it is already rounded
Write the number shown in standard form and expanded notation
Given:
Standard form and expanded notation
Find-:
The number shown in standard form and expanded notation
Explanation-:
The standard form is
Standard form = The standard form is
[tex]abcde=a.bcde\times10^4[/tex]For example, is
[tex]5326.6=5.3266\times10^3[/tex]The expanded form is
The expanded = Expanded form is a way to write a number by adding the value of its digits. We can use a place value chart to determine the value of a number's digits.
For example
[tex]7229=7000+200+20+9[/tex]I need to find the volume and surface area of this 3d composite figure
Volume:
To find the volume we notice that this figure is made of a cube minus a cone.
The volume of a cube is given as:
[tex]V=l^3[/tex]Here the length of each side is 6 cm.
The volume of a cone is given as:
[tex]V=\frac{1}{3}h\pi r^2[/tex]here the radius of the cone is 2 cm (half the diameter shown) and its height is 6 cm.
Hence the volume of the composite figure is:
[tex]V=(6)^3-\frac{1}{3}(6)\pi(2)^2=190.87[/tex]Surface area:
The surface area of the figure is the surface area of the cube minus the surface area of the cone.
The surface area of the cube is given by:
[tex]SA=6l^2[/tex]in this case the lenght of each side is 6 cm.
The surface area of the cone is given by:
[tex]SA=\pi r^2+\pi rl[/tex]where r is the radius of the cone and l is the slant height. The radius of the cone is 2 cm. To find the slant height we need to remember that this slant height is the hypotenuse of a right triangle with one leg equal to the radius and the other leg equal to the height of the cone. Then, using the pythagorean theorem we have:
[tex]\begin{gathered} l^2=2^2+6^2 \\ l^2=4+36 \\ l=\sqrt[]{40} \end{gathered}[/tex]Once we have all the values we need we have that the surface area is:
[tex]SA=6(6)^2-\pi(2)^2-\pi(2)(\sqrt[]{40)}=163.70[/tex]Summing up we have that:
• The volume is 190.87 cubic cm.
,• The surface area is 163.70 squared cm.
Examine the following graph, where exponential function P(x) undergoes a transformation.The preimage of the transformation is labeled P(x), and the image is labeled I(x). 2 exponentially decreasing functions. P of x passes through (0,1) & has a horizontal asymptote at y=0. I of x has same horizontal asymptote & passes through (0, 9).© 2018 StrongMind. Created using GeoGebra. What is the function rule for I(x) that represents this transformation?
Solution
The answer is
Answer:
I(x)=9⋅P(x)
Step-by-step explanation:
I just did the workbook.
Solve the following simultaneous equation using elimination or substitution method
Answer:
(15, 10) and (10, 15)
Explanation:
The given system of equation is
x + y = 25
xy = 150
To solve the equation, we will use the subtitution method, so first, we need to solve the first equation for y
x + y = 25
x + y - x = 25 - x
x y= 25 - yx
Then, substitute y = 25 - x on the second equation, we get
xy = 150
x(25 - x) = 150
x(25) - x(x) = 150
25x - x² = 150
Now, we can rewrite the equation as
25x = 15 + x²
0 = 150 + x² - 25x
0 = x² - 25x + 150
Therefore, we need to find the values of x that satisfies
x² - 25x + 150 = 0
Now, we need to factorize this equation, so two numbers that multiply to 150 and add to -25 are -15 and -10. Then
(x - 15)(x - 10) = 0
So, the solutions are
x - 15 = 0
x = 15
or
x 10 = 0
x = 10
Then, the values of y are
If x = 15
y = 25 - x
y = 25 - 15
y = 10
If x = 10
y = 25 - x
y = 25 - 10
y = 15
Therefore, the solutions are (15, 10) and (10, 15)
I
will the square root of 42 be closer to 6 or 7? why?
The square root of 42 is written mathematically as:
[tex]\sqrt[]{42}[/tex][tex]\sqrt[]{42}=\text{ }6.48[/tex]We can round 6.48 to the
Solve the equation:
√x+8=2
(square root of x+8)
The solution of the given equation is x = -4.
