When the factors of a trinomial are (x-p) and (x+q) then the constant teen of the trinomial is

Answers

Answer 1

(x-p)(x-q)

y(x-q) .... let y = x-p

yx - yq ... distribute

x(y) - q(y)

x(x-p) - q(x-p) ... replace y with x-p

x^2 - px - qx + pq .... distribute

x^2 + (-p-q)x + pq

The last expression is in the form ax^2+bx+c with a = 1, b = -p-q and c = pq

The constant term is the term without any variable x attached to it (either x or x^2), so the constant term is pq


Related Questions


A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 4 centimeters long, and the height of the equilateral triangle is 3.5 centimeters. The pyramid's slant height is 8 centimeters. What is its surface area?

Answers

Answer:

The surface area is 55 cm².

Step-by-step explanation:

The formula to compute the surface area of the triangular pyramid is:

[tex]SA=(0.50\times \text{Base Perimeter}\times h)+\text{Base Area}[/tex]

Here h is the slant height.

Compute the Base perimeter as follows:

Perimeter of the equilateral triangle = 3 × side

                                                            = 3 × 4

                                                            = 12 cm

Compute the Base area as follows:

Area of the equilateral triangle = 0.50 × side × height

                                                    = 0.50 × 4 × 3.50

                                                    = 7 cm²

Compute the surface area as follows:

[tex]SA=(0.50\times \text{Base Perimeter}\times h)+\text{Base Area}[/tex]

     [tex]=(0.50\times 12\times 8)+7\\=48+7\\=55\ \text{cm}^{2}[/tex]

Thus, the surface area is 55 cm².

When a boy pulls his sled with a rope, the rope makes an angle of 70° with the horizontal. If a pull of 20 pounds on the rope is needed to move the sled, what is the horizontal component force?

7 lb
19 lb
20 lb
24 lb

Answers

Answer:

The answer to your question is 7 lbs.

Step-by-step explanation:

Data

angle = 70°

force = 20 lb

horizontal component

Process

To solve this problem just imagine a right triangle, where the force is the hypotenuse and the horizontal component is the adjacent side.

1.- Look for a trigonometric function that relates the adjacent side and the hypotenuse.

                  cos Ф = adjacent side / hypotenuse

- Solve for the adjacent side

                  adjacent side = hypotenuse x cosФ

- Substitution

                  adjacent side = 20 x cos 70

- Simplification

                  adjacent side = 20 x 0.342

- Result

                  adjacent side = 6.84 ≈ 7 lb  

find the positive square root of 26.77

Answers

Answer:5.173973328

Step-by-step explanation:

√ 26.77 = 5.17
Thus: 5.1739733 x 5.1739733 = 26.77

A golf analyst claims that the standard deviation of the 18-hole scores for a golfer is at most 3.5 strokes. State H_0 and H_a in words and in symbols. Then determine whether the hypothesis test for this claim is left-tailed, right-tailed, or two-tailed. Explain your reasoning. State the null hypothesis in words and in symbols.Choose the correct answer below.A. The null hypothesis expressed in words is. "the standard deviation of the 18-hole scores for a golfer is at least 3.5 strokes." The null hypothesis is expressed symbolically as. "H0:σ≥3.5."B. The null hypothesis expressed in words is. "the standard deviation of the 18-hole scores for a golfer is at most 3.5 strokes." The null hypothesis is expressed symbolically as. "H0:σ≤3.5."C. The null hypothesis expressed in words is. "the standard deviation of the 18-hole scores for a golfer is equal to 3.5 strokes." The null hypothesis is expressed symbolically as. "H0:σ=3.5."D. The null hypothesis expressed in words is. "the standard deviation of the 18-hole scores for a golfer is not 3.5 strokes." The null hypothesis is expressed symbolically as. "H0:σ≠3.5."

Answers

Answer:

The correct option is (C).

Step-by-step explanation:

The claim made by the golf analyst is:

Claim: The standard deviation of the 18-hole scores for a golfer is at most 3.5 strokes.

A standard deviation test is to be performed.

