Answer:
8 times
Step-by-step explanation:
We know that the radius of smaller sphere is r,
The volume of sphere is given by:
[tex]V_1=\frac{4}{3} \pi r^{3}[/tex]
where V_1 is the volume of the small sphere.
As we know that the radius of large sphere is double of the smaller sphere, the radius of large sphere will be 2r
Let V_2 be the volume of large sphere
[tex]V_2=\frac{4}{3}\pi (2r)^{3} \\ =\frac{4}{3}\pi *8r^3[/tex]
Separating 8 aside
[tex]V_2=8(\frac{4}{3}\pi r^{3})\\V_2=8V_1[/tex]
We can see that the volume of large sphere is eight times the volume of small sphere ..
Answer:
8 times
Step-by-step explanation:
Given
ratio of radii = a : b, then
ratio of volumes = a³ : b³
Here ratio of radii = 1 : 2, hence
ratio of volumes = 1³ : 2³ = 1 : 8
Thus the volume of the large sphere is 8 times the volume of the small sphere
Which equation is a linear equation?
Question 4 options:
a)
23xy − 34y = 0
b)
3a + 5b = 3
c)
x2+y2 = 0
d)
4m2 = 6
Answer:
b) 3a + 5b = 3
Step-by-step explanation:
It is an exact replica of the Standard Formula [Ax + By = C]. The Standard Formula is an example of a linear equation.
Answer:
3a + 5b = 1 is a linear equation
Step-by-step explanation:
Required?
To state which equation is linear...
An equation is said to be linear if it obeys the following.
1. For Single variables: y = b
An example is y = 4
2. For 2 Variables; it can take any of the following form: Ax + By = C.
An example 3x + 5y = 4
.from option A through D, only option B fits the description.
Note that the arithmetic sign could take the negative form and the position of x and y or any other constraints can take an interchanged forms.
The key thing to watch out when naming a linear equation is that the highest power is 1.
Hence, the 3a + 5b = 1 is a linear equation
Subtract the equations 5x+4y=25 (5x+2y=3)
Answer:
0x + 2y = 22 ✔️
Step-by-step explanation:
To substract the equations, we should do the following:
5x + 4y = 25
5x + 2y = 3
----------------------------
0x + 2y = 22 ✔️
The value of y is: y = 11 ✅✅
The value of x is: x = 3.8 ✅✅
Answer:
To substract the equations, we should do the following:
5x + 4y = 25
5x + 2y = 3
----------------------------
0x + 2y = 22
Step-by-step explanation:
can someone help me please
Answer:
Attached below
Step-by-step explanation:
Given f(x) =1/x and g(x) = x-2 then;
f.g (x) = f (g(x) )
=f(x-2)
=1/x⇒⇒⇒1/x-2
f.g(x) =
[tex]\frac{1}{x-2}[/tex]
given the measure of arc dc is 120 the measure of arc ADC is?
Answer:
120°
Step-by-step explanation:
The arc ABC is twice that of the angle created at D. This is the central angle theorem extension.
So we can say that arc ABC = 2* 120 = 240
We know total circle angle is 360 degrees so, arc ADC + arc ABC = 360
Hence,
arc ADC + 240 = 360
arc ADC = 360 - 240 = 120
Given: ∠1 = ∠2 If AB = 10, AC = 6, and BC = 6, find AD:
5
10
15
Answer: AD = 5
because AB equals 10, logically we assume AD equals 5, hopefully this helps you.
Answer:
AD=5
Step-by-step explanation:
We are given that
[tex]\angle 1=\angle 2[/tex]
AB=10, AC=6 BC=6
We have to find the value of AD.
Let AD=x
BD=AB-AD
BD=10-x
By angle bisector theorem
[tex]\frac{AC}{AD}=\frac{BC}{BD}[/tex]
Substitute the values then we get
[tex]\frac{6}{x}=\frac{6}{10-x}[/tex]
[tex]\frac{10-x}{x}=\frac{6}{6}[/tex]
[tex]\frac{10-x}{x}=1[/tex]
[tex]10-x=x[/tex]
[tex]x+x=10[/tex]
[tex]2x=10[/tex]
[tex]x=\frac{10}{2}=5[/tex]
Hence, the value of AD=5 units
Quinton tried to transform triangle FGH according to the rule (x, y) → (–y, x). Which best describes his attempt? Correct. He transformed the triangle according to the rule (x, y) → (–y, x). Incorrect. He transformed the triangle according to the rule (x, y) → (y, –x) Incorrect. He transformed the triangle according to the rule (x, y) → (–y, –x) Incorrect. He transformed the triangle according to the rule (x, y) → (–x, –y)
Answer:Correct. He transformed the triangle according to the rule (x, y) → (-y, x).
