Can you help me with problem #1 I think I remember how to do it but just want to make sure
Answers
1)
[tex]3x-2y=-16[/tex]To convert this equation into slope-intercept form we have to isolate y. Subtracting 3x at both sides of the equation:
[tex]\begin{gathered} 3x-2y-3x=-16-3x \\ -2y=-3x-16 \end{gathered}[/tex]Dividing by -2 at both sides of the equation:
[tex]\begin{gathered} \frac{-2y}{-2}=\frac{-3x-16}{-2} \\ y=\frac{-3x}{-2}+\frac{-16}{-2} \\ y=\frac{3}{2}x+8 \end{gathered}[/tex]Related Questions
Select all prime numbers 2,4,6,7,9,5
Answers
The Solution:
Given the set of numbers below:
[tex]2,4,6,7,9,5[/tex]We are asked to select all the prime numbers in the set.
A prime number is a number that can only be divided by 1 and itself. That is, it is a number that has only two factors.
So, the prime numbers in the set are:
[tex]2,7,5[/tex]Since these numbers only have two factors each.
Therefore, the correct answer is {2,7,5}
Answer:
The prime numbers would be 2, 5, and 7.
Step-by-step explanation:
Prime numbers are numbers that can only be multiplied by 1 and itself.
Here is a list of the common factors of each number:
2: 1, 2
4: 1, 2, 4
6: 1, 2, 3, 6
7: 1, 7
9: 1, 3, 9
5: 1, 5
So, our prime numbers are 2, 5, and 7.
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The florist charge $31.75 for eight roses and five carnations. For one rose and three carnations,it costs $5.75. What is the cost for each type of flower?
Answers
Let's use the variable x to represent the cost of one rose and y to represent the cost of one carnation.
If 8 roses and 5 carnations cost $31.75, we can write the following equation:
[tex]8x+5y=31.75[/tex]If 1 rose and 3 carnations cost $5.75, we can write a second equation:
[tex]x+3y=5.75[/tex]From the second equation, we have x = 5.75 - 3y.
Using this value of x in the first equation, we have:
[tex]\begin{gathered} 8(5.75-3y)+5y=31.75\\ \\ 46-24y+5y=31.75\\ \\ -19y=31.75-46\\ \\ -19y=-14.25\\ \\ y=0.75 \end{gathered}[/tex]Now, calculating the cost of one rose, we have:
[tex]x=5.75-3y=5.75-3\cdot0.75=5.75-2.25=3.5[/tex]Therefore the cost of one rose is $3.50 and the cost of one carnation is $0.75.
amir drove from Jerusalém to the lowest on place on Earth , the dead Sea His altitude relative to sea level as a function of time is graphed what was amir's altitude at the begining of the drive?
Answers
Explanation
Step 1
define
Convert this rational number
to its decimal form and round
to the nearest tenth
2/5
Answers
Answer:
0.4
Step-by-step explanation:
First, divide 2 by 5. You should but a decimal because 5 doesn't go into 2, so you get 20. 5 does go into 20, 4 times.
The following list gives the number of pets for each of 14 students.1, 4, 4, 2, 3, 4, 3,0,0,0,3,0,0,1Send data to calculatorFind the modes of this data set.If there is more than one mode, write them separated by commas.If there is no mode, click on "No mode."
Answers
Given:
The number of pets for each of 14 students is,
1, 4, 4, 2, 3, 4, 3,0,0,0,3,0,0,1.
Mode: It is the number that appears the most.
In the given data,
0 appears the most that is for 5 times.
So, the mode of the given data is 0.
Answer: Mode is 0.
Solve for a if the line through the two given points has the given slope.(a, 6) and (0, 1), m = 1a=
Answers
Given:
Two points are,
[tex](a,6),(0,1)[/tex]The slope is,
[tex]m=1[/tex]To find:
The value of a.
Explanation:
Using the slope-intercept form of a line equation,
[tex]y=mx+c[/tex]Substituting y-intercept c = 1 and slope m = 1 we get,
[tex]y=(1)x+1[/tex]Then substituting the first point we get,
[tex]\begin{gathered} 6=a+1 \\ a=6-1 \\ a=5 \end{gathered}[/tex]The value of a is 5.
Final answer:
The value of a is 5.
An equation is shownn-5=17What is the value for n that makes the equation true
Answers
Simplify the equation n-5=17.
[tex]\begin{gathered} n-5=17 \\ n=17+5 \\ =22 \end{gathered}[/tex]So value of n is 22.
