The height of the tree is such that it cast a shadow 40 feet 6 inches long and maintains the given ratio will be 36 feet.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
As per the given question,
The height of a person is 5 feet and 4 inches.
Since 1 feet = 12 inches so 4 inches = 1/3 feet
Therefore,height of a person = 5 + 1/3 = 16/3 feet
Its shadow length = 6 feet
The ratio of the height to shadow length = (16/3)/6
Now, the shadow of the tree = 40 feet and 6 inches so 40.5 feet
Let's say its length was x feet.
Then x/40.5 = (16/3)/6
x = 36 feet
Hence "The height of the tree is such that it cast a shadow 40 feet 6 inches long and maintains the given ratio will be 36 feet".
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Solve the following simultaneous equation with elimination or substitution method
So, to solve the system:
To solve it, we could substitute the first equation in the second one and then solve for x:
We could solve the previous quadratic by factoring:
To find the values of y, just replace each vaue of x:
Therefore, the solutions of the system are
(x,y) = (-3,-1)
(x,y)=(1,3)
A
Y
+
B
X
Z
Given the diagram shown with AB|| XZ
AY = 7
AX = 6
AB= 14
find XZ.
Step-by-step explanation:
due to AB being parallel to XZ, we know that ABY and XZY are similar triangles.
therefore, they have the same angles, and there is one common scale factor for all side lengths from one triangle to the other.
so,
AY / XY = AB / XZ
XY = AY + AX = 7 + 6 = 13
7/13 = 14/XZ
XZ×7/13 = 14
XZ×7 = 14×13
XZ = 14×13/7 = 2×13 = 26
Question
Refer to section 1.3.2, Credit scores, beginning on page 22 of the report.
Arrange the five tiers of credit scores in order, starting with the lowest tier of credit scores.
The five credit score tiers are listed in ascending order, starting with the lowest tier:
Deep Subprime < Subprime < near prime < prime < super prime
A consumer's credit score may have a big impact on their ability to receive credit. These interactive infographics show how lending practices have changed for borrowers with various credit score profiles.
We focus on the five credit score levels that are commercially available.
The range of subprime credit scores is 580 to 619.
The range of Prime's credit score is from 660 to 719.
Deep subprime credit scores fall below 580.
Near prime credit scores range from 620 to 659.
Super prime credit is defined as having a score of 720 or higher.
The following are the five credit scores, listed from lowest to highest:
Deep Subprime < Subprime < near prime < prime < super prime
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find a b c d e f from the picture
Given data:
The value of a is (3+4+2)=9
The value of b is (5+1+2)=8
The value of c is (1+8+1)=10
The value of d is (
I am studying for the big test tomorrow and just need someone to go through this sheet I made with me.Sorry
SOLUTION
Let us solve the simultaneous equation
[tex]\begin{gathered} -2x-y=0 \\ x-y=3 \end{gathered}[/tex]using elimination
To eliminate, we must decide which of the variables, x or y is easier to eliminate. The variable you must eliminate must be the same and have different sign. Looking above, it is easier to eliminate y because we have 1y above and 1y below. But to eliminate the y's, one must be +y and the other -y. So that +y -y becomes zero.
So to make the y's different, I will multiply the second equation by a -1. This becomes
[tex]\begin{gathered} -2x-y=0 \\ (-1)x-y=3 \\ -2x-y=0 \\ -x+y=-3 \end{gathered}[/tex]So, now we can eliminate y, doing this we have
[tex]\begin{gathered} -2x-x=-3x \\ -y+y=0 \\ 0-3=-3 \\ \text{This becomes } \\ -3x=-3 \\ x=\frac{-3}{-3} \\ x=1 \end{gathered}[/tex]Now, to get y, we put x = 1 into any of the equations, Using equation 1, we have
[tex]\begin{gathered} -2x-y=0 \\ -2(1)-y=0 \\ -2-y=0 \\ \text{moving -y to the other side } \\ y=-2 \end{gathered}[/tex]So, x = 1 and y = -2
Using substitution, we make y or x the subject in any of the equations. Looking at this, It is easier to do this using equation 2. From equation 2,
[tex]\begin{gathered} x-y=3 \\ \text{making y the subject we have } \\ y=x-3 \end{gathered}[/tex]Now, we will put y = x - 3 into the other equation, which is equation 1, we have
[tex]\begin{gathered} -2x-y=0 \\ -2x-(x-3)=0 \\ -2x-x+3=0 \\ -2x-1x+3=0 \\ -3x+3=0 \\ -3x=-3 \\ x=\frac{-3}{-3} \\ x=1 \end{gathered}[/tex]So, substituting x for 1 into equation 1, we have
[tex]\begin{gathered} -2x-y=0 \\ -2(1)-y=0 \\ -2\times1-y=0 \\ -2-y=0 \\ y=-2 \end{gathered}[/tex]Substituting x for 1 into equation 2, we have
[tex]\begin{gathered} x-y=3 \\ 1-y=3 \\ y=1-3 \\ y=-2 \end{gathered}[/tex]Now, for graphing,
In 2002, the population of Isosceles City was 200,000. If expected growth is 10% per year, what will the expected population be in 2010?
