The equation is rearranged so that \(y\) is expressed in terms of[tex]\(x\): y= 5x - 26[/tex]
To rearrange the given equation so that x is the independent variable, you need to solve for y. Here's how you can do it step by step:
1. Start with the given equation:
[tex]\[y + 6 = 5(x - 4)\][/tex]
2. Expand the right side of the equation:
[tex]\[y + 6 = 5x - 20\][/tex]
3. Move the constant term (6) to the right side by subtracting 6 from both sides:
[tex]\[y = 5x - 20 - 6\]\\y = 5x - 26\][/tex]
Now, the equation is rearranged so that \(y\) is expressed in terms of[tex]\(x\): y= 5x - 26[/tex]
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Use what you know about domain to select all of
the following functions that could be the one
graphed.
f(x) - 3
f(x) - V1
Ax) = VX+1
(x) = 3x-3
Answer:A & B
Step-by-step explanation:
A box contains 50 cups. It is a mix of plastic and paper cups. Simon chooses a cup out of the bag, without looking, records the cup type, and then places that cup back in the bag. Simon has recorded 24 plastic cups and 26 paper cups. Using these results, predict the number of plastic cups in the bag.
Answer:
I think the plastic cup are 24
Find lim x -2 f(x) for: a . f(x) = 9 b. f(x) = x
Answer:
Step-by-step explanation:
Given the limit function
Lim x → 2: f(x)
1. When f(x) = 9
Then,
From limit theorem
Lim x → xo: K = K
Where k is a constant. Then, the limit of a constant is that constant.
Lim x → 2: 9 = 9
So limit is 9.
2. Lim x → 2: f(x)
Lim x → 2: x
When x = 2
Lim x → 2: 2 = 2
Then, x = 2.
I think the answer is letter C, can someone check me and make sure that is correct.
Answer:
You're Correct
Step-by-step explanation:
Keep up your good work
Find the area of the figure. Round to the nearest tenth
What are the restrictions of the domain gºh?
Answer:
The restrictions partly depend on the type of function.
You can’t divide by 0
You can’t take the square (or other even) root of a negative number, as the result will not be a real number.
In what kind of functions would these two issues occur?
the function is a rational function and the denominator is
0
for some value or values of x,
f ( x ) = x + 1 2− x
is a rational function
the function is a radical function with an even index (such as a square root), and the radic and can be negative for some value or values of x.
f ( x ) = √ 7 − x
is a radical function
The following table gives examples of domain restrictions for several different rational functions.
Hope this helped
Answer:
The answer is 6.
Step-by-step explanation:
Solve triangles using the law of cosines
Find AB.
Round to the nearest tenth.
Answer:
From the Law of cosines we see that Line AB^2 (or side c^2) equals
AB^2 = a^2 + b^2 -2ab *cos (C)
AB^2 = 6*6 + 7*7 -2*6 * 7 * cos(59)
AB^2 = 85 -84 * 0.51504
AB^2 = 85 - 43.26336
AB^2 = 41.73664
AB = 6.4603900811
AB = 6.5 (rounded)
Step-by-step explanation:
The equation h(t)= -16t^2+864t models the path of a rocket shot into the air. After how many seconds does the rocket hit the ground?
Answer:
t = 54 seconds
Step-by-step explanation:
The equation that models the path of a rocket into the air is given by :
[tex]h(t)= -16t^2+864t[/tex]
It is required to find the time after which the rocket will hit the ground. When it hits the ground, the height of the rocket will becomes zero. It means,
h(t) = 0
i.e.
[tex]-16t^2+864t=0\\\\16t(-t+54)=0\\\\16t=0, -t+54=0\\\\t=0\ and\ t=54\ s[/tex]
It means after 54 seconds, the rocket will hit the ground.
Each half of the drawbridge is about 284 feet long. How high does the drawbridge rise when x is 30?? The drawbridge rises about feet. Question 2 How high does the drawbridge rise when x is 45?? Round the answer to the nearest hundredth. The drawbridge rises about feet. Question 3 How high does the drawbridge rise when x is 60? ? Round the answer to the nearest hundredth. The drawbridge rises about feet.
Answer:
height = 142.00 ft
height ≈ 200. 82 ft
height ≈ 245.95 ft
Step-by-step explanation:
The picture below represent the image of the draw bridge. The illustration will form a right angle triangle. The hypotenuse is each half of the drawbridge which is 284 ft long. The opposite side of the triangle is facing the drawbridge half leg and the adjacent side is horizontal length. This is the side that made the angle with the drawbridge half leg(hypotenuse).
The question ask us to find the height of the drawbridge when it rise which is the opposite sides of the triangle when the angle is 30° , 45° and 60°.
