The measure of NP is 4 inches and perimeter of triangle MNP is 21.6 inches.
What is the CRPT theorem?Corresponding parts of congruent triangles or crpt tell us that the corresponding sides and corresponding angles of the two triangles which are congruent are equal.
Given here: Since the two triangles are similar therefore we have
LM/MN =NM/NP
8/NP=16/8
NP=4
Again if perimeter of LMN is 43.2 then measure of LN=19.2 inches
∴ LN/MP=2
MP=19.2/2
MP=9.6
Therefore perimeter of the triangle MNP is 9.6+4+8=21.6 inches
Hence, The measure of NP is 4 inches and perimeter of triangle MNP is 21.6 inches.
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What is the y-coordinate of the ordered pair that satisfies the system of linear equations?
6x+4y= -14
-x - 5y=11
A. 2
B. 1
C. -1
D. -2
Answer:
D
Step-by-step explanation:
-3d - 6 = 6 solve for d
Answer:
Isolate the "d" variable by adding 6 to the left side of the equation, cancelling it out to 0. Subsequently, you would also add 6 to the right side of the equation to complete the transition.
-3d = 12
Next, divide by -3 to get the variable "d" all by itself.
d = -4
We can prove this equation is true by plugging -4 back into the original equation: -3(-4) - 6 = 6
Thus, we get 6 = 6, so this equation is correct.
rationalise the denominator
\( 1\div 7 + 3 \sqrt{2} \)
The final answer is (1 + 21√2)/(21√2). The process of rationalization involves changing the form of an expression to eliminate radicals from its Denominator, or to eliminate denominators from a radical expression.
To rationalize the denominator 1/7 + 3√2,
A rational number is a number that can be expressed as a ratio of two integers, with the denominator not equal to zero. The fraction 4/5, for example, is a rational number since it can be expressed as 4 divided by 5.
Step-by-Step SolutionTo rationalizes the denominator 1/7 + 3√2, we'll need to follow these steps.
Step 1: First, we need to create a common denominator for the two terms. The common denominator is 7. Thus, we can convert the expression to the following form:(1/7) + (3√2 × 7)/(7 × 3√2).
Step 2: Simplify the denominator to 7. (1/7) + (21√2)/(21 × 3√2).
Step 3: The numerator and denominator can now be simplified. (1 + 21√2)/(7 × 3√2).Step 4: Simplify further. (1 + 21√2)/(21√2).We have successfully rationalized the denominator!
The final answer is (1 + 21√2)/(21√2).
The final answer is (1 + 21√2)/(21√2). The process of rationalization involves changing the form of an expression to eliminate radicals from its denominator, or to eliminate denominators from a radical expression.
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A history teacher is writing a test worth 100 points. She uses multiple choice questions worth six points each and true false questions worth two points each. She wants to test to have three times as many multiple-choice questions as true false questions. M represent the number of multiple choice questions on a test and let T represent the number of true false questions. Which system of equations can be used to find how many of each type of question she should write?
Answer:
15 multiple choice 5 true false
Plzzzzz give me Brainliest!!!!!
A triangle has vertices A, B, and C. The measure of A is 2x degrees. The measure of B is twice the measure of A. The measure of C is three times the measure of A. What is the value of x
Answer: the value of x is 15°
Step-by-step explanation:
A is 2x. B is 2(2x), so 4x. C is 3(2x) so 6x.
The sum of all the angles of a triangle is 180°
Set up the equation:
2x + 4x + 6x = 180
12x = 180°
x = 15°
3. Find the volume of a
hemisphere with a radius of
11 inches. Round to the
nearest tenth.
Volume of a hemisphere is equals to 2786.3 cubic inches (nearest tenth).
What is volume of a hemisphere?" Volume of a hemisphere is the total space covered by a hemisphere in 3dimensional shape."
Formula used
Volume of a hemisphere = ( 2 /3) π r³
value of π = 3.14
According to the question,
Radius of hemisphere = 11 inches
Substitute the value of radius in the formula we get,
Volume of hemisphere = (2 /3) × 3.14 × (11)³
= (2 /3 ) × 3.14 × 1331
= 2786.3 cubic inches ( nearest tenth)
Hence, Volume of a hemisphere is equals to 2786.3 cubic inches (nearest tenth).
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Pls help me in this
Answer:
12 x 12 = 144
Step-by-step explanation:
12 times by 12 is 144
cards are dealt, one at a time, from a standard 52-card deck. (a) if the first 2 cards are both spades, what is the probability that the next 3 cards are also spades? (round your answer to four decimal places.) (b) if the first 3 cards are all spades, what is the probability that the next 2 cards are also spades? (round your answer to four decimal places.) (c) if the first 4 cards are all spades, what is the probability that the next card is also a spade? (round your answer to four decimal places.)
(a) The probability that the next 3 cards are also spades, given that the first 2 cards are both spades, is approximately 0.2200. (b) The probability, is approximately 0.2041. (c) The probability is approximately 0.1875.
To solve these probability problems, we need to consider the number of favorable outcomes and the total number of possible outcomes at each stage.
(a) If the first 2 cards are both spades, we have a favorable outcome of 11 cards remaining in the deck that are spades. The total number of possible outcomes is 50 cards remaining in the deck. So the probability of the next 3 cards being spades is:
Probability = count of favorable outcomes / count of all possible outcomes
Probability = 11 / 50 ≈ 0.2200
(b) If the first 3 cards are all spades, there are 10 spades remaining in the deck as favorable outcomes. The total number of possible outcomes is 49 cards remaining. Thus, the probability of the next 2 cards being spades is:
Probability = count of favorable outcomes / count of all possible outcomes
Probability = 10 / 49 ≈ 0.2041
(c) If the first 4 cards are all spades, there are 9 spades left in the deck as favorable outcomes. The total number of possible outcomes is 48 cards remaining. So the probability of the next card being a spade is:
Probability = count of favorable outcomes / count of all possible outcomes
Probability = 9 / 48 ≈ 0.1875
Remember to round your answers to four decimal places as requested.
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Prove everything you say and please have a readable handwritting. Prove that the set X c R2(with Euclidean distance is defined as: See Pictureconnected,but not path connected (X is connected,that is,it cannot be divided into two disjoint non-empty open sets.) X={x,0xe[0,1}U{1/nyneN,ye{0,1]}U{0,1} Prove that the set X C R2(with Euclidean distance) is connected,but not path connected X
X is a connected set but not a path-connected set. X={x,0xe[0,1}U{1/nyneN,ye{0,1]}U{0,1}.
To prove that X is connected, let us assume that X can be divided into two disjoint non-empty open sets A and B. Since X is the union of different points, any point in X will be in either A or B. Let us take an arbitrary point p in A. Since A is open, there is an open ball centered at p that is contained in A. Because B is disjoint from A, it follows that every point in this ball is also in A. By a similar argument, any point in B must have a ball centered at that point that is entirely contained in B. Thus, X must be either in A or B and hence, cannot be divided into two disjoint non-empty open sets. However, X is not path-connected since there is no path between points in [0,1] x {0} and {1} x {1}. Thus, it is connected but not path-connected.
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Mrs. Trevino has 3 red pens, 5 pink pens, and 8 blue pens. What is the probability that
she will choose a blue pen to grade papers?
Well, If you add them all up (3 + 5 + 8) it will be 16. Now we have to make it a fraction (out of blue pens). That will b 8/16. Now we simplify- 1/2. 1/2 as a percent is 50%. The probability is 50%.
A line passes through (-2, 5) and has a slope of what is the equation of the line in point-slope form?
y+ 2 = } (x - 5)
A.
B.
y-5= (x + 2)
O C. y= {x +
3
o
D.
y+5 = (– 2)
Answer:
it actually y=1/3x+17/3
Step-by-step explanation:
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
To start, you know what m is; it's just the slope, which you said was 1/3. So you can right away fill in the equation for a line somewhat to read:
y=1/3x+b.
Now, what about b, the y-intercept?
To find b, think about what your (x,y) point means:
(-2,5). When x of the line is -2, y of the line must be 5.
Because you said the line passes through this point, right?
Now, look at our line's equation so far: . b is what we want, the 1/3 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the the point (-2,5).
So, why not plug in for x the number -2 and for y the number 5? This will allow us to solve for b for the particular line that passes through the point you gave!.
(-2,5). y=mx+b or 5=1/3 × -2+b, or solving for b: b=5-(1/3)(-2). b=17/3.
The equation of the line that passes through the point (-2,5) with a slope of 1/3
is
y=1/3x+17/3
There's your explanation
Solve C=85x+60 for x
Answer:
it is 85x and I'm only in middle school
34.2 is what percent of 288? Round to the nearest hundredth.
Answer:
11.87%
Step-by-step explanation:
34.2/288=0.11875
Which is about 0.1187
So 11.87%
Answer:
11.87
Step-by-step explanation:
mental math and just big brain
Suppose that A and B are points on the number line.
If AB=9 and A lies at 7, where could B be located?
If there is more than one location, separate them with commas.
On the number line, if 'A' lies at 7 then 'B' could lie at -2, 16.
What is a number line?
A number line can be stretched in either direction indefinitely and is commonly displayed horizontally.
The numerals on the number line grow as one goes from left to right and drop as one moves from right to left.
Given, AB = 9 and 'A' lies at 7
So, basically 'B' can be at -2 on the number line which makes the distance between 'A' and 'B' 9 units. The same is possible for B at 16 on the number line.
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simplify the expression: -4x + 8 + 7x - 10
Help PLSSS.
please someone help me....
Answer: see proof below
Step-by-step explanation:
Use the following Product to Sum Identities:
2 sin A sin B = cos (A - B) - cos (A + B)
2 sin A cos B = sin (A + B) + sin (A - B)
Use the Unit Circle to evaluate: cos 120 = -1/2 & sin 60 = √3/2
Proof LHS → RHS
LHS: sin 20 · sin 40 · sin 80
Regroup: (1/2) sin 20 · 2 sin 40 · sin 80
Product to Sum Identity: (1/2) sin 20 [cos(80-40) - cos (80+40)]
Simplify: (1/2) sin 20 [cos 40 - cos 120]
Unit Circle: (1/2) sin 20 [cos 40 + (1/2)]
Distribute: (1/2) sin 20 cos 40 + (1/4) sin 20
Product to Sum Identity: (1/4)[sin(20 + 40) + sin (20 - 40)] + (1/4) sin 20
Simplify: (1/4)[sin 60 + sin (-20)] + (1/4) sin 20
= (1/4)[sin 60 - sin 20] + (1/4) sin 20
Unit Circle: (1/4)[(√3/2) - sin 20] + (1/4) sin 20
Distribute: (√3/8) - (1/4) sin 20 + (1/4) sin 20
Simplify: √3/8
LHS = RHS: √3/8 = √3/8 \(\checkmark\)
We are given the equation cos(20°)(cos(40°)(cos(60°)(cos(80°) = √3 / 8. Let's once again start by applying the identity 'sin(s)sin(t) = - cos(s + t) + cos(s - t) / 2. In this case if we focus on the expression 'cos(20°)(cos(40°),' s would be = 20°, and t = 40°.
\(\mathrm{Use\:the\:following\:identity}:\quad \sin \left(s\right)\sin \left(t\right)=\frac{-\cos \left(s+t\right)+\cos \left(s-t\right)}{2}\)
\(\sin \left(20^{\circ \:}\right)\sin \left(40^{\circ \:}\right)=\frac{-\cos \left(20^{\circ \:}+40^{\circ \:}\right)+\cos \left(20^{\circ \:}-40^{\circ \:}\right)}{2}\)
\(\mathrm{Substitute}:\frac{-\cos \left(20^{\circ \:}+40^{\circ \:}\right)+\cos \left(20^{\circ \:}-40^{\circ \:}\right)}{2}\sin \left(80^{\circ \:}\right)\)
\(\mathrm{Multiply\:fractions}:\frac{\sin \left(80^{\circ \:}\right)\left(-\cos \left(60^{\circ \:}\right)+\cos \left(-20^{\circ \:}\right)\right)}{2}\)
Remember that cos(- x) = cos(x). Respectively cos(- 20°) = cos(20°). Let's substitute and afterwards apply the identity 'cos(60°) = 1 / 2.'
\(\frac{\sin \left(80^{\circ \:}\right)\left(-\cos \left(60^{\circ \:}\right)+\cos \left(20^{\circ \:}\right)\right)}{2} = \frac{\sin \left(80^{\circ \:}\right)\left(-\frac{1}{2}+\cos \left(20^{\circ \:}\right)\right)}{2}\)
And if we further simplify the expression, we should receive the following...
\(\frac{\sin \left(80^{\circ \:}\right)\left(-1+2\cos \left(20^{\circ \:}\right)\right)}{4}\)
Now we want to prove that this expression = √3 / 8. The denominator here is 4 so we can multiply the whole thing by 2 to have a denominator of 8. 2((sin(80°)(- 1 + 2cos(20°)) when simplified = √3. Therefore the expression is true.
General Appliance corporation (GAC) produces refrigerators at two plants: Marietta, Georgia and Minneapolis, Minnesota. They ship them to major distribution centers in Cleveland, Baltimore, Chicago, and Phoenix. The accounting, production, and marketing departments have provided the information in Table 14.6, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands. GAC’s supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost, not exceed available capacity, and meet customer demand.
Plant Cleveland Baltimore Chicago Phoenix Capacity
Marietta $12.60 $14.35 $11.52 $17.58 1,500
Minneapolis $9.75 $16.26 $8.11 $17.92 800
Demand 150 350 500 1,000
For the General Appliance corporation transportation model, suppose that the company wants to enforce a single sourcing constraint that each distribution center be served from only one plant. Setup and solve a model to find the minimum cost solution
Define decision variables and formulate the optimization model. Explain well the objective and each type of the constraints. Solve the model with EXCEL Solver and interpret the printouts obtained. Indicate any pertinent, interesting, or unusual results you may find.
Decision Variables and Objective:
The decision variables in this transportation model are the quantities to be shipped from each plant to each distribution center. Let's denote the quantity shipped from Marietta to Cleveland as X1, from Marietta to Baltimore as X2, and so on. Similarly, let's denote the quantity shipped from Minneapolis to each distribution center as Y1, Y2, and so forth.
The objective of the optimization model is to minimize the total transportation cost. The transportation cost is determined by multiplying the unit cost of shipping between each plant and distribution center by the corresponding quantity shipped and summing up these costs for all combinations.
How does the model ensure single sourcing constraint?To enforce the single sourcing constraint, we need to ensure that each distribution center is served from only one plant. This constraint can be represented by adding the following constraint for each distribution center:
X1 + X2 + X3 + X4 = Demand (for each distribution center)
Y1 + Y2 + Y3 + Y4 = Demand (for each distribution center)
These constraints ensure that the total quantity supplied from all plants to a particular distribution center is equal to the demand of that distribution center, effectively enforcing the single sourcing constraint.
Optimization Model and Interpretation of Results:
The optimization model can be formulated as a linear programming problem, where the objective is to minimize the total transportation cost while satisfying the capacity constraints and the single sourcing constraint.
The Excel Solver can be used to solve this model, providing the optimal solution for the decision variables and the corresponding minimum cost.
Interpreting the printouts, we can observe the values of the decision variables X1, X2, X3, X4, Y1, Y2, Y3, Y4, which represent the quantities shipped between each plant and distribution center. Additionally, we can see the total transportation cost, which is the objective value obtained by summing the costs of shipping for all combinations.
Pertinent results could include identifying the optimal shipping quantities that meet customer demand while minimizing costs. Interesting results might include identifying any significant differences in shipping costs between the plants and distribution centers. Unusual results could involve finding a scenario where the total transportation cost does not decrease proportionally with an increase in supply capacity or demand.
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answer this fast please
Answer:
negative
Step-by-step explanation:
b is a negative number because it is less than -1, so b/5 is a negative number because negative/positive = negative
Answer:
b/5 is negative
Step-by-step explanation:
Since b < -1 b must be less than zero
You can also look at this as b < 0 so b is less than 0, b is negative
b/5 is negative
Which equation represents a line which is parallel to the line 3x+y=8?
A. y=3x-4
B. y=−3x+2
C. y= 1/3x + 6
D. y= -1/3x-2
Answer:its A or C
Step-by-step explanation:i hope this helps
The library has 400 books. If each shelf can hold 100 books, how many shelves will the
library need to hold all of its books?
Answer: 4 shelves
Step-by-step explanation: Divide 400 books by 100 books which equals 4 shelves..
Each shelf contains 100 books,
so 1 shelf = 100 books, 2 shelves = 200 books, etc.
Find the distance FG between the points F(6,7) and G(8,9)
Answer:
2.828
Step-by-step explanation:
what is 29503.488rounded two decimal places
Answer:29503.49
Step-by-step explanation:
Answer:
29503.49
Step-by-step explanation:
since the number in the thousandths place is greater than four, you round the number in the hundredths place up to the number that would come after that. In this case, 8 rounds up to 9
Taylor was asked to solve the system of linear equations
3x - y = 12 and 10x + 5y = -10
by substitution. His solution is shown below.
Taylor's Solution:
Line 1: 10x + 5(-3x + 12)=-10
Line 2:10x - 15x + 60 = -10
Line 3: -5x +60 = -10
Line 4: -5x = -10 - 60
Line 5: -5x = -70
Line 6: x = 14
Which line is wrong? (pls help I’ll mark as brainliest)
What is the equation of this line in slope intercept form?
y = mx + b
m = slope
b = y-intercept
The equation of the line in slope intercept form is y = -4x + 1.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
Intercept of a line is the point where the line touches with one of the axis.
