I'm going to assume you start with
[tex]\dfrac{6^2 - 4 (3 - \sqrt{25})^2}{|4 - 8|}[/tex]
Let's simplify some pieces of this:
[tex]6^2 = 6\times6 = 36[/tex]
[tex]\sqrt{25} = \sqrt{5^2} = 5[/tex]
[tex](3 - \sqrt{25})^2 = (3 - 5)^2 = (-2)^2 = (-2)\times(-2) = 4[/tex]
[tex]|4 - 8| = |-4| = 4[/tex]
So as a first step we can reduce this to
[tex]\dfrac{6^2 - 4 (3 - \sqrt{25})^2}{|4 - 8|} = \dfrac{36-4\times4}4[/tex]
Now,
[tex]36 = 9\times4[/tex]
so every term contains a factor of 4 that we can cancel:
[tex]\dfrac{36-4\times4}4 = \dfrac{9\times4-4\times4}4 = \dfrac{9-4}1 = 9-4 = \boxed{5}[/tex]
as expected.
The domain of a function f(x) is x > 1, and the range is y< 2. what are the
domain and range of its inverse function, f '(a)?
o a. domain: * > - 2
range: y si
o
b. domain: x < -2
range: y > 1
c. domain: x > 1
range: y < -2
o d. domain: x = 1
range: y > -2
submit
Answer: Domain: x<-2 Range: y>1
Step-by-step explanation:
I don't know for sure but I am taking the test and that was the outcome of the answer.
Find the coordinates of P so that P partitions segment AB in the part-to-whole ratio of 1 to 5 with A(-9, 3) and B(1, 8). Explain.
Find point Z that partitions the directed line segment XY in the ratio of 2:1 where X(1, 2) and Y(7, 5). Explain.
For both problems, we can use the section formula.
1) [tex]P=\left(\frac{(1)(1)+(5)(-9)}{6}, \frac{(1)(8)+(5)(3)}{6} \right)=\boxed{\left(-\frac{22}{3}, \frac{23}{6} \right)}[/tex]
2) [tex]Z=\left(\frac{(2)(7)+(1)(1)}{3}, \frac{((2)(5)+(1)(2)}{3} \right)=\boxed{(5, 4)}[/tex]
A cylindrical pressure vessel has a height of 9 feet and a diameter of 6 feet. how much gas can the pressure vessel hold when full?
it is either, 54 pie cubic feet, 81 pie cubic feet, 108 pie cubic feet or 324 pie cubic feet
Step-by-step explanation:
the volume of a cylinder is as for any other regular 3D object :
ground area ×height
the ground area of a cylinder is a circle, so it is
pi×radius² × height
the radius is always half of the diameter (of the diameter is airways twice the radius).
radius = 6/2 = 3 ft.
the volume is then
pi × 3² × 9 = pi × 9 × 9 = pi × 81 ft³
so, the answer is 81pi ft³.
What is the inverse of the function f(x) = 2x + 1?
Answer:
:) The Inverse of the Function f(x) = 2x + 1 is f-1(x) = x/2 - 1/2.
Step-by-step explanation:
mark me brainlist^_^
Select the correct answer.
hich statement is false?
OA. The Inequality sign always opens up to the larger number.
OB.
The greater number in an inequality is always above the other number on the vertical number line.
OC. The smaller number in an inequality is always located to the left of the other number on the horizontal number line.
OD. The Inequality sign always opens up to the smaller number.
Reset
Next
Answer:
d
Step-by-step explanation:
the inequality sign opens up to the bigger number
Ezra has a square brick patio. he wants to reduce the width by 6 feet and
increase the length by 6 feet.
6 ft
6 ft
6 ft
6 ft
let x represent the length of one side of the square patio. write expressions
for the length and width of the new patio. then find the area of the new patio
if the original patio measures 13 feet by 13 feet.
The area of the new patio if the original patio measures 13 feet by 13 feet is 133 ft².
Ezra has a square brick patio. he wants to reduce the width by 6 feet and
increase the length by 6 feet.
What is the area of the square?The area of the square is the measure of the space occupied by it. It is equal to the product of the measure of its two sides.
We need to write the expression for the new patio and the area of the new patio if the original patio measures 13 feet by 13 feet.
let x be the measure of the side of a square.
The length increased by 6 ft, so the new length=x+6.
The width decreased by 6 ft, so the new width=x-6.
The area is the product of length and width, so the new area is
l×w = (x+6)×(x-6)
Since the original side is 13 ft, the new length is 13+6 = 19 ft, and the new width is 13-6=7 ft.
So, the area is (19 ft)×(7 ft) = 133 ft²
Hence, the area of the new patio if the original patio measures 13 feet by 13 feet is 133 ft².
