Simplify this algebraic expression.
y-3/3 +12
O A. y-11
O B. y + 13
O c. y-5
O D. y+ 11

Answer:

y = -6x + 1

Step-by-step explanation:

y = mx + b

b = slope = (-5 - (-17))/(1 - 3) = 12/(-2) = -6

y = -6x + b

-5 = -6(1) + b

b = 1

y = -6x + 1

Answer:

[tex]y=-6x+1[/tex]

Step-by-step explanation:

The linear equation with slope m and intercept c is given as follows:

[tex]y=mx+c[/tex]

The formula for slope of line with points [tex](x_{1} ,y_{2} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] can be expressed as,

[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

The line passes the points that are [tex](1,-5)[/tex] and [tex](3,-17)[/tex]

The slope of the line can be obtained as follows:

[tex]m=\frac{-17-(-5)}{(3)-1}[/tex]

[tex]m=\frac{-12}{2}[/tex]

[tex]m=-6[/tex]

The slope of the line is [tex]-6[/tex]

The line passes through the point [tex](3,-17)[/tex]

Substitute 3 for x, - 6 for m and -17 for y in equation [tex]y=mx+c[/tex] to obtain the value of c.

[tex]-17=-6(3)+c[/tex]

[tex]-17=-18+c[/tex]

[tex]-17+18=c[/tex]

[tex]1=c[/tex]

The equation is [tex]y=-6x+1[/tex]

Hence, the equation of the line that passes through the points [tex](1,-5)[/tex] and [tex](3,-17)[/tex] is [tex]y=-6x+1[/tex]

Answer:

LP ⊥ PN

Step-by-step explanation:

Given

[tex]L = (-4, 1)[/tex]

[tex]M = (2, 4)[/tex]

[tex]N = (3, 2)[/tex]

[tex]P = (-3, -1)[/tex]

See attachment

Required

What proves LMNP is a rectangle

The additional information needed is LP ⊥ PN

Because:

[tex](a)\ LM= \sqrt{45}; MN = \sqrt{5}[/tex]

This can be true for other shapes, such as trapezoid, etc.

[tex](b)\ m(LP) = m(MN) = -2[/tex]

The slopes of LP and MN will be the same because both sides are parallel; However, this is not peculiar to rectangles alone. Same as option (c)

(d) LP ⊥ PN

This must be true i.e. LP must be perpendicular to PN

Answer:

d

Step-by-step explanation:

Answer:

(21.064 ; 23.136)

Step-by-step explanation:

Given :

Sample, n = 80

Mean, xbar = 22.1

Standard deviation, s = 5.6

Standard Error, S. E = 0.63

Confidence interval :

Xbar ± Zcritical * S.E

22.1 ± (1.645 * 0.63)

22.1 ± 1.036

Lower boundary = 22.1 - 1.036 = 21.064

Upper boundary = 22.1 + 1.048 = 23.136

(21.064 ; 23.136)

Answer:

"Add equations A and B to eliminate [tex]y[/tex]. Add equations A and C to eliminate [tex]y[/tex]".

Step-by-step explanation:

Let be the following system of linear equations:

[tex]4\cdot x + 4\cdot y + z = 24[/tex] (1)

[tex]2\cdot x - 4\cdot y +z = 0[/tex] (2)

[tex]5\cdot x - 4\cdot y - 5\cdot z = 12[/tex] (3)

1) We eliminate [tex]y[/tex] by adding (1) and (2):

[tex](4\cdot x + 2\cdot x) +(4\cdot y - 4\cdot y) + (z + z) = 24 + 0[/tex]

[tex]6\cdot x +2\cdot z = 24[/tex] (4)

2) We eliminate [tex]y[/tex] by adding (1) and (3):

[tex](4\cdot x + 5\cdot x) +(4\cdot y - 4\cdot y) +(z -5\cdot z) = (24 + 12)[/tex]

[tex]9\cdot x -4\cdot z = 36[/tex] (5)

Hence, the correct answer is "Add equations A and B to eliminate [tex]y[/tex]. Add equations A and C to eliminate [tex]y[/tex]".

9514 1404 393

Answer:

  (t, u, w) = (1, -2, -2)

Step-by-step explanation:

A graphing calculator makes short work of this, giving the solution as ...

  (t, u, w) = (1, -2, -2)

__

There are many ways to solve this "by hand." Here's one of them.

Add the first and third equations. Their sum is ...

  -3t +4w = -11 . . . . . [eq4]

Add this to twice the second equation. That sum is ...

