Question 18 of 25
Line s is the perpendicular bisector of JK. If line s intersects JK at point L.
which of the following statements must be true?
Check all that apply.
O A. JL = KL
B. Line sis perpendicular to JK
C. Point L is the midpoint of JK
OD. Line s intersects JK at a 180° angle
O E. Line sis parallel to JK
SUBMIT

Hello,

[tex]m\ \widehat{ABC}=x\\m\ \widehat{BAC}=2*x\\\\So:\\ x+2x=90^o\\x=30^o\\[/tex]

[tex]cos(30^o)=\dfrac{\sqrt{3} }{2} \\[/tex]

In the triangle ABC,

[tex]cos(30^o)=\frac{BC}{BA} \\\\BA=\dfrac{cos(30^o)}{BC} \\\\BA=\frac{\dfrac{\sqrt{3} }{2} }{24} =16*\sqrt{3} \\\\[/tex]

[tex]sin(30^o)=\dfrac{1 }{2} =\dfrac{AC}{AB} \\\\AC=\dfrac{1}{2} *16\sqrt{3} =8\sqrt{3}[/tex]

In the triangle ACB,

[tex]cos(30^o)=\dfrac{AC}{AL} \\\\AL=\dfrac{8\sqrt{3} *2}{\sqrt{3} } =16\\[/tex]

Answer:

110x -200y

Step-by-step explanation:

10(x - 20y) + 100x

Distribute

10x-200y +100x

Combine like terms

110x -200y

Answer:

110x−200y

Step-by-Step Explanation:

Given:

10(x−20y)+100x

First Step: Distribute

(10)(x)+(10)(−20y)+100x

10x+−200y+100x

Second Step: Combine Like Terms:

10x+−200y+100x

(10x+100x)+(−200y)

110x+−200y

Answer:

=110x−200y

Answer:

4x^3 + 6x^2 -10x - 15

Step-by-step explanation:

* means multiply

4x^3 + 6x^2 -10x - 15

2x * 2x^2 = 4x^3

2x * -5 = 10x

3 * 2x^2 = 6x^2

3 * -5 = -15

Answer:

4x³ + 6x² - 10x - 15

Step-by-step explanation:

(2x+3) (2x²-5)

4x³ - 10x + 6x² - 15

4x³ + 6x² - 10x - 15

Answer:

19

Step-by-step explanation:

(-6)-(-25)=(-6) +25 = 19

[tex]\bold{{Answer:}}[/tex]

Tropical Rain Forest

1.B

2.A

3.Di ko alam

Coral Reefs

1.C

2.E

3.I

Mangrove Swamps

1.D

2.H

3.G

pa tama nalang kung mali ah

tao lang nag kakamali rin hehe

[tex]\bold\blue{{Answer:}}[/tex]

Tropical Rain Forest

1.B

2.A

3.F

Coral Reefs

1.C

2.E

3.I

Mangrove Swamps

1.D

2.H

3.G

Taga Pilipinas ka din ba o hindi?

Answer:

Multiples of 120 are 120, 240, 360, 480, 600, 720, 840 etc; Multiples of 150 are 150, 300, 450, 600, 750, 900 etc; Therefore, the least common multiple of 120 and 150 is 600.

Least common multiple (LCM) of 19600 and 19619 is 384532400.

Answer: 19600

Step-by-step explanation:

19600/120 = 160

Answer:

6a = 6 * a

2a * b = 2ab

Step-by-step explanation:

2a * 2b = 4ab not 2ab

6 * a is the same as 6a

5a = 5 * a not 5 + a

3ab has different variables then 3c therefore the expression cannot be true

2ab is the same as 2a * b

Answer:

16/8 + 24

Step-by-step explanation:

Answer:

$1,471.5625

Step-by-step explanation:

Monthly salary = $1850

Weekly salary = $1850/4 weeks

= $462.5

Hourly rate = $462.5/40 hours

= $11.5625

Overwork time = 62 hours - 40 hours

= 22 hours

Time and a half = 1.5 times the normal salary

Overwork time payment per hour = 1.5 × $11.5625

= $17.34375

Overwork time payment for 22 hours = 22 × $17.34375

= $381.5625

Last week salary = weekly salary + overtime payment

= $462.5 + $381.5625

= $84.0625

Gross salary for the month = 3 weeks regular salary + last week salary

= (3 × $462.5) + $84.0625

= $1387.5 + $84.0625

= $1,471.5625

Answer:

x = number of bicycles = 35

y = number of cars = 55

Step-by-step explanation:

Let

x = number of bicycles

y = number of cars

x + y = 80 (1)

2x + 4y = 270 (2)

From (1)

x = 80 - y

Substitute x = 80 - y into (2)

2x + 4y = 270 (2)

