Two numbers have a difference of 42 and a quotient of −6. What are the two numbers?

Answer:

y =x^2 +8x +15

factories form

y =( x+5 )( x+3 )

x intercept where the graph meet the x axis

y = x^2 +8x +15

let y =0

0 = x^2 +8x +15

0 = ( x + 5) (x+3)

o = x+5 or 0 = x+3

-5 = x or x = - 3

x intercept

(-5;0)

(-3 ;0)

axis of symmetry : where you will cut the graph into two half

x = - b/2a

x = - 8/2(1)

x = - 8/2

x = - 4

Domain

XER

Range

y > -1

Answer:

8.4 cm^2

Step-by-step explanation:

The area of the rectangle is

A = lw

A = 3x *5x = 15x^2

126 = 15x^2

126/ 15 =15x^2/15

42/5 = x^2

We want to find the area of the square

A = l*w

A = x*x

A = x^2 = 42/5 = 8.4 cm^2

Answer:

A is the answer to your question because it's the only answer in exponential form.

B and C are in slope forms.

D is in quadratic form.

Answer:

45 and 23

Step-by-step explanation:

Let x equal the first number and y equal the second number.

We can set the following equations up with our information:

[tex]x+y=68[/tex]

[tex]x-y=22[/tex]

Adding the two equations together, we get:

[tex]2x=90[/tex]

Dividing by two, we receive [tex]x=45[/tex]

We can plug this into our first equation to get [tex]45+y=68[/tex].

Subtracting 45 from both sides, we get [tex]y=23[/tex].

The two numbers are 45 and 23, solved using system of equations.

A system of equations is a set of equations, involving similar variables used to solve for the variables simultaneously.

In the question, we are asked to find the two numbers, whose sum is 68 and the difference is 22.

We assume the two numbers to be x and y.

The sum of the two numbers is given to be 68.

This can be shown as an equation, x + y = 68 ... (i).

The difference of the two numbers is given to be 22.

This can be shown as an equation, x - y = 22 ... (ii).

Equations (i) and (ii) together makes a system of equation in the variables x and y.

To solve for the system of equation, we add (i) and (ii), to get:

x + y = 68

x - y = 22

_________

2x  = 90,

or, x = 45.

Substituting x = 45 in (i), we get:

x + y = 68,

or, 45 + y = 68,

or, y = 23.

Thus, the two numbers are 45 and 23, solved using system of equations.

Learn more about system of equations at

https://brainly.com/question/13729904

#SPJ2

Answer:

90°

Step-by-step explanation:

Angle C = arccos((84²+13²-85²)/(2×84×13))

= arccos(0/2184)

= arccos(0)

= 90°

Answered by GAUTHMATH

Answer:

this is a 60 60 60 triangle, so one exterior angle is 120 degrees.

Step-by-step explanation:

hope it helps!

Answer:

[tex]x=-21y+5[/tex]

Step-by-step explanation:

Hi there!

[tex]7y=\frac{5-x}{3}[/tex]

We can isolate x by performing inverse operations on both sides of the equation and canceling values out.

First, multiply both sides by 3 to cancel 3 out on the right side and isolate 5-x:

[tex]7y*3=\frac{5-x}{3}*3\\21y=5-x[/tex]

Now, subtract 5 from both sides to isolate -x:

[tex]21y-5=5-x-5\\21y-5=-x[/tex]

Finally, multiply both sides by -1 to change -x to x:

[tex]-21y+5=x\\x=-21y+5[/tex]

I hope this helps!

Answer: A. The number 23 is prime, but 36 is composite.

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

Explanation:

Let's go through the possible answer choices

23 is indeed prime, and 36 is indeed composite.

33 is composite, and 42 is indeed composite.

21 is composite, and 25 is composite as well

27 is not prime, and 39 is composite.

Primes have only 2 factors: 1 and themselves.

And 33, 21 and 27 definitely have more than 2 factors. Hope this helps!

~Just a joyful teen

[tex]GraceRosalia[/tex]

Answer:

y=-70

Step-by-step explanation:

10.4/10y=-28.10

4y=-280

y=-70

[tex] \large \tt{{❃ \: S \: O \: L \: U \: T \: I \: O \: N : }}[/tex]

[tex] \large{ \tt{❁ \:x + x + 98 = 180 \degree \: [ Sum\: of \: angle \: of \: a \: triangle ]}}[/tex]

[tex] \large{ \tt{⟶2x + 98 \degree= 180 \degree}}[/tex]

[tex] \large{ \tt{⟶ \: 2x = 180 \degree - 98 \degree}}[/tex]

[tex] \large{ \tt{⟶ \: 2x = 82 \degree}}[/tex]

[tex] \large{ \tt{ ⟶x = \frac{82 \degree}{2} }}[/tex]

[tex] \large{ \tt{⟶ \: x = 41 \degree}}[/tex]

[tex] \large{ \tt{ ↔\angle \: 1 = x \degree = \boxed{41 \degree}}}[/tex] [ Being alternate angles ]

- Alternate angles are the non-adjacent interiors pair of angles lying to the opposite side of a transversal when it intersects two straight line segments. Alternate angles form ' Z ' shape.

