In the right triangle ABC angles B and C are congruent. What is the measure of B and C?
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
From Triangle ABC, we have that:
[tex]\begin{gathered} A=90^0(Right\text{ angle)} \\ B\text{ = x} \\ C\text{ = x} \\ \text{Because Angles B and C are congruent} \end{gathered}[/tex][tex]\begin{gathered} 90^0+x+x=180^0 \\ 90^{0\text{ }}+2x=180^0 \\ \text{collecting like terms, we have that:} \\ 2x=180^0-90^0 \\ 2x=90^0 \\ \text{Divide both sides by 2, we have that:} \\ \text{x = }\frac{90^0}{2} \\ \text{x = 45}^0 \end{gathered}[/tex]CONCLUSION:
The measure of B and C are: 45 and 45 degrees --- OPTION A
Related Questions
Which is the degree measure of an angle whose tangent is 1.19? Round the answer to the nearest whole number.
Answers
We know that:
[tex]\tan\theta=1.19[/tex]where theta is the angle we are trying to find; to get the angle we take the inverse tangent at both sides of the equation. Then:
[tex]\begin{gathered} \tan^{-1}(\tan\theta)=\tan^{-1}1.19 \\ \theta=50 \end{gathered}[/tex]Therefore, the angle we are looking for is 50°
Which of the following is equal to the rational expression when x + 1 or -1? 5(x-1) (x + 1)(x-1)
Answers
Answer
Option A is correct.
[tex]\frac{5}{(x+1)}[/tex]Explanation
We can see that the numerator and the denominator both contain (x - 1).
Hence, that expression cancels out and we are left with
5/(x + 1)
Hope this Helps!!!
I need to determine the length in feet of arc BC?? Is my answer correct?
Answers
l= π/2
1) To find out the length of the arc BC with a central angle ∠BAC, we'll use the following formula:
[tex]l=\frac{\alpha}{360}\cdot2\pi r[/tex]2) Now we can plug into that the given data, considering that ∠ BAC is a central angle then we can affirm:
[tex]m\widehat{BC}=m\angle BAC[/tex]
So we can plug into the formula below 45º as the angle of that arc, as it follows:
[tex]\begin{gathered} l=\frac{\alpha}{360}\cdot2\pi r \\ l=\frac{45}{360}\cdot2\pi\cdot2 \\ l=\frac{1}{2}\pi\text{ or }\frac{\pi}{2} \end{gathered}[/tex]3) Hence, as we can see the answer is the l= π/2
11 less than 4G leaves 37 translate into an expression
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In order to translate the phrase into an expression we need to divide it into 2 sections, the first part states 11 less than 4G, then,
[tex]4G-11[/tex]the second part states the result, then, we need to add an equal sign
[tex]4G-11=37[/tex]Answer:
[tex]4G-11=37[/tex]120 lb to 180 lb increase or decrease
Answers
We are asked to find out whether 120 lb to 180 lb is an increase or decrease?
Since the final amount (180 lb) is greater than the initial amount (120 lb) the difference will be positive.
A positve difference indictes an increase.
[tex]difference=180\: lb-120\: lb=60\: lb[/tex]Therefore, the difference is positive (that is 60 lb) and it is an increase.
Anthony is a waiter at a restaurant. Each day he works, Anthony will make a
guaranteed wage of $35, however the additional amount that Anthony earns from
tips depends on the number of tables he waits on that day. From past experience,
Anthony noticed that he will get about $7 in tips for each table he waits on. How
much would Anthony expect to earn in a day on which he waits on 20 tables? How
much would Anthony expect to make in a day when waiting on t tables?
Total earnings with 20 tables:
Total Earnings with t tables:
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Answer:
His guaranteed wage is 35$, and he makes 7$per each table, so 7$*table.
1) if he waits on t (tables)= 20 --> 35$+7*20
so he makes 35$+140$= 175$
2) t tables: 35$+7*t
f(x) = x^2 - 8x + 7Find the vertexaxis of symmetrygraph itfind the domainfind the range
Answers
Answers:
Vertex: (4, -9)
axis of symmetry: x = 4
Domain: (-∞, ∞)
Range: [-9, ∞)
Explanation:
If we have a quadratic function with the form y = ax² + bx + c, the x-coordinate of the vertex will be at x = -b/2a
So, for f(x) = x² - 8x + 7, we get a = 1, b = -8 and c = 7, then the x-coordinate of the vertex will be:
[tex]x=\frac{-(-8)}{2(1)}=\frac{8}{2}=4[/tex]Then, the y-coordinate will be the value of f(x) when x = 4
[tex]\begin{gathered} f(x)=x^2-8x+7 \\ f(4)=4^2-8(4)+7 \\ f(4)=16-32+7 \\ f(4)=-9 \end{gathered}[/tex]Therefore, the vertex of the equation is the point (x, y) = (4, -9).
