Solve the simultaneous equations.
x^2+y^2=13
y=x+1

When the measure of two vertical angles are 8x-18 and 6x+14, x is A. 16.

It should be noted that vertically opposite angles are equal. In this case, we have to equate both angles given. This will be illustrated as:

Angle 1 = Angle 2

8x - 18 = 6x + 14

Collect like terms

8x - 6x = 14 + 18

2x = 32

Divide

x = 32/2

x = 16

The value of x is 16.

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Answer: 11.2

Step-by-step explanation: In order to find the length of n, you can use the given angle measure and base length as well as a trig ratio. Since 6.2 is adjacent to angle N, you can use tangent (opposite/ adjacent).

tan (61) = n/6.2

(multiply by 6.2 on both sides to isolate n)

• 6.2 • 6.2

tan (61) • 6.2 = n

11.185 = n

~11.2 = n.

Answer:

A B D

Step-by-step explanation:

C might be missing something.

but even without that it might be a trick question, as

15g + 5 could be considered to have the following terms :

15g

15

g

5

so, it depends on what convention your teacher defined with you. because internationally this is not precisely defined as my hint about 15g + 5 shows.

some people consider a multiplication or division a combination of several items into one term.

some don't.

some consider a multiplication or division a term, and then the parts of that again as terms (as in my example), and some don't.

it really depends on your teacher and his/her definitions.

A . [tex]\sqrt{37}[/tex]  falls between integers 6 and 7

B. The decimal to the nearest tenth = 6.1

A. How are the two integers calculated?

[tex]\sqrt{37}[/tex]  =  6.082 , falls between integers 6 and 7

What are integers?

B: Estimate The Decimal To The Nearest Tenth

[tex]\sqrt{37}[/tex]  =  6.082

            [tex]\sqrt{37}[/tex]  =  6.082 = 6.1

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The expression f(5)=10 tells us that if Polly is an artist and sells posters at a local cafe then it means that Polly makes 10 dollars when she sells 5 posters.

According to the question,

We have the following information:

Polly sells x posters then she makes f(x) dollars.

We have the following expression:

f(5) = 10

So, it simply means that in place of x in f(x) we have f(5) then we have 5 in place of x.

f(x) is the amount made in dollars. So, the total amount Polly made is 10 dollars.

Hence, the expression f(5) = 10 clearly states that Polly sold 5 posters as an artist and made 10 dollars out of it.

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2x³ + XY is a binomial with a degree of 3

An algebraic expression containing only two terms is called a binomial. This is a binomial polynomial. It is also called the sum or difference of two or more monomials. This is the simplest form of a polynomial. A binomial is a polynomial with only terms. For example, x 2 is a binomial where x and 2 are two separate terms. Also, the coefficient of x is 1, the exponent of x is 1, and 2 is a constant here. Therefore, an A-binomial is a two-term algebraic expression that contains a variable, a coefficient, an exponent, and a constant.

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Answer:

24[tex]x^{5}[/tex][tex]y^{6}[/tex]

Step-by-step explanation:

(3x²y) × (2xy³) × (4x²y²)

= 3 × 2 × 4 × x² × x × x² × y × y³ × y²

= 24 × [tex]x^{(2+1+2)}[/tex] × [tex]y^{(1+3+2)}[/tex]

= 24[tex]x^{5}[/tex][tex]y^{6}[/tex]

In order to determine how many millimeters the spool has, you take into account the following identity:

1 meter = 1000 millimeters (1 m = 1000mm)

Then, you can proceed as follow:

100 m = 100(1m) = 100 (1000 mm) = 100,000 mm

where you have multiplied by 1000 the given quantity in meters, that is, you replace the unit meter (m) by its equivalence in millimeters (1000 mm)

That is, 100 meters are equivalent to 100,000 millimeters

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Only relations a, c and e are functions.

Here, we are given 6 relations and we need to determine which of them are function.

