The product of two consecutive positive integers is 17 more than 5 times their sum. Find the numbers​

Answer:

Step-by-step explanation:

[tex]\begin{bmatrix}2 & -3\\ 1 & 2\end{bmatrix}^{-1}\times \begin{bmatrix}2 & -3\\ 1 & 2\end{bmatrix}\times \begin{bmatrix}x\\y \end{bmatrix}=\frac{1}{7} \begin{bmatrix}2 & 3 \\ -1 & 2\end{bmatrix}\times \begin{bmatrix}19\\ -1\end{bmatrix}[/tex]  

Since, [tex]\begin{bmatrix}2 & -3\\ 1 & 2\end{bmatrix}^{-1}=\frac{1}{7}\begin{bmatrix}2 & 3\\ -1 & 2\end{bmatrix}[/tex]

And [tex]A^{-1}A=I[/tex]

[tex]\begin{bmatrix}x\\y \end{bmatrix}=\frac{1}{7}\begin{bmatrix}2 & 3\\ -1 & 2\end{bmatrix}\times \begin{bmatrix}19\\-1 \end{bmatrix}[/tex]

[tex]\begin{bmatrix}x\\y \end{bmatrix}=\frac{1}{7}\begin{bmatrix}35\\ -21\end{bmatrix}[/tex]

[tex]\begin{bmatrix}x\\y \end{bmatrix}=\begin{bmatrix}5\\ -3\end{bmatrix}[/tex]                

Therefore, x = 5 and y = -3 will be the value of variables.

Answer:

edge ⬇️  

If   invested at the rate of 2.5% for one year. The amount that tyrell pay in additional interest each month is: c. $1,000.

First step

Amount for one year=Simple interest amount/Interest rate

Amount for one year=$300/0.025

Amount for one year=$12,000

Second step

Additional interest each month=$12,000/12 months

Additional interest each month=$1,000

Therefore the amount that tyrell pay in additional interest each month is: c. $1,000.

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Answer:

B) (x + 3)^2 = 17

Step-by-step explanation:

To complete the square you need to put x + or - half of the x coefficient.

So here it would be (x + 3)^2. However, we're trying to find x^2 + 6x - 8 = 0, not x^2 + 6x + 9 =  0, which is what (x + 3)^2 expands to. So we need to -9 from x^2 + 6x + 9 = 0 and add -8 from the original equation.

This simplifies to (x + 3)^2 - 9 - 8 = 0    --> (x + 3)^2 - 17 = 0

Then all you need to do is rearrange to give: (x + 3)^2 = 17

Answer:

it looks like c

Step-by-step explanation:

its not quite 50 but its extreemly close so its got to be c

[tex]12 {}^{2} = 9 {}^{2} + 8 {}^{2} - 2(9)(8)(cosx)[/tex]

[tex]144 = 81 + 64 - 2(72)(cosx)[/tex]

[tex]144 = 145 - 144(cosx)[/tex]

[tex] - 144(cosx) = 144 - 145[/tex]

[tex](cosx) = \frac{ - 1}{ - 144} [/tex]

[tex]arccos( \frac{1}{144} ) = > a = 89.6[/tex]

Answer:

[tex]\left \{ {{x=-2} \atop {y=1}} \right.[/tex]

Step-by-step explanation:

[tex]\left \{ {{y=-2x-3} \atop {y=2x+5}} \right.[/tex]

Substitute into one of the equations
[tex]-2x-3=2x+5[/tex]

Rearrange variables to the left side of the equation
[tex]-2x-2x=5+3[/tex]

Combine like terms
[tex]-4x=5+3[/tex]

Calculate the sum or difference
[tex]-4x=8[/tex]

Divide both sides of the equation by the coefficient of variable
[tex]x=-\frac{8}{4}[/tex]

Cross out the common factor
[tex]x=-2[/tex]

Substitute into one of the equations
[tex]y=-2\times\left(-2\right)-3[/tex]

Calculate
[tex]y=1[/tex]

The solution of the system is
[tex]\left \{ {{x=-2} \atop {y=1}} \right.[/tex]

I hope this helps you! Don't forget to check the picture I uploaded as well

:)

Answer:

[tex]\displaystyle [-2, 1][/tex]

Step-by-step explanation:

Use the Elimination method sinse both coefficients in the system are OPPOCITES:

[tex]\displaystyle \left \{{{y = -2x - 3} \atop {y = 2x + 5}} \right.[/tex]

2y = 2; 1 = y [Plug this y-coordinate back into the system to get the x-coordinate of −2 (−2 = x).]

