Which is an equivalent expression for 4 times d raised to the negative third power all over quantity 22 times d raised to the ninth power end quantity? 88 over d raised to the twelfth power 2 over quantity 11 times d raised to the twelfth power end quantity negative 2 over quantity 11 times d raised to the sixth power end quantity 0.2d12
The expression "4 times d raised to the negative third power all over quantity 22 times d raised to the ninth power end quantity" or 4d^(-3)/(22d^9) is equivalent to "2 over quantity 11 times d raised to the twelfth power end quantity" or 2/(11d^12).
An algebraic expression is a number, variable, or the combination of both and operational symbols.
To determine the equivalent of the expression "4 times d raised to the negative third power all over quantity 22 times d raised to the ninth power end quantity" or simply 4d^(-3)/(22d^9), combine all like terms and perform the necessary operations.
Using the following rules of exponents:
Quotient Rule for Exponents : a^m/a^n = a^(m - n)
Negative Exponent Rule : a^-m = 1/a^m
Simplify the expression.
4d^(-3)/(22d^9)
⇒ (4/22) [d^(-3)/d^9]
⇒ (2/11) [d^(-3 - 9)]
⇒ (2/11) d^-12
⇒ 2/(11d^12)
Hence, the equivalent expression is "2 over quantity 11 times d raised to the twelfth power end quantity" or 2/(11d^12).
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Answer:
2 over quantity 11 times d raised to the twelfth power end quantity" or 2/(11d^12).
Step-by-step explanation:
Use the properties of logarithms to evaluate each expression. log₁₅ 25+log₁₅9
Expression is [tex]log_{15}25[/tex] + [tex]log_{15} 9[/tex] = 2
The properties of logarithms are
log ab = log a + log b
log a/b = log a - log b
Evaluating it:
[tex]log_{15} 25[/tex] + [tex]log_{15} 9[/tex]
= [tex]log_{15} 25*9[/tex]
= [tex]log_{15} 225[/tex]
= [tex]log_{15}15^{2}[/tex]
= 2[tex]log_{15} 15[/tex]
= 2 × 1
= 2
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(25 points) Please help me I'm stuck on these 3 questions.
[tex] \bf\bigg( - 3 \frac{1}{4} d + \frac{3}{5} \bigg) - \bigg(2 \frac{7}{8} d + \frac{7}{10} \bigg)[/tex]
[tex] \bf \longrightarrow \boxed{ - \frac{49}{8}d - \frac{1}{10} } \: {\underline{\underline{ans}}}[/tex]
Step-by-step explanation:[tex] \bf \longrightarrow \bigg( - 3 \frac{1}{4} d + \frac{3}{5} \bigg) - \bigg(2 \frac{7}{8} d + \frac{7}{10} \bigg)[/tex]
[tex] \bf \longrightarrow \bigg( - \frac{4 \times 3 + 1}{4} d + \frac{3}{5} \bigg ) - \bigg(\frac{8 \times 2 + 7}{8} d + \frac{7}{10} \bigg)[/tex]
[tex] \bf \longrightarrow\bigg( \frac{ - 13}{4}d + \frac{3}{5} \bigg) - \bigg( \frac{23}{8}d + \frac{7}{10} \bigg)[/tex]
[tex] \bf \longrightarrow \frac{ - 13}{4}d + \frac{3}{5} + \frac{ - 23}{8} d + \frac{ - 7}{10} [/tex]
[tex] \bf \longrightarrow \bigg( \frac{ - 13}{4}d + \frac{ - 23}{8}d \bigg) + \bigg( \frac{3}{5} + \frac{ - 7}{10} \bigg)[/tex]
[tex] \bf \longrightarrow \bigg( \frac{(2 \times - 13) + (1 \times - 23) }{8}d \bigg) + \bigg( \frac{(2 \times 3) + (1 \times - 7)}{10} \bigg)[/tex]
[tex] \bf \longrightarrow \bigg( \frac{ (- 26) + ( - 23)}{8}d \bigg) + \bigg( \frac{(6) + ( - 7)}{10} \bigg) [/tex]
[tex] \bf \longrightarrow\bigg( \frac{ - 26 - 23}{8} d\bigg) + \bigg( \frac{6 - 7}{10} \bigg)[/tex]
[tex] \bf \longrightarrow\frac{ - 49}{8}d + \frac{ - 1}{10} [/tex]
[tex] \bf \longrightarrow \boxed{ - \frac{49}{8}d - \frac{1}{10} } \: {\underline{\underline{ans}}}[/tex]
