divide 16x³+31.6x²-6.8x-12 by x+2​

Answer:

C. y=4x+13

Step-by-step explanation:

To solve this equation first find the slope. Do this by using the slope formula, m=\(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\), so plug in the points\(\frac{1+3}{-3+4}\) which equals 4/1 or 4. Since now we know the slope is 4 we can put the equation into slope-point form, I will be using (-4,-3) for this equation. y+3=4(x+4), then solve for y. After solving you get y=4x+13.

Answer:

32

8

Not enough info

Step-by-step explanation:

4/5 of 40 is 32

40 - 32 = 8

We don't know the total number of marbles in the bag

Therefore , as a result Two of a triangle's sides and the included  SAS angle are said to be congruent if they match the corresponding sides and angles of another triangle.

The Side-Angle-Side rule is applied to check the congruence of a set of triangles. The SAS rule states that a triangle is congruent if its two sides and included angles match those of another triangle.

Here,

if the first triangle's two sides and one of its included angles are equal to the second triangle's sides and one of its included angles.

Consequently, the SAS declares two triangles to be congruent. Two triangles are said to be congruent if their matching two sides and their included angles are found in a single triangle, according to the SAS theorem of congruence.

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The area of the figure ABDECA, and the coordinates of the points on the quadrilateral are;

1. The area is about 15.16 units²

2. The coordinates of the points are;

(i) B(5, 8)

(ii) C(8.58, 4)

(ii) D(8,58, 1.21)

A quadrilateral is a four sided polygon.

1. The coordinate of the point C can be found as follows;

Let (x, y) represent the coordinates of the C, we get;

(x + 8)/2 = 5

x = 2 × 5 - 8 = 2

(y + 8)/2 = 6

y = 2 × 6 - 8 = 4

The coordinates ot the point C (2, 4)

The length of the segment BC = √((8 - 2)² + (8 - 4)²) = 2·√(13)

Length of the side AB = √((8 - 6)² + (8 - 11)²) = √(4 + 9) = √(13)

The area of the triangle ABC = (1/2) × 2·√(13) × √(13) = 13

CE is perpendicular to DE, let (a, b), represent the coordinates of the point E, therefore;

(4 - y)/(2 - x) = -(5 - x)/(6 - y)

y - 4 = (-4/7)(x - 2)

y - 6 = (7/4)(x - 5)

(-4/7)(x - 2) + 4 = (7/4)(x - 5) + 6

x = (17/5) = 3.4

y = (7/4)((17/5) - 5) + 6 = 3.2

The coordinates of the point E is (3.4, 3.2)

The length of the side DE = √((5 - 3.4)² + (6 - 3.2)²) = √(10.4)

Length of the side CE = √((3.2 - 2)² + (3.4 - 4)²) = √(1.8)

Area of the triangle ΔCDE = (1/2) × √(10.4) × √(1.8)

Area of the figure is therefore;

2. The equation of the line AB is; y - 6 = (1/3)·(x - (-1))

y - 6 = (1/3)·(x + 1)

y = (1/3)·(x + 1) + 6

The slope of the segment AE = (4 - 6)/(3 - (-1)) = -1/2

Slope of the segment BE = -1/(-1/2) = 2

Equation of BE is; y - 4 = 2·(x - 3)

y = 2·(x - 3) + 4 = (1/3)·(x + 1) + 6

Therefore, x = 5

y = (1/3)·(5 + 1) + 6 = 8

(ii) Area of the triangle EBC = 24 unit²

EB = (1/2) × √((5 - 3)² + (8 - 4)²) = √20

Therefore;

BC = 24/(√20) = 12/√5 = 12·√5/5 = √(28.8)

(x - 5)² + (y - 8)² = 28.8

y = 4, therefore;

(x - 5)² + (4 - 8)² = 28.8

(x - 5)² = 28.8 - (4 - 8)² = 12.8

x = √(12.8) + 5

(iii) The equation of the segment AD is; y - 4 = (-1/2)(x - 3)

x = √(12.8) + 5

Therefore;

y - 4 = (-1/2)((√(12.8) + 5) - 3)

y = (-1/2)((√(12.8) + 5) - 3) + 4 ≈ 1.21

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Answer:

x=0

Step-by-step explanation:

You can combine the equation to get 2sin(3/2 +x) = -2

divide both sides by 2 and you get the equation equal to -1. sin is equal to -1 when the value inside is 3/2 so this is the answer.

