△DEF is an isosceles triangle. If m∠D = (3x + 5)° , m∠E = (4x − 15)° and m∠F = (2x + 10)° , what is the measure of one of the congruent base angles?

Answer:

The measure of arc FG is 148°

Step-by-step explanation:

Since the measure of an arc is equal to the measure of the central angle that subtends it, and the measure of central angle CG is 148°, the measure of arc FG is 148°. This is because the arc FG is subtended by the central angle CG.

The complete table will be;

Minutes              15   30

Cages cleaned   2    4

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

The owner of Paradise Pets works hard to keep her store clean. It takes her 15 minutes to clean 2 hamster cages.

Now,

Since, The owner of Paradise Pets works hard to keep her store clean. It takes her 15 minutes to clean 2 hamster cages.

Hence, By definition of proportion we get;

Let the time to clean 4 hamster cages = x

So, We get;

⇒ 15 / 2 = x / 4

⇒ 15×4 / 2 = x

⇒ 30 = x

⇒ x = 30

Thus, It take 30 minutes to clean the 4 hamster cages.

Learn more about the proportion visit:

https://brainly.com/question/870035

#SPJ1

The inequality is [tex]115\leq x\leq 495[/tex]

What is inequality?

A connection is termed an inequality if two real numbers or algebraic expressions are connected by the symbols ">", "<", "≥". Inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols.

Given [tex]60\leq 0.5x+2.5\leq 250[/tex]

splitting the equation:

[tex]60\leq 0.5x +2.5[/tex] and [tex]0.5x +2.5\leq 250[/tex]

[tex]60-2.5\leq 0.5x\\57.5\leq 0.5x\\115\leq x\\x\geq 115[/tex]

also

[tex]0.5x +2.5\leq 250\\0.5x\leq 247.5\\x\leq 495[/tex]

therefore the equation is

[tex]115\leq x\leq 495[/tex]

To learn more about inequality checkout https://brainly.com/question/28823603

#SPJ1

The equation of each of the lines are:

1. y = 1/3x - 1

2. y = 3x + 1

3. y = 2/3x - 1

4. y = 3x

5. y = -2/3x - 1

6. y = 1/3x - 1

7. y = -3x + 2

To write the equation of a line, find the following:

1. Slope (m) = rise/run = 1/3

y-intercept (b) = -1.

To write the equation, substitute m = 1/3 and b = -1 into y = mx + b:

y = 1/3x - 1

2. Slope (m) = rise/run = 3/1 = 3

y-intercept (b) = 1.

To write the equation, substitute m = 3 and b = 1 into y = mx + b:

y = 3x + 1

3. Slope (m) = rise/run = 2/3

y-intercept (b) = -1.

To write the equation, substitute m = 2/3 and b = -1 into y = mx + b:

y = 2/3x - 1

4. Slope (m) = rise/run = 3/1 = 3

y-intercept (b) = 0.

To write the equation, substitute m = 3 and b = 0 into y = mx + b:

y = 3x

5. Slope (m) = rise/run = -2/3

y-intercept (b) = -1.

To write the equation, substitute m = -2/3 and b = -1 into y = mx + b:

y = -2/3x - 1

6. Slope (m) = rise/run = 1/3

y-intercept (b) = -1.

To write the equation, substitute m = 1/3 and b = -1 into y = mx + b:

y = 1/3x - 1

7. Slope (m) = rise/run = -3/1 = -3.

y-intercept (b) = 2.

To write the equation, substitute m = -3 and b = 2 into y = mx + b:

y = -3x + 2

Learn more about the equation of a line on:

https://brainly.com/question/25969846

#SPJ1

The area of the circle would be 36π.

What is the area of a circle?

If the circle has a radius then the area of the circle can be computed by using the formula

area = π * radius²

The perimeter of the square = 24

4 * side = 24

Side of a square = 24/4 = 6

Side of a square = radius of the circle

Substituting the radius of 6 into this formula gives:

area = π * 6²

Which simplifies to:

area = π * 36

Hence, the area of the circle would be 36π.

