To calculate the initial value of the equation we have to equal it when x = 0
\(\begin{gathered} y=0.75x-2 \\ y=0.75(0)-2 \\ y=-2 \end{gathered}\)The value for x =0 would be y = -2
Given the two functions, which statement is true? f(x) = 3x, g(x) = 3x + 5 Question 12 options: g(x) is translated up 5 units compared to f(x) g(x) is translated left 5 units compared to f(x) g(x) is translated down 5 units compared to f(x) g(x) is translated right 5 units compared to f(x)
The correct statement is: g(x) is translated up 5 units compared to f(x).
The correct answer is A.
To determine the translation between the two functions, we can observe that the only difference between them is the constant term.In f(x) = 3x, there is no constant term, so the graph of f(x) passes through the origin (0, 0).In g(x) = 3x + 5, there is a constant term of 5 added to the function. This means that the graph of g(x) is shifted vertically upward by 5 units compared to the graph of f(x).Therefore, g(x) is translated up 5 units compared to f(x).The correct answer is A.
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Determine the possible side lengths of the third side of a triangle with known side lengths of 5 and 8.
Question 3 options:
A)
–5 < c < –8
B)
–3 < c < –13
C)
3 < c < 13
D)
5 < c < 8
Answer: 3 < c < 13 (choice C or third answer choice)
======================================================
Explanation:
Consider a triangle with sides: a,b,c
Furthermore, we'll have a = 5 and b = 8 as the two known sides.
Due to a modification of the Triangle Inequality Theorem, the third side will have the condition that:
b-a < c < b+a
where b ≥ a must be the case.
----------
Let's plug in those a & b values to determine the range for c.
b-a < c < b+a
8-5 < c < 8+5
3 < c < 13
This points us to Choice C as the final answer.
Answer: 9.43398113206
Step-by-step explanation:
A^2 + B^2 = C^2
5^2 + 8^2 = √89
= 9.43398113206
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The width of a rectangular field is represented by x meters. The length of the field is 10 more than twice its width . The area of the field is 5500m^2
Part A
Write an equation that can be used to determine the dimensions, in meters, of the field.
Part B
What is the width, in meters, of the field?
The width is ( ) meters.
Part A: The equation that can be used to determine the dimensions, in meters, of the field is 5500 = 2x² + 10x
Part B: width is 50 meters.
How to determine the valueThe formula for calculating the area of a rectangle is expressed with the equation;
A = lw
Such that the variables are expressed as;
A is the areal is the lengthw is the widthWe then have that;
l = 2x + 10
Substitute the values
5500 = (2x + 10)(x)
expand the bracket
5500 = 2x² + 10x
2x² + 10x - 5500
x² + 5x - 2750
x² + 55x - 50x - 2750
x(x + 55) - 50(x + 55)
x = 50 meters
Length = 2(50) + 10
Length = 100 + 10 = 110 meters
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Which is the best definition of mathematical proof?
Answer:
it will 3rd one. hope it helps
Which choice is the solution to the inequality below?
6x>72
OA. x< 12
OB. x> 12
OC. x2 72
OD. x>72
The solution to the inequality 6x > 72 is option B x > 12
What is an inequality?
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
A is not equivalent to b in any scenario. Since a is strictly less than or strictly greater than b, these relationships are known as stringent inequalities. Equivalence is not considered.
There are two forms of inequality relations that are not strict, in contrast to strict inequalities:
The notation a ≤ b or a ⩽ b means that a is less than or equal to b (or, equivalently, at most b, or not greater than b).
The notation a ≥ b or a ⩾ b means that a is greater than or equal to b (or, equivalently, at least b, or not less than b).
Given, the inequality is 6x>72
6x > 72
Dividing by 6 on both sides of inequality, we get,
6x/6 > 72/6
⇒ x > 12
Hence, option B is correct.
The solution to the inequality 6x > 72 is option B, x > 12
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Which property is demonstrated?
16 + 7 + 9 = 7 + 9 + 16
The correct option is option C i.e., associative property of addition.
A mathematical expression is given which is 16 + 7 + 9 = 7 + 9 + 16.
We have to find out which property is used in the above expression.
What is the associative property of addition ?
The associative property of addition states that sum of three or more numbers remains same regardless of the way in which they are grouped.
