Answer:
x=1
y=−2
z=5
(heres how i got the answer)
Step-by-step explanation:
x+2y+3z=12
x−3y+4z=27
−x+y+2z=7
Solve x+2y+3z=12 for x.
x=−2y−3z+12
Substitute −2y−3z+12 for x in the second and third equation.
−2y−3z+12−3y+4z=27
−(−2y−3z+12)+y+2z=7
Solve equations for y and z respectively.
y=−3+
5
1
z
z=
5
19
−
5
3
y
Substitute −3+
5
1
z for y in the equation z=
5
19
−
5
3
y.
z=
5
19
−
5
3
(−3+
5
1
z)
Solve z=
5
19
−
5
3
(−3+
5
1
z) for z.
z=5
Substitute 5 for z in the equation y=−3+
5
1
z.
y=−3+
5
1
×5
Calculate y from y=−3+
5
1
×5.
y=−2
Substitute −2 for y and 5 for z in the equation x=−2y−3z+12.
x=−2(−2)−3×5+12
Calculate x from x=−2(−2)−3×5+12.
x=1
The system is now solved.
x=1
y=−2
z=5
In January, Joanna deposited $250
into her savings account. In
February, she deposited an
additional $100. If her account has
an APR of 6% compounded monthly,
how much interest did Joanna earn
in the first two months?
The interest that Joanna earned in the first two months is $4.26.
What is the interest earned?Interest earned in the first month = future value - amount deposited.
Future value = amount deposited x (1 + monthly interest)
Monthly interest = 6/12 - 0.5% = $252.50
Interest = $252.50 = 250 = $2.50
Interest earned in the second monthly = future value of the first month + amount deposited x (1.005)
(252.50 + 100) x 1.005 = 354.26
Interest = 354.26 = 352.50 = $1.76
Total interest = $1.76 + $2.50 = $4.26
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1. Sue made a cookie cake for her friend's birthday. The diameter is 8 inches. The area of the cake is
inches² (round to the nearest hundredths place)
Answer:
50.24 inches^2
Step-by-step explanation:
D=8 inches, r=D/2, r=8/2=4 inches
Area of circle= πr^2
=3.14×4×4
=3.14×16
=50.24
I don’t know how to solve
Answer:
line it, then try to add each number going from the top, my mother gave me that advice before, it works (:
Step-by-step explanation:
Answer:
X go's first then Y
Step-by-step explanation:
I did this before and got 100% promise and mark me brainiest
Does the equation xy + 6y = 9 define y as a function of x?
O Yes
O No
Answer:
no. a function doesnt contain an = sign
Step-by-step explanation:
Answer:
Yes, it is a function.
Explanation:
xy + 6y = 9
y(x + 6) = 9
y = 9/(x + 6)
It is a inverse variation function.
Where equation: xy = k ["k" is constant]
Each value of x corresponds to a single value of y.Given g(x)=^3√x+6, on what interval is the function negative?
A (-∞, -6)
B (-∞, 6)
C (-6, ∞)
D (6, ∞)
The interval which the function is negative is (-∞, -6)
How to determine the interval?The equation of the function is given as:
[tex]g(x) = \sqrt[3]{x + 6}[/tex]
When the function is negative.
It means that g(x) is less than 0
i.e. g(x) < 0
So, we have:
[tex]\sqrt[3]{x + 6} < 0[/tex]
Take the cube of both sides
x + 6 < 0
Subtract 6 from both sides
x < -6
The above represents a value from negative infinity to -6
i.e. (-∞, -6)
Hence, the interval which the function is negative is (-∞, -6)
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12. Find the solution to the system of equations by
using
substitution.
y = -2x + 13
4x + 8y = 20
A)(-7,-1)
B)(4,5
C)(7,-1)
D)(-3,7)
Find the 9th term of the geometric sequence 8,32,128,
[tex]\text{First term,}~ a = 8\\\\\text{Common ratio,}~ r= \dfrac{32}8 = 4\\\\\text{nth term} = ar^{n-1} \\\\\text{9th term} = 8\cdot 4^{9-1}\\\\\\~~~~~~~~~~~~~=8 \cdot 4^8\\\\\\~~~~~~~~~~~~~=524288\\\\\text{The 9th of the geometric sequence is 525288.}[/tex]
if a person paid rs 32 as VAT to buy an article of cost Rs 2750 then how much money he /she pay? find it
The total amount paid for the article is Rs2782
How to determine the amount paid?The given parameters are:
Article = Rs 2750
VAT = Rs 32
The amount paid is calculated using:
Amount = Article + VAT
This gives
Amount = 2750 + 32
Evaluate
Amount = 2782
Hence, the total amount paid for the article is Rs2782
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The White Russian cocktail contains vodka, Tia Maria and milk in the ratio of 5:2:3. To make the cocktail for a party the barman used 180ml of milk. What was the total volume of the cocktail? If this was served in 60ml glasses, how many glasses would it serve?
