(SAT Prep) In the figure, what is the length of BC?
A. 25
B. 15
C. 18
D. 22

Given:

Given that the triangle ABC has vertices A(-2,3), B(0,3) and C(-1,-1).

We need to determine the coordinates of the image after a reflection over the x - axis.

Let A'B'C' denote the coordinates of the triangle after a reflection over the x - axis.

Coordinates of the point A':

The general rule to reflect the coordinate across the x - axis is given by

[tex](x,y)\rightarrow (x,-y)[/tex]

Substituting the point A(-2,3), we get;

[tex](-2,3)\rightarrow (-2,-3)[/tex]

Thus, the coordinates of the point A' is (-2,-3)

Coordinates of the point B':

The general rule to reflect the coordinate across the x - axis is given by

[tex](x,y)\rightarrow (x,-y)[/tex]

Substituting the point B(0,3), we get;

[tex](0,3)\rightarrow (0,-3)[/tex]

Thus, the coordinates of the point B' is (0,-3)

Coordinates of the point C':

The general rule to reflect the coordinate across the x - axis is given by

[tex](x,y)\rightarrow (x,-y)[/tex]

Substituting the point C(-1,-1), we get;

[tex](-1,-1)\rightarrow (-1,1)[/tex]

Thus, the coordinates of the point C' is (-1,1)

Hence, the coordinates of the image after a reflection over the x - axis is A'(-2,-3), B(0,-3) and C(-1,1)

Answer:

A - (-2,-3)

B - (0,-3)

C - (-1,1)

Step-by-step explanation:

Given:

For cylinder A:

Radius = 3 unit

Height = 4 unit

For cylinder B:

Radius = 4 unit

Height = 3 unit

To find the ratio of the volume of cylinder A to the volume of cylinder B.

Formula

The volume of a cylinder is,

[tex]V = \pi r^{2} h[/tex]

where, r be the radius and

h be the volume of the cylinder.

Now,

For cylinder A

Putting, r = 3 and h = 4 we get,

Volume [tex]V_{A}[/tex] = [tex]\pi (3^{2} )(4)[/tex]

or, [tex]V_{A} = 36\pi[/tex]

For cylinder B

Putting, r = 4 and h = 3 we get

Volume [tex]V_{B}=\pi (4^{2} )(3)[/tex]

or, [tex]V_{B}= 48\pi[/tex]

Now,

The ratio [tex]\frac{V_{A} }{V_{B}} = \frac{36\pi}{48\pi}[/tex]

or, [tex]\frac{V_{A} }{V_{B}} = \frac{3}{4}[/tex]

Hence,

The ratio of the volume of Cylinder A to the volume of Cylinder B is [tex]\frac{3}{4}[/tex]. Option A

Answer:

4(6)+12=36

Step-by-step explanation:

The required, Tracy has a total of 36 ounces of juice in her refrigerator.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,

The expression for the total ounces of juice Tracy has in her refrigerator is:

4(6) + 12

The expression shown above shows the sum of the ounces of juice in the four cans that have 6 ounces each, plus the ounces of juice in the fifth can that has 12 ounces.

Evaluating this expression:

4(6) + 12 = 24 + 12 = 36

Therefore, Tracy has a total of 36 ounces of juice in her refrigerator.

Learn more about models here:
https://brainly.com/question/22591166
#SPJ3

Answer: 30%

Step-by-step explanation:

Subtract the original cost from the on sale price.

21.50 - 15.05 = 6.45

Divide the savings by the original cost.

6.45/21.50 = .3

Multiply by 100

.3 * 100 = 30

Answer:

30% percent

Step-by-step explanation:

21.50-15.05=6.45

21.50÷6.45=3.

3×100=30%

we times 100 because 1 equal 100%.So you need to do is just to multiply the number by 100 and add at the end symbol %

The range of the function y=|x-1|+7 is all real numbers greater than or equal to 7, as the absolute value ensures non-negative values to which 7 is added.

The range of the function y=|x-1|+7 can be determined by analyzing the nature of the absolute value function and the constant term. The absolute value function, |x-1|, ensures that the output is always non-negative for any value of x, since it represents the distance from 1 on the number line, which cannot be negative. Therefore, when we add 7 to this non-negative value, the smallest value y can take is when |x-1|=0, which is when x=1. So, at x=1, y will be 7 since we have 0+7. For any other value of x, |x-1| will be positive, and when adding 7, y will be greater than 7. Hence, the range of y is all values greater than or equal to 7.

Answer:

-1/2

Step-by-step explanation:

The first thing you do is cross cancel because when you cross cancel 4 and 16 it would be  -1/5 * 10/4 then you cross cancel 5 and 10 and then you faction would look like  -1/1 * 2/4 then you multiply those fractions together and get -2/4 but simplified would be -1/2.

Answer: Elizabeth and Manuel have a distance of 4 meters between them.

Step-by-step explanation: Please refer to the picture attached.

From the information given, Elizabeth is directly behind Hannah and directly left of Manuel. That means we have three points which are HEM, that is, we now have triangle HEM. The longest side (hypotenuse) which is the distance between Hannah and Manuel is given as 5 meters while the other side the distance between Hannah and Elizabeth is given as 3 meters.

We shall apply the pythagoras theorem in solving for the unknown side, EM.

The Pythagoras theorem states thus;

AC² = AB² + BC²

Where AC is the hypotenuse, and AB and BC are the other two sides.

Substituting for the known values, we now have;

5² = 3² + EM²

25 = 9 + EM²

Subtract 9 from both sides of the equation

16 = EM²

Add the square root sign to both sides of the equation

√16 = √EM²

4 = EM

Therefore the distance between Elizabeth and Manuel is 4 meters

Final answer:

To calculate the distance between Elizabeth and Manuel, the Pythagorean theorem is used. Given the 3-meter distance between Hannah and Elizabeth, and the 5-meter distance between Hannah and Manuel, the distance between Elizabeth and Manuel is calculated to be the square root of 34, which is approximately 5.83 meters.

Explanation:

The question pertains to finding the distance between Elizabeth and Manuel, given their respective positions on a stage in relation to Hannah.

To find the distance between Elizabeth and Manuel, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Here, the distances between Hannah and the other two dancers form two sides of a right-angled triangle with Elizabeth and Manuel's positions marking the ends of the hypotenuse.

Since Hannah is 3 meters from Elizabeth and 5 meters from Manuel, we can calculate the distance between Elizabeth and Manuel (hypotenuse) with the following equation:
c^2 = a^2 + b^2

Where c is the distance between Elizabeth and Manuel, a is the distance between Hannah and Elizabeth (3 meters), and b is the distance between Hannah and Manuel (5 meters).

So, c^2 = 3^2 + 5^2 which simplifies to c^2 = 9 + 25, and further to c^2 = 34. This implies that c = [tex]\sqrt{34}[/tex].

Therefore, the distance between Elizabeth and Manuel is the square root of 34, which is approximately 5.83 meters. We can round this to the nearest hundredth for a precise measurement.

The distance between Elizabeth and Manuel is approximately 5.83 meters.

Answer:

it would be A and C because they are the lowest

Step-by-step explanation:

The correct option is C

Percentage point : It is defined as a unit for the arithmetic difference of two percentages and greater the difference more will be the error range.

So, the most reliable error range is the one whose percentage point is minimum.

Now, among the provided options , 2 percentage points is minimum so it will be the most reliable error range.

Hence, Option C. 2 percentage points is correct

Read more about Error ranges here brainly.com/question/3958017

#SPJ7

Answer:

You get $5727.27

Step-by-step explanation:

At the start, you have 2000

After you are attacked, stampeded and have trouble finding water, you have lost 10% of your cattle

2000 * 10% is 200

2000 - 200 is 1800

Multiply 1800 cattle by $35 per cow

1800 * $35 = $63000

10 cowboys + 1 (you) is 11 people

Divide $63000 by 11

63000 / 11 = $5727.27

You get $5727.27

Answer:

y = 4[tex](9)^{x}[/tex]