Please help me thank you I’ll send tutor a chart that goes with the question
Answers
Answer:
As time increases, the number of flyers Justin has increased.
3 flyers per minute
62 flyers at t
Explanation:
Based on the table, we can see that when the time is greater the number of flyers is also greater. So, as time increases, the number of flyers Justin has increased.
Then, to know the rate, we need to use two columns of the table, so the rate will be equal to:
[tex]\frac{Flyers_2-Flyers_1}{Time_2-Time_1}[/tex]So, if we replace Time1 by 10, Flyers1 by 92, Time2 by 15, and Flyers2 by 107, we get:
[tex]\text{rate}=\frac{107-92}{15-10}=\frac{15}{5}=3[/tex]Therefore, the rate is 3 flyers per minute.
Now, to know how many flyers he has when he started printing, we need to extend the table. We see that every 5 minutes, the flyers increase by 15. So, at 0 and 5 minutes the number of flyers was:
Time 0 5 10
Flyers 77-15 = 62 92-15 = 77 92
Therefore, the number of flyers that he has when he started printing was the number of flyers at 0 minutes. So the answer of part b is 62 flyers
is 16.5 a rational or irrational number
Answers
a rational number can be expressed by a fraction, if you cant is am irrational number
so
16.5 can by expressed like
[tex]\frac{165}{10}[/tex]so is a rational number, you can simplify the fraction
[tex]\frac{165}{10}\longrightarrow\frac{33}{2}[/tex]ΔABC - ΔDEE B D X = [?] Ente
Answers
Triangle ABC = Triangle DEF
Both triangles are similar
Hence, we will be using the similarity theorem
AB / DE = BC / EF
x / 3 = 8/6
Cross multiply
6 * x = 8 * 3
6x = 24
Divide both sides by 6
6x / 6 = 24/ 6
x = 24/ 6
x = 4
The answer is 4
given: ∠D ≅ ∠C and ∠CAB ≅ ∠DBA. Prove ΔABC ≅ ΔBAD
Answers
To prove that
[tex]\Delta ABC\cong\Delta BAD[/tex]We have to prove that they share at least 2 angles.
1.
[tex]\angle D\cong\angle C[/tex]This is a given fact.
2.
Notice that
[tex]\Delta ADE\cong\Delta\text{BEC}[/tex]Since they already share two angles: DEA and CEB (They are vertically opposite)
This way, we can conclude that:
[tex]\angle DAE\cong\angle\text{CBE}[/tex]In other words, the two angles on top of A and B are equal.
Therefore, we can conclude that
[tex]\angle DAB\cong\angle CBA[/tex]And since ΔABC and ΔBAD share two of their angles, we can conclude that they also share their third and that:
[tex]\Delta ABC\cong\Delta BAD[/tex]Q.E.D
2 points6. Which system of questions can be used to find the number of smallboxes, x, and the number of large boxes, y, on the pallet?*Small boxes and large boxes are stacked together on a pallet.The total number of boxes is 10.• The small boxes weigh 5 pound each.The large boxes weigh 12 pounds each.The total weight of the boxes is 78 pounds.O a. x + y = 7 and 5x + 12y = 10b. x + y = 10 and 5x + 12y = 10Ο Ο Ο ΟC. X + y = 10 and 5x + 12y = 78O d. x + y = 78 and 5x + 12y = 78
Answers
Let x be the number of small boxes and y be the number of large boxes. Then, for the first statement, we can write
[tex]x+y=10[/tex]For the second statement, we can write
[tex]5x+12y=78[/tex]Then, the answer is option C.
