Find domain and range please! Also, due tmrw!

Answer:

(4) (-1,6)

Step-by-step explanation:

f(x) = x² - 3x + 4

1) (0,4) ==>x=0 and f(x)=4

4 = 0² - 3(0) + 4

4 = 0 + 4

4 = 4 ==> true X

2) (1.5,1.75)==> x=1.5 and f(x)=1.75

1.75 = (1.5)² - 3(1.5) + 4

1.75 = 2.25 - 4.5 + 4

1.75 = 2.25 - 0.5

1.75 = 1.75 ==> true  X

3) (5,14)

14 = (5)² - 3(5) + 4

14 = 25 - 15 + 4

14 = 10 + 4

14 = 14  ==> true X

4) (-1,6)

6 = (-1)² - 3(-1) + 4

6 = (|-1|)² - (-3) + 4  ==> the square of a negative number is equal to the square

                              of the absolute value of that number since the square of

                             a real number is always positive

6 = (1)²+ 3 + 4  ==> subtracting a negative number is equivalent to adding

                          the positive number

6 = 1 + 3 + 4

6 = 4 + 4

6 = 8  ==> false √√

Hence, the answer is (4) (-1,6).

The value of  [tex]\sqrt{0.9}[/tex] is 0.94868329805. You can't get an accurate answer since the square root is an irrational quantity. But I suppose you could just make it simpler.

The value that a number produces when it is multiplied by itself is known as the square root of the number. The square root is denoted by the radical sign. For instance, 16 Equals 4. The root symbol or surds is another name for the radical symbol.

The radical symbol for the number's root is "" in this instance. The square of the positive number is represented by multiplying it by itself. The original number is obtained by taking the square root of the square of a positive number. For instance, the square of three is nine. and the square root of 9, √9 = 3.

Since, 3*3*0.1

= 9*0.1

= 0.9

[tex]\sqrt{3*3*0.1} \\[/tex]

= 3([tex]\sqrt{0.1}[/tex])

[tex]\sqrt{0.9}[/tex] ≈ 0.94868329805

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Correct Question:

What is the value of  [tex]\sqrt{0.9}[/tex]

Answer:   6^1/3x6^1/4=6^x/y

X= ,y=

Step-by-step explanation:

Answer:

x = 7 , y = 12

edge 2023

Answer:

AAA

Step-by-step explanation:

There's no angle angle angle (AAA) because all triangle's angles add up to 180

Hence, the three side length of two triangles are same so they are congurent.  

What is the congurency?

Two shapes are congruent if they are the same (shape and size)- in other words, if the lengths of the sides and the angles are the same.

It is often useful to know when two triangles are congruent.

Here given coordinates of the triangle [tex]FGH[/tex] and triangle [tex]JKL[/tex] are

[tex]F(-5, 10), G(-2, 2), H(-9, -7), J(0, -5), K(9, 2), L(-8, -2)[/tex].

So, the distance formula is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Distance between [tex]FG[/tex]  is

[tex]d=\sqrt{(-2-(-5))^2+(2-10)^2}\\\\d=\sqrt{(-2+5)^2+(2-10)^2}\\\\d=\sqrt{(3)^2+(-8)^2}\\\\d=\sqrt{9+64}\\\\d=\sqrt{73}[/tex]

Distance between [tex]GH[/tex]  is

[tex]d=\sqrt{(-9-(-2))^2+(10-(-7))^2}\\\\d=\sqrt{(-9+2)^2+(10+7)^2}\\\\d=\sqrt{(-7)^2+(-9)^2}\\\\d=\sqrt{49+81}\\\\d=\sqrt{130}[/tex]

Distance between [tex]HF[/tex]  is

[tex]d=\sqrt{(-5-(-9))^2+(10-(-7))^2}\\\\d=\sqrt{(-5+9)^2+(10+7)^2}\\\\d=\sqrt{(4)^2+(17)^2}\\\\d=\sqrt{16+289}\\\\d=\sqrt{305}[/tex]

Distance between [tex]JK[/tex]  is

[tex]d=\sqrt{(9-0)^2+(2-(-5))^2}\\\\d=\sqrt{(9)^2+(2+5)^2}\\\\d=\sqrt{(9)^2+(7)^2}\\\\d=\sqrt{81+49}\\\\d=\sqrt{130}[/tex]

Distance between [tex]KL[/tex]  is

[tex]d=\sqrt{(-8-9)^2+(-2-2)^2}\\\\d=\sqrt{(-17)^2+(-4)^2}\\\\d=\sqrt{289+16}\\\\d=\sqrt{305}[/tex]

Distance between [tex]LJ[/tex]  is

[tex]d=\sqrt{(0-(-8))^2+(-5-(-2))^2}\\\\d=\sqrt{(8)^2+(-5+2)^2}\\\\d=\sqrt{(8)^2+(-3)^2}\\\\d=\sqrt{64+9}\\\\d=\sqrt{73}[/tex]

Since, [tex]FG[/tex]≅[tex]LJ-GH[/tex]≅[tex]JK-HF[/tex]≅[tex]KL[/tex]

Hence, the three side length of two triangles are same so they are congurent.  

