The circle is:[tex]x^2+y^2 = 5^2 = 25[/tex]This circle has center (0,0) and radius 5 units. Therefore, it is a circle with a radius of 5 units, and every point that lies on the circumference of this circle is 5 units away from the center of the circle.
the distance between any point on the circle and the center of the circle is always 5 units. This is because the equation of a circle is
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where the center is (a,b) and the radius is r units. In this case,
a=b=0 and r=5.
Algebraically show that the point (6, 8) lies on the circle.
To show that the point (6, 8) lies on the circle, we need to substitute the values of x and y in the equation of the circle and verify whether the equation holds true or not.So,
substituting x=6 and y=8 in the equation of the circle, we
[tex]get:6^2 + 8^2 = 36 + 64 = 100[/tex]
Now, we can see that the LHS of the equation is equal to 100, which is also equal to the square of the radius of the circle. Therefore, the point (6, 8) lies on the circumference of the circle with center (0,0) and radius 5 units.
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M5|L15
...
zearn.org
Dive into Dimensions
Solve on paper. Then check your work on Zearn. 4>
AA C
Jordan made a quilt for his cousin's doll. The quilt had a 7 x 7 array of different color squ
patches. If each patch is 3 - in long, what is the area of the whole quilt?»
The area of the whole quilt is
û
in².
The area of the whole quilt is 441 in². of the whole quilt is 441 in².
We are given that;
Measure= 7*7
Now,
To find the area of the whole quilt, you need to multiply the length and width of the quilt.
The length and width of the quilt are both 7 times 3 in,
which is 21 in. So, the area of the quilt is 21 in x 21 in
= 441 in².
Therefore, by the area the answer will be 441 in².
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Name this polygon in as many ways as possible.
a four-sided figure
rhombus
trapezoid
pentagon
quadrilateral
Answer and Step-by-step explanation:
The given polygon can be referred to in multiple ways, though not all names may prove to be an accurate description:
1. Quadrilateral: A four-sided figure is accurately called a quadrilateral, as it includes any shape with four sides.
2. Rectangle: A type of quadrilateral with four right angles and opposite sides parallel.
3. Square: A special type of rectangle with all sides equal in length.
4. Parallelogram: A quadrilateral with opposite sides that are parallel.
5. Rhomboid: A parallelogram with no right angles and sides of unequal length.
6. Kite: A quadrilateral with two pairs of adjacent sides that are of equal length.
7. Irregular Quadrilateral: A quadrilateral that does not fit in any of the defined categories above.
It's important to note that some names provided in the question do not correctly classify a four-sided polygon:
- Rhombus: A quadrilateral with all sides of equal length and opposite sides parallel. However, it has been provided as a separate entry.
- Trapezoid: A quadrilateral with one pair of parallel sides. However, it has been provided as a separate entry.
- Pentagon: An incorrect classification for a four-sided figure as it refers to a five-sided polygon.
Hope that helps.
HELP PLEASE DUE SOON
Answer: 6
Step-by-step explanation:
set up a box plot.
To find the interquartile range: 3rd tile value subtracted by the first tile value. Basically: Q3-Q1=IQR
Q= Quartile
3 and 1 is the number
IQR = interquartile range
if you do incorrectly you should get 6 if not add me as a friend and I’ll show you and explain it better!
For the quadratic equation 2x² - 6x + 7 = 0, enter the correct values of a, b, and c.
X =
-b ± √√b² - 4ac
2a
The values of a is 2, b is -6 and c is 7 from the quadratic equation 2x² - 6x + 7 = 0
The given quadratic equation is 2x² - 6x + 7 = 0
A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
When we compare the given quadratic equation with standard form we get the values of a , b and c
a=2
b=-6
c=7
Hence, the values of a is 2, b is -6 and c is 7 from the quadratic equation 2x² - 6x + 7 = 0
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The manager of a pizza shop has $750 in tips
to distribute among its employees. He has
already distributed $550. If x equals the
amount that is left to distribute, choose the
equation to solve the problem.
