When the number k is multiplied by 5, the result is the same as when 5 is added to k. What is the value of k?

Answer:

10.

Step-by-step explanation:

x^2 + 5x = 150

x^2 + 5x - 150 = 0

This equation will factor:

(x - 10)(x + 15) = 0

x - 10 = 0 or x + 15 = 0, so:

x = 10 or -15.

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

Work Shown:

First get everything to one side

[tex]x^2 + 5x = 150\\\\x^2 + 5x - 150 = 0\\\\[/tex]

Now use the quadratic formula

Plug in a = 1, b = 5, c = -150.

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(5)\pm\sqrt{(5)^2-4(1)(-150)}}{2(1)}\\\\x = \frac{-5\pm\sqrt{625}}{2}\\\\x = \frac{-5\pm25}{2}\\\\x = \frac{-5+25}{2} \ \text{ or } \ x = \frac{-5-25}{2}\\\\x = \frac{20}{2} \ \text{ or } \ x = \frac{-30}{2}\\\\x = 10 \ \text{ or } \ x = -15\\\\[/tex]

Factoring, completing the square, or graphing are alternative methods to get these two answers. We see that the positive root is x = 10.

Answer:

Domain: (-11, 4)

Step-by-step explanation:

Domain is the set of all x-values that can be inputted into a function.

So we look at x-values that can be inserted into the graph.

We notice that we cannot input x = -11 or x = 4 as it is open-pointed but everything inbetween works, so we have (-11, 4) as our domain.

Answer:

One of the sides is 6 cm and the other is 8 cm

Step-by-step explanation:

Let's call the unknown sides a and b. From the perimeter information (24 cm) we have:

a + b + hypotenuse = 24

a + b + 10 = 24

a + b = 14

b = 14 - a

So now we can right the Pythagorean theorem as follows:

[tex]a^2 + b^2 = hypotenuse^2\\a^2 + (14-a)^2=10^2\\a^2+ 14^2-28\,a+a^2=100\\2\,a^2-28\,a +96=0\\2\,(a^2-14\,a+48)=0\\2\,(a^2-6\,a-8\,a+48)=0\\2(a\,(a-6)-8\,(a-6))=0\\2\,(a-6)\,(a-8)=0[/tex]

and from this expression in factor form to be zero a must be 6 or a must be 8.

Therefore the solutions are a = 6 (and therefore b = 14 - 6 = 8)

or a = 8 (and therefore b = 14 - 8 = 6)

Perimeter of triangle = Sum of all sides.

One side of triangle = 10 cm

Measure of other two sides will be → 24-10

Other two sides sum will be = 14 cm

Let's assume one side as x and other as 14-x

Now hypotenuse is of 10 cm

According to Pythagorean theoram

Hypotenuse² = Perpendicular ² + base²

→ 10² = (x)² + (14-x)²

→ 100 = x² + (14-x)²

(a-b)² = a²+b² -2ab

→ 100 = x² + 196 + x² -28 x

→ 100 = 2x² + 196 - 28x

Taking 2 commen both sides

→ 50 = x² -14x + 98

→ 0 = x² -14x +98-50

→ x² -14 x +48 = 0

Factorising :-

→ x² - 6x - 8x + 48 = 0

→ x( x -6) -8(x -6) = 0

→ (x-6)(x-8) = 0

→ x = 6 or x = 8

So x is 6 or 8

Other two sides of triangle are 6 cm and 8 cm

Answer:

y =2x+1

Step-by-step explanation:

The slope intercept form is

y = mx+b where m is the slope and b is the y intercept

y = 2x+b

Substituting the point into the equation

5 = 2(2)+b

5 = 4+b

5-4 =b

b=1

y =2x+1

Answer:

0-2 x-intercepts and 0-1 y-intercepts

Step-by-step explanation:

A quadratic function can have anywhere from 0 to 2 x-intercepts. This is possible because a function can have 0, 1, or 2 solutions.

A parabola can also have either 0 or 1 y intercepts. It is possible for the function to not intercept the y axis at all, and it is also possible for it to intercept it exactly one time.

Answer:

3 x (14-3) = 33

Step-by-step explanation:

The algebraic expression will be : 3(x - 4) = 33

Given,

3 times the difference of a number and 4 is 33

Now,

Let the number be x .

So,

Three times the difference of x and 4 will be 33 .

So,

First subtract x-4

Then thrice of this is 33

So,

3(x - 4) = 33

Thus the algebraic expression is 3(x - 4) = 33 .

