Answer:
Function • Quadratic Function •
Absolute Value Inequalities • Linear Function
A large tree casts a shadow that is 51 feet long. A 6-foot-tall person standing next to the tree casts a shadow that is 4.5 feet long. How tall is the tree?
Answer:
68 feet tall
Step-by-step explanation:
Imagine the shadows for both the tree and the person are set up like right triangles. The length of their shadows are the bases of the triangles, while the actual heights of the tree and person are the heights of the triangle. We can set up proportions since "height of the person" divided by " their shadow's length" should equal "height of tree" divided by "tree shadow length".
Set up a proportion of the person's high height relative to their shadow's length (which is 6/4.5). Set this equation equal to the tree's proportion (which is x/51).
Solve for x.
[tex]\frac{6}{4.5} = \frac{x}{51}\\Isolate x by multiply 51 to both sides\\\\(306/4.5)=x\\68=x[/tex]
The proportion is solved and the height of the tree is A = 68 feet
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the proportion be represented as A
Now , the value of A is
Now , we can set up the following proportion:
Height of tree / length of tree's shadow = height of person / length of person's shadow
On simplifying , we get
A / 51 = 6 / 4.5
Now we can solve for A by cross-multiplying and simplifying:
A = 51 x 6 / 4.5
A = 68 feet
Therefore, the tree is 68 feet tall
Hence , the proportion is solved
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Solve each system by elimination: 4x-7y=10 3x+2y=-7
Using the elimination method, the solution to the system of equations is as follows:
x = 19 / 13 and y = - 74 / 13
How to solve system of equation?System of equations can be solved using different methods such as the elimination method, substitution method, and graphical method.
Let's use the elimination method to solve the system of equations as follows:
The elimination method is the process of eliminating one of the variables in the system of equations using the addition or subtraction methods in conjunction with the multiplication or division of coefficients of the variables.
Therefore,
4x - 7y = 10
3x + 2y = -7
multiply equation(ii) by 3.5
4x - 7y = 10
10.5x - 7y = 24.5
subtract equation(i) from equation(ii)
6.5x = 14.5
x = 14.5 / 6.5
x = 145 / 65
x = 19 / 13
Let's find y
3(19 / 13) + 2y = -7
57 / 13 + 2y = -7
2y = - 7 - 57 / 13
2y = -91 - 57 / 13
2y = - 148 / 13
cross multiply
26y = - 148
y = - 148 / 26
y = - 74 / 13
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Help!! Please!!!!
Helppp
Answer: 60
Step-by-step explanation:
The square root of 144 is 12.
12 = x/5
You multiply 5 on BOTH sides (make sure when you do something to one side you do it to the other)
60 = x
A total of 1,043 players signed up for a citywide soccer league. Each team in the league can have up to 18 members. How many teams will be needed?
Answer:
58 teams
Step-by-step explanation:
This is a division problem. There are a total of 1043 players and there is a max number of 18 members per team. 1043 divided by 18 = 57 and a remainder. Because there is a remainder you add one more team for the remaining members.
Answer: 57.9
Step-by-step explanation:
Based on the given conditions, formulate: 1043 / 18
Evaluate the equation/expression: 57.9444
get the result: 57.9444
After rounding: 57.9
Answer: 57.9
This Venn Diagram represents the Science subjects studied by students.
Students
Physics
Biology
CO
6
7
6
2
3
8
4
5
Chemistry
What is the probability that a student, chosen at random,
studies Physics or Chemistry or both?
The probability that a student chosen at random studies physics and chemistry or both is 35/41 = 0.85
What is the probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.
What is the formula for probability?The formula for probability states that the possibility of an event happening, or P(E), equals the ratio of the number of favorable outcomes to the number of total outcomes. Mathematically, it looks like this: P(E) = favorable outcomes/total outcomes.
The Venn diagram shows:
There are 2 students studying both biology and physics.
Six students study biology and chemistry together.
There are 4 students who study physics and chemistry.
There are 5 students who just study physics.
There are 7 students who just study biology.
There are 8 students who just study chemistry.
There are 6 students that study none.
As a result, there are a total of 41 students, which is equal to 2 + 6 + 4 + 5 + 7 + 8 + 3 + 6 students.
There are 21 students who study chemistry, which is equal to 8 + 6 + 3 + 4 students.
The number of students that studies physics is = 14
The number of students that studies chemistry is = 21
Probability = number of favorable outcomes / total number of outcomes
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Find all of the prime numbers between 10 and 20
Answer:
11, 13, 17, and 19!