The general equation of a line in slope intercept form is,
y = mx + d, where m is the slope and d is the y intercept.
y intercept point touches the y axis.
Take any two points from the line.
Let it be (0, 1) and (-1, 5).
Slope = (5 - 1) / (-1 - 0) = 4 / (-1) = -4
m = -4
We have the point (0, 1), where the line touches the Y axis.
y intercept, d = 1.
Equation of the line is,
y = -4x + 1
Hence the equation of the line is y = -4x + 1, when slope is -4 and y intercept is 1.
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Jason has read 70% of the 310 pages how many has he read, how many has he not read?
Answer:
He has read 217 pages. He has not read 93 pages.
Step-by-step explanation:
310x70% = pages read = 217
310x30% = pages not read = 93
Complete the equation of the line through (-6, 5) and (-3, -3)
Answer:
y = -8/3x - 11
Step-by-step explanation:
(-6, 5) and (-3, -3)
Slope:
m=(y2-y1)/(x2-x1)
m=(-3-5)/(-3+6)
m=(-8)/3
m= -8/3
Slope-intercept:
y - y1 = m(x - x1)
y - 5 = -8/3(x + 6)
y - 5 = -8/3x - 16
y = -8/3x - 11
helppp mee look at the picture
Answer:
x=20
Step-by-step explanation:
bc 25 divided by 10 is 2.5 so you just multiply 8 by 2.5
Answer: X= 20
If solving for x
Step-by-step explanation:
x/25= 8/10
1= reduce the fraction to x/25= 4/5
2= cross multiply 5x=100
3= divide both sides X=20
Hope this helps. pls mark me brainliest
Find the zero of the function f (x) = -2x +2.
Answer:0 = 3x - 21
Step-by-step explanation:
From this given function we can take an
x
common from its expression
i.e
x
2
−
6
x
=
x
(
x
−
6
)
As we know that the product of two numbers is zero,when either one of them is zero
then in the above expression that we just factorised
the function can be zero when either
x
=
0
or when
x
=
6
i.e when
x
=
0
,
0
(
0
−
6
)
=
0
when
x
=
6
,
6
(
6
−
6
)
=
6
(
0
)
Finally, our prize of all that math, the zeroes of the function are
0
and
6
these numbers are called the zeroes of the function because when you put these values in
x
the function gives zero.
There is a 15 days tour of visiting 5 national parks. There is a
stay of two day at each park. So, 2 multiplied by 5 = 10 days are
spent at staying in those 5 parks. Now the remaining days left are
15
The final itinerary will depend on your preferences, the specific national parks you plan to visit, and the distances between them.
Let's clarify the itinerary for the 15-day tour visiting 5 national parks.
You have a 15-day tour, and you plan to visit 5 national parks. Each park will have a stay of two days.
When you multiply the number of parks (5) by the number of days spent in each park (2), you get a total of 10 days allocated for staying in those 5 parks.
However, there seems to be a discrepancy in the calculation because allocating 10 days for park stays leaves only 5 days remaining, not 15.
To resolve this issue and ensure a 15-day tour, we need to reevaluate the itinerary. Let's assume you want to spend two days at each park, which gives you a total of 10 days for park stays.
To fill the remaining 5 days, you have a few options:
1. Travel Days: You can allocate a day for travel between each park, which would require an additional 4 days. This accounts for the transportation time and allows you to enjoy the journey between the parks.
2. Additional Park Visits: If there are other nearby national parks or attractions in the area, you can extend your tour to include visits to these places. This would allow you to explore more diverse locations and make the most of your 15-day tour.
3. Rest and Relaxation: Alternatively, you might choose to use the extra days for relaxation or leisure activities. You can spend some time enjoying the amenities and attractions available near the parks, such as hiking trails, wildlife observation, or local cultural experiences.
Ultimately, the final itinerary will depend on your preferences, the specific national parks you plan to visit, and the distances between them. Make sure to consider travel times, desired activities, and any additional locations you wish to explore when creating your 15-day tour.
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A group of neighbors is holding an end of summer block party. They buy ppp packs of hot dogs, with 888 hot dogs in each pack. All together, they have 565656 hot dogs for the party.
Write an equation to describe this situation.
How many packs of hot dogs did the neighbors buy?
Answer:
565656÷8=p
So the answer is 637:D