Answers
Answer: x = 15
Step-by-step explanation: The first thing to note is that what we have here are two similar triangles. First we have triangle ABC and secondly we have triangle EDC. Line BD is a transversal that cuts line AE at point C. Hence we can deduce that angle ACB is equal in measurement to angle ECD (opposite angles). Next we also observe that the other two angles are right angles, that is, 90° in size. Therefore we can conclude that the other two angles (angle ABC and angle EDC) are also of the same measurement.
We can now establish the ratio of the similar sides.
Line AB = Line ED
Line AC = Line EC
AB/ED = AC/EC
24/40 = 2x/3x + 5
3/5 = 2x/3x + 5 {the left hand side has been reduced to it's simplest form}
Next we cross multiply and that gives us
3(3x + 5) = 5(2x)
9x + 15 = 10x
Subtract 9x from both sides of the equation
15 = 10x - 9x
15 = x
Related Questions
list the sample space for odd numbers between 20 and 30
Answers
The sample space for odd numbers between 20 and 30 is {21, 23, 25, 27, 29}. These are integers that are not wholly divisible by 2.
Explanation:The sample space is a term used in mathematics, specifically in statistics and probability, to describe all possible outcomes of an experiment. In this case, the experiment is to find all odd numbers between 20 and 30. An odd number is an integer that is not exactly divisible by 2. The odd numbers between 20 and 30 are: 21, 23, 25, 27, and 29. Therefore, the sample space you are looking for is {21, 23, 25, 27, 29}.
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Typically, what percentage of the home cost should you have available for a down payment? 5%, 50%, 25%, 30%
Answers
Answer:
25%
Step-by-step explanation:
Answer:
25%
Step-by-step explanation:
I had this question on a test and i made an 100%
In 2000 the median home price in a certain city was about $290,000, and from 2000 to 2006, home prices in the city rose in an average of about 11.3% per year. If prices continue to rise at that rate what would be the median home price would have been in 2018? Compare to the actual median price of about $400,000 in 2018. (median home price would be approximately ____ minion in 2018.
Answers
Answer:
5000
Step-by-step explanation:
What is slope = 3/4 goes through the point (0,6)
Answers
Answer:
y=3/4x+6
Step-by-step explanation:
y-y1=m(x-x1)
y-6=3/4(x-0)
y-6=3/4(x)
y-6=3/4x
y=3/4x+6
To make a ribbon and bow for a hat, Stacey needs 5/6 yard of black ribbon and 2/3 yard of red ribbon. How much total ribbon does she need
Answers
A 500-kilogram horse runs at 5 meters/second. The horse’s kinetic energy is (blank)joulese g = 9.8 N/kg.)
Answers
Answer:
KE = 6250 Joule.
Step-by-step explanation:
Every moving body has kinetic energy and it is given by the expression
[tex]KE = \frac{1}{2}mv^{2}[/tex]
where the moving body has m as the mass and v as the velocity.
If m is in Kg and v is in meter/sec, then KE will be expressed in Joule.
Now, in this case, m = 500 and v = 5 meter/sec.
So, [tex]KE = \frac{1}{2} \times 500 \times (5)^{2} = 6250[/tex] Joule. (Answer)
Write a ratio as a ratio of whole numbers in lowest terms
$1.00 to $1.50
Answers
Answer:
Step-by-step explanation:
50
The ratio of the whole numbers in its lowest term is ratio $2 to $3 i.e. [tex]\mathbf{\dfrac{2}{3}}[/tex]
A ratio of two integers a and b can be represented into a fraction as numerators and denominators.
[tex]\mathbf{\dfrac{a \to numerator}{b \to denominator}}[/tex]
To recognize and determine the ratio of the whole numbers in their lowest terms, we will multiply both the numerator and the denominator by 10.
i.e.