Answer:
Option A.
Step-by-step explanation:
Consider the below diagram is attached with this question.
Quinton tried to transform triangle FGH according to the rule (x, y) → (–y, x).
From the below figure it is clear that the vertices of triangle FGH are F(3,2), G(1,2) and H(4,5).
The vertices of image after transformation are F'(-2,3), G'(-2,1) and H'(-5,4).
The relation between preimage and image is defined by the rule
[tex](x,y)\rightarrow (-y,x)[/tex]
Since Quinton transformed the triangle according to the rule (x, y) → (–y, x), therefore he is correct.
Thus the correct option is A.
computing the probability of rolling two dice in succession face value of two rolls are added together is the sum greater than 7
Answer:
5/12 ≈ 0.41667
Step-by-step explanation:
If the first die rolls a 1 and the second die rolls a 1, then the sum is 2.
If the first die rolls a 1 and the second die rolls a 2, then the sum is 3.
Repeating this, we can build a table showing all the possible outcomes:
[tex]\left[\begin{array}{ccccccc}&1&2&3&4&5&6\\1&2&3&4&5&6&7\\2&3&4&5&6&7&8\\3&4&5&6&7&8&9\\4&5&6&7&8&9&10\\5&6&7&8&9&10&11\\6&7&8&9&10&11&12\end{array}\right][/tex]
As we can see, of the 36 possible outcomes, 15 are greater than seven. So the probability is 15/36, which reduces to 5/12.
Mike is making a scale model of his favorite car. The actual car is 8 feet long and 4 feet wide. Mike wants his model to be 12 inches in length. Which could be used to find the width of his model if he uses the same ratio?
Mike can determine the width of his scale model car by setting up and solving a proportion. Using the ratio of the actual car's dimensions, calculate an equivalent ratio for the model. The width of the model car should be 6 inches.
Explanation:To solve this problem, you can set up a proportion based on the known dimensions of the actual car and Mike's model. Given the actual car's length and width are 8 feet and 4 feet, and Mike's model length is 12 inches, we can set up the proportion like this:
8 feet : 4 feet = 12 inches : X
First, we need to convert all measurements to the same unit. Let's use inches since Mike's model is in inches (remember that 1 foot equals to 12 inches). So, the car's length is 96 inches and its width is 48 inches. Now, the proportion would be:
96 inches : 48 inches = 12 inches : X
To find the value of X (the width of the model), we can cross-multiply:
(96 * X) = (48 * 12)
Solve for X by dividing each side by 96, we get:
X = 6 inches
So, Mike's model car should be 6 inches wide to maintain the same ratio as the actual car.
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Help Please..............................................
Answer:
0 and 1 have the same y values for the x values.
Giovanna used the calculations below to determine the height of a stack of 7 books that are each 2 5/8
inches thick what
was her error?
C. There should be a subtract step not an addition step
D. Two should have been multiplied by 5/8
Answer:
Option C. Seven was not multiplied by 5/8
Step-by-step explanation:
we know that
To determine the height of a stack of 7 books that are each 2 5/8 inches thick. multiply 7 by 2 5/8
so
[tex]7(2\frac{5}{8})\\ \\7(2+\frac{5}{8})\\ \\7*2+7*\frac{5}{8}\\ \\14+\frac{35}{8}\\ \\14+4+\frac{3}{8}\\ \\18\frac{3}{8}\ in[/tex]
therefore
Seven was not multiplied by 5/8
Answer:
Option B.
Step-by-step explanation:
Giovanna did the calculations to determine the height of a stacks of 7 books having [tex]2\frac{5}{8}[/tex] inches thickness of each book.
[tex]7(2\frac{5}{8})[/tex]
[tex]=7(2+\frac{5}{8})[/tex]
[tex]=(7\times 2)+7(\frac{5}{8})[/tex]
[tex]=14+\frac{35}{8}[/tex]
[tex]=14+4+\frac{3}{8}[/tex]
=18+[tex]\frac{3}{8}[/tex]
[tex]=18\frac{3}{8}[/tex]
Now when compare this solution with Giovanna's solution we find error in 3rd step, in which she hasn't mutiplied the fraction [tex]\frac{5}{8}[/tex] by 7.
Therefore, option B is the correct one.
if 5x-3y=23 and 4x-4y=20, which is the value of x+y?