As per the question ;
The mathematical expression given is ;
16 + 7 + 9 = 7 + 9 + 16
Simplifying both sides , we get ;
32 = 32
Here ;
Sum of three or more numbers is same regardless of the way in which we have arranged them.
So , property used is associative property of addition.
Thus , the correct option is option C i.e., associative property of addition.
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Describe how to sketch the graph of y = –tan(2x) + 3 using the parent function.
Answer:
Start by graphing the tangent function.
Compress the graph horizontally by making the period one-half pi.
Reflect the graph over the x-axis.
Shift the graph up 3 units.
Step-by-step explanation:
Just did it but it’s the sample response
please i’ll fail if i don’t get this right. please i’ll give brainlyist The current temperature of 15°F below zero is 18°F below the high temperature of the day. What is the high temperature for the
day?
OA. 5°F
ов. 33°F
OC. 3°F
OD. 33°F
Answer:
I think its C
Step-by-step explanation:
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Launch realize. 8-2: Find Volume of Cylinders (LMS graded)
8.2.PS-13
The cylinder shown has a volume of 824 cubic inches.
a. What is the radius of the cylinder? Use 3.14 for .
b. If the height of the cylinder is changed, but the volume
stays the same, then how will the radius change? Explain.
a. The radius of the cylinder is about 8.2 in³.
(Type an integer or decimal rounded to the nearest tenth as needed.)
10.7 in.
Question Help
◇
To find the radius of the cylinder, we can use the formula for the volume of a cylinder:
V = πr²h
Given that the volume is 824 cubic inches, we can rearrange the formula to solve for the radius:
824 = πr²h
Since the height is not given, we cannot find the exact radius. However, we can still determine the relationship between the height and radius if the volume remains the same.
b. If the height of the cylinder is changed, but the volume stays the same, the radius will change inversely proportional to the height. This means that as the height increases, the radius will decrease, and vice versa. This relationship ensures that the volume remains constant.
Therefore, we cannot determine the exact radius without knowing the height, but we can conclude that the radius and height have an inverse relationship.
A first number plus twice a second number is 19. Twice the first number plus the second totals 20. Find the numbers
The smaller of the two numbers is ____
The larger of the two numbers is ____
Answer:
a first number plus twice a second number is 19
find the bearing of a from b
find the bearing of b from a
Answer:
130° and 310°
Step-by-step explanation:
the bearing of A from B is the measure of the clockwise angle from a north line at B to A
the angle at B and A are same- side interior angles and sum to 180°
angle at B = 180° - 50° = 130°
the bearing of A from B is then 130°
the bearing of B from A is the measure of the clockwise angle from the north line at A to B
the complete angle about A = 360° then clockwise angle from north line at A to B is
360° - 50° = 310°
the bearing of B from A is 310°
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BRAINLIEST!!!!! AND 100 POINTS!!!!!
Answer:
option 3
Step-by-step explanation:
As long as both lines are rotated the same direction and the same angle, then the angle between the two lines will not change.
What is the equation of the line at passes?
What is the slope of the line that produced the following table on your calculator?
Answer:
7. y=1/4x
8. m= 2
Step-by-step explanation:
i hope this helps :)
this question is proving to be very difficult so I'm here to request assistance on it?
...
SOLUTION
Given the figure below;
The radius of the inscribed circle is DE;
\(\begin{gathered} To\text{ determine DE;} \\ CE\text{ is divided into CD:DE}\rightarrow2:1 \\ DE=\frac{1}{3}\times CE \\ DE=\frac{1}{3}\times8.7 \\ DE=2.9 \\ The\text{ radius of the inscribed circle is 2.9} \end{gathered}\)The radius of the circumscribed circle is CD;
\(\begin{gathered} To\text{ determine CD:} \\ CD=\frac{2}{3}\times CE \\ CD=\frac{2}{3}\times8.7=5.8 \\ The\text{ radius of the circumscribed circle is 5.8} \end{gathered}\)
During optimal conditions, the rate of change of the population of a certain organism is proportional to the population at time t, in hours. At time t = 0 hours, the population is 300. At time t = 24 hours, the population is 1000. At what time t is the population 500?
