Final answer:
Using the Pythagorean theorem, the length of the longest side of right-angled triangle CDE, which is the hypotenuse DE, is found to be 39 units.
Explanation:
In triangle CDE, angle C is given as 90 degrees, making this a right-angled triangle. According to the information provided, side CD is 15 units long, and side DE is 3 units more than side CE. We are asked to find the length of the longest side, which would be the hypotenuse in a right-angled triangle. To find the hypotenuse, which we'll designate as side DE, we must first establish the relationship between the sides. Let's call CE 'x'; therefore, DE will be 'x + 3'. Since we've established that the triangle is right-angled at C, we can use the Pythagorean theorem, which states that in a right-angled triangle the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
So, the equation becomes CD² + CE² = DE², or 15² + x² = (x + 3)². If we solve for 'x' we have:
225 + x² = x² + 6x + 9216 = 6xx = 36As a result, CE = 36 units and DE, the longest side, equals 36 + 3, which is 39 units.
By applying the Pythagorean theorem correctly, we've found that the length of the longest side of triangle CDE is 39 units.
what is the slope the line cantains the points (-1,2) and (3,3)?
∠E and ∠F are vertical angles with m∠E=8x+8 and m∠F=2x+38 . What is the value of x? Enter your answer in the box.
Answer:
x = 5
Step-by-step explanation:
We need to remember that vertical angles are opposite to each other when two lines cross. The vertical angles that result from two lines crossing have the same measure.
In this problem we have angle E which measures 8x + 8 and angle F which measure 2x + 38.
Since they are vertical angles, we know that they have the same measure and therefore we can equal them both and solve for x:
[tex]8x+8=2x+38\\8x-2x=38-8\\6x=30\\x=5[/tex]
Therefore, x = 5 (and ∠E = ∠F = 48)
What is the equation of a line passing through the points 6,3 and -4,3 so y=?
Answer:
y=3
Step-by-step explanation:
The required line will be y = 3 which is passing through points (6,3) and (-4,3)
What is the slope of the line?The slope of the line is defined as the gradient of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Assume two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)
To determine the line of passing through points (6,3) and (-4,3)
We have been given two points :(6,3) and (-4,3)
Let the required line will be:
(y - y₁) = [(y₂ - y₁)/(x₂ -x₁ )](x -x₁ )
Here
x₁ = 6, y₁ = 3
x₂ = -4, y₂ = 3
(y - y₁) = [(y₂ - y₁)/(x₂ -x₁ )](x -x₁ )
Substitute values in the above formula
(y - 3) = [(3 - 3)/(-4 -6 )](x -6 )
(y - 3) = [(0)/(-10 )](x -6 )
(y - 3) = 0
y = 3
Therefore, the required line will be y = 3
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If you have a distribution of 50 scores, and you want 5 intervals, what should be the size of your class interval?
If be bisects abd find x and m angle abe
Which figure shows how a shape can be rotated about an axis to form the given object?
The figure that shows how a shape can be rotated about an axis to form a disc is (c) rectangle
How to determine the figure?The shapes in the figures are given as:
A. Rectangle
B. Semicircle
C. Inscribed semicircle
D. Another Rectangle
When the first rectangle is rotated about the axis, it forms a spiral shape
Rotating a semi-circle and the inscribed semi-circle about its axis would form a hemisphere
However, when a rectangle that has one of it sides on the axis is rotated, it forms a cylinder or disc
Hence, the figure is (d) rectangle
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does anyone know
2x=8y=7
4x-2y=9
You are offered an item for $17.85. If the seller states he normally sells the same item for $19.95, what percentage discount is he offering you?
Answer:
Find out the what percentage discount is seller offering you .
To prove
Formula
[tex]Discouunt\ percentage = \frac{Discount\times 100}{Marked\ price}[/tex]
Discount = Marked price - Selling price
As given
You are offered an item for $17.85. If the seller states he normally sells the same item for $19.95 .
