For the quadrilateral ABCD diagonal BD is an angle bisector for angles B and D. Find the m∠DAC if m∠ADB = 20°, m∠DBC = 60°.

The answer is 810

10% of a number is 81.

All you need to do is multiply 81 by 10 (810) to see that 10% of 810 is 81.

Best of luck

Answer:

810

Step-by-step explanation:

Multiply 81 by 100 (8,100).

The decimal for 10% is 0.10.

Then multiply 8,100 by 0.10.

Keep in mind that:

With this information, I have created a diagram. I encourage you to always draw a diagram when you can - it aids in the solving process.

Now, to find a, set the measures of the interior angles equal to 180.

(a + 15) + 7a + 7a = 180

Solve for a.

a + 15 + 7a + 7a = 180

15 + 15a = 180

15a = 165

a = 11

Find the angle measures by plugging 11 for a.

a + 15

(11) + 15

26

7a

7(11)

77

Check your work by adding the angles measures.

77 + 77 + 26 = 180

a = 11

Each base angle measures 77 degrees and the vertex angle measures 26 degrees.

Final answer:

To find the unknown angles in the isosceles triangle, we set up an equation using the fact that the sum of angles in a triangle is 180°, which gives a value of 11° for 'a.' Consequently, the vertex angle is 26°, and each base angle is 77°.

Explanation:

The question involves finding the unknown angle measures in an isosceles triangle when given the vertex angle and one of the base angles as algebraic expressions. Since we are dealing with an isosceles triangle, two base angles are equal, and the sum of all angles in a triangle is 180°. The vertex angle is given as (a+15)° and one of the base angles as 7a°. According to the properties of an isosceles triangle, the other base angle is also 7a°. Therefore, we can set up the equation:

(a+15)° + 7a° + 7a° = 180°

Combining like terms, we get:

15° + 15a° = 180°

Subtracting 15° from both sides:

15a° = 165°

Dividing by 15:

a = 11°

Now we can find each angle:

Vertex angle = a + 15° = 11° + 15° = 26°

Each base angle = 7a° = 7(11°) = 77°

The measures of the angles are therefore 26° (vertex angle) and 77° (each base angle).

Answer:

X is 18, and Y is 10.5

Step-by-step explanation:

The 92 degree measure is an example of a vertical angle relationship with the (6x-16) which means that that expression would have to equal 92. Solve for X by adding 16 and then dividing by 6. The 92 and 8y together nake a straight line which is equal to 180 degrees. (180-92) divided by 8 to get y

Writing in scientific notation is writing in power form.

Writing in power form is usually in the form:

X.y × 10ⁿ

We now write 3 920 000 000 000 in this form.

3.92 × 10¹²

Answer :

3.92 × 10¹²

This is the scientific notation.

Hope I helped :)

3,920,000,000,000 in scientific notation is 3.92×10^12.

To express a large number in scientific notation, we need to move the decimal point to the right until there is only one non-zero digit to the left of the decimal point. In this case, we start with the number 3.92 and move the decimal point to the right 10 places.

Therefore, 3,920,000,000,000 in scientific notation is written as 3.92×1012.

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Answer:

Variable

Step-by-step explanation:

A variable is a letter that takes the place of a number.

Answer:

Variable

Step-by-step explanation:

A variable is a letter that represents a number. It can also be solved for. As in 2x+3=100. You would have to solve for the x.

Answer:

21: 7*3

22: 11*2

23: prime

24: 2^3 * 3

25: 5^2

26: 13*2

27: 3^3

28: 2^2*7

29: prime

30: 3*2*5

Answer: Hello there!

initially Maria has 6 red marbles, 6 blue marbles, and 4 green marbles.

You know that in the first pick, Maria gets a green marble ( this means that now there are 3 green marbles left)

Now we want to know the probability that she gets a red marble on the second pick.

Now there are 6 + 6 + 3 = 15 marbles in the bag, and 6 of them are red ones. Then the probability of getting one red is the number of red ones divided by the total amount ( which is the ratio of red marbles to total marbles)

this is 6/15.

now you can see that there is no 6/15 in the options, so we need to see which one is equivalent.

if we took the option C, 2/5, and multiply both denominator and numerator by 3, we get (3*2)/(3*5) = 6/15, then 2/5 and 6/15 are equivalents.

Then the correct answer is C.

