It is proved that CM will be perpendicular to AB if M is midpoint of AB.
It is given that ΔABC is a right isosceles triangle with hypotenuse AB and M is midpoint of AB.
We have to prove that CM is perpendicular to AB.
What is an isosceles triangle ?
An isosceles triangle ΔABC is a triangle that has at least two sides of equal length i.e., AC= BC
As per the question ;
ΔABC is a right isosceles triangle with hypotenuse AB.
⇒ AC = BC (by the definition of isosceles triangle)
Also ;
M is midpoint of AB.
⇒ CM = CM (reflexive property)
So ;
ΔACM ≅ Δ BCM (by SSS)
∠A = 45° and ∠B = 45° because of right isosceles triangle.
Also ;
∠ACM = ∠BCM
because they are corresponding angles of congruent triangles
i.e.,
∠ACB = 90°
Now ;
∠ACM + ∠BCM = ∠ACB
because they are adjacent angles.
∵
∠ACM = ∠BCM , so ;
∠ACM + ∠ACM = ∠ACB
2∠ACM = 90°
∠ACM = 45 °
∵
∠A = 45 ° and ∠ACM = 45°
⇒ ∠AMC = 90°
because the sum of angles in a triangle is 180°.
So ,
If ∠AMC = 90° , then CM is perpendicular to AB because perpendicular lines form 90° angles.
Thus , CM will be perpendicular to AB if M is midpoint of AB.
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f(x) = 13 - x
h(x) = x² - 6x - 18
Write (fo h) (x) as an expression in terms of a x.
(ƒ○h)(x) =
Solve each equation for y .
12 y=3 x
After solving the equation, the value of y = x/4 for the equation 12 y=3 x.
⇒ 12 y=3 x
⇒ y = 3x/12
⇒ y = x/4
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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In an examination for the final year student of a school 60 offered history 50 offered economics and 48 offered literature,30 offered history and economics 16 offered history and literature 22 offered economics and literature if 10 candidate offered all the three subject find the number that offered only history
Answer:
Step-by-step explanation:
History(H),Economics(E),Literature(L)
1a).To find History(H) only is
H only =H-HE-HL+HEL
H only =60-30-16+10=24
b).E only=50-30-22+10=8
c). L only=48-22-16+10=20
2).no of candidates who sat for the exam is 24+8+20=52
Racha of Meghna’s cat has fleas, Her veterinarias recommended a treatment plan that includes combing out her cats fur every day. Meghna kept track of the number of fleas that she removed from her cats while combing them, on day 0, the day she started the treatment, she removed a total of 87 fleas. On day 6, she removed a total of 14 fleas. If Meghna keeps up the treatment and the number of fleas can be modeled by an exponential function, approximate the number of fleas she should expect to remove from the cats on Day 14, write the exponential function and show your work
The approximate number of fleas she should expect to remove from the cats on Day 14 is 1
How to approximate the number of fleas she should expect to remove from the cats on Day 14?The given parameters are
Function type: exponential function
Day 0 = 87
Day 6 = 14
An exponential function is represented as
y = ab^x
Where
y = a, when x = 0
This means that a = 87
So, we have
y = 87b^x
Day 6 = 14 means that
When x = 6, y = 14
So, we have
87b^6 = 14
This gives
b^6 = 0.161
Take the 6th roots of both sides
So, we have
b = 0.74
Subsitute b = 0.74 in y = 87b^x
y = 87(0.74)^x
On day 14, we have
y = 87(0.74)^14
Evaluate
y = 1.28
Approximate
y = 1
Hence, the approximate number of fleas she should expect to remove from the cats on Day 14 is 1
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Solve equation by using the Quadratic Formula. Round to the nearest tenth if necessary. x² = x + 12
The quadratic equation of the form ax² + bx + c = 0.
The value of x = 4 and x = -3
No solution
No real-valued solution
What is meant by quadratic equation?The quadratic equation of the form
ax² + bx + c = 0.
