If a system of linear equations has exactly one solution then the slopes of both the lines should be different.
Given A system of linear equations has exactly one solution.
Linear equation is a type of equation when when plotted on the graph gives a straight line. The slope is the ratio of the vertical change to the horizontal change between two distinct points on a line.
let two equations be who have one solution
2x+3y=7
5x+6y=1
solving them
x=7-3y/2
put the value of x in second equation
5(7-3y)/2+6y=1
35-15y/2+6y=1
35-15y+12y=2
-3y=-33
y=11
put the value of y in x=7-3y/2
x=7-3*11/2
x=7-33/2
x=-26/2
x=-13.
There is only one solution which is (-13,11)
Taking equations and convert them into standard form
first
y=7/3-2/3x
second
y=1/6-5/6x
The standard form is y=a+bx where b is slope
from the above equations we can find that the slope of first equation is -2/3 and the slope of second equation is -5/6. In this way we are able to conclude that slopes should be different for one solution.
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What is 3/4 divided by 1/2
Answer:
1 1/2
Step-by-step explanation:
Convert both fractions into decimals
⇒ 3/4 (0.75) and 1/2 (0.50)
Divide the decimals:
⇒0.75 ÷ 0.50
Find the quotient
⇒ 1.5
Convert the quotient to a fraction
⇒ 1 1/2
Terms:
Operations with fractions
Given m = -1/2 and the point (3, -6), which of the following is the point-slope form of the equation
Answer:
y + 6 = -1/2(x-3)
Step-by-step explanation:
let me know if you want an explanation
What is x, the distance between points A and A'? D.15
The value of x that fills the coordinate are 7 or -5
Distance between two pointsThe formula for calculating the distance between two points is expressed as:
D = √(x2-x1)² +(y2-y1)²
Substitute the given coordinates
10 = √(15-7)² +(1-x)²
100 = 8² +(1-x)²
(1-x)² = 100 - 64
(1-x)² = 36
1- x = -6
x = 7 or -5
Hence the value of x that fills the coordinate are 7 or -5
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Complete question
If the distance between two points (x, 7) and (1, 15) is 10, find the value of x.
La diferencia de las medidas de dos ángulos suplementarios es 20% determina el complemento del menor de dichos ángulos
Smaller angle = 50
Larger angle = 130
Let smaller angle be x degree
=> larger angle= [tex]3x - 20[/tex]
Since these angles are supplementary , So
[tex]= > x + 3x - 20 = 180\\= > 4x = 200\\= > x = 50\\= > 3x - 20\\ = > 150 - 20 = 130[/tex]
So smaller angle would be 50 deg & larger angle would be 130 deg.
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the height of a plant in centimeters is modeled as a function of time, in days. consider this graph of the function enter the average rate of change for the height of the plant measured in centimeters per day between day 0 and day 20
The average rate of change for the height of the plant measured in centimeters per day between day 0 and day 20 is 1.32 cm per day.
What is average height?The average height is the ratio of change in height of the plant and the time taken taken for that change.
Given is the height of a plant in centimeters is modeled as a function of time, in days.
For day 0, the height is 18cm and the height for day 20 is 42 cm, then the average height change is
height per day = 42 - 18/ 20 -0
height per day = 1.2 cm/day
Thus, the average height of plant is 1.2 cm/day.
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6 out of 11 players played well on the baseball team. What percent is it?
Answer: 54%
Step-by-step explanation:
You will need to divide these numbers.
[tex]6/11=0.54[/tex]
After you divide that, simplify that to a percentage by multiplying it by 100.
[tex]0.54 *100=54%[/tex]%
I hope this helps!!
Expand each expression A ( x+1)^2 B(x-3)^2. C ( x+4)^2 D (x-1/2)^2
The expanded expressions are shown below:
(x + 1)² = x² + 2 · x + 1(x - 3)² = x² - 6 · x + 9(x + 4)² = x² + 8 · x + 16(x - 1/2)² = x² - x + 1/43 · (x - 5)² = 3 · (x² - 10 · x + 25) = 3 · x² - 30 · x + 75(1/2) · (x - 2)² = (1/2) · (x² - 4 · x + 4) = (1/2) · x² - 2 · x + 2How to expand perfect square trinomials
Perfect square trinomials are polynomials of grade 2 with the form (a + b)² = a² + 2 · a · b + b². In this case, we have to expand six perfect square trinomials:
a) (x + 1)² = x² + 2 · x + 1
b) (x - 3)² = x² - 6 · x + 9
c) (x + 4)² = x² + 8 · x + 16
d) (x - 1/2)² = x² - x + 1/4
e) 3 · (x - 5)² = 3 · (x² - 10 · x + 25) = 3 · x² - 30 · x + 75
f) (1/2) · (x - 2)² = (1/2) · (x² - 4 · x + 4) = (1/2) · x² - 2 · x + 2
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a die is tossed twice and the number of dots facing up in each toss is counted and noted in the order of occurrence. (a) find the sample space. (b) find the set a corresponding to the event “number of dots in first toss is not less than number of dots in second toss.” (c) find the set b corresponding to the event “number of dots in first toss is 6.” (d) does a imply b or does b imply a? (e) find and describe this event in words. (f) let c correspond to the event “number of dots in dice differs by 2.”
A die is tossed twice and a number of dots facing up in each toss are counted and noted in the order of occurrence.
a) The sample space is given as:
Sample Space (S)= {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5),(2,6),(3,1),(3,2),(3,3)(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1)(5,2)(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),c),(6,6)}.
What is the sample space?A sample space is a collection of a set of possible outcomes of a random experiment. The sample space is represented using the symbol S.
b) the set corresponding to the event number of dots in the first toss is not less than the number of dots in the second toss.
{(6,6),(6,5)(6,3)(6,2)(6,1)(6,4),(5,1)(5,2)(5,3),(5,4),(5,5),(4,1),(4,2),(4,3),(4,4),(3,1),(3,2), (2,1), (2,2),(1,1)}
c) find the set b corresponding to the event number of dots in the first toss is 6.
{(6,1),(6,2),(6,3),(6,4),c),(6,6)}.
e) a does not imply b or does b imply a.
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A dairy farmer wants to make 45% protein supplement and a standard 15% protein ration to make 1800 pounds of high grade 35% protein ration how many pounds of each should be used.
1200 pounds of protein supplement and 600 pounds of standard protein is used.
Let a be the protein supplement and b be the standard protein.
Given that protein supplement and standard protein make 1800 pounds of high grade protein.
i.e., a+b = 1800 ------- (1)
45% a + 15% b = 35% 1800
0.45a + 0.15b = 1800 (3.5)
By (1), a = 1800 - b
Substituting, we get
0.45 (1800-b) + 0.15b = 630
810 - 0.45 b + 0.15b = 630
- 0.3 b = - 180
b = -180/-0.3
b = 600
Substituting b = 600 in (1),
we get
a = 1200.
Hence, 1200 pounds of protein supplement and 600 pounds of standard protein is used.
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pls help i forgot how to do this :)
Answer:
in picture
Step-by-step explanation:
added in the picture
Given the function f ( x ) = x 2 − 6 x + 10 , what is the average rate of change of the function over the interval [ 4 , 8 ] ?
The rate of change of the function over the interval [ 4, 8 ] will be 6.
What is the rate of change of the function?
The rate of change function represents the rate at which one quantity changes in relation to another. Simply put, the rate of change is the difference between the amount of change in one item and the comparable amount of change in another.
Given function:-
F(x) = x² - 6x + 10The formula for calculating the rate of change will be given as:-
[tex]ROC = \dfrac{F(x_2)-F(x_1)}{x_2-x_1}[/tex]
We have x₁ = 4 and x₂ = 8 given in the question
F(x₂) = x²₂ - 6x₂ + 10 = (8)² - ( 6 x 8 ) + 10 =
F(x₂) = 64 - 48 + 10
F(x₂) = 26
F(x₁) = x²₁ - 6x₁ + 10 = (4)² - ( 6 x 4 ) + 10 =
F(x₁) = 16 - 24 + 10
F(x₁) = 2
[tex]ROC = \dfrac{F(x_2)-F(x_1)}{x_2-x_1}[/tex]
[tex]ROC = \dfrac{26 -2}{8-4}=\dfrac{24}{4}=6[/tex]
Therefore the rate of change of the function over the interval [ 4, 8 ] will be 6.
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What is the horizontal and vertical shift for the absolute value function below f(x)=3[x+9]+6
We will see that we have a shift of 9 units to the left and 6 units upwards
How to identify the translations?For any given function H(x), we define a vertical shift of N units as:
g(x) = H(x) + N.
