[tex]\huge\boxed{45^\circ}[/tex]
See the attached diagram.
Together, angles BDC and ADB form a right angle, which is 90 degrees.
The angles are split straight down the middle, meaning they're equal to each other. This means each one is equal to half of 90 degrees, which is 45 degrees.
From the diagram below, if AC =40, CD=10, and DB=8, then what would be the length of AB?
The length of AB would be 38 units
How to determine the length AB?The attached image represents the missing piece in the question
Considering the triangle BCD;
Calculate the length BC using the following Pythagoras theorem
BC^2 = CD^2 + BD^2
This gives
BC^2 = 10^2 + 8^2
Evaluate
BC^2 = 164
Considering the triangle CBA;
Calculate the length AB using the following Pythagoras theorem
AB^2 = AC^2 - BC^2
This gives
AB^2 = 40^2 - 164
Evaluate
AB^2 = 1436
Take the square root
AB = 38 (approximated)
Hence, the length of AB would be 38 units
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How do you solve this?
Answer:
No solutions
Step-by-step explanation:
First ADD 4 /(X+4) to both sides of the equation to get
( x+4)/ (x+ 4) = 3
1 = 3 ???? There are no solutions
[tex]\dfrac{x}{x+4}=3-\dfrac{4}{x+4}\qquad(x\not=-4)\\\\x=3(x+4)-4\\x=3x+12-4\\2x=-8\\x=-4[/tex]
Which contradicts initial assumption, therefore [tex]x\in\emptyset[/tex].
A plane takes off from an airport on a bearing of 270° and travels at a speed of 320 mph. after sometime and flight, space the plane encounters a 35 mph wind blowing directly north. Find the speed of the airplane after it encounters the wind.
A.322mph B.330mph C.285mph D.355mph
The speed of the plane after it encounters the wind is C.285mph
How to calculate the speed of the plane when it encounters the wind?Since the plane takes off from an airport on a bearing of 270° and travels at a speed of 320 mph it's velocity is v = (320cos270°)i + (320sin270°)j
= (320 × 0)i + (320 × -1)j
= 0i - 320j
= - 320j mph
Also, the plane encounters a 35 mph wind blowing directly north. The velocity of the wind is v' = 35j mph
So, the velocity of the plane after it encounters the wind is the resultant velocity, V = v + v'
= -320j mph + 35j mph
= -285j mph
So, the speed of the plane after it encounters the wind is the magnitude of V = |-285j| mph
= 285 mph
So, the speed of the plane after it encounters the wind is C.285mph
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Which of the following represents the unlike terms? 8m and 12a,2x and 3x,3m and 6m,6a and 9a.
8m and 12a
Step-by-step explanation:Like terms are terms that can be combined to condense a mathematical expression or equation.
Unlike Terms
Unlike terms are defined as terms that have different variables or powers.
This means that for terms to be unlike they must either be multiplied by a different variable, like x and y, or have different exponents.If terms meet either of these requirements, they are unlike. On the other hand, for terms to be like they must have both the same variable and power. The coefficients for the terms are not important.
Final Answer
All of the answer choices are to the first power, so the exponents are not important for this question. However, the last 3 answer choices all share the same variable. This means that they are all like terms.
The first answer choice, 8m and 12a, have different variables. This means that they cannot be combined and are unlike terms.
I set off on a 15 miles cycle ride at a speed of 10mile per hour. how long does the ride take me
The ride takes 1.5 hours for a speed of 10 miles per hour.
What is speed?The rate at which an object travels a certain distance can be described using the speed formula. The distance that a body travels in a certain amount of time is a common way to measure speed.
A body's speed can be defined as how quickly it is going. The equation for a given body's speed can be written as,
Speed=Distance/Time
According to the question,
Speed=10 miles per hour
Distance=15 miles
Time=[tex]\frac{15}{10}[/tex]=1.5 hours
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Listen
If 2/3 is the fraction representing the ratio of corresponding sides of two similar
triangles, the ratio of the areas of the triangles would be:
2/3
3/2
1.41/1.73
4/9
Question 3 (1 point)
6
the the value of x, if the perimeter of the rectangle is 98ft
Answer:
98/22 or 4.4545
Step-by-step explanation:
Perimeter of a rectangle: 2*width+2*length
4x*2+7x*2 = 98
8x+14x = 98
22x = 98
x = 98/22 or 4.4545
Student Name:
Lesson Number: 22
4th Proportion
Directions:
Complete the following constructions. Leave all construction arcs on your paper.
a
Math Assignment
Level: 1007
b
1 Given a, b, and c, the length of three segments. Find the fourth proportional.
Find the fourth proprtional to r, s, and t.