The total principal and interest payment that Nelson will have to pay after 2 months is $4665.50.

To calculate the total principal and interest payment, we need to determine the interest amount and add it to the principal.

First, let's find the interest amount:

Interest = Principal x Interest Rate x Time

Given:

Principal = $4650

Interest Rate = 2% per year

Time = 2 months

Since the interest rate is given on an annual basis, we need to convert the time from months to years. There are 12 months in a year, so 2 months is equivalent to 2/12 = 1/6 years.

Interest = $4650 x 0.02 x (1/6) = $15.50

Now, we can calculate the total principal and interest payment:

Total Payment = Principal + Interest

Total Payment = $4650 + $15.50 = $4665.50

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Answer:

10.7

Step-by-step explanation:

Since this is a right triangle, we can use trig functions to calculate the hypotenuse.

We know the opposite side from the angle labeled 59 degrees.

sin 59 = opp side / hypotenuse

sin 59 = 9.2/x

x = 9.2/ sin 59

x = 10.733

Answer:

Here's the general rule for rounding:

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. Example: 38 rounded to the nearest ten is 40. ...

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down. Example: 33 rounded to the nearest ten is 30.

The answer is:

g(x + 1) = 6x + 1

g(4x) = 24x -5

Work/explanation:

To evaluate, I plug in x + 1 into the function:

\(\sf{g(x)=6x-5}\)

\(\sf{g(x+1)=6(x+1)-5}\)

Simplify

\(\sf{g(x+1)=6x+6-5}\)

\(\sf{g(x+1)=6x+1}\)

------------------

Do the same thing with g(4x)

\(\sf{g(4x)=6(4x)-5}\)

\(\sf{g(4x)=24x-5}\)

Hence, these are the answers.

Answer:

a number divided by 7=x÷7

Answer:

Step-by-step explanation:

NM=26

LM=\(\sqrt{26^{2} +33^{2} }\)

LM=42.0

Answer:

f(g(x)) = 50x² + 140x + 93

Step-by-step explanation:

f(g(x)) means that within the f(x) equation, you want to replace all of the x variables with the g(x) equation.

So,

f(g(x)) = 2 (5x+7)² -5

= 2 ( 25x²+ 70x + 49) - 5

= 50x² + 140x + 93

:)

To find the value of x, we can set the two angle measures equal to each other and solve for x.

Given:

mZA = (4x - 2)°

mZB = (6x - 20)°

Setting them equal to each other:

4x - 2 = 6x - 20

Now, we can solve for x:

4x - 6x = -20 + 2

-2x = -18

Dividing both sides by -2:

x = -18 / -2

x = 9

Therefore, the value of x is 9.

Answer:

The answer is 9.

Step-by-step explanation:

We need to use the fact that the sum of the angles in a triangle is 180 degrees. Let A, B, and C be the three angles in the triangle. Then we have:

mZA + mZB + mZC = 180°

Substituting the given values, we get:

(4x - 2)° + (6x - 20)° + mZC = 180°

Simplifying the left side, we get:

10x - 22 + mZC = 180°

Next, we use the fact that angles opposite congruent sides of a triangle are congruent. Since we know that segment AC and segment BC are congruent, we have:

mZA = mZB

Substituting the given values and simplifying, we get

4x - 2 = 6x - 20

Solving for x, we get:

x = 9

Therefore, the value of x is 9.

Answer: To convert liters of fuel oil burned in hours to gallons, we can use the conversion factor that 1 gallon is equal to 3.785 liters. The formula for the conversion can be represented as a function:

def liters_to_gallons(liters):

   return liters / 3.785

Here, the input liters represents the number of liters of fuel oil burned in hours, and the output of the function is the equivalent number of gallons. The function performs the conversion by dividing the input value (in liters) by the conversion factor (3.785).

Answer:

-------------------

As per recipe, 700 g apples is enough to make apple crumble for 8 people.