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Four lines are drawn on a coordinate plane to form trapezoid wxyz. Which statements are true about the lines? Select three options
The statements that are true for Trapezoid WXYZ are:
Line WZ has the same slope as line XY.Line XW has a lesser slope than line YZ.Line ZW has the same y-intercept as line WZ.Line XY has a greater y-interceptHow to Interpret Line Coordinates?
We are told that;
Shape is a trapezoid WXYZ.
Now, In a trapezoid, one pair of opposite sides are parallel and parallel lines have the same slope.
Lastly, the slope of line parallel to x axis is 0 and so If the line starts at the bottom left and goes towards the top right it has negative slope. Thus, all the statements that are true for Trapezoid WXYZ are:
Line WZ has the same slope as line XY.Line XW has a lesser slope than line YZ.Line ZW has the same y-intercept as line WZ.Line XY has a greater y-interceptComplete question is;
Four lines are drawn on a coordinate plane to form trapezoid WXYZ. Which statements are true about the lines? Select all that apply.
Line WZ has the same slope as line XY.
Line YX has a greater slope than line ZY.
Line XW has a lesser slope than line YZ.
Line ZW has the same y-intercept as line WZ.
Line XY has a greater y-intercept than line XW
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Shandra bought 24 chicken wings for $50.40. If Shandra spent $10.50, how many chicken wings did she buy?
Answer:
56
Step-by-step explanation:
Because i'm always right.
Shandra can buy 5 chicken wings for $10.50.
Given that, Shandra bought 24 chicken wings for $50.40 and Shandra spent $10.50.
We need to find out how many chicken wings Shandra brought for $10.50.
What is a unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Now, the cost of 1 chicken wing=Total cost of chicken wings/Number of chicken wings
=50.40/24=2.1
The cost of one chicken wing=$2.1
Now, the number of chicken wings for $10.50=10.50/2.1=5
Therefore, Shandra can buy 5 chicken wings for $10.50.
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I NEED HELP ASAPPPPPP
Its height (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=−(t−12)2+81
. Which of the following statements is true?
The airplane reaches its minimum height of 12 feet in 81 seconds.
The airplane reaches its maximum height of 81 feet in 12 seconds.
The airplane reaches its minimum height of 81 feet in 12 seconds.
The airplane reaches its maximum height of 12 feet in 81 seconds.
Considering the given quadratic equation, the correct statement is given by:
The airplane reaches its maximum height of 81 feet in 12 seconds.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
In this problem, the equation is given by:
h(t) = -(t - 12)² - 81.
The vertex is (12,81), with a negative leading coefficient, hence it is a maximum point and the correct statement is given by:
The airplane reaches its maximum height of 81 feet in 12 seconds.
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The first graph represent a=450-20t, which describes the relationship between gallons of water in tank and time in minutes. a. Where on the graph can we see 450? Where can we see the -20? b. What do these numbers mean in this situation?
Answer:450 is the intercept. We see it when t=0 (where the line cross the y axis). -20 is the slope
Step-by-step explanation: y = 20 is a thing no one would ever solve for but to do it, 20=450-20t -> y =20 when t=(20-450)/20. I don’t know why anyone would ever need to find this value
A family of 4 gets 505 text messages per month. Which of the following best describes the most even way these texts can be divided?
2 family members get 124 text messages each
2 family members get 125 text messages each
2 family members get 126 text messages each
2 family members get 125 text messages each
3 family members get 126 text messages each
1 family member gets 127 text messages
3 family members get 125 text messages each
1 family member gets 126 text messages
Answer:
3 family members get 126 text messages each
1 family member gets 127 text messages
Step-by-step explanation:
If you were finding the exact division of texts, 505 texts / 4 people, you would end up with 126.25 texts.
However, you can't get 0.25 of a text. If we take back each family member's 0.25 text, they will all be left with 126 texts (with an extra text leftover)
This extra text is considered the "remainder", meaning the amount left over when a number is divided [when it doesn't go into the larger number evenly]. The only importance/relevancy of a remainder is when a value cannot be split, such as a dog or a text.
So, we can give each family member 126 texts, and then we can give one family member an additional text, so that all texts are distributed.
This means that 3 family members get 126 texts, and 1 family member gets 127 texts
hope this helps!!
Sheryl makes $7 per pair of
earrings, e, and $13 per necklace,
n, she sells. What expression
represents
her total income?
70+13n
An expression is defined as a set of numbers, variables, and mathematical operations. The expression that can represent the total income of Sheryl is 7e+13n.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Since Sheryl makes $7 per pair of earrings and $13 per necklace, therefore, the expression that can represent her total income of Sheryl is 7e+13n.
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The circumference of a circular garden is 78.5 feet. What is the radius of the garden? Use 3.14 for it and do not round your answer.
?
