Answer:
Step-by-step explanation:
A direct variation equation is of the form
y = kx,
where, in words, it reads "y varies directly with x" or "y varies directly as x". In order to use this as a model, we have to have enough information to solve for k, the constant of variation. The constant of variation is kind of like the slope in a straight line. It rises or falls at a steady level; it is the rate of change.
We have that a vet gives a dose of three-fifths mg to a 30 pound dog. If the dose varies directly with the weight of the dog, then our equation is
d = kw and we need to find k in order to have the model for dosing the animals.
[tex]\frac{3}{5} =k(30)[/tex]
Divide both sides by 1/30 to get k alone.
[tex](\frac{1}{30})(\frac{3}{5})=k[/tex] and
[tex]k=\frac{1}{50}[/tex]
Our model then is
[tex]d=\frac{1}{50}w[/tex]
This means that for every pound of weight, the dog will get one-fiftieth of a mg of medicine.
Answer:
A
Step-by-step explanation:
what does x mean in algebra?
Answer:
The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown". In x + 2 = 7, x is a variable, but we can work out its value if we try! A variable doesn't have to be "x", it could be "y", "w" or any letter, name or symbol.
Step-by-step explanation:
It is called a "variable" or sometimes an "unknown"
What is variable?A variable is an abstract storage location paired with an associated symbolic name, which contains some known or unknown quantity of information referred to as a value; or in simpler terms, a variable is a named container for a particular set of bits or type of data.
here, we have,
The letter "x" is often used in algebra to mean a value that is not yet known.
It is called a "variable" or sometimes an "unknown".
In x + 2 = 7, x is a variable, but we can work out its value if we try!
A variable doesn't have to be "x", it could be "y", "w" or any letter, name or symbol.
Hence, x is called a "variable" or sometimes an "unknown".
To learn more on variable click:
https://brainly.com/question/19585043
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a group of 42 children all play tennis or football or both sports, the same number play tennis as play just football, twice as many play both tennis and football as play just tennis, how many children play football (answers 7,14,21,28,35)
Answer: Football = 35 children
Step-by-step explanation:
I created a Venn diagram and labeled it as follows:
Tennis only = x
Both Tennis & Football = y
Football only = x + y
Total children = x + y + x + y
42 = 2x + 2y
We are also given that y = 2x (twice as many play both tennis & football as just play tennis)
Now we have two equations and can use substitution to solve for x & y:
42 = 2x + 2y
y = 2x
42 = (y) + 2y
42 = 3y
14 = y
Now let's find x:
y = 2x
14 = 2x
7 = x
We are asked to find how many children play football.
Football = x + y
Both Tennis & Football = y
Total Football = x + 2y
= 7 + 2(14)
= 7 + 28
= 35
Answer: 35 children
Step-by-step explanation:
Let the number of children who play only football be f , the number of children who play only
tennis be t and the number of children who play both sports be b.
Since there are 42 children, f + t + b = 42.
Also, since the number of children who play tennis is equal to the number of children who play
only football, t + b = f . Therefore f + f = 42. So f = 21 and t + b = 21.
Finally, twice as many play both tennis and football as play just tennis. Therefore b = 2t.
Substituting for b, gives t + 2t = 21. Hence t = 7.
Therefore the number of children who play football is 42 − t = 42 − 7 = 35.
Your bowling ball weighs 14 14 pounds. How much does it weigh in ounces? CLEAR CHECK 0.875 0 . 875 ounces 112 112 ounces 140 140 ounces 224 224 ounces
Answer:
224 ounces.
Step-by-step explanation:
There are 16 ounces in a pound. Since the bowling ball weighs 14 pounds, we need to multiply it by 16 to get the weight in ounces.
14 * 16 = 224
The bowling ball should weigh 224 oz.
Consider that △ABC is an equilateral triangle, and AD is a perpendicular bisector of △ABC. Equilateral triangle A B C is cut by perpendicular bisector A D. If AB = 2x, complete the statements below. 2 + (AD)2 = (2x)2 (AD)2 = x2 – x2 (AD)2 = x2 AD =
Answer: AD = x√3
AD² = 3x²
Step-by-step explanation:
If ΔABC is equilateral and is cut by a perpendicular, then the resulting two triangles (ΔBDA & ΔBDC) are both 30°-60°-90° triangles where
∠A = 30°
∠D = 90°
∠B = ∠C = 60°
In a 30° - 60° - 90° triangle, the corresponding sides have lengths of
↓ ↓ ↓
b b√3 2b
Thus: BD = CD = b
AD = b√3
AB = AC = 2b
Since it is given that AB = 2x, replace the "b" above" with an "x"
BD = x, CD = x
AD = x√3
AB = 2x, AC = 2x
I'm not sure what the statements are because they are squished together but hopefully the information I provided will allow you to finish answering the question.
