To find the answers, we can put the numbers as x.
A) f(x)= -2x+7, when f(3)
f(3) = -2(3)+7
=-6+7
=1
Therefore f(3) = 1
B) f(x)= -2x+7, when f(-5)
f(-5)= -2(-5)+7
=10+7
=17
Therefore f(-5) = 17
Hope it helps!
Which is the simplified form of the expression 3(7/5x + 4) - 2(3/2 - 5/4x)
Answer:
Step-by-step explanation:
I think you meant 3([7/5]x + 4) - 2(3/2 - [5/4]x). If that's the case, then identify the LCD: It is 20. Multiply both [7/5]x + 4 and 3/2 - [5/4]x by 20 and then divide the resulting expression by 20:
3(28x + 80) - 2(30 - 25x)
------------------------------------
20
Next, perform the indicated multiplication:
84x + 240 - 60 + 50x
----------------------------------
20
This simplifies to:
34x + 180 17x + 9
---------------- = ----------------
20 10
Next time, please share the answer choices.
Answer:
67x/10 + 9
Step-by-step explanation:
Simplify 7/5x to 7x/5
3(7x/5 + 4) -2(3/2 - 5/4x)
Simplify 5/4x to 5x/4
3(7x/5 + 4) -2(3/2 - 5x/4)
Expand
21x/5 + 12 - 3 + 5x/2
Collect like terms
(21x/5 + 5x/2) + (12 - 3)
Simplify
67x/10 + 9
what expression represents the profit, and what is the profit if 240 cell phones are sold
Answer: $16.850
Step-by-step explanation:
Subtract 2x^2+55x+10 - (2x^2 -15x-40)
70x+50
Then put in 240 for x
What is the first quartile of the data set?
10, 11, 12, 15, 17, 19, 22, 24, 29, 33, 38
A. 12
B. 19
C. 29
D. 10
Answer:
A
Step-by-step explanation:
First find the median of the data set.
The median is the middle value of the data set arranged in ascending order
10, 11, 12, 15, 17, 19, 22, 24, 29, 33, 38
The median = 19
The first quartile ( lower) is the middle value of the data to the left of the median.
10, 11, 12, 15, 17
The first quartile is 12 → A
The total cost of Anja’s trip to the dentist was $628.35. She paid a flat fee of $89.95 which included the checkup and cleaning and then had 4 cavities filled, each of which cost the same amount. Which shows the correct equation and value of x, the cost of each cavity filling?
Answer:
89.95 + 4x =628.35
x = 134.60
Step-by-step explanation:
The trip to the dentist had a flat fee plus 4 cavities for a total cost of 628.35
fee + 4 * cost of cavity = 628.35
Let x = the cost of each cavity
89.95 + 4x =628.35
Subtract 89.95 from each side
89.95-89.95 + 4x =628.35-89.95
4x =538.40
Divide each side by 4
4x/4 =538.40/4
x =134.60
Choices to pick are : y=3x
And y=2x+2 can someone please help out ??
Answer:
y = 2x + 2
Step-by-step explanation:
Start at point (2, 6).
Go up 2 units up (rise = 2) and 1 unit right (run = 1). Now you are at point (3, 8) which is on the graph.
slope = rise/run = 2/1 = 2
The slope of the graph is 2. m = 2
Now look at point (0, 2). The y-intercept is 2. b = 2
The equation is
y = mx + b
y = 2x + 2
Answer:
y = 2x + 2
Step-by-step explanation:
Here we're asked to come up with a linear function relating x and y.
First we find the slope of the line. As we move from (0, 2) to (3, 8), x increases by 3 and y by 6. Thus, the slope is
m = rise / run = 6 / 3 = 2.
Plugging givens into the slope-intercept formula y = mx + b, we find b:
2 = 2(0) + b, so that b = 2.
Then the desired relationship between x and y is y = 2x + 2.
what is equivalent to (3 root 8^1/4 x) ?
