I can write a system of linear equations and inequalities from context.
One smartphone plan costs $40 per month and an
extra $3.50 per gigabyte of data used each month.
Another smartphone plan costs $75 per month and
$0.50 per gigabyte of data used each month.
Let c represent the cost of a phone plan, m represent
number of months, and g represent the number of
gigabytes of data used each month. Write a system of
two linear equations that could be used to determine
the number of gigabytes used in a month so that the
two phone plans cost the same amount.
Equation 1:
Equation 2:
An equation is formed of two equal expressions. The number of gigabytes that is used in a month so that the two phone plans cost the same amount is 11.6667 Gigabyte.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let c represent the cost of a phone plan, m represent the number of months, and g represent the number of gigabytes of data used each month.
Equation1: C = 40m + 3.5mg = (40+3.5g)m
Equation2: C = 75m + 0.5mg = (75+0.5g)m
Equating C,
(40+3.5g)m = (75+0.5g)m
40 + 3.5g = 75 + 0.5g
3g = 35
g = 11.6667 gigabyte of data per month
Hence, the number of gigabytes that is used in a month so that the two phone plans cost the same amount is 11.6667 Gigabyte.
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A cylinder has a height of 16 cm and a radius of 5 cm. A cone has a height of 12 cm and a radius of 4 cm. If the cone is placed inside the cylinder
as shown, what is the volume of the air space surrounding the cone inside the cylinder? (Use 3,14 as an approximation of "pl.)
Answer:
Given:
Cylinder: height = 16 cm ; radius = 5 cm
cone: height = 12 cm ; radius = 4 cm
Volume of cylinder = 3.14 * (5cm)² * 16cm = 1,256 cm³
Volume of cone = 3.14 * (4cm)² * 12cm/3 = 200.96 cm³
Volume of air space = 1256 cm³ - 200.96 cm³ = 1,055.04 cm³
Evaluate this function at the given value using the remainder theorem.
F(x)=x^4+5x^3-18x+1 at x=-4
Please show work , I give brainliest. :)
Answer:
9
Step-by-step explanation:
[tex]f(x) = x^4 +5x^3 -18x +1\\\\f(-4) = (-4)^4 +5(-4)^3 -18(-4) +1\\\\~~~~~~~~~=256+5(-64)+72+1\\\\~~~~~~~~~=329-320\\\\~~~~~~~~~=9[/tex]
Find the slope of the line graphed below.
to get the equation of any straight line, we simply need two points off of it, let's use the ones provided in the picture below.
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{-7}{2}[/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}{4}=\stackrel{m}{-\cfrac{7}{2}}(x-\stackrel{x_1}{1}) \\\\\\ y-4=-\cfrac{7}{2}x+\cfrac{7}{2}\implies y=-\cfrac{7}{2}x+\cfrac{7}{2}+4\implies y=-\cfrac{7}{2}x+\cfrac{15}{2}[/tex]
(05.05 mc)
~
a a food truck did a daily survey of customers to find their food preferences. the data is partially entered in the frequency table. complete the table to analyze the data and answer the to
questions:
likes hamburgers does not like hamburgers total
likes burritos
29
41
does not like burritos
54
135
total
110
205
part a: what percentage of the survey respondents do not like both hamburgers and burritos? (2 points)
part b: what is the marginal relative frequency of all customers that like hamburgers? (3 points)
part c: use the conditional relative frequencies to determine which data point has strongest association of its two factors. use complete sentences to explain your answer. (5 points)
The data point that has the strongest association of its two factors is Ratio of those who like Hamburgers but not burritos
How to find the percentage?A) The percentage of respondents who do not like both hamburgers and burritos is; 33/250 * 100% = 16.09%
B) Marginal relative frequency of all customers that like hamburgers will be the ratio of the sum of the customers that like hamburgers to the total number of respondents. Thus;
MRF = 134/205 = 0.65
C) Let us first find the ratio of all the four data with the total;
Ratio of those who like Hamburgers and burritos = 39/134 = 0.29
Ratio of those who like Hamburgers but not burritos = 95/134 = 0.71
Ratio of those who like burritos but not Hamburgers = 38/71 = 0.53
Ratio of those who do not like burritos or Hamburgers = 33/71 = 0.47
Thus, The data point that has the strongest association of its two factors is Ratio of those who like Hamburgers but not burritos
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Decide whether quadrilateral ABCD with vertices 4(-3,0), B(-4,1), C(-1.4), and D(0,3) is a rectangle, rhombus, square, or parallelogram.
Answer: rectangle
Step-by-step explanation:
The options imply the figure is a parallelogram. Furthermore, we can tell that not all the sides are congruent, so we can rule out the possibility that it is a rhombus or a square.
