Answer:
4
Step-by-step explanation:
18 - 2= 16
16/4=4
Suppose that x and y vary inversely. Write a function that models the inverse variation.
x=-12 when y=4
y = -48 (1/x) is the variation equation.
How to write the function that models the relationship?A relationship between a set of values for one variable and a set of values for other variables is known as a variation.
One of the most fundamental concepts in mathematics is the idea of a function, in part because functions are a useful tool for describing and illuminating patterns.
given that
x and y vary inversely that means x = k 1/y or y = k 1/x.
so, x= k(1/y)
xy = k
from the question x=-12 when y=4
-12(4) = k
k = -48
now,
y = K (1/x)
y = -48 (1/x)
This is the variation equation.
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The diameter of a circle is 20 cm. Find its area to the nearest whole number?
Answer:314
Step-by-step explanation:
radius=diameter divided by 2
area=[tex]\pi radius^{2}[/tex]
a=[tex]\pi 10^{2}[/tex]
a=314.16
rounded to the nearest whole
a=314
which statement must be true to prove 180
Answer: B
Step-by-step explanation: If you look at the phrase m<1 + m<2=180 - m<3 you realize that you can subtract m<3 from both sides so the equation becomes m<1 + m<2 + m<3=180
Convert them please
Answer:
a) 1.999 moles He
b) 0.50 moles Cu
Step-by-step explanation:
Step-by-step explanation:
1 km = 1000 m = 0.621371 miles
so,
786.3 m = 0.7863 km (simply divide by 1000).
40 km/h = 40×0.621371 mph (as the reference of 1 hour stays the same).
= 24.8548 mph
always consider the direction of the conversion rate : are you going from a smaller to a larger unit, or from a larger to a smaller unit ?
if we would have said
1 m = 0.001 km
then we would have converted 786.3 m by multiplying it by 0.001 (also getting 0.7863 km as result, of course).
but because we defined it the other way around, we had to divide by 1000. it is clear that this is the same operation, yes ?
in the same way, if we would have said
1 mile = 1.60934 km
then we would have converted 40 km to miles by dividing 40 by 1.60934. again getting the same result, of course.
the midpoint of line ab is m (-1,-1) if the coordinates of a are (3,-6) what are the coordinates of b
The coordinates of point b ( x, y) are ( - 5, 4 ).
The midpoint of the line ab is m( -1, -1 ).
The coordinates of the endpoints of the line are a( 3, -6) and b( x, y).
Now, the midpoint of the line with two endpoints A(x, y) and B( c, d) is given as:
m = [ ( x + c) / 2 , ( y + d) / 2 ]
Therefore,
m = [ ( 3 + x) / 2, ( - 6 + y ) / 2 ]
( -1 , - 1) = [ (3 + x / 2 ), ( -6 + y / 2 ) ]
Therefore,
(3 + x) / 2 = - 1
3 + x = - 2
x = - 2 - 3
x = - 5
And;
-6 + y / 2 = - 1
- 6 + y = - 2
y = - 2 + 6
y = 4
Therefore, ( x, y) = ( - 5, 4).
Therefore, the coordinates of point b are ( - 5, 4 ).
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The table represents a quadratic function. Write an equation of the function in
standard form.
X- -3,-2,-1,0
f(x)-2,0,2,8
An equation of the function in standard form is equal to 2x²/3 + 16x/3 + 8 = 0.
What is a quadratic function?A quadratic function can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.
In Mathematics, the standard form of a quadratic equation is given by;
ax² + bx + c = 0
y = f(x) = ax² + bx + c
Next, we would formulate a system of equations from the data contained in the table above:
-2 = a(-3)² + b(-3) + c ⇒ -2 = 9a - 3b + c .......equation 1.
0 = a(-2)² + b(-2) + c ⇒ 0 = 4a - 2b + c .......equation 2.
8 = a(0)² + b(0) + c ⇒ 8 = c .......equation 3.
Substituting the value of c into equation 1 and equation 2, we have:
-2 = 9a - 3b + 8 ⇒ 9a - 3b = -10 .......equation 4.
