Answer:
22 meters
Step-by-step explanation:
Let x = width of the rectangle
Let y = length of the rectangle
Equation 1
If the length of the rectangle is 6 meters shorter than four times the width then:
⇒ y = 4x - 6
Equation 2
Perimeter of a rectangle = 2(width + length)
If the perimeter is 58 inches, then:
⇒ 58 = 2(x + y)
Solve by substitution
Substitute Equation 1 into Equation 2 and solve for x:
⇒ 58 = 2(x + 4x - 6)
⇒ 58 = 2(5x - 6)
⇒ 58 = 2 · 5x - 2 · 6
⇒ 58 = 10x - 12
⇒ 58 + 12 = 10x -12 + 12
⇒ 10x = 70
⇒ 10x ÷ 10 = 70 ÷ 10
⇒ x = 7
Substitute found value of x into Equation 1 and solve for y:
⇒ y = 4(7) - 6
⇒ y = 28 - 6
⇒ y = 22
Conclusion
The dimensions of the rectangle are:
width = 7 meterslength = 22 metersTherefore, the length of the longer side is 22 meters
The length of the longer side is 22 meters.
Let, one side of the rectangle is x meters.
According to the problem, the other side is 6 meters shorter than four times this side, which means the length of the second side is (4x - 6) meters.
The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (length + width)
In this case, the perimeter is 58 meters:
58 = 2 * (x + 4x - 6)
Now, let's solve for x:
58 = 2 * (5x - 6)
58 = 10x - 12
Add 12 to both sides:
58 + 12 = 10x
70 = 10x
Now, divide both sides by 10 to isolate x:
x = 70 / 10
x = 7
So, one side of the rectangle is 7 meters.
Now, we can find the length of the longer side:
Length of the longer side = 4x - 6
Length of the longer side = 4 * 7 - 6
Length of the longer side = 28 - 6
Length of the longer side = 22 meters
Therefore, the length of the longer side is 22 meters.
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Find g'(t) for the function g(t) = 7/t^4
The differentiation of the function g(t) = 7/t⁴ will be equal to g¹(t)=-28/t⁵
What is differentiation?
The method of determining the derivative, or rate of change, of a function in mathematics.is termed as the differentiation.
Given that:-
[tex]g(t)= \dfrac{7}{t^4}[/tex]
The derivative will be calculated as:-
[tex]g'(t)=7 \dfrac{d}{dt}(t^{-4})\\\\\\g'(t)=7\times (-4t^{-5})\\\\\\g'(t)=\dfrac{-28}{t^5}[/tex]
Therefore the differentiation of the function g(t) = 7/t⁴ will be equal to g¹(t)=-28/t⁵
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A diver jumps off a 20 foot high diving board with an initial upward velocity of 4 feet per second. Use the vertical motion model
h=-16t² + vt + s.
PART A:
Using the information above, the vertical motion model of the diver is h-
PART B:
The solutions of the model are t =
and t=
PART C:
Choose the letter that best fits the scenario.
A. There are no real solutions, because the solutions found do not make sense.
B. There is only one solution, because the solutions indicate time and time cannot be negative.
C. There are two solutions, because when solving, there were two solutions that occurred.
D. None of the above because there is not enough information.
Answer: ______
The height is represented by h = -16t² + 4t + 20 and There is only one solution, because the solutions indicate time and time cannot be negative.
How to solve vertical motion models?
We are given the vertical model of the diver's jump as;
h = -16t² + vt + s
where;
h is height
t is time
v is velocity
s is distance
A) We are given;
Distance; s = 20 ft
velocity; v = 4 ft/s
Thus;
h = -16t² + 4t + 20
B) The solution of the model is gotten from;
-16t² + 4t + 20 = 0
Solving this quadratic equation gives;
t = 1.25 seconds or -1 second
C) B. There is only one solution, because the solutions indicate time and time cannot be negative.
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Which expression is a possible leading term for the polynomial function graphed below?
A group of kids just finished trick-or-treating. The number of pieces of candy collected by each of the 5 kids is listed below.
