The quotient of the given problem using laws of exponents is; 6 * 10⁰
How to use the law of exponents?
We want to express the quotient of the quantity 30 times ten raised to the negative twenty fourth power end quantity divided by the quantity 5 times ten raised to the negative twenty fourth power end quantity.
This is;
(30 * 10⁻²⁴)/(5 * 10⁻²⁴)
Now, we can break this down into like terms to get;
(30/5) * (10⁻²⁴/10⁻²⁴)
= 6 * 1
Now, 1 can also be written as;
10⁰ = 1
Thus, the solution of the given problem is; 6 * 10⁰
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Question 38.
Write the first six terms of the arithmetic sequence with the first term, a1 = 240, and common difference, d= 24.
The first six terms are a1 = ,a3= , a4= ,a5= , and a6= .
[tex]a(1) = 240 \\ a(2) = a(1) + d = 240 + 24 = 264 \\ a(3) = a(2) + d = 264 + 24 = 288 \\ a(4) = a(3) + d = 288 + 24 = 312 \\ a(5) = a(4) + d = 312 + 24 = 336 \\ a(6) = a(5) + d = 336 + 24 = 360[/tex]
two vertices of an obtuse triangle are $(6,4)$ and $(0,0)$. the third vertex is located on the negative branch of the $x$-axis. what are the coordinates of the third vertex if the area of the triangle is 30 square units?
Since the third vertex is located on the negative branch of the x-axis, the coordinates of the third vertex of this triangle is equal to (-15, 0).
The types of triangle.In Geometry, there are different types of triangle based on the length of their sides and angles, and these are;
Equilateral triangleScalene triangleIsosceles triangleObtuse triangleRight-angled triangleHow to calculate the area of a triangle?Mathematically, the area of a triangle can be calculated by using this formula:
Area = 1/2 × b × h
Where:
b is the base area.h is the height.Note: The height of this triangle is the y-axis of (6, 4).
Substituting the given parameters into the formula, we have;
Area = 1/2 × b × h
30 = 1/2 × b × 4
2b = 30
b = 30/2
b = 15 units.
Since the third vertex is located on the negative branch of the x-axis, the coordinates of the third vertex of this triangle is equal to (-15, 0).
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Complete Question:
Two vertices of an obtuse triangle are (6,4) and (0,0). The third vertex is located on the negative branch of the x-axis. What are the coordinates of the third vertex if the area of the triangle is 80 square units?
What is the distance between -6 2/3 and 4 1/3 on a number line, in units?
Select ALL that apply.
The distance between the points = |-6 2/3 - 4 1/3| = |-20/3 - 13/3| = |-33/3| = |-11| = 11 units.
How to Find the Distance between Two Points on a Number Line?The distance between two points on a number line is the absolute difference between their coordinates.
Given the following points are on a number line:
-6 2/3 and 4 1/3
The distance between the points = |-6 2/3 - 4 1/3|
The distance between the points = |-20/3 - 13/3|
The distance between the points = |(-20 - 13)/3|
The distance between the points = |-33/3| = |-11|
The distance between the points = 11 units.
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you perform an experiment to determine how many breaths a fish takes per minute. your experiment yields the following data: minute 1:65 breaths; minute 2:73 breaths; minute 3:67 breaths; minute 4:71 breaths; minute 5:62 breaths. calculate the average number of breaths that a fish takes per minute.
The average breaths taken per minute by the fish is 22.53. This is obtained using the previous knowledge of average.
What do you mean by average?
An average is a single number that is used to represent an entire group of things. Averages are calculated by dividing the sum of all values by the total number of values.
Calculation of average number of breaths taken by a fish per minute
Given:
Breaths in 1 minute are 65
Breaths in 2 minutes are 73
Breaths in 3 minutes are 67
Breaths in 4 minutes are 71
Breaths in 5 minutes are 62
Total breaths = 65 + 73 + 67 + 71 + 62
= 338
Total time taken = 1 + 2 + 3 + 4 +5
= 15 minutes
The average number of breaths = total breaths / total time taken
= 338 / 15
= 22.53 breaths per minute
Hence, the average breaths taken per minute by the fish is 22.53.
