solve the system of equations (how many solutions are there
1. x + y = 3
x - y = -3
2. 5x + y = 7
10x + 2y = 16

The area for each part of the figure is given as follows:

The area of a right triangle is given by half the multiplication of it's sides.

Triangle A has the side lengths given as follows:

Hence the area is given as follows:

A = 0.5 x 4 x 10 = 20 units squared.

Triangle D is has the side lengths given as follows:

Hence the area is given as follows:

D = 0.5 x 2 x 6 = 6 units squared.

The total area is given by the sum of the areas of each part of the figure, hence:

20 + 2 + 4 + 6 = 32 units squared.

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Answer:

0.2

Step-by-step explanation:

as 0.2 is greater than 1

Answer:

0.2

Step-by-step explanation:

The diagram = 0.1

0.1 < 0.2

The amount that will be in the account in 25 years is $16,282.298.

Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.

Given that,

Principal amount, P = $3000

Rate of interest, r = 7% = 0.07

Number of years, n = 25

The final amount in a compound interest where the interest is compounded annually is,

A = P (1 + r)ⁿ

Substituting the given values,

A = 3000 (1 + 0.07)²⁵

   = 3000 (1.07)²⁵

   = 16,282.298

Hence the final amount after 25 years is $16,282.298.

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Answer:

The number with the highest sum of prime factors is 27, as it has only two prime factors: 3 and 3. The sum of its prime factors is 6, so if you choose 27, you can move 6 spaces. The number 25 has two prime factors as well, but only 5 + 5 = 10. 26 is not a prime number, so it wouldn't be the best choice. So, if you want to move as many spaces as possible, you should choose 27.

The total amount spent on tickets by Edgar is $15.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Let x be the cost of one game ticket and y be the cost of one ride ticket.

From the table, we can form two linear equations regarding the total amount spent by Erica and Penny.

10x + 5y = 10

15x + 10y = 16.25

Multiplying the first equation throughout with 2,

20x + 10y = 20

Subtracting 15x + 10y = 16.25 from the above equation,

(20x + 10y) - (15x + 10y) = 20 - 16.25

5x = 3.75

x = 0.75

Substituting x = 0.75 in 10x + 5y = 10,

7.5 + 5y = 10

5y = 2.5

y = 0.5

Cost of a game ticket is $0.75 and cost of a ride ticket is $0.50.

Total cost by Edgar = (12 × 0.75) + (12 × 0.5) = $15

Hence the total money spent by Edgar for both game and ride tickets is $15.

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Answer:

8

Step-by-step explanation:

f(4) = 3(4) - 4

f(4) = 12 - 4

f(4) = 8

Answer:

b

Step-by-step explanation:

:)

Answer:

YOUR ANDWER MIGHT BE D

Step-by-step explanation:

Answer: 11

Step-by-step explanation:

3x2=6

6+5=11

The temperature at noon is equal to -0.1°C.

Mathematically, the standard form or slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Note: Let x represent the time.

Next, we would write an equation that models the situation based on the rate of change (slope) and y-intercept (initial value) as follows;

y = mx + c

y = -0.8x - 2.5

y = -0.8(3) - 2.5

y = -2.4 - 2.5

y = -0.1°C

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The statements that are true are:

Clayton could use the relationship (x, y) right-arrow (y, x) to find the points of the image.

Clayton could negate both the x and y values in the points to find the points of the image.

C’ will move because all points move in a reflection.

The image and the pre-image will be congruent triangles.

The image and pre-image will not have the same orientation because reflections flip figures.

Options A, B, D, E, and F.

There are two ways of reflection.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

Clayton could use the relationship (x, y) → (y, x) to find the points of the image.

This is the y = x reflection rule.

This is true.

Clayton could negate both the x and y values in the points to find the points of the image.

Reflection of (x, y) along the x-axis and y-axis consecutively will give us

(-x, -y).

This is true.

C’ will remain in the same location as C because it is on the line of reflection.

This is not true.

C’ will move because all points move in a reflection.

This is true.

The image and the pre-image will be congruent triangles.

This is true.

The image and pre-image will not have the same orientation because reflections flip figures.

This is true.

Thus,

All statements are true except the statement:

C’ will remain in the same location as C because it is on the line of reflection.

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The value of x is approximately 3.875.

