Answer:
x= -8 , y = 5
x= 25/4 , y = 1/4
Step-by-step explanation:
substitute first eqn into the second eqn:
(7 - 3y)^2 -y^2 = 39
49 - 42y + 9y^2 - y^2 = 39
8y^2 - 42y +10 =0
4y^2 - 21y + 5 = 0
(4y-1) (y-5) = 0
y= 1/4 , 5
when y=1/4
x = 7- 3/4
=25/4
when y= 5
x = 7- 15
= -8
The required solution of the given simultaneous equations are x = -8, 25/4 and y = 5, 1/4.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
x = 7 – 3y - - - - -(1)
x² - y² = 39 - - - - (2)
Put x from equation 1 in equation 2
(7 - 3y)² -y² = 39
49 - 42y + 9y² - y² = 39
8y² - 42y +10 =0
4y² - 21y + 5 = 0
(4y-1) (y-5) = 0
y= 1/4 , 5
Substitute this values in the equation 1,
x = -8 and 25/4
Learn more about simultaneous equations here:
https://brainly.com/question/16763389
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|-6+8| = simplify the expression
Answer:
2
Step-by-step explanation:
|-6+8|
Add/subtract the numbers: -6 + 8 = 2
= |2|
Apply the absolute value rule: |a| = a, a ≥ 0
= 2
Each lap around a park is 1 1⁄5 miles. Kellyn plans to jog at least 7 1⁄2 miles at the park without doing partial laps. How many laps must Kellyn jog to meet her goal?
Answer:
She must jog 7 laps in order to meet her goal.
Step-by-step explanation:
A more accurate answer would be that she needs to run 6 1/4 laps to meet her goal. However, because the problem states that she will not be running partial laps, then the number of laps she runs must be a whole number, which in this case works out to be 7 laps.
What is the volume of this rectangular prism?
3 cm
cm
1
cm
Answer:
.75cm³
Step-by-step explanation:
To find the volume of a shape like this it is,
base×height×width.
In this case it is .5×.5×3=.75cm³
Answer:
3/4 or 0.75
Step-by-step explanation:
Length times width times height:
1/2 * 1/2 * 3
= 3/4
How many centigrams are in 6.2 dekagrams?
Answer:
6200
Step-by-step explanation:
1 Dekagram = 1000 Centigram
6.2 x 1000 =
6200
Answer:
6200 centigrams
Step-by-step explanation:
deka means 10
centi means 100th
simplify 6(x - 4) +9
To simplify use the distributive property first. Multiply 6 by each value inside the parentheses:
6(x-4) + 9
6x -24 + 9
Now combine like terms to get the final answer:
6x - 15
Please answer question now
Answer:
67.02
Step-by-step explanation:
Bryce is making a model building. He raises the walls of the building by 2centimeters five times. By how many centimeters does Bryce raise the walls all together?
Answer:
C. 10cm
Step-by-step explanation:
Bryce is making a model building.
He raises the walls of the building
by 2 centimeters five times. By how
many centimeters does Bryce raise
the walls all together?
(A) 2 cm
(C) 10 cm
(B) 5 cm
(D) 20 cm
Bryce raises the walls of the building 2centimeters five times
This means, he raises the walls 2centimeters five different times
By how many centimeters does Bryce raise the walls all together?
We can solve this by finding the product of 2centimeters five times
The total centimeters Bryce raises the walls altogether= 2 centimeters × 5 times
=2cm × 5
=10cm
Simplify
(3x + 14) + (19x - 35)
Answer:
22x -21
Step-by-step explanation:
(3x + 14) + (19x - 35)
Combine like terms
3x+19x + 14-35
22x -21
Carlos pagó una cuenta de $300 con billetes de $5 y de $10. En total empleó 45 billetes para hacer el pago, ¿cuántos billetes de cada valor utilizó
Answer:
30 billetes de 5 dólares y 15 billetes de 10 dólares
Step-by-step explanation:
I don't speak spanish but take it in school, so I understand the question but cannot respond back in spanish.