If N > 0, the shift is upwards.If N < 0, the shift is downwards.While a horizontal shift is written as:
g(x) = H(x + N).
If N > 0, the shift is to the left.if N < 0, the shift is to the right.Here we know that:
f(x) = 3*|x + 9| + 6
If the original function was:
H(x) = 3*|x|
Then we can write:
f(x) = H(x + 9) + 6
So we have a shift of 9 units to the left and 6 units upwards.
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an animal shelter takes in an average of 5 animals per day. the shelter must keep its total occupancy below 300. currently the shelter has 165 animals. if none of the animals get adopted which inequality represents how many more days, x, the shelter can continue to take in animals without exceeding its occupancy limit?
Answer:
y= 5x+165
Step-by-step explanation:
the slope is 5, so five per day, plus the y-intercept, or when x = 0
Brainliest pls
look at the picture
4
Jake is the starting quarterback on his school's football team. He has completed 38 of his 79 passes this season. Which of the
following values is closest to his percentage of pass completions this season?
OA. 51%
OB. 48%
OC. 38%
OD. 30%
Reset
Submit
Session Timer: 7:52
Session Score:?
Please help
Answer: A) 51%
Step-by-step explanation:
We can estimate the percentage of pass completions by rounding both values. While estimation does not give an exact answer it will give one that is close.
38 rounds up to 40 and 79 rounds up to 80.
Now it is easier to divide.
40/80=1/2
1/2=50%
The closest answer to 50% is 51% which must be the answer.
Answer:
A)
Step-by-step explanation:
To which subsets of the Real Numbers does square root of 36 belong.
Answer:
The square root of 36 is a rational number. A rational number is a number that can be written as a fraction, a/b, where a and b are integers.
Answer:
Step-by-step explanation:
Hi, let me help you out.
The square root of 36 is 6.
6 belongs to the following subsets.
Natural Numbers (All numbers greater than 1, except fractions or decimalsWhole Numbers (All Natural Numbers + 0; fractions are still NOT included)Integers (All Whole Numbers + negative numbers; this set includes neither fractions nor decimals, like the two number sets aboveRational Numbers (All integers plus - wait for it - fractions & decimals!)Overall, 6 belongs to 4 sub-sets.
__________________
Hope I helped! Best wishes.
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NEED HELP ASAP WILL MARK BRAINLIEST!
Answer:
log_{b} (5b) = 2.609
Given that:
log_{b} (3) = 1.099
log_{b} (5) = 1.609
Evaluating with that:
[tex]\sf log_b (5b) = log_b\left(5\right)+log_b\left(b\right)[/tex]
[tex]= \sf 1.609 + 1[/tex]
[tex]= \sf 2.609[/tex]
Rule Used:
[tex]\rm \log _a\left(xy\right)=\log _a\left(x\right)+\log _a\left(y\right)[/tex]
ASSIGNMENTS
COURSES
2.(-4)2
3.42
Assignment 5. Solving Equations with Exponents
Attempt 10 of 7
Evaluate each expression. Determine if the final simplified form of the expression is positive or negative
1.-42
NEXT QUESTION
SECTION
Answer:
-16, 16, 16
Step-by-step explanation:
1) -16
2) 16
3) 16
A cell phone towerbcast a shadow that is 40 feet long . An 10- foot- tall stop sign located near the tower casts a shadow that is 8 feet long. How tall is the cell phone tower?
Using proportions, considering the relation between the height and the shadow, it is found that the cell phone tower is 50 feet.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
When the shadow is of 8 feet, the height is of 10 feet. What is the height when the shadow is of 40 feet? The rule of three is:
8 feet - 10 feet
40 feet - h feet
Applying cross multiplication:
8h = 10 x 40
Simplifying by 8:
h = 10 x 5 = 50 feet.
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What is the remainder of x^5+2x^4+9x^3-6x^2+3x+3165 divided by x-5
Answer:
8530
Step-by-step explanation:
The remainder is 5⁵ + 2(5)⁴ + 9(5)³ - 6(5)² + 3(5) + 3165 = 8530
RATS is a parallelogram. M
Answer:
Answer:
x = 12
Step-by-step explanation:
m∠S + m∠T = 180
8x + 7x = 180
15x = 180
x = 12
does this help?
