For a project in his Geometry class, Levi uses a mirror on the ground to measure the height of his school’s football goalpost. He walks a distance of 12.05 meters from the goalpost, then places a mirror flat on the ground, marked with an X at the center. He then walks 2 more meters past the mirror, so that when he turns around and looks down at the mirror, he can see the top of the goalpost clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.15 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.
Answer:
\text{ m} m
attempt 2 out of 2
Griffin Heaton
Word Problems, Similar Triangles (Level 2)
Oct 20, 9:06:20 PM
Watch help video
For a project in his Geometry class, Levi uses a mirror on the ground to measure the height of his school’s football goalpost. He walks a distance of 12.05 meters from the goalpost, then places a mirror flat on the ground, marked with an X at the center. He then walks 2 more meters past the mirror, so that when he turns around and looks down at the mirror, he can see the top of the goalpost clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.15 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.
The goalposts are 6.92m tall.
Angle of incidence Equals Angle of reflection, according to the physics principle of reflection.
Both angles ( θ) are equal, as seen in the attached image.
m<ABC = mADC = 90° - θ
m<ACB = mECD = 90°
detailed explanation?
Angle of incidence Equals Angle of reflection, according to the physics principle of reflection.
Both angles ( θ) are equal, as seen in the attached image.
m<ABC = mADC = 90° - θ
m<ACB = mECD = 90°
Thus, the ABC triangle and the EDC triangle will both be similar.
Their corresponding sides will also be proportionate due to the property of comparable triangles
AB/BD = CB/CD.
1.15/ED = 2.0/12.5
ED = 1.15 * 12.05 /2.0
ED= 6.92
ED = ED = 6.92 m
The goalposts are 6.92m tall.
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A mother dog weighs 75 pounds. One of her puppies weighs
6 pounds. How many times greater is the mother dog's weight
than her puppy's weight?
Answer: 12.5 pounds
Step-by-step explanation:
How many times greater, 75=6x
divide by 6
7sufifiglhofsufigif7dufig
Using a proportional relationship, it is found that:
a) The independent variable is x.
b) The dependent variable is y = 12x.
c) The domain is of 0 ≤ x ≤ 25.
d) The range is of 0 ≤ y ≤ 300.
What is a direct proportional relationship?A direct proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality k, as shown below:
y = kx
In which:
x is the independent variable.y is the dependent variable.For this problem, Jennifer makes $12 an hour, hence the constant is of k = 12 and the equation is:
y = 12x.
She can work between 0 and 25 hours, hence:
The domain is 0 ≤ x ≤ 25, which is the set that contains all possible input values for the function.The range is 0 ≤ y ≤ 300, as 25 x 12 = 300, which is the set that contains all possible output values for the function.More can be learned about proportional relationships at https://brainly.com/question/10424180
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How many adults and children were at the show
There is 100 students in a class 60 take math 40 take physics 10 take none then how many learn both math and physics
Answer: None
Step-by-step explanation: Trick question the total is 110 and none took both math and physics
To make bread, 2 teaspoons of yeast are needed for 500 grams of flour. How many teaspoons of yeast are needed for 750 grams of flour?
Answer:
3 teaspoons.
Step-by-step explanation:
500/2=250 grams per teaspoon
750/250=3
3 teaspoons
help me guys please I will give brainliest
Answer:
[tex]\textsf{1.} \quad 3x^2-4x+12[/tex]
[tex]\textsf{2.} \quad 3x^2-8x+4[/tex]
[tex]\textsf{3.} \quad 6x^3-8x+32[/tex]
[tex]\textsf{4.} \quad \dfrac{3x^2-6x+8}{2x+4}[/tex]
[tex]\textsf{5.} \quad 12x^2+36x+32[/tex]
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=3x^2-6x+8\\g(x)=2x+4\end{cases}[/tex]
Function composition is an operation that takes two functions and produces a third function.
