₁ = x-x₁/x₂-x₁

where (x₁, y₁) = (-4,-5) and (x₂, y₂) = (-6,3), the equation is:

y-(-5) / 3-(-5) = x-(-4)/-6-(-4)

y+5 / 3+5 = x+4 /6+4

(y+5)/8 =  (x+4)/10       cross multiply:

10(y+5) = 8(x+4)

10y + 50 = 8x + 32

10y = 8x +32 - 50

10y = 8x - 18

y = 8x/10 - 18/10

y = 4x/5 - 9/5

Comparing y = 4x/5 - 9/5 with y=mx+b

b = -9/5

Therefore, the value of b is -9/5

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Answer:

76

Step-by-step explanation:

Answer:

100% - 80%=20%

Step-by-step explanation:

that's the answer

Proportionately, it would take the restaurant 22.75 avocadoes to make 14 orders of guacamole since it takes 6.5 avocados to make 4 orders.

Proportion refers to the quantity of a value or variable contained in another value.

Proportion is a fractional value like a ratio that shows the numerical relationship between two or more values.

Proportions are depicted using fractions, decimals, or percentages.

The number of avocados required for 4 orders of guacamole = 6.5

The total number of orders of guacamole required = 14

The number of avocados to make 1 order = 6.5/4

The number of avocadoes required to fill 14 orders = 22.75 (6.5/4 x 14)

Thus, in proportion, it would take 22.75 avocados to make 14 orders of guacamole.

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Graph for the equation ( y = -300x +  1200 ) below

y-intercept = ( 0, 1200 )

x-intercept = ( 4, 0 )

Hope this helps! :)

The y-intercept is ( 0, 1200 ) and the x-intercept is ( 4, 0 ).

The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.

In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.

Given:

y=-300x+ 1200

Now, for y- intercept put x=0

y= 1200

and, for x- intercept put y= 0

0 = -300x +1200

x= 4

Hence, the y-intercept is ( 0, 1200 ) and the x-intercept is ( 4, 0 ).

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Step-by-step explanation:

so, we have 2 cost functions. each consisting of 1 large centerpiece, and x smaller arrangements.

cost1(x) = 19x + 50

cost2(x) = 23x + 42

to get the value for x we know that the cost is the same either way.

that means

cost1(x) = cost2(x) = 19x + 50 = 23x + 42

19x + 50 = 23x + 42

50 = 4x + 42

8 = 4x

x = 2

so, she orders 2 small arrangements.

the total cost is

19×2 + 50 = 38 + 50 = $88

cross check with the other function :

23×2 + 42 = 46 + 42 = $88

correct

The equation 6(x + 5) = 6x + 5 has NS (No Solution) and the equation -4x = 7x - 33 has IM (Infinite Many solutions).

Let us take the given equation

6(x + 5) = 6x + 5

⇒ 6x + 30 = 6x + 5

⇒ 6x - 6x = 5 - 30

⇒ 0 = -25

Hence, the given equation has No Solution (NS)

Let us take the given equation

-4x = 7x - 33

-4x - 7x = -33

-11x = -33

x = 3

Hence, the given equations has Infinite Many solutions (IM)

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⇒Note this is a fraction.

⇒For a fraction to be undefined that is of when the denominator is equal to 0

⇒Now equate what is  in the denominator with 0

⇒ [tex]k+3=0\\k=-3[/tex]

⇒So that the denominator is 0 that is of when k is equal to -3..it is then that the whole expression will be undefined.

⇒The expression is undefined when k=-3

The value of n is A. -1/2

The inequality that does not represent the position of 2 numbers on a number line is A. 4 1/2 > 25/4

A number line is a horizontal representation of number parts with equal intervals

The numbers in a number line is arranged to be increasing from left to right , hence drawing a number line will have the smaller values to the left of the bigger values

n is the negative side of the line and it is half (1/2) way between 0 and -1 hence should be -1/2

for the inequality, 4 1/2 > 25/4

4 1/2 = 4.5

25/4 = 6.25

4.5 should less than 6.25, and hence do not represent the correct position of two numbers

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The maximum and minimum measurements are 5 and -3 respectively.