0 = 4a - 2b + 8 ⇒ 4a - 2b = -8 .......equation 5.
Multiplying equation 5 by 1.5 and solving simultaneously, we have:
9a - 3b = -10
6a - 3b = -12
3a = 2
a = 2/3
For the value of b, we have:
4a - 2b = -8
4(2/3) - 2b = -8
8/3 - 2b = -8
2b = 8 + 8/3
2b = 32/3
b = 32/6
b = 16/3.
Substituting the values of a, b and c into the standard form of a quadratic equation:
ax² + bx + c = 0
2x²/3 + 16x/3 + 8 = 0
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How do positive and negative numbers help us to represent mathematical ideas?
If two positive numbers are multiplied or divide then the result is always positive but if we take one positive and one negative number and then after multiply or divide we get always negative number.
What is Number system?
A system of writing to express the number with positive or negative sign is called number system.
Now, There are many applications for the use of positive and negative numbers to represent mathematical ideas.
⇒ Negative and positive numbers are used to describe the distance from a reference point.
⇒ If two positive numbers are multiplied or divide then the result is always positive but if we take one positive and one negative number and then after multiply or divide we get always negative number.
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Sierra has a bucket that originally contained 340 fl oz of water and is being filled at a rate of 5 fl oz per
minute. Brian has a bucket that originally contained 650 fl oz of water and is being drained at a rate of 8 fl oz
per minute. What is x, the number of minutes that need to pass in order for the two buckets to contain the
same amount of water?
Answer:
It will take 20 minutes for both buckets to have the same amount of water
Step-by-step explanation:
A cylindrical vase has a diameter of 6 inches. At the bottom of the vase, there are 7 marbles, each of diameter 3 inches. The vase is filled with water up to a height of 12 inches.
Which of the following could be used to calculate the volume of water in the vase?
The volume of water in the vase is 103.5π inches³.
Diameter (d) of Cylindrical vase = 6 inches
Radius (r) of Cylindrical vase = d/2 = 3 inches
Height (h) of Cylindrical vase = 12 inches
Volume of Cylindrical vase (V) = πr²h
= π × 3 × 3 × 12
= 108π inches³
As we know that at the bottom of the vase, there are 7 marbles,
and, Diameter of Marbles = 3 inches
Radius of Marbles = 1.5 inches
Marble is a shape of sphere, so
The Volume of Marble = 4/3 (πr³)
= 4/3 ( π × 1.5 × 1.5 × 1.5)
= 4/3 ( 3.375π)
= 4.5π inces³
To find the volume of water in the vase, we have to subtract the volume marbles from the volume of cylindrical vase,
The volume of water in the vase = 108π inches³ - 4.5π inces³
= 103.5π inches³
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Answer:
n(3in)2(12in) - 7(4/3n(1.5in)3)
Step-by-step explanation:
X raised to power 2 minus 16 =0 using factorisation method
Answer:
X= 4 or -4
Step-by-step explanation:
factor out from mathematical technique of difference of two squares.
2π(3.5)(6)+ 2π3.52 in terms of pi
The equivalent expression of the expression given as 2π(3.5)(6)+ 2π3.52 in terms of π is 49.04π
How to rewrite the expression?The expression is given as
2π(3.5)(6)+ 2π3.52
Rewrite the above expression properly as follows
So, we have
2 * π * (3.5) * (6) + 2 * π * 3.52
Evaluate the products of the factors of the above expression
So, we have
42 * π + 7.04 * π
Evaluate the products of the constants in the above expression
So, we have
42π + 7.04π
Evaluate the sum in the above expression
So, we have
49.04π
Hence, the equivalent expression of the expression given as 2π(3.5)(6)+ 2π3.52 in terms of π is 49.04π
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If Maths equation3x plus 6 equals 21, what does Maths equationequal?
