Answer:
Her age is 15.
Step-by-step explanation:
13 + 14 + 15 = 42
Julia is the oldest and 15 is the greatest of the 3 numbers
therefore Julia is 15
What is the correct form of the partial fraction decomposition for the expression StartFraction 7 x + 18 Over x squared + 9 x EndFraction?
The correct form of the partial fraction decomposition for the expression 7x+18/x^2+9x is 2/x + 5/(x + 9).
What is the Fraction?
The numerator and the denominator are the two components of a fraction. The number displayed above the fractional bar is known as the numerator. As an illustration, the numerator in 6/7 is 6. Denominator: The fractional bar's lowermost number is designated as the denominator.Here,
x ² + 9x = x (x + 9), so the partial fraction decomposition would be
(7x + 18) / (x ² + 9x) = a/x + b/(x + 9)
where a, b are some constants. To find them, multiply both sides by x ² + 9x :
7x + 18 = a (x + 9) + bx
Solve for a and b :
7x + 18 = (a + b) x + 9a
[ a + b = 7
[ 9a = 18
→ a = 2, b = 5
So
(7x + 18) / (x ² + 9x) = 2/x + 5/(x + 9)
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You roll 3 dice. What is the probability that the outcome of at least two of the dice will be less than or equal to 4 ? Explain your reasoning.
6 out of 36 or I in 6 is the probability that the outcome of at least two of the dice will be less than or equal to 4 .
In statistics, what does a probability mean?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.Probability is the branch of mathematics concerning the occurrence of a random event, and four main types of probability exist: classical, empirical, subjective and axiomatic.There are 36 possible outcomes for rolling two dice.
There are six possible ways that the two dice will land on the same number, so the probability is 6 out of 36 or I in 6.
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Write the specified type of proof.
Flow proof of Corollary 4.1
The Corollary 4.1 states that , the acute angles of a right triangles are complementary.
What is Corollary ?A corollary can be defined as a theorem that follows a direct result of an another theorem. With an original theorem, a corollary can be used as a reason to proof it. There are two main corollaries which follow directly from the Triangle Angle-Sum theorem. These are defined below :
Corollary 4.1
It states that the " acute angles of the right triangle are always complementary".
Abbreviation : Acute ∠s of rt. Δ are comp.
Corollary 4.2
It states that, "there is at most only one right angle or an obtuse angle in triangle".
Flow Proof of Corollary 4.1Given : a triangle ABC, right angled at A
To Prove: ∠B and ∠C are complimentary
Proof :
step 1 : ∠A = 90°
step 2: According to angle-sum theorem
∠A + ∠B + ∠C = 180
step 3: 90 + ∠B + ∠C = 180
step 4: ∠B + ∠C = 180 - 90
step 5: ∠B + ∠C = 90
Thus, Corollary 4.1 is proved.
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What are the coordinates of D'' if -CD with vertices C(2,4) and D(8,7) is translated along <-6,2> and then reflected over the y -axis?
The coordinates of Parallelogram CDEF after a reflection across y = x are C'(-1,2), D'(1,7), E(-2,6) and (-4,1)
What does coordinate mean in this case?
To coordinate is to make plans for things to come together or to collaborate with another person to achieve a goal. Coordination occurs when all the details of a journey are planned. When you and a friend divide up a large science project and decide who will do what, that is an example of coordination.We want to find the coordinates of Parallelogram CDEF with vertices C(2, -1), D(7,1), E(6,-2), and F(1,-4) after a reflection across y = x.
We can find these coordinates by following the following rule:
Reflection over y = x rule : ( x , y ) ---> ( y , x )
the x and y values simply swap places .
Applying rule to coordinates:
C(2,-1) --- swap 2 and - 1 ---> C'(-1,2)
D(7,1) --- swap 7 and 1 ---> D'(1,7)
E(6,-2) --- swap 6 and -2 ---> E'(-2,6)
F(1,-4) --- swap 1 and -4 ---> F'(-4,1)
The coordinates of Parallelogram CDEF after a reflection across y = x are C'(-1,2), D'(1,7), E(-2,6) and (-4,1)
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A telephone tree is used to send messages. the person at the top calls 2 people. each person calls 2 more people. suppose it takes 1 min to call someone. a message is relayed until the bottom row of the tree has 256 people. how long did this take? how do you know? the tree has 8 rows because each time a person calls 2 people, they call two more people.
