Lin created a scaled copy of Triangle A with an area of 72 square units. How many times larger is the area of the scaled copy compared to that of Triangle A

Answer:

[tex]tan(A) = \frac{2\sqrt{15}}{11}[/tex]

Step-by-step explanation:

Given:

Right ∆ABC

AB = 61

BC = 60

AC = 11

Required:

Value of tan A in radical form

SOLUTION:

[tex] tan(A) = \frac{opposite}{adjacent} [/tex]

Opposite = 60

Adjacent = 11

[tex] tan(A) = \frac{60}{11} [/tex]

[tex] tan(A) = \frac{\sqrt{4*15}}{11} [/tex]

[tex]tan(A) = \frac{2\sqrt{15}}{11}[/tex]

Answer:

y= ½ x + 5

Step-by-step explanation:

[tex] (-4,3) \: (6,8). \\ x_1 = - 4 \\ y_1 = 3 \\ x_2 = 6[/tex]

[tex]y_2 = 8 \\ \frac{y - y_1}{x - x_1} = \frac{y_2 -y_1}{x_2 - x_1} [/tex]

[tex] \frac{y - 3}{x - ( - 4)} = \frac{8 - 3}{6 - ( - 4)} = \frac{y - 3}{x + 4} = \frac{5}{10} [/tex]

[tex]10(y - 3) = 5(x + 4) \\ 10y - 30 = 5x + 20 \: \\ 10y = 5x + 20 + 30 = 10y = 5x + 50 \\ [/tex]

[tex] \frac{10y}{10} = \frac{5}{10} x + \frac{50}{10} \\ y = \frac{1}{2} x + 5[/tex]

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the line can be written as y = (1/2)x+5.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is the y-intercept.

To write the equation of the line, we need to firstly find the slope of the equation. Therefore, the slope of the equation can be written as,

Slope = (8 -3)/[6 - (-4)] = 5/10 = 1/2

Now, substitute the value of the slope and the any point in the general equation of a line. Therefore, we can write,

y = mx + c

8 = (1/2)(6) + C

8 = 3 + C

C = 5

Hence, the equation of the line can be written as y = (1/2)x+5.

Learn more about Equation of Line:

https://brainly.com/question/21511618

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Answer:

Amna is the fastest typist.

Step-by-step explanation:

Amna = 710 words/15 minutes = 47.3 words per minute

Sara = 810 words/18 minutes = 45 words per minute

Uzma = 780 words/20 minutes = 39 words per minute

Answer:

12.5 kilograms

Step-by-step explanation:

Given:

Half of the granola served with breakfast.

Let the amount of Granola present initially = [tex]x[/tex] kg

Half of it ([tex]\frac{x}{2}[/tex]) served with breakfast, so remaining granola :

[tex]x-\dfrac{x}{2} = \dfrac{x}{2}[/tex]

After dinner, the remaining granola 6,250 gm granola was served with yogurt dessert.

First of all, let us convert it to kilogram because the answer is required in Kilograms.

We know that:

1000 gms = 1 kilograms

1 gms = 0.001 kilograms

6250 gms  = 6250 [tex]\times[/tex] 0.001 = 6.250 kilograms

Now, as per given question statement:

[tex]\dfrac{x}{2} = 6.250\ kg\\\Rightarrow x = 2 \times 6.250\\\Rightarrow \bold{x = 12.5\ kg}[/tex]

So, the answer is:

Girl scout camp started with 12.5 Kilograms of granola.

Answer:

16m²

25m²

9m²

Step-by-step explanation:

4 × 4 = 16m²

5 × 5 = 15m²

3 × 3 = 9m²

Answer:

a.three

b.the line containing them lies in the plane.

c.one point

Answer:

-1/8

Step-by-step explanation:

Convert 1/4 into 2/8.

Then, minus -3/8 and 2/8

Answer:

-3/8 + 1/4 = 1/8

Step-by-step explanation:

-3/8 + 1/4

1/4 = 2/8

then:

2/8 - 3/8 = -1/8

Answer:

[tex]y=-\frac{2}{3}x+12[/tex]

Step-by-step explanation:

Step 1: Rule out answers

The answer cannot be B or D because the y-intercept is at 12(b = 12) and in a linear equation y=mx+b, b is the y intercept.

B has the y intercept at 18

D has the y intercept at 18

Step 2: Find the slope

The slop is the change in y over the change in x.  We can also write this as [tex]\frac{rise}{run}[/tex]

We see it lowers by 2 so we will put -2 as the numerator

We also the x value increase by 3 every time it gets lowered by 2 so the run is 3

Therefore the slope is [tex]-\frac{2}{3}[/tex]

Step 3: Plug in the the variables to get the linear equation

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

[tex]y=-\frac{2}{3}x+12[/tex]

Therefore the answer is A. [tex]y=-\frac{2}{3}x+12[/tex]

Answer:

[tex]\Large \boxed{{y=-\frac{2}{3}x +12}}[/tex]

Step-by-step explanation:

y = mx + b (slope-intercept form of a line)

m is slope

b is y-intercept

The y-intercept of the line is (0, 12) or 12.

y = mx + 12

The slope of the line can be found through rise over run.

(0, 12) and (18, 0) are two points on the line.

m = (y2-y1)/(x2-x1)

m = (0-12)/(18-0)

m = -12/18

m = -2/3

The slope of the line is -2/3.

y = -2/3x + 12

Answer:

Step-by-step explanation:

[tex] \sf{Given}[/tex]

[tex] \sf{hypotenuse = 5}[/tex]

[tex] \sf{base = 2.1}[/tex]

[tex] \sf{perpendicular = x}[/tex]

Now, Let's find the value of x

Using Pythagoras theorem

[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]

Plug the values

⇒[tex] \sf{ {5}^{2} = {x}^{2} + {2.1}^{2} }[/tex]

Evaluate the power

⇒[tex] \sf{25 = {x}^{2} + 4.41}[/tex]

Swap the sides of the equation

⇒[tex] \sf{ {x}^{2} + 4.41 = 25}[/tex]

Move constant to R.H.S and change it's sign

⇒[tex] \sf{ {x}^{2} = 25 - 4.41}[/tex]

Calculate the difference

⇒[tex] \sf{ {x}^{2} = 20.59}[/tex]

Squaring on both sides

⇒[tex] \sf{x = 4.54}[/tex]

Hope I helped!

Best regards!!

Answer:

[tex]P(T_1\ n\ T_2) = \frac{2}{21}[/tex]

Step-by-step explanation:

From the comments in your question; we have

Stars = 4

Triangles = 5

Circles = 3

Squares = 3

Required  

Determine the probability of both shapes being triangles

First, calculate the total

[tex]Total = 4 + 5 + 3 + 3[/tex]

[tex]Total = 15[/tex]

Next, calculate the probability of the first selected shape being a triangle;

P(T₁) = Number of triangles divided by total number of shapes

[tex]P(T_1) = \frac{5}{15}[/tex]

[tex]P(T_1) = \frac{1}{3}[/tex]

Next, calculate the probability of the second selected shape being a triangle;

P(T₂) = Number of triangles divided by total number of shapes

Because it's probability without replacement. the number of triangle left is 4 and the number of shapes left is 14;

So:

[tex]P(T_2) = \frac{4}{14}[/tex]

[tex]P(T_2) = \frac{2}{7}[/tex]

Hence:

[tex]P(T_1\ n\ T_2) = P(T_1) * P(T_2)[/tex]

[tex]P(T_1\ n\ T_2) = \frac{1}{3} * \frac{2}{7}[/tex]

[tex]P(T_1\ n\ T_2) = \frac{2}{21}[/tex]