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Which relation is a function?
Can someone help me please?!!!
Answer:
The second one is a function.
Step-by-step explanation:
The other 3 have one-to-many mappings.
For example the first relation has 1 mapping to 2, 3, 4 and 5.
from the top of a 160-ft lighthouse, the angle of depression to a ship in the ocean is 26°. how far is the ship from the base of the lighthouse? (round your answer to the nearest foot.)
The distance of ship from the base of the lighthouse is 328.54m, as found with the help of angle of depression.
What is Angle Of Depression?The angle of depression is the angle formed by the horizontal line and the horizontal line's observation of the item. When we know the angles and the distance of an object from the ground, it is primarily utilized to find the distance between the two objects.Given:
Height of lighthouse = 160 feetAngle of depression = 26°To find: Distance of ship from the base of the lighthouse.
Finding:
Let 'x' be the distance of the ship from the base of the lighthouse and θ be the angle of depression.
Then, tanθ = [tex]\frac{160}{x}[/tex]
=> x = [tex]\frac{160}{tan26}[/tex]
=> x = [tex]\frac{160}{0.487}[/tex]
=> x = 328.54m
Hence, The distance of ship from the base of the lighthouse is 328.54m, as found with the help of angle of depression.
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7. The top of a tree is 35 feet above ground level. The roots reach down 22 feet below ground
level. What is the difference between the top of the tree and the bottom of the roots?
Answer:
57?
Step-by-step explanation:
35-(-22)
Rewrite: [tex]15\frac{1}{6}[/tex]% as a decimal. Round to the nearest thousandths.
Answer:
15.17
Step-by-step explanation:
Multiply whole number by denominatorAdd product to the numeratorDivide the sum by the denominatorRound your number to the neaests thousandthPls help I dont get this
Answer:
Step-by-step explanation:
In 2006, the population of the country was 33.3 million. This represented an increase in population of 6.5% since 2001. What was the population of the country in 2001? Round to the nearest hundredth of a million.
The population of the country in 2001 to the nearest hundredth of a million is 24.31 million
What was the population in 2001?If the population grows by 6.5% every year, the population grows at a compound rate. The equation that can be used to determine the population in 2001 would be an exponential equation. The equation that can be used to represent an exponential equation is: a = [tex]mx^{b}[/tex]
When a population grows at a compound rate, it means that both the existing population and the increase in the population increase by 6.5 every year.
The equation that can be used to determine the population of Tacoma in 2017 is:
P = FV / (1 + r)^n
Where:
FV = Future value P = Present populationR = rate of growthN = number of years : 2006 - 2001 = 533.3 / ( 1 + 0.065)^5
33.3 / (1.065^5) = 24.30503 million
In order to round 24.30503 million to the nearest hundredth , look at the thousandth figure, if it is greater or equal to 5, add one to the hundredth digit and change the thousandth digit to 0. So, 24.30503 million becomes 24.31 million
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Pls show steps on how u got the answer and thank u
Answer:
A=3
Step-by-step explanation:
-7a+28=7
subtract 28 from both sides to eliminate it from the first side
-7a=-21
Two negatives equals a positive
7a=21
divide both sides by 7
a=3
HELP ME PLEASE!!!!
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WITH QUESTION A!
Answer:
Cohesion and Adhesion. The complementary action of these two forces allows water to rise in a narrow capillary tube such as the xylem tissues of plants.
Step-by-step explanation:
Cohesion: the water molecules attract each other and are responsible for the surface tension of water.
Adhesion: the water molecule is also able to attract other non-water molecules. This allows water to be able to ‘cling’ to the sides of a capillary tube.
The complementary action of these two forces allows water to rise in a narrow capillary tube such as the xylem tissues of plants.
please let me know if you need a deeper/ more complex explanation, i am always happy to help :)
What is 943,158,670.3491 rounded to the 100 millions? PLEASE ANSWER ASAP!
Answer:
I believe the answer is 943,158,670.349
Step-by-step explanation:
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!
