Answers
Hello and Good Morning/Afternoon:
Let's take this step-by-step:
By looking at this diagram:
[tex]\hookrightarrow \text {angle C is 45 degrees, angle A is 90 degrees}[/tex]
[tex]\hookrightarrow \text{We know that the sum of all the angles is 180 degrees in a triangle}[/tex]
[tex]a + b + c = 180\\90 + b + 45 = 180\\b + 135 = 180\\b = 45[/tex]
[tex]\hookrightarrow \text {Therefore angle B is also 45 degrees}[/tex]
With all these angles' measures:
⇒ we have a 45-45-90 triangle
⇒ which has some special properties (look at the diagram attached)
Based on the diagram:
[tex]\hookrightarrow \text{the longest side/ hypotenuse (BC)} = \text{ length of leg (AC)} * \sqrt{2} =14\sqrt{2}[/tex]
Answer: [tex]14\sqrt{2}[/tex]
Hope that helps!
#LearnwithBrainly
Related Questions
the vertices of ABC are points A(1,1), B(4,1), and C(4,5). find the cosines of the angles of the triangle.
Answers
Answer:
cos(A) = 3/5cos(B) = 0cos(C) = 4/5Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relation between the cosine of an angle and the sides of the triangle.
Cos = Adjacent/Hypotenuse
__
Angle AIn the given triangle, the hypotenuse is AC. The side adjacent to angle A is AB, so its cosine is ...
cos(A) = AB/AC
cos(A) = 3/5
__
Angle BThe right angle in the triangle is angle B. The cosine of a right angle is 0.
cos(B) = 0
__
Angle CThe side adjacent to angle C is CB, so its cosine is ...
cos(C) = CB/AC
cos(C) = 4/5
Answer:
cos <ABC=0
cos <BAC=3/5
cos<ACB=4/5
GIVE 5 STARS IF YOU DO RSM!!!
Marcus works as a salesman at a car dealership. He is paid a base salary of $1,137.89 each month, and he receives a commission of $212.69 for each vehicle he sells. If last month Marcus earned $9,220.11, how many cars did he sell last month?
Answers
Answer:
He sold 38 cars
Step-by-step explanation:
first we subtract his base salary from how much he made, 9,220.11 - 1,137.80 = 8,082.22
then we divide that by the commission he gets from selling 1 car which is 212.29, the equation looks like: 8,082.22 / 212.69 and that equals 38 which means he sold 38 cars.
Given the rhombus ABCD, what is ECB
Answers
The football team played 15 games this season and won three more games than it lost. How many games did the team lose?
Answers
w = won game
l = lost game
w + l = 15
and
w = I + 3
so
l + 3 + l = 15
2l = 12
l = 6
lost = 6
won = 9
Answer:
The ratio of wins to losses is 3 to 1, out of 32 total games. 3:1 has a total of 4 parts (3+1).
Total games divided by total parts is 32/4 = 8.
Now multiplying number of parts to divisor gives us 3x8 : 1x8 or 24:8. Therefore they won 24 games, lost 8.
Step-by-step explanation:
The local college has a swimming pool that measures 50m long and 25m wide if u swam from one corner to the other how far would u swim
Answers
Answer:
55.9 m
Step-by-step explanation:
If you swam from one cornee to the other, you divide the rectangle into 2 right triangles
the diagonal is a common hypothenus of the triangles
applying pytha
C² = A² + B²
C² = 25² + 50²
C² = 625 + 2500
C² = 3125
C = sqrt 3125
C = 55.9 m
Answer:
105 cubic meters
Step-by-step explanation:
In a survey of 950 people, it was found that 420 people prefer Pepsi, 380 people prefer Coca Cola, and
the remaining people prefer other drinks, what percentage of the people prefer Pepsi and Coca Cola?
Answers
Answer:
84.2%
Step-by-step explanation:
420 + 380 = 800
800 / 950 = .842
.842 * 100 = 84.2
84.2 = 84.2%
A triangle has two sides of length 19 and 15. What is the largest possible whole-number length for the third side?
Answers
Answer: 33
To maximize the length of the third side, which I'll call x, it needs to be the longest side.
So by the triangle inequality theorem, 19+15>x, meaning the maximum whole number value of x is 33.
What is the area of this rectangle?
11.2 cm
5.1 cm
Answers
Answer :-
Area of Rectangle is 57.12 cm² .Explanation :-
As per the provided information in the given question, we have been given that the Length of Rectangle is 11.2 cm . Its Breadth is given as 5.1 cm . And, we have been asked to calculate the Area of Rectangle .
