Answer:
300-6x
Step-by-step explanation:
Trust me
A child’s building set contains a brick with dimensions 63 x 31 x 18mm . Assume this brick is a replica of a real brick that has a greatest side length of 23 cm, determine the surface area and volume of the real brick. (Please can someone help me )
The surface area and volume of the real brick will be 983.2 cm²and 1738.11 cm³ respectively.
What is volume?The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic cm.
The scale factor is ;
r = 630 cm /23
r = 27
L = 23 cm
b = 310 / 27 = 11.48 cm
h = 180/27 = 6.6 cm
The surface area of the brick;
A = 2(lb+bh+hl)
A = 2( 23 ×11.48+11.48×6.6+6.6×23)
A= 983.2 cm²
The volume of the brick is;
V= lbh
V=23 × 11.45 ×6.6
V=1738.11 cm³
Hence the surface area and volume of the real brick will be 983.2 cm² and 1738.11 cm³ respectively.
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What is another way to write
MP
Answer:
I am not completely sure if this is correct, but I believe the answer should be PM.
This is because the order of the letters that represents a point can be swapped, since they are still forming the same line.
The graph below shows the solution to which system of inequalities?
OA. y> 2 and y≤ x
B. x> 2 and y≤ x
C. y≥ 2 and y< x
D. y≤ 2 and y< x
Answer:
C
Step-by-step explanation:
The horizontal line, y=2, is solid and shaded above, so it represents
[tex]y \geqslant 2[/tex]
The slanted line, y=x is dashed and shaded below, so it represents y<x.
Find the maxima and minima of the following function:
[tex]\displaystyle f(x) = \frac{x^2 - x - 2}{x^2 - 6x + 9}[/tex]
To find the maxima and minima of the function, we need to calculate the derivative of the function. Note, before the denominator is a perfect square trinomial, so the function can be simplified as
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f(x) = \frac{x^2 - x - 2}{(x - 3)^2}} \end{gathered}$}[/tex]
So the derivative is:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f'(x) = \frac{(2x - 1)(x - 3)^2 - 2(x - 3)(x^2 - x - 2)}{(x - 3)^4} } \end{gathered}$}[/tex]
Simplifying the numerator, we get:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f'(x) = \frac{(x - 3)(-5x + 7)}{(x - 3)^4} = \frac{-5x + 7}{(x - 3)^3} } \end{gathered}$}[/tex]
The function will have a maximum or minimum when f'(x) = 0, that is,
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f'(x) = \frac{-5x + 7}{(x - 3)^3} = 0 } \end{gathered}$}[/tex]
which is true if -5x + 7 = 0. Then x = 7/5.
To determine whether x = 7/5 is a maximum, we can use the second derivative test or the first derivative test. In this case, it is easier to use the first derivative test to avoid calculating the second derivative. For this, we evaluate f'(x) at a point to the left of x = 7/5 and at a point to the right of it (as long as it is not greater than 3). Since 1 is to the left of 7/5, we evaluate:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f(1) = \frac{-5 + 7}{(1 - 3)^3} = \frac{2}{-8} < 0} \end{gathered}$}[/tex]
Likewise, since 2 is to the right of 7/5, then we evaluate:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \displaystyle \bf{\frac{-10 + 7}{(2 - 3)^3} = \frac{-3}{-1} > 0} \end{gathered}$}[/tex]
Note that to the left of 7/5 the derivative is negative (the function decreases) and to the right of 7/5 the derivative is positive (the function increases).
The value of f(x) at 7/5 is:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f\left(\tfrac{7}{5}\right) = \frac{\tfrac{49}{25} - \tfrac{7}{5} - 2}{\tfrac{49}{25} - 6 \cdot \tfrac{7}{5} + 9} = -\frac{9}{16} } \end{gathered}$}[/tex]
This means that [tex]\bf{\left( \frac{7}{5}, -\frac{9}{16} \right)}[/tex] is a minimum (and the only extreme value of f(x)).
[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
Answer:
[tex]\text{Minimum at }\left(\dfrac{7}{5},-\dfrac{9}{16}\right)[/tex]
Step-by-step explanation:
The local maximum and minimum points of a function are stationary points (turning points). Stationary points occur when the gradient of the function is zero. Differentiation is an algebraic process that finds the gradient of a curve.