Answer:

-w²+49x²-8wx

Step-by-step explanation:

if you want how I did this it's quite lengthy so let me know if you want the process

Answer:

-w^2 + 21xw - 64x ^2

Step-by-step explanation:

Answer:

70 days

Step-by-step explanation:

that is the procedure above

[tex] \\ \tt \longmapsto2x + 15 + 7 - 8x + 3x - 41 = 30 \\ \\ \tt \longmapsto 2x - 8x + 3x + 15 + 7 - 41 = 30 \\ \\ \tt \longmapsto - 3x - 19 = 30 \\ \\ \tt \longmapsto 3x + 19 = - 30 \\ \\ \tt \longmapsto 3x = - 30 -19 \\ \\ \tt \longmapsto 3x = - 49 \\ \\ \tt \longmapsto x = - \frac{49}{3}[/tex]

Answer:

Step-by-step explanation:

2x + 15 + 7 - 8x + 3x - 41 = 30

2x  - 8x + 3x + 15 + 7 - 41 = 30

Combine like terms

-3x - 19 = 30

Add 19 to both sides

-3x = 30 + 19

-3x = 49

Divide both sides by (-3)

x = 49/-3

x = -[tex]16\frac{1}{3}[/tex]

Answer:

5

Step-by-step explanation:

Answer: -1

Step-by-step explanation:

12x^2-7x-12 = (4x+3)(3x-4)

4x+3=0. X = -3/4

3x-4=0. X = 4/3

(-3/4) (4/3) = -1

Answer:

The answer is 18 feet...

Step-by-step explanation:

C. 18ft is the answer

Answer:

-5, - 2, 3

Step-by-step explanation:

y=2x+3, y=-7, x=-5; y=-1, x=-2, y=9, x=3

Answer:

or,

3/4×2/3=6/8

or, 3/4×3/3=9/12

Answer:

Step-by-step explanation:

1/3×2/8=2/24

1/2×5/12=5/42

5/6×3/4=15/24

Hope it is helpful to you

Answer:

x = 35

Step-by-step explanation:

Let x be the one of the other angles

X is also the third angle since we know they are equal

The sum of the angles of a triangle is 180

110+x+x = 180

110 +2x= 180

2x = 180-110

2x= 70

Divide by 2

2x/2 = 70/2

x = 35

Answer:

[tex]x = 35 \degree[/tex]

Step-by-step explanation:

Let the unknown angle be x

Unknown Angles are equal to each other so,

[tex]x + x + 110 = 180[/tex]

sum of the interior angles in a triangle is 180°

[tex]2x + 110 = 180 \\ 2x = 180 - 110 \\ 2x = 70 \\ \frac{2x}{2} = \frac{70}{2} \\ x = 35 \degree[/tex]

[tex]\bf \large \rightarrow \: \:2x \: + \: 8 \: = \: 0[/tex]

[tex]\bf \large \rightarrow \: \:x \: = \: \frac{8}{2} \\ [/tex]

[tex]\bf \large \rightarrow \: \:x \: = \: \cancel\frac{ 8}{ 2} \: \: ^{4} \\ [/tex]

[tex]\bf \large \rightarrow \: \:x \: = \: 4[/tex]

Option ( A ) is the correct answer.

Answer:

a) Hence the equation of the sinusoidal function that describes the height of the shorts in terms of time is [tex]y = 9 + 7* sin(\pi * t / 15 - \pi / 6)[/tex]

b) Hence the height of the shorts at exactly t = 10 minutes, to

the nearest tenth of a meter is 5.5 meters

Step-by-step explanation:

a) The wind turbine blade traverses a circular path as it rotates with time (t), whose time variation is given by the following trajectory equation :

[tex]x^2 + (y-yc)^2 = R^2[/tex] ,

where  

R = (16 m - 2 m)/2 (since diameter = maximum height - minimum height of the pink short)

= 14 m / 2

= 7 m (radius of the circle)

Also, center of the circle will be at (0, 2 + R) i.e (0,9)

So,  is the trajectory path equation to the circle

Let [tex]x = 7* cos(w*t + \phi ) & y = 9 + 7* sin(w* t + \phi)[/tex] be the parametric form of the above circle equation which represent the position of the pink shorts at the tip of the blade at time t  

At t= 10s, y = 16 m so we have,

[tex]9 + 7 * sin(10* w + \phi) = 16[/tex] ---------------(1)

Also, at t= 25s, y =2 m so we have,

[tex]9 + 7* sin(25 * w +\phi) = 2[/tex]--------------(2)

