Answer:
Basic Concept used:
Since D is the mid-point of EF,
ED will be equal to DF since D is in the middle of the line segment
We are given the following values for ED and DF
ED = 4x + 6 and DF = 7x - 9
Solving for x:
Since ED = DF (D is the mid point)
4x + 6 = 7x - 9
9 + 6 = 7x - 4x
15 = 3x
x = 5
Finding the values of ED , DF and EF:
we know that x = 5 (from the last section)
we are given the following values of the line segments:
ED = 4x + 6
DF = 7x - 9
EF (ED + DF) = (4x + 6) + (7x - 9)
Replacing x with 5 in each of these equations:
ED = 4(5) + 5 = 26
DF = 7(5) - 9 = 26
EF = (4(5) + 6) + (7(5)-9) = 26 + 26 = 52
allen was making trail mix but he only wanted to make 1/3 of the recipe if the whole recipe called for 1/2 of a cup of peanuts how many cups will he need to make 1/3 of the recipe choose the model that matches the situation.
Answer:
the last one 1/6
Step-by-step explanation:
1/2 x 1/3 = 1/6
Question content area top
Part 1
A new bank customer with $ wants to open a money market account. The bank is offering a simple interest rate of %.
a. How much interest will the customer earn in years?
Find the inverse function for
Answer:
a. ∛(x+4)/3
Step-by-step explanation:
y = 3x³ -4
step 1: x = 3y³ - 4 (swap x and y)
step 2: 3y³ = x + 4
y³ = (x + 4) / 3
y = ∛(x+4)/3 (solve y)
f⁻¹(x) = ∛(x+4)/3 (inverse notation)
Ian suffered a loss of 10% when his watch was sold at $90. How much should he have sold his watch if he wanted to make a gain of 20%?
Explanation:
This problem is a simple percent chage problem. The absoluge change in price was $12−$8=$4. Relative to the original price, it was 412, which is 0.3333 or 33.33%.
Simplify the expression by combining like terms.
4/3a - 1/2b + 1/3a + 5/2b
Answer: 5/3a + 4/2b
Step-by-step explanation:
\(\dfrac{4}{3} a-\dfrac{1}{2} b+\dfrac{1}{3} a+\dfrac{5}{2} b\)
Rearrange:
\(\dfrac{4}{3} a+\dfrac{1}{3} a-\dfrac{1}{2} b+\dfrac{5}{2} b\)
Combine Like Terms:
\(\dfrac{4}{3} a+\dfrac{1}{3} a=\dfrac{5}{3} a\\-\dfrac{1}{2}b+\dfrac{5}{2} b=\dfrac{4}{2} b\)
\(\fbox{$\dfrac{5}{3}$a + $\dfrac{4}{2}$b}\)
a playground is 750 M long and 250 m broad find the cost of levelling at rupees 16 per 100 square metres
Answer:
Area of play ground = Length × Breadth = 750 × 250 = 187500. a Cost of levelling the ground = 187500 × 16 100 = Rs . 30000
Eight gardeners equally share 1/2 of a pile of pine needles. What fraction of the pile does each gardener receive?
Answer:
Each gardner will get 1/16 of a pile of pine needles.
Step-by-step explanation:
1/2 ÷ 8
*Switch the division to multiplication and flip the 8 (or 8/1) upside-down.
= 1/2 · 1/8
= 1/16
HELP ASAP PLS GIVE EXPLANATION/STATEMENT AND REASON FORM
Explanation:
Glue the two right triangles together to form one larger triangle.
The angle adjacent to the 60 degree angle is 180-60 = 120 degrees.
The angle adjacent to x is 180-x
The larger triangle has the interior angles of:
35120180-xThose three angles add to 180 (which is true of any triangle)
35+120+180-x = 180
335-x = 180
-x = 180-335
-x = -155
x = 155
Or you can note that 35+120 = 155 which is the summation of the interior angles that aren't adjacent to exterior angle x (refer to the remote interior angle theorem, aka the exterior angle theorem).
Write an equation for the word problem below
You purchased 4 DVD's and a CD. The CD costs $14.50 and you spend a total of $52.50. How much does each DVD cost?