An algebraic expression is an expression which should include at least one variable connected by at least a single arithmetic operator. These operators can be addition(+), subtraction(-), multiplication(*) or division(/).
an algebraic equation or polynomial equation is an equation of the form
where p = 0
where P is a polynomial with coefficients in some field, often the field of the rational numbers. For many authors, the term algebraic equation refers only to univariate equations, that is polynomial equations that involve only one variable. On the other hand, a polynomial equation may involve several variables. In the case of several variables (the multivariate case), the term polynomial equation is usually preferred to algebraic equation.
We have given that √x+8= 2
To remove the root on the left side of the equation square both sides of equation.
so we get x+8= 4
by solving the equation we will get x= -4.
Thus the solution of the given equation is x= -4.
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Evaluate the expression how do you get to (2^-1 x 3^0)^3 times (2^0 x 5^3) ^5
we have the expression
[tex](2^{-1}\cdot3^0)^{-3}\cdot(2^0\cdot5^3)^5[/tex]Remember that
[tex]\begin{gathered} 2^{-1}=\frac{1}{2} \\ 3^0=1 \\ 2^0=1 \\ 5^3=125 \end{gathered}[/tex]substitute in the original expression
[tex]\begin{gathered} (\frac{1}{2}\cdot1)^{-3}\cdot(1\cdot125)^5 \\ (\frac{1}{2}\cdot)^{-3}\cdot(125)^5 \end{gathered}[/tex][tex]\begin{gathered} (\frac{1}{2})^{-3}=2^3=8 \\ \end{gathered}[/tex]substitute
[tex]\begin{gathered} 8\cdot(125)^5 \\ 8\cdot30,517,578,125 \\ 244,140,625,000 \end{gathered}[/tex]therefore
The answer is
244,140,625,000What are the coordinates of Y if (5, 12) is 1/3 of the way from X to Y?
Answer:
Step-by-step explanation:
The coordinates of point Y are (9 , 12)
Step-by-step explanation:
* Lets explain how to solve the problem
- If point (a , b) divides a line whose end points are (c , d) and (e , f) at
ratio p : q from the point (c , d), then
and
∵ Segment XY has one endpoint at X (0 , 0)
∵ Point (3 , 4) is 1/3 of the way from X to Y
∴ Point (3 , 4) divides the segment XY, where the distance from X
to the point (3 , 4) is 1 part and from point (3 , 4) to Y is 2 parts
∴ Point (3 , 4) divides segment XY to the ratio 1 : 2 from X
- Let point (a , b) is (3 , 4)
- Let point (c , d) is X (0 , 0)
- Let point (e , f) is Y
- Let p : q = 1 : 2
* Lets find e and f
∵
∴
∴
- Multiply both sides by 3
∴ 9 = e
∴ The x-coordinate of point Y is 9
∵
∴
∴
- Multiply both sides by 3
∴ 12 = f
∴ The y-coordinate of point Y is 12
* The coordinates of point Y are (9 , 12)
Which statement best describes the areas and perimeters of the figures?
O They have the same area and same perimeter.
O
They have the same area but different perimeters.
They have different areas but the same perimeter.
O They have different areas and different perimeters.
Statement (D) "they each have unique perimeters and areas" best describes the areas and perimeters of the figures.
What are the area and perimeter?The measurement that expresses the size of a region on a plane or curved surface is called an area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.A closed path that encompasses, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.So, according to the given image, we can easily conclude that both the figures have different areas and different perimeters.
Therefore, statement (D) "they each have unique perimeters and areas" best describes the areas and perimeters of the figures.
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The correct question is given below:
Which statement best describes the areas and perimeters of the figures below?
Figures 1 and 2 both have the same perimeter but have different numbers of units inside of the shape.
A. They have the same area and the same perimeter.
B. They have the same area but different perimeters.
C. They have different areas but the same perimeter.
D. They have different areas and different perimeters.
Find the slope intercept form of a line with a slope of -5 and goes through the point(1,9)
Answer:
y=-5x +14
Explanation:
Given a point on the line and the slope, we can obtain the equation of the line using the formula:
[tex]y-y_1=m(x-x_1)[/tex]In this case:
[tex]\begin{gathered} \text{Slope, m=}-5 \\ (x_1,y_1)=(1,9) \end{gathered}[/tex]Substitution in the formula above gives:
[tex]\begin{gathered} y-9=-5(x-1) \\ y-9=-5x+5 \\ y=-5x+5+9 \\ y=-5x+14 \end{gathered}[/tex]Note that the slope-intercept form of a line is given as: y=mx+b.
