2. What is the new correction equation using the Equal Values Method for the following system below?
y=2x+1
y = 6-3x

[tex]\\ \rm\Rrightarrow \dfrac{AB}{AD}=\dfrac{BC}{CD}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{18}{x}=\dfrac{19}{11}[/tex]

[tex]\\ \rm\Rrightarrow 19x=198[/tex]

[tex]\\ \rm\Rrightarrow x=10.4[/tex]

Answer:

x = 10.4 (nearest tenth)

Step-by-step explanation:

Angle Bisector Theorem

The angle bisector of any angle in a triangle will divide the side opposite the bisected angle in the ratio of the sides containing the angle.

Therefore:

AD : DC = BA : BC

Given:

Substituting the given values into the ratio and solving for x:

[tex]\implies \sf x : 11 = 18 : 19[/tex]

[tex]\implies \sf \dfrac{x}{11}=\dfrac{18}{19}[/tex]

[tex]\implies \sf 19x=18 \cdot 11[/tex]

[tex]\implies \sf 19x=198[/tex]

[tex]\implies \sf x=\dfrac{198}{19}[/tex]

[tex]\implies \sf x=10.4 \: (nearest\:tenth)[/tex]

Answer:

8.318

Step-by-step explanation:

writing a number in three decimal places means writing the number in a way that there will be three digits in the number after the decimal point.

to three decimal places= 8.318

1,005.44

Pir^2h

3.142*8*8*5

1,005.44

Answer:

option 3, [tex]972\pi in^{3}[/tex]

Step-by-step explanation:

The formula to find the volume of a sphere is [tex]\frac{4}{3} \pi r^{3}[/tex]

where r os the radius

given: diameter = 18in

radius = diameter / 2

radius = 18 / 2

r = 9in

Plug in radius:

[tex]\frac{4}{3} \pi (9)^{3}\\\\\frac{4\pi (9)^{3}}{3} \\\\Factor (9)^{3}: (3)^{6}\\\\\frac{(3)^{6} * 4\pi }{3} \\\\[/tex]

cancel common factor: 3

[tex]3^{5} * 4\pi \\3^{5} = 243\\243 * 4\pi\\972\pi[/tex]

Let me know if you have any questions !

The regression line is y = 10x + 125, and the value of calories is 135, and when x = 12 the value of y = 245 from the regression line, butbut the actual value is 225.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dot's relationship.

Here the scatter plot is not given, but we can draw the scatter plot using the data which is given with two variables such as (x, y) and the line which is best fit of the given data.

From the data given, we can write the line of best fit in slope and y-intercept form:

y = mx + b

Plug m = 10 and b = 125

y = 10x + 125

The number of fat grams in an item having that number of fat calories.

As we have the regression line:

y = 10x + 125

Put x = 1 in the regression line:

y = 10(1) + 125

y = 135 calories

For x = 12

y = 10(12)+125 = 245

But the actual value from the graph is 225.

Thus, the regression line is y = 10x + 125, and the value of calories is 135, and when x = 12 the value of y = 245 from the regression line, but but the actual value is 225.

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Step-by-step explanation:

x - 2y = -3,____1 , 8x - 6y = 16____ 2

x - 2y = -3

x = 2y -3 ____ equation 3

eqn 3 in 2

2=> 8x - 6y = 16

8(2y-3) - 6y = 16

16y - 24 - 6y = 16

10y = 16 + 24

10y = 40

y = 40 / 10

y = 4

y=4 in eqn 3

3=> x = 2y - 3

x = 2(4) - 3

x = 8 - 3

x = 5

x = 5 , y = 4

-2y-2y = 20 , x - 7y = 14___ 1

-2y-2y = 20

-4y = 20

y = 20/ -4

y = -5

y = -5 in eqn 1

1=> x - 7y = 14

x - 7(-5) = 14

x - (-35) = 14

x + 35 = 14

x = 14 - 35

x = -21

x = -21 , y = -5

Answer:

y = 2x – 10

Step-by-step explanation:

ΔY divided by ΔX

= 5-7/0-4

= 2/1 = 2 (simplified)

plug in 2 into; 0=2(5)+b

= -10=b

so we have: y=2x-10

Answer:

Step-by-step explanation:

A is 3 You have to minus Clares age by two to get Mary's age

B is 1 You have to divide the price in half

C is 2 the only one left

Answer:

9/19  or  47.4% (nearest tenth)

Step-by-step explanation:

A roulette wheel is numbered 1 to 36 with 0 and 00.

