Solve the system.
x - 5y + 4z=27
4x-3y-z-23
3x + 3y - 6z=-9
Answer:
Step-by-step explanation:
Step by step solution of a set of 2, 3 or 4 Linear Equations using the Substitution Method x-5y+4z=27,4x-3y-z=23,3x+3y-6z=-9 Tiger Algebra Solver.
Question is down below, match the answer choices with the units.
whichWe define:
• A = original area = 100 sq units,
,• A' = dilated area.
If we dilate a trapezoid in a scale factor k, the area scales as:
[tex]A\rightarrow A^{\prime}=k^2\cdot A\text{.}[/tex]Using the area A = 100 sq units, we have:
[tex]\begin{gathered} A^{\prime}=k^2\cdot100\text{ sq units,} \\ k^2=\frac{A^{\prime}}{100\text{ sq units}}, \\ k=\sqrt[]{\frac{A^{\prime}}{100\text{ sq units}}}\text{.} \end{gathered}[/tex]This formula gives as the scale factor k for witch we must dilate the trapezoid to have an area A'.
1) For A' = 6400 sq units, we have:
[tex]k=\sqrt[]{\frac{6400\text{ sq units}^{}}{100\text{ sq units}}}=\sqrt[]{64}=8.[/tex]2) For A' = 100 sq units, we have:
[tex]k=\sqrt[]{\frac{100\text{ sq units}^{}}{100\text{ sq units}}}=\sqrt[]{1}=1.[/tex]3) For A' = 25 sq units, we have:
[tex]k=\sqrt[]{\frac{25\text{ sq units}^{}}{100\text{ sq units}}}=\sqrt[]{\frac{1}{4}}=\frac{1}{2}.[/tex]4) For A' = 900 sq units, we have:
[tex]k=\sqrt[]{\frac{900\text{ sq units}^{}}{100\text{ sq units}}}=\sqrt[]{9}=3.[/tex]Answers
• 8
,• 1
,• 1/2
,• 3
How to turn “the number with the units digit equal to x and the tens digit three more than the ones digit” into a algebraic problem
The number with the unit digit equal to x and the tens digit three more than the one's digit is; 30 + 11 X
How to identify the place value of a digit in a number?The place values on the left of the decimal point start as ones, tens, hundreds, and so on. The place value on the right of the decimal point starts from the point and goes to the right as tenths, hundredths so on...
Given the statement as“the number with the units digit equal to x and the tens digit three more than the ones digit”
We need to convert the statement into the algebraic expression.
We know that unit digit number = X × 1
Then Tens digit number = (3 + X ) 10
Thus, the number = 30 + 10X + X
Hence, the Number = 30 + 11 X
The number with the unit digit equal to x and the tens digit three more than the one's digit is; 30 + 11 X
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Find the value of r in the equation below.X-17 = 12
Answer : x = 39
We are given the equation
x - 17 = 12
First, isolate the value of x
When you isolate the value of x, the figure 17 cross the equality sign and change to positive
x = 12 + 17
x = 39
What situation cannot be represented by the equation x + 10 = 45?
A. Nicholas rode his bike 45 miles last week. He rode 10 miles on Tuesday and the rest of the miles on Wednesday. What is x, the number of miles Nicholas rode his bike on Wednesday?
B. Two players scored a total of 45 points in a game. One player scored 10 points. What is x, the number of points scored by the other player?
C. Marissa spent $45 on a hat and a shirt. The hat cost $10. What is x, the cost of the shirt in dollars?
D. There are 45 students in a group. There are also 10 adults in the group. What is x, the total number of students and adults in the group?
Jeffrey rolled a 12-sided dice 15 times. It landed on a number greater than 10 three times. How
does the experimental probability of Jeffrey's rolls compare to the theoretical probability of
rolling a number greater than 10?
The experimental probability of the roll is greater than the theoretical probability
How to compare the experimental probability and theoretical probability?
Probability is the likelihood of a desired event happening.
Experimental probability is a probability that relies mainly on a series of experiments.
