123,000,000 as a multiple of a power of 10 is 1.23 x 10⁸.
What is power of 10?The large values when shortened, they are written in the form of power of 10 by shifting decimals.
123,000,000 has eight zeroes to reduce and taken to the power of 10. Put decimal after counting eight digits from the right.
123,000,000 can be written as 1.23 x 10⁸.
Thus, 123,000,000 as a multiple of a power of 10 is 1.23 x 10⁸.
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To express 123,000,000 as a multiple of a power of 10, we identify it as 1.23 x 10^7.
The question asks to express 123,000,000 as a multiple of a power of 10. To do this, we need to understand how exponents of 10 work. The exponent tells us how many zeros are added to the right of 1 to create the number. For instance, 10^2 equals 100 because there are two zeros.
In the case of 123,000,000, we count the zeros following the initial digit(s). There are 7 zeros. Therefore, we can express 123,000,000 as 1.23 x 10^7. Here, 1.23 is the coefficient (a value greater than or equal to 1 but less than 10), and 10^7 indicates that the decimal point in 1.23 is moved 7 places to the right to get the original number, 123,000,000.
This method of notation is commonly used in scientific notation, which simplifies large numbers by expressing them as a multiple of a power of 10. It's a useful way to work with very large or very small numbers efficiently.
Joanne is making punch. She uses 1/2 gallon of orange juice, 3 quarts of
lemonade, and 11/4 gallons of apple cider. How many quarts of punch will she
have all together? **Remember 4 quarts=1 gallon.
Your answer
Answer:
1/2 gallon=2 quarts plus 3 quarts so 5 quarts then 11/4 would be 11 quarts so 11+2+3=16 quarts
Step-by-step explanation:
If the 11/4 part is confusing you on how many quarts it actually is it simply means that for every 4 quarts you get a gallon and you have 11 quarts so you can also look at it as 2 3/4 gallons if that somehow clarifies it.
156 times 0.20 times 6
Answer: 187.2
Step-by-step explanation:
Answer:
187.2
Step-by-step explanation:
A cylinder has a diameter of 5 centimeters and a height of 50 millimeters. Which of the following steps should be done first in order to find the surface area of the cylinder?
convert the diameter and the height to the same unit
determine the radius and multiply by 2
calculate the circumference of the circle
multiply the circumference of the circle by the height of the cylinder
Answer:
B determine the radius and multiply by 2pi
Step-by-step explanation:
Answer:
The first guy is rite. ♥☻
what is the length of a rectangle whose perimeter is 140 ft if its width-to-length is 2 : 5
Answer:
50 ft.
Step-by-step explanation:
It is given that the ratio of width-to-length is 2 : 5.
Let,
Width = 2x ft
Length = 5x ft
Perimeter of the rectangle is
[tex]Perimeter=2(lenght+width)[/tex]
[tex]Perimeter=2(5x+2x)[/tex]
[tex]Perimeter=2(7x)[/tex]
[tex]Perimeter=14x[/tex]
It is given that the perimeter of the rectangle is 140 ft.
[tex]14x=140[/tex]
Divide both sides by 14.
[tex]x=10[/tex]
The value of x is 10.
[tex]Length=5x=5\times 10=50[/tex]
Therefore, the length of the rectangle is 50 ft.
A flying disc has has a circumference of 81.64 cm what is the area of the flying disc used 3.14 for pie
Answer:
530.66 cm squared
Step-by-step explanation:
c = 2(3.14)r
81.64 = 2(3.14)r
Divide both sides by 6.28
The radius is 13
a = 3.14(13 squared)
a = 530.66
Answer: 530.39 cm²
Step-by-step explanation:
C=2πr, Substitute 81.64 in for C then divide 2π t get 12.99. A=πr². Plug in 12.99 for r, solve, and get 530.39 cm
Which dimensions can create only one unique triangle?
three angles measuring 25 degrees, 65 degrees, and 90 degrees
three angles measuring 50 degrees, 50 degrees, and 50 degrees
three sides measuring 5 in., 12 in., and 14 in.
three sides measuring 4 ft, 8 ft, and 14 ft
Three sides measuring 5 in., 12 in., and 14 in.
