Tell whether each system of equations has no solution, one solution, or infinitely many solutions. Show how you arrived at your conclusion for each.
a. y = 5x + 11 and y = 5x
b. y = 6x + 3 and y = 3x
c. x + 4y = 8 and y = -1/4x + 2

Answer:

1. 1/3 and 3

2. 4 and 4

Step-by-step explanation:

Step-by-step explanation:

Solution 1 :-

> Scale = 12/4 = 3 .

> x/ 9 = 4/12

> x = 1/3 × 9

> x = 3 in .

Solution 2 :-

> Scale = 8/2 = 4

> y / 1 = 8/2

> y = 4 ft .

Answer:

The inverse function is [tex]y = -\frac{x}{4}[/tex]

Step-by-step explanation:

Inverse of a function:

To find the inverse of a function, we exchange x by y, then we isolate y.

y = -4x

Finding the inverse:

[tex]x = -4y[/tex]

[tex]4y = -x[/tex]

[tex]y = -\frac{x}{4}[/tex]

So

The inverse function is [tex]y = -\frac{x}{4}[/tex]

Answer:

Price-Town

Step-by-step explanation:

:D

Answer:

1) draw a line from (2,4) to (6,4)

2) 27.5

3) 16

4) 43.5

5) $97.88

Step-by-step explanation:

1) draw a line from (2,4) to (6,4)

2) (7+4)/2=5.5x5=27.5

3) 4x4=16

4) 27.5+16=43.5

5) 43.5x2.25= 97.875 = $97.88

Answer:

Step-by-step explanation:

Required volume is:

Answer:

2h

Step-by-step explanation:

You can solve this one by adding their rates, but you have to invert the numbers they give you to find the rate.  Rate is measured in something per unit of time, and "per" indicates division.  So the rates are: 1/3 of an hour (Sally) and 1/6 of an hour (Steve).  So add the rates: 1/3 + 1/6 = 1/2.  (1/3 is 2/6, and 2/6 + 1/6 = 3/6).  Since their combined rate is 1/2 of a room in one hour, it takes them two hours to paint the room.  

Answer:

C=10

Step-by-step explanation:

Answer:

sin 40 - sin 20 = ​0.3007674664 approximately

Step-by-step explanation:

We cannot write the given expression in exact form, so you have to use the calculator, which works out to be 0.3007674664 approximately.

Answer:

Angle × =180 - 126

Angle × = 54

Answer:

The actual SAT score is 2024.

The equivalent ACT score is 29.49.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

SAT score that is in the 95th percentile

Scores on the SAT test are normally distributed with a mean of 1511 and a standard deviation of 312, which means that [tex]\mu = 1511, \sigma = 312[/tex]

95th percentile is X when Z has a pvalue of 0.95, so X when Z = 1.645. The score is:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.645 = \frac{X - 1511}{312}[/tex]

[tex]X - 1511 = 1.645*312[/tex]

[tex]X = 2024[/tex]

The actual SAT score is 2024.

Equivalent ACT score:

The equivalent ACT score is the 95th percentile of ACT scores.

Scores on the ACT test are normally distributed with a mean of 21.1 and a standard deviation of 5.1, which means that [tex]\mu = 21.1, \sigma = 5.1[/tex]. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.645 = \frac{X - 21.1}{5.1}[/tex]

[tex]X - 21.1 = 1.645*5.1[/tex]

[tex]X = 29.49[/tex]

The equivalent ACT score is 29.49.

Answer:

15 and -20

Step-by-step explanation:

The zeros/ roots are the x intercepts of the graph

Answer:

The common difference is 4.

Step-by-step explanation:

[tex]a_n=a_1+(n-1)d[/tex]  You get to term number n by starting with term number 1 and adding the common difference  d  n-1 times.

[tex]a_1=3\text{, and }a_8=31[/tex]

[tex]a_8=a_1+(8-1)d\\\\31=3+7d\\\\28=7d\\\\d=4[/tex]

Answer:

i had a stroke while reading this

Step-by-step explanation:

Answer:

son: 19

mother: 38

father: 43

Step-by-step explanation:

x + 2x + 2x+5 = 100

5x = 95

x = 19

The measure of the angle (θ) is equivalent to sin⁻¹(6.3/14.5).

The Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. Mathematically, it can be written as -

(hypotenuse)² = (base)² + (perpendicular)²

Given is a right angle triangle with hypotenuse as 14.5 meters and

opposite side as 6.3 meters.

We can write sine of the angle (θ) as -

sin(θ) = P/H

sin(θ) = Opposite side/Hypotenuse

sin(θ) = 6.3/14.5

(θ) = sin⁻¹(6.3/14.5)

Therefore, the measure of the angle (θ) is equivalent to sin⁻¹(6.3/14.5).

To solve more questions on Pythagoras theorem, visit the link below -

brainly.com/question/343682

#SPJ1

Answer:

Pattern is: +4

Step-by-step explanation:

an arithmetic series/ pattern since the next number is got by adding 4 to tge previous number

Answer:

108°

Step-by-step explanation:

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]35^{2}[/tex] = [tex]11^{2}[/tex] + [tex]30^{2}[/tex]

[tex]\frac{204}{-660}[/tex] = [tex]\frac{-660 cos}{-660}[/tex]

cos = -0.309

The measure of the greatest angle in the triangular fence is approximately 108.5 degrees. To find the measure of the greatest angle in the triangular fence, you can use the Law of Cosines.

The Law of Cosines states:

[tex]c^2 = a^2 + b^2 - 2ab * cos(C)[/tex]

where c is the side opposite the angle C, and a and b are the other two sides of the triangle.