I am joyous to assist you at any time.

Answer:

a is the answer

Step-by-step explanation:

The equation of P(E1 ∪ E2) that represents the condition that the mutually exclusive events is one of the events occurs, or both occur which is correct option(A).

Mutually Exclusive events is defined as in probability the particular addition rule is applicable when two occurrences are incompatible with one another. It claims that the probability of either event is equal to the probability of each event separately.

If E₁ and E₂ are said to be mutually exclusive events then the probability of an event E₁ occurring or the probability of event E₂ occurring is given as P(E₁) + P(E₂) :

P(E₁ ∪ E₂) = P(E₁) + P(E₂)

Hence, the equation of P(E1 ∪ E2) that represents the condition that the mutually exclusive events is one of the events occurs, or both occur.

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Answer:

1/125

Step-by-step explanation:

Answer:

6 hours

Step-by-step explanation:

356-56

=300

300/50

=6

Answer:

4x+6y³

Step-by-step explanation:

give me thanks, please;)

Answer:

NOTHING

Step-by-step explanation:

Answer:

x = 22-3y/5-y

y=-22-5x/x-3

Step-by-step explanation:

Solve for x:

1)  Subtract 3y from both sides.

5x - xy = 22 - 3y

2) Factor out the common term x.

x(5 - y) = 22 - 3y

3) Divide both sides by 5 - y.

x = 22-3y/5-y

Solve for y:

1) Subtract 5x from both sides.

=xy + 3y = 22 - 5x

2) Factor out the common term y.

- y=(x-3)=22-5x

3) Divide both sides by x-3.

-y=22-5x/x-3

4) Multiply both sides by -1.

y=-22-5x/x-3

Answer:

24 Ohms

Step-by-step explanation:

Resistance is a function of amperes. For each amp, there is one and only one value for resistance.

It works the other way, too.

E=IR (well-known relationship). If IR=12, R=12/I

R=E* (1/I)

When the current is 0.5 amp, R=12/0.5 - 24 ohms

Answer:

16/100 or simplified is 4/25

Step-by-step explanation:

Answer:

x= 9.3 but im not to sure this is right

Step-by-step explanation:

Answer:

6×6

=36

Step-by-step explanation: Negative multiplied by negative is positive.

Answer:

36

Step-by-step explanation:

6 times -2 = -12

-12 times -3 = 36

Answer:

hey Hey Im the Hero to you 2x⋅(y−z+w)

Answer :D

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

 x • ((3y -  2 • (z - w)) -  y)

STEP

2

:

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  2y - 2z + 2w  =   2 • (y - z + w)  

Final result :

 2x • (y - z + w)

Answer:

Step-by-step explanation:

h(t) = 32 = -16t^2 + 50t + 5

-16t^2 + 50t - 27 = 0

Drawing a graph gives time = 0.7 seconds.

The ball is 32 feet above the ground after 2.9 seconds

We have,

To determine the time at which the ball is 32 feet above the ground, we can set the height function h(t) equal to 32 and solve for t:

h(t) = 32

-16t² + 50t + 5 = 32

-16t² + 50t + 5 - 32 = 0

-16t² + 50t - 27 = 0

We can solve this quadratic equation using various methods, such as factoring, completing the square, or the quadratic formula.

Let's use the quadratic formula:

t = (-b ± √(² - 4ac)) / (2a)

Plugging in the values a = -16, b = 50, and c = -27, we have:

t = (-50 ± √(50² - 4(-16)(-27))) / (2(-16))

Simplifying further:

t = (-50 ± √(2500 - 1728)) / (-32)

t = (-50 ± √(772)) / (-32)

Now, we can calculate the two possible solutions:

t ≈ (-50 + √772) / (-32) ≈ 2.85 seconds (rounded to the nearest tenth)

t ≈ (-50 - √772) / (-32) ≈ 0.18 seconds (rounded to the nearest tenth)

Based on the graph of the function, the ball is 32 feet above the ground after approximately 2.9 seconds (rounded to the nearest tenth).