Letting x = $5 bills and y = $10 bills,
x + y = 45
5x + 10y = 300
Solving the system by substitution,
y = -x + 45
5x + 10(-x+45) = 300
5x - 10x + 450 = 300
-5x = -150
x = 30
Substituting the x-value back into the equation,
x + y = 45
30 + y = 45
y = 15
Checking my solutions, tells me that they are correct.
Hope this helped! If you don't understand the text, please us a translator!
can someone explain this please?
Answer:
Hey there!
Our equation can be: 2y+3=4y+2
Hope this helps :)
Answer:
2y+3=4y+2
I hope you got it..
Which pairs of polygons are congruent?
Answer:
pair3
Step-by-step explanation:
it is when they have same number of sides .
Answer:
1 and 3.
Step-by-step explanation:
Pair 1 and pair 3.
If we reposition one of them we see that it exactly fits onto the other.
I already found the vertex, but can someone help me find the latus rectum of this parabola?
Answer:
Step-by-step explanation:
y=x²+7
vertex(0,7)
the length of latus rectum in a parabola equal to four times the focal length :
y=x²+7
focus X=-b/2a=0
focus Y=c- (b²-1)/4a=7+1/4=29/4
focus (0 , 29/4)
latus rectum is 29/4
(x-h)^2 = 4p (y-k) 4p is the length of the latus rectum with vertex(0,7)
(0-0)²=4p(29/4-7)
0=29p-28p=1p
the length of the latus rectum is 1
Answer:
1
Step-by-step explanation:
The short answer is that the length of the latus rectum is the reciprocal of the magnitude of the leading coefficient.
In y = x^2 +7, the leading coefficient is 1.
latus rectum = 1/|1| = 1
The grades on the last art exam had a mean of 75%. Assume the population of grades on art exams is known to be distributed normally, with a standard deviation of 7%. Using the empirical rule, approximately what percent of students earn a score between 75% and 82%? 68% 16% 32% 34%
Find the z-score for both 75% and 82% then subtract them.
Z-score for 75%:
75 -75 /7 = 0-7 = 0
Using empirical rule, This translates to a percentile if 50%
Z-score for 82%
82-75 /7 = 7/7 = 1
Using empirical rule, this translates to 84.13%
Answer = 84.13-50 = 34.13% round to 34%
Answer:
34%
Step-by-step explanation:
Well 75+7=82 and one hop on the graph is 34%.
A culture of bacterial triples in size every four hours. If the bacteria population is estimated to be three million now, what will it be one day from now?
A. 4,238,000,000
B. 6,561,000,000
C. 243,000,000
D. 2,187,000,000
Answer:
1 day = 24 hours
we cam divide in 6 periods of 4 hours
if bacteria triples in size every four hours
3 millions at begining
3^7 = 2'187'000'000 bacteria
Espero que te sirva
Answer: Geometric progression
Step-by-step explanation:
0h -> 3x10^6 /4h-> 9x10^6 / 8h-27x10^6 / 12h->81x10^6 / 16h->243x10^6 / 20h-> 729x10^6 / 24h->2187x10^6 = 2.187.000.000.:
When writing a equation how do you know where to put the equal sign ?
Answer:
The equal sign is generally placed at the separation between the left hand side and the right hand side
Step-by-step explanation:
Basically a typical equation has two parts, and one part is seen to be equal to the other part, and they are:
1. The left hand side2. The right hand sideGenerally equations are expressed algebraically,that is using letters/ alphabets and symbols to express mathematical relations
The left hand side mostly is the solution of the equation, while the right hand side contains symbols, alphabets used to find solution to the equation.
what is the answer to x2 = 121.
Answer:
11 if you mean x^2
Step-by-step explanation:
Since we are solving for x, we need to just get x by its self. The only thing we have to do is get rid of the exponent of (^2). to do this, we have to take teh square root of both sides:
The square root of x^2 is x
The square root of 121 is 11
So the asnwer is x = 11
Step-by-step explanation: A common mistake in this problem would be to say that if x² = 121, x must equal 11.
However, you must set the equation equal to 0 first.
So our first step is to subtract 121 from both sides to get x² - 121 = 0.