Answer:
3
Step-by-step explanation:
5x-3y=23
4x-4y=20
---------------I'm going to try to set this up for elimination. I notice the bottom equation contains terms that are divisible by 4 so I'm going to divide both sides by 4 on that last equation only...
5x-3y=23
x- y= 5
Now I'm going to multiply the bottom equation by -3 so the y terms will be opposite. When you add opposites you do get 0. That is the whole point of elimination.
5x-3y=23
-3x+3y=-15
------------------ adding
2x+0=8
2x =8
x =4
So using that second equation x-y=5 I will find y given that x=4.
4-y=5
-y =1
y=-1
So the solution to the system is (4,-1)
You are asked to find x+y
So x+y=4+(-1)=3
find the value of 2x-10 given that -5x-9=6
If f(x) = 2x2 - 5 and g(x) = x2 - 4x - 8, find (f - g)(x).
Answer:
= x^2 +4x +3
Step-by-step explanation:
f(x) = 2x^2 - 5
g(x) = x^2 - 4x - 8
(f - g)(x)=2x^2 -5 - (x^2 -4x-8)
Distribute the minus sign
= 2x^2 -5 -x^2 +4x+8
Combine like terms
= x^2 +4x +3
Which points could be on the line that is parallel to
and passes through point J? Check all that apply.
(-3,5)
(1,5)
(3,-2)
(3, 2)
(5,1)
Answer:
(-3, 5), (3, 2), (5, 1)Step-by-step explanation:
Parallel lines have the same slope.
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the coordinates of the given points G(-4, 1) and H(2, -2):
[tex]m=\dfrac{-2-1}{2-(-4)}=\dfrac{-3}{6}=-\dfrac{1}{2}[/tex]
J(1, 3). Let other point (x, y).
Substitute to the slope:
[tex]\dfrac{y-3}{x-1}=\dfrac{-1}{2}[/tex] cross multiply
[tex]2(y-3)=-1(x-1)[/tex] use the distributive property
[tex]2y+(2)(-3)=-x+(-1)(-1)[/tex]
[tex]2y-6=-x+1[/tex] add 6 to both sides
[tex]2y=-x+7[/tex] divide both sides by 2
[tex]y=-\dfrac{1}{2}x+\dfrac{7}{2}[/tex]
Check the equality for coordinates of each point:
[tex](-3, 5)\\\\5=-\dfrac{1}{2}(-3)+\dfrac{7}{2}\\\\5=\dfrac{3}{2}+\dfrac{7}{2}\\\\5=\dfrac{10}{2}\\\\5=5\qquad\bold{CORRECT}[/tex]
[tex](1,\ 5)\\\\5=-\dfrac{1}{2}(1)+\dfrac{7}{2}\\\\5=-\dfrac{1}{2}+\dfrac{7}{2}\\\\5=\dfrac{6}{2}\\\\5=3\qquad\bold{FALSE}[/tex]
[tex](3,\ -2)\\\\-2=-\dfrac{1}{2}(3)+\dfrac{7}{2}\\\\-2=-\dfrac{3}{2}+\dfrac{7}{2}\\\\-2=\dfrac{4}{2}\\\\-2=2\qquad\bold{FALSE}[/tex]
[tex](3,\ 2)\\\\2=-\dfrac{1}{2}(3)+\dfrac{7}{2}\\\\2=-\dfrac{3}{2}+\dfrac{7}{2}\\\\2=\dfrac{4}{2}\\\\2=2\qquad\bold{CORRECT}[/tex]
[tex](5,\ 1)\\\\1=-\dfrac{1}{2}(5)+\dfrac{7}{2}\\\\1=-\dfrac{5}{2}+\dfrac{7}{2}\\\\1=\dfrac{2}{2}\\\\1=1\qquad\bold{CORRECT}[/tex]
To identify which points could be on a line that is parallel to another and passes through a specific point, we need to know the slope of the original line or the coordinates of the given point. Without this information, it is impossible to accurately determine which points from the list might be on the parallel line.
Explanation:The question asks, Which points could be on the line that is parallel to and passes through point J? This problem is a part of geometry in mathematics where we study about points, lines, and planes.
The location of point J was not specified, but the line that is parallel to another would have the same slope, regardless of its y-intercept. As such, to find the points that can lie on a line that is parallel, we must know the slope of the primary line. If we are given the slope 'm', any points that fall on the line would satisfy the equation of a line, y = mx + b, where 'b' is the y-intercept. The points whose 'y' value remains constant in the given x-y pairs would lie on the line parallel to the original line.
Without the proper information about the slope of the line or the position of point J, it is impossible to accurately determine which points from the given list can lie on the line that is parallel and passes through point J.