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The pints of each of the two existing types of drink must be used to make 180 pints of a mixture that is 75% pure fruit juice is 72 and 108 pints respectively.

Let juice A = a

60% pure fruit juice

Let juice B = b

85% pure fruit juice

We need to make 180 pints of juice from both

a + b = 180

represented in terms of pure fruit

a = 0.60; b = 0.85 ;

Our mixed fruit juice from a and b should be 75% pure fruit = 0.75

Mathematically,

0.60a+ 0.85b = 180(0.75)

0.60a + 0.85b =135

Multiply this equation by 100

60a+ 85b = 13500

Now we have two equations for two variables,

a + b = 180 and

60a+ 85b = 13500

Multiply equation 1 by 60,

we get,

60a + 60b = 10800

On solving these equations we get,

b = 108

Substitute b = 108 into the second equation

60a+ 85(108)= 13500

60a+ 9180 = 13500

a = 72

Therefore , the pints of juice A required is 72 pints and the pints of juice B required is 108 pints.

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Answer:

Step-by-step explanation:

The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 85% pure fruit juice. The company is attempting to produce a fruit drink that contains 75% pure fruit juice. How many pints of the two existing types of drink must be used to make 60 pints of a mixture that is 75% pure juice?

The length AC of the triangle ABC is approximately 12.083 centimeters.

The law of sine is a relationship between the sides and the angles of the triangle, which is defined below:

AB / sin C = AC / sin B = BC / sin A

Where:

First, determine the measure of angle C:

AB / sin C = BC / sin A

sin C = (AB / BC) · sin A

sin C = (8.2 / 13.5) · sin 81°

C ≈ 36.865°

Second, determine the measure of angle B:

B = 180° - A - C

B = 180° - 81° - 36.865°

B = 62.135°

Third, determine the length of side AC:

AC / sin B = BC / sin A

AC = BC · (sin B / sin A)

AC = 13.5 · (sin 62.135° / sin 81°)

AC ≈ 12.083 cm

The length AC is approximately equal to 12.083 centimeters.

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Answer:

12

Step-by-step explanation:

Using the side splitter theorem, [tex]\frac{x}{32}=\frac{9}{24} \implies x=12[/tex].

The value of x is 12, option (B) is correct.

A line parallel to one side of a triangle splits the other two sides of the triangle proportionally if the line also crosses the other two sides.

Given that,

Two lines are parallel to each other,

And length of sides are,

32 , x , 24 and 9.

By angle proportionality theorem,

32 / x = 24 / 9

x = (32 × 9) / 24

x = (4 × 9) / 3

x = 4 × 3

x = 12

The required length of x is 12.

Hence, option (B) is correct.

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The expression to determine the number of bags is 2/3 x = 2 1/2 and the number of bags requited is 3 3/4 bags

Information from the problem

Maya rakes up the leaves and wants to put them into bags that hold 2\3 of a cubic yard

she rakes 2 1\2 cubic yards of leaves

one bag = 2/3 cubic yard

total leaves raked = 2 1/2 cubic yard

the number of bags required is how many 2/3 cubic yards are there in 2 1/2 cubic yard. this is solved by division

let the number of bags be x

2/3 cubic yard * x = 2 1/2 cubic yard

2/3 x = 2 1/2

x = (2 1/2) / (2/3)

x = 15/4

x = 3 3/4 bags

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The value of AC is 22.5

The property of three parallel lines and their transversals is used to solve this sum. The property explains that if the ratio of the corresponding intercepts made on any other transversal by the same parallel lines is the same as the ratio of the intercepts made on a transversal formed by three parallel lines.

XY ║seg AC

2AX = 3BX

XY = 9

Since, 2AX =3BX

∴ AX÷ BX = 3÷2

AX + BX÷ BX = 3+2÷2

AB ÷ BX = 5÷2

Δ BCA ~  ΔBYX (SAS test of similarity)

( The SAS similarity test determines whether two triangles are similar if the ratio of the lengths of two sides of one triangle equals the ratio of the lengths of two sides of another triangle, and the included angles are equal.)