Time taken by people in 8rows of given tree with each time a person calls 2 people and it takes 1 min to call someone is 510 minutes.
As given,
Given tree: Person at the top calls 2 people. each person calls 2 more people
Time taken by each person to call someone=1minute
Row wise
First1 +1=2
Second2+2=4
Third4+4=8
Fourth8+8=16
Fifth16+16=32
Sixth32+32=64
Seventh64+64=128
Eighth128+128=256
Total time
2 +4+8+16+32+64 +128 +256=510 minutes
Therefore, time taken by people in 8rows of given tree with each time a person calls 2 people and it takes 1 min to call someone is 510 minutes.
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The temperature in the mountains at 3 PM is 5°C. By 8 PM, the temperature has fallen 7°. What is the temperature at 11PM?
Answer:
-6.2
=
7°c ÷ 5hrs (difference between 3pm to 8pm)= 1.4
3×1.4= 4.2
7+4.2=11.2
5-11.2=-6.2
(sorry if it's wrong)
Solve each equation. 7+b=11(b-3)
The solution of the above equation 7 + b = 11(b - 3) is b = 4.
According to the given question.
We have a linear equation in one variable
7 + b = 11(b - 3)
Since, we have to solve the above equation for b.
As we know tha, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Thereofore, the solution of the above equation 7 + b = 11(b - 3) is given by
7 + b = 11(b - 3)
⇒7 + b = 11b - 33 ( distributive property)
⇒ 7 = 11b - b - 33 (subtract b from both the sides)
⇒ 7 = 10b -33
⇒ 7 + 33 = 10b ( adding 33 both the sides)
⇒ 40 = 10b
⇒ 40/10 = b ( dividing by 10 both the sides)
⇒ 4 = b or b = 4
Therefore, the solution of the above equation 7 + b = 11(b - 3) is b = 4.
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The figure above shows a graph of a line that goes through the origin. What is the value of (k)/(h) ? (A) 4 (B) 3 (C) (4)/(3) (D) -(4)/(3) (E) "-4"
The value of (k)/(h) from the graph of a line that goes through the origin is 4.
What is a graph of a line?A line graph joins distinct data points that generally show quantitative values across an interval. Line graphs have two axes:
The x-axis (horizontal), andThe y-axis (vertical), which are visually expressed as (x,y).From the image attached below, the value of (h,k) as translated on the graph in the negative x and y axis shows that:
(h,k) = (-1,-4) in terms of (x,y) respectively.However, we are to determine the value of (k)/(h):
i.e.
(k)/(h) = -4/-1
(k)/(h) = 4
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What is the rate of change? x intercept is (-1,0) and b is -4 if that helps at all
Answer:
-4
Step-by-step explanation:
In this case, rate of change will be equivalent to the gradient of the line.
Standard form of Equation of Line:
y = mx + c
where
m = Gradient
c = y - intercept
From the given information, we can substitute x = -1 and y = 0, and c = b = -4 (y-intercept) to find m (Gradient)
0 = -1m - 4
m = -4
Therefore, the rate of change is -4.
Evaluate each function for the given value of x , and write the input x and output f(x) as an ordered pair.
f(x) = (7/3)x-9 for x=3
f (3) = -2 is the output for the given input .
How can you tell whether a function is linear or not?
Looking at a function's graph will reveal if it is linear or not with the greatest ease.When a linear function is plotted on a graph, a straight line is formed. A nonlinear function is curved in some way; it does not form a straight line.f(x)= (7/3)x- 9
Put x = 3 ⇒ 7 * 3/3 - 9
⇒ 7 - 9
⇒ -2
Therefore f (3) = -2
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Combining functions to write a new function that models a real-world situation
The new function of T that models the real-world situation in terms of N is T = 560N + 750
How to write a new function that models the real-world situation?The equations of the functions are given as
A = 165N + 750
B = 395N
From the question, we understand that
T = A + B
Substitute the known values in the above equation
So, we have
T = 165N + 750 + 395N
Collect the like terms in the above equation
So, we have
T = 165N + 395N + 750
Evaluate the like terms in the above equation
So, we have
T = 560N + 750
Hence, the new function of T that models the real-world situation in terms of N is T = 560N + 750
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Which represents the inverse of the function f(x) = 4x?
