Step-by-step explanation:
parallel means it has the same slope.
the slope is always the factor of x : -3/2
I guess the needed equation is in slope-intercept form :
y = ax + b
"a" being the slope, "b" being the y intercept (the y value when x = 0).
but since we have a point on the line and its slope, we can start with the point-slope form
y - y1 = a(x - x1)
"a"is again the slope, (x1, y1) is the given point.
and then we transform this into the slope-intercept form.
in our case we have
y - -1 = -3/2 × (x - 6)
y + 1 = -3x/2 + 18/2 = -3x/2 + 9
y = -3x/2 + 8
or
y = -3/2 x + 8
or
y = -1/2 × (3x - 16)
The period of a periodic function is 8 s . How many cycles does it go through in 30 s ?
(F) (4/15) cycle (G) 3.75 cycles (H) 22 cycles (I) 240 cycles
The number of cycles of the periodic function is 3.75 cycles if the period of a periodic function is 8 s option (G) 3.75 is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The period of a periodic function is 8 s
From the question:
8n = 30
n = 30/8
n = 3.75 cycles
Thus, the number of cycles of the periodic function is 3.75 cycles if the period of a periodic function is 8 s option (G) 3.75 is correct.
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Someone pls help me with these
Answer:
y = (1/6)x - 11
Step-by-step explanation:
y = (1/6)x + 7; Point: (12, -9)
(x₁, y₁)
y - y₁ = m (x - x₁)
y - (-9) = (1/6) (x - 12)
y + 9 = (1/6)x - 2
-9 -9
y = (1/6)x - 11
I hope this helps!
What is the inverse of the function f(x)=√x-4 ?
(F) f⁻¹(x)=x²-4, x ≥ 0 (H) f⁻¹(x)= √x+4 (G) f⁻¹(x)=x²+4, x ≥ 0
(I) f⁻¹(x)= √x-4 / x-4
The inverse of [tex]f(x) = \sqrt{x - 4}[/tex] is [tex]f^{-1}(x) = x^{2} +4[/tex] that is option G) is correct
According to the question we have been given the function which is :
[tex]f(x) = \sqrt{x - 4}[/tex]
To find the inverse of this function we will solve this step by step
First we will convert it into equation form
[tex]y = \sqrt{x - 4}[/tex]
Then we will interchange the variables x and y
[tex]x = \sqrt{y - 4}[/tex]
Then we will solve for y, we get
Taking square on both sides of the equation, we get
[tex]x^{2} = y - 4[/tex]
[tex]y = x^{2} + 4[/tex]
Now replacing variable y with [tex]f^{-1} (x)[/tex] , we get
[tex]f^{-1}(x)[/tex] = [tex]x^{2} +4[/tex]
Thus the inverse of [tex]f(x) = \sqrt{x -4}[/tex] is [tex]f^{-1} = x^{2} +4[/tex] that is option G) is correct
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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
Help me on this question in the photo asap
Answer:
a. -5 b. 23 c. 871 d. -5
Step-by-step explanation:
f(x) = x^2 + 6x and g(x) = x - 4
a). (fog)(3) = (x - 4)^2 + 6(x - 4)
= (3 - 4)^2 + 6(-1)
= 1 -6
= -5
b). (gof)(3) = ( x^2 + 6x) - 4
= (9 + 18) - 4
= 23
c). (fof)(3) = (x^2 + 6x)^2 + 6(x^2 + 6x)
= 27^2 + 27(6)
= 871
d). (gog)(3) = (x - 4) -4
= (3 - 4) - 4
= -5
What does the slope tell you about the rate of change in elevation during Ryan's uphill climb? What was the total elevation change?
It should be noted that the slope shows that the rate of change in elevation rise at first but later reduced.
The total change in elevation is 10500 feet
How to explain the information?It should be noted that from the table, the time and the elevation has been given.
Therefore, the total elevation will be the addition of all the values given. This will be 10500 feet.
Also, the slope shows that the rate of change in elevation rise at first but later reduced.
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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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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:
f(x)=x
3
−9xf, left parenthesis, x, right parenthesis, equals, x, cubed, minus, 9, x
Over which interval does fff have a positive average rate of change?
The interval in which the function has positive average rate of change is x > √3
How to determine the interval which the function has positive average rate of change?The function is given as
f(x) = x^3 - 9x
Differentiate the above function to determine the average rate of change
So, we have
f'(x) = 3x^2 - 9
Set the function to greater than 0
So, we have
3x^2 - 9 > 0
Add 9 to both sides
3x^2 > 9
Divide by 3
x^2 > 3
Take the square root of both sides
x > √3
Hence, the interval in which the function has positive average rate of change is x > √3
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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:
Please help me out please please please
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
The factors 8 and 5 are a factor pair of 49.
O A. True
OB. False
Answer: ob false
Step-by-step explanation: look at a calculator and it will show 8 is not a 5 is not 8 times five is 40 hope this helps
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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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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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:
Factor each expression.
4 x²-9
The required factors of the expression, 4x² - 9 are 4, x, x, -3, 3.
What are the factors of an expression?
Any number or expression that completely divides another number or expression is called as the factor of an expression. These can be positive or negative depending upon the given expression.
Calculating the factor of expression. 4x² - 9
Given an expression, 4x² - 9
Terms of an expression are 4x², - 9
Further breaking the terms to factors, we obtain,
4, x, x, -3, 3
Hence, the required factors of the expression, 4x² - 9 are 4, x, x, -3, 3.
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What is the result of adding these two equations?
2x+3y=-5
5z-y = -12
In equation form and not fraction
7x +2y= -17 is the result of adding these two equations 2x+3y=-5 and 5z-y = -12
What is equation ?
An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic, etc.
given equations
2x+3y=-5
5z-y = -12
we have to add these two equations
Add 2x and 5x to get 7x
Add the y's
3y + (-1y) OR 3y - y
Which gives you 2y
add the (-5 and -12)
-12 + (-5) or -12 - 5 giving you -15
7x+2y=-17
Hence ,7x +2y= -17 is the result of adding these two equations 2x+3y=-5 and 5z-y = -12
the complete question is
What is the result of adding these two equations?
2x+3y= -5
5x - y = - 12
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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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the sum of 2 consecutive numbers are 55. what are the numbers?
Answer:
the numbers are 27,28
Step-by-step explanation:
Let the numbers be x,x+1
The sum is 55
⟹x+x+1=55
2x+1=55
2x+54
x=27
So the numbers are 27,28
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?
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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−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]
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
x² - 10 - 3 x² + 5×-8
hello please solve and give a solution thankyou!!
Answer:
-2x2 - 50
Step-by-step explanation:
First, you collect the like terms:
x2 - 3x2 + 5 x -8 -10
Do multiplication first:
x2 - 3x2 + (-40) - 10
Combine the terms:
-2x2 - 50
Answer:
5 star of you
Step-by-step explanation:
you are cool dictator
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.
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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If Maths equation3x plus 6 equals 21, what does Maths equationequal?
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.
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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