Answer:
x = 1 , x = 13
Step-by-step explanation:
(x - 7)² = 36 ( take square root of both sides )
x - 7 = ± [tex]\sqrt{36}[/tex] = ± 6 ( add 7 to both sides )
x = 7 ± 6
then
x = 7 - 6 = 1
x = 7 + 6 = 13
each book in a certain library is classified in one of three categories: fiction, nonfiction, or biography. the ratio of the number of fiction books to the number of nonfiction books is 4 to 3, and the ratio of the number of nonfiction books to the number of biographies is 3 to 2. if there are at least 10,000 books in the library, what is the least number of books that could be in the library?
The number of fiction books in the library is equal to 16
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given the ratio of fiction to nonfiction books in a classroom, the library is 2 to 3, and then the total ratio of both books will be 2+3 = 5. If there are 24 books non-fiction books in the library, to get the number of fiction books that are there we will follow the following steps.
First, we will calculate the total number of books in the shelf;
3/5 x Total number of books = total non fiction books
3/5 * Total number of books = 24
3*Total number of books = 5*24
3*Total number of books = 120
Total number of books = 120/3
Total number of books = 40
Therefore there are 40 total books on the shelf.
Total number of fiction books = 2/5 * 40
Total number of fiction books = 2* 8
Total number of fiction books = 16 books
Hence there are 16 fiction books on the shelf.
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UU UN INSUL OUUU Convert a fration: m=- 4444 21 x= -2 3 2 91 40 = IU m=-5 2 and 3 32°+x- Which two integers does V5 go between? 1 and 2 49 x=100 x=180 7 and 8 4 and
I'll get the slope of the arrow on the graph
P1 = (-1, 1)
P2 = (-4, 3)
slope = m = (3 - 1) / (-4 + 1)
m = 2/-3
slope = m = -2/3
Function g is represented by the table.
-1
0
24
4
X
g(x)
1
0
2
-
10
3
-24
to
Which statement correctly compares the two functions?
OA. They have different x- and y-intercepts but the same end behavior as x approaches.
OB.
They have the same x- and y-intercepts.
C.
They have the same y-intercept and the same end behavior as x approaches".
D. They have the same x-intercept and the same end behavior as x approaches".
The functions have the same x-intercept and the same end behaviour as x approaches infinity.
We are given two functions, f(x) and g(x). A function connects an input with an output. It is analogous to a machine with an input and an output. And the outcome is somehow connected to the input.
The function f(x) is represented in the graph. The function g(x) is represented by the data in the table. We have to find the correct comparison between the two functions.
The comparison is to be done on the basis of the lengths of the x-intercept and y-intercept and the end behaviour of both functions. From the given values, we conclude that the x-intercepts for both functions are the same, but the y-intercepts are different. The end behaviour of both functions becomes similar as x approaches infinity.
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5. A shipping company is sending a fragile package with these dimensions: 6 in. x 7 in. * 2 in. If the boxthey use to send it is 9 in. x 9 in. x 3 In., how many cubic Inches of packing peanuts can they fit into thebox?
First, we need to calculate the volume of the package and the volume of the box
Package
[tex]V_P=6\times7\times2=84in^2[/tex]Box
[tex]V_B=9\times9\times3=243in^3[/tex]we need to subtract the volume of the package from the volume of the box
[tex]V=V_B-V_P=243-84=159in^3[/tex]159 in^3 of packing peanuts will fill into the box
If a triangle has 2 sides measuring 10 and 64 then the 3rd side must be less than what value
Answer:
It must be less than 180º.
Step-by-step explanation:
A triangle always adds up to 180º which then means that since two angles have already been stated that means the total of those two angles is 74º which you subtract from 180º to get 106º which is the measure of the third angle.
Write an equation of the line that passes through $\left(18,\ 2\right)$ and is parallel to the line $3y-x=-12$.
The equation of the line which is parallel to the given line is 3y - x = -12.
What is an equation?An equation is a mathematical formula containing an equal sign. Equations often involve algebra. Algebra is used in mathematics when we don't know the exact number in a calculation. In its simplest form in algebra, the definition of an equation is the mathematical statement that two mathematical expressions are equal. For example, 3x + 5 = 14 is an equation where 3x + 5 and 14 are two terms separated by an equal sign. An equation is a mathematical expression consisting of two expressions connected by an equal sign. For example, 3x + 5 = -16 is an example of equation. Solving this equation gives the value of the variable x as x = 7.given that
x = 18 and y = 2
putting the value in equation 3y-x = -12
this saisfied he equation perfectly.