Hence, the required probability is [tex]\frac{2}{21}[/tex]

Answer:

2/21

Step-by-step explanation:

There are 4 stars, 5 triangles, 3 circles, and 3 squares

For the first drawing there are 5 triangles and a total of 15 shapes.

p(first triangle) = 5/15 = 1/3

Since there is no replacement, for the second drawing, and one triangle has been taken, now there are 4 triangles left and 14 total shapes left.

p(second triangle) = 4/14 = 2/7

p(two triangles) = p(first triangle) * p(second triangle)

p(two triangles) = 1/3 * 2/7

p(two triangles) = 2/21

Answer:

the 3'd power

Step-by-step explanation:

4x4=16 16x4=64

Answer:

[tex]\Huge \boxed{\mathrm{3}}[/tex]

Step-by-step explanation:

Let the power be x.

[tex]\mathrm{4^x=64}[/tex]

Take log of both sides.

[tex]\mathrm{log(4^x)=log(64)}[/tex]

[tex]\mathrm{x \cdot log(4)=log(64)}[/tex]

Divide both sides by log(4).

[tex]\displaystyle \mathrm{x=\frac{log(64)}{log(4)} }[/tex]

[tex]\mathrm{x=3}[/tex]

Answer:

[tex]2xy-5xz+x[/tex]

Step-by-step explanation:

I'm going to assume you wanted to multiply these terms.

To do this, we distribute [tex]x[/tex] into each term in the parentheses.

[tex]2y \cdot x = 2xy\\\\-5x \cdot x = -5xz\\\\1 \cdot x = x[/tex]

Combining these terms, we get [tex]2xy-5xz+x[/tex].

Hope this helped!

Answer:

B

Explanation:

Line segments do not extend or extract, they come together to form 1 line instead of going in one/two directions forever.

Answer:

1. 7.5 hours

2. TV

3. Computer

4. All electronic usage except for the heater would decrease because summer is usually when people go outside and don't really stay indoors. While in winter, most people stay inside their houses.

Answer:

$3 Each

Step-by-step explanation:

27 Spent Toatal.

Soft Drink for 3.

27-3 = 24

He bought eight candy bars, so divide 24 by 8.

24/8 = 3

So each was 3 dollars.

Answer:

6

Step-by-step explanation:

3 x 2

Answer:

5     3

6     4

4     2

Step-by-step explanation:

So in this case "number" will be "x"

Triple means multiply by 3 = 3x

1 less means minus 1.

3x-1

===========================================

Plug in x = 0

f(x) = 2x^2 + 5

f(0) = 2(0)^2 + 5

f(0) = 5

Plug in x = 2

f(x) = 2x^2 + 5

f(2) = 2(2)^2 + 5

f(2) = 13

Now use the formula below to find the average rate of change (AROC) from x = a to x = b

AROC = ( f(b) - f(a) )/( b-a )

AROC = ( f(2) - f(0) )/( 2-0 )

AROC = ( 13 - 5 )/( 2 - 0)

AROC = 8/2

AROC = 4

-----------------

This is the same as finding the slope of the line through (0,5) and (2,13)

m = (y2 - y1)/(x2 - x1)

m = (13-5)/(2-0)

m = 8/2

m = 4

Answer:

Student Ticket: $8

Adult $28

Step-by-step explanation:

To find out the price of each ticket create 2 equations, then solve for x & y

x = student tickets

y = adult tickets

25x + 28y = 984

25x + 25y = 900

To do this first put x on one side of the equation

25x = 900 - 25y

x = 36 - y

Now substitute this equation in x for the first equation

25(36 - y) + 28y = 984

Now distribute 25 in 36 - y, 900 - 25y + 28y = 984

After this combine like term, then subtract 900 from each side, 3y = 84

Then divide 3 on each side, y = 28

Lastly substitute 28 for y in any equation to solve for x, x = 8

x & y are the price of each ticket

Answer:

Yes, the bridge will hold 1 ton.