Step-by-step explanation:

Using the given points to find a and b

Using (0, 4), then

4 = a[tex]b^{0}[/tex] ⇒ a = 4, thus

y = 4[tex]b^{x}[/tex]

Using (3, 2916), then

2916 = 4 b³ ( divide both sides by 4 )

729 = b³ ( take the cube root of both sides )

b = [tex]\sqrt[3]{729}[/tex] = 9

Thus

y = 4 [tex]9^{x}[/tex] ← is the exponential function

Answer:

6 hours

Step-by-step explanation:

2 option for letter

10 for each digit

2×10×10×10

2000 trials

2000×10

20,000 seconds

20000/3600

5.5555555556 hours

The total number of combinations is 2000. Testing each one at a rate of 10 seconds per test would take approximately 20,000 seconds, which is around 6 hours when rounded to the nearest hour.

This problem deals with the concept of combinations in mathematics. To find out how long it would take to try all possible combinations, you first need to determine how many combinations there are. The door code consists of either A or B (2 options) followed by a three-digit code (10 options for each digit, from 0-9). Therefore, there are 2 * 10 * 10 * 10 = 2000 possible combinations. If each combination takes 10 seconds to try, it would take 2000 * 10 = 20,000 seconds. To convert this to hours, divide by 3600 (as there are 3600 seconds in one hour), rounding to the nearest whole number, would give approximately 6 hours.

https://brainly.com/question/39347572

#SPJ12

Answer:

56 [tex]in^{3}[/tex]

Step-by-step explanation:

Volume of bigger rectangular prism is 4*3*4 (48[tex]in^{3}[/tex]).

Volume of smaller rectangular prism is 1*2*4 (8[tex]in^{3}[/tex]).

48 + 8 = 56[tex]in^{3}[/tex].

Answer:

It falls between √7 and √8

Step-by-step explanation:

Please kindly check the attached file for explanation.

Answer:

residual = - 4

Step-by-step explanation:

The residual is the difference between the actual mass of the falcon chick and the mass our regression line would have predicted.

residual = actual mass - predicted mass

actual mass = 29 grams

The predicted mass of 40 mm breadth of egg can be calculated by using the regression equation Danila came up with.

predicted mass

y = -47 + 2(40)

y = -47 + 80

y = 33 grams

residual = actual mass - predicted mass

residual =  29 - 33

residual = - 4

Answer:

-4

Step-by-step explanation:

trust me.

Answer:

72 feet

Step-by-step explanation:

This is an example of a regular hexagon. A hexagon is  a polygon that has 6 sides. It is regular because all the sides are equal.

Perimeter of a Regular Hexagon=6l

Length of one side, l=12 feet

Therefore:

Perimeter of the deck = 6 X 12 =72 feet

Answer:

7 units

Step-by-step explanation:

use the distnce formula to get the riangles legs, multiply them and divide by two

Answer: 25%

Step-by-step explanation:

Bc I’m smort boi

A randomly chosen quadrilateral has four right angles, has a probability that the quadrilateral also has four equal side lengths is 33%.

Probability is a measure of the likelihood of an event to occur.

Many events cannot be predicted with total certainty.

We can predict only the chance of an event to occur i.e. how likely they are to happen, using it.

Given is a Venn diagram,

In the Venn diagram, we can see that we have 9 elements, 6 of these belong to the set R, 3 of them belong to the set E, and 2 belong to both sets.

Now we want to find the probability that, if a figure has four right angles (belongs to R) it also has 4 equal side lengths (belongs to E).

So, given that an element belongs to R (6 elements there).

The probability that it also belongs to E,

2 out of these 6 elements belong to E, so the probability will be:

P = 2/6 = 1/3 = 0.33

To get this in percent form, we need to multiply it by 100%, we will get:

0.33x100% = 33%

Learn more about probability,

brainly.com/question/251701

#SPJ7

Answer:

C.

Step-by-step explanation:

[tex]116.5^{3}[/tex]

The approximate total volume of the silo is 116.9 m^3, the correct option is C. 116.5 m^3.