∴ BA ÷ BX = AC ÷ XY ( Corresponding sides)

∴ 5÷ 2 = AC ÷ 9

∴ AC = 22.5

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Answer:

Step-by-step explanation:

Solve for x:

2 cos* (2) =

Divide both sides by 2:

cost (2) =

Take the logarithm base cos(2) of both sides:

Answer:

2inn

X=

iT+ log(-cos(2))

log(2)

i7+ log(-cos(2))

for NE Z

Answer: 1280 Kg

Step-by-step explanation:

The weight of the object given = 128 Kg

Time 1 = 10 hr

Time 2 = 1 hr

Cancel the hours,

128×10 = 1280 Kg

The minimum value, Q1, Median, Q3 and maximum value of the data are 2, 5, 12, 14 and 16 respectively

Given the data: 2, 4, 4, 5, 8, 10, 12, 12, 12, 13, 14, 14, 15, 16

The minimum value of the data is 2. Thus, Min = 2

The maximum value of the data is 16. Thus, Max = 16

The median is the data value in the middle.

2, 4, 4, 5, 8, 10, 12, 12, 12, 13, 14, 14, 15, 16

So the median (Q2) of the data is (12+12)/2 = 12. Thus, Med = 12

Consider the values to the left of the median with one of the median numbers included (since we have numbers in the middle):

2, 4, 4, 5, 8, 10, 12

Find the median of this set of numbers. The median is 5.  Q1 = 5

Also, consider the values to the right of the median with one of the median numbers included: 12, 12, 13, 14, 14, 15, 16. The median is 5. Q3 = 14

To create a box and whiskers plot use Min, Max, Q1, Median(Q2) and   Q3 (Check the attached image)

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Answer:

533

Step-by-step explanation:

3 hours = 180 minutes

2400 : 180 = x : 40

x = 2400 * 40 / 180

x = 2400 * 4 / 18

x = 2400 * 2 /9

x = 800 * 2 / 3

x = 1600/3

x = 533.333333

x = 533

365 sets of people born on the same day, with each set containing no more than 5 people.

Assuming everybody was born on a different day, then you could have 365 people where nobody was born on the same day. the 366 person, however, would have to have been born on the same day as somebody else in the group. therefore, the minimum number of people in the group would have to be 366 to guarantee that at least 2 people were born on the same day but you wanted to guarantee that at least 6 people were born on the same day. assuming you had 5 * 365 people together, with every 5 of them being born on the same day.

you would have a total of 365 * 5 = 1825 people, with no more than 5 people being born on the same day.

Add 1 more person and you will be guaranteed that at least 6 people were born on the same day that comes out to be 1826 people.

1825 / 5 = 365 sets of people born on the same day, with each set containing no more than 5 people.

set 1 is the number of people born on day 1.

set 2 is the number of people born on day 2 etc.

that next person had to be added to one of the sets of 5 to make it a set of 6.

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Answer:

7/20 miles

Step-by-step explanation:

get a common denominator

subtract the numerators

then you have the fraction she biked

According to the uniform distribution, there is a 0.1= 10% chance that a worker selected at random will have an annual wage between $45,000 and $60,000.

Uniform Distribution:

In statistics, uniform distribution refers to a type of probability distribution in which all outcomes are equally likely. A deck of cards has within it uniform distributions because the likelihood of drawing a heart, a club, a diamond, or a spade is equally likely.

An uniform distribution has two bounds, a and b.  

The probability of finding a value between c and d is:

P(c ≤ X ≤ d) = [tex]\frac{d-c}{b-a}[/tex]

given that , workers' salaries in your company are uniformly distributed between $10,000 and $60,000 per year

a = 10,000 , b= 60,000 , c = 45,000 and d = 50,000

The probability is

P(45,000 ≤ X ≤ 50,000) = [tex]\frac{50,000-45,000}{60,000-10,000}[/tex]

                                       = 0.1

0.1 = 10% probability that a randomly chosen worker earns an annual salary between $45,000 and $60,000

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Part (a)

Part (b)

Yes, the triangles are congruent by RHS.

Answer:

x= 9

Step-by-step explanation:

2(x + 5 ) = 3x + 1

expand the bracket first

2x + 10 = 3x + 1

then collect like terms

2x-3x = 1 - 10

-1x = - 9

and the last step is divide both side by -1

then x = 9

The increase in the orbital period is by a factor of k^3/2. Option D

From the Kepler's laws, we know that the square of the period of the planet is directly proportional to the cube of the distance of the planet from the sun. We can see that this has been typified by the expression; T^2 =A^3 where T is the period of the planet and A is the distance between the planet and the sun.

Now, we can see that from the relationship, If planet Y is k times the mean distance from the sun as a planet X then the orbital period would be increased by a factor of about k^3/2.

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The number of points of intersection for the graphs of the equations is infinite.

Point of intersection refers to the point at which two lines intersect on a graph. The graph of the equation refers to the visual demonstration of the equation obtained by plotting all the points of an equation on a graph. If there is only one variable, the graph is on a number line. If there are two variables, the graph is on the coordinate plane. If there are three variables, the graph is in three-dimensional coordinates.