The expected population in [tex]2010[/tex] will be [tex]428,717.762[/tex].
In [tex]2002[/tex] the population of Icosceles city was [tex]200,000[/tex].
The expected growth per year [tex]=10%[/tex]%
We have to find the expected population in [tex]2010[/tex].
From [tex]2002[/tex] to [tex]2010[/tex] the total years are [tex]8[/tex].
Since the population is increased every year so the population of previous year added. So we can see that the population is increased compound. We can find the total population by multiplying the population in 2002 with the rate assembled by one. So we can use the formula
Total population in [tex]2010=[/tex]Population in [tex]2002(1+\frac{rate}{100})^{year}[/tex]
Total population in [tex]2010=[/tex] [tex]2010=200,000(1+\frac{10}{100})^{8}[/tex]
Total population in [tex]2010=200,000(1+\frac{1}{10})^{8}[/tex]
Total population in [tex]2010=200,000(\frac{11}{10})^{8}\\[/tex]
Total population in [tex]2010=200,000(\frac{214,358,881}{100000000} )[/tex]
Total population in [tex]2010=200,000(2.14,358,881)[/tex]
Total population in [tex]2010=428717.762[/tex]
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22 8(11 + 2r) = 126r + 3
8(11 + 2r) = 126r + 3
first open the parenthesis
88 + 16r = 126r + 3
88 - 3 = 126r - 16 r
85 = 110r
divide both-side of the equation by 110
85/110 = r
r= 17/22
help meeeee pleaseeeee!!!
thank you
The values of f(0), f(2) and f(-2) for the polynomial f(x) = [tex]-x^{3} +7x^{2} -2x+12[/tex] are 12, 28 and 52 respectively.
According to the question,
We have the following function:
f(x) = [tex]-x^{3} +7x^{2} -2x+12[/tex]
Now, in order to find the value of f(0), we will put 0 in place of x.
f(0) = [tex]-0^{3} +7(0)^{2} -2(0)+12[/tex]
f(0) = 0+7*0-0+12
(More to know: when a number is multiplied with 0 then the result is always 0 even the number being multiplied with zero is in lakhs.)
f(0) = 0+0-0+12
f(0) = 12
Now, in order to find the value of f(2), we will put 1 in place of x:
f(2) = [tex]-2^{3} +7(2)^{2} -2(2)+12[/tex]
f(2) = -8+7*4-4+12
f(2) = -8+28-4+12
f(2) = 40 -12
f(2) = 28
Now, in order to find the value of f(2), we will put -2 in place of x:
f(-2) = [tex]-(-2)^{3} +7(-2)^{2} -2(-2)+12[/tex]
f(-2) = -(-8) + 7*4+4+12
f(-2) = 8+28+4+12
f(-2) = 52
Hence, the value of f(0) is 12, f(2) is 28 and f(-2) is 52.
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A popcorn stand offers buttered or unbuttered popcorn in three sizes: small, medium, and large. What is the P(buttered)
The popcorn we can order is either buttered or unbuttered.
Therefore, the probability of choosing buttered popcorn is 1/2
The number line below shows the values of x that make the inequality x > 1 true. Select all the values of x from this list that make the inequality x> 1 true. a. 3 b. -3c. 1 d. 700 e. 1.052. Name two more values of x that are solutions to the inequality.
Answer:
(a)3, 1, 700 and 1.05
(b)6 and 9
Explanation:
(a)The values of x from the list that make the inequality x> 1 true are:
3, 1, 700 and 1.05
(b)Two more values of x that are solutions to the inequality x>1 are:
6 and 9.
