the area of an issoseles triangle is 240 if the base is 24cm find the length of each sides
Answers
Answer:
Both of the two unknown sides of the triangle are 23.32 cm
Step-by-step explanation:
"Isosceles" means that the triangle has two equal sides. It is quite symmetrical. If we draw in the height, the base will be cut right in half by it. See image.
First use area formula:
A = 1/2bh
to find the measure of the height (Area and base were both given)
Then use the Pythagorean Theorem to solve for the hypotenuse, which is the side of the triangle. See image.
Related Questions
What is the missing reason in the proof?
given
transitive property
alternate interior angles theorem
converse alternate interior angles theorem
Answers
Two students created a list of steps for the following construction. Which student has steps in the correct order, and which does not? Explain.
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The steps of student B are in the correct order but the steps of student A are in the incorrect order.
What is a perpendicular and parallel line?Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines and the lines that never intersect are known as parallel lines.
We have:
You are given AB and point C. Construct a line parallel to AB that passes through point C
The correct way to draw a parallel line to AB that passes through point C is:
1. Draw a line that intersects points B and C.2. Place the compass on point B, and swing an arc that crosses line AB and line BC. Label the points D and E.3. Keep the compass at the same width, and place it on point C.4. Swing an arc that crosses line BC, and label the point F.5. Open the compass to the width between points D and E.6. Keeping the compass at the same width, place it on point F.7. Swing an arc that intersects the arc created from line BC at point C.8. Mark the intersection of the two arcs as point G.9. Draw a line through point C and point G.The steps of student B are in the correct order but the steps of student A are in the incorrect order.
Thus, the steps of student B are in the correct order but the steps of student A are in the incorrect order.
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It's very urgent plss answer
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The solution of the equation 4p – [(2p – 3) / 2] = 6 with variable p will be 1.5.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
The equation is given below.
4p – [(2p – 3) / 2] = 6
On simplifying, we have
(8p – 2p + 3) / 2 = 6
6p + 3 = 12
6p = 9
p = 1.5
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A line passes through the points (6, 8) and (5, 5). What is its equation in slope-intercept form?
Answers
Answer:
b6,4
Step-by-step explanation:
becust tehf sdj
2 inches tall on week 4 3 inches tall on week 6 4 inches tall on
week 8
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The linear relation of the height as a function of the number of weeks is:
y = 0.5*x
How to find the linear relation?A general linear relation is written as:
y = a*x + b
Where a is the slope.
If we know that the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
In this case, we have the points of the form (week, height).
(4, 2)
(6, 3)
(8, 4)
If we use any two of these we can get the slope, so using the first two:
a = (3 - 2)(6 - 4) = 1/2 = 0.5
y = 0.5*x + b
To get the value of b, we can use the first point, it says that when x = 4, we have y = 2, then:
2 = 0.5*4 + b
2 = 2 + b
0 = b
Then the linear relation of the height as a function of the number of weeks is:
y = 0.5*x
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Prove that for all integers n ≥ 3, n+1P3 −n P3 = 3 · n P2
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The permutation equation [tex]^{n+1}P_3 - ^nP_3= 3 * ^nP_2[/tex] is true for all integers n ≥ 3
How to prove the equation?We have:
[tex]^{n+1}P_3 - ^nP_3= 3 * ^nP_2[/tex]
Apply the following permutation formula
[tex]^{n}P_r = \frac{n!}{(n- r)!}[/tex]
So, we have:
[tex]\frac{(n + 1)!}{(n + 1 - 3)!} - \frac{n!}{(n - 3)!} = 3 * \frac{n!}{(n - 2)!}[/tex]
Evaluate the difference
[tex]\frac{(n + 1)!}{(n - 2)!} - \frac{n!}{(n - 3)!} = 3 * \frac{n!}{(n - 2)!}[/tex]
Expand
[tex]\frac{(n + 1)!}{(n - 2)(n - 3)!} - \frac{n!}{(n - 3)!} = 3 * \frac{n!}{(n - 2)(n - 3)!}[/tex]
Multiply through by (n - 3)!
[tex]\frac{(n + 1)!}{(n - 2)} - n! = 3 * \frac{n!}{(n - 2)}[/tex]
Expand
[tex]\frac{(n + 1) * n!}{(n - 2)} - n! = 3 * \frac{n!}{(n - 2)}[/tex]
Divide through by n!
