Answers
There exists two opposite sets of angles ( antipodal angles are equal).
What is meant by antipodal angles?The diametrically opposed points on a sphere are known as antipodal points in mathematics (the specific qualities of such a definition are that a line drawn from the one to the other passes through the center of the sphere so forms a true diameter).
If two separate points on a sphere lie along the same line passing through the center of the sphere, they are said to be diametrically opposed points. Antipodal points on the sphere are also known as diametrically opposed points.
We may determine from the image that the two triangles above are isosceles triangles ( the bottom angles one equal).
There are two sets of opposite angles ( antipodal angles are equal).
Let the equation be
[tex]$x & =180^{\circ}-\left(\frac{180^{\circ}-a}{2}+b\right) \\[/tex]
substitute the values in the above equation, we get
[tex]$& =180^{\circ}-\left(\frac{180^{\circ}-62^{\circ}}{2}+63^{\circ}\right) \\[/tex]
simplifying the equation, then
[tex]& =180^{\circ}-\left(59^{\circ}+63^{\circ}\right) \\[/tex]
= 58°
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The value of x in the following triangles is 59 degrees.
What is the sum of interior angles of triangle?One of the fundamental shapes in geometry is the triangle. The smallest polygon is a triangle. It has three vertices and three edges. The symbol for a triangle having the vertices P, Q, and R is PQR. The three sides and three angles that make up a triangle are referred to as its elements. The two crucial properties of a triangle are the external angle property and the angle sum property.
Given that,
a = 62 degree and
b = 62 degrees.
From the given figure we see that the two sides containing angle a are equal.
Thus, the value of the two angles containing angle a is:
a + x + x = 180
a + 2x = 180
62 + 2x = 180
2x = 180 - 62
2x = 118
x = 59
The value of x is 59. The angle x and the exterior angle of x form a straight line.
Thus,
x + y = 180
59 + y = 180
y = 121
The sum of angle y and the interior angle of triangle containing angle x is 180:
y + z = 180
121 + z = 180
z = 59
Now, for triangle containing angle b, the two sides are equal hence the angle corresponding to the side is b = 62.
The angle b and its exterior angle form a straight line. Thus,
b + c = 180
62 + c = 180
c = 118
The angle c and one interior angle of triangle form a straight line thus,
c + d = 180
118 + d = 180
d = 62
Now, the angles of the triangle containing angle x is:
z = 59 and d = 62
The sum of all the sides of triangle is 180, thus:
x + z + d = 180
x + 59 + 62 = 180
x = 59
Hence, the value of x is 59.
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Related Questions
Use The General Slicing Mothod To Find The Volume Of The Following Solid. The Solid With A Semicircular Base Of Radius 9 Whose Cross Section Is...
Answers
The volume of the solid can be found by using the general slicing method which involves slicing the solid into multiple thin slices, computing the volume of each slice.
The general slicing method can be used to find the volume of the solid with a semicircular base of radius 9 whose cross section is a triangle. This method involves slicing the solid into multiple thin slices, computing the volume of each slice, and then summing up the volumes of all the slices. To find the volume of each slice, we first need to determine the area of the cross-section for each slice. The area of the cross-section can be found by multiplying the base of the triangle by its height. For each slice, the base of the triangle is equal to 2πr/N, where r is the radius of the semicircle and N is the number of slices. The height of the triangle is equal to the thickness of each slice. Once the area of the cross-section is calculated, we can find the volume of each slice by multiplying the area by the thickness of the slice. Finally, the volume of the solid is equal to the sum of the volumes of all the slices.
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if a =determine the values ofx and y for which a^2 = a
Answers
Answer: - 14.4
Step-by-step explanation:
Matrices are used to represent data in rows and columns. The values of x and y are 9 and -14.4 respectively.
