What is the measure of ∠DAE? 45° 46° 91° 146°

Answer:

It is 70

Step-by-step explanation:

Both angles have to add up to 90 and I did the lesson ight

Answer:  The correct option is (a) [tex]2x^2+3x-5.[/tex]

Step-by-step explanation:  We are given to find the quotient in the following division :

[tex]Q=\dfrac{2x^3-3x^2-14x+15}{x-3}.[/tex]

To find the quotient, first we will try to factorize the numerator and then we will try to divide by the denominator.

We have

[tex]Q\\\\\\=\dfrac{2x^3-3x^2-14x+15}{x-3}\\\\\\=\dfrac{2x(x-3)+3x(x-3)-5(x-3)}{x-3}\\\\\\=\dfrac{(x-3)(2x^2+3x-5)}{(x-3)}\\\\=2x^2+3x-5.[/tex]

Thus, the required coefficient is [tex]2x^2+3x-5.[/tex]

Option (a) is CORRECT.

If 100 envelopes cost $0.70 then it would cost $1.75 for 250 envelopes.

If 100 envelopes cost $0.70, we can set up a proportion to determine the cost of 250 envelopes:

100 envelopes / $0.70 = 250 envelopes / x

Cross-multiplying:

100 × x = 250 × $0.70

Simplifying:

100x = 175

Dividing both sides by 100:

x = 175 / 100

x = $1.75

Therefore, it would cost $1.75 for 250 envelopes.

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The measure of angle m∠3 would be 60°.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.

Given;

g ∥ h, m∠1 = (4x + 36)°,

m∠2 = (3x – 3)°.

m∠2 = m∠3 ( alternate interoir angle)

we know that

m∠1 + m∠2 = 180

4x + 36 + 3x – 3 = 180

7x + 33 = 180

7x = 147

x = 21

Substituting

m∠2 = 3x – 3

m∠2 = 3(21) - 3

m∠2 = 63 - 3

m∠2= 60

Therefore, m∠3 = m∠2 = 60

Hence, The measure of angle m∠3 would be 60°.

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36 is least number of each for which this was possible.

The smallest positive integer that is divisible by both a and b is known as the least common multiple, lowest common multiple, or smallest common multiple of two integers, or lcm(a, b), in mathematics and number theory.

4 is the LCM of 2 and 4. To get the smallest multiple that is exactly divisible by 2 and 4, i.e. 4, we must first determine the multiples of 2 and 4 (multiples of 2 = 2, 4, 6, 8; multiples of 4 = 4, 8, 12, 16).

Given:

Hot dogs cam in pack of 9.

Buns came in pack of 12.

Now, to find least number of each bought the same number of hot dogs as buns.

So, LCM(9, 12)

9= 3x 3

12= 2 x2 x 3

Thus, LCM(9, 12) = 3 x 3 x 2 x 2 = 36

Hence, 36 is least number of each for which this was possible.

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The solutions to the quadratic equation x² + 5x + 3 = 0 are:

x = (-5 + √13) / 2

x = (-5 - √13) / 2

To solve the quadratic equation x² + 5x + 3 = 0, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this equation, a = 1, b = 5, and c = 3. Substituting these values into the quadratic formula, we get:

x = (-5 ± √(5² - 4×1×3)) / (2×1)

Simplifying further:

x = (-5 ± √(25 - 12)) / 2

x = (-5 ± √13) / 2

Therefore, the solutions to the quadratic equation x² + 5x + 3 = 0 are:

x = (-5 + √13) / 2

x = (-5 - √13) / 2

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The number of  each type of bill or coin the wallet contains is:

                                   4

It is given that:

A wallet holds $ 25 in total.

Also, the number of $ 1 bills,$ 5 bills and qaurters are present in equal number in the wallet.

Let the number of each coin or bill in the wallet be: x

Also, we know that:

1 quarter= 1/4 dollar

i.e.

1 quarter= 0.25 dollar

Hence, we get:

 x+5x+0.25x=25

i.e.

6.25 x=25

On dividing both side of the equation by 6.25 we get:

   x=25/6.25

i.e.

x=4

Hence, the number of each kind of coin or bill are: 4

The conversion of a percentage to a decimal number, divide the percentage by 100 it means that 275% represents 2.75 times the original quantity.

To convert a percentage to a decimal number,

divide the percentage value by 100.

Here's the step-by-step explanation for converting 275% to a decimal:

Take the percentage value (275%) and divide it by 100.

275 ÷ 100 = 2.75

So, 275% as a decimal is 2.75.

It means that 275% is equal to 2.75 times the whole quantity.

For example, if you have 100 dollars and increase it by 275%, you will end up with 100 + (2.75 × 100) = 375 dollars.

Therefore, the 275% as a decimal number is equal to 2.75.

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The triangle is isosceles.

A triangle is a polygon that has three vertices on each of its three sides. The angle that is created within the triangle is 180 degrees. It indicates that the sum of a triangle's interior angles is 180 degrees. This is a polygon with the fewest sides. At the end of the day, a triangle is characterized as a three-sided two-layered figure whose inside points are equivalent to 180°.

Given a triangle let the triangle be ΔABC

given angles (4x + 8), (5x + 2) and (6x - 10)

let ∠A = (4x + 8), ∠B =  (5x + 2) and ∠C  = (6x - 10)

we know that sum of angle of triangle is 180⁰

∠A + ∠B + ∠C = 180

4x + 8 + 5x + 2 + 6x - 10 = 180

15x = 180

x = 180/15 = 12

∠A = 4x + 8 = 4(12) + 8 = 56⁰

∠B = 5x + 2 = 5(12) + 2 = 62⁰

∠C = 6x - 10 = 6(12) - 10 = 62⁰

since ∠B = ∠C

it is the property of an isosceles triangle, An isosceles triangle is a triangle with any two sides that are the same length and angles on opposite sides that are the same size.

Hence the Given triangle is isosceles.

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