Answer:
each dvd costs $9.5
Step-by-step explanation:
first 52.5-14.5=38
then 38 divided by 4
and you answer
A pencil at a stationery store costs $1, and a pen costs $1.50. Shawn spent $12 at the store. He bought a total of 9 items. Which system of equations can be used to find the number of pencils (x) and pens (y) he bought? (5 points)
1.5x + y = 12
x = 9y
x + 1.5y = 12
x + y = 9
x + 9y = 12
x = 1.5y
9x + y = 12
x = 1.5y
Answer:
9 = x + y
1x + 1.5y = 12
Step-by-step explanation:
9 (number of items) = x (number of pencils) + y (number of pens)
1x (cost of x number of pencils) + 1.5y (cost of y number of pen s)= 12 (total cost)
the relation between x^n and n! . Is x^n and n! are equal?you can use taylor series.
Which statement about the value of x is true?
O x>38
Ox<39
Ox=77
OX > 103
Answer:
x = 77 and x > 38
Step-by-step explanation:
Sum of all angles in a triangle is 180.
The angle PNO will hence be:
180 - 38 - 39 = 103 degrees.
The angle PNO + angle x = 180 degrees (straight line)
So 103 + x = 180, therefore x = 180 - 103 = 77.
Which is also greater than 38, so x > 38 is also correct.
The solution is : x = 77 and x > 38
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
here, we have,
Sum of all angles in a triangle is 180.
The angle PNO will hence be:
180 - 38 - 39 = 103 degrees.
The angle PNO + angle x = 180 degrees (straight line)
So 103 + x = 180,
therefore x = 180 - 103 = 77.
Which is also greater than 38,
so x > 38 is also correct.
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Please help me find the area
Step-by-step explanation:
1/2×28×(21+16)
calculate then u get the answer
Answer: 213
Step-by-step explanation: U are beautiful in the picture u showed
In a sports competition, Alyssa received −16 points. She got these
points evenly in 4 events. How many points was she penalized for
each event?
Answer:
-4
Step-by-step explanation:
You deposit $6000 into an account that earns simple interest at an annual rate of 5%. How much interest does the account earn after 3 months?
The interest earned after 3 months is $75
What is simple interest?
The simple interest on a deposit is the principal deposited multiplied by the interest and the time the deposit lasted
I=PRT
I=interest=unknown
P=principal=$6000
R=interest rate=5%
T= 3 months=0.25 year
I=$6000*5%*0.25
I=$75
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Answer:
75 dollars
Step-by-step explanation:
i got it right
Suppose that the function h is defined, for all real numbers, as follows.
h(x) = (x+1)²
{
if x ≤-2
if-2
-x-2 ifx>2
h(-2) = 0
h(-1) = 0
h (3) = 0
Find h(-2), h(-1), and h (3).
0/0
믐
X
3
please help 15 points to whoever does
In light of this, 1,0,8 is the value of the function h(x) = (x+1)2 where h is defined for all real integers.
what is function ?The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
given
h(x) = (x+1)²
h(-2) = 1
h(-1) = 0
h(3) = 8
In light of this, 1,0,8 is the value of the function h(x) = (x+1)2 where h is defined for all real integers.
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write an exponential function that has a y-intercept of -4 and passes through the points (1, -1.6) and (2, -0.64)
The function can be used to model the exponential growth or decay that occurs in real-life situations that fit this particular pattern is y = 4(-0.4)ˣ + -4
An exponential function is a mathematical function that has the form
=> y = abˣ,
where a is a constant and b is the base of the exponential.
To start, we will use the first point, (1, -1.6), to write an equation that relates x and y. Let's call the constant a in our exponential function "k". Using the point (1, -1.6), we can write the equation:
=> -1.6 = k * b¹
Next, we will use the second point, (2, -0.64), to write another equation that relates x and y. Using the point (2, -0.64), we can write the equation:
=> -0.64 = k * b²
Now that we have two equations, we can solve for the two unknowns, k and b, by dividing the two equations:
=> (-0.64) / (-1.6) = k * b² / k * b¹
b = (0.64 / -1.6)¹
b = -0.4
With b determined, we can substitute it back into one of the equations and solve for k:
=> -1.6 = k * (-0.4)¹
=> k = -1.6 / (-0.4)
=> k = 4
So our exponential function that passes through the points (1, -1.6) and (2, -0.64) and has a y-intercept of -4 is:
y = 4 * (-0.4)ˣ + -4
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Round 0.00076511 to one significant figure
Answer: 0.0008
Step-by-step explanation: Hope this helps :)
Naji is trying to draw an isosceles triangle. He is
given point A at (-4,-2) and point B at (2,-2).
