Answer:
The solution to the system is S= (-2, -4).
Step-by-step explanation:
Given the system
−4x+5y=−12
x−6y=22
The first step is to solve x from the first equation for example, and substitute the expression in the second equation.
1) -4x + 5 y = -12 ⇒ -4x = -12 - 5y ⇒ x = (-12 - 5y)/-4 ⇒ x = 3 + (5/4)y
2) x - 6y = 22 ⇒ (3 + (5/4)y) - 6y = 22 ⇒ 3 + (5/4)y - 6y = 22
⇒ 3 - (19/4)y = 22 ⇒ (-19/4)y = 22- 3 ⇒ y = 19/(-19/4) ⇒ y =-4.
Finally, with the value obtained for "y", you have to return to the original equations and replace it to obtain the "x" value.
-4x + 5y = -12 ⇒ -4x + 5(-4) = -12 ⇒ -4x - 20 = -12 ⇒ -4x = -12 + 20
⇒ -4x = 8 ⇒ x = 8/-4 ⇒ x = -2.
Summarizing, the solution to this system is S = (-2, -4).
The midpoint CD of is E(-1,0) . One endpoint isC (5, 2) .
What are the coordinates of the other endpoint?
For this case we have that by definition, the midpoint formula is given by:
[tex](\frac {x_ {1} + x_ {2}} {2}, \frac {y_ {1} + y_ {2}} {2}) = (x_ {m}, y_ {m})[/tex]
We have to:
[tex](\frac {5 + x_ {2}} {2}, \frac {2 + y_ {2}} {2}) = (- 1,0)[/tex]
So:
[tex]\frac {5 + x_ {2}} {2} = - 1\\5 + x_ {2} = - 2\\x_ {2} = - 2-5\\x_ {2} = - 7[/tex]
On the other hand:
[tex]\frac {2 + y_ {2}} {2} = 0\\2 + y_ {2} = 0\\y_ {2} = - 2[/tex]
Finally we have to:
[tex]D (-7, -2)[/tex]
Answer:
[tex]D (-7, -2)[/tex]
Answer: The required co-ordinates of the other endpoint D are (-7, -2).
Step-by-step explanation: Given that the midpoint CD of is E(-1,0) . One endpoint is C(5, 2) .
We are to find the coordinates of the other endpoint D.
Let (x, y) represents the co-ordinates of the point D.
We know that the co-ordinates of the midpoint of a line segment with endpoints (a, b) and (c, d) are given by
[tex]\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right).[/tex]
So, according to the given information, we have
[tex]\left(\dfrac{5+x}{2},\dfrac{2+y}{2}\right)=(-1,0)\\\\\\\Rightarrow \dfrac{5+x}{2}=-1\\\\\Rightarrow 5+x=-2\\\\\Rightarrow x=-2-5\\\\\Rightarrow x=-7[/tex]
and
[tex]\dfrac{2+y}{2}=0\\\\\Rightarrow 2+y=0\\\\\Rightarrow y=-2.[/tex]
Thus, the required co-ordinates of the other endpoint D are (-7, -2).
Help me please I got 55 questions to go in I’m not really good at math
Answer:2 hr 30 min
Step-by-step explanation:
Answer:
D) 2 hr 30 min
Step-by-step explanation:
The current time on the clock says 6:30 pm. Sherry's mom says that she must go to bed at 9:00 pm. Note that there are 60 minutes in an hour. Subtract:
9:00 pm = 8:60 pm
Subtract:
8:60 pm - 6:30 pm = 2:30
2 hours 30 minutes is your answer, or D).
~
fredric worked 46 hours last week. his hourly rate is $8.50. What was his gross pay?
Final answer:
Fredric's gross pay for working 46 hours at an hourly rate of $8.50 is $391.00.
Explanation:
The question asks about calculating Fredric's gross pay given the number of hours he worked and his hourly rate. To find Fredric's gross pay, we multiply the number of hours worked by his hourly rate.
Fredric worked 46 hours last week and his hourly rate is $8.50. Therefore,
Gross Pay = Hours Worked × Hourly Rate
= 46 hours × $8.50/hour
= $391.00
So, Fredric's gross pay for the week is $391.00.
Fredric's gross pay for working 46 hours at $8.50 per hour is $391.00.
To find Fredric's gross pay, we multiply his hours worked by his hourly rate.