Hence, the equation in parallel to 3y-x = -12
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Which is the domain and range of the parabola with the equation… Thanks
Okay, here we have this:
Considering the provided equation of the parabola, we are going to find the requested domain and range, so we obtain the following:
Domain: Corresponds to all the values that x can take in the function. Given that in this case no value of x indeterminates the function, and that x can take any value, then its domain will be: (-∞, ∞).
Range: Corresponds to all the values that the dependent variable can take. In this case, since it is a parabola of the form ax^2+bx+c, and that a is less than or greater than 0, its range will be all values greater than or equal to its y-coordinate of the vertex, which for this case is (5, -15). So its range is: [-15, ∞).
Therefore finally we obtain that the correct answer is the fourth option.
Which region has a population density less than 60 animals per square mile
Explanation
We will have to find the population density of each of the regions
To get the population density, we will have to divide the population of each region and then divide by the area of the of each region
For part A
[tex]Area=\frac{1}{2}\times40\times35=700mi^2[/tex]The population density of region A is
[tex]\frac{42500}{700}=60.71\text{ animals per square miles}[/tex]For region B
The area of region B is
[tex]\frac{1}{2}\times50\times38=950mi^2[/tex]The population density of region B is
[tex]\frac{60800}{950}=64\text{ animals per square miles}[/tex]For region C
[tex]area=\frac{1}{2}\times42\times49=1029mi^2[/tex]The population density of region C
[tex]\frac{57300}{1029}=55\text{ animals per square mile}[/tex]Thus, we can observe that Region C has a population density lower than 60 animals per square miles
Thus, option C is correct
1. (5 points) The arc of a football thrown by Patrick Mahomes is modeled by the equation h=-16t2 + 36t + 6, where h = the height of the ball and t = the time in seconds. Will the ball reach a height of 24 feet?
In order to determine if the ball reaches the 24 ft, replace h = 24 and solve the quadratic equation. If the solutions are real, then, the ball does reach 24ft.
Proceed as follow:
h = 16t² + 36t + 6
24 = 16t² + 36t + 6
16t² + 36t + 6 - 24 = 0
16t² + 36t - 18 = 0
use he quadratic formula, given by:
[tex]t=\frac{-b\pm\sqrt[]{b^{2}-4ac}}{2a}[/tex]In this case, a = 16, b = 36 and c = -18
[tex]\begin{gathered} t=\frac{-36\pm\sqrt[]{(36)^{2}-4(16)(-18)}}{2(16)} \\ t=\frac{-36\pm49.47}{32} \\ t_1=-2.67 \\ t_2=\text{0}.42 \end{gathered}[/tex]negative times do not have physical meanning, then, the available solution is
t = 0.42
Hence, you can conclude that the ball reaches 24 ft for a time of 0.42 seconds.
What is the radian equivalent of 90 degrees?
Answer:
The Radiant Equivalent of 90 degrees, would be 1.57079633.
An empty bucket is being filled at a constant rate. after 4 minutes, the depth of the water is 12 inches. the water continues to be filled at that same rate. what is the relationship between the time in minutes, x, and the depth of the water, y?
Every 4 minutes, the depth of the water increases 12 inches. Like let's say after another 4 minutes it'll be 24 inches. I may be wrong but I may be right.
Answer:
See below
Step-by-step explanation:
Every minute 'x' produces 12/4 = 3 inches of 'y' water depth
y = 3 x
Heyyy.......please i need help with this
√ 1-cos²θ/1-sec²θ=cosθ, cosθ is the simplified form of √ 1-cos²θ/1-sec²θ
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
We know that ,
Trigonometric identities
sin²θ+cos²θ=1
so 1-cos²θ= sin²θ
sec²θ+tan²θ=1
1-sec²θ=tan²θ
So √ 1-cos²θ/1-sec²θ
√ 1-cos²θ/1-sec²θ=√sin²θ/tan²θ
The square root will get cancelled
=sinθ/tanθ
=sinθ/sinθ/cosθ (because tanθ=sinθ/cosθ)
=cosθ
Hence √ 1-cos²θ/1-sec²θ=cosθ, cosθ is the simplified form of √ 1-cos²θ/1-sec²θ
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Line segment EF has endpoints at (2,-4) and (5,-9)
If ST is congruent to EF and has one endpoint at (4,9), which of the following points could be the second endpoint?
