let's say the number is "a", so
[tex]\stackrel{doubled}{2a}~~ \stackrel{decreased}{-} ~~\stackrel{by~this~much}{13.7} ~~ \stackrel{greater~than}{ > } ~~ 125.28 \\\\\\ 2a > 125.28-13.7\implies 2a > 111.58\implies a > \cfrac{111.58}{2}\implies a ~~ > ~~ 55.79[/tex]
Answer:
56
Step-by-step explanation:
Solving Linear Equations: Variable on One Side
ssignment Active
Determining the Input Value That Produces the Same Output
Value for Two Functions
If f(x) = -3x + 4 and g(x) = 2, solve for the value of x
for which f(x) = g(x) is true.
ty
X =
y = f(x)
y = g(x)
x
2 3
Done
-2
Intro
-1
4
3
2
1
1
answer 2/3
check the attachments for more info
hope it helps :)
The functions f(x) and g(x) are equal for the x = 2/3
What is a function?A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given that, are two functions, f(x) = -3x + 4 and g(x) = 2, we need to find the value of x for which both are equal,
So,
For f(x) = g(x) we should equate the two functions to get the value of x.
f(x) = g(x)
-3x + 4 = 2
-3x + 4 - 4 = 2 - 4
-3x = -2
Dividing by -3 on both sides;
(-3x)/-3 = (-2)/-3
x = 2/3
Hence, the functions f(x) and g(x) are equal for the x = 2/3
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Solve for D: 70D + 6 - 9D= 35 + 4D - 20.
Answer:
The answer is D = 9/57
Step-by-step explanation:
Get the variable D by itself as stated to solve for D.
I got the other numbers to the other side.
70D + 6 - 9D = 35 + 4D - 20.
(70D - 9D - 4D) = (35 - 20 - 6)
57D = 9
D = 9/57
identify the matrix transformation of angle TUV, which has coordinates T(0,1), U(1,2), and V(2,0) for 90 degree rotation clockwise. Then identify the correct vertices of the image
9, 16, 23, ...
Find the 46th term.
Answer:
324
Step-by-step explanation:
Formula: [tex]a_{n} =a_{1} +(n-1)d[/tex]
=> [tex]a_{46} =9_{1} +(n-1)7\\[/tex]
= [tex]9_{1} +(46-1)7\\[/tex]
= [tex]9+(45)7\\[/tex]
= [tex]9+315[/tex]
= [tex]324[/tex]
:D
x y
-1 -10
3 14
Complete the slope-intercept form of the linear equation that represents the relationship in the table.
to get the equation of any straight line, we simply need two points off of it, let's use the ones in the table.
[tex]\begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} -1&-10\\ 3&14\\ \cline{1-2} \end{array}\hspace{5em} (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-10})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{14}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{14}-\stackrel{y1}{(-10)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-1)}}} \implies \cfrac{14 +10}{3 +1}\implies \cfrac{24}{4}\implies 6[/tex]
[tex]\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-\stackrel{y_1}{(-10)}=\stackrel{m}{6}(x-\stackrel{x_1}{(-1)}) \\\\\\ y+10=6(x+1)\implies y+10=6x+6\implies y=6x-4[/tex]
A line, y mx + b, passes through the point (2, 3) and is parallel to y 2x + 5. What is the value of b?
Answer:
Step-by-step explanation:
If a line is parallel to another it must have the same slope
The slope/intercept form of a line is y = mx + b where m is the slope and b the y intercept
The line y = 2x + 5 has slope 2
So the slope of the line that passes through (2,3) must also have the slope 2
We have
y = 2x + b; Substituting x =2, y =3 in this equation gives us
3 = 2 (2) + b or b = -1
Hence the equation of the line is
y = 2x -1
Cross-check
Substitute for x = 2 ==> y = 2(2) - 1 = 3 which is consistent
If Bank A charges a monthly service
fee of $2.50 and a per-check fee of
$0.15, while Bank B charges a
monthly service fee of $4 and a per-
check fee of $0.05, which bank will
charge a customer more in fees if
she writes 18 checks per month, and
by how much?
