1. Madison's work is correct. Her there is no mistake
2. Kaleb's work is not correct. His mistake was when he divided by 4
The owners of a recreation area are filling a small pond with water. Let W be the total amount of water in the pond (in liters). Let T be the total number of minutes that water has been added. Suppose that w= 35T +300 gives W as a function of T during the next 70 minutes.Identify the correct description of the values in both the domain and range of the function. Then, for each, choose the most appropriate set of values.
Given:
[tex]W=35T+300[/tex]To find:
The domain and the range when t = 70 minutes.
Explanation:
When t = 70, we get
[tex]\begin{gathered} W=35(70)+300 \\ W=2750l \end{gathered}[/tex]The ordered pair of the solution is,
[tex](70,2750)[/tex]As the domain is the set of all input values, so the domain will be,
[tex][0,70][/tex]As the range is the set of all output values, so the range will be,
[tex][300,2750][/tex]Final answer:
The domain is,
[tex][0,70][/tex]The range is,
[tex][300,2750][/tex]Select all prime numbers 2,4,6,7,9,5
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.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
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)
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 milesState the null and alternative hypotheses for the claimThe average score of high school basketball games is less than 88.
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?
Explanation
Step 1
define
is 16.5 a rational or irrational number
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]An equation is shownn-5=17What is the value for n that makes the equation true
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.
Together 2 people earn $28000. One earned $2000 more than the other. How much is the smaller income?
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.
Convert this rational number
to its decimal form and round
to the nearest tenth
2/5
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.
ΔABC - ΔDEE B D X = [?] Ente
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
19. Does the following system have a unique solution? Why?4x-6y=-7-2x + 3y = 18
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.
Help Please! Will give brainliest and 45 points!
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?
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.
Write a piecewise function describing your weekly pay P, in terms of the number of hours worked, h.
SOLUTION
the wage for less that 40 hours of work is
[tex]12h[/tex]The wage for more than 40 hours is:
[tex]1.5\times12=18h[/tex]Therefore the piecewise function is
[tex]\begin{cases}12h{,0\lt h\le40} \\ 18h{,h\gt40}\end{cases}[/tex]
Solve for a if the line through the two given points has the given slope.(a, 6) and (0, 1), m = 1a=
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.
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
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.
which of the following expressions is equal to 5^6/5^2?
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]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.
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
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
Can you help me with this assignment
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)
given: ∠D ≅ ∠C and ∠CAB ≅ ∠DBA. Prove ΔABC ≅ ΔBAD
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
The vertex of parabola that opens downwards is at (0,4)
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)
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)
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?
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 $0.75.
A certain state uses the following progressivetax rate for calculating individual income tax:Income ProgressiveRange ($)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.
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
Given the exponential equation:, find a common base and solve for x.
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]Identify the arc length of MA in terms of pi and rounded to the nearest hundredth.
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.
In the diagram, A CAT ~ADOG. Find the value of I.С161810215DT248.3I =
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
question provided in photo only need help with system b
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
Please help me thank you I’ll send tutor a chart that goes with the question
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
hi I'm having trouble on solving systems and graphing them
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)