Graph each of the following lines without using a table of values. a. y = 2⁄3x - 5 b. 6x - 2y + 5 = 0

Answer:

The picture isn't very clear but I think this is the answer.

1. 15 cents

2. $1.31

3. 30 cents

Step-by-step explanation:

1. 10+5

2. 50+50+10+10+10+1

3. 25+5

Answer:

 $624.90

Step-by-step explanation:

The total cost is the integral of the marginal cost. Here, you're asked to approximate that integral using 5 equal-width rectangles. The area of each rectangle is the product of its height and width. The height is given by the function value at the left end of the interval.

The table shows the function values at the left end of each of the 5 intervals. The intervals have width 1600/5 = 320. The total estimated cost is the sum of products of 320 and each of the table values. (Of course, 320 can be factored out of the sum to make the math easier.)

The estimated cost is ...

  320(58 + 50.576 + 41.104 + 29.584 +16.016) = 62,489.6 . . . cents

  ≈ $624.90 . . . . cost of manufacturing 1600 yards of fancy ribbon

Answer:

8/9

Step-by-step explanation:

The proportion of the treasure which Johnny got [tex]= \dfrac{1}{3}[/tex]

The proportion of the treasure which  Elizabeth got [tex]=\dfrac{5}{9}[/tex]

Together, the proportion of the treasure which they got

[tex]= \dfrac{1}{3}+\dfrac{5}{9}[/tex]

Take the LCM of the denominators

LCM of 3 and 9 is 9.

Therefore:

[tex]\dfrac{1}{3}+\dfrac{5}{9} \\\\=\dfrac{3+5}{9}\\\\=\dfrac{8}{9}[/tex]

Together, Johnny and Elizabeth got 8/9 of the treasure.

Answer:

Step-by-step explanation:

Given:

AB║DC and BC║AE

To prove:

[tex]\frac{\text{BC}}{\text{EA}}=\frac{\text{BD}}{\text{EB}}[/tex]

                Statements                  Reasons

1). ∠ABE ≅ ∠CDB                    1). Alternate interior angles

2). ∠AEB ≅ ∠CBD                  2). Alternate interior angles

3). ΔCBD ~ ΔAEB                   3). AA property of similarity

4). [tex]\frac{\text{BC}}{\text{EA}}=\frac{\text{BD}}{\text{EB}}[/tex]                             4). Property of similarity [Corresponding sides                                                          of two similar triangles are proportional]

Answer:

The percent of increase is 25%

Step-by-step explanation:

Percentage increase = increase in price/original price × 100 = ($250 - $200)/$200 × 100 = $50/$200 × 100 = 25%

Answer:

For the function [tex]f(x)=\frac{1}{x} +3[/tex]. The domain is [tex]\left(-\infty \:,\:0\right)\cup \left(0,\:\infty \:\right)[/tex] and the range is  [tex]\left(-\infty, 3\right) \cup \left(3, \infty\right)[/tex].

For the function [tex]g(x) =\sqrt{x+6}[/tex]. The domain is [tex]\left[-6, \infty\right)[/tex] and the range is [tex]\left[0, \infty\right)[/tex].

Step-by-step explanation:

The domain of a function is the set of input or argument values for which the function is real and defined.

The range of a function is the complete set of all possible resulting values of the dependent variable, after we have substituted the domain.

[tex]f(x)=\frac{1}{x} +3[/tex] is a rational function.  A rational function is a function that is expressed as the quotient of two polynomials.

Rational functions are defined for all real numbers except those which result in a denominator that is equal to zero (i.e., division by zero).

The domain of the function is [tex]\left(-\infty \:,\:0\right)\cup \left(0,\:\infty \:\right)[/tex].

The range of the function is [tex]\left(-\infty, 3\right) \cup \left(3, \infty\right)[/tex].

[tex]g(x) =\sqrt{x+6}[/tex] is a square root function.