Step-by-step explanation:
Answer:
11, 13,17 and 19
Step-by-step explanation:
prome numbers are natural numbers that are greater than 1 and not a product of two natural numbers eg 2×5 =10 so it's not a prime number 2×6 or 3×4 =12 it's not also a prime number e.t.c
what is m% of n? HII PLS HELP! :0
Answer:SLOPE
Step-by-step explanation:M in a equation is slope
Adnan bought
pounds of apples for $0.72 per pound and
pounds of bananas for $1.60 per pound.
a%2Bb=12 [1]
.75a%2B1.05b=10.20 [2]
Use elimination: multiply the first equation by .75 and then compare the two equations (i.e., subtract one equation from the other):
.75a%2B.75b=9
.75a%2B1.05b=10.2
.3b=1.2
3b=12
b=4
ANSWER: He bought 4 pounds of bananas, which means 8 pounds of apples.
CHECK: 8($.75)+4($1.05) = $6+$4.20 = $10.20
Help pls explain!!!!!!!!!!!!
The exact value of the logarithmic expression 12 · ㏒₃ [z⁷ / (y⁵ · t²)] is equivalent by logarithm properties to -711 / 5.
How to determine the result of logarithmic expression by logarithmic properties
In this question we must determine the exact value of a logarithmic expression by means of logarithm properties, which are described below:
Logarithm of a product
㏒ (a · b) = ㏒ a + ㏒ b
Logarithm of a division
㏒ (a / b) = ㏒ a - ㏒ b
Logarithm of a power
㏒ aⁿ = n · ㏒ a
Now we proceed to determine the exact value of the expression:
12 · ㏒₃ [z⁷ / (y⁵ · t²)]
12 · [㏒₃ z⁷ - ㏒₃ (y⁵ · t²)]
12 · (㏒₃ z⁷ - ㏒₃ y⁵ - ㏒₃ t²)
12 · (7 · ㏒₃ z - 5 · ㏒₃ y - 2 · ㏒₃ t)
12 · (7 · 7.74 - 5 · 11.03 - 2 · 5.44)
-711 / 5
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Are the two functions inverse of one another ?
A train takes 16 hours to travel a distance of 35,376 km. Find the distance travelled in one hour if it covers the same distance every hour
Adam currently run about 20 mile per week, and he want to increae hi weekly mileage by 10%. How many mile will Adam run per week? He will run mile per week
Andre wanted to measure the width of a creek by his camp but cannot get to the other side of the creek. Andre decided to construct two triangles to determine the width of the creek indirectly. Sighting the position of a tree on the opposite bank of the creek and placing 4 wooden pegs at point N, O, P, and Q as shown in the figure, such that MN is perpendicular to NP, NP is perpendicular to PQ, and O is the midpoint of NP. Andre claims that triangle MNO and triangle QPO are congruent.
Part A: Provide a valid argument, using geometry theorems or postulates, to validate
Andre's claim that AMNO and APQO are congruent.
Part B: Which segment should Andre measure to determine the width of the creek? Explain why.
Use the space below to answer Parts A and B of the question above. Use the CER (Claim, Evidence, Reasoning) method as a guide to your response. You may also upload a screenshot of your work
Triangles MNO and QPO are congruent.
What is congruent triangle?When two triangles are congruent, their three sides and their three angles match precisely.If there is a turn or a flip, the equal sides and angles might not be in the same place, but they are still present.Formally speaking, two sets of points are said to be congruent if—and only if—they can be changed into one another by an isometry, which is a combination of rigid motions like translation, rotation, and reflection. Therefore, if two separate plane figures on a piece of paper can be cut out and then perfectly fitted up, they are congruent.It is given that
O is the midpoint of NP,
NP is perpendicular to MN, and
NP is perpendicular to PQ.
When two lines intersect at a specific point, the opposite angles formed in this situation are equal.Then ∠MNP =∠QPO=90°∠MON=∠QOP∠MOP=∠QONTherefore, Triangles MNO and QPO are congruent.
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Select the correct text.
A spherical ball for a machine was made with a radius of 2 centimeters.
If the ball has a mass of 278.1 grams, which material was used to make the ball?
Copper-8.3 g/cm³
Brass -8.6 g/cm³ Iron - 7.8 g/cm³
The mass of the ball is 278.1 g, the material used to make the ball must be brass which having density of 8.6 g/cm³.
How to find mass of the ball ?To determine the material used to make the ball, we need to first calculate the volume of the ball.
