Answer:
y=-5/6
Step-by-step explanation:
-24y=20
y=-5/6
alternate:
-0.83
Last night, the temperature fell from 0°F to -13 1/5 in 4 2/5 hours What was the average temperature change per hour? the problem: -13 1/5 divided by 4 2/5
The temperature drop per hour can be represented by ___?
Answer:
What was the average temperature change per hour -3 degrees per hour
Step-by-step explanation:
Take the temperature drop and divide by the time
-13 1/5 ÷ 4 2/5
Change to improper fractions
-(13 *5+1)/5 ÷ (4*5+2)/5
-66/5 ÷22/5
Copy dot flip
-66/5 * 5/22
Rewrite
-66/22 * 5/5
-3 degrees per hour
Since we are looking for a drop
3 degrees per hour
What is a counterexample to this claim? Dividing a number by 2 always results in a smaller number.
Given:
Dividing a number by 2 always results in a smaller number.
To find:
The counterexample to the given claim.
Solution:
If 0 is divided by is divided by any non-zero real number [tex]a[/tex], then
[tex]\dfrac{0}{a}=0[/tex]
Let us consider the unknown number be 0. Then dividing a number by 2, we get
[tex]\dfrac{0}{2}=0[/tex]
Here, the result is not a smaller number because [tex]0=0[/tex].
Therefore, the counterexample to the given claim is "Dividing 0 by 2".
Answer:
-1
Step-by-step explanation:
Given OSALE, solve for x.
3
3x + 4
5x-6
S
3
A
Answer:
x=5
Step-by-step explanation:
The sides have to be equal length
3x+4 = 5x-6
Subtract 3x from each side
3x+4-3x = 5x-6-3x
4 = 2x-6
Add 6 to each side
4+6 = 2x-6+6
10 = 2x
Divide by 2
10/2 =2x/2
5 =x
Two parallel sides is 3x + 4 = 5x - 6
[tex]\bf \large \longrightarrow \: \: 3x \: + \: 4 \: = \: 5 x \: - \: 6[/tex]
[tex]\bf \large \longrightarrow \: \:6 \: + \: 4 \: = \: 5x \: - \: 3x[/tex]
[tex]\bf \large \longrightarrow \: \:10 \: = \: 2x[/tex]
[tex]\bf \large \longrightarrow \: \: \frac{10}{2} \: = \: x \\ [/tex]
[tex]\bf \large \longrightarrow \: \: \cancel\frac{10}{2} \: \large \: ^{5} \: = \: x \\ [/tex]
[tex]\bf \large \longrightarrow \: \:x \: = \: 5[/tex]
Option ( B ) is the correct answer.
I need help plz I don’t understand
Answer:
Step-by-step explanation:
If AD is an altitude, then by definition it drops from the vertex angle (the top angle) and meets the base at a right angle, which measures 90 degrees. That means that 17x + 73 is a right angle:
17x + 73 = 90 and
17x = 17 so
x = 1
Solve the following system of equations. -5x - 4y= -11 7x + 3y = 18
Step-by-step explanation:
-5x - 4y= -117x + 3y = 18
-5x +117x = 3y + 4y = 18
112x = 7y = 18
Agnes Hammer is a senior majoring in management science. She has been interviewing with several companies for a job when she graduates, and she is curious about what starting salary offers she might receive. There are 140 seniors in the graduating class for her major, and more than half have received job offers. She asked 12 of her classmates at random what their annual starting salary offers were, and she received the following responses: $28,500 $35,500 $32,600 $36,000 $34,000 $25,700 $27,500 $29,000 $24,600 $31,500 $34,500 $26,800 Assume that starting salaries are normally distributed. Compute the mean and standard deviation for these data and determine the probability that Agnes will receive a salary offer of less than $27,000.
Answer:
Mean = 30516.67
Standard deviation, s = 3996.55
P(x < 27000) = 0.0011518
Step-by-step explanation:
Given the data:
28500 35500 32600 36000 34000 25700 27500 29000 24600 31500 34500 26800
Mean, xbar = Σx / n = 366200 /12 = 30516.67
Standard deviation, s = [√Σ(x - xbar) / n-1]
Using calculator, s = 3996.55
The ZSCORE = (x - mean) / s/√n
Zscore = (27000 - 30516.67) / (3996.55/√12)
Zscore = - 3516.67 / 1153.7046
Zscore = - 3.048
P(x < 27000) = P(Z < - 3.049) = 0.0011518
Which graph represents the function f(x) = √x+3 – 1?
