A function f(x) has x-intercepts of -3 and -5 what is the constant term in the function f(x)=x^2+8x+

Answer:

A, B, A

Step-by-step explanation:

(3)

Given

- 2x² + 10x + 12 ← factor out - 2 from each term

= - 2(x² - 5x - 6) ← factor the quadratic

Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (- 5)

The factors are - 6 and + 1, since

- 6 × 1 = - 6 and - 6 + 1 = - 5, thus

x² - 5x - 6 = (x - 6)(x + 1) and

- 2x² + 10x + 12 = - 2(x - 6)(x + 1) → A

(4)

[tex]x^{4}[/tex] - 81 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b), thus

[tex]x^{4}[/tex] - 81

= (x² )² - 9²

=(x² - 9)(x² + 9) ← note that x² - 9 is also a difference of squares

= (x - 3)(x + 3)(x² + 9) ← in factored form

x² - 3 is not a factor → B

(5)

Given

5[tex]x^{4}[/tex] - 320 ← factor out 5 from each term

= 5([tex]x^{4}[/tex] - 64) ← difference of squares

= 5(x² - 8)(x² + 8) → A

Answer:

5.83 ft

Step-by-step explanation:

Given that

Scale factor, n = 10

Wall in blueprint = 7 in

To find:

Length of actual wall = ?

Solution:

Whenever a blueprint is created for any house or building, it is made smaller by a scale factor.

Here this factor is 10 times.

That means, the blueprint size is 10 times smaller than that of its actual size.

Or we can say that actual wall of building is 10 times the wall of blueprint.

So, wall of building = 10 [tex]\times[/tex] 7 = 70 inches

Now, we know that 12 inches = 1 ft

1 inch = [tex]\frac{1}{12}\ ft[/tex]

70 inches = [tex]\frac{1}{12}\times 70\ ft = 5.83\ ft[/tex]

so, the answer is Wall of building is 5.83 ft.

====================================================

Explanation:

This is a visual example of the pythagorean theorem. We add the areas of the two squares to get

13+29.25 = 42.25

Then we apply the square root to this to get the value of x, which is the hypotenuse of the right triangle

x = sqrt(42.25) = 6.5

---------

Side note: if you're curious about finding the other lengths of the triangle, apply the square root to those areas. The blue area 29.25 will lead to a side length of approximately sqrt(29.25) = 5.4083269; the red square will follow the same idea.

Answer:

Step-by-step explanation:

area of a square=a²

A=29.25

a=side=√29.25 first square

second square =a=√13

find x(c)

right triangle: a²+b²=c²

(√29.25 )²+(√13)²=c²

29.25+13=c²

c=√(29.25+13)=6.5 unit

Answer:

work is shown and pictured

The solution to the system of linear equation is (x, y) = (6, 2)

3x - 2y = 14 (1)

3x - 2y = 14 (1)5x + y = 32 (2)

From (2)

y = 32 - 5x

Substitute y = 32 - 5x into (1)

3x - 2y = 14 (1)

3x - 2(32 - 5x) = 14

3x - 64 + 10x = 14

13x = 14 + 64

13x = 78

x = 78/13

x = 6

Substitute x = 6 into (2)

5x + y = 32 (2)

5(6) + y = 32

30 + y = 32

y = 32 - 30

y = 2

(x, y) = (6, 2)

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Answer:

<BAC ≅ BCA by rule Base angle theorem

Step-by-step explanation:

What we know:

BAC = DAC

BC = BA

ΔBCA is an isosceles so ∠BCA  =  ∠DCA and ∠BAC

and we found that out by base angle theorem since

Base angle Theorem  = Two base angles of a icosceles triangle are equal.

And since ΔBCA is an isoceles then ∠A and ∠C will be equal. And so we can prove BC is a parallel to AD

The proof that BC ∥ AD from the given statements is that;

BC ∥ AD because of the definition of alternate angles

We are given;

AB = BC  

 AC is ∠ bisector of ∠BAD

Since AC is the angle bisector of ∠BAD, it means that;

∠BAC  = ∠DAC (definition of a bisected angle)

Now, since AB = BC, it means that ΔBCA is an isosceles triangle.