The bank which will charge a customer more in fees if she writes 18 checks per month, and by how much is Bank A by $0.30
How to write and solve equation?let
x = number of checksBank A = 2.50 + 0.15x
= 2.50 + 0.15(18)
= 2.50 + 2.7
= $5.20
Bank B = 4 + 0.05x
= 4 + 0.05(18)
= 4 + 0.9
= $4.9
Difference in charges = $5.20 - $4.90
= $0.30
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What is the volume of the cylinder below?
-----
-
2112
O O
A. 408 units3 B. 2448 units3
O
C. 204772 units 3
O
D. 20471 units
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve ~
We need to find volume of the given Cylinder, with information :
radius (r) = 12 units height (h) = 17 units[tex]\qquad \sf \dashrightarrow \:Volume_{(Cylinder)} = \pi r²h[/tex]
[tex]\qquad \sf \dashrightarrow \:Volume_{(Cylinder)} = \pi \sdot(12) {}^{2} \sdot17[/tex]
[tex]\qquad \sf \dashrightarrow \:Volume_{(Cylinder)} = \pi \sdot144{}^{} \sdot17[/tex]
[tex]\qquad \sf \dashrightarrow \:Volume_{(Cylinder)} = 2448 \pi \: \: unit {}^{3} [/tex]
So, correct choice is B
The volume of the given cylinder is 2448π cubic units
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
We have to find the volume of the given cylinder
Radius is 12 units
Height is 17 units
Volume of cylinder= πr²h
Plug in the values of radius and height
Volume = π×12²×17
=π×144×17
=2448π cubic units
Hence, the volume of the given cylinder is 2448π cubic units
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Khloe goes to a store an buys an item that costs xx dollars. She has a coupon for 15% off, and then a 8% tax is added to the discounted price. Write an expression in terms of xx that represents the total amount that Khloe paid at the register.
Answer:
0.93x
Step-by-step explanation:
the total amount is:
x(1-15%+8%)=0.93x
so the answer is 0.93x
5 ⟌94.3
108.86
18.86
188.6
18.68
Answer:
18.86
Step-by-step explanation:
5 ⟌94.3
90 ÷ 5 = 18
18
5 ⟌94.3
-90
-----------------
4.3
cant divide by 4 so add a decimal
5 × 0.8 = 4
18.8
5 ⟌4.3
- 4.0
---------------
0.3
5 × 0.06 = 0.3
18.86
5 ⟌0.3
- 0.3
--------------
0
I hope this helps!
Howard and Jane are surveying their neighbors about the community garden. Their questions, written on the survey, are below: Howard: Did you visit the garden this month? Jane: How many times do you visit the garden in a month? Who wrote a statistical question and why?
Answer:
Step-by-step explanation:
Note
Answer: Jane's question
Howard merely asked if a visit had taken place. There isn't a number anywhere or one that can be implied.
Jane asked for a number. It requires that the responder gives a number with no embellishment. The question asks for the number of times something has occurred and there is a time frame for the answer. That usually is the characteristic of a statistical survey.
volunteers for a fair prepared 12 1/2 liters of smoothies. At the end of the day, the volunteers had 2 5/8 remaining. How many liters of smoothies were sold?
The liters of smoothies sold is 9 7/8 liters.
What is an Equation?An equation is a statement formed when two algebraic expressions are equated by an equal sign.
The volunteer prepares 12 1/2 = 25/2 liters of smoothies
The remaining amount of smoothies is 2 5/8 = 21/8 liters of smoothies
Let the amount of smoothies sold is x liters
Then the equation formed to determine the value of x is
x = (25/2) - (21/8)
x = 79/8
x = 9 7/8 liters
Therefore, the liters of smoothies sold is 9 7/8 liters.