[tex]\mathbf{=\dfrac{1.00}{1.50}}[/tex]
[tex]\mathbf{=\dfrac{1.00\times 10}{1.50 \times 10}}[/tex]
[tex]\mathbf{=\dfrac{10}{15}}[/tex]
DIvide both the numerator and denominator by 5;
[tex]\mathbf{=\dfrac{2}{3}}[/tex]
Therefore, we can conclude that the ratio of the whole numbers in its lowest term is ratio $2 to $3 i.e. [tex]\mathbf{\dfrac{2}{3}}[/tex]
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Two people working together can complete a job in 5 hours. If one of them works
twice as fast as the other, how long would it take the faster one working alone?
Answers
Answer:
5 hours
Step-by-step explanation:
because he is working twice as fast which means he will get the job done faster
So your awnser would therefore be 5
Graph f(x)=1/2x+2. Use the line tool and select two points to graph the line.
Answers
Step-by-step explanation:
Since f is a linear function then its graph must be a line
to draw a line ,all you need is plotting two points.
f(0)=1/2(0)+2=0+2=2 then the line passes through the point (0,2)
f(2)=1/2(2)+2=1+2=3 then the line passes through the point (2,3)
look ok at the photo below for the graph.
How can this 12×2+2³ make 120
Answers
Step-by-step explanation:
[tex]12\times(2+2^3)\qquad\text{use PEMDAS}\\\\\text{first power}\\\\=12\times(2+8)\\\\\text{next addition in parentheses}\\\\=12\times10=120[/tex]
Read this scene from The Miracle Worker Act 2.
(ANNIE insists, and HELEN gets rid of ANNIE’S hand by jabbing it with the needle. ANNIE gasps and moves to grip HELEN’S wrist; but KATE intervenes with a proffered sweet, and HELEN drops the card, crams the sweet into her mouth, and scrambles up to search her mother’s hands for more.)
How do these stage directions add meaning to the play?
The stage directions explain the characters’ facial expressions.
The stage directions illustrate the appearance of the room.
The stage directions describe how characters react to Helen.
The stage directions reveal Annie’s manner of speaking.
Answers
Answer:
The stage directions describe how characters react to Helen.
Step-by-step explanation:
In the given scene, the different characteristics of Helen as well as how other characters react when they see Helen is depicted in the scene. Other characters in the scene react differently to Helen when they come in contact with her. This is the main objective of the stage direction. It shows the interaction between Helen and others.
The stage directions represent the additions of the meaning to the play in terms of the stage directions describe how characters react to Helen.
The following information should be considered:
In the given situation, there is various characters of Helen and how the other character react at the time of seeing when Helen represent in the scene. The other characters scene react in a different way at the time of contacting. It represents the main aim of the stage directon. Also, it shows the interaction that lies between Helen and others.Learn more: brainly.com/question/17429689
Combine like terms to create an equivalent expression 2/5m - 4/5 - 3/5m
Answers
Answer:
-1/5m-4/5
Step-by-step explanation:
2/5m-4/5-3/5m
2/5m-3/5m-4/5
-1/5m-4/5
Write the equation.
During the year,
Myong travels 5,678
miles by airplane.
He travels twice as
many miles by train.
How many miles
does Myong travel
by train?
Answers
Answer:
11,356
Step-by-step explanation:
We multiply 5,678 by 2 because the word 'twice' is the same as multiplying by 2
Kyle is purchasing a refurbished phone. He is looking at the phone models 4, 5, and 6, with a protective case in red (R), blue (B), or camo (C). What are all of the different choices he has? A) {4, 5, 6} B) {4R, 5B, 6C} C) {4R, 4B, 4C, 5R, 5B, 5C} D) {4R, 4B, 4C, 5R, 5B, 5C, 6R, 6B, 6C}
Answers
Answer:
The choices Kyle has are option D.) {4R, 4B, 4C, 5R, 5B, 5C, 6R, 6B, 6C}
Step-by-step explanation:
The choices available to Kyle either of the models 4, or 5 or 6 and each model can have a protective case which can be either red(R) or blue(B) or camo(C).