O x + 750 = 550
Ox+ 550 = 750
Ox-550 = 750
O x-750 = 550
Answer:
Step-by-step explanation:
The equation to solve the problem is:
x + 550 = 750
Explanation:
The manager has already distributed $550, and the remaining amount to distribute is represented by the variable x. Adding the distributed amount to the remaining amount should equal the total amount of tips the manager has, which is $750. Therefore, the correct equation is x + 550 = 750.
100 points asap step by step What is the value of x in the equation x/-3 = 2?
Answer:
-6
Step-by-step explanation:
[tex]\frac{x}{-3} = 2\\x = 2 * (-3)\\x = -6[/tex]
The answer is x equals negative 6
Determine the equation of the given conic xy-coordinates when the aces are rostered through the given angle
x^2-y^2=2y , o/ = cos^-1 3/5
Precalc helppp
The final equation of the given conic, after rotating the axes through the angle θ = arccos(3/5), is:
x^2 * cos(2θ) + y^2 * cos(2θ) = 2y
The equation of the conic in xy-coordinates when the axes are rotated through the given angle can be determined by using a rotation matrix. Given that the conic is represented by the equation:
x^2 - y^2 = 2y
And the rotation angle is θ = arccos(3/5), we can proceed as follows:
1. Rewrite the given equation in matrix form:
[x, y] * [1 0] * [x] = [2y]
[-1 0] [y] [0]
2. Define the rotation matrix using the given angle θ:
R(θ) = [cos(θ) -sin(θ)]
[sin(θ) cos(θ)]
3. Apply the rotation matrix to the equation:
[x, y] * R(θ)^T * R(θ) * [x] = [2y]
[1 0] [-1 0] [y] [0]
[x, y] * R(θ)^T * [1 0] * R(θ) * [x] = [2y]
[-1 0] [y] [0]
[x, y] * [cos(θ) sin(θ)] * [1 0] * [cos(θ) -sin(θ)] * [x] = [2y]
[-sin(θ) cos(θ)] [-1 0] [sin(θ) cos(θ)] [y] [0]
Simplifying the expression:
[x * cos(θ) + y * sin(θ)] * [x * cos(θ) - y * sin(θ)] - [x * sin(θ) - y * cos(θ)] * [x * sin(θ) + y * cos(θ)] = 2y
Expanding and rearranging terms:
x^2 * cos^2(θ) - y^2 * sin^2(θ) - x^2 * sin^2(θ) + y^2 * cos^2(θ) = 2y
Combining like terms:
x^2 * (cos^2(θ) - sin^2(θ)) + y^2 * (cos^2(θ) - sin^2(θ)) = 2y
Using the trigonometric identity cos^2(θ) - sin^2(θ) = cos(2θ):
x^2 * cos(2θ) + y^2 * cos(2θ) = 2y
The final equation of the given conic, after rotating the axes through the angle θ = arccos(3/5), is:
x^2 * cos(2θ) + y^2 * cos(2θ) = 2y
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Solve for x. You must show all of your work to receive credit.
V
5r+17
W
23x-5
37x+5
U
The solution for x in the circle is:
x = 6
How to solve for x in the circle?Tangent-tangent theorem states that "The measure of an angle formed by a two tangents drawn from a point outside the circle is one-half the difference of the intercepted arcs".
Using the above theorem. We can say:
5x + 17 = 1/2 * [(37x+5) - (23x-5)]
5x + 17 = 1/2 * [37x + 5 - 23x + 5]
5x + 17 = 1/2 * [14x + 10]
5x + 17 = 7x + 5
7x - 5x = 17 - 5
2x = 12
x = 12/2
x = 6
Therefore, the solution for x is 6.
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Complete Question
Check attached image
Range: 5 -> 18
Which of the following is the correct statement?
a. Mean is less than 6
b. Range is greater than 18
c. Median is less than or equal to 18
d. IQR is greater than or equal to 6
The correct statement is: c. Median is less than or equal to [tex]18[/tex].