To find the stationary points of a function:
Differentiate f(x)Set f'(x) = 0Solve f'(x) = 0 to find the x-valuesPut the x-values back into the original equation to find the y-values.[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $y=\dfrac{u}{v}$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=\dfrac{v \dfrac{\text{d}u}{\text{d}x}-u\dfrac{\text{d}v}{\text{d}x}}{v^2}$\\\end{minipage}}[/tex]
[tex]\text{Given function}: \quad \text{f}(x)=\dfrac{x^2-x-2}{x^2-6x+9}[/tex]
Differentiate the function using the Quotient Rule:
[tex]\text{Let }u=x^2-x-2 \implies \dfrac{\text{d}u}{\text{d}x}=2x-1[/tex]
[tex]\text{Let }v=x^2-6x+9 \implies \dfrac{\text{d}v}{\text{d}x}=2x-6[/tex]
[tex]\begin{aligned}\implies \dfrac{\text{d}y}{\text{d}x} & =\dfrac{(x^2-6x+9)(2x-1)-(x^2-x-2)(2x-6)}{(x^2-6x+9)^2}\\\\& =\dfrac{(2x^3-13x^2+24x-9)-(2x^3-8x^2+2x+12)}{(x^2-6x+9)^2}\\\\\implies \text{f}\:'(x)& =\dfrac{-5x^2+22x-21}{(x^2-6x+9)^2}\\\\\end{aligned}[/tex]
Set the differentiated function to zero and solve for x:
[tex]\begin{aligned}\implies \text{f}\:'(x)& =0\\\\\implies \dfrac{-5x^2+22x-21}{(x^2-6x+9)^2} & = 0\\\\-5x^2+22x-21 & = 0\\\\-(5x-7)(x-3) & = 0\\\\\implies 5x-7 & = 0 \implies x=\dfrac{7}{5}\\\\\implies x-3 & = 0 \implies x=3\end{aligned}[/tex]
Put the x-values back into the original equation to find the y-values:
[tex]\implies \text{f}\left(\frac{7}{5}\right)=\dfrac{\left(\frac{7}{5}\right)^2-\left(\frac{7}{5}\right)-2}{\left(\frac{7}{5}\right)^2-6\left(\frac{7}{5}\right)+9}=-\dfrac{9}{16}[/tex]
[tex]\implies \text{f}(3)=\dfrac{\left(3\right)^2-\left(3\right)-2}{\left(3\right)^2-6\left(3\right)+9}=\dfrac{4}{0} \implies \text{unde}\text{fined}[/tex]
Therefore, there is a stationary point at:
[tex]\left(\dfrac{7}{5},-\dfrac{9}{16}\right)\:\text{only}[/tex]
To determine if it's a minimum or a maximum, find the second derivative of the function then input the x-value of the stationary point.
If f''(x) > 0 then its a minimum.If f''(x) < 0 then its a maximum.Differentiate f'(x) using the Quotient Rule:
Simplify f'(x) before differentiating:
[tex]\begin{aligned}\text{f}\:'(x) & =\dfrac{-5x^2+22x-21}{(x^2-6x+9)^2}\\\\& = \dfrac{-(5x-7)(x-3)}{\left((x-3)^2\right)^2}\\\\& = \dfrac{-(5x-7)(x-3)}{(x-3)^4}\\\\& = -\dfrac{(5x-7)}{(x-3)^3}\\\\\end{aligned}[/tex]
[tex]\text{Let }u=-(5x-7) \implies \dfrac{\text{d}u}{\text{d}x}=-5[/tex]
[tex]\text{Let }v=(x-3)^3 \implies \dfrac{\text{d}v}{\text{d}x}=3(x-3)^2[/tex]
[tex]\begin{aligned}\implies \dfrac{\text{d}^2y}{\text{d}x^2} & =\dfrac{-5(x-3)^3+3(5x-7)(x-3)^2}{(x-3)^6}\\\\& =\dfrac{-5(x-3)+3(5x-7)}{(x-3)^4}\\\\\implies \text{f}\:''(x)& =\dfrac{10x-6}{(x-3)^4}\end{aligned}[/tex]
Therefore:
[tex]\text{f}\:''\left(\dfrac{7}{5}\right)=\dfrac{625}{512} > 0 \implies \text{minimum}[/tex]
Use the multiplication law for logarithm to expand the following expression:[tex]log_{8} (21)[/tex]
- worth 20pt
Answer:
[tex]\log_8{(3)} + \log_8{(7)}[/tex]
Step-by-step explanation:
Product Rule for Logarithms
[tex]\log_b{(mn)} = \log_b{(m)} + \log_b{(n)}[/tex]
Instead of 21 you can write 3 · 7, because 21 = 3 · 7.