To determine if it is a rectangle, we can use the slope formula to determine if there is a pair of perpendicular sides. If this is the case, then this will be a parallelogram with a right angle, making it a rectangle.
[tex]m_{\overline{AB}}=\frac{1-0}{-4-(-3)}=-1\\m_{\overline{BC}}=\frac{4-1}{-1-(-4)}=1\\\therefore \overline{AB} \perp \overline{BC}[/tex]
So, the most specific classification is a rectangle
What is the value of ax² + bx + c at x = a ?
[tex]a\cdot a^2+b\cdot a+c=a^3+ab+c[/tex]
The equation of the line with slope = 3, going through point (2, 4) is:
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ -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-\stackrel{y_1}{4}=\stackrel{m}{-3}(x-\stackrel{x_1}{2}) \\\\\\ y-4=-3x+6\implies y=-3x+10[/tex]
I need the x axis to solve this
Answer:
As a fraction:
x | y
________
|
7/3 | 2
3 | 4
11/3 | 6
13/3 | 8
As a mixed fraction:
x | y
________
|
2 ⅓ | 2
3 | 4
3 ⅔ | 6
4 ⅓ | 8
As a decimal:
x | y
___________
|
2.33.. | 2
3 | 4
3.66.. | 6
4.33.. | 8
You should start with x values since the y values will be easier to plot. x's will not be easy to represent.
For example:
x | y
________
|
0 | -5
1 | -2
2 | 1
3 | 4
4 | 7
5 | 10
find the height of the trapezoid
Answer:
h = 19
Step-by-step explanation:
The are is given so we can use the area to find the height because the area of a trapezoid is calculated by the following formula:
1/2 * (a+b)*h (a: base, b: base, h: height)
We already know the bases; 37 and 51
1/2*(37+51)*h = 836 first multiply both sides by 2
(37+51)*h = 1672 now divide both sides by 88 (sum of bases)
h = 19
A certain 300-term geometric sequence has first term 1337 and common ratio $-\frac12$. How many terms of this sequence are greater than 1
There are 6 terms in the sequence greater than 1.
What is a geometric series ?A geometric series is sum of infinite numbers which has a common ratio between its successive terms.
The missing common ratio value is -1/2
It is given in the question that
the number of terms in the sequence = 300
Sum = a₁ (1-rⁿ)/(1-r)
nth term is given by
aₙ = a₁r⁽ⁿ⁻ ¹⁾
1337(1/2)^(n - 1) = 1
(1/2)^(n - 1) = 1/1337
Applying log on both sides
log (1/2)^(n - 1) = log (1/1337)
(n - 1) log(1/2) = log(1/1337)
n = log (1/1337)/ log (1/2) + 1 ≈ 11.384
the 11th term is 1337(-1/2)^(10) ≈ 1.305
and
And the 12th term is 1337(-1/2)^11 = -.653
As the even terms are negative , they are less than 1 and , therefore the odd terms from 1 - 11 term will be positive and greater than 1.
Therefore there are 6 terms in the sequence greater than 1.
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−4(4x-6)= 3(-7x-1)
How do I solve this step by step when trying to solve for x?
[tex]-4(4x-6)=3(-7x-1)[/tex]
[tex]-16x+24=3\left(-7x-1\right) [/tex]
[tex]-16x+24=-21x-3 [/tex]
[tex]-16x+24+21x=-3 [/tex]
[tex]5x+24=-3 [/tex]
[tex]5x=-3-24 [/tex]
[tex]5x=-27 [/tex]
[tex]x=\frac{-27}{5} [/tex]
[tex]x=-\frac{27}{5} [/tex]
Explanation:
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Using the digits 0 to 9
Supplementary Angles:
[tex]\boxed{100°} and \boxed{80°}[/tex]
Arithmetically speaking, the closest 2 supplementary angles can get (in 3 and 2 digits respectively) is the upwritten.
Complementary Angles:
[tex]\boxed{45°} and \boxed{45°}[/tex]
Simply, in this case, for angles to be numerically as close as possible - make both the angles 45°.
The length of a rectangle is units greater than twice its width. if its width is w, which expression gives the perimeter of the rectangle in terms of w?
a. 2(5w/2) + w
b. 5w/2 + w
c. 3w + 10/2
d. 6w + 5
please help me quickly
Answer:
d
Step-by-step explanation:
the length is how many units greater than twice the width ?
you skipped that information from us.
so, all we can say
length = 2×width + x
the perimeter is
2×length + 2×width
with width = w we get by using the first equating in the second :
2×(2×w + x) + 2×w = 4w +2x + 2w = 6w + 2x
so the right answer must be d.
it is the only option with "6w".
it means that 2x = 5 and x = 2.5.
so it was that the length is 2.5 units greater than twice the width
The model represents x2 – 9x + 14.