Question 1The composite function (f + g)(x) means to add function f(x) and g(x):
[tex]\begin{aligned}\implies (f+g)(x) & = f(x)+g(x)\\&=(3x^2-6x+8)+(2x+4)\\ &=3x^2-6x+2x+8+4\\ &=3x^2-4x+12\end{aligned}[/tex]
Question 2The composite function (f - g)(x) means to subtract function g(x) from function f(x):
[tex]\begin{aligned}\implies (f-g)(x) & = f(x)-g(x)\\&=(3x^2-6x+8)-(2x+4)\\&=3x^2-6x+8-2x-4\\ &=3x^2-6x-2x+8-4\\ &=3x^2-8x+4\end{aligned}[/tex]
Question 3The composite function f(x) · g(x) means to multiply functions f(x) and g(x):
[tex]\begin{aligned}\implies f(x)\cdot g(x) & =(3x^2-6x+8)(2x+4)\\ &=3x^2(2x+4)-6x(2x+4)+8(2x+4)\\&=6x^3+12x^2-12x^2-24x+16x+32\\&=6x^3-8x+32\end{aligned}[/tex]
Question 4The composite function f(x)/g(x) means to divide function f(x) by function g(x):
[tex]\begin{aligned}\implies \dfrac{f(x)}{g(x)} & = \dfrac{3x^2-6x+8}{2x+4}\\\end{aligned}[/tex]
Question 5The composite function f(g(x)) means to substitute the function g(x) in place of the x in function f(x):
[tex]\begin{aligned}\implies f(g(x))&=3(g(x))^2-6(g(x))+8\\&=3(2x+4)^2-6(2x+4)+8\\&=3(2x+4)(2x+4)-12x-24+8\\&=3(4x^2+16x+16)-12x-16\\&=12x^2+48x+48-12x-16\\&=12x^2+48x-12x+48-16\\&=12x^2+36x+32\end{aligned}[/tex]
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how many solution does 3(2x+1)=2(2x+1) have
Answer:
1 solution
Step-by-step explanation:
please help!! due tmr morning!!
Answer:
6, -2, and-1
Step-by-step explanation:
f(2) means that x is 2, so looking in the left column find x as 2, and then find the corresponding number beside it.
f(x)=0 so look for 0 in the right column and find the number corresponding to it in the left.
Answer:
#8 is equal to 6
#9 is equal to -2
#10 is equal to -1
Step-by-step explanation:
If you look in the x column for 2 the outcome is 6
If you look in the f(x) column for 0 the income is -2
If you look in the f(x) column for 1.5 the income is -1
The algebraic expression of 9+11g
The mathematical statement of the expression 9 + 11g is the sum of 9 and 11g
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the expression?The algebraic expression is given as
9 + 11g
The above mathematical representation is an algebraic expression that is already in its most simplified form
This means that the algebraic expression cannot be further simplified
However, the algebraic expression can be rewritten as a mathematical statement
Recall that, we have
9 + 11g
The pronunciation of the above expression is:
9 plus 11g
In expressions, plus represents sum
So, we have
9 + 11g can be represented as the sum of 9 and 11g
Hence, the representation of the algebraic expression given as 9 + 11g is the sum of 9 and 11g
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Hello I really need help with this and this would help me a lot
Answer:
1.divide
2.minus
3.times
solve for x
please huryy
Answer:
X = 31
Step-by-step explanation:
180 = 2x + 9 + 3x +16
180 = 5x + 25
180 + -25 = 5x
155 = 5x
5x/5 = 0 (Cancel out)
155 /5x = 31
X = 31
Check math by :
2 x 31 = 62 + 9 = 71
3 x 31 = 93 + 16 = 109
109 + 71 = 180
Therefore, X = 31
Therfore we can derive the equation:
[tex]2x+9+3x+16 = 180[/tex]Next, we group like terms.[tex]2x+3x+9+16 =180[/tex]
Now, we combine like terms.[tex]5x+25 = 180[/tex]
Then, we move 25 to the right side.5x = 155
Finally, we divide both sides by 5.[tex]x = 31[/tex]
-) Written as products of their prime factors, N = 2^px5^qx7^r and 500=2² × 5³.
The highest common factor of N and 500 is 2^2 x 5²
The lowest common multiple of N and 500 is 2^3 x 5³ x7.
