Answers
The value of x in given figure is 85°
What do you mean by Exterior angle of a triangle ?An exterior angle of a triangle is the angle formed by one side of the triangle and the extension of an adjacent side. In other words, if you extend one of the sides of a triangle, the angle formed between the extended side and the adjacent side of the original triangle is the exterior angle for that vertex. Each vertex of a triangle has one exterior angle. The exterior angle is always supplementary to the interior angle adjacent to it, meaning that the sum of the exterior angle and the interior angle is equal to 180 degrees.
Let ABC is a triangle
and side BC is extended to D
Now, ∠ACD ≅ ∠A + ∠B (∴ An exterior angle of a triangle is equal to the sum of the two interior opposite angle)
120° = 35 + x
x = 120° - 35°
x = 85
So the option D is correct the value of X = 85
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Related Questions
A violin player broke a string on her violin.The string was 6/8 foot long When she got to the store to buy a new string, she found out that strings were only sold in sizes of one foot,1/8 foot, 1/2 foot and 3/4 foot.what size string should she buy at the store so that it matches the string that broke on her violin? Prove your answer.
Answers
Answer:
The string she needs to buy is the 3/4 string.
Step-by-step explanation:
Seeing how the string is 6/8 foot long, she needs to simplify the fraction from 6/8 to 3/4, which is in simplest form. After that she needs to buy the 3/4 string.
2 - 14. What is the equation of the line perpendicular to y - 4 = (x - 6) and passes through the point - (-3,2)? 5 5 - 2 5 = O -2= O A. y-2=-(x + 3) x OB. y + 3 = -(x - 2) (- 2 O c. y - 2 = = (x + 3) OD. y + 3 = (x - 2) 2 2 2 5
Answers
Solution:
The equation of a line that passes through a point is expressed as
\(\begin{gathered} y-y_1=m(x-x_1)\text{ ---- equation 1} \\ where \\ m\Rightarrow slope\text{ of the line} \\ y\Rightarrow y-intercept\text{ of the line} \\ (x_1,y_1)\Rightarrow coordinate\text{ of the point through which the line passes} \end{gathered}\)Two lines A and B are said to be perpendicular if the slope of line A is equal to the negative reciprocal of the slope of line B.
Thus, lines A and B are perpendicular if
\(m_A=-\frac{1}{m_B}\text{ ---- equation 2}\)Let the line equation
\(y-4=\frac{2}{5}(x-6)\)represent the line A.
step 1: Evaluate the slope of line A.
Comparing the equation of line A with equation 1, we can conclude that the slope of the line A is
\(m_A=\frac{2}{5}\)step 2: Evaluate the slope of line B.
Since lines A and B are perpendicular, we have
\(\begin{gathered} From\text{ equation 2,} \\ \begin{equation*} m_A=-\frac{1}{m_B} \end{equation*} \\ where \\ m_A=\frac{2}{5} \\ thus, \\ \frac{2}{5}=-\frac{1}{m_B} \\ cross-multiply \\ -2m_B=5 \\ divide\text{ both sides by -2} \\ \frac{-2m_B}{-2}=\frac{5}{-2} \\ \Rightarrow m_B=-\frac{5}{2} \end{gathered}\)step 3: Evaluate the line B.
Since the line B passes through the points (-3,2), recall from equation 1
\(\begin{equation*} y-y_1=m(x-x_1)\text{ } \end{equation*}\)where
\(\begin{gathered} x_1=-3 \\ y_1=2 \\ m=m_B=-\frac{5}{2} \end{gathered}\)Substitute these values into equation 1.
Thus,
\(\begin{gathered} y-2=-\frac{5}{2}(x-(-3)) \\ \Rightarrow y-2=-\frac{5}{2}(x+3) \end{gathered}\)Hence, the equation of the line is
\(y-2=-\frac{5}{2}(x+3)\)The correct option is A
The boca grande causeway in florida is about 1 4/9 times as long as the golden gate bridge in san francisco golden gate bridge is about 9000 feet long about how long is the boca grande causeway
Answers
The length of the Boca Grande Causeway = 13,000 feet.
When do we use multiplication ?Repeated addition of the same number is made easier by multiplying the numbers. When we need to merge groups of similar sizes, we employ it. For instance, if there are 5 baskets, each containing 4 apples, we can use multiplication to get the total number of apples, which is 5 x 4 = 20 apples.
We can rapidly determine the total number of things by multiplying. When multiplying, we'll consider the number of groups with similar sizes and the number of items in each group.
Given: The boca grande causeway in florida = 1 4/9 times golden gate bridge
Length of the Golden Gate Bridge = 9000 feet
Thus the length of the Boca grande causeway = 1 4/9 × 9000
= 13/9 × 9000
On further solving we get
= 13 × 1000
= 13,000 feet .
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Use ruler and compasses to draw a triangle ABC with:
AB of length 3 cm, AC of length 4.5 cm and BC of length 2 cm.
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According to the information we can infer that the triangle and its internal angles are: 76.7°, 125.2°, and 21.9°.
How to draw the triangle with the given measurements?To draw the triangle with the given measures we must take into account the internal angles so that the triangle is correct. Additionally we must take into account that it is a scalene triangle.
In this case, the internal angles are the most important part because it gives the shape of the triangle. These angles are:
76.7°125.2°21.9°So, according to the above, this triangles is scalene and its sides are:
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Marcus has been running a beverage cart on weekends at the beach, selling water and soda. Last Saturday, he sold 40 bottles of water and 25 sodas, bringing in $110. Sunday, he sold 50 bottles of water and 45 sodas, making $165. What are the prices for each beverage option?
Answers
Answer:
$2 for soda and $1.5 for a bottle of water
Step-by-step explanation:
You start by turning both situations into an equation
Let x represent bottles of water and y represent sodas
Saturday:
\(40x+25y=110\)
Sunday:
\(50x+45y=165\)
You then want to start by cancelling out the x in this equation, to do that you want 40x to become -50x so you:
50÷40=1.25
You then times the whole equation by -1.25
40x+25y=110
×-1.25
-50x+-31.25y= -137.5
You then add this equation by Sunday's equation
50x+45y=165
-50x+-31.25y=-137.5
13.75y=27.5
You now want to make the co-efficient of y a whole number (for example 15) so you divide 15/13.75=1.09 recurring
13.75y=27.5
×1.09 recurring
15y=30
15y/15=30/15
y=2
Now that we know y = 2
We can use either Saturday or Sunday's equation to figure out the value of \(x\)
Let's use Sunday's:
50x+45×2=165
50x+90=165
50x+90-90=165-90
50x/50=75/50
x=1.5
Let's check our answer with Saturday's equation
40×1.5+25×2=110
This equation is correct
Therefore the prices for each beverage option is $1.5 for a bottle of water and $2 for a soda
the half-life of radon-222 is 3.83 d. if a sample of radon initially contains 6.00 × 108 radon atoms, how many of them are left after 10.0 d?
Answers
Answer:
I THINK 64.8
Step-by-step explanation:
A cylinder has a height of 17 feet and a radius of 6 feet. What is its volume? Use ≈ 3.14
and round your answer to the nearest hundredth.
Answers
Answer:
1921.68 \(ft^{3}\)
Step-by-step explanation:
V = pi*r*r*h
= 3.14*6*6*17
= 1921.68
I NEVER LEARNT THIS BEFORE BUT I AM GOING TO GET A DETENTION IF I DON'T DO IT
Answers
Answer:
On side of the square is 20 cm.
Step-by-step explanation:
6x-1=4x+6
2x-1=6
2x=7
x=3.5
6(3.5)-1
21-1
Side 1 = 20
4(3.5)+6
14+6
Side 2 = 20
HELP MEEE ASAP PLEASE
Answers
Answer:
1. 3/10, 0.30
2. 21/50, 0.42
3. 9/50, 0.18
4. 7/20, 0.35
5. 1/1, 1.00
6. 29/100, 0.29
7. 14/25, 0.56
8. 200/3, 6600.66
9. 1/4, 0.25
Step-by-step explanation:
What is the time 100 minutes after 13:15
Answers
Therefore the time is 14:55.
Hope it helps : )
What is the justification for each step in the solution of the equation? 4(4x+6)−7=77−4x Select from the drop-down menus to correctly justify each step.
Answers
Answer:
x=3
Step-by-step explanation:
4(4x+6)-7=77-4x
open brackets and multiply by 4
16x+24-7=77-4x
16x+17=77-4x
like terms takes on one side and solve for x
16x+4x=77-17
20x=60
x=60/20
x=3
What is the relationship between the line of reflection and the segments connecting the corresponding points?
Answers
The relationship between the line of reflection and the segments connecting the corresponding points is perpendicular bisector.
Here we have to find the relationship between the line of reflection and the segments connecting the corresponding points
In order to find the relationship we must know what is meant by line of reflection.
The term line of reflection is defined as a line that lies in a position between two identical mirror images so that any point on one image is the same distance from the line as the same point on the other flipped image.
As per the definition of the term we have identified that the relationship between these two element is perpendicular to the segment and bisects it. Because the line of reflection is the perpendicular bisector of the segment joining corresponding points of the preimage and image.
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A 3 to 1
B 6 to 2
C 7 to 2
D 9 to 3
Answers
Answer:
yo what is your question??????
Step-by-step explanation:
Maybe c 7 to 2
vertex of y = -4(x + 3)^2 - 1
Answers
Answer:
(-3, -1)
Step-by-step explanation:
The equation is already in vertex form.
y = a(x-h)^2 + k where (h,k) is the vertex.
Therefore the vertex is (-3, -1)
A two-sample t-test for a difference in means will be conducted to investigate whether the average length of a cell phone call is shorter this year compared with 5 years ago. From a random sample of 35 phone call records this year, the average length was 25 minutes with a standard deviation of 4 minutes. From a random sample of 32 phone call records from 5 years ago, the average length was 27 minutes with a standard deviation of 5 minutes. The difference (this year minus five years ago) in means will be calculated With a null hypothesis of no difference in length, which of the following is a correct test statistic for the test?
A. t = 25-27/(√4^2/35+5^2/32)
B. t = 25-27/(√4/35+5/32)
C. t = 25-27/(√4^2/35+√5^2/32)
D. t = 27-25/(√4^2/35+5^2/32)
E. t = 27-25/(√4/35+5/32)
Answers
The correct test statistic is: A. t = (25-27)/(√4²/35+5²/32)
What is test statistic?
The correct test statistic for the two-sample t-test is:
t = (x1 - x2) / √[s1²/n1 + s2²/n2]
where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.
Using the given values, we have:
x1 = 25, x2 = 27, s1 = 4, s2 = 5, n1 = 35, n2 = 32
Substituting these values into the formula, we get:
t = (25 - 27) / √[(4²/35) + (5²/32)]
Simplifying, we get:
t = -2 / √[0.4632 + 0.7813]
t ≈ -2.64
Therefore, the correct test statistic is:
A. t = (25-27)/(√4²/35+5²/32)
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solvable problems for which no polynomially bounded algorithms exist are called ____.
Answers
Solvable problems for which no polynomially bounded algorithms exist are called NP-hard problems.
In computer science, the class of problems known as NP (nondeterministic polynomial time) consists of decision problems that can be verified in polynomial time, meaning that the time it takes to verify a solution to the problem grows at most polynomially with the size of the input. NP-hard problems are a subset of NP that are at least as hard as the hardest problems in NP.
An algorithm for an NP-hard problem is considered polynomially bounded if the time it takes to solve the problem grows at most as a polynomial function of the size of the input. This means that for large inputs, the running time of the algorithm does not increase too quickly. NP-hard problems are of particular interest because, although they may not have a polynomial time solution, they can be used to model many real-world problems and can provide insights into the complexity of computational problems.
Examples of NP-hard problems include the traveling salesman problem, the subset sum problem, and the knapsack problem. These problems have been shown to be NP-hard through a process called reduction, in which a problem can be transformed into another problem that is known to be NP-hard. By showing that the original problem can be reduced to an NP-hard problem, it can be concluded that the original problem is also NP-hard.
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help!!!!
the possible answers are below:
a: x=-1/4, y=-1/2
b: x=-1/2, y= -1/4
c: x=1/2, y=1/4
d: x= 1/4, y= 1/2
Answers
Answer: Based on the graph, I believe that the answer is a. x = -1/4, y = -1/2
Step-by-step explanation:
What is the value of the expression 1 2 3 4 5?
Answers
The value of the given and completed expression in this problem is
-1
What are combined operations?Combined operations are defined as a set of operations applied to the same problem, for example addition, subtraction, multiplication, are frequently used in arithmetic polynomials.
In this case we have an arithmetic polynomial.
We complete the expression as follows:
1 + 2 - 3 + 4 - 5
We group the positive terms on one side and negative terms on the other:
(1 + 2 + 4) - (3 + 5)7 - (8)-1The value of the expression (1 + 2 - 3 + 4 - 5) is -1
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4x + 10 = 2x + 24
PLEASE HELP AHHH
Answers
Answer:
x = 7
Step-by-step explanation:
subtract 10 by both sides
4x + 10 = 2x + 24
4x + 10 -10 = 2x + 24 -10
simplfy
4x = 2x + 14
subtract 2x from both sides of the equation
4x -2x = 2x + 14 -2x
simplify
2x = 14
divide both sides of the equation by the same term
2x / 2 = 14 / 2
simplify
x = 7
Help please stuck on this
Answers
Answer:
a) 314 m²
b) Estimate is 5 bags
c) Estimate for b is an underestimate (choice B)
Step-by-step explanation:
The garden is in the shape of a circle so the area of the garden will be the area of the circle
Part a
The area of a circle given radius r is
A = πr²
The diameter is given as 20m so radius = diameter/w = 20/2 = 10m
With π = 3.14
Area of the garden is 3.14 x 10² = 3.14 x 100 = 314 m² (Answer a)
Part b
We are asked to provide an estimate of the number of bags required to seed the garden by rounding to 1 significant figure
314 estimate to 1 significant figure = 300
58 estimate to 1 significant figure = 60
Estimate of number of bags = 300/60 = 5 (Answer b)
Part c
To determine if the estimate is over or under let's calculate the actual number of bags required.
= 314/58 ≈ 5.41
Our estimate of 5 bags is below the true requirement of 5.41 bags
So our estimate for b) is an underestimate (Choice B)
Help please.
Algebra.
Answers
Answer:
I'm pretty sure Its D i think-
hey i’ll give brainliest please help
Answers
Answer:
I believe it would be C if not then im sorry
Step-by-step explanation:
okay I bearly even know what a function is and this is practice I have a test monday!?
Answers
Answer:
A.
Step-by-step explanation:
A. because an input cannot have two outputs. However, two different inputs can have the same output.
Write the domain of the following graph.
Answers
Answer:
See below ( MIGHT choose (-2,+2) but it is incorrect)
Step-by-step explanation:
DOMAIN is the values of 'x' a function can have
NONE of the answers are correct
it should be (-3,+3) <=====not an option
5x - 2 = 10 - x
Please help fast thankyou
Answers
Answer:
5x-2=10-x
5x+x=10+2
6x=12
x=12/6
x=2
Step-by-step explanation:
Answer:
x =2
Step-by-step explanation:
5x-2 = 10-x
6x = 12
then x = 2
2. Use powers to rewrite these problems:
Example: 5 x 5 = 5^2
a. 4 * 4 * 4 * y * y * y
b. 7 * 7 * 7
c. 3 * 3 * 3 * x * x * x
Answers
Answer:
\( {4}^{3} {y}^{2} \\ {7}^{3} \\ {3}^{3} {x}^{3} \)
(gof)(x) = x2 + x + 1
(gºf)(x) = (x + 1)?
(gof)(x) = x2 + 1
(gof)(x) = x²(x + 1)
pls help i need asap!
Answers
Answer:
\(the \: answer \: is \: b\)
Step-by-step explanation:
\((gof)x = {(x + 1)}^{2 } = {x}^{2} + 2x + 1 \)
Find the x,y,z
For 10points
Answers
Answer:
x = y = 110°z = 70°Step-by-step explanation:
You want to know angles x, y, and z in the given figure where parallel lines 'a' and 'b' are crossed by a transversal. The sum of these angles is 290°.
Consecutive interior anglesAngles y and z are called consecutive interior angles. As such, they are supplementary, so their sum is 180°.
x + y + z = 290°
x + 180° = 290°
x = 110°
Vertical anglesAngles x and y are vertical angles, so are congruent.
y = x = 110°
Then z is found from ...
y + z = 180°
110° + z = 180°
z = 70°
The measures of x, y, and z are 110°, 110°, and 70°, respectively.
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7.
The manager of a water park keeps track of the amount of money collected,
m, and the number of tickets sold, 1, each day. Which best describes the
variables m and ?
A. The variable t is the independent variable because it affects the
amount of money collected, m, each day.
1
B. The variable t is the dependent variable because it depends on
the amount of money collected, m, each day.
C. The variable m is independent of variable i, and variable i is
independent of variable m.
D. The variable m is the independent variable because it depends on
the number of tickets sold, t.
Answers
Answer:
Step-by-step explanation:
A.
Use basic identities to simplify the following expression.
\(\frac{tan^2x-sec^2x}{cosx}\)
A. tanx
B. - tanx
C. secx
D. - secx
Answers
The simplified expression is \(\tan x+\sec x\), we arrive at this after performing mathematical calculations using basic identities.
What are basic mathematical identities?
Basic mathematical identities refer to fundamental equations or relationships between mathematical functions that are true for all values of the variables involved.
For example, a + b = b, a x 0 = 0 are basic identities. Applying the same principle we can simply the mathematical expression with the basic identities provided below:
\(= \frac{\tan^2x-\sec^2x}{\cos x}\)
= \(\frac{\sin^2x-\cos^2x}{\cos x\cdot\cos^2x} \quad\text\)
\(=\frac{\sin^2x}{\cos^2x}\text{ and }\sec^2x\)
= \(\frac{1}{\cos^2x} \ =\frac{(\sin x+\cos x)(\sin x-\cos x)}{\cos^3x}\)
factoring the numerator using the difference of squares.
\(=\frac{\sin x}{\cos^2x}+\frac{\cos x}{\cos^2x} \\)
\(&=\tan x+\sec x\)
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