[tex]\log_8{(21)} = \\= \log_8{(3 \cdot 7)} =\\= \log_8{(3)} + \log_8{(7)}[/tex]
Under her cell phone plan, Sarah pays a flat cost of $69 per month and $4 per gigabyte. She wants to keep her bill at $83.80 per month. Write and solve an equation that can be used to determine g, the number of gigabytes of data Sarah can use while staying within her budget.
Answer:
83.80 = 69 + 4x
x = 3.7
Sarah can use up to 3.7 gigabytes per month to stay within her budget
Step-by-step explanation:
83.80 = 69 + 4x
14.8 = 4x
x = 3.7
The number of gigabytes of data Sarah can use while staying within her budget is 3.7 gigabyte.
Given that, Sarah pays a flat cost of $69 per month and $4 per gigabyte.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of gigabyte be g.
69+4g=83.80
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Now, 4g=83.80-69
⇒ 4g=14.8
⇒ g=14.8/4
⇒ g=3.7 gigabyte
Therefore, the number of gigabytes of data Sarah can use while staying within her budget is 3.7 gigabyte.
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What are the zeros of this function?
Can someone explain this?
Answer:
false
Step-by-step explanation:
if the 2 shorter segments dont add up to be equal or greater to the longest segment, then its impossible for a triangle to be formed :)
Answer:
True
Step-by-step explanation:
General formulas and concepts:
Subject: Geometry
Unit: Triangular Line Segments
Definitions:
Triangle Inequality Theorem
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.Steps:
Use the triangle inequality theorem:
9 + 4 > 11
13 > 11 ⇒ True
9 + 11 > 4
20 > 4 ⇒ True
4 + 11 > 9
15 > 9 ⇒ True
Conclusion:
Because the 3 segments that are given satisfy the statements of the triangle inequality theorem, they can therefore form a triangle.
Which statement could be used to explain why f(x) = 2x – 3 has an inverse relation that is a function?
The graph of f(x) passes the vertical line test.
f(x) is a one-to-one function.
The graph of the inverse of f(x) passes the horizontal line test.
f(x) is not a function.
If g(x) is the inverse of f(x), what is the value of f(g(2))?
–6
–3
2
5
Answer:
1st q answer is f(x) is one- to -one function and 2nd q answer is 2
Answer:
1) f(x) is one - to - one function2) 2Step-by-step explanation:
inverse of f(x)Let f(x) = y
y = 2x - 3
x = y + 3 / 2
inverse of f(x) = x + 3 / 2
g(x) = inverse of f(x)f [g(2)]
f [2+3/2]
f [5/2]
(2×5/2)-3
5-3
= 2
Therefore f [g(2)] = 2What is the solution to the system of equation
Answer:
[tex]x=(-2,\frac{5}{3} )[/tex]
Step-by-step explanation:
1) We will use the matrix method to solve this problem.
[tex]\left[\begin{array}{ccc}-2/3&1&3\\1&0&-2\\\end{array}\right][/tex]
2) Swap Row₁ and Row₂ to make row reduction easier.
[tex]\left[\begin{array}{ccc}1&0&-2\\-2/3&1&3\\\end{array}\right][/tex]
3) Apply to Row₂ : Row₂ + [tex]\frac{2}{3}[/tex] Row₁.
[tex]\left[\begin{array}{ccc}1&0&-2\\0&1&5/3\end{array}\right][/tex]
4) Simplify rows.
[tex]\left[\begin{array}{ccc}1&0&-2\\0&1&5/3\\\end{array}\right][/tex]
Note: The matrix is now in row echelon form.
The steps below are for back substitution.
5) Apply Row₁ : Row₁ - 0 Row₂.
[tex]\left[\begin{array}{ccc}1&0&-2\0\\0&1&5/3\end{array}\right][/tex]
6) Simplify rows.
[tex]\left[\begin{array}{ccc}1&0&-2\\0&1&5/3\\\end{array}\right][/tex]
Note: The matrix is now in reduced row echelon form.
7) Therefore,
[tex]x=-2\\x=\frac{5}{3}[/tex]
What trigonometric ratio would you use to find the distance from the base of the tower of your keys ? Identify your choice, then calculate the distance
The choice is tangent rule and the distance from the base to the tower is 3. 98 meters
How to determine the distanceThe trigonometric ratio to use is
tan α = opposite side/ adjacent side
This is so because the angle 86° is facing the side of the distance from the top to the base
The choice is tangent rule
adjacent = x
Angle = 86°
Opposite side = 57
We have
tan 86° = 57/x
14. 300= 57/x
x = 57 ÷ 14.300
x = 3.98meters
Thus, the choice is tangent rule and the distance from the base to the tower is 3. 98 meters
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what is the square root of 36/196
√36/169
Answer:
The square root of 36/196 is 3/7.
