Which of the following functions is graphed me below ?
Answer:
[tex]y = |x - 2| + 3[/tex]
The correct answer is C.
On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (2, negative 1). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
y > 2x + 3
y < 2x + 3
y > −2x + 3
y < −2x + 3
The correct linear inequality represented by the graph is:
y < -2x + 3. Option D
To determine which linear inequality is represented by the graph of the dashed straight line with a negative slope and going through (0, 3) and (2, -1), we can start by finding the slope of the line.
The slope of a line can be calculated using the formula:
m = (y2 - y1) / (x2 - x1).
Using the coordinates (0, 3) and (2, -1), we have:
m = (-1 - 3) / (2 - 0),
m = -4 / 2,
m = -2.
So, we know that the slope of the line is -2.
Next, we need to determine the y-intercept of the line. To do this, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
Using the point (0, 3), we can substitute the coordinates into the equation and solve for b:
3 = -2(0) + b,
3 = b.
Therefore, the y-intercept is 3.
Now that we have the slope and y-intercept, we can write the equation of the line in slope-intercept form:
y = -2x + 3.
Since we are shading everything to the left of the line, we want the region where y is less than the line. Option D is correct.
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12. Write the coordinates of Triangle ABC.
A. 2 B.5 C. 6
13. Translate the Triangle (-2, 5). Draw the new image on the grid above.
14. Each coordinate will move how many on the x-axis? 8
Direction right
I
15. Each coordinate will move how many on the y-axis?
ordinates to the translated triangle image.
Given the following diagram: We need to find the coordinates of triangle ABC, translate the triangle (-2, 5) and draw the new image on the grid above, and determine the amount each coordinate will move on the x-axis and y-axis during translation.
1. Coordinates of triangle ABC:A = (2, 6)B = (5, 8)C = (6, 3)2. Translation of triangle (-2, 5)The translation of a triangle can be done by adding or subtracting a constant value from the x-coordinates and y-coordinates of each vertex of the original triangle.
For example, if we want to translate a triangle by 3 units to the right and 2 units up, we would add 3 to the x-coordinates and add 2 to the y-coordinates of each vertex of the original triangle. Using this method, we can translate the triangle (-2, 5) as follows:
New coordinates of A = (2 + (-2), 6 + 5) = (0, 11)New coordinates of B = (5 + (-2), 8 + 5) = (3, 13)New coordinates of C = (6 + (-2), 3 + 5) = (4, 8)3. New image of triangle (-2, 5)The new image of the triangle (-2, 5) is shown in the following diagram:4. Amount each coordinate moves on x-axis During translation, each coordinate moves 2 units to the right (from -2 to 0).5. Amount each coordinate moves on y-axis During translation, each coordinate moves 6 units up (from 5 to 11).
Therefore, the coordinates of the translated triangle image are (0, 11), (3, 13), and (4, 8).
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i need help in sparx
The rule that makes the machine work is *-5 + 6 * -5
How to make the machine work for the pair of input and outputFrom the question, we have the following parameters that can be used in our computation:
4 -50
-8 10
-3 -15
A linear equation is represented as
y = mx + c
Using the points, we have
4m + c = -50
-8m + c = 10
Subtract the equations
So, we have
12m = -60
m = -5
Next, we have
-8 * -5 + c = 10
So, we have
c = 10 - 40
c = -30
This means that the operation is
-5x - 30
When expanded, we have
*-5 + 6 * -5
Hence, the rule that makes the machine work is *-5 + 6 * -5
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find the value of b
A. 14
B. 15
C. 64
D. 289
[tex] \sf \hookrightarrow \: {8}^{2} + {b}^{2} = {17}^{2} [/tex]
[tex] \sf \hookrightarrow \: 8 \times 8 + {b}^{2} = 17 \times 17[/tex]
[tex] \sf \hookrightarrow \: 8 \times 8 + {b}^{2} = 289[/tex]
[tex] \sf \hookrightarrow \: 64 + {b}^{2} = 289[/tex]
[tex] \sf \hookrightarrow \: {b}^{2} = 289 - 64[/tex]
[tex] \sf \hookrightarrow \: {b}^{2} = 225[/tex]
[tex] \sf \hookrightarrow \: b = \sqrt{225} [/tex]
[tex] \sf \hookrightarrow \: b = \sqrt{15 \times 15} [/tex]
[tex] \sf \hookrightarrow \: b = 15[/tex]
B) b = 15 ✅Find the total surface area of the pyramid.
