Given: ∆KLM, KL ≅ LM A∈ KM , B ∈ KM AK ≅ BM Prove:△AKL ≅ △BML ΔALB is isosceles

Answer:

5/1

Step-by-step explanation:it goes up 5 and over 1

Answer:

Solution,

Let the points be A and B

A ( 8 , 2 ) -----> (X1 , y1 )

B ( 9 , 7 ) -------> (x2 , y2)

Now,

Slope =[tex] \frac{y2 - y1}{x2 - x1} [/tex]

[tex] = \frac{7 - 2}{9 - 8} [/tex]

[tex] = \frac{ 5}{1} [/tex]

[tex] = 5[/tex]

Hope this helps..

Good luck on your assignment...

Answer

260 kilograms

Step-by-step explanation:

the correct answer is 260 kg

Answer: 12.6 kg

Step-by-step explanation: add the amounts of food for her farm, and just search for how many kg are in 1,260 grams

Answer:

The answer is

Step-by-step explanation:

(x+3)(2x-4)(x-6)

Expand

We have

(x + 3) ( 2x² - 12x - 4x + 24)

(x + 3)( 2x² - 16x + 24)

2x³ - 16x² + 24x + 6x² - 48x + 72

Simplify

Group like terms

2x³ - 16x² + 6x² + 24x - 48x + 72

We have the final answer as

Hope this helps you

Answer:

the total amount is £ 756.

hope it helps..

Answer:

[tex]4 \frac{1}{10}[/tex]

Step-by-step explanation:

=> [tex]\frac{1305}{31828} * 100[/tex]

=> 0.041 * 100

=> 4.1

=> [tex]4 \frac{1}{10}[/tex]

Answer:

B. rotation 90° counterclockwise about the origin.

Step-by-step explanation:

Transformation is the process by which the size or orientation of a given figure is altered without any effect on its shape. Examples are; rotation, reflection, translation and dilation.

Rotation is the process of turning a figure about a reference point called the origin. While reflection is turning a figure about a line to produce its image.

In the given question, ∆ABC is  mapped onto ∆A'B'C' by rotating it at 90° counterclockwise about the origin.

The correct option is (B). rotation 90°counterclockwise about the origin.

Given, ∆ABC and ∆A'B'C' are shown in attached figure.

We have to map ∆ABC onto ∆A'B'C',.

A transformation is a general term for four specific ways to manipulate the shape and or position of a point, a line, or geometric figure.

Transformation is  also the process by which the size or orientation of a given figure is altered without any effect on its shape.

A rotation is a transformation in which the object is rotated about a fixed point.The direction of rotation can be clockwise or anticlockwise.

It is clear from the fig that the ∆ABC can be mapped over ∆A'B'C' by the rotation of  90°counterclockwise about the origin.

Hence the correct option is (B). rotation 90°counterclockwise about the origin.

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Answer:

Step-by-step explanation:

Here is another example :

Answer:

The probability is 0.2423.

Step-by-step explanation:

Given mean per capita = 19292 dollars

Given the variance = 540225

Now find the probability that the sample mean will be less than 19269 dollar when the sample is 499.

Below is the calculation:

[tex]\bar{X} \sim N(\mu =19292, \ \sigma = \frac{\sqrt{540225}}{\sqrt{499}}) \\\bar{X} \sim N(\mu =19292, \ \sigma = 32.90) \\\text{therefore the probability is:} \\P (\bar{X}< 19269) \\\text{Convert it to standard normal variable.} \\P(Z< \frac{19269-19292}{32.90}) \\P(Z< - 0.6990) \\\text{Now getting the probability from standard normal table}\\P(Z< -0.6990) = 0.2423[/tex]

Answer:

52 inches

Step-by-step explanation:

Answer:

we have, 1 feet =12 inches

13/3 foot =12×13/3 inches

=52 inches.

thereforethe , the answer is 52 inches.

Answer:

£380

Step-by-step explanation:

Consider the initial win of £4750

Sum the parts of the ratio, 1 + 4 = 5 parts

Divide the win by 5 to find the value of one part of the ratio.

£4750 ÷ 5 = £950 ← value of 1 part of the ratio

Thus Jim's share is £950

Sum the parts of the ratio shared in his family, 2 + 6 + 2 = 10 parts

Divide his share by 10 to find the value of one part

£950 ÷ 10 = £95 , thus

2 parts = 2 × £95 = £190 ← sons share

6 parts = 6 × £95 = £570 ← wife's share

£570 - £190 = £380

Wife gets £380 more than the son

Answer:

Step-by-step explanation:

Givens

Petri Dish A sees a double ever 10 minutes

Petri Dish B sees a double ever 6 minutes

Consequences

A doubles 60 / 10 = 6 times.