The probability that she gets a red marble on her second pick is 2/5.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that she gets a red marble on her second pick = [number of red marbles / (total number of marbles - 1)]

6 / 15 = 2/5

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Answer:

K is the midpoint of AB

Step-by-step explanation:

The line AB is 10 units long. KB is 5 units long. that makes AK 5 units long.

Add them together, you get 10 units long for AB.

Answer:

K is the midpoint of AB

Step-by-step explanation:

I would because the B is much closer to the T which mess with every other answer making it unpropartional.

Answer:

6,75

Step-by-step explanation:

It's necessary the addition of all numbers, divided between the number of the numbers.  It means: 8 +7 +5 +7 +4 +7 +6 +7 +8 +8 +8 +6 = 81, then we'll divide 81 between 12 (because there are 12 numbers), and the result is 6,75

Mean = ∑numbers/n numbers

Answer: c

Step-by-step explanation: because the first number has to be greater then 1 less then 10

Option C (0.21 X 10^7) is not in scientific notation.

The number that is NOT in scientific notation is 0.21 X 10^7 (option C).

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Final answer:

To find the number of new games rented, set up an equation using the given information. Assume all 6 games rented were new games, and solve for the number of new games.

Explanation:

To find the number of new games rented, we can set up an equation using the information given.

Let x represent the number of new games rented and y represent the number of older games rented.

We know that the total cost of renting 6 games is $22. Therefore, we can write the equation:

4x + 2y = 22

To find the number of new games rented, we want to solve for x. We can do this by substituting a value for y and solving for x.

Let's assume all 6 games rented were new games, so y = 0.

Substituting this value into the equation gives:

4x + 2(0) = 22

Simplifying, we get:

4x = 22

Dividing both sides by 4, we find that x = 5.5.

Since we can't rent a fractional number of games, the student rented 5 new games.

Final answer:

The ordered pair that must also be on the graph of y=f(x−2)−3 is (3, -1), which is the result of shifting the original point (1,2) to account for the horizontal and vertical transformations.

Explanation:

To determine the corresponding point on the graph of y=f(x−2)−3, we begin with the given point (1,2) on the graph of f(x). This point means that f(1)=2. The function y=f(x−2)−3 shifts the graph of f(x) two units to the right and three units down. Therefore, to find the x-value for the new function that will give us the y-value of 2, we add 2 to the original x-value of 1, giving us 3. Then to find the new y-value, we subtract 3 from the original y-value of 2, giving us -1. So the new point is (3, -1).

The ordered pair that must also be on the graph of y = f(x−2)−3, given that (1,2) is a point on the graph of f(x), is (-1, -1).

When you have the transformation y = f(x−2)−3, it implies two transformations are applied to the original function f(x): a shift to the right by 2 units and a downward shift by 3 units. To find the corresponding point on the transformed graph, we need to reverse these transformations.

The original point (1,2) on the graph of f(x) represents f(1) = 2. Applying the transformation x−2 shifts the x-coordinate by 2 units to the right, resulting in f(1−2) = f(-1). This gives us the x-coordinate for the transformed point on y = f(x−2)−3.

To account for the downward shift by 3 units, we subtract 3 from the y-coordinate of the original point. Hence, f(1) = 2 becomes f(1)−3 = 2−3 = -1. This provides the y-coordinate for the transformed point on y = f(x−2)−3.

Therefore, combining the x and y coordinates, the point (-1, -1) corresponds to (1,2) on the graph of f(x), satisfying the transformations of x−2 and -3 on y, hence making it a point on the graph of y = f(x−2)−3.

1. -√8, -2.1, 3/2, 12/6, 4

sorry man I'm tired but here's ya first set of answers

Answer: 15

Step-by-step explanation:

3x5 is 15

To find the total number of squares in 5 rows, multiply the number of squares in each row, which is 3, by the number of rows, which is 5.

To find the total number of squares in 5 rows, we need to multiply the number of squares in each row by the number of rows. Since there are 3 squares in each row, we can multiply 3 by 5 to get the answer.

Step 1: Multiply the number of squares in each row, which is 3, by the number of rows, which is 5: 3 x 5 = 15.

Step 2: Therefore, there are 15 squares in 5 rows.

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Answer:

5 inches

Step-by-step explanation:

The formula for a cube's volume is its side length cubed. So to get the side length when given the volume, you can take the cube root of the volume. [tex]\sqrt[3]{125}  = 5[/tex] inches.

Check the picture below.