(A) t = 2112
(B) t = 24 In 500 In 1000
(D) t = 300e (9)
Answer:
The population is of 500 after 10.22 hours.
Step-by-step explanation:
The rate of change of the population of a certain organism is proportional to the population at time t, in hours.
This means that the population can be modeled by the following differential equation:
\(\frac{dP}{dt} = Pr\)
In which r is the growth rate.
Solving by separation of variables, then integrating both sides, we have that:
\(\frac{dP}{P} = r dt\)
\(\int \frac{dP}{P} = \int r dt\)
\(\ln{P} = rt + K\)
Applying the exponential to both sides:
\(P(t) = Ke^{rt}\)
In which K is the initial population.
At time t = 0 hours, the population is 300.
This means that K = 300. So
\(P(t) = 300e^{rt}\)
At time t = 24 hours, the population is 1000.
This means that P(24) = 1000. We use this to find the growth rate. So
\(P(t) = 300e^{rt}\)
\(1000 = 300e^{24r}\)
\(e^{24r} = \frac{1000}{300}\)
\(e^{24r} = \frac{10}{3}\)
\(\ln{e^{24r}} = \ln{\frac{10}{3}}\)
\(24r = \ln{\frac{10}{3}}\)
\(r = \frac{\ln{\frac{10}{3}}}{24}\)
\(r = 0.05\)
So
\(P(t) = 300e^{0.05t}\)
At what time t is the population 500?
This is t for which P(t) = 500. So
\(P(t) = 300e^{0.05t}\)
\(500 = 300e^{0.05t}\)
\(e^{0.05t} = \frac{500}{300}\)
\(e^{0.05t} = \frac{5}{3}\)
\(\ln{e^{0.05t}} = \ln{\frac{5}{3}}\)
\(0.05t = \ln{\frac{5}{3}}\)
\(t = \frac{\ln{\frac{5}{3}}}{0.05}\)
\(t = 10.22\)
The population is of 500 after 10.22 hours.
By finding the population as a function of time, we will see that the population will be 500 after 10.2 hours.
How to find the population equation.Let's say that the population equation is p(t).
We know that the rate of change is proportional to the population, so we have the differential equation:
p'(t) = a*p(t).
This means that p(t) is an exponential function of the form:
p(t) = A*e^(a*t)
Now we know that:
p(0) = A*e^(a*0) = A = 300
And:
P(24) = 300*e^(a*24) = 1000
e^(a*24) = 1000/300
a*24 = ln(1000/300)
a = ln(1000/300)/24 = 0.05
Then the population equation is:
p(t) = 300*e^(0.05*t)
Now we want to find the value of t such that the population is 500, so we need to solve:
p(t) = 300*e^(0.05*t) = 500
e^(0.05*t) = 500/300
0.05*t = ln(500/300)
t = ln(500/300)/0.05 = 10.2
So the population will be 500 at t = 10.2 hours.
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Please help me so stressed
Answer:
Meron ka nang loptap bakit humihingi ka pa nang answer
A game card handed out at a grocery store states the probabilities of winning a prize: 0.2 for $10, 0.1 for $5, and 0.7 for $0. What is the probability of winning any amount of money?
Answer:
Step-by-step explanation:
To calculate the probability of winning any amount of money, we need to sum up the probabilities of winning each individual prize.
Given the probabilities stated on the game card:
Probability of winning $10 prize = 0.2
Probability of winning $5 prize = 0.1
Probability of winning $0 prize = 0.7
To find the probability of winning any amount of money, we add these probabilities together:
0.2 + 0.1 + 0.7 = 1
The sum of the probabilities is 1, which indicates that the total probability of winning any amount of money is 1 or 100%.
Therefore, the probability of winning any amount of money in this game is 100%.
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What are the points of the image of the line in Q4 after the dilation?
Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)
How is this so ?To rotate a point 90 degrees clockwise about a given point,we can follow these steps -
Translate the coordinates of the given point so that the center of rotation is at the origin. In this case,we subtract the coordinates of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).
Perform the rotation by swapping the x and y coordinates and changing the sign of the new x coordinate. In this case,we swap the x and y coordinates of (-5, 3) to get (3, -5).
Translate the coordinates back to their original position by adding the coordinates of the center (0,1) to the result from step 2. In this case, we add (0,1) to (3, -5) to get (3, -4).