Where:
• m=slope
,• b=y-intercept
The price of regular rice is $1 per pound; that of premium rice is $2. Mix 300 pounds
of regular rice with 400 pounds of premium rice. What is the price of the mixture?
Answer:
1200 dollars
Step-by-step explanation:
2x400 is 800 + 1x400 =1200
Find the length of the shorter leg of a right triangle if the longer leg is 3 feet more than the shorter leg and the hypotenuse is 3 feet less
than twice the shorter leg.
The length of the shorter leg of the right triangle is 6 feet.
What is a right triangle?A right triangle is one that has an interior angle of 90 degrees. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The height and base make up the two arms of the right angle. A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a specific angle, and its "adjacent" side is the one that faces the angle in question.So, the formula of the hypotenuse: c = √a²+b²
Let, the shorter leg be 'x' and the larger leg be 'x+3' and the hypotenuse be '2x-3'.Now, put these values in the formula as follows:
c = √a²+b²2x-3 = √(x+3)²+x²2x-3 = √x² + 3² + x²2x-3 = 2x+3= 6So, the length of the shorter leg of the right triangle is 6 feet.
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Find the perimeter of the window to the nearest hundredth. 3ft
Answer:
7.71
Step-by-step explanation:
1/2 pi * 3 + 3
3.14 * 3 = 9.42
1/2 of 9.42 = 4.71
4.71 + 3 = 7.71 ft
What is the rectangular form of the parametric equations?x(t)=t+3, y(t)=2t^2−4, where t is on the interval [−4,0].Enter your answer, in standard form, by filling in the boxes.
1. Solve t in the first equation:
[tex]\begin{gathered} x=t+3 \\ t=x-3 \end{gathered}[/tex]2. Substitute the t in the second equation by (x-3):
[tex]\begin{gathered} y=2t^2-4 \\ y=2(x-3)^2-3 \end{gathered}[/tex]3. Write the equation you get in previous step in standard form:
[tex]\begin{gathered} (a-b)^2=a^2-2ab+b^2 \\ \\ y=2(x^2-2*x*3+3^2)-3 \\ y=2(x^2-6x+9)-3 \\ y=2x^2-12x+19-3 \\ \\ y=2x^2-12x+16 \end{gathered}[/tex]To find the inverval of x use the equation x=t+3 and the interval of t
[tex]\begin{gathered} t\lbrack-4,0\rbrack \\ x=t+3 \\ x=-4+3=-1 \\ x=0+3=3 \\ \\ x\lbrack-1,3\rbrack \end{gathered}[/tex]Answer:[tex]\begin{gathered} y=2x^2-12x+16 \\ \lbrack-1,3\rbrack \end{gathered}[/tex]Determine the domain and range of (g ○ f)(x) if f of x is equal to 4 over the quantity x squared minus 4 end quantity and g(x) = x + 2.
For the function (gof)(x) the Domain is {x∈ R| ,x ≠ –2, 2} , the Range is {(–∞, 1)∪(2, ∞)} .
In the question ,
it is given that
the function f(x) is given as "4 over the quantity x squared minus 4" ,
which means
f(x)=4/(x²-4)
and g(x)=x+2
we know ,
(gof)(x) = g(f(x))= f(x) + 2
= 4/(x²-4) + 2
taking LCM as (x²-4) and solving further ,
we get
= [tex]\frac{4+2x^{2} -8}{x^{2} -4}[/tex]
= (2x²-4)/(x²-4)
the fraction is defined only when the denominator is non zero,
So for Domain
x²-4 ≠ 0
x² ≠ 4
x ≠ +2,-2
So, the domain is all real numbers except the numbers 2,-2 .
For Range , the graph of the function (gof)(x) is plotted below ,
From the graph we can see that the function does not have any value from y=1 to 2 .
So, the Range will be R={(∞, 1)∪(2, ∞)}.
Therefore , for the function (gof)(x) ,the Domain is {x∈ R| ,x ≠ –2, 2} , the Range is R:{(–∞, 1)∪(2, ∞)} .
