Solve the system of linear equations.

y=−16x+5
x+6y=30

Answer:

The temperature decreased by 28%

Step-by-step explanation:

How did the temperature change if :

At first it decreased by 60%

Then increased by 80%

Assume that the temperature before decreasing is 100%

∵ The temperature before decreasing = 100%

∵ It decreased by 60%

→  Before decreasing  :  decreasing  :    after decreasing

→  100%                         :  60%              :    100% - 60% = 40%

∴ The temperature after decreasing = 40%

Assume that the temperature after decreasing is 100%

∵ The temperature after decreasing = 100%

∵ It increased by 80%

By using the ratio method

→  After decreasing  :  increasing  :    after increasing

→  100%                      :  80%             :   100% + 80% = 180%

→  40%                        :                       :   x%

By using cross multiplication

∴ 100% × x% = 40% × 180%

- Divide both sides by 100%

∴ x% =

∴ x% = 72%

∵ At first the temperature = 100%

∵ At last the temperature = 72%

∵ The first the temperature > the last the temperature

∴ The decreasing in temperature = 100% - 72% = 28%

Answer:

Probability means Possibility. It states how likely an event is about to happen. The probability of an event can exist only between 0 and 1 where 0 indicates that event is not going to happen i.e. Impossibility and 1 indicates that it is going to happen for sure i.e. Certainty.

The higher or lesser the probability of an event, the more likely it is that the event will occur or not respectively. For example – An unbiased coin is tossed once. So the total number of outcomes can be 2 only i.e. either “heads” or “tails”. The probability of both outcomes is equal i.e. 50% or 1/2.

Answer:

The linear equation modeling the given function is P(t)=1700t+45000.

Step-by-step explanation:

In the question it is given that a town's population has been growing linearly. In 2003, the population was 45000, and the population has been growing by 1700 people each year.

It is required to write an equation P(t), for the population t years after 2003.

To solve this question, substitute the given slope , or change in population in the equation with the initial population . Thus, formulate the equation modeling the given function.

Step 1 of 1

Formulate the equation in the slope-intercept form.

[tex]$$\begin{aligned}&y=m x+b \\&P(t)=1700 t+45000\end{aligned}$$[/tex]

The correct option is to show that the ratios HL/JL = IL/KL = HI/JK are equivalent. Option A is correct.

For two triangles to be similar, the ratio of the measure of similar sides of the triangle must be equal to a constant known as a scale factor.

From the given figures, the expression that can be used to prove that the triangles are similar is as shown;

HL/JL = IL/KL = HI/JK

Hence the correct option is to show that the ratios HL/JL = IL/KL = HI/JK are equivalent

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I can Confirm A is correct

Step-by-step explanation:

The probability that none of them are spades is c(39,5) / c(48,5).

Probability is without a doubt how probable something is to show up. whenever we are uncertain about the final results of an occasion, we can talk about the possibilities of sure outcomes and how probable they are. The analysis of events governed by opportunity is referred to as records.

A chain of moves in which the results are usually unsure. The tossing of a coin, selecting a card from a deck of playing cards, throwing a cube. occasion. it is a single final result of an experiment. Getting a Head whilst tossing a coin is an event.

Simple chance is the calculation of an outcome or the chance of an event ever taking place. Coverage companies use possibility statistics to determine the possibility of having to pay out a declaration. A simple chance is calculated by way of dividing a particular outcome by all of the feasible outcomes.

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Answer:c

Step-by-step explanation:

c

Answer:

D.

Step-by-step explanation:

The equation must be true to have a proportion.

12/20 = 0.6

21/34 = 0.62

A. No

10/15 = 0.666666...

34/60 = 0.566666...

B. No

13/23 = 0.565217...

26/56 = 0.46428...

C. No

25/15 = 1.6666...

85/51 = 1.6666...

D. Yes

Answer: D

Steps 4 and 5 describe the errors Stephen made.

Stephen evaluated [tex](6.34\times 10^{-7})(4.5\times 10^3)[/tex].  

