Answer:
a) (-2,2), (-1,-1), (1,-1), (3,7)
b) x=1.4
Answer:
a) (-2, 2), (-1, -1), (1, -1), (3, 7)
b) x = 1.4
Step-by-step explanation:
a) Plug in your x & solve for y.
[tex]y = (-2)^2 - 2\\y = 2\\y = (-1)^2 - 2\\y = -1\\y = (1)^2 - 2\\y = -1\\y = (3)^2 -2\\y = 7[/tex]
b) Same thing as a, but just plug in 0 for y & solve for x
[tex]0 = x^2 -2\\2 = x^2\\\sqrt(2) = x\\1.4 = x[/tex]
On a map, 1 inch represents 100 feet. How many inches would
represent 350 feet? (Hint: answer will be a decimal) *
Answer:
3.5
Step-by-step explanation:
3.5 inches would represent 350 feet.
Inches and feetRelationship between inches and feet is that one inch is equal to [tex]\boldsymbol{100}[/tex] feets as per the map.
So,[tex]350[/tex] feet represent [tex]\frac{350}{100}=3.5[/tex] inches.
Therefore, [tex]\boldsymbol{3.5}[/tex] inches would represent [tex]350[/tex] feet in decimal.
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Write the linear equation in Slope-Intercept Form y = mx + b of the line that passes through the given points, then graph
the line.
Answer:
y = 3x + 7.
To graph the line mark off the 2 points and draw a line through them.
Step-by-step explanation:
The slope = (-2-7) / (-3-0)
= -9/-3
= 3.
The value of b is found using the point-slope form of a line:
y - y1 = m(x - x1)
using m = 3, (x1, y1) = (0, 7):
y - 7 = 3(x - 0)
y = 3x + 7.
will give brainliest!!! hurry up and solve it plzz
Answer:
8
Step-by-step explanation:
we can say that AD is congruent to DC
so your equation for x is: 4x - 1 = 2x
solve this to get x = 0.5
plug x into and equation and multiply you answer by 2 to find the hypotenuse of triangle ABC and DEF
4(0.5) - 1 = 1
hypotenuse: 1 x 2 = 2
since we know x is 0.5, plug this into 4x + 1 to find the length of the leg FE,
4(0.5) + 1 = 3
In the diagram, it shows that the legs of triangle are congruent
this means that FE, ED, BA, and BC are all congruent
since we know FE is 3, we know that all the other sides are 3 as well
this means that the perimeter of the triangle is: leg + leg + hypotenuse
so 3 + 3 + 2
the perimeter is 8
Use the elimination method to solve the system of equations. Choose the correct ordered pair. 2y = x + 2 x - 3y= -5 O A. (2, 2) O B. (4,3) O C. (6,4) O D. (8,5)
Answer:
(4,3)
Step-by-step explanation:
2y = x + 2
x - 3y = -5
Rearrange the second equation to equal y.
x - 3y = -5
x + 5 = 3y
(x+5)/3 = y
Substitute into the first equation.
2y = x +2
2[(x+5)/3] = x + 2
(2x + 10)/3 = x + 2
2x + 10 = 3(x + 2)
2x + 10 = 3x + 6
10 - 6 = 3x - 2x
4 = x
Therefore, the correct ordered pair is (4,3) since x is equal to 4.
A mosquito is walking at random on the nonnegative number line. She starts at $1$. When she is at $0$, she always takes a step $1$ unit to the right, but, from any positive position on the line, she randomly moves left or right $1$ unit with equal probability. What is the expected number of times the mosquito will visit $0$ before the first time she visits $4$?
The expected number of times the mosquito will visit 0 before the first time she visits 4 is 3/4 by using concept of probability and geometric series.
Given that repeatedly throwing a fair tetrahedral die, trying to get a 4 (success) before getting a number from 1 to 3 (failure), which follows a geometric distribution.
To find the expected number of visits to 0 before reaching 4, analyze two cases:
success (reaching 4 before 0) and failure (reaching 0 before 4).By the given data, the probabilities of two cases are:
P(success) p = 1/4,
P(failure)=3/4.