An algebra tile configuration showing only the Product spot. 24 tiles are in the Product spot: 1 is labeled + x squared, 9 are labeled negative x, and 14 are labeled +.
Which is a factor of x2 – 9x + 14?
x – 9
x – 2
x + 5
x + 7
the awnser is B x-2
HURRY GIVING BRAINLIEST
Answer:
12 or 7??
Step-by-step explanation:
it depends if they are being spinned at the same time because then you can get for eg. 'A,1' 'A2' etc.
Give the domain and range.
X
-2
0
2
y
-1
0
1
a.
b.
domain: (2, 0, 2), range: (1, 0, 1)
domain: {-2, 0, 2), range: {-1, 0, 1)
domain: {-1, 0, 1), range: (-2, 0, 2}
d. domain: {1, 0, 1), range: {2, 0, 2)
C.
DI
at the host answer from the choices provided
1
2
3
4
5
Answer:
(b) domain: {-2, 0, 2}, range: {-1, 0, 1}
Step-by-step explanation:
For the function defined by the table ...
[tex]\begin{array}{|cccc|}\cline{1-4}x&-2&0&2\\\cline{1-4}y&-1&0&1\\\cline{1-4}\end{array}[/tex]
we want the function's domain and range.
__
domainThe domain is the list of x-values for which the function is defined. Here, that list is ...
domain = {-2, 0, 2}
__
rangeThe range is the list of y-values the function produces. Here, that list is ...
range = {-1, 0, 1}
_____
The domain and range sets are most conveniently listed in order, with duplicates removed.
7. Write the equation -3x +2y = 7 in slope-intercept form.
Answer:
y = 3/2x + 7/2
Step-by-step explanation:
Slope-intercept form is when y is the subject. So we make y the subject:
Add 3x to both sides :
2y = 3x + 7
Now we divide both sides by 2 :
y = 3/2x + 7/2
This is our final answer.
Hope this helped and brainliest please
Hi student, let me help you out! :)
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We are asked to write the equation -3x+2y=7 in slope-intercept form.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
The equation for slope-intercept form is y=mx+b, where m= slope (gradient) of the line, b=y-intercept of the lineSo let's write this equation, -3x+2y=7, in slope-intercept form...
///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\\////\\\\///\\\////\\\///\\\///\\\////\\\\////\\\\
First, we add -3x to both sides of the equal sign:
[tex]\large\pmb{2y=7+3x}[/tex]
We can switch the order of the terms:
[tex]\large\pmb{2y=3x+7}[/tex]
This is starting to look like the slope-intercept equation. In fact, all we have to do is divide both sides by 2:
[tex]\large\pmb{y=(3x+7)\div2}[/tex]
Which simplifies to...
[tex]\large\pmb{y=\cfrac{3}{2}x+\cfrac{7}{2}}[/tex]
That's the equation in slope-intercept form.
Hope this helps you out! :D
Ask in comments if any queries arise.
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Chester scored 84, 88, and 80 on his first 3 math tests. How can you find Chester's mean, or average, score on these tests?
Answer:
Add and Divide.
Mean = 84
Step-by-step explanation:
Mean ( math word) and average (common usage word) tell us to ADD up the numbers in the list of data and DIVIDE by the number of pieces of data.
Here we add:
(80 + 84 + 88)
then divide by 3, because there's 3 numbers in this list.
(80 + 84 + 88)/3
= 252/3
= 84
The mean, or average is 84.
A fogpole casts a 13-foot shadow on the ground when the sun is at a 68° angle of elevation. Which of the following expressions can be used to determine the height (h), in feet, of the fogpole? (Assume the flagpole is perpendicular to the ground.) Draw a picture
Answer:
see below
Step-by-step explanation:
You didn't include the choices but here is a solution
tan 68 = opp/adj = height / 13
13 Tan 68 = height of pole
Sequence A: 4;9;16;25;36; ... ; ...
a) write the next two numbers
b) describe how sequence A is being formed
Answer:
49,64
Step-by-step explanation:
Every time the number changes there is an addition of two. for instance, from 4 to 9 the was an addition of 5 and from 9 to 16 there was an addition of 7. Thats how it works
What is the summation notation for the geometric series 1/2+2+8+32+128?
Answer ( k=1 ∑ 5 ) 1/2(4)^k-1
The summation notation is ∑ [tex](4^{n} -1)\\[/tex]/2.
What is geometric progression?The common ratio multiplied here to each term to get the next term is a non-zero number.
Given: 1/2+2+8+32+128
Using,
[tex]a_n= a_1r^{n-1}[/tex]
We have,
a1 =1/2 and r= 4
notation is : An= ∑ [tex](4^{n} -1)\\[/tex]/2
Hence, the notation is An= ∑ [tex](4^{n} -1)\\[/tex]/2.
