What is the measure of the missing side of the right triangle? Sad see is the hypotenuse. Sides a and b are the legs
Answers
Using the Pythagorean theorem, the formula is:
[tex]a^2+b^2=c^2[/tex]Where:
a = 7.1 km
c = 8.4 km
And we will find the side b.
Substitute the values:
[tex]7.1^2+b^2=8.4^2[/tex]And solve for b:
[tex]\begin{gathered} 50.41+b^2=70.56 \\ \text{subtract 50.41 on both sides} \\ 50.41+b^2-50.41=70.56-50.41 \\ b^2=20.15 \\ b=\sqrt[]{20.15}=4.5 \end{gathered}[/tex]Answer: b = 4.5 km
Related Questions
Point 0 is the center of the circle, What is the value of X
Answers
Answer: x = 22
Explanation:
From the information given. O is the center of the circle. The distance from the center of the circle to the circumference is the radius. This means that
OQ = radius
O to the vertex where angle 56 is formed is also a radius
This means that two sides the triangle formed insides the circle are equal. This also means that this triangle is an isosceles triangle. The base angles of an isosceles triangle are equal. This means that
angle 56 = angle Q because they are the base angles of the isosceles triangle
Recall, the sum of the angles in a triangle is 180 degrees. This means that
angle O + 56 + 56 = 180
angle O + 112 = 180
angle O = 180 - 112
angle O = 68
Recall, the angle formed by a tangent with the radius of the circle is 90 degrees. This means that angle Q = 90 degrees
Considering triangle POQ,
angle P + angle O + angle Q = 180
x + 68 + 90 = 180
x + 158 = 180
x = 180 - 158
x = 22
Use a 30 - 60 - 90 triangle to find the tangent of 60 Degrees
Answers
Let's put more details in the given figure to better understand the solution:
Let's now determine the Tangent of 60 degrees:
[tex]\text{ Tangent (60}^{\circ})\text{ = }\frac{\text{ Opposite}}{\text{ Adjacent}}[/tex][tex]\text{ = }\frac{\text{ }\sqrt[]{3}}{1}[/tex][tex]\text{ Tangent (60}^{\circ})\text{ = }\sqrt[]{3}[/tex]Therefore, the tangent of 60 degrees is √3.
The answer is Option 1 : √3
In the regular octagon below, if AP = 10 cm. and BC = 15 cm, find it's area.
Answers
Given:
There is a regular octagon given as below
Required:
We want to find the area of given regular octagon if AP = 10 cm. and BC = 15 cm
Explanation:
As we can see in the figure that there 8 triangles which are exactly same
so if we find area of 1 triangle and multiply with 8 we get the area of whole regular octagon
The area of 1 triangle is
[tex]a=\frac{1}{2}*10*15=75\text{ cm}^2[/tex]now to find area of regular octagon
[tex]A=8a=75*8=600\text{ cm}^2[/tex]
Final answer:
600 sq cm
A. Determine and then compare the rate of change (slope) for each function in terms of the quantities compared.b. Determine and the compare the y-intercept of each function in terms of the quantities.
Answers
A.
Pavilion's line:
[tex]y=10x+50[/tex]The slope of the line is the coefficient multiplying x, so it is m=10
Heliophobia's line:
To determine the slope of this line you have to use the following formula:
[tex]m_p=\frac{y_1-y_2}{x_1-x_2}[/tex]Where
(x₁,y₁) are the coordinates of one point on the line
(x₂,y₂) are the coordinates of a second point on the line
I'll choose to use points (1,85) and (0,70) but you can use any pair of points on the given line:
[tex]m_h=\frac{85-70}{1-0}=\frac{15}{1}=15[/tex]The slope of the Pavillion's line is m=10 → it indicates that y increases 10 units for every unit increase of x.
The slope of the Heliophobia's line is m=15 → it indicates that y increases 15 units for every unit increase of x.
The increase of Heliophobia's line is greater than the increase of Pavillion's line.
B.
