The length of ED is half the length of AB.
What is the length?Distance is measured by length. Length is a quantity with the dimension distance in the International System of Quantities. Most measurement systems use a base unit for length from which all other units are derived. The meter is the foundation unit of length in the International System of Units.Reasons:
The given parameters are;
In ΔABC, point E is the midpoint of AC
The midpoint of BC is the point D
Segment ED = s
Segment CE = p
Segment EA = r
Segment CD = q
Segment DB = t
Segment ED = s
Segment AB = u
Required:
The expression that represents the value of [tex]s[/tex].
Solution:
CE = 0.5 × AC Definition of midpoint
CD = 0.5 × CB Definition of midpoint
Therefore, we have;
[tex]\frac{CE}{AC} =\frac{CD}{CB} =0.5[/tex]
Therefore, given that ∠C ≅ ∠C, by the reflexive property, we have;
ΔABC is similar to ΔCDE by Side-Angle-Side similarity
Which gives;
[tex]\frac{CE}{AC} = \frac{CD}{CB} = \frac{ED}{AB} =0.5=\frac{1}{2}[/tex]
ED = s and AB = u which gives;
[tex]\frac{ED}{AB}=\frac{s}{u} =0.5=\frac{1}{2}[/tex]
[tex]\frac{s}{u} =\frac{1}{2}[/tex]
Which gives:
[tex]s=\frac{1}{2} *u[/tex]
The expression that represents the value of s is; s = one-half u
Therefore, the length of ED is half the length of AB.
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The question you are looking for is here:
If point E is the midpoint of segment AC and point D is the midpoint of segment BC, which expression represents the value of s? triangle CAB, point E is on segment AC between points A and C and point D is on segment BC between points B and C, creating segment ED, CE equals p, EA equals r, CD equals q, DB equals t, ED equals s, and AB equals u s equals p over q s = one half s equals q over p s = 2u
Subtract. Simplify your answer
(-8k^2-6)-(6k^2-5k)
Answer:
-14[tex]k^{2}[/tex] + 5k -6
Step-by-step explanation:
(-8[tex]k^{2}[/tex] -6) - (6[tex]k^{2}[/tex] - 5k) Distribute the negative sign
-8[tex]k^{2}[/tex] - 6 -6[tex]k^{2}[/tex] + 5k Combine like terms
-14[tex]k^{2}[/tex] + 5k -6
Answer: -14k^2+15k-6
Step-by-step explanation:
(-8k^2-6)-(6k^2-5k)
-8k^2-6-6k^2+5k
-14k^2-6+5k
-14k^2+15k-6
What is a residual and how is it used in finding the line of best fit?
Residual is the difference between the expected and actual y values, so r I = y I y i. A negative residual indicates that the anticipated value is excessively high, whereas a positive residual indicates that the projected value was excessively low. The goal of a regression line is to reduce the total amount of residuals.
What is Mcq, or salvage value?
When an item reaches the end of its useful life, its salvage value—or potential market value—is estimated. It can also be described as the asset's book value after depreciation has been taken into account.
What does the depreciation formula's residual value mean?
The asset's final worth is its residual value. To obtain the entire amount, it is therefore deducted from the starting value. Consequently, we are given the depreciation figure. This sum is divided by the usable years of the asset using the straight-line depreciation technique.
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A ray , and an angle is two . The measure of an angle related to the length of its sides. So, the measure of an angle the same at all distances from its vertex.
The combination of two rays with the same terminal is called an angle. The vertex of the angle is the common terminal of the rays, which are referred to as the sides of the angle.
What is the relation between angle and rays?A ray is a segment of a line with one endpoint and an endlessly extending end. Two rays can be linked at their starting points to create an angle, and their other ends can stretch indefinitely.
According to the question,
the proportion of an angle's measurement to the width of its sides.
Therefore, an angle's measure is constant regardless of how far it is from its vertex.
Due to the fact that adjacent angles are two angles with a shared vertex, and side, but not interior points.
Therefore,
The combination of two rays with the same terminal is called an angle.
The vertex of the angle is the common terminal of the rays, which are referred to as the sides of the angle.
Hence the measure of an angle is the same at all distances from its vertex.
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Answer:
Step-by-step explanation:
100 POINTS! PLEASE HELP
Given that one of the factors is (x-5), which graph represents the polynomial function?
y=-x^4 +6x^3 +11x^2 -60x -100
The graph on the bottom left represents the polynomial function
y = -x⁴ + 6x³ + 11x² - 60x - 100.
What is graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.
The relationships between two or more items are frequently represented by the points on a graph.
Given:
An equation,
y = -x⁴ + 6x³ + 11x² - 60x - 100.
And one of the factors of the equation is (x-5).
That means, x = 5 is one of the roots of the equation.
From the given graphs,
we can eliminate top left graph and bottom right graph.
Because, the graphs of the equation do not touch the x-axis at x = 5.
Let x = -2,
Then,
y = -(-2)⁴ + 6(-2)³ + 11(-2)² - 60(-2) - 100.
y = -16 -48 + 44 + 120 - 100
y = 0
That means,
x = -2 is one of the roots of the equation.
And the graph is given in the attached image.
And the graph is the bottom left graph.
Therefore, the graph in the bottom left is the required graph.
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Which of the following equations has no real roots?A x 2+4x+3 2=0B x 2 +4x−3 2 =0C x 2 +5x+3 2 =0D 3x2 +4 3x+4=0
The equation x² - 4x + 3√2 = 0 has no real roots.
Roots of Quadratic EquationThe roots of a quadratic equation are the values of variables satisfying the given quadratic equation.
There are three types of roots in quadratic equations, they are:
Real and distinct roots.Real and equal roots.Complex roots.Difference between real and non-real roots
How many roots f(x) has can be seen from the discriminant's value : -
If b2 - 4ac > 0, the quadratic function has two unique real roots.
If b2 - 4ac = 0, then the quadratic function has one repeating real root.
If b2 - 4ac < 0, then the quadratic function has non-real roots.
Discriminant ; D = b² - 4ac
According to the given question, we have to find the nature of the roots of the equation, so finding the nature of the roots of all the equations separately
1. x² - 4x + 3√2 = 0
Here, a = 1, b = -4 and c = 3√2
∵ D = b² - 4ac
∴ D = (-4)² - 4(1)(3√2)
⇒ D = 16 - 12√2
⇒ D = 16 - 12(1.414) = 16 - 16.968
∴ D = -0.968
⇒ D < 0
Consequently, there are no real roots in the equation.
2. x² + 4x - 3√2 = 0
Here, a = 1, b = 4 and c = -3√2
∵ D = b² - 4ac
∴ D = (4)² - 4(1)(-3√2)
⇒ D = 16 + 12√2 > 0
⇒ D > 0
As a result, the equation has two unique real roots.
3. x² + 5x + 3√2 = 0
Here, a = 1, b = 5 and c = 3√2
∵ D = b² - 4ac
∴ D = (5)² - 4(1)(3√2)
⇒ D = 25 - 12√2 = 8.029
⇒ D > 0
As a result, the equation has two unique real roots.
4. 3x² + 4√3x + 4 = 0
Here, a = 3, b = 4√3 and c = 4
∵ D = b² - 4ac
∴ D = (4√3)² - 4(3)(4)
⇒ D = 48 - 48 = 0
⇒ D = 0
As a result, the equation has two roots that are equal.
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Reflection: State if the figure has a reflection that carries onto itself. If so state how many lines of symmetry the figure has.
This refers to objects that can be divided into two identical halves. The line that divides the object into its identical halves is known as the line of symmetry.
Line of symmetry is of three types: vertical symmetry, horizontal symmetry, and diagonal symmetry.
Irregular shapes have no equal sides. Thus, they can not be split into two identical halves.
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Evaluate. 12/3+3/4÷(−1/3)−1/2
The fraction 12/3+3/4÷(−1/3)−1/2is evaluated to give -114/10
What is a fraction?A fraction can be defined as part of a whole element, variable or number
The several types of fractions in mathematics are;
Mixed fractionsProper fractionsImproper fractionsSimple fractionsComplex fractionsFrom the information, we have that;
12/3+3/4÷(−1/3)−1/2
The fraction given is a mixture of proper fractions and improper fractions
Expand the bracket, we get;
12/3 + 3/4 ÷ -1/3 -1/2
Find the lowest common denominator
48 + 9 /12 ÷ -2 - 3 /6
Add the numerators
57/12 ÷ -5/6
Take the inverse of the divisor and multiply
57/12 × 6/-5
-114/10
Hence, the value evaluated from the fraction is -114/10
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How do you find the legs of a 30 60 90 triangle given the long leg?
Answer:
A 30-60-90 triangle is a special type of right triangle where the angles are 30 degrees, 60 degrees, and 90 degrees. The side opposite the 30 degree angle is called the "short leg", the side opposite the 60 degree angle is called the "medium leg", and the side opposite the 90 degree angle is called the "long leg".
The ratios of the sides in a 30-60-90 triangle are always in the proportion of 1 : √3 : 2 . To find the legs of a 30-60-90 triangle when given the long leg, you can use these ratios.
If the long leg is "x", then the short leg is x/2 and the medium leg is x*√3/2.
For example, if the long leg is 8 cm, you can use these ratios to find the short leg and medium leg:
The short leg is 8 cm / 2 = 4 cm
The medium leg is 8 cm * √3 / 2 = 4 * √3 cm = 4 * 1.732 cm = 6.928 cm (approx)
So, in this example, the short leg is 4cm and the medium leg is 6.928cm (approx).
It's always a good idea to draw a diagram and label the sides to help you visualize the problem and check your answer.
Step-by-step explanation:
Norman earns $8 for every dog he washes plus25% of the cost of the dog wash. Write an expression that represents the total amount of money Norman earns for one dog wash with a cost, c.
Answer:
y = 0.25c + 8
Step-by-step explanation:
Let's y represent the total cost
We know
25% = 0.25
So, we will write this in the slope-intercept form y= mx +b
So, we have m = 0.25, and b = 8, so our equation is
y = 0.25c + 8
The scores of 10 students on a history test are 85, 79, 65, 72, 86, 66, 90, 98, 78, and 76. Which box plot represents the given data?.
The box will start at 72 and end at 86. At 78.5, a vertical line will be drawn through the box. Arrows will appear at both ends of the box. The one on the left will come to a halt at 65 miles per hour, while the one on the right will come to a halt at 98 miles per hour.
What is box plot?A box plot, often known as a boxplot, is a method in descriptive statistics for graphically displaying the localization, spread, and skewness groups of numerical data through their quartiles. A box plot is a graphical representation of statistical data that uses the lowest, first quartile, median, third quartile, and maximum values. The name "box plot" refers to how the graph resembles a rectangle with lines extending from the top and bottom. Box and whisker plots, often known as box plots, are an excellent graphic for displaying the distribution of data points over a specified metric. These graphs show ranges within variables that have been measured. Outliers, the median, the mean, and where the majority of the data points fall inside the "box" are all included.
Here,
65, 66, 72, 76, 78, 79, 85, 86, 90, 98
Q1 = 72
(78 + 79) / 2 = 78.5 Q2 (median)
Q3 = 86
min = 65
max = 98
So the box plot will look like this:
The box will begin at 72 and conclude at 86. At 78.5, a line will be drawn vertically through the box. Arrows will emerge from both ends of the box. The one on the left will come to a stop at 65, while the one on the right will come to a rest at 98.
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A Question 1 (1 point) Retake question
The ratio of the measures of the three angles in a triangle is 14:5:11.
Find the measures of the angles.
Please helllopppp
The measures of the three angles in a triangle is 84°, 30° and 66° respectively.