For calculating the Area , we will use the Formula :-
[tex] \bigstar \: \: \: \boxed {\sf { \: Area \: of \: Rectangle \: = \: Lenght \: \times \: Breadth \: }} [/tex]
Therefore , by Substituting the given values in the above Formula :-
[tex] \dag \: \: \: \sf {Area \: of \: Rectangle \: = \: Lenght \: \times \: Breadth} [/tex]
[tex] \longmapsto \: \: \: \sf {Area \: of \: Rectangle \: = \: 11.2 \: \times \: 5.1} [/tex]
[tex] \longmapsto \: \: \: \textbf {\textsf {Area \: of \: Rectangle \: = \: 57.12 }} [/tex]
Hence :-
Area of Rectangle = 57.12 cm² .[tex] \underline {\rule {205pt} {4pt}} [/tex]
Additional Information :-
[tex] \begin{gathered} \begin{gathered} \begin{gathered}\begin{gathered}\boxed{\begin{array}{c} \\ \underline{ { \textbf {\textsf \red{ \dag \: \: More \: Formulas \: \: \dag}}}} \\ \\ \\ \footnotesize \bigstar \: \bf{Area \: _{Square} = Side \times Side} \\ \\ \\ \footnotesize\bigstar \: \bf{Area \: _{Rectangle} = Lenght \times Breadth} \\ \\ \\ \footnotesize \bigstar \: \bf{Area \: _{Triangle} = \frac{1}{2} \times Base \times Height } \\ \\ \\ \footnotesize \bigstar \: \bf{Area \: _{Parallelogram} = Base \times Height} \\ \\ \\ \footnotesize \bigstar \: \bf{Area \: _{Trapezium} = \frac{1}{2} \times [ \: A + B \: ] \times Height } \\ \\ \\ \footnotesize \bigstar \: \bf {Area \: _{Rhombus} = \frac{1}{2} \times Diagonal \: 1 \times Diagonal \: 2}\end{array}}\end{gathered}\end{gathered} \end{gathered} \end{gathered} [/tex]
[tex] \underline {\rule {205pt} {4pt}} [/tex]
Note :-
Kindly Scroll the Screen from Right to Left for Better View .The area of the given rectangle.
Solution:[tex]a = length \times width[/tex]
[tex]a = 11.2 \times 5.1[/tex]
[tex]a = 57.12 \: {cm}^{2} [/tex]
Therefore, the area of the given rectangle is 57.12 square centimeters.
Seven more than the quotient of a number b and 45 is greater than 5.
Answers
Answer/Step-by-step explanation:
Given:
Seven more than the quotient of a number b and 45 is greater than 5
So:
Seven more than the quotient of a number b and 45 is greater than 5
=
7 + b/45 > 5
Solve if needed:
[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:b > -90\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-90,\:\infty \:\right)\end{bmatrix}[/tex]
[tex]\mathrm{Subtract\:}7\mathrm{\:from\:both\:sides}[/tex]
[tex]7+\frac{b}{45}-7 > 5-7[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]\frac{b}{45} > -2[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}45[/tex]
[tex]\frac{45b}{45} > 45\left(-2\right)[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]b > -90[/tex]
~Lenvy~
Select the correct answer.
Given the formula below, solve for x.
A.
B.
C.
D.
help me please
Answers
Answer:
C is the answer
Good luck! :)
help me please if you know it
Answers
Only 0.6% of the students at a high school did not attend the first football game. Write 0.6% as a fraction and as a decimal
Answers
Answer:
here my answer
Step-by-step explanation:
hope this helps
The ratio of daisies to roses is 14 daisies to 16 roses.
If there are 8 roses, how many daisies are there?
Answers
Answer:There are 7 daises
Step-by-step explanation: half of 16 roses is 8 and half of 14 daises is 7. given the ratios from roses to daises is 8:7
Answer:
10 daisies
Step-by-step explanation:
Find the radius. ddddddddddddddddddddddddddddd
Answers
Answer:
Its 3 because the radius if half of the diameter
Step-by-step explanation:
Nidah writes down two different prime numbers.
She adds together her two numbers.
Her answer is a square number less than 30
Find two prime numbers that Nidah could have written down.
Mathematician
Answers
Answer:
2 and 3
Step-by-step explanation:
prime numbers=2,3,4,5,...
taking 2 and 3
2+3=5
5²=25
hence the different prime numbers are 2 and 3
The numbers can be (2, 7), (2, 23), (3, 13), (5, 11)
What are Prime Numbers?A prime number is a whole number greater than 1 whose only factors are 1 and itself.
