find f(6) when using the function f(x)=3x+47
Answers
Answer: f(6) = 65
Step-by-step explanation:
plug in 6 for x
f(6) = 3(6) + 47
f(6) = 18 + 47
f(6) = 65
Related Questions
4(-8x + 5) – (-33x – 26) =
Answers
Answer:
1x + 46 or x + 46
Step-by-step explanation:
4(-8x + 5) – (-33x – 26)
-32x + 20 + 33x + 26
1x + 46
or x + 46
the question above or below states
The triangle has an area of 90cm^2 what size can angle x be
Answers
Answer:
\(x=30°\)
Step-by-step explanation:
\(Area=\frac{18*20sinx}{2} \\ \Leftrightarrow 90=\frac{18*20sinx}{2} \\ \Leftrightarrow sinx=\frac{90*2}{18*20}=\frac{1}{2}\\ \Leftrightarrow x=30°\)
help please asap i
show step by step !
Answers
Answer:
a = \(4\sqrt{3}\)
b= 4
Step-by-step explanation:
It's a 30-60-90 triangle based on the given picture. A right triangle too
Use sine, cosine, and tangent to solve for the side.
To find b, you can use sin(30) = b/8 because sin(angle) = opposite/hypotenuse.
OR you can use the rule for 30-60-90 triangle, which is x for short leg, 2x for hypotenuse, and \(x\sqrt{3}\) for long leg
So either way, b = 4
To find a, you can use cos(30) = a/8 because cos(angle) = adjacent/hypotenuse.
OR you can use the same rule, 30-60-90 triangle to save time
a will end up = \(4\sqrt{3}\)
Suppose that 18 inches of wire costs 72 cents.
At the same rate, how much in cents) will 41 inches of wire cost?
Answers
You divide the amount of wire by cost, and multiply that by 41
Answer:
1.61
Step-by-step explanation:
72/18 = 4cents per inch
4*41 = 161
1.61$
a prism and a cone have the same base area and the same height. the volume of the prism is 1. what is the volume of the cone?
Answers
The volume of the cone is 1/3.
If a prism and a cone have the same base area and the same height, we can use the formula for the volume of each shape to find the volume of the cone.
The volume of a prism is given by V_prism = base area × height. Since the volume of the prism is given as 1, we can write:
1 = base area × height
The volume of a cone is given by V_cone = (1/3) × base area × height. Since the base area and the height are the same as the prism, we can substitute them into the formula:
V_cone = (1/3) × base area × height = (1/3) × 1 = 1/3
Therefore, the volume of the cone is 1/3.
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solve the initial value problem below using the method of laplace transforms. y′′−2y′−3y=0, y(0)=1, y′(0) = 2
Answers
To solve the initial value problem y'' - 2y' - 3y = 0, with y(0) = 1 and y'(0) = 2, we can use the method of Laplace transforms.
First, we take the Laplace transform of the given differential equation to obtain an algebraic equation in terms of the Laplace transform of the unknown function y(t). Then, we solve the algebraic equation for the Laplace transform of y(t) using standard algebraic techniques. Finally, we take the inverse Laplace transform to obtain the solution y(t) in the time domain.
Applying the Laplace transform to the given differential equation, we have s²Y(s) - sy(0) - y'(0) - 2(sY(s) - y(0)) - 3Y(s) = 0, where Y(s) represents the Laplace transform of y(t). Simplifying this equation, we get (s² - 2s - 3)Y(s) - (s - 2) = s²Y(s) - 3s - 4. Rearranging the equation, we have Y(s) = (s - 2) / (s² - 2s - 3).
To solve this equation for Y(s), we can decompose the expression into partial fractions, which yields Y(s) = 1 / (s - 3) - 1 / (s + 1). Taking the inverse Laplace transform of Y(s), we obtain y(t) = e^(3t) - e^(-t), which is the solution to the initial value problem.
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The point A(-2, 3) is translated using T: (x,y) (x+4, y+2).What is the distance from Ato A?
Answers
Ok, so
Here we have this linear transformation as follows:
\(T\colon(x,y)=(x+4,y+2)\)And we're going to translate the point A:
\(A(-2,3)\)This is: (We replace the values of x and y of the point A in the transformation):
\(\begin{gathered} T\colon(-2,3)=(-2+4,3+2) \\ T\colon(-2,3)=(2,5) \end{gathered}\)The point A translated will give us a new point B, which is (2 , 5) (After applying the transformation).
Now, let's find the distance between A (-2,3) and B (2,5).