The volume of a sphere with radius r is given by:
V = (4/3) * π * r^3
Plugging in the given values, we get:
V = (4/3) * π * (2 cm)^3
= (4/3) * π * 8 cm^3
= (4/3) * 8π cm^3
= 32π cm^3
We can then use the density of each material (given in g/cm³) to calculate the mass of the ball if it were made of that material:
Copper: 8.3 g/cm³ * 32π cm³ = 266.4 g
Brass: 8.6 g/cm³ * 32π cm³ = 275.2 g
Iron: 7.8 g/cm³ * 32π cm³ = 250.4 g
Since the mass of the ball is 278.1 g, the material used to make the ball must be brass.
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which function has the same domain as
[tex]y = 2 \sqrt{x} [/tex]
Both have a domain of [tex][0, \infty)[/tex] which in other words, is the set of nonnegative real numbers. I recommend using a graphing calculator to verify both of these functions have the same domain.
The reason for this is because we need to avoid negative numbers under the square root. So it leads us to [tex]\text{x} \ge 0[/tex]
T (6,2) T’ (9,3 find the scale factor was used in the dilation shown
The scale factor of the transformation is 1.5
What is the scale factor of the dilationFrom the question, we have the following parameters that can be used in our computation:
Point T (6,2) T’ (9,3)
Also, see attachment for the missing graph in the question
This means that
The scale factor of the transformation = T'/T
Substitute the known values in the above equation, so, we have the following representation
Scale factor = (9, 3)/(6, 2)
Evaluate
Scale factor = 1.5
Hence, the scale factor is 1.5
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1. Consider this system of linear equations: -
y=4/5 x-3
y=4/5 x+1
a. Without graphing, determine how many solutions you would expect this system of equations to have. Explain your reasoning.
b. Try solving the system of equations algebraically and describe the result that you get. Does it match your prediction
The system of linear equations have no solution
System of Linear EquationThe system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables.
In the problem, given the system of linear equations are
y = 4/5x - 3 ...eq(i)
y = 4/5x + 1 ...eq(ii)
a) Since there are two unknown variables(x, y) the number of solutions expected is 2.
b)
From equation (i)
y = 4/5x - 3
Put eq(i) into equ(ii)
4/5x - 3 = 4/5x + 1
0 = 4
There's no solution for x and y
In the calculation, there's no solution for both x and y because the variables in both equation are equal to one another and hence cancel out.
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Graph y=-2x+5y=−2x+5y, equals, minus, 2, x, plus, 5. NEED HELP PLS
The graph for the linear equation y = -2x + 5 is plotted and shown in the image attached below.
How to Graph an Equation?If we are given an equation of a line that is expressed in slope-intercept form as y = mx + b, it means that the graph will have a slope = rise / run = the value of m, while it would cut across the y-axis at b, that is the y-intercept.
Given the equation in slope-intercept form as y = -2x + 5, it means that the graph will have a slope that has a ratio of the rise to the run as -2, while the line will intercept the y-axis at y = 5.
Therefore, the graph in the image attached below shows the equation, y = -2x + 5.
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use rounding or compatible numbers to estimate each product or quotient.
5 x 2 3/5
a. about 10
b. about 10 3/5
c. about 15
d. about 20
im guessing b
Answer: c.
Step-by-step explanation:
I used rounding: 3 is closer to 2 3/5 than 2 and 5 * 3 is 15, so the answer is about 15.
A movie streaming service charges a set fee for
membership each month, plus an additional fee
for the number of movies streamed each
month. If 2 movies are streamed, the cost is
$14 per month, however if 6 movies are
streamed, the cost is $20. Write an equation to
model the cost, y, based on the number of
movies streamed x.
The equation to model the cost 'y' based on the number of movies streamed 'x' would be 14 = 2x and 20 = 6x.
What is a linear equation in one variable?
The linear equation 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.
For the first case:
If 2 movies are streamed, the cost is $14 per month
So the cost = number of movies * cost per movie
y = 2*x
14 = 2x
For the second case:
If 6 movies are streamed, the cost is $20 per month
So the cost = number of movies * cost per movie
y = 6*x
20 = 6x
Hence the equation to model the cost 'y' based on the number of movies streamed 'x' would be 14 = 2x and 20 = 6x.
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The sum of two numbers is 33. One number is 2 times as large as the other. What are the numbers?
Question What is the decibel level of the noise from a motorcycle with intensity 10-2 watts per square inch? Use a logarithmic model to solve. Provide your answer below: 100 dB
The decibel level of the noise from a motorcycle with intensity 10⁻² watts per square inch (W/in²) is equal to 50 dB.