Next, factor the left side to get (x + 11)(x - 11) = 0
So either x + 11 = 0 or x - 11 = 0.
Solving each equation from here, we find that x = -11 or x = 11.
So our answer is not just 11, it's {11, -11}.
Helen made a scale drawing of the middle school. The gym is 195 inches long in the drawing. The actual gym is 104 feet long. What scale did Helen use?
Answer:
5 inches on the drawing = 32 actual inches
Step-by-step explanation:
195 inches
104 x 12 = 1248 inches
1/39
Answer:
she used a scale of 5 inches to represent 32 inches actual length
Step-by-step explanation:
We are told that helen made the gym to be 195 inches long in the drawing.
Now, we are told that the actual length of the gym is 104 ft long.
Thus, converting to inches,
1ft = 12 inches
So, 104ft = 104 × 12 = 1248 inches
Which means that 194 inches represented 1248 inches.
So the scale is:
195:1248
Dividing both by a common factor of 39 to give a scale of (195/39):(1248/39)
This gives;
5:32
So she used a scale of 5 inches to represent 32 inches actual length
PLEASE HELP !! what is the domain of f(x)=1/3x ?
Answer:
all real numbers
Step-by-step explanation:
f(x)=(1/3)^x
The domain is the values that x can take
X can take any value
Answer:
all real numbers
Step-by-step explanation:
For the function F(x)= 1/x-2 whose graph is shown below, what is the relative value of F(x) when the value of x is close to 2?
Answer:
10,000
Step-by-step explanation:
A taxi company charges a fee of $4 plus $0.50 per kilometer. Write a formula for $C, the cost of d journey.
Answer:
C = 4 + 0.5d
Step-by-step explanation:
General equation: y = ax + b, with b is fixed term and a is rate per x.
Here,
C = y
fixed term b = 4
rate a = 0.5 per kilometer (d)
please help me on this!! i’ll mark u the brainliest
PLEASE help me with this question! No nonsense answers please. This is really urgent.
Answer:
32
Step-by-step explanation:
This is because you would want the feet and the radium kinda meeting up in a way and would need to make sure you can fill it in with th e drive way as it will be on a horizontal base so you would need X2 of the driveway to make it into a standing up horizontal base
Hope this helps
If this seems incorrect please comment with the answer that it should be and I shall change my answer thanks you :)
Someone pls help me . I also need to show work just in case my teacher ask me to send her a photo of my notebook .
Answer: (i) 3
(ii) 10
(iii) 1080
Step-by-step explanation:
(i) Coefficient is the number written before any variable.
Coefficient of x in [tex]3x+10=36[/tex] is 3.
(ii) Constant is a numerical term written without any variable.
Constant in [tex]2x+10=5x[/tex] is 10.
(iii) Let x be the number of miles Katie's family drive.
Since they charge $30 combined with $0.25 per mile drive.
So, Total charge = 0.25 x +30 ( in dollars)
If they charged $300, then
[tex]0.25 x +30 =300[/tex]
Subtract 30 from both sides, we get
[tex]0.25x=270[/tex]
Divide both sides by 0.25, we get
[tex]x=1080[/tex]
Hence, Katie drove 1080 miles.
Write an expression for two times the difference of eight and d.