The hypothesis for the test will be defined as follows:

H₀: The standard deviation of the 18-hole scores for a golfer is 3.5 strokes, i.e. σ = 3.5.

Hₐ: The standard deviation of the 18-hole scores for a golfer is at most 3.5 strokes, i.e. σ ≤ 3.5.

Thus, the correct option is (C).

While traveling in England, Sonia noticed that the price of gas was 1.4 pints per liter. She wondered how that compares to the price of gas in Atlanta, where she lives. On that day, the exchange rate was £1= $1.56. Set up and evaluate a conversion expression to find the equivalent price in dollars per gallon. Use the conversion factor 1L=0.26 gal.

Answers

Answer:

The price in dollars per gallon is 8.4

Step-by-step explanation:

The ratio is a comparison between two quantities that is made using a quotient. In other words, a ratio is a comparison between two or more quantities that can be expressed as a fraction. If the quantities to be compared are a and b, the ratio between them is written as: [tex]\frac{a}{b}[/tex]

You know that the price in England is 1.4 pounds per liter and the current exchange rate is 1 pound = 1.65 dollars. So, being the following reasons:

[tex]\frac{1.4 pounds}{1 liter}[/tex][tex]\frac{1.56 dollars}{1 pound}[/tex]

and being the conversion factor 1 L = 0.26 gal expressed as a ratio:

[tex]\frac{1 liter}{0.26 gal}[/tex]

you can see that the expression to find the equivalent price in dollars per gallon is:

[tex]\frac{1.4 pounds}{1 liter}*\frac{1.56 dollars}{1 pound}*\frac{1 liter}{0.26 gal}[/tex]

Taking into account that all unwanted units of measure are canceled and solving:

[tex]\frac{1.4 pounds}{1 liter}*\frac{1.56 dollars}{1 pound}*\frac{1 liter}{0.26 gal}=\frac{2.184 dollars}{0.26gal}= 8.4 \frac{dollars}{gal}[/tex]

The price in dollars per gallon is 8.4

5 of 17Questions Question 5 Safiya needs to find a number that can be multiplied by 18−−√3 to result in a rational product. Which values could she use? Select all that apply.

Answers

Answer:

18 + √3

Step-by-step explanation:

The product of a surd and its conjugate gives a rational number. Hence;

(18 - √3) (18 + √3)

=324 + 18√3 - 18√3 - 3

=321

A rational number does not contain any surd, hence the answer.

Answer: cube root 1/18 & cube root 12

Use the Law of Sines to find the missing angle of the triangle.

Find m < C to the nearest tenth if the c= 102, a = 71 and m < A=40

Answers

Answer:

66.9 degrees

Step-by-step explanation:

The Law of Sines states that a/sinA = c/sinC. Plugging in the values for c, a, and M < A, we get:

71/sin40 = 102/sinC

Cross multiplying, we get:

102(sin40deg) = 71(sinC)

Now, we simplify the left side and get:

65.56 = 71(sinC)

Next, we divide 65.56 by 71 to get:

0.92 = sinC

Taking the inverse sign we get:

C = 66.9 degrees

1,400 is 10 times as much as 140- true or false

Answers

Answer:

True

Step-by-step explanation:

140 * 10 = 1400

True

After taking off from the landing pad, a helicopter flies 3 miles west, then 2 miles southeast. How far is the helicopter from the landing pad? If someone could explain to that would be very helpful

Answers

Answer:

When the plane makes its turn to fly southeast, it makes a 45º angle at point a, making angle abc also equal to 45º.  

Line ab is the 2 miles southeast the plane flies.

Line ac = line cb

sine (45º) = opposite / hypotenuse = cb / 2

.70711 = cb / 2

cb = 1.41422  miles = line ac

Line cs = 3 - 1.41422 = 1.58578

Line x^2 = cs^2 + cb^2

Line x^2 = 2.5146982084  + 2.0000182084

Line x^2 = 4.5147

Line x = 2.1248

Step-by-step explanation:

Verify the identity. cos quanity x plus pi divided by two = -sin x

Answers

Answer:

see below

Step-by-step explanation:

cos ( x+pi/2) = -sinx

We know that

cos(A + B) = cos A cos B - sin A sin B

Let x = A and pi/2 = B

cos x cos pi/2 - sin x sin pi/2 = -sin x

We know cos pi/2 = 0  and sin pi/2 = 1

cos x * 0 - sin x *1 = -sin x

- sin x = - sin x

1/4x + 2/3 =19/12 I don’t understand how to do this equation

Answers

Answer:

X=11/13

Step-by-step explanation:

First, convert the non-variable fractions to a common denominator.