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given that (-2,-8) is on the graph of f(x), found the corresponding point for the function f (x)-1
Answer:
(- 8, - 2)
Step-by-step explanation:
Assuming you mean the inverse function
Then any coordinate point (x, y ) in f(x) → (y, x) in the inverse
Given
(- 2, - 8 ) is on the graph of f(x), then
(- 8, - 2) is on the graph of [tex]f^{-1}[/tex](x)
The corresponding point on the graph of function f(x)-1 for a given point (-2,-8) from the graph of function f(x) is (-2, -9). All corresponding x-values remain the same, while the y-values are decreased by 1.
Explanation:The given point (-2,-8) is on the graph of the function f(x). Now, you're asked to find the corresponding point for the function f(x)-1. When we modify a function like this, it affects the y-values (output) of the function. The x-values (input) remains constant.
In this case, for any x-value in the function f(x), the corresponding y-value in the function f(x)-1 is simply the y-value of f(x) minus one. So the corresponding point on the graph of f(x)-1 for the given point (-2,-8) from the graph of f(x) would be (-2, -9), because -8 (the y-value from f(x)) minus 1 equals -9 (the y-value for f(x)-1). Hence, the point (-2, -9) is on the graph of the function f(x)-1.
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Can someone PLEASE help me :((
What is the measure of AC?
Answer:
5 blocks
Step-by-step explanation:
Since the triangle is right use Pythagoras' identity to solve for AC
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
AC² = AB² + BC² ← substitute values
AC² = 3² + 4² = 9 + 16 = 25 ( take the square root of both sides )
AC = [tex]\sqrt{25}[/tex] = 5
A colony contains 1500 bacteria. The population increases at a rate of 115% each hour. If x represents the number of
hours elapsed, which function represents the scenario?
f(x) = 1500(1.15)"
f(x) = 1500(115)
f(x) = 1500(2.15)
f(x) = 1500(215)
Answer:
Step-by-step explanation:
A colony contains 1500 bacteria. The population increases at a rate of 115% each hour. If x represents the number of hours elapsed, which function represents the scenario?
f(x) = 1500(1.15)x
f(x) = 1500(115)x
f(x) = 1500(2.15)x
f(x) = 1500(215)x
The answer to this problem is a f(x) = 1500(2.15)x
Answer:
[tex]f(x) = 1500(2.15)^x[/tex]
Step-by-step explanation:
Let the function that represents the population of bacteria after x hours is,
[tex]f(x)=ab^x[/tex]
For x = 0, f(x) = 1500,
[tex]1500=a(1+r)^0[/tex]
[tex]1500=a[/tex]
Now, the population increases at a rate of 115% each hour,
So, the population after 1 hour = (100+115)% of 1500 = 215% of 1500 = 3225,
That is, for x = 1, f(x) = 3225,
[tex]3225 =ab[/tex]
[tex]3225=1500(b)[/tex]
[tex]\implies b =2.15[/tex]
Hence, the function that represents the given scenario is,
[tex]f(x)=1500(2.15)^x[/tex]
Two garden plots are to have the same
area. One is square and one is
rectangular. The rectangular plot is 4
meters wide and 9 meters long.
Answer:
6m
Step-by-step explanation:
The area of the rectangular plot is
A = l*w
= 4*9
= 36 m^2
To find the area of the square plot
A = s^2
36 = s^2
Take the square root of each side
sqrt(36) = sqrt(s^2)
6 = s
The length of the side of the square plot is 6 m
Yasmin purchased 6 heads of cabbage that each weighed 2 3/8 pounds how much did the cabbage way all together
Answer:
14 1/4
Step-by-step explanation:
what is missing sequence number?
5 6 9 - 25 40
Answer:
15
Step-by-step explanation:
term 1 is equal to 5.
term 2 is equal to 5 + (1) = 5 + 1 = 6
term 3 is equal to 6 + (1 + 2) = 6 + 3 = 9
term 4 is equal to 9 + (1 + 2 + 3) = 9 + 6 = 15
term 5 is equal to 15 + (1 + 2 + 3 + 4) = 15 + 10 = 25
term 6 is equal to 25 + (1 + 2 + 3 + 4 + 5) = 25 + 15 = 40
If 8y-8=24 find the value of 2y
Answer:
8
Step-by-step explanation:
8y-8=24
+8 +8
8y=32
32/8 = 4
y=4
4*2=8
Answer:
8
Step-by-step explanation:
8 y - 8 = 24
( + 8 )
8 y = 32
( ÷ 4 )
y = 4
Find the value of 2 y
y = 4 so 2 y = 8
Find the rate of change for the line that passes through the point (-2, 6) and (-5, 9).