[tex]\frac{(n + 1)}{(n - 2)} - 1 = \frac{3}{(n - 2)}[/tex]
Take the LCM
[tex]\frac{n + 1 - n + 2}{(n - 2)} = \frac{3}{(n - 2)}[/tex]
Evaluate the like terms
[tex]\frac{3}{(n - 2)} = \frac{3}{(n - 2)}[/tex]
Both sides of the equations are the same.
Hence, the permutation equation [tex]^{n+1}P_3 - ^nP_3= 3 * ^nP_2[/tex] is true for all integers n ≥ 3
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prove that Cos4x=8Cosx -8Cosx
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Which expression is a factor of this polynomial? x^3 + 2x^2 - 9x - 18
A (x+2)
B (x+1)
c (x-2)
d (x-6)
Answers
Answer:
(x+2)(x-3)(x+3) this is ans
Answer:
a. (x + 2)
Step-by-step explanation:
x^2(x + 2) - 9(x + 2)
(x + 2)(x^2 - 9)
(x + 2)(x - 3)(x + 3)
Therefore the answer is (x + 2)
please help!!!!!!!
picture below
Answers
can someone please help mee
Answers
For the graphed function we can see:
domain = set of all real numbersrange = set of all real numbers.How to get the range and domain?For a function y = f(x), the domain is the set of the possible inputs "x" and the range is the set of the possible outputs "y".
In this case, we can see that in the right side we have a parabola, and on the left side a linear equation which increases up to the left (so it has a negative slope).
Then the domain will be the set of all real numbers.
Similar for the range, as we can see that on the left side, the line goes upwards, while on the right side, the parabola goes downwards. So this function has a range of all real numbers.
Then:
domain = set of all real numbers
range = set of all real numbers.
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Suzy invests $2,600 in an account that earns 2.3% annual interest, compounded continuously. What is the value of the account after 10 years? Round to the nearest dollar
Answers
Answer:
$3,272
Step-by-step explanation:
Continuous Compounding Formula
[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]
where:
A = Final amountP = Principal amounte = Euler's number (constant)r = annual interest rate (in decimal form)t = time (in years)Given:
P = $2,600r = 2.3% = 0.023t = 10 yearsSubstitute the given values into the formula and solve for A:
[tex]\sf \implies A=2600e^{(0.023 \times 10)}[/tex]
[tex]\sf \implies A=2600e^{0.23}[/tex]
[tex]\implies \sf A=3272.360026...[/tex]
Therefore, the value of the account after 10 years is $3,272 to the nearest dollar.
Which of the following sets of ordered pairs below represent a function?
{(0,0),(1,10),(10,4),(-1,-7)}
{(0,0),(4,1),(4,10),(7,1)}
{(0,0),(10,-1),(4,-10),(10,-2)}
{(0,0),(0,1),(0,10),(0,-1)}
Answers
The ordered pair that represents a function is {(0,0),(1,10),(10,4),(-1,-7)}.
How to identify ordered pairs?A set of ordered pairs that defines a function will be the one that has exactly one y-value that assigned to every x-value. This means that none of its x-values can have two corresponding y-values.
All the sets of ordered pairs don't have exactly one y-value that corresponds to each of its x-value except {(0,0),(1,10),(10,4),(-1,-7)}.
Thus, we can say that the ordered pair that represents a function is {(0,0),(1,10),(10,4),(-1,-7)}.
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Given the sequence in the table, which of the following represents the sum for term 5 through term 11 in sigma notation? (1 point)
a an
1 2
2 −10
3 50
Answers
Answer:
Given sequence in the table is a Geometric sequence and The sum for term 5 through term 11 in sigma notation is given by:
[tex]$\sum_{n=5} ^{\111} 2(-5)^n^-^1$[/tex]
Step-by-step explanation:
Geometric sequence - it is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio
here the given terms :
a1 = 2, a2 = -10, a3 = 50
you can see it is a geometric sequence as the ratio is constant [tex]\frac{a2}{a1}{=}\frac{a3}{a2}{=}{-5}[/tex]
now the nth term for geometric sequence :
[tex]a_{n} {=}{a}{r}^{n-1}[/tex]
here,
a = first term.r = common ratio of the given terms.n = number of terms in geometric sequence.now substituting the given values in the expression,
[tex]a_{n} {=}{2}{{(}-5}{)}^{n-1}[/tex]
we have to find the sum from term 5 to term 11,
therefore using sigma notation and putting n= 5 and n=11 at the below and above the sigma respectively,
[tex]$\sum_{n=5} ^{\111} 2(-5)^n^-^1$[/tex]
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Section B, Q5
please answer, it is urgent
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Mandy used the input and output in this table to write ratios. She concluded that because they are not all equivalent, this is not a proportional relationship. Is she correct? Explain.