Square root functions are defined for all real numbers except those which result in a negative expression below the square root.

The expression below the square root in [tex]g(x) =\sqrt{x+6}[/tex] is [tex]x+6[/tex]. We want that to be greater than or equal to zero.

[tex]x+6\geq 0\\x\ge \:-6[/tex]

The domain of the function is [tex]\left[-6, \infty\right)[/tex].

The range of the function is [tex]\left[0, \infty\right)[/tex].

Answer:

The value of the radius is 4.46cm.

Step-by-step explanation:

Given the perimeter is 28 cm. So, if we want to find the radius then we should consider this perimeter as the circumference of the circle. Thus, we have to equate this value with the circumference (perimeter of the circle).

The perimeter of the circle or circumference = 2π r  

Here, π = 22/7

r = radius

Now, 2π r = 28

r = 28 / 2π

r = 4.46 cm

Answer:

A and B are independent because P(A) * P(B) = P(A and B).

Step-by-step explanation:

If A and B are independent, then P(A) * P(B) = P(A and B)

since

P(A)*P(B) = (2/3*1/4) = 2/12 = 1 / 6 = P(A and B)

A and B are independent.

Answer:

YES THANKS FOR 30

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

For point-slope form, you need a point and the slope.

y - y₁ = m(x - x₁)

Looking at the graph, the points you have are (4, 0) and (-4, -4).  You can use these points to find the slope.  Divide the difference of the y's by the difference of the x's/

-4 - 0 = -4

-4 - 4 = -8

-4/-8 = 1/2

The slope is 1/2.  This cancels out choices C and D.

With the point (-4, -4), A is the answer.

the equation of the line in slope-intercept form is:

y = (1/2)x - 2

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

From the graph, two points on the line are (-4, -4) and (4,0),

The formula for the slope of a line is:

m = (y₂ - y₁) / (x₁ - x₁)

where (x₁, y₁) and (x₂, y₂) are two points on the line.

Using the given points (-4, -4) and (4, 0), we can calculate the slope:

m = (0 - (-4)) / (4 - (-4))

m = 4 / 8

m = 1/2

Now that we know the slope, we can use the slope-intercept form of a line, which is:

y = mx + b

where m is the slope and b is the y-intercept.

To find the y-intercept, we can use one of the given points on the line. Let's use the point (-4, -4):

y = mx + b

-4 = (1/2)(-4) + b

-4 = -2 + b

b = -2

Therefore, the slope-intercept form of the line is y = (1/2)x - 2.

Learn more about Linear equations here:

https://brainly.com/question/11897796

#SPJ7

Answer: k = 12

Step-by-step explanation:

x² + kx + 36 = 0

In order for x to have exactly one solution, it must be a perfect square.

(x + √36)² = 0

(x + 6)² = 0

(x + 6)(x + 6) = 0

x² + 6x + 6x + 36 = 0

x² + 12x + 36 = 0

 k = 12

Answer:

1. Vertex (-3,2)

A) (x+3)² + 5

B) (x-3)² + 2

C) (x-1)² -5

I hope these are all correct

Step-by-step explanation:

Answer:

The statistic is misleading because Christopher collects his sample from a population (voters in his state) and make inferences about another population (voters in his city).

Step-by-step explanation:

The statistic is misleading because Christopher collects his sample from a population (voters in his state) and make inferences about another population (voters in his city).

He should make inferences about the population that is well represented by his sample (voters in his state), or take a sample only from voters from his city to make inferences about them.

Answer:

The general term for the given sequence is:

[tex]a_n=(-1)^{n+1}\dfrac{n}{(n+1)^2}[/tex]

Step-by-step explanation:

The given series is:

[tex]\dfrac{1}4, - \dfrac{2}9, \dfrac{3}{16}, - \dfrac{4}{25}, ......[/tex]

First of all, let us have a look at the positive and negative sign of the sequence.

2nd, 4th, 6th ..... terms have a negative sign.