Factor each expression completely. x²-18 x+81
The factoring of the expression x²-18 x+81 is (x-9)²
To solve this exercise, we have to follow the rules of factoring:
x²-18 x+81
1. Looking for the a and b number that state the following equations:
a + b = -18a * b = 81Analyzing that (a*b) is a positive number, it means that (a) and (b) have the same signs, and due to the results of (a+b) is negative the sings of (a) and (b) should be negative.
The number could be:
a = - 9
b = - 9
Confirming:
a + b = -9 + (-9) = -18
a * b = (-9) * (-9) = 81
2. Rewriting the factored expression (x+a)(x+b) with the obtained values, we get:
(x-9)(x-9)
3. Rewriting as the square of a binomial, we get:
(x-9)²
What is factoring?Is a technique that consist of decomposition of a factor into a product of another factor, which when multiplied together give the original number.
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9 - 3/4x = 57
I know this is really simple, but my teacher wants me to do the thing where we do the stuff to both sides and I don't know how to write that.
-5 (5a+36+4c) +5(5a+3b-4c)
Answer:
Step-by-step explanation:
1)Distribute. (-25a+180-20c)(25a+15b-20c). 2) Combine like terms. -625a+180+15b+400c.
If p and q vary inversely, and p=10 when q=-4 , what is q when p=-2 ?
(A) 20 (B) 4/5 (C) -4/5 (D) -20
If p and q vary inversely, and p=10 when q=-4 , the value of q will be 20 when p=-2.
What is a constant?A mathematical constant is a significant integer that has a steady value and is specified by a precise definition.
What is inverse variation?relationship between two variables in mathematics that may be represented by an equation where the product of their products equals a constant
Inverse variation is y = k. 1/x
given p = -4
q = 10
So, 10 = k. 1/-4
So, the value of k = -40
We can conclude that the value of constant variation is -40
Value of q, when p = -2
⇒ q = -40 / -2
⇒ q = 20
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Find 95% of 3000 kilograms.
Answer:
2850 kilograms
Step-by-step explanation:
step 1)
change the percent to a decimal
by moving the decimal over to spots to the left
95.0% to 0.95
step 2
Multiply tge decimal with the amount you were given
0.95 × 3000 = 2850
If you want to double check, do this
2850 ÷ 3000 = 0.95
To find the height of an object that is dropped off a 350350 foot cliff tt seconds after it is dropped, you can use the polynomial -16 t^{2}+350−16t 2 +350. Find the height of the object at t = 1.5t=1.5 seconds after it is dropped.
The height of an object dropped off a 350 foot cliff after 1.5 seconds is 314 feet
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let h(t) represent the height of an object after t seconds, hence:
h(t) = -16t² + 350
Hence:
At time t = 1.5:
h(1.5) = -16(1.5)² + 350 = 314 feet
The height of an object dropped off a 350 foot cliff after 1.5 seconds is 314 feet
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a jewlery box company offers simple jewlery boxes with decorative tiles. the top and bottom of each box are adorned with heart tiles while the sides consists of diomand tiles. the figures show the first 3 jewlery box designs and their corresponding tile layouts
In design 8, number of hearts = 2 × 8 × 8 = 128 and number of diamonds is 32.
a) The offered designs show that the height always remains 1 cube, but the length and width both grow by 1 cube.
In design 1,
Number of hearts = 2 and number of diamonds = 4
In design 2,
Number of hearts = 8 and number of diamonds = 8
In design 3,
Number of hearts = 18 and, number of diamonds = 12
We have hearts at top and bottom and diamonds along the side walls.
b)
In deisgn 1 l× b × h = 1 × 1 × 1
Hearts = 2 = 2 × l ×b
Diamonds = 4 = l × 4
In deisgn 2 1 × b × h = 2 × 2 × 1
Hearts = 8 = 2 × l × b
Diamonds = 8 = l × 4
In deisgn 3 l × b × h = 3 × 3 × 1
Hearts = 18 = 2 × l × b
Diamonds = 12 = l × 4
So for any design,
number of hearts = 2 × l × b
number of diamonds = l × 4
c)
Company have 4 times hearts as diamonds.
So we can write,
2 × l × b = 4(l × 4) =
We can see in every case l=b. so
2 × l^2 = 16l
l = 8
So company have to advertise 8 × 8 × 1 design and put it on sale.