Answer:
X
4
3
X
Step-by-step explanation:
Correct on Edge 2020
A survey of students at a particular college showed that 33% of them prefer the American Heritage Dictionary (as opposed to Webster's or Random House). If 30 students are randomly surveyed, find the probability that exactly 6 of them prefer the American Heritage Dictionary.
Answer:
.066 = 6.6 percent chance
Step-by-step explanation:
1 in 5 chance to get 6, so that is .20 multiply .20 and .33 and you get .066
Find the equation of the line through point (2,−4) and parallel to −6x+2y=4. Use a forward slash (i.e. "/") for fractions (e.g. 1/2 for 12). Y=
Answer:
y = 3x - 10
Step-by-step explanation:
Step 1: Rewrite 1st equation
2y = 6x + 4
y = 3x + 4
Step 2: Find 2nd equation
y = 3x + b
-4 = 3(2) + b
-4 = 6 + b
b = -10
Step 3: Rewrite 2nd equation
y = 3x - 10
And we have your parallel equation!
which of the following best describes the number below?
Answer:
perfect square
Step-by-step explanation:
It is not positive because it is negative.
Answer:
D. IMAGINARY
Step-by-step explanation:
That is an imaginary number.
Lexie has dimes and ten dollar bills in her pocket. The number of dimes is six more than two times the number of ten dollar bills. Let t represent the number of ten dollar bills. Write an expression for the number of dimes
Answer:
d=6+2t
Step-by-step explanation:
Let
t=number of ten dollar bills
d=number of dimes
Number of dimes is six more than two times the number of ten dollar bills
d=6+2*t
d=6+2t
Simplify x^2÷x^-5. What is the exponent?
Answer:
[tex]7[/tex]
Step-by-step explanation:
[tex]x^2 \div x^{-5}[/tex]
[tex]x^{2-(-5)}[/tex]
[tex]x^{2+5}[/tex]
[tex]x^7[/tex]
WILL GIVE BRAINLIEST AND 20 POINTS IF ANSWERED FULLY AND CORRECTLY. Two bikers meet at a park. Biker A needs to stop at the store that is 12 miles east of the park. Biker B heads southeast at a 61° angle at the same time for 24 miles. Once biker A leaves the store he heads southwest at an angle of 89° for 21 miles. Do NOT use the law of cosines, use your knowledge from the content of this course(geometry). a. Use your knowledge of triangles to figure out if the two bikers will be able to meet up if each biker travels the distance given. b. If they do not meet up, how much farther would one of the bikers have to travel to meet the other? c. What is the measure of the angle between the bikers? d. What is the relationship between the measure of the angles and the paths the bikers took? e. Classify the triangle the paths created. f. How many miles did they travel together?
Answer:
See below
Step-by-step explanation:
See attached for reference
The path has been created by bikers is almost a right triangle with sides of 12, 21 and 24 miles and angles of 61, 89 and 30 deg
a) Biker A travels a straight line (hypotenuse of triangle)
It is likely the bikers meet at the bottom point of the triangle
They make almost same displacement from the start point:
24 miles ≈ √12²+21² miles
b) they meet each other
c) 30 deg
d) e) as per picture attached, it is almost right triangle
f) Together they traveled 12+21+24= 57 miles
the terms of this sequence increase by the same amount each time _,_,17_,_,29
Answer:
9, 13, 17, 21, 25, 29
Step-by-step explanation:
Since there is an equal increase of the same amount, the sequence is arithmetic with n th term
Substituting a = 9 and d = 4 into the n th term expression
[tex]a_{n}[/tex] = 9 + 4(n - 1) = 9 + 4n - 4 = 4n + 5
[tex]a_{n}[/tex] = a + (n - 1)d
where a is the first term and d the common difference
The third term and sixth term are therefore
a + 2d = 17 → (1)
a + 5d = 29 → (2)
Subtract (1) from (2) term by term, eliminating a, that is
3d = 12 ( divide both sides by 3 )
d = 4
Substitute d = 4 into either of the 2 equations and solve for a
Substituting into (1)
a + 2(4) = 17
a + 8 = 17 ( subtract 8 from both sides )
a = 9
Thus the first term is 9 and the common difference d = 4
The sequence of terms is therefore
9, 13, 17, 21, 25, 29
Substituting a = 9 and d = 4 into the n th term expression
[tex]a_{n}[/tex] = 9 + 4(n - 1) = 9 + 4n - 4 = 4n + 5
what is the solution to this inequality 7 x -4 < 4 (x + 3)
D and AC are chords that intersect at point Y. A circle is shown. Chords B C and A C intersect at point Y. The length of B Y is 3, the length of Y D is 8, the length of A Y is x, and the length of Y C is 6. What is the length of line segment AY? 2 units 3 units 4 units 6 units
Answer:
4 units
Step-by-step explanation:
see attachment for the missing figure.
to find the value of AY or x
We'll use intersecting chord theorem i.e the product of line segment of each chord are equal.
