Answers
Answer:
The domain of the function is x>=-7
Step-by-step explanation:
The domain is all the values that x can take so the function is defined, that means we can find a value of y
The sqrt is defined only for positive values and zero. So the expression in the sqrt must satisfy that
6x + 42 >=0
We only have to find x
6x >=-42
x>=-42/6
x>=-7
So the answer is D x>=-7
Related Questions
What is the slope of a line that is parallel to the line y = x + 2?
Answers
y = x + 2
⇒ slope = 1
⇒Slope of the parallel line = 1
Answer: 1
Answer:
I’m going to assume you didn’t put the 3/4x in your equation, if you had, the answer would’ve been 3/4.
Step-by-step explanation:
REMEMBER
If the equation is parallel, it will have the same slope as the other equation parallel to it.
What is the value of x in the equation x + 10 = 13?
Answers
Megan uses a credit card with a 24.9% APR compounded monthly to pay for car repairs totaling $583.75. She can pay $240 per month on the card. What will the total cost of this purchase be
Answers
Her total expense is $605.80.
the correct answer is $605.80
Find the equation of the straight line passing through the point (0, 2) which is perpendicular to the line
y = 1/4x + 5
Answers
Find the slope:
y = 1/4 x + 5
Slope = 1/4
Slope of perpendicular line = -4
Substitute m = -4 into the equation:
⇒ y = -4x + b
Find y-intercept:
At point (0, 2) ⇒ y-intercept = 2
Substitute b = 2 into the equation
y = -4x + 2
Answer: y = 4x + 2
Answer:
y=-4x+2
Step-by-step explanation:
The line passes through (0,2), so chuck these numbers in and you get a value of 2 for c. If you're sharp, you might spot that this point is the y-intercept of the line since the x- coordinate is 0, this point is on the Y-axis, and you don't even have to throw numbers in.
Therefore the equation of the line is:
y = -4x + 2
Hope that was clear!
Suppose a triangle has 3,4, and 5 sides.Which of the following must be true
Answers
Answer:
A. The triangle in question is a right triangle
Step-by-step explanation:
Select the property that allows the statement 10 = y to be written y = 10.
Commutative - addition
Distributive
Associative - multiplication
Symmetric
Commutative - multiplication
Associative - addition
Identity - addition
Answers
This is the symmetric property
Hope this helps!
The property that allows the statement 10 = y to be written y = 10 is:
Symmetric
Step-by-step explanation:We know that for any set A. if a and b are two elements of the set A.
Then if a is related to b by some relation then by the symmetric property b must be related to a by the same property.
Here 10 is related to y by the equality relation.
i.e. 10=y
Hence, by the symmetric property we have that y must be related to 10 by the same equality relation.
i.e. y=10
If 75% of the students in Toby’s grade voted, how many students are in Toby’s grade?
Answers
Answer:
The total number of students in Toby's grade is 200.
Answer:number of students who voted= 75%= 150
75% of total number of students= 150
The total number of students in Toby's grade is 200.
Step-by-step explanation:
Using a straightedge, or using technology, sketch an obtuse, scalene triangle. Make sure to include your sketch in your answer.
Answers
If Tom, George and Mario work together, they can paint a 600 ft2 room in 4 hours. When only George and Mario work together, it takes 8 hours to paint the room. Tom and George, working together, take 6 hours to paint the room. How long would it take Tom to paint the room alone? Hint: Write the system of equations shown below in augmented form, then solve the system for T (Tom's painting rate). Next, use the equation Painted Area = Painting Rate× Time and solve for Time to determine how long it would take Tom to paint the room alone.
4(T+G+M)=600
8(0+G+M)=600
6T+G+0)=600
Answers
T = Tom's paiting rate [tex]( \frac{ ft^{2} }{h} )[/tex]
G = George's paiting rate [tex]( \frac{ ft^{2} }{h} )[/tex]
M = Mario's paiting rate [tex]( \frac{ ft^{2} }{h} )[/tex]
As the first statement says that they can work together, then:
T + G + M = Painting rate working together, that is the surface area they paint per hour.