1/4x+8/12=19/12

1/4x=19/12-8/12

1/4x=11/12

x=11/12*4/1

x=44/12

x=11/3

A card is chosen at random from a standard deck of 52 cards. What is the probability that the card is a Queen or a $\diamondsuit$ (or both)?

Answers

Answer:

probability that the card is a Queen or a diamond= 0.3269

Step-by-step explanation:

There are 4 queen in a deck of cards and 13 diamond in a deck of cards.

And a deck of cards contains 52 cards total.

Probability of the card selected to be a queen = number of queen/total number of cards

Probability of the card selected to be a queen =4/52

Probability of the card selected to be a queen= 1/13

Probability of the card selected to be a diamond= number of diamond/ total number of cards

Probability of the card selected to be a diamond=13/52

Probability of the card selected to be a diamond=1/4

probability that the card is a Queen or a diamond= Probability of the card selected to be a queen + Probability of the card selected to be a diamond

probability that the card is a Queen or a diamond= 1/13+1/4

probability that the card is a Queen or a diamond= 0.3269

To celebrate the first day of a leap year, I taught my dog to jump through a hoop. It was a Sunday. When he taught me the same trick the first day of the next year, it was a ?

Answers

Answer:

Tuesday

Step-by-step explanation:

364/7 = 52, meaning that 364 days later will also be a Sunday. 2 days after that (366 as it is a leap year) would be a Tuesday.

There will be Tuesday when the dog jumps the next year.

What is the reasoning?

the process of applying logical reasoning to examine a situation in order to identify the optimal strategy for solving a specific problem, then using this approach to develop and justify a solution.

Reasoning is a tricky but interesting problem in mathematics that required relations of variables to solve.

Since when the dog jumped it was Sunday

Next Sunday will be at

364/7 = 52

So, after 52 weeks or 364 days, there will be next Sunday.

Since leap year is 366 days years

366 - 364 = 2

So, two days after Sunday is Tuesday.

Hence the day after next year when the dog jump will be Tuesday.

For more about reasoning,

https://brainly.com/question/2923977

#SPJ2

There are (43)2⋅ 40 strawberries on a farm. What is the total number of strawberries on the farm?

Answers

Answer:

3,440 strawberries

Step-by-step explanation:

Because of PEMDAS you want to start with the parentheses, and want to treat them like the distributive property.

So,

43 x 2 = 86

Then,

86 x 40 = 3440.

I hope that helps!!

Answer: 3440 strawberries on the farm.

Step-by-step explanation: (43)(2)⋅40                                                                     (86)(40)                                                                                                                     3440

Alexander bought a box of crackers at the store. He ate half of the crackers in the box on Monday, and he ate 1/2 of what was left on Tuesday. On Wednesday, he ate 1/3 of what was left after he was finished eating the crackers on Tuesday.
1) What fractional part of the total crackers originally in the box did Alexander
eat on Wednesday?
2) what fractional part of the total crackers originally in the box are left. 3) if there are 4 crackers left in the box after Alexander finished eating crackers on wensday, how many crackers were in the box before it was opened. (Please help!)

Answers

Answer:

1. 1/12x

2.1/6x

3. 18

Step-by-step explanation:

Let

x=number of crackers in the box

On Monday, Alexander are 1/2 of the crackers

1/2 of x

=1/2x

Remaining

x-1/2x=2x-1/2

=1/2x

Tuesday=1/2 of what was left

=1/2 of 1/2x

=1/2×1/2x

=1/4x

Remaining

1/2x-1/4x

=2x-x/4

=1/4x

Wednesday=1/3 of what was left

=1/3 of 1/4x

=1/12x

Remaining

1/4x-1/12x

=3x-x/12

=2/12x

=1/6x

1. What fractional part of the total crackers originally in the box did Alexander eat on Wednesday?

1/12x

2. what fractional part of the total crackers originally in the box are left.