From the figure, we can say that:
BY x YD = AY x YC
[tex]BY \times YD = AY \times YC\\3\times 8=x\times 6\\24=6x\\x=\frac{24}{6}\\x=4[/tex]
Therefore, AY = 4 units
Answer:
4 units
Step-by-step explanation:
We'll use intersecting chord theorem i.e the product of line segment of each chord are equal.
From the figure, we can say that:
BY x YD = AY x YC
so the answer is 4 units
hope this helps
p.s the guy above mine deserves brainliest
Karthik goes to office at 9.30 am and returns back at 6:00 pm.His lunch timings are 12:00 noon to 12:45 p.m.Rewrite these timings in the 24- hour clock format. pls answer to my questions
Answer:
Karthik goes to office at 09.30 and returns back at 18:00. His lunch timings are 12:00 to 12:45
If f(x) = –x2 + 3x + 5 and g(x) = x2 + 2x, which graph shows the graph of (f + g)(x)?
Answer:
Step-by-step explanation:
hello,
[tex]f(x)=-x^2+3x+5\\g(x)=x^2+2x \ \ \ so \ \ \ \\\(f+g)(x)=f(x)+g(x)=-x^2+3x+5+x^2+2x=5x+5\\[/tex]
this is a line, graph below
hope this helps
Answer:
D on edge
Step-by-step explanation:
What is the domain of f(x)=3^x
Answer:
B
Step-by-step explanation:
This is an exponential function. These types of functions have asymtotes. Asymtotes are when x or y is approaching a specific value, but it's not touching it. If you put your function in a graphing calculator, you will find that the y is approaching 0, but it's not quite touching it. What we're looking for, however is domain (x), and there are no asymtotes for x because as you can see, every value on the x axis has a y point. Therefore the domain is all real numbers.
Answer: B. All real numbers
Step-by-step explanation:
f(x) = 3ˣ
There is NO restriction on x .
x can be positive, negative, fractions, square roots, etc.
--> x is All Real Numbers.
Note: There IS a restriction on f(x) --> f(x) > 0
Check whether 15028 is a perfect square? If not find the smallest number by which 15028 be divided to make it a perfect square. Also, find the square root of the new number formed.
Answer:
8
Step-by-step explanation:
hope this helps.
15028 is not a perfect square.
Step-by-step explanation:
15028 is not a perfect square.
Smallest number by which 15028 can be divided to make it perfect square is 13.
If, we divide 15028 by 13, answer is 1156.
Therefore,
√1156 = 34.
Which expressions are equivalent to j+j+2k
Answer:
[tex]2j+2k[/tex]
Step-by-step explanation:
You didn't give any options so:
j+j+2k=
Combine like terms
2j+2k
help please
2 decks of cards 1st deck has red(R) and black (B)
2nd deck has hearts(H) clubs(C) diamonds(D) and spades(S) how many different combinations are there
Answer:A) (1 x 4) + (1 x 4) = 8
There are 8 possible combinations
B) BC:RD:RS:BH:BS:RH:BD:RC
Step-by-step explanation:
Hope it helps. Step by step in on the top. :)
what is the distance between 3,0 and 6,-13
Answer:
√178
Step-by-step explanation:
Distance formula: [tex]d = \sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]
Simply plug in your coordinates into the distance formula to find the distance between them.
Anne, Becky and Charlotte had sums of money in the ratio 7:6:5. One of them gave £9 to one of the others and this changed the ratio (in the same order of names) to 6:5:4. The total sum of money remained the same; what was it?
Answer:
The total sum of money is £810
Step-by-step explanation:
The parameters given are;
The ratio of the sum Anne, Becky and Charlotte had = 7:6:5
One of them gave one of the others £9 and the new ratio becomes 6:5:4
The total sum of money remains the same = M
The initial fraction amount of the total sum of money each had is given as follows;
Anne = 7/(7 + 6 + 5)×M = 7/18·M = 0.389·M
Becky = 6/18·m = 1/3·M
Charlotte = 5/18·M = 0.278·M
After one of them gave £9 to one of the others, the fraction amount of the total sum of money each had became;
Anne = 6/(6 + 5 + 4)×M = 6/15·M = 0.4·M
Becky = 5/15·m = 1/3·M
Charlotte = 4/15·M = 0.267·M
Therefore, given that Anne's fraction of the total sum of money increased while Charlotte's fraction of the total sum of money decreased, it was Charlotte that gave Anne £9
Therefore, the fraction of the total sum of money equivalent to £9 is found s follows;
5/18·M - 4/15·M = 1/90·M = £9
Therefore;
M = 90 × £9 = £810
The total sum of money = £810.