B doubles 60 / 6 = 10 times.SolutionIf you work best with numbers then suppose there are 100 bacteria in both dishes at the beginningA = 100 * 2^6B = 100 * 2^10A will have 100 * 64 = 6400 bacteria growing inside AB will have 100 * 1024 = 102400 bacteria growing inside BB/A = 102400 / 6400 = 16There are 16 times as many in B than in A

Answer:

16.66cm²

Step-by-step Explanation:

Given:

∆LMN with m<N = 38°

Length of side NL = 7.2cm

Length of side ML = 4.8cm

Required:

Area of ∆MNL

Solution:

Step 1: Find Angle LMN using the sine rule sin(A)/a = sin(B)/b

Where sin(A) = Sin(M) = ?

a = NL = 7.2cm

sin(B) = sin(N) = 38°

b = ML = 4.8cm

Thus,

Sin(M)/7.2 = sin(38)/4.8

Cross multiply

4.8*sin(M) = 7.2*sin(38)

4.8*sin(M) = 7.2*0.6157

4.8*sin(M) = 4.43304

Divide both sides by 4.8

sin(M) = 4.43304/4.8

sin(M) = 0.92355

M = sin-¹(0.92355) ≈ 67.45°

Step 2: Find m<L

angle M + angle N + angle L = 180 (sum of angles in a triangle)

67.45 + 38 + angle L = 180

105.45 + angle L = 180

Subtract 105.45 from both sides

Angle L = 180 - 105.45

Angle L = 74.55°

Step 3: Find the area of ∆MNL using the formula ½*a*b*sin(C)

Where,

a = NL = 7.2 cm

b = ML = 4.8 cm

sin(C) = sin(L) = sin(74.55)

Thus,

Area of ∆MNL = ½*7.2*4.8*0.9639

= ½*33.31

= 16.655

Area of ∆MNL ≈ 16.66cm²

Answer:

So for the first few small values of n, we have proven by demonstration that f(n) = n / (n+1).

Our task is to prove that if it works for any positive integer value of n, then it works for n + 1. This way, it must by induction work for all subsequent values of n.

Formally said, we need to prove that if for some positive integer n we can show that f(n) = n / (n+1), then we can conclude that f(n+1) = (n + 1) / (n + 2).

We begin the real "proof" by expanding f(n + 1):

f(n + 1) = f(n) + 1 / ((n+1)((n+1)+1)) because that's based on the construction.

= n / (n+1) + 1 / ((n+1)(n+2)) because f(n) = n / (n+1); this is called "using what you know from earlier".

= n(n+2) / ((n+1)(n+2)) + 1 / ((n+1)(n+2)) because we can multiply the left fraction by (n+2)/(n+2).

= (n2 + 2n + 1) / ((n+1)(n+2)) because we have a common denominator and can combine the numerators.

= (n+1)2 / ( (n+1)(n+2)) because we can factor the numerator now; it is a perfect square.

= (n+1) / (n+2) because we can cancel the common (n+1) factor from the numerator and denominator.

Q.E.D. (which means "that which was to be proven", in other words: "voilà")

Step-by-step explanation:

Answer:

-3 + 12x

Step-by-step explanation:

3 - 2(-6x + 3)

3 + 12x - 6

-3 + 12 x

Hope this helped! :)

Answer:

let me know when you have the anwser

Step-by-step explanation:

Answer:

~1.8 mile

Step-by-step explanation:

Michael lives at the closest  point to the school (the origin) on Maple Street,  which can be represented by the line  y = 2x – 4.

This means Michael's house will be the intersection point of line y1 (y = 2x - 4) and line y2 that is perpendicular to y1 and passes the origin.