Plot these two points, then help Naji make the
isosceles triangle ABC by ploting point C. Give
your coordinates for point C. It must be on the
grid provided.
Answ
Step-by-step explanation:wirugf4
Suppose the figure shows f(t), the interest rate on an investment t years after the initial deposit. The straight line is tangent to the graph of y=f(t) when t=8. How fast was the internet rate riding at that time?
Concept:
The slope of the tangent to the curve at any point gives the instantaneous rate of change of the function.
From the given graph, it is observed that the line is tangent to the curve at point (8,9).
So the slope of this line will give the rate of change of the function i.e. interest rate at that instant.
The slope (m) of the line joining (0,0) and (8,9) is given by,
\(\begin{gathered} m=\frac{9-0}{8-0} \\ m=\frac{9}{8} \\ m=1.125 \end{gathered}\)Since the slope comes out to be positive, it means that the function is increasing with respect to time.
Thus, the interest rate is increasing at the rate 1.125, at the given time instant.
5.3 MATHEMATICS HOLIDAY PACKAGE-TERM 2(2023) Instructions: Attempt ALL items 1. Your family has seven siblings; peter, John, Sarah, Joy, Ali, Mary and Ivan. There is an interval of 2 years between the ages of the children from Ivan to peter. Ivan is three years old. Task: Using an arrow diagram, explain the information about your family.
Use the table to answer the question that follows.
ROR Portfolio 1 Portfolio 2 Portfolio 3
12.6% $1,250 $950 $900
2.8% $575 $2,025 $2,350
10.4% $895 $1,185 $310
1.8% $800 $445 $1,600
−5.6% $1,775 $625 $2,780
Calculate the weighted mean of the RORs for each portfolio. Based on the results, which list shows a comparison of the overall performance of the portfolios, from best to worst?
Portfolio 1, Portfolio 2, Portfolio 3
Portfolio 3, Portfolio 2, Portfolio 1
Portfolio 2, Portfolio 3, Portfolio 1
Portfolio 2, Portfolio 1, Portfolio 3
Based on the results, the below list shows a comparison of the overall performance of the portfolios, from best to worst:
Portfolio 2, Portfolio 1, Portfolio 3
Portfolio 1:
total investment=$1250+$575+$895+$800+$1775
total investment = $5295
weighted average ROR= (12.6%*$1250/$5295 + 2.8%*$575/$5295 + 10.4%*$895/$5295 +1.8%*$800/$5295 - 5.6%*$1775/$5295)
weighted average ROR = 3.23%
Portfolio 2:
total investment = $950 + $2025 + $1185 + $445 + $625
total investment = $5230
weighted average ROR= ( 12.6%*$950/ $5230 + 2.8% *$2025/ $5230 + 10.4%*$1185/ $5230 + 1.8%* $445/ $5230 - 5.6%*$625/ $5230)
weighted average ROR = 5%
Portfolio 3:
total investment = $900 + $2350 + $310 + $1600 + $2780
total investment = $7940
weighted average ROR = ( 12.6%*$900/$7940 + 2.8% *$2,350/$7940 + 10.4%*$310/ $7940 + 1.8%* $1600 / $7940 −5.6% *$2780/$7940)
weighted average ROR = 1%
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lionfish are considered an invasive species, with an annual growth rate of 67%. A scientist estimates there are 8,000 lionfish in a certain bay after the first year.
Part A: Write the explicit equation for f (n) that represents the number of lionfish in the bay after n years. Show all necessary math work.
Part B: How many lionfish will be in the bay after 6 years? Round to the nearest whole number and show all necessary math work.
Part C: If scientists remove 1,200 fish per year from the bay after the first year, what is the recursive equation for f (n)? Show all necessary math work.
