Which congruence theorems can be used to prove ΔABR ≅ ΔACR? Select three options.

Triangles A B R and A C R share side A R. Angles A B R and A C R are right angles. Sides A B and A C are congruent. Sides B R and C R are congruent.

HL
SAS
SSS
ASA
AAS

Answer:

Step-by-step explanation:

Let's first find the rate of increase for each period which is 3 months here.

According to the table at month [tex]x=0[/tex] value is [tex]2000[/tex]dollars and at month [tex]x=3[/tex] value is [tex]2012[/tex]dollars.

∴[tex]2012=2000(1+\frac{r}{100} )^1[/tex]

⇒[tex]1+\frac{r}{100} =\frac{2012}{2000}=1.006[/tex]

⇒[tex]r=0.006*100[/tex]

⇒[tex]r=0.6[/tex]%

Now the question is to find how long it will take for the investment value to increase 10 percent.

[tex]y=2000(1+0.006)^\frac{x}{3}[/tex]

[tex]2000(1+0.1)=2000(1.006)^\frac{x}{3}[/tex]

⇒[tex](1.006)^\frac{x}{3} =1.1[/tex]

⇒[tex]\frac{x}{3}=\frac{log(1.1)}{log(1.006)}[/tex]

⇒[tex]x=3(\frac{log(1.1)}{log(1.006)} )[/tex]

⇒[tex]x=47.7979126....[/tex]

∴at [tex]x=48[/tex] the value will slightly cross 10 percent increase.

Answer:

We can conclude that Δ GHI ≅ Δ JKL by SAS postulate.

Step-by-step explanation:

Δ GHI and Δ JKL are congruents because:

1. Their sides GH and JK are equal (9 units = 9 units)

2. Their included angles ∠G and ∠J are equal (62° = 62°)

3. Their sides GI and JL are equal (17 units = 17 units)

Now, we can conclude that Δ GHI ≅ Δ JKL by SAS postulate.

Answer:

The answer is 52.2

Step-by-step explanation:

The equation of the line that passes through the points (0, 2) and (5, 8) will be y = (6/5)x + 2.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂). Then the equation of the line is given as,

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

The point given that lie on the line are mentioned below.

(0, 2) and (5, 8)

Then the equation of the line that passes through the points (0, 2) and (5, 8) will be given as,

(y - 2) = [(8 - 2) / (5 - 0)](x - 0)

y - 2 = (6/5)x

y = (6/5)x + 2

The equation of the line that passes through the points (0, 2) and (5, 8) will be y = (6/5)x + 2.

More about the line passing through two points link is given below.

https://brainly.com/question/12740817

#SPJ3

Final answer:

To find the equation of the line passing through (0,2) and (5,8), we calculate the slope as 6/5 and use the y-intercept of 2 to write the equation as y = (6/5)x + 2.

Explanation:

To find an equation of the line that passes through the points (0,2) and (5,8), we need to calculate the slope and use one of the points to write the equation in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

First, let’s find the slope of the line using the formula m = (y2 - y1) / (x2 - x1). Substituting the given points, we get m = (8 - 2) / (5 - 0), which simplifies to m = 6 / 5. This is the slope of the line.

Now, we can use the slope and one of the points to find the y-intercept. Since the line passes through (0,2), we know that the y-intercept b is 2. Therefore, the equation of the line is y = (6/5)x + 2.

Answer:

The value of g(x) at x  = -3 is 18.

Step-by-step explanation:

Here, the given function is:

g(x) = - 5 x + 3

Now, for the value of x = -3 ,

g (-3) : Substitute the value of x  = -3 in g(x) , we get

g (-3)  =  -5 (-3) + 3

          =  15 + 3 = 18

or, g ( -3) = 18

Hence, the value of g(x) at x  = -3 is 18.

Answer:

Two such numbers are  10  , 2 .

Step-by-step explanation:

Here, the question is INCOMPLETE.

Here is the Complete question:

One number is 1/5 of another number. The sum of the two numbers is 12. Find the two numbers. Use a comma to separate your answers.

We can solve the given problem as follows:

Here, : One number is   1/5  of another number.