The fourth proportionals are bc/a and st/r
How to determine the fourth proportional?Segments a, b and c
Let the fourth segment be x.
So, we have the following equivalent ratio
a : b = c : x
Express as fraction
a/b = c/x
Make x the subject
x = bc/a
Segments r, s and t
Let the fourth segment be x.
So, we have the following equivalent ratio
r : s = t : x
Express as fraction
r/s = t/x
Make x the subject
x = st/r
Hence, the fourth proportionals are bc/a and st/r
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Sarah has 15 naira and bobo has 39 naira .how much must Sarah give to bobo so that bibo shall have 5 times as much as Sarah
HELP THIS IS MY LAST QUESTION
Answer:
0.71
Step-by-step explanation:
- Please see the attached picture for full solution!:)
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A bank employee is filling an empty cash machine with bundles of $100.00,$500.00 and $1000.00 bills each bundle has 100bills in it and the machine hold 10 bundles of each type. What amount of money is required to fill the machines?
Answer:
65fghxtt
Step-by-step explanation:
ΔABC has the following angle measures: A = 40 degrees, B = 60 degrees, and C = 80 degrees. The triangle is reflected across the x-axis to obtain ΔA’B’C’. What is the measure, in degrees, of angle B' ?
Answer:
60 degrees.
Step-by-step explanation:
A reflection does not alter the size of the angles of the triangle so B = 60 degrees.
Can some one help !!???
Answer:
Yes
Step-by-step explanation:
help me please, anwser me fast please
Answer:
Yes, it is a function
Step-by-step explanation:
A function has only one output for each input. So a function can have the same output for different input, but one input can only have one output. In this case none of the inputs output more than one output, so it is a function.
NEED HELP LAST DAY TO SUMMIT
Answer:
A 3.5
Step-by-step explanation:
To Break it down there 1 3/4 so to put in halve it would be 1/2 1/2 1/2 1/4 so u have 3 feet because 1/2 in is 3 feet then u have a 1/4 inch so that is half of a feet 1 + 1 + 1 + 1/2 is 3 1/2 converted to decimal is 3.5.
Create an inequality:
The sun of the numbers is not more than 12
Answer:
x + y ≤ 12
Step-by-step explanation:
Inequality:
Not more than 12 means less than or equal to 12
x + y ≤ 12
Look at this triangle.
A
Work out length BC.
13 cm
8 cm
B
С
In the given triangle, the length of BC is 10.25 cm
Solving a right triangle
From the question, we are to determine the length BC
The triangle is a right triangle, then we can write that
/AB/² = /AC/² + /BC/² (Pythagorean theorem)
From the given information,
/AB/ = 13 cm
/AC/ = 8 cm
Putting the parameters into the equation, we get
13² = 8² + /BC/²
169 = 64 + /BC/²
/BC/² = 169 - 64
/BC/² = 105
/BC/ = √105
/BC/ = 10.25 cm
Hence, the length of BC is 10.25 cm
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Find the area of the shaded region. (drawing is not to scale) GEOMETRY!!! HELP PLEASE
Answer:
150
Step-by-step explanation:
The area of the trapezoid is (½)(14+10)(2) = 24.
The area of the rectangle is (14)(9) = 126.
Adding these together, we get 126 + 24 = 150.
Reperesent 1.235 as P/q.
Answer:
[tex]\frac{247}{200}[/tex]
Step-by-step explanation:
1.235
= 1 + 0.235 ( the place value of the 5 is thousandths ) , then
= [tex]\frac{1000}{1000}[/tex] + [tex]\frac{235}{1000}[/tex]
= [tex]\frac{1235}{1000}[/tex] ( divide numerator/denominator by 5 )
= [tex]\frac{247}{200}[/tex] ← in simplest form
A store sells both cold and hot beverages. Cold beverages, c, cost $1.50, while hot beverages, h, cost $2.00. On Saturday, drink receipts totaled $360, and 4 times as many cold beverages were sold as hot beverages.
Which system of linear equations represents the beverage sales on Saturday?
Answer:
There are two equations and two variables, so this is a system of linear equations.
c + h = 360
4c = h
Step-by-step explanation:
Answer:
The linear equations would be c = 4h and 1.5c + 2h = 360.
Step-by-step explanation:
First we have to create a table for our data.
c = total number of cold beverages sold.
h = total number of hot beverages sold.
The total cost of both beverages sold -
1.5c + 2h = 360
The amount of cold beverages -
c = 4h
Now we just need to substitute the second equation to the first one.
1.5 * (4h) + 2h = 360
= 6h + 2h = 360
= 8h = 360
= h = 45
Now we need to find the value of c.
c = 4* 45 = 180
Therefore 180 cold beverages were sold and 45 hot beverages were sold.
But the linear equations would be c = 4h and 1.5c + 2h = 360.
Hope this helped! :D
What is the length of PR?
Answer:
D
Step-by-step explanation:
By observation we just know that one of the angles of two triangles is the same.
There are two sides that are not equal in ability to determine similarity.
HELP
Given: ABCD is a parallelogram and AC bisects BD.
Prove: AC bisects
2) [tex]ABCD[/tex] is a rhombus (a parallelogram with perpendicular diagonals is a rhombus)
3) [tex]\overline{AC}[/tex] bisects [tex]\angle BCD[/tex] (diagonals of a rhombus bisect the angles from which they are drawn)
Which is equivalent to (3/125)*?
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Question reads:}[/tex]
[tex]\large\textbf{Which is equivalent to }\rm{\bf \dfrac{3}{125}}\large\textbf{ ?}[/tex]
[tex]\huge\textbf{Solving for your fraction:}[/tex]
[tex]\mathbf{\dfrac{3}{125}}[/tex]
[tex]\mathbf{= \dfrac{3\times2}{125\times2}}[/tex]
[tex]\mathbf{\approx \dfrac{3 + 3}{125 + 12{5}}}[/tex]
[tex]\mathbf{= \dfrac{6}{250}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{\dfrac{6}{250}}}\huge\checkmark[/tex]
[tex]\large\text{By the way, they are a lot more fractions that are equivalent to}\\\large\text{the given equation (}\rm{\dfrac{3}{125}}\large\text{) but we only labeled one that is the very}\\\large\text{first fraction that is equal to it. }[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Please help! will give 14 points and brainliest!
Answer:
EF = 22 , AB = 1
Step-by-step explanation:
the midsegment of a trapezoid is equal to half the sum of the parallel bases
EF = [tex]\frac{1}{2}[/tex] (AB + DC ) ← substitute values
x + 6 = [tex]\frac{1}{2}[/tex] (2x - 9 + x + 5) ← multiply both sides by 2 to clear the fraction
2x + 12 = 3x - 4 ( subtract 3x from both sides )
- x + 12 = - 4 ( subtract 12 from both sides )
- x = - 16 ( multiply both sides by - 1 )
x = 16
Then
EF = x + 6 = 16 + 6 = 22
Similarly
EF = [tex]\frac{1}{2}[/tex] (AB + DC ) , that is
x + 3 = [tex]\frac{1}{2}[/tex] (4x - 3 + 2x + 5 ) ← multiply both sides by 2 to clear the fraction
2x + 6 = 6x + 2 ( subtract 6x from both sides )
- 4x + 6 = 2 ( subtract 6 from both sides )
- 4x = - 4 ( divide both sides by - 4 )
x = 1
Then
AB = 4x - 3 = 4(1) - 3 = 4 - 3 = 1
So this is not a school related question, I am a trader looking to see my APY if I take an initial investment amount and make 5% on it every day of the year. I've tried the compound interest formula but it doesn't work, I only get about a 64.8% increase which I know is false. So here is what I'm looking for: I need to know the official APY of making 5% everyday on a 1,000 investment for 1 year and then the final amount your left with.
Answer:
um tbh me dont know
Step-by-step explanation:
What is the volume of the sphere shown below with a radius of 9? OA. 108 cu. units B. 972* cu units OC. 2916 cu units D. 1458, cu units
The volume of the sphere shown below with a radius of 9 is 3052.08 cubic units
Volume of a sphereThe formula for calculating the volume of a sphere is expressed as;
V = 4/3πr³
where
r is the radius of the sphere
Substitute
V = 4/3π(9)³
V = 4/3(3.14)*729
V = 3052.08 cubic units
Hence the volume of the sphere shown below with a radius of 9 is 3052.08 cubic units
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PLEASE HELP Which of the following expressions could not be used to determine the exact value of cos 60°?
The trigonometric expression cos 60° is equivalent to the expressions cos² 30° - sin² 30°, 2 · cos² 30° - 1 and 1 - 2 · sin² 30°. Then, not equivalent to 2 · sin 30° · cos 30°. (Correct choice: A)
How to find an expression not equivalent to a trigonometric equation
In this question we have a trigonometric equation and we are supposed to find an expression not equivalent to the former. Herein we have that the cosine of a double angle is equivalent to the following expressions:
cos 2θ = cos² θ - sin² θ (1)
cos 2θ = 2 · cos² θ - 1 (2)
cos 2θ = 1 - 2 · sin² θ (3)
The trigonometric expression cos 60° is equivalent to the expressions cos² 30° - sin² 30°, 2 · cos² 30° - 1 and 1 - 2 · sin² 30°. Then, not equivalent to 2 · sin 30° · cos 30°. (Correct choice: A)
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In 2012, the population of a city was 6.93 million. The exponential growth rate was 2.18% per year.
