Answer:
x - 8 < -17
8. 8
x > -9
Step-by-step explanation:
make sure to put a Line under the sign srry
consider the following equation:
2x−6y=9
Determine if the given ordered pair, (2,1/2), satisfies the given equation
yes or no
Answer:
The solution to a system of linear equations is the ordered pair (or pairs) that satisfies all equations in the system. The solution is the ordered pair(s) common to all lines in the system when the lines are graphed.
Lines that cross at a point (or points) are defined as a consistent system of equations. The place(s) where they cross are the solution(s) to the system.
Parallel lines do not cross. They have the same slope and different y-intercepts. They are an example of an inconsistent system of equations. An inconsistent system of equations has no solution.
Two equations that actually are the same line have an infinite number of solutions. This is an example of a dependent system of equations.
Step-by-step explanation:
Solve the system of equations graphically.
3x + 2y = 4
−x + 3y = −5
Solution
Graph each line and determine where they cross.
The lines intersect once at (2, −1).
A graphic solution to a system of equations is only as accurate as the scale of the paper or precision of the lines. At times the point of intersection will need to be estimated on the graph. When an exact solution is necessary, the system should be solved algebraically, either by substitution or by elimination.
Substitution Method
To solve a system of equations by substitution, solve one of the equations for a variable, for example x. Then replace that variable in the other equation with the terms you deemed equal and solve for the other variable, y. The solution to the system of equations is always an ordered pair.
Example
Solve the following system of equations by substitution.
x + 3y = 18
2x + y = 11
Solution
Solve for a variable in either equation. (If possible, choose a variable that does not have a coefficient to avoid working with fractions.)
In this case, it's easiest to rewrite the first equation by solving for x.
x + 3y = 18
x = −3y + 18
Next, substitute (−3y + 18) in for x into the other equation. Solve for y.
2( 3y + 12x + y = 11
2(−3y + 18) + y = 11-------Substitute -3y + 18 in for
−6y + 36 + y = 11-------Distribute.
2(3y −5y + 36 = 11-------Combine like terms.
2(3y + 18−5y = −25-----Subtract 36 from both sides
2(3y + 18) + y = 5---- -Divide both sides by -5.
Then, substitute y = 5 into your rewritten equation to find x.
x = −3y + 18
x = −3(5) + 18
x = −15 + 18
x = 3
Identify the solution. A check using x = 3 and y = 5 in both equations will show that the solution is the ordered pair (3, 5).
Elimination Method
Another way to solve a system of equations is by using the elimination method. The aim of using the elimination method is to have one variable cancel out. The resulting sum will contain a single variable that can then be identified. Once one variable is found, it can be substituted into either of the original equations to find the other variable.
Example
Find the solution to the system of equations by using the elimination method.
x − 2y = 9
3x + 2y = 11
Solution
Add the equations.
x − 2y = 9
3x + 2y = 11
4x + 2y = 20
Isolate the variable in the new equation
4x = 20
x = 5
Substitute x = 5 into either of the original equations to find y.
x − 2y = 9
(5) − 2y = 9
−2y = 4
y = −2
Identify the ordered pair that is the solution. A check in both equations will show that (5, −2) is a solution.
It may be necessary to multiply one or both of the equations in the system by a constant in order to obtain a variable that can be eliminated by addition. For example, consider the system of equations below:
3x + 2y = 6
x − 5y = 8
Both sides of the second equation above could be multiplied by −3. Multiplying the equation by the same number on both sides does not change the value of the equation. It will result in an equation whereby the x values can be eliminated through addition.
Special Cases
In some circumstances, both variables will drop out when adding the equations. If the resulting expression is not true, then the system is inconsistent and has no solution.
4x + 6y = 13
6x + 9y = 17
3(4x + 6y = 13)
2(6x + 9y = 17)
12x + 18y = 39
12x + 18y = 34
0 = 5
The equation is false. The system has no solution.
If both variables drop out and the resulting expression is true, then the system is dependent and has infinite solutions.
6x + 15y = 24
4x + 10y = 16
2(6x + 15y = 24)
3(4x + 10y = 16)
12x + 30y = 48
12x + 30y = 48
0 = 0
The equation is true. The system has an infinite number of solutions. (Notice that both of the original equations reduce to 2x + 5y = 8. All solutions to the system lie on this line.)
Simplify the expression. n+3(n−1)
Answer:
4n - 3
Step-by-step explanation:
[tex]n+3(n-1)\\n+3n-3\\4n-3[/tex]
A woman can bicycle 78 miles in the same time as it takes her to walk 24 miles. She can ride 9 mph faster
than she can walk. How fast can she walk?
mph
Answer:
4mph
Step-by-step explanation:
what is equation of the line shown in this graph
Since this is a horizontal line, the equation for this is simply
[tex]y = -3[/tex]
If 11% of a number equals 4, find 66% of that number.
Answer:
363/20,000
.................................................................................
Answer:
24
Step-by-step explanation:
Let the number be " x ".
11 % of x = 4
( 11 / 100 ) * x = 4
x = 4 * ( 100 / 11 )
x = 400 / 11
66 % of that number
= 66 % of x.
= 66 % of 400 / 11
= ( 66 / 100 ) x ( 400 / 11 )
= ( 66 x 400 ) / ( 100 x 11 )
= 6 x 4
= 24
Express 0.03 as a percentage of 1
Answer:
3%
Step-by-step explanation:
[tex] \frac{0.03}{1} \times 100[/tex]
0.03=3/100 So
[tex] \frac{3}{100} \div 1 \times 100[/tex]
=3%
what is 5/8 divided 6
[tex]\sf \longmapsto \frac{5}{8} \div6[/tex]
[tex]\sf \longmapsto \frac{5}{8} \times \frac{1}{6} [/tex]
[tex]\sf \longmapsto \frac{5 \times 1}{8 \times 6} [/tex]
[tex]\sf \longmapsto \frac{5}{48} [/tex]
Answer In DECIMAL:
[tex]\sf \longmapsto0.1041[/tex]
The basic wage earned by a truck driver for a 40-hour week is $560.00
(i) Calculate his hourly rate
For overtime work, the driver is paid one and a half times the basic hourly rate.
(ii) Calculate his overtime wage for 10 hours overtime.
(iii) Calculate the TOTAL wages earned by the truck driver for a 55-hour week.
Answer:
i: 14
ii: 140
iii: 770
(In question iii I didn't put the 10 hours overtime in it and if I put it its 910.
Step-by-step explanation:
i: 650/40=14
ii: 14x10=140
iii: 14x55=770
What is the slope of any line that is perpendicular to the line that contains the points (8,8) and (12,12)
Answer: 1
Step-by-step explanation:
12-8=4
12-8=4
4 over 4 is 1
if it perpendicular then it's the opposite reciprocal
hope that help
Find the exact values of cos 2x and tan 2x if sin x =4/5 and x is a quadrant II angle.
Answer:
Step-by-step explanation: 3-4-5 triangle
If sinx = 4/5, then cosx = -3/5 and tanx = 4/-3 x is approximately 126.87°
cos2x = cos²x - sin²x = (-3/5)² - (4/5)² = 9/25 - 16/25 = - 7/25
tan2x = 2tanx / (1 - tan²x) = 2(4/-3) / (1 - (4/-3)²) = (8/-3) / (1 - 16/9) = (-8/3) / (-7/9)
tan2x = (-8/3) • (-9/7) = 72/21 = 24/7
40.75 in word form.
Answer:
forty and seventy-five hundredths
Step-by-step explanation:
first number with always stay the same. after decimal each number you go up a thenths place. so in this case ten, hundreths
Four students were scheduled to get a book report in 1 hour. after the first report 2/3 hour remind. The next two reports took 1/6 hour and 1/4 hour. what fraction of the hour remained?
HELP please!!!! Due in 5 min
Find x intercept
(0, 24) (4,0)
Answer:
bt.ly/d97sjdu8 there is your answer!
Step-by-step explanation:
Answer:
x-intercept is 0
Step-by-step explanation:
(0, 24) (4,0)
(x, y)
0/4=0
someone help me on these 2 questions asap! 50 points!!