Explanation:First of all, you need to know some facts about every triangle:
FIRST FACT:
If two sides of a triangle are [tex]a \ and \ b[/tex], then the third side must be less than [tex]a+b[/tex]. Why? because if its length is exactly [tex]a+b[/tex], then you can't build up a triangle, but you'll have a line segment. In other words:
[tex]a<b+c \\ \\ b<a+c \\ \\ c<a+b[/tex]
SECOND FACT:
The internal angles of any triangle add up to 180°. So if ∠A, ∠B and ∠C are the internal angles of a triangle, then:
[tex]\angle A +\angle B+ \angle C=180^{\circ}[/tex]
__________________________
So let's analyze each case:
Case 1. Three angles measuring 25 degrees, 65 degrees, and 90 degrees :
[tex]\angle A=25^{\circ} \\ \\ \angle B=65^{\circ} \\ \\ \angle C=90^{\circ} \\ \\ \\ \angle A +\angle B+ \angle C=25^{\circ}+65^{\circ}+90^{\circ}=185^{\circ} \neq 180^{\circ}[/tex]
The sum is greater than 180 degrees, so these angles can't form a triangle
Case 2. Three angles measuring 50 degrees, 50 degrees, and 50 degrees [tex]\angle A=50^{\circ} \\ \\ \angle B=50^{\circ} \\ \\ \angle C=50^{\circ} \\ \\ \\ \angle A +\angle B+ \angle C=50^{\circ}+50^{\circ}+50^{\circ}=150^{\circ} \neq 180^{\circ}[/tex]The sum is less than 180 degrees, so these angles can't form a triangle
Case 3. Three sides measuring 5 in., 12 in., and 14 in. [tex]a=5 \\ \\ b=12 \\ \\ c=14 \\ \\ \\ 5<12+14\rightarrow 5<26 \\ \\ 12<5+14 \rightarrow 12<19 \\ \\ 14<5+12 \rightarrow 14<17[/tex]The inequalities are true, so these sides form a triangle.
Case 4: Three sides measuring 4 ft, 8 ft, and 14 ft
[tex]a=4 \\ \\ b=8 \\ \\ c=14 \\ \\ \\ 4<8+14\rightarrow 4<22 \\ \\ 8<4+14 \rightarrow 8<18 \\ \\ 14<4+8 \rightarrow 14<12 \ NOT \ TRUE![/tex]
Since the third inequality is not true, then we can't form a triangle with these sides.
[tex]f(x)=16t^2+32t[/tex]The function f(x)=-16t^2+32t represents the height of a pumpkin t seconds after it is launched from a catapult. When does the pumpkin reach its maximum height? What is the maximum height of the pumpkin?
Answer:
- time = 1second
- maximum height = 16m
Step-by-step explanation:
Given the height of a pumpkin t seconds after it is launched from a catapult modelled by the equation
f(t)=-16t²+32t... (1)
The pumpkin reaches its maximum height when the velocity is zero.
Velocity = {d(f(x)}/dt = -32t+32
Since v = 0m/s (at maximum height)
-32t+32 = 0
-32t = -32
t = -32/-32
t = 1sec
The pumpkin reaches its maximum height after 1second.
Maximum height of the pumpkin is gotten by substituting t = 1sec into equation (1)
f(1) = -16(1)²+32(1)
f(1) = -16+32
f(1) = 16m
The maximum height of the pumpkin is 16m
What would 6×6×6 equal with an exponent
Answer:
6³
Step-by-step explanation:
Answer:
6^3
Step-by-step explanation:
6*6*6
The base is 6
There are 3 sixes multiplied together so the exponent is 3
Which of the following is a simpler way to write StartFraction cosine theta Over sine theta EndFraction?
A. Tan E
B. Sec E
C. Csc E
D. Cot E
Pls help me with this problom asap!!!!
Answer:
4 1/2. Root 18 simplifies to 4.242640687, which is less than 4.50
Answer:
4and 1/2
Step-by-step explanation:the square for of 18 is 4.24264 and 4 and a half is 4.5
Please Help
Solve for the missing side (z)
This homework is making me crazy!
What is another name for Angle 2?
Lines EH and DF intersect at point G. Angle 2 is formed by line segments DG and GE and angle 1 is formed by line segments EG and GF.
a. Angle DGE
b. Angle GED
c. Angle EGF
d. Angle GEF
Answer:
a is the answer
Step-by-step explanation:
In the given scenario, angle 2 is formed by line segments DG and GE. Another name for angle 2 is Angle DGE (Option a).
What is the angle?Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
As mentioned in the question, Lines EH and DF intersect at point G. Angle 2 is formed by line segments DG and GE, and angle 1 is formed by line segments EG and GF. So angle 2 is constituted by segments jointly as DGE.
Thus, Another name for angle 2 is Angle DGE (Option a).
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What is 5/15+3\5=? For the sum
Answer:
14/15
Step-by-step explanation:
make both bases the same number
5/15 + 9/5
add like normally
14/15
Answer:
14/15 is your answer
Step-by-step explanation:
An angle measures 156° less than the measure of its supplementary angle. What is the measure of each angle?