4) Which expression is equal to[tex] \bf\bigg( - 2 \frac{1}{2} n + \frac{1}{4} \bigg) + \bigg(3 \frac{3}{4} n - \frac{5}{8} \bigg)[/tex]
[tex] \bf \longrightarrow \boxed{\frac{5}{4}n - \frac{3}{8} } \: {\underline{\underline{ans}}}[/tex]
5) Which expression is equal to[tex] \bf\frac{1}{5}(3x + 10) - \frac{11}{15}x[/tex]
[tex] \bf \longrightarrow \boxed{\frac{-2}{15}x + 2} \: {\underline{\underline{ans}}}[/tex]
Step-by-step explanation:[tex] \bf\longrightarrow\frac{1}{5}(3x + 10) - \frac{11}{15}x[/tex]
[tex] \bf\longrightarrow\frac{1}{5}(3x) + \frac{1}{5}(10) + \frac{-11}{15}x[/tex]
[tex] \bf\longrightarrow\frac{3}{5}x + 2 + \frac{-11}{15}x[/tex]
[tex] \bf\longrightarrow\bigg(\frac{3}{5}x + \frac{-11}{15}x\bigg) + 2[/tex]
[tex] \bf \longrightarrow \boxed{\frac{-2}{15}x + 2} \: {\underline{\underline{ans}}}[/tex]
b. What is another equation in point-slope form of the line through the points (-5,0) and (0,7) ? Explain.
0 - 7 = 7/5(-5 - 0) is the another equation in point-slope form of the line through the points (-5,0) and (0,7)
What is a slope of line?A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.
The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.
Therefore,
m = y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.
Be aware that tan ∅ = y/x
We also refer to this tan as the line's slope
If we reverse the point (-5,0) and (0,7) as (0,7) and (-5,0) line we will get another equation for (-5,0) and (0,7)
We know that point-slope form = y₂ - y₁ = m(x₂ - x₁)
But first we will find slope(m)
We know that slope = m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
For the pairs of points (0,7) and (-5,0)
⇒ m = [tex]\frac{0- 7}{-5 - 0}[/tex]
⇒ m = [tex]\frac{7}{5}[/tex]
⇒ m = 7/5
After we substitute the given information we get
0 - 7 = 7/5(-5 - 0)
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1, Find the difference
63-93
2, Find the difference
-4-5
3, Find the difference
-156-(-45)
Answer:
63-93=-30
-4-5=-9
-156-(-45)=-111
Step-by-step explanation:
63-93=-30
-4-5=-9
-156-(-45)=-156+45=-111
Hope this helps!
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Alexi walks 27 meters south and 38 meters east to get around a lake. Her sister swims directly across the lake. How many meters to the nearest tenth did Alexi's sister save by swimming?
Alexi’s sister saved about 18.4 meters by swimming across the river.
In this question,
Alexi walks 27 meters south and 38 meters east to get around a lake. Her sister swims directly across the lake.
The south and east directions are perpendicular.
The distance across the south, east and across the river form a right triangle, with the distance across the river as hypotenuse of right triangle.
Let x be the distance across the river.
Using Pythagoras theorem,
27² + 38² = x²
729 + 1444 = x²
2173 = x²
x = 46.6
The distance saved would be the difference between the sum of the two legs of the triangle and the hypotenuse (distance across the river).
distance saved = (27+38) - 46.6
= 18.4
Therefore, Alexi’s sister saved about 18.4 meters by swimming across the river.
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Write the first four terms of an arithmetic sequence with a common difference of 3 and a third term of 10 . Then write both a recursive definition and an explicit formula for this sequence.