The form is called the standard form of the quadratic equation.
Let the given equation be x² = x + 12
By using quadratic equation, ax² + bx + c = 0
ax² + bx + 12 = 0
x² = x + 12
⇒ x² - x - 12 = 0
Let the quadratic equation be
[tex]$x=\frac{\left(-b\right)\pm \sqrt{\left(b)^2-4\cdot \:a\cdot \left(c)}}{2\cdot \:a}[/tex]
a = 1, b = -1 and c = -12
Substitute the values in the above equation, we get
[tex]$x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{\left(-1\right)^2-4\cdot \:1\cdot \left(-12\right)}}{2\cdot \:1}[/tex]
simplifying the above equation, we get
[tex]$x_{1,\:2}=\frac{-\left(-1\right)\pm \:7}{2\cdot \:1}[/tex] and
[tex]$x_{1,\:2}=\frac{-\left(-1\right)\a++ \:7}{2\cdot \:1}[/tex]
[tex]$x_{1,\:2}=\frac{-\left(-1\right)\a+- \:7}{2\cdot \:1}[/tex]
x = 4 and x = -3
Therefore, the value of x = 4 and x = -3
No solution
No real-valued solution
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p²m ÷ 4; use m = 4, and p = 7
Answer:
[tex] \sf{49}[/tex]
Step-by-step explanation:
Given that,
m => 4
p => 7
Let us solve the given expression by using the given values.
[tex] \sf \: {p}^{2} m \div 4 \: \: \: \: \: \\ \sf{(7)}^{2} \times 4 \div 4 \\ \sf 49 \times 4 \div 4 \\ \sf196 \div 4 \: \: \: \: \: \: \\ \sf49 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Find the value of x.
Answer:
1 15 degrees
Step-by-step explanation:
Exterior angle is equal to sum of opposite interior angles
Select the correct answer.
Triangle ABC represents a triangular property lot where the measure of ZA is 50°, the measure of ZB is 68°, and the measure of ZC
is 62⁰:
What is the longest side of the property?
Cannot be determined
O
BC
O AC
O
AB
Answer:
AC is the longest side
Step-by-step explanation:
• the longest side is side opposite largest angle in the triangle
• the shortest side is opposite the smallest angle in the triangle
the largest angle is ∠ B = 68°
the longest side is then AC
volume=1/8π ft r=1/3ft what is the height?
Answer:
Need to know the shape of object (cylinder, cone, etc)
Find the geometric mean between pair of numbers.
36 and 24
The value of the geometric mean of the numbers 36 and 24 is.
Gm ( 36, 24) = 12√6
How is the geoemetric mean determined?The definition of geometric mean is a calculation that is performed on a set of numbers which consists of calculating the square root of the product between them, the equation is as follows:
Gm (a,b) = √ab
Then in our case that we have the values 40 and 15, these are equivalent to the variables a and b
a = 36b = 24We substitute and solve for the square root
Gm (36, 24) = √ab = √36×24
Gm (36, 24) = √864
Gm (36, 24) = √6×144
Gm ( 36, 24) = 12√6
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Find four solutions of the equation. Write the solutions as ordered pairs. 3x-y=-6
Solving the Question
We're given:
3x-y=-6Find 4 solutionsWe can start by isolating one of the variables, like y:
[tex]3x-y=-6\\-y=-3x-6\\y=3x+6[/tex]
Now we can find four solutions by plugging in any number for x:
[tex]y=3x+6\\y=3(1)+6\\y=3+6\\y=9[/tex]
First solution: (1,9)
[tex]y=3x+6\\y=3(2)+6\\y=6+6\\y=12[/tex]
Second solution: (2,12)
[tex]y=3x+6\\y=3(3)+6\\y=9+6\\y=15[/tex]
Third solution: (3,15)
[tex]y=3x+6\\y=3(4)+6\\y=12+6\\y=18[/tex]
Fourth solution: (4,18)
Possible AnswersFirst solution: (1,9)
Second solution: (2,12)
Third solution: (3,15)
Fourth solution: (4,18)
Here is the picture it says xxxxxxxxxxxxxxxxxxx
Answer:
Step-by-step explanation:
given: 5^3/5^7
= 1/5^(7-3)
= 1/5^4
= 1/625
final answer: 1/625
Answer:
[tex]5^{-4}[/tex]
Step-by-step explanation:
using the rules of exponents
• [tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]
• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
given
[tex]\frac{5^{3} }{5^{7} }[/tex]
= [tex]5^{(3-7)}[/tex]
= [tex]5^{-4}[/tex]
= [tex]\frac{1}{5^{4} }[/tex] ← if required with a positive exponent
Write an explicit formula for each sequence. Then generate the first five terms. a₁ =4, r=0.1
The given geometric sequence, with first term = 4 and ratio = 0.1, has the formula for its nth term: a(n) = 4 . 0.1ⁿ⁻¹. The first five terms are: 4, 0.4, 0.04, 0.004, 0.0004
The formula of the nth term of a geometric sequence is:
a(n) = a₁ . r^(n-1)
with a₁ is the first term and r is the ratio. In a geometric sequence, the ratio is constant and equal to a(n)/a(n-1).
In the given problem, a₁ =4, r=0.1, therefore:
a(n) = a₁ . r^(n-1)
a(n) = 4 . 0.1ⁿ⁻¹
To find the first five terms, replace n with 1, 2, 3, 4, and 5.
a₁ = 4
a(2) = 4 . 0.1²⁻¹
= 4 . 0.1¹ = 0.4
a(3) = 4 . 0.1³⁻¹
= 4 . 0.1² = 0.04
a(4) = 4 . 0.1⁴⁻¹
= 4 . 0.1³ = 0.004
a(5) = 4 . 0.1⁵⁻¹
= 4 . 0.1⁴ = 0.0004
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Determine whether each sequence is arithmetic, geometric, or neither. Then find the tenth term. 23,27,31,35,39, . . . .
The sequence 23,27,31,35,39, . . . . is arithmetic and the tenth term is: 59
We can determine that the sequence is arithmetic, because two consecutive terms differ by "d".
To solve this exercise we are going to apply the formula of the arithmetic sequence:
aₙ= a + (n-1) * dd = aₙ₊₁ - aₙWhere:
a = first termd = common difference of the sequencen= number of termsInformation about the problem:
Sequence = 23,27,31,35,39, . . . . Tenth term = ?Calculating the "d" term, we have:
d = aₙ₊₁ - aₙ
d = 27 - 23
d = 4
Calculating the tenth term, we get:
aₙ= a + (n-1) * d
a₁₀= 23 + (10-1) * 4
a₁₀= 23 + (9) * 4
a₁₀= 23 + 36
a₁₀= 59
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.
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Which input value produces the same output value for
the two functions?
O x=-3
O x=-1
O x=0
O x = 1
x = -2 is input value produces the same output value for the two functions .
What are the function's input values?
The domain of the function is the collection of input values. The range of the function is the collection of output values.
What input and output functions are used?
The fundamental functions for input and output are getchar, putchar, puts, scanf, and printf. To transfer single characters, utilize the first two functions, getchar and putchar.
Which four sorts of functions are there?
Four main categories can be used to classify different sorts of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.
The input value which produces the same input .
value for two function is x = -2
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Can y’all please help me on question 23 please I need help
Every day, the Randolph Pet Store uses 2/3 of a bag of dog food to feed the dogs. How many days will 1 1/3 bags of dog food last?
Write your answer as a fraction or as a whole or mixed number.
The dance committee consisted of 10 students. The committee will select three officers at random. What is the probability that Alice, David, and Carlene are selected?
The probability that Alice, David, and Carlene are selected is 1/120.