Theoretical probability is the theory behind probability. To find the probability of an event, an experiment is not required. Instead, we should know about the situation to find the probability of an event occurring.
Given that:
Jeffrey rolled a 12-sided dice 15 times and it landed on a number greater than 10 three times
Experimental probability = 3/15 = 1/5
But theoretically, a number greater than 10 in 12-sided dice have the probability of 2 out of 12 as illustrated with the numbers below:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
Theoretical probability = 2/12 =1/6
Therefore, the experimental probability (1/5) of rolling a number greater than 10 is greater than the theoretical probability (1/6)
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if the measure of angle ADC is 59 , what is the measure of angle BDC
The angle of BDC is 60 degrees.
The Angle Sum Property: What Is It?The angle sum property of a triangle states that the sum of a triangle's three internal angles is 180 degrees. A triangle is a closed figure made up of three line segments that have both internal and external angles. When the values of the other two angles are known, the measure of an unknown interior angle can be determined using the angle sum property.
The data listed above can be inserted into our diagram. ADB and BDC complement one another, therefore their combined degree measurement is 180. Thus, m∠ADB is equal to 180 – 60, or 120 degrees.
Given,
∠ADC = 59
∠BDC = ?
∠ADB = ∠BCD
∠BCD = 90
∠ADB = 90
∠ADC = 59
∠ADB + ∠BDC = 59
90 + ∠BDC = 59
∠BDC = -31
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Convert the following repeating decimal to a fraction in simplest form .38
The answer is : 7/18
Step by step:
(0.38 x 10) - 0.3/9
3.5 = 35
---- ----
9 90
= 7/18
8. Un vendedor de bebidas en un conocido pueblo mágico analiza sus ventas en días festivos
y encuentra que si vende x bebidas en un día su utilidad (en pesos) está dada por.
y=-0.015x² +45x-2700
¿Cuál es la utilidad máxima por día festivo?
Answer: the maximum profit per holiday is 31050 pesos
Step-by-step explanation:
y=-0,015x²+45x-2700 (1)
It`s a quadratic equation like y=ax+bx+c
Therefore, the value of x at which y is maximal is:
[tex]\displaystyle\\x=\frac{-b}{2a} \\\\x=\frac{-45}{2(-0.015)} \\\\x=\frac{-45}{-0.03} \\\\x=\frac{45(100)}{0.03(100)}\\\\x=\frac{4500}{3} \\\\x=\frac{3(1500)}{3} \\\\x=1500[/tex]
Substitute the value of x into equation (1):
[tex]y=-0,015(1500^2)+45(1500)-2700\\\\y=-0.015(15*10^2)^2+67500-2700\\\\y=-0.015(15^2)(10^4)+64800\\\\y=-0,015*225*10^4+64800\\\\y=-150*225+64800\\\\y=-33750+64800\\\\y=31050 \ pesos[/tex]
What is the slope of a line perpendicular to the line whose equation is 2x+3y=24
simplify
please help asap love you if u do ;)
The slope of the line perpendicular to the line whose equation 2x+3y= 24 is 3/2
The equation of the line is
2x+3y = 24
The standard form of the linear equation is
Ax + By = C
Where A, B and C are the integers
By comparing the standard form of the linear equation with the given equation
A = 2
B = 3
C = 24
The slope of the equation in standard form m = - A/B
Substitute the values in the equation
The slope of the equation in standard form m = -2/3
Slope of a line perpendicular to the line = -1/m
= -1/(-2/3)
= 3/2
Hence, the slope of the line perpendicular to the line whose equation 2x+3y= 24 is 3/2
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1 7
_ + _
6 10
Ayuda por favor
Answer: no entiendo la estructura de la operacion
Step-by-step explanation:
write each expression as a product
(2x+y)^2-(x-2y)^2
Answer:3x^ - 3y^ + 8xy (^ is ^2 !!)
Step-by-step explanation:
(2x+y)^ - (x-2y)^(2x+y)(2x+y) - (x-2y)(x-2y)4x^ + 2xy + 2xy + y^ - x^ + 2xy + 2xy - 4y^
need help btw the last two i guessed the last to boxes so yea
Answer:
Everything is right. No need to change anything.