The first fur terms of an arithmetic sequence are 4, 7, 10, 13
What is a arithmetic sequence?
It is a series of numbers where the gap between succeeding phrases is always the same. for instance, 5, 7, 9, 11, 13, and 15. An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d.
Given, common difference = 3
third term = 10
formula of arithmetic sequence is an = a + (n-1)d
a3 = a + (3-1)3
10 = a + 6
a = 4
a1 = 4
a2 = a + (n-1)d
a2 = 4 + (1)3
a2 = 7
a4 = a + 3d
a4 = 4 + 3.3
a4 = 13
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I am 3 units less than -3
Hi!
your answer is 0
hope this helps!
What is each number in scientific notation?
Drag the answer into the box to match each number.
Answer: the 1st one is 8.55 X 10^-5 the second one is 8.55 X 10^5
Step-by-step explanation:
when the decimal goes to the left, the exponents it's negative; when it's to the right, the exponent is positive. so one the 1st problem the decimal moved 5 spaces to the left giving it the value of 8.55 X 10^-5
Choose the equation that represents the graph.
PLS NEED FAST IF CORRECT ILL AWARD U
y = −2x − 4
y = 2x + 4
y = −2x + 4
y = 2x − 4
Answer:
y=-2x - 4
Step-by-step explanation:
The slope is 2 and the y-intercpt is -4
A car gets miles per gallon of gas. It travels for 45 minutes at miles per hour. How many gallons of gas does the car use during that time? Show your work using units and Giant Ones.
Answer:
A car gets 25 miles per gallon of gas. It travels for.45 minutes at 65 miles per hour. How many gallons of gas does the car use during that time?
Answer:
25 miles per gallon of gas
travels 45 minutes and 65 miles per hour
Step-by-step explanation:
100%
Tia left at 4:30 p.m. to drive to school. It took her 25 minutes to drive there.
What time did Tia get to school? Move numbers to the clock to show the time.
URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answer: The decimal moves 9 places left- 1.322 x 10^-9
Step-by-step explanation:
Answer: The decimal moves 9 places left 1.322 x 10^9 so option 5
Step-by-step explanation:
Solve each formula for the indicated variable. v = s² + 1/2 s h , for h
The solution of the formula v = s² + 1/2sh for the indicated variable h is 2(v - s²)/s.
According to the given question.
We have a formula v = s² + 1/2sh.
Since, we have to solve the above formula v = s² + 1/2sh for the indicated variable h.
Therefore, the solution of the above formula v = s² + 1/2sh for the indicated variable h is given by
v = s² + 1/2sh
⇒ v - s² = 1/2sh (subtracting s² from both the sides)
⇒ 2(v - s²) = sh (multiplying both the sides by 2)
⇒ 2(v - s²)/s = h (dividing both the sides by s)
⇒ h = 2(v - s²)/s
Hence, the solution of the formula v = s² + 1/2sh for the indicated variable h is 2(v - s²)/s.
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Name the property of real numbers illustrated by the equation. -(a-b) = (-1)(a-b)
The equation -(a-b) = (-1)(a-b) has used the property of real numbers is Distributive Property.
Property of Real numbers:
A real number is a value that represents a quantity along a continuous number line. Real numbers can be ordered.
The properties of real numbers are,
Commutative propertyAssociative propertyDistributive propertyIdentity propertyGiven,
The equation is
-(a-b) = (-1)(a-b)
Now we have to find the property used here.
Based on the properties of real number,
The one that exactly matches the equation is Distributive property.
Because the definition of Distributive property is explained through the following,
For three numbers m, n, and r, which are real in nature, the distributive property is represented as:
m (n + r) = mn + mr
The same will be applied in the given equation also.
Therefore, the Distributive property is used in the equation.
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2,2y÷3-5y^2÷3+5y^3÷2,-4÷3+2y^2-y÷2,5y^2÷3+3y^3+3y+6÷5
Answer:
27#(2828282(2(282)2828282828282827
How many ways can five of the nine U.S supreme court justices agree? (With solution)
Mathematics: Combinations and Permutations
The number of ways can five of the nine us supreme court justices agree is 3024 ways.