A.(-4,-3)
B.(-1,12)
C.(22,-3)
D.(-4,11)
Please show work so I can understand how to do it.
The second endpoint of ST is B(-1,12).
It is given in the question that:-
Endpoints of line segment EF are (2,-4) and (5,-9).
One of the endpoint of ST is (4,9).
We have to find the second endpoint of ST.
As both of the line segments are congruent hence, the length of each line segment will be same.
We can find the length of the line segment EF using the distance formula.
Length of the line segment EF :-
[tex]\sqrt{(-9-(-4)^2+(5-2)^2}=\sqrt{(-9+4)^2+3^2}=\sqrt{25+9}=\sqrt{34} units[/tex]
Hence, length of the line segment ST should also be the same.
We can check that from the options and get B(-1,12) as the answer.
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Convert the polar equ what is the angle between the ropes? Round to the nearest degree.ation r = 16 sin θ to a rectangular equation.
The angle between the ropes is 53°.
We are given that a barge is being towed by two tugboats using ropes. The force vectors of the two tugboats are represented by F1 and F2. A vector is an entity that has both a magnitude and a direction. The vectors are F1 = 11000i + 5000j and F2 = 14500i + -8000j. We need to find the angle between the ropes. The best method is to find the dot product. Let the angle between the ropes be θ. We can say that cos(θ) = F1.F2/(|F1|*|F2|) = (11000*14500 + 5000*-8000)/[√[(11000)² + (5000)²] * √[(14500)² + (-8000)²]] = (11*14.5 + 5*-8)/[√[(11)² + (5)²] * √[(14.5)² + (-8)²]] = 119.5/[√146*√274.25] = 119.5/200.1 = 0.597. So, the value of θ is 53°.
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Help with my algebra please.
t + b = 38
6t + 4b = 188 is the equation to calculate the system of the restaurant .
Restaurants must foster an atmosphere of delicious food, attractive surroundings, and courteous living. In order to maintain the restaurant's financial viability, it is crucial for the owners to choose the seating arrangement, chairs, and sofas with an eye toward projecting a certain image.
What is seat arrangement problems?The most typical categories of seating arrangement queries. There are intricate row arrangements, double rows, rectangular rows, linear rows, and circular rows.
Theatre. The simplest and most popular seating arrangement for events is the theater style setup.
Classroom.Herringbone.a U-shape.Equine shoeSquare HollowBoardroom.Banquet.n distinct things permuted (when repetition is not allowed) Repetition when it is acceptable. When the objects are not distinct, permutation (Permutation of multi sets)
The following formula determines how many permutations of n objects, taken r at a time: (n,r)! P(n,r)=n!
The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation.
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Kathleen took a total of 20 quizzes over the course of 4 weeks. After attending 7 weeks of school this quarter, how many quizzes will Kathleen have taken in total?
To determine the number for a unit value the unitary method is used.
The number of quizzes Kathleen will take in 7 weeks is 35.
What is Unitary method ?In order to solve a problem for two different values of a quantity, its unit value is first derived. This method is known as unitary method.
Given that,
Total number of quizzes in 4 weeks = 20
Total number of weeks the school is attended = 7
In order to find total number of quizzes in 7 weeks, apply unitary method to find the number of quizzes per week and then multiply it by 7 as follows,
Since, total number of quizzes in 4 weeks is 20
The number of quizzes in 1 week is 20 / 4 = 5.
Thus, the number of quizzes in 7 weeks is 5 × 7 = 35.
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Will mark Brainliest for right answer
Answer:
Toni had the highest score.
Step-by-step explanation:
Terri - 45/50 = 90%
Toni - 92%
Tina - 8/9 = 89%
Warm-up:
Determine the Cost of Goods Sold for one Holiday Basket:
1 basket $24.00 per dozen
2 lbs. Cheddar cheese $1.50 per pound
1 canned ham $60.00 per dozen
3 jars of jelly $1.00 each
6 oranges $2.00 per dozen
1 box crackers 2.00 per box
cellophane wrap $.50 each
Note: Each basket has only one of each item in it.
Cost of Goods Sold: $
Suggested selling price: $
The cost of Goods Sold will be $93.5
What is Addition?
A process of combining two or more numbers is called addition.