Find p, q and r.
The highest common factor of N and 500 is 2²x5² and The lowest common multiple of N and 500 is [tex]2^{3}[/tex]x[tex]5^{3}[/tex]x7. p, q and r is p =2 , q =2 , r =1
What is prime factorization ?Prime factorization is the technique of expressing a number as the product of prime numbers. The only two components in prime numbers are the number itself and the number itself. Prime numbers include, for instance, 2, 3, 5, 7, 11, 13, 17, 19, and so forth. Any number can be represented as a sum of prime numbers by "prime factorizing" it.
Given that : Written as product of their prime factors N= [tex]2^{p}[/tex] x[tex]5^{q}[/tex]x[tex]7^{r}[/tex] and 500= 2² x 5³ The highest common factor of N and 500 is 2² x 5³? The lowest common multiple of N and 500 is 2²x5²x7.
N= [tex]2^{p}[/tex] x[tex]5^{q}[/tex]x[tex]7^{r}[/tex]
500= 2² x 5³
highest common factor of N and 500 is 2²x5²
p ≥ 2
q = 2
r ≥ 0
The lowest common multiple of N and 500 is 2²x5²x7.
HCF x LCM = N * 500
=> 2²x5² x 2²x5²x7 = [tex]2^{p}[/tex] x[tex]5^{q}[/tex]x[tex]7^{r}[/tex] x 2² x5³
=> 2²x5x7 = [tex]2^{p}[/tex] x[tex]5^{q}[/tex]x[tex]7^{r}[/tex]
p = 2
q = 1 but q = 2 as per HCF
r = 1
There is mistake in data
As LCM should have [tex]5^{3}[/tex] atleast as 500 has 5^2
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PQRSTUVW is a cuboid.
Find the angle between the line PV and the plane PTWS.
Give your answer correct to 1 decimal place.
The angle between the line PV and the plane PTWS is 29.4°
In this question we have been given a cuboid PQRSTUVW
We need to find the angle between the line PV and the plane PTWS.
First we find the length of the line PW which is diagonal of rectangular surface PTWS.
In right triangle PWS by Pythagoras theorem,
PW² = PS² + SW²
PW² = 19² + 16²
PW² = 361 + 256
PW² = 617
PW = 24.84 cm
now, consider a right triangle PWV.
Consider tangent of angle VPW
tan(∠VPW) = VW / PW
tan(∠VPW) = 14 / 24.84
∠VPW = tan^{-1}(0.5636)
∠VPW = 29.4°
Therefore, the angle between the line PV and the plane PTWS is 29.4°
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0.35x – 4.8 < 5.2 – 0.9x
The solution to the given linear inequality expression is equivalent to x < 8
Inequality expressionsInequality expressions are expressions that are not separated by an equal sign. They are separated by the signs <, >, ≤ and ≥.
Given the inequality below:
0.35x – 4.8 < 5.2 – 0.9x
Collect the like terms;
0.35x + 0.9x < 5.2 + 4.8
Simplify the result to have:
(0.35+0.9)x < 10.0
1.25x < 10.0
Divide both sides by 1.25
1.25x/1.25 < 10.0/1.25
x <8
This gives the solution to the linear inequality shown.
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Laqueta has a $50 gift card for an online music store. Each song costs ss dollars. Write an algebraic expression that represents the amount left on her card after Laqueta buys 7 songs. How much money will be left on her card if each song costs $1.25?
1. The algebraic expression that represents the amount left on her card after Laqueta buys 7 songs is 50 - 7s
2. The money that will be left on her card if each song costs $1.25 is $41.25.
How to illustrate the information?From the information given, Laqueta has a $50 gift card for an online music store and each song costs s dollars.
In this case, the algebraic expression that represents the amount left on her card after Laqueta buys 7 songs will be:
= Total amount - Cost of songs
= 50 - (7 × s)
= 50 - 7s
where s = number of songs
The money that will be left on her card if each song costs $1.25 will be:
= 50 - 7s
= 50 - (7 × 1.25)
= 50 - 8.75
= $41.25
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GIVING 100 POINTS IF U ANSWER ASAP
A mobile company has the following plans on their website. STANDARD PLAN: $40 for 5GB (potential starting point) and $15/GB thereafter (this is a rate of change, so it could be a slope)
UNLIMITED PLAN: $80 Always, with no additional charges.