Answer:
12° and 168°
Step-by-step explanation:
If x is the angle, and y is the supplementary angle, then:
x + y = 180
x = y − 156
Solve the system of equations using substitution:
y − 156 + y = 180
2y = 336
y = 168
Plug back into either equation to find x:
x = 12
Final answer:
The measure of angle A is 12° and the measure of its supplementary angle B is 168°. This is determined by setting up the equation based on the property that the sum of supplementary angles is 180°.
Explanation:
The question asks to find the measures of two supplementary angles when one angle is 156° less than the other. Supplementary angles sum up to 180°. Let's designate angle A as the unknown angle and angle B as its supplementary angle. According to the given information, angle B is 156° more than angle A. Therefore, we can set up the equation A + B = 180°, where B = A + 156°.
Solving the equation A + (A + 156°) = 180° gives us 2A + 156° = 180°, and when we subtract 156° from both sides, we get 2A = 24°. Dividing both sides by 2 will give us A = 12°. To find angle B, we add 156° to angle A, resulting in B = 12° + 156°, which equals 168°.
Therefore, angle A is 12° and angle B is 168°. These are the measures of the two supplementary angles.
I have 5 math question
1: A zoo measured the height, in feet, of 9 giraffes?
18, 16, 22, 14, 17, 19, 15, 19, 22
A.16ft
B.17ft
C.18ft
D.19ft
----------------------------------------------------------------------------------------------------------------------------
2: This table shows the size, in acres, of four large water parks. What is the median of the sizes of the four water parks?
A.60 acres
B.63 acres
C.64 acres
D. 65 acres
----------------------------------------------------------------------------------------------------------------------------
3: What is the median of the ages in this stem-and-leaf plot?
A.43
B.45
C.46
D.47
----------------------------------------------------------------------------------------------------------------------------
4: What is the median of this data in this stem-and-leaf plot?
A.21
B.22
C.23
D.24
----------------------------------------------------------------------------------------------------------------------------
5: What is the median of the data set represented by the dot plot?
( )
The answer for question 1 is C. 18ft
for question 2 is B. 63ft
for question 3 is B. 45
and for question 4 is C. 23
Lastly for question 5 the answer is 14
What is the equation of the line that is perpendicular to the
given line and passes through the point (3, 4)?
Answer:
I am pretty sure that the answer is
y = 3x -2
Step-by-step explanation:
given a line with slope m then the slope of a line perpendicular to it is
where m is the slope and b the y-intercept
I hoped this helped!!!
Answer: y=3x-5
Step-by-step explanation:
Got ot right on my test!!
i need help with this
plz anwswer right away ill mark you brainiest if done.
Answer:
4 x 2 x 3
Step-by-step explanation:
[tex]l = 4\\\\w = 2\\h = 3\\[/tex]
Answer:
you can solve this by finding the volume of the block
Step-by-step explanation
V= lxwxh
= 3x4x2
= 24
therefore there are 24 blocks in this figure
Have a great day
Given that (3,3,-2) is a solution to the given system, which of the following statements are possibly true of the system? Check all the boxes that apply.
Answer: the system is consistent
The system is independent
Step-by-step explanation:
Nancy rode her bike for 154
miles on Saturday. On Sunday,
she rode 0.7 fewer miles. How
many miles did she ride on
Sunday?
Answer:
153.3
Step-by-step explanation:
154-0.7
Answer:
153.3
Step-by-step explanation:
154.0-0.7=153.3
Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number.
N(t)=⎧⎩⎨⎪⎪⎪⎪f(t)25t+150200+80t2+0.05tfor0≤t<6for6≤t<8fort≥8
The number of fish in a pond at time t years is modeled by the function N defined above, where f is a continuous function such that f(0)=80.
(a) Find limt→∞N(t). Explain the meaning of limt→∞N(t) in the context of the problem.
(b) Is the function N continuous at t=8 ? Justify your answer.
(c) The function N is continuous at t=6 . Is there a time t , for 0≤t≤6 , at which N(t)=250 ? Justify your answer.
Answer:
See Below
Step-by-step explanation:
The function is a piecewise function defined as:
[tex]N(t)=\left \{ {{25t+150} \ 0 \leq t \leq 6 \atop {\frac{200+80t}{2+0.05t} \ t \geq 8}} \right.[/tex]
a)
We need to find the limit of the function as t goes to infinity. This means what is the max value of fish in the pond given times goes to infinity (on an on).
We will take the 2nd part of the equation since t falls into that range, t is infinity, which is definitely greater than 8.
