Answers
We are given a right triangle and we have to find the length of one of its sides. It will be useful to remember the definition of the tangent of an angle inside a right triangle. For an angle α<90° in a right triangle we have:
[tex]\tan \alpha=\frac{\text{opposite side}}{\text{adjacent side}}[/tex]If α is the 26° angle in the image then its opposite side is 11 and its adjacent side is x. Then we get:
[tex]\tan 26^{\circ}=\frac{11}{x}[/tex]We can multiply both sides of this equation by x:
[tex]\begin{gathered} \tan 26^{\circ}\cdot x=\frac{11}{x}\cdot x \\ \tan 26^{\circ}\cdot x=11 \end{gathered}[/tex]And we divide both sides by tan(26°):
[tex]\begin{gathered} \frac{\tan 26^{\circ}\cdot x}{\tan 26^{\circ}}=\frac{11}{\tan 26^{\circ}} \\ x=\frac{11}{\tan26^{\circ}}=22.6 \end{gathered}[/tex]Then the answer is 22.6.
Related Questions
3m^2-13m+20=0 what is the discriminant? use the discriminant to determine the number and type of solutions of the given equation ,3m^2-13m+20=0 is this equation one rational number, two irrational numbers, two nonreal complex numbers ,two rational numbers? The given equation ,3m^2- 13m+20=0, can be solved using the quadratic formula or zero-favtor property?
Answers
The discriminant is -71
The discriminant is less than zero, the equation has no real roots
Explanation:Given the equation:
[tex]3m^2-13m+20=0[/tex]The discriminant is given as:
[tex]D=b^2-4ac[/tex]where a = 3, b = -13, c = 20
[tex]\begin{gathered} D=(-13)^2-4(3)(20) \\ \\ =169-240 \\ =-71 \end{gathered}[/tex]The discriminant is less than zero, the equation has no real roots
Volume with PI math problem, we are looking at number two. The sentence says, Pam served her apple pie on a 13 inch diameter dish, she wanted to tie a ribbon around the dish to make it a little bit more festive. How long does the ribbon need to be in order to fit around the dish?
Answers
81.68 inches
Explanation
Step 1
Let
diameter=13 inches
so, to find the length of the ribbon find the circumference of the pizza
[tex]\text{Circumference}=2\cdot\pi\cdot radius[/tex]Let
radius=13 inches
replace,
[tex]\begin{gathered} \text{Circumference}=2\cdot\pi\cdot radius \\ \text{Circumference}=2\cdot\pi\cdot13\text{ inches} \\ \text{Circumference}=26\pi\text{ inches} \\ \text{Circumference}=81.68\text{ inches} \end{gathered}[/tex]so, the ribbon has to be 81.68 inches
I hope this helps you
If Jacoby spins the spinner below 120 times, how many times can heexpect is to land on red?
Answers
Answer:
20 times
Explanation:
The spinner has 6 colors and 1 of them is red. So, the probability to land on red is
P = 1/6
Then, the expected number of times that the spinner will land on read can be calculated as the probability times 120, so
E = (1/6) x 120
E = 20
Therefore, the answer is 20 times
Translate the sentence into an equation:seven less than the product of four and a number is equal to 3use the variable x for the unknown number
Answers
Given:
seven less than the product of four and a number is equal to 3
Let the number = x
So, the product of four and a number = 4x
seven less than the product of four and a number will be 4x - 7
so, the expression will be:
4x - 7 = 3
use the figure two parallel lines cut by a transvesal.
Answers
Answer:
a. 137°
Explanation:
∠1 and ∠8 are corresponding angles. They are in the same relative position with respect to the parallel lines and the transversal.