Answer:
look at the png below
Step-by-step explanation:
A machine with velocity ratio of 5 is used to raise a load with an effort of 500N . If the machine is 80% efficient , determine the magnitude of the load.
Answer:
Solutions given:
Velocity ratio V.R =5
effort =500N
efficiency =80%
magnitude of load=?
mechanical advantage [M.A ]
we have
efficiency =M.A/V.R*100%
80=M.A./5*100
80/100*5=M.A
M.A.=4
again
we have
M.A =load/effort
4=load/500
load=500*4
load=2000N
the magnitude of the load is 2000N.Consider the following 8 numbers, where one labelled
x
is unknown.
12, 46, 31,
x
, 49, 24, 41, 14
Given that the range of the numbers is 63,
work out 2 values of
x
.
Put the data set in order:
12, 14, 24, 31, 41, 46, 49
In order to find a value of x using the range, x has to be on either end of the data set. Meaning:
x, 12, 14, 24, 31, 41, 46, 49 or 12, 14, 24, 31, 41, 46, 49, x
Since the range is the highest value minus the lower value, you can set two equations for x:
x - 12 = 63
x = 75
49 - x = 63
x = -14
Thus, x = 75, -14
Two values of x are -14 & 75
What is range of numbers ?The difference between highest and lowest numbers of the set of numbers is called the range of numbers.
What are the values of x ?The given values are 12, 46, 31, 49, 24, 41, 14
Arranging all the values in ascending order we get,
12, 14, 24, 31, 41, 46, 49
If x will be included, then x is in the 1st position or in the last position.
Then the values are x, 12, 14, 24, 31, 41, 46, 49 or 12, 14, 24, 31, 41, 46, 49, x
The range of the number is 63
So, we get two equations from it.
1 ) 49-x = 63
2 ) x-12 = 63
Solving eq. (1) we get, x = 49-63 = -14
Solving eq. (2) we get, x = 63+12 = 75
So the values of x are -14 & 75
Learn more about range of number here :
https://brainly.com/question/10081172
#SPJ2
can yaweeeeeeeee hlp
Answer:
( 25 x 100 )
option 1 is the answer
Step-by-step explanation:
Remaining options are not correct since they don't have 100 as a factor.
GUYS I NEED HELP URGENTLY!!!!!
Answer:
y = 4x-3
Step-by-step explanation:
First we need to determine the slope
Using two points on the line (0,-3) (1,1)
Using the slope formula
m = (y2-y1) /(x2-x1)
= (1- -3)/(1-0)
(1+3)/ (1-0)
4
We know the y intercept, -3
y = mx+b where m is the slope and b is the y intercept
y = 4x-3
1. The diagram shows a triangle OAB and point M is a point on AB. Rajah menunjukkan segi tiga OAB dan titik M ialah satu titik pada AB. A 5 5a M 0 B ub Given OA= 5a , OB = 4b and 2 AM =3MB, find vector Diberi OA=5a, OB = 4b dan 2 AM =3MB, cari vektor (a) AB [4b – 5a (b) OM 12 2a +
we have to find the value of the x°=<GHC
In the triangle BDH,
<D=31°
<B=47°
we know that,
Sum of three angle of a triangle is 180°
According to the question,
<D+<B+<BHD=180°
31°+47°+<BHD=180°
78°+<BHD=180°
<BHD=180°-78°
<BHD=102°
But,
<GHC and <BHD forms a straight line
so,
<GHC+<BHD=180°
102°+x=180°
x=180°-102°
x=78°
Therefore,
The value of x is 78°
Please help me with this question please and thank you ❤️
Answer:
x = -1
Step-by-step explanation:
3x - 1/9 (27) = 18
3x - 3
Divide both sides be 3
x = -1
Answer:
x = 7
Step-by-step explanation:
to solve this equation we are given the value of y which 27. just substitute 27 for y in the equation :
3x - 1/9(27) = 18
3x - 3 = 18
3x = 21
x= 7
What is the solution to the system of equations represented by these two lines?