Thus; ∠BCA = ∠BAC  (base angle theorem)

Now, since ∠BCA = ∠BAC, and ∠BAC  = ∠DAC, we can say that;

∠BCA = ∠DAC

This means  ∠BCA and ∠DAC are alternate angles. Thus, we can say that AC is the transversal line carrying the two equal angles.

Thus, we can say that BC is parallel to AD as they are the parallel lines cut by the transversal line AC.

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Answer:

45.29 miles per hour

Step-by-step explanation:

Speed is the distance over time.  To find the average rate of speed for a trip, we simply need to take the total distance divided by the total time.

Avg. Speed = (188 miles + 197 miles) / (4 hours + 4.5 hours)

Avg. Speed = 45.29 miles per hour

Hence the average rate of speed for the trip was 45.29 miles per hour.

Cheers.

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

Edit:  Thanks to Chegsnut36 for calculation correction

Answer:

≅45.29

Step-by-step explanation:

Hey there!

To find the average rate speed we need to add all the same number.

188 + 197 = 385

4 + 4.5 = 8.5

Now to find the average rate we do,

385 ÷ 8.5 ≅ 45.29

Hope this helps :)

Answer:

Step-by-step explanation:

Total cookies = 12

Ate = 3 cookies

Now,

Percentage of the cookies that James are:

[tex] \frac{3}{12} \times 100 \: percent[/tex]

Calculate:

[tex] = 25 \: percent[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

answer is 25

Step-by-step explanation:

Answer:

Time taken (t) = 2.67 s (Approx)

Step-by-step explanation:

Find:

Time taken (t)

Given:

Initial velocity (u) = 0 m/s

Acceleration due to gravity(a) = -9.8 m/s²

Distance (d) = -35 m

Computation:

Using 2nd equation of motion,

d = ut + (1/2)at²

-35 = (0)t + (1/2)(-9.8)t²

-35 = -4.9 (t²)

t² = 7.1428

t = 2.6726

Time taken (t) = 2.67 s (Approx)

Answer:

The perimeter of the figure is: 8x + 34.

Step-by-step explanation:

The perimeter of a shape is the sum of the length of all its sides. In this case there is one side missing, we need to find its length. To do that we will have to use Pythagora's theorem, because we will create a right triangle as shown in the attached picture. Where a, b and c are the sides of the right triangle. We can determine the lengths of a and c. If we pay close attention to the figure we will realize that a is:

[tex]a = 2x + 5 - 2x = 5[/tex]

While c is:

[tex]c = 2(x + 7) - (x + 5) - (x - 3)\\c = 2x + 14 -x - 5 -x + 3\\c = 2x - 2x + 12\\c = 12[/tex]

We can now apply Pythagora's theorem:

[tex]b^2 = a^2 + c^2\\b^2 = 5^2 + 12^2\\b^2 = 25 + 144\\b = 13[/tex]

With this we can sum all the sides and calculate the perimeter of the shape.

[tex]2x + 5 + x - 3 + 2x + x + 5 + 13 + 2(x + 7)\\2x + x + 2x + x + 2x + 5 - 3 + 5 + 13 + 14\\8x + 34[/tex]

Answer:

No

Step-by-step explanation:

He's not correct because 5a² isn't a factor of a³ or 35b⁴; in order for something to be the GCF of a polynomial, all of the terms must be evenly divisible by it.

Answer:

a^3 – 25a^2b^5 – 35b^4

He is incorrect since the coefficient of the a^3 term is 1, the GCF cannot contain a coefficient of 5. Also, there is no a in all terms, so a^2 is also not a common factor.

Answer:

WX = 8 mm

Step-by-step explanation:

To be able to solve for WX, we need to first find the size of angle [tex]\angle z[/tex].