Let's analyze the given range of values, which is [tex]5 \ to \ 18[/tex], and evaluate the statements:
a. Mean is less than [tex]6[/tex]:
To determine if the mean is less than [tex]6[/tex], we need to find the average of the given range.
The mean can be calculated as:
[tex]\[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} \][/tex]
In this case, the sum of the values is [tex]5 + 6 + 7 + \ldots + 18[/tex], and the number of values is [tex]18 - 5 + 1[/tex] (inclusive).
b. Range is greater than [tex]18[/tex]:
The range is the difference between the maximum and minimum values in a dataset. In this case, the range is [tex]18 - 5 = 13,[/tex] which is less than 18.
c. Median is less than or equal to [tex]18[/tex]:
The median is the middle value in a dataset when the values are arranged in ascending order. In this case, since the range starts from [tex]5[/tex] and ends at 18, the median is less than or equal to [tex]18[/tex].
d. IQR is greater than or equal to [tex]6[/tex]:
The interquartile range (IQR) is the difference between the first quartile (Q1) and the third quartile (Q3) of a dataset. Since we don't have the actual dataset or specific values beyond the range, we cannot determine if the IQR is greater than or equal to [tex]6[/tex].
Therefore, based on the given range, the correct statement is:
c. Median is less than or equal to [tex]18[/tex].
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find the quadratic equations
please help
brainleist alsoo
Answer:
[tex]y = (x-1)^2-9[/tex]
Step-by-step explanation:
The form of a quadratic equation is [tex]y = a(x-h)^2+k[/tex]. Lets identify each change in words before switching to the formula:
Shifted 1 right
Shifted 9 down
No stretch horizontally
No stretch vertically.
Our equation will be [tex]y = (x-1)^2-9[/tex].
Jenny wanted to study how the area of a rectangle changes with the length if its width is fixed. She computed the areas of several rectangles that have the same width and different lengths. She then plotted the results and connected them with a line, as shown below. The graph shows the area (in ) versus the length (in ).
Find the range and the domain of the function shown.
Area
()
y12345678910x1234567890
Length ()
Write your answers as inequalities, using or as appropriate.
Or, you may instead click on "Empty set" or "All reals" as the answer.
look at picture
The domain and range of a function for the area of a rectangle indicates;
(a) Range; 0 ≤ y < ∞
(b) Domain; 0 ≤ x < ∞
What is a function?A function is a definition or rule that maps the values of an input unto the values of the output variables.
The area of a rectangle, A = Length, L × Width, W
Therefore;
The area of a rectangle is directly proportional to the width of a rectangle
A ∝ W
The graph of the area to the length of the width of the rectangle indicates that we get;
(a) The domain is the set of the possible x-values of the function
The proportional relationship between the area and the width of a rectangle indicates;
The domain is; 0 ≤ x < ∞
(b) The range is the set of the possible output values of the graph, which is the set of the y-values
The proportional relationship between the area, y and the width, x , the range is; 0 ≤ y < ∞
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Give your answer in degrees (°).
35°
44°
x
Find X
The value of x is 53.
We have,
From the figure,
There are two parallel lines.
This means,
44 and angle M are corresponding angles.
And,
We can consider a triangle as:
M + P + P = 180
Where P is the angle opposite to the equal sides.
So,
44 + P + P = 180
44 + 2P = 180
2P = 180 - 44
2P = 36
P = 18
Now,
x is the exterior angle.
This means,
x = 35 + P
x = 35 + 18
x = 53
Thus,
The value of x is 53.
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Select all the sets of transformations that result in the same image when performed in any order. Select 3 choices.
A. translation, dilation with center (0,0)
B. two translations.
C. vertical translations, reflection over the y-axis.
D. refelction over the y-axis, dilation with center (2,2)
E. two reflections over the x-axis
The commutative sets of transformations are two translations, refelction over the y-axis, dilation with center (2,2) and two reflections over the x-axis. B, D, and E.