Answer:

= (a^2 + ab + ab + b^2)

Step-by-step explanation:

Distribute the first a to the second a and b

Distribute the first b to the second a and b

Answer:

7

Step-by-step explanation:

3x14+7=28

Answer:

Use fraction circles to add: 1% + 1% | Use fraction circles to model 1% and 1%. Whole and 1 Whole and 1 Whole and 1 eighth equals 3 wholes and 1 eighth. - Add the fractions and add the whole numbers separately. or: 0 Write each mixed number as an improper fraction, then add.

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Starting from the y-intercept of [0, 1], you do rise\run by either moving one block south over one block west or one block north over one block east. Either way, you will still get a rate of change [slope] of 1.

I am joyous to assist you anytime.

Answer:

The total area of Ohio is about 30 times the total area of Rhode Island

Step-by-step explanation:

Let

x -----> the total area of Ohio in square miles

y -----> the total area of Rhode Island in square miles

we know that

[tex]x=4.5*10^{4}\ mi^{2}[/tex]  

[tex]y=1.5*10^{3}\ mi^{2}[/tex] (searched in Google)

To find out approximately how many times the total area of Ohio is compared to the area of Rhode Island, divide the area of Ohio by the area of Rhode Island

[tex]\frac{x}{y}[/tex]

substitute the values

[tex]\frac{4.5*10^{4}}{1.5*10^{3}}=(\frac{4.5}{1.5})( 10^{4-3}) =3*10^{1}=30[/tex]

therefore

The total area of Ohio is about 30 times the total area of Rhode Island

Ohio is approximately 37.5 times larger than Rhode Island.

To find out how many times larger Ohio is compared to Rhode Island, we need to know the area of both states and then divide the area of Ohio by the area of Rhode Island.

The total area of Ohio is given as[tex]\( 4.5 \times 10^4 \)[/tex]square miles.

The area of Rhode Island is approximately[tex]\( 1.2 \times 10^3 \)[/tex] square miles.

Now, we divide the area of Ohio by the area of Rhode Island to find the factor by which Ohio is larger:

[tex]\[ \frac{\text{Area of Ohio}}{\text{Area of Rhode Island}} = \frac{4.5 \times 10^4}{1.2 \times 10^3} \][/tex]

[tex]\[ = \frac{4.5}{1.2} \times \frac{10^4}{10^3} \][/tex]

[tex]\[ = 3.75 \times 10 \][/tex]

[tex]\[ = 37.5 \][/tex]

Answer:

Discount = $1,464  New Price =$16,836

Step-by-step explanation:

The initial price is given as $18,300.

The price is reduced by a discount of 8%.

Discount = 8% of 18300

                = 8/100 =0.08 x 18300 =$1,464.

New price = $18,300 -$1,464

                  = $ 16,836

This can also be worked out as follows:

After the discount of 8%, the new price is 92% of the initial price.

92% = .92 x  $18300 = $16,836

Answer:

Discount = $1,464  New Price =$16,836

Answer:

Step-by-step explanation:

[tex]y=2^x\\\\\text{Put}\ x=5\ \text{to the equation of the function:}\\\\y=2^5=2\cdot2\cdot2\cdot2\cdot2=32[/tex]

The output, or the result when we input x=5 into the function y=2^x, is 32. This is found by substituting the given input into the function.

The function you've provided is y=2 to the power of x . It is an exponential function. The output for a function is simply the result you get when you substitute a given input into the function. In this case, the function is defined as y = 2^x. To find the output when x=5, replace x in the function with 5. So y = 2^5 = 32. Therefore, the output for an input of x=5 in your function is 32.

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Answer:

True

Step-by-step explanation:

The n th term rule for an arithmetic sequence is

[tex]a_{n}[/tex] = a + (n - 1)d

where a is the first term and d the common difference

here d = 9 - 7 = 2 and a = 7, thus

[tex]a_{n}[/tex] = 7 + 2(n - 1)

Answer:

Jamar should hit the wall opposite to the side of the barrier(if there is a space), which will cause the ball to bounce off the wall at an angle and into Target.

Aiming for the coordinate (0, 2.5) along the plane AB would ensure that the ball hits the plane AB and travels diagonally to the point T which is the target.

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Answer:

1.25 gallons per second

Step-by-step explanation:

To figure this out divide 50 by 40

I don't know how to explain this further, hope this is good enough.