Then, corresponding angles have the same measure, so:
∠8 = ∠1
∠8 = 43°
Now, ∠8 and ∠6 form a straight line, so the sum of these angles is 180°. Therefore, the measure of ∠6 can be calculated as:
∠6 = 180 - ∠8
∠6 = 180 - 43
∠6 = 137°
So, the answer is a. 137°
can I take a pictureSolve:8^8 / 8^3
Answers
Since both bases are equal (8) to divide we have to subtract the exponents:
[tex]8^{(8-3)}[/tex][tex]8^5[/tex]bleSolve the given linear system of equations:5arthinking Onlinecoring421-62 +бу9y15Drary ResearchuidesOne solution:CD No solutionInfinite number of solutions> Next Question
Answers
Let one of the angles is x
so, second angle is 3 times as large as x
The third angle is 45 more than the smallest angles
So, the angles are x , 3x and (x + 45)
We should know that the sum of the angles of the triangle = 180
so,
x + 3x + (x + 45) = 180
Solve to find x
So,
x + 3x + x + 45 = 180
5x = 180 - 45
5x = 135
Divide both sides by 5
x = 135/5 = 27
So, the angles are 27 , 81 and 72
so, the smallest angle = 27
The middle angle = 72
The largest angle = 81
I am a rectangle with an area of 100 cm, what is the area of the one of my triangles A. 50 in B. 50 cm C. 100 cm D. 25 cm
Answers
the area of a triangle is half the area of the rectangle:
100 cm / 2 = 50 cm
is this true or false ????????????,
Answers
Answer:
False
Step-by-step explanation:
Becuase the coefficient of “X” are not the same.
I'm learning about Samples With the Mean Absolute Deviation but I have been having trouble with this type of math could you help me with my math?
Answers
Solution
For 3a)
[tex]\begin{gathered} \frac{30.1}{7.9}=\frac{3.81}{x} \\ \\ \Rightarrow x=\frac{7.9\times3.81}{30.1}=1 \end{gathered}[/tex]Sample W and Sample Z
A bus traveled on a level road for 6 hours at an average speed of 20 miles per hour faster than it traveled on a winding road. The time spent on the winding road was 2 hour find the average speed on the level road if the entire trip was 360 miles.
Answers
Given:
A bus traveled on a level road for 6 hours at an average speed of 20 miles per hour .
The distance is calculated as,
[tex]\begin{gathered} d_1=r\times t \\ d_1=6\times20 \\ d_1=120\text{ miles} \end{gathered}[/tex]The distance covered by bus on level road is faster than it raveled on a winding road.
The time spent on the winding road was 2 hour. So, the distance is,
[tex]\begin{gathered} d_2=r\times t \\ d_2=2r\text{ miles} \end{gathered}[/tex]The total distance was 360 miles.
[tex]\begin{gathered} d_1+d_2=360 \\ 120+2r=360 \\ 2r=360-120 \\ 2r=240 \\ r=120 \end{gathered}[/tex]Answer: the average speed on the level road is 120 mph
What is the perimeter of the composite figure?6 cm9 cm2 cm10 cm
Answers
As the given figure can be considered as two rectangles,
Consider the first rectangle,
The length is, 9-2 = 7 cm,
The width is, 10-6 = 4 cm.
Therefore, the perimeter is,
[tex]P=2(l+w)=2(7+4)=22\text{ cm}[/tex]For the second rectangle,
[tex]P=2(l+w)=2(10+2)=24\text{ cm}[/tex]Therefore, the total perimeter is,
22 cm + 24 cm = 46 cm.
Enrique borrowed $23,500 to buy a car he pays his uncle 2% interest on the $4,500 he brought from him and he pays the bank 11.5% interest on the rest wherever interest rate does he pay the toll 23,500
Answers
Total borrowed: $23,500
$4,500 borrowed from his uncle: (2% interest)
Amount of interest paid to his uncle:
4,500 x 2/100 = $90
Amount borrowed from the bank: $23,500-$4,500 = $19,000
(11.5% interest)
Amount of interest paid to the bank:
19,000 x (11.5 /100) = 19,000 x 0.115 = $2,185
Total amount of interest:
23,500 (x/100) = 235 x
235x = 90+2185
Solve for x
235x = 2,275
x= 2,275/235 = 9.7
9.7 %
Divide: (x with exponent of 4 – 3xwith exponent of 3 - 1,000) divided by (x+5).
Answers
we have the expression
x^4-3x^3-1,000 : (x+5)
-----------
x^3-8x^2+40x-200
-x^4-5x^3
----------------------
-8x^3-1,000
+8x^3+40x^2
----------------------
40x^2-1,000
-40x^2-200x
--------------------
-200x-1,000
200x+1,000
--------------------
0
therefore
the answer is
x^3-8x^2+40x-200Use this graph of y = 2x2 - 12x + 19 to find the vertex. Decide whether thevertex is a maximum or a minimum point.A. Vertex is a minimum point at (3, 1)B. Vertex is a maximum point at (1,7)C. Vertex is a minimum point at (1,3)D. Vertex is a maximum point at (3,1)
Answers
Hello there. To slve this question, we'll have to remembrer some properties about maximum and minimum in a quadratic function.