Matrix A is represented as: ( x -5, y -8)
Calculate A2: A2: (x 5, y -8) x (x 5, y -8)
Recall that A2 = A
This means that: (x2 + 5y, 5x - 40) = (x 5)
( xy - 8y, 5y + 64) = (y -8)
So, by comparison:
5x - 40 = 5
5x = 40 + 5
5x = 45
x = 9
Similarly:
5y + 64 = -8
5y = -64 - 8
5y = -72
y = -14.4
Hence, the values of x and y are 9 and -14.4 respectively.
The equation a² = a is true, when the value of "x = 1" and "y = 1".
An equation is a mathematical statement that asserts that two expressions are equal.
When we are given an equation like
=> a² = a
it means that the value of a² on the left side is equal to the value of "a" on the right side.
Here we need to find the values of "x" and "y" for which this equation is true.
Let's start by assuming that the value of "a = 1".
In that case, the equation
=> a² = a
=> 1² = 1.
And since 1 raised to the power of 2 is equal to 1, this equation is true. Therefore, we have found a solution for the equation: "a = 1".
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Simplify the expression 4(5+1 x)
Answers
Answer: 4x+20
Step-by-step explanation:
4x5=20
4x1x=4x
3. A girl is 12 years older than her daughter. 4 years ago when she gave birth to her daughter while in SHS 1, she was 4 times as old as her daughter. How old are they now?
Answers
Answer:
The mother is now 20 years old and the daughter is 8 years old. Let the mother's age be x and the daughter's age be y. We can write the equation x - 12 = y and x - 4 = 4y. Solving these equations simultaneously gives us x = 20 and y = 8.
Step-by-step explanation:
Write the equation in Slope-Intercept Form (solve for y).
Identify the y-intercept.
Put that point on the graph
3x +9y = 9
Answers
Answer:
y=-1/3x+1
Step-by-step explanation:
3x+9y=9
First take your x and transfer it to the other side of the = by doing the opposite.
3x+9y=9
-3x -3x
9y=9-3x
You must then switch the -3x and 9 so that it stays in y intercept form
9y=-3x+9
Then you need to get y by itself by dividing both sides by 9.
y=-3x/9+1
Lastly simplify the fraction left from the division.
y=-1/3x+1
Please help me with math problem!! Will give brainliest!! :)
Answers
The amount of feet saved is given as follows:
24 feet.
What is the Pythagorean Theorem?The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.
Applying the Pythagorean Theorem, the diagonal length for this problem is given as follows:
d² = 35² + 50²
d = square root (35² + 50²)
d = 61 feet.
Without the diagonal, the distance would be of:
35 + 50 = 85 feet.
Hence the amount saved is given as follows:
85 - 61 = 24 feet.
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Find the area of the shaded regions below. Give
your answer as a completely simplified exact value
in terms of pi (no approximations).
Helppp pls
Answers
The area of the shaded regions in the given figure is 4.56 cm².
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
From the given figure,
Here, ΔLMN is isosceles triangle, ML=MN=4 cm
Now, area of a ΔLMN =1/2 ×Base×Height
= 1/2 ×4×4
= 8 cm²
By using Pythagora's theorem, we have
LN²=LM²+MN²
LN²=4²+4²
LN²=32
LN=4√2 cm
Area of semicircle = πr²/2
Here, radius =2√2 cm
Now, 3.14×(2√2)²/2
= 12.56 cm²
Area of shaded region = 12.56-8
= 4.56 cm²
Therefore, the area of the shaded regions in the given figure is 4.56 cm².
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HELP PLEASE ASAP!!!!!!
Answers
Answer:
26582
Step-by-step explanation:
Need help on this hurry!! :)))
Answers
Based on the given graph:
The y-intercepts is $20 and represents the fixed cost of the data usage. The slope of the linear function is 1/25 and represents the variable cost of each megabites of data usage used. The linear equation of this case is: y = 0.04x + 20Based on the given graph, we can know the relationship between the cost per month and data usage used per megabites.
On the graph, the line intercepts with y-axis on point (0, 20). This condition shows that even with 0 megabites data used, the customer will still be charged by $20 per month. This cost is known as a fixed cost. The y-intercepts is at 20.