The basic property of a function is that a function from a set X to a set Y assigns to each element of X exactly one element of Y.

a. In this relation all elements in A are assigned only one value in B, thus, this relation is a function.

b. In this relation -1 in A has two values in B, that is, 5 and 2. Thus, this relation is not a function.

c. In this relation all elements of the first set are assigned only one value in set 2, thus, this relation is a function.

d. In this relation, 9 in set 1 has two values in set 2, that is, 9 and 5. Thus, this relation is not a function.

e. In this, relation, from the graph, we can see that all the x values have exactly one y value corresponding to them. Thus, the relation is a function.

f. In this relation we see that when x = 2, y can be 2 or 7. Thus, this relation is not a function.

Hence, we conclude that only relations a, c and e are functions.

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Answer: If John gives the cashier $40 he will get 9.02 change back because $40.98 - $30.98 = $9.02

The graph that shows the in the table is option (D)

From the table

The cost for hiring a plumber for zero hours = $50

The cost for hiring a plumber for 1 hours = $80

The cost for hiring a plumber for 2 hours = $110

The cost for hiring a plumber for 3 hours = $140

The domain is the set of all possible inputs.

The range is the set of all possible output

Here we have to plot the graph using the number of hours in the x axis and cost of hiring a plumber in y axis

The graph on option (D) matches the values in table. Because

At x= 0, y=50

At x= 1, y=80

At x= 2, y= 110

At x= 3, y= 140

Hence, the graph that shows the in the table is option (D)

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Answer:

the ratio is 17/323 equals 19, therefore there would be 19 players per team.

An online place has the highest price for a board game because it costs $4.28 and a store costs $4.18 for each game respectively.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

From the data given:

At the toy store, you could get 2 board games for $8.36.

Each board game cost = 8.36/2 = $4.18

Online the price for 3 board games is $12.84.

Each board game costs = 12.84/3 = $4.28

4.28 > 4.18

Thus, an online place has the highest price for a board game because it costs $4.28 and a store costs $4.18 for each game respectively.

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Considering Annie bought 5 pounds of apples, 4 pounds of oranges, and 3 pounds of bananas, and each pound of apple costed $1.75, orange $2.35 and bananas $1.50,

(i) Annie had to spend an exact amount of $22.65, to buy all the above mentioned fruits.

(ii) The amount of money that Annie spent on the fruits, can be represented by the expression [(1.75 * 5) + (2.35 * 4) + (1.50 * 3)]

(iii) Rounding the prices to the nearest whole dollar and estimating the total amount Annie spent, our estimation is an overestimation compared to the actual price Annie had spent.

As per the question statement, no information is provided about Annie's expenditure, and hence, we are considering that, Annie bought 5 pounds of apples, each pound costing $1.75, 4 pounds of oranges, each pound costing $2.35 and 3 pounds of bananas, each pound costing $1.50.

We are required to calculate:

(i) The exact amount Annie spent on the fruits.

(ii) A mathematical expression to represent the amount of money that Annie spent.

(iii) To determine whether it is an overestimation or underestimation if we round the prices to the nearest whole dollar and estimate the total amount Annie spent.

Starting with (i) and (ii),

Total amount Annie actually spent on her fruits

= [{(price of per pound apple) * (number of pounds of apple she bought)} + {(price of per pound orange) * (number of pounds of orange she bought)} + {(price of per pound banana) * (number of pounds of bananas she bought)}

= $[(1.75 * 5) + (2.35 * 4) + (1.50 * 3)]

= $(8.75 + 9.40 + 4.50)

= $22.65

And, the amount of money that Annie spent on the fruits, can be represented by the expression [(1.75 * 5) + (2.35 * 4) + (1.50 * 3)].

Now solving (iii), first, we need to round off the prices to the nearest whole dollar and then estimate the total amount Annie spent.

Now, $1.75 dollars rounded off the prices to the nearest whole dollar will become $2.

Similarly, $2.35 dollars rounded off the prices to the nearest whole dollar will become $2,

And, $1.50 dollars rounded off the prices to the nearest whole dollar will become $2.