A. 87.6 cm2
B. 39.6 cm2
C. 72 cm2
D. 24 cm2
The total surface area of the pyramid is option c [tex]72 cm^2[/tex].
The total surface area of a pyramid is given by the formula;S= ½Pl + BWhere B is the area of the base and P is the perimeter of the base.
To find the perimeter, add the length of all the sides of the base. Here, the base of the pyramid is a square with sides measuring 6 cm each.Therefore, its perimeter = 6 + 6 + 6 + 6 = 24 cm.
Now, to find the total surface area, we need to find the area of all four triangular faces. To find the area of one of the triangular faces, we can use the formula:
A = 1/2bhWhere b is the base of the triangle and h is the height.
To find the height, we can use the Pythagorean theorem:
[tex]h = \sqrt(6^2 - 3^2) = \sqrt(27) = 3 \sqrt(3)[/tex]
Therefore, the area of one of the triangular faces is:
A = 1/2bh = [tex]1/2(6)(3\sqrt(3)) = 9\sqrt(3)[/tex]
We have four triangular faces, so the total area of the triangular faces is:
[tex]4(9\sqrt(3)) = 36\sqrt(3)[/tex]
Finally, we can find the total surface area by adding the area of the base and the area of the triangular faces:
S = ½Pl + B = [tex]1/2(24)(3\sqrt(3)) + 6^2 = 36\sqrt(3) + 36 = 36(\sqrt(3) + 1).[/tex]
Therefore, the total surface area of the pyramid is 36(sqrt(3) + 1) cm², which is approximately 72 cm². Hence, the correct option is C. [tex]72 cm^2[/tex].
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Suppose for 40 observations, the variance is 50. If all the observations are increased by 20, the variance of these increased observation will be
Select one:
a. 50
b. 70
c. 50/20
d. 40
e. 50-20=30
Note: Answer D is NOT the correct answer. Please find the correct answer. Any answer without justification will be rejected automatically.
Answer:
a) 50
Step-by-step explanation:
The variance will not change as all the observations are increased uniformly.
Proof:
Variance formula:
[tex]s^{2} = \frac{\sum x_i^{2} }{n} -\frac{(\sum x_i)^{2} }{n^{2} }[/tex]
When the obervations are inc by 20,
[tex]s_1^{2} = \frac{\sum (x_i + 20)^{2} }{n} -\frac{(\sum (x_i + 20))^{2} }{n^{2} }\\\\=\frac{\sum(x_i^{2} + 2*20*x_i + 20^{2} )}{n} - \frac{(\sum x_i +20n)^{2} }{n^{2} } \\\\=\frac{\sum x_i^{2} + 40\sum x_i + 20^{2}n }{n} - \frac{(\sum x_i)^{2} +2*20n\sum x_i + 20^{2} n^{2} }{n^{2} } \\\\= \frac{\sum x_i^{2}}{n} - \frac{(\sum x_i)^{2}}{n^{2} } +\frac{40\sum x_i}{n} + 20^{2} - \frac{40\sum x_i}{n} - 20^{2}\\\\s_1^{2}= \frac{\sum x_i^{2}}{n} - \frac{(\sum x_i)^{2}}{n^{2} }\\\\=s^{2}[/tex]
Therefore variance doesn't change
Please awnser asap I will brainlist
The row operation on the matrix [tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right][/tex] is [tex]\left[\begin{array}{ccc|c}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]
How to perform the row operation on the matrixFrom the question, we have the following parameters that can be used in our computation:
[tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]
The row operation is given as
1/2R₁
This means that we divide the entries on the first row by 2
Using the above as a guide, we have the following:
[tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right] = \left[\begin{array}{ccc|c}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]
Hence, the row operation on the matrix is [tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right] = \left[\begin{array}{ccc|c}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]
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John can ride his bide 4 miles in 30
minutes. At his current rate, what is the
distance, in miles, John can ride his
bike in 12 minutes?
The distance John can ride his bike in 12 minutes is approximately 1.6 miles.
To find out the distance John can ride his bike in 12 minutes, we can use the information given about his rate of riding.
We are told that John can ride his bike 4 miles in 30 minutes. This implies that his rate of riding is 4 miles per 30 minutes.
To calculate the distance John can ride in 12 minutes, we need to determine the proportion of time he is riding compared to the given rate.
We can set up a proportion to solve for the unknown distance:
(4 miles) / (30 minutes) = (x miles) / (12 minutes)
Cross-multiplying, we get:
30 minutes * x miles = 4 miles * 12 minutes
30x = 48
Now, we can solve for x by dividing both sides of the equation by 30:
x = 48 / 30
Simplifying the fraction, we have:
x = 8/5
So, John can ride his bike approximately 1.6 miles in 12 minutes, at his current rate.
Therefore, the distance John can ride his bike in 12 minutes is approximately 1.6 miles.
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If two opposite sides of a square are increased by 13 meters and the other sides are decreased by 7 meters, the area of the rectangle that is formed is 69 square meters. Find the area of the original square.
Answer:
(x + 13)(x - 7) = 69
x² + 6x - 91 = 69
x² + 6x - 160 = 0
(x + 16)(x - 10) = 0
x = 10, so the area of the original square is 100 m².
(3x-1)(x-2)=5x+2 ecuación cuadrática incompleta
Hence, the arrangements to the quadratic equation (3x-1)(x-2) = 5x + 2 are x = and x = 4.
Quadratic equation calculation.
To unravel the quadratic equation (3x-1)(x-2) = 5x + 2, let's to begin with grow the cleared out side of the equation:
(3x - 1)(x - 2) = 5x + 2
Growing the condition:
3x^2 - 6x - x + 2 = 5x + 2
Streamlining the condition:
3x^2 - 7x + 2 = 5x + 2
Another, let's move all terms to one side of the condition:
3x^2 - 7x - 5x + 2 - 2 =
Combining like terms:
3x^2 - 12x =
Presently, we have a quadratic condition in standard shape: ax^2 + bx + c = 0, where a = 3, b = -12, and c = 0.
To fathom the quadratic equation, able to calculate out the common calculate of x:
x(3x - 12) =
From this equation, we are able see that the esteem of x can be or unravel for 3x - 12 = 0:
3x - 12 =
Including 12 to both sides:
3x = 12
Isolating both sides by 3:
x = 4
Hence, the arrangements to the condition (3x-1)(x-2) = 5x + 2 are x = and x = 4.
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determine the surface area and volume
The surface area of a cylinder is 284m² and it's volume is 366.9m³
What is the surface area and volume of a cylinder?To find the surface area and volume of a cylinder, we need to know the radius (r) and height (h) of the cylinder. The formulas for the surface area (A) and volume (V) of a cylinder are as follows:
Surface Area (A) = 2πr² + 2πrhVolume (V) = πr²hFrom the given question, the data are;
radius = 4mheight = 7.3ma. The surface area of the cylinder is;
SA = 2π(4)² + 2π(4)(7.3)
SA = 283.999≈284m²
b. The volume of the cylinder is
v = πr²h
v = π(4)²(7.3)
v = 366.9m³
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NO LINKS!!! URGENT HELP PLEASE!!!
Please help with #15
Answer:
area = 8π/3
arc length = 4π/3
Step-by-step explanation:
θ = 60°
r = 4
Area of sector :
[tex]\frac{\theta}{360} \pi r^{2} \\\\=\frac{60}{360} \pi 4^{2} \\\\= \frac{1}{6} 16\pi \\\\= \frac{8}{3} \pi[/tex]
arc length:
[tex]\frac{\theta}{360} 2\pi r\\ \\= \frac{60}{360} 2(4)\pi \\\\= \frac{1}{6} 8\pi \\\\= \frac{4}{3} \pi[/tex]
Answer:
A ≈ 8.4 cm² , arc length ≈ 4.2 cm
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{60}{360}[/tex] ( r is the radius of the circle )
= π × 4² × [tex]\frac{1}{6}[/tex]
= [tex]\frac{16\pi }{6}[/tex]
≈ 8.4 cm² ( to 1 decimal place )
arc length is calculated as
arc = circumference of circle × fraction of circle
= 2πr × [tex]\frac{60}{360}[/tex]
= 2π × 4 × [tex]\frac{1}{6}[/tex]
= [tex]\frac{8\pi }{6}[/tex]
≈ 4.2 cm ( to 1 decimal place )
Read the following conditional statement:
If one of the angles of a triangle equals 90º, then the triangle is classified as a right triangle.
Which of the following choices is the first step of an indirect proof?
If the triangle is a right triangle
If the triangle is not a right triangle
If the triangle equals 90º
None of these choices are correct.
Answer/Step-by-step explanation:
C., the first proof we would be given if a little box is shown, which indicates a 90 degree angle at the place where to lines touch in a T kind of manor. So C is the answer.
The principal P is borrowed at a simple interest rate r for a period of time t. Find the loans future value A, or the total amount due at time t. P equals $9,000, r eeuals 10%, t equals 6 months. The loans future value is
The future value of the loan, or the total amount due at the end of 6 months, is $9,450.
We can use the following formula to calculate the future value of a loan:
[tex]A = P + P * r * t[/tex]
Given: $9,000 principal (P).
10% interest rate (r) = 0.10
6 months is the time period (t).
When we enter these values into the formula, we get:
A=9,000+9,000*0.10*6/12
First, compute the interest portion:
Interest is calculated as = 9,000*0.10*6/12=450
We may now calculate the future value:
A=9,000+450=9,450
As a result, the loan's future value, or the total amount payable in 6 months, is $9,450.
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Lola has 37 in Saint in her pocket. Then she finds these coins in the couch
Answer:
?
Step-by-step explanation:
?
please help
Use the quadratic formula to find the solution to the quadratic equation given
below.
Hello!
[tex]x^2 - 3x + \dfrac{9}{4} = 0\\\\4x^2 - 12x + 9 = 0\\\\\\x = \dfrac{-b\±\sqrt{b^2 - 4ac} }{2a} \\\\\\x = \dfrac{-(-12)\±\sqrt{(-12)^2 - 4 \times 4 \times 9} }{2 \times 4} \\\\\\\\boxed{x = \dfrac{3}{2} }[/tex]
help please its due in 50 minutes ill mark brainliest answer too and no need to show work
The function f(x) and the inverse function h(x) for which the function f(x) is defined by the values (0,3), (1,1), (2,-1) are f(x) = 3 -2x and h(x) = [tex]\frac{3 - x}{2}[/tex]
What is a Function?A function is a rule which takes each member x of a set and assigns, or maps it to the same value y known at its image.x → Function → yA letter such as f, g or h is often used to stand for a function.
The Function which squares a number and adds on a 3, can be written as f(x) = x2+ 5.
Let the linear function be f(x) = mx + cwhen x = 0, f(x) = 33 = m(0) + cTherefore, c = 3
when x = 1, f(x) = 11 = m(1) + c but c = 31 = m + 3
Therefore m = 1 - 3, which is -2
The linear equation f(x) = 3 - 2x
To solve for inverse function h(x)let y = 3 - 2xmaking x the subject of the equation2x = 3 - yx =[tex]\frac{3 - y}{2}[/tex]replacing x with h(x) and y with x, we haveh(x) = [tex]\frac{3 - x}{2}[/tex]
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The equation 4x – 4 – 5x = 7 – x + 5 has what type of solution set? Question 3 options: A) No solutions B) Two solutions C) One solution D) Infinitely many solutions
Answer:
A) No solutions
Step-by-step explanation:
First of all, we know that option B will always be incorrect. You cannot have two solutions. To illustrate this, try drawing two lines. You will find that they will either intersect once (one solution), or they will not intersect, (no solutions, parallel lines), or they are the same line and thus they will always intersect (infinitely many solutions).
With that in mind, let's solve the equation.
4x-4-5x=7-x+5
First, combine all like terms.
-x-4=12-x
Now add 4 to both sides to leave x by itself.
-x=16-x
This statement cannot be true. Therefore, this equation has no solutions (parallel lines. One line starts from 0, or the origin. That line is -x. The other line starts from 16. That line is -x+16.)
Hope this helps!
Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
6-3x+=x+5
5
12
Therefore, the value of x that solves the equation is 2/7, after eliminating the fractions and solving the resulting equation.
To eliminate fractions in the equation 6 - 3x + (1/2)x = x + 5, we can multiply each term by a number that will clear the denominators. In this case, the denominator is 2 in the term (1/2)x. The least common multiple (LCM) of 2 is 2 itself, so we can multiply each term by 2 to eliminate the fraction.
By multiplying each term by 2, we get:
2 * (6 - 3x) + 2 * ((1/2)x) = 2 * (x + 5)
Simplifying this expression, we have:
12 - 6x + x = 2x + 10
Now, the equation is free of fractions, and we can proceed to solve it.
Combining like terms, we have:
12 - 5x = 2x + 10
To isolate the variable terms, we can move the 2x term to the left side by subtracting 2x from both sides:
12 - 5x - 2x = 10
Simplifying further:
12 - 7x = 10
Next, we can move the constant term to the right side by subtracting 12 from both sides:
12 - 7x - 12 = 10 - 12
Simplifying again:
-7x = -2
Finally, we solve for x by dividing both sides by -7:
x = (-2) / (-7)
Simplifying the division of -2 by -7 gives us the solution:
x = 2/7
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5 hr, 30 min, 12 sec + 2 hr, 16 min, 25 'sec
The sum of the two time durations is 7 hours, 46 minutes, and 37 seconds.
To add the given time durations, we start by adding the seconds:
12 sec + 25 sec = 37 sec.
Since 60 seconds make a minute, we carry over any excess seconds to the minutes place, which gives us a total of 37 seconds. Moving on to the minutes, we add 30 min + 16 min = 46 min.
Again, we carry over any excess minutes to the hours place, resulting in a total of 46 minutes.
Finally, we add the hours: 5 hr + 2 hr = 7 hr.
Thus, the sum of the two time durations is 7 hours, 46 minutes, and 37 seconds.
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Find the area to the right of the z-score 0.41 under the standard normal curve.
z0.20.30.40.50.000.57930.61790.65540.69150.010.58320.62170.65910.69500.020.58710.62550.66280.69850.030.59100.62930.66640.70190.040.59480.63310.67000.70540.050.59870.63680.67360.70880.060.60260.64060.67720.71230.070.60640.64430.68080.71570.080.61030.64800.68440.71900.090.61410.65170.68790.7224
The area to the right of the z-score 0.41 under the standard normal curve is approximately 0.3409.
To find the area to the right of the z-score 0.41 under the standard normal curve, we need to calculate the cumulative probability or area under the curve from 0.41 to positive infinity.
Since the standard normal distribution is symmetric around the mean (z = 0), we can use the property that the area to the right of a z-score is equal to 1 minus the area to the left of that z-score.
From the given z-table, we can look up the area to the left of 0.41, which is 0.6591.
The area to the right of 0.41 is then:
Area = 1 - 0.6591
Area = 0.3409
Therefore, the area to the right of the z-score 0.41 under the standard normal curve is approximately 0.3409.
This means that approximately 34.09% of the data falls to the right of the z-score 0.41 in a standard normal distribution.
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NO LINKS!! URGENT HELP PLEASE!!
Please help with 35
Answer:
x = 4
Step-by-step explanation:
By property, if two tangents are drawn from an external point , then they are equal
⇒ 2x + 3 = 11
⇒ 2x = 11 - 3
⇒ 2x = 8
⇒ x = 8/2
⇒ x = 4
Answer:
x = 4
Step-by-step explanation:
To find the value of x, we can use the Two-Tangent Theorem.
The Two-Tangent Theorem states that if two tangent segments are drawn to a circle from the same external point, the lengths of the two tangent segments are equal.
Therefore:
[tex]\begin{aligned}AD &= AB\\\\2x+3&=11\\\\2x+3-3&=11-3\\\\2x&=8\\\\\dfrac{2x}{2}&=\dfrac{8}{2}\\\\x&=4\end{aligned}[/tex]
Therefore, the value of x is 4.
Jimmy's lunch box in the shape of a half cylinder on a rectangular box.
Find the total volume of metal needed to manufacture it
Answer:10cm 5cm 7 Jim's lunch box is in the shape of a half cylinder on a rectangular box. To the nearest whole unit, what is a The total volume it contains? b The total area of the sheet metal in 10 in needed to manufacture it? This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts
Step-by-step explanation:
Let {X₁} be independent standard normal random variables. Let Y = (X₁ + X3 + X5 + X7)² + (X₂ + X₁ + X6 + X8)². Determine a value c such that the random variable cY will have an x² distribution
The value of "c" such that the random variable cY has an x² distribution is 4.
To find the value of "c" such that the random variable cY has a chi-squared (x²) distribution, we need to consider the properties of the chi-squared distribution and the given expression for Y.
The chi-squared distribution with "k" degrees of freedom is obtained by summing the squares of "k" independent standard normal random variables. Each standard normal variable contributes one degree of freedom to the chi-squared distribution.
In the given expression for Y, we have two squared terms: (X₁ + X₃ + X₅ + X₇)² and (X₂ + X₁ + X₆ + X₈)². To obtain an x² distribution, we need to rewrite the expression in terms of squared standard normal random variables.
To achieve this, we can divide each squared term by its corresponding degrees of freedom and take the square root:
Y = (X₁ + X₃ + X₅ + X₇)² + (X₂ + X₁ + X₆ + X₈)²
= (1/4)(X₁ + X₃ + X₅ + X₇)² + (1/4)(X₂ + X₁ + X₆ + X₈)²
Now, we can rewrite Y as:
Y = (1/4)χ²₁ + (1/4)χ²₁
Here, χ²₁ and χ²₂ represent chi-squared random variables with 1 degree of freedom each.
To obtain an x² distribution, we need to make the coefficients of the chi-squared random variables equal to their degrees of freedom. In this case, we want the coefficient to be 1.
So, setting the coefficient of χ²₁ to 1, we get:
(1/4) = 1/c
Solving for "c", we find:
c = 4
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APQR-ASTU. Solve for x. Enter the number only.
The length of the unknown side x using the concept of similar triangles is: x = 4
How to find the side lengths of similar triangles?Similar triangles are referred to as triangles that have the same shape but different sizes. All equilateral triangles and squares of any side length are examples of similar objects. In other words, if two triangles are similar, their corresponding angles are the same and their corresponding side proportions are the same.
Now, we are told that triangle PQR is similar to Triangle STU and as such their corresponding sides are similar and therefore to find the missing side x, we have:
12/x = 15/5
x = (12 * 5)/15
x = 60/15
x = 4
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8. Amy has $30 to spend. She wants to buy pounds of lemons at $2 per pound, a box for $4, and 7 frozen dinners for $3 each Choose True or False for each statement. A She will not have enough money to buy everything O True O False 8 She will have $1 left over. O True O False C The total cost is $39. O True O False
Answer:she will actually need 1 dollar because all of that would be 31 dollars.
Step-by-step explanation:
3 pounds of lemons= $6
1 box of rice= $4
7 frozen diners= $21
6+4=10
10+21=31
Hannah and Becky are learning to type on a computer keyboard. Hannah's
typing speed is represented by the equation y = 11x where y is the number of
words she types and x is the number of minutes. Becky's typing speed is
given by the graph.
Number of words
60
48
36
24
12
2
3
Time (minutes)
Choose the statement that correctly compares their unit rates.
Adr
A. Hannah's unit rate is 2 more words per minute than Becky's unit
rate.
B. Hannah's unit rate is 1 more word per minute than Becky's unit
rate.
C. Hannah's unit rate is equal to Becky's unit rate.
D. Hannah's unit rate is 1 fewer word per minute than Becky's unit
rate
The correct statement is D. Hannah's unit rate is 1 fewer word per minute than Becky's unit rate.
To compare the unit rates, we need to determine the rate at which each person types words per minute.
For Hannah, the equation y = 11x represents her typing speed, where y is the number of words and x is the number of minutes. This means that Hannah types 11 words per minute (11 words/minute).
Looking at Becky's graph, we can determine her unit rate by calculating the change in the number of words divided by the change in time.
The change in words is 48 - 2 = 46, and the change in time is 3 - 2 = 1. So, Becky's unit rate is 46 words per minute (46 words/minute).
Comparing the unit rates:
Hannah's unit rate: 11 words/minute
Becky's unit rate: 46 words/minute
Therefore, Hannah's unit rate is 35 words per minute less than Becky's unit rate.
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Find f−1′ (0) for f(x) = 4x3 + 6x − 10
Answer:
Sure. First, we need to find the inverse function of f(x). We can do this by using the following steps:
1. Let y = f(x).
2. Solve the equation y = 4x3 + 6x - 10 for x.
3. Replace x with y in the resulting equation.
This gives us the following inverse function:
```
f^-1(y) = (-1 + sqrt(1 + 12y)) / 2
```
Now, we need to find f^-1′ (0). This is the derivative of the inverse function evaluated at y = 0. We can find this derivative using the following steps:
1. Use the chain rule to differentiate f^-1(y).
2. Evaluate the resulting expression at y = 0.
This gives us the following:
```
f^-1′ (0) = (3 * (1 + 12 * 0) ^ (-2/3)) / 2 = 1.5
```
Therefore, f^-1′ (0) = 1.5.
Step-by-step explanation:
A rigidly tie bar in a heating chamber has a diameter of 10 mm and is tensioned
The initial stress is 1.273 × [tex]10^9[/tex] N/[tex]m^2[/tex], the resultant stress is 1.273 × [tex]10^9[/tex] N/[tex]m^2[/tex] and the induced force in the bar when the temperature reaches 50°C is 100.03 kN.
To calculate the initial stress in the tie bar, we can use the formula:
Stress = Load/Area
The area of the tie bar can be calculated using the formula for the area of a circle:
Area = π * [tex](diameter/2)^2[/tex]
Plugging in the values, we get:
Area = π * [tex]10 mm^{2}[/tex] = π *[tex](5 mm)^2[/tex] = 78.54 [tex]mm^2[/tex]
Converting the area to square meters, we have:
Area = 78.54 [tex]mm^2[/tex]* (1 m^2 / 1,000,000 [tex]mm^2[/tex]) = 7.854 × 1[tex]0^-5 m^2[/tex]
Now we can calculate the initial stress:
Initial Stress = 100 kN / 7.854 ×[tex]10^-5 m^2[/tex] = 1.273 × [tex]10^9 N/m^2[/tex]To calculate the resultant stress when the temperature rises to 50°C, we need to consider the thermal expansion of the tie bar. The change in length can be calculated using the formula:
ΔL = α * L0 * ΔT
Where ΔL is the change in length, α is the coefficient of linear expansion, L0 is the initial length, and ΔT is the change in temperature.
The induced force in the bar can be calculated using the formula:
Induced Force = Initial Stress * Area + E * α * ΔT * Area
Plugging in the values, we get:
Induced Force = (1.273 × 10^9 N[tex]m^2[/tex] * 7.854 × [tex]10^-5 m^2[/tex]) + (200 × [tex]10^9[/tex] N/[tex]m^2[/tex] * 14 × [tex]10^-6[/tex] /K * (50 - 15) K * 7.854 × [tex]10^-5 m^2[/tex])
Simplifying the equation, we find:
Induced Force = 100.03 kN
Therefore, the initial stress is 1.273 × [tex]10^9[/tex] N/[tex]m^2[/tex], the resultant stress is 1.273 × [tex]10^9[/tex] N/[tex]m^2[/tex], and the induced force in the bar when the temperature reaches 50°C is 100.03 kN.
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The probable question may be:
A rigidly held tie bar in a heating chamber has a diameter of 10 mm and is tensioned to a load of 100 kN at a temperature of 15°C. What is the initial stress, the resultant stress and what will be the induced force in the bar when the temperature in the chamber has risen to 50°C? E= 200 GN/ m2 and the coefficient of linear expansion of the material for tie bar = 14 × 10−6 /K.