Remember that the distance between two points:
\(\begin{gathered} A(x_1,y_1) \\ B(x_{2,}y_2) \end{gathered}\)Can be found applying the following formula:
\(D=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}\)Replacing our values:
\(\begin{gathered} D=\sqrt[]{(5-3)^2+(2-(-2))^2} \\ D=\sqrt[]{(2)^2+(2+2)^2} \\ D=\sqrt[]{4+16} \\ D=\sqrt[]{20} \end{gathered}\)Therefore, the distance between the points A and B, is √(20) units. (This is, approximately, 4.47)
What is the least common multiple of 46, 49, and 17?
Answers
Answer:
38318
Step-by-step explanation:
Break the numbers into prime factors
46 = 23*2
49 = 7*7
17 = 17*1
The least common multiple is
23*2*7*7*17 = 38318
Find measure of angle E
Answers
The measure of ∠E will be equal to 38°.
Given,
m∠BFE = 118° and m∠C = 86°
And BF bisects ∠ABD
From the Property of Linear Pair,
∠AFB + ∠BFE = 180°
=> ∠AFB + 118° = 180°
=> ∠AFB = 62°
Now, we can see that ∠AFB and ∠FBD are equal because they are alternate angles.
And ∠FBD and ∠ABF are equal because BF bisects ∠ABD.
So, In ∆ABF,
∠AFB + ∠ABF + ∠BAF = 180° (because of the angle sum property of a triangle)
=>62° + 62° + ∠BAF = 180°
=>∠BAF = 180° - 124°
=> ∠BAF = 56°
Similarly, in ∆ABE,
∠A +∠C +∠E = 180°
=> 56° + 86° + ∠E = 180°
=> ∠E = 38°
Therefore, m∠E = 38°.
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on the first day of a measles outbreak at a school, 5 students were identified to have the measles. each day for the following two weeks, the number of new cases doubled from those identified with the disease the day prior. how many students are identified to have measles in all at the end of the 6th day of the outbreak?
Answers
160 students are identified to have measles in all at the end of the 6th day of the outbreak.
On the first day of a measles outbreak at a school, 5 students were identified to have the measles. Each day for the following two weeks, the number of new cases doubled from those identified with the disease the day prior. Here is the calculation below:
Number of cases of measles on the first day of outbreak = 5
Total number of cases of measles on day 2 = 5 x 2 = 10
Total number of cases of measles on day 3 = 10 x 2 = 20.
Total number of cases of measles on day 4 = 20 x 2 = 40
Total number of cases of measles on day 5 = 40 x 2 = 80
Total number of cases of measles on day 6 = 80 x 2 = 160
Therefore, 160 students are identified to have measles in all at the end of the 6th day of the outbreak.
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given your answer to (i), if jim chooses to buy 4 pints of beer and 9 cups of coffee, what must be the ratio of the price of pints of beer to the price of cups of coffee?
Answers
The ratio of the price of pints of beer to the price of cups of coffee if Jim chooses to buy 4 pints of beer and 9 cups of coffee is: b/c = 4b/9c , b/c = 1.125
Jim bought 3 pints of beer and 7 cups of coffee for $14, and the ratio of the price of pints of beer to the price of cups of coffee is 2:3,
To determine the cost of one pint of beer and one cup of coffee, let's solve the system of equations.
2b + 3c = 7 (dividing both sides of the equation by 7)
2b/7 + 3c/7 = 1b/3.5 + c/2.333
= 1b + 1.5c
= 4.666... (dividing both sides of the equation by 3.5)
b/3.5 × 4 + c/2.333 × 9
= 14b/0.875 + c/0.259
= 14.666...
Therefore, the ratio of the price of pints of beer to the price of cups of coffee if Jim chooses to buy 4 pints of beer and 9 cups of coffee is:
b/c = 4b/9c (multiplying both sides by 9c)
b/c = 1.125
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Question 5 of 10
Which pair of functions are inverses of each other?
O A. f(x) = 2 + 15 and g(x) = 12x - 15
O B. f(x) = √3x and g(x) = () ³
O c. f(x) = 3 - 10 and g(x) = +10
3
D. f(x) = 11x-4 and g(x) = +4
Answers
The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11
To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.