How do you calculate a triangle's ratio?α + β + γ = 180° . From this, you can calculate the angles: ax, bx, and cx, as well as the unknown x. We translate these ideas into a detailed procedure for using ratios to locate missing angles in triangles in the following section.
The ratios are:
∠A = 14, ∠B = 5, ∠C = 11
Total ratio = 14 + 5 + 11= 30
The total angle in a triangle = 180°
So,
∠A= 14 / 30 × 180°= 0.46× 180°= 84°
∠B= 5/30 × 180°= 0.16 × 180°=30°
∠C= 11/30 × 180°= 0.366× 180°= 66°
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Algebra 2, I remember doing this but i’m confused bc I remember like (f)g)(x) something like that so do I multiply or what?
If the function g(t) is -4t + 5 then (g o g)(t) will be 16t - 15.
What is a function?A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain. Originally, functions were the idealization of how a varying quantity depends on another quantity.f(g(x)) means so wherever there is an x in the function f, the function g(x) is substituted.Here given function,
g(t) = -4t + 5
We have to find (g o g) (t)
(g o g)(t) = g(g(t))
= g(-4t + 5)
= -4(-4t + 5)+ 5
= 16t -20 +5
= 16t - 15
Therefore the function (g o g)(t) is 16t - 15.
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Jean sold 32 boxes of
cookies. If this is 40% of
her goal how many boxes
does Jean want to sell?
Answer:
80 boxes of cookies
Step-by-step explanation:
First, we have to find 1% by taking
32 divided by 40 = 0.8
Then we take it times 100%
0.8 x 100 = 80 boxes of cookies
Jean want to sell 80 boxes of cookies
ITS COMPOUND INTERSERT ITS URGENTT
Mike's car will be worth £4116 at the start of 2017 as the car decreases in value by 30% every year
How to evaluate for the decreased value of the carAt the start of 2014, Mike's car is worth £12000,
we shall calculate the decreased worth of the same car to the start of 2017 as follows:
At the end of 2014, 30% of £12000 is calculated as;
£12000 × 30/100 = £3600
At the start of 2015, the car will be worth
£12000 - £3600 = £8400
At the end of 2015, 30% of £8400 is calculated as;
£8400 × 30/100 = £25200
At the start of 2016, the car will be worth
£8400 - £2520 = £5880
At the end of 2016, 30% of £5880 is calculated as;
£5880 × 30/100 = £1764
At the start of 2017, the car will be worth
£5880 - £1764 = £4116
Therefore, Mike's car will decrease in value to worth £4116 at the start of 2017.
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Solve For Each Variable 17n+8=104+5n
The solution of the expression 17n + 8 = 104 + 5n for the variable n is given as follows:
n = 8.
How to solve the expression?The expression for this problem is defined as follows:
17n + 8 = 104 + 5n
Combining the like terms, the expression is given as follows:
17n - 5n = 104 - 8.
12n = 96.
The inverse operation of the multiplication is the division, hence the value of n is obtained as follows:
n = 96/12
n = 8.
Which is the solution of the expression for the variable n.
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eliminate the parameter t to find a Cartesian equation for:
x=t2
y=2+3t
x=Ay2+By+C
Where A=________ B=__________ and C=________
Cartesian equation for x=t2,y=2+3t, x=Ay2+By+C, Where
A=1, B=0, and C=0
To eliminate the parameter t and find a Cartesian equation for the given equation, we need to solve for t in terms of x and substitute it into the equation for y.
We start by solving for t in terms of x:
t = √x
Now, we substitute this into the equation for y:
y = 2 + 3√x
Therefore, the equation for x and y becomes:
x = x
y = 2 + 3√x
Which can be represented as a Cartesian equation:
Ay2 + By + C = 0
where A=1, B=0, and C=0.
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what are 2 numbers that can multiply to 14 and add up to sum -9
Answer: -2, -7
Step-by-step explanation:
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 13, 19,25,... Find the 48th term.