[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{9}) \\\\\\ \stackrel{\textit{average rate of change}~\hfill }{slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}}\implies \cfrac{9-6}{-5-(-2)}\implies \cfrac{9-6}{-5+2}\implies \cfrac{3}{-3}\implies -1[/tex]
What is the solution to this system of equations?
4x + 5y = 7
3x – 2y = –12
Answer:
x = -2 and y = 3
Step-by-step explanation:
It is given that,
4x + 5y = 7 -----(1)
3x – 2y = –12 ----(2)
To find the value of x and y
eq(1) * 3 ⇒
12x + 15y = 21 ----(3)
eq(2) * 4 ⇒
12x - 8y = -48 ---(4)
eq(3) - eq(4) ⇒
12x + 15y = 21 ----(3)
12x - 8y = -48 ---(4)
0 + 23y = 69
y = 69/23 = 3
Substitute the value of y in eq(1)
4x + 5y = 7 ----(1)
4x + 5*3 = 7
4x = 7 - 15 = -8
x = -8/4 = -2
Therefore x = -2 and y = 3
Answer:
x = -2 and y = 3
Step-by-step explanation:
What is the purpose of this chart?
A. to show the populations of the largest cities in the world
B. to show the populations of major cities today
C. to show the populations of major cities in 1500
D. to show the populations of major cities in Europe
C. to show the populations of major cities in 1500
Answer:
C. to show the populations of major cities in 1500
Step-by-step explanation:
correct on edge
vertical angles must check all that apply
Vertical Angles have to be congruent and have the same vertex.
The correct options are:
B. Have the same vertex.
C. be congruent.
Step-by-step explanation:Vertical Angles--
These are formed by the intersection of two lines.When two lines intersect then four angles are formed such that each pair of the opposite angles are called vertical angles.The vertical angles have a common vertex.Since, one vertex is obtained when the lines intersect.They could never be adjacent angles.Also, they may be obtuse, acute or right angles.The measure of each of the vertical angles are always equal i.e. the angles are congruent.Solve this equation: m- 10 = -6
m=
Answer:
m=4
Step-by-step explanation:
add 10 to both sides m-10+10=-6+10
m=4
Answer:
Step-by-step explanation:
Mac is 5 feet tall and casts a 4 foot 6 inch shadow. At the same time, a nearby tree casts a 20
foot shadow
Which is the closest to the height of the tree?
I will convert feet to inches.
4 feet, 6 inches = 54 inches
20 feet = 240 inches
5/x = 54/240
Let x = closest height of tree
54x = 5(240)
54x = 1,200
x = 1200/54
x = 22.2222222222
The tree is about 22 feet tall.
Answer:
22 inches
Step-by-step explanation:
Height of Mac = 5 feet
Height of shadow of Mac = 4 foot 6 inches = [tex]4+\frac{6}{12}= 4.5[/tex] inches .
We are given that At the same time, a nearby tree casts a 20 foot shadow .
Let the height of the tree be x
ATQ
[tex]\frac{5}{4.5}=\frac{x}{20}[/tex]
[tex]\frac{5}{4.5} \times 20=x[/tex]
[tex]22.22=x[/tex]
Hence the height of the tree is approximately 22 inches .
Write 4.3125 as a fraction in simplest form and explain
Answer: [tex]\bold{\dfrac{69}{16}}[/tex]
Step-by-step explanation:
[tex]4.3125=\dfrac{43125}{10000}\\\\\\\dfrac{43125}{10000}\div\dfrac{625}{625}=\large\boxed{\dfrac{69}{16}}[/tex]
Solve the equation by completing the square. Round to the nearest hundredth if necessary. x^2 + 3x - 5= 0
Answer:
[tex]\large\boxed{x\approx-4.19\ \vee\ x\approx1.19}[/tex]
Step-by-step explanation:
[tex]x^2+3x-5=0\qquad\text{add 5 to both sides}\\\\x^2+3x=5\\\\x^2+2(x)(1.5)=5\qquad\text{add}\ 1.5^2=2.25\ \text{to both sides}\\\\x^2+2(x)(1.5)+1.5^2=5+2.25\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+1.5)^2=7.25\Rightarrow x+1.5=\pm\sqrt{7.25}\\\\x+1.5\approx\pm2.69\\\\x+1.5\approx-2.69\ \vee\ x+1.5\approx2.69\qquad\text{subtract 1.5 from both sides}\\\\x\approx-4.19\ \vee\ x\approx1.19[/tex]