Question 7 options:
(0, 4)
(2, 0)
(4, 2)
(2, 3)
The answer is: (2, 3) :)
what is the value of the expression below? (8^5/3)^1/5
Answer:
8^1/3
Step-by-step explanation:
(8^5/3)^1/5
8^5/3×1/5
8^5/15
8^1/3
Answer:
Step-by-step explanation:
Exponent Rule: [tex](a^{m})^{n}=a^{m*n}[/tex]
[tex](8^{\frac{5}{3}})^{\frac{1}{5}}= 8^{\frac{5}{3}}*{\frac{1}{5}}\\\\\\=8^{\frac{1}{3}}\\\\= \sqrt[3]{8} \\\\= \sqrt[3]{2*2*2}\\\\= 2[/tex]
Ayuda
Which of the following represents the isolate the variable "r" from the following formula?
V = K * q / r
Answer:
r = K * q / V
Step-by-step explanation:
V = K * q / r
i need help in this plzz
Answer:
[tex]8x^{4}[/tex]
3n-10
(a÷5)+12
Step-by-step explanation:
Numbers listed as in the picture.
70) 8 * [tex]x^{4}[/tex]= [tex]8x^{4}[/tex]
71) 3 * n -10= 3n-10
72) 12+ a/5= (a÷5)-12
Matt covers a distance of 300 miles in 10 hours. Given that he covers an equal distance every hour, find the distance covered by him in 4 hours.
It cost David $16.75 to fill his 5-gallon gas can.
1. Write two different rates.
2. What is the best unit rate to use?
3. If David decided to fill up his car that has a 22-gallon gas tank, would $73 be enough to cover it? If so, how much does he have leftover? If not, how much is he short?
Answer: I divided 16.75 by 5
Step-by-step explanation:
For every 1 gallon hes using 3.35
So 22 x 3.35 is 73.70 so hell need 70 cent more
Use the data in the table to complete the sentence.
х
-2
-1
0
1
y
7
6
5
4
The function has an average rate of change of ______.
Answer:
-1
Step-by-step explanation:
Increasing the x-value by one results in the y-value decreasing by 1. Therefore, the average rate of change is -1.
Answer: -1
Step-by-step explanation: ;)
14 less than 8 times a number is 3 more than 4 times the number. What is the number?
Answer:
x = 17/4
Step-by-step explanation:
Let x = the number
8x-14 = 4x+3
Subtract 4x from each side
8x -14-4x = 4x+3-4x
4x-14 = 3
Add 14 to each side
4x-14+14 = 3+14
4x = 17
Divide by 4
4x/4 = 17/4
x = 17/4
Given quadrilateral ABCD, where the diagonals AC and BD intersect at point E. AE⎯⎯⎯⎯⎯⎯⎯≅EC⎯⎯⎯⎯⎯⎯⎯⎯AE¯≅EC¯ and BE⎯⎯⎯⎯⎯⎯⎯≅DE⎯⎯⎯⎯⎯⎯⎯⎯BE¯≅DE¯. Can you prove can you prove that the figure is a parallelogram? Explain.
Given:
In a quadrilateral ABCD, diagonals AC and BD intersect at point E.
[tex]AE\cong EC[/tex]
[tex]BE\cong DE[/tex]
To prove:
The figure is a parallelogram.
Solution:
We know that if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
In a quadrilateral ABCD, diagonals AC and BD intersect at point E.
[tex]AE\cong EC[/tex]
[tex]BE\cong DE[/tex]
Since the diagonals AC and BD of a quadrilateral ABCD bisect each other, therefore the quadrilateral ABCD is a parallelogram.
Hence proved.
Absolute value equations HELP PLEASE! ALGEBRA!
