It is given that the scale used in the map is,
[tex]3\text{ in}\equiv50\text{ miles}[/tex]For 9 inches,
[tex]9\text{ inches=3}\times(\text{3 inches)}\equiv\text{3}\times(\text{50 miles)}=150\text{ miles}[/tex]Thus, a distance of 9 inches on the map corresponds to 150 miles in actual.
For 15 inches,
[tex]15\text{ inches=5}\times(\text{3 inches)}\equiv5\times(\text{50 miles)}=250\text{ miles}[/tex]Thus, a distance of 15 inches on the map corresponds to 250 miles in actual.
For 21 inches,
[tex]21\text{ inches=7}\times(\text{3 inches)}\equiv7\times(\text{50 miles)}=350\text{ miles}[/tex]Thus, a distance of 21 inches on the map corresponds to 350 miles in actual.
Last weekend, 5% of the tickets sold at Seaworldwere discount tickets. If Seaworld sold 60 tickets inall, howmany discount tickets did it sell? Use thepercent proportion.
Let:
N = Total tickets
d = discount tickets
r = percent of discount tickets sold
so:
[tex]\begin{gathered} d=N\cdot r \\ where\colon \\ N=60 \\ r=0.05 \\ so\colon \\ d=60\cdot0.05 \\ d=3 \end{gathered}[/tex]3 discount tickets were sold
How to find the value of X in problem 15
We are asked to determine the value of "x" and "y".
To determine the value of "y" we will use the facto that since WP is a median this means that:
[tex]AP=PH[/tex]Substituting the values in terms of "y" we get:
[tex]3y+11=7y-5[/tex]Now, we solve for "y". To do that we will first subtract "7y" from both sides:
[tex]\begin{gathered} 3y-7y+11=7y-7y-5 \\ -4y+11=-5 \end{gathered}[/tex]Now, we subtract 11 from both sides:
[tex]\begin{gathered} -4y+11-11=-5-11 \\ -4y=-16 \end{gathered}[/tex]Now, we divide both sides by -4:
[tex]\begin{gathered} y=-\frac{16}{-4} \\ \\ y=4 \end{gathered}[/tex]therefore, the value of "y" is 4.
Now, to determine the value of "x" we will use the fact that since WP is an angle bisector we have that:
[tex]m\angle HWP+m\angle PWA=m\angle HWA[/tex]We also have the:
[tex]m\angle PWA=m\angle HWP[/tex]Therefore, we have:
[tex]\begin{gathered} m\operatorname{\angle}HWP+m\operatorname{\angle}HWP=m\operatorname{\angle}HWA \\ 2m\operatorname{\angle}HWP=m\operatorname{\angle}HWA \end{gathered}[/tex]Now, we substitute the values:
[tex]2(x+12)=4x-16[/tex]Now, we divide both sides by 2:
[tex]x+12=2x-8[/tex]Now, we subtract 2x from both sides:
[tex]\begin{gathered} x-2x+12=2x-2x-8 \\ -x+12=-8 \end{gathered}[/tex]Now, we subtract 12 from both sides:
[tex]\begin{gathered} -x+12-12=-8-12 \\ -x=-20 \\ x=20 \end{gathered}[/tex]This means that the value of "x" is 20.
To determine if WP is an altitude we need to determine if the angle APW is 90 degrees. To do that we use the fact that the sum of the interior angles of a triangle always adds up to 180, therefore:
[tex]m\angle WPA+m\angle PWA+m\angle PAW=180[/tex]We substitute the values in terms of "x":
[tex]m\angle WPA+(x+12)+(3x-2)=180[/tex]Now, we substitute the value of "x":
[tex]m\angle WPA+(20+12)+(3(20)-2)=180[/tex]Solving the operations:
[tex]m\angle WPA+90=180[/tex]now, we subtract 90 from both sides:
[tex]\begin{gathered} m\angle WPA=180-90 \\ m\angle WPA=90 \end{gathered}[/tex]Since WPA is 90 degrees and WP is a median and bisector this means that WP is an altitude.