f ( x ) = -x^3 +3x^2+ 45 x + 10

f' l x ) = 0

0 = - 3x^2 +6x +45

x = 5,- 3.

f ( 4 ) = - ( 4 )^3+ 3( 4 )^ 2 + 45 ( 4 ) + 10 = 174

f ( - 4 ) = - ( - 4 )^3 + 3( - 4 )^2 + 45(- 4) + 10 = - 58

f ( - 3 ) = -(- 3 )^3 + 3 ( - 3)^2 + 45 (- 3) + 10 = - 7 1

+ ( 5 ) = -(5)^3 + 3(5 )^2 +45(5)+ 10 = 185

Absolute maximum = maxis{ f(4 ),f(5),f(-4),f( - 3 )}

                        = 185 at x=5

Absolute mininum=minis{f(4 ),f(5),f(-4),f( - 3 )}

                      = - 71 at x= -3

In light of this, the maximum and minimum values are 5 and -3, respectively.

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Answer:

  shifted down 4 units

Step-by-step explanation:

You want to know the effect on the graph of changing y=2x+2 to y=2x-2.

The constant in the equation y=2x+2 is the y-intercept. The line described by this equation crosses the y-axis at y=2.

When the equation is changed to y=2x-2, the y-intercept changes from +2 to -2, a shift down of 4 units. The shifted line has the same slope as the original, so is parallel to it.

The effect on the graph is to move it down 4 units.

Answer:

Divide by Three Trick

This is a fun trick. If the sum of the digits in a number can be divided by three, then the number can as well.

Examples:

1) The number 12. The digits 1+2=3 and 12 ÷ 3 = 4.

2) The number 15. The digits 1+5 = 6, which is divisible by 3. It turns out that 15 ÷ 3 = 5

Answer:

7+2/8+5

Step-by-step explanation:

The initial 4 gallons and the fractions of [tex]\frac{1}{2}[/tex] and [tex]1\frac{1}{4}[/tex] gallons of paint used on the first day indicates;

A fraction is the representation of a number in quotient form such that the value of the number is obtained by dividing the numerator by the denominator.

The amount of paint Lyle and Ming started painting the room with = 4 gallons

Amount of paint Lyle used on the first day = [tex]\dfrac{1}{2}[/tex] gallons of paint

The amount of paint Ming used on the first day =  [tex]1\frac{1}{4}[/tex] gallons of paint

Required; The amount of paint remaining after the first day of painting

The paint left after the first day of painting, V, is the difference between the amount of paint with which the painting was started and the amount used by Lyle and Ming on the first day

Therefore; [tex]V = 4 - \left(\dfrac{1}{2} + 1\dfrac{1}{4} \right) = 4 - \left(\dfrac{1}{2} +\dfrac{5}{4} \right) = 4 - \dfrac{7}{4}[/tex]

[tex]V = 4 - \dfrac{7}{4} = \dfrac{16-7}{4} = \dfrac{9}{4} = 2\dfrac{1}{4}[/tex]

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Answer:

The area of the dount is about 35.325 in²

Step-by-step explanation:

In order to find the area of a donut with a hole on the center we need to find the area of the center and the area of the circle of the donut (as if the donut was whole)

*The radius is half of the diameter or r = d/2

The area of a circle is A = n(3.14) r² or pi(3.14)× radius

The correct statement regarding the proportional relationships is given as follows:

Boat A travels at a faster rate than Boat B.

A proportional relationship is a special case of a linear function with intercept zero in which the output variable is given by the multiplication of the input variable and the constant of proportionality, in the case of a direct relationship, as follows:

y = kx

The function for boat A is:

d = 10.5t.

Hence the rate is:

10.5 miles per hour.

From the graph, the rate for boat B is obtained as follows:

k = 90/10 = 9 miles per hour.

A higher constant means a faster rate, 10.5 is greater than 9, hence boat A travels faster.

The problem is given by the image shown at the end of the answer.