The equation for the unlimited plan is y=80.
Write an equation (y=mx+c) for the standard plan.
IT IS NOT Y=15X+40
Answer:
y = 15x - 35
Step-by-step explanation:
STANDARD PLAN information:
$40 for 5GB.$15 per GB thereafter.Define the variables:
Let x be the number of GB.Let y be the cost in dollars.If it costs $40 for the first 5GB then y = 40 when 0 ≤ x ≤ 5.
It costs $15 per GB after the first 5GB. Therefore:
When x = 6, y = 40 + 15 = 55.When x = 7, y = 40 + 15(2) = 70.When x = 8, y = 40 + 15(3) = 85.Therefore:
⇒ y = 40 + 15(x - 5)
⇒ y = 40 + 15x - 75
⇒ y = 15x - 35
Roger ran 13.2 miles in 1.6 hours. Ana ran 10.85 miles in 1.4 hours. In miles per hour, how much faster was Roger's average speed than Ana's?
Roger has a faster speed at 8.25 miles per hour compared to Ana who ran with a speed of 7.75 mph.
What is Average speed?
The average speed is the total distance traveled by any object in a particular time interval.
Given that;
Distance covered by Roger = 13.2 miles
Time is taken by Roger = 1.6 hours
Distance covered by Ana = 10.85 miles
Time is taken by Ana = 1.4 hours
Now, Calculate the speed of Roger and Ana as;
Speed = Distance / Time
For Roger,
Speed = 13.2/1.6 = 8.25 mph
For Ana,
Speed = 10.85/1.4= 7.75 mph
Hence, Roger has a faster speed at 8.25 miles per hour compared to Ana who ran with a speed of 7.75 mph.
Solve: 3(x+4)= 3x+12
Ox=0
Ox=4
Oall real numbers
Ono solution
Correct option is C, The solution is set of all real numbers.
When x=0, 0=0 and 24 Equals 24 when x = 4.
This equation holds true for all real numbers since both sides of the equation are the same. When 0=0, the solution reveals that the equation is an identity, a specific kind of equation that is true regardless of the value of x.
Identity equation: What is it?Identity equations are described as equations that are true regardless of the value of the inserted variable.
3(x+4)=3x+12
3x+12=3x+12
When x = 0
3(0)+12=3(0)+12
12=12
When x = 4
12+12=12+12
The set of all real numbers is the answer as a result.
Y - = m is an equation for a line given a slope and a point ( x - )
or y - 7 = 1 ( x - 1) ( x - 1)
or y - 7 = x -1
or y = x + 6
Consequently, a line parallel to the line y = x + 4 has the equation y = x + 6.
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A liquid storage container is being filled at a constant rate. The container is being filled at a rate of 1
3
gallon per 1
4
minute.
As per unit rate of storing liquid in a container , the equivalent rate for 4 minutes is equal to (16/3) gallons.
As given in the question,
Liquid storage container is being filled at a constant rate.
Rate of filling a container = 1/3 gallon per 1/4 minute
Unit rate = (1/3 gallons)/ (1/4 minutes)
= (4/3) gallons per minute
Equivalent rate for 4 minutes is equal to
= [ ( 4 / 3) × 4 ] gallons per 4 minutes
= ( 16 / 3) gallons
Therefore, as per unit rate of storing liquid in a container , the equivalent rate for 4 minutes is equal to (16/3) gallons.
The complete question is :
A liquid storage container is being filled at a constant rate. The container is being filled at a rate of 1/3 gallon per 1/4 minute.
Unit rate = (1/3 gallons)/ (1/4 minutes)
= (4/3) gallons per minute
Find the equivalent rate for 4 minutes.
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The population of a city decreases by 1.7% per year. If this year's population is 366,000, what will next year's population be, to the nearest individual?
The population of the city next year, after decreasing, will be 359,778
Here, we are given that the population of a city decreases by 1.7 percent per year.