31,33,36,41,34
Find the standard deviation of the data set. Round your answer to the nearest hundredth.
4. Evaluate e^-2 to one decimal place
A) 0.7
B) -1.4
C) 0.1
D) 1.4
Expand and simplify: (-7y - 8) (y - 4)
Answer:
[tex] { - 7y}^{2} + 20y + 32[/tex]
Step-by-step explanation:
1.) -7y times y = -7y(squared)
2.) -7y times -4 = 28y
3.) -8 times y = -8y
4.) -8 times -4 = 32
5.) Combine like terms
[tex] { - 7y}^{2} + 28y - 8y + 32 = { - 7y}^{2} + 20y + 32[/tex]
Find the length of the arc in terms of pi
Answer:
see the attachment photo!
Henry flies from Washington, D.C., to Boston, MA. The first flight from Washington, D.C., to New York City is 1 h 12 min. The layover in New York City lasts 2 h 41 min. The flight from New York City to Boston lasts 1 h 10 min. How long is it from the time the first flight takes off to the time Henry touches down in Boston?
Answer:
5 hours 3 minutes
Step-by-step explanation:
Add all of the times together, but remember that minutes only goes up to 60 minutes. So when you add all the minutes and you get 63, subtract 60 and add an hour, and you are left with 3 minutes.
Michael and Zach are hiking in the mountains. They left Michael’s car in the parking lot and walked northwest for 12.4 km to a campsite. Then they turned due south and walked another 7.0 km to a glacier lake. The weather was taking a turn for the worse, so they decided to plot a course directly back to the parking lot. Zach remembered, from the map in the parking lot, that the angle between the path to the campsite and the path to the glacier lake measures about 30°. What compass direction should they follow to return directly to the parking lot?
Answer:
about 101°
Step-by-step explanation:
The bearing back to the parking lot is the reverse of the bearing from the parking lot to the lake. That bearing can be found two ways. One of them uses the bearing and distance of each leg of the hike. The other uses what Zach remembers about the map.
__
sum of vectorsThe location of the lake from the parking lot can be found by adding the vectors to the campsite from the lot and to the lake from the campsite. That sum will be ...
12.4∠315° +7.0∠180° ≈ 8.94∠281.4°
A suitable calculator can be used to find this sum, as shown in the second attachment. (Angles are displayed by the calculator in the range (-180°, 180°].)
__
The direction of the parking lot from the lake will be the opposite direction. It can be found by subtracting 180° from the angle:
bearing to parking lot = 281.4° -180° = 101.4°
Michael and Zack should follow a compass direction of about 101°.
__
map memoryNorthwest is a compass bearing of 315°. Points south of that bearing will have a smaller angle. Zach remembers the direction of the lake to be about 30° less than that angle, so at 315° -30° = 285°.
The bearing back to the parking lot is the opposite direction, so ...
285° -180° = 105°
Based on Zack's memory, they should follow a compass direction of about 105°.
They will come within about 560 meters of the parking lot using this heading.
_____
Additional comments
When doing these vector calculations by hand, a couple of different methods can be used. One is to convert the vectors to component form, add the components, then convert back to polar form. The other is to make use of the Law of Cosines and the Law of Sines to solve the relevant triangles.
Here, the lake-lot distance is the third side of a triangle with two sides and the included angle known. The Law of Cosines applied to this situation is ...
c² = a² +b² -2ab·cos(C) . . . . . generic Law of Cosines equation
c² = 12.4² +7.0² -2(12.4)(7.0)cos(45°) ≈ 80.0063
c ≈ √80.0063 ≈ 8.9446
Using the Law of Sines, we find the obtuse angle of the triangle to be ...
sin(L)/12.4 = sin(C)/8.9446 . . . . . L and C are vertex angles in the diagram
L = 180° -arcsin(12.4/8.9446×sin(45°)) ≈ 101.4°
__
If translation to rectangular coordinates is used, this can be done using the usual translation ...
(x, y) = (r·cos(θ), r·sin(θ)) . . . . rectangular coordinates for r∠θ
The value of θ used can be the bearing angle (measured clockwise from north), or it can be the corresponding Cartesian plane angle (measured counterclockwise from +x). As long as the angles are consistently measured, the math works either way.