For this we can use the following

[tex](-1)^{n+1}[/tex]

i.e. Whenever 'n' is odd, power of (-1) will become even resulting in a positive term for odd terms i.e. (1st, 3rd, 5th ........ terms)

Whenever 'n' is even, power of (-1) will become odd resulting in a negative term for even terms i.e. (2nd, 4th, 6th ..... terms)

Now, let us have a look at the numerator part:

1, 2, 3, 4.....

It is simply [tex]n[/tex].

Now, finally let us have a look at the denominator:

4, 9, 16, 25 ......

There are squares of the (n+1).

i.e. 1st term has a square of 2.

2nd term has a square of 3.

and so on

So, it can be represented as:

[tex](n+1)^2[/tex]

[tex]\therefore[/tex] nth term of the sequence is:

[tex]a_n=(-1)^{n+1}\dfrac{n}{(n+1)^2}[/tex]

Answer:

7

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

Multiply 3 quarts to 7 hours

Which is 21

Mark me as brainliest

Step-by-step explanation:

Edith picks 3

Rupert picks 3

3 + 3 = 6 quarts of blueberries in 1 hour

6 blueberries = 1 hour

x. =. 7 hours

x = 7 hours ÷ 1 hour × 6 blueberries

x =. 42 quarts of blueberries

Answer:

69.9 mg

Step-by-step explanation:

A = A₀ (½)^(t / T)

where A is the final amount,

A₀ is the initial amount,

t is time,

and T is the half life.

A = 400 (½)^(4000 / 1590)

A = 69.9 mg

Answer and Step-by-step explanation:

Variance is the measurement of the spread bewteen the numbers of the data set and can be calculated by the formula:

σ² = ∑(x  - ⁻x)² / n

1) With the data, find its mean (⁻x) by adding all the values and dividing the sum by total number of elements the data has;

2) Subtract each value of the data to the mean;

3) Square the result of the subtractions;

4) Add the squares;

5) Divide the sum by the total number of elements of the set;

6) The result is the Variance (σ²);

Standard Deviation is the measure of how far the values of the data set are from the mean and it is the square root of Variance:

σ = [tex]\sqrt{(variance)^{2}}[/tex]

So, to calculate standard deviation, you just take the square root of the variance.

Answer:

no solution

Step-by-step explanation:

y=-1/2x+4

2y=-x-8, t=-1/2x-4

These are parallel so no solution

Answer:

The correct answer is no solution.

Step-by-step explanation:

y = -1/2x + 4

x + 2y = -8 → -1/2x + 4

The lines are parallel therefore, leaving us with no solution.

Hope this helped! :)

Answer:

B. No solution.

Step-by-step example

I will try to solve your system of equations.

3x−y=4;6x−2y=7

Step: Solve3x−y=4for y:

3x−y+−3x=4+−3x(Add -3x to both sides)

−y=−3x+4

−y

−1

=

−3x+4

−1

(Divide both sides by -1)

y=3x−4

Step: Substitute3x−4foryin6x−2y=7:

6x−2y=7

6x−2(3x−4)=7

8=7(Simplify both sides of the equation)

8+−8=7+−8(Add -8 to both sides)

0=−1

Therefore, there is no solution, and the lines are parallel.

Answer:

Rate of change of function 1: ZERO

Rate of change of function 2: TWO

The rate of change of function 2 is 2 more than the rate of change of function 1.

Step-by-step explanation:

Hope this helps and please mark as brainiest!

Answer:

The answer is 2.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Area of a rectangle = l × w

where

l is the length

w is the width

The length is seven times the width is written as

l = 7w

Area of the rectangle = 175 cm²

7w × w = 175

7w² = 175

Divide both sides by 7

w² = 25

Find the square root of both sides

w = √25

w = 5cm

But l = 7w

l = 7(5)

l = 35cm

The length is 35cm

The width is 5cm

Hope this helps you.