The slope of the given line can be calculated by taking 2 different points from the graph:
(500, 40)
(1000, 60)
We use the slope formula, which:
m = y₂ - y₁
x₂ - x₁
m = 60 - 40
1000 - 500
m = 20 / 500
m = 1/25
The slope shows the additional cost the customer needs to pay for each megabites of data he used. This cost is also known as a variable cost.
Based on the given graph and the value of both slope and y-intercept, we can formulized a linear equation for this graph as:
y = 1/25 x + 20
y = 0.04x + 20
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decreasing the sample size, while holding the confidence level the same, will do what to the length of your confidence interval?
Answers
As a result, the confidence level widens as the sample size shrinks, indicating an inverse connection between the confidence interval and sample size.
How does interval depend on confidence interval?A broader interval will come from increasing the margin of error, which will also enhance the confidence. A tighter interval results from lowering the margin of error as confidence increases.The breadth of the confidence interval reduces as the confidence level rises.The interval widens when the sample size is reduced because the term s/sqrt(n) turns out to be higher as it gets larger. As a result, the confidence level widens as the sample size shrinks, indicating an inverse connection between the confidence interval and sample size.Because the standard error is reduced as sample size increases, confidence intervals are narrower.To learn more about confidence interval refer to:
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the probability that she hears her 2 favorite songs can be found using a number of
Answers
The probability that she hears her 2 favorite songs will be 0.01
How to calculate the probabilityProbability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.
The probability of hearing the first favorite song is 1/10.
The probability of also hearing the next favorite song is 1/10.
The probability will be:
= 1/10 × 1/10
= 1/100
= 0.01
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Serena has a playlist of 10 songs .she plays 2 songs . Find the probability that she hears her favorite song first and her next favourite second.
Let a = (0, 0), b = (7, 2), c = (3, 4), d = (3, 7), and e = (−1, 5). Cameron walks the polygonal path abcdea, writing down the number of degrees turned at each corner. What is the sum of these five numbers? notice that abcde is not a convex pentagon
Answers
Sum of angles at 5 corners of a polygonal path abcdea is 360 degrees (assuming convex polygon).
What is vector ?
Vector is a term that refers colloquially to some quantities that cannot be expressed by a single number, or to elements of some vector spaces.
The sum of the angles at the corners of a polygon is equal to (n-2) times 180 degrees, where n is the number of sides of the polygon. In this case, n = 5, so the sum of the angles at the corners is (5-2) * 180 = 360 degrees.
However, this assumes that the polygon is convex. Since abcde is not a convex pentagon, need to calculate the angles at each corner separately.
The angle between two lines can be calculated using the dot product formula:
cos(θ) = (u⋅v) / (||u|| * ||v||)
where u and v are the vectors representing the lines, and ||u|| and ||v|| are their magnitudes. The angle θ is between 0 and 180 degrees.
For example, to find the angle between the lines ab and bc,use the vectors b-a and c-b:
cos(θ) = (b-a⋅c-b) / (||b-a|| * ||c-b||)
Sum of angles at 5 corners of a polygonal path abcdea is 360 degrees (assuming convex polygon).
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The sum of these five numbers is 66.59 degrees.
To find the sum of the angles turned at each corner, we need to find the angle between each pair of adjacent sides.
First, we find the slope of the line segment between each pair of points:
AB: slope = (2-0)/(7-0) = 2
BC: slope = (4-2)/(3-7) = -2
CD: slope = (7-4)/(3-3) = 3
DE: slope = (5-(-1))/(-1-3) = -6
EA: slope = (0-5)/(0-(-1)) = 5
Next, we find the angle between each line segment using the inverse tangent function (atan).
AB: angle = atan(2) = 63.43 degrees
BC: angle = atan(-2) = -63.43 degrees
CD: angle = atan(3) = 71.57 degrees
DE: angle = atan(-6) = -84.97 degrees
EA: angle = atan(5) = 79.56 degrees
Adding up all the angles, we get:
63.43 + (-63.43) + 71.57 + (-84.97) + 79.56 = 66.59 degrees
So the sum of the five angles is 66.59 degrees.