We use the law of sines in the blue triangle to do such:

[tex]\frac{sin(z)}{11} =\frac{sin(133)}{20} \\sin(z)=\frac{11\,sin(133)}{20} \\sin(z)=0.4022[/tex]

Now we can use this value in the larger right angle triangle where WX is the opposite side to angle  [tex]\angle z[/tex], and the 20 mm side is the hypotenuse:

[tex]sin(z)=\frac{opposite}{hypotenuse} \\sin(z)=\frac{WX}{20}\\0.4022=\frac{WX}{20}\\WX=20\,(0.4022)\\WX=8.044\,\,mm[/tex]

which rounded to the nearest integer gives

WX = 8 mm

How can we tell? Look at the vertical lines inside the box. This is where the median is located. For movie A, the inner vertical line is somewhere between 30 and 40 (perhaps 35 or so). So this is the median for movie A. Meanwhile, the median for movie B is somewhere between 40 and 50. I'd say maybe 46 or 47 as its a bit higher than the halfway point.

-----------

Extra info:

Answer:

Hey there!

We must use what we are given, so even though it looks like there might be four isosceles triangles, we are only given CA=CE, so that only allows us to conclude mathematically that there is only 1 isosceles triangle.

Hope this helps :)

As x approaches infinity,

The function with the lowest output is graph A

The function with the greatest output is graph B

===========================================================

Explanation:

As the graphs head to the right, they go up forever. However, the growth rate (how fast they go upward) varies. The red straight line (line A) goes up the slowest. The growth rate is the same throughout the entire function. The rate is the slope of the line. In contrast, the purple curve B goes up the fastest as it has the steepest increase among the four graphs. The graph steadily gets steeper as you move to the right.

The exponential graph will grow the fastest compared to a linear one or parabolic one. Graphs B and C are exponential, where graph B has a steeper curve compared to graph C.

Answer: The function with the lowest output values as x approaches infinity is Graph A.

The function with the greatest output values as x approaches infinity is Graph B.

Step-by-step explanation: I can’t give you a step-by-step explanation, but this is right!

Answer:

The function is:

y = 150*x

where y is the number of calories consumed, and x is the number of pieces of candy consumed.

Now, the domain of a function is the possible values of x that you can input in the function.

For this particular case you can have:

x = 0 (no pieces candy)

x = 1 (one piece of candy)

x = 2 (two pieces of candy)

Notice that x can be only whole numbers because, in principle, you can't eat a fraction of a piece of candy.

So we only use x = whole numbers.

Then the domain of the function is equal to all the natural numbers plus the zero, or:

D = {x ∈ N ∪ {0}}

"x belongs to the union between the set of the natural numbers and the zero"

The amount of candies can only be positive values, hence the domain of the value exists on all natural numbers that are x≥0

The domain of a function is the input values of the function for which it exists.

Given the expression that relates the number of calories you consume after eating x pieces of candy as shown:

y = 150x

The amount of candies can only be positive values, hence the domain of the value exists on all natural numbers that are x≥0

The function is also discrete because the number of candies can be counted. Note that the domain of all discrete functions is countable.

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Answer:

10,000 panels

Step-by-step explanation:

A TV panel is being produced by two factory plants

Plant A produced 5000 fewer panels than plant B

Let a represent the number of panels produced by plant A and b represent the number of panels produced by plant B

a= b-5000............equation 1

5% of the panels from plant A were defective

= 5/100

= 0.05

2% of the panels from plant B were defective

= 2/100

= 0.02

The total defective panels of both plants is 450

0.05a + 0.02b= 450..............equation 2

Substitute b-5000 for a in equation 2

0.05(b-5000) + 0.02b= 450

0.05b - 250 + 0.02b= 450

Collect the like terms

0.05b+0.02b= 450+250

0.07b= 700

Divide both side by the coefficient of b which is 0.07

0.07 b/0.07= 700/0.07

b= 10,000

Hence plant B produced 10,000 panels

Answer:

$200 at 2%.

