Answer:
7p^15 / q^12
Step-by-step explanation:
7p^9+6 q^-5-7 / 3 #28 is divided by 12
7p^15 / q^12 #Answer
Answer:
7p^15/3q^12 is equivalent to 28p^9 q^-5/12p^-6 q^7
Step-by-step explanation:
Given Parameter:
28p^9 q^-5/12p^-6 q^7
Required; To simplify.
To simplify the above expression, we'll apply 2nd law of indices.
But first, let's rewrite the expression.
28p^9 q^-5/12p^-6 q^7 becomes
(28 * p^9 * q^-5) / (12 * p^-6 * q^7)
Then we collect similar indices. This is done as follows
(28/12) * (p^9/p^-6) * (q^-5/q^7)
From second law of indices (law of division);
If the two terms have the same base () and are to be divided their indices are subtracted.
For instance x^a/x^b = x^(a - b).
Applying this law; we have
(28/12) * (p^9/p^-6) * (q^-5/q^7) becomes
(28/12) * (p^(9 - (-6))) * (q^(-5-7))
(28/12) * (p^(9+6)) * (q^-12)
(28/12) * p^15 * q^-12
Simplify 28/12
(4*7)/(4*3) *p^15 * q^-12
(7/3) * p^15 * q^-12
(7/3) * p^15 * 1/q^12
7p^15/3q^12
Hence, 7p^15/3q^12 is equivalent to 28p^9 q^-5/12p^-6 q^7
The unicorns: Stardust, Umo, Windthorn and Highflyer are enjoying themselves playing in the forest. They notice 8 spiders in the tree, 5 cockroaches, 7 bees, 3 deer, 4 cows and a pair of antlers behind a bush. How many legs do all the numbered creatures amount to all together?
There are 188 legs in all
Step-by-step explanation:Let's solve this problem step by step:
1. First of all, there are 4 unicorns enjoying themselves playing in the forest, they are: Stardust, Umo, Windthorn and Highflyer are enjoying themselves playing in the forest. Each unicorn has 4 legs, so:
[tex]4 \ unicorns \times 4 \ legs=\boxed{16 \ legs}[/tex]
2. The unicorns notice 8 spiders in the tree, so each spider has 8 legs. Accordingly:
[tex]8 \ spider \times 8 \ legs=\boxed{64 \ legs}[/tex]
3. There are 5 cockroaches, so each cockroach has 6 legs. Accordingly:
[tex]5 \ cockroaches \times 6 \ legs=\boxed{30 \ legs}[/tex]
4. There are 7 bees, so each bee has 6 legs. Accordingly:
[tex]7 \ bees \times 6 \ legs=\boxed{42 \ legs}[/tex]
5. There are 3 deer, so each deer has 4 legs. Accordingly:
[tex]3 \ deers \times 4 \ legs=\boxed{12 \ legs}[/tex]
6. There are 4 cows, so each cow has 4 legs. Accordingly:
[tex]4 \ cows \times 4 \ legs=\boxed{16 \ legs}[/tex]
7. They notice a pair of antlers behind a bush, so this means there are 2 more deers, and each having 4 legs. Accordingly:
[tex]2\ deers \times 4 \ legs=\boxed{8 \ legs}[/tex]
7. They notice a pair of antlers behind a bush, so this means there are 2 deers, and each having 4 legs. Accordingly:
[tex]2\ deers \times 4 \ legs=\boxed{8 \ legs}[/tex]
Adding all the amounts of legs we have:
[tex]Total=16+64+30+42+16+12+8=\boxed{188 \ legs}[/tex]
x – 4 = 12.5 can be written in words as
Answer:
a number subtracted by four equals twelve and five tenths
Step-by-step explanation:
You have a map of an area in France. The scale used is 2cm:8km. You want to ride to a national park. The park is shown on the map as 16 cm away.
How far is that in kilometres?
Divide the distance on the map by 2 to get the number of 8km segments there are, then multiply that by 8km for total distance.
16 cm / 2cm = 8
8 x 8km = 64km total.
1. Graph the function f (x) =
The graph is attached.
Why?To solve the given piecewise function, we need to graph each of the functions that compound the main function with their respective domain restrictions.
So, solving we have:
- First function: Positive slope line (red line).
[tex]f(x)=x+1=y\\\\y=x+1, if x<0[/tex]
Let's find the axis intercepts in order to be able to graph the function.
Finding the x-axis intercept, we need to make "y" equal to 0, so:
[tex]y=x+1\\\\0=x+1\\x=-1[/tex]
So, we have that the x-axis intercept is located at the point (-1,0)
Finding the y-axis intercept, we to mate "x" equal to 0, so:
[tex]y=x+1\\\\y=0+1\\y=1[/tex]
So, we have that the y-axis intercept is located at the point (0,1)
Hence, we have that the function exists from the values of "x" less than 0 to the negative infinite or (-∞,0)
- Second function: Horizontal line (blue line).
[tex]y=2,if0\leq x\leq 1[/tex]
Since there is not variable, we know that it's a horizontal line that passes through y equal to 2.
Hence, we have that the function exists between the values of "x" from 0 to 1 or [0,1]
- Third function: Positive slope line (green line).
[tex]y=x,ifx>0[/tex]
Let's find the axis intercepts in order to be able to graph the function.
Finding the x-axis intercept, we need to make "y" equal to 0, so:
[tex]0=x+\\\\0=x+\\x=0[/tex]
So, we have that the x-axis intercept is located at the point (0,0)
Finding the y-axis intercept, we to make "x" equal to 0, so:
[tex]y=x\\\\y=0\\y=0[/tex]
We have that the function only pass through the point (0,0) or origin.
Hence, we have that the function exists from the values of "x" greater than 2.
So, the graph of the given function is attached.
Have a nice day!
Determine the equation of the line with the points (–13,10) and (16, 15).
[tex]\bf (\stackrel{x_1}{-13}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{16}~,~\stackrel{y_2}{15}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{15-10}{16-(-13)}\implies \cfrac{5}{16+13}\implies \cfrac{5}{29}[/tex]
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-10=\cfrac{5}{29}[x-(-13)] \\\\\\ y-10=\cfrac{5}{29}(x+13)\implies y-10=\cfrac{5}{29}x+\cfrac{65}{29}\implies y=\cfrac{5}{29}x+\cfrac{65}{29}+10 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=\cfrac{5}{29}+\cfrac{355}{29}~\hfill[/tex]
Between noon and 9pm the temperature dropped 10°F. If the temperature was -4°F at 9pm what was the temperature at noon ?
Answer:
6F
Step-by-step explanation:
Let x be the temperature at noon
dropping means we subtract
The temperature at 9 pm was -4. That goes on the right hand side of the equals
x-10 = -4
Add 10 to each side
x-10+10 = -4+10
x = 6
The temperature at noon was 6 F
Find x in the following right triangle.
Helppp
Answer:
15 ft
Step-by-step explanation:
Use Pythagorean Thm. If I have two sides:
Then I do this to find the third:
If looking for leg, do sqrt(big square - small square)
If looking for hyp, do sqrt(leg square+leg square)
So what this means since x is a leg, I'm going to do sqrt(17^2-8^2)
17 was bigger than 8 that's why it went first
Anyways now we can just whip out the calculator
sqrt(17^2-8^2)=15
Since this is a right triangle you may use Pythagorean theorem which is [tex]a^{2} +b^{2} =c^{2}[/tex]
a and b are the legs (two sides that FORM the right angle) of the right triangle while c is the hypotenuse (the side that is opposite the right angle)
In this case...
a = x
b = 8
c = 17
Plug these numbers into the formula and solve for x
[tex]x^{2} +8^{2} =17^{2}[/tex]
[tex]x^{2}[/tex] + 64 = 289
[tex]x^{2}[/tex] + (64 - 64) = 289 - 64
[tex]x^{2}[/tex] = 225
To remove the squared from the x take the square root of both sides
x = 15
Hope this helped!
