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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What are the solutions of the equation 2 log x = log (5x-6)? Select all that apply.
A x=1
B. x=2
C. x= 3
D. x = 5
E. x=6
Answer:
B, C
Step-by-step explanation:
x^2 = 5x - 6
x = 2 or x = 3
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
5/4 = h/44, so h = 55
The height of the tree is 55 feet.
D is correct.
The length and breadth of a rectangular flower bed are 16m and 9 m, respectively. How many plants can be planted in it, if each plant requires a space of 1.2m x 1m?
The calculated number of plants the flower bed can contain is 120
Calculating hw many plants can be planted in itFrom the question, we have the following parameters that can be used in our computation:
Dimensions = 16 m by 9 m
So, the area of the flower bed is
Area = 16 * 9
Evaluate
Area = 144
Also, we have
Each plant requires a space of 1.2m x 1m?
This means that
Plant area = 1.2 * 1
Plant area = 1.2
So, we have
Plants = 144/1.2
Evaluate
Plants = 120
Hence, the number of plants is 120
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Answer:
Step-by-step explanation:
To calculate the number of plants that can be planted in the rectangular flower bed, we need to calculate the area of the flower bed and divide it by the space required for each plant.
The area of the flower bed is calculated by multiplying its length and breadth.
So, the area of the flower bed is 16m x 9m = 144 sq.m.
Each plant requires a space of 1.2m x 1m = 1.2 sq.m.
Therefore, the number of plants that can be planted in the flower bed is:
144 sq.m. ÷ 1.2 sq.m./plant = 120 plants.
So, you can plant 120 plants in the rectangular flower bed.
................................................
Answer:
4,12,36,108,324.....
Step-by-step explanation:
The sequence represented by the equation [tex]a=4(3)^{n-1}[/tex]is a geometric sequence with first term 5 and common ratio 3. The first 4 terms of the sequence are:
[tex]a_1 = 4(3)^{1-1} =4(3)^0 = 4[/tex]
[tex]a_2 =4(3)^{2-1} = 4(3)^1 = 12[/tex]
[tex]a_3 =4(3)^{3-1} = 4(3)^2 = 36[/tex]
[tex]a_4 = 4(3)^{4-1} =4(3)^3 = 108[/tex]
[tex]a_5=4(3)^{5-1} =4(3)^4=324[/tex]
The sequence can be written as:
[tex]a_n = 4(3)^{n-1}[/tex]
where n is the term number.
Therefore, the sequence is 4,12,36,108,324.....
Answer:
The answer is 4,12,36,108,324
Step-by-step Explanation:
a1=4(3)¹‐¹=4(3)⁰=4
a2=4(3)²‐¹=4×3=12
a3=4(3)³‐¹=4(3)²=4×9=36
a4=4(3)⁴‐¹=4(3)³=4×27=108
a5=4(3)⁵‐¹=4(3)⁴=4×81=324
3.3.4√20+5-43 calculate
Here are the steps to calculate the expression √20 + 5 - 43 :
Step 1: Simplify the square root of 20:
[tex]\sqrt{20}[/tex]
Step 2: Calculate the value of the square root:
[tex]\sqrt{20} = 2\sqrt{5}[/tex]
Step 3: Substitute the value of the square root into the expression:
[tex]2\sqrt{5} + 5 - 43[/tex]
Step 4: Perform addition:
[tex]2\sqrt{5} + 5 = 2\sqrt{5} + \frac{5}{1} = \frac{2\sqrt{5} + 5}{1}[/tex]
Step 5: Perform subtraction:
[tex]\frac{2\sqrt{5} + 5}{1} - 43 = \frac{2\sqrt{5} + 5 - 43}{1}[/tex]
Step 6: Simplify the numerator:
[tex]\frac{2\sqrt{5} - 38}{1}[/tex]
Step 7: Simplify the expression:
[tex]2\sqrt{5} - 38[/tex]
Therefore, the calculation √20 + 5 - 43 simplifies to 2√5 - 38.
The algebraic expression below is a polynomial. x-1^k, where k is a real number
Answer: True
Step-by-step explanation:
Will give you brainly! :) Thank you for taking time out of your day to answer this!