Find the missing rational expression.382x + 6(x-3)(x + 1)X-332x + 6(x-3)(x + 1)(Simplify your answer.)X-3
a) rewrite each equation using function notation f(x) b) find f(3)
Hello there. To solve this question, we'll simply have to isolate y and plug in the value for x.
Given the equation:
4x - 3y = 8
To rewrite it using the notation y = f(x), subtract 4x on both sides and divide the equation by -3
-3y = 8 - 4x
y = - 8/3 + 4x/3
Now, plug in x = 3 in order to find f(3)
f(3) = -8/3 + 4 * 3/3 = -8/3 + 12/3 = 4/3
Can someone help me with this please? If the painting is 18 inches high, how wide would it be?
The ratio of width to height is :
[tex]\frac{w}{h}=\frac{1+\sqrt[]{5}}{2}[/tex]If h = 18 inches, the value of w will be :
[tex]\begin{gathered} \frac{w}{18}=\frac{1+\sqrt[]{5}}{2} \\ \text{Cross multiply :} \\ 2w=18(1+\sqrt[]{5}) \\ w=\frac{18(1+\sqrt[]{5})}{2} \\ w=9(1+\sqrt[]{5}) \\ w=9+9\sqrt[]{5}\quad or\quad 29.12 \end{gathered}[/tex]The answer is w = 29.12 inches
May I please help with this. I have tried to find the correct answers but still couldn’t get them right
Solution
[tex]1cm\text{ to 7in}[/tex]We can use ratio to solve the problem
Part A
5cm to x in
[tex]\begin{gathered} 1cm\colon7in \\ 5cm\colon x\text{ in} \end{gathered}[/tex]Now
[tex]\begin{gathered} 1\colon7 \\ 5\colon x \\ \therefore\frac{1}{7}=\frac{5}{x} \\ \\ \text{cross multiply} \\ 1\times x=5\times7 \\ x=35 \end{gathered}[/tex]The final answer
[tex]5cm\text{ to 35inches}[/tex]Part B
Similar step as part a
[tex]\begin{gathered} 1\colon7 \\ y\colon63 \\ \frac{1}{7}=\frac{y}{63} \\ \\ \text{cross multiply} \\ 7y=63 \\ \text{divide both sides by 7} \\ \frac{7y}{7}=\frac{63}{7} \\ y=9 \end{gathered}[/tex]The final answer
[tex]9cm\text{ to 63inches}[/tex]Summary
I need help please and thank you and you have to graph it
From the graph provided we can determine two points which are;
[tex]\begin{gathered} (x_1,y_1)=(0,-3) \\ (x_2,y_2)=(2,0) \end{gathered}[/tex]For the equation of the line given in slope-intercept form which is;
[tex]y=mx+b[/tex]We would begin by calculating the slope which is;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]We can now substitute the values shown above and we'll have;
[tex]\begin{gathered} m=\frac{(0-\lbrack-3\rbrack)}{2-0} \\ m=\frac{0+3}{2} \\ m=\frac{3}{2} \end{gathered}[/tex]Now we have the slope of the line as 3/2, we can substitute this into the equation and we'll have;
[tex]\begin{gathered} y=mx+b \\ \text{Where;} \\ x=0,y=-3,m=\frac{3}{2} \end{gathered}[/tex]We now have the equation as;
[tex]\begin{gathered} -3=\frac{3}{2}(0)+b \\ -3=0+b \\ b=-3 \end{gathered}[/tex]We now have the y-intercept as -3. The equation now is;
[tex]\begin{gathered} \text{Substitute m and b into the equation,} \\ y=mx+b \\ y=\frac{3}{2}x-3 \end{gathered}[/tex]The graph of this is now shown below;
We shall now draw lines to indicate the 'rise' and 'run' of this graph.
ANSWER
Observe carefully that the "Rise" is the movement along the y-axis (3 units), while the "Run" is the movement along the x-axis (2 units).
This clearly defines the slope of the equation that is;
[tex]\frac{\Delta y}{\Delta x}=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{3}{2}[/tex]please try to answer quickly because my brainly app keeps crashing before i get the answer.