That is, the rounded-off per pound cost of apples is $2, that of oranges is $2 and of bananas is also $2.

Therefore, on the same consideration that, Annie bought 5 pounds of apples, 4 pounds of oranges, and 3 pounds of bananas, the estimated total amount she spent on the fruits based on the above mentioned rounded-off per pound costs will be equal to

$[(2 * 5) + (2 * 4) + (2 * 3)] = ${10 + 8 +6) = $24

Since (24 > 22.60), thus, we can conclude that rounding-off the prices to the nearest whole dollar and estimating the total amount Annie spent, our estimation is an overestimation compared to the actual price Annie had spent.

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The correct options are:

B. The slope of Function W is greater than the slope of Function Z.

F. The y-intercept of Function W is greater than the y-intercept of Function Z.

Let's find the slope (m) and y-intercept (b) of each function to see which one compares the two functions accurately.

Function W:

The slope of Function B, using two points on the line, (0, -1) and (2, 0):

m = ( y₂ - y₁ )/ (x₂ - x₁ )

m = [ 0 - (- 1 )]/( 2- 0 ) = 0.5

The y-intercept will be when x = 0. Therefore, from the graph, the y-intercept is b = -1.

For Function Z:

The slope of Function Z, using two pairs of values from the table of values for function Z, ( 0, - 2 ) and ( 2, - 1.5 ):

m = ( y₂ - y₁ )/ (x₂ - x₁ )

m = ( - 1.5 - ( -2 ) )/( 2 - 0 )

m = 0.5/2 = 0.25

The y-intercept is the value of y when x = 0.

From the table when x = 0, y = - 2. Therefore, the y-intercept is b = - 2.

Thus, the following statements that compare both functions are TRUE:

B. The slope of Function W is greater than the slope of Function Z.

F. The y-intercept of Function W is greater than the y-intercept of Function Z.

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The Value of the horizontal asymptote is 0

What is horizontal asymptote?

The horizontal asymptote of a function y = f(x) is a line y = k and to calculate the horizontal asymptote please substitute [tex]x=[/tex]±∞. We can also find the vertical asymptote.

now we are given a function

[tex]f(x)=2(3)^{-x}[/tex]

Now substitute x=±∞ in the equation, as the x in denominator we get

f(x)= 0

This is the value of the horizontal asymptote

Hence the value of horizontal asymptote comes out to be 0

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Answer:

is 2000:4 because they Miles se divide en 150

The equation of the line is y = -x + 3

Equation of a straight line is usually of the form y = mx + c

where:

m = slope

c = y intercept

slope = ( 5 - -2 ) / ( -2 - 5 )

= ( 5 + 2 ) / -7

= 7 / -7

= -1

The y intercept is found from the graph to be 3

the equation of lthe line is

y = -1 ( x ) + 3

y = -x + 3

Therefore the equation of the line as gotten from the graph is y = -x + 3

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The length of the segment  BZ is approximately 2.78

The above value is obtained by using the following process:

The given parameters of the triangle are;

The angle bisectors of the triangle = BY and CZ

The point at which BY and CZ meet = The point I

The length of CY = 4

The length of AY = 6

The length of AB = 8

The unknown parameter;

The length of the segment BZ

Method:

Apply the angle bisector theorem

According to the angle bisector theorem we have;

AY/CY = AB/BC

BZ/AZ = BC/AC

From AY/CY = AB/BC,  we get;

6/4 = 8/BC

6 × BC = 8 × 4 = 32

BC = 32/6 = 16/3 =  5.33

BC = 5.33

From BZ/AZ = BC/AC, we have;

AC = CY + AY

∴ AC = 4 + 6 = 10

AZ = AB - BZ

∴ AZ = 8 - BZ

Therefore;

BZ/8 - BZ = 5.33/10

10 × BZ =  ×(8 - BZ) = (16/3) × 8 -  (16/3)·BZ

10·BZ + (16/3)·BZ = (16/3) × 8

(46/3)·BZ = 128/3

BZ = 128/46 = 64/23

Length of the line BZ = 64/23 = 2 ≈ 2.78

Therefore, the length of the segment  BZ is approximately 2.78.

