How to simplify algebraic expression 8z+4f-6 using z=3 and f=9
Peter is 2 years older than Winnie. Peter's age is 16 years less than seven times Winnie's age. The equations below model the relationship between Peter's Age (p) and Winnie's age (w):
p=w+2
p=7w-16
Which is a possible correct method to find Peter's and Winnie's ages?
A. Solve w+2 = 7w-16 to find the value of w
B. Solve p+2 =7p-16 to find the value of p
C. Write the points where the graphs of the equations intersect the x axis
D. Write the points where the graphs of the equations intersect the y axis
Answer:
A. Solve w+2 = 7w-16 to find the value of w.
Step-by-step explanation:
Here p represents the age of Peter and w represents the age of Winnie,
Given,
Peter is 2 years older than Winnie.
⇒ p = w + 2 -----(1)
Also, Peter's age is 16 years less than seven times Winnie's age.
⇒ p = 7w - 16 -----(2),
By equating right sides of equation (1) and (2),
We get,
w + 2 = 7w - 16,
Since, this equation is only in the variable w,
Thus, we can find the value of w with help of the above equation,
After putting this value in either of equation (1) or (2),
We can find the value of p.
Hence, option A is correct.
Note : From equation (1) and (2),
w = p - 2 and [tex]w=\frac{p+16}{7}[/tex]
[tex]\implies p-2=\frac{p+16}{7}[/tex]
⇒ Option B is incorrect.
Now, let x represents w and y represents p in the graph,
Then, the solution will be the intersection point of lines y=x+2 and y=7x-16,
Which is shown below,
⇒ Options C and D are incorrect.
A tennis ball bounces so that its initial speed straight upwards is b feet per second. Its height s in feet at time t seconds is given by s = bt − 16t^2 a) Find the velocity v = ds/dt at time t. b) Find the time at which the height of the ball is at its maximum height. c) Find the maximum height. d) Make a graph of v and directly below it a graph of s as a function of time. Be sure to mark the maximum of s and the beginning and end of the bounce.
A prism with a volume of 360 yd³ is scaled down to a volume of 45 yd³. What is the scale factor? Enter your answer, as a decimal or a fraction in simplest form, in the box.
Answer:
The scale factor is equal to [tex]\frac{1}{2}[/tex] or [tex]0.5[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
Let
z-----> the scale factor
[tex]z^{3}=\frac{45}{360}= \frac{1}{8}\\ \\z=\sqrt[3]{\frac{1}{8}}\\ \\z=\frac{1}{2}[/tex]
help. i don’t understand this at all!!!!!
Convert 0.656 to a fraction. A. 21⁄32 B. 22⁄30 C. 20⁄33 D. 23⁄12
Write and graph an equation in two variables that shows the relationship between the time and distance traveled
Answer:
1=1
Step-by-step explanation:
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Baileigh is using a piece of string to hang a painting on the wall. The back of the painting is diagrammed below. 36 cm 36 cm 15 cm 15 cm Note: Figure is not drawn to scale. What is the length of the string? A. 78 centimeters B. 102 centimeters C. 39 centimeters D. 51 centimeters
What is the answer to this problem
Julie has read 27 pages out of an 80-page book. What percent of the pages has she read?
Suppose the probability that a randomly selected man, aged 55-59, will die of cancer during the course of the year is StartFraction 300 Over 100 comma 000 EndFraction . How would you find the probability that at least 1 man out of 1,000 of this age will die of cancer during the course of the year?
The question is an example of binomial distribution.
P(x=r) = nCr* p^r* q^(n-r) ( nCr = n! / ( (n-r)!*r! )
p = probability of die = 300/100000 = .003
P ( at least one man would die) = 1-P(at most one man would die)
= 1 - [ P(X =0) + P(X= 1)
= 1- [ {1000C0(.003)^0 *(.997)^1000} + { 1000C1(.003)^1 *(.997)^999} ]
= .801
What is the surface area of the rectangular prism below?
A. 823 u
B. 740
C. 700
D. 1260
Answer:
C) 700 unit².
Step-by-step explanation:
Given : A rectangular prism .
To find : What is the surface area of the rectangular prism below.