Let's test each option:
Option A:
f(x) = x/2 + 15
g(x) = 12x - 15
f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x
g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x
Option B:
f(x) = ∛3x
g(x) = (x/3)^3 = x^3/27
f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x
g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x
Option C:
f(x) = 3/x - 10
g(x) = (x + 10)/3
f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x
g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x
Option D:
f(x) = 11x - 4
g(x) = (x + 4)/11
f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x
g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x
Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:
D. f(x) = 11x - 4 and g(x) = (x + 4)/11
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Transform this equation to standard from. No decimals, fractions or negatives as leading coefficients
Y = -2x - 3/2
Answers
Answer:
3/4 or 0.75
Step-by-step explanation: y+-2x3/2
0= -2x 3/2=2x-3/2=x+-3/4=X=3/4 or 0.75
match each trig function to a ratio. tan(A)=
Answers
Answer:
\(\frac{y}{x}\), the fourth option.
Step-by-step explanation:
Tan means \(\frac{opposite}{adjacent}\) or opposite side divided by adjacent side.
Tan A equals the opposite side of the angle A divided by its adjacent side.
The side opposite of A is y and side adjacent to it is x.
So, Tan A equals \(\frac{y}{x}\)!
A total of 379 tickets were sold for the school play. They were either adult tickets or student tickets. There were 71 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answers
A total of 225 tickets were sold to adults for the school play.
How many tickets were sold to adults?
In this problem we see the case of 379 tickets being sold to adults and students and there was 71 tickets more sold to adults. This situation is defined by following equations:
x + y = 379
x + 71 = y
Where:
x - Tickets sold to students.y - Tickets sold to adults.Now we proceed to solve the system of linear equations:
x + (x + 71) = 379
2 · x = 308
x = 154
And the number of tickets sold to adults is:
y = x + 71
y = 154 + 71
y = 225
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simplify the expression. be sure to show or explain how you arrived at your answer (-6i)(4i)
Answers
Answer:
hi no ugh I pero Eresi me gusta la
By definition i^2=-1
Simplify
-24•(-1)
Solution
24
Can I get Brainly pls
if the work required to stretch a spring 3 ft beyond its natural length is 6 ft-lb, how much work (in ft-lb) is needed to stretch it 18 in. beyond its natural length?
Answers
A total of 2.25 ft-lb work is needed to stretch it 18 in. beyond its natural length.
One foot is equal to 12 inches, so 3 ft is equal to 36 inches. To stretch the spring 18 inches beyond its natural length, we need to perform work on it to stretch it an additional 18/36 = 1/2 of the 3 ft distance. If the work required to stretch it 3 ft is 6 ft-lb, then to stretch it 1/2 of that distance, we would need 1/2 of the work, or 6/2 = 3 ft-lb. The work needed to stretch the spring 18 inches beyond its natural length is 3 ft-lb * 18 inches/12 inches/ft = 2.25 ft-lb.
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If m∠XWZ = 90, what is x?
Right angle X W Z is divided into 2 acute angles labeled 5 x plus 5 degrees and 2 x plus 8 degrees.
Answers
Answer: x=11
Step-by-step explanation:
If m∠XWZ = 90 and is divided into 2 acute angles labeled 5x+5 degrees and 2x+8 degrees then the value of x is 11.
Given,
m∠XWZ = 90.
Right angle ∠XWZ is divided into 2 acute angles labeled as:
- 5x + 5 degrees
- 2x + 8 degrees.
We need to find the value of x.
What is an acute angle?An acute angle means angles that are less than 90 degrees.
If an angle is divided, the sum of the divided angles must be equal to the angle divided.
Find the right angle.
m∠XWZ = 90
Find the acute angles that are being divided.
= 5x + 5° and 2x + 8°
Find x.
Since m∠XWZ is divided we have,
90° = 5x + 5° + 2x + 8°
Now,
Add the like terms.
90 = 7x + 13
Subtract 13 on both sides.
90 - 13 = 7x
77 = 7x
Divide both sides by 7.
11 = x
x = 11
We can crosscheck the angles:
90° = 5x + 5° + 2x + 8°
90 = 5x11 + 5 + 2x11 + 8
90 = 55 + 5 + 22 + 8
90 = 60 + 30
90 = 90
Thus if m∠XWZ = 90 and is divided into 2 acute angles labeled 5x+5 degrees and 2x+8 degrees then the value of x is 11.
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The graph represents the cost y (in dollars) to open an online gaming account and buy x games. Write an equation in slope-intercept form that represents the graph
Answers
Answer:
y=10x+15
Step-by-step explanation:
The slope intercept form is represent by this equation
\(y = mx + b\)
Where m is the slope, and b is the y intercept( when x is zero).
Looking at the graph, we already found the y intercept.