Work Shown:
C = 2*pi*r
78.5 = 2*3.14*r
78.5 = 6.28r
r = (78.5)/(6.28)
r = 12.5
6.75 into a mixed number
Answer:
6 3/4
Step-by-step explanation:
Answer:
6 3/4
Explanation:
0.75 is the result of dividing 3 by 4, which is the previous point but inversed.
Alan is on the swim team. Each week he swims a total of 6000 meters. How many kilometers does he swim each week
Answer:
6 km
Step-by-step explanation:
1000 meters equals 1 kilometer
A summer job as a life guard at lincoln pool pays 9.50 per hour how much willl you earn for working 6 hours
57
Step-by-step explanation:
$ 9.50 -> 1 hr
? -> 6 hrs
9.50(6) = $ 57
What is the equation of the linear function represented by the table?
Garden a and garden b are two rectangular gardens that are each surrounded by 120 feet of fencing. garden a has one side length of 25 feet and garden b has one side length of 50 feet. which garden has the largest area? show all of your work.
The garden with the largest area is garden b with an area of 6000 feet squares
What is the area of a rectangle?The area of a rectangle is simply known as the number of unit squares that can fit into the rectangle.
The formula for calculating the area of a rectangle is written thus;
Area of a Rectangle = (Length × Breadth)
How to determine the areaUsing the formula:
Area of a Rectangle = (Length × Breadth)
For garden a;
Length = 25 feet
Breadth = 120 feet
Substitute the values into the formula
Area of garden a = 25 × 120 = 3000 feet squares
For garden b;
Length = 50 feet
Breadth = 120 feet
Substitute the values into the formula
Area of garden b = 50 × 120 = 6000 feet squares
Therefore, the garden with the largest area is garden b with an area of 6000 feet squares.
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The mean of 19 numbers is 35.
One of these numbers is 70.
Determine the mean of the other 18 numbers.
Give your answer correct to 1 decimal place.
Submit Answer
To sell 300 notebooks and 120 pens quickly, a store decided to create two types of gift sets. one set is to include 2 notebooks and 1 pen, and the other will consist of 1 pen and 3 notebooks. the first set will be sold for $8, while the second will be sold for $11.50. it is unprofitable to sell more than 20 of any gift set. how many gift sets of each type must the store sell to obtain the biggest possible income?
The store must sell 60 of each set each to obtain the biggest possible income
How to determine the number of each gift set?The given parameters can be represented using the following table:
Set 1 Set 2 Available
Notebook 2 3 300
Pen 1 1 120
Selling price 8 11.5
Using the above data values, we have:
Objective function: Max P = 8x + 11.5y
Subject to:
2x + 3y ≤ 300
x + y ≤ 120
Next, we plot the graph of the above inequalities (see attachment)
From the attached graph, we have:
(x,y) = (60,60)
Hence, the store must sell 60 of each set each to obtain the biggest possible income
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A timer is started and a few moments later a model airplane is launched from the ground. Its height (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=−(t−10)2+95. Which of the following statements is true?
The airplane reaches its maximum height of 10 feet in 95 seconds.
The airplane reaches its maximum height of 95 feet in 10 seconds.
The airplane reaches its minimum height of 95 feet in 10 seconds.
The airplane reaches its minimum height of 10 feet in 95 seconds.
Considering the given quadratic function, the correct statement is given by:
The airplane reaches its maximum height of 95 feet in 10 seconds.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient. If a > 0, the vertex is a minimum point, and if a < 0 it is a maximum point.
In this problem, the function is:
h(t) = -(t - 10)² + 95.
Hence the vertex is (10, 95), and since a < 0, the correct statement is given by:
The airplane reaches its maximum height of 95 feet in 10 seconds.
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I need help on this pleas,what is 9 ÷ 1/5
Answer:
45
Step-by-step explanation:
Flip the fraction, 1/5 to 5/1, and reverse the equation to a multiplication problem.
[tex]1/5 \rightarrow 5/1\\9 \cdot 5/1 = 45[/tex]
Let me know if you have questions or concerns.
Find x, I’ll give brainliest I promise.
Answer:
x=16.5(or 17)
Step-by-step explanation:
2(x)+2(x-4)=58
2x+2x-8=58
4x-8=58
4x=66
x=16.5(if rounded to the nearest whole number will be 17)
ur welcome :)
brainliest please?
Question 5 of 5
Select the correct answer from each drop-down menu.
The area of this rectangle is 54 square inches. Create an equation to find the value of n.
3(n-1)
54 square inches n+2
rẻ tint
▼ = 0
Answer:
[tex]3n^2+3n-6=54[/tex]
Step-by-step explanation:
Total Area=54 square inches. Area=length*width.
Because the length is [tex][3(n-1)][/tex], and the width is [tex](n+2)[/tex], you can plug that into the equation for area. In this case, because the total area is 54, we can plug that in for area.