Using SOHCAHTOA principle,
Angle 30°
sin 30° = opposite/hypotenuse
sin 30° = height/284
cross multiply
height = 0.5 × 284
height = 142.00 ft
Angle 45°
sin 45° = height/284
height = 284 × 0.70710678118
height = 200.818325857
height ≈ 200. 82 ft
Angle 60°
sin 60 = height/284
cross multiply
height = 0.86602540378 × 284
height = 245.951214675
height ≈ 245.95 ft
The question asks about the height a drawbridge rises at different angles. This is a trigonometry problem that can be solved by using the sine of the angle to calculate the height of the bridge when raised. The height corresponds to the 'opposite' side in a right triangle formed by the raised drawbridge.
Explanation:This question appears to be asking about how high a drawbridge rises based on an angle, x, which is a trigonometry problem. Assuming that the drawbridge forms a right triangle when it rises, the height can be calculated using the sine of the angle, x. Sine of x is equal to the opposite side (height of the bridge when it is raised) over the hypotenuse (half of the drawbridge's length).
Applying these trigonometric principles, calculations for each scenario would look like the following:
For x = 30 degrees: Height = sin(30) * 284 feet = 142 feet. For x = 45 degrees: Height = sin(45) * 284 feet = 200.71 feet (rounded to the nearest hundredth). For x = 60 degrees: Height = sin(60) * 284 feet = 245.98 feet (rounded to the nearest hundredth). Learn more about Trigonometry here:
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What is equivalent to (3x^2y)(10x^5y^3)???
Answer:
[tex]30x^{7} y^{4}[/tex]
Step-by-step explanation:
simplify
Final answer:
The equivalent expression for (3x^2y)(10x^5y^3) is 30x^7y^4, obtained by multiplying the coefficients and adding the exponents of like bases.
Explanation:
The question asks for the equivalent expression of the product (3x^2y)(10x^5y^3).
To find the equivalent expression, we need to apply the properties of exponents, which state that when multiplying two powers with the same base, we add the exponents. We can also multiply the coefficients in a usual way. Let's break it down into steps:
Multiply the coefficients (numbers outside the exponents): 3 × 10 = 30.
Add the exponents of x: x^2 × x^5 = x^(2+5) = x^7.
Add the exponents of y: y^1 × y^3 = y^(1+3) = y^4.
Combine the results: 30x^7y^4.
Therefore, the equivalent expression for (3x^2y)(10x^5y^3) is 30x^7y^4.
What dose equal -7+4(-4)=?
Answer:
-23
Step-by-step explanation:
PEMDAS says to multiply first, so we multiply 4 by -4 and get -16.
Now the equation is -7 - 16. Change the subtraction sign into addition and the negative 16 into a positive, and the equation is -7 + -16.
-7 + -16 is -23.
André buys 12 apples at $1 each. He uses a coupon for $1.50 off the total purchase. How much did André spend on apples?
A $10.50 B $11.00 C $11.50 D $12.00
A train leaves at 11.15 and arrives at its destination at 12.23. If the train travelled 95 km, what was it's average speed in km/h? Give your answer rounded to 1 dp.
Answer:
Average speed v = 83.8 km/h
Step-by-step explanation:
Given;
Distance travelled = 95 km
Time taken t = 12.23 - 11.15 = 1 hour 8 minutes
t = 1 + 8/60 hours = 1.133 hours.
Average speed v = distance travelled/time taken
substituting the values;
v = 95 km ÷ 1.133 hours
Average speed v = 83.8 km/h
Which operation should be used to solve x + 3 = 7?
Answer:
You can use the Subtraction property of equality
You have to subtract 3 on both sides to have x alone, which will give you x=4
Answer:
SUbtraction
7-3=4 so X is 4
Step-by-step explanation:
Please help me I have been stuck on this question for ages
Answer:28 green and 35 red
Step-by-step explanation:
Given
If there are r red counter and g green counter then
Probability of drawing a green counter is [tex]P(g)=\frac{4}{9}[/tex]
and [tex]P(g)=\frac{\text{No of g counter}}{\text{Total no of counter}}[/tex]
Thus [tex]\frac{\text{No of g counter}}{\text{Total no of counter}}=\frac{4}{9}[/tex]
[tex]\frac{g}{g+r}=\frac{4}{9}[/tex]
[tex]\Rightarrow 9g=4g+4r[/tex]
[tex]\Rightarrow 5g=4r\quad \ldots(i)[/tex]
Also if 4 red and 2 green counter is added the probability of drawing a green counter is
[tex]P(g)=\frac{10}{23}=\frac{\text{No of g counter}}{\text{Total no of counter}}[/tex]
[tex]\Rightarrow \frac{10}{23}=\frac{g+2}{g+2+r+4}[/tex]
[tex]\Rightarrow \frac{10}{23}=\frac{g+2}{g+r+6}[/tex]
[tex]\Rightarrow 10g+10r+60=23g+46[/tex]
[tex]\Rightarrow 10r+14=13g\ quad \ldots(ii)[/tex]
Substitute the value of g in equation (ii)[/tex]
[tex]\Rightarrow 10\times \frac{5}{4}g+14=13g[/tex]
[tex]\Rightarrow \frac{25}{2}g+14=13g[/tex]
[tex]\Rightarrow g=28[/tex]
Therefore [tex]r=35[/tex]
Thus there 28 green counter and 35 red counter
Mark, Paul and Brian share some sweets in the ratio 1:3:5. Mark gets 14 sweets. How many did Brian get?