When x=0, y is at 15 so our y intercept is 15 so our equation updated look like
\(y = mx + 15\)
Now let find the slope
Slope is
\( \frac{change \: of \: y}{change \: of \: x} \)
Let use two arbitrary points to find the slope
Let use (3,45) and 6,75).
\( \frac{75 - 45}{6 - 3} = \frac{30}{3} = 10\)
So our slope is 10 so our equation look like
\(y = 10x + 15\)
The table for the quadratic functions f(x) and g(x) are given.
x f(x) g(x)
−6 36 4
−3 9 1
0 0 0
3 9 1
6 36 4
Determine the type of transformation and the value of k.
1. g(x) = 3f(x)
2. g(x) = f(3x)
3. g of x equals one third times f of x
4. g of x equals f of one third times x
Answers
The value of k is 1, which is the value of g(x) (and f(x)) when x = -3 or x = 3.
We can determine the type of transformation and the value of k for each of the aforementioned functions using the tables provided for f(x) and g(x).
g(x) = 3f(x) (x)
Here, there occurs a vertical stretch/compression transformation. The function g(x) is a three-fold vertical expansion or contraction of f(x). G(x) has a value of 4, which is identical to the value of k, whether x = -6 or = 6.
g(x) = f(3x) (3x)
Here, there occurs a horizontal stretch/compression transformation. A horizontal stretch or compression of f(x) by a factor of 1/3 results in the function g(x). When x = -3 or x = 3, the value of k is 1, which is also the value of g(x) and f(x).
g(x) = (1/3)f(x) (x)
Here, there occurs a vertical stretch/compression transformation. A vertical stretch or compression of f(x) by a factor of 1/3 results in the function g(x). G(x) has a value of 4, which is identical to the value of k, whether x = -6 or = 6.
g(x) = f(x/3)
Here, there occurs a horizontal stretch/compression transformation. The function g(x) is a three-fold horizontal stretching or compression of f(x). When x = -3 or x = 3, the value of k is 1, which is also the value of g(x) and f(x).
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How do you know if a curve is positive or negative?
Answers
Positive curve graphs will be upward-sloping.
Negative curve graphs will be downward-sloping.
Both graphs in the first image attached below, show curves sloping upward from left to right. As with upward-sloping straight lines, we can say that generally the slope of the curve is positive. While the slope will differ at each point on the curve, it will always be positive.
In the graphs in the second image attached, both of the curves are downward sloping. Straight lines that are downward sloping have negative slopes; curves that are downward sloping also have negative slopes. The slopes change from point to point on a curve, but all of the slopes along these two curves will be negative.
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Straight lines that are downward sloping have negative slopes; curves that are downward sloping also have negative slopes. The slopes change from point to point on a curve, but all of the slopes along these two curves will be negative.
ROC and intro to slopes guided notes:
This graph represents the linear relationship between time and distance for both Car 1 and Car 2.
Slope of Car 1 = 1 Speed of Car 1 = 1 mi
min
Speed of Car 2 = 1 mi 2 min
How can you determine by looking at the graph which car is moving at a faster rate? The the line, the the slope.
Car 1 is moving at a speed than car 2.
Answers
Answer:
Step-by-step explanation:
The steeper the line (graph), the greater the slope and the greater the speed of that particular car. It is instantly obvious that of the two lines shown, the yellow graph has the greater slope and thus the greater speed.
"The steeper the line, the greater the slope(speed). "Car 1 is moving at a speed than car 2."
Answer:
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Step-by-step explanation:
prove that triangle fgh ≅ triangle Ijh
options for 1: Given, Vertical angles are congruent, or linear pair angles are supplementary.
options for 3: same as 1
options for 4: angle-angle- side, Angle-side - angle, Side-angle-side, or SSS
Answers
Answer:
Statements and Proofs
1) m∠G= m∠J=39° | Given
2) FG=IJ=6 | Given
3) ∠GHF≅∠JHI | Vertical angles are congruent.
4) △FGH≅△IJH | Angle-angle-side congruence
I hope this works! Thanks and have a great day!
The triangle FGH ≅ triangle IJH using angle angle side congruency.
In the figure of the triangles FGH and IJH,
Measure of angle G = 39 degree
Measure of angle J = 39 degree
⇒ m ∠G ≅ m ∠J
Measure of side FG = 6 units
measure of IJ = 6 units
⇒FG ≅ IJ
Measure of ∠GHF ≅Measure of ∠IHJ as both are vertically opposite angles.