So Kyle can have model 4 in red protective case, 4R, or model 4 in blue protective case(4B), or model 4 in camo protective case (4C) or
Kyle can have model 5 in red protective case, 5R, or model 5 in blue protective case(5B), or model 5 in camo protective case (5C) or
Kyle can have model 6 in red protective case, 6R, or model 6 in blue protective case(6B), or model 6 in camo protective case (6C).
So the choices Kyle has are option D.) {4R, 4B, 4C, 5R, 5B, 5C, 6R, 6B, 6C}
Answer:
D
Step-by-step explanation:
I need to know the answers to these please
Answers
The answer is 40.
7/8=x/40. We had to multiply 8 by 5 to get 40.
Whatever you do to denominator you must do to numerator. Multiply 7 and 5 to get 35.
Now we have 7/8 is equal to 35/40.
Next, for the 9/10 part. We multiplied 10 and 4 to get 40 so multiply the numerator by 4 as well and you get 36.
Now we have 9/10 is equal to 36/40
The problem is now 35/40 and 36/40
35/40 < 36/40
Which is the same as
7/8 < 9/10
The Outstanding O's cereal box has been redesigned with a new size and shape.
20 cm
30 cm
8 cm
How much material will it take to make the new box with no overlaps?
Answers
Answer:
Step-by-step explanation:
2(20x30)+ 2(8x30) + 2(20x8) - I > 1200 + 480 + 320= 2000 hope this helps :D
The material required for making a new cereal box with new dimensions is 2000 sq. cm. This is obtained by calculating the total surface area of the box with new dimensions.
The surface area of the cuboid:Cuboid has 6 faces (each face looks like a rectangle)To get the surface area of the cuboid, add the areas of all the 6 faces of the cuboid.For the length (L), width (W), and height (H), the surface area is given as S.A=2(LW + WH + LH). Since the area of the rectangle is L×W, adding areas of each face.Calculating the required material:It is given that,
The Outstanding O's cereal box has been redesigned with the new size and shape
The new dimensions are,
L=20 cm
W=8 cm
H=30 cm
To get the required material, the surface area of the box with new dimensions is to be calculated.
So,
S.A=2(LW + WH + LH)
=2(20×8+8×30+30×20)
=2(160+240+600)
=2(1000)
=2000 sq. cm
Therefore, the material required for the new box is 2000 sq. cm
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How to solve systems using elimination
Answers
See explanations below on solving simultaneous equations by elimination.
Step-by-step explanation:
In solving simultaneous equations by elimination, you make one side of the variables equal and eliminate that side by either addition or subtraction, then solve the remaining variable whose value is then used in one of the equations to find the other variable. For example;
(i) 4x - 2y= 10
(ii) x+ y =4
Making the x variable part equal to eliminate x
1(4x-2y=10)--------multiply by 1
4(x+y=4) ---------multiply by 4
4x -2y =10
4x+4y=16
Apply subtraction to eliminate the x variables
0 +6y =6
6y=6
y=6/6 = 1
Use the value of y =1 in the equation x+y= 4
x+y=4
x+1=4
x=4-1 = 3
x= 3, and y=1
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Use the remainder to divide 5x^2+9x-2 by x+3. What is the remainder?
Answers
Answer:
16
Step-by-step explanation:
Using the Remainder theorem
f(x) divided by (x + h) then the remainder is the value of f(- h)
here the divisor is (x + 3), thus remainder is f(- 3)
remainder = 5(- 3)² + 9(- 3) - 2 = 5(9) - 27 - 2 = 45 - 29 = 16
Dave works for 5 hours double time and he earns $98 find his normal hourly year rate
Answers
Answer: $9.8 per hour
Step-by-step explanation:
If Dave works for 5 hours at double time, then he gets paid for 10 hours of work. If he earned $98 for 10 hours of work, all you need to do is divide the amount of money earned by the hours of work. [tex]\frac{98}{10}[/tex]=9.8 dollars per hour.
