The direction cosines of the line are:
x = 8 / √116
y = 6 / √116
z = -4 / √116
What are direction ratios?Direction ratio helps in knowing the components of a line or a vector with reference to the three-axis, the x-axis, y-axis, and z-axis respectively.
We have,
Let the direction ratio of the line be (x, y, z)
The line is perpendicular to the lines whose direction cosines are proportional to 3,-2,3 and 1,-2,-1.
Now we have,
3x - 2y + 3z = 0 _____(1)
x - 2y - z = 0 _____(2)
We will find the value of x, y, and z using cross product.
x / 2 + 6 = y / 3 + 3 = z / -6 + 2
x / 8 = y / 6 = z / -4
We get,
x = 8
y = 6
z = -4
The direction cosines of the line are:
x = 8 / √8² + 6² + (-4)²
x = 8 / √64 + 36 + 16
x = 8 / √116
y = 6 / √116
z = -4 / √116
Thus the direction cosines of the line are:
x = 8 / √116
y = 6 / √116
z = -4 / √116
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Find the cost of 1 can of soda if 12 cans cost $5.75. Round to the nearest cent
$0.48 or 48₵
Divide $5.75 by 12 cans
[tex]5.75/12[/tex]
Equaling = 0.479...
⬆️
Round to the nearest cent
[tex]0.48[/tex] ✅
Hope this was helpful! (✿◠‿◠)
10. During the hockey season, Elena
averaged 5.625 assists per game. What is
5.625 written in expanded form? How is
it written with number names?
Answer:
5 + 6*10^-1 +
Step-by-step explanation:
I got you started... If you still need extra help, let me know.
Which value of d would make the
expression 9 1/3 divide d/6 equivalent to a
whole number?
Answer: 5
Step-by-step explanation:
(9 × 3 + 1)× 6 over 3d (Cancel out 3 in both numerator and denominator)
2(1 + 3 × 9 ) over d (Multiply 3 and 9 to get 27)
2(1 + 27) over d (Add 1 and 27 to get 28)
2×28 over d (Multiply 2 and 28 to get 56)
If the price-demand equation for milk is q = 4,800 600p, find the price that will pro-
duce revenues of
(A) $9,300 (B) $10,500
Answer:
Probably A!
Step-by-step explanation:
What is the coefficient of t in the expression? −3t50+16
Answer:
-3/50
Step-by-step explanation:
The coefficient is the dependent or standalone integer(s) that are either multiplied by the variable or go along with the variable in the expression. Thus, this(the answer) is the coefficient.
Hope this helps!
Answer: Hello: )✨-3/50
Step-by-step explanation:
The coefficient is the dependent or standalone integer(s) that are either multiplied by the variable or go along with the variable in the expression. Thus, this(the answer) is the coefficient.
: Have an amazing Day/Night<3
Question 7 of 10
4
If f(x) = 3(x+5) +-, what is f(a+ 2)?
Answer:
There you go!
Step-by-step explanation:
184.36 9027.83 which number is the larger value of the 8. How many times larger is it
The number with the larger value of 8 is 184.36 and it is 100 times larger.
What is place value?Place value of a digit can be defined as the position of the particular digit in a given number.
Example;
The place value of 5 in 2850 is 50
Given the digits;
184.36
9027.83
Place value of 8 in 184.36 is 80
Place value of 8 in 9027.83 is 0. 8
Let's find the ratio;
= 80/ 0. 8
= 100 times
Thus, the number with the larger value of 8 is 184.36 and it is 100 times larger.
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Use properties of exponents to write an equivalent expression. Write the
correct exponent for each box.
The correct exponent is 12 for the equivalent expression [tex]5^{12}[/tex].
Which are the Power Rules?Knowing some of the main power rules.
Multiplication with the same base: you should repeat the base and add the exponents. Division with the same base: you should repeat the base and subtract the exponents. Power. For this rule, you should repeat the base and multiply the exponents. Exponent negative - For this rule, you should write the reciprocal number with the exponent positive. Zero Exponent. When you have an exponent equal to zero, the result must be 1.For solving this question, you should apply the power rule - Multiplication with the same base - in the expression
[tex]5^{10}[/tex]*5*5.
Here you have the same base (5), therefore you should repeat the base 5 and add the given exponents (10 +1 +1=12). Thus, the answer will be [tex]5^{12}[/tex].
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can somone help me with these fractions will give u brainliest :'(
Answer:
9/5=1/4/5
7/3=2/1/3
12/10=1/1/5
3. A question on a course evaluation survey for an introductory statistics course asked, "How
do you rate the class textbook on a scale from 1 to 10, where 1 = Not Helpful and 10 =
Very Helpful?" The distribution below summarizes the students' responses to this
question. (3 pts)
Frequency
8
"
H▬▬▬▬▬▬▬▬▬▬▬o
2 0
9
1
2
3 4
6 7 8 9 10
5
Rating
If you estimate the median and the mean, which statement is the appropriate statement for
the mean and the median?
a. Median=2 and mean = 5
b. Median=3 and mean = 3.5
c. Median = 3.5 and mean = 3
IMAGE ABOVE
The correct statements regarding the mean and the median of the distribution are given as follows:
b. Median = 3 and Mean = 3.5.
What are the mean and the median of a distribution?The mean of a data-set is given by the sum of all values in the data-set, divided by the cardinality of the data-set, which is the number of values in the data-set.The median of a data-set is given by the middle value of the data-set, which is the value for which 50% of the data-set is less than and 50% of the data-set is greater than.From the frequency table, we have that:
5 observations have a value of 1.7 observations have a value of 2.8 observations have a value of 3.6 observations have a value of 4.5 observations have a value of 5.3 observations have a value of 6.1 observations have a value of 7.1 observations have a value of 10.The number of values in the data-set is:
5 + 7 + 8 + 6 + 5 + 3 + 1 + 1 = 36.
Hence the mean is given by:
M = (5 x 1 + 7 x 2 + 8 x 3 + 6 x 4 + 5 x 5 + 3 x 6 + 1 x 7 + 1 x 10)/36 = 3.5.
The median will be the 36/2 = 18th value, which is of 3.
Hence the correct statement is:
b. Median = 3 and Mean = 3.5.
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7th grade!!!!
Pls show work ty :]
Will give brainliest ty!!!
5.625
I can't really show my work bc since I'm in high school we don't solve division problems on paper we use a calculator so I forgot how to do it normally
Please Hurry !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The prepositional phrases that are in the sentences include:
In his hands.
To cheer
To the pinata.
With candy.
What is a preposition?To indicate direction, time, place, location, spatial relationships, or to introduce an object, a preposition is a word or set of words used before a noun, pronoun, or noun phrase. Prepositions include phrases like "in," "at," "on," "of," and "to."
Prepositions, their objects, and any words used to modify the objects make up a prepositional phrase. A prepositional phrase usually modifies a verb or a noun.
Therefore, the prepositional phrases that are in the sentences include:
In his hands.
To cheer
To the pinata.
With candy.
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In which number is the value of the 6 ten times as great as the value of the 6 in 162,398
The value of the 6 ten times as great as the value of the 6 in 162,398 is 600,000.
The value of 6 in 162,398 is 60,000. And we have to find the value of the 6 ten times as great as the value of the 6 in 162,398. Simply multiply the value of 6 in 162,398 i.e., 60,000 by 10.
⇒60,000x10
⇒600,000
∴ 600,000 is the value of the 6 ten times as great as the value of the 6 in 162,398.
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I am absolutely stumped. Can someone help figure this out?
Answer:
Hmmm, the x in the first one is 4.8
The x in the second x is 18.5
Which means that the length for 48x m is 230.4 and the length for 12x m is 33.6
The length for the second image is 4x cm is 74 and 12x cm is 222
Step-by-step explanation:
Solve for x hrlpppppppppppppppppppppppppp
Answer:
x = 4
Step-by-step explanation:
The two angles labeled on the diagram are alternate exterior angles and by the Alternate Exterior Angles Theorem, they are congruent. So we can set up an equation like this to solve for x.
2x + 19 = x + 23
x = 4
21. A room has a rectangular floor plan as laid out below. Answer the following questions. What is the perimeter of the room in feet?
Answer:
[tex]50ft[/tex]
Step-by-step explanation:
you have to find the missing side by subtract
[tex]14.8 - 7 = 7.8[/tex]
and
[tex]10.2 - 4.5 = 5.7[/tex]
then you add all these to find the perimeter
[tex]p = 14.8 + 4.5 + 7.8 + 5.7 + 7 + 10.2 [/tex]
[tex]p = 50ft[/tex]
do not leave out your signs
If 2+sqrt(3) is a polynomial root, name another root of the polynomial, and explain how you know it must also be a root
Answer:
2 - √3
Step-by-step explanation:
Find other root. Use x as a substitute.
[tex]x = 2 + \sqrt{3}\\x - 2 = \sqrt{3}\\\left(x - 2\right)^2 = 3\\x^2 = 4 - 2 \times x \times 2 = 3\\x^2 - 4x + 1 = 0[/tex]
Now, we must use the quadratic formula to find the rest of the solution.