$2200 at 3.5%.

Step-by-step explanation:

Let the two amounts be x and y.

x earns 2% interest, and y earns 3.5% interest.

Since the total is $2400, then

x + y = 2400

Now we can solve for y and express the second amount in terms of x.

y = 2400 - y

The two amounts are x and 2400 - x.

In one interest period, the amount of interest earned is the amount of money in the account multiplied by the interest.

2% = 0.02; 3.5% = 0.035

The x amount earns 0.02x interest.

The y amount earns 0.035y interest.

The total interest earned is the sum of the interest amounts of the two accounts.

0.02x + 0.035y

We now replace y with 2400 - x, and we set the sum of the interest amounts equal to the total interest earned, $81.

0.02x + 0.035(2400 - x) = 81

The equation above is the linear equation.

Now we solve it. Distribute on the left side.

0.02x + 84 - 0.035x = 81

Combine like terms on the left side.

-0.015x + 84 = 81

Subtract 84 from both sides.

-0.015x = -3

Divide both side by -0.015.

x = 200

$200 was deposited in the account earning 2%.

y = 2400 - x

y = 2400 - 200

y = 2200

$2200 was deposited in the account earning 3.5%.

Answer:

2 28ounce cans and 4 15ounce cans

Step-by-step explanation:

28+28=56 and 15+15+15+15=60

56+60=116

Answer:

your answer is the second option

Step-by-step explanation:

Answer:

7√2 cm

Step-by-step explanation:

Aquí, estamos interesados ​​en encontrar la longitud del lado de un cuadrado que tiene una longitud diagonal de 14 cm.

Una diagonal es una línea que se extiende desde un borde del cuadrado hasta el otro borde del cuadrado internamente.

Ahora, una diagonal de un cuadrado junto con dos lados de un cuadrado forman un triángulo rectángulo isósceles, siendo la diagonal la hipotenusa de este triángulo rectángulo.

Sabemos que los lados de un cuadrado tienen la misma longitud y, por lo tanto, llamemos a este lado desconocido x cm.

Matemáticamente, según el teorema de Pitágoras, el cuadrado de la hipotenusa es igual a la suma de los cuadrados de los otros dos lados.

Por lo tanto, tenemos;

14 ^ 2 = x ^ 2 + x ^ 2

196 = 2x ^ 2

dividir ambos lados por 2

98 = x ^ 2 x = √98

x = √ (49 * 2)

x = 7√2 cm

Por lo tanto, la longitud del lado del cuadrado es de 7√2 cm

Answer:

Option A is the correct option

Step-by-step explanation:

[tex]5x = 35[/tex]

Divide both sides of the equation by 5

[tex] \frac{5x}{5} = \frac{35}{5} [/tex]

Calculate

[tex]x = 7[/tex]

Hope this helps...

Best regards!!

Answer:

Option A

Step-by-step explanation:

5x = 35

5x/5 = 35/5

x = 7

Answer:

Part 2:

The shape of a banana cut in 45° angle is that of a curve that is closed with the appearance of a flattened circle or an oval similar to an ellipse therefore having two focal points

The drawing of the angle cross section of a cylinder representing the banana is attached

Part 3:

When the banana is cut in half, perpendicular to the base of the banana, the shape formed is circular withe the center of the banana being about the same location as the center of the circle

The drawing of the perpendicular cross section of a cylinder representing the banana is

Step-by-step explanation:

Answer:

x + y = 500

215x + 615y = 187,500

Step-by-step explanation:

The first equation can show the amount of land.  The farmer has 500 acres to plant corn, x, and cotton, y.

x + y = 500

The second equation can show the cost.  The farmer has $187,500 to invest when corn costs $215 per acre and cotton costs $615 per acre.