What is meant by probability?
Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.
3 people can be chosen from 10 people in 10C3 ways and Alice, David, and Carlene can be chosen in only one way.
10C3 = 10! / (10 - 3)! 3!
= (10 [tex]*[/tex] 9 [tex]*[/tex] 8 [tex]*[/tex] 7!) / (7! [tex]*[/tex] 3 [tex]*[/tex] 2 [tex]*[/tex] 1)
= 120
So, the number of possible outcomes is 120 and the number of favorable outcomes is 1. Therefore, the probability is 1/120.
The probability that Alice, David, and Carlene are selected is 1/120.
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dell has a small bag containing 50 centimeters of potting soil. her planter has a volume of 46,300 cubic millimeters. does dell have enough soil to fill the planter? explain.
Answer:
No, Dell does not have enough soil to fill the planter.
Step-by-step explanation:
SOLVE THE Word problem involving average rate of change
Answer:
[tex]{ \rm{rate \: of \: change = \frac{R _{2}(t) - R _{1}(t) }{t _{2} - t _{1}} }} \\ [/tex]
For 0 < t < 10; 226.6 < R(t) < 205.6
[tex]{ \rm{ = \frac{205.6 - 226.6}{10 - 0} }} \\ \\ { \rm{ = - \frac{21}{10} }} \\ \\ = { \rm{ - 2.1}} \\ \\ = 2.1[/tex]
Negative indicates an inverse proportionality, or decrease in temperature
For 30 < t < 50; 157.6 < R(t) < 119.6
[tex] = { \rm{ \frac{119.6 - 157.6}{50 - 30} }} \\ \\ = { \rm{ - \frac{38}{20} }} \\ \\ = { \rm{1.9}}[/tex]
difference of two sqaures
The difference of squares is a quadratic polynomial of the form is a² - b² = (a + b) · (a - b).
What is a difference of two squares?
Difference of two squares is a particular case of a second order polynomial whose form is the following:
a² - b² = (a + b) · (a - b)
Now we proceed to demostrate the equivalence between the two expressions:
a² - b² → (a + b) · (a - b)
a² - b² Given
(a² - b²) + 0 Modulative property
(a² - b²) + a · b - a · b Existence of additive inverse
(a² + a · b) + (- b² - a · b) Associative property
a · (a + b) - b · (a + b) Definition of power / Distributive property / (- a) · b = - a · b
(a + b) · (a - b) Commutative and distributive property /
(a + b) · (a - b) → a² - b²
(a + b) · (a - b) Given
(a + b) · a + (a + b) · (- b) Distributive property
a² + a · b - a · b - b² Distributive property / (- a) · b = - a · b / Definition of power
(a² - b²) + (a · b - a · b) Associative property
a² - b² Existence of the additive inverse / Modulative property / Result
Hence, the difference of squares is a quadratic polynomial of the form is a² - b² = (a + b) · (a - b).
RemarksThe statement is incomplete. The complete form is: What is a difference of two squares?
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A question paper has two parts, a and b, each containing 10 questions. if a student has to choose 7 from part a and 4 from part b, in how many ways can he choose the questions?
Combinations exist ways to select elements from a collection in mathematics where the order of the selection exists irrelevant. He can choose the question in 28 ways.
What is meant by combinations?
Combinations exist mathematical operations that count the number of potential configurations for a set of elements when the order of the selection exists is irrelevant. You can select the components of combos in any order.
The combination formula is used to determine how many options there are for choosing things from a collection so that the order in which they are chosen is irrelevant. Combination, to put it simply, is the choosing of items or things from a bigger group when the order doesn't important.
Given: Number of questions in part A = 10
Number of questions in part B = 10
A student chooses 7 from part A and 4 from part B
Required number of ways = ( 10C7 × 10C4) × ( 10C3 × 10C6)
= 5040 × 24/ 6 × 720
= 28
He can choose the question in 28 ways.