Given a quadratic function f as follows:
[tex]f(x)=ax^2+bx+c[/tex]We can determine whether or not the vertex is a maximum or minimum by the signal of the leading coefficient a.
If a < 0, the concavity ofthe parabolai is facing down, hence it admits a maximum value at its vertex.
If a > 0, the concavity of the parabola is facing up, hence it admits a minimum value at its vertex.
As a cannot be equal to zero (otherwise we wouldn't have a quadratic equation), we use the coefficients to determine an expression for the coordinates of the vertex.
The vertex is, more generally, located in between the roots of the function.
t is easy to prove, y comlpleting hthe square, that the solutions of the equation
[tex]ax^2+bx+c=0[/tex]are given as
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Taking the arithmetic mean of these values, we get the x-coordinate of the vertex:
[tex]x_V=\dfrac{\dfrac{-b+\sqrt{b^2-4ac}}{2a}+\dfrac{-b-\sqrt{b^2-4ac}}{2a}}{2}=\dfrac{-\dfrac{2b}{2a}}{2}=-\dfrac{b}{2a}[/tex]By evaluating the function at this point, we'll obtain the y-coordinate of the vertex:
[tex]f(x_V)=-\dfrac{b^2-4ac}{4a}[/tex]With this, we can solve this question.
Given the function:
[tex]y=2x^2-12x+19[/tex]First, notice the leadin coefficient is a = 2 , that is positive.
Hence it has a minimum point at its vertex.
To determine these coordinates, we use the other coefficients b = -12 and c = 19.
Plugging the values, we'll get
[tex]x_V=-\dfrac{-12}{2\cdot2}=\dfrac{12}{4}=3[/tex]Plugging ths value in the function, ewe'll get
[tex]y_V=f(x_V)=2\cdot3^2-12\cdot3+19=2\cdot9-36+19=1[/tex]Hence we say that the final answer is
Vertex is a minimum point at (3, 1)
As you can see in the gaph.
This is all the information I was given. O. 2.5.
Answers
The equation of a line in the slope-intercept form is y = mx + b, where m is the slope and b the y-intercept.
If it is known:
- The equation of a parallel line
- One point of the equation
To find the equation of the line, follow the steps:
1. Parallel lines have the same slope. So, use the slope of the parallel line to find the slope of the line.
2. Substitute the point in the equation to find b.
3. Since m and b are known, you found the equation of the line.
Unit cost of ring: $375Markup: 75%Retail Price?
Answers
Answer:
[tex]Retail=\text{ \$656.25}[/tex]Step-by-step explanation:
The retail price is represented by:
[tex]\text{ Retail= Cost*\lparen1+Markup \lparen as decimal\rparen\rparen}[/tex]Therefore, by the given information:
[tex]\begin{gathered} Retail=375*(1+0.75) \\ Retail=\text{ \$656.25} \end{gathered}[/tex]Find the 10th term of the geometric sequence whose common ratio is 3/2 and whose first term is 3.
Answers
ANSWER:
59049/512
EXPLANATION:
Given:
Common ratio(r) = 3/2
First term(a) = 3
Number of terms(n) = 10
To find:
The 10th term of the geometric sequence
We can go ahead and determine the 10th term of the sequence using the below formula and substituting the given values into it and evaluate;
[tex]\begin{gathered} a_n=ar^{n-1} \\ \\ a_{10}=3(\frac{3}{2})^{10-1} \\ \\ a_{10}=3(\frac{3}{2})^9 \\ \\ a_{10}=3(\frac{19683}{512}) \\ \\ a_{10}=\frac{59049}{512} \end{gathered}[/tex]Therefore, the 10th term of the sequence is 59049/512
I need help with all of these I’m in 8th grade and I’m so confused and they are due today and I can’t fail this class!!!