[tex]\lim_{t \to \infty} \frac{200+80t}{2+0.05t} \\\lim_{n \to \infty} \frac{80t}{0.05t}\\ \lim_{n \to \infty} \frac{80}{0.05} =1600[/tex]
This means the maximum number of fish at this pond is 1600, no matter how long it goes on.
b)
A function is continuous at a point if we have the limit and the functional value at that point same.
Functional value at t = 8 is (we use 2nd part of equation):
[tex]\frac{200+80t}{2+0.05t}\\\frac{200+80(8)}{2+0.05(8)}\\=350[/tex]
We do have a value and limit also goes to this as t approaches 8.
So, function is continuous at t = 8
c)
We want to find is there a "time" when the number of fishes in the pond is 250, during t from 0 to 6. We plug in 250 into N(t) and try to find t. Make sure to use the 1st part of the piece-wise function. Shown below:
[tex]N(t)=25t+150\\250=25t+150\\25t=250-150\\25t=100\\t=4[/tex]
The time is 4 years when the number of fishes in the pond is 250
One gallon of water weighs 8.34 pounds. How much does 6 gallons of water weigh? Show your work, including labeling your answer with the appropriate units of measure
Answer:
50.04 pounds
Step-by-step explanation:
If 1 gallon weighs 8.34 pounds,
all you have to do is multiply 8.34 by 6
to get what 6 gallons would weigh.
To determine the weight of 6 gallons of water, multiply the weight of one gallon (8.34 pounds) by 6. Thus, 6 gallons of water weigh 50.04 pounds.
To find out how much 6 gallons of water weigh, you simply need to multiply the weight of one gallon by the number of gallons.
Since we know that one gallon of water weighs 8.34 pounds, the calculation is as follows:
6 gallons × 8.34 pounds/gallon = 50.04 pounds.
Therefore, 6 gallons of water weigh 50.04 pounds.
What is the product?
Answer:
5/4k^2
Step-by-step explanation:
P=5\dfrac{k}{6}\times \dfrac{3}{2k^3}.
We will be using the following property of exponents:
\dfrac{a^x}{a^y}=a^{x-y}.
We have
P\\\\\\=5\dfrac{k}{6}\times\dfrac{3}{2k^3}\\\\\\=\dfrac{5}{6}\times\dfrac{3}{2}k^{1-3}\\\\\\=\dfrac{5}{4}k^{-2}=\dfrac{5}{4k^2}.
Thus, the required product is \dfrac{5}{4k^2}.
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Answer: 5/4k^2
Step-by-step explanation:
Just multiply the fractions then simplify by a common factor of 3, then cancel out the common variable of k
The area of a triangle is 40 square centimeters. The height is 10 centimeters. What is the length of the base of the triangle?
Answer:
20cm.
Step-by-step explanation:
so the answer is 8cm
Hope this will help u...
Can someone help with this
Answer:
50
Step-by-step explanation:
YOU WILL GET BRAINLIST!!!!!!!!!1111
Rewrite the following fraction as a decimal. 4/5
The answer is 0.8. What I did was I put 4 divided by 5 in my calculator
Answer:
0.8
Step-by-step explanation:
First, we have to find out what 1/5 is, so we divide 1 by 5:
Divide:
1/5=.2
Multiply by 4:
.2 times 4= .8
I hope this helps u pls give a brainliest and a thx ;)
Part B
The hospital is 3.1 miles west of the fire station. What is the length of a straight line between the school and the hospital? Round to the nearest tenth. Enter your answer in the box.
miles
Answer:
Part A) The length of a straight line between the school and the Fire Station is [tex]4.6\ miles[/tex]
Part B) The length of a straight line between the school and the hospital is [tex]2.1\ miles[/tex]
Step-by-step explanation:
The complete question in the attached figure
Let
The positive x-coordinates ----> East
The positive y-coordinates ----> North
The negative x-coordinates ----> West
The negative y-coordinates ----> South
take the point A (0,0) as the Middle School (reference point)
Part A) we have
Town Hall is located 4.3 miles directly east of the Middle School
so
The coordinates of Town Hall are B(4.3,0)
The Fire Station is located 1.7 miles directly North of Town Hall
so
The coordinates of Fire Station are C(4.3,1.7)
What is the length of a straight line between the school and the Fire Station?
Remember that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
A(0,0) and C(4.3,1.7)
substitute
[tex]d=\sqrt{(1.7-0)^{2}+(4.3-0)^{2}}[/tex]
[tex]d=\sqrt{(1.7)^{2}+(4.3)^{2}}[/tex]
[tex]d=4.6\ miles[/tex]
Part B) we have that
The hospital is 3.1 miles west of the fire station
so
The coordinates of the hospital are D(4.3-3.1,1.7)
D(1.2,1.7)
What is the length of a straight line between the school and the hospital?