The expected count of failures, X, can be found in terms of success probability p as
[tex]E[X]=\sum_{x=0}^{+\infty}[x(1-p)^xp][/tex]
On substituting p = 1/4 gives:
[tex]E(X) = 0(1/4)+1(3/4)(1/4)+2(3/4)^2(1/4)+3(3/4)^3(1/4)+.........[/tex]
On taking (1/4) gives
[tex]E(X) = 1/4[3/4+(3/4)^2+(3/4)^3+......+\infty]----(1)[/tex]
Consider [tex]3/4+(3/4)^2+(3/4)^3+......+\infty[/tex]
This forms a geometric series tends to infinity and the sum is given by :
[tex]S_\infty = a/(1-r)[/tex]
Here: a= 3/4
r = 3/4
Plugging these values into formula gives:
[tex]3/4+(3/4)^2+(3/4)^3+......+\infty = S_\infty[/tex]
[tex]S_\infty= 3/4/(1-3/4)[/tex]
On subtracting the denominator gives:
= 3/4/(1/4)
On taking reciprocal gives:
= 3/4 * 4
On simplifying gives:
= 3
Substituting these value into given equation 1 gives:
E(X) = 1/4*[3]
On multiplying gives:
E(X) = 3/4.
Therefore, the expected number of times the mosquito will visit 0 before the first time she visits 4 is 3/4 by using concept of probability and geometric series.
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Nicole has x dimes and y nickels. She has at least 15 coins worth a maximum of $1
combined. Solve this system of inequalities graphically and determine one possible
solution.
Answer:
Step-by-step explanation:
[tex]X + Y \geq 15\\\\10X + 5Y \leq 100[/tex]
we want to put it into terms of Y
[tex]y \geq 15 - x\\and\\5y \leq 100 - 10x\\y \leq 20 - 2x[/tex]
the graph is in the attached image. Any point in the shaded overlap region where x is greater than or equal to 0 (assuming you cannot have negative coins) works, e.g. (2, 14)
The solution of the inequalities is required.
One of the solutions is [tex](5,10)[/tex]
Number of dimes is [tex]x[/tex]
Number of nickels is [tex]y[/tex]
Minimum number of coins is 15.
So, [tex]x+y\geq 15[/tex]
Maximum total value of the coins is $1
So, [tex]0.1x+0.05\leq 1[/tex]
The equations are
[tex]x+y=15[/tex]
[tex]0.1x+0.05y=1[/tex]
Points of the first equation
[tex](0,15)[/tex] and [tex](15,0)[/tex]
Graph the points and draw a line through them.
Points of the second equation
[tex]x=0[/tex]
[tex]y=\dfrac{1}{0.05}=20[/tex]
[tex]y=0[/tex]
[tex]x=\dfrac{1}{0.1}=10[/tex]
[tex](0,20)[/tex] and [tex](10,0)[/tex]
Graph the points and draw a line through them.
The shaded regions can be determined by substituting the point in the equations.
One of the solutions is [tex](5,10)[/tex]
This means there are 5 dimes and 10 nickels.
[tex]5+10=15\geq 15[/tex]
[tex]0.1\times 5+0.05\times 10=1\leq 1[/tex]
Hence, one of the solutions is [tex](5,10)[/tex].
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i'm doing a math worksheet and its asking me to describe the stair of a slope. what does that mean??
Answer:
i believe its the rise and the run of the slope.
Step-by-step explanation:
i believe its something similar to this photo
A person has $28,000 invested in stock A and stock B. Stock A currently sells for $50 a share and stock B sells for $60 a share. If stock B triples in value and stock A goes up 50%, his stock will be worth $69,000. How many shares of each stock does he own?