The y-intercept is the value of y when x=0
For Pavillion's line the y-intercept is
[tex]\begin{gathered} y=10\cdot0+50 \\ y=50 \end{gathered}[/tex]The coordinates are (0, 50)
For the Heliophobia's line the y-intercept is given in the table (0,70)
May I please get help with finding weather they are quadrilaterals, parallelograms, or rectangles
Answers
Given:
Three diagrams are given.
Diagram VWXY:
Quadrilateral, Parallelogram,Rectangle
Diagram IJGH:
Quadrilateral
Diagram ABCD:
Quadrilateral , Parallelogram
seven more than the product of 22 and a number
Answers
Answer:
22n + 7
Step-by-step explanation:
We can let n represent the number being multiplied by 22 (products imply multiplication).
We put the seven after the multiplication since "seven more" means that we're adding the 7 to the product.
All you have to do to find the answer is
find first four terms of an arithmetic series if last term is 10 times first term and sum to n terms is 121
Answers
Answer: 120
Step-by-step explanation:
S = n/2 (a(1) + a(n)), where n is the number of terms (10), a(1) is the first term (3), and a(n) is the last term (21).
By substitution, we have,
S = 10/2 (3 + 21)
S = 120
Find the difference: 75.12 - 2.1 O A. 7.302O B. 73.02O C. 75.11 O D. 54.12
Answers
Then, the answer is number B.
what is the value of 6 × 7 – 3^2 × 9 + 4^3
Answers
Starting with the given expression:
[tex]6\cdot7-3^2\cdot9+4^3[/tex]Follow the hierarchy of operations to find the value.
First, solve potencies and roots. Solve the powers 3^2 and 4^3:
[tex]6\cdot7-3^2\cdot9+4^3=6\cdot7-9\cdot9+64[/tex]Next, solve the multiplications and divisions:
[tex]6\cdot7-9\cdot9+64=42-81+64[/tex]Solve the sums and substractions:
[tex]42-81+64=-39+64=25[/tex]Therefore:
[tex]6\cdot7-3^2\cdot9+4^3=25[/tex]If mQR = 80° and mQS = 150°, what is m
Answers
we have that
m
by exterior angle
so
substitute given values
m
mWrite a recursive formula for the sequence: 8, 4, 2, 1,...Tn + 1 = Tn × 12Tn + 1 = Tn × (2)Tn + 1 = Tn - 4(n - 1)Tn + 1 = Tn + 4(n - 1)
Answers
Given:
The sequence is:
8, 4, 2, 1,...
Required:
Find a recursive formula for the given sequence.
Explanation:
The given sequence is:
8, 4, 2, 1,...
The common ratio of the sequence is:
[tex]\begin{gathered} \frac{4}{8}=\frac{1}{2} \\ \frac{2}{4}=\frac{1}{2} \\ \frac{1}{2} \end{gathered}[/tex]Since the common ratio for the given series is 1/2.
[tex]\begin{gathered} \frac{T_{n+1}}{T_n}=\frac{1}{2} \\ T_{n+1}=\frac{1}{2}T_n \end{gathered}[/tex]Final Answer:
The recursive formula for the given sequence is
[tex]T_{n+1}=\frac{1}{2}T_{n}[/tex]use the circle graph to answer the following questionhow many more pop/rock records than soul records were sold in the year shown?
Answers
We are given the record sales of varous types.
67 million records were sold.
We are asked to find out how many more Pop/Rock records than Soul records were sold in the year?
From the given information we see that
Pop/Rock records = 56%
Let's find out 56% of 67 million
[tex]67\times\frac{56}{100}=37.52\: \text{million}[/tex]Sour records = 17%
Let's find out 17% of 67 million
[tex]67\times\frac{17}{100}=11.39\: \text{million}[/tex]Now find the difference between Pop/Rock records and Soul records
[tex]difference=37.52-11.39=26.1\: \text{million}[/tex]Therefore, about 26.1 million more Pop/Rock rethan Soul records were sold in the year
157 - 95x + 72 + 13x =
Answers
given equation
157-95x+72+13x
First arrange the variables terms together and constant terms together,
157+72-95x+13x
Now simplify constant terms together and variable terms together
229-82x
82x=229
x=229/82
x=2.79
f(x)=(0.13x⁴+0.22x³)-0.88x²-0.25x-0.09for this polynomial use a graph to state the number of turning points
Answers
The graph of the function is:
From this, we can conclude that the polynomial has three turning points
A recent study of 28 city residents showed that the mean of the time they had lived at their present address was 9.3 years. The standard deviation of the population was 2 years. Find the 90% confidence interval of the true mean? Assume that the variable is approximately normally distributed. Show all your stepsVery confused in this exercise I’m self teaching myself
Answers
Given that:
- The sample size is 28 city residents:
[tex]n=28[/tex]- The mean of the time (in years) they had lived at their present address was:
[tex]\mu=9.3[/tex]- The standard deviation (in years) of the population was:
[tex]\sigma=2[/tex]Then, you need to use the following formula for calculating the Confidence Interval given the Mean:
[tex]C.I.=\mu\pm z\frac{\sigma}{\sqrt{n}}[/tex]Where μ is the sample mean, σ is the standard deviation, "z" is the z-score, and "n" is the sample size.
By definition, the z-score for a 90% confidence interval is:
[tex]z=1.645[/tex]Therefore, you can substitute values into the formula and evaluate:
[tex]C.I.=9.3\pm(1.645)(\frac{2}{\sqrt{28}})[/tex]You get that the lowest value is:
[tex]9.3-(1.645)(\frac{2}{\sqrt{28}})\approx8.678[/tex]And the highest value is:
[tex]9.3+(1.645)(\frac{2}{\sqrt{28}})\approx9.922[/tex]Hence, the answer is:
[tex]From\text{ }8.678\text{ }to\text{ }9.922[/tex]2(4+-8)⁶+3 evaluate the Expression
Answers
The given expression is
2(4+-8)⁶+3
The first step is to evaluate the bracket.
4 + - 8 = 4 - 8 = - 4
The expression becomes
2(-4)^6 + 3
= 2(4096) + 3
= 8192 + 3
= 8195
What is the equation of the parabola shown below, given a focus at F(1, 5) and a directrix of x = −3? In addition, identify the vertex and the equation of the axis of symmetry for the parabola.
Answers
EXPLANATION
First, let's find the vertex.
From the graph, the vertex is (-1, 5).
It is symmetric about y = 5
Length of the Latus rectom (a) =2 x 4 = 8
Therefore, the equation of the graph is;
[tex]y=\frac{1}{a}(y-5)^2-1[/tex]Substitute a = 8
[tex]x=\frac{1}{8}(y-5)^2-1[/tex]Point M is the midpoint of AB. The coordinates of point A are (-7,2) and the coordinates of M are (-3, 1).What are the coordinates of point B?The coordinates of point B are
Answers
We have three points that lie on a line namely, A M B, in a cartesian coordinate system.
The coordinates of each point are as such:
[tex]A\text{ ( -7 , 2 )}[/tex]The mid-point of a line segment ( AB ) is given by coordinate ( M ) as follows:
[tex]M\text{ ( -3 , 1 )}[/tex]We will define the coordinates of point ( B ) in terms of cartesian coordinates as follows:
[tex]B\text{ ( x , y ) }[/tex]Here the line ( A B ) with points [ A, M , B ] are colinear. This means they all lie on the same line passing through all three points.
A straight line always have a constant slope/gradient ( m ) . This slope is determined between two points that lie on the line.
The formulation of calculating the slope ( m ) of the line in a cartesian coordinate system is as follows:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]The respective cartesian coordinates of each of the two points are represented by sub-scripts of ( x and y ).
Here we will take two points ( A and M ) to determine the slope ( m ) of the line passing throgh all three points as follows:
[tex]\begin{gathered} m\text{ = }\frac{1\text{ - 2}}{-3\text{ -(-7)}}\text{ = }\frac{1-2}{-3+7} \\ m\text{ = }\frac{-1}{4} \end{gathered}[/tex]This slope ( m ) holds true for the entire line and must satisfy all consecutive points that lie on the line.
