Answers
Answer:
x = 6 cmy ≈ 14.5°Step-by-step explanation:
The given diagram shows two points labeled B. Rename the one on segment CD as E.
We assume that AE is supposed to be the bisector of angle A. Since triangle ABC is isosceles, segment AE will be perpendicular to BC. In that case, triangle EBC is also isosceles, which means BE is also 6 cm.
Angle ABC is exterior to triangle BCD, so has a measure that is the sum of angles BDC and BCD. That is, angle ABC is 2y+y=3y. Angle CBE is also y, so angle ABE will be 3y+y=4y. This exterior angle to triangle BED is the sum of angles BED and BDE. We know BDE is 2y, so BED is 4y-2y=2y, which means triangle BED is isosceles and BD=BE=EC=x=6 cm.
__
Finding the measure of angle y is a bit tricky. We know that angle ABC is 3y, and angle EBC is y. If we say X is the midpoint of BC, where AE crosses BC, then we can write the trig relations ...
BX=BA·cos(3y)
BX=BE·cos(y)
Filling in the measures of BA and BE, we can equate expressions for BX to get ...
8cos(3y) = 6cos(y)
Using the trig identity for cos(3y), we can write this as ...
8(4cos(y)³ -3cos(y)) = 6cos(y)
32cos(y)³ -30cos(y) = 0
2cos(y)(16cos(y)² -15) = 0
This has solutions cos(y)=0 and cos(y) = ±√(15/16). We are interested in the positive solution only:
y = arccos(√15/16) ≈ 14.478°
The value of y is about 14.5°.
Related Questions
Brita cuts a block of wood along the red line. When she looks at the newly
exposed face, what is the shape of the cross-section?
6 in
4 in
8 in
O A. A rectangle, 4 inches by 6 inches
O B. A rectangle, 8 inches by 6 inches
O C. A square, 4 inches by 4 inches
O D. A rectangle, 8 inches by 4 inches
Answers
Answer:
D is the answer
Step-by-step explanation:
because only the hight is changing not leanth or breath
The shape of the cross-section is rectangle, 8 inches by 4 inches.
What is Surface Area?The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface.
Now, from the figure we cut the figure from red line.
As the figure is a three dimensional figure called Cuboid.
We know that cuboid is formed by rectangle surfaces.
Then, the shape of the cross-section is Rectangle whose length is 8 inches and width 4 inches.
Learn more about Surface area here:
https://brainly.com/question/29101132
#SPJ7
1) A wallet is full of $5 and $10 bills. He has a total of 25 bills and a total of $230. How many of each bill do you have?
Answers
Answer:
6 $5 dollar bills, and 20 $10 dollar bills
Step-by-step explanation:
Five pens cost £3.25. What is the cost of 9 pens?
Answers
Answer:
3.25/5*9= 5.85
Step-by-step explanation:
3.25euros divided by 5pens times 9pens= 5.85euros
Compare the shapes of the two distributions from Louise and Aiden’s experiments.
Answers
To compare the shapes of the distributions from the experiments, a z-test can be used.
What is a z-test?Your information is incomplete as the distributions aren't given. Therefore, an overview will be given. It should be noted that a z-test is a statistical test that's us used to determine if the means of two population are different when their variances are known.
Z-tests simply test the mean of a distribution. To compare the distributions, the error in the mean will be calculated by dividing the dispersion by the square root of the number of data points.
Learn more about z-test on:
https://brainly.com/question/15728178
The sum of two numbers is equal to 11 and the difference is 19. What are the two numbers?