1/6x

3. if there are 4 crackers left in the box after Alexander finished eating crackers on wensday, how many crackers were in the box before it was opened.

1/6x=3

Divide both sides by 1/6

1/6x ÷ 1/6 = 3 ÷ 1/6

x=3÷1/6

=3 × 6/1

=18

x=18

Answer:

1) 1/12

2) 1/6

3) 18

Step-by-step explanation:

An online company wants to establish ratings for the products they provide. To do so, they ask visitors to their website to evaluate the products and leave a "thumbs up" or a "thumbs down." What type of sample is this? Explain why.

Answers

Answer:

This is a group specific influence sample, it only shows a demographic sample of those that are influenced by the reviews in the first place.

Step-by-step explanation:

How many equations are thereof: 70 divided by h equals 10?
What are those equations?

Answers

Answer:

We have:

"70 divided by h equals 10"

We can write it in only one equation:

70/h = 10.

This is a rational equation because our variable is in the denominator of a quotient.

To solve it we can multiply by h on both sides of the equation and get:

(70/h)*h = 10*h

70 = 10*h

now we divide both sides by 10.

70/10 = (10*h)/10

7 = h.

cual es el area de un rectangulo

Answers

Answer:

Use this formula:

a = b * h

Where: "a", the area of the rectangle is equal to its "b" (base), multiplied by "h" (height)

Step-by-step explanation:

Usa esta formula:

a = b * h

Donde: "a", el área del rectángulo es igual a su "b" (base), multiplicado por "h" (su altura).

hi! i need to know the cube root of minus one!! just let me know down there!

Answers

Answer:

[tex]\large \boxed{\mathrm{-1}}[/tex]

Step-by-step explanation:

[tex]\sqrt[3]{-1}[/tex]

Apply radical rule:

[tex]\sqrt[n]{-1}=-1[/tex]

If [tex]n[/tex] is odd.

[tex]\sqrt[3]{-1}=-1[/tex]

8 times the sum of a and b

Answers

Answer:

c

Step-by-step explanation:

i did the quiz

Answer:

8(a + b)

Step-by-step explanation:

Sun of a and b = a + b

8 times of (a + b) = 8(a + b)

Determine the measure of the interior angle at vertex D. A. 27 B. 162 C. 20 D. 36

Answers

Answer:

162°

Step-by-step explanation:

The shape is a hexagon, so the interior angles equal 720. (N-2)*180=720

9x+9x+9x+2x+9x+2x=720

40x=720

x=720/40

x=18

D=9x=9(18)=162°

The sum of interior angles of a polygon with n sides is [tex](n-2)\cdot180[/tex]

In this case [tex]n=6[/tex]

Therefore

[tex]4\cdot9x+2\cdot2x=(6-2)\cdot180\\36x+4x=4\cdot180\\40x=720\\x=18[/tex]

[tex]9x=9\cdot18=162[/tex]

So B

Evaluate 1 3 m − 1 − 1 2 n 3 1 ​ m−1− 2 1 ​ nstart fraction, 1, divided by, 3, end fraction, m, minus, 1, minus, start fraction, 1, divided by, 2, end fraction, n when m = 2 1 m=21m, equals, 21 and n = 1 2 n=12n, equals, 12.

Answers

Answer:

  0

Step-by-step explanation:

Apparently, you want the value of ...

  [tex]\dfrac{1}{3}m-1-\dfrac{1}{2}n = \dfrac{m}{3}-\dfrac{n}{2}-1\\\\=\dfrac{21}{3}-\dfrac{12}{2}-1=7-6-1\\\\=\boxed{0}[/tex]

The value of the given expression for the given variable values is zero.

(-9) - 9n= (-45) please helpppp!