215x + 615y = 187,500

The system of equations is

x + y = 500

215x + 615y = 187,500

The correct system of represents this scenario will be,

⇒ x + y = 500

⇒ 215x + 615y = 187,500

Where,' x' is plant acres of corn and 'y' is acres of cotton.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A farmer has 500 acres to plant acres of corn, x, and acres of cotton, y.

And, Corn costs $215 per acre to produce, and cotton costs $615 per acre to produce. He has $187,500 to invest this season.

Now,

Let us take  'x' is plant acres of corn and 'y' is acres of cotton.

Since, A farmer has 500 acres to plant acres of corn, x, and acres of cotton, y.

So, we can formulate;

⇒ x + y = 500

And, He has $187,500 to invest this season for corn costs $215 per acre to produce, and cotton costs $615 per acre to produce.

So, We can formulate;

⇒ 215x + 615y = 187,500

Thus, The correct system of represents this scenario will be,

⇒ x + y = 500

⇒ 215x + 615y = 187,500

Where,' x' is plant acres of corn and 'y' is acres of cotton.

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Answer:

50

Step-by-step explanation:

The value of P(A|B) = 0.50 which is correct option(B)

What is independent events?

Independent events is defined as an event that is not affected by other events.

A and B are independent events.

P(A) = 0.50

P(B) = 0.20

P(A|B) = P(A∩B)/P(B)

P(A|B) = P(A).P(B)/P(B)

P(A|B) = P(A)

Substitute the value of P(A) = 0.50,

P(A|B) = 0.50

Hence, the value of P(A|B) = 0.50

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Answer:

Option (4)

Step-by-step explanation:

In the given picture,

Trapezoid PQRS has two points T and U as the midpoints of sides PS and RQ.

Segment TU joins the midpoints of the sides PS and RQ.

Mid-segment theorem states that "If a line joining midpoints of a trapezoid is parallel to the bases, length of this segment is half the sum of lengths of the bases."

Therefore, m(TU) = [tex]\frac{1}{2}(m\text{PQ}+m\text{SR})[/tex]

7x - 26 = [tex]\frac{1}{2}[(3x+23)+(9x-3)][/tex]

7x - 26 = 6x + 10

7x - 6x = 26 + 10

x = 36

m(TU) = 7x - 26

          = 7(36) - 26

          = 252 - 26

          = 226

Therefore, Option (4) will be the answer.

Answer:

[tex]\frac{\sqrt{3} }{4} a^2[/tex]

Step-by-step explanation:

To find the area of an equilateral triangle, we can apply a formula.

[tex]A=\frac{\sqrt{3} }{4} s^2[/tex]

[tex]A= area\\s=side \: length[/tex]

The side length is given a.

Plug a in the formula as the side length.

[tex]A=\frac{\sqrt{3} }{4} a^2[/tex]

Answer:

3 square root over 4 a square

Step-by-step explanation:

Step-by-step explanation:

v= 4/3πr³

4/3×314/100×8×8×8

•

= 2,143.573

Step-by-step explanation:

this is substitution method

Answer:

2x + y = 21

+

x - y = 6

_________

3x = 27

x = 27 ÷ 3

x= 9

x - y = 6

9 - y = 6

9 - 6 = y

3 = y

Therefore, x= 9 and y = 3

Answer:

The angle created between the ladder and tree is [tex]15.5^{0}[/tex].

Step-by-step explanation:

The required sketch is shown in the attachment to this answer.

Applying the appropriate trigonometric function to the question, we have;

Tan θ = [tex]\frac{Opposite side}{Adjacent side}[/tex]

         = [tex]\frac{5}{18}[/tex]

         = 0.2777777777

⇒ θ = [tex]Tan^{-1}[/tex] 0.2777777777

      = 15.5241

      = [tex]15.5^{0}[/tex]

Therefore, the angle created between the ladder and tree is [tex]15.5^{0}[/tex].

Answer:

Step-by-step explanation:

inequality is a equation with |x|

a inequality equation is like this..

|x|>7

Answer:

what expressions?

Step-by-step explanation: