The equation of tangent plane to the surfacez = 8x² - 9y² at the point (2,1,23) is 32(x - 2) - 18(y - 1) -1(z - 23) = 0
Here, the equation of the surface is
z = 8x² - 9y²
Let us assume that f(x, y, z) = 8x² - 9y² - z
The partial derivative of f(x, y, z) would be:
[tex]\frac{\partial f}{\partial x}[/tex] = 16x
[tex]\frac{\partial f}{\partial y}[/tex] = -18y
[tex]\frac{\partial f}{\partial z}[/tex] = -1
At point (2, 1, 23) the partial derivative of f(x, y, z),
[tex]\frac{\partial f}{\partial x}[/tex] = 32
[tex]\frac{\partial f}{\partial y}[/tex] = -18
[tex]\frac{\partial f}{\partial z}[/tex] = -1
So, the equation of tangent plane would be,
32(x - 2) - 18(y - 1) -1(z - 23) = 0
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Multiply 6c(8 − 3c).
Answer:-30c
Step-by-step explanation:
you subtract 8 from 3c which is -5c than multiply by 6 which is -30c
A coupon book has a coupon for 10% off a ticket at a theme park. A ticket usually costs $80. How much would a visitor save with the coupon?
Answer: the visitor would save $8 with the coupon.
Step-by-step explanation: 10% of $80 = 0.1 x $80 = $8
The velocity v of a meteorite approaching earth is givin by v=k/
The velocity of the meteorite is 4 km per sec.
Given that, a meteorite is approaching the earth and is 10000 km away from earth,
we need to find the velocity,
v = k / √d
v = 400 / √10000
v = 400 / 100
v = 4 km per sec.
Hence, the velocity of the meteorite is 4 km per sec.
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The velocity at a distance of 6,889 kilometers is 6.795 Km/ sec.
We have,
The velocity v of a meteorite approaching earth is V = k/√d.
The distance from center of Earth = 8836
and, Velocity = 6 Km/ s
So, using the formula for velocity
6 = k/√8836
6 = k/94
k= 564 Km
Now, velocity at 6689 Km
V = 564/ √6889
V =6.795 km/sec
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A machine produces metal pieces that are cylindrical in shape. A sample of these pieces is taken and the diameters are found to be 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 0.99, 1.01, and 1.03 centimeters. Use these data to calculate three interval types and draw interpretations that illustrate the distinction between them in the context of the system. For all computations, assume an approximately normal distribution. The sample mean and standard deviation for the given data are ¯x = 1.0056 and s = 0.0246. (a) Find a 99% confidence interval on the mean diameter. (b) Compute a 99% prediction interval on a measured diameter of a single metal piece taken from the machine. (c) Find the 99% tolerance limits that will contain 95% of the metal pieces produced by this machine. (Complete step by step process)
This interval is wider than the confidence interval in part (a) and the prediction interval in part (b) because it is based on the entire population of metal pieces, not just a sample.
(a) To find a 99% confidence interval on the mean diameter, we can use the t-distribution with n-1 degrees of freedom since the population standard deviation is not known. The formula for the confidence interval is:
CI = x ± tα/2,s/√n
where x is the sample mean, s is the sample standard deviation, n is the sample size, and tα/2 is the t-value with (n-1) degrees of freedom for the desired level of confidence α.
Plugging in the values, we get:
CI = 1.0056 ± t0.005/2,0.0246/√9
= 1.0056 ± 0.025
= (0.9806, 1.0306)
Therefore, we can be 99% confident that the true mean diameter of the metal pieces produced by the machine is between 0.9806 and 1.0306 centimeters.
(b) To compute a 99% prediction interval on a measured diameter of a single metal piece taken from the machine, we can use the formula:
PI = x ± tα/2,s(1 + 1/n)√(1 + 1/n)
where x is the point estimate of the diameter (in this case, the sample mean), s is the sample standard deviation, n is the sample size, and tα/2 is the t-value with (n-1) degrees of freedom for the desired level of confidence α.
Plugging in the values, we get:
PI = 1.0056 ± t0.005/2,0.0246(1 + 1/9)√(1 + 1/9)
= 1.0056 ± 0.052
= (0.9536, 1.0576)
Therefore, we can be 99% confident that a single metal piece produced by the machine will have a diameter between 0.9536 and 1.0576 centimeters.