The axis of symmetry is located in the vertex, since the parabola opens up, the axis of symmetry is the vertical line x = 4.
To graph the function, we need to find some points before and after the vertex. So, we will give values to x as 2, 3, 5, and 6. Then, we can calculate f(x) as:
[tex]\begin{gathered} f(2)=2^2-8(2)+7=4-16+7=-5 \\ f(3)=3^2-8(3)+7=9-24+7=-8 \\ f(5)=5^2-8(5)+7=25-40+7=-8 \\ f(6)=6^2-8(6)+7=36-48+7=-5 \end{gathered}[/tex]So, to graph the function, we will use the points (2, -5), (3, -8), (5, -8), (6, -5) and the vertex (4, -9). Therefore, the graph is:
Finally, the domain is the set of values that the variable x can take. In this case, x can be any number, so the domain is the set of all real numbers or written as an interval
(-∞, ∞)
And the range is the set of all values that f(x) can take. In this case, f(x) is always greater than -9, so the range is the set [-9, ∞)
Find the greatest number that divides 30 and 60 without leaving a remainder.
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The greatest number that divides 30 and 60 without leaving a remainder is its GCF.
Find the GCF of 30 and 60 by listing their factors. We get the following:
The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Since the greatest common factor of the two numbers is 30, then the greatest number that divides 30 and 60 without remainder is 30.
Statistics approximating the mean of a data set given a frequency distribution
Answers
Solution
- The mean formula is given as:
[tex]\begin{gathered} \bar{x}=\sum_{i=1}^n\frac{fix_i}{f_i} \\ \\ where, \\ x_i=\text{ The ith data point} \\ f_i=\text{ The frequency of the ith data point} \end{gathered}[/tex]- Thus, we can find the mean as follows:
[tex]\begin{gathered} \text{ We have been told to use the midpoint of the classes. Thus, we can say:} \\ x_i=\lbrace3,8,13,18,23,28\rbrace \\ fi=\lbrace22,21,15,9,4,3\rbrace \\ \\ \text{ Thus, the mean commute distance for students is:} \\ \bar{x}=\frac{3(22)+8(21)+13(15)+18(9)+23(4)+28(3)}{22+21+15+9+4+3} \\ \\ \bar{x}=\frac{767}{74} \\ \\ \bar{x}=10.36486486...\approx10.4\text{ \lparen To 1 decimal place\rparen} \end{gathered}[/tex]Final Answer
The mean distance is 10.4 miles
The figure below is a net for a right rectangular prism. Its surface area is 384 cm2 andthe area of some of the faces are filled in below. Find the area of the missing faces,and the missing dimension.Yes
Answers
Solution
For this case we know the total surface area given by:
384 cm^2
And we have the following: 108+48 +108+48 = 312 cm^2
the ramianing area is:
384 -312= 72 cm^2
And we can do the following:
2*9*? = 72
Solving for ? we got:
? = 72/18 = 4 cm
the final answer is:
The area of each missing face is: 36 cm^2
The lenght of each missing edge is: 4 cm
Write a compound inequality for the graph shown below.Use x for your variable.++><++-10-9-8-7-65 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 x0Dand<>D400 050 020XC
Answers
STEP - BY - STEP EXPLANATION
What to do?
Write the compound inequality of the given graph.
Given:
Step 1
Determine the two inequality separately.
[tex]x\ge4[/tex][tex]x<6[/tex]Step 2
Combine the two inequalities
[tex]4\leq x<6[/tex]ANSWER
The compound inequality is
4≤x < 6
blake needed at least 225 votes to become president of his seventh-grade class. if three-fourths of the seventh-grade students voted for him and he won. how many seventh-grade students could there be?im looking for the inequality and answer. thank you.
Answers
Given :
The number of votes to win is at least 225 votes
three-fourths of the seventh-grade students voted for him and he won.
Let the number of students = x
So, the inequality will be:
[tex]\frac{3}{4}x\ge225[/tex]Solve the inequality :
Multiply both sides by 4/3
[tex]undefined[/tex]What percentage is 1 m longer than 1 yard? Round to one tenth percent. 1 yard = 91.4 cm
Answers
1 Find the area of the triangle given below and type your result in the empty box. 19 cm 15 cm 12 cm
Answers
We have a right triangle with sides 12 cm, 15 cm and 19 cm.