The square root of 36/169 is 6/13.
What is the slope of = -x +7 ?
Answer:
I assume you meant "y = -x+7" not "= -x +7". If that is correct then the slope is -1.
Step-by-step explanation:
The slope is the coefficient of the x in slope-intercept form. Therefore, the slope is -1.
Please give me Brainliest if this answer is correct.
Which statement best explains the relationship
between lines AB and CD?
They are parallel because their slopes are equal.
• They are parallel because their slopes are negative
reciprocals.
They are not parallel because their slopes are not
equal.
They are not parallel because their slopes
are
negative reciprocals.
Answer:
They are parallel because their slopes are equal.
Step-by-step explanation:
See attached image.
Work out (6 × 10²) ÷ (3 × 105)
Give your answer in standard form.
Answer: 40/21
Step-by-step explanation:
[tex]3 \times 105=315\\\\6 \times 10^{2}=600\\\\\implies \frac{6 \times 10^{2}}{3 \times 105}=\frac{600}{305}=\boxed{\frac{40}{21}}[/tex]
Jamaal knows that it is certain that he will win the election because he is the only person who is running for class treasurer. which value represents the probability that he will win the election? 0 one-fourth three-fourths 1
The correct answer is option D which is the probability is 1.
The complete question is given below:-
Jamaal knows that it is certain that he will win the election because he is the only person who is running for class treasurer. Which value represents the probability that he will win the election?
0
1/4
3/4
1
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
The probability of Event E is given by,
P = favourable outcomes / Total outcomes
Jamaal is the only candidate running in the class treasurer election.
There for Total No. of outcomes = 1
Here Event E is Jamaal winning the Election.
So, No. of favorable outcome = 1
P(E) = 1 / 1
P(E) = 1
This type of event is called a SURE EVENT Because the probability of a sure event is always 1.
The Probability of Jamaal winning the election is 1. So, Option D is correct.
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The probability that he will win the election will be 1. Then the correct option is D.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
The value of the probability of an event will be varying from zero to one.
Jamaal knows that it is certain that he will win the election because he is the only person who is running for class treasurer.
Then the probability that he will win the election will be
If the event will certainly happen, then the probability will be one.
P = 1
Then the correct option is D.
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Find x and y.
help please ty:)
Please, make sure you understand the solution:
We can notice that x + (x - 28) = 90
2x - 28 = 90
2x = 118
x = 59
Now for y:
We can notice that y + 90 + x = 180
y + 90 + 59 = 180
y + 149 = 180
y = 180 - 149
y = 31
Find the missing side of each triangle. Leave your answers in simplest radical form.
2√3 m
A) √ 19 m
c) √5 m
O a
a
Ob b
Oc
√7m
C
Od d
B) √17 m
D) √√2 m
Answer:
C [tex]\sqrt{5}[/tex]
Step-by-step explanation:
Use pythagorean theorem.
[tex]x^{2}[/tex] +[tex]\sqrt{7} ^{2}[/tex] = (2[tex]\sqrt{3}) ^{2}[/tex]
[tex]x^{2}[/tex] + 7 = 12 Subtract 7 from both sides
[tex]x^{2}[/tex] = 5 Take the square root of both sides to solve
x = [tex]\sqrt{5}[/tex]
What must be the value of x so that lines a and b are parallel lines cut by transversal f? 10 20 22 32.
Answer: Option 3 or C. 22
Step-by-step explanation:
I got the answer correct on Edge 2022 quiz. Trust me the answer is correct I screenshot it using the prt sc key then uploaded it. The proof is in the pic below. :)
The sum of the reciprocals of the first four consecutive positive integers is greater than two. What is the least number of consecutive positive integers necessary to make the sum of the reciprocals greater than three?
The least number of consecutive positive integer that is required to make the sum of the reciprocals greater than three is 7.
What is an integer?An integer is simply a number that is not a fraction.
The first four consecutive positive integers are:
1, 2, 3 , 4.