3+9(5)
8
2 is equal to
Answer:768
Step-by-step explanation:
(PLEASE HELP) -5 - (-5/3)
Answer:
steps
-5-5(-5/3)
=-5-(-25)
=10/3
=3 1/3
Step-by-step explanation:
Grace has read 2 chapters in each of her 9 books. How many chapters has read in all
Answer:18
Step-by-step explanation:2*9=18 hope this helps
Answer:
18 chapters have been read in total.
Step-by-step explanation:
What is the slope of the line that passes through the points (1,-6) and (-2,-8) ?
We can conclude that the slope of the line is (-2, -3).
What do we mean by the slope?The slope of a line indicates its steepness. The slope is calculated mathematically as "rise over run" (change in y divided by change in x).The formula of slope: y₂ - y/x₂ - x₁
Put the values in the formula as follows:
y₂ - y/x₂ - x₁-8 - (-6)/-2 -1-2/-3Therefore, the slope of the line is (-2, -3).
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try these using the above pattern, find the value of the following. (i) 73 – 63 (ii) 123 – 113 (iii) 203 – 193 (iv) 513 – 503
The value of the given question by using the above pattern is (i)127, (ii)397, (iii)1141, (iv)7651.
What do you mean by pattern?In the real world, in artificial design, or in abstract concepts, a pattern is a regularity. As a result, a pattern's components repeat in a predictable way. Any of the senses can directly witness patterns, which are types of patterns made of geometric shapes and frequently repeated like wallpaper designs. On the other hand, abstract patterns in science, math, or language might only be visible through analysis. In actuality, direct observation entails recognizing visual patterns, which are common in both nature and art. Natural visual patterns are frequently chaotic, hardly ever precisely repeat, and frequently contain fractals. Spirals, meanders, waves, foams, tilings, fissures, and patterns produced by rotational and reflective symmetries are examples of natural patterns.
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The image of the point (2, -3)under a translation is (1, -6)Find the coordinates of the image of the point (9, -5)under the same translation.
The image of the point (2, -3)under a translation is (1, -6). the coordinates of the image of the point (9, -5)under the same translation is (9,-8).
With the aid of mirror-related concepts, we will first build a diagram of the image position in order to determine the coordinates of the image location. We will use trigonometry to determine the necessary coordinates after sketching the diagram.
Without needing to change its orientation, a translation relocates an item from its original location on the coordinate grid.
An illustration of a transformation is translation. A transformation is a technique for moving or repositioning a shape.
Image of the point (2,-3)
under the translation (2,-6)
2+a=2
a=2-2
a=0
-3+b=-6
b=-6+3
b=-3
By applying the translation (x+0,y-3) to (9,-5)
(9+0,-5-3)
(9,-8)
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Write an
inequality that represents the
temperatures (in degrees Fahrenheit)
of the interior of the iceberg.
-20°C to
-15°C
The inequality representation can be expressed as: -4 < x < 5
Representation of real number into inequality.An inequality is a mathematical connection that exists between two expressions and may be expressed by one of the following:
"greater than >" "less than < ""less than or not equal to ≤: "greater than or equal to" ≥:From the given expression, the conversion of °C to F is estimated by using the formula:
(°C × 9/5) + 32
For -20°C , we have:
= (-20°C × 9/5) + 32
= -4 F
For -15°C, we have:
= (-15°C × 9/5) + 32
= 5 F
Therefore, this can be represented in inequality form as: -4 < x < 5.
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K'
Write the coordinates of the vertices after a reflection over the x-axis.
304
-10 4
L'=
M'=
6
-8
0
4
2
2
6
Answer:can you right It all together?
Step-by-step explanation:
A cell phone company charges an initial price of $500 for a new phone and then $60 each month after the purchase. if c (t) is a rational function that represents the average monthly cost of owning the cell phone, what is the range of the function? (2 points) r: (0, 500) r: (60, 560) r: ℠r: (−[infinity], [infinity])
The range of the given function is: (500, ∞).
What is the range of a function?The collection of potential output values for a function is known as its range.