The sets of transformations that result in the same image when performed in any order are called "commutative."
A set of transformations is commutative if the order of the transformations doesn't matter;
Performing the transformations in a different order still results in the same final image.
Based on this definition can select the commutative sets of transformations from the given choices:
Translation and dilation with center (0,0) are not commutative.
The order of the transformations matters.
Two translations are commutative.
The order of the transformations doesn't matter.
Vertical translations and reflection over the y-axis are not commutative. The order of the transformations matters.
Reflection over the y-axis and dilation with center (2,2) are commutative.
The order of the transformations doesn't matter.
Two reflections over the x-axis are commutative.
The order of the transformations doesn't matter.
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In Exercises
frequencies.
9.
Gender
9 and 10, find and interpret the marginal
(See Example 1.)
Male
Female
Set Academic Goals
No
168
142
Yes
64
54
suport
no sas8
09. The total sample, 118 individuals set academic goals (regardless of gender), while 310 individuals did not set academic goals.
10. The total sample, 290 individuals have cats, while 306 individuals do not have cats. Furthermore, 312 individuals have dogs, while 284 individuals do not have dogs.
In order to find the marginal frequencies, we need to calculate the totals for each category separately.
For question 9:
The marginal frequency for "Set Academic Goals - yes" is 64 + 54 = 118. This represents the total number of individuals who answered "yes" to setting academic goals.
The marginal frequency for "Set Academic Goals - no" is 168 + 142 = 310. This represents the total number of individuals who answered "no" to setting academic goals.
The marginal frequency for "Male" is 64 + 168 = 232. This represents the total number of males.
The marginal frequency for "Female" is 54 + 142 = 196. This represents the total number of females.
Interpretation:
The marginal frequencies provide us with the total counts for each category in a contingency table. In this case, we can see that out of the total sample, 118 individuals set academic goals (regardless of gender), while 310 individuals did not set academic goals. Additionally, there were 232 males and 196 females in the sample.
For question 10:
The marginal frequency for "Cat - yes" is 104 + 186 = 290. This represents the total number of individuals who have cats.
The marginal frequency for "Cat - no" is 208 + 98 = 306. This represents the total number of individuals who do not have cats.
The marginal frequency for "Dog - yes" is 104 + 208 = 312. This represents the total number of individuals who have dogs.
The marginal frequency for "Dog - no" is 186 + 98 = 284. This represents the total number of individuals who do not have dogs.
Interpretation:
The marginal frequencies reveal the total counts for each category in the contingency table. In this case, we can observe that out of the total sample, 290 individuals have cats, while 306 individuals do not have cats. Furthermore, 312 individuals have dogs, while 284 individuals do not have dogs.
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Anika has an outdoor storage bin shaped like a rectangular prism that holds her pool toys and inflatables. The base of the storage bin measures 5.5 feet by 3 feet. The total surface area of the storage bin is 75.5 square feet. What is the height of the storage bin in feet?
Answer:
Step-by-step explanation:
20=17+12+9 so the answer is 4982
What do you know about the graphs of polynomials with positive end behavior compared to the graphs of polynomials with negative end behavior?
If "positive" end behavior:
1. The graph hits the x-axis
2. The arrows point in opposite directions
3. The arrows point in the same direction
4. The right arrow is up
5. The graph hits the y-axis
6. The right arrow is down
If "negative" end behavior:
1. The graph hits the x-axis
2. The right arrow is down
3. The graph hits the y-axis
4. The right arrow is up
5. The arrows point in the same direction
6. The arrows point in opposite directions
The correct statements are:
If "positive" end behaviour:
The arrows point in the same direction.
The right arrow is up.
The graph hits the y-axis.
If "negative" end behaviour:
The arrows point in opposite directions.
The right arrow is down.
The graph hits the X-axis.
In mathematics, a graph is a visual representation of a set of data, which consists of points, called vertices or nodes, and lines connecting them, called edges or arcs.