His work is shown below.

Step 1 - [tex](6.34\times 10^{-7})(4.5\times 10^3)[/tex]

Step 2 - [tex]=(6.34\times 4.5)(10^{-7} \times 10^3)[/tex]

Step 3 - [tex]=(28.53)(10^{-4})[/tex]

Step 4 - [tex]20.53\times 10^4[/tex]

Error is the step as 4 sign is negative.

So correct step is [tex]=(28.53)(10^{-4})[/tex]

Step 5 - [tex]=(28.53)(10^{-4})[/tex]

Error is the step as there are 4 in place of 3.

So correct step is [tex]=(28.53)(10^{-4})[/tex]

Steps 4 and 5 describe the errors Stephen made.

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The function y = x + 1 has a slope (rate of change) of 1 as well as an y intercept of 1.

An equation is an expression that shows the relationship between two or more numbers and variables.

The standard form for a linear function is:

y = mx + b

Where m is the slope and b is the y intercept.

Given the function y = x + 1

The function y = x + 1 has a slope (rate of change) of 1 as well as an y intercept of 1.

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The attached graph represents the line plot of the dataset

The frequency table is given as:

Amount        3   3.5    4  4.5  5

Frequency   1      2     3   3    1

To create the line plot, we represent the frequency by dots.

Take for instance:

See attachment for the line plot

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The approximate depth of water for a tsunami traveling at 200 kilometers per hour, given the equation S=356√d, where S is the speed in kilometers per hour and d is the average depth of the water in kilometers, is 0.32 km. Hence, option A is the correct choice.

To solve for the average depth of water, when the water is traveling at 200 kilometers per hour, we substitute speed S = 200, in the relation S = 356√d.

This will be solved in the following way:

S = 356√d,

or, 200 = 356√d {Substituting S = 200},

or, 200/356 = (356√d)/356 {Dividing both sides by 356},

or, √d = 0.5618 {Simplifying},

or, d = 0.32 kilometers.

Therefore, the approximate depth of water for a tsunami traveling at 200 kilometers per hour, given the equation S=356√d, where S is the speed in kilometers per hour and d is the average depth of the water in kilometers, is 0.32 km. Hence, option A is the correct choice.

The provided question is incomplete.

The complete question is:

"The speed that a tsunami can travel is modeled by the equation S=356√d, where S is the speed in kilometers per hour and d is the average depth of the water in kilometers. What is the approximate depth of water for a tsunami traveling at 200 kilometers per hour?

A. 0.32 km

B. 0.75 km

C. 1.12 km

D. 3.17 km"

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The amount in pounds of Type A coffee used is 36 pounds.

Type A coffee costs Susan $5.45 per pound, and type B coffee

costs $4.05 per pound.

Therefore,

Let x = the number of pounds of Type A coffee.

total pounds = x + 3x

total cost = 5.45(x) + 3x(4.05)

633.60 =  5.45(x) + 3x(4.05)

633.60 =   5.45x + 12.15x

633.60 = 17.6x

divide both sides by 17.6

x = 633.60 / 17.6

x = 36

Pounds of Type A coffee used = 36 pounds

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The acute angle is 40.40 degrees

The cosine of the angle is given as:

cos(x) = 0.7620

Take the arc cos of both sides

[tex]x = \cos^{-1}(0.7620)[/tex]

Evaluate the arc cos

x = 40.359

Approximate

x = 40.40

Hence, the acute angle is 40.40 degrees

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None of the expressions is equivalent to 78

The number is given as:

Number = 78

Next, we evaluate the expressions in the options using a calculator

2 × (10 × 3 + 32) = 124

2 × (13 + 32) = 90

(10 × 3 + 32) =62

2 × (10 × 3 + 3) = 66

None of the options equals 78

Hence, none of the expressions is equivalent to 78

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Answer: Infinite

Step-by-step explanation:

Answer:

one solution, r = - 2

Step-by-step explanation:

4(2r - 1) = - 2(3r + 16) ← distribute parenthesis on both sides

8r - 4 = - 6r - 32 ( add 6r to both sides )

14r - 4 = - 32 ( add 4 to both sides )

14r = - 28 ( divide both sides by 14 )

r = - 2

Answer:

In the SAS congruence criterion, you must show that two pairs of sides are equal and their included angles are equal as well. But In the SAS similarity criterion, you must show that two pairs of sides are proportional and their included angles are equal.