Answers
According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together., it is =a (b+c) =ab+ac
1) -6( a+8)
using distributive property
-6(a+8)= -6*a +(-6)*(8)
-6(a+8)=(-*+) (6*1)+(-*+)(6*8)
-6(a+8) = -6*a +(-6)*8
-6(a+8) =-6a -48
2. Fill in the blanks below to show the sum of (2x2 + 4x) and (x2 + 8).
Answers
Given the function (2x^2+4x) and (x^2+8), we are to find the sum of both functions. This is as shown below;
(2x^2+4x) + (x^2+8) [sum means addition]
Next is to collect the like terms based on the power
= (2x^2+x^2)+4x +8
Evaluate the expression in parenthesis
= 3x^2 + 4x + 8
Hence the sum of (2x2 + 4x) and (x2 + 8) is 3x^2 + 4x + 8
You will have to fil the blanks with the corresponding coefficient of x^2 and x and the constant.
The first blank will be 3 (coefficient of x^2)
The second blank will be 4 (coefficient of x)
The third blank will be 8 (the constant value)Y
In a class of students, the following data table summarizes how many students playan instrument or a sport. What is the probability that a student chosen randomlyfrom the class does not play a sport?Plays an instrument Does not play an instrumentPlays a sport34Does not play a sport136
Answers
First, let's calculate the total number of students in the class:
[tex]3+4+13+6=26[/tex]Out of those 26 students we have
[tex]13+6=19[/tex]19 that do not play a sport.
Therefore the probability that a student chosen randomly
from the class does not play a sport is:
[tex]\frac{19}{26}[/tex]fill in the blank summataion notation
Answers
we have the sequence
5+9+13+...
we have an arithmetic sequence
a1=5
a2=9
a3=13
a2-a1=9-5=4
a3-a2=13-9=4
the common difference is d=4
the general expression is equal to
[tex]a_n=a_1+d\cdot(n-1)[/tex]we have
a1=5
d=4
substitute
[tex]\begin{gathered} a_n=5+4\cdot(n-1) \\ a_n=4n+1 \end{gathered}[/tex]therefore
the notation is equal to
see the attached figure
please wait a minute to fill the image
The sum of two numbers is 95. If the larger number is increased by twice the smaller number the result is 120 what is the largest number
Answers
Let x represent the smaller number
Let y represent the larger number
The sum of the two numbers is 95. This means that
x + y = 95
If the larger number is increased by twice the smaller number, the result is 120. This means that
2x + y = 120
The system of equations representing the word problem is
x + y = 95, 2x + y = 120
Josie sold 965 tickets to a local car show for a total of $4,335.00. A ticket for childrencosts $3.00 and an adult ticket costs $5.00. How many of each ticket did she sell?
Answers
Answer:
[tex]\begin{gathered} 245\text{ children tickets were sold.} \\ \text{ 720 adult tickets were sold.} \end{gathered}[/tex]Step-by-step explanation:
To approach this situation, we need to create a system of linear equations.
Let x be the number of children
Let y be the number of adults
For equation 1)
Since the sum of the tickets sold are 965, it means children plus adults is 965
[tex]x+y=965[/tex]For equation 2)
Since the price for children is $3, the adult ticket costs $5, and the total of tickets sold is $4,335:
[tex]3x+5y=4335[/tex]Now, we can solve this by using the substitution method, isolating one of the variables in equation 1 and plugging it into equation 2.
[tex]y=965-x[/tex]Plug it into equation 2:
[tex]3x+5(965-x)=4335[/tex]Solve for x.
[tex]\begin{gathered} 3x+4825-5x=4335 \\ 5x-3x=4825-4335 \\ 2x=490 \\ x=\frac{490}{2} \\ x=245 \\ 245\text{ children tickets were sold.} \end{gathered}[/tex]Knowing the value for x, we can plug it into equation 1, and solve for y.
[tex]\begin{gathered} y=965-245 \\ y=720\text{ } \\ \text{ 720 adult tickets were sold.} \end{gathered}[/tex](x+3)^2+(y-4)^2=16please provide the center and the radius
Answers
Given:
Given the equation of the circle
[tex](x+3)^2+(y-4)^2=16[/tex]Required: Radius and center of the circle
Explanation:
The standard form of an equation of a circle is of the form
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h, k) is the center and r is the radius.
Re-write the given equation of circle in standard form.
[tex](x-(-3))^2+(y-4)^2=4^2[/tex]Comparing with the standard form,
center: (h, k) = (-3, 4)
Radius: r = 4
Final Answer: Center = (-3, 4) and radius = 4.