Given that, Nidah writes down two different prime numbers.
She adds together her two numbers.
Her answer is a square number less than 30
Square numbers less than 30 are = 1, 4, 9, 16, 25
The pairs of numbers that can satisfy the given condition are;
2 + 7 = 9
2 +23 = 25
3 + 13 = 16
5 + 11 = 16
Hence, Nidah could have chosen from these numbers (2, 7), (2, 23), (3, 13), (5, 11)
For more reference on Prime numbers, click;
https://brainly.com/question/15048606
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can someone help me plsea and i mean if its right what i wrote?
Answers
Answer:
Area = 201.1
Cicumference = 50.27
Your answers are correct
Step-by-step explanation:
A = Area = ?
C = Circumference = ?
SInce both the "Area" and "Circumference" are unknown, we use the formula:
[tex]\mathrm{A = \dfrac{ 1 }{ 4 } \pi { d }^{ 2 }}[/tex]
Remember that:
The diameter is the length of the line through the center
and
The radius is half the diameter
Given:
Diameter = 16
Now we substitute "16" for "d" into the formula and solve
[tex]\mathrm{A = \dfrac{ 1 }{ 4 } \pi {( 16) }^{ 2 }}[/tex]
Calculate 16 to the power of 2 and get 256
[tex]\mathrm{A = \dfrac{ 1 }{ 4 } \pi \times 256}[/tex]
Multiply [tex]\frac{1}{4}[/tex] and 256 to get [tex]\frac{256}{4}[/tex]
[tex]\mathrm{A = \dfrac{ 256 }{ 4 } \pi}[/tex]
Divide 256 by 4 to get 64
[tex]\mathrm{A=64\pi }[/tex]
Multiply 64 and π to get 201.06192983
[tex]\mathrm{A=201.06192983}[/tex]
Round to the nearest tenth and get 201.1
[tex]\mathrm{A=201.1}[/tex]
Next we need to find the "Circumference"
Formula for finding circumference is:
C = πd
Given:
Diameter = 16
Now we substitute "16" for "d" into the formula and solve
C = π(16)
Multiply 16 and π to get 50.265482457
C = 50.265482457
Round to the nearest hundreth and get 50.27
C = 50.27
So, your answers are correct.
The only mistake that could happen is whether you need to round to the nearest hundreth or tenth.
Juan went shopping for a new pair of sneakers because of a sale. The price on the tag was $28, but Juan paid $23.80 before tax. Find the percent discount.
Answers
Answer:
15% off
Step-by-step explanation:
28-23.80 = 4.2$
23.8/28 = 0.85
100-85 = 15
15%
help please and please hurry this assignment is due 11:59
Answers
Then lower shape, triangle: 13.5
Then you add both:
B) 58.5 square feet:))
PLEASE HELP!!! Sari stood at a point measured 20 meters away from the base of building A. Turning 40° to building B, she determined that the base
of that building was 25 meters away. How far apart were the buildings? Use a calculator if needed.
Answers
Answer:
x = 16.71m
Step-by-step explanation:
KL² = KX² + LX² - 2KX × LX × cos(KXL)
x² = 26² + 20² - 2 × 26 × 20 × cos(40°)
x = 16.713m ≈ 16.71m
PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY :)
The base of a triangle is (x - 3) inches. The height of a triangle is 4.5 inches. If the area is 27 square inches, what is the value of x?
Answers
Answer:
x=15 inches
Step-by-step explanation:
Area of ∆ is 27sq inches
Height is 4.5 inches
base is (x-3) inches
Area of ∆= ½×b×h
27= ½×(x-3)×4.5
27=2.25×(x-3)
27=2.25x-6.75
2.25x=27+6.75
2.25x=33.75
x=33.75/2.25
x=15 inches
Paul is running Tennis shop. He sells balls and rackets. Rackets (R) cost $1.20 each and Balls (B) cost $2:0 each. At the end of a month, Paul made a total of $70 and sold a total of 90 Rackets and Balls combined. Which system of equations represents this situation?
A. 2R + 1.20B = 90, B - R = 160.
B. 1.20R + 2B = 90, R - B = 90
C. 1.20R + 2B = 70, and R + B = 90
D. 1.20B + 2R = 90 and 2B + R = 70
Answers
The system of equations that represent the situation are 1.20R + 2B = 70, and R + B = 90.