A tree is making a shadow 22 feet long. The angle of elevation from the tip of
the shadow to the top of the tree is 50°.
feet. Round your answer to the nearest
The height of the tree is about
foot.
Answer:
26.2 feet
Step-by-step explanation:
tan(50°) = h/22
h = 22 × tan(50°) = 26.2 feet
A bedroom measures 9 feet long and 11 feet wide. A scale drawing is made using a scale factor of 112.
What is the length of the bedroom in the scale drawing?
3/4 11/12 5/3
multiply the actual length by the scale:
9 x 1/12 = 9/12 = 3/4
Answer: 3/4
Solve 8x + c = k for x.
A. x=8(k-c)
OB. x=
_k+c
8
O C. x = 8(k+c)
O D. x=
k-c
8
Answer: [tex]x=\frac{c-k}{8}[/tex]
Step-by-step explanation:
[tex]1) \text { } 8x+c=k \text{ (given)}\\\\2) \text { }8x=c-k \text{ (subtract } k \text{ from both sides)}\\\\3) \text { } \boxed{x=\frac{c-k}{8}} \text{ (divide both sides by 8)}[/tex]
Find x
proportions with similar triangles.
Answer:
32
(this is just an approximation due to the left triangle)
The price p in dollars that a store sets for an items is given by the equation p=c + 1/10c where c dollars is the stores cost for the items if the store sets a price of $55 for an ideal what is the cost for the item
The cost of the item whose price $ 55 is $ 50.
What is Cost Price?The cost price is the price paid by an individual to buy an item or any other commodity. Or this can also be taken as the total amount of money spent by the manufacturer to assemble a product or deliver a service.
Here, Price equation in terms of cost
P = C + C/10
P = (10C+C)/10
P = 11C/10
C = 10P /11
For P = $ 55, the cost will be
C = 10 X 55 / 11
C = 10 X 5
C = $ 50
Thus, the cost of the item whose price $ 55 is $ 50.
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PLEASE HELP WITH THIS PROBLEM!
Answer: Options 1 and 2
Step-by-step explanation:
To model exponential decay, the base of the exponential has to be less than 1.
Model exponential decay equation are
y = 0.34(0.98)^x
y = 8 (0.28)^x
Model exponential decay equation
Model exponential decay equation has the base value which is less than 1.Exponential decay is the process of reducing amount by consistent percentage rate over a time period. It can be expressed by the equation y=a(1-b)x where y is the final amount, a original amount, b decay factor, and x is the amount of time that has passed.Option C and D have the base value greater than 1. So it can't be model exponential decay equation.
Hence, the model exponential decay equation are
y = 0.34(0.98)^x
y = 8 (0.28)^x
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Eli read 1 book in 5 months If he read constantly how many books did he read?
Answer:
(life span - age when he started reading)/5months =number of books he read
Step-by-step explanation:
(life span - age when he started reading)/5months =number of books he read
Which algebraic expression is a trinomial?
O x³ + x²-√x
O 2x³-x²
○ 4x³ + x²-1/x
O x-x+√6
Answer:
D. x^6 - x + √6
Step-by-step explanation:
Last option:
⇒ x^6 - x + √6
Cannot be simplified further and has three terms.
Therefore is a trinomial.
The algebraic expression that is a trinomial is 2x³-x².
What is a polynomial?An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
A trinomial is a polynomial that has three terms.
In the given options, the only expression that has three terms is "2x³-x²". It has the terms 2x³, -x², and 0x (which is often omitted).
The other options have different numbers of terms or they have terms with fractional or radical exponents, which do not fit the definition of a trinomial.
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2. Mike is looking to purchase a Ford Explorer, which has a sticker price of $32,415. He's able to negotiate $3,000
off sticker price, and the tax rate is 6.5%. License and title fees are $395. If he trades in his minivan for $9,000
(deducted from the negotiated price before taxes), the monthly payment will be $500.95 for 60 months. He is
also offered a lease with $2,900 down and payments of $429 for 36 months.
a) How much will Mike pay total if he chooses the lease option?
b) How much more will he pay in the first three years if he chooses to buy instead?
c) How much interest will he pay if he buys?
d) Which option would you choose? Explain.
3. Maya bought a new Ford Focus for $17,400. She made a down payment of $4,000 and made monthly payments
of $396 for three years. Find the APR.
Answer:
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Step-by-step explanation:
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