How to compute the value?The number of ways that five of the nine us supreme court justices agree will be calculated thus:
= 9! / 5!
= (9 × 8 × 7 × 6 × 5 × 4 × 3 × 2) / (5 × 4 × 3 × 2)
= 3024
There'll be 3024 ways.
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Determine whether y varies directly with x. if so, find the constant of variation k. 6y = 2x
Given the equation 6y = 2x, y varies directly with x and the constant of variation k has a value of 1/3.
There are two kinds of variations: direct and inverse.
Direct variation is a linear function defined by an equation of the form y = kx where variable y varies directly as x. On the other hand, inverse variation is a nonlinear function defined by an equation in the form y = k/x where variable y varies inversely as x.
Transforming 6y = 2x into a function of y,
y = 2/6 x
y = 1/3 x
where k = 1/3
Notice that it resembles the form y = kx which describes a direct variation between x and y.
Hence, the equation 6y = 2x shows that y varies directly with x and k = 1/3.
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Katherine is very interested in cryogenics (the science of very low temperatures).
With the help of her science teacher she is doing an experiment on the affect of low
temperatures on bacteria. She cools one sample of bacteria to temperature of -51°C
and another to -76°C. What was the temperature difference in the two experiments?
Temperature difference of experiments is -25°C.
Step-by-step explanation:
Given that
Katherine is very interested in cryogenics (the science of very low temperatures).With the help of her science teacher she is doing an experiment on the affect of low temperatures on bacteria.She cools one sample of bacteria to temperature of -51°C and another to -76°C.To find
Temperature difference in the two experimentsSo, according to the question
we have,
Temperature of 1st experiment = -51°C, andTemperature of 2nd experiment = -76°CWe have to find Temperature difference of experiments
So, we can say that
Temperature difference of experiments
= Temperature of 2nd experiment - Temperature of 1st experiment
Now, putting the all given values,
We, will get
Temperature difference of experiments = -76 - (-51)
= -76+51
= -25°C,
Answer:
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The red snake is 12 inches long. It is 3 times as long as the green snake. Let n represent the green snake. Which number sentence below will solve for n?
A 3x6 inches = 18 inches
B 12 inches x 3 = 36 inches
C 12 inches divided 3= 4 inches
D 12 inches divided 4 = 3 inches
Answer: Your answer would be C.
Step-by-step explanation:
4 x 3 is 12 so, if you divide the 12 by 3 you will get 4 making C your answer.
Mr. Delgado gets paid $40 per breaking
gig. If he has $120 saved, how many
breaking gigs will it take him to have
$400 if he doesn't spend any money?
Write AND Solve the Equation.
Answer:
7
Step-by-step explanation:
→ Write the equation
40x + 120 = 400
→ Minus 120 from both sides
40x = 280
→ Divide by 40 on both sides
x = 7
The number of breaking gigs that it takes him to have is $400 will be 7 breaking gigs.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Mr. Delgado gets paid $40 per breaking gig. If he has $120 saved. If he doesn't spend any money.
Then the number of breaking gigs that it takes him to have is $400 will be
40x + 120 = 400
Simplify the equation then we have
40x = 280
x = 280/40
x = 7
The number of breaking gigs that it takes him to have is $400 will be 7 breaking gigs.
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For each function, find the y -intercept
y=-3(x+2)²-4 .
Answer:
-16
Step-by-step explanation:
The y-intercept is when x=0.
[tex]y=-3(0+2)^2-4 \\ \\ =-3(4)-4 \\ \\ =-16[/tex]
Write a two-column proof for each case of Theorem 10.6 Case 3
Given: P lies outside
Prove: m< ABC = 1/2m AC
The measure of an inscribed angle is one-half the measure of the central angle.
What is the inscribed angle and the circumscribed angle?An inscribed angle in geometry is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle formed by two given points on a circle at a given point on the circle.
The measure of an inscribed angle is one-half the measure of the central angle. The measure of a circumscribed angle is 180 degrees minus the measure of the central angle.