Solution : We have given that a rectangular prism with
Length = 14 units,
Width = 12 units
Height = 7 units.
Surface area of rectangular prism = [tex]2(length* width\ +\ height*width\ +\ height*length})[/tex].
Plugging the values
Surface area of rectangular prism = 2 ( 14* 12 + 7 *12 + 7 *14)
Surface area of rectangular prism = 2 ( 168 + 84 + 98)
Surface area of rectangular prism = 2 ( 350).
Surface area of rectangular prism = 700 unit².
Therefore, C) 700 unit².
What is the distance between y = -x+2 and y = -x+4?
Answer:
√2
Step-by-step explanation:
You want the distance between the lines y = -x +2 and y = -x +4.
Distance to a lineThe distance from point (x, y) to line ax +by +c = 0 is given by the formula ...
[tex]d=\dfrac{|ax+by+c|}{\sqrt{a^2+b^2}}[/tex]
ApplicationRewriting the equation of the second line to general form, we have ...
y = -x +4
x +y -4 = 0 . . . . . . . a=1, b=1, c=-4
The equation of the first line is written in slope intercept form, so we can identify the y-intercept as (0, 2). Using this point in the formula for the distance to the second line, we have ...
[tex]d=\dfrac{|1(0)+1(2)-4|}{\sqrt{1^2+1^2}}=\dfrac{|-2|}{\sqrt{2}}=\sqrt{2}[/tex]
The distance between the lines is √2 units.
__
Additional comment
As you can see from the graph, the distance between the lines is the length of the diagonal of a unit square, √2.
Polygon D is a scaled copy of Polygon C using a scale factor of 6. How many times larger is the area of Polygon D than the area Polygon CCC?
Answer:
Yup...it's 36.
Step-by-step explanation:
Use the equation p=8.31/v where p = pressure and V = volume. What happens to the pressure as the volume approaches 0? Explain your reasoning.
Answer:
1 The pressure approaches infinity.
2 The function is undefined for V = 0.
3 There is an asymptote at V = 0.
The pressure tends to infinity.
Given information,
The equation [tex]p=\frac{8.31}{v}[/tex]
Where p= pressure,
v= volume
If the volume approaches [tex]0[/tex] then the pressure [tex]p=\frac{8.31}{v}[/tex] will reach to infinity.
Therefore, the pressure tends to infinity.
For further details refer to the link:
https://brainly.com/question/356585
a volleyball reaches its maximum height of 13 feet, 3 seconds after its served. Which of the following quadratics could model the height of the vollyball over time after it is served. Select all that apply.
A: f(x)=2x^2+12x+5
B: f(x)=-2x^2+12x-5
C: f(x)=-2x^2-12x+5
D: f(x)=-2(x-3)^2+13
E: f(x)=-2(x+3)^2+13
Answer:
D.
Step-by-step explanation:
Intuitively it's a volleyball game reaching its maximum height, then we must discard the 1st option because of its parameter a >0, and whenever a>0 the parabola makes a curve, rather different than in a volleyball game.
Also, considering Vertex of this parabola by (-b/2a, -Δ/4a) given the fact that the question says the maximum height.
Taking
y= height in feet
x= time in second
Function Vertex (-b/2a, -Δ/4a)=(-3, -13)
A: f(x)=2x²+12x+5 False
B: f(x)=-2x²+12x-5 Function Vertex (-b/2a, -Δ/4a) = (3,23) False
C: f(x)=-2x²-12x+5 Function Vertex (-b/2a, -Δ/4a) = (-3,23) False
D: f(x)=-2(x-3)²+13 Function Vertex (-b/2a, -Δ/4a) = (3,13) True
E: f(x)=-2(x+3)²+13 Function Vertex (-b/2a, -Δ/4a) =(-3,13) False
the sears tower of Chicago is 1450 feet high. a model is 24 inches tall. what is the ratio of the height of the model to the height of the actual sears tower?
Explain how two angles can be complementary angles.
PLSSS HELP!!!
What is the exact volume of the sphere?
56.3⎯⎯π ft³
274.625π ft³
366.16⎯⎯π ft³
1464.6⎯⎯π ft³
Answer:
366.16
Step-by-step explanation:
i promise
what is 16×45÷2
[tex]12 \times 4 + 23 \div 2 + 13 \div 4[/tex]
Value times frequency equals product.
