SAS
HL
State how the triangles can be proven
congruent, if possible.
AAS
ASA

She invested $1000 at 2% and 2200 at 5% simple interest.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Given, P₁ = 1000, P₂ = 2200, assuming r₁ = x% and r₂ = (x + 3)% and the sum of simple interest obtained from both these investments is $130.

∴ (1000×x×1)/100 + {(2200×(x + 3)×1}/100 = 130.

10x + 22x + 66 = 130.

32x = 64.

x = 2.

So, the rate of interest is 2% and 5%.

learn more about simple interests here :

https://brainly.com/question/11564235

#SPJ1

The sum of the arithmetic sequence 1, 3, 5, 7, … , 99 is 2525

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given sequence is 1, 3, 5, 7, … , 99.

It is a arithmetic sequence, the difference between two consecutive terms will be same

d=3-1=2

first term a=1

l=last term =99

We need to find 99 is which term in the sequence

Aₙ = a + ( n - 1 ) d

99=1+(n-1)2

99=1+2n-2

99=2n-1

100=2n

Divide both sides by 2

50=n

Now we need to find the sum of 50 terms

Sₙ=n/2(l+d)

=50/2(99+2)

=25(101)

=2525

Hence, the sum of the arithmetic sequence 1, 3, 5, 7, … , 99 is 2525

To learn more on Sequence click:

https://brainly.com/question/21961097

#SPJ1

Answer:

7.5 cups of grapes

Step-by-step explanation:

4o:3g:2b

With 5b, there's an increase in 2.5 from 2b. (divide 5b/2b)

Since the increase in all the other fruits is proportional by the same amount of 2.5.

This leaves you with 10o:7.5g:5b

Answer:

domain { a ∈ R , a ≠ - 5 }

Step-by-step explanation:

the denominator of f(a) cannot equal zero as this would make f(a) undefined. Equating the denominator to zero and solving gives the value that a cannot be.

a + 5 = 0 ( subtract 5 from both sides )

a = - 5 ← excluded value

domain { a ∈ R, a ≠ - 5 }

Answer:

133, 412500, 500, 1.184, 37.8, 10, 0.6

Step-by-step explanation:

If we think about how many centimeters are in a meter, we know that

1m = 100cm

Using this, we can see that

20m = 2000cm

Now divide by 15:

2000 ÷ 15 ≈ 133

She can make roughly about 133 ribbons.

To solve the next question, we need to know how many kilometers are in a meter

1km = 0.001m

Let's covert 0.75 into m:

0.75 × 1000 = 750

Now solve for the area:

750 × 550 = 412500

The area of the rectangle is 412500

If he is selling the home for 206,250,000 pesos,

206,250,000 divided by 412500

206,250,000 ÷ 412500 = 500

The price per square meter is 500

If each glass is 148 milliliters, and we need to convert that into liters, we can use the equation:

1L = 1000mL

So converting 148 into liters,

148mL = 0.148L

Now, multiply by 8.

0.148 × 8 = 1.184L

We need to convert 100 Fahrenheit to Celsius.

100 F ≈ 37.8

This is definitely not a normal body temperature.

We can convert grams to kilograms using the equation:

1kg = 1000 g

Converting 2.5kg to g would look like this:

2.5kg = 2500g

250g × 10 = 2500g

We need to buy 10 packs of sugar.

If 120 grams of powdered milk can produce 60 cups of milk, and we need to figure out how many kg can produce the same amount, we use the equation:

1kg = 1000g

Converting 120g to kg would look like this:

120 ÷ 1000 = 0.120

Now, we need to figure out how many times 12 goes into 60.

12 × 5 = 60

Now we multiply 0.120 by 5

0.120 × 5 = 0.6

I hope this helps!

Answer:

x = -3; y = -4

Step-by-step explanation:

We can start by eliminating x, which will give us y:

[tex]9(-4x +11y=-32)\\-4(-9x+4y=11)\\\\-36x+99y=-288\\36x-16y=-44\\\\83y=-332\\y=-4[/tex]

Now we can plug in -4 for y in the first equation to find x:

[tex]-4x+11(-4)=-32\\-4x-44=-32\\-4x=12\\x=-3[/tex]

The domain and the range of the function are given as follows:

The domain of a function is composed by the set that contains all possible values assumed by the input of the function.

On a graph, the input of the function is given by the values of x, hence the domain of the graphed function is given by the following interval:

(-2,3].

The meaning of the circles on the intervals is of:

The range is composed by the set containing all the values assumed by the output of the function.