Let one such number = m

⇒ The other number = 1/5 (m)

Sum of both the given number = 12

[tex]\implies  m + \frac{1}{5}  m = 12\\\implies \frac{5m + m}{5}  = 12\\\implies \frac{6m}{5}  = 12[/tex]

or, 6  m = 12 x (5) = 60

or, m = 60 / 6  =  10

or, m = 1 0

Hence, the first number = m = 10

Second number is [tex]\frac{1}{5} m =  \frac{1}{5} \times 10 = 2[/tex]

Hence, two such numbers are 10  , 2 .

There are 27 purple marbles

Step-by-step explanation:

Let p be the purple marbles

and

w be the white marbles

Then according to given statements

[tex]p+w = 34\ \ \ Eqn\ 1\\p = 4w-1\ \ \ Eqn 2[/tex]

Putting p = 4w-1 in equation 1

[tex]4w-1 +w = 34[/tex]

Adding one on both sides

[tex]5w-1+1 = 34+1\\5w = 35[/tex]

Dividing both sides by 5

[tex]\frac{5w}{5} = \frac{35}{5}\\w = 7[/tex]

Putting w = 7 in equation 2

[tex]p = 4(7)-1\\p = 28-1\\p = 27[/tex]

Hence,

There are 27 purple marbles

Keywords: Linear equation

Learn more about linear equations at:

#LearnwithBrainly

The inequality for the given condition is x ≥ 42 inches

Solution:

Given that, the condition is you must be at least 42 inches tall to ride the bumper cars at an amusement park.  

We have to write an inequality that represents this situation.

Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are deemed equal which is shown by the symbol =

Where as in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥

Let "x" represent the heights of people who are allowed to ride the bumper cars

Height of people who are allowed to ride the bumper cars should be at least 42 inches

Height of people ≥ 42 inches [ since at least condition holds even at 42 value also ]

x ≥ 42 inches

Hence, the inequality for the given condition is x ≥ 42 inches

Answer:

I believe it is 7

Step-by-step explanation:

Final answer:

To find the dimensions of a rectangle with an area of 24 sq. inches and a perimeter of 50 inches, we set up a system of linear equations and solve for the length and width. The dimensions are found to be either 24 inches by 1 inch or 1 inch by 24 inches.

Explanation:

The question given by a student involves finding the dimensions of a rectangle given its area and perimeter. Given the area (24 sq. inches) and the perimeter (50 in.), we can set up two equations to solve for the length and width:

Area = length imes width = 24 sq. inches

Perimeter = 2 imes (length + width) = 50 inches

We can divide the perimeter by 2 to get the sum of the length and width:

25 = length + width

Since we have two equations, this forms a system of linear equations which we can solve simultaneously. First, assume the length is the larger dimension and let us represent it by 'L' and the width by 'W'. We have:

L imes W = 24

L + W = 25

To solve for L and W, we can use substitution or elimination methods. Let's assume we solve for W in terms of L using the first equation, W = 24/L, and then we substitute it into the second equation:

L + 24/L = 25

Multiplying both sides by L to clear the fraction, we get:

L² + 24 = 25L

Then we rearrange the terms to set the equation to zero:

L² - 25L + 24 = 0

Now we can factor this quadratic equation to find the values of L:

(L - 1)(L - 24) = 0

So, L can be either 1 inch or 24 inches. If L is 24 inches, then W will be 1 inch (since 24 imes 1 = 24), and if L is 1 inch, then W will be 24 inches. Either way, the dimensions that satisfy both the area and perimeter equations are 24 inches by 1 inch.

The dimensions of the rectangle are [tex]\( {24 \text{ inches} \text{ by } 1 \text{ inch}} \)[/tex].

To find the dimensions of the rectangle, let's denote the length by l and the width by w.

Given:

1. The area of the rectangle is 24 square inches:

[tex]\[ l \cdot w = 24 \][/tex]

2. The perimeter of the rectangle is 50 inches, which gives us the equation:

[tex]\[ 2l + 2w = 50 \][/tex]

Let's solve these equations step by step.

From the perimeter equation:

[tex]\[ 2l + 2w = 50 \][/tex]

Divide the entire equation by 2 to simplify:

[tex]\[ l + w = 25 \][/tex]

Now we have two equations:

[tex]\[ l + w = 25 \]\[ l \cdot w = 24 \][/tex]

Let's solve for l and w using substitution or elimination.