Answer:
1) 600cm^3 2) 10 glasses
Step-by-step explanation:
x = total amount in ml
(3/10)x = 180ml (MILK)
x = 600ml
(2/10)600 = 120ml (TIA MARIA)
(1/2)600 = 300ml (VODKA)
1) 600cm^3
2) 600ml : 60ml = 10 (GLASSES)
A car and a motor bike are priced at $33090. If the value of the car is three times the value of the motor bike, how much is the car worth?
jason was surveying students about their use of the new software lab in a school. Which question in the survey is a statistical question? How many hours do you spend developing software in the software lab? What is the number of learning stations at the software lab? Where is the software lab located in the school? What are the times the software lab is open?
HELP 10 MIN/ 66 points!
hope you can understand
Jim is designing a seesaw for a children's park. The seesaw should make an angle of 30° with the ground, and the maximum height to which it should rise is 1 meter, as shown below:
A seesaw is shown with one end on the ground and the other in the air. The seesaw makes an angle of 30 degrees with the ground. The height of the seesaw from the ground, at the other end, is labeled 1 meter.
What is the maximum length of the seesaw?
Using the slope concept, it is found that the maximum length of the seesaw is of 1.73 meters.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
In this problem:
The vertical change is of 1 m.The horizontal change is the length l.The angle is of 30º.Hence:
tan(30º) = 1/l
l = 1/tan(30º)
l = 1.73.
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i need help i’m failing math!!!
Answer:
[tex]\huge\boxed{\bf\:2\sqrt{5} \:\: units }[/tex]
Step-by-step explanation:
We have a figure given in the shape of a square with a diagonal (x) passing from one edge to another. We need to find the measure of its diagonal if the side of the square is [tex]\sqrt{10}[/tex] units.
We know that, a square has all equal sides. Then, all the sides of the square will be equal to [tex]\sqrt{10}[/tex] units.
Now, let's find the diagonal.
To find the diagonal of a sqaure from one of its sides, we need to know the formula ⟶ Diagonal = side [tex]\bf\:\sqrt{2}[/tex].
By using this formula,
[tex]Diagonal (x)\\= side *\sqrt{2} \\= \sqrt{10} *\sqrt{2}\\ = \sqrt{5*2*2} \\= \boxed{\bf\:2\sqrt{5} \:units}[/tex]
→ The diagonal of the square = 2√5 units.
[tex]\rule{150pt}{2pt}[/tex]
If two variables have a correlation coefficient of r=0.625 which statement below best represents the relationship?
Answer:
There is a moderate positive linear association between the variables
Step-by-step explanation:
Since 0.5<r<0.7, there is a moderate positive linear association between the variables. The closer r is to 1, the stronger the positive linear association.
Kurt and Courtney are playing basketball. Kurt makes 2 baskets in the first game and 4 baskets in each game after that. Courtney makes 4 baskets in the first game and 2 baskets in each game after that. The table below shows the number of baskets each made in the first 4 games. Which graph shows the ordered pairs of the total number of baskets each has made after each game?
Answer:
Kurt 10 Courtney 10 Mark brainiest
Step-by-step explanation:
I did this too
Answer:
they each have 10 if you count mark me brainiest, please
Step-by-step explanation:
What type of quadrilateral is shown below? What do the symbols on the sides of this quadrilateral tell you? A quadrilateral with one pair of congruent sides.
The type of quadrilateral shown is called A kite. The symbols on the sides tell us that two pairs of adjacent sides are equal.
How to Identify a Quadrilateral?A quadrilateral is defined as a closed shape and a type of polygon that has four sides, four vertices and four angles.
Now, from the attached quadrilateral shown, we can say that it is called a Kite. This is because a kite is a quadrilateral that has 2 pairs of equal-length sides and these sides are adjacent to each other.