Denote equation of y2 is y = ax + b,

with a is equal to negative reciprocal of 2 => a = -1/2

y2 pass the origin (0, 0) => b = 0

=> Equation of y2:

y = (-1/2)x

To find location of Michael's house, we get y1 = y2 or:

     2x - 4 = (-1/2)x

<=> 4x - 8 = -x

<=> 5x = 8

<=> x = 8/5

=> y = (-1/2)x = (-1/2)(8/5) = -4/5

=> Location of Michael' house: (x, y) = (8/5, -4/5)

Distance from Michael's house to school is:

D = sqrt(x^2 + y^2) = sqrt[(8/5)^2 + (-4/5)^2) =  ~1.8 (mile)

Answer:

[tex]m=-\frac{13}{20.8}=-0.625[/tex]

Nowe we can find the means for x and y like this:

[tex]\bar x= \frac{\sum x_i}{n}=\frac{16}{5}=3.2[/tex]

[tex]\bar y= \frac{\sum y_i}{n}=\frac{35}{5}=7[/tex]

And we can find the intercept using this:

[tex]b=\bar y -m \bar x=7-(-0.625*3.2)=9[/tex]

So the line would be given by:

[tex]y=-0.625 x +9[/tex]

Step-by-step explanation:

We have the following data:

X: 3,3,2,1,7

Y:6,7,8,9,5

We want to find an equationinf the following form:

[tex] y= bX +a[/tex]

[tex]a=m=\frac{S_{xy}}{S_{xx}}[/tex]

Where:

[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}[/tex]

[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}[/tex]

So we can find the sums like this:

[tex]\sum_{i=1}^n x_i = 3+3+2+1+7=16[/tex]

[tex]\sum_{i=1}^n y_i =6+7+8+9+5=35[/tex]

[tex]\sum_{i=1}^n x^2_i =72[/tex]

[tex]\sum_{i=1}^n y^2_i =255[/tex]

[tex]\sum_{i=1}^n x_i y_i =99[/tex]

With these we can find the sums:

[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=72-\frac{16^2}{5}=20.8[/tex]

[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=99-\frac{16*35}{5}=-13[/tex]

And the slope would be:

[tex]m=-\frac{13}{20.8}=-0.625[/tex]

Nowe we can find the means for x and y like this:

[tex]\bar x= \frac{\sum x_i}{n}=\frac{16}{5}=3.2[/tex]

[tex]\bar y= \frac{\sum y_i}{n}=\frac{35}{5}=7[/tex]

And we can find the intercept using this:

[tex]b=\bar y -m \bar x=7-(-0.625*3.2)=9[/tex]

So the line would be given by:

[tex]y=-0.625 x +9[/tex]

Based on Evelyn's response, it can be said that she predicts that there is a 50% chance of the coin landing on tails and a 50% chance of the coin landing on heads.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that the coin lands on tails is half of the number of times the coin is tossed. This means she belives that there is an equal chance that the coin would land on either heads or tails.

To learn more about probability, please check: https://brainly.com/question/13234031

Answer:

150 cal

Step-by-step explanation:

5x30=150

Answer:

150 calories.

Step-by-step explanation:

Assuming there is the same amount of chocolate as well as cookie dough throughout the whole cookie.

You know that 1/5 of a chocolate chip cookie has 30 calories.

Find one cookie, by multiply 5 to both numbers. Set the equation:

1/5x = 30

Isolate the variable. Multiply 5 to both sides:

(1/5x) * 5 = (30) * 5

x = 30 * 5

x = 150

150 calories is your answer.

Answer:

x^2+y^2=25

Step-by-step explanation:

x^2+y^2=25 graphs a circle. A relation is a function if every x only has one y value. This is not true in a circle.

Answer:

d) x^2 + y^2 = 25.

Step-by-step explanation:

D is the equation of a circle so it fails the vertical line test for a function. If a relation is a function then any vertical line passing through it's graph will only intersect it once. This is not true of a circle.

Answer:

Coin A : [tex]V(t)=25(1.07)^t[/tex]

Coin B : [tex]V(t)=40(1.05)^t[/tex]

Step-by-step explanation:

Consider the given formula is  

[tex]V(t)=P(1+r)^t[/tex]

where, P is current value, V(t) is the value of the coin in t years, and r is annual appreciation rate.

For coin A, current value is 25 dollars and annual appreciation rate is 7%.

[tex]V(t)=25(1+0.07)^t[/tex]

[tex]V(t)=25(1.07)^t[/tex]

For coin B, current value is 40 dollars and annual appreciation rate is 5%.

[tex]V(t)=40(1+0.05)^t[/tex]

[tex]V(t)=40(1.05)^t[/tex]

Therefore, the required equations for coin A and B are [tex]V(t)=25(1.07)^t[/tex] and [tex]V(t)=40(1.05)^t[/tex] respectively.