Hence, on the graph, the range is composed by the values of y of the function, which are given as follows:

[-8, 2).

More can be learned about the domain and range of functions at brainly.com/question/2264373

#SPJ1

The statement that best describes the functions represented in the graphs is B. Only function p is continuous and linear.

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

A function at a place can only be continuous if it is defined there, has a limit there, and its value at that point is equal to the value of the limit there.

The graph of function p is linear and continuous

Learn more on continuous functions at:

https://brainly.com/question/13205114

#SPJ1

The quadratic equation y = x² - 8 · x + 18 represents the parabola shown in the figure.

In this problem we find a representation of a parabola, which is described algebraically by quadratic equations, that is, polynomials of the form:

y = a · x² + b · x + c

Where a, b, c are the coefficients of the polynomial.

We can determine the value of the coefficients from the knowledge of three points set on Cartesian plane. First, select the points from Cartesian plane:

(x₁, y₁) = (0, 18), (x₂, y₂) = (4, 2), (x₃, y₃) = (7, 11)

Second, create a system of linear equations with three variables and three equations by replacing the variables x and y on the quadratic equation:

c = 18

16 · a + 4 · b + c = 2

49 · a + 7 · b + c = 11

Third, solve the system by numerical methods:

(a, b, c) = (1, - 8, 18)

Fourth, write the resulting quadratic equation:

y = x² - 8 · x + 18

To learn more on parabolas: https://brainly.com/question/21685473

#SPJ1

Answer:

283 cm^2

Step-by-step explanation:

hi your welcome

Answer:

Step-by-step explanation:

radius = r = 17

height = h = 13

First calculate the total surface area =

2πr (r + h)

2 (3.14) 17 (17 + 13)

2 (3.14) 17 (30)

6.28 (17)(30)

106.76 (30)

3202.80  cm²

Then subtract the area of the bottom base of the cake:

Base of the cake is the area of the round base

π r² = 3.14 (17)²

3.14 (289) = 907.46 cm²

Subtract area of base from total surface area:

I am rounding:

3203 - 908 = 2295 cm²

Second option or B

Answer:

ten is the fight one

Step-by-step explanation:

True

Answer:

39%

Step-by-step explanation:

126.28 minus 77 is 49.28.

49.28 divided by 126.28 is 0.39 and a bunch of other numbers but round it up and its 0.39. move the decimal to the right two places and youve got 39%

hope this helped!

Answer:

R would equal 12

Step-by-step explanation:

If the rotation is clockwise the angle is 120°.

If the rotation is counterclockwise the angle is 240°

The correct options are A and D.

We assume that the rotation is clockwise.

First, we can see that the rotation from P to F is just a rotation of 90°.

(point P as at 9 on a clock and point F is at 12 on a clock).

To go from point F to G, we need to move one of the sections defined by the dashed lines, and we know that each one of these measures 30°, then we need to add another 30° to the angle.

90° + 30° = 120°

Then the angle of rotation to map P to G is 120°.

The correct option is D.

Then if the rotation is counterclockwise, the rotation will be of 240°.

Learn more about rotations:

https://brainly.com/question/26249005

#SPJ1

Answer:

Sydney will have to pay -5, and her brother will have to pay -7. Her brother will have to pay $2 more than Sydney.

Step-by-step explanation:

Answer: There are multiple answers.

Step-by-step explanation: To find x...simply ad together what you have (The numbers given) and subtract from 180.

(I did this a while ago, don't take my word  for it)

The break-even point under the old situation is 680000, the break-even point under the proposed situation is 806451 and the birr sales volume must be obtained under the proposed plan to make as much profit as last year is 1129032.

In economics, business, and particularly cost accounting, the break-even point is the point at which total cost and total income are equal, or "even." Although opportunity costs have been paid and capital has obtained the risk-adjusted, projected return, there is no net loss or gain, and one has "broken even."

In the given question, last year sales=  birr 100000

net profit= 8% of sales

Fixed costs= birr 170000

Estimated sales increase= 25%

Estimated net profit= birr 30000

Increase in fixed cost due to moving to low-rent warehouse= birr 30000

(a) The break-even point under the old situation (X):

   = 100,000 * a - 170,000

   =1,000,000 * 8%

   a= 25% (net profit)

   X*a= 1170,000

   X=680,000

   That is, the break-even point under the old situation is 680000.