From ( l + w = 25 ), we can express l as:

[tex]\[ l = 25 - w \][/tex]

Substitute [tex]\( l = 25 - w \)[/tex] into [tex]\( l \cdot w = 24 \)[/tex]:

[tex]\[ (25 - w) \cdot w = 24 \][/tex]

Expand and rearrange the equation:

[tex]\[ 25w - w^2 = 24 \]\[ w^2 - 25w + 24 = 0 \][/tex]

Now, solve this quadratic equation using the quadratic formula [tex]\( w = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \)[/tex], where ( a = 1 ), ( b = -25 ), and ( c = 24 ):

[tex]\[ w = \frac{{-(-25) \pm \sqrt{{(-25)^2 - 4 \cdot 1 \cdot 24}}}}{{2 \cdot 1}} \]\[ w = \frac{{25 \pm \sqrt{{625 - 96}}}}{2} \]\[ w = \frac{{25 \pm \sqrt{{529}}}}{2} \]\[ w = \frac{{25 \pm 23}}{2} \][/tex]

So, we get two possible values for w:

[tex]\[ w = \frac{{25 + 23}}{2} = 24 \]\[ w = \frac{{25 - 23}}{2} = 1 \][/tex]

Now, find l for each value of w:

1. If ( w = 24 ):

 [tex]\[ l = 25 - 24 = 1 \][/tex]

2. If ( w = 1 ):

[tex]\[ l = 25 - 1 = 24 \][/tex]

Answer:

[tex]\large\boxed{k=\dfrac{2m+3}{7-r}\ \text{for}\ r\neq7}[/tex]

Step-by-step explanation:

[tex]7k+2m=kr+4m+3\qquad\text{subtract}\ 2m\ \text{from both sides}\\\\7k+2m-2m=kr+4m-2m+3\\\\7k=kr+2m+3\qquad\text{subtract}\ kr\ \text{from both sides}\\\\7k-kr=kr-kr+2m+3\\\\7k-kr=2m+3\qquad\text{distribute}\\\\k(7-r)=2m+3\qquad\text{divide both sides by}\ (7-r)\neq0\\\\k=\dfrac{2m+3}{7-r}[/tex]

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

Explanation:

The x intercept is (-2,0) which is where the graph crosses the x axis.

The y intercept is (0,-6) which is where the graph crosses the y axis.

-----

Find the slope of the line through those two points

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

m = (-6-0)/(0-(-2))

m = (-6-0)/(0+2)

m = -6/2

m = -3

-----

The y intercept (0,-6) leads to b = -6

Both m = -3 and b = -6 plug into y = mx+b to get

y = mx+b

y = -3x+(-6)

y = -3x-6

-----

Now add 3x to both sides

y = -3x-6

y+3x = -3x-6+3x

3x+y = -6

-----

Lastly, multiply both sides by -2 so that the "-6" on the right hand side turns into "12" (each answer choice has 12 on the right hand side)

3x+y = -6

-2(3x+y) = -2(-6)

-2(3x)-2(y) = 12

-6x-2y = 12

which is what choice B shows.

Answer:

C.)

Step-by-step explanation:

Denominator is the bottom part of a fraction

Answer:

V=349525.333*pi

Step-by-step explanation:

Volume of a sphere: V=(4/3)*pi*r^3 where r=radius.

r=64

V=(4/3)*pi*(64)^3=(4/3)(262144)pi=349525.333*pi

Answer:It cost 2100 dollars

Step-by-step explanation:I did the math on calculator very very simple buddy

Answer:

903 1/8

Step-by-step explanation:

Just divide 7225 by 8. :) I put it in fraction form but decimal form is just 903.125. I hope this helps you out. :)

Answer:

its 903 with 1 left over

the inequality representing the fewest number of cars she must wash is [tex]\( x \geq 13 \).[/tex]

To find the fewest number of cars the employee must wash, we need to determine the minimum number of cars that will allow her to have at least $100 in spending money after saving $50.

Let's denote the number of cars she must wash as( x \).

Given:

- Earnings per car washed: $12

- Amount saved: $50

- Desired spending money: at least $100

Step 1: Calculate her earnings from washing cars:

The total earnings from washing cars will be ( 12x ) dollars.

Step 2: Calculate her spending money after saving:

She saves $50 of her weekly earnings, so her spending money will be her total earnings minus $50, which is \( 12x - 50 \) dollars.

Step 3: Write the inequality:

Since she wants to have at least $100 in spending money, we can write the inequality:

[tex]\[ 12x - 50 \geq 100 \][/tex]

This inequality states that her spending money after saving must be greater than or equal to $100.

Now, to solve for [tex]\( x \), we'll isolate \( x \)[/tex] on one side of the inequality.

Step 4: Solve the inequality:

[tex]\[ 12x - 50 \geq 100 \][/tex]

Add 50 to both sides:

[tex]\[ 12x \geq 150 \][/tex]

Now, divide both sides by 12:

[tex]\[ x \geq \frac{150}{12} \][/tex]

[tex]\[ x \geq 12.5 \][/tex]

Step 5: Interpret the result:

Since the number of cars washed must be a whole number (you can't wash half a car), the fewest number of cars she must wash to have at least $100 in spending money is 13.

So, the inequality representing the fewest number of cars she must wash is [tex]\( x \geq 13 \).[/tex]

Answer:

The simplified form would be [tex]6x^5[/tex]

Step-by-step explanation:

Given:

[tex]\frac{(3x^4)(12x^2)}{6x}[/tex]

Now multiplying the numbers and variable we get,

[tex]\frac{(3x^4)(12x^2)}{6x}\\\\\frac{(36x^{2+4})}{6x}\\\\\frac{36x^6}{6x}[/tex]

Now Dividing 36 by 6 we get,

[tex]\frac{6x^6}{x}=6x^6\times x^{-1} = 6x^{6-1}= 6x^5[/tex]

Hence the simplified form would be [tex]6x^5[/tex]

Answer:

[tex]\large \boxed{24; 12; 8}[/tex]

Step-by-step explanation:

1. Calculate the number of milkshakes

[tex]\text{Number of milkshakes}= \dfrac{\text{Total volume}}{\text{Volume of each milkshake}} = 3 \div \dfrac{1}{8}[/tex]

Invert the denominator and change division to multiplication

[tex]3\div\frac{1}{8} = 3\times \dfrac{8}{1}  = \mathbf{24}\\\\\text{LiAnn can make $\large \boxed{\mathbf{24}}$ milkshakes}[/tex]

2. Calculate the number of double milkshakes

[tex]\text{Number of double milkshakes}= \dfrac{\text{Total volume}}{\text{Volume of each double milkshake}} = 3 \div \dfrac{1}{4}[/tex]

Invert the denominator and change division to multiplication

[tex]3\div\dfrac{1}{4} = 3\times \dfrac{4}{1}  = \mathbf{12}\\\\\text{LiAnn can make $\large \boxed{\mathbf{12}}$ milkshakes}[/tex]

3. Calculate the number of triple milkshakes

[tex]\text{Number of triple milkshakes}= \dfrac{\text{Total volume}}{\text{Volume of each triple milkshake}} = 3 \div \dfrac{3}{8}[/tex]

Invert the denominator and change division to multiplication

[tex]3\div\dfrac{3}{8} = 3\times \dfrac{8}{3}[/tex]  

Cancel the 3s

[tex]3\times \dfrac{8}{3} = \mathbf{8}\\\\\text{LiAnn can make $\boxed{\mathbf{8}}$ triple milkshakes}[/tex]

The scale is likely to show the mass is either 270.9g or 245.1g

Step-by-step explanation:

Actual mass = 258g

Percent error = 5% = ±0.05

Mass shown by scale = Actual mass*percent error

[tex]Mass\ shown\ by\ scale=258*(\±0.05)\\Mass\ shown\ by\ scale=\±12.9g[/tex]

Therefore,

Mass shown by scale = 258+12.9 , Mass shown by scale = 258-12.9

Mass shown by scale = 270.9g , Mass shown by scale = 245.1g

The scale is likely to show the mass is either 270.9g or 245.1g

Keywords: error, percentage

Learn more about percentages at:

#LearnwithBrainly

Answer:

A scale has a percent error of 5%. The actual mass of a rock is 258 g.

Select from the drop-down menus to correctly complete the statement.

The scale is likely to show the mass is either

245.1

g or

270.9

g.

Step-by-step explanation:

I copied an pasted from k-12

Final answer:

To find how long it takes Jordan to run 6.21 miles, multiply the per-mile time (8.4 minutes) by the total miles (6.21), resulting in approximately 52.164 minutes.

Explanation:

To calculate how long it would take Jordan to run 6.21 miles based on the information that Jordan can run a mile in 8.4 minutes, we use the following steps:

Time for 1 mile = 8.4 minutes

Total distance = 6.21 miles

Total time = 8.4 minutes/mile × 6.21 miles

Total time = 52.164 minutes

Therefore, it would take Jordan approximately 52.164 minutes to run 6.21 miles. This straightforward multiplication provides a precise estimate, illustrating the application of the mile pace to calculate the overall running time for the specified distance.

Answer:

[tex]x=\frac{8}{3}\ cm[/tex]

Step-by-step explanation:

we know that

The area of the right triangle ABC is equal to

[tex]A=\frac{1}{2}(AB)(BC)[/tex]

we have

[tex]A=17\ cm^2[/tex]

[tex]AB=(3x-2)\ cm[/tex]

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

substitute the values

[tex]17=\frac{1}{2}(3x-2)(x+3)[/tex]

[tex]34=(3x-2)(x+3)[/tex]

[tex]34=3x^2+9x-2x-6[/tex]

[tex]3x^2+7x-6-34=0[/tex]

[tex]3x^2+7x-40=0[/tex]

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]3x^2+7x-40=0[/tex]

so

[tex]a=3\\b=7\\c=-40[/tex]

substitute in the formula

[tex]x=\frac{-7(+/-)\sqrt{7^{2}-4(3)(-40)}} {2(3)}[/tex]

[tex]x=\frac{-7(+/-)\sqrt{529}} {6}[/tex]

[tex]x=\frac{-7(+/-)23} {6}[/tex]

[tex]x=\frac{-7(+)23} {6}=\frac{16}{6}=\frac{8}{3}[/tex]

[tex]x=\frac{-7(-)23} {6}=-5[/tex]

therefore

The solution is

[tex]x=\frac{8}{3}\ cm[/tex]

Answer:

$40,$60

Step-by-step explanation:

Let the money in the first month be x.

2x+20=100

x=40

The area of the given figure is 864 square feet.

To find the area of the given figure, we can break it down into two rectangles and then sum their areas.

The figure consists of two rectangles with dimensions:

1. The first rectangle has a length of 36 ft and a width of 18 ft.

2. The second rectangle has a length of 12 ft and a width of 18 ft.

The area (A) of a rectangle is calculated using the formula: [tex]\(A = \text{length} \times \text{width}\).[/tex]

For the first rectangle:

[tex]\[ A_1 = 36 \, \text{ft} \times 18 \, \text{ft} = 648 \, \text{ft}^2 \][/tex]

For the second rectangle:

[tex]\[ A_2 = 12 \, \text{ft} \times 18 \, \text{ft} = 216 \, \text{ft}^2 \][/tex]

Now, add the areas of both rectangles to find the total area (A) of the figure:

[tex]\[ A = A_1 + A_2 = 648 \, \text{ft}^2 + 216 \, \text{ft}^2 = 864 \, \text{ft}^2 \][/tex]

The question probable maybe :-

Find the combined area of two rectangles with side 36 ft 18 ft ,12 ft

18 ft​ respectively .

Answer:

Each girl gets 2/3 yd of ribbon.

Step-by-step explanation:

12 2/3=38/3

(38/3)/19

(38/3)(1/19)

(2/3)(1/1)=2/3

112 different area codes can be made.

Given, In a different plan for area codes, the first digit could be any number from 0 through 6 ,  

So, total 7 digits are possible for 1st place (i.e. 0 1 2 3 4 5 6)

The second digit was either 7 or 8,  

So, total 2 digits are possible for 2nd place (i.e. 7 8)

And the third digit could be any number except 0 or 6.  

So, total possible digits are 8 for 3rd place (i.e. 1 2 3 4 5 7 8 9)

With this plan, we have to find how many different area codes are possible?

[tex]\text { total possible combinations }=7 \text { possibilities for } 1 \text { st place } \times 2 \text { for } 2 \text { nd place } \times 8 \text { for } 3 \text { rd place }[/tex]

[tex]\text { Total possible area codes }=7 \times 2 \times 8=14 \times 8=112[/tex]

Hence, 112 different area codes can be made.

Answer:

(A) 40.67

(B) 57.98

Step-by-step explanation:

I did it in my head