Which statement is true about the climbers heights?
Answer:
D
Step-by-step explanation:
Because on the data, it shows that the climbers, Abby and Brynn rest in different height but both rest two minutes.
Answer:
option no D is correct in my view
What is 2x-4. I really don’t understand
Answer:
2 * -4 = -8
Step-by-step explanation:
2 * -4 = -8
It is just like multiplying two numbers like... 2 * 4 = 8
You must need to know that:
+a * -b = -c
-a * -b = +c
+a * +b = +c
In your question;
+a * -b = -c
a = 2
b = -4
c = -8
therefore:
2 * -4 = -8
A tv costs £1300. Work out the price after a 4.2% price increase.
Answer:
Step-by-step explanation:
1300 x 1.042 = $1354.6
help ASAP i need help
Answer:
Isosceles Right Triangle
Step-by-step explanation:
We look at the sides first. Two sides are equal, which means that the triangle is isosceles (equilateral means three equal sides, and scalene means no sides equal). Then we look at the only angle indicated, which is the right angle. Thus, we come to the conclusion that the triangle is an Isosceles Right Triangle.
I will give brainliest to the first person to get it right :)
Answer:
Transverse axis
Step-by-step explanation:
Just search it up and you will see...
Brainliest! like you promised!
Answer:
Transverse axis.......
Step-by-step explanation:
hope it's helpful....
Find the equation of the circle whose center and radius are given.
center (7.-3), radius = 7
Answer:
(x - 7)² + (y + 3)² = 7
Step-by-step explanation:
The equation of a circle is denoted by: [tex](x -x_1)^2+(y-y_1)^2=r^2[/tex], where [tex](x_1,y_1)[/tex] is the centre and r is the radius.
Here, the centre is (7, -3), which means [tex]x_1=7[/tex] and [tex]y_1=-3[/tex]. The radius is r = √7. Plug these values into the formula:
[tex](x -x_1)^2+(y-y_1)^2=r^2[/tex]
[tex](x -7)^2+(y-(-3))^2=(\sqrt{7}) ^2[/tex]
[tex](x -7)^2+(y+3)^2=7[/tex]
Thus, the answer is (x - 7)² + (y + 3)² = 7.
~ an aesthetics lover
Given that y varies inversely with x, if x =7 and y = 4, what is y when x = 2?
Answer:
y = 14
Step-by-step explanation:
y ∝ [tex]\frac{1}{x}[/tex]
=> y = [tex]\frac{k}{x}[/tex] -------------(1)
Where k is the constant of proportionality
Now,
x = 7, y = 4
Putting in (1)
4 = [tex]\frac{k}{7}[/tex]
So,
=> k = 28
Now y = ? when x = 2
Putting x and k in (i)
y = [tex]\frac{28}{2}[/tex]
y = 14
Answer:
[tex]y=14[/tex]
Step-by-step explanation:
[tex]y \propto 1/x[/tex]
[tex]y=k/x[/tex]
[tex]4=k/7[/tex]
[tex]4 \times 7 = k[/tex]
[tex]28=k[/tex]
[tex]y=28/x[/tex]
[tex]y=28/(2)[/tex]
[tex]y=14[/tex]
Can someone help me please? Thanks!!
Answer:
Since this triangle is isosceles, we know that the base angles are both x so we can write:
x + x + 32 = 180
2x + 32 = 180
2x = 148
x = 74°
Answer:
m∠x = 74°
Step-by-step explanation:
We are given 2 side lengths are are the same. This means that the triangle is an isosceles triangle and the other angle is also x (and congruent to the given x). Therefore,
2x + 32 = 180
2x = 148
x = 74
find the area of a square with a side length of 9 m
Answer:
81
Step-by-step explanation:
To find the area of a square, you multiply the known side length by the same number the known side length is. So in this case it would be
9x9 which equals 81.
equation therefore is:
9x9=81
I hope this helps you!!
Answer:
81 m^2
Step-by-step explanation:
The area of a square can be found using the folllowing formula:
A=s^2
where s is the side length.
In this problem, the square has a side length of 9 meters. Therefore,
s=9 meters
Substitute this value into the formula
A=(9 meters)^2
Evaluate the exponent.
(9 meters)^2= 9 meters *9 meters= 81 meters^2
A=81 meters^2
The area of the square is 81 square meters.
