An exterior angle of a triangle is equal to sum of the opposite interior angles, hence it will be greater than each of the opposite interior angles. The statement is correct. therefore, Correct option is C.
How to find which statement is true?
(A) A triangle's third angle becomes zero angle if there are already two right angles. The statement is false.
(B) If all angles of the triangles are greater than 60 degree, then sum of angles in triangle will be greater than 180 degree. The statement is false.
(C) An exterior angle of a triangle is bigger than each of the opposing interior angles because it is equal to the total of the interior angles on either side. The statement is correct.
(D) If all angles of the triangles are less than 60 degree , then sum of angles in triangle will be less than 180 degree. The statement is false.
Hence, the right response is option (C).
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(assuming that question is-
Which of the following statements is correct?
A) A triangle's third angle becomes zero angle if there are already two right angles. The statement is false.
(B) If all angles of the triangles are greater than 60 degree , then sum of angles in triangle will be greater than 180 degree.
(C) An exterior angle of a triangle is bigger than each of the opposing interior angles because it is equal to the total of the interior angles on either side.
(D) If all angles of the triangles are less than 60 degree , then sum of angles in triangle will be less than 180 degree. )
PLZZ HELP WITH ALGEBRA..
PART A
what is the equation of line 1?
Enter the correct answer in the box by replacing the values of m and b
PART B
what is the equation of line 2?
Enter the correct answer in the box by replacing the values of m and b
PART C
Use your answers from part A and B and the substitution method to solve the system shown in the graph.
What is the solution to the system?
Answer:
A: y= 2x -2
B: y= 1/3x +2
C: set the two = to each other and solve
2x-2= 1/3x +2
1 2/3x -2= 2
1 2/3x = 4
x= 12/5
y= 1/3 (12/5) +2
y= 14/5
answer to C is (12/5 , 14/5)
Answer:
answering so they get brainest
Step-by-step explanation:
A container holds an unknown number of pints of water. Let p represent this unknown amount. Nari pours three-fourths of this volume into an empty pot. She then adds another 2 pints of water. The pot now holds a total of 11pints of water. Set up and solve an equation to find the value of p.
Answer: 12
Step-by-step explanation:
Let p represent this unknown amount.
Nari pours three-fourths of this volume into an empty pot. This can be written as:= 3/4 × p = 3/4p = 0.75p
She then adds another 2 pints of water and the pot now holds a total of 11pints of water. This means we will add 2 to 0.75p and equate to 11. This will be:
0.75p + 2 = 11
0.75p = 11 - 2
0.75p = 9
p = 9/0.75
p = 12
P equals to 12
This question is based on solving linear equation.Therefore, the answer is 12 pints of total amount of water.
Given:
Nari pours three-fourths of this volume into an empty pot.She then adds another 2 pints of water. The pot now holds a total of 11 pints of water.
Let the unknown amount of pints of water is p.
According to the question,
She pours three-fourths of this volume into an empty pot. This can be written as:
\(\dfrac{3}{4}\times p= \dfrac{3}{4} p = \bold{0.75p}\)
She add on 2 pints of water to 0.75 p in pot, then it becomes total of 11 pints of water.
In ,mathematically expressed as,
\(\begin{alligned}0.75p+2&=11\\0.75p&=11-2\\0.75p&=9\\p&=\frac{9}{0.75}\\\bold{p&=12}\end{alligned}\)
Therefore, there is total amount of 12 pints water.
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Last week at a gym, 120 people participated in a biking class. The number of people who ran on a treadmill was 150% of the number of people who participated in a biking class. How many people ran on a treadmill at the gym last week?
Answer:
180.
Step-by-step explanation:
Trust me.
15 x = -27 + 6x cuál es la respuesta de la ecuación, ¿me ayudan? gracias!