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Find all solutions.
x +4x=0
Answer: x = 0
Step-by-step explanation:
Given:
x + 4x = 0
Combine like terms:
5x = 0
Divide both sides of the equation by 5:
x = 0
We can also check our work by graphing. See attached, intercepts of the x-axis are solutions.
question 14, thank you
The parametric equation that represents the same path as the original equation is x = 3 + cos(2θ) and y = 2sin(2θ).
Path of the parametric equations
The given parametric equation can be expressed as follows;
x = 3 + cosθ
y = 2sinθ
From the given options, a plot of the various equation can be used to determine the paths of the equation.
For; x = 3 + cos(2θ) and y = 2sin(2θ), its parametric plots is same as original equation since the equation [3 + cos(2θ) and y = 2sin(2θ)] changed at equal rate of the angles.
Thus, the parametric equation that represents the same path as the original equation is x = 3 + cos(2θ) and y = 2sin(2θ).
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Which shows one way to determine the factors of Which shows one way to determine the factors of x3 + 4x2 + 5x + 20 by grouping? by grouping?
The factored expression of the expression x^3 + 4x^2 +5x + 20 is (x^2 + 5)(x + 4)
How to determine the factors?The expression is given as:
x^3 + 4x^2 +5x + 20
Group the expression into two
(x^3 + 4x^2) + (5x + 20)
Factorize each group
x^2(x + 4) + 5(x + 4)
Factor out x + 4
(x^2 + 5)(x + 4)
Hence, the factored expression of the expression x^3 + 4x^2 +5x + 20 is (x^2 + 5)(x + 4)
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Question 15(Multiple Choice Worth 1 points)
(01.05 MC)
Which expression is rational?
04.121221222...
by
√36
O√21
O1.192744502...
Answer:
Second option
Step-by-step explanation:
Given the following question:
We are given four choices and we need to determine which choice is a rational number. In order for any integer to be a rational number you have to be able to write it as a fraction.
In this case, options one and four are immediately excluded since they are repeating decimals. They cannot be written as a fraction which leaves us with the second option or the third option.
[tex]\sqrt{36}[/tex]
[tex]\sqrt{36} =6\times6[/tex]
[tex]=6=\frac{6}{1}[/tex]
[tex]=\frac{6}{1}[/tex]
Your answer is the second option or "sqrt36."
Hope this helps.
The equation of a curve is y = x³ + 4x. Show that the value of y increases when x increases. ² is a decreasing function.
We will see that f'(x) > 0, which means that f(x) is an increasing function.
How to prove that the function is increasing?
For any function f(x), if f'(x) > 0, then f(x) is increasing for any value of x.
Here we have the cubic function:
f(x) = x³ + 4x
If we differentiate this, we get:
f'(x) = df(x)/dx = 3x² + 4.
And notice that x² is always positive, then f'(x) > 0, which means that f(x) is an increasing function.
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The mean price of a textbook is $82, and the range of prices are $16. What are the possible prices for the textbook?
$82, $82, $82, $82, $98
$90, $90, $74, $74, $74
$82, $82, $88, $76, $82
$82, $84, $90, $80, $74
Answer: D (82, 84, 90, 80, 74)
Finding Range:
To find range, you must subtract the smallest number to the highest number in that number pattern.
For example, the highest in D is 90, and the smallest is 74. 90-74 is 16, which matches the range for a possible price (16 = 16).
Range is basically the most easiest to find out of median, mean, and mode. You just have to find the greatest-smallest = range.
Finding Mean:
To find mean, you must add all the numbers up then divide the sum by the QUANTITIY of all the numbers.
For example, if we add 82, 84, 90, 80, and 74, we would get 410. Since there are 5 numbers that make up 410, we divide 410 by 5, and therefore getting 82. This matches the mean of the price of a textbook (82 = 82).
Mean is basically easy to find as you just add all the numbers and divide it by how much numbers make that sum.
Conclusion:
In conclusion, the mean and range all match a possible price of the textbook, having a range of $16 and a mean of $82. Thus, D is the right answer.