Answers
[tex]\bold{\huge{\pink{\underline{ Solution }}}}[/tex]
We have given in the question that,
The sum of 2 numbers is equal to 11 The difference between two numbers is 19 .[tex]\bold{\underline{ To \: Find }}[/tex]
We have to find the value of x and y.[tex]\bold{\underline{ Let's \: Begin }}[/tex]
Let the two numbers be x and y
According to the question,
[tex]\sf{ x + y = 11......eq(1) }[/tex]
[tex]\sf{ x - y = 19......eq(2) }[/tex]
Solving eq( 1 ) we get :-
[tex]\sf{ x + y = 11 }[/tex]
[tex]\sf{ x = 11 - y ......eq(3 ) }[/tex]
Subsituting eq(3 ) in eq(2) :-
[tex]\sf{ x - y = 19 }[/tex]
[tex]\sf{ ( 11 - y) - y = 19 }[/tex]
[tex]\sf{ 11 - y - y = 19 }[/tex]
[tex]\sf{ 11 - 2y = 19 }[/tex]
[tex]\sf{ - 2y = 19 - 11 }[/tex]
[tex]\sf{ - 2y = 8}[/tex]
[tex]\sf{ y = 8/(-2) }[/tex]
[tex]\sf{ y = - 4 }[/tex]
[tex]\sf{\red{Thus ,\: the\: value\: of \: y = -4}}[/tex]
Now, Subsitute the value of y in eq( 3 ) :-
[tex]\sf{ x = 11 - y }[/tex]
[tex]\sf{ x = 11 - (-4 ) }[/tex]
[tex]\sf{ x = 11 + 4 }[/tex]
[tex]\sf{ x = 15 }[/tex]
Hence, The value of x and y are 15 and (-4) .
HELP AND HURRY UP pleas
Answers
Answer:
I believe the answer is 0, -1
Helped by QueenTLoveHave an nice day
Eighty percent of students in your school own a bike. Of a sample of students in your school, the ratio of students who own a bike to students who do not own a bike is 8 : 2. Does the sample closely estimate the percentage of students in your school who own a bike? yes or no
Answers
Answer:
Yes, the sample's estimation about the percentage is accurate.
Answer:
yes
Step-by-step explanation:
It does because 10 would be 100% 8 is 80% and 2 is 20% that is why it closely estimates the percentage.
which simplest formula can assist me in solving the determinant of a matrice?
Answers
Answer:
Step-by-step explanation:
For a 2 by 2 matrix,
This is the formula for a 2 by 2 matrix determinant.
For a 3 by 3 matrix, the formula is
For 4 by 4 matrices, and higher, i suggest you use a calculator.
There is a pair of parallel sides in the following shape.
What is the area of the shape?
Answers
Answer:
Parallelogram
Step-by-step explanation:
Please mark me as brainliest
Please help me solve this problem -5= -32 please and thank you
Answers
Answer: false
Step-by-step explanation: Compare -5 and -32. They do not equal each other.
a business woman bought a refrigerator from manufacturer for $1378. Calculate the selling price if she makes a profit of 17.5 precent
Answers
Answer:
= 1619.15
Step-by-step explanation:
Hope this is correct :)
select all numbers that are rational
a. 8.23234231
b. 1/23
c. 5.12121212
d. -0.129
e. -0.9
f. 4.62
Answers
Answer:
All the numbers are technically, rational.
Step-by-step explanation:
Triangle DEF contains right angle E. If angle D measures 55° and its opposite side measures 7.6 units, what is the measure of side
DF? Round your answer to the nearest hundredth.
A. 5.34 units
B. 6.38 units
C. 9.06 units
D. 9.28 units
Answers
Answer:
D. 9.28 units
Step-by-step explanation:
DF is the hypotenuse of the triangle.
[tex]\frac{sin(A)}{a} =\frac{sin(B)}{b}[/tex]
[tex]\implies \frac{sin(55)}{7.6} =\frac{sin(90)}{DF}[/tex]
[tex]\implies DFsin(55) =7.6sin(90)[/tex]
[tex]\implies DF =\frac{7.6sin(90)}{sin(55)}[/tex]
[tex]\implies DF =9.277886875...[/tex]
[tex]\implies DF =9.28\ \textsf{units (nearest hundredth)}[/tex]
A piece of rural land sold ten years ago for $40,000. This year, the same piece of land can sell for $60,000. If the price increase is $800 per acre, what is the size of the piece of land in acres??
Answers
well, the price difference is 60000 - 40000 = 20000.
so, we're told that the price increase acres wise is 800 bucks per acre, but we also know it's a total of 20000, so how may times does 800 go into 20000?