Therefore, the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).
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Find the value of x.
Answer:
x=21
Step-by-step explanation:
Following the vertical angles, we can assume that the equation that has x and 87 are equal to each other. From then, you set them equal to each other and solve for x.
87=4x+3
84=4x subtract 3 from both sides
21=x divide by 4 to get the x alone on both sides
THIS IS MY SISTER LAST QUESTION TAKE YOUR TIME1
Answer:
B
Step-by-step explanation:
\([(8+15) \times 3] \div 3\\= \frac{(8+15) \times 3}{3}\\= \frac{8 + 15}{1}\\= 8 + 15 = 23\)
write a linear equation in slope-intercept form. slope=1/2 and y-intercept= -6
Answer:
y=1/2x-6
Step-by-step explanation:
Slope intercept form is y=mx+b so plug it into the equation and it is y=1/2x-6.
y=1/2-6
Solution:Since we're given the line's slope and y-intercept, we can easily determine its equation.Remember, slope-intercept looks like so: y=mx+bIn this formula, the letter "m" stands for the slope, and "b" stands for the y-intercept.Therefore, the line's equation is:y=1/2-6Hope it helps.
Do comment if you have any query.
Two consecutive even numbers are such that five times the smaller number , subtracted from eight times the bigger gives 58. Find the two Numbers? show working
Answer:
\(14\text{ and }16\)
Step-by-step explanation:
Let the smaller number be \(x\). Since they are consecutive even numbers, the larger number can be represented by \(x+2\).
Therefore, we have the following equation:
\(8(x+2)-5x=58,\\8x+16-5x=58,\\3x=42,\\x=\boxed{14}\)
Thus, the larger number is \(x+2=\boxed{16}\)
10. Convert. 12 kg = _______ g
Answer:
12,000 grams
Step-by-step explanation:
hope this helps
50 Points! Multiple choice algebra question. Photo attached. Which represents the correct synthetic division of (x^2-4x+7) divided by (x-2)? Thank you!
Option D is the correct synthetic division of (x^2-4x+7) divided by (x-2)
What is the synthetic division?Synthetic division is a shorthand procedure used to divide a polynomial by a linear factor of (x - a) form, in which "a" is constant. This method gives an expedient way to locate the quotient and remainder without carrying out long division.
x - 2 | x^2 - 4x + 7
x^2 - 2x
---------
-2x + 7
-2x + 4
-------
3
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Demtermine the degree of the polynomial_57
Answer:
The degree of polynomial of 57 is 0.
The diameter of a circle is 8cm. Find its circumference to the nearest tenth.
Answer:
\(C = 25.1 \text{ cm}\)
Step-by-step explanation:
We can find the circumference of the circle by plugging the given radius value 8 cm into the formula:
\(C = \pi d\)
Note: This formula can also be written as \(C = 2\pi r\) because \(2r = d\).
↓ plugging in the given radius
\(C = 8\pi \text{ cm}\)
↓ rounding to the nearest tenth
\(\boxed{C = 25.1 \text{ cm}}\)
What is the value of r?
If angle 1= 36 degrees and angle 4= 115 degrees what is the measurement of angle 2 ?
Which function is represented by this graph?
-10 -8 -6 -4 -2
-10
-2
-6
-8
-10
2
4
6
8
10
The standard absolute value graph has been shifted 7 units to the right and 3 units down to get this graph.
That means we have answer B: f(x) = | x - 7 | - 3
Remember that the left-right shifts are opposite from what they would appear to be in the equation.
| x - 7 | shifts it right 7 units.
| x + 7 | shifts it left 7 units.
Write a two column proof (Given: x is the midpoint of WY and VZ) (Prove: VW=ZY)
Bruce and Felicia would have a unique solution to the given equation. The value of x that satisfies the equation is 15.
To determine if the equation 6x + 2 = 5x + 17 has a unique solution, we need to check if the variable x has a consistent value that satisfies the equation.
By simplifying the equation, we can see that the equation becomes:
6x - 5x = 17 - 2
Simplifying further, we have:
x = 15
Since the variable x has a specific value, in this case, x = 15, the equation does have a unique solution. When x is substituted with 15 in the equation, both sides are equal.
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