Therefore, there is a total of 38 evenly-spaced pockets.

The number of odd numbers from 1 to 36 is 18

(1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35)

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

[tex]\implies \textsf{Probability of odd number}= \sf \dfrac{18}{38}=\dfrac{9}{19}=47.4\%[/tex]

Roulette wheel contains 1 to 36 numbers excluding 0 and 00

Total odd nos

{1,3,5,7,9,11,13,15,17,19,21,23,25,29,31,33,35}

Probability

Answer:

78m

Step-by-step explanation:

6942 ÷ 89 = 78, here you go!

Answer:

11/15

Step-by-step explanation:

To find probability, you divide whatever you're looking for over your total. In this case, you have 11 marbles that are not red, and 15 marbles total, so your answer would be 11/15.

Answer:

V ≈ 68.63 cm³

Step-by-step explanation:

the volume (V) of a sphere is calculated as

V = [tex]\frac{4}{3}[/tex]πr³

the volume of a hemisphere is half the volume of a sphere, so

V = [tex]\frac{1}{2}[/tex] × [tex]\frac{4}{3}[/tex] πr³ = [tex]\frac{2}{3}[/tex] πr³ , then

V = [tex]\frac{2}{3}[/tex] π × 3.2³

  = [tex]\frac{2}{3}[/tex] π × 32.768

  ≈ 68.63 cm³ ( to 2 dec. places )

Answer:

y = 2x + 7

Step-by-step explanation:

Answer:

240

Step-by-step explanation:

see photo for solution

Answer:

1) 9y^10

2) 560u^16 v^15

Step-by-step explanation:

√a × √b = √ab

only if at atleast one among a,b is positive

here both a,b is non negative so not possible

Step-by-step explanation:

Remember when expanding radicals,

[tex] \sqrt{ab} = \sqrt{a} \times \sqrt{b} [/tex]

When expanding radicals into two radicals, we don't let our radicand have two negative answers.

[tex]i = \sqrt{ - 1} [/tex]

[tex] {i}^{2} = - 1[/tex]

We don't do this

[tex] (\sqrt{ - 1} ) {}^{2} = \sqrt{ - 1 \times - 1} [/tex]

[tex] - 1 = \sqrt{1} [/tex]

[tex] - 1 = 1[/tex]

Answer:

x=+-√10+3

Step-by-step explanation:

x^2=6x+1

x^2-6x=1

To create a trinomial square on the left side of the equation, find a value that is

equal to the square of half of b

a is the number next to x^2

b is the number next to x

c is the last number

b is -6

half of b is -3

square of half of b is 9

put 9 on both sides of the = sign

x^2-6x+9=1+9

x^2-6x+9=10

(x-3)^2=10

take the square root of both sides of the = sign

√(x-3)^2=√10

x-3=√10

x=+-√10+3

(x_1+x_2)=-b/a=18/3=6

x_1x_2=c/a=-21/3=-7

So

(x_1-x_2)²

x_1-x_2=8

Answer:

[tex]x{_1}^2+x{_2}^2=50[/tex]

[tex]|x_1-x_2|=8[/tex]

Step-by-step explanation:

Given equation:

[tex]3x^2-18x-21=0[/tex]

Factor to find the roots:

[tex]\implies 3(x^2-6x-7)=0[/tex]

[tex]\implies x^2-6x-7=0[/tex]

[tex]\implies x^2+x-7x-7=0[/tex]

[tex]\implies x(x+1)-7(x+1)=0[/tex]

[tex]\implies (x-7)(x+1)=0[/tex]