Answer:
x = -3
Step-by-step explanation:
If the equation is correctly written as 15·x = -27 + 6·x
Then we have;
15·x = -27 + 6·x
We subtract 6·x from both sides to have all the variables (x) on one side as follows;
15·x - 6·x= -27 + 6·x - 6·x
Which gives;
x·(15 - 6) = -27 + x·(6 - 6)
We note that 6 - 6 = 0, therefore, we have;
x × 9 = -27 + x × 0
We not that x × 0 = 0, therefore;
x × 9 = -27
We now divide both sides with the 9 to get the value of x alone as follows;
x×9/9 = -27/9
Which gives;
x = -27/9 = -3
x = -3
A box of cereal states that there are 87 calories in a 3/4 cup serving. What is the unit rate for calories per cup? How many calories are there in 4 cups of cereal?
Find the period, range, and amplitude of the cosine function. Y = -5 cos 6x
Answers are in the picture
In conclusion, the function's range is [-5, 5], its amplitude is 5, and its phase is /3.
what is range ?The set of all potential output values for a function is referred to as the range in mathematics. It is the entire collection of values that the function is capable of accepting as its input changes throughout its domain. Typically, we begin by determining a function's domain, which is the collection of all possible input values for the function. Then, we determine the collection of all output values by evaluating the function for each input value in the domain. Consider the case where f(x) = x2 is a function that is defined for all real integers x. Since any real number can be squared to produce a legitimate input, all real numbers fall within the domain of this function.
given
y = -5cos is the formula provided (6x). The cosine function in its standard form can be used to determine its time, range, and amplitude:
y = A cos(Bx - C - D)
A represents amplitude, B represents frequency, C represents phase shift, and D represents vertical shift.
When we contrast the provided function with the usual version, we can observe that:
The magnitude is A = |-5| = 5
The frequency is B = 6, so
The phase change is given by C = 0.
The downward shift is D = 0.
The function's duration is determined by:
T = 2π/B = 2π/6 = π/3
Consequently, the interval is /3.
The cosine function has a range between -1 and 1, which can be used to determine the function's range. Using the magnitude of 5 to multiply this range, we obtain:
Number = [-5, 5]
As a result, the function's range is [-5, 5].
In conclusion, the function's range is [-5, 5], its amplitude is 5, and its phase is /3.
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Daisy filled a bucket with 7/6 gallon of rain.water.
later she poured out 1/6 of gallon of of the water. how much water is left in the bucket?
I'll mark you brilliantest
Mr. Snow keeps a list of vocabulary terms that he wants his students to memorize from the textbook.
He began the year with 15 terms on the list. Of the 35 new terms in each chapter, Mr. Snow puts the definition of 10 terms on the wall and adds the remaining terms to the vocabulary list to be memorized.
question:
the number of terms on the vocabulary list can be represented by a linear function. Identify the rate of change and initial value of this function. Explain what these value represent in term of the situation.
Answer:
Step-by-step explanation:
35(6)x12=224
27
Lalculate the projected balance or casn at the end or August. A. \( \$ 23000 \) B. \( \$ 29000 \) C. \( \$ 107000 \) D. \( \$ 38000 \)
The projected balance of cash at the end of August is $38,000. The correct option is D.
To calculate the projected balance of cash at the end of August, we need to consider the cash balance at the beginning of the month, cash collections, and cash payments for August.
Given that the cash balance on July 31 was $32,000.00, we start with this amount.
Cash collections for August are $52,000.00, which means this amount is added to the cash balance.
Next, we consider cash payments for August, which include purchases of direct materials and operating expenses. The total cash payments for August are $20,000 (purchases of direct materials) + $26,000 (operating expenses) = $46,000.00. This amount is subtracted from the cash balance.
Finally, we calculate the projected balance of cash at the end of August by adding the cash collections and subtracting the cash payments from the beginning cash balance:
Projected cash balance at the end of August = Beginning cash balance + Cash collections - Cash payments
= $32,000 + $52,000 - $46,000
= $38,000
Therefore, correct option is D.
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Complete question is:
Berman Company is preparing its budget for the third quarter. Cash balance on July 31 was $32,000.00. Assume there is no minimum balance of cash required and no borrowing is undertaken. Additional budgeted data are provided here:
July Aug Sep
Cash collections $51,000.00 $52,000.00 $50,000.00
Cash payments
Purchases of direct materials 23,000 20,000 24,000
Operating expenses 32,000 26,000 22,000
Capital expenditures 7,000 9,000 13,000
Calculate the projected balance of cash at the end of August.
A. $23000
B. $29000
C. $107000
OD. $38000
GEOLOGY Shan used a surveying tool to map a region of land for his science class. To determine the height of a vertical rock formation, he measured the distance from the base of the formation to his position and the angle between the ground and the line of sight to the top of the formation. The distance was 43 meters, and the angle was 36°. What is the height of the formation to the nearest meter? 36° 43 m
The formation's height is 31 meters to the closest meter.
What exactly is meant by height?In mathematics, height is defined as the vertical distance between an object's top and bottom. It is also referred to as 'altitude.' The term height in geometry refers to the measurement of an object along the y-axis in coordinate geometry.
Height, altitude, and elevation all refer to the vertical distance between the top and bottom of something or between a base and anything above it. Height is a standard bodily measurement that is commonly measured in feet (ft) + inches (in) in the United States and centimeters (cm) abroad. Because they are length measurements, the SI unit would be meters.
We can use the tangent function to calculate the formation's height, h.
tan ( 36°) = h/43
Here, we have to multiply both sides by 43 we get,
43tan (36°)= h
h=31m
Therefore, the height of the formation to the nearest meter is 31m.
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What are the coordinates of the vertex
Answer:
(-1,1)
Step-by-step explanation:
The vertex is the tip of the parabola.
-hope it helps
Simplify \(\frac{sec(a)-csc(a)}{sec(a)+csc(a)}\)
The simplified version of (sec a - cosec a) / (sec a + cosec a) is cosec 2a(cosec 2a - 2) / (sec²a - cosec²a).
What is trigonometry?The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.
Given:
(sec a - cosec a) / (sec a + cosec a)
Multiply the numerator and denominator by (sec a - cosec a)
(sec a - cosec a) / (sec a + cosec a) × (sec a - cosec a)
(sec²a + cosec²a -2sec a cosec a) / (sec²a - cosec²a)
As we know,
\(sec^2a + cosec^2a = sec^2a \ cosec^2a\)
sec² a cosec² a - 2sec a cosec a / (sec²a - cosec²a)
sec a cosec a (sec a cosec a - 2) / (sec²a - cosec²a)
cosec 2a(cosec 2a - 2) / (sec²a - cosec²a)
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A confectionery company mixes three types of toffees to form one kilogram " toffee packs. the pack is sold at rs. 17. the three types of toffees cost rs.20, rs. 10, rs. 5 per kg. resp. the mixture must contain atleast 300 gms of first type. also weight of first two types must be at least be equal to weight of third type. find the optimal mix for maximum profit.answer
The maximum profit is 6 and it is obtained when we mix 0.6 kg of type A, 0 kg of type B, and 0.4 kg of type C.
The optimal mix for the maximum profit can be found as follows:
The company mixes three types of toffees, A, B, and C. Let the weights of type A, B, and C be a, b, and c kg, respectively. Let us assume that we are making 1kg of toffee pack. Therefore, the weight of type C should be 1 - (a + b) kg. Also, the mixture must contain at least 300 gms of type A i.e a >= 0.3 kg
Also, the weight of the first two types (A and B) must be at least equal to the weight of type C, i.e a + b >= c. This condition can also be written as a + b - c >= 0
Let us now calculate the total cost of making 1kg of toffee pack.
Cost = 20a + 10b + 5c
If the pack is sold at Rs. 17, then the profit per 1kg of toffee pack is by
Profit = Selling Price - Cost = 17 - (20a + 10b + 5c)
Now we have the following linear programming problem:
Maximize P = 17 - (20a + 10b + 5c)
Subject to constraints: a + b + c = 1 (since we are making 1kg of toffee pack)
a >= 0.3a + b - c >= 0a, b, c >= 0
We can use the simplex method to solve this linear programming problem. However, to save time, we can solve it graphically. The feasible region is as follows:
We can see that the corner points of the feasible region are: (0.3, 0, 0.7), (0.6, 0, 0.4), (0, 0.5, 0.5), and (0, 1, 0).
Let us calculate the profit at each of these corner points. For example, at the point (0.3, 0, 0.7), we have a = 0.3, b = 0, and c = 0.7. Therefore, the profit is
P = 17 - (20(0.3) + 10(0) + 5(0.7)) = 3.5
Similarly, we can calculate the profit at the other corner points as well. The corner point (0.3, 0, 0.7) gives a profit of 3.5
Corner point (0.6, 0, 0.4) result in a profit of 6
Corner point (0, 0.5, 0.5) results in a profit of 5
Corner point (0, 1, 0) gives a profit of 3
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if p(a) = 0.62, p(b) = 0.47, and p(a è b) = 0.88, then p(a ç b) =
a. 0.2914
b. 1.9700
c. 0.6700
d. 0.2100
Answer: a
Step-by-step explanation:a
— 8х + 3y = 17
8x — 9y = — 19
Answer:
x= 83y−17 and y= 83x+17
hope it helps
2x + 5 - 3 +8x combine like terms
Answer:
10x+2
Step-by-step explanation:
Hope you have a good day, Loves!~
what is order of the likelihood of the following events, from most to least likely : winning a lottery with 1 million (106) contestants five times in a row (the probability is (1/106)5). most likely. guessing a 64-bit key on the first try. second most likely. guessing a 128-bit key on the first try. third most likely. being hit by lightening this year (the probability is 1/105)
Winning lottery 5 times most likely, guessing 64-bit key, 128-bit key, hit by lightening.
What is probability ?
Probability is a measure of the likelihood of an event occurring. It is typically expressed as a decimal or fraction between 0 and 1, with 0 indicating that an event is impossible, and 1 indicating that an event is certain.
1) Being hit by lightning this year (probability is 1/105) - The probability is the lowest because the odds of being hit by lightning in a given year are relatively low.
2) Guessing a 128-bit key on the first try - The probability of guessing a 128-bit key on the first try is very low because of the large number of possible key combinations.
3) Guessing a 64-bit key on the first try - The probability of guessing a 64-bit key on the first try is lower than guessing a 128-bit key, but still relatively low because of the large number of possible key combinations.
4) Winning a lottery with 1 million (106) contestants five times in a row (the probability is (1/106)5) - The probability of winning a lottery with such large number of contestants is relatively low, but it is still much higher than the first three events.
So the order is:
1) Being hit by lightning this year
2) Guessing a 128-bit key on the first try
3) Guessing a 64-bit key on the first try
4) Winning a lottery with 1 million contestants five times in a row,
Winning lottery 5 times most likely, guessing 64-bit key, 128-bit key, hit by lightening.
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FInd the equation of a perpendicular line to y=-2 that passes through the points (4,-2)
Answer:
x = 4
Step-by-step explanation:
y=-2 is a horizontal line so x must be a vertical line through (4,-2)
I need help with points!!!!!!
Answer:
It's the red option.
Help its urgent!!!!!!!!!!
Answer:A>
Step-by-step explanation:
I NEED AN ANSWER ASAP PLEASE
Step-by-step explanation:
the correct answer is option a 6a-7
I need help with this please
Answer:
5nStep-by-step explanation:
5, 10 ,15, 20
it is going up in 5
so 5n
−8 (1 + x) + 7x PLEASE HELP
Answer:
-8-x or -x-8 or x=-8
Step-by-step explanation:
Distribute the -8 to the (1+x)
-8-8x+7x
then add the -8x+7x
-8-x or -x-8
and if you want to solve for x
x=-8
I need help!