(06.04)The line of best fit for a scatter plot is shown:A scatter plot and line of best fit are shown. Data points are located at 1 and 4, 2 and 6, 2 and 3, 4 and 3, 6 and 1, 4 and 5, 7 and 2, 0 and 6. A line of best fit passes through the y-axis at 6 and through the point 4 and 3.What is the equation of this line of best fit in slope-intercept form? (4 points)y = −6x + three fourthsy = 6x + three fourthsy = negative three fourthsx + 6y = three fourthsx + 6
Answer:
[tex]y\text{ = -}\frac{3}{4}x\text{ + 6}[/tex]Explanation:
Given the y-intercept and a point, we want to get the equation of the line of best fit
We have the slope-intercept form as:
[tex]y\text{ = mx + b}[/tex]where m is the slope and b is the y-intercept:
[tex]y\text{ = mx + 6}[/tex]Now, to get m, we substitute the point (4,3)
We substitute 3 for y and 4 for x
We have that as:
[tex]\begin{gathered} 3\text{ = 4m + 6} \\ 3-6\text{ = 4m} \\ 4m\text{ = -3} \\ m\text{ = -}\frac{3}{4} \end{gathered}[/tex]Thus, the equation of the line of best fit is:
[tex]y\text{ = -}\frac{3}{4}x\text{ + 6}[/tex](a) Find an angle between 0 and 2pi that is coterminal with 10pi/3.(b) Find an angle between 0° and 360° that is coterminal with -300°.Give exact values for your answers.(a) __ radians(b) __ °
To find a coterminal angle between 0 and 2pi, you can subtract 2pi from the given angle, like this
[tex]\frac{10\pi}{3}-2\pi\text{ }[/tex]To do the subtraction, you can convert 2pi into a fraction, like this
[tex]\frac{2\pi\cdot3}{3}=\frac{6\pi}{3}[/tex]So, you have
[tex]\frac{10\pi}{3}-2\pi=\frac{10\pi}{3}-\frac{6\pi}{3}=\frac{4\pi}{3}[/tex]Therefore, 4pi/3 is the angle between 0 and 2pi that y is coterminal with 10pi/3.
For point (b), you can add 360° at the angle given, like this
[tex]360+(-300)=360-300=60[/tex]Therefore, an angle between 0° and 360° that is coterminal with -300° is 60°.
How does g(t) = 1/2t change over the interval t = 0 to t = 1?
we have the equation
[tex]g(t)=\frac{1}{3^t}[/tex]Find out the rate of change over the interval [0,1]
Remember that
the formula to calculate the rate of change is equal to
[tex]\frac{g(b)-g(a)}{b-a}[/tex]In this problem
a=0
b=1
g(a)=g(0)=1
g(b)=g(1)=1/3
therefore
the function decreases by a factor of 3NEED ANSWER ASAP Solve this system of equations:3x - 2y = - 8y= 3/2x - 2I NEED ALL THE STEPS
Let's solve it by replacing in the first equation.
3x-2y=-8
y=3/2x-2
So,
3x-2(3/2x -2)=-8
3x-3x+4=-8
Erica is given the diagram below and asked to prove that AB DF. What would be the missing step of the proof? Given: Point B is the midpoint of EF, and point A is the midpoint of ED. Prove: AB DF
Given
To find the missi
Convert the radical to exponential form. Assume variables represent positive real numbers.