(c) To find the 99% tolerance limits that will contain 95% of the metal pieces produced by this machine, we can use the formula:
TL = x ± kσ
where x is the sample mean, σ is the population standard deviation (which is estimated by the sample standard deviation s), k is the number of standard deviations from the mean that will contain the desired percentage of the population (in this case, 95% or 1.96 standard deviations for a normal distribution).
Plugging in the values, we get:
TL = 1.0056 ± 1.96(0.0246)
= (0.9573, 1.0539)
Therefore, we can be 99% confident that 95% of the metal pieces produced by the machine will have diameters between 0.9573 and 1.0539 centimeters. This interval is wider than the confidence interval in part (a) and the prediction interval in part (b) because it is based on the entire population of metal pieces, not just a sample.
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Two concentric circles form a target. The radii of the two circles measure 8 cm and 2 cm. The inner circle is the bullseye of the target. A
point on the target is randomly selected.
What is the probability that the randomly selected point is in the bullseye?
?
—
?
The probability that the randomly selected point is in the bullseye = 15/16.
How do we determine the probability that the point randomly selected is in the bullseye?To calculate the probability that the randomly selected point is in the bullseye, we shall first evaluate the area of each of the circles:
The area of the larger circle (outer circle) with radius 8 cm is given:
A_outer = πr² = π(8)² = 64π
The area of the smaller circle (inner circle) with radius 2 cm is given:
A_inner = πr² = π(2)² = 4π
The area of the bullseye (the region between the two circles) = the difference between the areas of the two circles:
A_bullseye = A_outer - A_inner
= 64π - 4π = 60π
Therefore, the probability that a randomly selected point is in the bullseye:
P = A_bullseye / A_outer
= (60π) / (64π)
P = 15/16
x
Therefore, the probability that the randomly selected point is in the bullseye = 15/16.
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Pls help
The shape below contains a triangle and a semi circle.
Round your response to two decimal places.
What is the perimeter of the shape above?
What is the area of the shape above?
The perimeter of the shape above is 22.22 units
the area of the shape above is 26 square units
How to determine the valuesWe can see from the diagram shown, that the shape is made up of a semicircle below and a triangle above.
Now, the formula for calculating the area of a triangle is expressed as;
A = 1/2bh
Such that the parameters are;
A is the areab is the base h is the height of the triangleNow, substitute the values
Area = 1/2 × 7 ×6
Multiply the values
Area = 42/2
Area = 26 square units
The formula for perimeter of a triangle is;
Perimeter = (a + b + c)
Perimeter = 6 + 7 + 9. 22
Add the values
Perimeter = 22. 22 units
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Graph the line with slope
3/4
passing through the point (-4,-1)
.
Answer: See attached.
Step-by-step explanation:
First, we will create an equation with the slope given.
y = [tex]\frac{3}{4}[/tex]x + b
Then, we will substitute this value in and solve for b (our y-intercept). Then we will graph the equation.
y = [tex]\frac{3}{4}[/tex]x + b
(-1) = [tex]\frac{3}{4}[/tex](-4) + b
-1 = -3 + b
b = 2
Our final equation:
y = [tex]\frac{3}{4}[/tex]x + 2
See attached for the graph. We will plot the point (0, 2) for our y-intercept and then move 3 units up for every four units right, according to the slope.
35 POINTS ANSWER FOR BRAINLIST
Colbie solved the equation below by completing the square. Did she complete the square correctly? Explain why or why not? Correct the mistake(s) – if there are any.
Answer:
Colbie did not complete the square correctly.
Colbie failed to add the square of half the coefficient of the term in x to both sides of the equation. She only added 25 to the left side of the equation. She also factored x² + 10x + 25 incorrectly by using a subtraction sign in the binomial rather than an addition sign.
Step-by-step explanation:
Given quadratic equation:
[tex]2x^2+20x-48=0[/tex]
As the leading coefficient is not one, to complete the square we must first divide both sides of the equation by the leading coefficient, 2:
[tex]\dfrac{2x^2+20x-48}{2}=\dfrac{0}{2}[/tex]
[tex]x^2+10x-24=0[/tex]
Now move the constant to the right side of the equation by adding 24 to both sides of the equation:
[tex]\begin{array}{rcr}x^2+10x-24&=&0\\\vphantom{\dfrac12}+24 & &+24\\\cline{1-3}\vphantom{\dfrac12}x^2+10x\phantom{-24.}&=&24\end{array}[/tex]
We need to make the left side of the equation a perfect square trinomial. To do this, add the square of half the coefficient of the term in x to both sides of the equation.
The coefficient of the term in x is 10. Therefore, the square of half of this is 25:
[tex]\left(\dfrac{10}{2}\right)^2=5^2=25[/tex]
This is the point at which Colbie made her first mistake. She didn't add the square of half the coefficient of the term in x to both sides of the equation - she only added it to the left side.
Add 25 to both sides of the equation:
[tex]x^2+10x+25=24+25[/tex]
[tex]x^2+10x+25=49[/tex]
To continue to solve the equation, factor the perfect square trinomial on the left side of the equation:
[tex](x+5)^2=49[/tex]
↑ Colbie made her second mistake here. She factored x² + 10x + 25 incorrectly by using a subtraction sign in the binomial rather than an addition sign.
Square root both sides:
[tex]\sqrt{(x+5)^2}=\sqrt{49}[/tex]
[tex]x+5=\pm7[/tex]
Subtract 5 from both sides:
[tex]x+5-5=-5\pm7[/tex]
[tex]x=-5\pm7[/tex]
Therefore, the solutions are:
[tex]x=-5+7=2[/tex]
[tex]x=-5-7=-12[/tex]
How do I solve this?
Answer:
Step-by-step explanation:
A = length x width = (2w + 5)(w) = 2w² + 5w
P = 2(2w + 5) + 2w = 6w + 10
To graph: sorry, Brainly doesn't have graphing tools so I'll just have to describe it
A: parabola, opens up, vertex at (-1.25, -3,124), crosses x axis at (-2.5, 0) and (0,0)
P: straight line, slants up, with a slope of 6, y-intercept of 10, crosses x axis at (-1.667, 0)
FYI, the 2 graphs intersect at 2 points: (-2, 2) and (2.5, 25)
A middle school took all of its 6th-grade students on a field trip to see a play at a theater that has 3260 seats. The students filled 95% of the seats in the theater. How many 6th graders went on the trip?
There were 3097 6th-grade students who went on the field trip to see the play at the theater.
We have,
If 95% of the 3260 seats in the theater were filled by the 6th-grade students,
We can find the total number of students by multiplying the total number of seats by the fill percentage as a decimal:
Number of 6th graders = 3260 x 0.95
Number of 6th graders = 3097
Therefore,
There were 3097 6th-grade students who went on the field trip to see the play at the theater.
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SOLVE ASAP!!
On the same coordinate plane, mark all points (x, y) that satisfy each rule.
a) y= -3-x
b) y= x-3
c) y= 3x+2
d) y= 3x-2
e) y= -3x+2
(SHOW COORDINATE PLANE GRAPH)
(WILL AWARD BRAINLIEST)
The point that satisfies y = -3-x is (0,-3), the point that satisfies y = x-3 is (0,-3), the point that satisfies y = 3x+2 is (0,2), the point that satisfies y = 3x -2 is (0,-2), the point that satisfies y = -3x+2 is (0,2). The graph is shown below.
To find the points that satisfy the equation y = -3 - x, we can substitute different values of x and solve for y.
When x = 0, y = -3 - 0 = -3, so one point is (0, -3).
When x = 1, y = -3 - 1 = -4, so another point is (1, -4).
When x = -1, y = -3 - (-1) = -2, so another point is (-1, -2).
By repeating this process for different values of x, we can find more points that satisfy the equation.
To find the points that satisfy the equation y = x - 3, we can again substitute different values of x and solve for y.
When x = 0, y = 0 - 3 = -3, so one point is (0, -3).
When x = 1, y = 1 - 3 = -2, so another point is (1, -2).
When x = -1, y = -1 - 3 = -4, so another point is (-1, -4).
To find the points that satisfy the equation y = 3x + 2, we can once again substitute different values of x and solve for y.
When x = 0, y = 3(0) + 2 = 2, so one point is (0, 2).
When x = 1, y = 3(1) + 2 = 5, so another point is (1, 5).
When x = -1, y = 3(-1) + 2 = -1, so another point is (-1, -1).
To find the points that satisfy the equation y = 3x - 2, we can once again substitute different values of x and solve for y.
When x = 0, y = 3(0) - 2 = -2, so one point is (0, -2).
When x = 1, y = 3(1) - 2 = 1, so another point is (1, 1).
When x = -1, y = 3(-1) - 2 = -5, so another point is (-1, -5).
To find the points that satisfy the equation y = -3x + 2, we can once again substitute different values of x and solve for y.
When x = 0, y = -3(0) + 2 = 2, so one point is (0, 2).
When x = 1, y = -3(1) + 2 = -1, so another point is (1, -1).
When x = -1, y = -3(-1) + 2 = 5, so another point is (-1, 5).
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Find the median of 61, 55, 56, 61, 57, 55, 54
Check the picture below.
The discussion above offers a third tip for saving money on purchases. Write a short paragraph, consisting of 125 words or more, that applies these techniques to purchasing a television.
When we create a budget for television purchase as a technique, this can help you avoid overspending and ensure that you stay within your means.
How to save money when purchasing a Television?It is best to ensure we you are purchasing a television that meets your needs and is within your budget. We can look for reviews, compare prices and features of different models to make an informed decision.
One can also try to purchase during sales, holidays and special events which is when retailers offer discounts and promotions.
Finally, when we create a budget, this can help you avoid overspending and ensure that you stay within your means. By setting a limit on how much you're willing to spend, you can focus on finding the best deal within your budget.
Full question "The discussion above offers a third tip for saving money on purchases which is create a budget. Write a short paragraph, consisting of 125 words or more, that applies these techniques to purchasing a television".
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A different sample box has a height that is twice as long as the original box described in Problem 1. What is the
volume of this sample box? How does the volume of this sample box compare to the volume of the sample box ins
Problem 1
The original sample box had a volume of 343 cubic cm, which is half the volume of the new sample box.
Since the height of the new sample box is twice as long as the original box, its height will be 2×7=14 cm.
The length and width remain the same at 7 cm.
The volume of the new sample box is given by the formula:
V = lwh
Substituting the values, we get:
V = (7)(7)(14) = 686 cubic cm
Therefore, the volume of the new sample box is 686 cubic cm.
Comparing the volumes of the two boxes, we see that the new sample box has a larger volume than the original sample box.
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Need help on this classwork
Answer: 9
Step-by-step explanation: volume is l x w x h, so 9 x 9 x height = 729
9 x 9 = 81, so 81 x height = 729
by dividing 729 / 81, you get 9
Answer: The answer is H=9.
The reason of this is because the branch of mathematics concerned with the shape of individual objects, spatial relationships among various objects, and the properties of surrounding space.
Hence,
We can see that thats the answer because volume is l x w x h, so 9 x 9 x height = 7299 x 9 = 81, so 81 x height = 729by divide 729 / 81, you get 9
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Step-by-step explanation: Please give Brainliest.
Hope this helps!!!!
I can answer more questions if you want.
A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 25 pounds each. The small boxes weigh 50 pounds each. There are 105 boxes in all. if the truck is carrying a total of 3,875 pounds in boxes, how many of each type of box is it carrying?
The solid below is dilated by a scale factor of 4. Find the volume of the solid created
upon dilation. Answer in terms of TT.
Answer:
units³
3
Submit Answer
Step-by-step explanation:
the volume of a sphere is
4/3 × pi × r³
the original sphere had a radius of 3.
now, after a dilation of factor 4 the radius is 3×4 = 12.
the volume of that sphere is then
4/3 × pi × 12³ = 4/3 × pi × 1728 = 2304pi
1. The domain for f(x) and g(x) is the set of all real numbers.
Let f(x) = 2x²+x-3 and g(x) = x - 1.
Find f(x) · g(x).
a. 2x³-x²+4x-3
b. 2x³-4x²+3
c. 2x³-x²-4x+3
d. x² - 4x +3
The solution to the multiplication of both functions is:
2x³ - x² - 4x + 3
How to find the product of functions?To multiply a function by another function, multiply their outputs. For example, if f (x) = 2x and g(x) = x + 1, then fg(3) = f (3) × g(3) = 6 × 4 = 24. fg(x) = 2x(x + 1) = 2x² + x.
We are told that the domain for f(x) and g(x) is the set of all real numbers.
The functions are given as:
f(x) = 2x² + x - 3
g(x) = x - 1
Thus:
f(x) · g(x) = (2x² + x - 3) * (x - 1)
= 2x³ + x² - 3x - 2x² - x + 3
= 2x³ - x² - 4x + 3
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The graph below shows a company's profit tox), in dollars, depending on the price of erasers x, in dollars, sold by the company
300+10x)
270
240
210-
180
150
120
90
60
Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit? (4 points)
Part B: What is an approximate average rate of change of the graph from x-1 tox-4, and what does this rate represent? (3 points)
Part C: Describe the constraints of the domain. (3 points)
The x-intercepts represent a zero profit.
The maximum value of the graph represents the maximum profit.
How to explain the informationThe function increases up till the vertex and decreases after it.
This means that the profit increases as it reaches the peak at the vertex.
It decreases after the vertex up till it reaches zero.
On the left of the first zero and on the right of the second zero, the profits are negative.
An approximate average rate of change of the graph from x = 3 to x =5 represents the reduction in profit from 3 to 5
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Carlos does 138 jumping jacks during gym class. John only does 89. How many more jumping jacks did Carlos do than John?
Answer:
Carlos did 49 more jumping jacks than John.
Step-by-step explanation:
Carlos = 138
John = 89
138 - 89 = 49
Which linear equation shows a proportional relationship?
y = 2x
y equals one third times x plus 2
y equals negative two fifths times x minus 1
y = 1
A linear equation which shows a proportional relationship include the following: A. y = 2x.
What is a proportional relationship?In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
y = kx
Where:
y represents the x-variable.x represents the y-variable.k is the constant of proportionality.Next, we would determine the constant of proportionality (k) by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 2/1 = 4/2 = 6/3 = 8/4
Constant of proportionality, k = 2.
Therefore, the required linear equation is given by;
y = kx
y = 2x
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Which figure has two more faces than a rectangular prism ?
The figure that has two more faces than a rectangular prism is a Square pyramid.
How many faces does it have ?There are precisely six faces that a rectangular prism contains, which consists of a pair of identical rectangles for its top and bottom planes as well as four lateral faces consisting of corresponding right-angled, congruent rectangles. Hence, a solid figure that has two more sides than the aforementioned rectangular prism could only have eight total faces without exception.
An example of such an entity is a square pyramid whose base constitutes of four equal-length sides with four corresponding triangular surfaces converging at one single vertex on the summit's tip. Within this context, it possesses five faces (one square and four isosceles triangles), thus exceeding by two faces compared to the former geometric model.
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Explain the J curve effect when domestic currency is appreciated?
The J curve impact is an financial wonder that happens when domestic currency increases in value in esteem relative to other monetary forms within the remote trade advertise. The J curve impact is named for the shape of the bend that's made when the adjust of exchange and the esteem of a country's currency are plotted against time.
What occur to the J curve effect when domestic currency is appreciated?Within the brief run, when a country's money increases in value, its sends out ended up more costly and imports ended up cheaper. This implies that the request for a country's sends out will diminish, whereas the request for imports will increase. As a result, the adjust of exchange will at first
compound, which implies that the nation will have a exchange shortfall.
Be that as it may, within the long run, the J curve impact predicts that the adjust of exchange will in the long run progress, and the exchange shortage will turn into a exchange overflow. This happens because the increment within the cost of sends out due to the appreciation of the currency will in the long run lead to a diminish within the amount of trades requested. At the same time, the diminish within the price of imports due to the appreciation of the money will in the long run lead to an increment within the amount of imports requested. Over time, these changes in request will cause a move within the adjust of exchange, coming about in a exchange excess.
In this manner, the Jcurve impact portrays the short-term weakening within the adjust of exchange that happens when a money increases in value, taken after by a long-term enhancement within the adjust of exchange. This impact is named after the shape of the bend that's shaped when the adjust of exchange and the esteem of a country's cash are plotted against time, which looks like a "J" shape.