Given that;
The Cost of Goods Sold for one Holiday Basket:
1 basket = $24.00 per dozen
2 lbs. Cheddar cheese = $1.50 per pound
1 canned ham = $60.00 per dozen
3 jars of jelly = $1.00 each
6 oranges = $2.00 per dozen
1 box crackers = 2.00 per box
Cellophane wrap = $.50 each
Now,
Since, Each basket has only one of each item in it.
So, The total cost = $24 + $1.50 x 2 + $60 + $1 x 3 + $1 + $2 + $0.50
= $93.5
Thus, The cost of Goods Sold will be $93.5
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On the number line above, if x is a number that lies between a and a + 10, which of the following must betrue?lx - al > 5lx - a -51 < 5lx - a - 101 < 5lx - a + 101 < 5
We are given an inequality proble. Our approach is to test our options.
We begin with the second option.
[tex]\begin{gathered} |x-a-5|<5 \\ \text{This translates to:} \\ -5<|x-a-5|<5 \end{gathered}[/tex]We'll solve it in parts and compare to our number line
[tex]\begin{gathered} -5<(x-a-5) \\ \text{Adding 5 to both sides gives us:} \\ -5+5On the other hand, we have:[tex]\begin{gathered} (x-a-5)<5 \\ \text{Adding 5 to both sides} \\ x-a<5+5 \\ x-a<10 \\ \text{Adding a to both sides} \\ x<10+a \end{gathered}[/tex]The range of x is therefore: a < x < 10 + a
SECOND OPTION
Can someone please help me?
Part A) The definition of speed can be used to establish the equation of the line that depicts the relationship between distance and time, which is (y = 62x).
Part B) Option c
What is a speed, exactly?
Velocity is the rate and direction of an object's movement, whereas speed is the time rate at which an object is moving along a path.
Given:
In 3 hours and 186 miles, Car X goes.
To find the equation of the line that represents the relationship between distance and time, perform the following steps:
Step 1: Assume that car X traveled a total distance of y miles and traveled that amount in x minutes.
Step 2: The speed is determined by the distance to time ratio.
speed = distance / time
Step 3: Add the distance and time values to the equation above.
Speed = y/x —— (1) (1)
Step 4 - Based on the provided information, the speed is determined by:
speed = 186/3 = 62
Step 5: Adding the speed value to the equation (1).
y/x = 62
y = 62x
(Y = 62x) is the equation of the line that depicts the relationship between space and time.
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For trapezoid WXYZ shown below, points U and V are the midpoints of the legs. Use this information to find UV, the length of the mid segment.
Given:
[tex]\begin{gathered} WX=x+7 \\ ZY=6x+5 \\ UV=8x-3 \end{gathered}[/tex][tex]\begin{gathered} UV=\frac{1}{2}(WX+ZY) \\ 8x-3=\frac{1}{2}(x+7+6x+5) \\ 2(8x-3)=(7x+12) \\ 16x-6=7x+12 \\ 16x-7x=12+6 \\ 9x=18 \\ x=\frac{18}{9} \\ x=2 \end{gathered}[/tex][tex]\begin{gathered} \text{Length of the midsegment=8x-3} \\ =8(2)-3 \\ =16-3 \\ =13 \end{gathered}[/tex]13 is the final answer.
In this question, assume that the car uses the same amount of petrol for each mile it travels.
A car uses 55 litres of petrol to travel 495 miles.
How much petrol would the car use on a trip of 160 miles?
Give your answer to the nearest litre.
The quantity of petrol used to travel 160 mile is 17.78 liters
The quantity of petrol used to travel 495 miles = 55 liters
Here we have to use the unitary method
The unitary method is defined as the method that uses to find the unit rate
The quantity of petrol used to travel 1 mile = The quantity of petrol used to travel 495 miles / 495
Substitute the values in the equation
The quantity of petrol used to travel 1 mile = 55 / 495
= 1 /9 liters
The quantity of petrol used to travel 160 mile = The quantity of petrol used to travel 1 mile × 160
Substitute the value in the equation
The quantity of petrol used to travel 160 mile = (1 / 9) × 160
= 17.78 liters
Hence, the quantity of petrol used to travel 160 mile is 17.78 liters
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Use the ALEk calculator to write 3/32 as a percentage
Answer:
9.4%
Step-by-step explanation:
To convert any given imporper fraction into a percentage, we multiply it by 100. This way, we can convert the fraction given as following:
[tex]\frac{3}{32}\times100\rightarrow9.4\%[/tex]estimate the quotient .. 19 4/8 divided 4 5/8
about 3
about 6
about 5
about 4
The quotient 19 4/8 divided 4 5/8 is about 3
We need to estimate the quotient .. 19 4/8 divided 4 5/8
19 4/8 ÷ 4 5/8
Converting the mixed fraction 19 4/8 into improper fraction
(19x8 + 4)/8 = 154/ 8
Converting the mixed fraction 4 5/8 into improper fraction
(4x8 + 5)/ 8 = 45/8
Dividing 154/ 8 with 45 / 8
(154/8) / (45/8)
Multiplying both numerator and denominator with 8
154 / 45
3.2 = 3 (approx)
Therefore, the quotient .. 19 4/8 divided 4 5/8 is about 3
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-2(-3.4)what is the answer
6.8
1) Let's calculate this product by distributing the factor -2 multiplying the number within the parentheses.