Since the problem says that they last four hours painting a [tex] 600ft^{2} [/tex] room, then we need to multiply the amount of hours times the painting rate that is equal the surface area of the room, so:
4(T + G + M) = 600
Applying a similar reasoning, the George and Mario's painting rate is:
0 + G + M
Note that 0 implies that Tom didn't work in this case.
As they last eight hours painting the room, then:
8(0 + G + M) = 600
The same reasoning is applied to Tom and George working together. In this case 0 implies that Mario didn't work, so:
6(T + G + 0) = 600
We have a system of linear equations in three variables T, G, M:
4(T+G+M)=600
8(0+G+M)=600
6(T+G+0)=600
Solving:
(1) T + G + M = 150
(2) G + M = 75
(3) T + G = 100
Substitute (3) in (1):
100 + M = 150 ∴ M = 50
Replace M in (2):
G + 50 = 75 ∴ G = 25
Substitute G in (3)
T + 25 = 100 ∴ T = 75
Then, the painting rates are:
Tom = 75 [tex]( \frac{ ft^{2} }{h} )[/tex]
George = 25 [tex]( \frac{ ft^{2} }{h} )[/tex]
Mario = 50 [tex]( \frac{ ft^{2} }{h} )[/tex]
Solving for Time to determine how long it would take Tom to paint the room alone:
Painted Area = Painting Rate×Time, so:
[tex]Time Tom = \frac{Painted Area}{Painting Rate (T)} [/tex]
[tex]Time Tom = \frac{600}{75} = 8 hours [/tex]
Answer:
A. 8 hours
Step-by-step explanation:
The area of a rectangular television screen is 3456 in^2. The width of that screen is 24 inches longer than the length. What is a quadratic equation the represents the area of the screen? What are the dimensions of the screen?
Answers
x^2 + 24x - 3456 = 0 is the equation you require
(x - 48(x + 72) = 0
x = 48
Dimensions are width 48 and length 72 in
A single 6-sided dice is being rolled. What is the probability of rolling a 5 or an odd number?
Answers
S = set of all possible outcomes
S = {1,2,3,4,5,6}
E = event space
E = set of items we want to happen (rolling a 5, or rolling an odd number)
E = {1, 3, 5}
note: the event of "rolling a 5" is a subset of "rolling an odd number" because 5 is odd
n(S) = number of items in the sample space
n(S) = 6
n(E) = number of items in event space
n(E) = 3
Divide the values to get the probability
P(E) = n(E)/n(S)
P(E) = 3/6
P(E) = 1/2
P(E) = 0.50
P(E) = 50%
The answer in fraction form is 1/2
The answer in decimal form is 0.50
The answer as a percentage is 50%
These three values all represent the same idea, just written in different forms.
note: writing "P(E)" means "the probability of event E occurring", which I've defined as the event space above
The difference of a number and 8 is the same as 34 less the number. find the number.
Answers
34 less the number is 34-n.
n-8=34-n
2n=34+8
2n=42
n=21
The question is a simple algebra problem. By setting up and solving the equation 'x - 8 = 34 - x', we find that the number is 21.
Explanation:The subject of this question is algebra, and involves setting up and solving an equation. Let's denote the unknown number as 'x'. Following the question, we can set up the equation as 'x - 8 = 34 - x'.
To solve the equation, let's add 'x' to both sides to get 2x - 8 = 34. Then, add 8 to both sides to get 2x = 42. Finally, divide each side by 2, so that 'x = 21'.
So, the number that satisfies the equation is 21.
Learn more about Algebra here:https://brainly.com/question/24875240
#SPJ3
What is the positive solution of x2 – 36 = 5x?
Answers
Answer:
The positive solution is x=9
Step-by-step explanation:
Given the equation
[tex]x^2-36=5x[/tex]
we have to find the positive solution of above equation.
[tex]Equation: x^2-5x-36=0[/tex]
By splitting middle-term method
[tex]x^2-5x-36=0[/tex]
[tex]x^2-9x+4x-36=0[/tex]
[tex]x(x-9)+4(x-9)=0[/tex]
[tex](x+4)(x-9)=0[/tex]
[tex]x+4=0, x-9=0[/tex]
The solution is x=-4 and x=9
Hence, the positive solution is x=9
What is the answer? Please help.
Answers
_______________________________________________
Explanation:
_______________________________________________
Given:
_______________________________________________
(x − 2) = √(2x + 1) ;
→ "Square" each side of the equation; that is, raised EACH SIDE of the equation to the power of "2" ; to get rid of the "radical" ; as follows:
_______________________________________________
[(x - 2)]² = [ √(2x + 1) ] ² ;
to get:
→ (x - 2)² = (2x - 1) ;
Expand the " (x - 2)² " ;
→ (x - 2)(x -2) = ?
NOTE: (a + b)(c + d) = ac + ad + bd .
→ = (x * x) + (x * -2) + (-2 * x) + (-2 * -2) ;
= (x²) + (-2x) + (-2x) + (4) ;
= x² − 2x − 2x + 4 ;
= x² − 4x + 4 ;
______________________________________________
Now, rewrite the entire question:
→ (x − 2)² = (2x − 1) ;
→ as follows:
______________________________________________
→ " x² − 4x + 4 = 2x − 1 " ;
Now, subtract "2x" from each side of the equation;
& add "1" to each side of the equation:
→ " x² − 4x + 4 − 2x + 1 = 2x − 1 − 2x + 1 " ;
to get:
→ " x² − 6x + 5 = 0 " ; Solve for "x" ;
Let us if : " x² − 6x + 5 " can be factors:
_____________________________________
What factors of "positive 5" ; add up to "-6" ;
-5 ,-1 ; → -5 + (-1) = - 6; YES.
5, 1 ; → 5 + 1 = 6 ; NO.
_____________________________________
So, we have: " (x − 5) (x − 1) = 0 " .
x = 5, and -1 .
_________________________________________
A painter is placing a ladder to reach the third story window, which is 12 feet above the ground and makes an angle of 80 degrees.how far out from the building does the base of the ladder need to be positioned
Answers
tan ∅=opposite side angle ∅/adjacent side angle ∅
adjacent side angle ∅=opposite side angle/tan ∅
in this problem
see the attached figure to better understand the problem
angle ∅=80°
opposite side angle ∅=12 ft (AB)
adjacent side angle ∅=? (AC)
adjacent side angle ∅=12/tan 80°------> 2.12 ft
the answer is
2.12 ft
f(x)=3 cos (2x-pi) -1
HELP PLS!!
Answers
I sadly do not know what they mean by " smallest rate of change.
(Financial Algebra workbook 10-3)
Under his "Household expenses" Budget category, Mark has allocated $60 per month for pet food. He can purchase "wet food" for $1.50 per can or "dry food" for $3 per bag.
D.) Name a combination of bags and cabs that will allow him to meet his budget exactly.
Answers
We can find answers by creating this equation.
$1.50c + $3.00b = $60
where c and b represent the number of "wet food" cans and "dry food" bags, respectively. We can easily substitute numbers and solve for the other quantity that will satisfy the condition of total cost adding up to $60.
Final answer:
The question asked for a combination of wet and dry pet food that meets a monthly budget of $60. One such combination would be buying 10 bags of dry food and 20 cans of wet food, as 3(10) + 1.5(20) equals $60, which fits the budget exactly. There are also other combinations that can fulfill the budget constraint.
Explanation:
The student asked for a combination of bags and cans of pet food that would allow Mark to meet his monthly budget of $60 exactly. With wet food costing $1.50 per can and dry food costing $3.00 per bag, we can create a simple algebraic equation to find multiple combinations. Let's let x represent the number of bags and y represent the number of cans. The equation can be written as 3x + 1.5y = 60.
To find a combination that fits exactly into Mark's budget, consider the following example:
If Mark buys 10 bags of dry food, that would cost 10 × $3 = $30. He would then have $30 left of his budget. At $1.50 per can, he could buy 20 cans of wet food (because 20 × $1.50 = $30). Thus, one possible combination would be 10 bags and 20 cans. The equation for this would be 3(10) + 1.5(20) = 30 + 30 = 60, which satisfies Mark's budget constraint.
It's important to note that there are other combinations that would also meet Mark's budget exactly. The student could experiment with different numbers of bags (x) and cans (y) to find additional combinations. The key is that the total cost must not exceed $60.
You roll a number cube and flip a coin. find the probability of rolling an even number and flipping heads. write your answer as a fraction in simplest form.