There are two functions that can be used to describe the percent of people 25 years and older who have completed at least high school. For both functions f(x)=0.44x + 87.5 and g(x)=0.008x^2 + 0.42x + 87.5 is the number of years since 2008, and any y (or f(x) or g(x)) is the percent of people 25 and older completing at least high school. Assume that the trend of g(x) continues. Find g(15) and describe in words what this means.
g(15)=
Answers
Answer:
[tex]g(15)=93.8\%[/tex]
see the explanation
Step-by-step explanation:
Let
x ----> the number of years since 2008,
g(x) ----> the percent of people 25 years and older who have completed at least high school
we know that
[tex]g(x)=0.008x^2+0.42x+87.5[/tex]
so
For x=15 years since 2008
substitute
[tex]g(15)=0.008(15)^2+0.42(15)+87.5=93.8\%[/tex]
That means
In the year 2023 (2008+15) the percent of people 25 and older completing at least high school will be 93.8%
Final answer:
To find g(15), we substitute x with 15 in the function g(x) = [tex]0.008x^2 + 0.42x + 87.5[/tex], yielding g(15) = 95.6%. This means that in 2023, it's projected that 95.6% of people 25 and older will have completed high school according to the given quadratic trend.
Explanation:
The student is asking for the evaluation of the function g(x) = [tex]0.008x^2[/tex] + 0.42x + 87.5 at x = 15, which represents the number of years since 2008. To find g(15), we need to substitute x with 15 in the given function:
g(15) = 0.008(15)2 + 0.42(15) + 87.5
Calculating the value step by step:
152 = 225
0.008 × 225 = 1.8
0.42 × 15 = 6.3
1.8 + 6.3 + 87.5 = 95.6
Therefore, g(15) = 95.6.
In words, this means that if the trend described by function g(x) continues, then in the year 2023 (15 years after 2008), 95.6% of people aged 25 and older will have completed at least a high school education. This is a projection of graduation rates over time.
F is directly proportional to a.
If F = 24 when a = 8 find,
a when F = 18
Answers
Answer:
K = 3
a = 6
Step-by-step explanation:
F is directly proportional to a
That’s F = Ka
K is the constant
Divide both sides by a to get the constant k
K = F/a
When F = 24 and a =8
K = 24/8
= 3
When F = 18
a = ?
F = Ka
18 = 3 x a
18 = 3 x a
Divide both sides by 3
18/3 = 3 x a /3
6 = a
a = 6
Mrs. Rivera ate 3/8 of a
pizza and Ms. Carter ate 4/8
of a pizza. How much pizza
did they eat altogether?
Answers
Answer:
They ate 7/8 of a pizza altogether.
Step-by-step explanation:
So, you know Mrs. Rivera ate 3/8 of a pizza and Ms. Carter ate 4/8 of a pizza.
You add 3/8 + 4/8 and you get 7/8.
The ate 7/8 of a pizza altogether.
The quantity of pizza that Mrs. Rivera and Ms. Carter ate altogether is equal to [tex]\frac{7}{8}[/tex]
Given the following data:
Fraction Rivera ate = [tex]\frac{3}{8}[/tex]Fraction Carter ate = [tex]\frac{4}{8}[/tex]To calculate how much (quantity) pizza they ate altogether:
A fraction can be defined as a numerical quantity that isn't a whole number.
Hence, a fraction is simply a part of a whole number.
In this exercise, we would add up the two fractions, so as to calculate how much (quantity) pizza they ate altogether.
[tex]Total \;quantity = \frac{3}{8} + \frac{4}{8}[/tex]
Lowest common multiple (LCM) = 8
[tex]Total\;quantity = \frac{4\;+\;3}{8} \\\\Total\;quantity = \frac{7}{8}[/tex]
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what is the measurement of
Answers
Answer: Angle A = 120° and angle C = 45°
Step-by-step explanation: The first thing to note at the back of our minds is that the sum of the interior angles of a triangle equals 180°. Given that the three angle are available, we can start by adding them all together. Hence,
{12x + 12} + 15 + {3x + 18} = 180
12x + 12 + 15 + 3x + 18 = 180
By collecting like terms, we arrive at,
12x + 3x + 12 + 15 + 18 = 180
15x + 45 = 180
Subtract 45 from both sides of the equation
15x = 135
Divide both sides of the equation by 15
x = 9
At this point, we can now substitute for the value of x = 9 in the expressions representing angles A and C.