-2(-3.4) Equal signs yield positive and remove the parentheses
6.8
2) So 6.8 is the answer for that product.
Which two consecutive integers does[tex] - \sqrt{214} [/tex]fall between?
Answer
-√214 is between -15 and -14.
Explanation
To solve this, we need to first obtain the value of the -√214
-√214 = -14.63
Hence, we can see that this number is between -15 and -14.
Hope this Helps!!!
what is 91 divided by 7 ??
Answer:
13
Step-by-step explanation:
[tex]\frac{91}{7}=\frac{70+21}{7}=10+3=13[/tex]
The solution of 91 divided by 7 in simplest form is,
⇒ 13
We have to given that,
To simplify 91 divided by 7 in simplest form.
It can be written as,
⇒ 91 ÷ (7)
⇒ 91 / 7
⇒ 13
Therefore, The solution of 91 divided by 7 in simplest form is,
⇒ 13
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The storage area in an art room has 24 separate bins. Each bin can hold 8 packs of markers, crayons, or colored pencils. Each pack holds 8 items. The art teacher has 240 markers, 320 crayons, and 336 colored pencils. How many empty bins will the art teacher have once all of the markers, crayons, and pencils are put away?
In order to find the number of empty bins, let's calculate how many packs will be made with the given material.
240 markers can be organized in 240/8 = 30 packs
320 crayons can be organized in 320/8 = 40 packs
336 colored pencils can be organized in 336/8 = 42 packs
In total we have 30 + 40 + 42 = 112 packs
Each bin can hold 8 packs, to in order to hold 112 packs, we need 112/8 = 14 bins.
We have 24 bins. Since 14 will be used, we will have 24 - 14 = 10 empty bins.
What is the slope of the line that passes through the points (-2, 6)(−2,6) and (-12, 2)(−12,2)? Write your answer in simplest form.
Answer:Given points are (6, -2) and (12, -2). Find the slope of the line using the formula m = (y2 - y1)/(x2 - x1) Here, y1 = -2, y2 = -2, x1 = 6 and x2 = 12
⇒ m = (-2 - -2)/(12 - 6) = 0/6 = 0
Step-by-step explanation: i hoped i helped a little :)
What is the value of Arc cosine (negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction)?
StartFraction pi Over 6 EndFraction
StartFRaction pi Over 4 EndFraction
StartFraction 3 pi Over 4 EndFraction
StartFraction 5 pi Over 6 EndFraction
The value of arccos(-√3/2) is 5π/6.
In the given question,
We have to find the value of [tex]arccos(-\frac{\sqrt{3}}{2})[/tex].
The given term is [tex]arccos(-\frac{\sqrt{3}}{2})[/tex].
We using the quadrant rule.
The value is in negative so we check in which quadrant the value of cos negative.
As we now that in second quadrant only the value of sine and cosine is positive and all value are negative.
The second quadrant of 180 degree or we can also write 180 degree as π.
From the trigonometry table we know that at 30 degree or (π/6) the value of cos is √3/2.
So the value of cos at which -√3/2 is
-√3/2 = cos(π - π/6)
-√3/2 = cos(π×6/6 - π/6)
-√3/2 = cos(6π/6 - π/6)
-√3/2 = cos{(6π- π)/6}
-√3/2 = cos 5π/6
So we can write it as
arccos(-√3/2)=arccos(cos 5π/6)
Since there is a arccos and cos both so only left 5π/6.
arccos(-√3/2)=5π/6
Hence, the value of arccos(-√3/2) is 5π/6.
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Answer:
d
Step-by-step explanation: