The values of the variables are x = 23, y = 41/3, and z = -22/3.
The matrix equation Ax = b for the given set of linear equations is:
```
| -3 0 -6 | | x | | 11 |
| 5 -2 3 | * | y | = | 17 |
| 2 -1 -7 | | z | | -3 |
```
Where A is the coefficient matrix, x is the column matrix of variables, and b is the column matrix of constants.
To find the inverse of matrix A, we perform row operations on the augmented matrix [A|I]:
```
| -3 0 -6 | 1 0 0 |
| 5 -2 3 | 0 1 0 |
| 2 -1 -7 | 0 0 1 |
```
First, we divide the first row by -3:
```
| 1 0 2 | -1/3 0 0 |
| 5 -2 3 | 0 1 0 |
| 2 -1 7 | 0 0 1 |
```
Then, we subtract 5 times the first row from the second row, and 2 times the first row from the third row:
```
| 1 0 2 | -1/3 0 0 |
| 0 -2 -7 | 5/3 1 0 |
| 0 -1 -3 | 2/3 0 1 |
```
Next, we divide the second row by -2:
```
| 1 0 2 | -1/3 0 0 |
| 0 1 7/2 | -5/6 -1/2 0 |
| 0 -1 -3 | 2/3 0 1 |
```
And then we add the second row to the third row:
```
| 1 0 2 | -1/3 0 0 |
| 0 1 7/2 | -5/6 -1/2 0 |
| 0 0 1/2| 1/6 -1/2 1 |
```
Finally, we divide the third row by 1/2, and subtract 2 times the third row from the first row, and 7/2 times the third row from the second row:
```
| 1 0 0 | 0 1 -2 |
| 0 1 0 | -4/3 2 -7/2|
| 0 0 1 | 1/3 -1 2 |
```
So, the inverse of matrix A is:
```
| 0 1 -2 |
| -4/3 2 -7/2|
| 1/3 -1 2 |
```
Now, we can perform matrix multiplication A^-1b to get the values of the variables:
```
| 0 1 -2 | | 11 | | x |
| -4/3 2 -7/2| * | 17 | = | y |
| 1/3 -1 2 | | -3 | | z |
```
```
| x | | 1(17) + (-2)(-3) | | 23 |
| y | = | (-4/3)(11) + 2(17) + (-7/2)(-3) | = | 41/3 |
| z | | (1/3)(11) + (-1)(17) + 2(-3) | = | -22/3 |
``
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I paid $9.54 for 1.2 pounds of fresh fish.
How much did the fresh fish cost per pound?
Determine whether the following trinomial is a perfect square trinomial. 16a^(2)-40ab+25b^(2)
Yes, the given trinomial is a perfect square trinomial.
To determine whether a trinomial is a perfect square trinomial, we can use the formula:
(a-b)^(2) = a^(2) - 2ab + b^(2)
In this case, we can compare the given trinomial with the formula and see if it matches.
16a^(2)-40ab+25b^(2) = (4a)^(2) - 2(4a)(5b) + (5b)^(2)
This matches the formula, so we can conclude that the given trinomial is a perfect square trinomial.
Another way to determine whether a trinomial is a perfect square trinomial is to factor it and see if it can be written as a binomial squared.
In this case, we can factor the given trinomial as follows:
16a^(2)-40ab+25b^(2) = (4a-5b)(4a-5b) = (4a-5b)^(2)
Since the trinomial can be written as a binomial squared, we can conclude that it is a perfect square trinomial.
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Can somebody help with this problemo
Answer: end balance: $8,496.95
total interest: $1,496.95
Step-by-step explanation: total interest = $7000 × 8.554% × 30 ÷ 12 = $1,496.95
end balance = $7000 + $1,496.95 = $8,496.95
Find the missing variable and indicated
angle measure.
A
X =
51°
(3x)°
B
C
mzBDC =
This is the last one for me to be done with the assignment please answer fast:) will mark brainiest
Answer:x=a
Step-by-step explanation:
Write an equation for a line perpendicular to y = - 5 x - 2 and passing through the point ( 10 , 5 ) . Express your answer in slope-intercept form. y =
For a line perpendicular to y = - 5 x - 2 and passing through the point ( 10 , 5 ), the equation in slope-intercept form is y = (1/5)x + 3.
To write an equation for a line perpendicular to y = -5x - 2 and passing through the point (10, 5), we first need to find the slope of the new line. The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. The slope of the original line is -5, so the slope of the new line is 1/5.
Next, we can use the point-slope form of an equation to write the equation for the new line. The point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in the values we have, we get:
y - 5 = (1/5)(x - 10)
Finally, we can rearrange this equation to put it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. To do this, we'll distribute the 1/5 and then add 5 to both sides of the equation:
y - 5 = (1/5)x - 2
y = (1/5)x + 3
So the equation for the new line is y = (1/5)x + 3. This is our final answer.
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The pizza shown has a radius of 13 cm. What is the approximate area of the pizza? (Use 3.14 for .)
Answer:
530.66 cm²
Step-by-step explanation:
Pizza has a circle shape
The formula for the area of the circle is
A = π · r²
r = 13 cm
π = 3.14
3.14 x 13² = 3.14 x 169 = 530.66 cm²
So, the area of the pizza is 530.66 cm²
Answer:
530.66cm^2
Step-by-step explanation:
since a pizza is in the shape of a circle, we can use the formula π[tex]r^{2}[/tex] and here the radius is r which is 13cm, and since you asked to use 3.14 as pi's value,
=3.14*(13^2)cm
=3.14*169cm
is approximately = 530.66cm^2
Find the missing dimension in the figure below if the surface area is given as 216.18 m2
Answer:
x=4.3m
Step-by-step explanation:
It is made up by six graphics.
Two triangles=1/2*x*5.6*2=5.6x
Base rectangular: 11.3x
Back rectangular: 11.3*5.6=63.28
Front rectangular:11.3*7.1=80.23
Add together: 5.6x+11.3x+63.28+80.23=216.18
16.9x=72.67
x=4.3m
p(x)=7x^(3)-10x^(2)+8x-5 According to the rational zero theorem, the possible zeros for p(x) are +-((1,5)/(1,7))
Yes, according to the Rational Zero Theorem, the possible zeros of the polynomial p(x) are +-(1,5/1,7). The only factorization that works in this case is p/q = 1.5/1.7, which yields the zeros +-(1,5/1,7).
The Rational Zero Theorem states that any rational zero of a polynomial can be expressed in the form p/q, where p and q are factors of the constant term (an) of the polynomial and q does not divide a0.
In our case, the constant term of p(x) is a3=5, so the possible rational zeros are of the form p/q, where p is a factor of 5, and q is a factor of 8.
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Based on the following figure, determine which value below is correct.
The correct measure is given as follows:
x = 6.
What are vertical angles?Vertical angles are angles that are opposite by the same vertex on crossing segments, hence they share a common vertex, thus being congruent, meaning that they end up having the same angle measure.
Over vertex C, the two angles are congruent, hence the value of x is obtained as follows:
12x - 9 = 6x + 27
6x = 36
x = 6.
(as the vertical angles are congruent, we can just equal the measures of the two angles and then solve the expression for the value of x).
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Three clocks ring once at the same time. After that, the first clock rings after every 90 minutes,
the second after every 30 minutes, and third after every 60 minutes. After how many minutes will they again ring together?
Answer:
me no habla ingles?
Step-by-step explanation:
The top rectangle has a base b and a height h. The bottom rectangle has a base that is 1/3 of the length of the base of the top rectangle and a height that is 1/2 of the length of the height of the top rectangle. Devin writes the area of the smaller rectangle as the product 1/3 b • 1/2 h. Tracy rewrites this as 1/6 bh. Which of the students’ expressions makes it easier to see how the areas of the rectangles are related? Explain.
Tracy's expression makes it easier to see how the areas of the rectangles are related i.e. 1/6 bh.
What is a Rectangle?
The opposite sides of a quadrilateral are equal and parallel, and all the angles are equal. Around us, there are several rectangle-shaped items. Two dimensions, the length and breadth, define each rectangle shape. The width and length of a rectangle are its longer and shorter sides, respectively.
Dimensions of top rectangle :
base = b
height = h
So, area = b × h
Dimensions of bottom rectangle :
base = b/3
height = h/2
So, area = b/3 × h/2 = (b × h) 6
Hence, area of bottom rectangle is 1/6th of that top rectangle.
Devin writes the area of the smaller rectangle as the product 1/3 b • 1/2 h. Tracy rewrites this as 1/6 bh.
Hence, Tracy's expression represents more easier way to see how the rectangle's area is related.
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The question is in the screenshot:
The value of the trigonometric function sin A, tan A, and sec A will be 3/5, 3/4, and 5/4.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Use the triangle to evaluate each function.
Hypotenuse AB has a length of 5, BC has a length of 4, and side AC has a length of 3.
Then the value of the trigonometric function will be
sin A = BC / AB
sin A = 3 / 5
tan A = BC / AC
tan A = 3 / 4
sec A = AB / AC
sec A = 5 / 4
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given an "Armfield pump rig" to find the characteristics and efficiency of a pump experimentally. In this context, the pump is an energy converter that converts electrical power into hydraulic power.
the sample points are logged with a constant setting of rotational speed (angular velocity). power data is registered along the way - electric power into the electric motor, pressure from the pump and volume flow during throttling of the water flow out of the pump.
given data from EXCELbelow:
use EXCEL to solve the questions below, and explain step by step procedure
a) Calculate effects and efficiencies for all operating points.
b) Create a graph showing the delivery pressure (Pa) ("Pump 1") as a function of volume flow (Flow Rate Q) in (m3 / s)
c) Create a graph showing motor power (Pump 1) (W) as a function of volume flow (Flow Rate) Q (l / s) on an axis and efficiency (Pump 1 (%) on a secondary axis
To calculate the effect of the pump, use the formula: P = Q * ΔP / η and To calculate the efficiency of the pump, use the formula: η = P / P_e. Use the data provided in the EXCEL file.
To solve the questions, follow these steps:
a) Calculate effects and efficiencies for all operating points:
1. To calculate the effect of the pump, use the formula: P = Q * ΔP / η, where P is the power of the pump, Q is the volume flow rate, ΔP is the pressure difference across the pump, and η is the efficiency of the pump.
2. To calculate the efficiency of the pump, use the formula: η = P / P_e, where P is the power of the pump, and P_e is the electrical power input to the pump.
3. Use the data provided in the EXCEL file to calculate the effects and efficiencies for all operating points.
b) Create a graph showing the delivery pressure (Pa) ("Pump 1") as a function of volume flow (Flow Rate Q) in (m3 / s):
1. Select the data for the delivery pressure (Pa) and volume flow (Flow Rate Q) in the EXCEL file.
2. Click on the "Insert" tab in EXCEL and select the "Scatter" chart option.
3. Choose the "Scatter with Straight Lines" option to create a graph showing the delivery pressure (Pa) as a function of volume flow (Flow Rate Q).
c) Create a graph showing motor power (Pump 1) (W) as a function of volume flow (Flow Rate) Q (l / s) on an axis and efficiency (Pump 1 (%) on a secondary axis:
1. Select the data for the motor power (Pump 1) (W) and volume flow (Flow Rate) Q (l / s) in the EXCEL file.
2. Click on the "Insert" tab in EXCEL and select the "Scatter" chart option.
3. Choose the "Scatter with Straight Lines" option to create a graph showing the motor power (Pump 1) (W) as a function of volume flow (Flow Rate) Q (l / s).
4. Add a secondary axis to the graph by clicking on the "Format" tab in EXCEL and selecting the "Secondary Axis" option.
5. Select the data for the efficiency (Pump 1 (%) and add it to the secondary axis of the graph.
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Fix \( G \) a group. For elements \( g, h \in G \) set \( [g, h]:=g h g^{-1} h^{-1} \) and set \[ [G, G]:=\left\{\left[g_{1}, h_{1}\right] \cdots\left[g_{s}, h_{s}\right]: g_{1}, \ldots, g_{s}, h_{1},
([G,G]\) is a group, which is the subgroup of \(G \times G\) generated by the set of all commutators \([g,h]\).
To fix \(G\) as a group and set \([g,h]:=g h g^{-1} h^{-1}\), and then set
\[[G,G] := \left\{\left[g_{1}, h_{1}\right] \cdots\left[g_{s}, h_{s}\right]: g_{1}, \ldots, g_{s}, h_{1}, \ldots, h_{s} \in G\right\}\), we can start by noticing that this is a subset of the Cartesian product of \(G\) with itself, and since \(G\) is a group, this subset must also be a group. Therefore, \([G,G]\) is a group, which is the subgroup of \(G \times G\) generated by the set of all commutators \([g,h]\).
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use the body temperatures, in degrees in fahrenheit, listed in the accompanying table. the range of the data is 3.5 degrees F. use the range rule of thumb to estimate the value of the standard deviation. compare the result to the actual standard deviation of the data rounded to two decimal places, 0.72 degrees F, assuming the goal is to approximate the standard deviation within 0.2 degrees F.
The estimated value of the standard deviation using the range rule of thumb is 0.875 degrees F
The range rule of thumb is used to estimate the standard deviation of a data set using the range of the data. In this case, the range of the data is 3.5 degrees F. Using the range rule of thumb, the standard deviation of the data can be estimated by taking the range (3.5) and dividing it by 4, which gives us an estimated standard deviation of 0.875 degrees F.
This estimated value is within 0.2 degrees F of the actual standard deviation of the data (0.72 degrees F).
To compare this result to the actual standard deviation of the data, we subtract the estimated value from the actual value and take the absolute value of the result. This gives us the difference between the two values:
|0.72 - 0.875| = 0.155
Since the difference between the estimated and actual standard deviations is less than 0.2 degrees F, we can say that the range rule of thumb provides a reasonable approximation of the standard deviation for this data set.
In conclusion, the estimated value of the standard deviation using the range rule of thumb is 0.875 degrees F, and this value is within 0.2 degrees F of the actual standard deviation of 0.72 degrees F.
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can some one please help me with this
We can rewrite the inequality as:
95 ≤ u ≤ 155
How to solve the inequality?Here we have the absolute value inequality:
|125 - u| ≤ 30
Where the variable is u.
The absolute value can be decomposed into two inequalities:
(125 - u) ≤ 30
(125 - u) ≥ -30
Solving these two we will get:
125 - 30 ≤ u
125 + 30 ≥ u
Then the compound inequality is:
95 ≤ u ≤ 155
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Find the median of the solutions to the equation 3x^3+5x^2−6x−10=0. (A) −√2 (B) √2 (C) −5/9 (D) −3/5 (E) None of these
The median of the solutions to the equation 3x³ + 5x² − 6x − 10 = 0 is -√2. The correct answer is A.
To find the median of the solutions to the equation 3x³ + 5x² − 6x − 10 = 0, first find the solutions of the equation and then find the middle value of those solutions.
Group the terms and factor out (3x + 5).
(3x³ + 5x²) + (-6x − 10) = 0
(3x + 5)(x²) + (3x + 5)(-2) = 0
(3x + 5)(x² - 2) = 0
Factor (x² - 2).
(3x + 5)(x + √2)(x - √2) = 0
So the solutions of the equation are x = -5/3, x = -√2, and x = √2.
To find the median of these solutions, we need to order them from least to greatest:
-5/3 < -√2 < √2
The median of these solutions is -√2.
Therefore, the correct answer is (A) -√2.
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Find the point (x, y) on the unit circle that corresponds to the real number t. ON THE BLANK WRITE DOWN sqrt(2) for √2 or sqrt(3) for √3. t = 5????/6 the corresponding (x,y) is
The point (x, y) on the unit circle that corresponds to the real number t = 5π/6 is (-√3/2, 1/2).
The point (x, y) on the unit circle that corresponds to the real number t can be found using the following equations:
x = cos(t)
y = sin(t)
Since t = 5π/6, we can plug this value into the equations to find x and y:
x = cos(5π/6) = -√3/2
y = sin(5π/6) = 1/2
Therefore, the point (x, y) on the unit circle that corresponds to the real number t = 5π/6 is (-√3/2, 1/2).
Note: The unit circle is a circle with a radius of 1 that is centered at the origin (0, 0) of the coordinate plane. The x-coordinate of a point on the unit circle corresponds to the cosine of the angle formed by the positive x-axis and the radius connecting the origin to the point, while the y-coordinate corresponds to the sine of this angle.
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Find the measure of angle R.
17.2°
16.1°
70.1°
88.6°
Answer:
16.1 is the closest asnwer
Step-by-step explanation:
if you didn't understand feel free to send me a message bro
For a function f(x)f(x) and a particular input value x=ax=a, then we may write the difference quotient as
f(a+h)−f(a)/h
where h≠0
Now, let f(x)=x^3−15x and consider the input value a=3. We could now write the difference quotient as
f(3+h)−f(3)/h
where h≠0.
Use this difference quotient to calculate the average rate of change of f(x) from x=3 to x=3+h for the following particular values of h.
When h=0.2 the average rate of change of f(x) is __________ .
When h=0.1, the average rate of change of f(x) is ____________ .
When h=0.01, the average rate of change of f(x) is ____________ .
When h=−0.01, the average rate of change of f(x) is _____________ .
When h=−0.1, the average rate of change of f(x) is ______________ .
When h=−0.2, the average rate of change of f(x) is ______________ .
The average rate of change of f(x) for the given values of h are:
When h=0.2, the average rate of change of f(x) is 112.84.
When h=0.1, the average rate of change of f(x) is 206.41.
When h=0.01, the average rate of change of f(x) is 1850.5601.
When h=−0.01, the average rate of change of f(x) is -1807.5399.
When h=−0.1, the average rate of change of f(x) is -171.39.
When h=−0.2, the average rate of change of f(x) is -80.76.
To calculate the average rate of change of f(x) for the given values of h, we need to substitute the values of h into the difference quotient and simplify.
When h=0.2:
f(3+0.2)−f(3)/0.2 = [(3.2^3−15(3.2)) - (3^3−15(3))]/0.2 = (32.768 - 10.2) - (27 - 45)/0.2 = 22.568/0.2 = 112.84
When h=0.1:
f(3+0.1)−f(3)/0.1 = [(3.1^3−15(3.1)) - (3^3−15(3))]/0.1 = (29.791 - 9.15) - (27 - 45)/0.1 = 20.641/0.1 = 206.41
When h=0.01:
f(3+0.01)−f(3)/0.01 = [(3.01^3−15(3.01)) - (3^3−15(3))]/0.01 = (27.270601 - 8.765) - (27 - 45)/0.01 = 18.505601/0.01 = 1850.5601
When h=−0.01:
f(3+(-0.01))−f(3)/(-0.01) = [(2.99^3−15(2.99)) - (3^3−15(3))]/(-0.01) = (26.730399 - 8.655) - (27 - 45)/(-0.01) = 18.075399/(-0.01) = -1807.5399
When h=−0.1:
f(3+(-0.1))−f(3)/(-0.1) = [(2.9^3−15(2.9)) - (3^3−15(3))]/(-0.1) = (24.389 - 8.25) - (27 - 45)/(-0.1) = 17.139/(-0.1) = -171.39
When h=−0.2:
f(3+(-0.2))−f(3)/(-0.2) = [(2.8^3−15(2.8)) - (3^3−15(3))]/(-0.2) = (21.952 - 7.8) - (27 - 45)/(-0.2) = 16.152/(-0.2) = -80.76
Therefore, the average rate of change of f(x) for the given values of h are:
When h=0.2, value is 112.84.
When h=0.1, value is 206.41.
When h=0.01, value is 1850.5601.
When h=−0.01, value is -1807.5399.
When h=−0.1, value is -171.39.
When h=−0.2, value is -80.76.
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plsplsplsss im struggling so bad- does anybody know how to do the attached question?
By angle angle similarity ΔWYZ ≈ Δ WZX ≈ ΔZYX are similar.
Explain about the similarity of triangles?Triangles with exactly similar corresponding angle configurations are said to be similar triangles. This implies that equiangular triangles are comparable. All equilateral triangles are thus interpretations of similar triangles.
Two triangles are comparable if the determinations of their corresponding sides are proportionate. The same is true if the lengths of two sides for one triangle are proportional to the lengths of the corresponding sides inside a triangle and the included angles are congruent.In the given statements, thus the similar triangle are:
ΔWYZ ≈ Δ WZX ≈ ΔZYX
A,
∠Y is common
∠x = ∠z = 90°
Therefore, by angle angle similarity ΔWYZ ≈ Δ WZX ≈ ΔZYX are similar.
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Jane wants to buy 15 tomatoes. She asks for 1 kg of tomatoes at a shop. Jane assumes that each tomato has a weight of 75 g. (b) (i) If Jane's assumption is correct, will she get 15 tomatoes? You must show how you get your answer. (ii) If Jane's assumption is not correct, could she get 15 tomatoes? Justify your answer.
(i) If Jane's assumption is correct, she will not get 15 tomatoes.
(ii) If Jane's supposition about the body mass of the each tomato is wrong, she could not obtain 15 tomatoes to 1 kg of tomatoes.
What types of things are assumptions?
An presumption is something you believe to be true despite the lack of evidence. People might presume, for instance, that you are a geek if you wear spectacles, even though that is untrue.
(b) (i) If Jane's assumption is correct, then the weight of 15 tomatoes would be:
15 tomatoes × 75 g/tomato = 1125 g
Since 1 kg is equal to 1000 g, Jane would need to buy at least:
1125 g / 1000 g/kg = 1.125 kg of tomatoes
Therefore, Jane would need to ask for at least 1.125 kg of tomatoes to get 15 tomatoes if her assumption about the weight of each tomato is correct.
(b) (ii) If Jane's assumption about the weight of each tomato is not correct, it is possible that she could get 15 tomatoes with 1 kg of tomatoes, depending on the actual weight of each tomato.
For example, if each tomato actually weighs 67 g, then 15 tomatoes would weigh:
15 tomatoes × 67 g/tomato = 1005 g
This is less than 1 kg, so Jane would get 15 tomatoes with 1 kg of tomatoes.
On the other hand, if each tomato actually weighs 100 g, then 15 tomatoes would weigh:
15 tomatoes × 100 g/tomato = 1500 g
This is more than 1 kg, so Jane would not get 15 tomatoes with 1 kg of tomatoes if her assumption about the weight of each tomato is incorrect.
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Blake collects stamps. He collected a total of 250. If 84% of the stamps he collected were foreign, how many other stamps did he collect?
Put the function y=10x(x+1) in factored form f(x)=a(x-r)(x-s) and state the values of a,r, and s. (Assume r ≤ x)
The function y=10x(x+1) is already in factored form, with a=10, r=0, and s=-1.
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is termed the domain of the function and the set Y is called the codomain of the function. Initially, functions represented the idealized relationship between varied quantities and other variables.
To see this, we can rewrite the function as f(x)=10(x-0)(x-(-1)), which matches the form f(x)=a(x-r)(x-s). Therefore, the values of a, r, and s are:
a = 10
r = 0
s = -1
It is important to note that the values of r and s are the x-intercepts of the function, or the values of x that make the function equal to zero. In this case, the x-intercepts are 0 and -1, which correspond to the values of r and s.
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Suppose z varies inversely with t and that z=6 when t=8. What is the value of z when t=2 ?
The value of z when t=2 is 24
The value of z varies inversely with t, which means that the product of z and t is a constant. We can write this relationship as:
zt = k
Where k is the constant. We are given that z=6 when t=8, so we can plug these values into the equation to find k:
6*8 = k
k = 48
Now we can use this value of k to find the value of z when t=2. Plugging in these values gives us:
z*2 = 48
Solving for z gives us:
z = 48/2
z = 24
Therefore, the value of z when t=2 is 24.
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Javier is saving money at a constant rate to buy a new car. After saving for 2
months, Javier has $920
. After saving for 4
months, Javier has $1,030
.
Construct a function that models the relationship between the amount of money Javier has saved and the number of months he has saved for. Show or explain how you constructed the function.
Respond in the space provided.
Answer:
look in the comments and have a good
Step-by-step explanation:
look
The diagram shows a right triangle and the lengths of two of its sides in inches. Which measurement is closest to the value of d in inches?
Substituting in the given values for a and b, we can solve for d and find that it is approximately 9.48 inches.
What is Pythagorean theorem?Pythagorean Theorem is a mathematical formula that states that the square of the hypotenuse (the side opposite the right angle) of a right triangle is equal to the sum of the squares of the other two sides. It is expressed as a2 + b2 = c2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
The given diagram is a right triangle with two of its sides labeled in inches. To find the length of the third side (d), one must use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, d is the hypotenuse, so d2 = a2 + b2. Therefore, substituting in the given values for a and b, we can solve for d and find that it is approximately 9.48 inches.
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Find the exact value of each of the remaining trigonometric functions of \( \theta \). Rationalize denominators when applicable. \( \cot \theta=-\frac{\sqrt{3}}{7} \), given that \( \theta \) is in qu
The exact value of the remaining trigonometric functions of \( \theta \) are \( \sin \theta = \frac{7\sqrt{52}}{52} \), \( \cos \theta = \frac{-\sqrt{3}\sqrt{52}}{52} \), \( \tan \theta = \frac{-7\sqrt{3}}{3} \), \( \sec \theta = \frac{-\sqrt{52}\sqrt{3}}{3} \), and \( \csc \theta = \frac{\sqrt{52}}{7} \).
We can find the exact value of the remaining trigonometric functions of \( \theta \) by using the Pythagorean identity and the definition of the trigonometric functions. The Pythagorean identity states that \( \sin^2 \theta + \cos^2 \theta = 1 \). The definition of the trigonometric functions are \( \sin \theta = \frac{y}{r} \), \( \cos \theta = \frac{x}{r} \), \( \tan \theta = \frac{y}{x} \), \( \cot \theta = \frac{x}{y} \), \( \sec \theta = \frac{r}{x} \), and \( \csc \theta = \frac{r}{y} \).
Given that \( \cot \theta=-\frac{\sqrt{3}}{7} \), we can use the definition of the cotangent function to find the values of x and y. Let x = -\( \sqrt{3} \) and y = 7. Then, we can use the Pythagorean identity to find the value of r.
\( \sin^2 \theta + \cos^2 \theta = 1 \)
\( \frac{y^2}{r^2} + \frac{x^2}{r^2} = 1 \)
\( \frac{7^2}{r^2} + \frac{(-\sqrt{3})^2}{r^2} = 1 \)
\( \frac{49 + 3}{r^2} = 1 \)
\( \frac{52}{r^2} = 1 \)
\( r^2 = 52 \)
\( r = \sqrt{52} \)
Now, we can use the definition of the trigonometric functions to find the exact value of the remaining trigonometric functions of \( \theta \).
\( \sin \theta = \frac{y}{r} = \frac{7}{\sqrt{52}} = \frac{7\sqrt{52}}{52} \)
\( \cos \theta = \frac{x}{r} = \frac{-\sqrt{3}}{\sqrt{52}} = \frac{-\sqrt{3}\sqrt{52}}{52} \)
\( \tan \theta = \frac{y}{x} = \frac{7}{-\sqrt{3}} = \frac{-7\sqrt{3}}{3} \)
\( \sec \theta = \frac{r}{x} = \frac{\sqrt{52}}{-\sqrt{3}} = \frac{-\sqrt{52}\sqrt{3}}{3} \)
\( \csc \theta = \frac{r}{y} = \frac{\sqrt{52}}{7} = \frac{\sqrt{52}}{7} \)
Therefore, the exact value of the remaining trigonometric functions of \( \theta \) are \( \sin \theta = \frac{7\sqrt{52}}{52} \), \( \cos \theta = \frac{-\sqrt{3}\sqrt{52}}{52} \), \( \tan \theta = \frac{-7\sqrt{3}}{3} \), \( \sec \theta = \frac{-\sqrt{52}\sqrt{3}}{3} \), and \( \csc \theta = \frac{\sqrt{52}}{7} \).
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What happens when sample size is small and population S.D is unknown?
i. Values on the Z row on the table (or Z values) can't be used.( note that Z is normal distribution)
ii. we use the sample distribution
A. i only
B. i and ii only
C. ii only
D. None of the abov
When sample size is small and population S.D. is unknown, values on the Z row on the table (or Z values) can't be used (note that Z is normal distribution). The correct option is A, i only.
A small sample is a dataset that contains few observations, making it more difficult to generalize the outcomes to the broader population. When a sample size is small, the sample mean, standard deviation, and other statistical measures may be influenced by chance variations.
Larger samples may be required to represent the overall population precisely. The larger the sample size, the closer the sample mean is likely to be to the true population mean. Additionally, when the sample is large, the sample standard deviation is more likely to be an accurate estimate of the population standard deviation.
A standard normal distribution can be used to find out the probability of obtaining a score in a particular range for a normal distribution. The Z value, or the value on the standard normal distribution, is used to convert any regular distribution to a standard normal distribution, which has a mean of 0 and a standard deviation of 1. However, when the sample size is small and the population standard deviation is unknown, the values on the Z row on the table (or Z values) can't be used.
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At the movie theatre, child admission is $5.30 and adult admission is $8.70. On Saturday, 163 tickets were sold for a total sales of $1169.90. How many child tickets were sold that day?
The number of child tickets were sold that day are 73.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that;
Cost of child admission= $5.30
Cost of adult admission= $8.70
Now,
Let's assume that "c" represents the number of child tickets sold, and "a" represents the number of adult tickets sold. We can create two equations based on the given information:
c + a = 163 (equation 1: the total number of tickets sold)
5.30c + 8.70a = 1169.90 (equation 2: the total sales)
We can use equation 1 to solve for "a" in terms of "c":
a = 163 - c
Substituting this expression for "a" into equation 2, we get:
5.30c + 8.70(163 - c) = 1169.90
Simplifying and solving for "c", we get:
5.30c + 1418.10 - 8.70c = 1169.90
-3.4c = -248.20
c = 73
Therefore, by algebra the answer will be 73.
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