Answer:
Explanations:
The formula for calculating the surface area of a sphere is given as:
[tex]SA=4\pi r^2[/tex]Determine the radius of the sphere given the Circumference 4cm. Recall that;
[tex]\begin{gathered} C=4cm \\ 2\pi r=4 \\ r=\frac{4}{2\pi} \\ \end{gathered}[/tex]Substitute the resulting radius into the sphere's surface area
[tex]\begin{gathered} SA=4\pi\cdot(\frac{4}{2\pi})^2 \\ SA=4\pi\cdot\frac{16}{4\pi^2} \\ SA=\frac{16}{\pi} \\ SA=\frac{16}{3.14} \\ SA=5.096\approx5cm^2 \end{gathered}[/tex]Hence the surface area of the spherical object is 5 squar
Kayla wants to have new doors installed in herhome. A door company charges a one-time fee of$125 plus $ per window installed. Write anexpression that represents the total cost to installnew windows in terms of the number of windows(w) installed.
Kayla wants to have new doors installed.
The door company charges $125 as a one time fee.
They also charge $50 per window installed.
If the number of new windows installed is w, then it means that to install w new windows, they will charge an additional:
w * 50 = $50w
This will be in addition to the one time fee.
Let T be the total cost of installation.
Therefore, the total cost for installing w new windows (in dollars) is:
T = 125 + 50w
Question 1 of 10 - What is the value of the expression below when d= 5 and m = -2? d? + | dm|
Note the absolute value of any negative value is positive.
The value of a collectible coin can be represented by the equation+9 74 where x represents the number ofyears that Consuello has owned the coin and y represents the total value, in dollars, of the coin. What was the valueof the coin when Consuello originally purchased it?
Given:
The value of a collectible coin can be represented by the equation
[tex]y=2x+9.74[/tex]Required:
We need to find the original purchased value
Explanation:
To find the orginal value we just put
[tex]x=0[/tex][tex]\begin{gathered} y=2*0+9.74 \\ y=9.74 \end{gathered}[/tex]Final answer:
The original value is $9.74
Solve the inequality X - (5 - 3x) = 2x - 1
hi,
x - (5 - 3x) = 2x - 1
x - 5 + 3x = 2x - 1
x - 2x + 3x = -1 + 5
2x = 4
x = 4/2
x =< 2
[tex]\text{ x }\leq\text{ 2}[/tex]
The result is letter A, the first choice
Kirsten is driving to a city that is 400 miles away. When Kirsten left home, she had 15 gallons of gas in her car. Assume that her car gets 25 miles per gallon of gas. Define a function f so that f(x) is the amount of gas left in her car after she has driven x miles from home. What are intercepts for that function. What do they represent.
The equation that gives us the amount of gas left in her car, given the driven miles, is
[tex]f(x)=15-\frac{x}{25}[/tex]Notice that when x=25, there will remain 14 gallons of gas in the tank.
The x-intercept is
[tex]\begin{gathered} f(x)=0 \\ \Rightarrow0=15-\frac{x}{25} \\ \Rightarrow x=15\cdot25=375 \end{gathered}[/tex](375,0). This is the maximum distance one can drive when the amount of gas in the tank reaches zero gallons.
On the other hand, the y-intercept is
[tex]\begin{gathered} x=0 \\ \Rightarrow f(x)=15 \end{gathered}[/tex](0,15). This is the number of gallons in the tank when we have driven 0 miles.
The owner of a movie theater was countingthe money from 1 day's ticket sales. He knewthat a total of 150 tickets were sold. Adulttickets cost $7.50 each and children's ticketscost $4.75 each. If the total receipts for theday were $891.25, how many of each kind ofticket were sold?
65 adult's ticket and 85 children's ticket was sold
Explanation:Let the number of tickets for children = x
Let the number of adults ticket = y
Total tickets = 150
x + y = 150 ....equation 1
The cost of tickets per child = $4.75
The cost of tickets per adult = $7.50
Total revenue from tickets = $891.25
Total revenue from tickets = The cost of tickets per child × number of children ticket +
The cost of tickets per adult * number of adults ticket
891.75 = 4.75(x) + 7.5(y)
891.75 = 4.75x + 7.5y ...equation 2
x + y = 150 ....equation 1
891.75 = 4.75x + 7.5y ...equation 2
Using substitution method by making x the subject of formula in equation 1:
x = 150 - y
Substitute for x in equation 2:
891.25 = 4.75(150 - y) + 7.5y
891.25 = 712.5 - 4.75y + 7.5y
891.25 = 712.5 + 2.75y
891.25 - 712.5 = 2.75y
178.75 = 2.75y
y = 178.75/2.75
y = 65
Substitute for x in equation 1:
x + 65 = 150
x = 150 - 65
x = 85
Hence, 65 adult's ticket and 85 children's ticket was sold
Which expression is undefined? (9-9) A 2 -3) )B. O C. )D. 0
Answer:
Option B
Step-by-step explanation:
Undefined expression:
An undefined expression is a division by 0, or a fraction in which the denominator is 0.