We will now consider points ( A and B ) and determine the slope ( m ):
[tex]\begin{gathered} m\text{ = }\frac{y\text{ - 2}}{x\text{ - (-7)}} \\ \\ -\frac{1}{4}\text{ = }\frac{y\text{ - 2}}{x+7} \\ \\ -\text{ ( x + 7 ) = 4}\cdot(y-2) \\ -x\text{ - 7 = 4y - 8} \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 1 - 4y }}\textcolor{#FF7968}{\ldots}\text{\textcolor{#FF7968}{ Eq 1}} \end{gathered}[/tex]What we did above was calculated the slope ( m ) between two points ( A and B ) which resulted in an expression in terms of coordinates of point B ( x and y ). We equated that expression with the value of slope ( m ) that holds true for all points that lie on the line.
Then we used the slope equation and expressed the x-coordinate of point B in terms of y-coordinate of point B. This relaitonship is termed as Equation 1 ( Eq 1 ).
Next, we were also given that point M is the midpoint of line segment ( AB ). Using the definition of a mid-point ( M ) i.e the magnitude of line segments are:
[tex]|AM|\text{ = |MB|}[/tex]The magnitudes of line segment AM and MB must be equal for point ( M ) to be a mid-point of line segment ( AB ).
We will express the formulation of determining a magnitude of line segment using two points:
[tex]\text{length of line segment = }\sqrt{(\times_2-x_1)^2+(y_2-y_1)2}[/tex]So for equating the lengths (magnitudes) of line segments ( AM ) and ( MB ) we have:
[tex]\begin{gathered} A\text{ ( -7 , 2 ) , M ( -3 , 1 ) , B ( x , y )} \\ \sqrt{(-3-(-7))^2+(1-2)^2}\text{ = }\sqrt{(-3-x)^2+(1-y)^2} \end{gathered}[/tex]Square both sides of the equation:
[tex](4)^2+(-1)^2=(-1)^2\cdot(x+3)^2+(1-y)^2[/tex]Evaluate left hand side of equation and apply PEMDAS at right hnd side of the equation:
[tex]\begin{gathered} 16+1=(x^2+6x+9)+(y^2\text{ - 2y + 1 )} \\ 17\text{ = }x^2+y^2\text{ + 6x - 2y + 10} \\ \textcolor{#FF7968}{7}\text{\textcolor{#FF7968}{ = }}\textcolor{#FF7968}{x^2+y^2}\text{\textcolor{#FF7968}{ + 6x - 2y }}\textcolor{#FF7968}{\ldots Eq2} \end{gathered}[/tex]We have two equations with two unknows ( x and y ) as follows:
[tex]\begin{gathered} x\text{ = 1 - 4y }\ldots Eq1 \\ 7=x^2+y^2\text{ + 6x - 2y }\ldots Eq2 \end{gathered}[/tex]We will solve the two equation by simultaneous substitution method. Substitute Eq1 into Eq2 as follows:
[tex]\begin{gathered} 7=(1-4y)^2+y^2\text{ + 6}\cdot(1\text{ - 4y ) - 2y} \\ 7=(1-8y+16y^2)+y^2\text{ + ( 6 - 24y ) - 2y} \\ 7=17y^2\text{ -34y + 7 } \\ 0=17y^2\text{ -34y} \\ 0\text{ = y}\cdot(17y\text{ - 34 )} \\ \textcolor{#FF7968}{y}\text{\textcolor{#FF7968}{ = 0 OR y = }}\textcolor{#FF7968}{\frac{34}{17}}\text{\textcolor{#FF7968}{ = 2}} \end{gathered}[/tex]We will now plug the two values of coordinate ( y ) into ( Eq 1 ) and solve for ( x ):
[tex]\begin{gathered} y\text{ = 0, x = 1 - 4}\cdot(0)\text{ = 1} \\ y\text{ = 2, x = 1 -4}\cdot(2)=-7\text{ } \end{gathered}[/tex]We have two solutions for the coordinates of point ( B ) as follows:
[tex]B\text{ : ( 1 , 0 ) OR ( -7 , 2 )}[/tex]However, point B must have only one pair of coordinate. So we have to investigate both solutions given above and reject a redundant solution.