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Part 3 of 3 Graph the equation y=49x, where y represents the distance traveled over time, z, in hours is the relationship proportional? How many miles from home is the family after 5 hours?
Refer to the graph below for the graphical representation of the given equation y = 49x.
What is an equation, exactly?An equation, in its most basic form, is a mathematical statement that proves two mathematical expressions appear to be equal.The expressions 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14.Graph:
A diagram (such as a series of one or more points, lines, line segments, curves, or areas) that depicts the variation of one variable in comparison to another. A grouping of all points whose coordinates satisfy a given relationship (such as a function).Refer to the graph given below for the equation y=49x.
Therefore, the graph of the given equation y=49x is shown below.
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Marsha pays $20 each month for a car wash membership. Which of the following represents the total amount subtracted from her account after 6 months of having the membership?
|−20| − 6 = $14
|−20| − |6| = $14
−6|20| = −$120
6|−20| = $120
The total amount subtracted from her account after 6 months of having the membership is −6|20| = −$120. option C
Given:
Cost of membership
Cost per month for a car wash membership = $20
Number of months = 6 months
Total amount subtracted from her account = Number of months × Cost per month for a car wash membership
= 6 (-20)
= -120
Therefore, the total amount subtracted from her account after 4 months of having the membership is −6|20| = −$120.
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What is the squared root of 56 minus the squared foot of 189?
The squared root of 56 minus the squared root of 189 is -6.26 .
The square root of any number is equal to the number squared to give the original number. In mathematics, the square root function is defined as a one-to-one function that takes a positive number as input and returns the square root of the given input number.The square root symbol is usually represented by '√'. It's called a radical. To represent the number 'x' as a square root, this symbol can be written as "√x"We have given an statement that squared root of 56 minus the squared root of 189 which can be represented in expression as
[tex]\sqrt{56} -\sqrt{189}[/tex] ..(1)
Prime factorization 56 is given by
[tex]\sqrt{56} =\sqrt{2\times2\times2\times7} \\\sqrt{56} =2\sqrt{14} \\\sqrt{56} =2\times3.74\\\sqrt{56} =7.48[/tex]
Prime factorization 189 is given by
[tex]\sqrt{189} =\sqrt{3\times3\times3\times7} \\\sqrt{189} =3\sqrt{21} \\\sqrt{189} =3\times4.58\\\sqrt{189} =13.74[/tex]
Putting above values in equation (1) , we get
[tex]\sqrt{56} -\sqrt{189}=7.48-13.74\\\sqrt{56} -\sqrt{189}=-6.26[/tex]
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b. Use summation notation to write the related series for a triangle with 10 cans in the bottom row.
The series that is related to a triangle with 10 cans in the bottom row can be expressed in summation notation as [tex]\sum\limits^{10}_{n=1} {n}[/tex]
Let us consider the simpler triangle formed by stacking cans as in the attached picture.
As we can see in the picture, if the bottom row contains 3 cans, then the triangle will have 3 rows. The number of cans in each row decreases by 1. We can expand this idea for a triangle with 10 cans in the bottom row.
In this case, there will be 10 rows and the number of cans in each row decreases by 1.
10th row : 10 cans
9th row : 9 cans
and so on.
We can express the number of all cans in this triangle as a series, starting from the top row (the first row):
1 + 2 + 3 + ... + 10
The explicit formula of the nth term is: a(n) = n.
Hence, in the summation notation, it can be written as:
[tex]\sum\limits^{10}_{n=1} {a(n)} = \sum\limits^{10}_{n=1} {n}[/tex]
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NEED HELP WITH INEQUALITY PLEASE!!!!!!!!!!!!!!!!!!
Answer:
D
Step-by-step explanation:
If the light build can be 50 and less, the sign needs to be ≤ because it means less than or equal to.