Answer:
[tex]4.\\\text{E. }x=5, x=-6,\\\\5.\\\text{A. }x=7, x=-3\\\\\text{18.}\\\text{D. No mistakes.}[/tex]
Step-by-step explanation:
For [tex]a=|b|[/tex], there are two cases:
[tex]\begin{cases}a=b,\\a=-b\end{cases}[/tex]
Question 4:
Given [tex]5|2x+1|=55[/tex],
Divide both sides by 5:
[tex]|2x+1|=11[/tex]
Divide into two cases and solve:
[tex]\begin{cases}2x+1=11,2x=10, x=\boxed{5}\\-(2x+1)=11,2x+1=-11, 2x=-12, x=\boxed{-6}\end{cases}[/tex]
Therefore, the solutions to this equation are [tex]\boxed{\text{E. }x=5, x=-6}[/tex].
Question 5:
Given [tex]\frac{1}{2}|4x-8|-7=3[/tex],
Add 7 to both sides:
[tex]\frac{1}{2}|4x-8|=10[/tex]
Multiply both sides by 2:
[tex]|4x-8|=20[/tex]
Divide into two cases and solve:
[tex]\begin{cases}4x-8=20,4x=28, x=\boxed{7}\\-(4x-8)=20, 4x-8=-20, 4x=-12, x=\boxed{-3}\end{cases}[/tex]
Therefore, the solutions to this equation are [tex]\boxed{\text{A. }x=7, x=-3}[/tex]
Question 18:
There are no mistakes in the solution shown. The answer properly isolates the term with absolute value with no algebraic mistakes. Following that, the answer divides the equation into both absolute value cases and solves algebraically correctly. Therefore, the correct answer is [tex]\boxed{\text{D. No mistakes.}}[/tex]
Tim used a lever to lift a heavy box off the ground. His input work was 50 J and the output work was 40 J. What was the mechanical efficiency of the lever?
A.90%
B.30%
C.80%
D.10%
The 555 points plotted below are on the graph of y=\log_b{x}y=log
b
xy, equals, log, start base, b, end base, x.
Based only on these 555 points, plot the 555 corresponding points that must be on the graph of y=b^{x}y=b
x
y, equals, b, start superscript, x, end superscript by clicking on the graph.
Answer:
See attachment for graph
Step-by-step explanation:
See comment for correct question
Given
[tex]y = \log_bx[/tex]
Required
The corresponding points on [tex]y =b^x[/tex]
On the graph, we have:
[tex](x_1,y_1) \to (1,0)[/tex]
[tex](x_2,y_2) \to (2,1)[/tex]
[tex](x_3,y_3) \to (4,2)[/tex]
[tex](x_4,y_4) \to (8,3)[/tex]
[tex](x_5,y_5) \to (16,4)[/tex]
First, we solve for b in [tex]y = \log_bx[/tex]
Using laws of logarithm, the equivalent of the above is:
[tex]x = b^y[/tex]
[tex](x_2,y_2) \to (2,1)[/tex] implies that:
[tex]2 = b^1[/tex]
[tex]2 = b[/tex]
Rewrite as:
[tex]b =2[/tex]
So, the equation [tex]y =b^x[/tex] becomes:
[tex]y = 2^x[/tex]
Using the same values of x, we have:
[tex](x_1,y_1) = (1,2)[/tex]
[tex](x_2,y_2) = (2,4)[/tex]
[tex](x_3,y_3) = (4,16)[/tex]
[tex](x_4,y_4) = (8,256)[/tex]
[tex](x_5,y_5) = (16,65536)[/tex]
See attachment for graph
The points (1,2), (2,4), and (4,16) are plotted on the graph attached below and this can be determined by using the given data.
Given :
Logarithmic Function -- [tex]\rm y = log_b(x)[/tex] --- (1)
The following steps can be used in order to determine the corresponding points that must be on the graph [tex]\rm x = b^y[/tex]:
Step 1 - Now, substitute the value of x and y that is (2,1) in the expression [tex]\rm x = b^y[/tex].
[tex]\rm 2 = b^1[/tex]
b = 2
Step 2 - Now, substitute the value of b in the equation [tex]\rm y=b^x[/tex].
[tex]\rm y = 2^x[/tex] --- (2)
Step 3 - At (x = 1) the above expression becomes:
y = 2
Step 4 - At (x = 2) the expression (2) becomes:
y = 4
Step 5 - At (x = 4) the expression (2) becomes:
y = 16
The graph of [tex]\rm y = 2^x[/tex] is attached below.