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The formula for the Lateral Surface Area of a pyramid is LSA = (1/2) Pl; where 'P' is the perimeter of the base and 'l' is the slant height.
a. true
b. false
Answers
The formula for the Lateral Surface Area of a pyramid is LSA = (1/2) Pl; is true
What is the Surface Area of a Pyramid?
The total area of a pyramid's faces is referred to as the pyramid's surface area. In other terms, a pyramid's surface area is the whole area that the pyramid's surface occupies. Typically, it is measured in square units like m2, cm2, in2, and so forth.
The pyramid's two types of surface areas are:
A pyramid's lateral surface area (LSA) is the sum of its side faces' surface areas.LSA of the pyramid plus the base's area equals the pyramid's total surface area (TSA).Regular Pyramid Lateral Surface Area = (1/2) Pl Square Units
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True, the formula for the Lateral Surface Area of a pyramid is LSA = (1/2) Pl.
What is the Surface Area of a Pyramid?The total area of a pyramid's faces is referred to as the pyramid's surface area. In other terms, a pyramid's surface area is the whole area that the pyramid's surface occupies. Typically, it is measured in square units like m², cm², in², and so forth.
The pyramid's two types of surface areas are:
A pyramid's lateral surface area (LSA) is the sum of its side faces' surface areas.LSA of the pyramid plus the base's area equals the pyramid's total surface area (TSA).Refer to the attachment.
The base area of the pyramid is, B = a2
The base perimeter of the pyramid is, P = 4a
The area of each of the side faces = (1/2) × base × height = (1/2) × (a) × l
Therefore, the sum of all side faces = 4 [(1/2) × (a) × l] = (1/2) × (4a) × l
= (1/2) Pl.
Regular Pyramid Lateral Surface Area = (1/2) Pl Square Units
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How to convert 18 meters to feet?
Answers
18 meters = 59.0551 foot. Meter to Feet Conversion : One meter is approximately equal to 3.28084 feet. To convert meters to feet, multiply the given meter value by 3.28084 feet.
How do you convert meters to feet?One meter is roughly equivalent to 3.28084 feet. Multiply the given meter value by 3.28084 feet to convert meters to feet. 5 meters to feet, for example, is converted as follows: We know that multiplying 5 by 3.28084 converts 5 meters to feet.In most cases, all you need to know is that 1 meter = 3.28 feet, so simply divide a foot measurement by 3.28 to get the same length in meters.To convert meters to feet, we must first understand the difference in their lengths. According to the rule, one meter equals 3.28 feet and one foot equals 12 inches.To learn more about meters to feet conversion refer to:
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7. the soccer team had a fundraiser. they sold pizzas for $5.00 each and sub sandwiches for $3.00 each. they sold 11 more subs than pizzas and earned a total of $233. write and solve a system of equations to represent this situation and determine how many pizzas they sold.
Answers
The soccer team sold 25 pizzas.
Let x be the number of pizzas sold. Then, the number of subs sold would be x + 11.
The total amount of money earned from pizzas is $5.00 * x and the total amount of money earned from subs is $3.00 * (x + 11).
We can represent this situation using the following system of equations:
5x + 3(x + 11) = 233
Expanding the second equation:
5x + 3x + 33 = 233
Combining like terms:
8x + 33 = 233
Subtracting 33 from both sides:
8x = 200
Dividing both sides by 8:
x = 25
So, the soccer team sold 25 pizzas.
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The soccer team sold 25 pizzas.
Let x be the number of pizzas sold. Then, the number of subs sold would be x + 11.
The total amount of money earned from pizzas is $5.00 * x and the total amount of money earned from subs is $3.00 * (x + 11).
We can represent this situation using the following system of equations:
5x + 3(x + 11) = 233
Expanding the second equation:
5x + 3x + 33 = 233
Combining like terms:
8x + 33 = 233
Subtracting 33 from both sides:
8x = 200
Dividing both sides by 8:
x = 25
So, the soccer team sold 25 pizzas.
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The price of Stock A at 9 A.M. was $12.71. Since then, the price has been increasing at the rate of $0.12 each hour. At noon the price of Stock B was $13.46. It begins to decrease at the rate of $0.13 each hour. If the two rates continue, in how many hours will the prices of the two stocks be the same?
Answers
The prices of the two stocks will be the same after 3 hours from noon.
What is stock?A stock, also known as equity, is a security that represents the ownership of a fraction of the issuing corporation.
Given that, The price of Stock A at 9 A.M. was $12.71. Since then, the price has been increasing at the rate of $0.12 each hour. At noon the price of Stock B was $13.46. It begins to decrease at the rate of $0.13 each hour.
Let the hours when they equalize at h, then we have:
12.71 + 0.12h = 13.46 - 0.13h
0.25h = 0.75
h = 3
Hence, the prices of the two stocks will be the same after 3 hours from noon.
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If sides of a triangle are a = 3, b = 6, and c = 7, then what is the altitude of the triangle?
Answers
The triangle is 2.98142 meters high.
Explain about the altitude of the triangle?The height of a triangle is the perpendicular tracing from one side to the other of the triangle. The height of the triangle is also referred to as the altitude, which joins the base to form a right-angle triangle.
The formula h = xy, where x and y are the bases of the two analogous triangles formed when the height of the right triangle is drawn from one vertex to its hypotenuse, can be used to determine the altitude of a right triangle.
A line segment connecting a triangle's vertex to its opposite side is known as the triangle's altitude. In relation to the base or the side it touches, it is perpendicular. It is possible to draw three altitudes in a triangle because it has three sides. The Orthocenter is the location where the three heights of a triangle intersect.
s = a + b +c\2
hb = √ -a4 +2(ab)² + 2 (ac)² - b4 +2 (bc)² - c4/2b
=√-3 4 +2 .(3.6)² +2.(3.7)² - 6 4 +2.(6.7)²-7 4 / 2.6
=2.98142
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what is 0.9 is_______of 9?
Answers
Answer: 10
step by step explenation
I looked it up
suppose net income = $200 , depreciations = $10, and working capital went up by $70. what was cash from operations?
Answers
cash from operations is $140 when net income = $200 , depreciations = $10, and working capital went up by $70.
Cash from Operations = Net Income + Depreciation - Change in Working Capital
Plugging in the values:
Cash from Operations = $200 + $10 - $70
Cash from Operations = $140.
So, cash from operations is $140.
Cash from operations can be calculated by adding non-cash items such as depreciation and subtracting changes in working capital.
This means that the company generated $140 in cash from its operations during the given period. It is important to understand the cash from operations as it represents the cash generated from the day-to-day operations of the business and provides an indication of its ability to generate cash in the future.
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What is the next term of the following sequence?
12, 6, 3,.
6 124 0
00
a
Answers
The next term in the sequence is 1.5
What is an arithmetic sequence?It is a series of numbers that increase or decrease by a constant amount called the ratio of the progression. It is increasing when the ratio is positive and decreasing when it is negative.
The sequence given is: 12,6,3
We have to find the ratio or constant amount to find the next term:
12/2 = 6
6/2 = 3
We can see the successive term is half of the preceding one, so the general formula will be:
A(n+1)=A(n)/2
For the next term we get:
A(4th)= A(n)/2
A(4th) = 3/2
A(4th) = 1.5
The sequence is: 12, 6 ,3 , 1.5
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Correctly written question:
What is the next term of the following sequence? 12, 6, 3, ...
Using the Law of Cosines, in triangle QRP, if p= 28 km, q= 17 km, r= 15 km, find the measure of angle R
Answers
The measure of angle R is 106.5 degrees approximately when the
sides of the triangle are given.