True or False
Answer: The correct answer is true
Step-by-step explanation:
The lengths, in centimeters, of nine earthworms are shown below. 3, 4, 5, 5, 6, 7, 8, 9, 10 What is the median of the data?
Select the two equations that can be used to solve the following inequality
A cylinder has a radius of 12 m and a height of 9 m.
What is the exact volume of the cylinder?
A. 108π m³
B. 216π m³
C. 972π m³
D. 1296π m³
we are given
radius=r=12m
height=h=9m
now, we can use formula of volume of cylinder
[tex] V=\pi r^2 h [/tex]
now, we can plug values
and we get
[tex] V=\pi (12)^2 *9 [/tex]
we get
[tex] V=1296 \pi m^3 [/tex]
so, the exact volume of the cylinder is [tex] 1296 \pi m^3 [/tex]..........Answer
Answer:
(D)
Step-by-step explanation:
It is given that a cylinder has a radius of 12 m and a height of 9 m. Then,
Volume of the cylinder is given as:
[tex]V={\pi}r^{2}h[/tex]
⇒[tex]V={\pi}(12)^2(9)[/tex]
⇒[tex]V={\pi}(144)(9)[/tex]
⇒[tex]V=1296{\pi}m^3[/tex]
Therefore, the volume of the cylinder is [tex]1296{\pi}m^3[/tex].
Thus, Option D is correct.
GCF and LCM of 3 and 14
If 4 apples and 2 oranges equals $1 and 2 apples and 3 oranges equals $0.70, how much does each apple and each orange cost? (Can you do it step by step)
Tasha claims that her skateboard weighs about 3 pounds. is Tasha's claim reasonable? Explain
A line passes through the point (8, -1) and has a slope of -5/2
Write an equation in slope-intercept form for this line.
Final answer:
To find the slope-intercept form of a line with a given slope of -5/2 that passes through the point (8, -1), we use the point-slope form and then rearrange to get the final equation: y = (-5/2)x + 19.
Explanation:
To write the equation of a line in slope-intercept form (which is y = mx + b), we need to know the slope (m) of the line and the y-intercept (b). In this case, we are given the slope of the line as -5/2 and a point through which the line passes, which is (8, -1). Using the point-slope form, which is y - y1 = m(x - x1) where (x1, y1) is the given point and m is the slope, we can substitute the given slope and the coordinates of the given point to derive the slope-intercept form.
The equation starts with y - (-1) = (-5/2)(x - 8). Simplifying the equation, we get:
y + 1 = (-5/2)x + (5/2)*8
y = (-5/2)x + 20 - 1
y = (-5/2)x + 19
So, the equation of the line in slope-intercept form is y = (-5/2)x + 19.
To write an equation in slope-intercept form, substitute the given values of the slope and a point on the line into the equation. The equation of the line passing through the point (8, -1) with a slope of -5/2 is y = -5/2x + 19.
Explanation:To write an equation in slope-intercept form, we need to use the given slope and the coordinates of the point through which the line passes. The slope-intercept form is y = mx + b, where m represents the slope and b represents the y-intercept. We're given that the slope of the line is -5/2, so we can substitute this value for m. We're also given that the line passes through the point (8, -1), so we can substitute these coordinates to find the value of b.
Using the point-slope form of a line, we have y - y1 = m(x - x1). Substituting the given values, we get y - (-1) = -5/2(x - 8). Simplifying, we have y + 1 = -5/2x + 20. Moving the 1 to the other side, we have y = -5/2x + 19. This is the equation of the line in slope-intercept form.
HURRY!!!When are two triangles said to be in perspective?
a.
If the corresponding vertices of two triangles form three lines that intersect in a single point
c.
If the corresponding vertices of four triangles form three lines that intersect in a single point
b.
If the corresponding vertices of three triangles form three lines that intersect in a single point
d.
If the corresponding vertices of two triangles form three lines that intersect in two points.
What is the next number in the following sequence.
0, 1, 1, 2, 3, 5, 8...
a.
9
c.
10
b.
13
d.
11
reciprocal of 4 and 1/8 fraction