This, means that the city's population will decrease by 1.7% in 1 year, (1.7 × 1.7)% in 2 years and so on.
The population of the city this year is given to be 366,000.
Thus, next year, the population will decrease by-
1.7% of 366,000
= 1.7/100 × 366,000
= 17/10 × 3,660
= 17 × 366
= 6,222
Thus, the city's total population next year will be-
366,000 - 6,222
= 3,59,778
Hence, the city's population to the nearest individual comes out to be 359,778.
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PLEASE HELP ME WITH THIS QUESTION!
Triangle B is a reflection of triangle A across the axis y=-1
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.
The graph A is the original graph and it is transformed to B. Triangle B is a reflection of triangle A across the axis y=-1
Hence Triangle B is a reflection of triangle A across the axis y=-1
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As a football team kept winning, the attendance of their games increased. Use Demos (or calculator) to write a linear equation to model this data.
The data:
Game # ||| Attendance
1. 722
2. 763
3 772
4 826
5 815
6 857
7 897
A line of best fit (linear equation) to model this data is y = 27x + 699.43
What is a line of best fit?A line of best fit can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.
In this scenario, the game would be plotted on the x-axis of the scatter plot while the attendance would be plotted on the y-axis of the scatter plot.
By critically observing the scatter plot (see attachment) which models the data in the given table, we can reasonably and logically deduce that a linear equation for the line of best fit is given by:
y = 27x + 699.43
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please help and explain thank you
how does the speed at which you drive affect your fuel economy? to find out, researchers drove a compact car for 200 miles at speeds ranging from 35 to 75 miles per hour. from their data, they created the model fuel efficiency
Using linear function concepts, the interpretation of the slope of the model is:
The slope indicates that the Fuel Efficiency decreases by an amount of 0.15 mpg for every 1 mile per hour increase of speed.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
m is the slope of the function, which is the rate of change of the function.b is the y-intercept of the function, which is the initial value of the function.For this problem, the model is given as follows:
Fuel Efficiency = 32 - 0.15Speed.
The slope is of m = -0.15, meaning that for each mph that the average velocity increases, the fuel efficiency decays by 0.15 mpg.
What is the missing information?The model is missing, and is given as follows:
Fuel Efficiency = 32 - 0.15Speed.
The units are as follows:
Fuel Efficiency: mpg.Speed: mph.It asks for the interpretation of the slope.
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Find the value of f(4) for the function.
f(a) = 7(a + 2)-5
f(4) = (Simplify your answer.)
Answer:
f= 37 / 4
Step-by-step explanation:
I am using ( / ) to show a fraction
Let's solve your equation step-by-step.
f(4)=7(4+2)−5
Step 1: Simplify both sides of the equation.
f(4)=7(4+2)−5
4f=42+−5
4f=(42+−5)(Combine Like Terms)
4f=37
4f=37
Step 2: Divide both sides by 4.
4f / 4 = 37 / 4
f= 37 / 4
Answer:
f= 37 / 4
Hope this helps! :)
What is the equation of the line that passes through the point (6, 1) and has a slope
of -5/6
Answer:
y = -5/6x + c
Step-by-step explanation:
line equation is:
y = mx + c
y = -5/6x + c
sub in values:
1 =-5/6(6) + c
1 = -5 + c
6 = c
equation of line:
y = -5/6x + 6
The zeros of a quadratic function are 1 and 4. How would you use this information to write the equation for the function? If the equation cannot be written, explain why. Use complete sentences in your answer.
Answer:
The quadratic function is x²-5x+4=0
Step-by-step explanation:
To find a quadratic equation whose roots are given we use
x²-(sum of roots)x + (product of roots) =0
x²-(4+1)x + (4×1)=0
x²-5x+4=0
let us check if it is correct
x²-5x+4=0
x²-1x-4x+4=0
x(x-1)-4(x-1)=0
(x-4)(x-1)=0
(x-4)=0 and (x-1)=0
x=4 and x=1
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Identify the interval(s) on which each quadratic function is positive.