In this question, the undefined expression is given by option B.
The table shows the linear relationship between the average height in feet of trees on a tree farm andthe number of years since the trees were planted,Average Tree HeightNumber of Years Sincethe Trees were planted1361115Average Height (ft)10244580108m
Rate of change = change in y / change in x
From the table, number of years since the tree are planted are the x
They are; 1, 3, 6, 11 , 15
Average height are y, and they are;
10, 24, 45, 80, 105
Now, to calculate the rate of change, we will find the difference between two values of y then divide it by the difference between 2 values of x
If we are going to pick the first and second value of y, we must also pick the first and second value of x
If we are to pick the second and 3rd value of y, we must then pick the 2nd and 3rd value of x
That is;
rate of change = 24 -10 / 3-2
= 14/2
= 7 ft/yr
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100 POINTS!!!!!
Answer:
-45 is an integer
√100 = 10 is a whole number
√89 is an irrational number-root
4.919191... is a rational decimal
-2/5 is a rational number-ratio
.12112111211112... is an irrational decimal
Finnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn
Consider the following inequality:x < -2Step 2 of 2: What type of interval does the following inequality represent?
You have the following inequality:
x≤2
the prevous inequality can be written in interval notation as follow:
(-oo, 2]
then, you can conclude that the inequality is represented by a half-open interval (this happens when you have an open parentheses and a close parentheses)
Which lines are parallel?
M: y + 1 = -3 (x-1)
K: y =3(x+2)
P: y + 4 = 3x
The most appropriate choice for equation of line in slope intercept form will be given by-
line K is parallel to line P
line M is not parallel to both line K and line P.
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx +c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line
For M
y + 1 = -3(x - 1)
y + 1 = -3x + 3
y = -3x + 3-1
y = -3x + 2
Slope of M = -3
For K
y = 3(x+2)
y = 3x + 6
Slope of K = 3
For P
y + 4 = 3x
y = 3x - 4
slope of P = 3
Since Slope of K = Slope of P,
line K is parallel to line P
Since slope of M is different from slope of both K and P,
line M is not parallel to both line K and line P.
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A deep-dish pizza is cut into twelve equal slices. If you eat four slices, how manydegrees of pizza do you eat?240°120°45°90°
The shape of the pizza is circular. This means that the total angle possible is 360 degrees.
Since the pizza have 12 equal slices
Then each slice will represent
[tex]\frac{360}{12}=30^0[/tex]Therefore, If you decide to eat 4 four slices, then
you will eat
[tex]4\times30^0=120^0[/tex]Answer = 120 degrees
Help me to answer this question with vectors, thank you
To find:
The coordinates of a point P such that PA = PB.
Solution:
Given that A(4, 0) and B(0, 9) are the coordinates.
Let the point P is (x,0) because the point is on x-axis, and it is given that |PA| = |PB|.
So,
[tex]\sqrt{(4-x)^2+(0-0)^2}=\sqrt{(x-0)^2+(0-9)^2}[/tex]Now, squaring both the sides:
[tex]\begin{gathered} (4-x)^2=x^2+9^2 \\ 16+x^2-8x=x^2+81 \\ 8x=-65 \\ x=\frac{-65}{8} \end{gathered}[/tex]Thus, the coordinates of point P are (-65/8, 0).
Jake and Joshua go to different theme parks during the day. Jake must pay a fee of $30 for a ticket and additional 4$ for every food/beverage. Joshua has to pay 50$ for a ticket and additional 6$ for the food and drinks. How many beverages and food would it take for Joshua to have the same amount of pay as Jake? Graph the item.Write a system of equations, graph them, and type the solution.
To answer this question, we will set a system of equations, and we will solve the system by the graphical method.
Let x be the number of times Jake buys drinks and food, then the total amount he will pay is determined by the following equation:
[tex]T=30+4x\text{.}[/tex]Its graph is:
Now, let x be the number of times Joshua buys drinks and food, then the total amount he will pay is determined by the following equation:
[tex]T=50+6x\text{.}[/tex]Graphing both equations we get:
The intersection of the graphs is the point,