  (-3t +4w) +2(-4t -2w) = (-11) +2(0)

  -11t = -11

  t = 1

Substituting this into the second equation gives ...

  -4(1) -2w = 0

  w +2 = 0 . . . . divide by -2

  w = -2 . . . . add -2

Substituting for t in the third equation lets us find u.

  2(1) -2u = 6

  -1 +u = -3 . . . . . divide by -2

  u = -2 . . . . add 1

The solution is (t, u, w) = (1, -2, -2).

Answer:

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

95°=6r°+47(being vertically opposite angle)

or,48°=6r

or,48=/6=r°

or,r=8°

Answer:

She had 8 doubles.

Step-by-step explanation:

This question is solved by a system of equations.

I am going to say that:

x is the number of singles.

y is the number of doubles

z is the number of triples.

46 hits

This means that [tex]x + y + z = 46[/tex]

46 hits totaled 66 bases

This means that:

[tex]x + 2y + 3z = 66[/tex]

4 times as many singles as doubles

This means that [tex]x = 4y[/tex]

So

[tex]x + 2y + 3z = 66[/tex]

[tex]4y + 2y + 3z = 66[/tex]

[tex]6y + 3z = 66[/tex]

And

[tex]x + y + z = 46[/tex]

[tex]4y + y + z = 46[/tex]

[tex]5y + z = 46 \rightarrow z = 46 - 5y[/tex]

Then

[tex]6y + 3z = 66[/tex]

[tex]6y + 3(46 - 5y) = 66[/tex]

[tex]6y + 138 - 15y = 66[/tex]

[tex]9y = 72[/tex]

[tex]y = \frac{72}{9}[/tex]

[tex]y = 8[/tex]

She had 8 doubles.

Answer:

The number of fours divided by the total number of possibilities. If there are two fours and 8 spaces, the probability is 2/8 = 1/4.Step-by-step explanation:

Answer:

D, E, and F

Step-by-step explanation:

✔️Statement D is true:

Rationale: m<4 is more than 90°, while m<2 is less than 90°. Therefore m<4 is greater than m<2

✔️Statement E is true:

Rationale: m<4 is more than 90°, while m<1 is less than 90°. Therefore m<4 is greater than m<1

✔️Statement F is true:

Rationale:

m<4 is an external angle of the triangle.

m<1 and m<2 are interior angles that are opposite to m<4. Therefore, based on the external angle theorem of a triangle,

m<4 = m<1 + m<2

Answer:

-9

Step-by-step explanation:

(f-g) (x) = 2x²-7x+24-5x²-5x+3

= -3x²-12x+27

(f-g) (2) = -3(2)²-12(2)+27

= -12-24+27

= -9

[tex] \large{ \tt{❁ \: USING \: INTERNAL \: SECTION \: FORMULA: }}[/tex]

[tex] \large{ \bf{✾ \: P(x \:, y \: ) = ( \frac{m_{1}x_{2} + m_{2}x_{1}}{m_{1} + m_{2}} \: ,\: \frac{m_{1}y_{2} + m_{2}y_{1}}{m_{1} + m_{2}}) }}[/tex]

[tex] \large{ \bf{⟹ \: ( \frac{8m + 3n}{m + n} , \: \frac{9m -n}{m + n}) }}[/tex]

[tex] \large{ \bf{ ⟼\frac{8m + 3n}{m + n} - \frac{9m - n}{m + n} - 2 = 0 }}[/tex]

[tex] \large{ \bf{⟼ \: \frac{8m + 3n - 9m + n}{m + n} - 2 = 0 }}[/tex]

[tex] \large{ \bf{⟼ \: \frac{4n - m}{ m + n} - 2 = 0 }}[/tex]

[tex] \large{⟼ \: \bf{ \frac{4n - m}{m + n }} = 2} [/tex]

[tex] \large{ \bf{⟼ \: 4n - m = 2m + 2n}}[/tex]

[tex] \large{ \bf{⟼ \: 4n -2 n = 2m + m}}[/tex]

[tex] \large{ \bf{⟼2n = 3m}}[/tex]

[tex] \large{ \bf{⟼ \: 3m = 2n}}[/tex]

[tex] \large{ \bf{⟼ \: \frac{m}{n} = \frac{2}{3} }}[/tex]

[tex] \boxed{ \large{ \bf{⟼ \: m : \: n = 2: \: }3}}[/tex]

-Hope I helped! Let me know if you have any questions regarding my answer and also notify me , if you need any other help! :)

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Answer:

27

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

Identify

x = -3

y = 3

y - 8x

Step 2: Evaluate

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\large\textsf{y - 8x}\\\\\large\textsf{= 3 - 8(-3)}\\\\\large\textsf{8(-3) = \bf -24}\\\\\large\textsf{= 3 - \bf 24}\\\\\large\textsf{= \bf 27}\\\\\boxed{\boxed{\large\textsf{\huge\textsf{Answer: \bf 27}}}}\huge\checkmark\\\\\\\\\large\textsf{Good luck on your assignment and enjoy your day!}\\\\\\\\\\\frak{Amphitrite1040:)}[/tex]

Answer:

2b-7

Step-by-step explanation:

Given that,

Bernie's hamster completed the maze in b seconds.