Answer:
Number of stock A = 200
Number of stock B = 300
Step-by-step explanation:
Let :
Number of stock A shares = a
Number of stock B shares = b
Worth of stock A = 50 * a = 50a
Worth of stock B = 60 * b = 60b
50a + 60b = 28000 - - - (1)
Triple the value of stock B:
3 * 60 = 180
Value of stock A goes up by 50%
(100 + 50)% * 50 = 1.5 * 50 = 75
75a + 180b = 69000 - - - (2)
50a + 60b = 28000
75a + 180b = 69000
Multiply equation 1 by 3 and subtract
150a + 180b = 84000
75a + 180b = 69000
75a = 15000
a = 15000/75
a = 200
75(200) + 180b = 69000
15000 + 180b = 69000
180b = 69000 - 15000
180b = 54000
b = 300
The temperature has been dropping 2 degrees every hour and the current temperature is -15°F. How many hours ago was the temperature 0°F?
Answer: 6 1/2
Step-by-step explanation:
six and 1 half of a hour
What expression represents the decimal 72.603
Answer: 7 x 10 + 2 x 1 + 6 x 1/10+ 3 x 1/1000
Step-by-step explanation: just had this question on the test
Two rectangular boxes have the same volume. One box is a cube, and the other box has dimensions 8 ft by 4 ft by 16 ft. How many feet long is an edge of the cube?
Answer:
8 feet
Step-by-step explanation:
All you have to do is find the area of one box and find the root to find the cube edge, as it says they have the same volume.
Lets find the volume of the rectangular box.
8 x 4 x 16 =
32 x 16 =
512.
The volume of the cube is 512 feet cubed, but you are looking for the edge.
The edge cubed should be equal to 512 feet cubed.
So 512 cube root is 8, because 8 x 8 x 8 is 512.
8 feet.
Hope this helps!
Answer:
The answer to your question is 2744 ft³
Step-by-step explanation:
Data
length = 14 ft
width = 14 ft
height = 14 ft
- Volume of a Cube
Volume = length x width x height
-Substitution
Volume = 14 x 14 x 14
-Simplification
Volume = 2744 ft³
Conclusion
The volume of this cube is 2744 ft³
6. Examine the prism shown below.
which of the following statements is true?
a) Points G,F,D and H are Coplanar.
b) Segments BF and BC intersect at point B
c) Point A,B, and C are collinear
d) Planes ABC and BCG intersect at point C
How do I solve this equation?
Answer:
x = ± [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
[tex]|a|= \left \{ {a,if{a\geq 0} \atop-a, if {a<0}} \right.[/tex]
~~~~~~~~~~~~
7 | 3x | + 2 = 16
7 | 3x | = 14
| 3x | = 2
1). 3x = 2
x = [tex]\frac{2}{3}[/tex]
2). - 3x = 2
x = - [tex]\frac{2}{3}[/tex]
Which of the following is equivalent to 5x − 6y = 8?
A. y = -5/6x
B. y = 6/5x + 2
C. y = 5/6x - 4/3
D. y = 8/11x
Answer:
b
Step-by-step explanation:
i need help asap !!!
Answer:-15/28
Step-by-step explanation:
2/1*x5/7x-3/8=-30/56 ÷2=-15/28
How many solutions exist for the given equation? (x + 12) = 4x - 1 o zero infinitely many
determine the linear factors 18x^3-34x^2+16x
Answer:
good luck tho oh and dont forget to tell me the answer
Step-by-step explanation:
Answer:
2x(9x - 8)(x - 1)
Step-by-step explanation:
-5+22=r-4+3r+5
I need help please and thank u
Answer:
r = 4
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASEquality PropertiesStep-by-step explanation:
Step 1: Define equation
-5 + 22 = r - 4 + 3r + 5
Step 2: Solve for r
Combine like terms: 17 = 4r + 1Subtract 1 on both sides: 16 = 4rDivide 4 on both sides: 4 = rRewrite: r = 4Step 3: Check
Plug in r to verify it's a solution.
Substitute: -5 + 22 = 4 - 4 + 3(4) + 5Add/Subtract: 17 = 3(4) + 5Multiply: 17 = 12 + 5Add: 17 = 17What is 400,000 in scientific notation?
O A) 40 x 104
OB) 400 x 103
OC) 4 x 106
OD) 4 x 105
Answer:
4 x 10⁵
so that i think will be OD)
THANK YOU IF U HELPED!!!