In design 8,
number of hearts = 2 × 8 × 8 = 128 and number of diamonds = 4 × 8 = 32.
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Solve each equation. Round to the nearest ten-thousandth. Check your answers.
2³x⁻⁴=5
[tex]2^{3x-4}=5[/tex] => x = 2.106 , by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Given: [tex]2^{3x-4}=5[/tex]
Taking logarithm on both sides:
log ([tex]2^{3x-4}[/tex]) = log (5)
=> (3x - 4) log (2) = log (5) (As [tex]log_b(a)^m = m (log_b(a))[/tex])
=> 3x - 4 = [tex]\frac{log5}{log2}[/tex]
=> 3x - 4 = [tex]\frac{0.698}{0.301}[/tex]
=> 3x - 4 = 2.318
=> 3x = 6.318
=> x = 2.106
Hence, [tex]2^{3x-4}=5[/tex] => x = 2.106, by properties of logarithm.
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On an airplane, there are two seats on the left side in each row and three seats on the right side. There are 42 seats on the right side of the plane. How many seats are on the left side of the plane?
What is the relationship between 23 and 26?
Which statement about pulleys is not true?
1. Fixed pulleys increase the output force.
2. Movable pulleys reduce the input force.
3. Fixed pulleys change the direction of the output force.
4. Fixed and moveable pulleys can be combined.
Answer:
4. Fixed and movable pulleys can be combined.
Step-by-step explanation:
The sum of an integer and 4 times the next consecutive odd integer is 53. Find the
value of the lesser integer.
Answer:
The lesser integer is 9.
Step-by-step explanation:
[tex]x + 4(x + 2) = 53[/tex]
[tex]x + 4x + 8 = 53[/tex]
[tex]5x + 8 = 53[/tex]
[tex]5x = 45[/tex]
[tex]x = 9[/tex]
Solve each equation by factoring. Check your answers.
x²+9 x+20=0
The factors of equation are -4 and -5.
Rewriting the equation -
x² + 9x + 20 = 0
ax² + bx + c = 0
The mentioned equation will be factorized using the given two rules -
1. sum of the factors will be equal to numeral in middle expression b (9x in this case)
2. product of factors will be equal to product of a and c (20 in this case)
Using above rules, the appropriate factors should be 5 and 4.
Representing the factors in mentioned equation -
x² + 4x + 5x + 20 = 0
Taking common factors
x(x + 4) +5(x + 4) = 0
(x + 4) (x + 5) = 0
x = -4, -5
Hence, the two factors of given equation are -4 and -5.
To check the answer, we will keep each value of x in the equation -
When x = -4
x² + 9x + 20 = 0
(-4)² + 9(-4) + 20 = 0
16 -36 + 20 = 0
36 - 36 = 0
0 = 0
When x = -5
x² + 9x + 20 = 0
(-5)² + 9(-5) + 20 = 0
25 - 45 + 20 = 0
45 - 45 = 0
0 = 0
As both Left Hand Side and Right Hand Side of the equation are same for both values of x, the factors are correct.
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Jessica collects stamps. She has 26 stamps that represent countries and 45 stamps that represent famous people. Write a ratio in the simplest form that represents the number of stamps she has of famous people to the number of stamps she has in total.
Answer:
Step-by-step explanation:
26:45
PLS HELP
SHOW WORK
ALSO WRITE THE SOLUTION AND EQUATION
Answer:
P = 3.75x - 7
Step-by-step explanation:
the perimeter (P) is the sum of the 3 sides of the triangle
P = 1.5x - 3 + 1.5x - 3 + 0.75x - 1 ← collect like terms
= 3.75x - 7
Please help me out please please please
−2x+3y−z=−23x+y=4−2y+2z=4
Enter your answer, in the form (x,y,z), in the boxes in simplest terms.