To learn more about the area of the circle, visit:

https://brainly.com/question/14068861

#SPJ1

The value of x is 91/9.

What is the value of X triangle?

The two angles' combined angles are subtracted from 180 degrees. A triangle's total angles are always equal to 180 degrees. When you remove the total of the two angles from 180 degrees, note the difference you discovered. This is what X is worth. The algebraic expression should often take one of the following forms: addition, subtraction, multiplication, or division. Bring the variable to the left and the remaining values to the right to determine the value of x. To determine the outcome, simplify the values.

(9x+1)+ 88

Remove parentheses: (a)=a

9 x+1+88=180

Add the numbers: 1+88=89

9 x+89=180

Move 89 to the right side

9 x=91

Divide both sides by 9

[tex]\frac{9 x}{9}=\frac{91}{9}$$[/tex]

Simplify

[tex]x=\frac{91}{9}$$[/tex]

To learn more about triangle visit:https://brainly.com/question/2773823

#SPJ1

Answer:

  x = 5

Step-by-step explanation:

You want the value of x where one of the base angles in an isosceles triangle is marked (9x+1)° and the vertex angle is marked 88°.

Each base angle of an isosceles triangle is the complement of half the vertex angle. This one is ...

  9x +1 = 90 -(88/2)

  9x = 45 . . . . . . . . . . subtract 1

  x = 5 . . . . . . . . . divide by 5

The polynomial expression are P(x) = (x - 1)(x + 1)[(x - 3)² + 1] and P(x) = x⁴ - 6x³ + 9x² + 6x - 10

Factored form

The given parameters are

There are complex numbers in the above zeros

This means that, the other zero is

Zeros = 3 + i

The equation of the polynomial is then calculated as

P(x) = Leading coefficient * (x - zero)^multiplicity

So, we have

P(x) = (x - 1) * (x + 1) * (x - (3 + i)) * (x - (3 - i))

This gives

P(x) = (x - 1) * (x + 1) * (x - 3 - i) * (x - 3 + i)

Evaluate the products

P(x) = (x - 1) * (x + 1) * [(x - 3)² - (i)²]

So, we have

P(x) = (x - 1) * (x + 1) * [(x - 3)² + 1]

P(x) = (x - 1)(x + 1)[(x - 3)² + 1]

The standard form

In (a), we have

P(x) = (x - 1) * (x + 1) * [(x - 3)² + 1]

Expand

P(x) = (x² - 1) * (x² - 6x + 9 + 1)

So, we have

P(x) = (x² - 1) * (x² - 6x + 10)

Remove the brackets

P(x) = x⁴ - 6x³ + 10x² - x² + 6x - 10

Evaluate the like terms

P(x) = x⁴ - 6x³ + 9x² + 6x - 10

Hence, the equation is P(x) = x⁴ - 6x³ + 9x² + 6x - 10

Read more about polynomial at

brainly.com/question/17517586

#SPJ1

Number of years since 2003 x=5 years and number of jobs in thousand y=288.

In this method two equation are added or subtracted depending on the sign of variables. After adding or subtracting we create a new equation with one variable. Therefore, we easily get the solution.

while using addition method of algebra, we either add or subtract two equations to obtain a new equation by eliminating one variable. Hence, this method is called elimination method.

Given equation, 7.4x-y= -254

                         12.4x-y = -231

          using addition method

                -5x= -23

                  after solving x=4.6

            x= 5 (nearest whole number)

                     y = 288.04

                y =288

   hence, number of years 5

 number of jobs in thousand =288

to know more about addition method algebra visit:

https://brainly.com/question/25421984

#SPJ1

If 87. 5 percent of a sample of pure 131 I decays in 24 days, then the half-life of 131 i is 8 days.

In this question we have been given 87.5 percent of a sample of pure 131i decays in 24 days

We need to find the the half-life of 131i

We know that the rate constant expression is given as :

k = (2.303/t)*(log (a / a-x))

where, t = 24 days

a = 100

a -x = 100 - 87.5

      = 12.5 g

From the rate constant expression,

k = (2.303 / 24) * (log(100/12.5))

k = 0.0866

Now, the half life is given as :

k = 0.693 / t(1/2)

t1/2 = 0.693 / 0.0866

t1/2 = 8 days.