The area of the triangle is half the product of the legs, as they represent the base and height of the triangle:
[tex]A=\frac{b\cdot h}{2}=\frac{12\cdot15}{2}=6\cdot15=90\operatorname{cm}^2[/tex]NOTE: The legs are the shortest sides that form the right angle of the triangle.
Answer: the area of the triangle is 90 cm^2
Identify an angle That's congruent to < PQR in the given figure.
Answers
You need to rotate the figure to see the new orientation
Name the ordered pair for a fourth point. Q. so that points P.Q.R. and S will be the vertices of a Given: Points P6.-1), R(0.-1) and S(4.-5) rectangle Response
Answers
to find Q we need to make 2 distance measure
that they fulfill these conditions
PS=RQ and RS=QP
the formula of distances between 2 points is
[tex]\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]Distance PS
[tex]\begin{gathered} \sqrt[]{(6-4)^2+(-1-(-5))^2} \\ \\ PS=\sqrt[]{20} \end{gathered}[/tex]Distance RQ
[tex]\begin{gathered} \sqrt[]{(0-x)^2+(-1-y)^2} \\ \\ RQ=\sqrt[]{x^2+(1+y)^2} \end{gathered}[/tex]where x and y are de coordinates of Q
Distance RS
[tex]\begin{gathered} \sqrt[]{(0-4)^2+(-1-(-5))^2} \\ \\ RS=\sqrt[]{32} \end{gathered}[/tex]Distance QP
[tex]\begin{gathered} \sqrt[]{(x-6)^2+(y-(-1))^2} \\ \\ QP=\sqrt[]{(x-6)^2+(y+1)^2} \end{gathered}[/tex]now solve the equals
PS=RQ
[tex]\begin{gathered} \sqrt[]{20}=\sqrt[]{x^2+(1+y)^2} \\ 20=x^2+(1+y)^2 \end{gathered}[/tex]RS=QP
[tex]\begin{gathered} \sqrt[]{32}=\sqrt[]{(x-6)^2+(y+1)^2} \\ 32=(x-6)^2+(y+1)^2 \end{gathered}[/tex]if I subtract the two equations I will get
[tex]32-20=(x-6)^2-x^2[/tex]and i will solve to find x
[tex]\begin{gathered} 12=-12x+36 \\ 12x=36-12 \\ x=\frac{24}{12} \\ \\ x=2 \end{gathered}[/tex]the value of x is 2, then I can replace x on any equation to find y
so replacing
[tex]\begin{gathered} 20=x^2+(1+y)^2 \\ 20=(2)^2+y^2+2y+1 \\ y^2+2y+1-20+4=0 \\ y^2+2y-15=0 \end{gathered}[/tex]use factor to solve y
[tex]\begin{gathered} y=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \\ y=\frac{-2\pm\sqrt[]{4+60}}{2} \\ \\ y=\frac{-2\pm8}{2} \\ \\ y=-1\pm4 \end{gathered}[/tex]then y will have two values
[tex]\begin{gathered} y_1=-1+4=3 \\ y_2=-1-4=-5 \end{gathered}[/tex]the real coordinate is y=3 because if is y=-5 the point dont form a rectangle
if x=2 and y=3 the point Q is (2,3)
it says (6^2)^2 then it says select one Add, Subtract, Multiply
Answers
Multiply
Here, we want to select the arithmetic operation that could be used to evaluate the given indices expression
The key to solving this is to use an important indices relationship
That is;
[tex](a^x)^y=a^{xy}[/tex]Hence, we have to multiply the powers
So the correct option here is multiply
Here is a pattern of squares. S represents the number of small squares in the pattern as a function on n, the step number. Hint: create a table and use your graphing calculator. Step 1 Step 2 Step 3 Step 4 Which expression could define S? n²+3 n +3 n²+2 3n
Answers
In the given figure :
Step 1 has 3 square, step 2 has 6 number of square
step 3 has 11 number of squares
step 4 has 18 number of squares
So, the sequence is 3, 6, 11, 18
As we can see that the figure makes a complete square and two more squares
So the expression will be :
[tex]n^2+2[/tex]Answer : C)
[tex]n^2+2[/tex]What is the average rate of change of f(x) from x1=-10 to x2=-3? Please write your answer rounded to the nearest hundredth. f(x)= the square root of -9x+5
Answers
We have the following information
[tex]\begin{gathered} x_1=-10 \\ x_2=-3 \end{gathered}[/tex]and the function
[tex]f(x)=\sqrt[]{-9x+5}[/tex]In order to find the average rate, we need to find y1 and y2. Then, by substituting x1 into the function, we have
[tex]\begin{gathered} f(-10)=\sqrt[]{-9(-10)+5} \\ f(-10)=\sqrt[]{90+5} \\ f(-10)=\sqrt[]{95} \end{gathered}[/tex]Similarly, by substituting x2, we get
[tex]\begin{gathered} f(-3)=\sqrt[]{-9(-3)+5} \\ f(-3)=\sqrt[]{27+5} \\ f(-3)=\sqrt[]{32} \end{gathered}[/tex]Therefore, the average rate is given by
[tex]\frac{f(x_2)-f(x_1)}{x_2-x_1}=\frac{\sqrt[]{32}-\sqrt[]{95}}{-3-(-10)}[/tex]which gives
[tex]\begin{gathered} \frac{f(x_2)-f(x_1)}{x_2-x_1}=\frac{\sqrt[]{32}-\sqrt[]{95}}{7} \\ \frac{f(x_2)-f(x_1)}{x_2-x_1}=\frac{5.6568-9.7467}{7} \\ \frac{f(x_2)-f(x_1)}{x_2-x_1}=-\frac{4.0899}{7} \end{gathered}[/tex]Therefore, the average rate is
[tex]\frac{f(x_2)-f(x_1)}{x_2-x_1}=-0.58[/tex]Complete the conversion. 1 12, gal = qt Click the icon to view the customary units. 1 12 gal = 2 qt (Type an integer, fraction, or mixed number.)