Here
Marked price = $19.95
Selling price = $17.85
Discount = 19.95 - 17.85
= $2.1
Put in the formula
[tex]Discouunt\ percentage = \frac{2.1\times 100}{19.95}[/tex]
[tex]Discouunt\ percentage = \frac{210}{19.95}[/tex]
Discount percentage = 10.5% (Approx)
Therefore the discount is seller offering you is 10.5 % .
What is a methodical step by step procedure that guarantees solving a problem?
Write each rational number as a repeating decimal.
1. -7/9
2. 11/15
3. 8/3
Final answer:
To write a rational number as a repeating decimal, perform long division. -7/9 as a repeating decimal is -0.7777..., 11/15 is 0.7333..., and 8/3 is 2.6666...
Explanation:
To write a rational number as a repeating decimal, you need to perform a long division. Let's go through each of the given rational numbers:
1. -7/9
When you divide -7 by 9, you get -0.7777… with the 7s repeating. So, -7/9 as a repeating decimal is -0.7777…
2. 11/15
When you divide 11 by 15, you get 0.7333… with the 3s repeating. So, 11/15 as a repeating decimal is 0.7333…
3. 8/3
When you divide 8 by 3, you get 2.6666… with the 6s repeating. So, 8/3 as a repeating decimal is 2.6666…
classify each pair of labeled angles as complementary, supplementary, or neither.
Answer: supplementary, complementary, neither.
Step-by-step explanation:
How is the distance formula like the pythagorean theorem explain?
The distance formula is
simply a variation of the theorem. The method is the same with the Pythagorean
however we are now dealing with 2 sets of points instead of 2 lengths.
In the distance formula, the lengths are derived from the
(x1,y1)->(x2,y2) coordinate points and the formula simplified. We still
square the difference of x’s and difference of y’s to get our two squares then
square root the sum to give our length. While the Pythagorean theorem is
directly the sum of the square of the other two sides.
Nevertheless, both formulas work on the same principle.
Answer:
Both formulas can be used to find the distance between two points on the coordinate plane. The vertical leg of the right triangle represents the difference in the y values of the two points. The horizontal leg of the right triangle represents the difference in the x values of the two points. The hypotenuse of the right triangle represents the distance between the two points.
Step-by-step explanation:
Write the equation in slope -intercept form with slope of 4 that contains (-3, -6).
A population of flies grows according to the function p(x) = 5(2)x, where x is measured in weeks. A local spider has set up shop and consumes flies according to the function s(x) = 3x + 2. What is the population of flies after three weeks with the introduced spider?
x = 3 weeks
Growth: 5(2)(3) = 30 flies in 3 weeks
eaten: 3(3) +2 = 9+2 =11 flies eaten in 3 weeks
30-11 = 19 flies ( population after 3 weeks)
The rule (x,y)→(2x,2y) maps △DEF to △D′E′F′.
Which statement correctly describes the relationship between △DEF and △D′E′F′ ?
the triangles are congruent because △D′E′F′ is a rotation of △DEF , and a rotation is a rigid motion.
The triangles are congruent because △D′E′F′ is a reflection of △DEF , and a reflection is a rigid motion.
The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.
The triangles are not congruent because △D′E′F′ is a translation of △DEF , and a translation is not a rigid motion.
The scale on a map of Texas shows that 1 inch represents 20 miles. The actual distance from Austin to Dallas is 195 miles. On the map, how many inches apart are the two cities?
To calculate the map distance between Austin and Dallas with a scale of 1 inch representing 20 miles, and an actual distance of 195 miles, set up a proportion and solve to find that Austin and Dallas would be 9.75 inches apart on the map.
Explanation:To find out how many inches Austin is from Dallas on the map, we need to set up a proportion. The scale given on the map is 1 inch represents 20 miles. We know the actual distance between Austin and Dallas is 195 miles. To calculate the distance on the map, we use the proportion 1 inch / 20 miles = x inches / 195 miles.
Cross-multiply to solve for x:
(1 inch) * (195 miles) = (20 miles) * (x inches)
195 inch-miles = 20x inch-miles
Now, divide both sides by 20 miles to solve for x:
x = 195 inch-miles / 20 miles
x = 9.75 inches
So, on the map, Austin and Dallas would be 9.75 inches apart.