Given that angle JKL is inscribed in a circle and the measure of angle JKL is (16x-2)°, we can use the property of inscribed angles to find x. Inscribed angles that subtend the same arc have equal measure.

Let's call the measure of angle JKL "m". Then, the measure of angle JKL = m, the measure of angle KJL = m, and the measure of angle JLK = m.

The sum of the angles in a triangle is 180°, so we have:

m + m + m = 180°

3m = 180°

m = 60°

Substituting the value of m into the equation for the measure of angle JKL:

60° = (16x - 2)°

60 = 16x - 2

62 = 16x

x = 3.875

So, the value of x is approximately 3.875.

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a. The perimeter of the figure is:  61.4 cm

b. The area of the figure is: 160.69 cm²

The figure consists of two semicircles which makes one full circle and a rectangle. Therefore:

a. The perimeter of the given figure = circumference of a circle + 2w.

d = 8.6 cm

Circumference of the circle = 2 * pi * r = 2 * 3.14 * (8.6/2) = 27.00 cm

Perimeter = 27.00 + 2(17.2)

Perimeter = 61.4 cm

b. Area = area of circle + area of rectangle = 2πr + (length * width)

r = 7.9/2 = 3.95 cm

length = w = 17.2 cm

width = d = 7.9 cm

Area = 2*3.14*3.95 + (17.2*7.9) = 160.69 cm²

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Answer:

The length of the train can be calculated using the formula:

Length of the train = Speed x Time / 2

Where,

Speed = 60 km/hr = 60 x 1000/60 = 1000 m/min

Time = 9 sec = 9 / 60 min = 0.15 min

So,

Length of the train = 1000 x 0.15 / 2 = 75 m

Therefore, the length of the train is 75 meters.

Answer:

Length of the train shold be 75m

Step-by-step explanation:

The value of cosα is 2/5.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Given that, tanα= -2/5 and α is quadrant IV.

We know that, tan(−θ) = − tan(θ)

α= 2/5

As we know cos(−θ) = cos(θ)

cosα =2/5

Therefore, the value of cosα is 2/5.

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Answer:

they started trip at 10:00 am

Step-by-step explanation:

Let's call the starting time "S".

The arrival time is 11:37AM,

difference in time after break to park arrived : 11:37 am - 10:48 am = 49 minutes

remaining time : 97-49= 48 minutes

starting time= 10:48 am -48 minutes = 10:00 am

After 3 3/5 weeks, they will have the same number of pictures.

the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.

Given, Yuki and Roman are photographers for the yearbook. Yuki starts with 20 photos. She then takes 60 photos each week. Roman starts with 110 photos. He then takes 35 photos each week.

Let "w" the number of weeks they collected the pictures

For Yuki,

The total picture he has after 0 weeks = is 20

The total picture he has after 1 week = 20 + 60

The total picture he has after 2 weeks = 20 + 60*2

The total picture he has after w weeks = 20 + 60*w

For Roman,

The total picture he has after 0 weeks = is 110

The total picture he has after 1 week = 110 + 35

The total picture he has after 2 weeks =110 + 35*2

The total picture he has after w weeks = 110 + 35*w

To calculate the number of weeks when they have equals pictures:

20 + 60*w = 110 + 35*w

25w = 90

w = 3 3/5

Therefore, After 3 3/5 weeks, they will have the same number of pictures.

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The arena should be financed by selling $  320   million in bonds and borrowing $  480   million.

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

Work Shown:

Something like x = 27 means "27 million dollars of bonds were sold".

The variable x has the restriction of [tex]0 \le x \le 480[/tex] since $480 million is the ceiling for the bonds.

The variable y has the restriction of [tex]0 \le y \le 640[/tex] since $640 million is the ceiling for the money borrowed from the insurance company.

The two amounts, x and y, must add to 800 to represent the $800 million total that needs to be raised.

x+y = 800

y = 800-x

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

Let's calculate the interest for each item. Use the simple interest formula.

Bonds at 7% interest rate:

i = P*r*t

i = x*0.07*1

i = 0.07x

Borrowed money at 2% interest rate:

i = P*r*t

i = y*0.02*1

i = 0.02y

Total annual interest = 0.07x+0.02y = 32

The 32 at the end represents the $32 million of interest payout. This amount of money is paid to the bondholders and to the insurance company, and is done so yearly.

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

Apply substitution to solve for x.

