The distance between Ernie and Elmo is 20.38 feet.
Consider the distance between Ernie and Elmo be x
What is a law of sine?Law of sines is a formula relating the length of the sides of a triangle to the angles of the triangle.
[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]
The Sine rule is used to solve angles and sides of triangle.
If a triangle ABC has angles A, B and C at the vertices of the triangles with the sides facing each of these angles tagged a, b and c respectively, the sine rule is;
Given parameters;
A = 30°
a = x = ?
B = 105°
b = 12 m
Therefore, [tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b}[/tex]
0.5/ x = 0.9659 / 12
Cross multiplication;
0.9659x = (12) (0.5)
0.9659x = 6
Divide both sides by 0.9659;
(0.9659x/0.9659) = (6/0.9659)
x = 6.21 m
Since 1 m = 3.281 ft
Then;
6.21 m = (6.21) (3.281) = 20.38 ft
Hence, the distance between Ernie and Elmo is 20.38 feet.
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Q14
How can I prove (a)
AE is congruent to CE.We can prove by assuming two triangle in the given diagram and by using SAS rule.
How do you find congruent triangles?If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle then the two triangles are said to be congruent by SSS rule. In the above-given figure, AB= PQ, BC = QR and AC=PR, hence Δ ABC ≅ Δ PQR.
What is an alternate angle in a triangle?Alternate angles are angles that occur on opposite sides of the transversal line. If two parallel lines are cut by a transversal then the alternate angles are equal.The pair of angles formed on the inner side of the parallel lines but on the opposite sides of the transversal are called alternate interior angles.
Now we have
Given a triangle ABC.Where E is the midpoint of AC. We have to prove that AE is congruent to CE.
In ΔAED and ΔCED
ED=ED (∵Common side are equal)
∠AED=∠CED (∵Alternate angles)
∠A=∠C (∵Alternate angles)
By ASA rule, ΔAED≅ΔCED
By Corresponding Parts of Congruent triangles
AE=EC
Hence, AE is conruent to CE.
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Find the measure of the missing angles.
Answer:
Y:64
X:15
Hope this helps
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A student-athlete can run 10 yards in 6 seconds. Which equation shows the number of yards that can be run in s seconds
The equation for the maximum number of yards per second that can be run is y = 5/3 s.
Define the term Direct Variation?Two quantities are said to be fluctuating directly if they are coupled in a way that an increase for one quantity suggests an increase in the other and a drop in one implies a decrease in the other. The direct variation equation, which connects the two values y and x, looks like this: y=kx, where k is the variational constant.A direct variation measurement between distance covered and time taken can be composed as:
y=kx,
where,
y stands for the number of yards, s stands for the number of seconds, and k is really the constant of variation.This is because the athlete's distance travelled directly varies with the amount of time it takes.
Find k using the given values:
y=kx,
10 = k(6)
k = 10/6
k = 5/3
As a result, the equation for the maximum number of yards per second is y = 5/3 s.
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Tessa buy candy that cost $4 per pound. she will spend more than $40 on candy. what are the possible number of pounds she will buy?
Answer:
She will buy at least 10 pounds or more.
Step-by-step explanation:
If each pound costs $4 and she is spending $40 worth, she needs to buy 10 pounds in order to spend the minimum of $40. She can buy more than 10 pounds to keep spending more money. 11, 12, 13, 14, 15, and so forth are all possible numbers in pounds she will buy.
Factor each polynomial completely.
a. 5a²c - 3a²d + 5b²c-3b²d
b. x^2n+ 6x^n +9
lan solved the below problem He is confident his work is correct Checklar's work If he is correct, explain the work that he did. If he has made a mistake, idenufy his mistake and explain to lan host fint
Answer:
Correct steps given below:
511 = -7 (10x - 13)511 = - 70x - (-91)511 = -70x + 91-91 - 91---------------------420 = -70x420/-70 = -70x/-70-6 = xIan missed the step 3 above.
He wrongly added 91 to both sides instead of subtracting, this resulted in wrong solution.
Answer:
See below.
Step-by-step explanation:
The mistake Ian made was incorrectly distributing -(-91). When multiplying two negative numbers the result is always positive: [tex]-a \cdot -b=-a(-b)=ab[/tex].
This error meant he added 91 to both sides of the equation in Step 3 of his calculation, when he should subtract 91 from both sides.
Therefore, the correct calculation is:
[tex]\begin{array} { r l}511 & = -7(10x-13)\\\\511 & = -70x \phantom{)))}+91\\\\-91 & \phantom{))))))))))))} -91\\\\\cline{1-2}\\420 & = -70x\\\\\dfrac{420}{-70} & = \dfrac{-70x}{-70}\\\\-6 & = x\end{array}[/tex]
Please help! will give brainlist if correct answer. NO LINKS
find the unknown side length x. round your answer to the nearest tenth
A) 21.5
B) 12.8
C) 58
D) 48
Answer:
58 Use pathagreon theorem
Step-by-step explanation:
a^2 + b^2 = c^2
Answer:
58
Step-by-step explanation:
The Pythagorean theorem says
[tex]40^{2} + 42^{2} = x^{2}[/tex]
[tex]x^{2}[/tex] = 1600 + 1764
= 3364
x = [tex]\sqrt{3364}[/tex] = 58
Identify the term(s), coefficient(s), and
constant(s) in the expression
52 + 6 + ya.
Term(s) Coefficient(s) Constant(s)
In the expression 52 + 6 + ya,
"ya" is a term,The coefficient of "ya" is 1,"52" and "6" are constants.Describe Term(s), Coefficient(s), Constant(s).The terms are the individual parts of the expression that are being added together. The coefficient is the numerical factor that is multiplied by a variable in a term, and the constant is a term that has no variable.
Any expression with variables will either add or delete one or more variables. Any one of a variety of numbers to represent a generic idea. An absolute number is a constant. A constant is a number, whereas a coefficient is a number that is "in front of" a variable.
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Nina walks on the path around the pond at the city park.
When she walks around the path one time, Nina has completed one lap.
The table shows the distance Nina walks based on the number of laps she completes.
Answer: 0.5
Step-by-step explanation:
Answer:
First answer: 0.5
Second answer: 0.5
Third answer: show
Step-by-step explanation:
What is the effect on the graph of the parent function f(x) = x when f(x) is changed to x+6.
A) same slope, same y-intercept
B) same slope, different y-intercept
C) different slope, same y-intercept
D) different slope, different y-intercept
Need help please ?!!!
Answer:
should be C. No, there are no y-values that have more than one x-value
but if i'm wrong let me know!
The half-life of radium is 1620 years. If a laboratory has 12 grams of radium, how long will it take before it has 8 grams of radium left?
a 947.6 years
b 804.3 years
c 797.5 years
d 849.5 years
Step-by-step explanation:
A = A02^(-t/hl) ---> ln(A/A0) = -(t/hl)ln2
solving for t,
t = -(hl)ln(A/A0)/ln2
= -(1620 yrs)×ln(8/12)/ln2
= 947.6 yrs
974.6 years It will take before it has 8 grams of radium left,
Given that,
The half-life of radium is 1620 years
Laboratory has 12 grams of radium,
We have to determine,
How long will it take before it has 8 grams of radium left.
According to the question,
Laboratory has radium = 12 grams
Left radium = 8 grams
Half life of radium [tex]_t_\frac{1}{2}[/tex] = 1620 years.
[tex]N = N_o [\frac{1}{2}]^{n} \\\\8 = 12 [\frac{1}{2}] ^{n}\\\\\frac{8}{12} } =[ \frac{1}{2} ]^{n}\\\\ log2 - log3 = n( log1 - log2)\\\\0.30-0.47 = n (0 - 0.30)\\\\-0.17 = -0.30 n\\\\n = 0.56[/tex]
It will take before it has 8 grams of radium left,
[tex]t = n \times t_\frac{1}{2} \\\\t = 0.56 \times 1620\\\\t = 974.6 \ years[/tex]
Hence, 974.6 years It will take before it has 8 grams of radium left,
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Pls help me solve this
I have 2 standard, 6-sided dice; one is brown, and the other is black. I roll them both. What is the probability that the sum of the numbers that I roll is less than 4?
Answer:
1/36
Step-by-step explanation:
Since you have two six-sided die, you have 2 sets of 1-6.
Set 1: 1,2,3,4,5,6
Set 2: 1,2,3,4,5,6
Now, we need to find out how many items in the sets add up to equal a sum less than 4.
1 + 1 = 2
2 + 1 = 3
We can roll a 1 and a 1 with a 1/6 chance each.
We can also roll a 1 and a 2 with a 1/6 chance as well.
So, to get the final probability, we would multiply the two fraction together.
1/6 x 1/6 = 1/36
There is a 1/36 chance that the sum of the numbers you roll will be less than 4.
Answer:
1/36
Step-by-step explanation:
I am not a good explainer but im a genuis and when i put this as my answer for my homework i got it right
Na fazenda Santa Elisa onde a principal atividade a criação de gado cada hectare deve ser ocupado por 20 bois quantos bois podem ser criados no terreno de 70000 m²
Answer:
140 bois
Step-by-step explanation:
Observe que:
1 hectare = 10000m²
Na Fazenda Santa Elisa, principal atividade da pecuária, cada hectare deve ser ocupado por 20 bois
Isso significa:
10000m² = 20 bois
O número de bois que podem ser criados no local de 70000 m² é calculado como:
10000m² = 20 bois
70000m² = x
Multiplicação cruzada
10000m² × x = 70000m² × 20 bois
x = 70000m² × 20 bois / 10000m²
x = 140 bois
Portanto, 140 bois podem ser criados em um terreno com 70000m².
3m+2≤ 29
help.............................
Answer:
29-2 =27 divided by 3
m=9
Answer:
One option is:
m=3
Step-by-step explanation:
3x3=9
9+2=11
11<29
Overview
1 what is the value of 8 in the number of 4801
2
3
4
5
6
8
pls help i’m so confused!!
The areas of the squares adjacent to two sides of a right triangle are shown below.
What is the area of the square adjacent to the third side of the triangle?
Answer:
11 units^2
Step-by-step explanation:
We know that the area of a square is the side squared, so we can use the inverse of this formula to say the side of a square is the square root of the the area. This gives us√33 and √44 as the side lengths of the red and green squares respectively. Next, we use the pythagorean theorem to find the other side of the white right triangle, which is also a side of the blue square. So:
(√44)^2 - (√33)^2 = side^2
44 - 33 = side
side^2 = 11
side = √11
To find the area of a square, you just square the side, so we get (√11)^2 which is just 11 units^2.
answer quick its due in ten minutes
The number of grams of sugar that would be in a 200 ml glass of juice, given the carton, is 13. 2 grams of sugar
How to find the number of grams of sugar ?In a 250 ml glass of juice, we would see 16. 5 g of sugar. Given this information, we can find the amount of sugar in a 200 ml of juice by using direct proportion.
The amount of sugar in 200 ml of juice is :
= ( Amount of sugar in 250 ml x Quantity of juice ) / Quantity of base quantity of juice
= ( 16. 5 x 200 ) / 250
= 3, 300 / 250
= 13. 2 grams of sugar
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We have a drawer with 30 pairs of different socks. How many (individual) socks do we need to pull from the drawer before getting one pair for certain
Answer:
60 because their a 2 induivedinal in 1 sock.
Step-by-step explanation:
30 x 2 = 60
latifa writes down a number. she says
if i find a cube root of that number and then quadruple the answer, i get 16
what number did latifa write down?
Answer:
8
Step-by-step explanation:
the cubed root of 8 equals 2
if you quadruple 2 (multiply it by 4), you will get 8
Ceramic tile is being used to cover two 6 ft-by-4 ft rectangular walls. The tiles
are in the shape of equilateral triangles with 6-in. sides. A box of tiles contains
20 tiles. How many boxes of tiles will be needed to cover both walls?
Answer:
Approximately 5 boxes
Step-by-step explanation:
6x4=24 ft
24x2=48 ft
48x12=576 in
576/6=96
96/20=4.8 boxes
If I'm wrong I'm sorry
PLEASE HELP THIS IS URGENT!!!!!! Decide which of the following points are on the graph of the function y=2x+1
(0.1), (2,5), (1/2,2), (-1,-1) are the points on graph.
What is a graph, exactly?In mathematics, a graph is a visual representation or diagram that shows data or values in an ordered way. The relationships between two or more things are frequently represented by the points on a graph.
what a graph example?A graph is a type of non-linear data structure composed of nodes, also known as vertices and edges. Any two nodes, also referred to as vertices, in a graph are connected by edges. The vertex numbers in this graph are 1, 2, 3, and 5, and the edge numbers are 1, 2, 1, 3, 2, 4, and 5, respectively.
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Please help
Find the value of x
Find the measure of the two marked angles
PLEASE ALSO FIND X
The value of x is 8 and the measure of the two marked angles is 60°.
Which angles are corresponding and adjacent?When an angle's vertex and side are shared by another angle, the two angles are said to be neighboring angles. The vertex of an angle is the point where the rays come to a halt and create the sides of the angle. When two adjacent angles share a vertex and a side, they can be either complimentary or supplementary angles.
we know that ,
10x-20=7x+4 (it is corresponding opposite angle)
3x=24
x=8
the value of x is 8.
the measure of the two marked angles is 10*8-20= 80°-20°= 60°.
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Machines at a factory produce circular washers with a specified diameter. The quality control manager at the factory periodically tests a random sample of washers to be sure that greater than 90 percent of the washers are produced with the specified diameter. The null hypothesis of the test is that the proportion of all washers produced with the specified diameter is equal to 90 percent. The alternative hypothesis is that the proportion of all washers produced with the specified diameter is greater than 90 percent. Which of the following describes a Type I error that could result from the test
Proportion is the ratio of the two equal fractions. It compares the part of a whole to another part of another whole. Option c is the correct option which is, The test provides convincing evidence the proportion is greater than 90% but the actual proportion is equal to the 90%.
What is proportion?
proportion is the ratio of the two equal fraction. It compare the part of a whole to other part of of the another whole.
Given
Options for the following question are,
A) The test does not provide convincing evidence that the proportion is greater then 90 percent but the actual proportion is greater then 90 percent.
B) The test does not provide convincing evidence the proportion is greater than 90% but the actual proportion is equal to the 90%.
C)The test provides convincing evidence the the proportion is greater than 90% but the actual proportion is equal to the 90%.
D)The test provides convincing evidence that the proportion is greater then 90 percent but the actual proportion is greater then 90 percent.
E) All type 1 error is not possible for this hypothesis test.
The Null Hypothesis for the given question is,
The proportion of all washers produced with the specified diameter is equal to 90 percent. The Null Hypothesis for the given case is true and actual proportion is equal to 90 percent.
Hence, option c is the correct option which is, The test provides convincing evidence tha the proportion is greater than 90% but the actual proportion is equal to the 90%.
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Does a hyperbola have an inverse?
If the circle's center is in one of the foci, the inverse of the hyperbola is a Limaçon with an inner loop.
What is a hyperbola?A hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set.
A hyperbola is made up of two mirror images of one another that resemble two infinite bows.
These two sections are known as connected components or branches.
The hyperbola's equation is expressed as (y−k)2b2−(x−h)2a2=1.
The transverse axis is defined by b, the conjugate axis by a, and the center is defined by (h,k).
The section of a line that a hyperbola's vertices form.
The inverse of the hyperbola is a Limaçon with an inner loop if the circle's center is in one of the foci.
Therefore, if the circle's center is in one of the foci, the inverse of the hyperbola is a Limaçon with an inner loop.
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What is the slope of the line perpendicular to the line y = 3x+1
Answer:
-1/3
Step-by-step explanation:
Answer:
-1/3
Step-by-step explanation:
to find perpendicular you need to reverse the slope
For what value of k do the pair of linear equations KX − 4y 3 and 6x − 12y 9 have an infinite number of solutions?
The pair of linear equations KX − 4y = 3 and 6x − 12y = 9 have an infinite number of solutions when K = 0.
This can be shown by solving the two equations for K. Solving the first equation for K yields K = (4y/X) + 3. Substituting this into the second equation yields: 0 = (4y/X) + 3 - (12y/6x). Simplifying this yields 0 = (2y/X) - (9/6x). This equation simplifies to 0 = (2y - 9x)/X. Since the denominator of the right side of the equation is not equal to 0, the only way to get 0 = 0 is if the numerator is equal to 0 as well. This happens when 2y - 9x = 0. Since y and x are variables, the only way that this equation can be true for all values of x and y is if the coefficient of both of them is equal to 0. Thus, K = 0 is the only value for which this pair of linear equations has an infinite number of solutions.
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How do you calculate seed number?
To calculate seed number, divide the total number of inches available for crop by the in-row crop spacing. For example, 120 inches divided by one inch per pea seed equals 120 pea seeds.
What is seed?In botany, a seed is an undeveloped plant embryo and food reserve encased in a protective outer covering. In a broader sense, "seed" refers to anything that can be sown, such as seed and husk or tuber.
Seeds are formed when a ripened ovule is fertilised by pollen-derived sperm, resulting in a zygote. The embryo develops from the zygote within a seed, forming a seed coat around the ovule and growing to a certain size within the mother plant before growth stops.
The formation of seeds is a stage in the reproduction of seed plants (spermatophytes). Other plants, such as ferns, mosses, and liverworts, lack seeds and must reproduce exclusively through water.
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a) 3.2÷0.8 explain pls b) 7.5÷0.5 also explain pls