Step-by-step explanation:

Solution: In the SAS congruence criterion, you must show that two pairs of sides are equal and their included angles are equal as well. But In the SAS similarity criterion, you must show that two pairs of sides are proportional and their included angles are equal.

The equivalent equations to [tex]\frac{3}{5}(30x - 15) = 72[/tex] are given as follows:

Equivalent equations are equations that have the same solution.

First, we have to check the solution to [tex]\frac{3}{5}(30x - 15) = 72[/tex], hence:

[tex]\frac{3}{5}(30x - 15) = 72[/tex]

Applying the fraction:

18x - 9 = 72 -> first equivalent equation

Simplifying by 3:

3(6x - 3) = 72 -> second equivalent equation

The solution is:

18x - 9 = 72

18x = 81

x = 81/18

x = 4.5 -> third equivalent equation.

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Answer:

1400000

Step-by-step explanation:

This is very simple,

multiply the total tickets with this fraction which is

= 2/5x 3500000

= 1400000

Answer:

14,000,000.

Step-by-step explanation:

2 out 5  tickets are winners.

So number of winning tickets = 3,500,000 * 2/5

= 2 * 7,000,000

= 14,000,000

Answer:

(d) y≥-5

Step-by-step explanation:

first, we find the equation for the blue line:

a doesn't work as it goes diagonally, so as b, e, or f.

so it must be y≥-5 or y<-5

since the graph is shaded above the line, it must be greater than or greater than or equal to, so it must be D) y≥-5.

You can tell it must be D as greater or less than is dotted while greater equal or less equal would be a solid line.

The exponential equation for the growth is f(x)=57[tex]e^{0.51x}[/tex] where x is the number of days and the population on 21st march is 2069983.5 of microbes.

Given:

Days                   population

0                                57

1                                 95

5                               700

10                               8525

We have to form exponential equation which shows the growth of microbes.

We know that exponential equation which shows the sum is as under:

f(x)=P[tex]e^{rt}[/tex] where r is the rate of growth and x is the number of days, months or years depending on how things grows.

In the question when x=0 population is 57.

f(0)=57

P[tex]e^{0}[/tex]=57

P=57

When x=1, population is 95.

f(1)=95

P[tex]e^{r}[/tex]=95

57 [tex]e^{r}[/tex]=95

57=95/[tex]e^{r}[/tex]----1

when x=5,population is 700.

f(5)=700

P[tex]e^{5r}[/tex]=700

57[tex]e^{5r}[/tex]=700

57=700/[tex]e^{5r}[/tex]-----2

Equating 1&2

95/[tex]e^{r}[/tex]=700/[tex]e^{5r}[/tex]

[tex]e^{5x} /e^{x} =700/95[/tex]

[tex]e^{5r-r}[/tex]=7.36

[tex]e^{4r}[/tex]=7.36

[tex](2.7182)^{4r}[/tex]=[tex](2.7182)^{2}[/tex]

equating both sides

4r=2

r=0.5

put the value of t=21 in the exponential equation

f(21)=57[tex]e^{0.5*21}[/tex]

=57[tex]e^{10.5}[/tex]

=57*36315.5

=2069983.5

Hence the population on 21st march is 2069983.5.