Exponential Form of Radicals
A radical can be expressed in exponential form by using the equivalence:
[tex]\sqrt[m]{x^n}=x^{\frac{n}{m}}[/tex]We are given the expression:
[tex]\sqrt[4]{16a^4b^3}[/tex]It can be separated into several radicals:
[tex]\sqrt[4]{16a^4b^3}=\sqrt[4]{16}\cdot\sqrt[4]{a^4}\cdot\sqrt[4]{b^3}[/tex]Now we apply the equivalence on each individual radical:
[tex]\begin{gathered} \sqrt[4]{16a^4b^3}=\sqrt[4]{2^4}\cdot\sqrt[4]{a^4}\cdot\sqrt[4]{b^3} \\ \sqrt[4]{16a^4b^3}=2^{\frac{4}{4}}\cdot a^{\frac{4}{4}}\cdot b^{\frac{3}{4}} \end{gathered}[/tex]Simplifying:
[tex]\sqrt[4]{16a^4b^3}=2ab^{\frac{3}{4}}[/tex]solve the system by substitution type your stepsx=2y-53x-y=5
Answer:
The solution to the system of equations is
x = 3
y = 4
Explanation:
Given the pair of equations:
[tex]\begin{gathered} x=2y-5\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(1) \\ 3x-y=5\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(2) \end{gathered}[/tex]To solve these simultaneously, use the expression for x in equation (1) in equation (2)
[tex]\begin{gathered} 3(2y-5)-y=5 \\ 6y-15-y=5 \\ 6y-y-15=5 \\ 5y-15=5 \\ \\ \text{Add 15 to both sides} \\ 5y-15+15=5+15 \\ 5y=20 \\ \\ \text{Divide both sides by 5} \\ \frac{5y}{5}=\frac{20}{5} \\ \\ y=4 \end{gathered}[/tex]Using y = 4 in equation (1)
[tex]\begin{gathered} x=2(4)-5 \\ =8-5 \\ =3 \end{gathered}[/tex]Therefore, x = 3, and y = 4
Use the figure to find the measures of the numbered angles. 95 23 24 = Explain your reasoning.
The given angle and angle 3 are corresponding angles, that is, angles that are on the same corner at each intersection. Graphically,
Corresponding angles are congruent, so
[tex]\angle3=95\text{\degree}[/tex]On the other hand, angle 3 and angle 4 are supplementary angles, that is, add up to 180°. Graphically,
[tex]A+B=180\text{\degree}[/tex]So, you have
[tex]\begin{gathered} \angle3+\angle4=180\text{\degree} \\ 95\text{\degree}+\angle4=180\text{\degree} \\ \text{ Subtract 95\degree from both sides of the equation} \\ 95\text{\degree}+\angle4-95\text{\degree}=180\text{\degree}-95\text{\degree} \\ \angle4=85\text{\degree} \end{gathered}[/tex]Therefore, the measures of the numbered angles are
[tex]\begin{gathered} \angle3=95\text{\degree} \\ \angle4=85\text{\degree} \end{gathered}[/tex]a bag contains 30 marbles. 8 are pink, 11 are blue, 4 are yellow and 7 are purple. Calculate the probability of randomly selecting a marble that is not blue .
In order to find the probability of a marble not being blue, we need to find how many marbles are not blue.
To do so, we just need to sum the number of pink, yellow and purple marbles:
[tex]8+4+7=19[/tex]Now, to find the probability, we just need to divide the number of non-blue marbles by the total number of marbles.
[tex]\frac{19}{30}=0.6333=63.33\text{\%}[/tex]Given the following data, find the diameter that represents the 69th percentile.AnswerHow to enter your answer (opens in new window)Diameters of Golf Balls1.531.36 1.69 1.68 1.701.601.601.361.34 1.531.32 1.401.39 1.391.44
Given that there is a Table given of diameters
Complete the coordinate proof. Answer choices are on the bottom.
Given:
There are given that the triangle, ABC.
Where:
[tex]\begin{gathered} A=(3,6) \\ B=(5,0) \\ C=(1,0) \end{gathered}[/tex]Explanation:
According to the question, we need to prove that the isosceles triangle:
So,
From the concept of the isosceles triangle:
The isosceles triangle is defined when two sides of the length of any triangle are equal.