We see that solution B: ( -7 , 2 ) is redundant solution, hence, rejected. This is because it represents the coordinates of point A: ( -7 , 2 ) - given in question. So two different points can not attain the same set of coordinates! Hence,
The solution to the set of coordinates of point B is:
[tex]\textcolor{#FF7968}{B\colon}\text{\textcolor{#FF7968}{ ( 1 , 0 ) }}[/tex]
You flip a coin 100 times and record each outcome.You find that you land on heads 47 times and land ontails 53 times. What is the theoretical probability oflanding on heads?
Answers
If we were asked the "experimental probability", the answer would have been
[tex]\frac{47}{100}\text{ that is number of outcomes/total outcomes. }[/tex]But we were asked the "theoretical probability". And in theory, we can get either a head or a tail if a coin is flipped. So that makes it
[tex]\frac{1\text{ outcome }}{total\text{ outcomes of 2 }}\text{ = }\frac{1}{2}[/tex]Therefore, the answer is
[tex]\frac{1}{2}[/tex]a right cone has a radius of 27 cm and a height of 36cm. find the slant height of the cone. find the surface area of the cone. find the volume of the cone
Answers
A right triangle is formed where the radius is one leg, the height is the other leg and the slant height is the hypotenuse. Applying the Pythagorean theorem:
[tex]\begin{gathered} c^2=a^2+b^2 \\ s^2=27^2+36^2 \\ s^2=729+1296 \\ s^2=2025 \\ s=\sqrt[]{2025} \\ s=45\operatorname{cm} \end{gathered}[/tex]The surface area of a right cone is calculated as follows:
[tex]SA=\pi rs+\pi r^2[/tex]where r is the radius and s is the slant height. Substituting with r = 27 cm and s = 45 cm, we get:
[tex]\begin{gathered} SA=\pi\cdot27\cdot45+\pi\cdot27^2 \\ SA=1215\pi+729\pi \\ SA=1215\pi+729\pi \\ SA=1944\pi\approx6107.25\operatorname{cm} \end{gathered}[/tex]The volume of a right cone is calculated as follows:
[tex]V=\pi\cdot r^2\cdot\frac{h}{3}[/tex]where h is the height. Substituting with r = 27 cm and h = 36 cm, we get:
[tex]\begin{gathered} V=\pi\cdot27^2\cdot\frac{36}{3} \\ V=\pi\cdot729\cdot12 \\ V=8748\pi\approx27482.65\operatorname{cm}^3 \end{gathered}[/tex]In February of 2014, gas was about $3.37 per gallon. In February 2015, gas was about 2.25 per gallon. What is the percent decrease from 2014 to 2015?
Answers
According to the problem, the price decrease from $3.37 to $2.25. Let's find the difference
[tex]3.37-2.25=1.12[/tex]Then, we divide
[tex]\frac{1.12}{3.37}=0.33[/tex]Hence, the answer is 33%.Graph the line parallel to x= -1 that passes through (8,4).could you also draw a picture
Answers
The line x = -1 is a vertical line, since it has a specific x-coordinate and no y-coordinate.
A line parallel to a vertical line is also a vetical line, so our line will have the equation x = b, where we need to find the value of b.
Since our line passes through the point (8, 4), we know that its x-coordinate will be 8, so our line is x = 8.
Drawing the lines (x = -1 in blue and x = 8 in green), we have:
The answer that should be graphed is just the green line.
8 divided by 856 long division
Answers
Answer: look at the attachment bellow
(−2) × 36 × (−5) = ______.
Answers
we have 3 terms, two of them are negative
when operating multiplications, minus by plus gives minus and minus byminus gives plus, so the final result will be positive.