Answer:
The given expression is equivalent to 3(2^(3/8))x.
Step-by-step explanation:
The given expression (3 root 8^1/4 x) can be written as:
3√(8^(1/4))x
we know that 2^3 = 8
= 3√(2^(3/4))x
We know that √x = (x)^(1/2)
= 3(2^((3/4)(1/2))x
Powers multiply with each other, 3*1/4*2 = 3/8
= 3(2^(3/8))x
A direct variation function contains the points (-9, -3) and (-12, 4). Which equation represents the function"
y=-3x
0 y=-
Oy
y = 3x
You are measuring the height of a statue. You stand 10 feet from the base of the statue. You measure the angle of elevation from the ground to the top of the statue to be 76 degrees find the height h of the statue to the nearest foot
Answer:
h = (10 ft)(4.01) = 40.1 ft
Step-by-step explanation:
The tangent function relates this elevation to the horizontal distance (10 ft) and the angle of elevation (76 degrees):
opp h
tan 76 degrees = --------- = ------------- = 4.01
adj 10 ft
Therefore , h = (10 ft)(4.01) = 40.1 ft
Answer: 40 ft
Step-by-step explanation:
You can find the height of the statue by solving the right triangle.
In this case the adjacent side of the triangle is the horizontal distance to the statue (10 ft). The height of the statue is the opposite side to the angle of 76 °.
By definition, the tangent of an angle is:
[tex]tan(\theta) = \frac{opposite}{adjacent}[/tex]
In this case
[tex]\theta=76\°\\\\opposite = h\\\\adjacent = 10\ ft[/tex]
Therefore
[tex]tan(76) = \frac{h}{10}[/tex]
[tex]h=tan(76) * 10\\\\h=40\ ft[/tex]
Find the equation in slope-intercept form of a line with slope –2 and y-intercept 4.
Question 10 options:
a)
y = -2x
b)
y = 4x -2
c)
y = -2x+4
d)
y = 2x-4
Answer:
c)
Step-by-step explanation:
-2 is the slope so that y equals -2x and the y intercept is positive 4 so that the equation is y=-2x+4
Answer:
c) y = -2x+4
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
Substituting in
y = -2x +4
Which equation is equivalent to..
Answer:
D
Step-by-step explanation:
[tex]1/3)^{x}[/tex] = [tex]\frac{1}{3^{x} }[/tex] = [tex]3^{-x}[/tex]
and
[tex]27^{x+2}[/tex] = [tex](3^{3})^{x+2}[/tex] = [tex]3^{3(x+2)}[/tex] = [tex]3^{3x+6}[/tex]
Hence expression D is equivalent
What does Pythagoras’ famous theorem involve? A. pentagons B. polygons C. triangles D. rectangles
Answer:
C. triangles
Step-by-step explanation:
Pythagoras Theorem is a theorem which states you can work out a side of a right - angled triangle using the other 2 sides. Pythagoras will not work on shapes except from a right - angled triangle and square
which expression is equivalent to 2(a+3) when a=3
Answer:
12
Step-by-step explanation:
2(a+3)
Given a = 3, all you need to do is just plug in a = 3 into the expression
2(3 + 3)
= 2 (6)
= 12
Answer:
2(3+3)
6x2
12
Step-by-step explanation:
A sphere and a cylinder have the same radius and height the volume of the cylinder is 18cm3 what is the volume
Answer:
The volume of the sphere is 24 cm³
Step-by-step explanation:
* Lets explain the difference between the cylinder and the sphere
- The cylinder has two circular bases and a curved surface
- The bases of the cylinder have radius r and the curved surface has
a height h
- The volume of the cylinder = area of its base × its height
∵ The area of the circle is πr²
∴ The volume of the cylinder is V = π r² h
- A sphere is a perfectly round geometrical object in three-dimensional
space
