Answer
Domain of the function:
In interval notation: [6, ∞)
In set notation: {x: x∈R, x≥6}
Explanation
Remember that the the domain of the square root function are all the values such is is bigger than zero. We can express the later in set notation: {x: x∈R, x≥0}, or in interval notation: [0, ∞)
This is because the square root is not defined, in the real numbers, for negative values.
So, to find the domain of our function, we just need to set the thing inside the radical grater or equal than zero and solve for x:
The domain of the function is all the numbers bigger than 6, including 6.
Answer:
[6, infinity (use the symbol)
Step-by-step explanation:
i got this answer by graphing
The sign below is located at the start of Pinecone trail and shows the distances from the sign to different points of interest along the trail. Sage hiked from the start of the trail to Lookout Point. She then hiked back to Giant Boulder to camp for the night. What was the total distance, in miles, that Sage hiked?
Answer:
Total distance = 53/4 miles = 13.25 miles
Step-by-step explanation:
Sage hiked from the start of the trail to Lookout Point.
Distance = 8 3/4 miles = 35/4 miles
She then hiked back to Giant Boulder
This means she traveled an additional
8 3/4 miles - 4 1/4 miles = 35/4 mi - 17/4 mi = 18/4 mi = 9/2 mi
The total distance traveled by sage is the sum of both trajectories
Total distance = 35/4 miles + 9/2 miles = 53/4 miles
Total distance = 13.25 miles
3x2 + 7x + 2 how to factor
Answer:
(x+2)(3x+1)
Step-by-step explanation:
the factored form of the quadratic expression 3x² + 7x + 2 is (3x + 1)(x + 2).
To factor the quadratic expression 3x² + 7x + 2, you can use the factoring method or apply the quadratic formula. Let's use the factoring method:
1. Look for two numbers that multiply to give the product of the coefficient of x² (which is 3) and the constant term (which is 2). These numbers should also add up to the coefficient of x (which is 7).
The two numbers that meet these conditions are 1 and 6. They multiply to give 6, and they add up to 7.
2. Rewrite the quadratic expression using the two numbers found in step 1:
3x² + 1x + 6x + 2
3. Group the terms in pairs and factor out the greatest common factor from each pair:
x(3x + 1) + 2(3x + 1)
4. Notice that both pairs have a common factor of (3x + 1). Factor out this common binomial:
(3x + 1)(x + 2)
So, the factored form of the quadratic expression 3x² + 7x + 2 is (3x + 1)(x + 2).
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Solve the system of linear equations below. x − 3y = -3 x + 3y = 9 A. x = -12, y = 7 B. x = 3, y = 2 C. x = 6, y = 1 D. x = 6, y = 2
ANSWER
B. x=3,y=2
EXPLANATION
The given equations are
[tex]x - 3y = - 3...(1)[/tex]
and
[tex]x + 3y = 9...(2)[/tex]
We add the two equations to eliminate y.
This implies that that:
[tex] x + x - 3y + 3y = 9 + - 3[/tex]
Simplify:
[tex]2x = 6[/tex]
Divide both sides by 2.
[tex]x = 3[/tex]
We put x=3 into any of the equations to find y.
Let us substitute x=3 into equation (1) to get:
[tex]3 - 3y = - 3[/tex]
[tex] - 3y = - 3 - 3[/tex]
[tex] - 3y = - 6[/tex]
Divide both sides by -3 to get;
[tex]y = 2[/tex]
The solution is therefore x=,y=2.
Frank left his house at 7 a.m. and drove to the airport at a speed of 50 mph. Lance left his house at 6 a.m. and drove to the same airport at a speed of 55 mph. Frank's house is 150 miles from the airport and Lance's house is 220 miles from the airport. At what time did Frank arrive at the airport?
Answer:
10:00 AM
Step-by-step explanation:
Frank drove at a speed of 50 mph, and traveled a distance of 150 miles. This means he traveled for
150/50 = 3 hours.
7 AM + 3 hours = 10 AM
The solution is, at 10:00 AM Frank will arrive at the airport.
What is speed?Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).
Speed = Distance/ Time.
here, we have,
given that,
Frank left his house at 7 a.m. and drove to the airport at a speed of 50 mph.