1. **Calculate total earnings for the week:**
[tex]\[ \text{Total earnings} = \text{Hours worked} \times \text{Hourly rate} \][/tex]
[tex]\[ \text{Total earnings} = 46 \text{ hours} \times \$8.50/\text{hour} \][/tex]
2. **Perform the multiplication:**
[tex]\[ \text{Total earnings} = 46 \times \$8.50 \][/tex]
[tex]\[ \text{Total earnings} = \$391.00 \][/tex]
So, Fredric's gross pay for the week was $391.00.
Simplify these expression a.-8p + (-9p)+(-2p) b. -3jk+5jk+(-6jk)
Step-by-step explanation:
Combine like terms
a. -8p + (-9p) + (-2p) = -8p -9p -2p = (-8 - 9 - 2)p = -19p
b. -3jk + 5jk + (-6jk) = -3jk + 5jk - 6jk = (-3 + 5 - 6)jk = -4jk
Terms are called "like terms" if they have the same variable part (the same letters in the same powers). Like terms differ at most coefficient.
Answer:
a. –8p + (–9p) + (–2p)
Combine the coefficients of the like monomials.
[(–8) + (–9) + (–2) = –19]
Answer: –19p
b. –3jk + 5jk + (–6jk)
Combine the coefficients the like of monomials.
[(–3) + 5 + (–6) = –4]
Answer: –4jk
Step-by-step explanation:
straight from Penn
how do you simplify 2 2/3
Answer:2.66
Step-by-step explanation:
What is six,thousand,fifty,four in standard form
Answer:
6,054
Step-by-step explanation:
6000+50+4=6054 basically.
Hope this helps!!!
Brady
In school there are 500 students. 320 of the students are females. What is the ratio of female to male students? What is the ratio of the male students to the total number of students?
Answer:
9:25
Step-by-step explanation:
500 - 320 = 180
500:180
50:18
25:9
Answer:
female to male = 8:7
male to total = 14:25
Step-by-step explanation:
since no of boys= 500-320= 280
no of boys = 280
so
male : female = 8:7
male : total = 14:25
the difference of two odd numbers is always an odd number. true or false
it is false that the difference of two odd numbers is always an odd number.
How to determine the true statement
From the question, we have the following parameters that can be used in our computation:
the difference of two odd numbers is always an odd number
By definition:
Odd numbers cannot be divided by 2 evenly
Examples are
3 and 5
The difference between these numbers is
5 - 3 = 2
This means that the statement is false
False.
The difference of two odd numbers is always an even number.
Which type of fruit has a cost $1.20 per pound?
Answer:
Apples
Step-by-step explanation:
Answer: Apples cost $1.20 per pound of apples.
Step-by-step explanation:
6/5 = 1.20 per pound of apples
4/5 = 0.80 per pound of bananas
5/4 = 1.25 per pound of peaches
9/6 = 1.50 per pound of kiwis
For the function ƒ(x) = x2 + 3, what are the outputs for the inputs −3, 2, 0, and 5?
Good morning ☕️
_______
Answer:
12 , 7 , 0 , 28
___________________
Step-by-step explanation:
ƒ(x) = x² + 3
(1) ƒ(-3) = (-3)² + 3 = 9+3=12
(2) ƒ(2) = (2)² + 3 = 4+3=7
(3) ƒ(0) = (0)² + 3 = 0+3=0
(4) ƒ(5) = (5)² + 3 = 25+3=28.
:)
7. The value of x varies directly with y, and
when x =1/3, y = 12. Write an equation to
represent the direct variation. V- X
[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we also know that } \begin{cases} x= \frac{1}{3}\\ y= 12 \end{cases}\implies 12=k\left( \cfrac{1}{3} \right)\implies 12=\cfrac{k}{3} \\\\\\ 36=k~\hspace{10em}\boxed{y=36x}[/tex]
For direct variation, represented by y = kx, we replace y and x with the provided values. We solve for k to get 36. The direct variation equation is y = 36x.
Explanation:In the case of direct variation, the equation is usually presented in the form of y = kx, where k is the constant of variation. To write an equation to represent the direct variation between x and y with the given values, we will begin by replacing y and x in our equation with the given values 12 and 1/3 respectively.
That gives us 12 = k(1/3). By solving for k, we obtain k = 12 / (1/3) = 36. Thus, the equation representing the direct variation between x and y is y = 36x.
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A shipment of 8 computers contains 4 with defects. Find the probability that a sample of size 1, drawn from the 8, will not contain a defective computer. What is the probability that a sample of 1 of the 8 computers will not contain a defective computer?
Answer:
0.5
Step-by-step explanation:
Total computers in the shipment = 8
Number of computers with defects = 4
We have to find if the sample size of 1 is drawn from the 8 computers, what is the probability that it will not contain a defective computer.
Drawing a sample size of 1 is equivalent to selecting 1 computer on random. So, in short we have to find the probability of randomly selecting a computer which is not defective.
Since, out of 8 computers, 4 are defective, so, the remaining 4 will be without defects.
Probability is defined as ratio of favorable outcomes to total number of possible outcomes.
Possible outcome here is any of the 8 computers. So number of possible outcomes is 8.
Favorable outcome is selecting the computer without defect. So, number of favorable outcomes = 4
Thus, the probability of selecting a computer without defect = 4/8 = 0.5
The probability of drawing a non-defective computer from a sample size of 8, with 4 being defective, is 0.5 or 50%.
Explanation:The question is asking for the probability that a single computer from a shipment of eight will not be defective. With 4 defective computers out of 8, we know that the other 4 are not defective. The total number of outcomes when drawing one computer is 8. We are interested in the events where the drawn computer is not defective. As there are 4 such computers, there are 4 successful outcomes.
So, to find the probability, we construct a ratio of successful outcomes (not defective computers) to total outcomes (all computers). That would be 4 over 8, or 0.5, meaning there is a 50% chance that if you draw one computer, it will not be defective.
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72% and 89% confirm that the mean theses two are scores is 80.5%
Answer:
correct. the mean of 72 and 89 is 80?5
Step-by-step explanation:
find the mean to confirm it.
(a+b)/2
72+89= 161
161/2=80.5
find the area of a triangle with a base of 8 cm and a height of 10 cm
Answer:
A = 40 cm²Step-by-step explanation:
The formula of an area of a triangle:
[tex]A_\triangle=\dfrac{b\cdot h}{2}[/tex]
b - base
h - height
We have b = 8cm, h = 10cm.
Substitute:
[tex]A=\dfrac{(8)(10)}{2}=\dfrac{80}{2}=40\ (cm^2)[/tex]
18. Convert 9.268 to a fraction, the 6 and 8 are repeating
we'll start off by making the recurring decimal value to a variable, hmmm say "x", thus x = 9.268686868......
we'll next multiply that value by a power of 10 so that the recurring decimal part moves over to the left of the decimal point, the recurring decimals in this case are "68", but we need to bring the 2 in front along as well, so to move all those three fellows, we'll need 1000.
we'll next multiply the same value by a power of 10 that brings two of the recurring decimals over, so 1000 gives us one "68" over, we'll need "6868" over to the left, so we'll use 100000, let's proceed.
[tex]\bf x = 9.2\overline{68}\qquad \qquad \begin{array}{llll} 1000\cdot x&=&9268.\overline{68}\\\\ 100000\cdot x&=&926868.\overline{68} \end{array}~\hfill \begin{array}{rllll} \stackrel{100000x}{926868.\overline{68}}\\\\ -\stackrel{1000x}{9268.\overline{68}}\\ \cline{1-1}\\ 917600.00 \end{array} \\\\\\ 100000x-1000x = 917600\implies 99000x=917600 \\\\\\ x = \cfrac{917600}{99000}\implies x = \cfrac{4588}{495}[/tex]
What are the coordinates of point B on the pre-image
Answer: C)- (2,3)
Answer on edge
What integer is represented by ten feet
below sea level?
Factor 2X4 - 20x2 - 78.
Answer:
-110 = -2^1×5^1×11^1
Step-by-step explanation:
Factor the following integer:
-110
Hint: | Is 110 divisible by 2?
The last digit of 110 is 0, which means it is even. Therefore 110 is divisible by 2:
110 = 2 55:
-110 = -2×55
Hint: | Now try to factor 55. Is 55 divisible by 2?
55 is not divisible by 2 since 55 is odd and 2 is even:
-110 = -2×55 (55 is not divisible by 2)
Hint: | Is 55 divisible by 3?
The sum of the digits of 55 is 5 + 5 = 10, which is not divisible by 3. This means 55 is not divisible by 3:
-110 = -2×55 (55 is not divisible by 2 or 3)
Hint: | Is 55 divisible by 5?
The last digit of 55 is 5, which means 55 is divisible by 5:
55 = 5 11:
-110 = -2×5×11 (11 is not divisible by 2 or 3 since 55 is not)
Hint: | Now try to factor 11. Is 11 divisible by 5?