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Answer:

6 mm

Step-by-step explanation:

So, the area he needs to fill isn't really important, you don't need to calculate it. What is necessary is the individual dimensions of that area (width/length). The width and the length must be divisible by the lengths of the tiles. This is so you don't need to cut anything. For example let's say the area needed to be filled was 15 mm (width) by 10 mm (length). If I chose 3mm square tiles, it could perfectly fill up the width, but when it came to the length there would be a small 1 mm gap. And you would need to cut one of the square tiles, so it would have a length of 1 mm. In this case the 15mm was divisible by 3, but the 10 mm wasn't. So using this logic, it can't be the 4 mm square tile since 150mm / 4 mm = 37.5. It can be the 6m since 150mm / 6mm = 25 and 180 mm / 6mm = 30. It can't be the 8 mm since 150 mm / 8mm = 18.75 mm

Answer:

Step-by-step explanation:

Comments

AE = AT = 7                                                  Given

AT is a perpendicular bisector of OS        Property of a circle

AE is a perpendicular bisector of BR        Property of a circle

ER = 1/2 BR = 48/2 = 24                              Property of a bisector

TS = ER                                                        Property of a bisector and chord

TS = 24                                                        ER = 24 so TS = 24

AS^2 = TS^2 + TA^2                                   Pythagorean Theorem + rt angle

AS^2 = 24^2 + 7^2                                      Substitute values

AS^2 = 576 + 49                                         Combine

AS^2 = 625                                                 Take sqrt of both sides

√AS^2 = √625                                  

AS = 25

Answer

AS = 25

First part;

Following the transformation (x, y) → (3•x, 2•y), the images are;

A'(9, 10), B'(15, 6), C'(6, 4)

Second part;

The distance between points A and B is 2•√2 which is different from the distance between the image A' and B' which indicates that the transformation is a non rigid transformation.

First part;

The given points are;

The given transformation is presented as follows;

(x, y) → (3•x, 2•y)

Therefore, the images are;

A(3, 5) → A'(3 × 3, 2 × 5) = A'(9, 10)

B(5, 3) → B'(3 × 5, 2 × 3) = B'(15, 6)

C(2, 2) → C'(3 × 2, 2 × 2) = C'(6, 4)

Second part;

Length of AB = √((5-3)² + (3-5)²) = 2•√2

Length of A'B' = √((15-9)² + (6-10)²) = 2•√13

Given that the length of AB ≠ the length of A'B' then we have;

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The points of the image are (9, 10), (15, 6) and (6, 4) and the resulting image is a nonrigid motion.

The points are given as:

A = (3, 5)

B = (5, 3)

C = (2, 2)

The transformation is given as:

(x, y) ⇒ (3x, 2y)

So, we have:

A' = (9, 10)

B' = (15, 6)

C' = (6, 4)

Hence, the image of the transformation is (9, 10), (15, 6) and (6, 4)

See attachment for the image

Also, the resulting image is a nonrigid motion.

This is so because the lengths of the image and the preimage are not equal

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Answer:

2x-9=0

2x-9+9=0+9.add the inverse of subtraction /addition/ (+9)

2x=9....then divide by 2

x=9/2

x=4.5. will the final answer

Answer:

3072

Step-by-step explanation:

General form of a geometric sequence:

  [tex]a_n=ar^{n-1}[/tex]

where:

Given values:

Substitute the given values into the formula to create an equation for the nth term:

[tex]\implies a_n=3(4)^{n-1}[/tex]

To find the 6th term, substitute n = 6 into the equation:

[tex]\implies a_6=3(4)^{6-1}[/tex]

[tex]\implies a_6=3(4)^{5}[/tex]

[tex]\implies a_6=3(1024)[/tex]

[tex]\implies a_6=3072[/tex]

Therefore, the 6th term of a geometric sequence whose 1st term is 3 and whose common ratio is 4 is 3072.

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Answer: [tex]\frac{1}{4}[/tex]x - y = 2

Step-by-step explanation:

    Standard form is Ax + By = C where A, B, and C, are integers.

   Given:

y - 1 = 1/4(x - 12)

  Distribute:

y - 1 = [tex]\frac{1}{4}[/tex]x - 3

  Add 3 to both sides of the equation:

y  + 2 = [tex]\frac{1}{4}[/tex]x

  Subtract y from both sides of the equation:

2 =  [tex]\frac{1}{4}[/tex]x - y

   Apply the reflexive property:

[tex]\frac{1}{4}[/tex]x - y = 2

Answer:

its 3 grapes

Step-by-step explanation:

6-3=3 therefore the answer is 3

Answer:

3 grapes are left

Step-by-step explanation:

if you subtract 3 from 6 (6 - 3) you will find the answer you need to find how many grapes you have left.

By inclusion/exclusion,

[tex]n(P' \cup Q) = n(P') + n(Q) - n(P' \cap Q)[/tex]

We have

[tex]n(\xi) = n(P) + n(P') \implies n(P') = 28 - n(P)[/tex]

so that

[tex]n(P'  \cup Q) = (28 - n(P)) + n(Q) - 2n(P) = 28 - 3n(P) + n(Q)[/tex]

Now,

[tex]n(\xi) = 28 \implies n(P \cup Q) = 28 - 7 = 21[/tex]

and by inclusion/exclusion,

[tex]n(P \cup Q) = n(P) + n(Q) - n(P \cap Q)[/tex]

Decompose [tex]Q[/tex] into the union of two disjoint sets:

[tex]Q = (P \cap Q) \cup (P' \cap Q)[/tex]

Since they're disjoint,

[tex]n(Q) = n(P\cap Q) + n(P'\cap Q) \implies n(Q) = n(P\cap Q) + 2n(P)[/tex]

[tex]\implies n(P \cup Q) = n(P) + (n(P\cap Q) + 2n(P)) - n(P \cap Q)[/tex]

[tex]\implies 21 = 3n(P)[/tex]

[tex]\implies n(P) = 7[/tex]

From the Venn diagram, we see there are 3 elements unique to [tex]P[/tex] - by the way, this is the set [tex]P \cap Q'[/tex] - so [tex]n(P\cap Q) = 7-3 = 4[/tex], and it follows that

[tex]n(Q) = n(P\cap Q) + 2n(P) = 4 + 2\times7 = 18[/tex]

Finally, we get for (a)

[tex]n(P' \cup Q) = 28 - 3n(P) + n(Q) = 28 - 3\times7 + 18 = \boxed{25}[/tex]

For (b), we have by inclusion/exclusion that

[tex]n(P \cup Q') = n(P) + n(Q) - n(P \cap Q') = 7 + 18 - 3 = \boxed{22}[/tex]

Answer:

C = 29.7

Step-by-step explanation:

Remember to use a^2 + b^2 = c^2

21^2+ 21^2 = c^2

441 + 441 = c^2

882 = c^2

you square root both sides

c= 29.6984

Round it

C = 29.7

The system of inequalities that correctly represents this scenario is given by:

A system of inequalities is when two or more variables are related, and inequalities are built to find the values of each variable.

In this problem, the variables are given as follows:

The manager of the stand expects sales of a minimum of 100 items, hence:

[tex]x + y \geq 100[/tex].

The concession stand at a local high school sells nachos for $4 each and popcorn for $2 each. The manager wants a total of at least $225, hence:

[tex]4x + 2y \geq 225[/tex]

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For question 1 option C is the correct answer and for question 2 option A is the correct answer.

We need to find which transformation from the graph of a function f(x) describes the graph of 10f(x).

Here the transformation that describes the graph of g(x) is a vertical dilation of scale factor k = 10 of f(x).

We can start by defining the general vertical dilation.

For a given function f(x), a vertical dilation stretches or contracts the graph vertically, depending on the scale factor k.

And it is written as:

g(x) = k*f(x).

Then here we have:

g(x) = 10*f(x)

It is easy to see that this is a vertical dilation of scale factor k = 10. Therefore, option C is the correct answer.

We need to check from the given options which information is sufficient to prove that quadrilateral ABCD is a parallelogram.

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Therefore, option A is the correct answer.

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