~Just a girl in love with Shawn Mendes
The sum of -1 7/8 and 1 11/12
Answer:
1/24
Step-by-step explanation:
Step-by-step explanation:
-1 7/8+1 11/12
=-15/8+23/12 by taking Lcm as 24 we get:
=-45+46/24=1/24
which value is included in the solution set for the inequality graphed on the number line
Answer:
-5
Step-by-step explanation:
On the number line, the arrow is from -2 (opens) to the left; that means solutions will be any values less than -2
So
-5 < -2 : YES ( solutions will be any values less than -2)
-2 = -2 : NO (solutions will be any values less than -2)
0 > -2 : NO (solutions will be any values less than -2)
3 > -2 : NO (solutions will be any values less than -2)
Answer
- 5
Answer:
-5
Step-by-step explanation:
First
(open circle) means < or >
(closed circle) means < or >
SInce the arrow is pointing to the left the answer would be to the left.
So -3, -4, -5, -6, -7, -8, -9, -10etc
so -5 is one of them so thats ur answer
Simplify sqr 18
A 2 sqr 3
B 2 sqr 9
C 3 sqr 2
D 9 sqr 2
[tex]\bf \sqrt{18}~~ \begin{cases} 18=&2\cdot 3\cdot 3\\ &2\cdot 3^2 \end{cases}\implies \sqrt{2\cdot 3^2}\implies 3\sqrt{2}[/tex]
Answer:
C. 3√2
Step-by-step explanation:
√18
= √(9 x 2)
= √9 x √2
= 3√2
The air temperature at 2 pm was 12º. What was the air temperature at 8 pm, if it had dropped 15ºby
then?
Answer:
-3 degrees at 8 pm.
Step-by-step explanation:
That would be 12 - 15
= -3 degrees.
Answer:
-3
Step-by-step explanation:
The answer would be -3, because if it were to go down 15 degrees from when it was 2 PM. The equation you would have to do is 12 - 15. Which answsering that would be -3
Solve for x.......................
Answer:
D) x = 40.5
Step-by-step explanation:
When parallel lines create a smaller triangle inside a larger triangle, the triangles are similar. Triangle similarity means that side lengths are proportional, meaning to find x we must use dimensions of the smaller triangle to create a proportion.
The left side of the larger triangle is 12 + 15, so it is 27.
The left side of the smaller triangle is 12.
So, part of the proportion will be [tex]\frac{27}{12}[/tex]
The bottom side of the larger triangle is x.
The bottom side of the smaller triangle is 18.
So, part of the proportion will be [tex]\frac{x}{18}[/tex]
The full proportion will be:
[tex]\frac{27}{12}=\frac{x}{18}[/tex]
Cross multiply and solve for x.
27(18) = 12x
486 = 12x
40.5 = x
the perimater of the triangle is 30cm. its sides are in the ratios 1:3:2, then find its sides
Answer:
1 * 5 = 5cm
3 * 5 = 15cm
2 * 5 = 10cm
Step-by-step explanation:
1+3+2 = 6
then do 30 / 6 = 5 to find one part of the ratio
1 * 5 = 5
3 * 5 = 15
2 * 5 = 10
Answer: The lengths of the sides of the triangle are:
____________________________________
" 5 cm, 15 cm, and 10 cm " .
____________________________________
Step-by-step explanation:
____________________________________
1x + 3x + 2x = 30 ;
In which the sides are:
1x ; 3x, 2x ;
Find: 1x ; 3x; and 2x .