Answer:
[tex](x,y,z)=\left(-\dfrac{1}{11},\dfrac{21}{11},\dfrac{21}{11}\right)[/tex]
Step-by-step explanation:
Given:
[tex]-2x+3y-z=-23x+y=4-2y+2z=4[/tex]
Therefore:
[tex]\begin{cases}-2x+3y-z=4\\-23x+y=4\\4-2y+2z=4\end{cases}[/tex]
Rewrite Equation 2 to make x the subject:
[tex]\implies -23x+y=4[/tex]
[tex]\implies -23x+y-y=4-y[/tex]
[tex]\implies -23x=4-y[/tex]
[tex]\implies \dfrac{-23x}{-23}=\dfrac{4}{-23}-\dfrac{y}{-23}[/tex]
[tex]\implies x=-\dfrac{4}{23}+\dfrac{y}{23}[/tex]
Rewrite Equation 3 to make z the subject:
[tex]\implies 4-2y+2z=4[/tex]
[tex]\implies 4-2y+2z-4=4-4[/tex]
[tex]\implies -2y+2z=0[/tex]
[tex]\implies -2y+2z+2y=0+2y[/tex]
[tex]\implies 2z=2y[/tex]
[tex]\implies \dfrac{2z}{2}=\dfrac{2y}{2}[/tex]
[tex]\implies z=y[/tex]
Substitute the found expressions for y and z into Equation 1 and solve for y:
[tex]\implies -2x+3y-z=4[/tex]
[tex]\implies -2\left(-\dfrac{4}{23}+\dfrac{y}{23}\right)+3y-y=4[/tex]
[tex]\implies \dfrac{8}{23}-\dfrac{2}{23}y+2y=4[/tex]
[tex]\implies \dfrac{8}{23}+\dfrac{44}{23}y=4[/tex]
[tex]\implies \dfrac{8}{23}+\dfrac{44}{23}y- \dfrac{8}{23}=4- \dfrac{8}{23}[/tex]
[tex]\implies \dfrac{44}{23}y=\dfrac{84}{23}[/tex]
[tex]\implies \dfrac{44}{23}y \cdot \dfrac{23}{44}=\dfrac{84}{23}\cdot \dfrac{23}{44}[/tex]
[tex]\implies y=\dfrac{84}{44}[/tex]
[tex]\implies y=\dfrac{21}{11}[/tex]
Therefore, as y = z:
[tex]\implies z=\dfrac{21}{11}[/tex]
Substitute the found value of y into the found expression for x and solve for x:
[tex]\implies x=-\dfrac{4}{23}+\dfrac{y}{23}[/tex]
[tex]\implies x=-\dfrac{4}{23}+\dfrac{\frac{21}{11}}{23}[/tex]
[tex]\implies x=-\dfrac{4}{23}+\dfrac{21}{253}[/tex]
[tex]\implies x=-\dfrac{1}{11}[/tex]
Therefore, the final solution is:
[tex](x,y,z)=\left(-\dfrac{1}{11},\dfrac{21}{11},\dfrac{21}{11}\right)[/tex]
answer question on pdf
The equation of the parabola that has the same shape as [tex]f(x) = -8x^2[/tex], but with the vertex (4,9) is [tex]f(x) = -8(x - 4)^2 + 9.[/tex]
What is the standard equation of parabola ?The general equation of a parabola is given by
y = a(x – h)² + k
or x = a(y – k)² + h.
Here (h, k) denotes the vertex.
Now it is given that,
The parent function is [tex]f(x) = -8x^2[/tex]
The vertex of parabola is given as (4,9)
Thus, we have
h = 4
k = 9
Now since, the transformations form of a parabola is given as:
[tex]f(x) = a(b(x - h)) + k[/tex]
where:
a = vertical distance
b = horizontal distance
h = horizontal shift, x-coordinate of vertex
k = vertical shift, y-coordinate of vertex
Therefore, transformed equation of parabola is given as,
[tex]f(x) = -8(x - 4)^2 + 9[/tex]
this is the required equation of parabola with the vertex (4,9).
Thus, the required equation of the parabola that has vertex (4,9) is [tex]f(x) = -8(x - 4)^2 + 9[/tex].
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