- It the set of points that are all at the same distance r from a given point
that means its radius equals its height
- The volume of the sphere = 4/3 π r³
* Now lets solve the problem
∵ The cylinder and the sphere have the same radius and height
∵ The volume of the cylinder is 18 cm³
- Lets equate the rule of the volume of the cylinder by 18
∵ The volume of the cylinder = π r² h
∴ π r² h = 18 ⇒ divide both side by π
∴ r² h = 18/π
- The sphere and the cylinder have the same radius and height
∴ The radius and height of the sphere have the same value of the
cylinder
∵ The the height of the sphere is its radius
∴ r²h of the cylinder = r³ in the sphere
∴ r³ = 18/π
- Substitute this value in the rule of the volume of the sphere
∵ The volume of the sphere = 4/3 π r³
∴ The volume of the sphere = 4/3 π (18/π) ⇒ cancel π's
∴ The volume of the sphere = 4/3 (18) = 24 cm³
* The volume of the sphere is 24 cm³
Can anyone help me? Factorise: 81m^2-1
Answer:
(9m-1)(9m+1)
Step-by-step explanation:
This is a difference of squares
(9m)^2-1^2
Use a^2-b^2=(a-b)(a+b)
So the answer is (9m-1)(9m+1)
Answer:
81m² - 1 = (9m - 1)(9m + 1)Step-by-step explanation:
[tex]81m^2-1=9^2m^2-1^2=(9m)^2-1^2\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(9m-1)(9m+1)[/tex]
5x + 1y + 4z=-1
4x + 6y +9z= -68
9x + 1y + 4z = 27
Select one:
(7,-4, -8)
(-4,-8, 7)
(-8, -7, -4)
(-7,4, -8)
(-7, -4, -8)
Answer:
[7, -4, -8]
Step-by-step explanation:
Just simply plug in each choice into the equations to confirm their authenticities.
Please helpppp .......
Answer:
It would be (-2,11)
Step-by-step explanation:
I used desmos for this, since it says graphing.
desmos.com/calculator/glijhd4ksg
look at the link to view the graph and solution.
Normally, you would plot points from one line, connect them, then do the same for the other line.
Hope this helps!
When using a graph to find the solution you must look at where the lines intersect. Look at the graph provided below:
As you can see the graph below shows that the two lines intersect at point (-2, 11)
Hope this helped!
~Just a girl in love with Shawn Mendes
Which of the following shows the correct graph and solution of the system
y=-4x+2 and y + 2x = 0?
solution = (1.-2)
solution =(-1.-2)
solution
(-1.2)
solution - (1.-2)
Answer:
solution = (1.-2)
Step-by-step explanation:
put x= 1 and y = -2 in this system : y=-4x+2 and y + 2x = 0
you have : - 2 = - 4(1)+2 and -2 +2(1)=0
-2=-2 and 0=0 .....right
The required solution of the given system of equations is (1, -2), and a graph of the solution has been shown.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
y=-4x+2 - - - -(1)
y + 2x = 0 - - - (2)
Equating equations,
-4x +2 = -2x
x = 1
Put x = -2 in equation 1
y = -4(1) + 2
y = -2
Thus, the required solution of the given system of equations is (1, -2).
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What would X= to?
(89)
(39)
(26)
To solve this you must use Pythagorean theorem:
[tex]a^{2} +b^{2} =c^{2}[/tex]
a and b are the legs (the sides that form a perpendicular/right angle)
c is the hypotenuse (the side opposite the right angle)
In this case...
a = 5
b = 8
c = x
^^^Plug these numbers into the theorem
[tex]5^{2} +8^{2} =x^{2}[/tex]
simplify
25 + 64 = [tex]x^{2}[/tex]
89 = [tex]x^{2}[/tex]
To remove the square from x take the square root of both sides to get you...
√89 = x
(choice A)
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
The correct answer is first option √89
Step-by-step explanation:
Points to remember
Pythagorean theorem
For a right triangle,
Base² + Height² = Hypotenuse²
To find the vale of x
From the figure we can see a right triangle,
Base = 8 units and height = 5 units
Hypotenuse² = Base² + Height²
x² = 8² + 5²
= 64 + 25
= 89
x = √89
The correct answer is first option √89
Angle D is a circumscribed angle of circle O. what is the perimeter of kite OBDE?
Answer:
27
Step-by-step explanation:
Answer:
27 units on edge.
what is the vertex form of f(x) = x2 + 6x + 3
Answer: [tex]y=(x +3)^2 -6[/tex]
Step-by-step explanation:
The equation of a parabola in Vertex form is:
[tex]y=a(x-h)^2+k[/tex]
Where [tex](h,k)[/tex] is the vertex of the parabola
We can rewrite the function [tex]f(x)= x^2 + 6x + 3[/tex] as:
[tex]y= x^2 + 6x + 3[/tex]
In order to convert it into vertex form we need to Complete the square:
Take the coefficient of the x term, divide it by 2 and square it:
[tex](\frac{6}{2})=3^2[/tex]
Add and subtract 3² on the right side:
[tex]y= x^2 + 6x+3^2 + 3-3^2[/tex]
Now we must convert the right side to a squared expression, then we get:
[tex]y=(x +3)^2 -6[/tex]
square the following numbers 4 6 13 10
Answer:
16 36 169 100
Step-by-step explanation:
just square them
16, 36, 169, 100
square of 4
[tex]4^{2}=16[/tex]
square of 6
[tex]6^{2}=36[/tex]
square of 13
[tex]13^{2}=169[/tex]
square of 10
[tex]10^{2} = 100[/tex]
In the mathematics squaring is easy to understand. Squaring the number means multiplying it by itself. Squaring is written on mathematical symbols by putting a two above the number you are squaring to show that it is multiplied two times
What does it mean if you square something in math?acceleration, or length per square timecross section (physics), the area-dimensioned quantitycoupling constant (has square charge in the denominator, or may be expressed with square distance in the numerator)kinetic energy (quadratic dependence on velocity)specific energy, the (square velocity)-dimensioned quantityLearn more about square here https://brainly.com/question/14198272
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What is the ordered pair of X′ after point X (3, 4) is rotated 180°?
Answer with explanation:
Pre image= Coordinates of point X= (3,4)
When point ,(x,y) is rotated by an angle of 180°, then coordinates of image that is point (x,y) after rotation = (-x, -y)
⇒≡Coordinates of point X(3,4) after rotation by an angle of 180°=X'(-3,-4)
The coordinates after a rotation of 180 degrees about the origin is: X'(-3, -4)
How to find the transformation?There are different types of transformation such as:
Translation
Rotation
Reflection
Dilation
The transformation rule for the rotation about 180 degrees (180°) about the origin is (x,y)→(−x,−y) .
Thus:
X(3, 4) → X'(-3, -4)
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What is the solution to the system of equations?
y = 1/3x - 10
2x + y = 4
A) (-8,6)
B) (-6, 16)
C) (6,-8)
D) (16, -6)
ANSWER
C) (6,-8)
EXPLANATION
The equations are:
[tex]y = \frac{1}{3}x - 10[/tex]
and
[tex]2x+y=4[/tex]
We substitute the first equation into the second equation to get:
[tex]2x + \frac{1}{3}x - 10 = 4[/tex]
We multiply through by 3 to get:
[tex]6x + x - 30= 12[/tex]
Group similar terms,
[tex]6x + x = 30 + 12[/tex]
[tex]7x = 42[/tex]
Divide both sides by 7 to get,
[tex]x = \frac{42}{7} = 6[/tex]
Put this value of x into the first equation to get;
[tex]y = \frac{1}{3} (6) - 10[/tex]
[tex]y = 2 - 10 = - 8[/tex]
select the quadratic function with a graph that has the following features
x-intercept at (8,0)
y-intercept at (0,-32)
maximum value at (6,4)
axis of symmetry at x=6
A. f() = 1/2 x2 +6 - 32
B.f() = -x2 + 12x -32
C.f() = 1/2 x2 + 6x -16
D f() = -x2 + 12x -6
Answer:
Option B [tex]f(x)=-x^{2}+12x-32[/tex]
Step-by-step explanation:
we know that
For the given values, the quadratic function is a vertical parabola open downward (vertex is a maximum)
The equation in vertex form is equal to
[tex]f(x)=a(x-h)^{2} +k[/tex]
where
(h,k) is the vertex
a is a coefficient
we have
(h,k)=(6,4)
so
[tex]f(x)=a(x-6)^{2} +4[/tex]
Find the value of a
For x=8, y=0 -----> the y-intercept
substitute
[tex]0=a(8-6)^{2} +4[/tex]
[tex]0=a(2)^{2} +4[/tex]
[tex]0=4a +4[/tex]
[tex]a=-1[/tex]
substitute
[tex]f(x)=-(x-6)^{2} +4[/tex]
Convert to standard form
[tex]f(x)=-(x^{2}-12x+36) +4[/tex]
[tex]f(x)=-x^{2}+12x-36+4[/tex]
[tex]f(x)=-x^{2}+12x-32[/tex]
The graph in the attached figure
The number of potato chips in a bag is normally distributed with a mean of 75 and a standard deviantion of 5. Approximately what percent of bags contain between 65 and 85 potato chips?
a. 68%
b. 75%
c. 95%
d. 99.7%
The percentage of bags contain between 65 and 85 potato chips is 95%.
Step-by-step explanation:
A probability distribution that is symmetric and the data near the mean are more frequent than far is known as a normal distribution. Normal distributions are important in statistics and are often used to represent real-valued random variables.
The formula for finding the percentage of bags using normally distributed is given as
f(x) = (1 / sigma * square root 2 *pi) * e^((-1/2)*((x-u)/sigma))
Substituting the values of mean and standard deviation,
The percentage of bags contain between 65 and 85 potato chips is 95%.
Final answer:
Using the empirical rule, approximately 95% of potato chip bags will contain between 65 and 85 chips, as this range spans two standard deviations away from the mean in a normal distribution.
Explanation:
The question is regarding the percentage of potato chip bags that contain a specific number of chips based on a normal distribution. With a mean of 75 and a standard deviation of 5, the range of chips in the bags is between 65 and 85. To find this percentage, we use the empirical rule, sometimes referred to as the 68-95-99.7 rule, which states that approximately 68% of the data within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
Since the range from 65 to 85 chips spans two standard deviations from the mean (65 is 10 chips away from 75 which is two standard deviations as 5*2=10, and the same logic applies for 85), we can say that approximately 95% of the bags will contain between 65 and 85 potato chips.
Evaluate B2 for B = 9.
B^2 for B = 9 means squaring the value of 9, resulting in 9^2, which equals 81. Therefore, B^2 for B = 9 is 81.
To evaluate B^2 for B = 9, you simply substitute the value of B into the expression and then perform the calculation. Here's how it's done:
B^2 means "B squared," which is equivalent to multiplying B by itself. So, for B = 9, we have:
[tex]\(B^2 = 9^2 = 9 \times 9\)[/tex]
Now, calculate the product:
[tex]\(9 \times 9 = 81\)[/tex]
So, B^2 for B = 9 is equal to 81.
In summary, when you substitute B = 9 into the expression B^2, you get 9^2, which equals 81. Therefore, B^2 for B = 9 is 81.
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what is the value of expression -225 divided (-15)
Answer:
15
Step-by-step explanation:
-225/-15 = 15
A negative divided by a negative is a positive
225/15 = 15
Answer:
15
Step-by-step explanation:
The value of expression -225 divided (-15) :
-225/-15 = 15
Brooke found the equation of the line passing through the points (–7, 25) and (–4, 13) in slope-intercept form as follows.
Question:
What was Brooke’s error?
•She found the incorrect slope in step 1.
•She mixed up the x- and y-coordinates when she plugged in the point in step 2.
•She found the incorrect y-intercept in step 2.
•She mixed up the slope and y-intercept when she wrote the equation in step 3.
For this case we have that by definition, the equation of a line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
[tex]m = \frac {y2-y1} {x2-x1}[/tex]
We have the following points:
[tex](x1, y1): (- 7,25)\\(x2, y2): (- 4,13)[/tex]
Substituting the values:[tex]m = \frac {13-25} {- 4 - (- 7)} = \frac {-12} {- 4 + 7} = \frac {-12} {3} = - 4[/tex]
Thus, the line is of the form:
[tex]y = -4x + b[/tex]
We substitute one of the points and find "b":
[tex]13 = -4 (-4) + b\\13 = 16 + b\\b = 13-16 = -3[/tex]
Finally we have to:
[tex]y = -4x-3[/tex]
Answer:
The equation es [tex]y = -4x-3[/tex]
Answer:
She mixed up the slope and y-intercept when she wrote the equation in step 3.
Type the correct answer in each box. If necessary, round your answers to the nearest tenth.
Use the conversion formulas for Celsius and Fahrenheit to find the missing values in the table.
Temperature
Degrees Celsius Degrees Fahrenheit
10
87
Answer:
Part 1) [tex]10\°\ C=50\°\ F[/tex]
Part 2) [tex]87\°\ F=30.6\°\ C[/tex]
Part 3) [tex]-5\°\ C=23\°\ F[/tex]
Part 4) [tex]10\°\ F=-12.2\°\ C[/tex]
Step-by-step explanation:
we know that
The formula to convert degrees Celsius to degrees Fahrenheit is equal to
[tex]F=(\frac{9}{5}C)+32[/tex]
The formula to convert degrees Fahrenheit to degrees Celsius is equal to
[tex]C=(F-32)\frac{5}{9}[/tex]
Part 1) we have
10 degrees Celsius
Convert to degrees Fahrenheit
[tex]F=(\frac{9}{5}10)+32[/tex]
[tex]F=50\°[/tex]
Part 2) we have
87 degrees Fahrenheit
Convert to degrees Celsius
[tex]C=(87-32)\frac{5}{9}[/tex]
[tex]C=30.6\°[/tex]
Part 3) we have
-5 degrees Celsius
Convert to degrees Fahrenheit
[tex]F=(\frac{9}{5}(-5))+32[/tex]
[tex]F=23\°[/tex]
Part 4) we have
10 degrees Fahrenheit
Convert to degrees Celsius
[tex]C=(10-32)\frac{5}{9}[/tex]
[tex]C=-12.2\°[/tex]
Answer:
Degree Celsius: Degree Fahrenheit:
10 50
30.6 87
-5 23
-12.2 10
Step-by-step explanation:
Hope this helps!!
which equation represents an exponential function that passes through the point 2,36
Answer:
f(x)=4(3)^2
(2,36)
36=4(3)^2
36=4(9)
36=36
Step-by-step explanation:
Answer: Hi! here you want a function that pases through the point (2,36)
it means, a function f(x) so f(2) = 36.
Also, f(x) must be an exponential function, this means that f(x) = [tex]a^{x}[/tex]
where a is a real number.
then [tex]a^{2}[/tex] = 36
so a = [tex]\sqrt{36}[/tex] = ± 6.
then your function can be f(x) = [tex]-6^{x}[/tex] or [tex]6^{x}[/tex].
Notice that i used a very simplest example of exponential function. You actually can found lots of exponential functions F(x) that passes through the point (2,36).