Lance left his house at 6 a.m. and drove to the same airport at a speed of 55 mph.
Frank's house is 150 miles from the airport and Lance's house is 220 miles from the airport.
so, we get,
Frank drove at a speed of 50 mph,
and traveled a distance of 150 miles. This means he traveled for
150/50 = 3 hours.
Thus, it takes Frank 3 hours to reach the airport.
so, we get,
since he departed at 7:00 AM, he will arrive at the airport at
7 AM + 3 hours = 10 AM
Hence, The solution is, at 10:00 AM Frank will arrive at the airport.
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A rectangle has an area of 24 square centimeters. Select the three choices that show pairs of possible side lengths of the rectangle
Answer:
A, B, and C
Step-by-step explanation:
We can use guess-and-check.
A rectangle with the area 24 cm² has the sides that make the product of 24 (A = l * w)
1 * 24 is 24.
2 * 12 is 24.
3 * 8 is 24.
4 * 20 is 80.
12 * 12 is 144.
What is the value of x?
Answer:
x = 12.8
Step-by-step explanation:
To find the value of x, set up a proportion between the two similar triangles. Then solve for x.
[tex]\frac{32}{32+x} = \frac{40}{56}[/tex]
Solve by cross multiplying and isolating x.
32(56) = 40(32+x)
1792 = 1280 + 40x
512 = 40x
12.8 = x
If you had 150 subjects to work on and had 28 Days How many per day do you need to do?
Divide the total subjects by total days:
150 / 28 = 5.357 per day. Round the answer as needed.
Answer: Approximately 5 subjects per days.
Step-by-step explanation:
To solve the exercise and calculate the number of subjects you need to do per day you must keep on mind the information given in the problem. You know that:
- The total number of subjects is 150.
- You had 28 days left.
Therefore, you need to divide 150 subjects by 28 days.
Then, you obtain the following result:
[tex]=\frac{150subjects}{28days}=5.35\frac{subjects}{day}[/tex]≈ 5 subjects per days.
A diagonal path divides a square park in half. If the park is 50 yards on each side, how long is the path?
The length of the diagonal path is approximately 70.71 yards.
To find the length of the diagonal path that divides the square park in half, we can use the Pythagorean theorem. A square park of 50 yards on each side means we are dealing with a right-angled triangle with both legs equal to 50 yards.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b):
[tex]c^2 = a^2 + b^2[/tex]
Here, both a and b are 50 yards, so the equation becomes:
[tex]c^2[/tex] = 502 + 502 = 2500 + 2500 = 5000
Now we find the square root of 5000 to get the length of the diagonal:
c = √5000 ≈ 70.71 yards
Therefore, the length of the diagonal path is approximately 70.71 yards.
I need help with this question I dont get how to do it..
Answer:
If 300 lunches were served, then 90 students choose milk.
Step-by-step explanation:
The graph shows that 30% of students choose milk. So when 300 lunches are served, 300*.30 students choose milk. 300*.3 or 300*30% is equal to 90.
The answer for this question is the first option "if 300 lunches were served then 90 students would have milk".
A) If 300 lunches were served then 90 would chose milk as milk is represented and shown to have a popularity of 30%. 30% of 300 is equivalent to 90 making the statement true
B) If 200 lunches were served then 90 would choose milk however this is false as milk at 30% as votes and 30% of 200 is not 90
C) if if 300 lunches were served then 30 more students would chose water over juice however water has a population of 40% and 40% of 300 is 120 and juice has a population of 10% and 10% of 300 is 30 and 120-30=90 not 30.
D) if 200 lunches were served than 10 more students would choose tea over juice. Tea has a population of 20% and 20% of the 200 is 40 and juice has a population of 10% and 10% of 200 is 20 and 40-20=20 not 10
The only correct statement is If 300 lunches were served then 90 would chose milk.
I need to know how to find the mean for 77,82,87,85,32,78?
Answer:
73.5
Step-by-step explanation:
To find the mean, sum the data and divide by the amount of data
mean = [tex]\frac{77+82+87+85+32+78}{6}[/tex]
= [tex]\frac{441}{6}[/tex] = 73.5
The answer is 73.5. Just add all the numbers and divided by how many numbers there are. So you would add all the numbers and then divided by 6 since there are 6 numbers.
