Which system is equivalent to
O
O
O
[5-x=9x²
y = 5-x
[y=9y²-90y+225
1x=y-5
[5+x=9x²
y = 5+x
y = 3x
x+3x=5
y=9x²?
x+y=5
Answers
The first equation is a quadratic equation, and the second equation is a linear equation. The solution to the system is x = -2 and y = 7, which satisfies both equations.
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.
The system that is equivalent to:
O
O
O
[5-x=9x²
y = 5-x
is: x = -2, y = 7
In the given system, the first equation is a quadratic equation, and the second equation is a linear equation. The solution to the system is x = -2 and y = 7, which satisfies both equations.
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Related Questions
The sum of two numbers is -6. One number is 14 more than the other one. Find the numbers.
Answers
Answer:
The two numbers are -10 and 4
Step-by-step explanation:
[tex]x+y=-6\\y=14+x\\\\x+(14+x)=-6\\2x+14=-6\\2x=-20\\x=-10\\\\x+y=-6\\-10+y=-6\\y=4[/tex]
What is the apparent solution set for the system of equations:
x ^ 2 + 3x - 2;
- x ^ 2 + 2x + 4
A) {(- 3.5, 0) , (-1.2, 0), (0.5, 0), (3.3, 0)}
B) {(0, 2), (1.5, - 4.25)}
C) {(- 2, - 4), (1.5, 4.75)}
D) {(0, 4), (1, 5)}
Answers
There are no apparent solutions that satisfy both equations.
We have,
The system of equations is:
x² + 3x - 2 = 0
-x² + 2x + 4 = 0
To find the solutions, we can solve each equation separately:
x² + 3x - 2 = 0
This equation can be factored as:
(x + 2)(x - 1) = 0
Setting each factor equal to zero gives:
x + 2 = 0
x = -2
And,
x - 1 = 0
x = 1
-x² + 2x + 4 = 0
This equation does not factor easily, so we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
For this equation, a = -1, b = 2, and c = 4.
Plugging in the values into the quadratic formula:
x = (-2 ± √(2² - 4(-1)(4))) / (2(-1))
x = (-2 ± √(4 + 16)) / (-2)
x = (-2 ± √20) / (-2)
Simplifying further:
x = (-2 ± 2√5) / (-2)
x = 1 ± √5
Now,
let's check which of these solutions satisfies both equations:
For x = -2:
(-2)² + 3(-2) - 2 = 4 - 6 - 2 = -4 ≠ 0
-(-2)² + 2(-2) + 4 = -4 - 4 + 4 = -4 ≠ 0
x = -2 does not satisfy both equations.
For x = 1:
1² + 3(1) - 2 = 1 + 3 - 2 = 2 ≠ 0
-(1)² + 2(1) + 4 = -1 + 2 + 4 = 5 ≠ 0
x = 1 does not satisfy both equations.
For x = 1 ± √5:
We can substitute these values into the equations, but it can be seen that they will not satisfy both equations either.
Therefore,
There are no apparent solutions that satisfy both equations.
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Sofia and ella are both writing expressions to calculate the surface area of a rectangular prism however they wrote different expressions.
a. examine the expressions below, and determine if they represent the same value. explain why or why not.
sofia's expression
(3 cm x 4 cm ) + (3 cm x 5 cm) + (4 cm x 5 cm) + (4 cm x 5 cm)
ella's expression:
2(3 cm x 4 cm) + 2(3 cm x 5 cm) + 2(4 cm x 5 cm)
b. what fact about the surface area of a rectangular prism does ella's expression show more clearly than sofia's?
Answers
a ) The given expression from Sofia and Ella represents two different values.
b.) The fact about the surface area of prism that Ella's expression shows that is not in Sofia's expression is that the expression is according to the formula.