Now,
Given:
Initial price of the cell phone = $500Monthly charge = $60Let 't' be the number of months. Then, the function C(t) can be calculated as:
C(t) = 500 + 60t
For range:
The minimum value will be when t = 0, i.e., when no charge has been charged by for each month.
Thus, C(0) = 500 + 60(0)
=> C(0) = 500
The maximum value will be when t = ∞, i.e., for infinite number of months.
=> C(∞) = 500 + 60(∞)
=> C(∞) = 500 + ∞
=> C(∞) = ∞
Thus, the range of the function will be: (500, ∞).
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How many lines appear in a square
Answer: 4?
Step-by-step explanation:
1. Find the value of two numbers if their sum is 12 and their difference is 4.
Answer:
8 and 4
Step-by-step explanation:
Answer:
8+4
Step-by-step explanation:
8-4 is equal to 4 and 4+8 is equal to 12
Find the difference
-8 - 3
Answer:
-11
Step-by-step explanation:
Starting at -8 you subtract three, meaning you go three numbers lower which would be -11.
9. Royanne determined that it cost her $.75 a day to make her own lunch
for school. If she ate in the cafeteria, lunch would cost $2.25. In five days,
how much money would Royanne save by bringing her own lunch to
school?
O $5.50
O $7.50
$9.50
Select the correct answer. What is this expression in simplified form? 2√2-7√18 OA 18√5 OB. 84√2 OC. 84 OD. 14sqrt6
The expression in simplified form is -19√2
How to write this expression in simplified form?The expression is given as:
2√2 - 7√18
Express 18 as 9 * 2
So, we have:
2√2 - 7√18 = 2√2 - 7√(9 * 2)
Take the square root of 9
2√2 - 7√18 = 2√2 - 7 * 3√2
This gives
2√2 - 7√18 = 2√2 - 21√2
Evaluate the difference
2√2 - 7√18 = -19√2
Hence, the expression in simplified form is -19√2
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A regular hexagon is divided into 6 congruent triangles. If the perimeter of the hexagon. is 48 centimeters, what is the height of each triangle?
A 4 \mathrm{~cm}
B 4 \sqrt{3} \mathrm{~cm}
C 6 \sqrt{3} \mathrm{~cm}
D 8 \mathrm{~cm}
E 8 \sqrt{3} \mathrm{~cm}
Answer:Your answer would be E
Step-by-step explanation:8 times 6 would be 48
The measure of height of each triangle will be 4√3 cm. Then the correct option is B.
What is the perimeter of the regular polygon?All the sides of the regular polygon are congruent to each other. The perimeter of the regular polygon of n sides will be the product of the number of the side and the side length of the regular polygon.
P = (Side length) x n
A regular hexagon is divided into 6 congruent triangles. If the perimeter of the hexagon is 48 centimeters.
Then the Side length of each triangle will be given as,
48 = (Side length) x 6
Side length = 8 cm
Then the measure of the height of each triangle will be calculated as,
tan 60° = h / (8 / 2)
√3 = h / 4
h = 4√3 cm
The measure of height of each triangle will be 4√3 cm. Then the correct option is B.
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You move up 2 units and down 5 units. You end at (5, -4). Where did you start?
Answer:
(5,-1)
Step-by-step explanation:
a train is travelling at a speed of 90 miles per hour. the driver of the train plans on maintaining this speed for the next 120 miles, plus or minutes 15 miles. find the minimum and maximum numbers of hours the train will travel at that speed.
The minimum and maximum numbers of hours the train will travel at that speed are 1.17 and 1.5
How to find the minimum and maximum numbers of hours the train will travel at that speed?The given parameters are
Speed = 90 miles per hour
Current speed = next 120 miles, plus or minutes 15 miles.
Let the time travelled be x
So, we have the following equation
Speed * Time = Distance
This gives
|90x - 120| =15
Remove absolute bracket
90x - 120 = ±15
Add 120 to both sides
90x = 120 ±15
This gives
90x = (120 - 15, 120 + 15)
Evaluate
90x = (105, 135)
Divide by 90
x = (1.17, 1.5)
Hence, the minimum and maximum numbers of hours the train will travel at that speed are 1.17 and 1.5
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