Answers
Hope this helped!
Final answer:
To calculate the combined probability of rolling an even number on a number cube and flipping heads on a coin, you multiply the separate probabilities of each event, which are 1/2 and 1/2 respectively, resulting in a combined probability of 1/4.
Explanation:
The probability of rolling an even number on a number cube (which is a standard six-sided die) is 3 out of 6 since there are three even numbers (2, 4, 6) and six possible outcomes overall. This simplifies to 1/2. The probability of flipping heads on a coin is 1/2 since there are two possible outcomes, heads or tails, and both are equally likely if the coin is fair.
To find the combined probability of two independent events (rolling an even number and flipping heads), you multiply the probabilities of each event together. So, the probability of rolling an even number and flipping heads is 1/2 (for the number cube) times 1/2 (for the coin), which equals 1/4 or 25%.
In the simplest form, the fraction is written as 1/4.
Which of the following have the same value as the fraction below?
8/5 A.
Check all that apply.
A. 2.20
B. 220%
C. 1.60
D. 160%
Answers
20 POINTS!
Verify the identity.
Answers
[tex]R_s=\left(\dfrac{1}{\sin x}-1\right):\dfrac{\cos x}{\sin x}=\left(\dfrac{1}{\sin x}-\dfrac{\sin x}{\sin x}\right)\cdot\dfrac{\sin x}{\cos x}\\\\=\dfrac{1-\sin x}{\sin x}\cdot\dfrac{\sin x}{\cos x}=\dfrac{1-\sin x}{\cos x}\cdot\dfrac{1+\sin x}{1+\sin x}=\dfrac{1-\sin^2x}{\cos x(1+\sin x)}\\\\=\dfrac{\cos^2x}{\cos x(1+\sin x)}=\dfrac{\cos x}{1+\sin x} \\\\L_s=R_s[/tex]
[tex]Used:\\\csc x=\dfrac{1}{\sin x}\\\\\cot x=\dfrac{\cos x}{\sin x}\\\\\sin^2x+\cos^2x=1\to\cos^2x=1-\sin^2x\\\\(a-b)(a+b)=a^2-b^2[/tex]
How do you know the sum of a positive and negative integer will be negative?
Answers
[tex]8+(-3)=+5[/tex]
If what you're asking is, under what condition will the sum of a positive and negative be negative, then it's when the absolute value of the negative number is greater than the positive number. For example:
positive number: 8
negative number: -10
[tex]8+(-10)=-2[/tex]
This sum is negative. Note that [tex]\mid{-10}\mid\ \textgreater \ 8[/tex].
suppose you deposit 1,000 ina savings account that pays interest at an annual rate of 5%. if no money is added or withdrawn from the account answer the following questions. How much money will be in the account after 3 years? How much will be in the account after 18 years? How many years will it take for the account to contain 1,500? How many years will it take for the account to contain 2,000?
Answers
Time req'd for amount to reach $1500 from $1000:
1500=1000(1+0.05)^t, or 1.5=1.05^t
ln 1.5
ln 1.5 = t ln 1.05, so that t = ------------ = 8.31 years, or 8 yr 3 3/4 months
ln 1.05
How do I simplify this expression
Answers
= 4x(x + 5) - 3(x + 5)
= 4x^2 + 20x - 3x - 15
= 4x^2 + 17x - 15 Answer
If the selling price is $18 and the markup is 33% what is the dollar market
Answers
The data shows the number of grams of fat found in 9 different health bars.12, 14, 16, 16.5, 11, 18, 18, 14, 20 What is the IQR (interquartile range) for the data?
9
5
16
18
Answers
The interquartile range (IQR) for the given health bar fat content data set is 5 grams, calculated by subtracting the first quartile (13) from the third quartile (18).
To calculate the interquartile range (IQR) of the given health bar data set, first, we must organize the numbers in ascending order: 11, 12, 14, 14, 16, 16.5, 18, 18, 20. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).
Find the median (the middle value) of the dataset, which will also serve as the second quartile (Q2). The median of the dataset here is 16.
To find Q1, calculate the median of the lower half of the data (not including the median of the dataset if your dataset has an odd number of values). So the lower half of the data is 11, 12, 14, 14, and the median of this is 13.