[tex][3(n-1)](n+2)=54[/tex]
Distribute through the parenthesis in [tex]3(n-1)[/tex].
[tex](3n-3)(n+2)=54[/tex]
Then, multiply [tex]3n-3[/tex] and [tex]n+2[/tex] using whatever method you prefer. I used FOIL, which stands for First, Outer, Inner, Last. You multiply the first terms together, the outer terms together, the inner terms together, and the last terms together.
[tex]3n^2+6n-3n-6=54[/tex]
Simplify.
[tex]3n^2+3n-6=54[/tex]
Which of these graphs represents a function?
5NW&S
4
1
43-2-1₁ 1 2 3 4 5
-2
-3
-4
-5
W.
N.
1
-5-4-3-2-1 1 2 3 4 5
JANM
-5
-2
Y.
A
X
२४
-3-2-
>
८
4
3
1
-5-4-3-2-1 1 2 3 4
-2
-3
-4
-5
>
X.
V
5
4
-2
-3
-4
5
Z.
HE
४
+X
1 2 3 4 5
Answer: W
Step-by-step explanation:
The graph must pass the vertical line test.
Your friend is supposed to meet you at the beach between 12pm and 1:30pm. If you arrive at 12:25pm and you do not see you friend, what is the probability that you will have missed your friend? Express your answer as a percentage.
The probability that you will have missed your friend is 27.78%
How to determine the probability?The time of meeting is given as:
Time = 90 minutes (i.e 12pm and 1:30pm)
Your time of arrival is given as:
Arrival = 12:25pm
If you missed your friend, it means that your friend arrives earlier.
So, the time spent by your friend is:
Friend= 12:25 - 12 = 25 minutes
The probability that you will have missed your friend is:
P = 25 minutes/90 minutes
Evaluate
P = 27.78%
Hence, the probability that you will have missed your friend is 27.78%
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Find the value of y in the solution to the system of equations shown.
3y = 18x + 6
y = 2x + 14
A. y = 3
B. y = 4
C. y = 20
D. y = 26
Divide by 3
y=6x+2--(1)y=2x+14--(2)Equating
6x+2=2x+144x=12x=3Now
y=6(3)+2y=18+2y=20C
Answer:
C. y = 20
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}3y = 18x + 6\\y = 2x + 14\end{cases}[/tex]
Multiply the second equation by 3:
[tex]\implies (3)y=(3)2x+(3)14[/tex]
[tex]\implies 3y=6x+42[/tex]
Subtract this from the first equation to eliminate 3y:
[tex]\begin{array}{r l}3y & = 18x+6\\-\quad3y&=6x+42\\\cline{1-2}0&=12x-36\end{array}[/tex]
Solve the resulting equation for x:
[tex]\implies 12x-36=0[/tex]
[tex]\implies 12x=36[/tex]
[tex]\implies x=3[/tex]
Substitute the found value of x into the original second equation and solve for y:
[tex]\implies y=2(3)+14[/tex]
[tex]\implies y=6+14[/tex]
[tex]\implies y=20[/tex]
f(x)=x^2+2x-5
g(x)=2x+4
what is (f•g)(x)
The product of the functions is 2x³ + 8x² - 2x - 20. Then the correct option is C.
What is a function?A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.
The functions are given below.
f(x) = x² + 2x - 5
g(x) = 2x + 4
Then the product of the functions will be given as
(f•g)(x) = f(x) × g(x)
(f•g)(x) = (x² + 2x - 5) × (2x + 4)
(f•g)(x) = 2x³ + 8x² - 2x - 20
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help me please these dot plots show hourly earnings for a sample of workers in two different
careers
career a
0
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
career b
0
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
hourly eamings (5)
what are the differences between the centers and spreads of these earning
distributions?
select two choices: one for the centers and one for the spreads
a. spreads: the hourly earnings for career b are more spread out
b. spreads: the hourly earnings for career a are more spread out.
c. centers career bhas greater median hourly earnings than career
d. centers: career a has greater median hourly earnings than career
The hourly earnings for career a are more spread out.
Career a has greater median hourly earnings than career.
What is the spread and median of the data plots?Median is the number at the center of the dataset that is arranged either in ascending order or descending order.
The median of career A is 60.
The median of career b is 40
Spread refers to the range of the dataset. Career A has a greater range than career B.
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What type of Symmetry
Answer:
Line Symmetry, Horizontal and Vertical Lines, 90 and 180 degrees
Step-by-step explanation:
It is line symmetry because you can fold the H, and it would overlap perfectly.
Horizontal and vertical lines because if you were to place a line in the middle both horizontally and vertically it would overlap.
90 and 180 degrees because the H would still have have symmetry if you flipped it on its side or upside down.