Suppose a 50-foot ladder is leaning against a wall. Which statements about the base of the ladder are true? Choose two that apply.
A If the base is 24 feet from the wall, the ladder reaches 45 feet up the wall.
B If the base is 30 feet from the wall, the ladder reaches 40 feet up the wall.
C If the base is 27 feet from the wall, the ladder reaches 44 feet up the wall.
D If the base is 14 feet from the wall, the ladder reaches 48 feet up the wall.
Answer: 30-40-50, or B
Step-by-step explanation:
Think of this equation of a right triangle. We know that the hypotenuse is 50 feet and leaning.
Since right triangles follow a formula is 3-4-5, then, 30, 40 and 50 is the answer.
If the 50-foot ladder is leaning against a wall. Statement B about the base of the ladder is true.
What is the Pythagoras theorem?The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
It is given that, a 50-foot ladder is leaning against a wall.
Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines.
It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
The hypotenuse is 50 feet long and slopes, as is known.
Since right triangles have a formula of 3-4-5, the correct response is 30, 40, and 50.
Thus, if the 50-foot ladder is leaning against a wall. Statement B about the base of the ladder is true.
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Solve the system of linear equations by elimination.
4x+3y= -5
-x+3y= -10
The solution of given system of linear equations are x = 1 and y = -3.
Given system of linear equations are,
[tex]4x+3y=-5 ..........(1)\\\\ -x+3y=-10..............(2)[/tex]
Subtract equation 2 from equation 1.
[tex]4x+3y-(-x+3y)=-5+10\\ \\ 4x+3y+x-3y=5\\ \\ 5x=5\\ \\ x=5/5=1[/tex]
Substituting value of x in equation 1.
[tex]4(1)+3y=-5\\ \\ 3y=-5-4=-9\\ \\ y=-9/3=-3[/tex]
Hence, The solution of given system of linear equations are x = 1 and y = -3.
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What is the volume of the sphere?
25.12
75.36
150.72
904.32
Answer:
D
Step-by-step explanation:
Formula
V = 4/3 * pi * r^3
Givens
pi = 3.14
r = 6
Solution
V = (4/3) * 3.14 * 6^3 Expand the cube
V = (4/3) * 3.14 * 216 Multiply by 3.14
V = (4/3) * 678.24 Multiply by 4
V = 2712.96 / 3 Divide by 3
V = 904.32
Which of the following numbers is irrational?
Answer:
it is the 3rd choice
Step-by-step explanation:
3
➷ An irrational number cannot be written in the form of a fraction.
As you can see, the first two are already in fraction form, so it can't be those.
The square root of 4 is 2 which can be written as 2/1
This leaves the square root of 3, which is the answer.
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Which of the following equations represents the graph shown?
Answer:
[tex]y=\frac{3}{2}x[/tex]
Step-by-step explanation:
The given line passes through the origin.
Its equation is of the form;
[tex]y=mx[/tex]
where
[tex]m=\frac{3}{2}[/tex] is the slope of the line.
The required equation is
[tex]y=\frac{3}{2}x[/tex]
Answer: [tex]f(x)=\dfrac{3}{2}x[/tex].
Step-by-step explanation:
Assume one block in the graph takes one value.
From the given graph, it can be seen that the line is passing through two points (0,0) and (2,3).
We know that the equation of a line passing through points (a,b) and (c,d) is given by :-
[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]
Then , the equation of a line passing through points (0,0) and (2,3) is given by :-
[tex](y-0)=\dfrac{3-0}{2-0}(x-0)\\\\\Rightarrow y=\dfrac{3}{2}x[/tex]
Hence, the equations represents the given graph [tex]f(x)=\dfrac{3}{2}x[/tex].
Given that √x = -4, what is x?
Square on both sides..
x=16 !!!
[tex] \sqrt{x} = - 4 \\ { \sqrt{x} }^{2} = {( - 4)}^{2} \\ x = 16 [/tex]
(-) +(-) =+
All rectangles are parallelograms
how many different pairs can you make with four colors: red, blue, green purple?