hi I'm having trouble on solving systems and graphing them
Answers
The system of equations is
0 = 2y + 6 - x (1)
0 = 4y + 3x - 8 (2)
To solve it graphically we must find 2 points on each line
So let us choose values of x and find their corresponding values of y
Let x = 2
Substitute it in equation (1)
0 = 2y + 6 - (2)
Add the like terms on the right side
0 = 2y + (6 - 2)
0 = 2y + 4
Subtract 4 from both sides
0 - 4 = 2y + 4 - 4
-4 = 2y
Divide both sides by 2
-2 = y
The 1st point is (2, -2)
Let x = 4
Substitute it in the equation to find y
0 = 2y + 6 - (4)
0 = 2y + (6 - 4)
0 = 2y + 2
Subtract both sides by 2
0 - 2 = 2y + 2 - 2
-2 = 2y
Divide both sides by 2 to find y
-1 = y
The 2nd point is (4, -1)
Now you can plot these to points and join them to draw the 1st line
We will do the same with equation (2)
Let x = 4
Substitute it in the equation (2)
0 = 4y + 3(4) - 8
0 = 4y + 12 - 8
Add the like terms in the right side
0 = 4y + (12 - 8)
0 = 4y + 4
Subtract 4 from both sides
0 - 4 = 4y + 4 - 4
-4 = 4y
Divide both sides by 4
-1 = y
The 1st point on the second line is (4, -1)
Let x = -4
0 = 4y + 3(-4) - 8
0 = 4y -12 - 8
0 = 4y + (-12 - 8)
0 = 4y - 20
Add 20 to both sides
0 + 20 = 4y - 20 + 20
20 = 4y
Divide both sides by 4
5 = y
The 2nd point on the second line is (-4, 5)
Plot the two points and join them to form the second line
As you see the two lines have point (4, -1),
then the two lines will intersect at this point
The solution of the system is (4, -1)
About 53.6% of the students in the class got a AA. If 15 students got an A, estimate the number of students in the class B. If the students got an A, find the actual number of students in the class
Answers
For A.
we have that 15 students got an A that represents the 53.6%
In this case w need to find the 100%
15 is 53.6%
x is 100%
x is the total number of students in the class
[tex]x=\frac{\frac{100}{100}\times15}{\frac{53.6}{100}}[/tex][tex]x=\frac{15\cdot100}{53.6}[/tex][tex]x=27.98[/tex]19. Does the following system have a unique solution? Why?4x-6y=-7-2x + 3y = 18
Answers
Given,
The equations are
[tex]\begin{gathered} 4x-6y=-7..............(1) \\ -2x+3y=18............(2) \end{gathered}[/tex]To find: Does the following system have a unique solution? Why?
Solution:
The determinant of the given equations are
[tex]\begin{gathered} \begin{bmatrix}{4} & {-6} \\ {-2} & {3}\end{bmatrix}=\begin{bmatrix}{-7} & {} \\ {18} & {}\end{bmatrix} \\ 4\times3-(-6\times-2) \\ =12-12 \\ =0 \end{gathered}[/tex]For unique solutions, the condition is
[tex]\begin{gathered} \frac{a_1}{a_2}=\frac{b_1}{b_2} \\ \frac{4}{-2}=\frac{-6}{3} \\ -2=-2 \end{gathered}[/tex]Condition satisfied.
Hence, the given equations have a unique solution.
A certain state uses the following progressivetax rate for calculating individual income tax:Income ProgressiveRange ($)Tax Rate0 - 20002%2001 - 9000 5%9001 and up5.4%Calculate the state income tax owed on a $60,000per year salarytax = $[?]your answer to the nearest whole dollar amount.
Answers
Answer:
$3240
Explanation:
If the tax rate for $9001 and up is 5.4%, we can calculate the state income tax when the income is $60,000. So,
$60,000 x 5.4% = $60,000 x 5.4/100 = $3240
Therefore, the tax will be:
$3240
which of the following expressions is equal to 5^6/5^2?
Answers
Simplify the expression 5^6/5^2.
[tex]\begin{gathered} \frac{5^6}{5^2}=5^6\cdot5^{-2} \\ =5^{6-2} \\ =5^4 \\ =5\cdot5\cdot5\cdot5 \\ =625 \end{gathered}[/tex]Identify the arc length of MA in terms of pi and rounded to the nearest hundredth.
Answers
To answer this question we will use the following formula for the arc length of a central angle θ degrees:
[tex]\begin{gathered} \frac{\theta}{180}\cdot\pi r, \\ \text{where r is the circumference's radius.} \end{gathered}[/tex]Assuming that Y is the circumference's center we get:
[tex]m\hat{AM}+m\hat{MH}=180^{\circ}.[/tex]Substituting mMH=88degrees we get:
[tex]m\hat{AM}+88^{\circ}=180^{\circ}\text{.}[/tex]Therefore:
[tex]\text{m}\hat{\text{AM}}=92^{\circ}\text{.}[/tex]Then the arc length of MA is:
[tex]\frac{92}{180}\cdot\pi\cdot16m\approx8.18\pi m\approx25.69m\text{.}[/tex]Answer: First option.
Can you help me with this assignment
Answers
The question provides one endpoint and then the midpoint. The midpoint on the coordinate grid is (0, -7) and one endpoint is (-2,-6).