After solving the expression:

x- 4 = 11

x = 15

Know more about algebra,

https://brainly.com/question/16934260

#SPJ6

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

Explanation:

See the diagram below.

We start with triangle PQR with the given angles mentioned. Then you extend out segment QR to form line QR. It goes off infinitely in both directions.

The exterior angle x adds to the interior angle Q = 40 to get 180

x+40 = 180

x+40-40 = 180-40 ... subtract 40 from both sides

x = 140

The exterior angle is 140 degrees

Answer:

-10x+1.5

Step-by-step explanation:

-2(5x-0.75).... distributive property

-10x+1.5

Note:

-&-=+

+&+=+

+&-=-

-&+=-

Hope this helps ;) ❤❤❤

Answer:

d

Step-by-step explanation:

Answer:

[tex]-\frac{1}{28}[/tex]

Step-by-step explanation:

-1/2 ÷ 2(9+3)-4 - 3/4(8)

-0.5 ÷ 2(12)-4 - 3/4(8)

-0.5 ÷ 2(12)-4 - 6

-0.5 ÷ 24-4 - 6

-0.5 ÷ 14 = [tex]-\frac{1}{28}[/tex]

Answer:

39.75

Step-by-step explanation:

take the total cost multiply it by 1.08 then subtract that from the final cost hope it helps

Answer:

$39.75

Step-by-step explanation:

Step 1: multiply 43.20x.08=3.45

Step 2: subtract 43.20-3.45=39.75

All done!

im not going to give u the answer but all you do is

step by step :

#1. D2- (-6*2),(0*2)=(-12,0)

(3*2), (-9*2)= (6,-18)

(12*2),(4*2)=( 24,8)

Answer:

1 out of 6

Step-by-step explanation:

Answer:

-14 F

Step-by-step explanation:

Answer:

Answer = 25

Step-by-step explanation:

125 = 5f

125/5 = f

25 = f

Explanation:

The idea is to isolate y getting it by itself. We can do this a number of ways, but possibly the quickest way is to add y to both sides

x/2 - y + 6 = 0

x/2 + 6 = 0+y

x/2 + 6 = y

y = x/2 + 6

This is now in slope intercept form, more or less. We could rewrite the x/2 as (1/2)x to get

y = (1/2)x + 6

Then compare this to y = mx+b and note the slope is m = 1/2 and the y intercept is b = 6.

Side note: the quality of the snapshot is fairly good. I've seen much worse.

Answer:

if f(x)=0,

then 2x-7=0

so,x=7/2

Answer:

f−1(x)=12(y−7). Explanation: Given: f(x)=2x+7. Let y=f(x). y=2x+7. Expressing x in terms of y gives us the inverse of x. y−7=2x. 2x=y−7. x=12(y−7)

Answer:

250

Step-by-step explanation:

5000×5/100 =250

why because you times it for commission because it what you gain

Answer:

(5, 12, 13)

Step-by-step explanation:

Hello, please consider the following.

[tex](\forall (x,y) \in \mathbb{R}^2) \ \ (x^2-y^2)^2+(2xy)^2=(x^2+y^2)^2\\\\\text{You can develop both expressions to see that this is equal.}\\\\\text{After }(3,4,5)\text{ we can try the triple starting with }5\\\\\text{So, let's search x and y such that } 5=x^2-y^2=9-4=3^2-2^2\\\\\text{And, then, it comes}\\\\(3^2-2^2)^2+(2*3*2)^2=(3^2+2^2)^2\\\\<=> 5^2+12^2=13^2\\ \\\text{So, }(5,12,13)\text{ is a Pythagorean triple}[/tex]

Is it a primitive one?

5 = 1 * 5

12 = 1 * 2 * 2 * 3

13 = 1 * 13

So this is a primitive one.

Thanks

Answer:

5, 12, 13

Step-by-step explanation:

Answer:

4ab² + 20b - 3a

Step-by-step explanation:

This question most likely asks us to simplify the expression, as factoring is not possible...

(ab² + 13b - 4a) + (3ab² + a + 7b),

ab² + 13b - 4a + 3ab² + a + 7b,

ab² + 3ab² + 13b + 7b - 4a + a,

Solution : 4ab² + 20b - 3a

Answer:

1). Option (3)

2). Option (D)

Step-by-step explanation:

1). Integers are the numbers which are whole numbers with negative or positive notations.