Therefore:

[tex]\implies (x-7)=0 \implies x=7[/tex]

[tex]\implies (x+1)=0 \implies x=-1[/tex]

Therefore, the roots of the quadratic equation are:

[tex]x = 7,\quad x = -1[/tex]

Let  [tex]x_1 = 7[/tex]

Let  [tex]x_2 = -1[/tex]

[tex]\implies x{_1}^2+x{_2}^2=7^2+(-1)^2=50[/tex]

[tex]\implies |x_1-x_2|=|7-(-1)|=8[/tex]

Answer:

bridget types at the fastest rate as he can type 60 words per minute

Answer:

76°

Step-by-step explanation:

Taking the cosine ratio of the angle of depression :

Answer:

{27.5, 29, 34}.

Step-by-step explanation:

In order they are

24 27 28 28 29 31 32 36 38

The Median = middle value = 29.

Lower quartile =  mean of 27 and 28 =  27.5.

Upper quartile =  mean of 32 and 36 = 34.

Answer:

{27.5, 29, 34}

Step-by-step explanation:

Arrange in increasing order :

Lower Quartile :

Median :

Upper Quartile :

Answer:

Step-by-step explanation:

The value of a, b and c from the given expression above are 15, 1 and 4 respectively

Indices are written in form of exponential expression. Given the expression

[tex]\sqrt[4]{15}[/tex]

We are to write the expression in the form

[tex]a^{b/c}[/tex]

This is simplified as shown

[tex]\sqrt[4]{15}= 15^{1/4}[/tex]

Compare both expression

a = 15

b = 1

c = 4

Hence the value of a, b and c from the given expression above are 15, 1 and 4 respectively

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area of rectangle= length × width

= 19×33

= 627 sq units

Answer:

133°

Hope this helps!!!

Using the binomial distribution, we have that:

a) The distribution is given by:

b) 0.3125 = 31.25%.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem, we have that:

The distribution is given by the probability of each outcome, hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{4,0}.(0.5)^{0}.(0.5)^{4} = 0.0625[/tex]

[tex]P(X = 1) = C_{4,1}.(0.5)^{1}.(0.5)^{3} = 0.25[/tex]

[tex]P(X = 2) = C_{4,2}.(0.5)^{2}.(0.5)^{2} = 0.375[/tex]

[tex]P(X = 3) = C_{4,3}.(0.5)^{3}.(0.5)^{1} = 0.25[/tex]

[tex]P(X = 4) = C_{4,4}.(0.5)^{4}.(0.5)^{0} = 0.0625[/tex]

The probability of at least 3 daughters is given by:

[tex]P(X \geq 3) = P(X = 3) + P(X = 4) = 0.25 + 0.0625 = 0.3125[/tex].

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Answer:

Let DC be the tower and BC be the building. Then,

∠CAB=45

o

,∠DAB=60

o

,BC=20 m

Let height of the tower, DC=h m.

In right △ABC,

tan45 o = AB/BC

1=20/AB

AB=20m

In right∆ABD,

tan 60°=BD/AB

√3=h+20/20

h=20(√3-1)m

Answer:

a.

Step-by-step explanation:

the area of a whole circle (360°) is

pi×r²

in our case

pi×10² = 100pi

but here we don't need the full circle. we only need a fraction of the whole circle : 128/360

so, the area of the sector is

100pi × 128/360 = 100pi × 16/45 = 20pi × 16/9 =

= 111.7010721... cm² ≈ 111.7 cm²

Answer:

x = 27.4

Step-by-step explanation:

[tex]\sf \angle Q+ \angle R+ \angle S=180^{o} [/tex]

[tex]\sf 34.6 + 118 + x = 180[/tex]

Add 34.6 and 118 = 152.6

[tex]\sf 152.6+x=180[/tex]

Subtract 152.6 from both sides.

[tex]\sf x=180 - 152.6[/tex]

Subtract 152.6 from 180 = 27.4.

Therefore, the missing angle "x" is 27.4.