What is sound intensity?In Science, sound intensity can be defined as a measure of the power of a sound wave per unit area. This ultimately implies that, sound intensity is a quantity that is typically be used for measuring the energy of sound and its unit of measurement is Watts per square meter (W/m²) or .
How to calculate the sound intensity level?Mathematically, sound intensity level or decibel level can be calculated by using this formula:
[tex]\beta = 10 log(\frac{I}{I_{ref}} )[/tex]
Note: The reference value of sound intensity is equal to 1.0 × 10⁻¹² watts per square inch (W/in²).
Since the intensity of the noise from this motorcycle is 10⁻² W/in², the decibel level (in dB) would be calculated as follows:
Decibel level, β = 10 × log(10⁻²/10⁻¹²)
Decibel level, β = 10 × log(10¹⁰)
Decibel level, β = 10 × 10
Decibel level, β = 100 dB.
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A competition mark is worked out by doubling the sum of the middle four scores, then adding the average of the top and bottom scores.
Martha scores: 7 7 6 8 5 9
What is her competition mark?
The required competition mark is given as 60, as of the given condition.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
A competition mark is calculated by doubling the sum of the top and bottom four scores and then averaging them.
According to the question,
Competition mark = 2 [7 + 6 + 8 + 5] + [7 + 9] / 2
Competition mark = 52 + 8 = 60
Thus, the competition mark is 60.
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Find the range of the function f(x)=x^2- 6x if the domain is (-7,-2, 1)
The range of the function will be;
⇒ Range = (91, 16, - 5)
What is Domain?The set of all inputs of the function is called Domain of set.
Given that;
The function is,
⇒ f (x) = x² - 6x
And, The domain = (- 7, - 2, 1)
Now,
Since, The function is,
⇒ f (x) = x² - 6x
We know that;
The range of the function gives the value of y.
Here, The domain (x) = (- 7, - 2, 1)
Put x = - 7;
⇒ f (-7 ) = (-7)² - 6 × - 7
= 49 + 42
= 91
Put x = - 2;
⇒ f (- 2) = (-2)² - 6 × - 2
= 4 + 12
= 16
Put x = 1;
⇒ f (1) = (1)² - 6 × 1
= 1 - 6
= - 5
Thus, The range = (91, 16, - 5)
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(a) The area of a rectangular parking lot is 6279 m². If the length of the parking lot is 91 m, what is its width? Width of the parking lot:
Answer:
The width of the parking is 69 meters
Step-by-step explanation:
Rectangle area = L*W
6279 = 91*W
Widht = 6279/91
W = 69 m
Pleas help me find the equation for this chart please
Answer: y = 1/12x
Step-by-step explanation:
(24, 2)
(12, 1)
find slope (y2 - y1) / (x2 - x1)
2 - 1 / 24 - 12
1 / 12
find y intercept
y = mx + b
1 = 1/12(12) + b
1 = 1 + b
b = 0
y = 1/12x + 0
y = 1/12x
Use the Rule of 72 to figure out how long it will take a $1,000 deposit to double at 7% interest. Following this rule will give you the number of years it will take for your money to double.
Using the formula of simple interest, the time period it takes to double the principal is approximately 14.29 years
Simple InterestSimple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.
The formula is given as
S.I = P(1 + rt)
S.I = Simple InterestP = Principalr = rate t = timeSubstituting the values into the simple interest formula
S.I = 1000(1 + 0.07 * t)
However, we are to calculate the time it takes to double the money
2000 = 1000(1 + 0.07 * t)
2 = 1 + 0.07t
0.07t = 2 - 1
t = 1 / 0.07
t = 14.29 years
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its a 50 50 question both A and B are wrong please help
Answer: d/ 30x +200 <= 1400
Step-by-step explanation:
It can't be the first two answers because the truck can only hold 1400
So it must be < or = 1400
It says that she loaded computers for 200 pounds and x number of books, 30 pounds each.
So the equation is 30x + 200 <=1400
PLEASE HELP SOON I NEED TO LEAVE TO MY LAB
Answer: 10: 6 is
ration add them 16
Step-by-step explanation:
rate?
2) James Bond took 4.5 minutes to complete a Grand Prix circuit when driving at an average speed.
97 mph. How long would it take to complete one circuit driving at a speed of 112 mph.
Answer: 30 meters
Step-by-step explanation:
A boy is standing on an elevator which is traveling downward with a constant velocity of 30 meters per second.