By applying Angle Angle side congruency,
ΔFGH ≅ΔIJH
Therefore, the triangle FGH and IJH are congruent to each other using Angle Angle side congruency.
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Two buildings are 18.5 meters apart. The angles of elevation from the top of one building to the top of the other is 18 degrees. If the taller building is 15 meters tall, how tall is the shorter building?
Answers
=
110.4
ft
Explanation:
Let the difference in heights of the buildings be
x
ft
The buildings are
200
ft apart - all the way up from the ground to the top of the buildings.
Draw in a triangle joining the tops of the buildings and show the angle of depression as
7
°
Le'ts find
x
:
x
200
=
tan
7
x
=
200
×
tan
7
x
=
24.557
ft
This is the difference in the heights of the buildings.
Height of shorter building =
135
−
24.6
ft
=
110.4
ft
To make bread, 2 teaspoons of yeast are needed for 500 grams of flour. How many teaspoons of yeast are needed for 750 grams of flour?
Answers
Answer:
3 teaspoons.
Step-by-step explanation:
500/2=250 grams per teaspoon
750/250=3
3 teaspoons
write the equation of the line in standard form. slope of 2/3 and passing through the points (-5, 1)
Answers
Answer:
Explanation:
The standard form of a linear equation is
\(Ax+By=C\)However, it is a lot easier if we find the equation in slope-intercept form
\(y=mx+b\)and then rearrange the above equation to write it in standard form.
We are told that the slope of the line is 2/3 which means m = 2/3; therefore, the above equation becomes
\(y=\frac{2}{3}x+b\)Moreover, fro the point (-5, 1) we know that when x = -5, then y = 1; therefore, the above equation gives
\(1=\frac{2}{3}(-5)+b\)Simplifying the above gives
\(1=-\frac{10}{3}+b\)adding 10/3 to both sides gives
\(1+\frac{10}{3}=-\frac{10}{3}+b+\frac{10}{3}\)\(\begin{gathered} \frac{3}{3}+\frac{10}{3}=b \\ \\ \end{gathered}\)\(\therefore b=\frac{13}{3}\)With the value of b in hand, we write the slope-intercept of the equation:
\(y=\frac{2}{3}x+\frac{13}{3}\)Now, to write the above in standard form, we multiply both sides by 3. This cancels out 3 in the denominator on the right-hand side and gives
\(3y=2x+13\)Finally, subtracting 2x from both sides gives
\(3y-2x=13\)Just shift the position of the terms on the left-hand the side and we get
\(\boxed{-2x+3y=13.}\)which is the standard form of our equation!
Fred sold 14 rolls of wrapping paper for a band fundraiser earning the band $17. 50. Sharon sold 16 rolls of wrapping paper and earned $20. 00 for the band. If this relationship is graphed with the number of rolls sold on the x-axis and the money earned on the y-axis, what is the slope of the graph in dollars per roll?.
Answers
Answer: $1.25 Per Roll
Step-by-step explanation:
(14,17.50) and (16,20)
math sucks....who wants the brainlyest???? answer correctly and you'll get it.
Answers
Answer:
Put 1/2x on the line going straight across which is x with is somewhere in between 0 and 1
put -7 on the line going up and down which is y
the second one put it on -1 which is -x going straight across
put 2 on the line going up and down which is y
Step-by-step explanation:
Answer: so y = 1/2 x-7 point is gonna go on 0,-7 and y=-x+2 is gonna be on 0,2....i used desmos.
Step-by-step explanation: Oh and i want brainlest lol...its been a long time so hopefully i get this right lol
Sam bought a Blu-ray disc that normally costs $20. The store was running a sale that was a 15% discount for the
disc. What was the amount of discount Sam got on his disc?
Answers
Answer:
15% of $20 is $3
So the price of his disc was reduced to $3
Step-by-step explanation:
Explain a few ways that placing figures in a coordinate plane can be helpful for solving different problems.
Answers
Use the coordinate plane to graph points, lines, and geometric forms in the different quadrants, and then use the absolute value to determine the distances between them.
What does ordinate math entail?
An exact position of a point in the coordinate plane can be demonstrated using a collection of values called coordinates. Meaning of a Coordinate Plane. The intersection of the x-axis and y-axis, two perpendicular lines that form a 2D plane known as a coordinate plane.
Which three coordinate systems are there?
Cartesian, cylindrical, and spherical are the three most often used coordinate systems. We'll discuss a cylinder-based coordinate system as well as a cartesian-based one in this chapter.
Learn more about co ordinate
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