The formula for calculting the midpoint is given as follows;
[tex]\begin{gathered} M=\frac{x1+x2}{2},\frac{y1+y2}{2} \\ Take\text{ the x coordinates and y coordinates one after the other,} \\ 0,7=\frac{-2+x2}{2},\frac{-6+y2}{2} \\ \text{The x coordinates and the midpoint coordinate are} \\ 0=\frac{-2+x2}{2} \\ \text{Cross multiply and you have;} \\ 0=-2+x2 \\ 2=x2 \\ \text{The y coordinates and the midpoint coordinates are;} \\ 7=\frac{-6+y2}{2} \\ \text{Cross multiply and you have;} \\ 14=-6+y2 \\ 14+6=y2 \\ 20=y2 \\ \text{Therefore, the coordinates for the other midpoint is derived as;} \\ (2,20) \end{gathered}[/tex]Therefore, the coordinates of B is calculated as (2, 20)
question provided in photo only need help with system b
Answers
Consistent dependent
Infinitely many solutions
Explanation:The given system of equations is:
[tex]\begin{gathered} y=-\frac{3}{2}x\ldots\ldots\ldots....\ldots\ldots\ldots\text{.}(1) \\ 3x+2y=0\ldots\ldots\ldots\ldots.......\ldots(2) \end{gathered}[/tex]A system of equations is consistent if it has at least one solution.
A system of equations is dependent if it has infinite number of solutions.
Considering the graph of the lines drawn in the question, the two lines are perfectly drawn on each other, which means that there are infinite numbers of solutions.
Therefore, the system of equations is consistent dependent.
This means that the system has infinitely many solutions. mber
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What is 12/10 as a fraction? What is 132/100 as a fraction? What is 546/100 as a fraction? What is 123/10 as a fraction? What is 872/100 as a fraction?
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What is 12/10?
6/5 or 1 1/5 or 1.2
________________
What is 132/100?
33/25 or 1 8/25 or 1.32
________________
What is 546/100?
273/50 or 5 23/50 or 5.46
________________
What is 123/10?
123/10 or 12 3/10 or 12.3
________________
What is 872/100?
218/25 or 8 18/25 or 8.72
Answer:
12/10 = 1.2132/100 = 1.32 546/100 = 5.46123/10 = 12.3 872/100 = 8.72Step-by-step explanation:
1) 12/10 as a decimal is?
→ 12/10
→ 6/5 = 1.2
2) 132/100 as a decimal is?
→ 132/100
→ 1.32
3) 546/100 as a decimal is?
→ 546/100
→ 5.46
4) 123/10 as a decimal is?
→ 123/10
→ 12.3
5) 872/100 as a decimal is?
→ 872/100
→ 8.72
Hence, these are the answers.
coefficient. | The (blank) factor that appears before a varible. constant of proportionality. | The value of the ratio between (blank) quantities that are in a proportional relationship. equation.| A mathematical statement equating two (blank). proportional. | a relationship between two quantities such that as one value increases or (blank), the other value will increase or decrease by the same multiple.
Answers
1st statement = constant number factor
2nd statement =variable
3rd statement = expression
4 th statement = decreses
In the diagram, A CAT ~ADOG. Find the value of I.С161810215DT248.3I =
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we where given two sides of the triangle without the third side
lets take the given sides to a and b
then let the third side be c which is also x
let a = 16
b = 10
c = x
using pythagoras theorem
x^2 = a^2 - b^2
x^2 = 16^2 - 10^2
x^2 = 256 - 100
x^2 = 156
therefore,
x = the square root of 156
x = 12
Together 2 people earn $28000. One earned $2000 more than the other. How much is the smaller income?
Answers
Let x be the smaller income and y be the bigger income.
So, if both earn together $28,000, then:
[tex]x+y=28000[/tex]If one earns $2000 more than the other, we can say the the bigger minus the smaller is equal to 2000, that is:
[tex]y-x=2000[/tex]Now, we can solve the second equation for y and input it into the first equation:
[tex]\begin{gathered} y-x=2000 \\ y=x+2000 \end{gathered}[/tex][tex]\begin{gathered} x+y=28000 \\ x+x+2000=28000 \\ 2x=28000-2000 \\ 2x=26000 \\ x=\frac{26000}{2} \\ x=13000 \end{gathered}[/tex]Thus, the smalle income is $13,000, alternative D.
Given the exponential equation:, find a common base and solve for x.