How to determine the surface area of a rectangular prism?To determine the surface area of a rectangle prism, the formula that should be used would be given below:
That is;
Surface area of rectangular prism;
= 2(wl+hl+hw)
when the formula is multiplied out the following is gotten;
= 2wl + 2hl + 2hw
From Ella's expression,
2(3 cm x 4 cm) + 2(3 cm x 5 cm) + 2(4 cm x 5 cm). This follows the order of the formula. And it's final answer = 94cm²
From Sofia's expression,
(3 cm x 4 cm ) + (3 cm x 5 cm) + (4 cm x 5 cm) + (4 cm x 5 cm). This doesn't follow the order of the formula and therefore is not correct and not the same final value with Ella's expression.
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A jewlary shop sells 240 necklaces in a month 180 of the necklaces were sold in a via the shops website the rest were sold in a high street shop .
Work out the ratio of online sales to shop sales
Give ur answers in its simplest form
Answers
180 were sold online and 60 were sold in shops
the ratio in its simplest form would be 3:1
Which graph has the same end behavior as f (x) = StartFraction 10 x cubed + x squared + 3 Over 2 x squared + 1 EndFraction?
On a coordinate plane, a line goes through (negative 2, negative 10), (0, 0), and (2, 10).
On a coordinate plane, a graph approaches the x-axis in quadrant 2, increases up to (0, 10), and then curves down and approaches the x-axis in quadrant 1.
On a coordinate plane, a parabola opens up. It goes through (negative 2, 8), has vertex (0, 1), and goes through (2, 8).
Answers
The function with the same end behavior as f(x) = (10x³ + x² + 3)/(2x² + 1) is given as follows:
On a coordinate plane, a line goes through (-2, -10), (0, 0), and (2, 10).
What is the end behavior of a function?The end behavior of a function refers to how the function behaves as the input variable approaches positive or negative infinity.
The function for this problem is given as follows:
f(x) = (10x³ + x² + 3)/(2x² + 1)
As we are looking for the end behavior, we look at the terms with the highest exponent, hence:
f(x) = 10x³.
Then the end behavior is given as follows:
As x -> - ∞, 10(-∞)³ -> -∞.As x -> ∞, 10(∞)³ -> ∞.Hence the function with the same end behavior is the increasing line, which is given by the first option.
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At a conference of educators, there ore 189 people total, and 128 are teachers. If the rest are principals, then how many principals are present?
Answers
Answer:
61 principals
Step-by-step explanation:
189 total - 128 teachers = 61 principals
A triangle has sides with lengths of 3 miles, 4 miles, and 6 miles. Is it a right triangle
Answers
Yes, the given triangle is a right triangle.
We have,
This can be determined by applying the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Now,
In this case, the squares of the side lengths are:
3² = 9
4² = 16
6² = 36
If the sum of the squares of the two shorter sides (9 + 16 = 25) is equal to the square of the longest side (36), then the triangle is a right triangle.
Thus,
In this case, since 25 is indeed equal to 36, the triangle with side lengths 3 miles, 4 miles, and 6 miles is a right triangle.
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Please help I don’t understand thank you have a blessed day
Answers
By evaluation, the values of the rational function are f(11) = - 1 / 12 and f(- 2) = 1, respectively.
How to evaluate a rational function
In this problem we find the case of a rational function that must be evaluated at two different x-values: x = 11, x = - 2. The procedure is summarized below:
Write the entire expression.Substitute on x with the given value.Simplify the expression by algebra properties.Now we proceed to present the complete procedure:
f(11) = 11 / (11 + 1) - 1
f(11) = 11 / 12 - 1
f(11) = 11 / 12 - 12 / 12
f(11) = (11 - 12) / 12
f(11) = - 1 / 12
f(- 2) = (- 2) / (- 2 + 1) - 1
f(- 2) = - 2 / (- 1) - 1
f(- 2) = 2 - 1
f(- 2) = 1
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answers
The exact value of the cosine of θ is given as follows:
a) 3/5.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are obtained according to the rules presented as follows:
Sine of angle = opposite side/hypotenuse.Cosine of angle = adjacent side/hypotenuse.Tangent of angle = opposite side/adjacent side = sine/cosine.Applying the Pythagorean Theorem, the hypotenuse length is given as follows:
x² = 6² + (-8)²
x² = 100
x = 10.