The given sequence is 13, 19, 25, ...
What comprises an arithmetic series?
An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.
This sequence appears to be increasing by 6 each time, so it is an arithmetic sequence. The common difference is 6. The nth term of an arithmetic sequence is given by the formula:
an = a1 + (n-1)d
where a1 is the first term, d is the common difference and n is the position of the term in the sequence.
We can use this formula to find the 48th term of the sequence:
a48 = a1 + (48-1)d
a48 = 13 + (48-1)6
a48 = 13 + 47*6
a48 = 13 + 282
a48 = 295
So, the 48th term of the sequence is 295.
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Simplify: (8^ 2/3)^4
Answer: 256
Step-by-step explanation:
Remove any grouping symbol such as brackets and parentheses by multiplying factors.Use the exponent rule to remove grouping if the terms are containing exponents.Combine the like terms by addition or subtraction.Combine the constants.
y=1.7952 × 2.0657^x
find x when y=1000
The value of x when y = 1000 is 8.59.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
y = 1.7952 x [tex]2.0657^x[/tex]
Substitute y = 1000
1000 = 1.7952 x [tex]2.0657^x[/tex]
10³ = 1.7952 x [tex]2.0657^x[/tex]
Taking logs on both sides.
log 10³ = log (1.7952 x [tex]2.0657^x[/tex])
3 log 10 = log 1.7952 + x log 2.0657
3 x 1 = 0.25 + 0.32x
3 = 0.25 + 0.32x
0.32x = 3 - 0.25
x = 2.75/0.32
x = 8.59
Thus,
The value of x is 8.59.
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∣x−7∣=∣2x−8∣ (there are 2 solutions for the positive one and the negative)
Answer:
x = 1, x = 5
Step-by-step explanation:
|x−7|=|2x−8| ==> there are 2 ways to simplify this equation:
1. x - 7 = 2x - 8
2. -(x - 7) = 2x - 8
Let's first solve equation 1:
x - 7 = 2x - 8
-7 = x - 8 ==> subtract x on both sides
x - 8 + 8 = -7 + 8 ==> add 8 on both sides
x = 1 ==> simplify
Now let's solve equation 2:
-(x - 7) = 2x - 8
-x - (-7) = 2x - 8 ==> distribute the negative sign to x and -7
-x + 7 = 2x - 8 ==> subtracting a negative number is equivalent to adding a
positive number
7 = 3x - 8 ==> add x on both sides
15 = 3x ==> add 8 on both sides
x = 5 ==> divide 3 on both sides
Hence, the answers are x = 1 and x = 5.
How do I Create a table in form?
Therefore , the solution of the given problem of table comes out to be we can create a table in form by following below steps.
Explain a table.A mathematical list is a list of numbers that represents the results of a calculation with several inputs. organized in rows and columns, data consists of numbers and descriptions. It is simple to recall the table and the 10 pattern. 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30 are the numerals in numerical order. Value mapping are used to illustrate the connections between various data elements.
Here,
Import the layout table by moving the pointer to the desired location on the form template.
Click Insert, followed by Layout Table, in the Tables toolbar.
The number of rows and rows to be included in the table should be entered with in Insert Table dialog box.
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please please please help me
Answer:
For the first one, the answer would be:
2/3 * 3/8 = 6/24 because, all you have to do is multiply straight across.
2 * 3 = 6 and 3 * 8 = 24
6/24 can be simplified to 1/4 because 6 with go into the denominator 4 times, so the simplified fraction will be 1/4.
(Im not so sure what to do about the second one, so I would need to see what the options look like)
For the third:
The answer would be 3/3, because:
2 * 3 = 6
5 * 3 = 15
And the result fraction is 6/15, which matches what the image shows!
Step-by-step explanation:
Hope it helps! =D
A rectangle has a width of 15 cm and a length of 25 cm. What is the perimeter of the rectangle?