20000 ÷ 800 = 25.
so we know that in 20000 bucks there are 25 acres, so how many will there be in 60000 bucks?
[tex]\begin{array}{ccll} \$&acres\\ \cline{1-2} 20000&25\\ 60000&x \end{array}\implies \cfrac{20000}{60000}=\cfrac{25}{x}\implies \cfrac{1}{3}=\cfrac{25}{x}\implies \stackrel{acres}{x=75}[/tex]
Answer:i have no idea!
Step-by-step explanation:
what is -2 1/3 - (-5) =?
Answers
Answer:
[tex]2\frac{2}{3}[/tex]
Step-by-step explanation:
Given the following question:
[tex]-2\frac{1}{3} -(-5)[/tex]
To find the answer to this question we will use KCF (Keep, Change, Change) because we are subtracting from a negative. Then we find the common denominator and subtract the numerators.
[tex]-2\frac{1}{3} -(-5)[/tex]
[tex]-5=\frac{-5}{1}[/tex]
[tex]-2\frac{1}{3} =3\times-2=-6+-1=-7=\frac{-7}{3}[/tex]
[tex]\frac{-7}{3} -\frac{-5}{1}[/tex]
[tex]\frac{-7}{3} \times1=\frac{-7}{3}[/tex]
[tex]\frac{-5}{1} \times3=\frac{-15}{3}[/tex]
[tex]\frac{-7}{3} -\frac{-15}{3}[/tex]
[tex]-7+15=\frac{8}{3} =8\div3=2\frac{2}{3}[/tex]
[tex]2\frac{2}{3}[/tex]
Hope this helps.
Kindly solve my question
Answers
Answer:
(a) AA Similarity using alternate interior angles
(b) 6.3
Step-by-step explanation:
(a)
Triangles ABD and BDC have a given pair of congruent angles, angles ABD and BCD.
With parallel lines AB and DC and transversal BD, then alternate interior angles ABD and BDC are congruent.
Now we have two pairs of congruent corresponding angles, so by AA Similarity, triangles ABD and BDC are similar.
(b)
Triangles ABD and BDC are similar.
The ratios of the lengths of corresponding sides are equal.
AB/BD = AD/BC
4/6 = 4.2/BC
4BC = 6 × 4.2
BC = 6.3
I WILL MARK BRAINLIEST 25 POINTS!!What is the value of the expressionshown below? . ( 2/3)^2+ 5 x 2 - 4
Answers
Answer:
x=4
Step-by-step explanation:
Hurrryy
A bag contains 8 blue marbles, 6 green marbles, 12 yellow marbles, and 10 orange marbles. A marble is drawn at random from the
bag
What is the probability that the marble drawn will not be blue?
19
o
الات
Answers
Add up to get the total number of marbles: (8 + 6 + 12 + 10) = 36
Then subtract the number of blue marbles from the total amount of marbles: 36 - 8 = 28.
28 signifies the amount of marbles that are NOT blue.
So the probability is: 28/36 = 0.77 = About 77%
The final answer is 7/9.
A regular polygon has 40 sides.
Find the size of each of its interior angles.
Answers
An interior angle of a polygon is found by subtracting 2 from the number of sides, multiplying that by 180 And then divide by the number of sides:
40-2 = 38
38 x 180 = 6840
6840/40 = 171
Answer : 171 degrees
divide the following. Put your answer in scientific notation.
(77) ÷ (4.9 × 10²)
Answers
Answer:
The answer is 0.1571428 I think
hello i don't get it pla help me i just want an answer
Answers
Answer:
-3
Step-by-step explanation:
y = 4x - 3
this equation is put in slope intercept form
y = mx + b
where m = slope and b = y intercept.
we want to find the y intercept
-3 takes the spot of b therefore the y intercept is -3
D
48°
C
61°
A
B
Find the measure of ZABD
Answers
Answer:
119
Step-by-step explanation:
Angle ABD and angle DBC are supplementary so their sum is equal to 180
therefore to find the measure of ABD we subtract 61 from 180
<ABD = 180 - 61
<ABD = 119
A section of fence is 2 feet wide. How many sections are needed to make a 9 foot fence?