A 2-column table with 4 rows. Column 1 is labeled x with entries 1, 2, 5, 10. Column 2 is labeled y with entries 5, 10, 25, 50.
StartFraction 5 over 1 EndFraction = StartFraction 10 over 2 EndFraction = StartFraction 25 over 5 EndFraction = StartFraction 10 over 50
Answers
Answer:
The conclusion derived by Mandy is incorrect.
Step-by-step explanation:
Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value time the other. That constant is known as the "constant of proportionality".
To determine if the input and output are proportional, we simply divide the output (y) by the corresponding input (x).
i.e. Ratio[tex]=\frac{y}{x}[/tex]
So, we have:
[tex]Ratio=\frac{5}{1}=5[/tex]
[tex]Ratio=\frac{10}{2}=5\\ Ratio =\frac{25}{5}=5\\ Ratio=\frac{50}{10} =5[/tex]
For the four input and output data, the ratios are equal. This means that the relationship is proportional.
Hence, Mandy's conclusion is incorrect.
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ratios are equal, so its proportionate Mandy's conclusion is incorrect.
3. The elevation of a hilltop is 250 feet above sea level. The
hill slopes gradually to a valley that is 100 feet below sea
level. The hilltop and the valley are 28,000 feet apart. What
is the average rate of change in elevation from the hilltop tot
the valley?
Answers
Answer:
0.00893 feet elevation per 1 foot distance.
Step-by-step explanation:
The hill reaches an elevation of 250 ft (above sea level) over the course of 28,000 feet. The average rate of change would be (250 ft)/(28,000 ft), or 0.00893 feet elevation/1 foot distance.
((0.00893 (feet up/foot distance))*(28,000 feet distance) = 250 feet up (elevation).
Line q and m are cut by transversal lines j and k. The line and the measures of some of the angles created by the intersections of the lines are shown in the diagram below. What is the measure, in degrees, of angle 1?
Answers
Answer:
70
Step-by-step explanation:
180 minus 110 is 70
straight lines are 180 degrees
what graph represents viable values for y = 2x, where x is the number of pounds of rice scooped and purchased from a bulk bin at the grocery store and y is the total cost of the rice?
Answers
A graph is a way to represent a lot of data in such a visual format. The graph for the given situation can be drawn as shown below.
What is a graph?A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.
The graph for the given situation can be drawn as shown below, where the x-axis represents the number of pounds of rice scooped and purchased from a bulk bin at the grocery store and the y-axis represents the total cost of the rice.
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Find the least common denominator for these
two rational expressions.
-4
-1
4y²
Enter the correct answer.
Answers
Answer:
4y^2
Step-by-step explanation:
least common denominator is 4y^2
The branches of a tree diagram are weighted probabilities.
True
Or
False
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Answer:
The correct answer is True
Answer:
True
Step-by-step explanation:
Each branch of a tree diagram is the likelihood of that outcome happening. You multiply as you go along the branch.
What are the slope and the y-intercept of the linear function that is represented by the graph?
The slope is Two-thirds, and the y-intercept is –2.
The slope is Two-thirds, and the y-intercept is 3.
The slope is Three-halves, and the y-intercept is –2.
The slope is Three-halves, and the y-intercept is 3.
Answers
The slope and the y-intercept of the linear function represented by the graph is given as follows:
The slope is two-thirds, and the y-intercept is –2.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Looking at the graph, when x = 0, y = -2, hence the y-intercept is of -2. The slope is given by change in y divided by change in x, hence considering that the graph also goes through (3,0), it is given by:
[tex]m = \frac{0 - (-2)}{3 - 0} = \frac{2}{3}[/tex]
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A triangle with vertices at A (0, 0) B (0, 4) and C( 5, 9) is dlated to yeld a triangle with vertices at A(0, 0) , B(0, 10) and C (15, 0) The origins the center of dilation. What is the scale factor of the dilation?