Answers
1 gal = 4 qt
Multiply by 4
12 1/2 (4) = 50 qt
write a linear equation that passes through the points (3,1) and (-2,6)
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The general equation of a line is
[tex]y=mx+b[/tex]where m is the slope and b the y-intercept
we can find m by the formula
[tex]m=\frac{y2-y1}{x2-1}[/tex]where (x2,y2) is a right point of (x1,y1) then if we replace the point of the exercise we can find the slope of the line
[tex]\begin{gathered} m=\frac{1-6}{3-(-2)} \\ \\ m=\frac{-5}{5}=-1 \end{gathered}[/tex]value of the slope is -1
now to find y-intercept or b we replace the slope and a point of the line on the general equation
for example i will use (3,1)
[tex]\begin{gathered} y=mx+b \\ (1)=(-1)(3)+b \\ 1=-3+b \\ b=1+3 \\ b=4 \end{gathered}[/tex]no we can replace the slope -1 and b 4 on the general equation to have the equation of the line to the exercise
[tex]\begin{gathered} y=-x+4 \\ \end{gathered}[/tex]2.write the equation of a circle with the following parameters Center at (0,-1)Passing through (-35,0)
Answers
Solution:
Given:
[tex]\begin{gathered} center\text{ }=(0,-1) \\ Through\text{ p}oint\text{ }(-35,0) \end{gathered}[/tex]The equation of a circle is gotten by;
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ where: \\ x=-35 \\ y=0 \\ h=0 \\ k=-1 \\ \end{gathered}[/tex]Substituting these values into the equation to get the value of r;
[tex]\begin{gathered} (-35-0)^2+(0-(-1))^2=r^2 \\ (-35)^2+(1)^2=r^2 \\ 1225+1=r^2 \\ r^2=1226 \end{gathered}[/tex]Thus, the equation of the circle is;
[tex]\begin{gathered} (x-0)^2+(y-(-1))^2=1226 \\ x^2+(y+1)^2=1226 \end{gathered}[/tex]Dean is on top of a 300 m high cliff. He sees Emily in her new sailboat. If dean calculates the angle of depression to the boat to be 25° how far from the base of the cliff is Emily’s boat
Answers
To answer this question we will use the following diagram as reference:
Let d be the distance from the base of the cliff to Emily's boat, then, from the above diagram we can set the following equation:
[tex]\tan 25º=\frac{300m}{d}\text{.}[/tex]Then:
[tex]d=\frac{300m}{\tan 25º}\text{.}[/tex]Simplifying the above result we get:
[tex]d\approx643.35m[/tex]Answer:
[tex]643.35m[/tex]What is an equation of the line that passes through the points (-1, -6), (6,1)?