0.07x+0.02y = 32

0.07x+0.02(800-x) = 32 ...... plug in y = 800-x

0.07x+16-0.02x = 32

0.05x+16 = 32

0.05x = 32-16

0.05x = 16

x = 16/(0.05)

x = 320

They should sell $320 million in bonds.

320 million = 320,000,000

Note how x = 320 is in the interval [tex]0 \le x \le 480[/tex]

y = 800-x

y = 800-320

y = 480

They should borrow $480 million at an interest rate of 2%

480 million = 480,000,000

Note how y = 480 is in the interval [tex]0 \le y \le 640[/tex]

Answer:

The arena should be financed by selling $320 million in bonds and borrowing $480 million.

Step-by-step explanation:

Simple interest is calculated by multiplying the principal by the interest rate (in decimal form) and the time (in years).

Let x be the amount raised by selling bonds that pay an annual simple interest rate of 7%.

Therefore:

As the total cost of the sports arena is $800 million, the amount raised from borrowing money from the insurance company at an annual simple interest rate of 2% is (800 - x).  Therefore:

To determine whether the arena can be financed so that the annual interest is $32 million, equate the sum of the two expressions for interest to 32 and solve for x:

[tex]\implies 0.07x+0.02(800-x)=32[/tex]

[tex]\implies 0.07x+16-0.02x=32[/tex]

[tex]\implies 0.05x+16=32[/tex]

[tex]\implies 0.05x=16[/tex]

[tex]\implies x=320[/tex]

As x is the amount raised by selling bonds, then the amount in bonds that should be sold is $320 million.

To calculate the amount to borrow, subtract the amount in bonds sold from $800 million:

[tex]\implies 800-320=480[/tex]

Therefore, the amount to be borrowed from an insurance company is $480 million.

As both these amounts are less than the maximum limits set, they are both valid.

Answer:pls brainly award

Step-by-step explanation:

The 330 feet of rope is equivalent to 330/3 = 110 yards.

The cost of the rope at SportsStuff.com is 110 * $5.50 = $605.

The cost of the rope at OutdoorHaven.com is 110 * $5.20 + $12.25 = $604.45.

Therefore, the cheapest price you can pay is $604.45.

Answer:

1) 9

2) 27

3) Read explanation below!

Step-by-step explanation:

1) Use the Pythagorean theorem to find AD. Show your working

To find '?' we first have to expand the indices...

Now work out '?'

2) Find AC. Show your working

We have found out that AD is 9 and to find AC we have to add 18!

3) Is ΔABC a right triangle? Explain

We can that ΔABC is not a right angle as none of the angles in the triangle are 90°!  If it was a right angled triangle we would see the ∟sign on one of the angles. Even though there are two of those in the middle it does not count as the question is asking about ΔABC!!

Have a lovely day :)

The original amount of water is 15 cups.

The change in David's water intake is 3 cups.

And, The percent change is 20%. This is a percent decrease.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

David is tracking the amount of water he drinks each day.

Here, On Thursday, he drinks 15 cups of water.

And, On Friday, he drinks 12 cups of water.

Hence, We get;

The original amount of water = 15 cups.

And, The change in David's water intake = 15 - 12

                                                               = 3 cups

And, The percent change in his water intake is,

⇒ Percent = 3 / 15 × 100

⇒ Percent = 20%

Thus, The original amount of water is 15 cups.

The change in David's water intake is 3 cups.

And, The percent change is 20%. This is a percent decrease.

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Answer:

see below

Step-by-step explanation:

a=50 because it's cut out of a full circle = 360, and it tells you what's left = 310

so 360-310=50

The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is given as follows:

0.5874 = 58.74%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

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

The parameters for this problem are given as follows:

[tex]\mu = 17.2, \sigma = 2.5, n = 40, s = \frac{2.5}{\sqrt{40}} = 0.3953[/tex]

The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is the p-value of Z when X = 18.1 subtracted by the p-value of Z when X = 17.1, hence:

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

By the Central Limit Theorem:

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

Z = (18.1 - 17.2)/0.3953

Z = 2.28

Z = 2.28 has a p-value of 0.9887.

Z = (17.1 - 17.2)/0.3953

Z = -0.25

Z = -0.25 has a p-value of 0.4013.

Hence:

0.9887 - 0.4013 = 0.5874 = 58.74%.