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The total number of dogs are 135.

The number of Retrievers dogs are 35.

The number of off leashed playing dogs are 47.

Determine the number of dogs that are not Retrievers.

Determine the number of dogs that are not retrievers and not lleashed.

So table can be filled as,

Not on a leash leashed Total

Retrievers 10 25 35

Not a Retrievers 37 63 100

Total 47 88 135

1.

The events are indpendent if occurence of event does not affect the other event. But it can be observed that not on a leash and retriever depend on each other. So event not on a leash and retriever are not indpendent.

4.

The number of dogs that are not retriever and is on a leash are 63. So probability is,

1. Reject the null.

2. Data is consistent with the null hypothesis.

3. Unable to tell using our staff confidence interval.

A confidence interval in frequentist statistics is a range of estimates for an unknown parameter. A confidence interval is calculated at a specified degree of confidence; the most popular level is 95%, but other levels, such 90% or 99%, are occasionally used. Confidence intervals are used by statisticians to assess a sample variable's level of uncertainty. For instance, a researcher might randomly select many samples from the same population, compute a confidence interval for each sample, and then examine how well each sample might reflect the true value of the population variable. The generated datasets are all unique, some of which contain the genuine population parameter and others which do not. An unknown population parameter is most likely to be found inside a range of values that is bounded above and below the statistic's mean.

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Two or more expressions with an Equal sign is called as Equation.  Price of each basket is 24.ice of each basket is 24.

Two or more expressions with an Equal sign is called as Equation.

Given A youth organization raised $15, 336 by selling gift baskets.

Martin's team sold : 48 baskets

Amy's team sold : 138 baskets

Sharon's team sold :77 baskets

Juan's team sold : 250 baskets

Dee's team sold : 126 baskets

Let x be the price of each basket.

Let us form a equation by given data

48x+138x+77x+250x+126x=$15, 336

639x=$15, 336

Divide both sides by 639

x=24

Hence price of each basket is 24.

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The measure of the angle indicated is as follows:

The measure of the angle indicated can be found using exterior angle theorem. The exterior angle theorem states that  If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.

Therefore,

m∠S + m∠T = 129

m∠S  = -3 + 6x

m∠T = 11x + 13

Therefore,

129 = - 3 + 6x + 11x + 13

129 = - 3 + 13 + 6x + 11x

129 = 10 + 17x

129 - 10 = 17x

119 = 17x

x = 119 / 17

x = 7

Therefore,

m∠S = - 3 + 6(7) = -3 + 42 = 39°

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T-Mobile charges a base fee of $15 per month plus $0.05 for each minute. 300 minutes long would you need to call for them to charge the same amount.

Given: While Verizon has a basic rate of only $10 per month but charges $0.10 for long-distance calls, T-Mobile has a base fee of $15 per month plus $0.05 for each minute you are on the phone.

We have to estimate how long would you need to call for them to charge the same amount.

Let the equation be 15 + 0.05 x = 0.10 x

⇒ 0.05 x - 0.10 x = -15

simplifying the above equation, we get

⇒ -0.05 x = -15

⇒ 0.05x = 15

⇒ x = 15 / 0.05

⇒ x = 300 minutes

Therefore, 300 minutes long would you need to call for them to charge the same amount.

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Three ratios that are equivalent to 3:2:20 are: 9:6:60  27:18:180 and 81: 54:540 .

When comparing two or more numbers, the mathematical concept of ratio is applied. It is a comparison tool to show how large or tiny a given quantity is. A ratio compares two amounts by dividing them. Here, the dividend is referred to as the "antecedent" and the "consequent" is the divisor.

Make sure to multiply the denominator and numerator by the same value each time to keep getting equal ratios.

Three ratios that are equivalent to 3:2:20 are: 9:6:60  

Multiply the ratios by 9

27:18:180 and 81: 54:540 .

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