Suppose that the radius of considered right circular cylinder be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

[tex]V = \pi r^2 h \: \rm unit^3[/tex]

Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.

We are given that;

Diameter=4.4m

Height=6.2meter

Now,

The radius of the silo is half of its diameter, which is 4.4/2 = 2.2 meters. So, plugging in the given values and using 3.14 for π, we get:

V = πr^2h + (2/3)πr^3

V = 3.14(2.2^2)(6.2) + (2/3)3.14(2.2^3)

V = 94.25 + 22.64

V = 116.89

Therefore, the volume of silo will be 116.5 m^3.

Learn more about volume of cylinder here:

https://brainly.com/question/12763699

#SPJ7

Answer:

  98,790

Step-by-step explanation:

The given relation is ...

  0.248 · (total employees) = 24,500

Dividing by the coefficient of the variable, we have ...

  (total employees) = 24,500/0.248 = 98,790

The company has 98,790 employees in total.

Answer:

Money earned after 30 days is $509455

Step-by-step explanation:

If on the first day, that is n = 1, where n is the day and you earn $1.

On the second day (n = 2), you earn $4, On the third day (i.e n = 3) you earn $9 and on the fourth day (n = 4) you then earn $16. That is the money earned on the nth day is given by:

Money earned on the nth day = n².

That is on the 30th day, the money earned = 30² = $900

Once you’ve completed the 30 days you receive a completion bonus of $500,000, in given by:

Money earned after 30 days = [tex]\Sigma}n^2 ;n=1 to30+$500000=(1^2+2^2+3^2+4^2+5^2+...+29^2+30^2)+500000\\=9455+500000=509455[/tex]

Money earned after 30 days = $509455

Answer:

y = x^2 = 30^2 = $900

He would earn $900 on the 30th day and the bonus of $500,000

Step-by-step explanation:

Given

let y represent the amount earned

x represent the day.

At x = 1 y = 1

x = 2 y = 4

x= 3 y = 9

x = 4 y = 16

This satisfies the function;

y = x^2

So, on the 30th day;

x = 30

y = x^2 = 30^2 = $900

He would earn $900 on the 30th day and the bonus of $500,000

Answer:

The number is 6

Step-by-step explanation:

Let the number be x

3 times a number plus 5 =  3x +5

Same number increased by 17 = x + 17

3x + 5 = x + 17

3x -x  + 5 = 17

2x + 5 = 17

2x = 17 - 5

2x = 12

x = 12/2

x = 6

The solution to the problem 3x + 5 = x + 17 is x = 6. This involves setting up an algebraic equation using the given conditions and then solving for x.

This problem seems to be a basic algebra problem. You can begin by setting up the equation based on the sentence given. The sentence translates into the equation: 3x + 5 = x + 17 where x is the unknown number you’re solving for. Then, you need to solve for x by isolating it on one side of the equation.

Step-by-step explanation: Subtract x from both sides of the equation to get 2x + 5 = 17. Then, subtract 5 from both sides to get 2x = 12. Finally, divide by 2 to solve for x. This will give you: x = 6. Therefore, the number that fits the condition in the problem is 6.

https://brainly.com/question/18322830

#SPJ3

Answer:

42.5

Step-by-step explanation:

so you start with adding 15 to the equations because that is how many days

1.5 15 +20

1.5 x 15 =22.5

22.5+20=42.5

so 42.5 is the answer

The predicted height of the plant 15 days from today is 42.5 cm.

The given expression for the height of a plant is 1.5t + 20, where t represents the number of days from today. To find the predicted height of the plant 15 days from today, we need to substitute t = 15 into the expression.

        height of the plant 15 days from today = 1.5(15)+20 cm

        height of the plant 15 days from today = 22.5 + 20 cm = 42.5 cm

Therefore, the predicted height of the plant 15 days from today is 42.5 cm.

Answer:

9 degrees.

Step-by-step explanation:

For ALL polygons, the exterior angles add up to 360 degrees.

Therefore the 8th exterior angle = 360 - (42+110+13+67+55+11+53)

= 360 - 351

= 9 degrees.