Answers
y = x - 5
Explanation:Given:
The points are (-1, -6) and (6, 1)
To find:
the equation of line that pass through the points
To determine the equation of the line, it will be in the form:
[tex]\begin{gathered} y\text{ = mx + b} \\ m\text{ = slope, b = y-intercept} \end{gathered}[/tex]The slope formula is given as:
[tex]$$m\text{ = }\frac{y_2-y_1}{x_2-x_1}$$[/tex][tex]\begin{gathered} x_1=-1,y_1=-6,x_2=6,y_2\text{ = 1} \\ m\text{ = }\frac{1-(-6)}{6-(-1)} \\ m\text{ = }\frac{1+6}{6+1}=\text{ }\frac{7}{7} \\ m\text{ = 1} \end{gathered}[/tex]To get the y-intercept, we will use any of the given points and the slope
[tex]\begin{gathered} Using\text{ point \lparen6, 1\rparen: x = 6, y = 1} \\ y\text{ = mx + b} \\ 1\text{ = 1\lparen6\rparen + b} \\ 1\text{ = 6 + b} \\ 1-6\text{ = b} \\ b\text{ = -5} \end{gathered}[/tex]Next substitute the slope and y-intercept
[tex]\begin{gathered} y\text{ = 1\lparen x\rparen + \lparen-5\rparen} \\ \\ The\text{ equation od the line becomes:} \\ y\text{ = x - 5} \\ \end{gathered}[/tex]Two times x, minus the quantity 7 times y, equals 20
Answers
In order to determine the associated algebraic equation of the given statement, you consider part by part.
Two times x: 2x
minus the quantity 7 times y: - 7y
equals 20: = 20
Which is equivalent to:
2x - 7y = 20
6. The line in each graph represente y = 2x Which grach represents 2> y?
Answers
Given the following question:
Which graph represents 2 > y
Both equations are graphed as follows
Since the sign is not less than or equal to it won't be a red line, but a dotted red line.
Your answer is option C.
Can you show the steps in how to solve it
Answers
To break even, the equations must satisfy that
[tex]C(x)=R(x)\text{.}[/tex]Substituting the explicit form of the equations, we get:
[tex]50x+1600=66x\text{.}[/tex]Subtracting 50x, we get:
[tex]\begin{gathered} 50x+1600-50x=66x-50x, \\ 1600=16x\text{.} \end{gathered}[/tex]Dividing by 16, we get:
[tex]\begin{gathered} x=\frac{1600}{16}, \\ x=100. \end{gathered}[/tex]Answer:
[tex]100\text{ units.}[/tex]In a textbook, 900 digits are used for the page numbers. How many pagesare in the textbook, starting with page 1? (Hint: First find how many digitsare used for pages 1-9 and 10-99.)
Answers
Given:
900 digits are used for the page numbers. How many pages are in the textbook, starting with page 1
We will find the number of the pages of the book as follows
The number of digits from 1 to 9 = 9
The number of digits from 10 to 99:
There are 90 numbers, each number has 2 digits
So, the number of digits from 10 to 99 = 90 x 2 = 180
The number of digits from 100 to 999:
There are 900 numbers, and each number has 3 digits
so, the number of digits from 100 to 999 = 900 x 3 = 2700
The overall digits are given = 900
So, number of digits from 1 to 99 = 9 + 180 = 189
Subtract 189 from 900 = 900 - 189 = 711
Divide 711 by 3 = 237
So, the number of pages that have 3 digits = 237
So, the number of pages of the book = 237 + 99 = 336
So, the answer will be 336 pages
A randomly generated list of integers from 1 to 5 is being used to simulate anevent, with the numbers 1, 2, 3, and 4 representing a success. What is theestimated probability of a success?
Answers
The theoretical probability is defined as the ratio of the number of favourable outcomes to the number of possible outcomes.
The randomly generated list has the numbers from 1 to 5, therefore, the total amount of elements is 5, which is the number of possible outcomes.
Our event consists of choosing from this list any of the numbers from 1 to 4, which is a total of 4 elements, which represents the number of favourable outcomes.4
Their ratio is:
[tex]\frac{4}{5}[/tex]Rewritting this ratio as a percentage, we have:
[tex]\frac{4}{5}=\frac{80}{100}=80\%[/tex]The answer is option B.
Use any method to add or subtract (1 point)
5/7 - (3/14 + 3/14)
Answers
Answer:
5/7 - (3/14 + 3/14) = 2/7See the steps of solution:
5/7 - (3/14 + 3/14) = Solve parenthesis first5/7 - (3 + 3)/14 = Add fractions with same denominator5/7 - 6/14 = Simplify5/7 - 3/7 = Subtract fractions with same denominator(5 - 3)/7 = Simplify2/7 AnswerAnswer:
2/7 (or) 0.285
Step-by-step explanation:
Given problem,
→ 5/7 - (3/14 + 3/14)
Let's solve the given problem,
→ 5/7 - (3/14 + 3/14)
→ (5/7) - (6/14)
→ ((5 × 2)/(7 × 2)) - (6/14)
→ (10/14) - (6/14)
→ (10 - 6)/14
→ 4/14 = 2/7
Hence, required answer is 2/7.