Step-by-step explanation:
earbuds
we have a 1in : 0.2in scale of drawing to reality.
0.2 = 2/10 = 1/5
so, 1in in the drawing is actually 1/5in in reality.
how long are the 4in in the drawing ?
well, 4 times the 1in thing.
4×1/5 = 4/5 = 0.8in long
again the similar triangles
similar triangles means that each pair of corresponding lines (sides, heights, ...) in the triangles follows the same scaling factor for the length.
so, what do I need to multiply the side of the large triangle with to get the corresponding side length of the small triangle ?
27 × x = 9
x = 9/27 = 1/3
and that is the scale factor.
Pls help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
numbers are 24 and 210
Step-by-step explanation:
the number are : 24(2x2x2x3) and 210 (3x2x5x7)
GCF of 24 and 210 is 6
LCM of 24 and 210 is 840
9514 1404 393
Answer:
a. numbers: 24, 210
b. GCF = 6
c. LCM = 840
Step-by-step explanation:
The number each circle represents is the product of the factors in that circle:
red circle: 2×2×2×3 = 24
blue circle: 2×3×5×7 = 210
The numbers represented in the diagram are 24 and 210.
__
The GCF is the product of the common factors--the factors in the portion of the diagram where the circles overlap:
GCF = 2×3 = 6
__
The LCM is the product of all of the factors shown in the diagram:
LCM = 2×2×2×3×5×7 = 840
_____
Additional comment
I personally find this a nice way to represent two numbers, their GCF, and their LCM. Note that there cannot be any numbers in the red (only) part of the diagram that are also in the blue (only) part of the diagram. Any common factors belong in the overlap portion of the diagram.
This diagram makes it easy to see that the LCM is the product of the numbers, divided by their GCF. (The product of the two numbers will have the center portion of the diagram appear twice in the product. It only appears once in the LCM.)
2/-2.5+4.1+1.2(3+6)/-0.1
Answer:
-104.7Step-by-step explanation:
2 : (-2.5) + 4.1 + 1.2 * (3+6) : (-0.1 ) =
-0.8 + 4.1 + 10.8 : (-0.1) =
-0.8 + 4.1 + (-108) =
3.3 - 108 =
-104.7
Please Help!! I can"t solve this ! Kendrick had 2/3 of an ice cream cake left. Each piece on the ice cream cake is 1/ 12 of the entire cake. How many pieces are left?
Answer:
8
Step-by-step explanation:
What is the volume of an oblique square pyramid with base edges 25 ft and height 24ft?
A. 5,000 ft^3
B. 7,500 ft^3
C. 10,000 ft^3
D. 15,000 ft^3
Check the picture below.
5. The recursive algorithm given below can be used to compute gcd(a, b) where a and b are non-negative integer, not both zero.
procedure gcd(a, b)
if a b then gcd(a, b) := = gcd (b, a)
else if a = 0 then gcd (a, b) = b
else if a = 1 then gcd (a, b) :
:=1
else if a and b are even then gcd(a, b) 2gcd(a/2, b/2) := else if a is odd and b is even then gcd(a, b) := gcd(a, b/2)
else gcd(a, b) := gcd(a, b - a)
Use this algorithm to compute
(a) gcd(124, 244)
(b) gcd (4424, 2111).u
Implementating the given algorithm in python 3, the greatest common divisors of (124 and 244) and (4424 and 2111) are 4 and 1 respectively.
The program implementation is given below and the output of the sample run is attached.
def gcd(a, b):
#initialize a function named gcd which takes in two parameters
if a>b:
#checks if a is greater than b
return gcd (b, a)
#if true interchange the Parameters and Recall the function
elif a == 0:
return b
elif a == 1:
return 1
elif((a%2 == 0)and(b%2==0)):
#even numbers leave no remainder when divided by 2, checks if a and b are even
return 2 * gcd(a/2, b/2)
elif((a%2 !=0) and (b%2==0)):
#checks if a is odd and B is even
return gcd(a, b/2)
else :
return gcd(a, b-a)
#since it's a recursive function, it recalls the function with new parameters until a certain condition is satisfied
print(gcd(124, 244))
print()
#leaves a space after the first output
print(gcd(4424, 2111))
Learn more :https://brainly.com/question/25506437
The formula for the area of a trapezoid is A= 1/2h(b1+b2), Where h is the height and b1 and b2 are the two bases. Rewrite the formula to solve for b1 in terms of A, h, and b2.