If ABC is a triangle, then as per the statement of the Law of Cosines, we have: a2 = b2 + c2 – 2bc cos α, where a,b, and c are the sides of triangle and α is the angle between sides b and c.
Here PQR is a triangle, then as per the statement of cosine law,
we will have: p2 = q2 + r2 – 2pqcos R,
where p, q and r are the sides of triangle and R is the angle between sides q and p.
therefore, [tex]28^{2} = 17^{2} +15^{2}[/tex] - 2(28)(17)cos R
cos R = -270/952
= -0.284
R = cos-1(-0.284)
therefore, R = 106.499 = 106.5 approximately.
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find
-x^2/5 - 2x^2/5
Answers
Answer:
Step-by-step explanation:
If
a
1
=
4
a
1
=4 and
a
n
+
1
=
−
5
a
n
+
5
a
n+1
=−5a
n
+5 then find the value of
a
4
a
4
I NEED THIS RN MY HW DUE
.
Answers
Answer:
I can't understand your question do comment the question.find a b, 2a 3b, |a|, and |a − b|. a = 3, −4 , b = −3, 4
Answers
10 , [ -3 , 4 ] and [ 0 , 0 ] are the values in linear equation .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
a = [ 3, -4 ]
b = [ -3,4 ]
a + b = [ 3, -4 ] + [ -3,4 ]
= [ 0 , 0 ]
2a + 3b = 2 [ 3, -4 ] + 3 [ -3,4 ]
= [6 , -8 ] + [-9 , 12 ]
= [ -3 , 4 ]
l a - b l = l [ 3, -4 ] - [ -3,4 ]
= l [ 6 , -8 ] l
= √36 + 64
= √100
= 10
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While walking her dog, Sylvia noticed that 32 houses had a pot of red flowers on their
front step and 24 had a pot of yellow flowers. Write the ratio of red to yellow pots of
flowers three different ways. There is part a part b and part c pls helppp
Answers
The ratio of red to yellow pots of flowers in three different ways are
16 : 12, 8 : 6, and 4 : 3
As per the given data Sylvia while walking with her dog, she noticed that the 32 houses had a pot of red flowers on their front step.
Also, 24 houses had a pot of red flowers on their front step.
Here we have to determine that the ratio of red pots of flowers to yellow pots of flowers in three different ways.
The three different ways will be part a part b and part c.
The ratio of red to yellow pots of flowers.
32 : 24
Simplify the above ratio.
16 : 12
Also, we have to simplify further.
We get:
8 : 6
Then:
4 : 3
Therefore the ratios are 16 : 12, 8 : 6, and 4 : 3
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a bowl contains 3 red balls, 2 white balls and 1 blue ball. a what is the expected number of white balls obtained if three balls are selected at random from the bowl?
Answers
As per the given details, the expected number of white balls obtained when three balls are selected at random from the bowl is 58/60.
We must first determine the probability of choosing various numbers of white balls, then multiply those numbers by the corresponding probabilities in order to determine the expected number of white balls that will be produced when three balls are randomly chosen from the bowl.
Choosing none of the white balls: The chance of choosing none of the white balls can be estimated by choosing all three of the red and blue non-white balls.
The bowl has a total of 6 non-white balls. It is possible to choose 0 white balls with a probability of (6/6) * (5/5) * (4/4) = 1.
By choosing one white ball and two non-white balls, it is possible to compute the likelihood of selecting one white ball.
In the bowl, there are two white balls and four colored balls. The odds of choosing just one white ball are (2/6) * (4/5) * (3/4) = 2/5.
By choosing two white balls and one non-white ball, it is possible to compute the likelihood of selecting two white balls. Selecting two white balls has a probability of (2/6) * (1/5) * (4/4) = 2/30.
You can figure out the likelihood of selecting three white balls by choosing all three of them. The likelihood of choosing three white balls is 1/60 (2/6) * (1/5) * (1/4).