Answer:

a) sinx = 3/5

b) cosx = 4/5

c) line OZ = 3cm

Step-by-step explanation:

Two different questions are stated here:

The first is rectangle ABCD where two of its sides are given and we are to find line OZ

The second is on trigonometry. We have been given the tangent ratio and we are to find the sine and cosine ratio.

1) Rectangle ABCD dimensions:

AB = 2cm

CD = 6cm

So we know when we are drawing the rectangle, the smallest side = 2cm and biggest side = 6cm

AO is perpendicular to OB

Line OZ cuts line AB into two

Find attached the diagram

To determine Line OZ, we would apply tangent rule since we know adjacent but opposite is missing.

All 4 angles in a rectangle = 90°

∠OAZ = 45

tan 45 = opposite/adjacent

tan 45 = OZ/3

OZ = 3 × tan45

OZ = 3×1

OZ = 3cm

2) tanx = 3/4

Tangent ratio = opposite/adjacent

opposite = 3, adjacent = 4

see attachment for diagram

Sinx = opposite/hypotenuse

Using Pythagoras theorem

hypotenuse² = opposite² + adjacent²

hypotenuse² = 3²+4² = 9+16 = 25

hypotenuse = √25

hypotenuse = 5

Sinx = opposite/hypotenuse

Sinx = 3/5

Cosx = adjacent/hypotenuse

Cosx = 4/5

a) 3/5

b) 4/5

c) 3cm

Answer:

The 68% confidence interval is (6.3, 6.7).

The 95% confidence interval is (6.1, 6.9).

The 99.7% confidence interval is (5.9, 7.1).

Step-by-step explanation:

The Central Limit Theorem states that if we have a population with mean μ and standard deviation σ and take appropriately huge random-samples (n ≥ 30) from the population with replacement, then the distribution of the sample-means will be approximately normally distributed.

Then, the mean of the sample means is given by,

[tex]\mu_{\bar x}=\bar x[/tex]

And the standard deviation of the sample means (also known as the standard error)is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}} \ \text{or}\ \frac{s}{\sqrt{n}}[/tex]

The information provided is:

[tex]n=400\\\\\bar x=6.5\\\\s=4[/tex]

As n = 400 > 30, the sampling distribution of the sample-means will be approximately normally distributed.

(a)

Compute the 68% confidence interval for population mean as follows:

[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]

    [tex]=6.5\pm 0.9945\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.1989\\\\=(6.3011, 6.6989)\\\\\approx (6.3, 6.7)[/tex]

The 68% confidence interval is (6.3, 6.7).

The margin of error is:

[tex]MOE=\frac{UL-LL}{2}=\frac{6.7-6.3}{2}=0.20[/tex]

(b)

Compute the 95% confidence interval for population mean as follows:

[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]

    [tex]=6.5\pm 1.96\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.392\\\\=(6.108, 6.892)\\\\\approx (6.1, 6.9)[/tex]

The 95% confidence interval is (6.1, 6.9).

The margin of error is:

[tex]MOE=\frac{UL-LL}{2}=\frac{6.9-6.1}{2}=0.40[/tex]

(c)

Compute the 99.7% confidence interval for population mean as follows:

[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]

    [tex]=6.5\pm 0.594\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.392\\\\=(5.906, 7.094)\\\\\approx (5.9, 7.1)[/tex]

The 99.7% confidence interval is (5.9, 7.1).

The margin of error is:

[tex]MOE=\frac{UL-LL}{2}=\frac{7.1-5.9}{2}=0.55[/tex]

Answer:

Step-by-step explanation:

g(x) = |x-3| is neither even nor odd; the graph is not symmetric about the y-axis (as characterizes even functions), and is not symmetric about the origin either.

g(x) = x + x is actually g(x) = 2x, which is an odd function.  The graph is symmetric about the origin.

Answer:

See Explanation

Step-by-step explanation:

(a)For matrices A and C, given that: [tex]CA=I_n[/tex].

