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Can someone plz help me solved this problem I need help ASAP plz help me! Will mark you as brainiest!

Answers

Answer 1

Answer:

Answer:

-1, 1

13, 15

Step-by-step explanation:

x and x+2 are the integers

x*(x+2)= 7(x+x+2) -1
x²+2x= 14x+14-1
x² - 12x -13= 0

Roots of the quadratic equation are: -1 and 13.

So the integers pairs are: -1, 1 and 13, 15

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Find the components of the vertical force Bold Upper FFequals=left angle 0 comma negative 4 right angle0,−4 in the directions parallel to and normal to the plane that makes an angle of StartFraction pi Over 3 EndFraction π 3 with the positive x-axis. Show that the total force is the sum of the two component forces.

Answers

Answer:

$F_p = < - √(3) , -3 >\n\nF_o = < √(3) , -1 >$

Step-by-step explanation:

- A plane is oriented in a Cartesian coordinate system such that it makes an angle of ( π / 3 ) with the positive x - axis.

- A force ( F ) is directed along the y-axis as a vector < 0 , - 4 >

- We are to determine the the components of force ( F ) parallel and normal to the defined plane.

- We will denote two unit vectors: ( $u_p$ ) parallel to plane and ( $u_o$ ) orthogonal to the defined plane. We will define the two unit vectors in ( x - y ) plane as follows:

- The unit vector ( $u_p$ ) parallel to the defined plane makes an angle of ( 30° ) with the positive y-axis and an angle of ( π / 3 = 60° ) with the x-axis. We will find the projection of the vector onto the x and y axes as follows:

$u_o$ = < cos ( 60° ) , cos ( 30° ) >

$u_o = < (1)/(2) , (√(3) )/(2) >$

- Similarly, the unit vector ( $u_o$ ) orthogonal to plane makes an angle of ( π / 3 ) with the positive x - axis and angle of ( π / 6 ) with the y-axis in negative direction. We will find the projection of the vector onto the x and y axes as follows:

$u_p = < cos ( (\pi )/(6) ) , - cos ( (\pi )/(3) ) >\n\nu_p = < (√(3) )/(2) , -(1)/(2) >\n$

- To find the projection of force ( F ) along and normal to the plane we will apply the dot product formulation:

- The Force vector parallel to the plane ( $F_p$ ) would be:

$F_p = u_p(F . u_p)\n\nF_p = < (1)/(2) , (√(3) )/(2) > [ < 0 , - 4 > . < (1)/(2) , (√(3) )/(2) > ]\n\nF_p = < (1)/(2) , (√(3) )/(2) > [ -2√(3) ]\n\nF_p = < -√(3) , -3 >\n$

- Similarly, to find the projection of force ( $F_o$ ) normal to the plane we again employ the dot product formulation with normal unit vector ( $u_o$ ) as follows:

$F_o = u_o ( F . u_o )\n\nF_o = < (√(3) )/(2) , - (1)/(2) > [ < 0 , - 4 > . < (√(3) )/(2) , - (1)/(2) > ] \n\nF_o = < (√(3) )/(2) , - (1)/(2) > [ 2 ] \n\nF_o = < √(3) , - 1 >$

- To prove that the projected forces ( $F_o$ ) and ( $F_p$ ) are correct we will apply the vector summation of the two orthogonal vector which must equal to the original vector < 0 , - 4 >

$F = F_o + F_p\n\n< 0 , - 4 > = < √(3), -1 > + < -√(3), -3 > \n\n< 0 , - 4 > = < √(3) - √(3) , -1 - 3 > \n\n< 0 , - 4 > = < 0 , - 4 >$ .. proven

50 points!!What are the factors of the following polynomial: x^2−x−56
Do not include any spaces in your answer. Use parentheses to separate your factors. A sample answer might be (x+1)(x-4).

Answers

Answer:

(x-8) (x+7)

Step-by-step explanation:

x^2 -x-56

We want to factor this problem.

What two numbers multiply to negative 56 and add to -1

-8 *7 = -56

-8+7 = -1

We can use -8 and 7

(x-8) (x+7)

Check:

FOIL

first: x*x =x^2

outer: 7x

inner:-8x

last: -8*7 = -56

Add this together

x^2 +7x-8x -56 = x^2 -x-56

1/2x + 1 ⥸ 5
show your work

Answers

Answer:

x ⥶ 8

Step-by-step explanation:

1/2x + 1 ⥶5

x + 2 ⥶ 10

x ⥶ 10 - 2

34.00 -A video game is on sale at Amazon for 35% off the original price of $28.50. Both Pat and Henri want to purchase the game, but they only have $21 each. They will have to pay 10% sales tax. Pat and Henri have different strategies to calculate the price and decide if they have enough money to get the game. Pat takes 35% of $28.50 and subtracts that from the original price. She takes 10% of the sale price and adds it to the sale price to find the total amount she would have to pay. Henri finds 65% of the original price and then calculates 110% of the sale price. What is the sale price of the video game with tax? (1 point) Will Pat's strategy calculate the correct total? Explain the calculations. (2 points) Will Henri's strategy calculate the correct total? Explain the calculations. (2 points) Do they each have enough to purchase the game? (2 points) Explain your answers using complete sentences and show your work

Answers

Answer:

Sale price of video game with tax = $20.3775

Yes, they both have enough money to purchase the video game.

Step-by-step explanation:

Given that:

Original price of video game = $28.50

Discount on original price = 35%

Sales tax = 10%

Money available with Pat and Henri = $21 each

First of all, let us find out the price as per Pat's method.

Step 1:

Taking 35% of $28.50

$\Rightarrow (35)/(100)* \$28.50 = \$9.975$

Step 2:

Subtract from $28.50 to find the sale price:

$28.50 - $9.975 = $18.525

Step 3:

Take 10% of sale price:

$\$18.525* (10)/(100) = \$1.8525$

Step 4:

Add to sale price to get the final amount to be paid:

$18.525 + $1.8525 = $20.3775

Now, let us use Henri's method:

Step 1:

Find 65% of original price:

$(65)/(100)* $28.50 = \$18.525$

Step 2:

Find 110%:

$(110)/(100)* \$18.525 = \bold{\$20.3775}$

Sale price of video game with tax = $20.3775

Yes, they both have enough money to purchase the video game.

If CD = EF, then CD ≅ EFDefinition of Congruence
Reflexive Property
Symmetric Property
Definition of Midpoint
Help quickly

Answers

Answer:

Definition of congruence

Step-by-step explanation:

According to this

If two sides are equal then they are ought to be congruent.

Here

CD is equal to EF

It means both have same lengths

Hence they are congruent

Final answer:

Based on the Definition of Congruence in mathematics, if two line segments are of equal lengths, then they are said to be congruent. So if CD = EF, then CD is congruent to EF (CD ≅ EF).

Explanation:

In this context, if CD = EF, then CD is indeed congruent to EF, written as CD ≅ EF.

This is based on the Definition of Congruence in mathematics, specifically geometry, which states that two objects (in this case, line segments) are congruent if they have the exact same size and shape, or, for line segments, the same length. So, if the lengths of two line segments are equal (CD = EF), then they are congruent (CD ≅ EF).

Learn more about Congruence here:

brainly.com/question/31992651

#SPJ2

1 . ( m →(N v Q)) →((M→N) v (M→Q))
2.((T v U) → V) → (T → (U → V))

Answers

. ( m →(N v Q)) →((M→N) v (M→Q))

2.((T v U) → V) → (T → (U → V)) wut tyhe hell is this

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