Remember that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
A(0,0) and D(1.2,1.7)
substitute
[tex]d=\sqrt{(1.7-0)^{2}+(1.2-0)^{2}}[/tex]
[tex]d=\sqrt{(1.7)^{2}+(1.2)^{2}}[/tex]
[tex]d=2.1\ miles[/tex]
what fraction multiplied by itself is equal to 4/25
Answer:
2/5 times 2/5 equals 4/25
Step-by-step explanation:
Lashonda bought some books for $6 each and received a discount of $8 off of her total purchase. She spent $58 after the discount. How many books did she buy?
Write an equation that could be used to answer the question above. Let b represent the number of books. Solve for b
Answer:
6b - 8 = 58
6b = 66
b = 11
Each book costs $11.
Lashonda bought 11 books.
To solve this problem, we can set up an equation based on the information given. Let [tex]\( b \)[/tex] represent the number of books Lashonda bought. Each book costs $6, so the total cost before the discount is [tex]\( 6b \)[/tex]. Lashonda received a discount of $8 off of her total purchase, and she spent $58 after the discount. Therefore, the equation representing the total cost before the discount minus the discount equals the amount she spent is:
[tex]\[ 6b - 8 = 58 \][/tex]
Now, we solve for [tex]\( b \)[/tex]:
[tex]\[ 6b = 58 + 8 \][/tex]
[tex]\[ 6b = 66 \][/tex]
[tex]\[ b = \frac{66}{6} \][/tex]
[tex]\[ b = 11 \][/tex]
So, Lashonda bought 11 books.
A parabola can be represented by the equation x2 = -20y.
What are the coordinates of the focus of the parabola?
Answer:
[tex]\mathrm{Parabola\:focus\:given}\:x^2=-20y:\quad \left(0,\:-5\right)[/tex]
Step-by-step explanation:
Given the equation
[tex]x2 = -20y[/tex]
A parabola is the locus of points such that the distance to a point the focus equals the distance to a line the directrix.
[tex]4p\left(y-k\right)=\left(x-h\right)^2[/tex] is the standard equation for an up-down facing parabola with vertex at (h, k), and a focal length |p|.
so
[tex]x^2=-20y[/tex]
[tex]\mathrm{Switch\:sides}[/tex]
[tex]-20y=x^2[/tex]
[tex]\mathrm{Factor\:}4[/tex]
[tex]4\cdot \frac{-20}{4}y=x^2[/tex]
[tex]4\left(-5\right)y=x^2[/tex]
[tex]\mathrm{Rewrite\:as}[/tex]
[tex]4\left(-5\right)\left(y-0\right)=\left(x-0\right)^2[/tex]
[tex]\left(h,\:k\right)=\left(0,\:0\right),\:p=-5[/tex]
Parabola is symmetric around the y-axis and so the focus lies a distance\ p from the center (0, 0) along the y-axis.
[tex]\left(0,\:0+p\right)[/tex]
[tex]=\left(0,\:0+\left(-5\right)\right)[/tex]
[tex]\mathrm{Refine}[/tex]
[tex]\left(0,\:-5\right)[/tex]
Therefore,
[tex]\mathrm{Parabola\:focus\:given}\:x^2=-20y:\quad \left(0,\:-5\right)[/tex]
Please check the attached figure too.
The focus of the parabola given by the equation x2 = -20y is at the coordinates (0,-5). This is calculated by finding the value of 'p' in the standard form x2 = 4py.
The equation x2 = -20y is notably a form of the parabola equation known as standard form. This version of a parabola equation is defined in the form x2 = 4py (or it could be y2 = 4px), where p is the distance from the vertex to the focus (and also to the directrix).
In the given equation, x2 = -20y, comparing it with the standard form, we find 4p = -20 by observing the coefficient of 'y'. Solving for 'p', we get p = -20/4 = -5. This means the focus of the parabola is (0,-5), because for a parabola that opens downwards (since 'p' is negative), the focus is located at the coordinates (h, k-p), where 'h' and 'k' are the coordinates of the vertex (which is the origin (0,0) in this case).
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If I like geometry, then I like math.
Choose the equivalent statement
Answer:
C
Step-by-step explanation:
If you don't like math you don't like geometry because geometry is math. Just like if you like geometry you like math because geometry is math
Answer:
C
Step-by-step explanation:
Since geometry is math, then if you don’t like math, you won’t like geometry.