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What is the quotient? startfraction t 3 over t 4 endfraction divided by (t squared 7 t 12)
A fraction is a way to describe a part of a whole. The quotient of the fraction is 1/(t+4)².
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
The quotient of [tex]\dfrac{\dfrac{t+3}{t+4}}{t^2+7t+12}[/tex] can be found by factorizing the denominator of the fraction. Therefore, the factors of the denominator are,
t² + 7t + 12
= t² + 4t + 3t + 12
= t(t+4) +3(t+4)
= (t+4)(t+3)
Now, quotient will be,
[tex]\dfrac{\dfrac{t+3}{t+4}}{t^2+7t+12}\\\\\\=\dfrac{\dfrac{t+3}{t+4}}{(t+4)(t+3)}\\\\\\=\dfrac{(t+3)}{(t+4)(t+3)(t+4)}\\\\\\= \dfrac1{(t+4)^2}[/tex]
Hence, the quotient of the fraction is 1/(t+4)².
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What is the range of the function [tex]y=\sqrt[3]{x+8}[/tex]?
A. -∞ < y < ∞
B. -8 < y < ∞
C. 0 ≤ y < ∞
D. 2 ≤ y < ∞
Answer:
-∞ < y ∞
The range is all real numbers.
Solve for h
-8 = - 2 (h - 6)
H=
The first step that we need to take before solving is to understand what the question is asking us to do and what is given to us to do that. Looking at this problem, we are given the goal of this problem which is to solve for h and we are given an expression to do so.
The next step that we need to take is to distribute the -2 to the contents inside of the parenthesis.
Distribute
[tex]-8 = - 2 (h - 6)[/tex][tex]-8 = (- 2 * h) + (-2 * - 6)[/tex][tex]-8 = (- 2h) + (12)[/tex]After we have distributed the -2 to the contents inside of the parenthesis we can move onto the next step to isolate h which is to subtract 12 from both sides which would just leave us with -2h.
Subtract 12 from both sides
[tex]-8 = - 2h + 12[/tex][tex]-8 - 12 = - 2h + 12 - 12[/tex][tex]-20 = - 2h[/tex]The next step that we will take to finish the problem is to divide both sides by -2 which will isolate h. Then we will simplify the expression and that will give us our final answer.
Divide both sides by -2
[tex]-20 = - 2h[/tex][tex]\frac{-20}{-2} = \frac{- 2h}{-2}[/tex][tex]\frac{-20}{-2} = h[/tex]Simplify the expression
[tex]\frac{-20/-2}{-2/-2} = h[/tex][tex]\frac{10}{1} = h[/tex][tex]10= h[/tex]We have now completed solving for h for the expression that was provided in the problem statement and we were able to determine that h is equal to 10.
Which number(s) below belong to the solution set of the equation? Check all
that apply.
X+ 6 = 45
A. 45
B. 39
C. 35
D. 3
E. 51
F.0
If ABCD is a parallelogram, which of the following statements must be true? (
Answer:
AB=CD and BC=AD because both of them are visually paired with the same longitude.
Answer:
AB = CD, BC = AD
Step-by-step explanation:
According to parallelogram properties,
Angle A = 180-Angle B; False
AB!=BC; False
AC==BD is only true when AB = BC, False
AB ==CD, BC == AD; True
What is the product?
The correct answer is option C which is [tex]\left[\begin{array}{cc}8&32\\39&15&\\\end{array}\right][/tex].
What is a matrix?Matrix is defined as the arrangement of the numbers variables and expressions in the table as rows and columns.
The multiplication of the matrix will be calculated as:-
M = [tex]\dfrac{1}{2}\left[\begin{array}{cc}12&64&\\78&30&\\\end{array}\right][/tex]
M = [tex]\left[\begin{array}{cc}\dfrac{12}{2}&\dfrac{64}{2}&\\\dfrac{78}{2}&\dfrac{30}{2}&\\\end{array}\right][/tex]
M = [tex]\left[\begin{array}{cc}8&32\\39&15&\\\end{array}\right][/tex].
Therefore the correct answer is option C which is [tex]\left[\begin{array}{cc}8&32\\39&15&\\\end{array}\right][/tex].
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HURRY for 100 points
If p is true and ~ q is false, then p -> ~ q is ____ false.
-sometimes
-always
-never
Find the quotient. Simplify your answer.
s + 1/
s²1
÷
s^2/
6s²
Enter the correct answer.
Let's see
[tex]\\ \rm\Rrightarrow \dfrac{s+1}{s^2+1}\div \dfrac{s^2}{6s^2}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{s+1}{s(s+1)}\div\dfrac{1}{5s^2}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1}{s}\times{5s^2}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{5s^2}{s}[/tex]
[tex]\\ \rm\Rrightarrow 5s[/tex]