2(80 - y) + 4y = 270

160 - 2y + 4y = 270

- 2y + 4y = 270 - 160

2y = 110

y = 110/2

y = 55

Substitute y = 55 into (1)

x + y = 80 (1)

x + 55 = 80

x = 80 - 55

x = 35

x = number of bicycles = 35

y = number of cars = 55

Answer:

B. neither perpendicular nor parallel

Step-by-step explanation:

to be perpendicular, the slopes have to be complete opposites. in this case, the second term would have to be y=-0.5x to be perpendicular. to be parallel, the two would have to have the same slopes; so y=2x and y=2x

Answer:

(3x + y)(3x - 4)

Step-by-step explanation:

9x² + 3xy - 12x - 4y ​=

There is no common factor in the 4 terms.

Since there are 4 terms, we try factoring by grouping.

Find a common factor in the first two terms, and find a common factor in the last two terms.

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

Now factor out the common factor 3x + y.

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

Answer:

4

Step-by-step explanation:

The distance between the points (-1,2) and (-5,2)

[tex] \sqrt{( - 5 - ( - 1)) ^{2} + (2 - 2) ^{2} } \\ = \: \sqrt{( - 4)^{2} + (0) ^{2} } \\ = \sqrt{16 + 0} \\ = \sqrt{16} \\ = 4[/tex]

Answered by GAUTHMATH

Answer:

150%

Step-by-step explanation:

15 / 10 =

1.5 =

150%

Step-by-step explanation:

X(x+6) - 6(x+6)

X+6x-6x-36

X-36

Answer:

BOXPLOT is a simple way of representing statistical data on a plot in which a rectangle is drawn to represent the second and third quartiles, usually with a vertical line inside to indicate the median value. The lower and upper quartiles are shown as horizontal lines either side of the rectangle.

Step-by-step explanation:

Example 1: Draw a box-and-whisker plot for the data set {3, 7, 8, 5, 12, 14, 21, 13, 18}.

From our Example 1 on the previous page, we had the five-number summary:

Minimum: 3, Q1 : 6, Median: 12, Q3 : 16, and Maximum: 21.

Notice that in any box-and-whisker plot, the left-side whisker represents where we find approximately the lowest 25% of the data and the right-side whisker represents where we find approximately the highest 25% of the data. The box part represents the interquartile range and represents approximately the middle 50% of all the data. The data is divided into four regions, which each represent approximately 25% of the data. This gives us a nice visual representation of how the data is spread out across the range.

Step-by-step explanation:

In descriptive statistics, a box plot or boxplot (also known as box and whisker plot) is a type of chart often used in explanatory data analysis. Box plots visually show the distribution of numerical data and skewness through displaying the data quartiles (or percentiles) and averages.

Answer:

[tex]x=1,\\y=9[/tex]

Step-by-step explanation:

When solving a system of equations, one of the faster methods to solve this system is the process of elimination. This process involves manipulating one of the equations (by multiplying it by a certain value), such that when one adds the two equations in the system, one of the variables cancels. One can then solve for the other variable in the system. Then backsolve for the other variable; by substituting the value of the found variable into the system, simplifying and using inverse operations to solve for the other variable.

[tex]-6x=48-6y\\\\-4x=50-6y[/tex]

Manipulate, multiply one of the equations by a certain value such that the coefficient of the like term in the other equation is the additive inverse of it.

[tex](-6x=48-6y)*(-1)\\\\-4x=50-6y[/tex]

Simplify,

[tex]6x=-48+6y\\\\-4x=50-6y[/tex]

Add the equations in the system,

[tex]6x=-48+6y\\\\-4x=50-6y[/tex]

[tex](6x)+(-4x)=(-48)+(50)+(6y)+(-6y)[/tex]

Simplify,

[tex](6x)+(-4x)=(-48)+(50)+(6y)+(-6y)[/tex]

[tex]2x=2[/tex]

Inverse operations,

[tex]2x=2[/tex]

[tex]x=1[/tex]

Backsolve to find the value of (y).

[tex]-4x=50-6y[/tex]

[tex]x=1[/tex]

Substitute,

[tex]-4(1)=50-6y[/tex]

Simplify,

[tex]-4=50-6y[/tex]

Inverse operations,

[tex]-4=50-6y[/tex]

[tex]-54=-6y[/tex]

[tex]9=y[/tex]

Answer:

508.8 seconds

Step-by-step explanation:

The most accurate determination mathematically is to assume that Lola will maintain an average of 5.3 seconds per signature as she signs all 96 invitations.