Answer:
6
Step-by-step explanation:
red blue green purple
red red/blue red/green red/purple
blue red/blue blue/green blue/purple
green red/green blue/green green/purple
purple red/ purple purple blue purple/green
i did not include red/red since the question asks for DIFFERENT PAIRS. same with the combinations that are repeated
plz give me a brainliesttttttt
To find the number of different pairs that can be made with four colors, we use the combinations formula C(4, 2), which calculates to 6. Thus, there are 6 different color pairs that can be made with red, blue, green, and purple.
To determine how many different pairs can be made with four colors: red, blue, green, purple, we use the concept of combinations from mathematics. A combination is a selection of items where the order does not matter. In this case, we are selecting two colors from the four available to form a pair.
To calculate the number of combinations without repetition, we can use the combination formula which is [tex]C(n, k) = \frac{n! }{ (k!(n - k)!)}[/tex], where n is the total number of items to choose from, k is the number of items to choose, and '!' represents the factorial of a number. For this scenario, n = 4 (four colors) and k = 2 (since we are forming pairs).
So, the number of combinations is C(4, 2) = [tex]\frac{4! }{2!(4 - 2)!} = \frac{4 \times 3 \times 2 \times 1 }{ 2 \times 1 \times 2 \times 1}[/tex] = 6. Therefore, there are 6 different color pairs that can be made with the colors red, blue, green, and purple.
measure each rectangle to the nearest 1/4 in with your ruler and label the dimensions use the area model to find the area
Answer:
can you attach a picture
Step-by-step explanation:
Do u have a picture so i could solve it
If m > n, which inequalities must be true? Check all that apply.
m + 2.1 > n + 2.1
m - (-4) > n -(-4)
m + 3 > n - 3
16.5 + m > 16.5 + n
m > n + 1/2
9 + m > 6 + n
Will give a rank if can be answered in 5 min
Answer:
It's A B and D, the brainliest is incorrect.
Step-by-step explanation:
Final answer:
If m is greater than n, then all the provided inequalities must be true, as they involve either adding the same amount to both sides or increasing the positive difference between m and n.
Explanation:
If m > n, then certain inequalities must hold true when we add, subtract, or compare these variables while keeping the inequality relationship consistent. Here are the inequalities that must be true based on the given condition:
m + 2.1 > n + 2.1: Adding the same number to both sides of an inequality does not change the relationship, thus this inequality must be true.
m - (-4) > n -(-4): Subtracting a negative is the same as adding a positive, so this inequality will also hold true.
m + 3 > n - 3: Adding a positive number to m and a negative to n will increase the difference between them, making this inequality true.
16.5 + m > 16.5 + n: Similar to the first point, adding the same number to both sides of an inequality maintains the inequality.
m > n + 1/2: Since m is greater than n, adding a positive fraction to n would still keep m greater than the modified n.
9 + m > 6 + n: Adding different numbers to m and n still preserves the inequality, if the number added to m is not smaller than the number added to n.
What happens to the graph of y=|x| when the equation changes to y=|x+3| - 1
If a figure is a square, then it is a regular quadrilateral. True or false? Explain.
Answer:
Yes, because a quadrilateral have four sided figure. So True.
Answer + Explanation:
True, because all quadrilaterals are four-sided figures. Squares have four equal sides, so they are regular quadrilaterals.
PLEASE HELP QUICK??!!!
Jordan is saving for a new laptop that costs $325. He uses the equation and table below to show the number of months he has been saving, m, and the total amount he has saved so far, d.
d=80+75m
Which is the first month in which Jordan will have saved enough money to buy the laptop?
Month 2
Month 3
Month 4
Month 5
Answer:
Month 4
Step-by-step explanation:
Given : Jordan is saving for a new laptop that costs $325.
Equation: d=80+75m
To Find: Which is the first month in which Jordan will have saved enough money to buy the laptop?
Solution:
Equation: [tex]d=80+75m[/tex]
where d is the total amount he has saved so far.
m shows the number of months he has been saving.
Now we are given that he needs to save $325.
So, To find the first month in which Jordan will have saved enough money to buy the laptop
Substitute d = 325 in the equation:
[tex]325=80+75m[/tex]
[tex]245=75m[/tex]
[tex]\frac{245}{75}=m[/tex]
[tex]3.266=m[/tex]
Thus,the first month in which Jordan will have saved enough money to buy the laptop is Month 4.
