Answer:
Step-by-step explanation:
Inverse variation is written as
[tex]y=\frac{k}{x}[/tex] which, in words, says "y varies inversely with x". If cavities varies inversely with time brushing, then
[tex]c=\frac{k}{t}[/tex]
We are given the initial condition for which we need to solve for k:
c = 4 when t = 30:
[tex]4=\frac{k}{30}[/tex] so
k = 120.
Now we will use that value of k to solve the problem of how many cavities, c, would she have if she brushed her teeth 120 seconds, t, each night:
[tex]c=\frac{120}{120}[/tex] (the 120 on top is the k value and the 120 on the bottom is the number of seconds she brushed) to get
c = 1
Answer:
1 cavity
Step-by-step explanation:
The inverse equation is x*y=k, where x is the amount of cavities, y is the time brushed, and k is a constant number. In your scenario, x is c and y is t, but you can really use any name for the variable. In the first equation 23 have 4*30=120, which is just a constant number. now that we know our constant, we can plug is into our second equation, and we get c*120=120. By dividing both sides by 120, c=1. This means that Paul will have 1 cavity.
At a parking lot, the ratio of people to cars is 3 : 5. If there are 30 people, how many cars are there? *
Answer:
50 cars
Step-by-step explanation:
Let's define p as the number of people and c the number of cars.
We know that p / c = 3/5 or in other words, there are 5 cars every 3 people. If we have 30 people means that p = 30 which implies 30/c = 3/5 which implies c = 5/3 * 30 = 50.
Answer:
Step-by-step explanation:people=30=3/5
30/5=6*3=18
car=30=5/3
30/3=10
10*5=50
so there are 50 cars there
1. The weight, wky, of a bag of sand is given as 5.6 kg correct to
1 decimal place. Find the range of values in which the actual
weight lies.
Answer:
5.56
Step-无by-step explanation:
Consider the following linear system.
-3x+7y=-16
-9x+5y=16
The y-value of the solution is:
a. -16/13
b. 4
c. 51/16
d. -4
Answer:
D) y=-4
Step-by-step explanation:
we can multiply the first equation by -3 to cancel out the x's
and then add the first equation and the second equation
9x-21y=48
-9x+5y=16
0x-16y=64
y=-64/16=-4
If sin Θ = 5 over 6, what are the values of cos Θ and tan Θ?
Answer:
Check explanation
Step-by-step explanation:
Sin∅=5/6
Opp=5. Hyp=6
Adj= (√6²+5²)
= √11
Cos∅=(√11)/6
Tan∅=5/(√11)
Andrea is comparing the prices charged by two different taxi firms.
Firm A charges £20 for a 5 mile journey and £30 for a 10 mile journey, and there is a linear relationship between the price and the length of the journey.
Firm B charges a pickup fee of £3 and then £2.40 for each mile travelled.
Find the length of the journey for which both firms would charge the same amount.
Answer: 17.5 miles
Step-by-step explanation:
P=price, L=length
Firm A:
P=2L+10
Firm B:
P=2.40L+3
2.40L+3=2L+10
L=17.5
The fare would be the same for 17.5 miles for both firms.
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here, Firm A charges £20 for a 5 mile journey and £30 for a 10 mile journey . let the fixed component of the fare be k and charge for travelling per mile be x then we have, 20=5x+k. . . (1)
30=10x+k. . . .(2)
solving these two equations we get x=2 and k = 10
Now let the length of the journey that both firm charge the same is equal to L and given here that firm B charges a pickup fee of £3 and then £2.40 for each mile travelled. Thus forming the equations we get
2L+10=2.40L+3
0.40L=7
L=17.5
Hence, The fare would be the same for 17.5 miles for both firms.
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in a group140 pupils 5/7 like swimming while the rest like football .find the fraction of the pupils who like football
Answer:
[tex]{ \sf{ \underline{it \: is \: \frac{2}{7} }}}[/tex]
Step-by-step explanation:
[tex] = \frac{7}{7} - \frac{5}{7} \\ \\ = \frac{2}{7} [/tex]
Find the value of tetha in 2 cos 3 tetha = 1
Answer:
Step-by-step explanation: 2cos3 theta=1. Cos 3theta=1/2. Since cos 60°= 1/2. Therefore cos 3theta=cos 60°. Theta=20°.
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Finance A bicycle shop hires road bikes for £25 per day and tandems for £40 per day. One day a family pays £155.
a Which type of bicycles did they hire?
b How many people are in the family?
Answer:
3 road bikes and 2 tandems
7 people
Step-by-step explanation:
25b + 40t = 155
b=3 and t = 2
Check
25*3 + 40*2 = 155
75+80 = 155
Assuming 1 person per road bike and 2 people per tandem
3*1 + 2*2 = 3+4 = 7
1. Define sets
2. What are the types of sets?
3. What are the operations used on sets?
Answer:
Set is a collection of specified object.The types of set are Finite Set. A set which contains a definite number of elements is called a finite set. ...Infinite Set. A set which contains infinite number of elements is called an infinite set. ...