For 6 people Shahina needs:

Since she has 550 grams of apple, which is more than 525 grams, she can make it for 6 people.

Answer:

With 550g of apples and enough other ingredients, Shahina can make apple crumble for 6 people according to the given recipe.

Step-by-step explanation:

Let's compare the recipe requirements with the available ingredients to determine whether Shahina can make apple crumble for 6 people with the given ingredients.

The recipe serves 8 people and requires the following quantities of ingredients:

Shahina has 550g of apples, which is sufficient to meet the apple requirement of the recipe.

Now, let's calculate the ratio of the other ingredients needed per person

For sugar:

240g / 8 people = 30g/person

For flour:

180g / 8 people = 22.5g/person

For butter:

40g / 8 people = 5g/person

Since the recipe is designed to serve 8 people, we can use these ratios to adjust the quantities for 6 people:

For sugar:

30g/person * 6 people = 180g

For flour:

22.5g/person * 6 people = 135g

For butter:

5g/person * 6 people = 30g

Comparing these adjusted quantities to the available ingredients, we see that Shahina has enough sugar, flour, and butter to make an apple crumble for 6 people.

Answer:

It takes the electrician 4 hours to complete the job

Step-by-step explanation:

This question can be solved using a rule of three.

In 2/3 of an hour, he completes a sixth of a job. So how many hours does it take for him to complete the job(which is 100% = 6/6 = 1)?

2/3 hour - 1/6 of the job

x hours - 1 of the job

\(\frac{1}{6}x = \frac{2}{3}\)

Applying cross multiplication

\(3x = 6*2\)

\(3x = 12\)

\(x = \frac{12}{3}\)

\(x = 4\)

It takes the electrician 4 hours to complete the job

Answer:

B. 11 1/4

Step-by-step explanation:

8 3/4 + 2 2/4 = 11 1/4

We want to sum two mixed numbers.

The correct option is D: 11 1/4

A mixed number is a number that is separated into a whole part and a rational part.

Here we want to sum:

(8 3/4) + (2 1/2)

This can be written as:

8 + 3/4 + 2 + 1/2

Now we group the whole numbers and we group the rational numbers:

8 + 3/4 + 2 + 1/2 = (8 + 2) + (3/4 + 1/2) = 10 + (3/4 + 1/2).

To perform the sum of the rational numbers, we can write:

1/2 = 2/4

Then we have:

10 + (3/4 + 1/2) = 10 + (3/4 + 2/4) = 10 + 5/4 = 10 + 4/4 + 1/4 = 11 + 1/4

Then we can see that the correct option is D.

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Answer:

5

Step-by-step explanation:

use the distributive property

6 * 1/2 = 3

6 * 1/3 = 2

3 + 2 = 5

Hope this helped! Have a nice rest of ur day! Plz mark as brainliest!!!

-Lil G

Answer:

Hence the possible values of m are m > 14

So, the dairy farm produced greater than 14 kg of cheese

Step-by-step explanation:

We have m = kg of cheese,

let y = yogurt

and i = ice cream,

The dairy farm also produced 28 kg more yoghurt than cheese

y = m + 28

3 times as much ice cream as cheese

i = 3m

The dairy farm produced more kilograms of ice cream than yoghurt last week

i > y

so we have,

y = m + 28  (i)

i = 3m  (ii)

i > y  (iii)

Now, using (i) and (ii) in (iii),

i > y

3m > m + 28     (i = 3m, y = m + 28)

subtracting m from both sides,

3m - m > m - m + 28

2m > 28

dividing by 2 on both sides,

m > 28/2

m > 14

Answer:

radius = 1.4

Step-by-step explanation:

The formula for circumference is as follows:

\(C = d\pi\)

or

\(C = 2r\pi\)

However, these formulas are the same, because the diameter is equal to the radius times 2. I prefer to use the first (it gives you less values to work with).

Anyhow, We would substitute like this:

\(8.8 = d\pi\)

We know that pi, is going to be equal to: 3.14159

So we work from there...

\(8.8=d(3.14159)\\2.8011=d\)

Diameter divided by 2 would be the radius, and thats:

1.4006

or 1.4

Answer:

17/20

Step-by-step explanation:

3/5+1/4=12/20+5/20 (you want to find a common denominater, so its easier to add up.)

12/20+5/20=17/20, so Carla has finished washing 17/20 of her laundry.

Answer:

B. The limits Lim x-->7 (x²-9x+14)/x-7  and  lim x--> 7 (x-2) equals the same number when evaluated using direct substitution. The limit of both functions is 5

Step-by-step explanation:

Find the complete question in the attachment.

Given the limit of the functions

Lim x-->7 (x²-9x+14)/x-7

To solve this, we will need to factorize the quadratic function at the numerator first.

x²-9x+14

= x²-2x-7x+14

= x(x-2)-7(x-2)

= (x-7)(x-2)

The expression therefore becomes:

= lim x-->7 (x-7)(x-2)/x-7

= lim x-->7 (x-2)

Now substitute the value of x into the simplified function

lim x-->7 (x-2) = 7-2

lim x-->7 (x-2) = 5

Hence Lim x-->7 (x²-9x+14)/x-7 = 5

From the calculation above, it can be seen that Lim x-->7 (x²-9x+14)/x-7 = lim x--> 7 (x-2) = 5

Hence the correct answer based on the explanation above is B.

The limits Lim x-->7 (x²-9x+14)/x-7  and  lim x--> 7 (x-2) equals the same number when evaluated using direct substitution.

Answer:

42 degrees

Step-by-step explanation:

We already have the two angles for the triangle, we just need the third. For triangles, the can only add up to 180 degrees. 101+37=138 degrees, now we subtract 138 from 180.

180-138=42.

Answer:

\( {5}^{ \frac{1}{12} } = \sqrt[12]{5} \)

Step-by-step explanation:

\( \frac{ \sqrt[3]{5} }{ \sqrt[4]{5} } = {5}^{ \frac{1}{3} } \div {5}^{ \frac{1}{4} } = {5}^{ \frac{4}{12} } \div {5}^{ \frac{3}{12} } = {5}^{ \frac{1}{12} } = \sqrt[12]{5} \)

THIS IS THE ANSWER: 5 to the power of one-twelfth (Take a look at the image if this does not make sense) :))

:))

:)))   HAPPY SLAPPY!!!!

:))))

"UPDATE" : This was correct on my test. Also I realized to see the image in this answer keep your cursor on the side of your screen, not on the image :D

Using double angle identity, we are able to prove tan(x)(1 + cos(2x)) = sin(2x).

To prove the identity tan(x)(1 + cos(2x)) = sin(2x), we can start by using trigonometric identities to simplify both sides of the equation.

Starting with the left-hand side (LHS):

tan(x)(1 + cos(2x))

We know that tan(x) = sin(x) / cos(x) and that cos(2x) = cos²(x) - sin²(x). Substituting these values, we get:

LHS = (sin(x) / cos(x))(1 + cos²(x) - sin²(x))

Next, we can simplify the expression by expanding and combining like terms:

LHS = sin(x) / cos(x) + sin(x)cos²(x) / cos(x) - sin³(x) / cos(x)

Simplifying further:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

Now, let's work on the right-hand side (RHS):

sin(2x)

Using the double angle identity for sine, sin(2x) = 2sin(x)cos(x).

Now, let's compare the LHS and RHS expressions:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

RHS = 2sin(x)cos(x)

To prove the identity, we need to show that the LHS expression is equal to the RHS expression. We can combine the terms on the LHS to get a common denominator:

LHS = [sin(x) - sin³(x) + sin(x)cos²(x)] / cos(x)

Now, using the identity sin²(x) = 1 - cos²(x), we can rewrite the numerator:

LHS = [sin(x) - sin³(x) + sin(x)(1 - sin²(x))] / cos(x)

    = [sin(x) - sin³(x) + sin(x) - sin³(x)] / cos(x)

    = 2sin(x) - 2sin³(x) / cos(x)

Now, using the identity 2sin(x) = sin(2x), we can simplify further:

LHS = sin(2x) - 2sin³(x) / cos(x)

Comparing this with the RHS expression, we see that LHS = RHS, proving the identity.

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