As the x-coordinate is used for the cosine, the cosine is given as follows:
cos(θ) = 6/10
cos(θ) = 3/5.
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Can someone answer and provide an explanation for these problems? Find the midpoint of the line segment with the given endpoints.
Answers
52) The midpoint of the line segment is (-0.5, 9).
53) The midpoint of the line segment is (3, -8.5).
52) To find the midpoint of the line segment with endpoints (8,9) and (-9,9), we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint (x, y) are the average of the corresponding coordinates of the endpoints.
For the x-coordinate:
(x₁ + x₂) / 2 = (8 + (-9)) / 2 = (-1) / 2 = -0.5
For the y-coordinate:
(y₁ + y₂) / 2 = (9 + 9) / 2 = 18 / 2 = 9
Therefore, the midpoint of the line segment is (-0.5, 9).
53) To find the midpoint of the line segment with endpoints (8,-10) and (-2,-7), we apply the same process using the midpoint formula.
For the x-coordinate:
(x₁ + x₂) / 2 = (8 + (-2)) / 2 = 6 / 2 = 3
For the y-coordinate:
(y₁ + y₂) / 2 = (-10 + (-7)) / 2 = -17 / 2 = -8.5
Hence, the midpoint of the line segment is (3, -8.5).
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A rectangular prism measures 8 inches in width, 12 inches in length, and 4 inches in height. What is the surface area of the prism?
Answers
Step-by-step explanation:
It has
two sides 8x12
two sides 12x4
two sides 4x8 total 352 in^2
Volume of Cone ___ mm3?
Answers
The volume of the cone is 301. 44mm³
How to determine the valueFirst, we need to know the formula
the formula that is used for calculating the volume of a cone is expressed as;
V = πr²h/3
Such that the parameters are;
V is the volume r is the radiush is the height of the coneSubstitute the values, we have;
Volume = 3.14 × 6² × 8/3
Multiply the values, we have;
Volume = 904.32/3
Divide the values
Volume = 301. 44mm³
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Zara's car depreciates at a rate of 14% per year.
By what percentage has Zara's car depreciated after 5 years?
Give your answer to the nearest whole number.
NO SPAM.
Answers
Answer:
53%
Step-by-step explanation:
You want to know the depreciation of car value after 5 years if it is 14% per year.
MultiplierThe multiplier of value each year is ...
1 + growth rate = 1 + (-14%) = 0.86
When the value has been multiplied by that 5 times, it has been multiplied by ...
0.86^5 ≈ 0.4704
This represents a change in value from the original value of ...
0.4704 -1 = -0.5296 = -52.96% ≈ -53%
Zara's car has depreciated by 53% after 5 years.
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A given triangle has vertices at (-3, 1) (2, 4) and (5, -3). If the triangle were rotated 360 degrees clockwise, the new coordinates would be:
Answers
New x-coordinate = x * cos(θ) - y * sin(θ)
New y-coordinate = x * sin(θ) + y * cos(θ)
Since we want to rotate the entire triangle 360 degrees, each point will be transformed using these formulas.
Let's calculate the new coordinates for each vertex:
For the first vertex (-3, 1):
New x-coordinate = -3 * cos(360°) - 1 * sin(360°) = -3 * 1 - 1 * 0 = -3
New y-coordinate = -3 * sin(360°) + 1 * cos(360°) = -3 * 0 + 1 * 1 = 1
For the second vertex (2, 4):
New x-coordinate = 2 * cos(360°) - 4 * sin(360°) = 2 * 1 - 4 * 0 = 2
New y-coordinate = 2 * sin(360°) + 4 * cos(360°) = 2 * 0 + 4 * 1 = 4
For the third vertex (5, -3):
New x-coordinate = 5 * cos(360°) - (-3) * sin(360°) = 5 * 1 - (-3) * 0 = 5
New y-coordinate = 5 * sin(360°) + (-3) * cos(360°) = 5 * 0 + (-3) * 1 = -3
Therefore, after rotating the triangle 360 degrees clockwise, the new coordinates would be (-3, 1), (2, 4), and (5, -3), which are the same as the original coordinates.
(x+3)(x+7)=0
Problem answered, solution and why!
Answers
[tex](x+3)(x+7)=0\\x=-3 \vee x=-7\\\\x\in\{-7,-3\}[/tex]
Help me solve this problem please
Answers
Answer:
450°
Step-by-step explanation:
Stuck on this and cant move along until I get it correct. Please help.
Fill in the missing value.
The measure of angle F is ___°
Answers
The solution is: the measure of angles 2, 3, and 4 are:
m∠2 = 95°
m∠3 = 85°
m∠4 = 95°
Vertical Angle Theorem:
When two straight lines intersect, the opposite vertical angles formed are always equal (congruent) to each other.
Therefore,
m∠3 = 85°
m∠2 = m∠4
Linear pair:
Two adjacent angles which, when combined, form a line, so the sum of a linear pair is 180°.
Therefore,
85° + m∠2 = 180°
m∠3 + m∠4 = 180°
If 85° + m∠2 = 180°
⇒ m∠2 = 180° - 85°
⇒ m∠2 = 95°
As m∠2 = m∠4 then m∠4 = 95°
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complete question:
Find the measure of angles 2, 3, and 4. input the measures then click done. i-ready
please help i missed a day of class i cant figure this out
how do I change 1/4 to a percentage .
Answers
Answer: You divide it, get your answer, move the decimal point to the right twice, and that's you're percent.
Step-by-step explanation:
1/4=.25
.25 > 25%
Answer:
The answer is 25%
Step-by-step explanation:
To change decimal to percentage multiply by 100
1/4×100%
=25%
Find the exact values of the six trigonometric functions of the angle O shown in the figure.
sin(0) -
X
cos(0) -
tan(0) -
csc(0) -
sec(0)-
cot(0) -
0
3
3
Answers
The values of
1. cosθ = √3/2
2. sinθ = √3/2
3. tanθ = 1
4. sec θ = 2/√3
5. cosec θ = 2/√3
6. cot θ = 1
What is trigonometric ratio?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
cosθ = adj/hyp
sinθ = opp/hyp
tanθ = opp/adj
sec θ = 1/cosθ
cosec θ = 1/sinθ
cot θ = 1/tanθ
We need to find the hypotenuse of the triangle
x² = 3² +3²
x = √9+9
x = √18
x = 2√3
cosθ = 3/2√3 = 6√3/12
= √3/2
2. sinθ = 3/2√3 = √3/2
3. tanθ = 3/3 = 1
4. sec θ = 2/√3
5. cosec θ = 2/√3
6. cot θ = 1
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A dentist was making note of her upcoming appointments with different aged patients and
the reasons for their visits.
Patients under 18
Patients 19-60
Patients over 60
Regular cleaning Broken tooth
Submit
5
3
3
2
6
2
What is the probability that a randomly selected appointment is not with a patient 19-60 or is
not for a broken tooth?
Simplify any fractions.
Answers
Probability that a randomly selected appointment is with patients over 60 years old and is for a regular cleaning = (5/21)
The probability of an event is calculated as the number of elements in that event divided by the total number of elements in the sample space.
For this question, we are told to find the probability that a randomly selected appointment is with patients over 60 years old and is for a regular cleaning.
Number of patients that are over 60 years and are for regular cleaning = 10
Total number of patients = 2 + 8 + 6 + 4 + 10 + 12 = 42
Probability that a randomly selected appointment is with patients over 60 years old and is for a regular cleaning = (10/42)
= (5/21)
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hey here is my algebra 13 homework, can someone please help! heres screenshot. QUICK PLSS
Answers
The graph of the given exponential function f(x) = 4(0.5)ˣ + 2 is g(x) = 5(1/6)ˣ + 2
Hence, the correct option is A.
An exponential function is a mathematical function of the form f(x) = aˣ, where "a" is a positive constant known as the base, and "x" is the independent variable. The exponential function is defined for all real values of x, and the output values of the function are always positive.
The exponential function is characterized by its unique property of having a constant rate of change with respect to its own value. This means that the function increases (or decreases) by a constant factor each time the independent variable is increased by a fixed amount.
For the given exponential function g(x) = 5(1/6)ˣ + 2 as the graph of f(x) and g(x) are same.
Hence, the correct option is A.
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Using the given scale 1:50, calculate the actual length of the wall if it is measured to be 15cm.
Answers
With a short time remaining in the day, a delivery driver has time to make deliveries at seven locations among the 8 locations remaining. How many different routes are possible? Question content area bottom Part 1 There are enter your response here possible different routes. (Simplify your answer.)
Answers
The number of different routes possible for the delivery driver, given the time to make deliveries at 7 out of the remaining 8 locations, is 8.
The number of different routes possible for the delivery driver can be calculated using combinatorics. Specifically, we need to determine the number of ways to choose 7 locations out of the remaining 8 locations. This can be found using the combination formula.
The combination formula, also known as "n choose k," is given by the expression C(n, k) = n! / (k! * (n-k)!), where n is the total number of items to choose from and k is the number of items to choose.
In this case, there are 8 locations remaining and the driver needs to choose 7 of them. Applying the combination formula, we have C(8, 7) = 8! / (7! * (8-7)!) = 8! / (7! * 1!) = 8.
Therefore, there are 8 possible different routes for the delivery driver to make deliveries at the remaining 8 locations, given that the driver has time to make deliveries at 7 of them.
To simplify the answer, we can state that there are 8 possible different routes for the driver.
In summary, the number of different routes possible for the delivery driver, given the time to make deliveries at 7 out of the remaining 8 locations, is 8.
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find the perimeter of a rectangle if: L= 12cm, W= 5cm.
(a) 34cm
(b) 21cm
(c) 14cm
(d) 17cm
Answers
Answer:
(a) 34 cm
Step-by-step explanation:
The formula for perimeter of a rectangle is
P = 2l + 2w, where
P is the perimeter,l is the length,and w is the width.Thus, we can plug in 12 for l and 5 for w in the perimeter formula and simplify to find the perimeter of the rectangle:
P = 2(12) + 2(5)
P = 24 + 10
P = 34
Thus, the perimeter of a rectangle with a length of 12 cm and a width of 5 cm is 34 cm.
What is the area of the shaded region?
Answers
Answer:
80 mm²
Step-by-step explanation:
Even for slanted triangles, the area is base x half height! The base is 10 mm, half the height is 8 mm, so the area is 8x10=80 mm.
Use the given data to make a box-and-whisker plot.
5, 4, 16, 21, 10, 6, 15
Answers
Answer:
To make a box-and-whisker plot, we first need to order the data from smallest to largest:
4, 5, 6, 10, 15, 16, 21
Next, we can find the median, which is the middle value of the ordered data set. In this case, the median is 10.
Then, we can find the lower quartile (Q1) and the upper quartile (Q3). The lower quartile is the median of the lower half of the data set, and the upper quartile is the median of the upper half of the data set. To find Q1 and Q3, we can split the data set into two halves:
4, 5, 6, 10 and 15, 16, 21
The median of the lower half is (5+6)/2 = 5.5, and the median of the upper half is (16+21)/2 = 18.5. Therefore, Q1 = 5.5 and Q3 = 18.5.
Now we can draw the box-and-whisker plot. The box represents the middle 50% of the data, with the bottom of the box at Q1 (5.5), the top of the box at Q3 (18.5), and the line inside the box at the median (10). The whiskers extend from the box to the smallest and largest values inthe data set that are not outliers. To determine whether there are outliers, we can use the following formula:
Outlier = Q1 - 1.5 * (Q3 - Q1) or Q3 + 1.5 * (Q3 - Q1)
Plugging in the values, we get:
Outlier = 5.5 - 1.5 * (18.5 - 5.5) = -13.25 or Outlier = 18.5 + 1.5 * (18.5 - 5.5) = 37.25
Since there are no values in the data set that are less than -13.25 or greater than 37.25, there are no outliers.
Therefore, the box-and-whisker plot for the given data is:
| 4
___|___
| |
| |
| 5.5 |-----
| | |
| | |
|------------| 10 |
| | |
| 15.5 |------
| | |
___|___
| 21
The box spans from Q1 (5.5) to Q3 (18.5), with the median line inside the box at 10. The whiskers extend from the box to the minimum value of 4 and the maximum value of 21, since there are no outliers.
Hope this helps!
I need help finding the Component form and Magnitude of the vector V.
Answers
To find the magnitude of the vector, we can use the Pythagorean theorem: ||V|| = sqrt((5 * √2 / 2)^2 + (5 * √2 / 2)^2) = 5.
To find the component form of a vector, you need to break it down into its x and y components. Let's say our vector V has a magnitude of 5 and is pointing in the direction of 45 degrees (measured from the positive x-axis).
To find its x component, we can use cosine: Vx = V cos(45) = 5 * √2 / 2. To find its y component, we can use sine: Vy = V sin(45) = 5 * √2 / 2. So the component form of vector V is (5 * √2 / 2, 5 * √2 / 2).
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need help on this math question
Answers
The expression which gives the number of months passed in terms of p is √300 -0.5p
Subject of formulaWe make t the subject of the formula in the expression
p = 600 - 2t²
subtract 600 from both sides in other to isolate 2t²
p - 600 = 600 - 2t² - 600
p - 600 = -2t²
Rearrange the equation
2t² = 600 - p
Divide both sides by 2 in other to isolate t²
2t²/2 = 600/2 - p/2
t² = 300 - 0.5p
Take the Square root of both sides in other to isolate t
√t² = √300 - 0.5p
t = √300 - 0.5p
Hence, the correct expression which gives the number of months t in terms of price p is t = √300 - 0.5p
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5. (6 pts pts) The displacement of a spring vibrating in damped harmonic motion is given by
y = 4e-3t sin(2πt)
Find the times when the spring is at its equilibrium position (y = 0). '
Answers
The times when the spring is at its equilibrium position (y = 0) are t = 0, 1/2, 1, 3/2, ... and so on.
To find the times when the spring is at its equilibrium position (y = 0), we can set the displacement equation equal to zero and solve for t:
[tex]4e^{(-3t)[/tex] sin(2πt) = 0
Since the product of two factors is zero if and only if at least one of the factors is zero, we have two cases to consider:
4[tex]e^{(-3t)[/tex] = 0
This equation has no solution since [tex]e^{(-3t)[/tex] is always positive and nonzero.
sin(2πt) = 0
The sine function is zero at integer multiples of π.
So, we can set 2πt equal to integer multiples of π:
2πt = 0, π, 2π, 3π, ...
Solving for t in each case, we get:
t = 0, 1/2, 1, 3/2, ...
Therefore, the times when the spring is at its equilibrium position (y = 0) are t = 0, 1/2, 1, 3/2, ... and so on.
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if x+y+z=27 and x+y=17 then Z=
Answers
Answer:
Step-by-step explanation:
x+y+z=27
x+y=17
z=?
since x+y=17
then
17+z=27
z=27-17
z=10