The correct option is D (82, 84, 90, 74)
What is range?Range is subtract the smallest number to the highest number in that number pattern.
What is mean?Mean is addition of all the numbers up then divide the sum by the quantities of all the numbers.
The highest in D is 90, and the smallest is 74. 90-74 is 16, which matches the range for a possible price (16 = 16).
Addition of 82, 84, 90, 80, and 74, we would get 410. Since there are 5 numbers that make up 410, we divide 410 by 5, and therefore getting 82. This matches the mean of the price of a textbook (82 = 82).
Therefore, the possible prices for the textbook is the possible prices for the textbook is (82, 84, 90, 74).
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Consider the graph of the function .
Match each transformation of function f with a feature of the transformed function.
vertical asymptote of
function decreases as x increases
y-intercept at
x-intercept at
arrowRight
arrowRight
arrowRight
g(x) = ¹/₂f(x - 2) -------> y-intercept at (0, - ¹/₂)
h(x) = f(x - ¹/₂) -------> x-intercept at (1.5, 0)
j(x) = f(x) - ¹/₂ -------> vertical asymptote at x = 0
m(x) = function decreases as x increases
How to Interpret Graphs?We are given the function;
f(x) = In (x)
Now, from the given tiles and when we punch the respective values for the given functions, we can say that;
g(x) = ¹/₂f(x - 2) -------> y-intercept at (0, - ¹/₂)
h(x) = f(x - ¹/₂) -------> x-intercept at (1.5, 0)
j(x) = f(x) - ¹/₂ -------> vertical asymptote at x = 0
m(x) = function decreases as x increases
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Cost of Bikes ($) at Bike Shop
312, 352, 480, 392, 368, 352, 416, 640
Ic. mode
The mode is.
Answer:
352
Step-by-step explanation:
it repeated more than once
Amalia and Alec are studying the growth of a plant over time. They measure the height of the plant at the end of each week for several weeks and display the data in a scatter plot. They then find the equation for the best-fit line to be y=2.5+ 1.25x
X=the number of weeks that have passed
Y = the height of the plant
How tall will with plant be after 7 weeks?
After 7 weeks the plant will 11.25 units tall if the equation for the best-fit line to be y = 2.5 + 1.25x.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2} \\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
We have a line of best fit:
y = 2.5 + 1.25x
Plug x = 7 weeks
y = 2.5 + 1.25(7)
y = 11.25 units
Thus, after 7 weeks the plant will 11.25 units tall if the equation for the best-fit line to be y = 2.5 + 1.25x.
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Solve the system of equations.
y=x²-5
y 2x+3
Answer:
[tex]x=4,\:x=-2[/tex]
Step-by-step explanation:
Both equations are equal to y, so we can simply set them equal to each other and solve for x:
[tex]x^2-5=2x+3\\\\x^2-8=2x\\\\x^2-2x-8=0\\\\(x-4)(x+2)=0\\\\x=4,\:x=-2[/tex]
ASAP HELP NOWWWWW
What are the solutions for the following system of equations? –3x2 + 4y = 21 4x2 + y = 10 (1, 6) and (0, 10) (–1, 6) and (1, 6) (1, 6) and (3, 12) (–1, 6) and (3, 12)
The solutions for the following system of equations will be (–1, 6) and (1, 6). Then the correct option is B.
What is the solution of the equations?The equations are given below.
–3x² + 4y = 21 ...1
4x² + y = 10 ...2
Multiply equation 1 by 4 and equation 2 by 3, then we have
–12x² + 16y = 84
12x² + 3y = 30
Add both equations, then we have
19y = 114
y = 6
From equation 2, we have
4x² + 6 = 10
4x² = 4
x² = 1
x = ±1
x = 1, –1
Then the correct option is B.