Therefore, the half-life of 131 i is 8 days.

Learn more about expression here:

https://brainly.com/question/28580620

#SPJ4

Answer:

72+20sqrt3

Step-by-step explanation:

check the attached file

The probability that a randomly chosen person from the united states can donate blood to maria is 0.50

considering blood to be of types A,B,AB and O

further all blood groups are equi probable

Probability of blood type A  = probability of blood type B = probability of blood type AB = probability of blood type O = x

Probability of blood type A  + probability of blood type B + probability of blood type AB + probability of blood type O = 1

⇒ 4x = 1

⇒ x = 1/4

Probability that a random person will have blood of type B or O = x+x

= 1/4 + 1/4

= 1/2

= 0.50

Hence we get the required answer.

Learn more about Probability here:

brainly.com/question/25870256

#SPJ4

Answer:

Step-by-step explanation:

Sorry if this is different, but based on what I read, here is the answer.

100 x 0.85 = 85

therefor it is 85%, which is significantly more than 80%

P(X=12) is the needed probability. P ( X = 12 ) . There is a 0.0042 percent chance that all 12 of them will use their smartphones during courses or meetings.

The possibility or likelihood of an event occurring is expressed numerically as probability. Probabilities are expressed as ratios (0 to 1) and percentages (0 to 100). It is founded on the likelihood that something will occur. The theoretical probability is built on the fundamental principle of probability justification. For instance, there is a 12 percent chance of receiving heads while flipping a coin.

P(X=12) is the needed probability. P ( X = 12 ) . There is a 0.0042 percent chance that all 12 of them will use their smartphones during courses or meetings.

To know more about probability visit:
https://brainly.com/question/30034780

#SPJ4

The scale factor, if The original photo is 4 inches by 6 inches, and the new photo is 3 yards by 4.5 yards, is 1.8.

The ratio of one object's scale to that of a new object, which has its representation but is larger, is known as a scale factor (bigger or smaller).

Given:

The original photo is 4 inches by 6 inches, and the new photo is 3 yards by 4.5 yards,

Calculate the scale factor as shown below,

Scale factor = Original dimension / new dimension

Scale factor = (4 × 6) / (3 × 4.5)

Scale factor = 1.8

To know more about scale factors:

https://brainly.com/question/28658657

#SPJ1

Answer:

y= -9

Step-by-step explanation:

Subtract 3 from both sides

-2y + 3-3= 21-3

-2y=18

Divide both sides by the same factor

-2y/-2 = 18/-2

y= -9

Answer: y = -9

Step-by-step explanation:

-2y+3=21

-2y=21-3

-2y=18

Divide that by -2:

y=-9

Answer:

Fraction: 4 1/4 = 17/4

Decimal: 17/4 = 4.25

Step-by-step explanation:

The solution of the system of equation is as follows;

when x = -2 , y = -4

when x = 4, y = 8

System of equation can be solved using different method such as elimination method, substitution method and graphical method.

Let solve the system of equation by substitution method.

Therefore,

y = 2x

y = x² - 8

Using substitution,

2x = x² - 8

x² - 2x - 8 = 0

x² + 2x - 4x - 8 = 0

x(x + 2) - 4(x + 2) = 0

(x - 4)(x + 2) = 0

x = -2 or 4

Hence,

when x = -2

y = 2(-2) = -4

when x = 4

y = 2(4) = 8

learn more on system of equation here: https://brainly.com/question/11713450

#SPJ1

Bob lifts a 15N rock through a distance of 1.7m, 25.5 J work does Bob do

An item should be converted to energy before being moved. The use of force is one way to transfer energy. The amount of energy used by a force to move an item is referred to as the work done.

The amount of the displacement and the component of the applied force of the object in the displacement direction is the work done by a force. Pushing a block with force "F" causes the body to move more quickly, meaning that work has been completed.