(b) The break-even point under the proposed situation is:

      = 1,250,000 x b - 170,000- 30,000

      = 80,000 + 30,000

      b= 24.8%

      X*b=200,00

      X=806451

      The break-even point under the proposed situation is 806451 and

(c) The birr sales volume must be obtained under the proposed plan to make as much profit as last year is:

        X*b -200,000= 80,000

        X*b = 280,00

        X= 1,129,032

The birr sales volume must be obtained under the proposed plan to make as much profit as last year is 1129032.

To know more about breakeven point, visit:

https://brainly.com/question/15406644

#SPJ1

Using the secant-secant theorem,

[tex]\frac{13x+7-60}{2}=5x-10 \\ \\ 13x-53=10x-20 \\ \\ 3x-53=-20 \\ \\ 3x=33 \\ \\ \boxed{x=11} \\ \\ m\angle RDB=5(11)-10=\boxed{45^{\circ}}[/tex]

The measure of the angle ∠RDB will be 45°.

In geometry, a chord of a circle is a straight line segment whose endpoints both lie on the circle. A diameter of a circle is the longest chord, and it passes through the centre of the circle.

Calculate the value of x as below,

( 13x + 7 - 60 ) / 2 = 5x - 10

13x - 53 = 10x - 20

3x - 53 = -20

3x = 33

x = 11

The measure of the angle ∠RDB is,

∠RDB = 5x - 10

∠RDB = ( 5 x 11 ) - 10

∠RDB = 45°

Therefore, the value of an angle ∠RDB will be 45°.

To know more about the angle of the chord follow

https://brainly.com/question/28270974

#SPJ2

Answer: the first one

Step-by-step explanation:

Answer: 23.1, 13.35718336 years or 14 rounded

Step-by-step explanation:

[tex]Given:A= 23.1e^{0.0152t}[/tex]

when A = end amount, and t = years after 2000

Part A).

What was the population of the state in 2000. According to our function, this would be when t = 0

[tex]23.1e^{0.0152(0)}\\\\=23.1(1)\\\\=\boxed{23.1}[/tex]

Part B).

When will the population of the state reach 28.3 million?

This would be when A = 28.3

[tex]28.3=23.1e^{0.0152t}\\\\\frac{28.3}{23.1} =\frac{23.1e^{0.0152t}}{23.1} \\\\\frac{28.3}{23.1} =e^{0.0152t}\\\\ln^{\frac{28.3}{23.1} }=ln^{e^{0.0152t}}\\\\ln^{\frac{28.3}{23.1} }=0.0152t\\\\t=\frac{ln^{\frac{28.3}{23.1} }}{0.0152} \\\\\boxed{t=13.35718336 \ \ years}[/tex]

Answer:

B: 25.75 times a number x, plus 10 | D: the product of 25.75 and x, plus 10

Step-by-step explanation:

B: 25.75 times "x" = 25.75x + 10

D: The product of 25.75 and x = 25.75x  + 10

Answer:

The carpenter will be paid $516.00

Step-by-step explanation:

1. Multiply

(Since the carpenter is being paid per hour, and the pay is $24.00, and the time it takes to work is 21.5, we can set up this equation):

21.5 x 24.00 = $516.00

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 3 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

The net asset value of the given mutual fund will be 2.29.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Division = divide any two numbers or variables called division.

Multiplication = to multiply any two or more numbers or variables called multiplication.

As per the given,

Total assets = $25,500,000

Liabilities = $2,100,000

Total shares = 10,200,000

Net asset = (total assets - total liability)/total shares outstanding

Net assets = (25,500,000 - 2,100,000)/10,200,000

Net assets = 2.29

Hence "The net asset value of the given mutual fund will be 2.29".

To learn more about the arithmetic operators,

brainly.com/question/25834626

#SPJ1

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

The inequalities that describe the constraints on the number of each type of hedge trimmer produced are:

x + y ≤ 200

2x + 10y ≤ 1000

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Total number of hours = 1000

Total number of trimmers = 200

Let x represent the number of cord-type models,

Let y represent the number of cordless models.

Now,

x + y ≤ 200

2x + 10y ≤ 1000

Thus,

The inequalities that describe the constraints on the number of each type of hedge trimmer produced are:

x + y ≤ 200

2x + 10y ≤ 1000

Learn more about inequalities here:

https://brainly.com/question/20383699

#SPJ1

Hence, the probability of selecting two Democrats is [tex]45[/tex].

What is the probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen.

The meaning of probability is basically the extent to which something is likely to happen.