Given: P lies outside
m ∠ABC = m ∠DBC – m ∠DBA ( Addition Postulate, Subtraction Property of Equality)
m ∠DBC = m 1/2(arc DC)
m ∠DBA = m 1/2(arc DA) (The measure of an inscribed ∠ whose side diameter is half the measure of the intercepted arc (Case 1)).
m ∠ABC = m 1/2 (arc DC) – m 1/2(arc DA) (Substitution)
m ∠ABC = 1/2 [m(arc DC) – m(arc DA)] (Factor)
m(arc DA) + m(arc AC) = m(arc DC) (Arc Addition Postulate)
m(arc AC) = m(arc DC) – m(arc DA) (Subtraction Property of Equality)
m ∠ABC = m 1/2 (arc AC) (Substitution)
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A soccer team brings a 4.5 -gallon cooler of water to their games. How many 4 -ounce cups can the team drink per game?
The number of 4 -ounce cups that the team can the team drink per game is 144.
It is given in the question that the soccer team brings a 4.5 gallon cooler of water to their games.
We have to find the number of 4 -ounce cups that the team can drink per game.
We know that,
1 gallon = 128 ounces
Hence, we can write,
4.5 gallon = 128*4.5 = 576 ounces
Hence, by using unitary method, we can write,
Number of 4 ounce cups the team can fill per game = ounces in 4.5 gallons/ounces in a cup = 576/4 = 144 cups.
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Simplify by combining like terms.
5+10 s-8 s
By combining the like terms, the simplified form of the expression 5+10s-8s is 2s+5
Given,
The algebraic expression = 5+10s-8s
Combine the like terms
5+10s-8s = 5+2s
Simplified form is 2s+5
Hence, by combining the like terms, the simplified form of the expression 5+10s-8s is 2s+5
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what property is 0x = 0
Answer:
Additive Identity Property of 0
Step-by-step explanation:
It means that additive identity is "0," as adding 0 to any number gives the sum as the number itself.
60 POINTS AND BRAINLIE$T
Is this table linear? I need help!
Given from the table below, Is the table linear or nonlinear?
Answer:
The table is linear because as x increases by 1, y changes by an average rate of |2|. You can also notice the tables both end in |+1|, which shows that the table has a constant rate of change between the two points at the end. Thus, the table is linear. If the table was nonlinear, there would be no constant rate of change between the 2 sets of data.
3. If the ratio of yellow pigment to blue pigment in a shade of green paint is 2:3, how many
drops of yellow pigment will be needed if 12 drops of blue are used?
Drops of yellow pigment is 8.
A ratio is a comparison of two identical values that makes it simple to compare them. This is how a fraction with a numerator and denominator comparison is expressed. Depending on the ratio formula employed in various parts of mathematical computation, the definitions of the numerator and denominator may change.
For a certain shade of green, y = yellow and b = blue, where y/b = 2/3.
How many yellow drips are needed if there are 12 drops of blue,
y/b = 2/3 = x/12
= 2 × 12 = 3 × x
= 24 = 3x
= 24/3 = x
= x = 8
If you have 12 droplets of blue, you will need 8 drops of yellow.
y/b = 2/3
y = 2/3 × b
Substituting the value b = 12
y = 2/3 × 12
y = 24/3 = 8
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Find the 10 th term of each geometric sequence. a₉ =-5, r=-1/2
The 10th term of the geometric sequence as described in the task content is; 5/2.
What is the 10tg term of the geometric sequence as given in the task content?It follows from the task content that the 10th term of the sequence is to be determined.
On this note, since the 10th term differs from the 9th term by a factor of r, common ratio.
Hence; a(10) = a(9) × r
= -5 × (-1/2)
a(10) = 5/2.
Ultimately, the 10th term is; 5/2.
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K
A woman traveled 2436.5 miles in 18 hours 15 minutes. Find the average speed of her flight in miles per hour. (Change
18 hours 15 minutes into hours and use the formula d=rt.)
The average speed of the woman's flight was mph.
(Do not round until the final answer. Then round to the nearest tenth of a mile per hour as needed?
Answer:
133.5
This is because transfer it to hours nd then divide and this is what you get