[tex]x = \frac{-b\pm \sqrt{b^2-4ac} }{2a}\\x = \frac{4\pm \sqrt{\left(-4\right)^2-4 \times 1 \times 1} }{2}\\\frac{4 \pm \sqrt{12} }{2} = 2 \pm 3[/tex]
If one root of this polynomial [root] is 2 - √3, the other will be 2 + √3. Inversing that rule, the answer is 2 - √3.
Here is a theorem: If A:B with B isn't equal to 0 and C:D with D isn't equal to 0 are equivalent, then they have the same value:A/B = C/D. This is essentially stating that if two ratios are equivalent, then their values are the same (when they have values). Can you provide any counterexamples to the theorem above?
Examples of the given theorem are [tex]\frac{2}{4} \ \& \ \frac{3}{6}[/tex] , [tex]\frac{4}{16} \ \& \ \frac{8}{32}[/tex] and so on .
Equivalent fractions can be defined as fractions that have different numerators and denominators but represent the same value. Two or more fractions are said to be equivalent if they simplify to the same fraction. Equivalent fractions are fractions that have the same value regardless of the numerator and denominator.For example, the equivalent fractions of 1/5 are 5/25, 6/30, and 4/20, which on simplification, result in the same fraction, that is, 1/5.According to the theorem .
if two ratios are equivalent, then their values are the same .
Let one ratio be [tex]\frac{2}{4}[/tex] and other be [tex]\frac{3}{6}[/tex] .
On simplifying and equating these ratios , we get
[tex]\frac{2}{4} =\frac{3}{6} \\\\\frac{1}{2} =\frac{1}{2}[/tex]
As the ration is same hence [tex]\frac{2}{4} \ \& \ \frac{3}{6}[/tex] are equivalent fractions .
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Write the equation of the line that passes through the points (-3,-1) and (5, -1).
Put your answer in fully simplified point-slope form, unless it is a vertical or
horizontal line. i need help
Answer:
y = -1
Step-by-step explanation:
Since the y-coordinates are the same, the equation is y=-1.
It is estimated that one honeybee can make about 1/12 teaspoon of honey in its lifetime. How many honeybees will it take to make 2 tablespoons of honey?
One tablespoon is equivalent to
3 teaspoons.
The number of honeybees which it will take to make the required 2 tablespoons of honey as required in the task content is; 72.
How many honeybees will it take to make 2 tablespoons of honey?It follows from the conversion factor given in the task content that;
3 teaspoons is equivalent to 1 tablespoon.
Hence, 1/12 teaspoons is equivalent to;
= (1/12 ×1) ÷ 3
= 1/36 tablespoons.
On this note, one honeybee can make 1/36 tablespoons of honey in its lifetime.
Hence, if 2 tablespoons of honey is needed, the number of honeybees required is; 2/(1/36)
= 2 ÷ 1/36
= 2 × 36
= 72 honeybees.
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find the cost of 200 shares of stock that sell for 11.3 per share
Beverly is buying hot dogs and hot dog buns for a picnic. She wants to buy 1 hot dog for each bun with none leftover. The hot dogs come packed 12 in a package. The buns come packed 8 in a package. what is the least amount of each Beverly needs to buy? How many packages of each item would Beverly have to buy?
The least amount of each hot dogs and hot dog buns Beverly needs to buy is 24
The least amount of each hot dogs and hot dog buns Beverly needs to buyHot dog = 12 in a packageHot dog buns = 8 in a packageFind the least common multiple (LCM) of 12 and 8
12 = 12, 24, 36, 48, 60, 72, 84, 96, 1208 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80The least common multiple (LCM) of 12 and 8 is 24
Number packages of each item would Beverly have to buy?
Hot dog = 12 in a package
= 24 /12
= 2 packages
Hot dog buns = 8 in a package
= 24/8
= 3 packages
Therefore, the number of packages of each hot dogs and hot dog buns would Beverly have to buy us 2 packages and 3 packages respectively.
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if the measure of arc CDE=118 degrees and the measure of arc EF=62 degrees calculate measure of angle FGE
The measure of angle FGE from the given figure is 28°.
Given that, the measure of arc CDE = 118° and the measure of arc EF = 62°.
How the measure of an arc and measure of an angle are related?The measure of an arc is equal to the measure of its corresponding central angle.
From the given figure, the measure of arc CDE = 118° = corresponding central angle (∠CAE)
So, ∠CAE = 118°
From the given figure, the measure of arc FE = 62° = corresponding central angle (∠FAE)
So, ∠FAE = 62°
As we know the radius of a circle is perpendicular to the tangent.
That is, AE ⊥ EG
So, ∠AEG = 90°
Now, ∠AGE+∠AEG+∠GAE = 180° (The sum of interior angles of a triangle is equal to 180°)
∠AGE + 90° + 62° = 180°
⇒ ∠AGE + 152° = 180°
⇒ ∠AGE = 28°
So, ∠AGE = ∠FGE = 28°
Therefore, the measure of angle FGE from the given figure is 28°.
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The angle FGE will be equal to 28 degrees.
What is an angle of chord theorem?The phrase "the intersecting chords theorem" refers to a relationship between the four-line segments formed by two intersecting chords inside of a circle. The products of the line segment lengths on each chord, according to this statement, are equal.
Given that if the measure of arc CDE=118 degrees and the measure of arc EF=62 degrees. The angle FGE will be calculated as:-
Angle CDE=118 then the angle AFE will be:-
AFE = 180 - 118 = 62
From the angle of chord theorem angle EBF = 31. Now the angle AFE and AEF will be 59 degrees. Angle GEF will be 31 degrees and angle EFG will be 121 degrees by supplementary property.
Angle EGF = 180 - 121 - 31 = 28
Therefore, the angle FGE will be equal to 28 degrees.
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f(4)
Help me with this please
Answer:
if its Derivative it is 0. if it's multiply then it's 4f.
Step-by-step explanation:
if this is not it tell me how you want it done
Choose the symbol that makes the statement true
A. =
B. <
C. >
PLEASE HELP THANK YOU :)
Answer:
B
Step-by-step explanation:
[tex]6\%=0.06 \\ \\ 7/100=0.07[/tex]
After it snows it takes Maria and her little sister Anita 1/2 of an hour to shovel the snow off of the sidewalks on their street. This is 2/3 of the time it takes Maria to do the same job by herself. How long does it take Maria to do this job by herself?
The time taken for Maria to do the job by herself is 3/4 of a hour which is 45 minutes.
How to compute the fraction?It should be noted that it was stated that Maria and her little sister Anita used 1/2 of an hour to shovel the snow off of the sidewalks on their street and that this is 2/3 of the time it takes Maria to do the same job by herself.
Therefore, the time taken for Maria to do the job will be represented by x
Therefore, 2/3x = 1/2
Divide
x = 1/2 ÷ 2/3
x = 1/2 × 3/2
x = 3/4
Therefore, the time taken for Maria to do the job by herself is 3/4 of a hour which is 45 minutes.
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Shae and John drive trucks for a produce company. One day Shae drove 102 miles in 112
1
1
2
hours. John drove 54 miles in 34
3
4
hour. Who drove at a faster rate?
when you add 102+112 you know that shae drove the fastest
help help help........
Answer: D
Step-by-step explanation:
Range affects y-coordinates
Range starts from -8 and ends at 7. -8 is included in the range, but 7 isn't.
Hence, the answer is -8<=y<7, but the best matching answer is -8<=y<8 since these two inequalities share the most number of solutions.
Hence, the answer is D
For ()=‾‾√, use the values of (144) and (169) to estimate the value of 155‾‾‾‾√.
The square root of 155 is estimate according to the following compound inequality:
12 < sqrt(155) < 13.
What is a compound inequality?A compound inequality is a combination of multiple inequalities, at least two, involving operations such as and and or, explained below.
The and operation between multiple sets is composed by the elements that belong to all the sets.The or operation between multiple sets is composed by the elements that belong to at least one of the sets.Hence one example of a compound inequality is:
a ≤ x ≤ b.
Which is read as follows:
x is greater or equal than a and less or equal than b.
For this problem, we have that:
12² = 144, hence sqrt(144) = 12.13³ = 169, hence sqrt(169) = 13.Considering that 155 is between 144 and 169, and the square root function is increasing over it's entire domain, the square root of 155 is estimate according to the following compound inequality:
12 < sqrt(155) < 13.
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Jane decides that he is spending too much money at his favorite coffee place. He finds that he can buy a bag of 24 ounces of ground coffee for $12 to make at home. It takes 2 tablespoons of ground coffee to make one cup of coffee. How much will each cup of coffee cost you? Note 2 tablespoons equals 1 ounce. Use the dimensional analysis method (use units in your calculations)
The amount that each cup of coffee cost you will be $0.5 per cup.
How to illustrate the information?It should be noted that the information illustrated that Jane decides that he is spending too much money at his favorite coffee place and she finds that he can buy a bag of 24 ounces of ground coffee for $12 to make at home.
It should be noted that since 2 tablespoons equals 1 ounce, the number of teaspoons will be:
= 24 × 2
= 48 teaspoons
Therefore, the amount that each cup of coffee cost you will be:
= Cost / Number of cups
= $12 / (48 / 2)
= $12 / 24.
= $0.5
Therefore, the amount that each cup of coffee cost you will be $0.5 per cup.
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