Then,
First, we need to find the length of the sides by using the distance formula:
So,
[tex]\begin{gathered} AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ AB=\sqrt{(5-3)^2+(0-6)^2} \\ AB=\sqrt{(2)^2+(-6)^2} \\ AB=\sqrt{4+36} \\ AB=\sqrt{40} \end{gathered}[/tex]Then,
[tex]\begin{gathered} AC=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ AC=\sqrt{(1-3)^2+(0-6)^2} \\ AC=\sqrt{(-2)^2+(-6)^2} \\ AC=\sqrt{4+36} \\ AC=\sqrt{40} \end{gathered}[/tex]And,
[tex]\begin{gathered} CB=\sqrt{(5-1)^2+(0-0)^2} \\ CB=\sqrt{(4)^2+0} \\ CB=4 \end{gathered}[/tex]Final answer:
Hence, the step and values of the sides are shown below;
[tex]\begin{gathered} CA=d \\ AB=d \end{gathered}[/tex]And,
The side CA and AB is congruence by the definition of h
And,
Triangle ABC is an isosceles triangle by the the defination of b.
Mr. Fowler's science class grew two different varieties of plants as part of anexperiment. When the plant samples were fully grown, the studentscompared their heights.PlantvarietyHeight of plant(inches)20, 17, 19, 18, 21Mean Mean absolute deviation(Inches)Variety A191.2Variety B13, 18, 11,9,14132.4Based on these data, which statement is true?O A. The maximum height for plants from variety B is greater than forvariety A.B. Plants from variety A always grow taller than plants from variety B.C. The height of a plant from variety B is likely to be closer to themean.D. The height of a plant from variety A is likely to be closer to themean.
Let's analyze all the statements and see why they are false or true.
A. FALSE
The tallest plant in variety B is just 18 tall, while the variety A we have 21.
B. FALSE
We do have plants in A that have the same height as B.
C. FALSE
The standard deviation measure how far it's from the mean, the variety B has a 2.4 standard deviation, which means that the height can be more distant from the mean than in variety A.
D. True
Justified by C. Variety A has a 1.2 standard deviation, which means it's more likely to be closer to the mean
2-18 72 20=34-To=315)-10=35 5)EXTENSION: a) In right A DEF, m D = 90 and mZF is 12 degrees less than twice mze. Find mZE. b) in AABC, the measure of ZB is 21 less than four times the measure of LA, and the measure of ZC is 1 more than five times the measure of ZA. Find the measure, in degrees, of each angle of ABC.
As given by the question
There are given that in the right triangle DEF, angle D is 90 degrees and angle f is 12 degrees less than angle E.
Now,
The sum of the three measures of a triangle is always 180 degree
So,
[tex]m\angle D+m\angle E+m\angle F=180[/tex]Where angle D is 90 degree
Then,
[tex]\begin{gathered} m\angle D+m\angle E+m\angle F=180 \\ 90+m\angle E+m\angle F=180 \\ m\angle E+m\angle F=90 \end{gathered}[/tex]Also we are given that
[tex]\begin{gathered} F+12=2E \\ F=2E-12 \end{gathered}[/tex]Therefore, substituting for F back into E+F=90
Then,
[tex]\begin{gathered} E+(2E-12)=90 \\ 3E-12=90 \\ 3E=102 \\ E=34 \end{gathered}[/tex]So, angle E is 34 degrees, which is the answer.
Simplify. Final answer should be in standard form NUMBER 18
4(2 - 3w)(w^2 - 2w + 10) =
(8 - 12w)(w^2 - 2w + 10) =
8w^2 - 16w + 80 - 12w^3 + 24w^2 - 120w =
- 12w^3 + 32w^2 - 123w + 80
If cos(0) = 24/25, and 0 is in Quadrant I, then what is cos(0/2)? Simplify your answer completely, rationalize the denominator, and enter it in fractional form.