Answers
Answer:
2 feet times nine equals 18
30 POINTS MARKING BRAINLEIST IF YOU ANSWER RIGHT AND QUICK!!
Answers
Answer:
5c^2+2cd−2d^2− 15
Step-by-step explanation:
this is as simplified as it gets
Hope this helps! :)
Answer:
[tex]5c^2+2cd-2d^2-15[/tex]
Step-by-step explanation:
Perimeter of a 2D shape = distance around the outside.
Therefore, to calculate the perimeter, sum the lengths of all the sides.
[tex]\textsf{perimeter} \ =(4c^2+4cd+12)+(c^2-d^2+1)+(3cd+4d^2-30)+(-5d^2-5cd+2)[/tex]
[tex]=4c^2+4cd+12+c^2-d^2+1+3cd+4d^2-30-5d^2-5cd+2[/tex]
[tex]=4c^2+c^2+4cd+3cd-5cd+4d^2-d^2-5d^2+12+1-30+2[/tex]
[tex]=5c^2+2cd-2d^2-15[/tex]
PLEASE HURRY AND GET THE ANSWER CORRECT I WILL MARK BRAINLIST
Evaluate and simplify the following complex fraction.
3/8/1/-7
screenshot below
Answers
Answer:
[tex]\cfrac{\frac{3}{8} }{\frac{1}{-7} } =\cfrac{3}{8} \times -\cfrac{7}{1}[/tex]
[tex]=\cfrac{-21}{8}[/tex]
[tex]=-2\cfrac{5}{8}[/tex]
Hope this helps u! :)
[tex]\\ \rm\rightarrowtail \dfrac{3/8}{1/-7}[/tex]
[tex]\\ \rm\rightarrowtail 3/8\div 1/-7[/tex]
[tex]\\ \rm\rightarrowtail 3/8\times -7[/tex]
[tex]\\ \rm\rightarrowtail -21/8[/tex]
[tex]\\ \rm\rightarrowtail -2\dfrac{5}{8}[/tex]
A Choir has
30 total members.
14 are boys.
How many are girls?
Choose the answer that shows the ratio of boys to girls in simplest form.
8
-10 12
о
8
15
o
7
15
Answers
Answer:
there are 12 boys because 32/8 =4 and the ratiots 3 to 8 which means you need to multiply 3 by 4 which gives you 12
Step-by-step explanation:
How can you use a protractor to prove that AB and DC are perpendicular?
Answers
Find the value of x in the triangle shown below.
Answers
Answer:
Isosceles triangle
62 + 62 + x = 180
124 + x = 180
-124 -124
x = 56 degrees
fhh earns 8 dollars per hour how much will he earn in 3/4 of an hour
Answers
Answer:
5.625
Step-by-step explanation:
3/4 of an hour is 45 minutes so if you divide 45 by 8 you will get 5.625
does this graph represent a function? why or why not?
Answers
Answer:
D. Yes, because it passes the vertical line test
Step-by-step explanation:
the vertical line test is a test you do by drawing a vertical line through the graph of the function if more than one point from the function lies on the line it does not represent a function
in this graph at any part if you draw a vertical line it passes through one point only
Answer:
Okay so what you need to know here is for a graph to be considered a function it has to pass the vertical line test. This means that if a vertical line is moved across the graph and touches the graph at only one point, then it is considered a function. But if the vertical line touches the graph at more than one point, then it is not considered a function.
Step-by-step explanation:
But for this graph, I know it wouldn't be A, B, or C...... This is because this and it touches the graph at only one point. We know the graph has to pass the vertical line test to be a function. But we can see here that it does because on the graph it only touches one point as you can see in that attachment. So, It would be D.... I'm pretty sure it is D though. Sorry if it's wrong. I tried to do what I could bcs I'm not really good at math lol
Please mark as brainliest pls and I have attached of graphs that pass the vertical line test to help you understand it better!