____________________________________
Let us begin by finding "x" :
____________________________________
1x + 3x + 2x = 30
1x + 3x + 2x = 6x ;
→ 6x = 30 ;
Divide each side of the equation by: " 6 " ;
to isolate "x" on each side of the equation; and to solve for "x" ;
→ 6x / 6 = 30 / 6 ;
to get:
→ x = 5 ;
______________________________________
Now, solve for the length of each side;
______________________________________
1x = x = 5 cm ;
3x = (3*5) = 15 cm ;
2x = (2*5) = 10 cm ;
______________________________________
Answer: The lengths of the sides of the triangle are:
5 cm, 15 cm, and 10 cm .
_______________________________________
Hope this helps!
Best wishes to you in your academic pursuits
— and within the "Brainly" community!
_______________________________________
Type the correct answer in each box. Round numbers to the nearest tenth, if necessary.
Solve the equation by filling out the table.
-0.5x − 2 = 2x−1 − 5
ANSWER
[tex]x = 1.6[/tex]
EXPLANATION
The given equation is:
[tex] - 0.5x - 2 = 2x - 1 - 6[/tex]
Group similar terms to obtain:
[tex] - 0.5x - 2x = - 5 - 1 + 2[/tex]
Simplify similar terms,
[tex] - 2.5x = - 4[/tex]
Divide both sides by -2.5
[tex]x = \frac{ - 4}{ - 2.5} [/tex]
[tex]x = 1.6[/tex]
Answer: see table completed.
Step-by-step explanation:
Hope this helps.
When a number is added to 1/5 of itself, the result is 24. The equation that models this problem is n +1/5 n = 24. What is the value n? n = 18 n = 20 n = 214/5 n = 234/5
For this case we must find the value of n of the following equation:
[tex]n + \frac {1} {5} n = 24[/tex]
Taking common factor "n" from the left side of the equation we have:
[tex]n (1+ \frac {1} {5}) = 24\\n \frac {6} {5} = 24[/tex]
Multiplying by 5 on both sides of the equation:
[tex]6n = 120[/tex]
Dividing between 6 on both sides of the equation:
[tex]n = 20[/tex]
Thus, the value of n is 20.
Answer:
[tex]n = 20[/tex]
Answer: Second Option
[tex]n = 20[/tex]
Step-by-step explanation:
Let's call n the number searched.
Then one fifth of this number is written as
[tex]\frac{1}{5}n[/tex]
Then at 1 / 5n the number n is added.
So, we have
[tex]n + \frac{1}{5}n[/tex]
Now we know that the result of this sum is equal to 24. Then we write the equation:
[tex]n + \frac{1}{5}n = 24[/tex].
Now we solve the equation:
[tex]\frac{6}{5}n = 24[/tex]
Muple both sides of equality by [tex]\frac{5}{6}[/tex]
[tex]\frac{5}{6} * \frac{6}{5}n = 24*\frac{5}{6}[/tex]
[tex]n = 20[/tex]
Simplify the expression. 2n/3n
[tex]\dfrac{2n}{3n}=\dfrac{2\cdot \not n}{3\cdot\not n}=\dfrac{2}{3}[/tex]
What is the range of this function
The range of a function is the output values ( Y values)
These would be the numbers the arrows are pointing at.
-8, -3 , 5 and 7
The answer is C.
The soccer team collected $800 at a car wash fundraiser. They charged $5 00 for small vehicles and $10 00 for larger
vehicles. The amount collected can be modeled by the equation 5x+10y 800, where x represents the number of small
vehicles and y represents the number of larger vehicles. If the number of larger vehicles washed was 50, how many small
vehicles were washed in total?
You are told Y is the number of large vehicles washed and that there were 50 large vehicles.
Replace Y with 50 in the given equation to solve for x ( the number of small cars.
5x + 10(50) = 800
5x + 500 = 800
Subtract 500 from both sides:
5x = 300
Divide both sides by 5:
x = 300/5
x = 60
There were 60 small cars washed.