Answer:
Step-by-step explanation:
Grove City = 45,032
Franklin = 41,064
Franklin < Grove City
5 thousands > 1 thousand
Byron's MP3 player holds 75 songs. He has space for 26 more songs. Write an equation to find how many songs are already on Byron's MP3 player.A.) 75 + s = 26 B.)75/s = 26 C.) 26s = 75 D.)s + 26 = 75
Answer:
D
Step-by-step explanation:
let the number of songs Byron have be s songs.
s + 26 = 75
Answer:
D
Step-by-step explanation:
s= number of songs played.
s+26=75
s-26=75-26
s=49
what is the measure of <x
Answer:
X=17
Step-by-step explanation:
73+x=90 90-73=17
rohit has two pieces of ribbon pices one 20cm long and other 65 cm long .he wants to cut them into smaller pices of equal length for craft project in such a way thaty no ribbon is left.
what is 3x^2+4-6x^2-18x+15=
Solve the system of equations.
\begin{aligned} &-6y+11x = -36 \\\\ &-4y+7x=-24 \end{aligned}
−6y+11x=−36
−4y+7x=−24
Answer:
The solutions to the system of equations will be:
[tex]y=6,\:x=0[/tex]
Step-by-step explanation:
Given the equation
[tex]-6y+11x=-36[/tex]
[tex]-4y+7x=-24[/tex]
solving the system of equations
[tex]\begin{bmatrix}-6y+11x=-36\\ -4y+7x=-24\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}-6y+11x=-36\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:-12y+22x=-72[/tex]
[tex]\mathrm{Multiply\:}-4y+7x=-24\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:-12y+21x=-72[/tex]
[tex]\begin{bmatrix}-12y+22x=-72\\ -12y+21x=-72\end{bmatrix}[/tex]
[tex]-12y+21x=-72[/tex]
[tex]-[/tex]
[tex]\underline{-12y+22x=-72}[/tex]
[tex]-x=0[/tex]
[tex]\begin{bmatrix}-12y+22x=-72\\ -x=0\end{bmatrix}[/tex]
solving for x
[tex]-x=0[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}-1[/tex]
[tex]\frac{-x}{-1}=\frac{0}{-1}[/tex]
[tex]x=0[/tex]
[tex]\mathrm{For\:}-12y+22x=-72\mathrm{\:plug\:in\:}x=0[/tex]
[tex]-12y+22\cdot \:0=-72[/tex]
[tex]-12y+0=-72[/tex]
[tex]-12y=-72[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}-12[/tex]
[tex]\frac{-12y}{-12}=\frac{-72}{-12}[/tex]
[tex]y=6[/tex]
Therefore, the solutions to the system of equations will be:
[tex]y=6,\:x=0[/tex]
A pound of chocolate cost six dollars . Donna buys P pound. Write an equation to represent the total cost c that Donna pays 
Answer:
c = 6P
Step-by-step explanation:
equation format: c = mP
c = the total cost Donna pays
m = the cost per pound of chocolate(6)
P = the amount of pounds Donna buys
Since we know the cost per pound is $6, we can input it into the equation format:
c = 6P
Now we have an equation that represents the total cost (c) that Donna pays for P pounds.
Let C = total cost that Donna pays.
Donna buys P pound at $6 per pound tells me to multiply.
C = 6P.
Understand?
On a spelling quiz, Lily got 16 out of 20 questions correct. Select all the expressions that show the ratio of Lily’s correct answers to incorrect answers.
Answer:
ACD
Step-by-step explanation:
VNQLW3M2L,Q;KJ52KQ
ANAWER ASAP NEED HELP ASAP!!!!!!
Answer:
1/3
Step-by-step explanation:
Is the relation in the mapping below a function? Explain.
Domain
1,3,5,7
Range
2,4,6
Answer: No
Step-by-step explanation:
The range and the Domain aren’t equal
What is the y-intercept of y = 4x?
Answer:
It depends on what x is
Step-by-step explanation:
I cant help
Answer:
0
Step-by-step explanation:
well if its just 4, then that means it doesnt have a y value