Step-by-step explanation:

The ratio of the scale of the model to the real bridge = 1:4

The test model shows the model can take 8000 ounces

The real bridge will therefore take 8000 x 4 = 32000 ounces

but,

16 ounces = 1 pound

32000 ounces = [tex]x[/tex] pounds

==> [tex]x[/tex] = 32000/16 = 2000 pounds

also,

2000 pounds = 1 ton,

therefore, the bridge will hold 1 ton

Answer:

it would be able to hold 1 ton

Step-by-step explanation:

Mike: From the school to the mall, we could count out 16 units. From the mall to the library, we could count out 29 units. When we add 16 and 29, we get the distance Mike traveled: 45 units.

Henry: He traveled from the school to the library. To find out how long this distance is, we look at our previous numbers. From the school to the mall: 16. From the mall to the library: 29

To solve, we need to know the Pythagorean Theorem. We use the formula a^2 + b^2 = c^2. Here, 16 is a and 29 is b. We need to square both numbers and add them together to get c^2.

[tex]16^2=256\\29^2=841\\256+841=1097\\1097=c^2[/tex]

Then, we have to square 1097 to find c.

√1097 ≈ 33

Total: We subtract Henry's distance from Mike's to get our final answer.

45 - 33 = 12

Mike traveled 12 more units than Henry.

Answer:

(-4+8) ÷ 2 = 2

uuujhhhhh

Greetings from Brasil...

Rewriting the problem sets

A = {-7, 4, 2, 14, 21, 34, 42}

B = {...; 2; 4; 6; 8; 10; 12; 14; 16; 18; 20; 22; 24; 26; 28; 30; 32; 34; 36; 38; 40; 42;...}

C = {...; -14; -7; 0; 7; 14; 21; 28; 35; 42; 49; 56; 63; 70; 77;...}

So, according to the statement, it is desired:

A ∩ B ∩ C - the intersection between the 3 sets, that is, which numbers are present simultaneously in the 3 sets....

Looking at the sets we conclude that

Answer:

Answer C: Reflecting over the line y = x

Step-by-step explanation:

A function and its inverse have always symmetry around the line y = x (called also the identity line)

Therefore answer C seems to be the only answer that addresses such.

Answer: Light blue

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]2\$ on \:each \:game\\10\$ on food\\Let \:x \:be the \:no \:of \:games \:he \:plays\\\\2x +10\\Must\: be \:less\: than\: or \:equal \:to\: 25\$\\\\= 2x+10\:\le 25[/tex]

Answer: Hi!

The value of the variable is 11.

The angles will be equal, as the lines intersect and make an X. To find the value of the angle, we would first subtract 2 from 35 and then divide by 3 to fill in the expression.

35 - 2 = 33

33 ÷ 3 = 11

The value of x is 11.

Hope this helps!

Step-by-step explanation:

It is given that,

A 2-liter bottle of juice costs $2.80.

It means that 1 liter bottle of juice costs $1.4.

A box containing six 12-liter bottles sells for $3.90.  

(6×12)l i.e. 72 liter bottles sells for $3.9

1 liter bottles sells for $0.05416

It is clear that "A box containing six 12-liter bottles sells for $3.90." have higher cost per liter. Its cost is $0.05416 per liter. Hence, the correct option is (D).

Answer:

D

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

h,n

m,n

n,o

j,k

k,l

k,i

Answer:

[tex] \frac{1}{76543^4} [/tex]

Step-by-step explanation:

We are given base that is raised to a negative power of 4, [tex] 76543^{-4} [/tex].

Another way to rewrite this is as indicated as follows: thus, [tex] a^{-x} = \frac{1}{a^x} [/tex], where, a is the base, and x is the exponent.

Therefore, an equivalent expression of [tex] 76543^{-4} [/tex] = [tex] \frac{1}{76543^4} [/tex]