Apply the distributive property to simplify the expression 8(12x – 20)
Answers
Answer:
[tex]\boxed{\bf {96x-160}}[/tex]
Step-by-step explanation:
[tex]\sf 8(12x - 20)[/tex]
Apply the Distributive Property :-
[tex]\boxed{\sf \:a\left(b-c\right)=ab-ac}[/tex]
[tex]\sf 8(12x - 20)[/tex]
[tex]\sf 8\times \:12x-8\times\:20[/tex]
[tex]\sf 8 \times 12x=\bf 96x[/tex]
[tex]\sf 8\times 20=\bf 160[/tex]
[tex]\bf 96x-160[/tex]
________________
Hope this helps!
Have a great day! :)
Answer:
96x - 160
Step-by-step explanation:
Given expression,
→ 8(12x - 20)
Let's simplify the expression,
→ 8(12x - 20)
→ (8 × 12x) - (8 × 20)
→ 96x - 160
Hence, answer is 96x - 160.
Find the value of x if A, B, and C are collinear points and B is between A and C.AB=5,BC=3x+7,AC=5x−2A. 6B. 12C. 7D. 14
Answers
C. 7
Explanation:Given:
AB = 5
BC = 3x + 7
AC = 5x - 2
Since the points A, B, and C are collinear:
AB + BC = AC
Substitute the given values into the equation above:
5 + 3x + 7 = 5x - 2
Collect like terms
5x - 3x = 5 + 7 + 2
2x = 14
Divide both sides by 2
2x/2 = 14/2
x = 7
Juan has a bag of candy with 20 pieces that are the same shape and size.
40% of the pieces are only chocolate.
20% of the pieces are only caramel.
•The remainder of the pieces are only toffee
Juan eats I piece of caramel candy from the bag and then gives the bag to her friend
Susanna. If Susanna takes one piece of candy from the bag without looking, what is the
probability the piece she takes will be chocolate?
Answers
The probability the piece Susanna takes will be chocolate 8/19
Juan has a bag of candy with 20 pieces
40% of the pieces are only chocolate
Number of only chocolate pieces = (40/100) 20 = 8 pieces
20% of the pieces are only caramel.
Number of only charamel pieces = (20/100) 20 = 4 pieces
The remainder of the pieces are only toffee
number of toffee = 20 - 8 - 4 = 8
Juan eats 1 piece of caramel candy from the bag
For Sussana
Now the number of caramel pieces are 3
and the number of candies present = 20 - 1 = 19
probability = number of desired outcomes/ sample space
P(chocolate) = 8/19
Therefore the probability the piece Susanna takes will be chocolate 8/19
To learn more about probability refer here
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the approximate weights of two animals are 8.16 x 10 4 lbs. and 9.2 x 10 4 lbs. find the total weight of the two animals. write the final answer in scientific notation with the correct number of significant digits. 1.2 x 103 lbs. 1.19 x 103 lbs. 11 x 102 lbs. 5.8 x 102 lbs.
Answers
The scientific notation of weight of animal is 1.736 × 10^5.
What is scientific notation?
The scientific notation helps us to represent the numbers which are very huge or very tiny in a form of multiplication of single-digit numbers and 10 raised to the power of the respective exponent. The exponent is positive if the number is very large and it is negative if the number is very small. Learn power and exponents for better understanding.
The numbers can be written as a×10ⁿ.
Given, the weight of one animal is 8.16 × 10^4 and other animal is 9.2×10^4
Therefore, the sum of the weights in scientific notation is
=8.16 × 10^4 +9.2×10^4
Since they have same power of exponent, hence
=(8.16+9.2)10^4 =17.32×10^4
or we can write it as
1.732×10^5.
To know more about scientific notation, visit:
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What are the coordinates of the point on the directed line segment from (-1,1) to (8, 10) that partitions the segment into a ratio of 2 to 1?
Answers
Point 1 = (x1,y1)= (-1,1)
Point 2 = (x2,y2)= (8,10)
xp,yp= ? (coordinates of the point)
a:b= 2:1
xp= x1+ a/a+b (x2-x1)
xp= -1+ 2/2+1 (8-(-1))
xp= -1+2/3 (8+1)
xp= -1+2/3(9)
xp= -1+ 6
xp= 5
yp= y1 + a/ a +b (y2-y1)
yp= 1 +2/3 (10-1)
yp =1+2/3 (9)
yp=1+6
yp=7
xp,yp = (5,7)