Work done (W) = F × s

Where, F = force

s = displacement

Now putting the values, we get-

or, W = 15 N × 1.7 m

or, W = 25.5 N-m or Joule

To know more about work refer to:

https://brainly.com/question/25573309

#SPJ1

V = 20,000 * 0.81^2 and V = 20,000 * (1 - 0.19)^2 are the equation(s) that represent the exponential relationship.

The value of the car two years later is represented by the variable V. The initial value of the car is represented by the constant 20,000. The relationship between the value of the car two years later and the initial value of the car is exponential, because the value of the car decreases by a fixed percentage each year.

One equation that represents this relationship is:

V = 20,000 * 0.81^2

This equation says that the value of the car two years later is equal to the initial value of the car multiplied by the decay factor of 0.81 raised to the power of 2. The decay factor represents the percentage by which the value of the car decreases each year.

Another equation that represents this relationship is:

V = 20,000 * (1 - 0.19)^2

This equation says that the value of the car two years later is equal to the initial value of the car multiplied by (1 - 0.19) raised to the power of 2. The term (1 - 0.19) represents the percentage by which the value of the car remains after it has depreciated.

Both of these equations represent the exponential relationship between the value of the car two years later and the initial value of the car.

To learn more about Depreciation,

visit; brainly.com/question/14682335

#SPJ4

Store B offers better $0.85 per-roll price than store A.

One type of operation is division in mathematics. The phrases or numbers are divided into the same number of components during this operation.

Given, two stores sell identical sandwich rolls in different size packages.

Store A sells a six-pack for $5.28.

To find the unit price,

we take division of 5.28 with number 6.

The unit price of sandwich roll for store A,

= 5.28 / 6

= $0.88

To find the unit price of sandwich roll for store B,

we take division of 3.40 with number 4.

= 3.40 / 4

= $0.85

And $0.85 < $0.88.

Therefore, Store B offers better per-roll price.

To learn more about the division;

https://brainly.com/question/13263114

#SPJ1

Answer:4

Step-by-step explanation:i did the quiz

The retail price of the car is  $ 9802.9.

A car dealership pays $8350 for a car.

They mark up the price by 17.4%

8350 * 17.4%  = 1452.9

retail price = 8350 + 1452.9 = $ 9802.9

To learn more about percentage   refer,

https://brainly.com/question/24877689

#SPJ1

Answer:

c = 14

Step-by-step explanation:

-3(7f + 3f + 9) - 4f

Distribute.

(−3)(7f) + (−3)(3f) + (−3)(9) + −4f

−21f + −9f + −27 + −4f

Combine like terms.

−21f + −9f + −27 + −4f

(−21f + −9f + −4f) + (−27)

−34f + −27

-34f + -27

Answer:

Bellow

Step-by-step explanation:

QS =√c2 - b2

= √202 - 15.0941916044552

= √172.16537980799

= 13.12118

Answer: 157.14

Step-by-step explanation: SDHU IK

Answer:

1155.52cm²

Step-by-step explanation:

A cylinder's volume is π r² h, and its surface area is 2π r h + 2πr²

radius(r) = 8cm

π = 3.14

height(h) = 15

2πrh + 2πr²

=2πr(h + r)

= 2 × 3.14 × 8 ( 15 + 8)

= 50.24(23)

= 1155.52cm²

pls rate as brainliest

Answer:

1,368

Step-by-step explanation:

4.56x36=164.16

164.16/0.12=1368

Answer:

1368

Step-by-step explanation:

1368

Answer:

D

Step-by-step explanation:

base area = (6 · 4)/2 = 24/2 = 12 cm²

half base length = 6 : 2 = 3 cm

leg = [tex]\sqrt{3^2+4^2} = \sqrt{9 + 16} = \sqrt{25} = 5[/tex] cm

perimeter = (5·2) + 6 = 10 + 6 = 16 cm

lateral area = 16 · 20 = 320 cm²

surface area = (2 · 12) + 320 = 24 + 320 = 344 cm²