Annic's hamster completed the maze 7 seconds less than twice the time it took Bernie's hamster to complete the maze.

Twice the time it took Bernie's hamster to complete the maze is 2b.

7 seconds less than twice the time it took Bernie's hamster = 2b-7

So, the correct option is (b) "2b-7".

Answer:

Step-by-step explanation:

Answer:

42 degrees

Step-by-step explanation:

We already have the two angles for the triangle, we just need the third. For triangles, the can only add up to 180 degrees. 101+37=138 degrees, now we subtract 138 from 180.

180-138=42.

Answer:

Step-by-step explanation:

Answer:

hope it will help u

Answer:

2nd choice

Step-by-step explanation:

Answer:

ok so its is 5 dollars for a pencil and 420 dollars for a pen(dang)

a40+2100=2140

now

b6 pencil 462 pen

60+3696=3756

Hope This Helps!!!

(a) Afua paid ¢44,500.00 for 8 pencils and 5 pens.

(b) Afua will pay ¢71,400.00 for 10 pencils and 8 pens after the price increase.

(a) To find how much Afua paid altogether for 8 pencils and 5 pens, we need to calculate the total cost for each item and then add them together.

Given:

Cost of a pencil, [tex]Pencil_{cost}[/tex] = ¢500.00

Cost of a pen, [tex]Pen_{cost}[/tex] = ¢42,000.00

Number of pencils bought, [tex]n_{pencils}[/tex] = 8

Number of pens bought, [tex]n_{pens}[/tex] = 5

Total cost of pencils,

[tex]Total_{pencil}_{cost} = Pencil_{cost} * n_{pencils}[/tex]

                      = ¢500.00 × 8

                      = ¢4,000.00

Total cost of pens,

[tex]Total_{pen}_{cost} = Pen_{cost} * n_{pens}[/tex]

                   = ¢42,000.00 × 5

                   = ¢210,000.00

Altogether, [tex]Total_{cost} = Total_{pencil}_{cost} + Total_{pen}_{cost}[/tex]                                      

                                  = ¢4,000.00 + ¢210,000.00

                                  = ¢214,000.00.

Therefore, Afua paid ¢214,000.00 for 8 pencils and 5 pens.

(b) Now, let's calculate the new total cost after the price increase.

The price of a pencil increased by 20%, which means the new pencil cost is:

[tex]New_{pencil}_{cost}[/tex] = [tex]Pencil_{cost}[/tex]+ (20% × [tex]Pencil_{cost}[/tex])

                                  = ¢500.00 + (0.20 × ¢500.00)

                                  = ¢500.00 + ¢100.00

                                  = ¢600.00

Similarly, the price of a pen increased by 10%, which means the new pen cost is:

[tex]New_{pen}_{cost}[/tex] = [tex]Pen_{cost}[/tex] + (10% × [tex]Pen_{cost}[/tex])

                          = ¢42,000.00 + (0.10 × ¢42,000.00)

                          = ¢42,000.00 + ¢4,200.00

                          = ¢46,200.00

Now, we can find the total cost for 10 pencils and 8 pens with the increased prices:

Number of pencils to be bought, [tex]n_{pencils}_{new}[/tex] = 10

Number of pens to be bought, [tex]n_{pens}_{new}[/tex] = 8

Total cost of pencils with new prices,

[tex]Total_{pencil}_{cost}_{new}[/tex] =[tex]New_{pencil}_{cost}[/tex] × [tex]n_{pencils}_{new}[/tex]

                                        = ¢600.00 × 10

                                        = ¢6,000.00

Total cost of pens with new prices,

[tex]Total_{pen}_{cost}_{new}[/tex] = [tex]New_{pen}_{cost}[/tex] × [tex]n_{pens}_{new}[/tex]

                                    = ¢46,200.00 × 8

                                    = ¢369,600.00

Altogether, [tex]New_{total}_{cost}[/tex] = [tex]Total_{pencil}_{cost}_{new}[/tex] + [tex]Total_{pen}_{cost}_{new}[/tex]

                                               = ¢6,000.00 + ¢369,600.00

                                               = ¢375,600.00

Therefore, Afua will pay ¢375,600.00 for 10 pencils and 8 pens with the increased prices.