Answer:  [tex]a)\ \text{Vertex}:y=-\dfrac{3}{2}(x+1)^2+6[/tex]

                [tex]b)\ \text{Standard}:y=-\dfrac{3}{2}x^2-3x=\dfrac{9}{2}[/tex]

              c) Transformations: reflection over the x-axis,

                                               vertical stretch by a factor of 3/2,

                                               horizontal shift 1 unit to the left,

                                               vertical shift 6 units up

Step-by-step explanation:

Intercept form: y = a(x - p)(x - q)

Vertex form: y = a(x - h)² + k

Standard form: y = ax² + bx + c

We can see that the new vertex is (-1, 6). Use the Intercept form to find the vertical stretch: y = a(x - p)(x - q) where p, q are the intercepts.

p = -3, q = 1, (x, y) = (-1, 6)

a(-1 + 3)(-1 -1) = 6

       a (2)(-2) = 6

                a  = -6/4

                 a = -3/2

a) Input a = -3/2 and vertex (h, k) = (-1, 6) into the Vertex form to get:

[tex]y=-\dfrac{3}{2}(x+1)^2+6[/tex]

b) Input a = -3/2 into the Intercept form and expand to get the Standard form:

[tex]y=-\dfrac{3}{2}(x+3)(x-1)\\\\\\y=-\dfrac{3}{2}(x^2+2x-3)\\\\\\y=-\dfrac{3}{2}x^2-3x+\dfrac{9}{2}[/tex]

c) Use the Vertex form to identify the transformations:

[tex]y=-\dfrac{3}{2}(x+1)^2+6[/tex]

Answer:

1.8 and 14.3

Step-by-step explanation:

Our equation is a quadratic equation so we will use the dicriminant method

Answer:

The pyramid's height h = 12 ft

Step-by-step explanation:

Notice that the slant height of the pyramid forms a right angle triangle with the segment that joins the bottom end of the slant height with the center of the pyramid's base, and with the pyramid height (h).

The segment joining the slant height with the center of the pyramid's base is one half of the side of the base in length, so that it; 16 feet.

then we have a right angle triangle with hypotenuse given by the pyramid's slant height (20 ft), a leg given by 16 ft, and we need to find the length of the second leg (pyramid's height (h).so we use the Pythagorean theorem:

[tex]hyp^2=leg_1^2+leg_2^2\\(20\,ft)^2= (16\,ft)^2+h^2\\h^2=400\,ft^2-256\,ft^2\\h^2=144\,ft^2\\h=12 \,ft[/tex]

Answer:

C.12ft

Step-by-step explanation:

for people on edmentum

Answer:

Step-by-step explanation:

The answer is B, the solution to your equation is at (2,1). Your solution is where the two lines meet.

Answer:

The second option.

Step-by-step explanation:

When two lines intersect, they usually intersect at just one point (unless they are parallel, where they never intersect; or no solutions when they infinitely intersect).

According to the graph provided, the lines are intersecting at one point: (2, 1).

So, your answer will be the second option!

Hope this helps!

Answer:

The unit prices will be within the range of $0.77 ≤x≤$0.78

Step-by-step explanation:

If a package 8-count AA batteries cost $6.16 and a package of same 20-count AA batteries cost $15.60, to calculate the unit price, the following steps must be carried out:

8 counts AA batteries = $6.16

A unit price (i.e 1 count) = x

Cross multiplying

8 × x = 6.16 × 1

x = 6.16/8

x = $0.77 for a unit price

Similarly, if 20-count AA batteries cost $15.60, then:

20 counta = $15.60

1 count = x

Cross multiplying

20 × x = $15.60 × 1

x = $15.60/20

x = $0.78 for a unit price

From above calculation, of can be seen that the unit price is almost similar but with a difference of $0.01 ($0.78-$0.77) which is insignificant. Based on this, we can conclude that a unit price of the battery is between the range

$0.77 ≤x≤$0.78

Answer:

The 8-count pack of AA batteries has a lower unit price of 0.77

per battery.

Step-by-step explanation:

Answer:

B: (3x + 81)(x - 1)

Step-by-step explanation:

Answer:

y= -3x+2

Step-by-step explanation:

Parallel lines have the same slope. We can form an incomplete equation:

y= -3x+b

(make sure to see why the slope is -3)

We can plug in the coordinates of (2, -4):

-4= -3(2)+b

-4= -6+b

2=b

b is 2! We can form an equation: y= -3x+2