A 1.5
B 2
C 2.5
D 3
Answers
So to find the scale factor:
You take any point listed and pick x or y value, we will be using C. For this point we must use x because y = 0 (side note: if any value = 0 you can not use it if the center of dialtion is on any point on the triangle). The original value of x was 5 and the new one is 15 so new/old. For this example it would be 15/5 which = 3. this number is the scale factor so the answer is D
Multiply 3.4x and 1.2x.
Answers
Answer:
telmhtkhknrkh
Step-by-step explanation:
eg
Answer:
4.08x^2
Step-by-step explanation:
Consider the steps for determining the quotient of ¹24 + x4
12
X-4
The quotient will be
expression.
Complete the statements to choose a numerator and denominator to represent the quotient.
The numerator of the simplified quotient is
The denominator of the simplified quotient is
Answers
The simplified form of the expression has a numerator (x + 9)(2x + 1) and the denominator (x + 7) and the expression doesn't exist at (x = 9).
How to illustrate the quotient?The given expression is:
= [(3x² - 27x)/(2x² + 13x - 7)]/(3x/4x² - 1)
Firstly, factorize the expression 4x² - 1.
4x² - 1 = (2x - 1)(2x + 1)
Then, factorize 2x² + 13x - 7.
2x² + 13x - 7 = 2x² + 14x - x - 7
2x(x + 7) - 1(x + 7)
= (2x - 1)(x + 7)
Then, factorize the equation 3x² - 27x.
3x² - 27x = 3x(x - 9)
The factorized terms will be substituted into the equation. This will be:
= [3x(x - 9)/(2x - 1)(x + 7)] / 3x[(2x - 1)(2x + 1)]
= (x + 9)(2x + 1)/(x + 7)
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Use the expression 8a+16c
What is the value of the expression when a = –5 and c = –1?
Answers
Answer:
i think its 8(a+2c)
Step-by-step explanation:
The GCF or greatest common factor of 8 and 16 is 8.
8a+16c
8(a+2c)
Therefore the answer is 8(a+2c)
What is the product of 4 and 5g + 2.34?
Answers
The product of 4 and 5g + 2.34 is 20g + 9.36
How to determine the product?The expressions are given as:
4 and 5g + 2.34
As a product expression, we have:
4 * (5g + 2.34)
Evaluate the product
20g + 9.36
Hence, the product of 4 and 5g + 2.34 is 20g + 9.36
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PLease help due today! I will give brainliest!!
Select the correct answer.
Simplify the expression.
[tex][tex]\sqrt[5]{224x^{11}yx^{8} }[/tex][/tex]
Answers
Hopes this helps
For the functions f(x) and g(x), determine the domain of (f ∙ g)(x) (the product of f and g).
f(x)= 12/x, g(x)= -8x ^3
Answers
Answer: Domain: (-∞, 0) U (0, ∞)
Step-by-step explanation:
[tex]\frac{12}{x} *-8x^{3}[/tex]
[tex]=-96x^2[/tex]
Domain: (-∞, 0) U (0, ∞)
If 1 < a ⩽ x , then the minimum value of [tex] \rm log_{a}(x) + log_{x}(x) [/tex] is ?
PLEASE HELP!!!!
Answers
The minimum value of the expression log_a(x)+log_x(x) is 2 because the minimum value of each term is 1.
What is a logarithm?It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.
[tex]\rm a^b = c\\log_ac =b[/tex]
We have:
1 < a ≤ x
We have an expression:
[tex]\rm log_a(x)+log_x(x)[/tex]
We know,
[tex]\rm log_aa = 1[/tex]
[tex]\rm log_a(x)+1[/tex]
If a = x
Then, [tex]\rm log_a(x)=1[/tex]
We cannot find the function value less than 1 because it goes infinitely in a negative direction.
So the minimum value of the expression:
= 1 + 1
= 2
Thus, the minimum value of the expression log_a(x)+log_x(x) is 2 because the minimum value of each term is 1.
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Please help 2 sorry for last one it didnt go through
Answers
Answer:
No, it's not.