a) Find the exponential growth function.
b) Estimate the population of the city in 2018.
e) When will the population of the city be 10 million?
d) Find the doubling time.
a) The growth function has the form:
[tex]P(x) = P*(1 + r)^x[/tex],where:
P(x) - population after x years, P- initial population, r - rate of change, x - number of years since 2012.Considering the values we get the function:
[tex]P(x) = 6.93*(1 + 2.18/100 ) ^x=6.93*1.0218^x[/tex]b) Number of years between 2012 and 2018 is:
x = 2018 - 2012 = 6Find the population, using the above equation:
[tex]P(6) = 6.93*1.0218^6 = 7.89[/tex] million (rounded)c) Find the value of x when P(x) = 10 million
[tex]10 = 6.93*1.0218^x[/tex][tex]1.0218^x = 10/6.93[/tex][tex]1.0218^x=1.443[/tex][tex]log1.0218^x=log1.443[/tex][tex]x = log1.443/log1.0218[/tex][tex]x=17[/tex] yearsd) Find the doubling time:
[tex]2*6.93 =6.93*1.0218^x[/tex][tex]1.0218^x=2[/tex][tex]x=log2/log1.0218[/tex][tex]x=32.14[/tex] yearsAnswer:
[tex]\textsf{a)} \quad f(x)=6.93(1.0218)^x[/tex]
b) 7.89 million (2 d.p.)
c) 2019
d) 32.14 years (2 d.p.) after 2012
Step-by-step explanation:
Exponential Function
[tex]y=ab^x[/tex]
where:
a is the initial value (y-intercept)b is the base (growth/decay factor) in decimal formx is the independent variabley is the dependent variableIf b > 1 then it is an increasing function
If 0 < b < 1 then it is a decreasing function
Part (a)
If the exponential growth rate was 2.18% per year, then each year there would be 102.18% of the previous year's population.
⇒ b = 1.0218
Given:
a = 6.93 millionb = 1.0218x = time (in years after 2012)y = population (in millions)Substitute the given values into the formula to create an exponential growth function:
[tex]f(x)=6.93(1.0218)^x[/tex]
Part (b)
To estimate the population of the city in 2018, determine the value of x:[tex]x = 2018 - 2012 = 6[/tex]
Substitute the found value of x into the found exponential function:
[tex]\implies f(6)=6.93(1.0218)^6=7.89 \: \sf million\:(2\:d.p.)[/tex]
Part (c)
To determine when the population of the city will be 10 million, set the function to 10 and solve for x:
[tex]\implies 6.93(1.0218)^x=10[/tex]
[tex]\implies (1.0218)^x=\dfrac{10}{6.93}[/tex]
[tex]\implies \ln (1.0218)^x= \ln \left(\dfrac{10}{6.93}\right)[/tex]
[tex]\implies x\ln (1.0218)= \ln \left(\dfrac{10}{6.93}\right)[/tex]
[tex]\implies x= \dfrac{\ln \left(\frac{10}{6.93}\right)}{\ln (1.0218)}[/tex]
[tex]\implies x=17.00496413...[/tex]
To find the year, add the found value of x to 2012:
[tex]\implies \sf 2012 + 17.00496413... = 2019[/tex]
Part (d)
To find the doubling time, set the function to double the initial population and solve for x:
[tex]\implies 6.93(1.0218)^x=6.93 \cdot 2[/tex]
[tex]\implies (1.0218)^x=2[/tex]
[tex]\implies \ln (1.0218)^x= \ln (2)[/tex]
[tex]\implies x \ln (1.0218)= \ln (2)[/tex]
[tex]\implies x = \dfrac{\ln (2)}{\ln (1.0218)}[/tex]
[tex]\implies x=32.14107014...[/tex]
Therefore, the doubling time is 32.14 years (2 d.p.) after 2012.
Help me with this problems
Answer:
its easy
Step-by-step explanation:
you should change all into degrees
Graph a system of equations to solve Log(-5.6x+1.3)=-1-x
From least to greatest the solutions are:
By seeing where the curves intercept, we conclude that the solutions are:
(0.22, -1.22) and (-2.12, 1.12)
How to solve the system of equations?
Here we just need to graph the equations:
y = log(-5.6*x + 1.3)
y = -1 - x
And see in which points the curves intercept.
The graph can be seen below:
There we can see that the intersections (and solutions) are the points:
(0.22, -1.22) and (-2.12, 1.12)
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