Which number is a MULTIPLE of both 12 and 24?
A: 6
B: 24
C: 12
D: 8
E: 2
Answer:B - 24
Step-by-step explanation:
12 x 2 = 24
24 x 1 = 24
1) Calculate the perimeter of
this triangle
7cm
4cm
10cm
6cm
Answer:
23cm
Step-by-step explanation:
in this problem the 4cm actually doesnt matter. so what you can dois 7cm+6cm+10cm=answer
7cm+6cm+10cm=23cm
simplify the expression . express using positive exponents.
The simplified expression of (5x⁶y²)³ is 125[tex]x^{18}y^{6}[/tex] which is expressed using the positive exponents.
What exactly is a positive exponent?A positive exponent indicates that the base should be multiplied by that many.
Give a good illustration of a positive exponent.For instance, 10 should be multiplied by 10x10x10, or 1000, if the number is 103. The variable x should be multiplied by itself nine times if the variable is x raised to 9.
What does "simplifying exponent" mean?It is possible to simplify exponents by putting exponent-containing algebraic formulas into a simpler form that prevents further simplification.
The given expression is (5x⁶y²)³
Simplifying it further we get,
(5x⁶y²)³ = 125[tex]x^{18}y^{6}[/tex]
Therefore, the simplified expression of (5x⁶y²)³ is 125[tex]x^{18}y^{6}[/tex] which is expressed using the positive exponents.
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in new york state, the mean salary for high school teachers in 2017 was $81,410 with a standard deviation of $9,500. only alaska’s mean salary was higher! assume new york’s state salaries follow a normal distribution.
The percentage of New Yorks state teachers that earn between $7000 and $75000 is 13.63%.
What will the percentage be?Let the salary of the teachers be represented as x.
Mean = $81410
Standard deviation = $9500
In this case, the probability for normal distribution will be used. This is illustrated as P(a < Z < b).
where a = lower number.
b = higher number
Therefore, the probability of earning the amount will be:
P(70000 < X < 75000)
= P[(70000 - 81410/9500) < Z < (75000 - 81410/9500)
= P(-1.20 < Z < -0.67)
Using the z table to look for the value
= 0.8849 - 0.7486
= 0.1363
= 13.63%.
Therefore, the probability is 13.63%.
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in new york state, the mean salary for high school teachers in 2017 was $81,410 with a standard deviation of $9,500. only alaska’s mean salary was higher! assume new york’s state salaries follow a normal distribution. What is the percentage of New Yorks state teachers that earn between $7000 and $75000?
Starting at sea level, a turtle descends at a constant rate to a depth of -yard relative to sea level in minute.
The turtle continues descending at this same rate.
What is the turtle's depth relative to sea level after the first minute?
Enter your answer as a simplified mixed number in the box
The turtle's depth relative to sea level after the first minute is 1.2 yards.
Given,
The depth where the turtle descends, d = -3/4 yards
The speed of turtle relative to sea level, t = 5/8 minutes.
We have to find the turtle's depth relative to sea level after the first minute.
The rate at which the turtle descends, r = d/t
r = d/t
r = (-3/4) / (5/8)
r = -3/4 × 8/5
r = -6/5 yards/minute
r = -1.2 yards/min
Now, the depth of turtle after the one minute, D = rt
Where, r = -1.2 yards/min and t = 1 min
Then,
D = -1.2 × 1 = -1.2 yards
That is,
The turtle's depth relative to sea level after the first minute is 1.2 yards
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Which represents the inverse of the function f(x)
4x?
O h(x) = x + 4
O h(x) = x -4
O h(x) = ›
h(x) = #x
Answer: Summary: The equation which represents the inverse of the function f(x) = 4x is h(x) = 1/4 x.
Step-by-step explanation: THERE IS NO EXPLANATION
(hope this helps) :)
Which term describes the red curve in the figure below?
A. Hyperbola
B. Ellipse
C. Circle
D. Parabola
The function H(X) equals 0.6X plus 3.8 models the height in inches of a stack of X cups. What key features is at H(0)?
The key feature of the function H(X) = 0.6X + 38 at H(0) is 3.8
Function:
A function is defined as the an expression, rule, or law that defines a relationship between one independent variable and another dependent variable.
Given,
Here we have the function H(X) = 0.6X + 3.8 models the height in inches of a stack of X cups.
And we need to find the key features is at H(0).
To find the key feature at H(0), then we have to simple apply the value of X as 0,
Like the following, we have to replace the X value in the function with 0, then we get the expression like the following,
=> H(0) = 0.6(0) + 3.8
=> H(0) = 0 + 3.8
H(0) = 3.8
Therefore, the key feature at H(0) is 3.8.
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in triangle ABC , angle A = 30 degrees and angle C = 35 degrees. what is angle B degrees?
Answer:
115°
Step-by-step explanation:
The sum of the three angles in a triangle is always 180°
m∠A + m∠B + m∠C = 180°
m∠B = 180 - m∠A - m∠C
m∠B = 180 - 30 - 35 = 115
3 c = (2b²)
What is this
Step-by-step explanation:
I hope this helps you with your answer
name the sampling method used in this data collection. a polling company wanted to study about hr personnel in tech companies. the pollster selects five tech companies and interviews all hr personnel in each of the 5 companies.
Cluster Sample is the sampling method used in this type of data collection.
Cluster sampling is a sampling technique used in statistics that divides the total population under consideration into externally homogeneous but internally heterogeneous groupings known as clusters. Each cluster essentially serves as a miniature representation of the overall population.
Using simple random sampling, some clusters are picked after the clusters have been identified, while the remaining clusters are left out of the study. A researcher must determine the right sampling strategy for each cluster after identifying the clusters.
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–8(y-7)=2y+6Simplify your answer as much as possible
You have the following equation:
-8(y -7) = 2y + 6
In order to solve for y, proceed as follow:
-8(y -7) = 2y + 6 expand the factor right side
-8y + 56 = 2y + 6 subtract 2y and subtract 56 both sides
-8y - 2y = 6 - 56 simplify
-10y = -50 divide by -10 both sides
y = -50/(-10)
y = 5
Hence, the value of y is 5
scientific notation. 3{,}868{,}000{,}000
Answer:
3.868 * 10^9
Step-by-step explanation:
3868000000
=3.868 * 10^9
:]
the mean monthly electric bill for 59 residents of the local apartment complex is $65. what is the best point estimate for the mean monthly electric bill for all residents of the local apartment complex?
In linear equation, the best point estimate of mean monthly electric bill is $65 .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.The sample mean is an unbiased estimate of the population mean μ.
Thus, the best point estimate of mean monthly electric bill is $65 .
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Main has $36 to spend on movie tickets. Each movie ticket costs $4.50. How many tickets can she buy? Write a multiplication equation and division equation to represent this situation.
Answer:
Main can buy 8 tickets.
Step-by-step explanation:
Use the equation total amount ÷ cost of each ticket
Input your information: $36 ÷ $4.50
The equation adds up to 8.
So therefore, Main can buy 8 tickets.
Write 72.4% as a decimal
Answer:
0.724
Step-by-step explanation:
percent means ' out of 100 ' , then
72.4% = [tex]\frac{72.4}{100}[/tex] = 0.724
Simplify three raised to the fourth power raised to the negative one power
one over three raised to the fourth power
one over three raised to the power of negative four
negative three raised to the fourth power
three raised to the power of the third power
The result of the given expression is one over three raised to the fourth power.
what is logarithmic equation ?
Logarithm , the exponent or power to which a base must be raised to yield a given number.
Simplifying exponential equation
Exponential equations are inverse of logarithmic equation. Exponential equation is expressed as y = ab^x
Given the expression below;
(3⁴)⁻¹ = 3⁻⁴
According to the law of indices
a^-n = 1/a^n
Using this law above, this will be expressed as;
(3⁴)⁻¹ = 3⁻⁴ = 1/3⁴
Hence the result of the given expression is one over three raised to the fourth power
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