3. (05.01)
A pair of linear equations is shown below:
y = -x + 1
y = 2x + 4
Which of the following statements best explains the steps to solve the pair of equations graphically? (4 points)
On a graph, plot the line y = -x + 1, which has y-intercept = -1 and slope = 1, and y = 2x + 4, which has y-intercept = 2 and slope = 4, and write the coordinates of the point of
Intersection of the two lines as the solution.
On a graph, plot the line y = -x + 1, which has y-intercept - 1 and slope = 1, and y = 2x + 4, which has y-intercept = 1 and slope = 4, and write the coordinates of the point of
intersection of the two lines as the solution.
On a graph, plot the line y = -x + 1, which has y-intercept = 1 and slope = -1, and y = 2x + 4, which has y-intercept = -2 and slope = 2, and write the coordinates of the point
of intersection of the two lines as the solution.
On a graph, plot the line y = -x + 1, which has y-intercept = 1 and slope = -1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of
intersection of the two lines as the solution.

Answer:

B.

Step-by-step explanation:

B.

- 9 ≤ - 3x - 6 ≤ 6

1 part.

- 9  +6 ≤ - 3x - 6 +6

- 3/(- 3) ≤ - 3x/(- 3)

1 ≥ x

2d part

- 3x - 6 +6≤ 6 + 6

- 3x ≤ 12

- 3x/(-3) ≥ 12/(-3)

x ≥ - 4

x ≥ - 4 and x≤ 1

Answer:

48x>+2

Step-by-step explanation:

Answer:

  2082.12 was the total invested

Step-by-step explanation:

Let x represent the amount invested at 14%. Then the amount invested at 12% was (x-580). The total accumulated amount was ...

  112%(x -580) +114%(x) = 2358.60

  2.26x -649.60 = 2358.60

  2.26x = 3008.20 . . . add 649.60

  x = 1331.06 . . . . . . divide by 2.26

  x -580 = 751.06

The total invested was 1331.06 +751.06 = 2082.12 cedis.

__

Check

The investment at 12% was 751.06, so the accumulated amount of that investment was 751.06×1.12 = 841.19.

The investment at 14% was 1331.06, so the accumulated amount of that investment as 1331.06×1.14 = 1517.41.

The accumulated total amount was 841.19 +1517.41 = 2358.60.

Answer:

Step-by-step explanation:

Wheres the question??

Answer: $7

Step-by-step explanation:

35/ 5 = 7

Answer:

$7

Step-by-step explanation:

Bc/ 35/5=7

Answer:

0.00420 is the answer

Step-by-step explanation:

The definition of sig figs is each of the digits of a number that are used to express it to the required degree of accuracy, starting from the first nonzero digit.

The rounding number of 0.004198223 to 3 significant figures is 0.0042

Here,

The number is 0.004198223.

We have to find,  0.004198223 to 3 significant figures.

What is Rounding number?

Rounding means making a number simpler but keeping its value close to what it was.

Here,

The number is 0.004198223.

To find 3 significant figures,

We round a number to three significant figures in the same way that we would round to three decimal places.

Then, We count from the first non-zero digit for three digits. We then round the last digit.

Here, the digit is 9 then it will be round.

We get, the number is;

0.0042

We fill in any remaining places to the right of the decimal point with zeros.

So, The rounding number of 0.004198223 to 3 significant figures is 0.00420

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Answer: the answer is A 5 units

The length of L'L in the dilated figure is 5 units.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Dilation is the increase or decrease in size of a figure.

Triangle JKL was dilated by 1/3 with M as the center of dilation to form J'K'L'.

Given that ML' = 2.5 units, hence:

L'L = (2.5 * 3) - 2.5 = 5 units

The length of L'L in the dilated figure is 5 units.

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Answer:

13.53% probability that no customers arrive in a five-minute period

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given time interval.

They arrive at a rate of two every five minutes

This means that [tex]\mu = 2[/tex]

What is the probability that no customers arrive in a five-minute period?

This is P(X = 0).