Simplifying the given equations:

i) x/2 + 5y = 6

x + 10y = 12

ii) 3x + 30y = 36

3(x + 10y) = 36

x + 10y = 12

As the equations are equal lines, they will intersect at infinite times.

Note: The question is incomplete. The complete question probably is: How many intersections are there of the graphs of the equations below? x/2 + 5y = 6 3x + 30y = 36 none one two infinitely many

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The change in Ms Smith's saving account balance each month due to her car payments is of:

-$267.75.

A proportion is a fraction of a total amount, and this fraction is used along with the basic arithmetic operations, especially multiplication and division, to find the desired measures in the context of a problem.

In this problem, the monthly balance change is obtained as follows:

Monthly balance change = Yearly balance change / 12.

(as an year is composed by 12 months).

As stated in the text, the yearly balance change of Ms. Smith's account is given as follows:

-$3,213.

The payments are equal each month, hence the monthly change is of:

Monthly balance change = -3213/12 = -$267.75.

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The simplified form can be written as -

7.8y + 1.4z

We have the following expression -

6(0.7y + 0.8z) − 4z − 6(−0.1z − 0.6y)

We have -

6(0.7y + 0.8z) − 4z − 6(−0.1z − 0.6y)

(6 x 0.7y + 6 x 0.8z) - 4z + 6 x 0.1z + 6 x 0.6y

4.2y + 4.8z - 4z + 0.6z + 3.6y

7.8y + 4.8z - 3.4z

7.8y + 1.4z

Therefor, the simplified form can be written as -

7.8y + 1.4z

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Answer: The ∠DEF= 75°

Step-by-step explanation:

The angle subtended by circumference is half of the angle subtended at the center by the same arc.

So , ∠DEF= 75°

[tex]~~~~~~~~~~~~\stackrel{\textit{\LARGE Sydney}}{\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}}}[/tex]

[tex]A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right) \\\\ \qquad \begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic payments}\dotfill & 100\\ r=rate\to 0.8\%\to \frac{0.8}{100}\dotfill &0.008\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &10 \end{cases}[/tex]

[tex]A=100\left[ \cfrac{\left( 1+\frac{0.008}{12} \right)^{12 \cdot 10}-1}{\frac{0.008}{12}} \right]\left(1+\frac{0.008}{12}\right) \\\\\\ A=100\left[ \cfrac{\left( \frac{1501}{1500} \right)^{120}-1}{\frac{1}{500}} \right]\left(\frac{1501}{1500}\right) \implies {\Large \begin{array}{llll} A \approx 12497.05 \end{array}}[/tex]

Answer:

112/1000

Step-by-step explanation:

Just put 1 under decimal point and just add as many zeros as digits after that

After doing the equitation the at rate of $15 per week.

How to do graph representation?

Graph representation is a way of visualizing data as a graph or chart. It is used to easily identify relationships between data points and to illustrate trends in the data. Graphs can be used to present data in a variety of ways, such as bar graphs, line graphs, pie charts, scatter plots and more. Graphs are especially useful when trying to compare two or more sets of data and to highlight any patterns or trends that may exist. Additionally, graphs are often used to represent numerical data in a more visually appealing way. By using graphs, it is easier to identify relationships, trends and outliers in the data. Graphs also help to make data easier to interpret and understand.

Carson owes = $110

At rate of $15 per week.

The graph representation will follows:

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Answer:

7

Step-by-step explanation:

Experimental probability is based on the actual results of an experiment (gathered by experimenting repeatedly).  

It is calculated by dividing the recorded number of times an event happens by the total number of trials in the actual experiment:

[tex]\boxed{\textsf{Experimental Probability} = \dfrac{\textsf{Number of times an event happens}}{\textsf{Total number of trials}}}[/tex]

As the number of trials increases, we would expect for the experimental probability to get closer to the theoretical probability.

Given:

The experimental probability of drawing a short straw is:

[tex]\implies \sf P(short\;straw)=\dfrac{35}{50}=\dfrac{7}{10}[/tex]

If Laura conducts 10 further trials of the experiment, based on the results in the table, the number of additional trials that will have a result of a short straw being drawn is:

[tex]\begin{aligned}\implies \textsf{Additional trials (short straw)} &=\sf experimental\;probability \times number\;of\;trials\\&= \sf \dfrac{7}{10} \times 10\\&= \sf 7\end{aligned}[/tex]

The table that contains only viable solutions if b represents the number of books he orders and w represents the total weight of the books, in ounces is the second table on the image given at the end of the answer.

The variables for this problem are given as follows:

To obtain the viable solutions, we must consider the input variable. The number of books is a countable amount, meaning that it can only assume non-negative integer values.

Thus the first table is incorrect, as it contains a negative amount of books, and the second table is the one that contains only viable solutions in the context of this problem.

The table is given by the image shown at the end of the answer.

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