We want to show that Ax=0 has only the trivial solution

If Ax=0

Multiply both sides by C

[tex]C(Ax)=C \times 0\\\implies (CA)x=0$ (Recall: CA=I_n)\\\implies I_nx=0 $ (Since I_n$ is the n\times n$ identity matrix)\\\implies x=0[/tex]

This means that the system has only the trivial solution.

(b)If the system has more columns than rows, a free variable would occur when a column does not have a pivot. This would lead to a non-trivial solution.

Answer:

a)

The object slowing down  S = -72 centimetres after t = 4 seconds

b)

The speed is decreasing at t = -2 seconds

The objective function  S = 36 centimetres

Step-by-step explanation:

Step(i):-

Given  S = t³ - 3 t² - 24 t + 8 ...(i)

   Differentiating equation (i) with respective to 'x'

       [tex]\frac{dS}{dt} = 3 t^{2} - 3 (2 t) - 24[/tex]

     Equating Zero

      3 t ² - 6 t - 24 = 0

 ⇒   t² - 2 t - 8   = 0

 ⇒  t² - 4 t + 2 t - 8 = 0

⇒ t (t-4) + 2 (t -4) =0

⇒  ( t + 2) ( t -4) =0

⇒ t = -2 and t = 4

 Again differentiating with respective to 'x'

   [tex]\frac{d^{2} S}{dt^{2} } = 6 t - 6[/tex]

Step(ii):-

Case(i):-

Put t= -2

[tex]\frac{d^{2} S}{dt^{2} } = 6 t - 6 = 6 ( -2) -6 = -12 -6 = -18 <0[/tex]

The  maximum object

S = t³ - 3 t² - 24 t + 8

S = ( -2)³ - 3 (-2)² -24(-2) +8

S = -8-3(4) +48 +8

S = - 8 - 12 + 56

S = - 20 +56

S = 36

Case(ii):-

   put  t = 4

[tex]\frac{d^{2} S}{dt^{2} } = 6 t - 6 = 6 ( 4) -6 = 24 -6 = 18 >0[/tex]

The object slowing down at t =4 seconds

The minimum objective function

S = t³ - 3 t² - 24 t + 8

S = ( 4)³ - 3 (4)² -24(4) +8

S =  64 -48 - 96 +8

S = - 72

The object slowing down  S = -72 centimetres after t = 4 seconds

Final answer:-

The object slowing down  S = -72 centimetres after t = 4 seconds

The speed is decreasing at t = -2 seconds

The objective function  S = 36 centimetres

Answer:

Step-by-step explanation:

x-4 greater or equal 0

x greater or equal 4

Answer:

The actual answer is x is greater than or equal to 6 (i used the answer that was on here and got it wrong so here is the correct answer!!)

just did the test on edg 2021

Hey there! I'm happy to help!

The domain is all of the x-values of a relation and the range is all of the y-values. When you write them out, you order the numbers from least to greatest and put it in brackets.

The domain of our relation is the x-values of these points, which are 11, 9, 7, and 5. The domain is  {5,7,9,11}.

The range is the y-values, which are 1, 2, 3, and 4. So, the range is {1,2,3,4}.

Now you can find the domain and range given a few ordered pairs!

Have a wonderful day!

Answer:

2

Step-by-step explanation:

Slope =( difference in the y coordinates)/ (difference in the x coordinates)

= 6/3

= 2

Answer:

[tex]approx. = 85.28 {ft}^{2} [/tex]

Step-by-step explanation:

You can think of this as adding the area of the rectangular portion of the deck (length x width) and the semicircular portion (πr^2)/2.

(l×w)+(πr^2)/2

(10×7)+((π2^2)/2

79+2π

[tex]approx. = 85.28 {ft}^{2} [/tex]

Answer:

13

Step-by-step explanation:

p^2 -6p +6

Let p=-1

(-1)^2 -6(-1) +6

1 +6+6

13