- Que

Answer:

It use 1.25 gallons of water per  second

Step-by-step explanation:

Amount of water used for car wash in 40 seconds = 50 gallons

Amount of water used for car wash in 1 seconds = [tex]\frac{50}{40}[/tex]

Amount of water used for car wash in 1 seconds = [tex]1.25[/tex]

So, Amount of water used in 1 second is 1.25 gallons

So, Unit rate = 1.25 gallons per second

Hence it use 1.25 gallons of water per  second

Answer:

A.2.251 cm , 2.349 cm, 2.295 cm

B. 0.023 meters.

Step-by-step explanation:

a. The possible actual measurements are 2.251 cm, 2.349 cm and 2.295 cm.

b. Rounded measurement in meters is 0.023 meters

a. To determine which measurements could be the actual measurement of the rainfall, we need to consider how rounding works.

When rounding to the nearest tenth of a centimeter, any measurement with a hundredth digit of 5 or greater rounds up, and any measurement with a hundredth digit less than 5 rounds down.

Given that the rounded measurement is 2.3 cm, let's evaluate the measurements:

2.251 cm: Rounds down to 2.3 cm

2.349 cm: Rounds up to 2.3 cm

2.352 cm: Rounds up to 2.4 cm

2.295 cm: Rounds down to 2.3 cm

So, the possible actual measurements are 2.251 cm, 2.349 cm and 2.295 cm.

b. To convert the rounded measurement to meters, we need to divide it by 100, since there are 100 centimeters in a meter.

Rounded measurement: 2.3 cm

Conversion to meters: 2.3 cm / 100 = 0.023 meters

Equation: Rounded Measurement (in meters) = Rounded Measurement (in centimeters) / 100

Rounded Measurement (in meters) = 2.3 cm / 100

= 0.023 meters

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The probability that the spinner landing on a number that is a multiple of 5 or 2 is 0.6, calculated by dividing the number of favorable outcomes (9) by total outcomes (15).

To find the probability that the spinner lands on either a multiple of 5 or a multiple of 2, we first need to identify these numbers.

The multiples of 5 between 1 and 15 are 5, 10, and 15. The multiples of 2 between 1 and 15 are 2, 4, 6, 8, 10, 12, and 14.

Note that 10 is both a multiple of 2 and 5. When we combine these sets, we have 9 unique numbers out of total 15. This gives us a total of 9 favorable outcomes.

The probability is the ratio of favorable outcomes to the total number of outcomes. So, the required probability would be 9/15 or 0.6 when simplified.

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The probability that the spinner lands on a multiple of 5 or a multiple of 2 is 9 out of 15, or 0.6 (60%).

The subject of this question is probability, which falls under Mathematics. To determine the probability that a spinner numbered from 1 to 15 would land on a multiple of 5 or a multiple of 2, we need to first identify the amount of numbers that meet these criteria. The multiples of 5 between 1 and 15 are 5, 10, and 15, which totals to 3 numbers. The multiples of 2 between 1 and 15 are 2, 4, 6, 8, 10, 12, and 14, which totals to 7 numbers.

However, the number 10 is a common multiple of both 5 and 2; to avoid counting it twice, we subtract 1 from our total. Therefore, there are 3 + 7 - 1 = 9 favorable outcomes. With 15 equally likely possibilities on the spinner, the probability is then 9/15 or 0.6, meaning there's a 60% chance the spinner lands on a multiple of 5 or a multiple of 2.

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Answer:

x = [tex]\frac{1}{12}[/tex] y²

Step-by-step explanation:

Any point (x, y ) on the parabola is equidistant from the focus and the directrix

Using the distance formula, then

[tex]\sqrt{(x-3)^2+(y-0)^2}[/tex] = | x + 3 |

Squaring both sides

(x - 3)² + y² = (x + 3)² ← expanding both sides

x² - 6x + 9 + y² = x² + 6x + 9 ← subtract x² + 6x + 9 from both sides

- 12x + y² = 0 ( subtract y² from both sides )

- 12x = - y² ( divide both sides by - 12 )

x = [tex]\frac{1}{12}[/tex] y²

Answer:

y²-12x = 0

Step-by-step explanation:

The formula for calculating the equation of a parabola is y² = 4ax

and x = a

To find the equation of the parabola with focus (3, 0) and directrix x = –3,

The point given (x,y) = (3,0) and x = -3

From the data given, it can be seen that a = -3 by simply comparing x = a with x = -3

Similarly, x = 3 from the given point.

Substituting the value of x = -3 in the formula for equation of a parabola gives;

y² = 4(-3)x

y²= -12x

y²-12x = 0