Answer:
Month 4 or C
Step-by-step explanation:
PogChamp
Mrs Jenkins picked some tomatoes from her garden. She used 5/9 of the tomatoes to make pasta sauce. Then she used 3/4 of the remainder to make a salad. What fraction of the tomatoes did mrs Jenkins use to make the salad?
Answer:
Final answer is 1/3.
Step-by-step explanation:
Given that Mrs Jenkins picked some tomatoes from her garden. She used 5/9 of the tomatoes to make pasta sauce. Then she used 3/4 of the remainder to make a salad. Now we need to find about what fraction of the tomatoes did Mrs Jenkins use to make the salad.
Since she used 5/9 of the tomatoes to make pasta sauce.
Then remaining amount of tomatoes = 1- 5/9 = 9/9 -5/9 = 4/9
Then she used 3/4 of the remainder to make a salad. So fraction of the tomatoes did Mrs Jenkins use to make the salad = (4/9)(3/4)=12/36=1/3
Hence final answer is 1/3.
Two numbers have a sum of 18. One number is 4 more than the other. Find the numbers
math help 20 points and brainliest
find the roots, and list the steps correctly
you need to show work and list the steps please
f(n)=n^2 -6n-16
ANSWER
[tex]n = 8 \: or \: n = - 2[/tex]
EXPLANATION
The given function is
[tex]f(n) = {n}^{2} - 6n - 16[/tex]
To find roots of the equation, we set the equation to zero.
[tex]{n}^{2} - 8n + 2n- 16 = 0[/tex]
Split the middle term with -8n+2n
We now factor to get,
[tex]n(n - 8) + 2(n- 8) = 0[/tex]
[tex](n - 8)(n + 2) = 0[/tex]
Using the zero product property,
[tex]n - 8 = 0 \: or \: n + 2 = 0[/tex]
[tex]n = 8 \: or \: n = - 2[/tex]
Find the value of x.
Answer options: 17, 7, 14, 10
Answer:
7
Step-by-step explanation:
Since both chords are congruent and the distance of the x and 7 are equidistant from the center, then the value of x will also be 7.
Left side chord will have a value of y + 10
The right side chord will have a value of y + 10
Now since the right angles on both sides are equal, then x = 7.
The value of x is 7.....
A recipe calls for 3/4 cup of sugar for every 1 1/2 cups of flour. How much sugar would be needed if the baker uses 4 1/2 cups of flour?
Answer:
Step-by-step explanation:
Area of regular hexagon
Check the picture below.
let's recall that a circle has 360°, so that means every two radii coming from the center of the hexagon, will split those 360° in 6 even pieces, 360/6 = 60, namely those two radii make up a 60° central angle, as you see in the picture.
running a perpendicular from the center, we end up with a 30-60-90 triangle, as you see there, and thus we can use the 30-60-90 rule to get the length of "a".
now, keeping in mind that the perimeter of the polygon is simply 4+4+4+4+4+4 = 24.
[tex]\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}dp~~ \begin{cases} d=apothem\\ p=perimeter\\[-0.5em] \hrulefill\\ d=2\sqrt{3}\\ p=24 \end{cases}\implies A=\cfrac{1}{2}(2\sqrt{3})(24)\implies A=24\sqrt{3}[/tex]
HELP QUICK!15 + 100 • [12 – (12 – 3 • 2)] + 6
Answer:
621
Step-by-step explanation:
Use PEMDAS.
15 + 100 * [12 - 6] + 6
15 + 100 * 6 + 6
15 + 600 + 6
621
Answer:
[tex]\boxed{\bold{621}}[/tex]
Step By Step Explanation:
Follow PEMDAS Order Of Operations
[tex]\bold{12-\left(12-3\cdot \:2\right): \ 6}[/tex]
[tex]\bold{15+100\cdot \:6+6}[/tex]
[tex]\bold{100\cdot \:6: \ 600}[/tex]
[tex]\bold{15+600+6}[/tex]
[tex]\bold{15+600+6: \ 621}[/tex]
[tex]\bold{621}[/tex]