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In Venn diagram All three papers 39,exactly two of the papers 189, exactly one of the papers 251 and  The Guardian alone 142.

A Venn diagram is a visual representation that makes use of circles to highlight the connections between different objects or limited groups of objects. Circles that overlap share certain characteristics, whereas circles that do not overlap do not. Venn diagrams are useful for showing how two concepts are related and different visually.

They frequently serve to visually group objects while highlighting how they differ and how they are similar.

(I) All three papers

(G∪P∪T) = G + P+T+G∩P+G∩T+P∩T-(G∩P∩T)

290=142+181+117+75+60+54-(G∩P∩T)

(G∩P∩T)=39

(ii) exactly two of the papers = 60+75+54=189

(iii) exactly one of the papers =251

(iv) The Guardian alone =142.

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Answer:

Step-by-step explanation:

W(40)x25  

This is a problem finding the slope of a line at some point "a"

It accomplishes this by doing an average rate of change formula over an area approaching 0.

We must know the format of this type of equation.

See first image.

The variables in this example don't match up.

Let the function input be x, and the limit being a --> 0

a = 2

f(x) = x^5

Answer:

[tex]\displaystyle{f(x)=x^4 \ \: \text{and} \ \: a =2}[/tex]

Step-by-step explanation:

The first principal of derivative:

[tex]\displaystyle{f'(x) = \lim_{h\to 0} \dfrac{f(x+h)-f(x)}{h}}[/tex]

Since the given problem represents f'(a), meaning:

[tex]\displaystyle{f'(a) = \lim_{h\to 0} \dfrac{f(a+h)-f(a)}{h}}[/tex]

If we compare:

[tex]\displaystyle{f'(a) = \lim_{h\to 0} \dfrac{f(a+h)-f(a)}{h}}[/tex]

and

[tex]\displaystyle{ \lim_{h\to 0} \dfrac{(2+h)^4-16}{h}}[/tex]

which can be rewriten as:
[tex]\displaystyle{f'(a) = \lim_{h\to 0} \dfrac{(2+h)^4-2^4}{h}}[/tex]

We can conclude by comparing that:

This would mean that:

[tex]\displaystyle{f(x)=x^4}[/tex]

Therefore:

[tex]\displaystyle{f(x)=x^4 \ \: \text{and} \ \: a =2}[/tex]

The equity of Company X's is $13,291.

The difference between assets and liabilities is the equity.

The equity is the portion of assets belonging to the owners.

Initial investment = $12,000

Retained Earnings = $1,291

Long-term loan = $9,982 ($12,000 - $2,018)

Land and building = $8,878

Equipment = $4,230

Cash $8,250

Inventory = $1,225

Accounts Receivable = $675

Accounts Payable = $485

Short-term loan = $500

Company X

As of current date

Cash                                 $8,250

Inventory                            1,225

Accounts Receivable          675  $10,150

Long-term investment  $1,000

Land and building          8,878

Equipment                      4,230    $14,108

Total Assets                               $24,258

Accounts Payable         $485

Short-term loan               500       $985

Long-term loan                         $9,982

Total liabilities                         $10,967

Initial capital           $12,000

Retained earnings       1,291  $13,291

Total liabilities and equity   $24,258

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Determine Company X's equity?

Therefore , the solution of the given problem of probability comes out to be likelihood that the full batch will be approved is therefore 0.832.

Probability theory is an area of mathematics that focuses on calculating the probability that a claim is accurate or that a particular occurrence will occur. Chance can be represented by any number range between 0 and 1, where 1 often denotes certainty and 0 typically denotes possibility. A probability diagram shows the possibility that a specific event will occur. The numerals 0 and 1, fractions with a ranging of 0% to 100%, or a few more characters can all be used to indicate probabilities.

Here,

Given that we've done it

Amount of CDs: 2100

50 faulty CDs total.

If every component of the sample is acceptable, the complete batch is accepted.

Therefore, we shall apply the "Binomial Theorem"

If there is no flaw, let p be the likelihood of success.

So, => p = 2100 - 50 / 2100

=> p = 2050/2100

=> p =0.97

q is the likelihood of a failure, or defect.

So,

=> q = 50/2100

=> q = 0.02

hence, the number of CDs chosen is 6.

Consequently, it is => P(X=6) = (0.97)6 = 0.832.

The likelihood that the full batch will be approved is therefore 0.832.

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