Graph the following inequality and then select the correct graph below. x + y < 1
( first answer choice is a dotted vertical graph shaded down)
(second answer is a vertical line graph shaded up)
plsss help
Answer:
Given inequality,
[tex]x+y<1[/tex]
For graphing the inequality :
The related equation of the given inequality,
x + y = 1
Having the x-intercept = (1,0),
y-intercept = (0,1),
Also, at (0,0),
0 + 0 < 1 ( True )
⇒ The area of the given inequality x + y < 1 must contain the origin.
Now, '<' show the dotted line.
Thus, by the above explanation we can plot the graph of the given inequality.
how do u solve using the ratios !
?PLEASE HELP!!!!
The table shows the relationship between the number of bracelets made and the number of beads used: Number of bracelets Number of beads 3 24 5 40 7 ? 9 72 The number of beads used to make 7 bracelets is _______.
The number of beads used to make 7 bracelets will be equal to 56 beads.
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the data given in the question,
Three bracelets have 24 beads, so start with the lowest number. Finding out how often beads are on a single bracelet will help you locate the solution the quickest. We shall know the answer on 24/3.
24/3=8.
Then multiplying 56 by 7 to get.
Then confirm that your response still makes sense.
3 x 8 = 24
5 x 8 = 40
7 x 8 = 56
9 x 8 = 72
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So I’m doing test corrections and I need help on the problem
Large reusable bottles cost $4 more than small ones. 8 large bottles cost $24 less than 12 small ones. How much does one small bottles cost?
solve the equation 17=-13-8x with steps
The solution for given equation 17=-13-8x is x = -15/4.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .
The given equation is,
17 = -13 - 8x
Now to solve the equation following steps are followed :
adding 13 both the sides of the equation,
17 + 13 = -13 - 8x + 13
or, 17 + 13 = -13 + 13 - 8x
Solving them we get,
30 = - 8x
or, - 8x = 30
multiplying -1 both side
- 8x*(-1) = 30*(-1)
Solving them we get,
8x = -30
dividing both side by 2
8x/2 = -30/2
Solving them we get,
4x = -15
dividing both side by 4
4x/4 = -15/4
Solving them we get
x = -15/4
Hence,the solution for given equation 17=-13-8x is x = -15/4.
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(f) how many ways are there to place a total of m indistinguishable balls into n distinguishable urns, with some urns possibly empty or with several balls?
You claim to have a magic coin that will land on heads whenever you want. Your friend dares you to prove it by tossing 4 heads in a row. Assuming the coin is fair, what is the probability that your magic will fail?
A) 50%
B) 62.5%
C) 75%
D) 93.75%
Convert the radian measure to degree measure. use the value of π found on a calculator and round answers to two decimal places. five pi divided by six
The measure of each interior angle of a regular polygon is 140 degrees, how many sides does the polygon have
The regular polygon with an interior angle of 140 degrees has 9 sides. This conclusion can be reached by using the formula for the interior angle of a polygon, which is (n-2)*180/n, where 'n' represents the number of sides.
Explanation:
The number of sides in a regular polygon can be determined using the formula for the interior angle of a polygon, which is (n-2)*180/n, where 'n' represents the number of sides. This formula comes from the fact that a polygon can be divided into (n-2) triangles, each of which has angles summing up to 180 degrees.
In this particular case, an interior angle of 140 degrees is given. So we will set up an equation: 140 = (n-2)*180/n. Solving for 'n', we get a value of 9.
Therefore, the regular polygon with an interior angle of 140 degrees has 9 sides.
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What is the sine of angle a?
a. 12/13
b. 5/13
c. 5/12
d. 13/12
Which of the following measurements is equivalent to 5 quarts? 25 cups 40 fl. oz. 10 pt. 1 gal.
Solve fro the Equation below:
7+2(x-3)=-3(x+1)-4
What is 42/100 simplified?