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Hence, 17-unit percent change is (45/19)×17% = 40.26%

12-unit percent change is (43/16)×12% = 32.25%

18-unit percent change is (-25/20)×18% = -22.5%

8-unit percent change is (-50/5)×8% = -80%

Given, that

The 19-unit percent change is 45 %

Now, 1-unit percent change is 45/19

17-unit percent change is (45/19)×17%

= 40.26%

The 16-unit percent change is 43 %

Now, 1-unit percent change is 43/16

12-unit percent change is (43/16)×12%

= 32.25%

The 20-unit percent change is -25%

Now, 1-unit percent change is -25/20

18-unit percent change is (-25/20)×18%

= -22.5%

The 5-unit percent change is -50 %

Now, 1-unit percent change is -50/5

8-unit percent change is (-50/5)×8%

= -80%

Hence, 17-unit percent change is (45/19)×17% = 40.26%

12-unit percent change is (43/16)×12% = 32.25%

18-unit percent change is (-25/20)×18% = -22.5%

8-unit percent change is (-50/5)×8% = -80%

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The range values for the domain of the functions are as follows

x   y

-2  7

0   3

1     1

3    -3

The domain are the input values of the graph the output values are solved using the given functions

The given function 2x-y=3

rearranging gives

y = 3 - 2x

solving for the range values using the domain values: (-2,0,1,3)

= 3 - 2x = 3 - 2 * -2 = 7

= 3 - 2 * 0 = 3

= 3 - 2 * 1 = 1

= 3 - 2 * 3 = -3

The graph is attached

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Answer:

x = -20

Step-by-step explanation:

x/4 + 8 = 3

subtract 8 from both sides:

x/4 + 8 - 8 = 3 - 8

x/4 = -5

multiply both sides by 4:

4(x/4) = 4(-5)

x = -20

The probability of an event is given by dividing the favorable outcomes by total number of outcomes. The sum of all the probabilities of events is always 1.

The probability that 2 red cards and 11 black cards are dealt is .

The probability of an event is given by dividing the favorable outcomes by total number of outcomes. The sum of all the probabilities of events is always 1. If for finding probability we have to select r out of n. Combination is used to select r items out of n, the formula is as follows,

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Finding the probability that 2 red cards and 11 black cards are dealt,

Number of favorable outcomes will be [tex]^{26}C_2\times^{26}C_{11}[/tex].

Total number of outcomes will be [tex]^{52}C_{13}[/tex]

Now, the probability will be,

[tex]P()=\frac{^{26}C_2\times^{26}C_{11}}{^{52}C_{13}} \\\\=\frac{325\times7726160}{635013559600} \\\\=0.00395[/tex]

Therefore, the probability that 2 red cards and 11 black cards are dealt is 0.00395.

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Answer:

14

Step-by-step explanation:

The model which model the dimensions of the bed has been attached.

Perimeter of the bed = 2(length + width)

= 2(6 + 4)

= 2(10)

= 20 feet

Area of the bed = Length × width

= 6 feet × 4 feet

= 24 square feet

Total perimeter = 14 + 10 + 10 + 6

= 40 feet

Therefore, the items listed can not all be underneath your bed because the total perimeter of the items is greater than the perimeter of your bed.

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Answer:

Y = 3/4x + 0

Step-by-step explanation:

Find the slope of the line = Rise/Run.

[tex]\frac{-3-6}{-4-8}[/tex]  = [tex]\frac{-9}{-12}[/tex]

= 0.75 or 3/4.

Therefore, insert into point slope form using one of the corresponding points; (8, 6) for example;

Y-6 = 3/4(x-8)

= Y-6 = 3/4x-6

and simplify the equation;

Y = 3/4x + 0 also just Y = 3/4x.  

Answer:

$1053

Step-by-step explanation:

If we have that £1 = $1.62, then we can multiply both sides by 650 in order to get £650 on the left side of the equality. We must multiply the right side also by 650, and so we get £650=$1.62 * 650.

To do this multiplication, we can break 1.62 down  simply into $1.00 +$0.6+$0.02

650*$1.00=$650, 650*$0.6=650*6/10=65*6=$390, and 650*$0.02=650*2/100=6.5*2=$13.

When we add these three products together, we get $650+$390+$13=$1053. And so, £650=$1053