What is the perimeter of the rectangle pictured below? Show all work for full credit.
Answer:
≈38.57 units.
Step-by-step explanation:
To find the perimeter of a rectangle, we need to add up the lengths of all its sides.
First, gather the coordinates:
R - (4, 5)
U - (8, -3)
F - (-6, 0)
O - (-2, -8)
Using the coordinates given, we can calculate the lengths of the sides of the rectangle using the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
So, for the rectangle with vertices R, U, F, and O, we have:
Side RU: d = √((8 - 4)^2 + (-3 - 5)^2) = √(16 + 64) = √80
Side UF: d = √((-6 - 8)^2 + (0 - (-3))^2) = √(196 + 9) = √205
Side FO: d = √((-6 - (-2))^2 + (0 - (-8))^2) = √(16 + 64) = √80
Side OR: d = √((-2 - 4)^2 + (-8 - 5)^2) = √(36 + 169) = √205
Since opposite sides of a rectangle are congruent, we have RU = FO and UF = OR. Therefore, the perimeter of the rectangle is:
Perimeter = RU + UF + FO + OR
Perimeter = √80 + √205 + √80 + √205
Perimeter ≈ 38.57
Therefore, the perimeter of the rectangle is approximately 38.57 units.
A scientist who studies teenage behavior was interested in determining if teenagers spend more time playing computer games then they did in the 1990s. In 1990s, the average amount of time spent playing computer games was 10. 2 hours per week. Is the amount of time greater than that for this year? twenty students were surveyed and asked how many hours they spent playing video games. The test statistics is equal to 1. 39. What is the p-value?.
0.3317 is the p-value .
What is the P value?
The likelihood, for a particular statistical model, that the statistical summary would be equal to or more extreme than the actual observed findings when the null hypothesis is true is known as the P value.The test hypothesis should be rejected if the result is statistically significant (P 0.05), which indicates that the test hypothesis is false. There was no effect, according to a P value greater than 0.05.H0 : Mu = 10.2
H1 : Mu > 10.2
Test statistic
t=0.45 (since n is small)
P value = 0.3317
Hence P is greater than 0.10
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Drag a company name into each box to show the total cost from least to greatest.
Answer:
Company A:
$3 each6% for shipping150*3*1.06 = $477 total costCompany B:
$3.10 each4% for shipping150*3.1*1.04 = $483.60 total costCompany C:
$3.20 eachNo shipping charge150*3.2 = $480 total costLeast cost | Medium cost | Greatest cost
Company A | Company C | Company B
alice ate 5 cookies and 2 carrots for a total of 590 calories; bob ate 3 cookies and 4 carrots for a total of 410 calories. how many calories are in one cookie?
Since, Alice ate 5 cookies and 2 carrots for a total of 590 calories; bob ate 3 cookies and 4 carrots for a total of 410 calories. Therefore, In a cookie there are 110 calories.
A calorie is a unit of energy that food and drink provide. we can usually find out how many calories are listed in foods, and wearables like the best fitness trackers let you monitor how many calories you're burning in different activities. Certain foods, such as processed foods, tend to be high in calories. Other foods, such as fresh fruits and vegetables, tend to be low in calories. there is not. Calories are needed to give you enough energy to move, keep warm, grow, work, think, and play. Our circulation and digestion also need to work well with the energy we get from calories.
Let x = calories in cookies.
y = calories in carrots.
Now, according to the question:
5x + 2y = 590 --------------------------------------- (1)
3x + 4y = 410 -------------------------------------- (2)
Multiplying equation(1) by 3 and equation(2) by 5:
15x + 6y = 1770 ---------------------------(3)
15x + 20y = 2050 ---------------------------(4)
Solving we get:
y = 280/14
or, y = 20 units.
Putting the value of y = 20 in equation (2)
3x + 4y = 410
⇒ 3x + 4 × 20 = 410
⇒ 3x = 410 - 80
⇒ x = 330/3
⇒ x = 110 Units
Therefore, the calories of cookies is 110 units .
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Find the amount of money required for fencing (outfield, foul area, and back stop), dirt (batters box, pitcher’s mound, infield, and warning track), and grass sod (infield, outfield, foul areas, and backstop). Need answers for each area.
The amount of fencing, dirt and sod for the baseball field are: length of Fencing & 1410.5 ft. Area of the sod ≈ 118017.13ft² Area of the field covered with distance ≈ 7049.6ft²
How did we determine the values?Area of a circle = πr²
Circumference of a circle = 2πr
where r is the radius of the circle
The area of a Quarter of a circle is therefore;
Area of a circle/ 4
The perimeter of a Quarter of a Circle is;
The perimeter of a circle/4
Fencing = ¼ x 2 x π x 380 + 2 x 15 +2 x 380 + ¼ x 2 x π x 15
Fencing = 197.5π + 190π = 1410.5 feet.
Grass =
π/4 x (380 - 6)² + 87 ² - π/4 × (87 + 30)² + 2 x 380 x 15 + π/4 x 15² - (3/4) x π x 10² - 25π
= 31528π + 18969 = 118017.13
The area Covered by the sod is about 118017.13Sq ft.
Dirt = π/4 x 380 ² - π/4 x (380 - 6)² + π/4 (87 + 30)² - 87² + π100 = (18613π - 30276)/4
= 7049.6
Therefore, the area occupied by the dirt is about 7049.6 Sq ft.
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Make subject of the formula
Answer:This is what i could solve hope it helps :)
Number17
\(H = \frac{m(v^2-u^2}{2gx} \\Cross - multiply\\2Hgx = m (v^2-u^2)\\2Hgx = mv^2-mu^2\\\frac{2Hgx+mu^2}{m} = \frac{mv^2}{m} \\Divide -both -sides-of-the-equation-by-m\\v^2 = \frac{2Hgx+mu^2}{m}\\Square - root-both -sides -to -eliminate the square\\v =\sqrt{\frac{2Hgx+mu^2}{m}}\)
Step-by-step explanation:
Number 19
\(T =2\pi \sqrt{\frac{1}{MH}}\\Divide - both - sides-of-the-equation-by 2\pi\\\frac{2\pi \sqrt{\frac{1}{MH}}}{2\pi }=\frac{T}{2\pi }\\\sqrt{\frac{1}{MH}}=\frac{T}{2\pi }\\SQUARE-BOTH -SIDES\\\left(\sqrt{\frac{1}{MH}}\right)^2=\left(\frac{T}{2\pi }\right)^2\\\frac{1}{MH}=\frac{T^2}{4\pi ^2}\\CROSS-MULTIPLY\\MHT^2={4\pi ^2\\\\DIVIDE BOTH SIDES OF THE EQUATION BY HT^2\\M=\frac{4\pi ^2}{HT^2}\)
Number 20 &21
\(A =\frac{1}{2} m(v^2-u^2)\\Divide both sides by \frac{1}{2} m\\\frac{\frac{1}{2}m\left(v^2-u^2\right)}{\frac{1}{2}m}=\frac{A}{\frac{1}{2}m}\\2Am = v^2-u^2\\Move- v^2- to- the -other -side- to- isolate- u\\\\u^2 = 2Am-v^2\\Square-root-both-sides-to -eliminate-the-square-on-u.\\u = \sqrt{2Am-v^2}\)
emma advertises a reward for the return of her lost dog. frank, who does not know of the reward, finds and returns the dog. frank cannot recover the reward because he
Frank cannot recover the reward because he was unaware of the reward being offered by Emma.
In order to claim the reward, one typically needs to have knowledge of the reward prior to finding and returning the lost item or fulfilling the specified condition. Since Frank was unaware of the reward, he would not have had the opportunity to intentionally seek the dog with the expectation of receiving the reward. As a result, Emma is not obligated to provide the reward to Frank in this situation.
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