Subset. ...
Proper Subset. ...
Universal Set. ...
Empty Set or Null Set. ...
Singleton Set or Unit Set. ...
Equal Set.
The operation used on sets are. 1 Intersection 2.Union 3.Difference 4.CompelementThe radius of a circle is 16 ft. Find its area in terms of pi
Step-by-step explanatio
Which of the variable expressions below is a trinomial with a constant term? A. 3x5 – 2x3 B. x5 – 3x2 + 5x C. 7x6 + 2x4 – x3 + 7 D. 4x2 – 3 + x3
Answer:
Option (D)
Step-by-step explanation:
Option (A).
3x⁵ - 2x³
There are two terms with the variable 'x' in the given expression. therefore, it's a binomial with no constant term.
Option (B).
x⁵ - 3x² + 5x
This expression has three terms with variable 'x'.
Therefore, it's a trinomial without no constant term.
Option (C).
7x⁶ + 2x⁴ - x³ + 7
It's a quadrinomial having 4 terms. '7' is the constant term in the given expression.
Option (D).
4x² + x³ - 3 ≈ x³ + 4x² - 3
It's a trinomial with a constant term 3.
Therefore, Option (D) is the answer.
Find the measure Of PR
Answer:
18
Step-by-step explanation:
The formula for this is a x b = c x d where a is SR, b is FR, c is QR and d is PR. This will give us the equation 9(16) = 8(5x + 8); 144 = 40x + 64; 80 = 40x; x = 2. Now, plug this into PR which will be 5(2)+8 = 18. This is your answer.
2 hundredths as a decimal
Answer:
0.02
Step-by-step explanation:
Answer:
.02
Step-by-step explanation:
Which of the functions below is not exponential or logarithmic?
Answer:
f(x) = 5x² + 3
Step-by-step explanation:
Exponential Function: [tex]a(b)^x+c[/tex]
Logarithmic Function: [tex]alog_bx+c[/tex]
5x² + 3 is a quadratic function. Therefore, it is not an exponential or logarithmic function and is incorrect.
log₅x is a logarithmic function. Therefore, it is correct.
5log₃x + 3 is a logarithmic function. Therefore, it is correct.
5ˣ + 3 is an exponential function. Therefore it is correct.
Please answer this question now
Answer:
11 yd
Step-by-step explanation:
To find the volume of a rectangular prism, we multiply the width, length and height.
We already know the length, 18, and the height, 11, and the volume, 2178, so we can easily solve for y.
[tex]18\cdot y\cdot11=2178\\192y=2178\\y = 11[/tex]
Hope this helped!
I need help on both answers. They’re different from my other problems so I’m kinda confused
f (x) = -x^2 + x + 14 Find f(2)
f(x) = -x² + x + 14
f(2) = -2² + 2 + 14 = -4 + 16 = 12
f(2) = 12
Answer:
12
Step-by-step explanation:
f (x) = -x^2 + x + 14
Let x= 2
f(2) = - (2)^2 +2+14
= -4 +2+14
= -2 +14
= 12
On a baseball field, the pitcher's mound is 60.5 feet from home plate. During practice, a batter hits a ball 214 feet at an
angle of 36° to the right of the pitcher's mound. An outfielder catches the ball and throws it to the pitcher. Approximately
how far does the outfielder throw the ball?
9514 1404 393
Answer:
169 ft
Step-by-step explanation:
The law of cosines can be used to find the distance from the outfielder to the pitcher. It tells you for triangle ABC, the length of side c can be found from ...
c² = a² +b² -2ab·cos(C)
Here, we hve a=60.5, b=214, and C=36°. Then the desired distance is ...
c = √(60.5² +214² -2·60.5·214·cos(36°)) ≈ √28507.56 ≈ 168.84
The outfielder throws the ball about 169 feet.
PLS HELP ME ON THIS QUESTION I WILLL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Which of the following measures is a measure of spread?
A. median
B. range
C. mode
D. mean
Answer:
B) Range
Step-by-step explanation:
Hope this will help you
Answer:
Range
Step-by-step explanation:
I hope this will help buddy
Please help quick pleaseeeeeeeeeeee
Answer:
think this one
Step-by-step explanation:
the answers there
i think
A son is 8 years old. His father is 5 times as old. How old was the father when his son was born?
Answer:
he was 32
Step-by-step explanation:
8x5 is 40 because he was born 8 years ago you subtract 8 from 40 to get 32
solving polynomial(2y-4)(3y+6)
Answer:
6y² - 24
Step-by-step explanation:
Expand. Follow FOIL method. FOIL =
First
Outside
Inside
Last.
First, multiply the first term of each parenthesis:
2y * 3y = 6y²
Next, multiply the outside terms from both parenthesis:
2y * 6 = 12y
Then, multiply the inside terms from both parenthesis:
-4 * 3y = -12y
Finally, multiply the last terms of each parenthesis:
-4 * 6 = -24
Combine like terms:
6y² + 12y - 12y - 24
6y² + (12y - 12y) - 24
6y² - 24
6y² - 24 is your answer.