Answer:
70
Step-by-step explanation:
mark = 1 1 times 14 = 14
Brian = 5 5 times 14 = 70
Brian receives 70 sweets, as Mark's 14 sweets represent 1 part of the ratio 1:3:5, indicating that 1 part equals 14 sweets and Brian's 5 parts equal 70 sweets.
Mark, Paul, and Brian share sweets in a ratio of 1:3:5, which means that for every sweet Mark gets, Paul gets 3, and Brian gets 5. Since Mark gets 14 sweets, we can use this information to calculate how many sweets Brian gets. First, let's find out what one 'part' of the ratio is worth by dividing the number of sweets Mark gets by his ratio number:
Mark's sweets (14) / Mark's ratio (1) = 14 sweets per ratio part.
Next, determine Brian's share by multiplying the sweets per ratio part by Brian's ratio number:
Brian's share = sweets per ratio part (14) * Brian's ratio (5) = 70 sweets.
Therefore, Brian gets 70 sweets.
Easy Question, Easy points
Topic: Volume
Use the other attached paper to help u find formula
Focus on question Scenario 3
Answer:
see below
Step-by-step explanation:
A can is a cylinder
V = pi r^2 h
The diameter is 6.4 we want the radius
r = d/2 = 6.4/2 = 3.2
V = 3.14 * (3.2)^ * 12.3
V =395.48928 cm^3
1 cm^3 = 1ml
V = 395.48928 mL
A can of soda has 355 mL
We are over estimating because the can narrows on the ends and the height is actually shorter because the ends do not have volume but are metal to contain the soda. We also did not take into account the curve in the bottom of a can of soda.
Answer:
395.48928 cm³
40.48928 cm³ greater than an actual can
Step-by-step explanation:
Volume of can:
pi × r² × h
3.14 × (6.4/2)² × 12.3
395.48928 cm³
Actual can: 355 cm³
395.48928 - 355 = 40.48928 cm³
What is the radian measure of an angle of 132°?
Answer:
11/15 pi radians
Step-by-step explanation:
To convert from degrees to radians, multiply by pi/180
132 * pi/180
11/15 pi
Answer:
2.304 radians
hope this helps :)
EASY QUESTION
Read question 7
Topic: Volume
Answer:
196 cent^3
Step-by-step explanation:
mark brainliest please :)
Answer:
190 cents skimpy simple
190 cent
Which decimal is equivalent to 2/9?
A. 2.2
B. 2.9
C. 22222
D. 0.2
Answer:
The answer is 0.2. It is an irrational number with a repeating 2. It should have a line over the two to represent it repeating.
Step-by-step explanation:
First divide 2 by 9.
Use a calculator or do it by hand.
You get your answer.
Option D is correct, the decimal which is equivalent to the fraction 2/9 is 0.2
The given fraction is two divided by nine, 2/9
Two is the numerator and nine is the denominator
We have to find the equivalent decimal number of fraction 2/9
To do this we have to divide 2 by number nine
When two is divided by nine we get 0.222
2/9 =0.22
=0.2
Hence, the decimal which is equivalent to the fraction 2/9 is 0.2, option D is correct.
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solve the system of equations y=2x -4,y = -x+2
Answer:
(2,0)
Step-by-step explanation:
Solve by graphing:
Use a graphing tool to graph the lines y=2x -4 and y = -x+2.
The lines intercept at point (2,0).
Therefore, the solution to the set of equations is (2,0).
[tex]x=2\\y=0[/tex]
Brainilest Appreciated!
Answer:
(0, -4) and (2,0)
Step-by-step explanation:
Bill plans to save for a pair of headphones that are $89.00. The sales tax rate is 8%. How much will Bill need to save? i'll give you brainliest and five star
Answer:
96.12
Step-by-step explanation:
89x.0.08 is 7.12 add that to 89 gives you 96.12
4/9 times 9/3 can someone please answer this question
Answer:
36/27
Step-by-step explanation:
simplified is 4/3
If r(x) = 2 – x2 and w(x) = x – 2, what is the range of (w circle r) (x)?