Graphs are often used to represent mathematical functions, data sets, or relationships between objects, and they can be used to model real-world phenomena.
Graphs can be drawn on a coordinate plane or in a more abstract form, and they can be used to analyze and understand complex systems and relationships.
The correct statements are:
If "positive" end behaviour:
The arrows point in the same direction.
The right arrow is up.
The graph hits the y-axis.
If "negative" end behaviour:
The arrows point in opposite directions.
The right arrow is down.
The graph hits the X-axis.
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Need help please
Find all the zeros of the polynomial p(x)=x^3+x^2+8x-60
--------------------------
Enter the zeros separated by commas. Enter exact values, not decimal approximations, using square roots as needed.
A bag has 2 red marbles and 2 blue marbles. Jade randomly selects two marbles
from the bag, one at a time. What is the probability that both marbles are the
same color? Show your work.
The probability that both marbles are the same color is 1/3.
How to solve for the probabilityP(R₂ | R₁) = 1/3
The probability of both events happening together (drawing two red marbles) is the product of the probabilities of each event:
P(R₁ and R₂) = P(R₁) * P(R₂ | R₁)
= (1/2) * (1/3)
= 1/6
P(B₁) = 2/4 = 1/2
P(B₂ | B₁) = 1/3
Probability of B₁ and B₂
P(B₁ and B₂)
= P(B₁) * P(B₂ | B₁)
= (1/2) * (1/3)
= 1/6
P(Same color)
= P(R₁ and R₂) + P(B₁and B₂)
= 1/6 + 1/6 = 2/6
= 1/3
So, the probability that both marbles are the same color is 1/3.
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Helpppp pleaseeeee :(
Answer:
[tex]\large {\mbox{R = 3.6}}[/tex]
Step-by-step explanation:
The formula for finding a magnitude of an earthquake on the Richter Scale is given as
[tex]R = \log\left(\dfrac{A}{A_0}\right)\\[/tex]
[tex]\rm{where}\\\textrm{A - measure of amplitude of quake wave}\\\textrm{$A_0$ = amplitude of smallest detectable wave}\\[/tex]
Given A = 0.3954 and A₀ = 0.0001, we can plug in these values into the R equation to get
[tex]R = \log\left(\dfrac{0.3954}{0.0001}\right)\\\\= \log(3954)\\\\= 3.597\\\\= 3.6\text { rounded to the nearest tenth}[/tex]
Write an equation for a function that has a graph with the given characteristics.
The shape of y= |x| that has been shrunk vertically by a factor of 2/9.
----------------------.
The absolute value function y = |x| looks like a "V" shape, with the vertex at the origin and the arms going off to positive and negative infinity. To shrink this function vertically by a factor of 2/9, we can multiply the entire function by 2/9:
y = (2/9)|x|
This new function has the same "V" shape, but the y-values are only two-ninths as large as they would be for the original function at any given value of x. The vertex of the new function is still at the origin, and the arms still go off to positive and negative infinity.
please help I'm confused, what's the area of the entire quadrilateral?
After considering the given data we conclude that the area of the given figure is 62.2 cm², under the condition that x = 5 cm
Since the given figure comprises of two right angled triangle and one rectangle we can split them and calculate their area separately then apply summation at the ending.