The given information is:
[tex]\begin{gathered} \cos (\theta)=\frac{24}{25} \\ \theta\text{ is in quadrant I} \end{gathered}[/tex]cos (theta/2) is given by:
[tex]\cos (\frac{\theta}{2})=\pm\sqrt[]{\frac{1+\cos\theta}{2}}[/tex]In Quadrant I, cos (theta) is positive, then the answer is positive. By replacing the known values:
[tex]\begin{gathered} \cos (\frac{\theta}{2})=\sqrt[]{\frac{1+\frac{24}{25}}{2}} \\ \cos (\frac{\theta}{2})=\sqrt[]{\frac{\frac{25+24}{25}}{2}} \\ \cos (\frac{\theta}{2})=\sqrt[]{\frac{\frac{49}{25}}{2}} \\ \cos (\frac{\theta}{2})=\sqrt[]{\frac{49}{25\times2}} \\ \cos (\frac{\theta}{2})=\sqrt[]{\frac{49}{50}} \\ \cos (\frac{\theta}{2})=\frac{\sqrt[]{49}}{\sqrt[]{50}} \\ \cos (\frac{\theta}{2})=\frac{7}{\sqrt[]{50}} \\ \cos (\frac{\theta}{2})=\frac{7}{\sqrt[]{50}}\cdot\frac{\sqrt[]{50}}{\sqrt[]{50}} \\ \cos (\frac{\theta}{2})=\frac{7\sqrt[]{50}}{50} \\ \cos (\frac{\theta}{2})=\frac{7\sqrt[]{25\times2}}{50} \\ \cos (\frac{\theta}{2})=\frac{7\cdot\sqrt[]{25}\cdot\sqrt[]{2}}{50} \\ \cos (\frac{\theta}{2})=\frac{7\cdot5\cdot\sqrt[]{2}}{50} \\ \text{Simplify 5/50} \\ \cos (\frac{\theta}{2})=\frac{7\sqrt[]{2}}{10} \end{gathered}[/tex]Which of the following rational expressions has the domain restrictions X = -6 and x = 1?
The domain of the function is possible values of independant varaible such that function is defined or have real values.
So the expression
[tex]\frac{(x+2)(x-3)}{(x-1)(x+6)}[/tex]is not defined for x = -6 and for x = 1, as expression becomes undefined for this values of x (Denominator becomes 0).
So answer is,
[tex]\frac{(x+2)(x-3)}{(x-1)(x+6)}[/tex]Option B is correct.
The number of visits to public libraries increased from 1.2 billion in 1990 to 1.6 billion in 1994. Find the average rate of change in the number of public library visits from 1990 to 1994.
Okay, here we have this:
Considering the provided information, we are going to calculate the requested rate of change, so we obtain the following:
We will replace in the rate of change formula with the following points: (1990, 1.2) and (1994, 1.6), then we have:
Rate of change=(f(b)-f(a))/(b-a)
Rate of change=(1.6-1.2)/(1994-1990)
Rate of change=0.4/4
Rate of change=0.1 Billion
Finally we obtain that the average rate of change in the number of public library visits from 1990 to 1994 is 0.1 billion.
8Suppose Z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of c so that the following is true.p=(-c ≤ Z ≤ c ) =0.9127Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.
The value of c such that [tex]P(-c\leq Z\leq c)=0.9127[/tex] is true is 0.0873 where Z follows the standard normal distribution.
It is given to us that -
[tex]P(-c\leq Z\leq c)=0.9127[/tex] is true
It is also given that Z follows the standard normal distribution.
We have to find out the value of c.
Since Z follows the standard normal distribution, so we can say that
Z ∼ N(0,1)
To find out c,
[tex]P(-c\leq Z\leq c)=0.9127\\= > P(Z\leq c)-P(Z\leq -c)=0.9127\\[/tex]
Since there is a symmetric z-distribution, the above equation can be represented as -
[tex][1-P(Z\leq -c)]-P(Z\leq -c) = 0.9127\\= > 1-P(Z\leq -c) - P(Z\leq -c) = 0.9127\\= > 1-2P(Z\leq -c)=0.9127\\= > 2P(Z\leq -c)=0.0873\\= > P(Z\leq -c)=0.04365[/tex]
=> -c ≈ 0.0873 (Using online calculator)
Therefore, the value of c such that [tex]P(-c\leq Z\leq c)=0.9127[/tex] is true is 0.0873 where Z follows the standard normal distribution.