Their reciprocals are:
1/1, 1/2, 1/3, 1/4; and
The sum of them are greater than 2; that is
1/1 + 1/2 + 1/3 + 1/4 = 2.08333333333 > 2
to make the expression >3
We would require the following integers
1/1 + 1/2 + 1/3 + 1/4+ (1/5) + (1/6) + (1/7) + (1/8)+ (1/9) + (1/10) + (1/11) = 3.01987734488
Thus, the additional consecutive reciprocal integers that is required to make the sum of the reciprocal of the fist four greater than 3 is 7.
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Based on an architectural drawing, a roof slopes to a drain along the function represented in the table that defines the edge of slope, where x is the horizontal distance in feet and f(x) is the vertical distance in feet.
If the drain is at the minimum point, how far is it from the wall defined by the y-axis?
0 feet
8 feet
80 feet
160 feet
The distance from the wall defined by the y-axis will be 8 feet. Then the correct option is B.
What is the equation of line?The equation of line is given as
y = mx + c
Where m is the slope and c is the y-intercept.
The table is given below.
Then the equation of the line will be
(y – 8) = [(8 – 6) / (0 – 20)](x – 0)
y = -0.1x + 8
If the drain is at the minimum point.
Then the distance from the wall defined by the y-axis will be 8 feet.
Then the correct option is B.
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Drag a statement or reason to each box to complete this proof.
Given: Quadrilateral ABCD with m∠A=(7x)°, m∠B=(5x)°, m∠C=(7x)°, and m∠D=(5x)°.
Prove: x = 15
2) [tex]m\angle A+m\angle B+m\angle C+m\angle D=360^{\circ}[/tex]
3) Substitution property
4) Combine like terms
Two measures of two supplementary angles are in the ratio of 2.3 find the measurments of the two angles.
Answer:
The angles are 72° and 108°
Step-by-step explanation:
Supplementary angles add up to 180°
Ratio of supplementary angles = 2 : 3
The angles are 2x , 3x
2x + 3x = 180
5x = 180
x = 180 ÷ 5
x = 36°
2x = 2*36 = 72°
3x = 3*36 = 108°
which statements about square roots are true ?check all that apply
Point A is located at (−2, 2), and point M is located at (1, 0). If point M is the midpoint of segment AB, find the location of point B.
(−0.5, 1)
(4, −2)
(−5, 4)
(−1, 1)
Answer:
B. (4, -2)
Step-by-step explanation:
Please see attachment.
Hope this helps!
If not, I am sorry.
Identify the method that will be used to solve for x for each equation.
4x = 20
x 119
5x + 6x = 22
5(x - 2) = 30
The solution of the equation 4x = 20, x – 11 = 9, 5x + 6x = 22, and 5(x – 2) = 30 will be 5, 20, 2, and 8.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
The equations are given below.
4x = 20
x = 5
x – 11 = 9
x = 20
5x + 6x = 22
11x = 22
x = 2
5(x – 2) = 30
x – 2 = 6
x = 8
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please please help ME!!!
Answer:
720 Course Schedules
Step-by-step explanation:
When you choose the first course, there are 6 to choose from. When you scoose the second, there are only 5. This keeps going until the 6th course where there is only 1 choice.
You multiply these choices together. You should get 6×5×4×3×2×1
6×5=30
30×4=120
120×3=360
360×2=720
720×1=720
You then end up with 720 course schedules.
18 A student has 273 matchsticks with which to make a pattern of nested triangles. Fig. 18.9 shows the first three triangles. Fig. 18.9 If all the matchsticks are used, how many matchsticks will each side of the biggest triangle contain? 18 A student has 273 matchsticks with which to make a pattern of nested triangles . Fig . 18.9 shows the first three triangles . Fig . 18.9 If all the matchsticks are used , how many matchsticks will each side of the biggest triangle contain ?
The number of matchsticks that each side of the biggest triangle contains is; 137 matchsticks
How to find the biggest side of a triangle?We know that for a diagram to be a triangle, then two smallest sides must not be greater than the third side.
Now, if there are 273 matchsticks, then the greatest side of the triangle must not be less than 273/2 = 136.5 ≈ 137
Thus, the largest side will have at least 137 matchsticks
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what is the measure of this angle
Answer:
135
Step-by-step explanation:
Depending on where you start, the protractor can read in different ways. Since the measure of this angle started from the left, you read the numbers at the top. If the measure would have started from the right, you read the numbers below.
A good rule of thumb is that if the angle appears to be greater than 90 degrees, or an obtuse angle, you would choose the only answer choice that is above 90 degrees.
Hope this helps!
Select two ratios that are equivalent to 2 : 9.
Choose 2 answers:
9:2
1881
12:54
18:4
20:45