Lyle is driving from home to his friend’s house, a distance of 720 km. He plans to drive at an average speed of 80 km per hour, take an hour for lunch, and take two 15- minute breaks. He must arrive at his friend’s house by 7:00 p.m. What is the latest possible time that Lyle could leave home in order to arrive at his friend’s house on time?
The latest possible time that Lyle could leave home in order to arrive at his friend’s house on time is 8:30 a.m
How to find the latest possible time that Lyle could leave home in order to arrive at his friend’s house on time?Given that Lyle is driving from home to his friend’s house, a distance of 720 km. He plans to drive at an average speed of 80 km per hour, take an hour for lunch, and take two 15- minute breaks and He must arrive at his friend’s house by 7:00 p.m.
The time it takes Lyle to drive to his friend's house is given by t = d/v where
d = distance travelled and v = average speedGiven that Lyle is driving from home to his friend’s house, a distance of 720 km. He plans to drive at an average speed of 80 km per hour, we have that
d = 720 km and v = 80 km/hSubstituting the values of the variables into t, we have
t = d/v
= 720 km/80 km/h
= 9 h
So, it takes Lyle 9 hours to drive.
Now, since Lyle takes an hour for Lunch and two 15 minutes breakes, this extra time is t' = 1 h + 2 × 15 min
= 1 h + 30 min
= 1 h + 30 min/60 min × 1h
= 1 h + 0.5 h
= 1.5 h
So, the total time Lyle takes to reach his friend's house is T = t + t'
= 9 h + 1.5 h
= 10.5 h
Since Lyle must reach his friend's place no later than 7:00 pm, 10.5 hrs from 7:00 pm is 8:30 am.
So, Lyle must leave no later than 8:30 a.m
So, the latest possible time that Lyle could leave home in order to arrive at his friend’s house on time is 8:30 a.m
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Which is one condition that must be present for an inverse relation to be a function?
A- The inverse relation must be a straight line.
B- The function must be a straight line.
C-The function must pass the vertical line test.
D- The inverse relation must pass the vertical line test.
the correct option is D, the inverse relation is only a function if it passes the vertical line test.
When an inverse relation is a function?A relation maps elements from one set (called the domain) into elements of another set (called the range).
A relation is a function only if each element in the domain is mapped into only one element of the range. So, there is something called the vertical line test.
It says that if at any part of the graph of the relation you can draw a vertical line that intercepts the graph of the relation more than once, then it is not a function. Passing the vertical line test means that no vertical line intercepts the graph more than once.
Then the correct option is D, the inverse relation is only a function if it passes the vertical line test.
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If line B is drawn such that it passes through Point P and is parralel to line A, what is the equation of line B?
Equation of line B is y=7/2x
A line is simply an object in geometry that is characterized under zero width object that extends on both sides. A straight line is just a line with no curves. So, a line that extends to both sides till infinity and has no curves is called a straight line.
Straight line formulas= y=mx+ c
= y-y1=m(x-x1)
slope, m= (y1-y2)/(x1-x2)
given that, B passes through P and parallel to A
so one of the points on the line is P(2,7)
and one more point is O(0,0) if we extend line B parallelly to A
So we can conclude that B passes through O and P
we know equation of straight line is y-y1=m(x-x1)
on solving we get equation of line B is, y=7/2x
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Answer:
Line B's equation is y=7/2x.
Step-by-step explanation:
An object in geometry known as a line is simply one that extends on all sides and has zero width. Simply put, a straight line is a line devoid of curves. A straight line is one that does not curve and extends to infinity on both sides.
Straight line formulas= y=mx+ c
= y-y1=m(x-x1)
slope, m= (y1-y2)/(x1-x2)
given that, B passes through P and parallel to A
so one of the points on the line is P(2,7)
Moreover, if we stretch line B parallel to A, the final position is O(0,0).
Therefore, we can say that B goes through O and P.
Y-y1=m is the straight line's known equation (x-x1)
After solving, we obtain the equation y=7/2x for line B.