~
[tex] \Large{ \boxed{ \rm{ \red{To \: solve?}}}}[/tex]
(2y - 4)(3y + 6)Solution:-⇛ (2y - 4)(3y + 6)
⇛ 2y(3y + 6) - 4(3y + 6)
⇛ 6y² + 12y - 12y - 24
⇛ 6y² - 24
☃️ So, Final answer = 6y² - 24
if 25% of a number is 75 find the number
Answer:
x = 300
Step-by-step explanation:
of means multiply and is means equals
25% * x = 75
Change to decimal form
.25x = 75
Divide each side by .25
.25x/.25 = 75/.25
x = 300
Answer:
300
Step-by-step explanation:
Assume the unknown value is 'Y'
75 = 25% x Y
75 = 25/100 x Y
Multiplying both sides by 100 and dividing both sides of the equation by 25 we will arrive at:
Y = 3 x 100/25
Y = 300%
Answer: 75 is 25 percent of 300
2(3x + 1) - (x - 5) = 42
Answer:
6x+2-1x+5=42
Step-by-step explanation:
Answer:
6x+2-x-5=42
Step-by-step explanation:
A dinner at a restaurant was advertised at $60 plus 18% tax. The total bill for this dinner was
Answer:
xjjvbbbnhzxb hai jhfVbfxkdXhxx
Herbert has sold 92, 28, 83 and 75 suits in the last four months, respectively. How many suits will he need to sell this month to maintain an average of at least 71 sales per month?
Answer: 77 suits
Step-by-step explanation:
Let sales of this month = x
Sales for last 4 months = 92, 28, 83, 75
Average = Sum of Observation ÷ No of Observation
Now, we can form an equation
(92+28 +83+75+x) ÷ 5 =71
(92+28 +83+75+x) = 71 × 5
278 + x = 355
x = 355 - 278
x = 77
5a - 2b for a = -2 and b = 5
Answer:
-20
Step-by-step explanation:
5a - 2b a=-2 b=5
5(-2)-2(5)
-10-10=-20
Answer:
The answer is - 20Step-by-step explanation:
5a - 2b
To find the value of the expression when
a = -2 and b = 5
Substitute the values of a and b into the expression
That's
5(-2) - 2(5)
-10 - 10
-20
We have the final answer as -20
Hope this helps you
I really need these answered!
Answer:
Step-by-step explanation:
#1) [tex]\arcsin \left(0.64958\right)=0.70703\dots \quad \begin{pmatrix}\mathrm{Degrees:}&40.51^{\circ \:}\end{pmatrix}[/tex]
∡C =62.49
[tex]\frac{\left(\sin \left(27^{\circ \:}\right)\right)}{3}=\frac{\sin \left(54^{\circ \:}\right)}{x}\quad :\quad x=\frac{3\left(\sqrt{5}+1\right)}{\sin \left(27^{\circ \:}\right)\cdot \:4}\quad \left(\mathrm{Decimal}:\quad x=5.34603\dots \right)[/tex]
Describe the transformation. A. (x,y)→(x+5,y−3) B. (x,y)→(x−3,y+5) C. (x,y)→(x+3,y−5) D. (x,y)→(x−5,y+3)
Answer:
Option(A)
Step-by-step explanation:
From the graph attached,
Quadrilateral USTR has been transformed to get the image quadrilateral U'S'T'R'.
Coordinates of point U → (-2, 6)
Coordinates of point U' → (3, 3)
Coordinates of U and U' show that quadrilateral USTR has been shifted by 5 units to the right and 3 units down.
Rule to be followed for the translation,
U(-2, 6) → U'[(-2 + 5), (6 - 3)]
U(x, y) → U'[(x + 5), (y - 3)]
Therefore, Option (A) describes the correct rule of transformation.
Which equation represents a population of 300 animals that decreases at an annual rate of 23%? A. p=300(1.23)t B. p=300(1.77)t C. p=300(0.77)t D. p=300(0.23)t
For a given initial quantity A, a decrease of x% can be written as:
A - A*(x%/100%) = A*(1 - x%/100%)
With this, we need to construct an exponential decrease equation for the given situation, and we will find that the equation is:
P(t) = 300*(0.77)^t
Now let's see how we found that.
In this case, we know that:
The initial number of animals is 300.
They decrease at an anual rate of 23%.
This means that after the first year, the population will be:
P(1) = 300 - 300*(23%/100$) = 300*( 1 - 0.23) = 300*(0.77)
After another year, the population decreases again, so we get:
P(2) = 300*(0.77) - 300*(0.77)*(23%/100$) = 300*(0.77)^2
Here we already can see the pattern, the population in the year t, we will get:
P(t) = 300*(0.77)^t
Then we can see that the correct option is C.
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