The probability values are P(30 ≤ Amount ≤ 59) = 0.43, P(Amount ≥ 60 or Amount < 30) = 0.57 and P(Amount ≥ 40) = 0.45
Calculating the probability valuesAt least $30 but not more than $59
This means that we use the money spent from 30 to 59
So, we have
30 to 59 = 76 + 58 + 67
30 to 59 = 201
Total = 85 + 98 + 201 + 84
Total = 468
Next, we have
P(30 ≤ Amount ≤ 59) = 201/468
P(30 ≤ Amount ≤ 59) = 0.43
At least $60 or less than $30
This means that we use the money spent less than 30 and greater than or equal to 60
So, we have
At least $60 or less than $30 = 84 + 85 + 98
At least $60 or less than $30 = 267
Next, we have
P(Amount ≥ 60 or Amount < 30) = 267/468
P(Amount ≥ 60 or Amount < 30) = 0.57
At least $40
This means that we use the money spent greater than or equal to 40
So, we have
At least $40 = 58 + 67 + 84
At least $40 = 209
Next, we have
P(Amount ≥ 40) = 209/468
P(Amount ≥ 40) = 0.45
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Please help due 5 min!!!!
b) tan 2A cot A-1 = sec 2A
The trigonometric equation is tan 2A cot A-1 = sec 2A
We have to prove the trigonometric equation
tan 2A cot A-1 = sec 2A
Now let us take LHS
tan 2A cot A-1
2tanA/1-tan²A - 1 . cotA - 1
2-1+tan²A/1-tan²A
1+tan²A/1-tan²A
sec2A
Hence, the trigonometric equation is tan 2A cot A-1 = sec 2A
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The product of a number and five added to 17
Answer:
The phrase "The product of a number and five added to 17" can be represented mathematically as:
5x + 17
In this expression, 'x' represents the unknown number. The product of the number and five is calculated by multiplying the number by 5, and then 17 is added to the result.
Identify the sequence graphed below and the average rate of change from n = 1 to n = 3.
coordinate plane showing the points 2, 10, point 3, 5, point 4, 2.5, and point 5, 1.25
a
an = 20(one half)n − 1; average rate of change is fifteen halves
b
an = 10(one half)n − 1; average rate of change is fifteen halves
c
an = 20(one half)n − 1; average rate of change is negative fifteen halves
d
an = 10(one half)n − 1; average rate of change is negative fifteen halves
The sequence based on the information would be: B. an = [tex]10 1/2^{-1}[/tex]average rate of change is negative fifteen halves.
How to explain the functionThis question is about exponent function/series. You are given 3 points from the function, point A (1,10), point B( 2, 5), and point C(4,1.25).
If you insert point A to the function, an will give a result of 10 for n=1.
For n=0, the result would be:
an= 10([tex]1/2^{-1}[/tex])
= 10 * 2
= 20
Then the average rate of change from n=0 to n=2 would be:
Rate of change= (y₂ -y₁)/ (x₂ -x₁)
Rate of change= (5-20)/ (2-0)
= -15/2
= negative fifteen halves
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A researcher performed an experiment with two groups. She found the difference of the means for each group. Then
she combined the groups, chose two new groups, and found the difference between the means of those groups. She
repeated this process 200 times. The normal distribution of the difference in the means she found is given below. How
great would the difference in means between the first two groups have to be in order to be considered significant?
At least 8
O At least 10
At least 9
At least 7
Answer:
Step-by-step explanation:
To determine the significance level for the difference in means between the first two groups, we need to refer to the provided normal distribution. However, you haven't provided the details or parameters of the normal distribution, such as the mean and standard deviation. Without this information, it is not possible to determine the exact significance level required.
In hypothesis testing, the significance level, typically denoted as α (alpha), is chosen by the researcher before conducting the experiment. It represents the threshold at which the researcher considers the results to be statistically significant. Commonly used significance levels are 0.05 (5%) or 0.01 (1%).
Please provide the necessary parameters or more information about the normal distribution to determine the specific significance level for the difference in means between the first two groups.
Simplify > (x)3(−x3y)2
−x9y2
x5y2
−x6y2
x9y2
The simplified expression of the expression (x)³(−x³y)² is x⁹y²
Simplyfing the expression using the common factorFrom the question, we have the following parameters that can be used in our computation:
(x)3(−x3y)2
Express properly
So, we have
(x)³(−x³y)²
Open the brackets
(x)³(−x³y)² = x³ * x⁶y²
Multiply (x)³ and x⁶ in the expression
So, we have the following representation
(x)³(−x³y)² = x⁹y²
Hence, the simplified expression is x⁹y²
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-49 = 7i, what number is the i.