To learn more about standard normal distribution visit https://brainly.com/question/14916937
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Answer:
The value of c such that is true is 0.0873 where Z follows the standard normal distribution.
Step-by-step explanation:
Which is the greatest number?A. 50 – 16piB. 16 - sqrt(410)C. -sqrt(20) + 1/2D. 7/3 - (7pi/3)فر
First, we need to develop each case or take care of the following:
One number is greater than another if it is more at the right of the Real Line.
A negative number is lower than a positive number.
Between two negative numbers, the greater is the one near to zero.
Let develop the numbers:
A. 50 - 16pi is approximately -0.265472
B. 16 - sqrt(410) approximately equals to -4.24845
C. -sqrt(20) + 1/2 is approximately equals to -3.97213
D. 7/3 - (7*pi)/3 is approximately equaled to -4.99705
So taking into account the previous reasons at the beginning, we have that the number near to zero is -0.265472, which is the first option. Option A.
F (x)=x^2+4 what is f(-4)
ANSWER
f(-4) = 20
EXPLANATION
To find f(-4) we just have to replace x by -4 in function f(x):
[tex]f(-4)=(-4)^2+4[/tex]First solve the exponents. Remember that if the exponent is even and the result is always positive, either the base is positive or negative:
[tex]f(-4)=16+4=20[/tex]is it option one or two I don't need to work
From the options, the function has the next form
[tex]y=a\cdot b^x[/tex]where a and b are two constants.
The function pass through the point (0, 2), then:
[tex]\begin{gathered} 2=a\cdot b^0 \\ 2=a\cdot1 \\ 2=a \end{gathered}[/tex]The function pass through the point (1, 10), then:
[tex]\begin{gathered} 10=2\cdot b^1 \\ \frac{10}{2}=b \\ 5=b \end{gathered}[/tex]Therefore, the function is:
[tex]y=2\cdot5^x^{}[/tex]There are 8 triangles and 20 circles. What is the simplest ratio of triangles to circles?
Answer:
2:5
Step-by-step explanation:
8:20
= 4:10 (simplifying)
= 2:5
Answer:
2:5
Step-by-step explanation:
8=2*2*2, 20=2*2*5
cancel out the numbers they have in common
8=2*2*2, 20=2*2*5
=2,5
as a ratio
2:5
For each ordered pair, determine whether it is a solution to the sytem of equations.
Given
We have the system of equations:
[tex]\begin{gathered} 3x\text{ - 2y = -4} \\ 2x\text{ + 5y = -9} \end{gathered}[/tex]The ordered pair that would be a solution to the given system of equations must satisfy both equations. There can only be one ordered pair and this can be obtained by solving the system of equations simultaneously
Using a graphing tool, the plot of the lines is shown below:
The point where the lines intercept is the solution to the system of equations.
Hence the ordered pair that is a solution is (-2, -1)
Answer:
(4,8) - No
(8, -5) - No
(0, 3) - No
(-2, -1) - Yes
what is the GCF of 20 and 32
Given the following numbers
[tex]20,32[/tex]To find the greatest common factor, G.C.F.