Integers can't be a fraction or a number with decimal.

Out of the numbers given,

-18 and 4 will be the integers

Option (3) is the correct answer.

2). Shaded portion of the diagram represents the rational numbers excluding integers,

By the definition of the rational numbers, any number which can be written as a fraction is a rational number.

Rational numbers → All numbers given are the rational numbers

Integers → [tex]\frac{16}{4}=4, -\frac{30}{5}=6, -\frac{32}{8}=-4[/tex]

Therefore, only one number [tex]\frac{30}{9}[/tex] will lie in the shaded region.

Option (D) will be the answer.

Answer:

Sparkle wands:  NO

Fairy wands:  YES

Glass wands:  NO

Step-by-step explanation:

To find the price per glitter wand, you have to divide the price of the wands by the amount of wands you have.

$50/8 = $6.25

Divide the price of the wands by the amount you get.

Sparkle wands:  $20/4 = $5

Fairy wands:  $37.50/6 = $6.25

Glass wands:  $65/10 = $6.50

The sparkle wands and the glass wands do not have the same price per wand as glitter wands.

The fairy wands have the same price per wand as glitter wands.

Answer:

Glow wands = no

Fairy Wands= yes

Sparkle Wands = No

Step-by-step explanation:

Khanacademy

Trust

Answer:

I dont get the question, is there suposed to be a chart?

Step-by-step explanation:

Answer:

-31

Step-by-step explanation:

-2((c+5)/(-2))=13*-2

c+5=-26

c=-31

Answer:

c = -31

Step-by-step explanation:

(c+5)/(-2)=13

Multiply each side by -2

(c+5)/(-2) *-2=13* -2

c+5 = -26

Subtract 5 from each side

c+5-5 = -26-5

c = -31

Answer:

12x² - 4x - 8

Step-by-step explanation:

Use FOIL method

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

                        = 12x² - 12x + 8x - 8   {add like terms}

                        = 12x² - 4x - 8

Hint: 3x * 4x  -----> Multiply the coefficients = 3 *4 = 12 and then multiply the variables and for multiplying the two variable, add the powers

x*x =[tex]x^{1+1)=x^{2}[/tex]

3x * 4x = 12x²

Answer:  see proof below

Step-by-step explanation:

Use the following Double Angle Identities: cos 2A = 1 - 2sin²A

                                                                        sin 2A = 2sinA · cosA

[tex]\text{Given:}\quad \tan A = \dfrac{x}{y}[/tex]

Proof LHS = RHS

y cos 2A + x sin 2A = y

                  x sin 2A = y - y cos 2A

                  x sin 2A = y(1 - cos 2A)

                  [tex]\dfrac{x}{y}=\dfrac{1-\cos2A}{sin\ 2A}[/tex]

                  [tex]\dfrac{x}{y}=\dfrac{1-(1-2sin^2A)}{2\sin A\cdot \cos A}[/tex]

                  [tex]\dfrac{x}{y}=\dfrac{2sin^2A}{2\sin A\cdot \cos A}[/tex]

                  [tex]\dfrac{x}{y}=\dfrac{\sin A}{\cos A}[/tex]

                  [tex]\dfrac{x}{y}=\tan A}[/tex]

This is a TRUE statement since it was given that  [tex]\tan A = \dfrac{x}{y}[/tex]  

Answer:

Step-by-step explanation:

studying Math       65

Studying science   50

studying both          35

student are studying in the college are:(65+50)-35=80 students

student studying math only= 65-35=30

student studying science only = 50-25=15

Answer:

23.4696 liters

Step-by-step explanation:

Answer: 6

Step-by-step explanation:

ax/ay=r^(x-y)

in this case it will be

a4/a1=r^(4-1)

24/3=r^3

8=r^3

r=2

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

an=a1×r^(n-1) ⇔ geometric sequence formula

a2=3×2^(2-1)

a2=3×2^1

a2=3×2

a2=6

Answer:

100 ml of concentrate and 350 ml of water

Step-by-step explanation:

2 + 7 = 9 total parts

450/9 = 50

2(50) = 100 ml concentrate

7(50) or 450 - 100 = 350 ml water

Hope it helped u if yes mark me BRAINLIEST!

Tysm!

Answer:

Leg₂ ≈ 6.481 or √42

Step-by-step explanation:

a² + b² = c²

(√7)² + b² = (7)²

7 + b² = 49

b² = 42

b = √42

b ≈ 6.481