O h(x) = x + 4
O h(x) = x-4
O h(x) = 3/4x
O h(x) = 1/4x
the answer to this question is
O h(x) = 1/4x
pls help will mark brainlyiest
Answer:
B
Step-by-step explanation:
3/5 multiplied by itself 4 times is a fraction exponent so it’s either b or c.
But C is [tex]\frac{3^{4}}{5}[/tex]. 3/5 multiplied 4 times means the bottom has a exponent too so it’s not c.
Find the missing term of each geometric sequence. It could be the geometric mean or its opposite. 2/5,||| 8/45
The missing item in the given geometric sequence is: [tex]\frac{4}{15}[/tex].
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Given: [tex]\frac{2}{5}[/tex], ___, [tex]\frac{8}{45}[/tex]
Here, Let b = missing term of the geometric sequence.
By using the concept of geometric mean, we can find the missing term; geometric mean is used to find the mean, i.e., the middle term between two terms.
GM = [tex]\sqrt{(term_1)(term_2)}[/tex]
Here, b = [tex]\sqrt{\frac{2}{5}\times\frac{8}{45}}[/tex]
=> b = [tex]\sqrt{\frac{16}{25\times9}}[/tex]
=> b = [tex]\frac{4}{5\times3}=\frac{4}{15}[/tex]
Hence, The missing item in the given geometric sequence is: [tex]\frac{4}{15}[/tex].
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Suppose a family drives at an average rate of 60 miles an hour on the way to visit relatives and then at rate of 40 miles an hour on the way back. The return trip takes 1 hour longer than the trip there. Let D be the distance in miles the family traveled. How many hours did it take to drive there?
Answer:
3 hours
Step-by-step explanation:
[tex]speed = \frac{distance}{time} \\ 60 = \frac{d}{t} \\ d = 60t \\ \\ speed = \frac{distance}{time} \\ 40 = \frac{d}{t + 1} \\ d = 40(t + 1)[/tex]
Since;
[tex]d = 60t \: \: \: and\\ d = 40(t + 1) \\ [/tex]
Therefore;
[tex]60t = 40(t + 1) \\ 60t = 40t + 40 \\ 60t - 40t = 40 \\ 20t = 40[/tex]
Divide both sides by 20
[tex] \frac{20t}{20} = \frac{40}{20} \\ t = 2 \: hours[/tex]
Since the return trip took an hour longer to get back home an hour will be added to the time
[tex]t + 1 = 2 + 1 \\ = 3 \: hours[/tex]
Which parent function is represented by the graph?
O A. Absolute value parent function
• B. Quadratic parent function
• C. Linear parent function
• D. Reciprocal parent function
Answer: D, reciprocal parent function
Step-by-step explanation:
I need done before school please help!!
: Write in standard form
(a) 567000
..... (1 mark)
The standard form of a given number is scientific notation which is given by the form of exponents of ten and written as 5.67 ×10⁵.
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9. Based on the basic value of its digits, different types of number systems exist.
What is the standard form?Standard form is a way of writing down in the easy form very large or very small numbers.
Let E is the standard form of a given number
E = 567000
E = 500000 + 67000 + 7000
E = 0.567 × 10⁶ = 5.67 ×10⁵
E = 5.67 × 10⁵
Hence, the standard form of a given number is 5.67 ×10⁵.
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Use your ruler and compasses to construct the angle bisector of angle ABC
Step-by-step explanation:
Step 1: Draw any angle, say ∠ABC. Step 3: Now, taking D and E as centers and with the same radius as taken in the previous step, draw two arcs to intersect each other at F. Step 4: Join B to F and extend it as a ray. This ray BF is the required angle bisector of angle ABC.
yael used to have a square garage with 356ft ^2 of floor space. She recently built an addition to it. The garage is still a square but it now has 50% more floor space. What was the length of one side of the garage originally? What is the length of one side of the garage now? What was the percent increase in the length of one side?
The answers are given below:-
The length of one side of the garage originally was 17.9 ft.
The length of one side of the garage now is 21.9 ft.
The percent increase in the length of one side was 22.35%.
What is the area of a square?The area of a square of side s is given by s squared, that is:
A = s².
The original area was 320 ft², hence the original length was:
s² = 320
s = √(320)
s = 17.9 ft.
The area increased by 50%, hence the new area is:
A = 1.5 x 320 = 480 ft².
The current length of one side is:
s² = 480
s = √(480)
s = 21.9 ft.