1. y= x^2 + 2x - 8
2. y= -x^2 +4x +12
3. y= 5x^2 - 3x - 8
Help on these three problems above would be greatly appreciated, thanks! ☜(ˆ▿ˆc)
Answer:
[tex]\textsf{1. \quad $x < -4$ or $x > 2$}[/tex]
[tex]\textsf{2. \quad $-2 < x < 6$}[/tex]
[tex]\textsf{3. \quad $x < -1$ or $x > \dfrac{8}[5}$}[/tex][tex]\textsf{3. \quad $x < -1$ or $x > \dfrac{8}[5}$}[/tex][tex]\textsf{3. \quad $x < -1$ or $x > \dfrac{8}{5}$}[/tex]
Step-by-step explanation:
The intervals on which a quadratic function is positive are those intervals where the function is above the x-axis, i.e. where y > 0.
The zeros of the quadratic function are the points at which the parabola crosses the x-axis.
If the leading coefficient of a quadratic function is positive, the parabola opens upwards.
If the leading coefficient of a quadratic function is negative, the parabola opens downwards.
Therefore, to find the intervals on which each quadratic function is positive:
Calculate the zeros.Determine if the parabola opens upwards or downwards.If the parabola opens upwards, the intervals are less than the smaller zero and greater than the larger zero.If the parabola opens downwards, the interval is between the zeros.Question 1Given function:
[tex]y=x^2+2x-8[/tex]
Factor the given function:
[tex]\implies y= x^2+4x-2x-8[/tex]
[tex]\implies y=x(x+4)-2(x+4)[/tex]
[tex]\implies y=(x-2)(x+4)[/tex]
Substitute y = 0 to find the zeros:
[tex]\implies (x-2)(x+4)=0[/tex]
[tex]\implies x-2=0 \implies x=2[/tex]
[tex]\implies x+4=0 \implies x=-4[/tex]
The leading coefficient is positive, so the parabola opens upwards.
Therefore, the interval on which the function is positive is:
Solution: x < -4 or x > 2Interval notation: (-∞, -4) ∪ (2, ∞)Question 2Given function:
[tex]y=-x^2+4x+12[/tex]
Factor the given function:
[tex]\implies y=-(x^2-4x-12)[/tex]
[tex]\implies y=-(x^2-6x+2x-12)[/tex]
[tex]\implies y=-(x(x-6)+2(x-6))[/tex]
[tex]\implies y=-(x+2)(x-6)[/tex]
Substitute y = 0 to find the zeros:
[tex]\implies -(x+2)(x-6)=0[/tex]
[tex]\implies (x+2)(x-6)=0[/tex]
[tex]\implies x+2=0 \implies x=-2[/tex]
[tex]\implies x-6=0 \implies x=6[/tex]
The leading coefficient is negative, so the parabola opens downwards.
Therefore, the interval on which the function is positive is:
Solution: -2 < x < 6Interval notation: (-2, 6)Question 3Given function:
[tex]y=5x^2-3x-8[/tex]
Factor the given function:
[tex]\implies y=5x^2-8x+5x-8[/tex]
[tex]\implies y=x(5x-8)+1(5x-8)[/tex]
[tex]\implies y=(x+1)(5x-8)[/tex]
Substitute y = 0 to find the zeros:
[tex]\implies (x+1)(5x-8)=0[/tex]
[tex]\implies x+1=0 \implies x=-1[/tex]
[tex]\implies 5x-8=0 \implies x=\dfrac{8}{5}[/tex]
The leading coefficient is positive, so the parabola opens upwards.
Therefore, the interval on which the function is positive is:
Solution: x < -1 or x > ⁸/₅Interval notation: (-∞, -1) ∪ (⁸/₅, ∞)Which of the following are rational numbers?
5.48
78.541
97
42.111...
Answer:
5.48
78.541
97
42.111...
(all of above)
Step-by-step explanation:
because a rational number is a number that can be written as a fraction
a decimal number that ends can be written as a fraction (ex: 5/4 = 1.25)
a decimal number that has a repeating number after the decimal point can also be written as a fraction (ex: 10/3 = 3.33...)