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Application of percentages
In an examination 25% of the candidates failed to obtain the pass mark The number of candidates who passed were 150 . How many candidates failed
Answer:
The answer is actually 50
Step-by-step explanation:
Based on the given conditions
formulate:
150 × 25% ÷ (1 - 25%)
150 × 0.35 = 37.5
1 - 0.25 0.75
Rewrite the fraction
3750 = 50
75
5/8 multiple by 4/10
Answer:
1/4
Step-by-step explanation:
[tex]\frac{5}{8}[/tex]x[tex]\frac{4}{10}[/tex]
multiply the numerators and denominators
[tex]\frac{20}{80}[/tex]
simplify
cancel the zeros and get 2/8
then simplify to 1/4
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to multiply 5/8 times 4/10.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
How do we multiply fractions? See below! ^-^///\\\\///\\\\////\\\\///\\\///\\\///\\\////\\\///\\\///\\\///\\\//\\\\////\\\\////\\\\///\\\\///\\\///\\\//\\
Multiplying fractions
Multiply the numerator of one fraction times the numerator of the other fraction:
5×4=20
Same with the denominator:
8×10=80
Put them together:
[tex]\pmb{\cfrac{20}{80}}[/tex]
Divide the numerator and denominator by 20:
[tex]\pmb{\cfrac{1}{4}}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students :)
[tex]\bf{\overline{\underline{\overline{\underline{Maribel\:Peri}}}}[/tex]
Elena and Jada are 24 miles apart on a path when they start moving toward each
other. Elena runs at a constant speed of 6 miles per hour, and Jada walks at a constant
speed of 4 miles per hour. How long does it take until Elena and Jada meet!
Answer:
Your friends' school and college
These equations represent the number of bacteria in four different dishes as a function of time, t, in days. Which equation represents the population with the greatest growth factor (also called common factor)?
SOMEONE ANSWER THIS ANS YOU’LL EARN FREE EASY POINTS FOR GIVING ME THE RIGHT ANSWER!!
The growth factor:
⇒ is the base in the exponent:
⇒ the larger it is ⇒ the greater the growth factor is!
Let's Analyze our choices:
c(t)'s growth factor: 5/2a(t)'s growth factor: 5/6d(t)'s growth factor: 3b(t)'s growth factor: 1/50The greatest growth factor is 3
Answer: d(t)
Hope that helps!
If 5 apples cost $1.15, find the cost of 16 apples
Answer:
3.68$Step-by-step explanation:
If 5 apples cost $1.15, find the cost of 16 apples
we can solve with an equation5 : 1.15 = 16 : x
x = 1.15 * 16 : 5
x = 18.04 : 5
x = 3.68
check
5 : 1.15 = 16 : 3.68
4.34 = 4.34
the answer is good
Opinions about a current event issue are recorded through responses given on a website. Opinions gathered in this fashion are an example of a ______________.
A. random sample
B. stratified random sample
C. self-selecting sample
D. systematic sample
Answer:
this is one of systematic sample and correct option is d
A multiple-choice examination has 10 questions, each with four possible answers, only one of which is correct. Suppose that one of the students who takes the examination answers each of the questions with an independent random guess. What is the probability that he answers at least six questions correctly?
Answer:
[tex]0.0197277[/tex]
Step-by-step explanation:
Consider the random variable X
Where X denotes the number of (success/having a correct answer)
in 10 identical and independent trials .
then
X follows the Binomial distribution with parameters
10 and p = p(success) = 1/4
[tex]p\left( X\geq 6\right) =\sum^{10}_{k=6} p\left( X=k\right)[/tex]
[tex]=\sum^{10}_{k=6} C^{k}_{10}\left( \frac{1}{4} \right)^{k} \left( \frac{3}{4} \right)^{10-k}[/tex]
[tex]=\frac{20686}{2^{20}} \\= 0.0197277[/tex]
What do you think are the biggest advantages & disadvantages regarding the kind of technology we have access to in the early 21st century?
The advantages and disadvantages of the kind of technology we have access to in the early 21st century include:
Advantages:
The improvement of productivity.
Better and easier communication between people.
Disadvantages:
Can be bad for the environment.
Technology might be able to replace humans in jobs.
What is technology?Technology is the result of accumulated knowledge and the application of skills, and processes used in industrial production and scientific research.
Technology is embedded in the operation of all machines for the intended purpose of an organization.
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(8 kg 300 g 120 mg) − (3 kg 500 g 480 mg) 4 kg 799 g 640 mg
The value of (8 kg 300 g 120 mg) − (3 kg 500 g 480 mg) is; 4 kg 799 g 640 mg
How to carry out Unit Conversions?We want to find the value of;
(8 kg 300 g 120 mg) − (3 kg 500 g 480 mg)
First of all, let us convert all units to kg as;
120 mg = 0.00012 kg
300 g = 0.3 kg
Thus;
8 kg 300 g 120 mg = 8 + 0.3 + 0.00012 = 8.30012 kg
Similarly, converting the second expression;
480 mg = 0.00048 kg
500 g = 0.5 kg
Thus;
3 kg 500 g 480 mg = 3 + 0.5 + 0.00048 = 3.50048 kg
Thus, we have;
8.30012 kg - 3.50048 kg = 4.77964 kg
Breaking down this gives;
4 kg 799 g 640 mg
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Can someone explain how to get the answer I’m confused on how to solve
Answer:
x=29
Step-by-step explanation:
The square notation indicates 90 degrees.
90=(x+3)+(x-1)+(x+1)
90=3x+3
87=3x
x=29
Answer:
x = 29
(x + 3)° = 32°
(x - 1)° = 28°
(x + 1)° = 30°
Step-by-step explanation:
(x + 3)° + (x - 1)° + (x + 1)° = 90°-> (x + x + x +3 -1 + 1)° = 90°-> (3x + 3)° = 90°-> 3x + 3= 90-> 3x = 90 - 3-> 3x = 87-> x = 87/3-> x = 29-> (x + 3)° = (29 + 3)° = 32°-> (x - 1)° = (29 - 1)° = 28°-> (x + 1)° = (29 + 1)° = 30°
To verify the associative property of addition, begin
by finding the sum of the polynomials:
(3x + 4) + ((5x²-1) + (2x + 6))
x² +
X +
DONE
The sum of the given polynomial is 5x²- 5x +9
Sum of polynomialPolynomials are expressions with a degree of 3 and above. Given the equation shown;
(3x + 4) + ((5x²-1) + (2x + 6))
Expand
(3x + 4) + ((5x²-1) + (2x + 6))
3x + 4 + 5x²-1 + 2x + 6
Collect the like terms
5x² + 5x + 4 - 1 + 6
5x²- 5x +9
Hence the sum of the given polynomial is 5x²- 5x +9
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Point G is on line segment FH. Given FG = 10 and GH =
10 and GH = 5, determine the
length FH.
Answer:
FH = 15
Step-by-step explanation:
G is lying between the point F & H on the line FH.
So, the distance of FH will be given by the sum of distance of FG and GH.
FH = FG + GH
= 10 + 5
= 15
1
Select the correct answer.
Find the quotient.
24-3÷1
7
I
=
1²
7
OA.
1(21 - 3)
OB.
71
21
3
-
O C.
21 3
-
71
OD. (213)
7
(2x² - 3x) / 7 is the quotient of the given division.
What is simplification?Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.
To divide by a fraction, we can multiply by its reciprocal. So to simplify the expression:
((2x-3)/x ) / (7/x²)
We can multiply the numerator by the reciprocal of the denominator:
((2x-3)/x ) * (x²/7)
Simplifying this expression, we can cancel out the common factor of x in the numerator and denominator:
(2x-3) * (x/7)
Expanding the product:
(2x² - 3x) / 7
Therefore, the quotient of ((2x-3)/x ) / (7/x^2) is (2x² - 3x) / 7.
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Please Help
Use the probability distribution table to answer the question.
X / P
0 / 0.03
1 / 0.13
2 / 0.70
3 / 0.10
4 / 0.04
What is P(2
Considering the given discrete probability distribution, it is found that [tex]P(2 < X \leq 4) = 0.14[/tex].
What does the discrete probability distribution gives?It give the probability of each outcome, and each outcome is represented by a countable number.
The desired probability is:
[tex]P(2 < X \leq 4) = P(X = 3) + P(X = 4)[/tex]
As there is an open interval at X = 2, it does not enter the calculation. The values are:
P(X = 3) = 0.1.P(X = 4) = 0.04.Hence:
[tex]P(2 < X \leq 4) = P(X = 3) + P(X = 4) = 0.1 + 0.04 = 0.14[/tex]
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