Answers

Answer: n=4

Step-by-step explanation:

[tex]\left(-9\right)-9n=\left(-45\right)[/tex]

add 9 to both sides

[tex]-9-9n+9=-45+9[/tex]

[tex]-9n=-36[/tex]

divide both sides by -9

[tex]n=4[/tex]

Brainliest please

━━━━━━━☆☆━━━━━━━

▹ Answer

n = 4

▹ Step-by-Step Explanation

(-9) - 9n = (-45)

Simple terms are written last:

-9 - 9 = -45

Group all the variable terms on one side, and all the constant terms on the other side:

(-9n - 9) + 9 = -45 + 9

n = 4

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Area of a trapeziod with a top base length of 6 cm a bottom base length of 12 cm and a height of 5 cm​

Answers

Answer:

A=45cm^2

Step-by-step explanation:

A= h/2(b1 + b2) for trapezoid

A=(5/2(6+12))cm^2

A=(2.5(18))cm^2

A=45cm^2

Describe the transformation. A. (x,y)→(x+5,y−3) B. (x,y)→(x−3,y+5) C. (x,y)→(x+3,y−5) D. (x,y)→(x−5,y+3)

Answers

Answer:

Option(A)

Step-by-step explanation:

From the graph attached,

Quadrilateral USTR has been transformed to get the image quadrilateral U'S'T'R'.

Coordinates of point U → (-2, 6)

Coordinates of point U' → (3, 3)

Coordinates of U and U' show that quadrilateral USTR has been shifted by 5 units to the right and 3 units down.

Rule to be followed for the translation,

U(-2, 6) → U'[(-2 + 5), (6 - 3)]

U(x, y) → U'[(x + 5), (y - 3)]

Therefore, Option (A) describes the correct rule of transformation.

a pizza shop offers 30% of the price of a large pizza every tuesday night. if the regular price is 25, what is the discount price?

Answers

Answer:

17.50

Step-by-step explanation:

First find the discount

25 * .3

7.5

Subtract this from the original price

25-7.5

17.50

If Jim Roller can paint a room in 3 hours while John Brush would take 5 hours, how long will they take if they work together?

Answers

Answer:

4 hrs

Step-by-step explanation:

half of Jim Rollers time is 1.5 hrs, and half of John Brushs time is 2.5 hrs. The two combined is 4 hrs. Therefore, the answer is four hours.

This is basically finding the average of two numbers, and you can use multiple different equations to find the same answer.

3/2 + 5/2 =4

(3+5)/2 =4

5-3=2, then 2/2=1, 5-1=4

Answer:

1 7/8 hours

Step-by-step explanation:

Help pleasee!!! Tyyyyy

Answers

Answer:

G. 7

Explanation:

The longest side must be less than the sum of the two shorter sides.

The difference between the longest and shortest sides must be less than the middle side.

l+a = 11

l < (a + 4) ... l < (11 - l + 4)

... 2 l < 15 ... l <  7.5

--Variables

l = 7 (Longest Side/Answer)

a = 4 (Other Missing Length)

m = 4 (Side Given)

multiplying polinomiyal(5x+2)(3x+4)​

Answers

Answer:

(5x+2) (3x+4)

= 15x²+20x+6x+8

= 15 x²+ 26x+8

Hope this helps ^_^

Answer:

Step-by-step explanation:

Use FOIL method

(5x + 2)(3x + 4) = 5x * 3x + 5x *4 + 2*3x +2*4

                        = 15x² + 20x + 6x + 8    { now add like terms}

                       = 15x² + 26x + 8

(3-1) (4+2) + 9 - 3 I need help

Answers

Answer:

18

Step-by-step explanation:

(3-1) (4+2) + 9-3 =

2 • 6 + 6 = 12 + 6

= 18

Answer:

[tex]\displaystyle 18[/tex]

Step-by-step explanation:

[tex]\displaystyle (3 - 1)(4 + 2) + 9 - 3 = [(2)(6)] + 9 - 3 = 12 + 9 - 3 = 12 + 6 = 18\:[OR\:21 - 3 = 18][/tex]

G - Grouping Symbols

E - Exponents

M\D - Division & Multiplication [left to right]

A - Subtraction & Addition [right to left OR vice versa]

I am joyous to assist you at any time.

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