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in order to store your suitcase in the overhead compartment the girth must not exceed 45 inches will you be able to store your suitcase in the overhead compartment explain and I don't have a frickin picture
Suitcase store 45 inches
Overhead
To estimate the height of a building, Ami walks 200 meters from its base and plants a 2m tall stick. Ami lines up the top of the building and the top of the stick. At this point, Ami is 5 meters from the stick. Estimate the height of the building if Ami's eye level is the ground. Show all work.
Using T- ratios, We concluded that the height of the building is 82m.
According to the given question,
the distance between stick and building is 200m,
height of the stick is 2m,
Ami is standing at 5m from the stick,
Let the height of the building = x
So, By observing the pictorial representation of the question through image attached,
And using T - ratios along with
we can conclude that
Tan A = Height of the building / distance between Ami and building
⇒ Tan A = x / 5 + 200 ......... (1)
Tan A = Height of the stick / Distance between Ami and stick
⇒ Tan A = 2 / 5 ............(2)
On equating (1) and (2)
x / 5 + 200 = 2 / 5
x / 205 = 2/5
x = 2/5 × 205
x = 82
∴ Height of the building is 82m
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Which of these is an example of combination?A. Selecting a president and a vice-president from a group of 8 members.B. Opening a combination lock.C. Picking a team of 5 people from a group of 15D. Arranging the letters of the word "mathematics without repetition.
By definition:
• a, combination, is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. ,In combinations, you can select the items in any order,.
• in ,permutations,, the order of the selected items is essential,. For example, the arrangements ab and ba are equal in combinations (considered as one arrangement), while in permutations, the arrangements are different.
From the list of examples we see that:
A) We select a president and a vice president, so order matters → permutation.
B) The order of the numbers of a lock's key matters → permutation.
C) The order of the members of the team doesn't matter → combination.
D) The order of the letter matters → permutation.
Answer: C
10. A mouse runs a distance of 2metres in 15 seconds. What is its speed?
We will use the formula;
speed = distance / time
from the question, d= 2 t=15
substitute the value into the formula:
speed = 2/15 = 0.13333 m/s
help meeeeeeeeeeeeeeeeeeeeeee
thank you
The function g(3) has a value of 0
How to determine the value of the function?The graphs represent the given parameters
The function definition is given as
g(3)
On the two graphs, we have the following highlights
First graph: The function of ySecond graph: The function of g(x)This means that we use the second graph to calculate the value of the function g(3)
The function g(3) means the value of x is 3
On the graph, we have
g(x) = 0 when x = 3
So, we have
g(3) = 0
Hence, the value of the function is 0
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1)There are fourteen shirts in your closet, four blue, five green, and five red. You randomly select one to wear. It is blue or green2)a magazine contains for teen pages.you open to a random page. The page number is eight to ten.find the probability
Given:
Total number of shirts is, N= 14.
Number of blue shirts is, n(b) = 4.
Number of green shirts is, n(g) = 5.
Number of red shirts is, n(r) = 5.
The objective is to find the probability of randomly selecting a blue shirt or green shirt.
The required probability ca be calculated as,
[tex]\begin{gathered} P(\text{blue or gr}een)=P(blue)+P(green) \\ =\frac{n(b)}{N}+\frac{n(g)}{N} \\ =\frac{4}{14}+\frac{5}{14} \\ =\frac{9}{14} \end{gathered}[/tex]Hence, the probability of randomly selecting a blue shirt or green shirt is 9/14.
Simplify 6.5/2 raised to the second power
What is the equation of the line that passes through the point (4,-7) and has a slope of -3
Answer: y=-3x+5
Step-by-step explanation:
1) List in a y = mx + b
y = -3x+b
2) Next fill in x and y with the points given
-7 = -3(4) + b
3) Solve
-7 = -3(4) + b
-7 = -12 + b
5 = b
4) Apply b to the y =mx + b
y=-3x+5
Answer: y= -3x +5
Step-by-step explanation:
Slope: y= mx+ b
m being the slope
b being the y intercept
You're given the slope, so you substitute m for -3
y=mx+b
y = -3x + b
You have the coordinates (4, -7) which you can substitute (the line passes through that point.)
-7 = -3(4) + b
-7 = -12 + b
+12 +12
5= b
y= -3x + b
Check:
-7 = -3(4) + 5
-7 = -12 + 5
-7 = -7
Answer the following.