__
We have assumed that "northwest" is a bearing of 315°. If the compass rose is divided into 32 segments, the name "northwest" will be given to any bearing within 5° of this value. This makes our detailed vector calculations be somewhat approximate, and means that Zach's memory of the required bearing may be sufficiently accurate after all. Or not.
The loudness L of sound in decibels is given by L=10log(I/I0) where I is the intensity of the sound, and I0 is the intensity of the least audible sound. If I0=10^-12 W/m^2 about how many times more intense is a 108 decibel sound than a 100 decibel sound?
A. 4.56
B. 6.31
C. 5.64
D. 7.82
The 108 decibel sound is 6.31 times more intense than a 100 decibel sound option (B) is correct.
What is a logarithm?It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.
[tex]\rm a^b = c\\log_ac =b[/tex]
We have:
The loudness L of sound in decibels is given by
[tex]\rm L=10log(\dfrac{I}{I_0})[/tex]
Here I is the intensity of the sound.
[tex]\rm I_0=10^{-12} \ W/m^2[/tex]
Loudness for 108 decibel sound:
[tex]\rm 108=10log(\dfrac{I}{10^-^1^2})[/tex]
I = 0.06309
Similarly, for:
100 decibel sound:
i = 0.01
I/i = 0.06309/0.01 = 6.31
I = 6.31i
Thus, the 108 decibel sound is 6.31 times more intense than a 100 decibel sound option (B) is correct.
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find the
-2
-4
-3
-1
-9-8
determinant OF
-15
- 5
6
Determinants are defined only for square matrices, so I assume you are given the 3×3 matrix
[tex]A = \begin{bmatrix}-2 & -4 & -3 \\ -1 & -9 & -8 \\ -15 & -5 & 6 \end{bmatrix}[/tex]
Let's compute the determinant by taking the cofactor expansion along the first column:
[tex]\det A = -2 \det\begin{bmatrix}-9 & -8 \\ -5 & 6\end{bmatrix} + \det\begin{bmatrix}-4 & -3 \\ -5 & 6\end{bmatrix} - 15 \det \begin{bmatrix}-4 & -3 \\ -9 & -8\end{bmatrix}[/tex]
[tex]\det A = -2 ((-9)\times6-(-8)\times(-5)) + ((-4)\times6 - (-3)\times(-5)) \\ ~~~~~~~~~~~~~~~- 15 ((-4)\times(-8)-(-3)\times(-9))[/tex]
[tex]\det A = -2(-54-40) + (-24 - 15) - 15 (32 - 27)[/tex]
[tex]\det A = \boxed{74}[/tex]
Shirley is drawing triangles that have the same area. The base of each triangle varies inversely with the height. What are the possible base and height of a second triangle if the first triangle's base is 14 and its height is 6?
The possible base and height of a second triangle are 12 and 7, respectively
How to determine the possible base and height of a second triangle?An inverse variation is represented as:
Base * Height = k
Where k is the constant of variation.
In this case, k is the area
So, we have:
Base * Height = Area
For the first triangle, we have:
14 * 6 = Area
Evaluate
Area = 84
Substitute Area = 84 in Base * Height = Area
Base * Height = 84
Express 84 as the product of two numbers
Base * Height = 12 * 7
By comparison;
Base =12 and Height = 7
Hence, the possible base and height of a second triangle are 12 and 7, respectively
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How many negative roots will this function have? f(x) = x^7 – 2x^4 + 7x^2 + 2x – 2
help plsss
There are two negative roots to the provided polynomial function
f(x) = x⁷ – 2x⁴ + 7x² + 2x – 2
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
We have a polynomial function:
f(x) = x⁷ – 2x⁴ + 7x² + 2x – 2
[tex]\rm f(x) =\left(x+1\right)\left(x^6-x^5+x^4-3x^3+3x^2+4x-2\right)[/tex]
Using the zero product property:
[tex]\rm \left x+1\right = 0 \ \ \ or \left x^6-x^5+x^4-3x^3+3x^2+4x-2\right = 0[/tex]
After solving:
x = -1, x = -0.853, and x = 0.418 (using the graph method)
Thus, there are two negative roots to the provided polynomial function
f(x) = x⁷ – 2x⁴ + 7x² + 2x – 2
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What are the domain and range of the function represented by the set of ordered pairs?