In this case, the sides of the triangle are:

a = 11 yards

b = 30 yards

c = 35 yards

Now, let's find the measure of angle C (the angle opposite the side with length 35 yards):

[tex]c^2 = a^2 + b^2 - 2ab * cos(C)\\35^2 = 11^2 + 30^2 - 2 * 11 * 30 * cos(C)\\1225 = 121 + 900 - 660 * cos(C)\\1225 = 1021 - 660 * cos(C)\\[/tex]

Now, isolate cos(C) by moving the terms around:

[tex]660 * cos(C) = 1021 - 1225\\660 * cos(C) = -204[/tex]

Now, divide by 660 to find cos(C):

[tex]\cos(C) \approx -0.3091[/tex]

Now, find the measure of angle C by taking the inverse cosine (cos^-1) of -0.3091:

[tex]C \approx cos^-1(-0.3091)\\C \approx 108.5 degrees[/tex] (rounded to one decimal place)

Since this is the angle opposite the side with length 35 yards, it is the greatest angle in the triangle.

So, the measure of the greatest angle in the triangular fence is approximately 108.5 degrees.

To know more about angle:

https://brainly.com/question/30147425

#SPJ2

Answer:

52 cm²

Step-by-step explanation:

There are 3 distinct faces:

one with sides 2 and 3

one with sides 2 and 4

one with sides 3 and 4

There are two of each distinct face (they are accros each other)

so we find their areas (we times by two as there are two of each face)

2×3×2=12

2×4×2=16

3×4×2=24

Finally we add the values:

12+16+24=52 cm²

Answer:

f(x) = 0.99x + 0.3

Step-by-step explanation:

f(x) = 1.29 + 0.99(x - 1)

Distribute

f(x) = 1.29 + 0.99x - 0.99

Combine like terms

f(x) = 0.99x + 0.3

Answer: 2.403 × 10^3 atoms

Step-by-step explanation:

10^13 x 6.02 = 6.02^23 and 6.02^23 x 4 = 2,403 turned into 2.403 x 10^3 atoms.

The division expression is equivalent to the given expression is (13/ 3)/ (-5/6)

What is expression ?

expression can be defined as with the minimum of two variables or numbers and at least one math operation.

Given expression,

= 4 1/3 / (-5/6 )

= (13/3 )/ (-5/6)

= 13*6 / -15

= -26/5

By evaluating the other expressions to find its equivalent,

(13 / 3) / (-5/6)

= 13 * 6 / -15

= -26/5

Hence , the expression 4 1/3 / (-5/6 ) is equivalent to (13 / 3) / (-5/6) .

To learn more about expression from the given link.

brainly.com/question/1859113

#SPJ1

The division expression is equivalent to the given expression is (13/ 3)/ (-5/6)

expression can be defined as with the minimum of two variables or numbers and at least one math operation.

Division is one of the four basic mathematical operations of arithmetic, along with addition, subtraction, and multiplication. The division operation is represented by the symbol ÷ or /, and it is the inverse operation of multiplication.

Given expression,

= 4 1/3 / (-5/6 )

= (13/3 )/ (-5/6)

= 13*6 / -15

= -26/5

By evaluating the other expressions to find its equivalent,

(13 / 3) / (-5/6)

= 13 * 6 / -15

= -26/5

Hence , the expression 4 1/3 / (-5/6 ) is equivalent to (13 / 3) / (-5/6) .

To learn more about expression from the given link.

brainly.com/question/1859113

#SPJ1

Note that in the attached Geometric Figure (Diagram) which features QR as parallel to NO, if NQ = 12, QR 20, and NO = 35, then the length of QP is equal to 16.

[tex]\overline {QR}[/tex] is Parallel to [tex]\overline {NO}[/tex]; therefore

QR/NO = PQ/PN

⇒ 20/35 = PQ/PQ +12

This is because:

PN = PQ + NQ; which is also
PN = PQ +12

(PQ + 12) x 20 = 35PQ
20PQ + 240= 35PQ ; Collect like terms

240= 35 PQ - 20 PQ

240 = 15PQ; Divide both sides by 15

⇒ 240/15 = 15PQ/15
⇒ 16 = PQ

Therefore, QP = PQ which is equal to 16.

Learn more about Geometric Forms:
https://brainly.com/question/29273438
#SPJ1

Answer:

E, 5, 3

Step-by-step explanation:

We just need to connect the rectangle with dots equally placed.

Answer:

(x + 1)^2 + (y + 2)^2 = 106

Step-by-step explanation:

The formula for a circle is

(x - h)^2 + (y - k)^2 = r^2

Where (h, k) is the center of the circle and r is the raadius

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

The center is the midpoint of the diameter end points

(h, k) = ( (-6 + 4)/2 , (-11 + 7)/2 )

(h, k) = (-1, -2)

The radius is the distance from the center to an endpoint

Using (h, k) and Q

r^2 = (4 - -1)^2 + (7 - -2)^2

r^2 = 5^2 + 9^2

r^2 = 106

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

Plug into the circle formula

(x + 1)^2 + (y + 2)^2 = 106

9514 1404 393

Answer:

  2∛7

Step-by-step explanation:

Putting the expression in simplest form will factor cubes from under the radical.

  [tex]\displaystyle\sqrt[3]{56}=\sqrt[3]{2^3\cdot7}=\boxed{2\sqrt[3]{7}}[/tex]

Answer:

a=0.2

Step-by-step explanation:

Let's solve your equation step-by-step.

2.8=14a

Step 1: Flip the equation.

14a=2.8

Step 2: Divide both sides by 14.

14a/ 14 = 2.8/ 14

a=0.2

Answer:

a=0.2

Answer:

here is your correct answer and listen question no four option are incorrect

Answer:

It's sales tax I believe

Answer:

8 and 5

Step-by-step explanation: