I cannot say that I am entirely sure of the answer so let me know if it doesn't make sense, but I will try to explain as best as I can nonetheless.
1. The graph of f''(x) represents the graph of the second derivative of f(x). Now, we know that the graph is continuous and decreasing. I think that the most important thing here is to mentally visualise the graph - if it is decreasing and has an x-intercept at x = -3, then we can say the following:
a) for all values of x before -3, f''(x) is positive
b) at x = -3, f''(x) is 0
c) for all values of x after x = -3, f''(x) is negative
2. What this means in terms of the graph f'(x) is the following:
a) for values of x less than -3, the gradient of the graph of f'(x) is positive and becoming less positive as x reaches 0
b) at x = -3, the gradient of the graph of f'(x) is 0
c) for values of x more than -3, the gradient of the graph of f'(x) is negative and becoming more negative as x reaches ∞
With this in mind, maybe try drawing a quick sketch to guide you (I would include one here but I have trouble adding attachments so I hope you'll forgive my lack of one) - it could perhaps look something similar to -(x + 3)^2 (but wouldn't be restricted to this - remember, it is just a visual aid).
3. Now, we need to work from the graph of f'(x) to the graph of f(x).
What we need to notice is that the graph of f'(x) takes the form of a concave down graph - this means that the gradient of the graph of f(x) immediately to either side of x = -3 changes from being either:
a) + >> ++ >> +++ >> ++ >> +
(Here, the number of + symbols signifies the strength of the positive gradient. >> represents an arrow.
So, the gradient starts off less positive, becomes more positives, reaches its peak, and then becomes gradually less positive again - imagine this being represented by f'(x) = -(x + 3)^2 + 5 (again, remember this is just a visual aid) )
b) --- >> -- >> - >> -- >> ---
(Likewise, the number of - symbols signifies the strength of the negative gradient.
So, the gradient starts off very negative, becomes less negative, reaches its peak, and then gradually becomes more negative again - you can see that this is effectively the same pattern as above: there is an increasing trend and then a decreasing trend. You can imagine this as being represented by the graph f'(x) = -(x + 3)^2 - 5)
c) -- >> - >> 0 >> - >> --
(Here, the gradient is negative, becomes less negative, reaches 0, then gradually becomes more negative - again, there is the same increasing trend followed by a decreasing trend. You can imagine this as being represented by the graph f'(x) = -(x + 3)^2)
It is this increasing trend in the gradient up to x = -3 followed by a decreasing trend that is crucial to take note of - this signifies that there is a point of inflection at x = -3. What we must remember here is that a point of inflection is characterised by a change in the curvature of the graph - either from concave up to concave down or from concave down to concave up. In our case, this would be a transition from concave up to concave down as the gradient gradually becomes more positive until it reaches its highest value at x = -3 and then gradually becomes less positive. Thus, we can say that answer B (the graph of f has an inflection point at x = -3) is correct.
Looking at the other answers:
A - The graph of f cannot be always concave down since there is a clear change in the gradient from less positive to more positive to less positive again (if it were always concave down the gradient would just gradually become more negative)
C - A relative minimum is characterised by the fact that the gradient to the left of the minimum is negative, the gradient at the minimum is 0, and the gradient to the right of the minimum is positive. Since this isn't the case for our graph, this is not the correct answer.
D - This is only a viable answer if none of the others are correct; since we have identified B as correct, this is incorrect.
I hope this helped but if you have any questions or problems with my working, please don't hesitate to comment below.
The correct statement about the function is,
⇒ The graph of f is always concave down.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Since, We have to given that;
The graph of f’’(x) is continuous and decreasing with an x-intercept at
x = - 3 .
We know that;
⇒ f(x) is a function then the solutions to the equation f′(x) = 0 gives the maximum and minimum values to f(x)
Hence, The value of x gives maximum if f′′(x) is negative and minimum if f′′(x) is positive.
- Inflection points of the function f(x) are found the solutions of the equation f′′(x) = 0
- The graph of f'(x) is continuous means that the graph is unbroken line
- The graph of f'(x) decreasing with an x-intercept at x = 2 means f'(2) = 0
- The differentiation of a function equal to zero at the critical point (minimum or maximum) of the function
Since, f'(x) = 0 at x = 2
Hence, The x-coordinate of the critical point of f(x) is 2
Now, If the differentiation of the function is decreasing, then the critical point of the function is maximum point.
Since, f'(x) is decreasing
Hence, The critical point of the f(x) is maximum point
That means the slope of curve is negative
Hence, The graph of f is concave down at x = 2
Thus, The correct answer is the graph of f is always concave down.
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Can someone plz help me
Answer:
a = 6, b = 5, c = 3
Step-by-step explanation:
Given
[tex]\frac{1}{6}[/tex] ÷ [tex]\frac{3}{5}[/tex]
Leave the first fraction, change division to multiplication and turn the second fraction upside down, that is
[tex]\frac{1}{6}[/tex] × [tex]\frac{5}{3}[/tex]
Compare with
[tex]\frac{1}{a}[/tex] × [tex]\frac{b}{c}[/tex]
To obtain a = 6, b = 5 and c = 3
a car had 3/4 of a tank and used 1/8 of a tank.how much is left?
336 dollar is divided between A&B so that A gets 5/16th of what B gets.What amount does A get???
Answer:
80 dollars.
Step-by-step explanation:
Let the amount that A get be [tex]x[/tex] dollars.
B will get the rest of the 336 dollars. That will be [tex]336 - x[/tex] dollars.
[tex]\displaystyle \frac{5}{16}[/tex] of what B get will be the same as what A gets. In other words,
[tex]\displaystyle \frac{5}{16}(336-x) = x[/tex].
Add [tex]\displaystyle \frac{5}{16}x[/tex] to both sides of the equation:
[tex]\displaystyle \frac{5}{16}\times 336 = (1 + \frac{5}{16})x[/tex].
[tex]\displaystyle x = \frac{\displaystyle \frac{5}{16}\times 336}{\displaystyle 1 + \frac{5}{16}} = 80[/tex].
In other words, A gets 80 dollars.
Answer:
80
Step-by-step explanation:
Evaluate the expression when a=3 and b=4
2
2a+ b =
The answer you are looking for could either be 16 or 40. To solve the equation, you would follow the steps of PEMDAS. Since the 2 above the equation is an exponent, you'd first solve there.
Fill in "a" and "b", the equation will now say 2^2 * 3 + 4 = ?. Assuming that the exponent is meant to go with the 2 alone, 2 * 2 = 4. This leaves the equation to say 4 * 3 + 4 = ? Multiply 3 and 4 to get 12, then add 4 to get 16.
OR
Fill in "a" and "b". This time, we're assuming that the exponent is going with 2 * 3 (originally 2a). Multiply 2 and 3 to get 6, then square 6 to get 36. Finally, add 4 to 36 to get 40.
I'm not quite sure where the exponent was meant to go, but I hope this helps!
Look for a pattern in the table to determine which model best describes the data.
exponential function
not a function
linear function
quadratic function
Answer:
linear function
Step-by-step explanation:
What is the value of x?
A. 52
B.60
C.86
D.26
Answer:
26
Step-by-step explanation:
x is a degree so it can't be no more then 60 so the angle should be 26
The value of x is 60 degrees, as determined through a series of geometric deductions based on the properties of triangles and semicircles. Here option B is correct.
The sum of the angles in a triangle is 180 degrees.
The sum of the angles in a semicircle is 180 degrees.
The angle opposite to the diameter of the circle is 90 degrees.
Therefore, the angle x in the first triangle is 180 - 90 - 52 = 38 degrees.
The angle x in the second triangle is 180 - 38 - x = 142 - x degrees.
The angle x in the second triangle is also equal to the angle x in the semicircle, which is 180 - 52 - x = 128 - x degrees.
Equating the two expressions for the angle x in the second triangle, we get 142 - x = 128 - x.
Solving for x, we get x = 60 degrees. Here option B is correct.
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Which of the following is a solution of y - x > -3?
(6, 2)
(2, 6)
(2, -1)
Answer:
(2, 6)
Step-by-step explanation:
For each of the 3 given points, substitute the coordinates into y - x > -3 and determine whether the resulting inequality is true or false:
(6, 2): 2 - 6 > - 3, or -4 > -3. This is FALSE, so (6, 2) is not a solution.
(2, 6): 6 - 2 > - 3, or 4 > -3. This is TRUE, so (2, 6) is a solution.
Answer: (2,6)
Step-by-step explanation:
The coordinates are in the form (x,y)
(6,2) 2-6=-3, -3≡-3 thus not the answer
(2,6) 6-2=3, 3>-3
(2,-1) -1-2=-3, -3≡-3 thus not the answer
Hope it helped!
find the distance between the points (6,-4) and (0,5)
Answer:
d = 10.8167
Step-by-step explanation:
The distance between two points can be easily found by using the following expression
d = √((x1-x2)^2 + (y1-y2)^2)
where
(x1,y1) = (6,-4)
(x2,y2) = (0,5)
d = √((6-0)^2 + (-4-5)^2)
d = √(36 + 81)
d = √(117)
d = 10.8167
Answer:
The distance between the points (6,-4) and (0,5) = 10.82 units
Step-by-step explanation:
Points to remember
Distance formula
Length of a line segment with end points (x1, y1) and (x2, y2) is given by,
Distance = √[(x2 - x1)² + (y2 - y1)²]
To find the distance between given points
Here, (x1, y1) = (6, -4) and (x2, y2) = (0, 5)
Distance = √[(x2 - x1)² + (y2 - y1)²]
= √[(0 - 6)² + (5 - -4)²]
=√[(-6)² + (9)²]
= √[36 + 81]
= √[117
= 10.82
The distance between the points (6,-4) and (0,5) = 10.82 units
I need help!
can someone help me?
thank you
Answer:
12
Step-by-step explanation:
For the sake of showing work I will replace the empty space with an x like so...
[tex]\frac{1}{6} =\frac{2}{x}[/tex]
To find out what x is you must cross multiply (aka butterfly)
1*x = 2*6
1x = 12
x = 12
***If you don't understand the "cross multiply" technique let me know in the comments and I'll be happy to explain.
To make these fractions equivalent the empty spot must be 12
[tex]\frac{1}{6} = \frac{2}{12}[/tex]
Hope this helped!
~Just a girl in love with Shawn Mendes
Please help! Answers are on the image attached!
Answer:
The exact values of sin2Ф and cos2Ф are as follows:
sin2Ф = 0.8983
cos2Ф = 0.4394
Step-by-step explanation:
sin Ф = 9/17 = perp/hyp = y/r
we know that:
r² = x²+y²
17² = x² + 9²
x² = 208
x = 4√13
cos Ф = base/hyp = x/r = (4√13)/17
Solving sin2Ф
we know that:
sin2Ф = 2 sinФ cosФ
= 2*(9/17)*((4√13)/17)
= (72√13)/289
= 0.8983
Solving cos2Ф:
we know that:
cos2Ф = 1 - 2sin²Ф
= 1 - 2(9/17)²
= 1 - 0.5606
= 0.4394
Find the volume and surface area of the following solid:
A Hemisphere attached on top of a cylinder.
I'm not sure if the picture resolution is clear for everyone to see and understand, so I'll describe its properties as well:
Hemisphere 's radius=7cm
Cylinder's height= 10cm
Cylinder 's radius= 7cm
Total height of the solid= 17cm
Please help me out with this question. I am in dire need of the answer, as my finals are nearing.
If there is any confusion with the question, please ask me. I'll be glad to elaborate.
Thank you.
Step-by-step explanation:
Here,
radius of hemisphere and cylinder(r)=7 cm
height of the cylinder(h)= 10 cm
Now the volume of cylinder(V1) is,
[tex]\pi {r}^{2} h \\ = \pi \times {7}^{2} \times 10 \\ = 1540 \: {cm}^{3} \\ [/tex]
And the volume of hemisphere(V2) is,
[tex] \frac{2}{3} \pi {r}^{3} = \frac{2}{3} \times \pi \times {7}^{3} \\ = 718.67 \: {cm}^{3} [/tex]
Total volume=V1+V2=1540+718.67= 2258.67 cu.cm
Surface area of cylinder(A2)=
[tex]2\pi \: rh + 2\pi {r}^{2} = 2\pi \: r(h + r) \\ = 2 \times \pi \times 7 \times (10 + 7) \\ = 44 \times 17 \\ = 748 \: {cm}^{2} [/tex]
Surface area of hemisphere(A2)=
[tex]2\pi {r}^{2} = 2 \times \pi \times {7}^{2} = 308 \: {cm}^{2} [/tex]
Then total Surface area=A1+A2
=748+308=1056 sq.cm
1. First, let us find the volume. Now the total volume is simply given by adding the volume of the cylinder to that of the hemisphere.
Let us revisit the formulas for the volume of a cylinder and hemisphere.
Cylinder: V = πr^(2)h
Hemisphere: V = (2/3)πr^3
Thus, the total volume is given by πr^(2)h + (2/3)πr^3
Using the values provided in the diagram, we can now say that:
Total volume = π(7)^(2)*10 + (2/3)π(7)^3
= 490π + 686π/3
= 2156π/3 cm cubed
Using π = 22/7, we can now see that:
Total volume = 2156*(22/7) / 3
= 2258.67 cm cubed (to two decimal places)
2. Now let's find the total surface area. Let's review the formulas for total surface area for a cylinder and a hemisphere:
Cylinder: SA = 2πr^2 + 2πrh (this is the area of the top and bottom, plus the area of the rectangle that is wrapped around)
However, since the top of the cylinder is covered by the hemisphere, we don't need to count its area in the surface area, thus we must use SA = πr^2 + 2πrh
Hemisphere: SA = πr^2 + 2πr^2 = 3πr^2 (this is the area of the bottom of the hemisphere plus the area of half of the sphere)
However, since the bottom of the hemisphere is on the cylinder, we don't count this in the total surface area either, therefor we must use SA = 2πr^2
Thus, total surface area is given by:
πr^2 + 2πrh + 2πr^2
= 3πr^2 + 2πrh
Now we can substitute the values of the radius and cylinder height into the formula above. So:
TSA = 3πr^2 + 2πrh
TSA = 3π(7)^2 + 2π(7)(10)
= 147π + 140π
= 287π cm squared
Using π = 22/7, we can now see that:
TSA = 287*(22/7)
= 902 cm squared
at a local soccer game, 6/7 of the people were fans. one-half of those fans were wearing hats. what fraction of the people was wearing hats?
What is 3log2 x-(log2 3-log2 (x+4)) written as a single logarithm?
Answer:
log_2((x^4+4x^3)/3)
Step-by-step explanation:
First step would be distribute that - into the ( )
3log_2(x)-log_2(3)+log_2(x+4)
Now take care of coefficients of the logs... bring them up as powers of the inside
log_2(x^3)-log_2(3)+log_2(x+4)
or
+log_2(x^3)-log_2(3)+log_2(x+4)
Now for the product and quotient rule! If it has a + in front of it, it will go on top. If it has a - in front of it, it will go on bottom.
Like this:
log_2 (x^3(x+4)/3)
or
log_2((x^4+4x^3)/3)
So inside that log base 2 thing the top is x^4+4x^3
and that bottom is 3
Answer:
[tex]log_{2}(\frac{x^{3}(x+4)}{3})[/tex].
Step-by-step explanation:
[tex]3log_{2}x-(log_{2}3-log_{2}(x+4))[/tex]
[tex]log_{2}x^{3}-log_{2}(\frac{3}{x+4})[/tex]
[tex]log_{2}(\frac{x^{3}}{\frac{3}{x+4}})[/tex]
[tex]log_{2}(\frac{x^{3}(x+4)}{3})[/tex].
Please help. Choose the equation that represents the graph below:
to get the equation of a straight line, all we need is two points on it... say hmmm this one has (0 , 6) and (6 , 2), so let's use those.
[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{2-6}{6-0}\implies \cfrac{-4}{6}\implies -\cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-6=-\cfrac{2}{3}(x-0) \\\\\\ y-6=-\cfrac{2}{3}x\implies y=-\cfrac{2}{3}x+6[/tex]
classify the system of equations -1/2x=3-y -7+y=1/2x-2
Answer: Inconsistent.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
Solve for "y" in each equation:
Equation 1
[tex]-\frac{1}{2}x=3-y\\\\y=\frac{1}{2}x+3[/tex]
Equation 2
[tex]-7+y=\frac{1}{2}x-2\\\\y=\frac{1}{2}x-2+7\\\\y=\frac{1}{2}x+5[/tex]
You can notice that the slope of the Equation 1 is:
[tex]m_1=\frac{1}{2}[/tex]
And the slope of the Equation 2 is:
[tex]m_2=\frac{1}{2}[/tex]
Observev that [tex]m_1=m_2[/tex], then you can conclude that the lines are parallel and the System of equations has No solution.
When there is no solution the classification of the system of equations is: "Inconsistent".
Typically a point in a three dimensional Cartesian coordinate system is represented by which of the following
Answers in the picture !
Answer: B (x, y, z)
Step-by-step explanation:
In a two-dimensional plane, a coordinate is represented as (x, y).
In a three-dimensional plane, a coordinate is represented the same as the two-dimensional plane, except we need to add the third coordinate (z).
--> (x, y, z)
Answer:
B. (x,y,z).
Step-by-step explanation:
We represent the coordinate of a point in one dimension as x on the line. We represent the coordinate of a point in two dimension (plane) as (x,y). Similarly we represent the coordinate of a point which lie in the space (three dimension) as (x,y,z) .Here x is the x-coordinate of the point,
y is the y-coordinate of the point,
and z is the z-coordinate of the point. Hence (x,y,z) represent a point a point in a three dimensional Cartesian System.
Divide 1,485/0.09. Please help me
Answer:
The answer is 16,500
Step-by-step explanation:
Answer:
THE ANSWER IS 16500!
Step-by-step explanation:
hopes this helped
Find the product. -3x^ 3(-2x^ 2 + 4x + 7)
6x6 - 12x4 + 21x3
6x5 - 12x4 - 21x3
6x5 + 12x4 + 21x3
For this case we must find the product of the following expression:[tex]-3x ^ 3 (-2x ^ 2 + 4x + 7)[/tex]
We apply distributive property to the terms within parentheses:
[tex](-3x ^ 3 * -2x ^ 2) + (- 3x ^ 3 * 4x) + (- 3x ^ 3 * 7) =[/tex]
We take into account that:
[tex]- * - = +\\- * + = -[/tex]
To multiply powers of the same base, put the same base and add the exponents.
[tex]6x ^ {3 + 2} -12x ^ {3 + 1} -21x ^ 3 =\\6x ^ 5-12x ^ 4-21x ^ 3[/tex]
Answer:
Option B
The circumference of Z is 104 cm. What is the length of xy (the minor arc)?
A. 13 cm
B. 416 cm
C. 52 cm
D. 208 cm
E. 6.5 cm
F. 26 cm
A full circle is 360 degrees.
XY is 45 degrees.
Multiply the circumference by the fraction of the angle:
104 x (45/360) = 13
The answer is A. 13 cm.
Answer:
Arc length = 13 cm.
Step-by-step explanation:
Given : A circle with circumferences = 104 cm , central angle = 45°.
To find : what is the length of arc AB.
Solution : We have given circle with circumference = 104 cm , central angle = 45°.
Arc length = [tex]\frac{theta }{360} * circumference[/tex].
Plug the values circumference = 104 cm , central angle = 45°.
Arc length = [tex]\frac{45 }{360} * 104[/tex].
Arc length = 0.125 * 104
Arc length = 13 cm .
Therefore, Arc length = 13 cm.
Which set of angle measures could be the measures of the interior angles of a triangle?
• 90°, 42°, and 58°
60°, 60°, and 60°
LO 100°, 48°, and 42°
31°, 75°, and 70°
Answer:
B
Step-by-step explanation:
The sum of the 3 interior angles of a triangle = 180°
Check the sums of the given sets of angles
90° + 42° +58° = 190° ≠ 180° ← not valid
60° + 60° + 60° = 180° ← Valid
100° + 48° + 42° = 190° ← not valid
31° + 75° + 70° = 176° ← not valid
Answer:
The answer is
60°, 60°, and 60°
What is the domain of the function graphed below?
Answer:
X<7
Step-by-step explanation:
It would be x is less than or equal to 7 if the dot to the far right was filled in. The furthest point to the left is an arrow meaning it continues.
Using it's concept, it is found that the domain of the function graphed is given by x < 7.
What is the domain of a function?It is the set that contains the input values for the function. In a graph, it is given by the values of the x-axis.
In this problem, to the left, there is an arrow, hence the function is calculated for all values of x to negative infinity. To the right, there is an open circle at x = 7, hence the domain is x < 7.
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Find the height h of the parallelogram.
1.5 units
1.125 units
1.175 units
The area of a parallelogram is base times height. Each side can be a base, and has a particular height associated with it.
Here the height associated with the 1.5 base is 2.7, and the height associated with the 3.6 base is h. So
[tex]1.5(2.7)=3.6 h[/tex]
[tex]h=15(27)/360= 1.125[/tex]
Answer: 1.125 units
Without the necessary details related to the parallelogram's area or base and side lengths, it is impossible to calculate the precise height of the parallelogram. The snippets provided relate to different mathematical problems and do not apply to the calculation of a parallelogram's height.
Explanation:To find the height h of the parallelogram, we have several different pieces of information provided in the snippets, and each one appears to address a distinct mathematical problem. However, none of the given pieces align directly with calculating the height of a parallelogram.
To calculate the height of a parallelogram, usually the area and the base length are given, or you would use trigonometric relationships if angles and side lengths are known. Since none of these crucial pieces of information are provided, we will focus on demonstrating a general approach to solve such a problem through a proportion method that was mentioned:
Set up a proportion to find the height of the actual model.
For example, if a scale model uses a 1 cm height to represent 0.5 m in reality, and the actual height in the model is 75 cm, then using the proportion:
1 cm / 0.5 m = 75 cm / x m Cross multiply to solve for x. 1x = 0.5 × 75 x = 37.5 m
This approach would yield the height x in the actual model. However, we cannot precisely find the height h of the provided parallelogram without specific details related to its area or base and side lengths.
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The density of a fish tank is 0.4 fish over feet cubed . There are 12 fish in the tank. What is the volume of the tank?
Answer:
=30 ft³
Step-by-step explanation:
From the scenario given the formula for density of the fish pod is
ρ= no. of fish/ volume
Making volume the subject of the formula we obtain the following equation:
Therefore volume = no.of fish/ρ
Using the values provided in the question:
=12 fish/0.4 fish/ft³
=30 ft³
= 4.8
Answer:
Step-by-step explanation:
Volume = 30 ft³
density = population/area
.4 = 12/ft³
(.4)(ft³) = 12/ft³ × ft³/1
.4 ft³ = 12
.4ft³ /.4 = 12/.4
ft³ = 30
30 ft³
28 POINT QUESTION!!
will give you brainliest for right answer!!
For the inverse variation equation p= 8/v what is the value of V when p = 4?
I’ve seen a lot of answers between C & D & I need to know asap!!!
Answer:
C
Step-by-step explanation:
[tex]p = \frac{8}{v} [/tex]
when we plug in 4 for P
we want to multiply V to (8/V) and 4 to get rid of the fraction
then we get
[tex]4v = 8[/tex]
we want V by itself so we defide 8 by 4.
8/4 should be simplified.
so we end up with 2.
For Bill's birthday his mom is bringing donuts to school.
She has a coupon to get 2 1/2 dozen donuts for $8.00.
How much would just one dozen donuts cost at this price?
36 donuts (2 1/2 dozen) = $8.00
So, you divide 8 by 36 and you get about 22¢ for each donut. Then, you do .22 x 12 which equals $2.64.
One dozen donuts = $2.64
The cost of the one dozen donuts will be $2.64.In one dozen their is 12 donuts.
What is an arithmetic operation?Arithmetic is an area of mathematics involving the study of numbers and the different operations that can be performed on them.
[tex]\rm 1 \ dozen = 12 \ donuts \\\\ 2\frac{1}{2} dozen = 2\frac{1}{2} \times 12\\ \\\\ 2\frac{1}{2} dozen = 36 \ donuts[/tex]
36 donuts= $8.00
1 donuts = $ 0.22
1 dozen donuts cost = 12 × $ 0.22
1 dozen donuts cost = $ 2.64
Hence,the cost of the one dozen donuts will be $2.64.
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9 Peter walked 8,900 feet from home to school.
1 mile = 5,280 feet
How far, to the nearest tenth of a mile, did he walk?
[tex]\bf \begin{array}{ccll} miles&feet\\ \cline{1-2} 1&5280\\ x&8900 \end{array}\implies \cfrac{1}{x}=\cfrac{5280}{8900}\implies 8900=5280x \\\\\\ \cfrac{8900}{5280}=x\implies 1.6856\approx x\implies \stackrel{\textit{rounded up}}{1.7=x}[/tex]
Answer:
I would try 1.7
A painter needs 5 gallons of paint to finish a house. He has 3 quarts and 1 pint. How much more paint does he
need?
Make a Selection:
A. 3 gallons
B. 4 gallons, 1 pint
C. 3 gallons, 1 pint
D. 4 gallons, 1 quart
NEXT >>
Answer:
4 1/4 gallons
Step-by-step explanation:
5 gallons are needed.
Convert one gallon into quarts and one quart into pints.
3 quarts and 2 pints, minus 3 quarts and 1 pint.
The result is 4 gallons and 1 pint.
He needs 4 galloons and 1 pint .
What is Unit Conversion?The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.
Given:
A painter needs 5 gallons of paint to finish a house.
He has 3 quarts and 1 pint.
Now, Convert one gallon into quarts and one quart into pints.
3 quarts and 2 pints
= 0.75 + 0.125
= 0.875 gallons
So, amount of paint needs = 5- 0.875
= 4.125
Hence, 4 gallons and 1 pint paint does he need.
Learn more about Unit Conversion here:
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Which arrow do I follow left or right?
6 < k
k is greater then 6. That means that you will go to the right of 6. This will show that k can be any number larger then 6
Hope this helped!
~Just a girl in love with Shawn Mendes
Solve for x with steps.
Answer:
no real solution is the answer
If you have to list your extraneous solutions somewhere, that would be x=0.
Step-by-step explanation:
Cool thing here is the radical, the thing with the square root, is already isolate.
So we need to square both sides as a first step. (Whenever you raise both sides to even power, you must definitely check your solutions as some might not actually be solutions to the original equation)
So upon squaring both sides I get:
x^4+16=(x^2-4)^2
Now I will write (x^2-4)^2 as (x^2-4)(x^2-4) and foil it! This gives me:
x^4+16=x^4-8x^2+16
Subtract x^4 and 16 on both sides:
0=-8x^2
Divide both sides by -8
0=x^2
Therefore x=0.
0 isn't actually a solution though because when you plug it in you get 4=-4 which is not true.
what is the domain of f(x) = log2(x + 3) + 2?
Answer:
(-3, infinity)
Step-by-step explanation:
The domain of the log function is (0, infinity). In other words, x must be greater than 0.
To determine the domain of f(x) = log2(x + 3) + 2, we set (x + 3) greater than 0 and solve for x: That set is x > -3, or (-3, infinity).
Answer:
the answer is x>-3