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PLEASE ANSWER
Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−1, −1), B′(1, 1), C′(0, 1). Determine the scale factor used.
1
one half
3
one third
Answer: B) 1/2
Step-by-step explanation: Hope this helps! :)
The answer is 1/3. I looked it up on gpt and also got a 100 on this quiz
Please help me asap need to get it done MANY POINTS WILL BE GIVEN
Answer:
Step-by-step explanation:
1. The line of best fit must have an equal number of points above and below the line
2. The line of best fit could be used as a predictions showing a trend in data
What is the radius of X?
The radius of the diameter X is 6cm. Option D
How to determine the radius
To determine the radius of the circle, we have;
It is important to that the formula for diameter
The formula for calculating the diameter is given as;
d = r/2
Such that the parameters are given as;
d is the diameter of the circle.r is the radius of the circle.From the information given, we have that;
Diameter, d = 12cm
Now, we have to substitute the values
Radius =diameter/2
Radius = 12/2
Radius = 6cm
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The ratio of union members to nonunion members working for a company is 4 to 7. If there are 108 union members working for the company, what is the total number of employees?
The total number of employees in the company is 297 if ratio of union members to nonunion members working for a company is 4 to 7
The given ratio of union members to nonunion members, which is 4 to 7. This means that for every 4 union members, there are 7 nonunion members.
We are also given that there are 108 union members working for the company.
The total number of employees in the company be "x".
Let us from a proportional equation
4/11 = 108/x
To solve for x, we can cross-multiply and simplify:
4x = 1188
x = 297
Therefore, the total number of employees in the company is 297.
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The price of 7 citrons and 9 fragrant wood apples is 135 units. The price of 9 citrons and 7 fragrant wood apples is 137 units. Find the price of a citron and the price of a wood apple.
The price of a citron is :
The price of a wood apple is :
Let's assume the price of a citron is "x" units and the price of a fragrant wood apple is "y" units.
From the given information, we can form two equations:
7x + 9y = 135 ...(1)
9x + 7y = 137 ...(2)
We can solve this system of equations using the elimination method. Multiplying equation (1) by 9 and equation (2) by 7, we get:
63x + 81y = 1215 ...(3)
63x + 49y = 959 ...(4)
Subtracting equation (4) from equation (3), we get:
32y = 256
y = 8
Substituting the value of y in equation (1), we get:
7x + 9(8) = 135
7x + 72 = 135
7x = 63
x = 9
Therefore, the price of a citron is 9 units and the price of a fragrant wood apple is 8 units.
Which statements are always true regarding the diagram? Select three options
The following statements are always true regarding the given diagram having angles: m<3+m<4+m<5=180, m<5+m<6=180, m<2+m<3=m<6.
Statement 2 is always true because the sum of the three angles in a triangle is always 180 degrees.
Statement 3 is always true because the sum of the angles on a straight line is 180 degrees.
Statement 4 is always true because angles 2, 3, and 6 are opposite angles, which means they are congruent.
Thus, statements 1 and 5 are not always true. The sum of angles 3, 4, and 5 could be greater or less than the measure of angle 5. The sum of angles 2, 3, and 5 could be greater or less than the measure of angle 3.
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Sebastian bought a 30-pack of mechanical pencils and plans to give the same number of pencils each to 6 friends. Which equation can he use to find p, the number of pencils each friend will receive?
[tex]p+6 = 30\\p-6 = 30\\6p = 30\\\frac{p}{6} = 30[/tex]
1.) [tex]6p=30[/tex]
2.) Sebastian bought a pack of 30 mechanical pencils and plans to give the same number of pencils each to 6 friends.
Let a varible such as p be the number of pencils given by him to each students.
Now we need to find p we need to divide 30 by 6, we get
[tex]p = \frac{30}{6}[/tex]
[tex]to[/tex]
[tex]6p = 30[/tex]
Thus, the equation can he use to find p, the number of pencils each friend will receive is: [tex]6p = 30[/tex]
Answer:
[tex]6p = 30[/tex]
Step-by-step explanation:
3dxnn have's the explanation.