Angle A = 12x + 12
= 12(9) + 12
= 108 + 12
= 120
Angle A = 120°
Angle C = 3x + 18
= 3(9) + 18
= 27 + 18
= 45
Angle C = 45°
An object is launched from a platform.
Its height (in meters), x seconds after the launch, is modeled by:
h(x)=-5x2verb +20x+60
What is the height of the object at the time of launch?
Answers
Answer:
60 feet
Step-by-step explanation:
The height, h (in meters), of the object launched from a platform is represented by the equation
[tex]h=h(x)=-5x^2+20x+60[/tex]
where x is the time (in seconds) passed after the launch.
The time of launch is [tex]x=0[/tex] (0 seconds passed after the launch)
Substitute [tex]x=0[/tex] to find the height:
[tex]h=h(0)=-5\cdot 0^2+20\cdot 0+60=60\ feet[/tex]
given S (-1,8), and T (7,-9) what is the length of ST?
Answers
Answer:
ST = √353 or 18.79
I can add a step-by-step explanation if you want me to.
The length of ST is approximately 18.79 units.
What is the distance between two points ( p,q) and (x,y)?The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
[tex]D = √[(x-p)² + (y-q)²] D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]
We are given that;
Points= S (-1,8), and T (7,-9)
Now,
x1=−1
y1=8
x2=7
y2=−9
Substituting these values into the formula, we get:
d=(7−(−1))2+(−9−8)2
d=(8)2+(−17)2
d=64+289
d=353
d= 18.79
Therefore, by the distance the answer will be 18.79 units.
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What is the value of t in the following equation? t + 14 = 2 712
Answers
Answer: t = 2698
Step-by-step explanation: Subtract 14 from 2712 to get the value of t
Please help I’ll give 50 points
The question is down below with the fractions please answer as fast as you can
Answers
Answer:
C
Step-by-step explanation:
(4√6)/(5√6)
= 6^(¼) ÷ 6^(1/5)
= 6^(1/4 - 1/5)
= 6^[(5-4)/20]
= 6^(1/20
When dividing roots, multiply them together: 4 x 5 = 20
Invert the product: 1/20
Raise the number under the root by that
Answer = 6 ^ 1/20
Rewrite the following in the form log(c).
log(6) – log(2)
Answers
Answer:
Step-by-step explanation:
㏒(6)-㏒(2)=㏒(6/2)=㏒ 3
The expression log(6) – log(2) in form of log(c) is log(12).
What is Logarithm?Logarithms are another way of writing exponents in mathematics. A number's logarithm with a base equals another number. Exponentiation is the inverse function of logarithm.
A logarithm is defined as the number of powers to which a number must be increased in order to obtain some other numbers. It is the simplest way to express enormous numbers.
We have to write the expression log(6) – log(2) in form of log(c).
Using product property for logarithms
log a + log b= log (ab)
Here, a= 6 and b= 2 then
ab = 6 . 2= 12
Thus, the required form of log(6) – log(2) is log(12).
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Jake paid $13.50 for admission to the country fair and bought 9 tickets to play games. If he spent a total of $36, what is the cost, c, of one ticket? Write and solve an equation.
Answers
Answer:
$2.50
Step-by-step explanation:
Jake's total expenditure is ...
total = admission + c × (number of tickets)
36 = 13.50 + 9c . . . an equation to solve
4 = 1.50 +c . . . . . . . divide by 9
2.50 = c . . . . the cost of one ticket
Each ticket cost Jake $2.50.
which point is an x intercept of the quadratic function f(x) =(x-8)(x+9)
Answers
Answer:
(- 9, 0) and (8, 0)
Step-by-step explanation:
To find the x- intercepts let f(x) = 0, that is
(x - 8)(x + 9) = 0
Equate each factor to zero and solve for x
x + 9 = 0 ⇒ x = - 9
x - 8 = 0 ⇒ x = 8
The x- intercepts are x = - 9 and x = 8