Answer:
Correct choice: B
Step-by-step explanation:
Equation Solving
The area of a trapezoid with height h and bases b1 and b2 is given by:
We must solve this formula for h.
First, multiply by 2 to eliminate denominators:
Now, divide by b1+b2:
Swapping sides:
Correct choice: B
2 (n - 1) + 47 = 2 (3n - 1)
[tex]\\ \sf\longmapsto 2(n-1)+47=2(3n-1)[/tex]
[tex]\\ \sf\longmapsto 2n-2+47=6n-2[/tex]
[tex]\\ \sf\longmapsto 2n+47=6n[/tex]
[tex]\\ \sf\longmapsto 4n=47[/tex]
[tex]\\ \sf\longmapsto n\approx 12[/tex]
Answer:
n = 11.75
Step-by-step explanation:
2(n - 1) + 47 = 2(3n - 1) Distribute the multiplier
2n - 2 + 47 = 6n - 2 Combine terms
47 = 4n divide
n = 11.75
2) Subtract and simplify. 11 7\10 − 7 3\10 =
Answer:
4 2/5
Step-by-step explanation:
11 7/10
- 7 3/10
----------------
4 4/10
4 4/10 = 4 2/5
NEED HELP PLS
Marques was out at a restaurant for dinner when the bill came. He wanted to leave a tip of 32%. What number should he multiply the cost of the meal by to find the total plus tip in one step?
Answer:
1.32
Step-by-step explanation:
1.32
0.45 is the result of finding the product of 3 and 12 minus a number. What is the number?
7/20
19/60
−1/60
−1/20
Answer:
The answer is 7/20
Step-by-step explanation:
This is for k-12!!
Currently taking the quiz just want to help others:)
Answer:
The answer is indeed 7/20 !!
Step-by-step explanation:
For the k12 5.17 Quiz: Model with Multistep Equations
Good luck on the rest of your quiz !!!
[tex] \frac{25}{ \sqrt[3]{5} } [/tex]write ^ as a power of 5
Answer:
[tex]5^{\frac{5}{3} }[/tex]
Step-by-step explanation:
Using the rules of exponent
[tex]\sqrt[3]{a}[/tex] = [tex]a^{\frac{1}{3} }[/tex]
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]
[tex]\frac{25}{\sqrt[3]{5} }[/tex]
= [tex]\frac{5^2}{5^{\frac{1}{3} } }[/tex]
= [tex]5^{\frac{6}{3}-\frac{1}{3} }[/tex]
= [tex]5^{\frac{5}{3} }[/tex]
Work out the length x. 14cm, 7cm , right angle triangle
The given triangle is a right angled triangle. So we can use the pythagorean theorem to solve this.
Hypotenuse = 14 cm
Altitude = 7 cm
Base = x cm
Using pythagorean theorem,
Hypotenuse² = Base² + Altitude²
14² = x² + 7²
14² - 7² = x²
196 - 49 = x²
147 = x²
√147 = x
12.124 = x (approx.)
_________
Hope it helps ⚜
Determine whether the inverse of F(x) is a function.
so i have 1,521,588 poker chips how much do i need to get 2 million (poker chips on a game called pokerstars vr)
Answer: 478,412
Step-by-step explanation:
In order to do this just take 2 million and subtract the number of chips you wanted to take away. For example, it'd be 2,000,00 - 1,521,588 which leaves you with 478,412.
A car travelling at a constant speed covers 585 km in 9 hours. In how much time will it cover in 520 km? I want the answer in direct or inverse proportion.
Answer:
It took eight hours to travel 520km
Step-by-step explanation:
all graphs range from -10 through 10 ;)
Answer:B
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
First, we want to find out what is X.3x = -6 ---> x = -2
X is -2 so we want the graph point to start at -2 and from there go down to -10.