Thus,

The ball is 32 feet above the ground after 2.9 seconds

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Answer:

2feet

Step-by-step explanation:

There brother is 2 feet and 6 inches

Formula: 12 inches = 1 foot

4'2 + 10 inches = 5 foot

Half of 5 foot would be 2'6 since there are 12 inches in a foot.

Answer:

Length = 18 cm

Width = 12 cm

Area = 216 cm^2

Step-by-step explanation:

The perimeter of a rectangle is twice it's length(l) plus twice it's width(w):

Perimeter = 2l + 2w

We are told that (l/w) = (3/2) [ratio of its length to its width is 3:2]

Therefore:

60cm = 2l + 2w

---

(l/w) = (3/2)

We can rewrite this as:  l = (3/2)w

----

Now substitute this expression into the perimeter equation:

60 cm = 2l + 2w

60 cm = 2((3/2)w) + 2w

60 cm = 3w + 2w

60cm = 5w

w = 12 cm

l = (3/2)w

l = (3/2)*12

l = 18 cm

Area = 1*w

Area = (12cm)(18cm) = 216 cm^2

Answer:

-40

Step-by-step explanation:

Answer:

-13

Step-by-step explanation:

Answer:

9*3.14=28.26

Step-by-step explanation:

Hope this Helps!

Answer:

[tex]C\approx28.27ft[/tex]

Step-by-step explanation:

[tex]C=\pi d\\C=\pi(9)\\C=9\pi\\C\approx28.27[/tex]

Thus, your circumference is about 28.27 ft

Answer:8.9

Step-by-step explanation: y=2.2 +3.5 =6.7 +0.18

y= 8.9

good luck

Both solutions are valid, so the solutions to the quadratic function [tex]f(x) = 4x^2 - 9[/tex] are x = -3/2 and x = 3/2.

To solve the quadratic function [tex]f(x) = 4x^2 - 9[/tex] by factoring, we set the expression equal to zero and then try to factor it.

Step 1: Set f(x) equal to zero:

[tex]4x^2 - 9 = 0[/tex]

Step 2: Factor the quadratic expression:

The expression [tex]4x^2 - 9[/tex] is in the form of a difference of squares, which can be factored as follows:

[tex]a^2 - b^2 = (a + b)(a - b)[/tex]

In our case, a = 2x and b = 3:

[tex]4x^2 - 9 = (2x + 3)(2x - 3)[/tex]

Step 3: Set each factor equal to zero and solve for x:

First factor: 2x + 3 = 0

Subtract 3 from both sides:

2x = -3

Divide both sides by 2:

x = -3/2

Second factor: 2x - 3 = 0

Add 3 to both sides:

2x = 3

Divide both sides by 2:

x = 3/2

Step 4: Check the solutions:

Plug the values of x back into the original equation to verify:

For x = -3/2:

[tex]f(-3/2) = 4(-3/2)^2 - 9\\f(-3/2) = 4(9/4) - 9\\f(-3/2) = 9 - 9\\f(-3/2) = 0\\For x = 3/2:\\f(3/2) = 4(3/2)^2 - 9\\f(3/2) = 4(9/4) - 9\\f(3/2) = 9 - 9\\f(3/2) = 0[/tex]

Both solutions are valid, so the solutions to the quadratic function f(x) = [tex]4x^2 - 9[/tex] are x = -3/2 and x = 3/2.

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h(x) = x^2 - 2

h(-3) = (-3)^2 - 2

= 9-2

= 7

Answer:

A. x>2

Step-by-step explanation:

11x>22

x>22/11

x>2

Answer:

the sale price will be 130% off

Step-by-step explanation:

Answer:

10x+2

Step-by-step explanation:

2×(2x+1+3x)

4x+2+6x

10x+2

Answer:

10x + 2

Step-by-step explanation:

The perimeter is the sum of the 4 sides of the rectangle, where opposite sides are equal in measure, thus

perimeter = 3x + 3x + 2x + 1 + 2x + 1 = 10x + 2

Answer:

10.) b. not a function

11.) a. function

Step-by-step explanation:

hope it helps. good luck :)