The factor that can divide through two or more numbers evenly is the G.C.F
The factors of 20 and 32 are as follows
[tex]\begin{gathered} 20\Rightarrow1\times2\times2\times5 \\ 32\Rightarrow1\times2\times2\times2\times2\times2 \end{gathered}[/tex]The common factors between 20 and 32 is
[tex]\begin{gathered} \text{Common factors }=2,2 \\ G\mathrm{}C\mathrm{}F=2\times2=4 \\ G\mathrm{}C\mathrm{}F=4 \end{gathered}[/tex]Hence, the GCF of 20 and 32 is 4
Alternatively
Finding the G.C.F using table to find the G.C.F of 20 and 32
Therefore, the G.C.F is
[tex]G.C.F\Rightarrow2\times2=4[/tex]Hence, the G.C.F of 20 and 32 is 4
a square pyramid has a base height edge length of 3m and a slant height of 6m. find the lateral area and surface area of the pyramid
hello
given that the pyramid has the shape of a triangle, we can easily find the height of the pyramid using pythagoran's theorem
from triangle b, let's use the formula and solve for y
[tex]\begin{gathered} x^2=h^2+z^2 \\ 6^2=h^2+1.5^2 \\ 36=h^2+2.25 \\ \text{collect like terms} \\ h^2=36-2.25 \\ h^2=33.75 \\ \text{solve for h} \\ h=\sqrt[]{33.75} \\ h=5.809\approx5.81m \end{gathered}[/tex]having known the value of the heigh of the pyramid, we can now proceed to solve for the lateral area and surface area
for the lateral area, the formula is given as
[tex]\begin{gathered} A_l=l\sqrt[]{l^2+4h} \\ l=\text{edge length} \\ h=\text{height of pyramid} \end{gathered}[/tex][tex]\begin{gathered} A_l=l\sqrt[]{l^2+4h} \\ l=3m \\ h=5.81m \\ A_l=3\sqrt[]{3^2+4\times5.81_{}} \\ A_l=17.03m^2 \end{gathered}[/tex]the lateral area of the figure is 17.03 squared meter.
let's solve for the surface area
the formula for the surface area of a square pyramid is given as
[tex]\begin{gathered} A=l^2+2l\sqrt[]{\frac{l^2}{4}+4h^2} \\ l=3m \\ h=5.81 \\ A=3^2+2\times3\sqrt[]{\frac{3^2}{4}+4\times5.81^2} \\ A=9+6\sqrt[]{\frac{9}{4}+135.0244} \\ A=79.298\approx79.3m \end{gathered}[/tex]15. Graph the rational function ya*-*Both branches of the rational function pass through which quadrant?Quadrant 2Quadrant 3Quadrant 1Quadrant 4
SOLUTION:
CONCLUSION:
Both branches of the rational function pass through Quadrant 1.
Graph AABC with A(4, 7), B(0,0), and C(8, 1).a. Which sides of AABC are congruent? How do you know?b. Construct the bisector of ZB. Mark the intersection of the ray and AC as D.c. What do you notice about AD and CD?
a) Two sides of a triangle are concruent when they are the same length. First calculate the lenght of each side
[tex]\begin{gathered} AC^2=\text{ (X\_c-X\_a)}^2+(Y_a-Y_c)^2=(8-4)^2+(7-1)^2=\text{ 52} \\ AC=\sqrt{52}=7.2 \end{gathered}[/tex][tex]\begin{gathered} AB^2=(X_a-X_b)^2+(Y_a-Y_b)^2=(4-0)^2+(7-0)^2=\text{ 65} \\ AB=\sqrt{65}=8.06\approx8 \end{gathered}[/tex][tex]\begin{gathered} BC^2=(X_c-X_b)^2+(Y_c-Y_b)^2=(8-0)^2+(1-0)^2=\text{ 65 } \\ BC=\sqrt{65}=8.06\approx8 \end{gathered}[/tex]Sides AB and BC aren congruent.
b)
The bisector divides the triangle in exact halves.
The bisector is the blue line, in green you'll se the length of each side.
c)
9. Find the volume of the triangular pyramid. (2pts)-10 mI9 m16 m
Answer:
240 m³
Explanation:
The volume of a pyramid is equal to:
[tex]V=\frac{1}{3}\times B\times H[/tex]Where B is the area of the base and H is the height of the pyramid.
Then, the base of the pyramid is a triangle, so the area of a triangle is equal to:
[tex]B=\frac{b\times h}{2}[/tex]Where b is the base of the triangle and h is the height of the triangle. So, replacing b by 16 m and h by 9 m, we get:
[tex]B=\frac{16\times9}{2}=\frac{144}{2}=72m^2[/tex]Finally, replacing B by 72 m² and H by 10 m, we get that the volume of the pyramid is equal to:
[tex]V=\frac{1}{3}\times72\times10=\frac{1}{3}\times720=240m^3[/tex]Therefore, the volume is 240 m³