(a) A certain solution has a hydrogen ion concentration of 6.53 x 10 moles per liter. Write this number in standard notation.
(b) An African bush elephant can weigh up to 28,000 pounds. Write this number in scientific notation.
Answer:
a) 65.3
b) 2.8 x [tex]10^{4}[/tex]
Step-by-step explanation:
a)
When you multiply by 10, you move the decimal 1 place to the right.
b)
You move the decimal so that the number will be between 1 and 10. You move the decimal point 4 places.
2.8 x [tex]10^{4}[/tex]
Which of the following are possible equations of a parabola that has no real solutions and opens downward?y > = -(x + 4)2 - 2y > = -(x + 4)2 + 2y > = -x2 - 2y > = (x - 4)2 + 2y > = -(x - 4)2 - 2
We have to identify the parabola that:
a) has no real solutions (it has complex roots).
b) opens downward.
The equations are in vertex form, so to have no real solutions and be downward, the vertex should have a value of y that is less than 0:
If the vertex had a value of y greater than 0, if it opens downward, there should be two values of x so that f(x) = 0. Then, this would be the real solutions.
The vertex form can be written as:
[tex]y=a(x-h)^2+k[/tex]where (h,k) are the coordinates of the vertex.
Then, we need k <= 0.
The equations that satisfy this are:
y = -(x + 4)² - 2
y = -x² - 2
y = -(x - 4)² - 2
The second condition is that the parabola opens downward. This means a quadratic coefficient "a" with negative value.
All this three equations satisfy this condition.
We can graph them and check if the conditions are satisfied:
Answer:
There are 3 equations that satisfy the two conditions:
y = -(x + 4)² - 2
y = -x² - 2
y = -(x - 4)² - 2
your solution as an inequality in the box below,using "<="fors or ">" for 2 if necessary
Help me!
Many black holes have diameters that are
relatively small, but those at the centers of
galaxies can have diameters of millions or
billions of kilometers. If two black holes have
each pair of diameters shown, is one of the
diameters 500 times the other?
Yes No
8 x 10^6 km and 4 x 10⁹ km ▢ ▢
2 x 10^7 km and 4 x 10^10 km ▢ ▢
1 x 10^8 km and 2 x 10^11 km ▢ ▢
3 x 10^10 km and 6 x 10^7 km ▢ ▢
5 x 10⁹ km and 1 x 10^6 km ▢ ▢
The correct option 8 x 10^6 km and 4 x 10⁹ km defines the diameter relation of 500 times to other for the black hole.
What is termed as the diameter?A circle's diameter would be any straight line segment which passes through center of a circle and has endpoints on the circle's circumference. The diameter also is known as the circle's longest chord.It is twice the length of the circle's radius. In other words, a circle's diameter is the line that runs through its center and divides it into two equal portions.For the given question;
There are black holes with very small diameters.
And also there are black holes with millions or billions of kilometres of diameter.
Now, the diameter of one black hole is 500 times the other.
Consider the first option;
Let the diameter of 1st black hole be 8 x 10^6 km.
Then, the diameter of 2nd black hole be 500 times of the 8 x 10^6 km.
= 500 × 8 x 10^6 km
= 4 x 10⁹ km
Thus, the option is the correct representation of the relation between both the diameters of black hole.
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How do I do this? , it doesn’t really explain
Given:
[tex]\sqrt{y^2}[/tex]To find:
The exponent of y
Explanation:
Using the exponential rule,
[tex]\begin{gathered} \sqrt{y^2}=y^{\frac{2}{2}} \\ =y^1 \end{gathered}[/tex]The exponent of y is 1.
Final answer:
The exponent of y is 1.
log base √2 8 = x . find the value of x
state if the givin binomial is a factor of the givin polynomial
19)
Given data:
The given polynomial is
[tex]x^3-5x^2-8x+8^{}[/tex]Substitute -2 for x in the above polynomial.
[tex]\begin{gathered} (-2)^3-5(-2)^2-8(-2)+8 \\ =-8-20+16+8 \\ =-4 \end{gathered}[/tex]As after substituting x=-2 in the polymial is not equal to zero.
Thus, (x+2) is not the factor of the polynomial