To find Q3, calculate the median of the upper half of the data. The upper half following our median is 16.5, 18, 18, 20, with a median value of 18.
The IQR is Q3 - Q1, which is 18 - 13 = 5.
Thus, the IQR for the health bars' fat content data is 5 grams.
You fly a hot air balloon 1.5 miles above the ground. What is the measure of BD⌢, the portion of Earth that you can see? Round your answer to the nearest tenth. (Earth's radius is approximately 4000 miles.)
Answers
Answer:
3.1
Step-by-step explanation:
If you are doing this for big ideas, the answer ended up being 3.1
I'm sorry if you wanted the work, I found the answer from something else that didn't show the work but this was the correct answer...
To find the measure of BD⌓, the visible portion of Earth's surface from a hot air balloon 1.5 miles above the ground, convert the height to kilometers and use the formula D = 112.88 km × √h to get the distance to the horizon, which is about 175.4 km. Then, calculate the semicircular distance visible by using C/2 = (π × D) / 2, which results in approximately 276.1 km for the measure of BD⌓.
Explanation:To calculate the measure of BD⌓, the portion of Earth's surface that is visible from a hot air balloon 1.5 miles above the ground, you can use the formula for the distance to the horizon, given as D = 112.88 km × √h, where h is the height above the Earth's surface. In this case, we must convert the height of 1.5 miles to kilometers before applying the formula, as the formula uses kilometers.
The conversion from miles to kilometers is 1 mile = 1.60934 kilometers, so 1.5 miles is approximately 2.414 km.
Inserting h = 2.414 km into the formula, we get:
D = 112.88 km × √2.414
D = 112.88 km × 1.5535 (approx)
D ≈ 175.4 km (rounded to the nearest tenth)
This is the straight-line distance to the horizon. To find the measure of the arc BD, which is the portion of the Earth's surface visible, we can treat this distance as the radius of a circle and calculate the circumference. However, since we are only looking at the visible part, which is a semicircle, we use half of the circumference C = π × D.
The measure of BD⌓ is therefore approximately:
C/2 = (π × 175.4 km) / 2
C/2 ≈ 276.1 km
Thus, the measure of BD⌓ to the nearest tenth is 276.1 km.
A person who is 55 feet tall is standing 168168 feet from the base of a tree, and the tree casts a 180180 foot shadow. the person's shadow is 1212 feet in length. what is the height of the tree?
Answers
A basket contains the following pieces of fruit: 3 apples, 2 oranges, 2 bananas, 2 pears, and 5 peaches. Jack picks a fruit at random and does not replace it. Then Bethany picks a fruit at random. What is the probability that Jack gets a peach and Bethany gets an orange?
Answers
You have to find the probabilities of them happening separately
To do this you do the amount of favorable outcomes over the total amount of outcomes
3 + 2 + 2 + 2 + 5 = 14 total fruit
The chance of Jack getting a peach is 5 / 14
The chance of Bethany getting an orange is 2 / 13 because Jack did not put the fruit back in so their is one less to choose from
You multiply the two probabilities to find the probability of them happening in a row
5/14 * 2/13 = 5/91
The answer is 5/91
Hope this helps!
simplify by 2
10/182 ÷ 2/2
5/91
5 over 91
find the solution of this system of equations
-6x-2y=8
7x-2y=-5
Answers
Simplify the expression, leave your answer in exponential form :
Can you show the steps!??
Answers
[tex]\bf \left( \cfrac{x^{\frac{1}{2}}}{16z^{-8}} \right)^{\frac{3}{4}}\implies \left( \cfrac{x^{\frac{1}{2}\cdot \frac{3}{4}}}{16^{\frac{3}{4}}z^{-8\cdot \frac{3}{4}}} \right)\implies \left( \cfrac{x^{\frac{3}{8}}}{(2^4)^{\frac{3}{4}}z^{-6}} \right) \\\\\\ \left( \cfrac{x^{\frac{3}{8}}}{2^{4\cdot \frac{3}{4}}z^{-6}} \right)\implies \left( \cfrac{x^{\frac{3}{8}}}{2^3z^{-6}} \right)\implies \cfrac{x^{\frac{3}{8}}z^6}{8}[/tex]