Answers
EXPLANATION:
Given;
We are given the exponential equation shown below;
[tex](\frac{125}{8})^{4x-1}=(\frac{4^2}{25^2})^{x+1}[/tex]Required;
We are required to
(i) Find a common base
(ii) Solve for x
Step by step solution;
To solve this problem we shall start with the following steps;
[tex][(\frac{5}{2})^3]^{4x-1}=[(\frac{2}{5})^4]^{x+1}[/tex]For the left side of the equation, we can refine by applying the rule of exponents;
[tex]\begin{gathered} Flip\text{ the left side of the equation:} \\ (\frac{2}{5})^{-3} \end{gathered}[/tex]Therefore, we now have;
[tex][(\frac{2}{5})^{-3}]^{4x-1}=[(\frac{2}{5})^4]^{x+1}[/tex][tex](\frac{2}{5})^{-12x+3}=(\frac{2}{5})^{4x+4}[/tex]We now have a common base and that means;
[tex]\begin{gathered} If: \\ a^x=a^y \\ Then: \\ x=y \end{gathered}[/tex]Therefore;
[tex]-12x+3=4x+4[/tex][tex]-12x-4x=4-3[/tex][tex]-16x=1[/tex]Divide both sides by -16;
[tex]x=-\frac{1}{16}[/tex]ANSWER:
[tex]x=-\frac{1}{16}[/tex]What should be done to these equations to solve the system of equations by elimination? [tex]2x + y = 12 \\ 5x - 3y = -3[/tex]A: Divide the first equation by 2.B: Divide the second equation by 2.C: Multiply the first equation by 3.D: Multiply the second equation by 3.
Answers
ANSWER:
C: Multiply the first equation by 3.
STEP-BY-STEP EXPLANATION:
We have the following the system of equations:
[tex]\begin{gathered} 2x+y=12 \\ 5x-3y=-3 \end{gathered}[/tex]To solve a system of equations by means of the elimination method, it must coincide in such a way that when adding equation 1 and equation 2, one of the variables are eliminated, that is, they are canceled.
Therefore, the option in this case is to multiply the first equation by 3, in this way, the first equation remains as 3y and the second remains as -3y, since when adding them, it is 0 and the variable y is canceled.
ED has a midpoint at C.If CD=6+x and CE = 2x +1, what is the length of ED?5112210
Answers
Answer: Length of ED = 22
Since according to the question and the diagram drawn above, C is the midpoint of ED;
ED = 2CE = 2CD
CE = CD
6 + x = 2x + 1
6 - 1 = 2x - x
x = 5
CD = 6 + x = 6 + 5
CD = 11
CE = 2x + 1
CE = 2(5) + 1 = 10 + 1
CE = 11
Also note from the line drawn that ED = CE + CD
Therefore, ED = 11 + 11
ED = 22
A woman is traveling in her car at 50 miles per hour. How far will that woman travel in fifteen minutes if her speed is constant? (Distance = Rate x Time)
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we know that
Distance=ratex Time
where
Rate=50 mph
Time=15 min
Convert the time to hours
1 hour=60 min
so
15 min=15/60=0.25 hours
substitute in the formula
Distance=50x0.25
Distance=12.50 milesThe vertex of parabola that opens downwards is at (0,4)
Answers
The true statement is that the points of intersection are of equal distance from the y-axis.
What is parabola?A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line which is known as the directrix.
Given that the vertex of a parabola that opens downward is at (0, 4).
The vertex of a second parabola is at (0, -4).
Therefore, the points of intersection are the distance from the y-axis.
This is because the symmetry axis of both parabolas is x = 0, thus the intersection points must be at same distance from x- axis and y-axis.
Learn more about this parabola here:
brainly.com/question/8158213
#SPJ1
The complete question is;
The vertex of a parabola that opens downward is at (0, 4). The vertex of a second parabola is at (0, –4). If the parabolas intersect at two points, which statement must be true?
The second parabola opens downward.
The second parabola opens upward.
The points of intersection are on the x-axis.
The points of intersection are of equal distance from the y-axis.
WCompare Function ValuesGiven the functions f(2) = 2:24 and g(x) = 11 - 2", which of the followingstatements is true?O f(3) > g(3)O f(3) < 9(3)Submit AnswerO f(3) = g(3)
Answers
Notice that
[tex]\begin{gathered} f(3)=2\cdot(3)^4=162 \\ g(3)=11\cdot2^3=88 \end{gathered}[/tex]Notice that
[tex]\begin{gathered} f(6)=6^2=36 \\ g(6)=2^6=64 \\ \end{gathered}[/tex]Then, f(6) < g(6)