Answer:

9°

Step-by-step explanation:

Always some of exterior angle of any polygon is 360

42 + 110 + 13 + 67 + 55 +11 + 53 + x = 360

351 +x = 360

x = 360 - 351

x = 9

Answer:

X=16

Y=5

Step-by-step explanation:

For equilateral triangle, length of both sides are equal hence 18y-41=3x+1=49

Solving for x

Given that 3x+1=49

Rearranging like terms

3x=49-1=48

x=48/3=16 units

Solving for y

Considering that 18y-41=49

18y=49+41=90

y=90/18=5 units

The value of x = 16 and y = 5.

Given that [tex]\( \triangle ABC \)[/tex] is an equilateral triangle, all sides are equal. Therefore, we have:

[tex]\[ AB = BC = AC \][/tex]

Given the side lengths:

[tex]\( AB = 49 \)[/tex] meters

[tex]\( BC = 3x + 1 \)[/tex] meters

[tex]\( AC = 18y - 41 \)[/tex] meters

Since [tex]\( AB = BC \)[/tex]:

[tex]\[ 49 = 3x + 1 \][/tex]

Solve for [tex]\( x \)[/tex]:

[tex]\[ 49 - 1 = 3x \][/tex]

[tex]\[ 48 = 3x \][/tex]

[tex]\[ x = \frac{48}{3} \][/tex]

[tex]\[ x = 16 \][/tex]

Next, since [tex]\( AB = AC \)[/tex]:

[tex]\[ 49 = 18y - 41 \][/tex]

Solve for [tex]\( y \)[/tex]:

[tex]\[ 49 + 41 = 18y \][/tex]

[tex]\[ 90 = 18y \][/tex]

[tex]\[ y = \frac{90}{18} \][/tex]

[tex]\[ y = 5 \][/tex]

The complete question is:

If ABC Is an equilateral triangle, solve for both x and y.

x = _____.

y = _____.

Answer:

f(x) should shifted Right by 4 units to obtain g(x) ⇒ B

Step-by-step explanation:

Let us put g(x) in the form of g(x) = (x - h)² + k, where h is the the horizontal shift (x - h) to right, (x + h) to left and k is the vertical shift (k) up and (-k) down

In the quadratic function y = ax² + bx + c, h = [tex]-\frac{b}{2a}[/tex]  and k = y at x = h

∵ g(x) = x² - 8x + 1

∵ a is the coefficient of x² and b is the coefficient of x

∴ a = 1 and b = -8

∵ h = [tex]-\frac{b}{2a}[/tex]

∴ h = [tex]-\frac{-8}{2(1)}=\frac{8}{2}[/tex]

∴ h = 4

∵ k = g(x) at x = h

- Substitute x by 4 in g(x) to find k

∴ k = (4)² - 8(4) + 1 = 16 - 32 + 1

∴ k = -15

- Substitute them in the form of g(x) = (x - h)² + k

∴ g(x) = (x - 4)² + (-15)

∵ h is the horizontal shift

∵ (x - h) means shift to right h units

∵ f(x) = x²

∵ g(x) = (x - 4)² + (-15)

- That means f(x) is shifted 4 units to the right

∴ f(x) should shifted right by 4 units to obtain g(x)

Answer:

B. Right by 4 units

Step-by-step explanation:

Answer: A2, B3, E1, C5, D4

Step-by-step explanation:

1. A is Maxium because it is the highest point on the graph

2.B is Midline because it is the “middle”

3.C is Peroid because the graph in a way ends or meets back in the middle

4.D is Minimum because it is the lowest point on the graph

5.E is Amplitude

Answer:

C. 6x² -45x + 21

Step-by-step explanation:

( x - 7) (6x - 3)

= x(6x - 3) -7 ( 6x - 3)

= 6x² - 3x - 42x + 21

= 6x² - 45x + 21

Hope it will help you :)

Answer

the answer is c

Step-by-step explanation:

Answer: a line parallel to one side of a triangle divides the other two sides proportionally. you’re welcome :)