Answer:
There would be 173,535 lionfish after 6 years.
Step-by-step explanation:
Since lionfish are considered an invasive species, with an annual growth rate of 67%, ya scientist estimates there are 8,000 lionfish in a certain bay after the first year, A) to write the explicit equation for f (n) that represents the number of lionfish in the bay after n years; B) determine how many lionfish will be in the bay after 6 years; and C) if scientists remove 1,200 fish per year from the bay after the first year, determine what is the recursive equation for f (n); the following calculations must be performed:
A)
8000 x 1.67 ^ n = f
B)
8000 x 1.67 ^ 6 = X
8000 x 21.691961596369 = X
173,535.692770952 = X
C)
(8000 - 1200 x 1 ^ n) x 1.67 ^ n = f
Therefore, there would be 173,535 lionfish after 6 years.
A florist sells roses for $5 each and carnations s for $3 each if she makes a bouquet containing a mixture of 15 roses and carnations and sells it for $61 how many of each flower should she use. ?
A florist sells roses for $5 each and carnations s for $3 each if she makes a bouquet containing a mixture of 15 roses and carnations and sells it for $61 how many of each flower should she use. ?
Let
x -----> number of roses
y ----> number of carnations
so
we have
x+y=15 -----> x=15-y -----> equation 1
5x+3y=61 -----> equation 2
solve the system
substitute equation 1 in equation 2
5(15-y)+3y=61
solve for y
75-5y+3y=61
2y=75-61
2y=14
y=7
x=15-7
x=8
therefore
roses 8carnations 7Last year , 375 students attended homecoming dance. The committee expects at least 500 to attend this year’s event. What is the expected cost for refreshments based on expected attendance?
Answer:
2362 dollars for all the students
Step-by-step explanation:
my big brain
Answer:
ya you are right okokgudcv
need help asap!
Mildred has a circular yard with a diameter of 145 feet
She wants to put a fence around the entire yard. How many feet of fence would it take to put Fence around the entire circular yard?
Approximately 456.3 feet of fence to surround the entire circular yard.
Now, For the amount of fencing needed to surround a circular yard, we have to calculate the circumference of the circle, which is the distance around the circle.
Since, The circumference of a circle is,
⇒ C = πd,
where, C is circumference, d is diameter,
Here, the diameter of the circular yard is 145 feet,
So the radius is half of that,
r = 145/2 = 72.5 feet.
So, Using the formula, we can calculate the circumference as:
C = πd
C = 3.14 x 145
C = 456.3 feet
Therefore, Approximately 456.3 feet of fence to surround the entire circular yard.
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HELP MEEE PLEASE I BEG U
Answer:it is either graph a or b but i sure its a
Step-by-step explanation:
Answer:
The first or second graph
Create an equation for a line that is parallel to the line �� = −32�� − 5.
Answer:
can u type it again
Step-by-step explanation:
Please solve this
∫ (log(1 + x ^ 2))/((x + 1) ^ 2) dx
The final result of the integral is:
∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,
where Li(x) is the logarithmic integral function and C is the constant of integration.
We have,
To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.
Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:
∫ (log(1 + (u-1)²) / u²) du.
Expanding the numerator, we have:
∫ (log(1 + u² - 2u + 1) / u²) du
= ∫ (log(u² - 2u + 2) / u²) du.
Now, let's split the logarithm using the properties of logarithms:
∫ (log(u² - 2u + 2) - log(u²)) / u² du
= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.
We can simplify the second integral:
∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.
Using the power rule for integration, we can integrate both terms:
∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.
Now, let's focus on the second integral:
∫ (log(u) / u³) du.
This integral does not have a simple closed-form solution in terms of elementary functions.
It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).
Therefore,
The final result of the integral is:
∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,
where Li(x) is the logarithmic integral function and C is the constant of integration.
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10-d=34-5d\(10-d=34-5d\)
Answer:
d = 6
Step-by-step explanation:
10 - d = 34 - 5d
add d to both sides to make all the d's on one side
10 = 34 - 4d
subtract 34 from both sides to isolate the d and its coefficient
-24 = -4d
divide both sides by -4 to isolate d
d = 6