Answer:
yes the answer would be B ✌
Which of the following is the converse of the statement “if it is my birthday, then it is September”
Answer:
The converse statement is "If its is September then it is my birthday"
Step-by-step explanation:
Answer:
If its is September then it is my birthday basically reverising it
Step-by-step explanation:
Solve this equation -4x = -60
x =
-4x = -60
x = -60 / -4
x = 15
The answer is
x = 15
Which best describes the range of the function f(x) = (6)x after it has been reflected over the x-axis
Answer:
all real numbers
Step-by-step explanation:
The range of the function f(x) = (6)x after it has been reflected over the x-axis is the single value y = -6, which represents a horizontal line at that height.
Explanation:The question asks about the range of the function f(x) = (6)x after it has been reflected over the x-axis. Since f(x) is a constant function, its graph is a horizontal line at the height of y = 6 for any value of x within the domain 0 ≤ x ≤ 20. When this function is reflected over the x-axis, the range becomes the set of values that f(x) takes on after the reflection, which would be a horizontal line at y = -6.
Now, let's formulate what happens after the reflection: If the original range of f(x) is a horizontal line at y = 6, then after reflecting over the x-axis, the new range will be a horizontal line at y = -6. Therefore, the range of the reflected function is the single value y = -6.
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Complete this sentence: The longest side of a triangle is always opposite the _______.
A. Second-longest side
B. Angle with the smallest measure
C. Angle with the greatest measure
D. Shortest side
Answer:
The answer is C. Angle with greatest measure
Step-by-step explanation:
In any triangle, there are two property that they always fulfill:
The shortest side is always opposite the smallest interior angle The longest side is always opposite the largest interior angleA classical example is in a right triangle: We know that the hypotenuse is the longest side, and also we know that the greatest angle is the right angle.
I have attached an image that shows the properties of the triangles.
Finally, the answer is C. Angle with the greatest measure.
Answer:
Angle with the greatest measure.
Step-by-step explanation:
please help, see pic attachment
Answer:
the answer is 30
Step-by-step explanation:
because it is an equilateral triangle all sides are the same so if you set 3x+15 equal to 7x-5 and solve for x you get 4x=20 and x= 5
when you plug 5 in to each equation you get 30 for both sides and so it proves that the answer is 30
Ramon invested $2,400 into two accounts. One account paid 3% interest and the other paid 6% interest. He earned 5% interest on the total investment. How much money did he put in each account?
Answer:
In the account that paid 3% Ramon put [tex]\$800[/tex]
In the account that paid 6% Ramon put [tex]\$1,600[/tex]
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]I=P(rt)[/tex]
where
I is the Final Interest Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
[tex]P(rt)=Pa(rat)+Pb(rbt)[/tex]
in this problem we have
[tex]t=t\ years\\ P=\$2,400\\ Pa=\$x\\ Pb=\$(2,400-x)\\r=0.05\\ra=0.03\\rb=0.06[/tex]
substitute
[tex]2,400(0.05t)=x(0.03t)+(2,400-x)(0.06t)[/tex]
solver for x
Simplify
[tex]2,400(0.05)=x(0.03)+(2,400-x)(0.06)[/tex]
[tex]120=0.03x+144-0.06x[/tex]
[tex]0.03x=24[/tex]
[tex]x=\$800[/tex]
therefore
In the account that paid 3% Ramon put [tex]\$800[/tex]
In the account that paid 6% Ramon put [tex]\$2,400-\$800=\$1,600[/tex]
To solve this problem, we set up an equation representing the total interest earned from the two different bank accounts. After doing a bit of algebra, we find that Ramon put $1200 into each account.
Explanation:This question falls into the category of the linear system in mathematics which deals with simple interest calculations. The total amount invested by Ramon is $2400 and we don't know how it was distributed into the two accounts, so we can name the amount in the account with 3% interest x and the other with the 6% interest 2400-x, as the total should be $2400.
We know the total interest earned was 5% of the whole sum, so we can set up the equation:
0.03x + 0.06(2400 - x) = 2400 * 0.05.
Solving the equation, we find that x, the amount in the first account, is $1200 and therefore, $1200 must have been put into the second account.
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if x+3y=-2 and 2x-6y=-8, which of the following equation is true?
A) 3X-3Y=-6
B) 12y=4
C) x-9y=-10
D) 3X=5
Final answer:
The correct equation is 3X-3Y = -6, Therefore option A is correct.
Explanation:
To find the correct equation, we can solve the given system of equations. We can do this by using the method of substitution or elimination. Let's use the method of elimination to solve the system.
Multiplying the first equation by 2 and the second equation by 3, we get:
2(x+3y) = 2(-2) ⟶ 2x + 6y = -4
3(2x-6y) = 3(-8) ⟶ 6x - 18y = -24
Adding these two equations together, we eliminate the variable 'x':
(2x + 6y) + (6x - 18y) = -4 + (-24)
8x - 12y = -28
Now, let's compare this equation to the options given. The correct equation is:
3X-3Y = -6
In physics, Ohm's law says that current through a wire, I, is directly proportional to voltage, V, and inversely proportional to resistance, R:
I=V/R.
It's also true that resistance is directly proportional to the length of the wire. We have a piece of wire. We pass 12 volts through this wire and measure 100 milliamps of current. If I cut the wire in half and pass 24 volts through it, how many milliamps of current will I measure?
If you cut the wire in half and pass 24 volts through it, you would measure 400 milliamps of current.
Ohm's law states that the current (I) through a wire is directly proportional to the voltage (V) and inversely proportional to the resistance (R). The formula is given by:
[tex]\[ I = \frac{V}{R} \][/tex]
If you double the voltage (V) and cut the wire in half, the length of the wire (which affects resistance) is also halved. Let's denote the original resistance as [tex]\( R_1 \)[/tex] and the halved resistance as [tex]\( R_2 \)[/tex]. The new equation becomes:
[tex]\[ I_2 = \frac{V_2}{R_2} \][/tex]
Now, since resistance is directly proportional to the length of the wire, we can write:
[tex]\[ R_2 = \frac{1}{2} \cdot R_1 \][/tex]
Substitute this into the previous equation:
[tex]\[ I_2 = \frac{V_2}{\frac{1}{2} \cdot R_1} \][/tex]
Now, let's use the information given. Initially, [tex]\( V_1 = 12 \)[/tex] volts and [tex]\( I_1 = 100 \)[/tex] milliamps. We can find [tex]\( R_1 \)[/tex] using Ohm's law:
[tex]\[ R_1 = \frac{V_1}{I_1} \][/tex]
Substitute the values:
[tex]\[ R_1 = \frac{12 \, \text{volts}}{100 \, \text{milliamps}} = 120 \, \text{ohms} \][/tex]
Now, substitute [tex]\( R_1 \)[/tex] into the equation for [tex]\( I_2 \)[/tex]:
[tex]\[ I_2 = \frac{24 \, \text{volts}}{\frac{1}{2} \cdot 120 \, \text{ohms}} \][/tex]
Simplify:
[tex]\[ I_2 = \frac{24 \, \text{volts}}{60 \, \text{ohms}} \][/tex]
[tex]\[ I_2 = 0.4 \, \text{amps} \][/tex]
To convert amps to milliamps, multiply by 1000:
[tex]\[ I_2 = 0.4 \, \text{amps} \times 1000 = 400 \, \text{milliamps} \][/tex]
Therefore, if you cut the wire in half and pass 24 volts through it, you would measure 400 milliamps of current.
By applying Ohm's law, the new current measured after cutting the wire in half and applying 24 volts is calculated to be 400 milliamps.
Explanation:According to Ohm's law, the current (I) through a resistor is directly proportional to the voltage (V) and inversely proportional to the resistance (R), as described by the equation I = V / R. Given the initial conditions of 12 volts and 100 milliamps of current, we can calculate the resistance of the wire using R = V / I. The resistance (R) would then be 120 ohms.
When the wire is cut in half, the resistance is halved because resistance is directly proportional to the length of the wire. Now, with a resistance of 60 ohms and applying 24 volts across it, the new current can be calculated with Ohm's law by I = V / R, which gives us I = 24 V / 60 Ω = 0.4 A, or 400 milliamps of current.
Which equation is the inverse of 5y+4 = (x+3)^2 + 1/2?
Answer:
[tex]f^{-1}(x)=-3(+/-)\sqrt{\frac{10x+7}{2}}[/tex]
Step-by-step explanation:
we have
[tex]5y+4=(x+3)^{2}+\frac{1}{2}[/tex]
Exchange x for y and y for x
[tex]5x+4=(y+3)^{2}+\frac{1}{2}[/tex]
Isolate the variable y
[tex]5x+4-\frac{1}{2}=(y+3)^{2}[/tex]
[tex]5x+\frac{7}{2}=(y+3)^{2}[/tex]
[tex]\frac{10x+7}{2}=(y+3)^{2}[/tex]
Take square root both sides
[tex](y+3)=(+/-)\sqrt{\frac{10x+7}{2}}[/tex]
[tex]y=-3(+/-)\sqrt{\frac{10x+7}{2}}[/tex]
Let
[tex]f^{-1}(x)=y[/tex]
[tex]f^{-1}(x)=-3(+/-)\sqrt{\frac{10x+7}{2}}[/tex]
a snake slithers 2/9 miles in 4/5 hours what is its speed in miles per hour
Answer:
5/18
Step-by-step explanation:
speed = distance / time
s = (2/9 miles) / (4/5 hours)
To divide by a fraction, multiply by the reciprocal:
s = (2/9) × (5/4)
s = 10/36
s = 5/18
So the snake's speed is 5/18 miles per hour.
Final answer:
To calculate the snake's speed, you divide the distance (2/9 miles) by the time (4/5 hours), resulting in a speed of 5/18 miles per hour.
Explanation:
To calculate the snake's speed in miles per hour, we divide the distance traveled by the time taken. The snake slithers 2/9 miles in 4/5 hours, which can be written as a rate equation:
Speed = Distance ÷ Time
Plugging in the numbers, we calculate:
Speed = (2/9) miles ÷ (4/5) hours
To find the speed in miles per hour, we solve the equation:
Speed = (2/9) ÷ (4/5)
To divide one fraction by another, we multiply by the reciprocal of the divisor:
Speed = (2/9) × (5/4)
Speed = (2×5) ÷ (9×4)
Speed = 10/36
When this fraction is simplified, it equals 5/18 miles per hour.
If we want to relate it to units of m/s as the reference information suggests, we can use an online unit converter or unit analysis, considering that 1 mile per hour is approximately equal to 0.44704 meters per second.
Which inequality does the graph below represent?
Answer:
A. [tex]y\le2x^2-8x+3[/tex]
Step-by-step explanation:
The given parabola has vertex at (2,-5).
The equation of this parabola in vertex form is given by:
[tex]y=a(x-h)^2+k[/tex], where (h,k)=(2,-5) is the vertex of the parabola.
We substitute the values to get:
[tex]y=a(x-2)^2-5[/tex]
The graph passes through; (0,3).
[tex]3=a(0-2)^2-5[/tex]
[tex]\implies 3+5=4a[/tex]
[tex]\implies 8=4a[/tex]
[tex]\implies a=2[/tex]
Hence the equation of the parabola is
[tex]y=2(x-2)^2-5[/tex]
We expand this to get:
[tex]y=2x^2-8x+8-5[/tex]
[tex]y=2x^2-8x+3[/tex]
Since the outward region was shaded, the corresponding inequality is
[tex]y\le2x^2-8x+3[/tex]
The correct answer is A
Please help
I’m bad at this
Hello There!
The Answer Would Be 0.25
This is because you have to multiply your original number 5.8 by 0.25 to get the new dilation.
The scale factor is 0.25