To know more about Price here

https://brainly.com/question/28005569

#SPJ2

(a) The region Y₁ < 1/2 and Y₂ > 1/4 corresponds to the rectangle,

{(y₁, y₂) : 0 ≤ y₁ < 1/2 and 1/4 < y₂ ≤ 1}

Integrate the joint density over this region:

[tex]P\left(Y_1<\dfrac12,Y_2>\dfrac14\right) = \displaystyle\int_0^{\frac12}\int_{\frac14}^1 (y_1+y_2)\,\mathrm dy_2\,\mathrm dy_1 = \boxed{\dfrac{21}{64}}[/tex]

(b) The line Y₁ + Y₂ = 1 cuts the support in half into a triangular region,

{(y₁, y₂) : 0 ≤ y₁ < 1 and 0 < y₂ ≤ 1 - y₁}

Integrate to get the probability:

[tex]P(Y_1+Y_2\le1) = \displaystyle\int_0^1\int_0^{1-y_1}(y_1+y_2)\,\mathrm dy_2\,\mathrm dy_1 = \boxed{\dfrac13}[/tex]

Y₁ and Y₂ are not independent because

P(Y₁ = y₁, Y₂ = y₂) ≠ P(Y₁ = y₁) P(Y₂ = y₂)

To see this, compute the marginal densities of Y₁ and Y₂.

[tex]P(Y_1=y_1) = \displaystyle\int_0^1 f(y_1,y_2)\,\mathrm dy_2 = \begin{cases}\frac{2y_1+1}2&\text{if }0\le y_1\le1\\0&\text{otherwise}\end{cases}[/tex]

[tex]P(Y_2=y_2) = \displaystyle\int_0^1 f(y_1,y_2)\,\mathrm dy_1 = \begin{cases}\frac{2y_2+1}2&\text{if }0\le y_2\le1\\0&\text{otherwise}\end{cases}[/tex]

[tex]\implies P(Y_1=y_1)P(Y_2=y_2) = \begin{cases}\frac{(2y_1+1)(2y_2_1)}4&\text{if }0\le y_1\le1,0\ley_2\le1\\0&\text{otherwise}\end{cases}[/tex]

but this clearly does not match the joint density.

Answer:

B

substract the variables

Answer:

B.

Step-by-step explanation:

there is not much to explain.

a strong correlation means there is a direct connection.

so, a change in a causes immediately a change in b.

and positive means that the changes go in the same sign direction. increase => increase. decrease => decrease.

Answer:

A

Step-by-step explanation:

Midpoints are found by averaging the coordinates.

Averaging " add all the numbers and divide by the number of numbers.

Here, there are only 2 numbers. So, you divide by 2.

(1,2) (1,-5)

[tex]\frac{1 +1}{2}[/tex] , [tex]\frac{2 + (-5)}{2}[/tex]

[tex]\frac{2}{2}[/tex] , [tex]\frac{-3}{2}[/tex]

(1, [tex]\frac{-3}{2}[/tex] )

Answer:

925



Step-by-step explanation:

Formula =592 x 100/64 = 925

Answer:

ii

Step-by-step explanation:

you have to look and read it it comes simple

Answer:

60 ft

Step-by-step explanation:

The answer has to be in feet units

Now that we know the height is 5 cm equivalent to 150 feet, what is the width of the building in feet units

5 cm = 150 ft

Rule: multiply cm by 30 to get the ft

2 cm = ?

2 cm × 30 = 60 ft

2 cm = 60 ft

Answer:

(-2, 2)

Step-by-step explanation:

(-2, 2) is the only ordered pair that makes both inequalities true.

Answer:

B

Step-by-step explanation:

got it right

Step-by-step explanation:

678-72=606/2=303+72=375

Answer:

1. x + 4 = 9

Hint: the word 'sum' generally refers to addition.

2. 10a = 70

3. [tex]\frac{3}{4} t[/tex] = 15

4. [tex]\frac{1}{4} x[/tex] - 4 = 4

Answer:

y = 2x

Step-by-step explanation:

Given that , the line passes through the point (0,0) and has a slope of 2. So here we can use the point slope form of the line as ,

[tex]\implies y- y_1 = m( x - x_1) \\\\\implies y - 0 = 2( x - 0 ) \\\\\implies y = 2(x) \\\\\implies \underline{\underline{y = 2x }}[/tex]