The last digit of 11 is not 5 or 0, which means 11 is not divisible by 5:
-110 = -2×5×11 (11 is not divisible by 2, 3 or 5)
Hint: | Is 11 divisible by 7?
Divide 7 into 11:
| | 1 | (quotient)
7 | 1 | 1 |
- | | 7 |
| | 4 | (remainder)
11 is not divisible by 7:
-110 = -2×5×11 (11 is not divisible by 2, 3, 5 or 7)
Hint: | Is 11 prime?
No primes less than 11 divide into it. Therefore 11 is prime:
-110 = -2×5×11
Hint: | Express -110 as a product of prime powers.
There is 1 copy of 2, 1 copy of 5 and 1 copy of 11 in the product:
Answer: -110 = -2^1×5^1×11^1
What is the area of a rectangle with length 1/12 ft and width 3/4 ft
Answer:
3/48 or reduced 1/16
Step-by-step explanation:
1/3 x 3/4 = 3/48
Reduced:
3/48 ÷ 3/3 = 1/16
Only put the reduced fraction if it asks.
Hope this helps :)
Final answer:
The area of a rectangle with a length of 1/12 ft and a width of 3/4 ft is calculated by multiplying the length by the width, resulting in an area of 1/16 square feet.
Explanation:
To find the area of a rectangle, you multiply the length by the width. For a rectangle with a length of 1/12 ft and a width of 3/4 ft, you would calculate the area as follows:
Area = length × widthArea = (1/12) ft × (3/4) ftArea = 3/48 ft²Area = 1/16 ft²Thus, the area of the rectangle is 1/16 square feet.
the vet put 2 litters of kittens in a cage with 5 other kittens she also put 3 litters of puppies in the cage next door with one other puppy if all the litters have the same number of animals and the cages now contain the same number of animals how many animals are in each litter
answer:
10
Step-by-step explanation:
if u add 5+3+2 that will equal 10
Each litter contains 4 animals.
Explanation:To find the number of animals in each litter, we need to use the given information. We know that the vet put 2 litters of kittens in a cage with 5 other kittens, so there are a total of 7 kittens in the first cage. In the second cage, there are 3 litters of puppies with 1 other puppy, so there are 4 puppies in the second cage. Since the cages now contain the same number of animals, we can set up an equation: 2 litters of kittens + 5 other kittens = 3 litters of puppies + 1 other puppy. Substituting the given numbers, we have 2x + 5 = 3x + 1, where x represents the number of animals in each litter. Solving this equation, we find that x = 4. Therefore, each litter contains 4 animals.
Find the absolute value l-7 -9il
(-3.2) to the power of 0
Answer:
1
Step-by-step explanation:
If the perimeter of International Space Station Base, which is rectangular in shape, is 720 cm and its length is 120cm, find the area of the International Space Station Base.
Answer:
Area = 28800 cm².
Step-by-step explanation:
Given : If the perimeter of International Space Station Base, which is rectangular in shape, is 720 cm and its length is 120cm,
To find : find the area of the International Space Station Base.
Solution : We have given
Perimeter = 720 cm .
Length = 120 cm .
Perimeter = 2 ( length + width ) .
Plugging the values
720 = 2 ( 120 + width )
On dividing both sides by 2
360 = 120 + width .
On subtracting both sides by 120.
240 cm = width.
Area = length * width .
Area = 120 * 240 .
Area = 28800 cm².
Therefore, Area = 28800 cm².
26. Higher Order Thinking Explain how
you know 437,160 is greater than 43,716.
Answer:
Step-by-step explanation:
Locate the decimal point.
Count to the left of the decimal point.
The number with the most number of digits is larger than the number with fewer digits.
437160 has six digits.
It is 10 times bigger then
43716 which only has 5 digits.
the question is y³+9y²
Find the
1. domain
2. range,
3. x-intercepts,
4. y-intercepts
5. the rate of change on |-1,4|
6.find the interval(s) where the graph is increasing
7. find the interval(s) where the graph is decreasing
8.find the interval(s) where the graph is positive
Answer:
I dont think you need the answer anymore, the question is from ages ago
Step-by-step explanation:
The absolute value function has a domain of all real numbers, a range of non-negative real numbers, a single x-intercept at (0, 0), no y-intercept, a constant rate of change of 1 over the interval [-1, 4], and is increasing for x greater than 0 and decreasing for x less than 0. Overall, the graph is positive over the entire real number line.