Expected number of white balls = (0 * 1) + (1 * 2/5) + (2 * 2/30) + (3 * 1/60) = 0 + 2/5 + 1/15 + 1/20 = 2/5 + 1/15 + 1/20
Expected number of white balls = (8/20) + (4/20) + (3/60) = 15/20 + 4/20 + 1/60 = 19/20 + 1/60 = 57/60 + 1/60 = 58/60
Therefore, the expected number of white balls obtained when three balls are selected at random from the bowl is 58/60, which can be further simplified to 29/30.
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Graph the line using slope and y intercept y=-1/3x - 7
Answers
Answer:
To graph the line using slope and y-intercept, we can follow these steps:
Identify the slope and y-intercept:
The slope of the line is -1/3.
The y-intercept is -7.
Plot the y-intercept:
Plot the point (0, -7) on the coordinate plane, since this is the point where the line intersects the y-axis.
Plot additional points using the slope:
Choose a convenient value for x (such as x = 1) and use the equation of the line to find the corresponding value of y.
Plot this point on the coordinate plane.
Repeat the process for several more values of x to obtain additional points on the line.
Connect the dots:
Draw a line through the points that you have plotted, connecting them to form the graph of the line.
Note: The line y = -1/3x - 7 will have a negative slope and will decrease as x increases, which means that the line will slope downward from left to right.
Question 4 (1 point) Quadrilateral DKLM is a rhombus. M A If DA = 4x and AL = 5x - 3, find DL. Blank 1:
Answers
The length DL of the rhombus is 24 units
How to determine the length DLThe figure that completes the question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
DA = 4x
AL = 5x - 3
This means that
DA = A:
So, we have
5x - 3 = 4x
Evaluate the like terms
x = 3
So, we have
DL = 2 * DA
This gives
DL = 2 * 4 * 3
Evaluate
DL = 24
Hence, the length is 24 units
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what is 2 x 4 + 82 - 18 divide by 8 x 9?
Answers
Answer:
1 because,
(2*4+82-18)/8*9
(8+82-18)/72
(90-18)/72
72/72
1
Answer:
Step-by-step explanation:
2 x 4 + 82 - 18 / 8 x 9
We want to use the PEMDAS rule for working math problems with more than one operation.
P = Parentheses first
E = Exponents second
M/D = Multiplication and division third
A/S= Addition and subtraction last
There are no parentheses, so we look for exponents next and there are none.
The next operations are multiplication and division.
Step 1
2 x 4 = 8
8 + 82 - 18 / 8 x 9
Step 2
8 x 9 = 72
Step 3
8 + 82 - 18 / 72
Before we can divide by 72, we need to add and subtract the top numbers from left to right.
Step 4
8 + 82 - 18 = 72
72/72
Now divide 72 by 72
Step 5
72/72 = 1
Two teams need to raise $100 each for their end-of-the-year field trips. Team A wants to sell popcorn at the Spring Fling Carnival, and Team B wants to sell cotton candy. It costs $15 to rent a popcorn machine, whereas it costs $25 to rent a cotton candy maker. The cost of additional supplies for the popcorn is $0.05 per bag, and the additional cost for the cotton candy is $0.10 per stick. Team A will sell the bags of popcorn for $0.75 each. Team B will sell the cotton candy for $0.80 per stick.
What is the least number of items Team A needs to sell to avoid losing money?
Answers
Team A needs to sell 255 bags of popcorn to reach their goal of $100.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Team A will sell the bags of popcorn for $0.50 each.
Team B will sell the cotton candy for $0.75 per stick.
Let the number of bags of popcorn sold by Team A be "x".
So, the total cost for the popcorn machine rental and supplies is
= $15 + 0.05x.
To reach their goal of $100
$100 = 0.5x - ($15 + 0.05x)
$100 = 0.5x - $15 - 0.05x
$115 = 0.45x
x = $115 / 0.45
x = 255 bags of popcorn
Thus, Team A needs to sell 255 bags of popcorn.
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