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]
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.
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]
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
HURRY for 100 points
If p is true and ~ q is false, then p -> ~ q is ____ false.
-sometimes
-always
-never
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
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.
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.
Learn more about Geometric series here:
https://brainly.com/question/23304333
#SPJ1
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
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
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.
Learn more about Equation:
https://brainly.com/question/2263981
#SPJ1
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].
To know more about matrix follow
https://brainly.com/question/1821869
#SPJ1
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
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°.
Using a trial and improvement method, find x correct to 1 decimal place.
3x² - x = 30
Answer:
x = 10/3
x = -3
Step-by-step explanation:
3x² - x = 30
3x² - x - 30 = 0
multiply 3 and -30 which =
-90
what are 2 numbers that when multiplied make
-90
and that when added make
-1
(-1 is the number in -x in the equation)
they are the numbers 9 and 10
namely -10 and +9
3(x-10/3)(x+9/3)=0
divide both sides by 3
(x-10/3)(x+9/3)=0
then split factors being multiplied
(x-10/3)=0
(x+9/3)=0
x = 10/3
x = - 9/3 = -3
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
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.
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
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
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! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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.
#StudyWithBrainly
~Just a smiley person helping fellow students :)
−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:
#CarryOnLearning
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
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.
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]
Segment BD is a median. Solve for x. Round to the nearest tenth, if necessary. (Image not necessarily to scale.)
Answer: 10
Step-by-step explanation:
By definition, the point at which a median intersects the side of the triangle opposite from the vertex from which it is drawn is the midpoint of that side.
If you draw four cards at random from a standard deck of 52 cards, what is the probability that all 4 cards have distinct characters (letters or numbers)
There are [tex]\binom{52}4[/tex] ways of drawing a 4-card hand, where
[tex]\dbinom nk = \dfrac{n!}{k!(n-k)!}[/tex]
is the so-called binomial coefficient.
There are 13 different card values, of which we want the hand to represent 4 values, so there are [tex]\binom{13}4[/tex] ways of meeting this requirement.
For each card value, there are 4 choices of suit, of which we only pick 1, so there are [tex]\binom41[/tex] ways of picking a card of any given value. We draw 4 cards from the deck, so there are [tex]\binom41^4[/tex] possible hands in which each card has a different value.
Then there are [tex]\binom{13}4 \binom41^4[/tex] total hands in which all 4 cards have distinct values, and the probability of drawing such a hand is
[tex]\dfrac{\dbinom{13}4 \dbinom41^4}{\dbinom{52}4} = \boxed{\dfrac{2816}{4165}} \approx 0.6761[/tex]
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
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.
Learn more about Fraction:
https://brainly.com/question/1301963
#SPJ1
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.