1. Domain:
The domain of a function is the set of all possible input values (x-values) for which the function produces a real output value (y-value). In the case of the absolute value function, the output is always real, so the domain is all real numbers. Therefore, the domain is:
(x) ∈ (-∞, ∞)
2. Range:
The range of a function is the set of all possible output values (y-values) that the function produces. The absolute value function always outputs a non-negative value, so the range is:
(y) ∈ [0, ∞)
3. x-intercepts:
The x-intercepts of a function are the points where the graph of the function crosses the x-axis. This happens when the output value (y) is zero. In the case of the absolute value function, the output is zero only when the input (x) is zero. Therefore, the x-intercept is:
(0, 0)
4. y-intercepts:
The y-intercept of a function is the point where the graph of the function crosses the y-axis. This happens when the input value (x) is zero. In the case of the absolute value function, the output is always non-negative, so there is no y-intercept.
5. Rate of change on |-1,4|:
The rate of change of a function at a point is the slope of the line tangent to the graph of the function at that point. The absolute value function is a piecewise function, so it has different slopes in different intervals. Over the interval |-1, 4| , the function is simply x + 1, so the rate of change is 1.
6. Intervals where the graph is increasing:
The graph of the absolute value function is increasing over the intervals where the expression inside the absolute value bars is positive. In other words, the graph is increasing when x > 0. Therefore, the interval where the graph is increasing is:
(x) ∈ (0, ∞)
7. Intervals where the graph is decreasing:
The graph of the absolute value function is decreasing over the intervals where the expression inside the absolute value bars is negative. In other words, the graph is decreasing when x < 0. Therefore, the interval where the graph is decreasing is:
(x) ∈ (-∞, 0)
8. Intervals where the graph is positive:
The graph of the absolute value function is always non-negative, so it is positive over the entire interval:
(x) ∈ (-∞, ∞)
the sum of twice y and 9 is 21
Answer:
so y equals 6 if thats your question. What you said wus a statement not a question.
Step-by-step explanation:
21-9=12
12/2=6
answer=6
y is 6
7
factors of 56
What are factors of 56
Answer: 1 , 2 , 4 , 7 , 8 , 14 , 28 , 56
Step-by-step explanation:
Answer:
1 , 2 , 4 , 7 , 8 , 14 , 28 , 56
Step-by-step explanation:
please mark me brainiest and like and rate 5 stars
Rocky simplified an expression in three steps, as shown:
x to the power of negative 5 multiplied by y to the power of 2, over y multiplied by x to the power of 3 multiplied by x to the power of 3 multiplied by y to the power of negative 5, the whole to the power of 2 equals x to the power of negative 10 multiplied by y to the power of 4, over y to the power of 2 multiplied by x to the power of 6 multiplied by x to the power of 6 multiplied by y to the power of negative 10 equals x to the power of negative 10 multiplied by y to the power of 4, over y to the power of negative 8 multiplied by x to the power of 12.
Which is the first incorrect step and why?
Step 1, all the exponents are increased by 2
Step 1, all the exponents are multiplied by 2
Step 2, the exponents in the denominator are added during multiplication
Step 3, the exponents of the same base are added during division
Answer:
Step three is wrong because when you divide use the quotient rule which is in division the exponents are subtracted and in this problem the exponents are added
Answer:
Step 3.
Step-by-step explanation:
The given expression is
[tex](\frac{x^{-5}y^2}{yx^3\cdot x^3y^{-5}})^2[/tex]
Step 1: Using distributive property of exponent we get
[tex]\frac{(x^{-5})^2(y^2)^2}{(y)^2(x^3)^2\cdot (x^3y^{-5})^2}[/tex] [tex][\because (ab)^x=a^xb^x][/tex]
[tex]\frac{x^{-10}y^4}{y^2x^6\cdot x^6y^{-10}}[/tex]
Ste 2: Using product property of exponent, we get
[tex]\frac{x^{-10}y^4}{y^{2-10}x^{6+6}}[/tex] [tex][\because a^ma^n=a^{m+n}][/tex]
[tex]\frac{x^{-10}y^4}{y^{-8}x^{12}}[/tex]
Step 3: Using quotient property of exponent, we get
[tex]x^{(-10-12)}y^{4-(-8)}[/tex] [tex][\because \frac{a^m}{a^n}=a^{m-n}][/tex]
[tex]x^{(-22)}y^{12}[/tex]
Therefore, the first incorrect step is 3.
A used boat is on sale for 2,400.Austin makes an offer equal to 2/3 of this price.How much does Austin offer for the boat
Answer:1600 he offered
Step-by-step explanation: 2400 / 3 x 2 = 1600