Let us proceed with the triangle
Let us first name the whole figure, ABCD is the whole diagram out of which first we will deal with triangle CDG,
In triangle CDG
The height length (DG) = 7.5 cm
The base length ( CG) = 2.4 cm
Then the area of the triangle CDG
[tex]Area =1/2 * base *height[/tex]
= 1/2 × 2.4 ×7.5
= 1/2 × 18
= 9 cm²
Now moving on to the other triangle ABE
The height length (AE) = 7.5 cm
The base length (EB) = 4.2 cm
Then the area of the triangle ABE
[tex]Area =1/2 * base *height[/tex]
= 1/2 × 4.2 × 7.5
=1/2 × 31.5
= 15.7 cm²
Finally moving onto the rectangle AEGD,
Given
Length of the rectangle (DG) = 7.5 cm
Breadth of the rectangle ( GE) = x = 5 cm
Placing the values in the formula
[tex]Area = length * breathe[/tex]
Area = 7.5 × 5
Area = 37.5 cm²
Now applying summation to evaluate the total area of the quadrilateral ABCD
Area of CDG + Area of ABE + Area of AEGD
= ( 9 + 15.7 + 37.5)
= 62.2 cm²
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Let a 5 kVA, 400/300V transformer be approximately by a 2Ω reactance referred to low voltage side. Considering the rated values as base quantities, express the transformer reactance as per unit quantity
The per-unit reactance of the transformer is 0.0444 pu.
To calculate the per-unit reactance of the transformer, we need to use the following formula:
Xpu = X / (Vbas[tex]e^2[/tex] / Sbase)
where X is the reactance in ohms, Vbase is the base voltage in volts, and Sbase is the base power in volt-amperes.
In this case, the rated power of the transformer is 5 kVA, and the rated voltage on the high side is 400V. Therefore, the base power and base voltage are:
Sbase = 5 kVA
Vbase = 400V
The reactance of the transformer referred to the low voltage side is given as 2Ω. To convert this to per-unit, we substitute the values in the formula:
Xpu = 2Ω / (300[tex]V^2[/tex] / 5 kVA)
Xpu = 0.0444 pu
Therefore, the per-unit reactance of the transformer is 0.0444 pu.
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John bought a shirt at ksh 500 and marked it at Ksh 600. A customer bought it at ksh 550. What was the percentage discount?
Answer:
The original price of the shirt was Ksh 500 and it was sold for Ksh 550.
The discount is the difference between the original price and the selling price, which is Ksh 500 - Ksh 550 = Ksh -50.
To find the percentage discount, we can use the formula:
percentage discount = (discount ÷ original price) × 100%
percentage discount = (-50 ÷ 500) × 100%
percentage discount = -10%
Therefore, the percentage discount is 10%.
the length of a rectangle is 5 meters longer than the width. if the area is 23 square meters, find the rectangles dimensions. round to the nearest tenth of a meter
Answer:
The rectangle is 7.9 meters by 2.9 meters.
Step-by-step explanation:
Let l be the length and w be the width
l = w + 5
A = 23 m²
Formula: A = lw
Solve for the dimensions
23 = (w+5)w
23 = w² + 5w
w² + 5w - 23 = 0
Use quadratic formula to find the possible value/s of w
[tex]w = \frac{-b+-\sqrt{b^2-4ac} }{2a}\\ w = \frac{-5+-\sqrt{5^2-4(1)(-23)} }{2(1)} \\w = \frac{-5+-\sqrt{25+92} }{2}\\ w = \frac{-5+-\sqrt{117} }{2} \\w = \frac{-5+-\sqrt{9(13)} }{2} \\w = \frac{-5+-3\sqrt{13} }{2}\\ w = \frac{-5+3\sqrt{13} }{2} = 2.9\\ w = \frac{-5-3\sqrt{13} }{2} = -7.9[/tex]
Since we're dealing with dimensions, take the positive value which is 2.9.
w = 2.9 m
Substitute the value to l = w + 5
l = 2.9 + 5
l = 7.9 m
expand using the Binomial Theorem: (2x+5y)^3
The Binomial coefficients, we get:
(2x+5y)^3 = 8x^3 + 60x^2y + 150xy^2 + 125y^3
Therefore, (2x+5y)^3 expands to 8x^3 + 60x^2y + 150xy^2 + 125y^3.
To expand (2x+5y)^3, we can use the Binomial Theorem, which states that:
(a + b)^n = nC0a^n + nC1a^(n-1)b + nC2a^(n-2)b^2 + ... + nCn-1ab^(n-1) + nCn b^n
where nCk represents the binomial coefficient, which is the number of ways to choose k items from a set of n items.