A. 50 cm
B. 75 cm
C. 100 cm
D. 125 cm
Answer:
The perimeter of a rectangle is the total distance around the outside of the rectangle. To find the perimeter of a rectangle, you add the lengths of all four sides.
In this case, the width of the rectangle is 15 cm and the length is 25 cm. To find the perimeter, we add the lengths of all four sides, which are:
15 cm + 15 cm + 25 cm + 25 cm = 75 cm
Therefore, the perimeter of the rectangle is 75 cm. The answer is B. 75 cm.
Step-by-step explanation:
The length of a basketball court is 84 feet, and the perimeter is 268 . What is the width of the basketball court?
Answer: 50 ft
Step-by-step Explanation:
First, subtract the given length from the perimeter:
*268 - (84 x 2) = 100
Then divide this by 2:
100 / 2 = 50
*We multiply the 84 by 2 since the court is assumed to have 4 sides meaning there are two sides with lengths and two sides with widths.
Need help on the question
- x/7 − 8 = 17
Show work
And check
Answer:
x = -175
Step-by-step explanation:
Given:
⇒ [tex]-\frac{x}{7}-8=17[/tex]
Solution:
Work:
[tex]-\frac{x}{7}-8=17[/tex]
[tex]-\frac{x}{7}-8+8=17+8[/tex] ⇒ Add 8 to both sides
[tex]-\frac{x}{7}=25[/tex]
[tex]7\left(-\frac{x}{7}\right)=25\cdot \:7[/tex] ⇒ Multiply both sides by 7
-x = 175
[tex]\frac{-x}{-1}=\frac{175}{-1}[/tex] ⇒ Divide both sides by -1
x = -175
Check:
Since, x = -175. We can substitute into the equation to check.
[tex]-\frac{-175}{7}-8=17[/tex]
[tex]-\frac{-175}{7}=25[/tex]
[tex]25-8=17[/tex] ⇒ Statement = True (25 minus 8 is 17.
Hence, x = -175
Lenvy~
What is called as factor of polynomial?
Therefore , the leading term 1 and constant 0 in the above function make it a polynomial function.
A polynomial function is what?A polynomial function can be defined in an equation that uses only real number exponents or non-negative integer powers of a variable. Examples of such equations include cubic and quadratic equations. The exponent of the polynomial 2x+5 is 1, for instance.
Here,
For the following polynomial function, exponents all positive integers in this case.
Exponent 1 applies to the positive number 2x.
, 1 where is an integer with positive exponent and and.
Among the coefficients of the function are real values like 5 and 1.
Thus, a polynomial characterizes the function.
It is a polynomials with a degree of five.
When writing a polynomial in standard form, the word with the largest exponent is used as the starting point, and the other terms are written in order of importance of expressions with lesser exponents.
The polynomial is expressed in standard form as f(x)=2x+1.
containing the leading word 1, the constant 0, and
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2y = 6x + 4
y = -2x + 2
find x and y
The value of x is 0.
The value of y is 2.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 9 is an equation.
We have,
2y = 6x + 4 _____(1)
y = -2x + 2 ______(2)
Substituting (2) in (1).
2 (-2x + 2) = 6x + 4
-4x + 4 = 6x + 4
4 - 4 = 6x + 4x
10x = 0
x = 0
Now,
x = 0 in (2)
y = -2 x 0 + 2
y = 0 + 2
y = 2
Thus,
The value of x and y is 0 and 2.
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Select ALL the correct answers. Select the expressions that are equivalent to the expression below. (375/345) 1/3
The equation is given by A = ∛ ( 375/345 ) and A = ( ∛375 ) / ( ∛ 345 )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = (375/345) ^ 1/3 be equation (1)
On simplifying the equation , we get
The number raised to the power ( 1/3 ) means it is the cube root of the number ,
So , A = ∛ ( 375/345 )
Now , taking the cube root on both the numerator and denominator ,
A = ( ∛375 ) / ( ∛ 345 )
Hence , the value of A is ( ∛375 ) / ( ∛ 345 )
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