For more information, refer to the link given below:
https://brainly.com/question/14375099
Which expression is equivalent to 6(3n-4)?
1)9n-10
2)18n-24
3)18n-4
4) 3n-24
Answer:
[tex]18n - 24[/tex]
Step-by-step explanation:
[tex]6(3n - 4) = 18n - 24[/tex]
Answer:
18n-24
Step-by-step explanation:
6(3n-4)
Open the brackets .......
(6×3n)-(6×4)
=18n_24
The second sail has one side of length 22 feet and another of length 2 feet. Determine the range of possible lengths of the third side of the sail.
Answer:
20 < L < 24
Step-by-step explanation:
We know that in any given triangle, the length of two sides is always greater than the length of the third side.
Since the sail is a triangle having length of one side as 22 feet and the length of another side as 2 feet, and let L be the length of the third side.
It follows from our triangle rule of sides above that
22 + 2 > L (1)
22 + L > 2 (2)and
L + 2 > 22 (3)
It follows that from (1)
22 + 2 > L
⇒ 24 > L (4)
It follows that from (2)
22 + L > 2
⇒ L > 2 - 22
⇒ L > - 44 (5) and
It follows that from (3)
L + 2 > 22
⇒ L > 22 - 2
⇒ L > 20 (6)
Since from (5) and (6),
L > -44 and L > 20
and 20 > -44 ⇒ L > 20
⇒ 20 < L (7)
From (4) 24 > L ⇒ L < 24 (8)
Combining (7) and (8), we have
20 < L < 24
So, the possible range of values of the third side are 20 < L < 24
in 10 words or fewer, what other numbers do you think are in the domain of this function?
Answer:
Numbers greater than or equal to 0.
Step-by-step explanation:
The domain of this function is {x∈R | x≥0}, meaning that x can be anything greater than or equal to 0.
QUICK HELP! ): 20 POINTS!
A group of friends goes Sky diving, using a parachute to fall in a straight line from (1,45) to (3,36). If they keep going in a straight line, at what coordinates will they land on the x-axis?
Answer:
at x = 11
0 =-4.5X +49.5
x = 49.5/4.5
x = 11
Step-by-step explanation:
x1 y1 x2 y2
1 45 3 36
(Y2-Y1) (36)-(45)= -9 ΔY -9
(X2-X1) (3)-(1)= 2 ΔX 2
slope= -4 1/2
B= 49 1/2
Y =-4.5X +49.5
!!kinda urgent!!
You decide to put $150 in a savings account to save for a $3,000 down payment on a new car. If the account has an interest rate of 2.5% per year and is compounded monthly, how long does it take you to earn $3,000 without depositing any additional funds?
Answer:
119.95 years
Step-by-step explanation:
The general equation is given by:
[tex]P = A*(1 + \frac{r}{n} )^{n*t}[/tex]
Where:
A is the initial amount, we know that the first deposit is of $150, then:
A = $150
t is the variable, in this case, is the number of years.
n = number of times that the interest is compounded in one unit of t, because the interest is compounded monthly, we have n = 12.
r = interest rate in decimal form.
r = 2.5%/100% = 0.025
Replacing these in our equation, we get that:
[tex]P = 150*(1 + \frac{0.025}{12} )^{12*t}[/tex]
Now we want to find the time such that his savings, P, are equal to $3000.
Then we need to solve the equation:
[tex]P = 150*(1 + \frac{0.025}{12} )^{12*t} = 3000[/tex]
[tex](1 + \frac{0.025}{12} )^{12*t} = 3000/150 = 20\\[/tex]
Now, remember that:
Ln(a^x) = x*ln(a)
So if we apply the natural logarithm to bot sides, we get:
[tex]Ln((1 + \frac{0.025}{12} )^{12*t}) = Ln( 20)\\\\(12*t)*Ln(1 + \frac{0.025}{12}) = Ln(20)\\\\t = \frac{Ln(20)}{12*Ln(1 + \frac{0.025}{12})} = 119.95[/tex]
So after 119.95 years you will have the $3000.