Therefore, multiply the time it takes her to sign each invitation (5.3 seconds) by the total number of invitations there are (96 invitations) to get the projected total amount of time that it will take Lola to sign all 96 invitations:[tex]96\cdot 5.3=\boxed{508.8\text{ seconds}}[/tex]

Answer:

508.8 seconds (8.48 minutes)

Step-by-step explanation:

96 × 5.3 = 508.8

Answer:

Subtraction property ; x = 3.25

Division property ; - 6

multiplication property ; - 125

Addition property ; 13

Step-by-step explanation:

A.)

x + 3.75 = 7

Using the subtraction property : subtract 3.75 from both sides

x + 3.75 - 3.75 = 7 - 3.75

x = 3.25

B. )

–3b = 18

According to the division property :

Divide both sides by - 3

-3b / - 3 = 18 / - 3

b = - 6

C.)

m/5 = - 25

Using the multiplication property :

m/5 * 5 = - 25 * 5

m = - 125

D.)

m – 4 = 9

Using the addition property :

Add 4 to both sides :

m - 4 + 4 = 9 + 4

m = 13

Answer:

A. Subtraction property ; x = 3.25

B. Division property ; - 6

C. multiplication property ; - 125

D. Addition property ; 13

Step-by-step explanation:

(x-2)(x+2) is factorize is given eq

Answer:

y=sqrt(x+12)

i hope this helped and have a nice day/night :)

Answer:

final cost of 3 pounds:  8 dollars  

final cost of p pounds:   3.75p - 3.25  dollars  

Step-by-step explanation:

Each pound costs $3.75, so 3 pounds cost 3*3.75 = 11.25 dollars. Subtract off the $3.25 to get the final cost to be 11.25-3.25 = 8 dollars. This takes care of the first part.

For the second part, the expression for the final cost is 3.75p - 3.25; where the 3.75p is the cost before the coupon is applied. If you plugged p = 3 into that expression, you should get 8 as a result. The variable p is some positive whole number. It's a place holder for the number of pounds of apples.

Answer:

Graph B

Step-by-step explanation:

The vertical intercept I am getting is (0,-1) and B is the only one with that point. Therefore, it should be B.

Second option is correct

Given:

A line passes through the points (-1, -1) and (5,8).

To find:

Which points lie on the same line?

Solution:

If a line passes through two points, then the equation of the line is:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

A line passes through the points (-1, -1) and (5,8). So, the equation of the line is:

[tex]y-(-1)=\dfrac{8-(-1)}{5-(-1)}(x-(-1))[/tex]

[tex]y+1=\dfrac{8+1}{5+1}(x+1)[/tex]

[tex]y+1=\dfrac{9}{6}(x+1)[/tex]

[tex]y+1=\dfrac{3}{2}(x+1)[/tex]

Multiply both sides by 2.

[tex]2(y+1)=3(x+1)[/tex]

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

[tex]2y=3x+3-2[/tex]

[tex]y=\dfrac{3}{2}x+\dfrac{1}{2}[/tex]

So, the equation of the line is [tex]y=\dfrac{3}{2}x+\dfrac{1}{2}[/tex].

Now, check each point for this equation.

Putting [tex]x=-3[/tex], we get

[tex]y=\dfrac{3}{2}(-3)+\dfrac{1}{2}[/tex]

[tex]y=\dfrac{-9+1}{2}[/tex]

[tex]y=\dfrac{-8}{2}[/tex]

[tex]y=-4[/tex]

Similarly,

For [tex]x=9,y=15[/tex].

For [tex]x=1,y=2[/tex].

For [tex]x=4,y=6.5[/tex].

For [tex]x=3,y=5[/tex].

For [tex]x=-2,y=-2.5[/tex].

Therefore, the points (-3,-4), (9,14), (1,2) and (3,5) lie on the same line but the points (4,7) and (-2,-2) are not on that line.

Given:

The polynomial is:

[tex]p(x)=x^2-1[/tex]

To find:

Whether [tex]x=-2[/tex] is a zero of the given polynomial or not.

Solution:

If [tex]x=c[/tex] is a zero of a polynomial, then [tex]f(c)=0[/tex].

We have,

[tex]p(x)=x^2-1[/tex]

Putting [tex]x=-2[/tex] in the given polynomial.

[tex]p(-2)=(-2)^2-1[/tex]

[tex]p(-2)=4-1[/tex]

[tex]p(-2)=3[/tex]

Since [tex]p(-2)\neq 0[/tex], therefore [tex]x=-2[/tex] is not a zero of the given polynomial.

Answer:

The single equation is [tex]y = 0[/tex]

Step-by-step explanation:

We are given the following system of equations:

[tex]x + y = 0[/tex]

[tex]x + 2y = 0[/tex]

From the first equation:

[tex]x = -y[/tex]

Replacing in the second equation:

[tex]-y + 2y = 0[/tex]

[tex]y = 0[/tex]

The single equation is [tex]y = 0[/tex]

Answer:

18 seconds

Step-by-step explanation:

5x9=45 so 2x9=18