The percent increase is the change divided by the initial length and multiplied by 100%, hence:
(21.9 - 17.9)/17.9 x 100% = 22.35%.
The percent increase in the length of one side was 22.35%.
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Factor completely. 2x³ - 4x² 30x
A (x+3)(x - 5)
B 2x(x² - 2x - 15)
2x(x+3)(x - 5)
- 5)
D 2x(x-3)(x
-
Hi! I'm just answering questions for points.
8x²2x (1+4x) +2. determined if the simplified expression is quadratic
The quadratic expression is 64[tex]x^{4}[/tex] + 16x³ + 2.
The quadratic expression:
Any expression with the variables of the highest exponent or the expression's degree as 2 is a quadratic expression.
The given expression is 8x²2x( 1 + 4x) + 2
An expression of the form ax² + bx + c, where a ≠ 0 is called a quadratic expression.
8x²2x( 1 + 4x) + 2
Now apply the distributive property we have
8x² × 2x + 8x² × 2x × 4x + 2
16x³ + 64 [tex]x^{4}[/tex] + 2
64[tex]x^{4}[/tex] + 16x³ + 2
Therefore the quadratic expression is 64[tex]x^{4}[/tex] + 16x³ + 2.
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If 7/2 meler of wire ris cut from a 2 piece of 10 meter long wire, how much wire is left?
The wire left is 16 1/2 meters.
How to calculate the fraction?From the information 7/2 wire is cut from piece of wire that is 2 piece of 10 meters.
Therefore, the wire that will be left will be:
= (2 × 10) - 7/2
= 20 - 7/2
= 20 - 3 1/2
= 16 1/2 meter
The wire left is 16 1/2 meters.
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A particle P moves with constant velocity v. Initially P is at the point with position vector a. t seconds later P is at the point with position vector b. Find v when:
a= 2i + 3j, b= 6i + 13j , t = 2
Answer:
correct
Step-by-step explanation:
So the acute angle between the vectors is 7.122° (3sf). Explanation: The angle θ between two vectors →A and →B is related to the modulus.
While shopping for books, Dominique spent $38 less than 3 times what Roberto
spent. Write an equation to represent the scenario if Dominique spent $10.
The equation to represent the scenario is 3y - 38 = 10
How to write an equation to represent the scenario?Represent the given parameters as
x = Dominique
y = Roberto
From the question, we have
Dominique spent $38 less than 3 times what Roberto spent
This means that
x = 3y - 38
Also, Dominique spent $10
So, we have
3y - 38 = 10
Hence, the equation to represent the scenario is 3y - 38 = 10
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i need help solving this angle problem
Answer:
corresponding angles are equal
Step-by-step explanation:
89*=(6x+5)*
89-5=6x
84=6x
x=14
I hope I could help.
Explain the difference between finding the vertex of a function written in vertex form and finding the vertex of a function written in standard form.
The equation in the vertex form will be y = (x + b/2a)² - b²/4a² + c/a and the equation in the standard form will be ax² + bx + c = 0.
What is a quadratic equation?The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.
Convert the standard equation into a vertex form, then we have
x² + (b/a)x + (c/a) = 0
x² + (b/a)x + b²/4a² - b²/4a² + c/a = 0
(x + b/2a)² - b²/4a² + c/a = 0
Put h = - b/2a and k = - b²/4a² + c/a, where (h, k) be the vertex of the parabola. Then the equation will be
(x - h)² + k = 0
The function written in vertex form will be y = (x - h)² + k and in the standard form will be ax² + bx + c = 0.
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Express 80 as the product of its prime factors
Write the prime factors in ascending order.
Answer:
Give brainliest - the crown thingy.
2*2*2*2*5
Or
2^4 * 5
The * is the symbol on my keyboard for the multiplication symbol.
Step-by-step explanation:
who is kay floxk i so confused so help me wit this
Do you mean Kay Flock? Because they are a rapper.
https://en.m.wikipedia.org/wiki/Kay_Flock
Anyone pls help me rq
Answer:
m<LHK = 101
Step-by-step explanation:
Ok, so the straight line is equal to 180 degrees. And we already know the side of one angle, that is 79 degrees. So, simply subtract 79 from 180, and you get 101 degrees. I took geometry last year, and this might not be the "correct" way to do it, but it is easier and you get the same correct answer
Answer:
<LHK = 101
Step-by-step explanation:
angle on a straight line add up to 180
180 - 79 = 101