Here given that,

Consider a political discussion group consisting of [tex]9[/tex] ​Democrats, [tex]9[/tex] ​Republicans, and [tex]5[/tex] Independents. Suppose that two group members are randomly​ selected, in​ succession, to attend a political convention.

Let us assume ,

The discussion of the democratic is [tex]x_1=9[/tex].

The discussion of the democratic is [tex]x_2=9[/tex].

The discussion of the democratic is [tex]x_3=5[/tex]

So, the total number of candidates are

[tex]x_t=x_1+x_+x_3\\\\=9+9+5\\\\=23[/tex]

Probability of independate candidate from the group of candidates is

[tex]P_1=\frac{x_3}{x_t}\\\\P_1=\frac{5}{23}\\\\[/tex]

As, the remaining number of candidates after the selectio of the independent candidate is

[tex]x_r=x_t-1\\\\x_r=23-1\\\\x_r=22[/tex]

Now, the remaining number of candidates from the group of total remaining candidates is

[tex]P_2=\frac{x_1}{x_r}\\\\P_2=\frac{9}{22}[/tex]

So, the probability of an independent Democrat using the probability is

[tex]P=P_1[/tex] × [tex]P_2[/tex]

[tex]P=\frac{5}{23}[/tex] ×[tex]\frac{9}{22}[/tex]

[tex]P=\frac{110(207)}{506}\\\\P=\frac{22770}{506}\\\\P=45[/tex]

Hence, the probability of selecting two Democrats is [tex]45[/tex].

To know more about the probability

https://brainly.com/question/12629667

#SPJ1

The volume of the canister is 36.7 in³. The volume of box is 482.6 cm³

To find the volume of a canister, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

In this case, the canister has a radius of 1.56 inches and a height of 6.93 inches,

volume of canister = π × (1.56 inches)² × 6.93 inches

volume of canister = 36.7 in³

To find the volume of a box, we can use the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height.

In this case, the box has a length of 15.5 cm, a width of 8.6 cm, and a height of 3.8 cm

volume of box = 15.5 cm × 8.6 cm × 3.8 cm

volume of box = 482.6 cm³

Learn more about the volume of cuboids here:

brainly.com/question/23118276

#SPJ1

Answer:

LM ≈ 15.8

Step-by-step explanation:

calculate the length d using the distance formula

d = [tex]}\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = L (- 6, - 7 ) and (x₂, y₂ ) = M (3, 6 )

LM = [tex]\sqrt{(3-(-6))^2+(6-(-7))^2}[/tex]

    = [tex]\sqrt{(3+6)^2+(6+7)^2}[/tex]

   = [tex]\sqrt{9^2+13^2}[/tex]

   = [tex]\sqrt{81+169}[/tex]

  = [tex]\sqrt{250}[/tex]

  ≈  15.8 ( to the nearest tenth )

Answer:

y=0.25x+3

Step-by-step explanation:

use desmos graphing calculator and put the coordinates into a table

The option that's a requirement for employees who must wear PPE is C. Participate in PPE training.

Personal protective equipment (PPE) is clothing that is comfortable to wear in order to reduce the risk of hazards at work that cause serious illnesses and injuries.

Personal protective equipment (PPE) will be divided into the following categories for this purpose: eye and face protection, hand protection, body protection, respiratory protection, and hearing protection.

Personal protective equipment (PPE) should be used when all other measures to control exposure are ineffective. It only protects the wearer while they are wearing it. PPE offers no protection if it fails.

All personal protective equipment should be designed and built safely, and it should be kept clean and reliable. It should be comfortable for workers to use. Personal protective equipment that does not fit properly can mean the difference between being safe and being dangerously exposed. Employers must provide personal protective equipment to their employees and ensure its proper use when engineering, work practices, and administrative controls are not feasible or provide adequate protection

Learn more about PPE on:

https://brainly.com/question/28178938

#SPJ1

Complete question

Which of the following is a requirement for employees who must wear PPE?

a. Speak to the. project manager.

b. Get necessary clothes.

C. Participate in PPE training.

From the area of a triangle, the height of the triangle is 12ft

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, which is given by

A = 1/2 b * h

In the given question, the base is two-thirds of the height.

b = 2/3h

Let's substitute the values into the formula

A = 1/2 * 2/3h * h

A = 2/6 * h²

A = 1/3h²

48 = 1/3h²

h² = 48 * 3

h = √144

h = 12ft

Learn more on area of a triangle here;

https://brainly.com/question/23945265

#SPJ1