Answer:
-7
Step-by-step explanation:
divide by 7 on both sides and you get i = -7
e
B
0
14. The table shows the number of inches of
rain over five months. What would be an
appropriate display of the data? Explain.
(Lesson 2)
Month
Number
of Inches
of Rain
Jan. Feb. Mar.
1.5
2.2
3.6
Apr.
5.3
May
4.8
The graph of the given function is attached.
Given is a function for the rainfall in 5 months in inches.
We need to display the data,
So, as we can see that the data is not showing any proportion or pattern,
So, it can be displayed as a line chart.
Hence the chart is attached for the function.
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Could someone help me with this? I have to double check I’m right thank you
Solving linear equations using matrices involves steps ranging from creating an augmented matrix, performing row operations, back substitution, and then interpreting results
To solve a system of linear equations using matrices:
Step 1: Write the system of linear equations in matrix form.
Represent the coefficients of the variables as a matrix (called the coefficient matrix), and the constants on the right side of the equations as another matrix (called the constant matrix).
Step 2: Create the augmented matrix.
Combine the coefficient matrix and the constant matrix into a single matrix by appending the constant matrix as an additional column. This combined matrix is called the augmented matrix.
Step 3: Perform row operations to achieve row-echelon form.
Use row operations (swapping rows, multiplying a row by a constant, or adding/subtracting rows) to manipulate the augmented matrix into row-echelon form. Row-echelon form has zeroes below the diagonal and non-zero elements on the diagonal.
Step 4: Perform back-substitution.
Starting from the last row of the row-echelon form matrix, solve for the variables using back-substitution. Substitute the values of the variables you find into the previous rows to determine the remaining variable values.
Step 5: Interpret the results.
Once you have solved all the variables, you have found the solution to the system of linear equations. If there are infinitely many solutions or no solutions, this will be indicated by the row-echelon form.
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A telephone pole is 54 feet tall. A guy wire runs 83 feet, from point A at the top of the telephone pole, to the ground at point B. The base of the telephone pole is at point C. Triangle ABC is a right triangle.
How far from the base of the telephone pole, to the nearest tenth of a foot, is the guy wire secured to the ground at point B?
Okay, let's break this down step-by-step:
* The telephone pole is 54 feet tall
* The guy wire runs 83 feet from point A (top of pole) to point B (ground)
* So the hypotenuse (AB) of the right triangle is 83 feet
* The opposite side (AC) is 54 feet (height of pole)
To find the adjacent side (BC), we use the Pythagorean theorem:
a^2 + b^2 = c^2
54^2 + BC^2 = 83^2
Solving for BC gives:
BC = sqrt(83^2 - 54^2) = sqrt(1296 - 2916) = sqrt(1620) = 40 feet
So the guy wire is secured 40 feet from the base of the telephone pole.
Rounded to the nearest tenth is 40.0 feet.
Therefore, the final answer is:
40.0
Let me know if you have any other questions!
5. [0.5/1 Points] DETAILS PREVIOUS ANSWERS SALGTRIG4 7.3.112.
A rectangle is to be inscribed in a semicircle of radius 4 cm as shown in the following figure.
10
4 cm-
(a) Find the function that models the area of the rectangle.
A(0) = 16 sin (20)
Need Help? Read It
MY NOTES
4
ASK YOUR TEACHER
(b) Find the largest possible area for such an inscribed rectangle. [Hint: Use the fact that sin(u) achieves its maximum value at u=/2.]
16
cm²
(c) Find the dimensions of the inscribed rectangle with the largest possible area. (Round your answers to two decimal places.)
smaller dimension 2
x cm
larger dimension 25
x cm
PR.
The Area function [tex]A(x) = 2x * \sqrt(16 - x^2).[/tex]
(a) For a rectangle inscribed in a semicircle of radius 4 cm, let half-length be x and height be y.
Therefore, the Area function [tex]A(x) = 2x * \sqrt(16 - x^2).[/tex]
(b) Maximum area occurs when x = [tex]4 * sin(\pi/4), so A(4 * sin(\pi/4)) = 16 cm^2.[/tex]
(c) Dimensions for the largest inscribed rectangle are smaller dimension (height) ≈ of 2.83 cm, a larger dimension (base) ≈ of 5.66 cm.
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Find the area of the composite figure
The area of the composite shape is 125units²
What is area of shape?The area of a figure is the number of unit squares that cover the surface of a closed figure.
A composite shape can be defines as a shape created with two or more basic shapes.
The composite shape can be divided into 2 equal squares and a rectangles.
Area of the square = l²
= 5× 5 = 25
For two squares it will be;
25 × 2
= 50 units²
area of the rectangle = l× w
where w is the width
A = 15 × 5
= 75 units²
Therefore the area of the composite shape = 50 + 75 = 125 units²
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Write the equation of a line perpendicular to the one above that passes through (-2, 9). You may use either slope intercept or point slope form.
Answer:
-3x + 3
Step-by-step explanation:
To find the equation of a line perpendicular to the line passing through (-2, 1) and (4, 3), we need to determine the slope of the original line first. Then, we can use the negative reciprocal of that slope to find the slope of the perpendicular line. Finally, we can use the point-slope form to write the equation of the perpendicular line.
Step 1: Find the slope of the original line.
Slope (m) = (change in y) / (change in x)
m = (3 - 1) / (4 - (-2))
m = 2 / 6
m = 1/3
Step 2: Determine the slope of the perpendicular line.
The slope of the perpendicular line is the negative reciprocal of the original line's slope.
Perpendicular slope = -1 / (1/3)
Perpendicular slope = -3
Step 3: Use the point-slope form to write the equation.
The point-slope form is given by:
y - y1 = m(x - x1)
Using the point (-2, 9) and the perpendicular slope (-3), we can write the equation as:
y - 9 = -3(x - (-2))
y - 9 = -3(x + 2)
y - 9 = -3x - 6
y = -3x + 3
Therefore, the equation of the line perpendicular to the line passing through (-2, 1) and (4, 3) and passing through (-2, 9) is y = -3x + 3.
A kid's size small T-shirt is designed to fit children
who weigh between 43 and 55 pounds.
a. Write an inequality to describe w, the weight
of a child who has outgrown the small T-shirt.
9 √
b. Write an inequality to describe y, the weight
of a child who is not ready for the small T-shirt
yet.
A) The inequality that the weight of a child who has outgrown the small T-shirt is w > 55. B) The inequality that the weight of a child who is not ready for the small T-shirt yet. Is y < 43
How to determine the inequalitiesa. To describe the weight (w) of a child who has outgrown the small T-shirt, we can use the inequality:
w > 55
This inequality states that the weight of a child (w) must be greater than 55 pounds for them to have outgrown the small T-shirt.
b. To describe the weight (y) of a child who is not ready for the small T-shirt yet, we can use the inequality:
y < 43
This inequality states that the weight of a child (y) must be less than 43 pounds for them to not be ready for the small T-shirt yet.
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Cameron surveyed her friends about the number of apps they use. The responses were 15, 16, 18, 9, 18, 4, 19, 20, 17, and 36 apps. Use the range and interquartile range to describe how the data vary.
The middle half of the data values vary by:
Interquartile = [tex]Q_3-Q_1[/tex] => 19.25 - 13.5 = 5.25
The given data is :
15, 16, 18, 9, 18, 4, 19, 20, 17, and 36 apps.
We have to find:
Use the range and interquartile range to describe how the data vary.
We have to arrange the data from smallest to largest.
4, 9, 15, 16, 17, 18, 18, 19, 20, 36
Range of the data is : Highest no. - lowest no.
Range of the data is: 36 - 4 = 32
The location of the [tex]Q_1[/tex] = (n + 1) × 0.25 (where n is the total no. in the data)
The location of the [tex]Q_1[/tex] = (10 + 1) × 0.25 = 11 × 0.25 = 2.75
∴[tex]Q_1[/tex] = 15 × 0.75 + 9 × 0.25 = 13.5
The location of the [tex]Q_3[/tex] = (n + 1) × 0.75
The location of the [tex]Q_3[/tex] = 11 × 0.75 = 8.75
∴[tex]Q_3[/tex] = 19 × 0.75 + 20 × 0.25 = 19.25
Hence, The middle half of the data values vary by:
Interquartile = [tex]Q_3-Q_1[/tex] => 19.25 - 13.5 = 5.25
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b) Find the sum of all the numbers between 0 and 207 which are exactly divisible by 3.
A popular brand has introduced a new design of jeans. All major stores have stocked the jeans because the brand usually sells very well. But the cost of these jeans is much higher than those of other brands, so people don't buy them.
The price of the jeans will decrease because supply is greater than demand hence the stores will sell them at discounted prices.
How do we calculate?The store owners would be forced to cut pricing if the jeans weren't purchased at all or as frequently as the other brands. Either they choose that choice, return the goods if possible or just toss the jeans away. It generally takes some trial and error to determine the proper price.
For instance, the owner may lower the price to $75 and test whether the 25% discount works or not if the jeans initially sell for $100 and nobody buys them for a week.
The price might remain there if people continue to buy and if not, the cost might decrease even further.
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some help is required
54° is the value of the given angle BAC.
As we know that the arc and angles formed by intersecting chords,
θ = (α + β)/2 .....(i)
According to the given figure, we have
θ = 10x+4
α =9x-12
β = 12x +15
Substitute the value in equation (1)
10x+4 = (9x-12+12x +15)/2
20x+8 = 21x +3
x = 8-3
x = 5
Thus,
∠BAC = θ
= 10*5+4
= 50 + 4
=54
Therefore, the value of the given angle will be 54°.
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During the winter, if the low temperature outside is a °C, the daily cost to heat a
building can be determined using the function f(x) = 5 (1.3) * . Find and
interpret the given function values and determine an appropriate domain for the function.
round all function values to the nearest hundredth.
f:7)= __, meaning when the low temp outside is __ celsius it would cost $__ to heat the building. this interpretation _______________ in the context of your problem.
f(9.5)=___, meaning when the low temp outside is ___ celsius it would cost & __ to heat the building. this interpretation _______________ in the context of the problem.
based on the observations above it is clear that an appropriate domain for the function is —————
PLEASE HELP
The values of the function are 5 and 1.5 and the domain is,
⇒ - ∞ < x < ∞
Here, The equation of the function is given as
f(x) = 5 (1.3)ˣ
The above function is an exponential function.
An exponential function is represented as
f(x) = abˣ
Where
a represents the initial value, b represents the rate of growth or decay
While x and f(x) are the input and output values
Hence, By comparison, we have
a = 5 and b = 1.3
This means that the function values are 5 and 1.3.
Since, the function is an exponential function.
The domain of an exponential function is the set of all real values
Hence, the domain of f(x) is the set of all real values.
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Find the Value of x. Round to the nearest tenth.
hyp = x
28°
11
The calculated value of x in the right triangle is 12.5
How to calculate the value of xFrom the question, we have the following parameters that can be used in our computation:
The right triangle
The value of x can be calculated using the following cosine rule
So, we have
cos(28) = 11/x
make x the subject of the formula
So, we have
x = 11/cos(28)
Evaluate the quotient
This gives
x = 12.5
Hence, the value of x is 12.5
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solve for v, PV/T=pv/t
No matter the values of P, V, T, p, and t, as long as the equation PV/T = pv/t holds true, the solution for v is always equal to V.
To solve for v in the equation PV/T = pv/t, we can manipulate the equation to isolate v on one side.
Starting with the given equation:
PV/T = pv/t
To isolate v, we can cross-multiply:
PVt = pVt
Next, we divide both sides of the equation by pt:
V = v
Therefore, the solution is v = V.
In other words, v is equal to V, which means they represent the same values.
This implies that v and V are interchangeable and can be used interchangeably in the equation.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
From the relationship of AC bar ≅ BD bar, we can tell that ABCD is a rectangle.
How is this a rectangle ?A quadrilateral with two sets of parallel sides is known as a parallelogram.
If ABCD is a parallelogram where AC and BD have equal lengths, then the opposite sides of ABCD are also equal. ABCD has two sets of sides that are parallel and have the same length.
The fact that ABCD possesses two sets of sides that are parallel and of equal length logically leads to the conclusion that it also has four angles that are right. One reason for this is that the angles opposite each other in a parallelogram are of equal measure, while the sum of the angles at each corner of a parallelogram is always 180 degrees.Therefore, ABCD is a rectangle.
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Find area of the shape
Answer:
130.4
Step-by-step explanation:
6 x 14 = 84
8 x 4 = 32
(4 x 7.2)/2 = 14.4