Answer: Choice C
(-19/2, -33/2)
=========================================================
Explanation:
We'll plug the second equation into the first one
In other words, we'll replace every copy of y with 3x+12 and solve for x
This is an example of the substitution rule.
x-y = 7
x-( y ) = 7
x - (3x+12) = 7
x - 3x - 12 = 7
-2x - 12 = 7
-2x = 7+12
-2x = 19
x = -19/2
Based on this alone, we can see the answer must be choice C. No other answer choice has this x coordinate.
-----------------------------------
If you want to find y based on this x value, then,
y = 3x+12
y = 3(-19/2)+12
y = -57/2 + 12
y = -57/2 + 24/2
y = (-57+24)/2
y = -33/2
This fully confirms choice C is correct.
So we have x = -19/2 and y = -33/2 pair up to get us (-19/2, -33/2)
In decimal form, this would be (-9.5, -16.5)
Answer:
3. (-19/3, -33/2)
You have to make a equation system :
[tex]\left \{{{x - y = 7} \atop { y = 3x + 12}} \right. <=> \left \{{{y = x - 7} \atop { y = 3x + 12}} <=> x-7 = 3x + 12 <=> 3x -x = -7 - 12 <=>[/tex] [tex]2x = -19 <=> x = -19/2[/tex]
Replacing x=-19/2 in the first equation (it's the easiest to solve) :
[tex]y = -19/2 - 7 <=> y =-19/2- 14/2 <=> y = -33/2[/tex]
What product is positive (2/5)(-8/9)(-1/3)(-2/7). (-2/5)(8/9)(-1/3)(-2/7). (2/5)(8/9)(1/3)(-2/7). (-2/5)(-8/9)(1/3)(2/7)
Answer:
d
Step-by-step explanation:
a. (2/5)(-8/9)(-1/3)(-2/7)= - 32/945
b. (-2/5)(8/9)(-1/3)(-2/7) = -32/945
c. 2/5 * 8/9 * 1/3 * - 2/7 = - 32/945
d. -2/5 * - 8/9 * 1/3 * 2/7 = 32/945
Answer:
D
Step-by-step explanation:
32/945 is the final answer
Evaluate Sigma 5 n=1 3(-2)^n-1
Answer choices
-93
-33
33
93
Answer:
93
Step-by-step explanation:
the answer is 93 no -93 i think so
Lmk if you understand thanks
Answer:
y = 100,000 (1 + 0.04) ²⁰
Step-by-step explanation:
Here:
100,000 = original amount.
0.04 = rate (a percent)
and
20 = number of times you need to run the simulation.
The president of the math club is conducting a survey to see where the 12th grade class wants to go to their field trip. Instead of asking the whole class, she surveys only the 12th grade members of the math club. She records the choices and plans to present the results to the school principal. what kind of sampling did she use?
Convenience sampling.
What is the slope of the line?
Answer:
1/2
slope = Δy/Δx
start at (-1,3) to get to the line from there you can go down 1 ( Δy = -1)
and left 2 (Δx = -2)
-1/-2 = 1/2
Step-by-step explanation:
An _____________________________ is an answer that falls outside of the domain of the function.
Answer:
irrelevant is the answer for it doesn't belong
Two cars that are 600km apart are moving towards each other. Their speeds differ by 6km per hour and the cars are 123km apart after 4.5 hours. Find the speed of each car
Answer: [tex]56\ kmph,\quad 50\ kmph[/tex]
Step-by-step explanation:
Given
Two cars are 600 km apart moving towards each other
Difference in their speed is 6 kmph
After 4.5 hr, they are 123 km apart that is, they covered a distance of [tex]600-123=477\ km[/tex] in 4.5 hours
Suppose their speeds is [tex]v_1\ \text{and}\ v_2[/tex]
[tex]\therefore v_1-v_2=6\quad \ldots(i)[/tex]
Also, distance traveled is given by
[tex]\Rightarrow 477=[v_1+v_2]4.5\\\Rightarrow v_1+v_2=106\quad \ldots(ii)[/tex]
Solve, (i) and (ii) , we get [tex]v_1=56\ kmph\ \text{and}\ v_2=50\ kmph[/tex]
what's the equation of a line with slope 5 and y-intercept -2
Answer
Slope-intercept form: y=5x-2
Standard form: 5x-y=2
Explanation
Slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept. You can just plug in the numbers to go y=5x-2.
Standard form is Ax+By=C. This form is usually used to find the x-intercept and y=intercept. You can rearrange the numbers to get standard form; 5x-y=2.
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
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
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.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
Someone please help me understand this question. Its timed and Im really confused and cant afford to miss questions.
Answer:
B For each x increase of 1, the y increases by a common factor of 3
Step-by-step explanation:
so it means that y is adding 3 every time x adds 1
Answer:D
The last one explanation of that graphic line is correct answer.
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
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]
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°
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
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.
!!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.
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
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
Solve for x.
8 - 2x = 5(x - 4)
X = [?]
Enter
Answer:
4
Step-by-step explanation:
8-2x=5(x-4)
8-2x=5x-20
28=7x
x=4
Answer: x=4
given equation: 8 - 2x= 5(x-4)
STEP 1: distribute the 5 with ONLY the parenthesis which is (x-4)
so it will be 5x-20 (-20 because 5 x -4= -20)
Now the equation is 8 - 2x= 5x - 20
STEP 2: ADD 20 on both SIDES
8+20= 28
New equation: 28 - 2x= 5x
STEP 3: ADD 2x on both sides 2x+5x= 7x
STEP 4: Now divide 28 by 7
28/7= 4
Therefor x= 4
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
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%
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
4. State one use of the following gases: a) Argon - b) Helium -
Step-by-step explanation:
HELIUM: To fill air balloon
ARGON: Used for filling incandescent metal filament electric bulbs
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.
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