(negative infinity, 0 right-bracket
(negative infinity, 2 right-bracket
Left-bracket 0, infinity)
Left-bracket 2, infinity)
Answer:
[tex](-\infty, 0)[/tex]
Step-by-step explanation:
(w circle r) (x) is the composite function(w of r(x)), that is, w(r(x))[/tex]
We have that:
[tex]r(x) = 2 - x^{2}[/tex]
[tex]w(x) = x - 2[/tex]
Composite function:
[tex]w(r(x)) = w(2 - x^{2}} = 2 - x^{2} - 2 = -x^{2}[/tex]
[tex]-x^{2}[/tex] is a negative parabola with vertex at the original.
So the range(the values that y assumes), is:
[tex](-\infty, 0)[/tex]
The range of (w circle r) (x) will be (-∞,0). Option A is correct.
What is a function?A connection between independent variables and the dependent variable is defined by the function.
Functions help to represent graphs and equations. A function is represented by the two variables one is dependent and another one is an independent function.
The relation between them is shown as y if dependent and x is the independent variable;
Given functions;
[tex]\rm r(x) =2- x^2 \\\\ w(x) =x-2[/tex]
The composite function is found as;
[tex]\rm w(r(x))=w(2-x^2 = 2-x^2-2)\\\\ w(r(x))= -x^2[/tex]
-x² is graphed and shows the negative parabola
The range of (w circle r) (x) will be (-∞,0).
Hence, option A is correct.
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The answers I don’t really understand the question
For step one, they want you to factor 5,000 into a 5 and ?. To find the missing value, we can divide:
5,000 / 5 = 1,000
So, 1000 goes in the first blank.
For step two, 1,000 also goes in the second blank since the first 2 numbers are being multiplied.
For step three, multiply the last two numbers.
30 * 1000 = 30,000
So, 30000 goes in the last blank.
Best of Luck!
Answer: 30000 goes in the last one
Step-by-step explanation:
Please HELP LOTS OF POINTS
Question:
Clay bought a baseball card in 2001 for $50. In 2016, the card's value was $500. Determine the average annual rate (r) of appreciation to the nearest whole percent. Show all work.
Answer:
67%
Step-by-step explanation:
500=50*x*15
500=750*x
500/750=x
.666666666=x
.67=x
67%=x
Three salesmen are working for the same company, selling the same product. And, although they are all paid on a weekly basis, each salesman earns his paycheck differently. Salesman A works strictly on commission. He earns $65 per sale, with a maximum weekly commission of $1,300. Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale. There are no limits on the amount of commission he can earn. Salesman C does not earn any commission. His weekly salary is $900.
1. For each salesman, write an equation showing the relationship between their weekly paycheck amount, p, and the number of sales, s, they had that week.
Answer:
A:
p = 65s, 0《s《20
p = 1300, s > 20
B:
p = 300 + 40s, s》0
C:
p = 900
Step-by-step explanation:
Salmesman A:
p = 65s
65s = 1300
s = 20
Salesman B:
p = 300 + 40s
Salesman C:
p = 900
Answer:
A:
p = 65s, 0《s《20
p = 1300, s > 20
B:
p = 300 + 40s, s》0
C:
p = 900
Step-by-step explanation:
Salmesman A:
p = 65s
65s = 1300
s = 20
Salesman B:
p = 300 + 40s
Salesman C:
p = 900
Step-by-step explanation:
Find the common ratio for the geometric sequence of, 162, 108, 72, 48 ......
A- -3/2
B- -2/3
C- 2/3
D- 3/2
2/3Answer:
Step-by-step explanation:
The graph shows the inverse of which function?
Josh has 25 classmates. He has 10 tickets to the movies. How many ways can he invite 9 friends to see a movie with him?
Answer:
2,042,975
Step-by-step explanation:
Josh can choose 9 of his 25 classmates using the function C(n,k), which tells the number of combinations of n objects taken k at a time.
__
Here, Josh wants to choose 9 from 25 classmates. The number of possible choices is ...
C(n, k) = n!/(k!(n-k)!)
C(25, 9) = 25!/(9!(25 -9)!) = 25·24·23·22·21·20·19·18·17÷(9·8·7·6·5·4·3·2·1)
= 2,042,975
__
Additional comment
In effect, the first ticket can go to any of 25 classmates, the second to any of 24, and so on. The last ticket can go to any of 17 classmates. This product 25·24·...·17 counts each group of classmates 9! times. Since the order in which they are chosen does not matter, the final number is then ...
25!/(16!·9!) = 2042975