In this case, we have:
a = 2x
b = 5y
n = 3
So, we can apply the Binomial Theorem as follows:
(2x+5y)^3 = 3C0 (2x)^3 + 3C1 (2x)^2(5y) + 3C2 (2x)(5y)^2 + 3C3 (5y)^3
Simplifying each term using the binomial coefficients, we get:
(2x+5y)^3 = 8x^3 + 60x^2y + 150xy^2 + 125y^3
Therefore, (2x+5y)^3 expands to 8x^3 + 60x^2y + 150xy^2 + 125y^3.
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175
m/1 =
m/2=
160°
determine the requested value below
The measures of angle 1 and angle 2 are 12.5 degrees
We have to find the measures of angle 1 and angle 2
The circle will have 360 degrees
The unknown arc length be taken as x
175+160+x=360
Add the like terms
335+x=360
Subtract 335 from both sides
x=360-335
x=25
So angle m∠1 = 1/2(25)
m∠1 is 12.5
m∠1 = m∠2 as both are equal.
m∠2 = 12.5 degrees
Hence, the measures of angle 1 and angle 2 are 12.5 degrees
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A piece of lumber 2.8 meters long weighs 24.5 kilograms. A piece 0.8 meter long is cut from
the 2.8-meter length. Determine the weight of the 0.8-meter piece.
The weight of the 0.8-meter piece is 19.6 kilograms.
We can use the ratio of length to weight to determine the weight of the 0.8-meter piece.
Let's call the weight of the 2.8-meter piece "W₁" and the weight of the 0.8-meter piece "W₂". Then we have:
W₁/2.8m = 24.5kg/1m
Solving for W₁, we get:
W₁ = (24.5kg/1m) x 2.8m = 68.6kg
Now we can use the same ratio to find W₂:
W₂/0.8m = 24.5kg/1m
Solving for W₂, we get:
W₂ = (24.5kg/1m) x 0.8m = 19.6kg
Therefore, the weight of the 0.8-meter piece is 19.6 kilograms.
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The sine of an angle 0 in the third quadrant is -0.5. What is the value of cos(0)?
The sine of an angle 0 in the third quadrant is -0.5. So the value of cos∅ is -√(3)/2.
In the third quadrant, both sine and cosine are negative. We know that the sine of ∅ is -0.5, so we can use the Pythagorean identity to find the cosine of ∅:
sin²(∅) + cos²(∅) = 1
Substituting -0.5 for sin(∅), we get:
(-0.5)² + cos²(∅) = 1
Simplifying:
0.25 + cos²(∅) = 1
cos²(∅) = 1 - 0.25
cos²(∅) = 0.75
Taking the square root of both sides:
cos(∅) = ±√(0.75)
Since we're in the third quadrant where cosine is negative, we take the negative square root:
cos(∅) = -√(0.75)
Simplifying the square root:
cos(∅) = -√(3/4)
cos(∅) = -√(3)/2
Therefore, the value of cos(∅) is -√(3)/2.
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you took out a loan for 5,000 and the interest rate was 5.9% which is charged every month if you make no payments how much will your total balance be after 2 months
+* Answer *+
$5,590
*+Step-by-step explanation:*+
$5,000 x 5.9% = $295
$95 x 2 (months), = 590
5,000 + 590 = 5,590
So therefore you have $5,590 dollars.
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What is the probability?
The true statements regarding the probability are:
It is likely that the bag has a black marbleIt is not unlikely that the bag has at least one pink marble (equivalently, it is likely that the bag has at least one pink marble)How to explain the probabilityBased on the given information, it is likely that the bag has at least one black marble (with a probability of 0.1). It is not certain or impossible, as the probability is not 0 or 1.
It is not certain or unlikely that the bag has at least one pink marble, as the probability is not 0 or 1. However, the probability of the bag having at least one pink marble is relatively high (0.79), so it is more likely than not that the bag has a pink marble.
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