Answer:
The answer is
2( 8 - d)Step-by-step explanation:
From the question difference in the statement means subtraction
So the statement
two times the difference of eight and d is written as
2( 8 - d)Hope this helps you
Answer:
the answer is 2( 8 - d) I got the same answer and got it right
Step-by-step explanation:
Find the smallest value of $x$ such that $x^2 + 10x + 25 = 8$. [tex]Find the smallest value of $x$ such that $x^2 + 10x + 25 = 8$.[/tex]
Answer:
[tex]x =-5\ - \sqrt{8}[/tex]
Step-by-step explanation:
Given
[tex]x^2 + 10x + 25 = 8[/tex]
Required
Find the smallest value of x
[tex]x^2 + 10x + 25 = 8[/tex]
Expand the expression on the right hand side
[tex]x^2 + 5x + 5x + 25 = 8[/tex]
Factorize
[tex]x(x+5)+5(x+5) = 8[/tex]
[tex](x+5)(x+5) = 8[/tex]
[tex](x+5)^2 = 8[/tex]
Take Square root of both sides
[tex]\sqrt{(x+5)^2} = \±\sqrt{8}[/tex]
[tex](x+5) = \±\sqrt{8}[/tex]
Remove bracket
[tex]x+5 = \±\sqrt{8}[/tex]
Subtract 5 from both sides
[tex]x+5-5 =-5\± \sqrt{8}[/tex]
[tex]x =-5\± \sqrt{8}[/tex]
[tex]x =-5\ + \sqrt{8}[/tex] or [tex]x =-5\ - \sqrt{8}[/tex]
Comparing both values of x;
The smallest value of x is
[tex]x =-5\ - \sqrt{8}[/tex]
Help quick anyone know this
Answer:
See step by step explantation
Step-by-step explanation:
Step 1. given
Step 2. Subtraction property of equality
Step 3. Simplification
Step 4. Subtraction property of equality
Step 5. Simplification
Step 6. Multiplication property of equality
Step 7. Simplification
can u help me with this?
Answer: Yes. The sales tax is 5% which equals $4.20 for $84
Step-by-step explanation:
[tex]\dfrac{0.60}{12}=0.05\qquad \rightarrow 5\%\\\\\\\dfrac{1.20}{24}=0.05\qquad \rightarrow 5\%\\\\\\\dfrac{1.80}{36}=0.05\qquad \rightarrow 5\%\\\\\\\dfrac{2.40}{48}=0.05\qquad \rightarrow 5\%[/tex]
The sales tax rate is proportional for the values in the table.
$84 x 0.05 = $4.20
The sales tax on a purchase of $84 is $4.20
A will states that 4/5 of estate is to be divided among relatives. Of the remaining estate1/4 goes to the American cancer society. What fraction of the estate goes to the American cancer Society
Answer:
1/9 of the estate is for American cancer societyStep-by-step explanation:
In this problem we are expected to calculate the fraction of a whole that belongs to a part. that is the fraction of the estate the belongs to American cancer society.
let us state as given that the total estate is 5
and 4 is to be divided among relatives, remaining 1
out of the remaining 1 estate,
1/4 belongs to American cancer society
Therefore the fraction of the 5 estates that belongs to American cancer society is = 1/4 of 1/5= 1/9
help me you im in danger right now
Answer:
B
Step-by-step explanation:
The student's mistake was between Step 1 and Step 2.
Here, on the left side, they added 6x and 2x. The result should be 8x, not 4x.
It should be 8x-15=3x-75, not 4x-15=3x-75.
There are 100 prize tickets in a bowl, numbered 1 to 100. What is the probability
that an even numbered prize ticket will be chosen at random, not replaced, then an
odd numbered prize ticket will be chosen? Does this represent an independent or
dependent event? Explain.
Answer:
25/99; Dependent event
Step-by-step explanation:
This is the probability that an even ticket will be chosen out of 100 tickets times the probability that an odd ticket will be chosen out of the remaining 99 tickets.
There 50 even out of 100 to start off with. After 1 even is chosen there are still 50 odd but only 99 more tickets.
(50/100)(50/99)=2500/9900= 25/99
This is a dependent event because an odd number should come after the even number only.
Answer:
25/99
Dependent event
Step-by-step explanation:
1. Multiply the possibilities
There are 50 even numbers out of 100 numbers. If one even number is drawn and not replaced, that would leave the odd ticket to be drawn out of 99 tickets. Because an even number was drawn first, all 50 odd numbers would remain.
[tex]\frac{50}{100}[/tex] · [tex]\frac{50}{99}[/tex] = [tex]\frac{2500}{9900}[/tex]
Simplify
[tex]\frac{2500}{9900}[/tex] = [tex]\frac{25}{99}[/tex]
2. This is a dependent event because the chances of an odd number being drawn was altered. If the even ticket was replaced, the probability of the odd number being drawn would not have been affected.