[tex]\begin{gathered} (-2)\cdot36\cdot(-5)=\text{?} \\ (-2)\cdot36\cdot(-5)=360 \\ \end{gathered}[/tex]The anwer is 360
Peter works at a sports store. On a particular day, he surveyed a random sample of 50 customers and observed that 30 customers liked to play tennis and 15 customers liked to play basketball.Which of the statements are likely true? Select all that are true.A. 30% of the equipment in the store should be related to basketball.B. 60% of the equipment in the store should be related to tennis.C. 30% of the sales at the sports store that day were related to basketball.D. 70% of the sales at the sports store that day were related to basketball.E. 40% of the sales at the sports store that day were related to tennis equipment. F. 60% of the sales at the sports store that day were related to tennis equipment.
Answers
Given data:
Total sample = 50
customers that liked tennis = 30
customers that liked basketball = 15
To select the answers that are true, we can check all the options
Step 1: Find the percentage of those who like tennis and basketball
[tex]\begin{gathered} \text{ The percentage of customers that like tennis is given by} \\ \frac{30}{50}\text{ x 100\% = 60\%} \end{gathered}[/tex][tex]\begin{gathered} \text{The percentage of customers that like basketball is given by} \\ \frac{15}{50}\text{ x 100\% = 30\%} \end{gathered}[/tex]Option A
Since 30% like basketball, then it will be reasonable to have 30% of the equipment related to basketball.
OptionB
Since 60% like tennis, then it will be reasonable to have 60% of the equipment related to tennis
Option C
Since 30% like basketball, then 30% of the sales is likely to be related to basketball
Option D
Since 30% like basketball, then IT IS NOT LIKELY to have 70% of the sales related to basketball.
Option E
Since 60% like tennis, then IT IS NOT LIKELY to have 40% of the sales related to tennis
Option F
Since 60% like tennis, then IT IS LIKELY to have 60% of the sales related to tennis
Hence, we select options
A, B, C, and F as True
I need to make sure this is correct please graph.
Answers
We have the expression:
[tex]y=\frac{4}{5}x+8[/tex]In order to plot the function we replace two values for x and we will get two values for y [Respectively], that is:
x = 0 => y =(4/5)(0)+8 => y = 8
x = 1 => y = (4/5)(1)+8 => y = 8.8
We then have the two points:
(0, 8)
(1, 8.8)
By looking at the fucntion we can tell is a function that describes a line, now we graph:
I need help with math I have dyscalculia and I don’t understand
Answers
The summation symbol means that we need to add the terms (n-1) for n = 1, 2, 3, and 4.
In other words, we have the following terms:
[tex]\begin{gathered} 1-1=0 \\ \\ 2-1=1 \\ \\ 3-1=2 \\ \\ 4-1=3 \end{gathered}[/tex]And we need to add them:
[tex]0+1+2+3=6[/tex]Therefore, the result is 6.
Mrs.Gall orders 240 folders and divides them equally among 3 classes. How many folders does each class receive? What basic fact did you use?
Answers
Answer:
80
Step-by-step explanation:
240 folders divided by 3 class
8. An urn contains 3 red, 2 blue, and 5 green marbles. If we pick 4 marbles with replacement and
count the number of red marbles in the 4 picks, the probabilities associated with this experiment are
P(0) = 0.24, P(1) = 0.41, P(2)= 0.265, P(3) = 0.076, and P(4) = 0.009. The probability of less than
2 red marbles is:
a. 0.41.
b. 0.65.
c. 0.915.
d 0.991
Answers
The probability of less than 2 red marbles is B. 0.65.
What is probability?Probability is the likelihood that an event will occur.
In this case, the urn contains 3 red, 2 blue, and 5 green marbles. Also, the probabilities associated with this experiment are give as:
P(0) = 0.24, P(1) = 0.41, P(2)= 0.265, P(3) = 0.076,
Therefore, the probability of less than 2 red marbles will be:
P(0) + P(1)
= 0.24 + 0.41
= 0.65.
Learn more about probability on:
brainly.com/question/24756209
#SPJ1
Determine if the following side lengths could form a triangle. Prove your answer with an inequality 3,3,7
Answers
According to the definition of triangle, the sum of two sides of a triangle must be greater than the third one.
In this case, the sum of 3 and 3 is 6 which is not greater than 7, it means that these length can't form a triangle:
[tex]3+3<7[/tex]That is the inequality that explains why they can form a triangle.