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353[/tex]

13.53% probability that no customers arrive in a five-minute period

Answer:

18×18×36

Step-by-step explanation:

According to the Question

108≥ 4h + w

Volume V is given by

V = wh^2

⇒V= (108-4h)h^2

⇒V= 108h^2 - 4h^3

Now differentiating and keeping = 0 we get

V' = 216h - 12h^2 = 0

h = 216/12 = 18

w = 108 - 4×18 = 36

V = 36×18^2 = 11664 from a box of 18×18×36.

Answer:  The probability if getting a head on the first flip is 1/2 or 50 percent,the probability of getting a tail on the second flip is also 1/2 and the probability of getting another head on the third flip is 1/2.

Step-by-step explanation:

Answer:

3/8

Step-by-step explanation:

Answer:

Step-by-step explanation:

Rational numbers are the result of dividing two integers. Intergers cannot be fractions. So 1.5 is rational but 3/2 is not.

Five rational numbers: 1.5, 6, 24.7, 384, 404.4, 1,980

I'm always happy to help :)

Answer:

Step-by-step explanation:

Area of rectangle = l × b

= 23 × 6

= 138 feet

hope this helps

plz mark it as brainliest!!!!!!!

Answer:

Read below.

Step-by-step explanation:

Questions are underlined

Answers are bolded

Which of the following statements is true?

If two polygons are similar then the corresponding sides are proportional and the corresponding angles are proportional.

If two polygons are similar, then the corresponding sides are proportional and  the corresponding angles are congruent.

If two polygons are similar, then the corresponding sides are congruent and the corresponding angles are proportional.

None of the choices are correct.

Which of the following sides are corresponding if ΔABC is similar to ΔMNL?

AC and ML, BC and NL, AB and MN is the correct answer but the answer choices are:

AB and MN, BC and NL, AC and ML

AC and MN, BC and NL, AB and ML

AB and ML, BC and NL, AC and MN

None of the choices are correct.

Answer:

The real number 'a' = 32

The real number 'b' = 0

Step-by-step explanation:

Product of a number of a number and its conjugate = a + bi

The number is = -4 + 4i

Conjugate of this number is = -4 - 4i

Product of the number and it's conjugate

= (-4 + 4i)(-4 - 4i)

= -4(-4 - 4i) + 4i(-4 - 4i) [By distributive property]

= 16 + 16i - 16i - 16i²

= 16 - 16(-1)

= 16 + 16

= 32

a + bi = 32 + (0)i

By comparing both the sides,

a = 32

b = 0

Answer:

30

Step-by-step explanation:

Since this is a right triangle, we can use a trig function

cos theta = adjacent/ hypotenuse

cos ? = 52/ 60

Take the inverse cos of each side

cos ^ -1 cos ? = cos ^ -1 ( 52/60)

? =29.92643487

To the nearest degree

? = 30

[tex]answer \\ 30 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]

Answer:

Is there a picture or graph or..

Step-by-step explanation:

Step-by-step explanation:

arc length = (radians * radians) . 90° is π/2 radians. Arc length is (π/2×4). So the answer is 2π.

Answer:

1/3 left

Step-by-step explanation:

The total sandwich is 1 or in fraction form 6/6

He ate 2/6

6/6 -2/6 = 4/6

Then he ate 2/6 more

4/6 -2/6 = 2/6

He has 2/6 left

Simplifying

2/6 =1/3

Answer:

a)0.2240

b)0.5768

Step-by-step explanation:

Given:

µ=3

Poison probability is given by :

[tex]f_k=\frac{\mu^ke^-^\mu}{k!}[/tex]

a) Evaluating at k=3

[tex]f(3)=\frac{3^3e^-^3}{3!} \approx 0.2240[/tex]

b)Evaluating at k=0,1,2:

[tex]f(0)=\frac{3^0e^-^3}{0!} \approx 0.0498[/tex]

[tex]f(1)=\frac{3^1e^-^3}{1!} \approx 0.1494[/tex]

[tex]f(2)=\frac{3^2e^-^3}{2!} \approx 0.2240[/tex]

Use complement rule:

P(x≥3)= 1 - f(0) - f(1) - f(2)= 1- 0.0498 - 0.1494 - 0.2240 =0.5768

Answer:

[tex]70 \: cm^2[/tex]

Step-by-step explanation:

Area of parallelogram.

[tex]A=bh[/tex]

[tex]b \times h[/tex]

[tex]14 \times 5[/tex]

[tex]=70[/tex]

Answer:

0

Step-by-step explanation:

In a suit of 52 cards

The experiment consists of drawing 1 card from the standard deck.

Since diamonds are red, there is no black jack of diamonds.

Therefore:

P(drawing a black jack of diamonds)

[tex]=\dfrac{0}{52}\\\\ =0[/tex]

Answers:

In photo below

Explanation:

I got it correct in my test :)

Answer:

[tex]74.8m[/tex]

Step-by-step explanation:

[tex]A=a^2\\P=4a\\P=4\sqrt{A} \\=4*\sqrt{349.69} \\=74.8m[/tex]

Hi

X-17 = -5

X = -5+17

X = 12

Answer:

Step-by-step explanation:

I'm pretty sure that you have to add 17 on both sides to keep the final number, not negative.  

So like:

x-17=-5

+17   +17

x-0=12            

and because 0 is nothing really, x=12

Answer:

When x = 1 and z = 4,   [tex]y=\frac{80}{9}[/tex]

Step-by-step explanation:

The variation described in the problem can be written using a constant of proportionality "b" as:

[tex]y=b\,\,x\,\,z^2[/tex]

The other piece of information is that when x = 5 and z = 1, then y gives 25/9. So we use this info to find the constant "b":

[tex]y=b\,\,x\,\,z^2\\\frac{25}{9} =b\,\,(5)\,\,(1)^2\\\frac{25}{9} =b\,\,(5)\\b=\frac{5}{9}[/tex]

Knowing this constant, we can find the value of y when x=1 and z=4 as:

[tex]y=b\,\,x\,\,z^2\\y=\frac{5}{9} \,\,x\,\,z^2\\y=\frac{5}{9} \,\,(1)\,\,(4)^2\\y=\frac{5*16}{9}\\y=\frac{80}{9}[/tex]

Answer:

[tex]t=\frac{25.5-26}{\frac{1}{\sqrt{8}}}=-1.414[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=8-1=7[/tex]  

The p value for this case is given by:

[tex]p_v =P(t_{(7)}<-1.414)=0.100[/tex]  

Since the p value is higher than the significance level of 0.06 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 25.5 and then the claim makes sense

Step-by-step explanation:

Information given

[tex]\bar X=25.5[/tex] represent the sample mean

[tex]s=1[/tex] represent the sample standard deviation

[tex]n=8[/tex] sample size  

[tex]\mu_o =26[/tex] represent the value to verify

[tex]\alpha=0.06[/tex] represent the significance level  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value

Hypothesis to est

We want to test if the true mean is at least 26 mpg, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 25.5[/tex]  

Alternative hypothesis:[tex]\mu < 25.5[/tex]  

The statistic for this case is given by;

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing the info given we got:

[tex]t=\frac{25.5-26}{\frac{1}{\sqrt{8}}}=-1.414[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=8-1=7[/tex]  

The p value for this case is given by:

[tex]p_v =P(t_{(7)}<-1.414)=0.100[/tex]  

Since the p value is higher than the significance level of 0.06 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 25.5 and then the claim makes sense

Answer:

57°

Step-by-step explanation:

According to theorem, "any two angles in the same segment of the circle are equal"

So,

m<BED = 57°

Answer:

B:

Step-by-step explanation:

Measure of ARC AFB is 180°

Why?

This is because AB is a diameter.

Answer:

[tex] \frac{1}{9 - 4i} [/tex]

I'm not sure

FINDING THE SURFACE AREA OF A COMPOSITE SOLID

About "Finding the surface area of a composite solid"

Finding the surface area of a composite solid :

A composite solid is made up of two or more solid figures.

To find the surface area of a composite solid, find the surface area of each figure. Subtract any area not on the surface.

Finding the surface area of a composite solid - Examples

Example 1 :  

Daniel built the birdhouse shown below. What was the surface area of the birdhouse before the hole was drilled ?

Solution :  

Step 1 :

Identify the important information.

• The top is a triangular prism with h = 24 cm. The base is a triangle with height 8 cm and base 30 cm.

• The bottom is a rectangular prism with h = 18 cm. The base is a 30 cm by 24 cm rectangle.

• One face of each prism is not on the surface of the figure.

Step 2 :  

Find the surface area of each prism.

Add the areas. Subtract the areas of the parts not on the surface.

Step 3 :  

Find the area of the triangular prism.

Perimeter  =  17 + 17 + 30  =  64 cm

Base area  =  (1/2)(30)(8)  =  120 sq.cm

Surface area  =  Ph + 2B

Surface area  =  64(24) + 2(120)

Surface area  =  1,776 sq.cm

Step 4 :  

Find the area of the rectangular prism.

Perimeter  =  2(30) + 2(24)  =  108 cm

Base area  =  30(24)  =  720 sq.cm

Surface area  =  Ph + 2B

Surface area  =  108(18) + 2(720)

Surface area  =  3,384 sq.cm

Step 5 :  

Add. Then subtract twice the areas of the parts not on the surface.

Surface area  =  1,776 + 3,384 - 2(720)  =  3,720 sq.cm

The surface area before the hole was drilled was 3,720 sq.cm.

The surface area before the hole was drilled was; 3,720 sq.cm.

A composite solid is made up of two or more solid figures.

To determine the surface area of a composite solid, find the surface area of each figure. Subtract any area not on the surface.

Given that the top is a triangular prism with h = 24 cm. The base is a triangle with height 8 cm and base 30 cm.

The bottom is a rectangular prism with h = 18 cm.

The base is a 30 cm x 24 cm rectangle.

One face of each prism is not on the surface of the figure.

Then the surface area of each prism.

Add the areas. Subtract the areas of the parts not on the surface.

The area of the triangular prism.

Perimeter  =  17 + 17 + 30  =  64 cm

Base area  =  (1/2)(30)(8)  =  120 sq.cm

Surface area  =  Ph + 2B

Surface area  =  64(24) + 2(120)

Surface area  =  1,776 sq.cm

Now the area of the rectangular prism.

Perimeter  =  2(30) + 2(24)  =  108 cm

Base area  =  30(24)  =  720 sq.cm

Surface area  =  Ph + 2B

Surface area  =  108(18) + 2(720)

Surface area  =  3,384 sq.cm

Now,

Surface area  =  1,776 + 3,384 - 2(720)  =  3,720 sq.cm

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Answer:

(1)  f(x,y) = 1-|x|-|y|

(a) 3d figure attached

(b) 2d figure attached

(2) f(x,y) = 6-2x-3y

(a) 3d figure attached

(b) 2d figure attached

Step-by-step explanation:

The Function is not given in the question. Lets solve this for 2 common function for the internet. Hopefully it can solves the given problem

(1)  f(x,y) = 1-|x|-|y|

(2) f(x,y) = 6-2x-3y

All the figures are labelled to avoid confusion. (a) part of both functions have 3D sketches. (b) part of both functions have 2d sketches

Answer:

dA/dt = 12 - 2A/(100 + t)

Step-by-step explanation:

The differential equation of this problem is;

dA/dt = R_in - R_out

Where;

R_in is the rate at which salt enters

R_out is the rate at which salt exits

R_in = (concentration of salt in inflow) × (input rate of brine)

We are given;

Concentration of salt in inflow = 4 lb/gal

Input rate of brine = 3 gal/min

Thus;

R_in = 4 × 3 = 12 lb/min

Due to the fact that solution is pumped out at a slower rate, thus it is accumulating at the rate of (3 - 2)gal/min = 1 gal/min

So, after t minutes, there will be (100 + t) gallons in the tank

Therefore;

R_out = (concentration of salt in outflow) × (output rate of brine)

R_out = [A(t)/(100 + t)]lb/gal × 2 gal/min

R_out = 2A(t)/(100 + t) lb/min

So, we substitute the values of R_in and R_out into the Differential equation to get;

dA/dt = 12 - 2A(t)/(100 + t)

Since we are to use A foe A(t), thus the Differential equation is now;

dA/dt = 12 - 2A/(100 + t)