{(-6, 12), (-3, -2), (1, 0), (14, -4)}
A. Domain: {-6, -3, 1, 14}
Range: {-4, -2, 0, 12}
B. Domain: -6 ≤ x ≤ 14
Range: -4 ≤ y ≤ 12
C. Domain: {-4, -2, 0, 12}
Range: {-6, -3, 1, 14}
D. Domain: -4 ≤ x ≤ 12
Range: -6 ≤ y ≤ 14
Answer:
A
Step-by-step explanation:
the domain is the definition of the valid x (input) values.
the range is the definition of the valid y (result) values.
as the function is defined by listing the specific points, the function only consists of individual points and not of connecting lines.
therefore the domain and range cannot be continuous intervals (otherwise the function would suddenly also include points not in the original list).
so, B and D are wrong.
and A is right, because the domain contains the x values, and the range the y values.
Suppose Z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of c so that the
following is true.
P(-C≤Z≤c)=0.9715
Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.
Using the normal distribution, considering it's symmetry, it is found that the value of C is of 2.19.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The standard normal distribution has mean and standard deviation given, respectively, by:
[tex]\mu = 0, \sigma = 1[/tex].
Hence, considering the symmetry of the normal distribution, the value of c is Z with a p-value of (1 + 0.9715)/2 = 0.98575, hence c = Z = 2.19.
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help me on this asap
Answer:
A
Explanation:
Formula for the volume of a cone :Volume (cone) = 1/3πr²h
=========================================================
Given :
⇒ r = 4 units
⇒ h = 21 units
=========================================================
Solving :
⇒ Volume (cone) = 1/3 × π x 4² × 21
⇒ Volume (cone) = 16 × 7 × π
⇒ Volume (cone) = 112π units²
Please help me with this!
Answer:
Yes, x = 0 is a solution to the given equation
Step-by-step explanation:
[tex]1^3+1(1-1)=1-x^2[/tex] (Given)[tex]L.H.S.=1^3+1(1-1)[/tex] [tex]= 1 +1(0)[/tex] [tex]= 1+0 [/tex] [tex]=1[/tex] [tex]R.H.S. =1-x^2[/tex] [tex]=1-(0)^2[/tex] (Plug x = 0)[tex]=1-0[/tex] [tex]=1[/tex] [tex]\implies L.H.S. = R.H.S.[/tex]Thus, x = 0 is a solution to the equation [tex]1^3+1(1-1)=1-x^2[/tex]Hi Student!
The goal of this question is to determine x = 0 is a solution of the expression that was provided. The first step that we must take is input 0 into all of the x's that we have in the expression. Then we just simplify both sides and determine if the end expression is true and if it is then x = 0 is a solution.
Plug in the values
[tex]1^3 + 1(1 - 1) = 1 - x^2[/tex][tex]1^3 + 1(1 - 1) = 1 - (0)^2[/tex]Simplify both sides
[tex]1^3 + 1(0) = 1 - 0[/tex][tex]1 + 0 = 1[/tex][tex]1 = 1[/tex]Looking at the final expression, we can see that 1 is indeed equal to 1 and since the expression is true, we can say that x = 0 is a solution of the expression that was provided in the problem statement.
A group of researchers wants to develop an experiment to determine whether a new drug effectively treats hypothyroidism. The researchers want to inject the drug in rabbits first to determine whether there are any potential serious side effects.
Part A: What are some possible ethical issues to this type of testing? (5 points)
Part B: While conducting the experiment, the researchers find the thyroid begins functioning properly, and they declare the new drug is causing the change. Is this a good assumption? Explain. (5 points)
Some possible ethical issues to this type of testing that they are subjected to unpleasant and hazardous procedures, as well as stress and injury.
What is experiment?Any well-defined method that yields an observable outcome that cannot be precisely predicted in advance is referred to as a experiment. To avoid any ambiguity or surprise, a experiment must be properly defined.
A) Because human experimentation is immoral, animal research has been employed as a research approach.
However, using animals is unethical because they are subjected to unpleasant and hazardous procedures, as well as stress and injury. The use of non-animal methods to substitute animal methods as much as possible will provide both ethical and technical benefits. Researchers should make the use of non-animal methods for a top priority experiments.
B) Even though the purpose of an experiment is to ensure success in rabbits, this is incorrect in people because action is what will operate properly.
The absence of thyroid-stimulating hormone in rabbit serum is a mistaken notion. As a result, it is preferable to test the drug further, and it was a success. As a result, there will be no dysfunctionality for humans.
Thus, some possible ethical issues to this type of testing that they are subjected to unpleasant and hazardous procedures, as well as stress and injury.
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If Toni wants to grow flowers in her garden, she will need a special type of top soil. If she wants the topsoil to be 1 foot deep, how much topsoil is needed? Remember, the length of the garden is 44 feet and the width is 2 feet.
Answer:
Depending on the unit your answer needs to be in, it would be 88 cubic feet or 3.25926 cubic yards
If your question asks you to round to the nearest hundredth it would be 3.26 cubic yards.
Step-by-step explanation:
To find the volume of soil:
Volume= Length x Width x Depth/Height
Volume= 44ft x 2ft x 1ft
Volume= 88 cubic feet or 3.25926 (there are 27 cubic feet in a cubic yard, 88/27=3.25926)
hope this helps! :)
Find sin A for the triangle below. Give the exact value as an expression and an approximation to the nearest ten-thousandth. Note: The triangle is not drawn to scale.
the exact value of sin A to the nearest ten- thousandth is 0. 6625
Using the pythagorean theorem
a² + b² = c²
The opposite side is unknown, so use the pythagorean theorem to find it
c = hypotenuse = 4
a= opposite site = ?
b= adjacent side = 3
Substitute into the formula
4² = a² + 3²
16 = a² + 9
a² = 16 -9 = 7
Find the square root
a =√7 = 2. 65
To find Sin A, use
Sin A = opposite side ÷ hypotenuse
Sin A = 2. 65 ÷ 4 = 0. 6625
Thus, the value of sin A is 0. 6625
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Can somebody please help with Khan Academy? Thx :)
Answer:
x ≤ 0
Step-by-step explanation:
The number line's direction is left, any number that is left on a number line behind zero has a less value. Greater than or equal!
A company lost $5,676 over a year. How much money did they lose each month to split evenly?
Answer:
$473
Step-by-step explanation:
We divide 5676 by 12 and we get 473
$473 they lose each month (?)
Step-by-step explanation:
calculator
help please, i need to turn this in
Answer:
a = -3
b = 9
c = -3
Step-by-step explanation:
[tex]a. (2^{5} )(2)^{-8} =2^{a} \\2^{(5-8)} =2^{a} \\2^{-3}=2^{a}[/tex]
[tex]a=-3[/tex]
[tex]b.\frac{4^{7} }{4^{-2} } =4^{b} \\4^{(7-(-2))} } =4^{b} \\4^{(7+2)} =4^{b}[/tex]
[tex]4^{9} =4^{b}[/tex]
[tex]b=9[/tex]
[tex]c. \frac{7^{9} }{7^{c} } =7^{12}[/tex]
[tex]7^{9-c} =7^{12}[/tex]
[tex]9-c=12[/tex]
[tex]c=9-12[/tex]
[tex]c=-3[/tex]
Hope this helps
Refer to image and please attach working out
The solution to the initial value problem is determined as y = e³ˣ.
Form auxiliary equationThe auxiliary equation is determined as follows;
y'' - 7y' + 12y = 0
m² - 7m + 12 = 0
m² - 3m - 4m + 12 = 0
m(m - 3) - 4(m - 3) = 0
m = 3 or 4
[tex]y = c_1e^{3x} + c_2e^{4x}\\\\y(0) = 1\\\\1 = c_1e^{3\times 0} + c_2e^{4\times 0}\\\\1 = c_1 + c_2 \ --(i)\\\\y' = 3c_1e^{3x} + 4c_2e^{4x}\\\\y'(0) = 3\\\\3 = 3c_1e^{3\times 0} + 4c_2e^{4\times 0}\\\\3 = 3c_1 + 4c_2 \ \ --(ii)[/tex]
solve (i) and (ii)
3 = 3c₁ + 4(1 - c₁)
3 = 3c₁ + 4 - 4c₁
3 = -c₁ + 4
c₁ = 1
c₂ = 0
[tex]y = e^{3x}[/tex]
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A rose garden is formed by joining a rectangle and semicircle. The rectangle is 25ft long and 29 ft wide. If the garden wants to build a fence around the garden, how much feet of fence are required
Step-by-step explanation:
normally the perimeter of a rectangle is
2×length + 2×width
in this case here one of the sides in that calculation has to be replaced by the outer circumference of the semicircle.
but which one ? you did not say, whether the semicircle is attached to a length or to a width of the rectangle.
the circumference of a circle is
2×pi×r
r being the radius (= half of the diameter).
so, the outer circumference of a semicircle is
2×pi×r/2 = pi×r
since we don't know the side of the rectangle, I am giving you both calculations here, and you have to pick the right one that fits your original problem definition.
if it is attached to a length (25 ft), then the radius of the semicircle is
25/2 = 12.5 ft
and the whole perimeter is
length + semicircle + 2×width =
= 25 + pi×12.5 + 2×29 =
= 25 + 39.26990817... + 58 = 122.2699082... ft
if it is attached to a width (29 ft), then the radius of the semicircle is
29/2 = 14.5 ft
and the whole perimeter is
2×length + semicircle + width =
= 2×25 + pi×14.5 + 29 =
= 50 + 45.55309348... + 29 = 124.5530935... ft
find the coordinates of the vertices of the figure after the given transformation T <2,4>
OA.J'(-2,-1),E'(-2,1),V'(1,3)
OB. J'(1, -1), E'(1, 1), V' (4, 3)
OC. J'(0, -2), E (0, 0), V' (3, 2)
OD. J' (-3, -2), E'(-3,0), V'(0, 2)
The correct answer is option A which is j'(1,3) , E'( -2,1) and V'( 1,3).
What is coordinate geometry?
A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
Given that:-
The coordinates of the vertices of the figure after the given transformation T <2,4>So we will transform the points given in the figure.
V(-1,-1) , J(-4,-5) and E(-4,-3).
The transformation will be given as:-
V(-1,-1) → V'(-1+2 , -1 + 4) → V'( 1,3 )
J(-4,-5) → J'( -4 +2 , -5 + 4 ) → J'( -2,-1 )
E(-4,-3). → E'( -4+2 , -3+4 ) → E' ( -2, 1 )
Therefore correct answer is option A which is j'(1,3) , E'( -2,1) and V'( 1,3).
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what does 7,124 ÷ 26 equal too explain with what you know
Answer:
274
Step-by-step explanation:
i used a calculator. You can try long division
Answer:
274
Step-by-step explanation:
7,124 ÷ 26 =274
0 2 7 4
2 6 7 1 2 4
0
7 1
5 2
1 9 2
1 8 2
1 0 4
1 0 4
0
The measure of an exterior angle of a regular polygon is 45º. How many sides does the polygon have?
Answer:The answer is 8 sides
Step-by-step explanation:
Manny drove 385 miles in 7 hours. How far will he go in 12 hours?
Answer:
660 miles.
Step-by-step explanation:
385 m/7 h = 55 m/h
55 m/h * 12 h = 660 m
Evaluate the expression when
x = 6.
x² +8x-3
Answer:
81
Step-by-step explanation:
Hello!
We can plug in 6 for x in x² + 8x - 3
Evaluatex² + 8x - 3(6)² + 8(6) - 336 + 48 - 384 - 381When x = 6, the expression evaluates to 81.