Solving we have, [tex]10* w + \phi = \pi/2 & 25*w + \phi = 3*pi/2[/tex]

[tex]15* w = \pi\\\\w = \pi/15 & \phi = \pi/2 - 10*\pi/15 = -\pi / 6[/tex]  

Therefore [tex]y = 9 + 7* sin(\pi * t / 15 - \pi / 6)[/tex] is the instantaneous height of the pink short at time t ( in seconds)

b) At t= 10minutes = 10 * 60 s = 600s, we have,

[tex]y = 9 + 7 * sin(\pi * 600/15 - \pi / 6)\\\\= 9 + 7 * sin(40* \pi - \pi / 6)[/tex]

= 5.5 meters (pink short will be at 5.5 meters above ground level at t= 10 minutes)

Answer:

65.3%

Step-by-step explanation:

what we want: p(2)+p(3)+p(4)

[tex]P(2)={5\choose2}*.4^2*.6^3\\P(3)={5\choose3}*.4^3*.6^2\\P(4)={5\choose4}*.4^4*.6\\P(2)+P(3)+P(4)= .6528[/tex]

which equal 65.28%

which rounds to

65.3%

Answer: 39°

Step-by-step explanation:

Angle of depression must be less than 90° but greater than 0°

So you pretty much have all you need. 1/3 represents slope, and slope is m. Initial value would be your y intercept which is b.

y=1/3x-3

Answer:

y = x/3 - 3

Step-by-step explanation:

x/3 is the equivalent of 1/3(x)

Answer:

if f(x) = ax + b then f-1(x) = (x - b)/a

Step-by-step explanation:

Now

f(x)=ax + b

then y = ax + b

interchanging x and y , we get

or, x = ay + b

or, x - b = ay

or, (x - b)/a = y

therefore,f-1(x) = (x - b)/a

Answer:

y-3

Problem:

What is the remainder when the dividend is xy-3, the divisor is y, and the quotient is x-1. ?

Step-by-step explanation:

Dividend=quotient×divisor+remainder

So we have

xy-3=(x-1)×(y)+remainder

xy-3=(xy-y)+remainder *distributive property

Now we just need to figure out what polynomial goes in for the remainder so this will be a true identity.

We need to get rid of minus y so we need plus y in the remainder.

We also need minus 3 in the remainder.

So the remainder is y-3.

Let's try it out:

xy-3=(xy-y)+remainder

xy-3=(xy-y)+(y-3)

xy-3=xy-3 is what we wanted so we are done here.

Answer:

Step-by-step explanation:

Given,

[tex] \frac{7}{3} = \frac{x}{49} [/tex]

[tex] = > x = \frac{7}{3} \times 49[/tex]

[tex] = > x = \frac{343}{3} (ans)[/tex]

Answer:

343/3 or 114 1/3

Step-by-step explanation:

7/3 = x/49

Using cross products

3x = 7*49

3x =343

Divide by 3

3x/3 = 343/3

x =343/3

x =114 1/3

Answer:

T = 60 degrees

Step-by-step explanation:

The dotted line is the height so it is a right angle

We are able to use trig functions since this is a right triangle

cos T = adj side / hyp

cos T = a/b

cos T = 8 sqrt(2) / 16 sqrt(2)

cos T = 1/2

Taking the inverse of each side

cos^-1 ( cosT) = cos^-1 ( 1/2)

T = 60 degrees

Answer:

[tex]\angle T=60^{\circ}[/tex]

Step-by-step explanation:

In all 30-60-90 triangles, the sides are in ratio [tex]x:x\sqrt{3}:2x[/tex], where [tex]x[/tex] is the side opposite to the 30 degree angle and [tex]2x[/tex] is the hypotenuse of the triangle. We know that two right triangles are created on both sides of the rectangle in the center. Notice that [tex]8\sqrt{2}\cdot 2=16\sqrt{2}[/tex] and since [tex]16\sqrt{2}[/tex] is the hypotenuse of the right triangle on the left, [tex]8\sqrt{2}[/tex] must be facing the 30 degree angle. Therefore, angle T must be 60 degrees.

Alternatively, the cosine of any angle in a right triangle is equal to its adjacent side divided by the hypotenuse.

Therefore, we have:

[tex]\cos \angle T=\frac{8\sqrt{2}}{16\sqrt{2}},\\\cos \angle T=\frac{1}{2},\\\angle T=\arccos(\frac{1}{2}),\\\angle T=\boxed{60^{\circ}}[/tex]

Answer:

133

Step-by-step explanation:

Given that :

Degree of confidence, α = 0.90 ; The Zcritical vlaue at α = 90% is 1.645

The margin of error, MOE = ±2

Standard deviation, s = 14

Using the relation :

n = (Zcritical * standard deviation) / MOE

n = ((1.645 * 14) / 2)²

n = (23.03 /2)²

n = 11.515²

n = 132.595

n = 133 samples