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A family plan for a cell phone has a monthly base price of $75 plus $10.99 for each additional family member added beyond the primary account holder. The linear function to model the monthly cost C(x) (in $) of a family for x additional family members added is C(x)=
The linear equation that models the cost for having x additional family members added is:
c(x) = $75 + $10.99*x
How to get the linear equation?
Here we know that the plan has a fixed price of $75 plus $10.99 for each family member added beyond the primary account holder.
Then if there are x family members added, the cost will be:
$75 + $10.99*x
Then the linear equation that models the cost for having x additional family members added is:
c(x) = $75 + $10.99*x
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6. A department store uses a
market research survey to
determine the types of products
various consumer groups are
buying.
Choose all that apply.
The characteristics that best
describe surveys are:
Answer choices:
Work with a wide variety of
formats
Involve studying subjects in their
environment, which is not
controlled in any way
May collect either facts or
opinions
A solid sphere is cut into 12 equal wedges. The volume of each wedge is
V=³. Solve the formula for r.
The complete question is
"A solid sphere is cut into 12 equal wedges. The volume of each wedge is V= 4/3πr³. Solve the formula for r."
A solid sphere is cut into 12 equal wedges. The volume of each wedge is V= 4/3πr³. The value of r is (9V/π)^1/3.
What is the volume of the sphere?It is given that;
The Volume of a sphere = V = 4/3πr³
Dividing into 12
4/3 x 1/12 πr³ = 1/9πr³
V = 1/9πr³
Cross multiply
9V = πr³
Divide both sides by π
9V/ π = πr³/ π
9V/ π = r³
Take the cube root of both sides
r = (9V/π)^1/3
Thus, The value of r is (9V/π)^1/3.
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Find the product 3 radical -3 and 3 radical -5
[tex]\left(\sqrt[3]{-3} \right) \left(\sqrt[3]{-5}\right)\\\\=\left( \sqrt[3]{-1}\right \sqrt[3]{3}) \left(\sqrt[3]{-1} \sqrt[3]{5} \right)\\\\=\sqrt[3]{(-1)(-1)} \cdot \sqrt[3]{(3)(5)}\\\\=\sqrt[3]{1} \cdot \sqrt[3]{15}\\\\=1\cdot \sqrt[3]{15}\\\\=\sqrt[3]{15}[/tex]
PLEASE HELP TIMER!!!!!!!!!!!!!
Answer:
Answer: -3/2
Step-by-step explanation:
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3. Find sin A and cos B exactly.
B
a
C
6
4
A
Check the picture below.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{6^2 - 4^2}=a\implies \sqrt{36-16}=a\implies \sqrt{20}=a\implies 2\sqrt{5}=a \\\\[-0.35em] ~\dotfill\\\\ sin(A )=\cfrac{\stackrel{opposite}{2\sqrt{5}}}{\underset{hypotenuse}{6}}\implies sin(A)=\cfrac{\sqrt{5}}{3} \\\\\\ cos(B )=\cfrac{\stackrel{adjacent}{2\sqrt{5}}}{\underset{hypotenuse}{6}}\implies cos(B)=\cfrac{\sqrt{5}}{3}[/tex]
Which point lies on the line described by the equation below? y+ 4 = 4(x-3) O A. (3,-4) O B. (2,9) O C. (0,0) O D. (1,-11) E. (1,11) OF. (-2, 3) PREVIOUS SUBMIT 22949
The point (3, -4) lie on the line y + 4 = 4(x - 3) because the point (3,-4) satisfy the line option (A) is correct.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have an equation of a line:
y + 4 = 4(x - 3)
A (3,-4)
Plug the above points in the equation of the line.
-4 + 4 = 4(3 -3)
0 = 0 (true)
The point lies on the line
Similarly checking for others points we will find that points (2,9), (0,0) , (1,-11), (1,11), and (-2, 3) does not lie on the line y + 4 = 4(x - 3)
Thus, the point (3, -4) lie on the line y + 4 = 4(x - 3) because the point (3,-4) satisfy the line option (A) is correct.
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