What are the system of equations?
The system of equations are sets of equations that have to be solved simultaneously in order to determine their required values. They are often referred to as simultaneous equations.
To learn more about simultaneous equations, please check: https://brainly.com/question/25875552
The two conditional relative frequency tables below show the results of a survey asking students whether they are taking a foreign language or not.
A 4-column table with 3 rows. The first column has no label with entries middle school, high school, total. The second column is labeled taking a foreign language with entries 0.34, 0.66, 1.0. The third column is labeled not taking a foreign language with entries 0.64, 0.36, 1.0. The fourth column is labeled total with entries 0.4, 0.6, 1.0.
Table B: Frequency of Foreign-Language Studies by Row
A 4-column table with 3 rows. The first column has no label with entries middle school, high school, total. The second column is labeled taking a foreign language with entries 0.68, 0.88, 0.8. The third column is labeled not taking a foreign language with entries 0.32, 0.12, 0.2. The fourth column is labeled total with entries 1.0, 1.0, 1.0.
Which table could be used to answer the question "Assuming a student is taking a foreign language, what is the probability the student is also in high school?”
Table A, because the given condition is that the student is in high school.
Table A, because the given condition is that the student is taking a foreign language.
Table B, because the given condition is that the student is in high school.
Table B, because the given condition is that the student is taking a foreign language
Answers
Answer:
B: Frequency of Foreign-Language Studies by Row
A set of stacked plates for serving weighs 12kg . If each plate weighs 1/2 kg how many plates are in the stack?
Answers
Answer:
24
Step-by-step explanation:
12 divided by 1/2 = 24
Hope this helped! :)
Write 9.33 as a mixed number and as an improper fraction. Do not try to simplify your answers.
Answers
Answer:
Improper Fraction:
933/100
Mixed Number:
9 33/100
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
Help as soon as possible thanks
Answers
3x14=42ft
Add the answers together
42+66
= 108 squared feet
What weighs more 5kg of feathers or 5kg of steel
Answers
Answer:
both weigh the same.
Step-by-step explanation:
you have 5kg of steel and 5kg feathers.
The weight is the same so both weigh the same.
P = $700, r = 5%, t = 8 years; compounded quarterly
HELP ME ASAP!!!
Answers
Answer:
$1,041.69
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 5/100
r = 0.05 rate per year,
Then solve the equation:
Forumla; P(1 + r/n)nt
700.00(1 + 0.05/4)(4)(8)
700.00(1 + 0.0125)(32)
$1,041.69
hope this helps!
Answer:
$1,041.69
Step-by-step explanation:
Compound interest formula: [tex]A=P(1+\frac{r}{n})^{nt[/tex]
A = amount (future value ($))
P = principal (orignal amount - $700)
R = rate (written as a decimal - 5%/100= 0.05)
N = compound (quarterly - 4) 4 quarters in 1 yr.
T = number of years (8)
[tex]A=P(1+\frac{r}{n})^{nt[/tex]
[tex]A=P(1+\frac{r}{n})^{nt}\\\\A=700(1+\frac{0.05}{4})^{4*8} < == start\ from\ the\ parenthesis\ and\ divide\ first\\\\A=700(1+0.0125)^{4*8} < == add\ the\ \#s\ in\ the\ parenthesis\\\\A=700(1.0125)^{4*8} < == multiply\ the\ exponents\\\\A=700(1.0125)^{32} < ==multiply\\\\A=700(1.488131) < ==multiply\\\\A=1041.691\\\\A=$1,041.69[/tex]
Hope this helps!
Find m∠O given m∠R = 46°.
Answers
Answer:
m∠O=67
Step-by-step explanation:
m∠O=180-m∠R-the other angle since it is not given we can assume that the other angle is the same as m∠O so you divide 134 by 2 to get 67 therefore m∠O=67
A school gym has an area of 4,641 square feet and a perimeter of 284 feet. What are the dimensions of the gym?
Answers
Answer:
dimensions are 51x91
Step-by-step explanation:
Assuming that the gym is rectangular in shape, then...
l*w=4641
and 2l+2w=284
We have two variables and two equations so to solve this we plug one equation into another.
Solve for one variable:
l*w=4641
w=4641/l
Plug into the other equation...
2l+2(4641/l)=284
Solve
l*(2l+9282/l)=284
2l^2+9282=284l
2l^2-284l+9282=0
Factor the trinomial:
2(l−51)(l−91)=0
l−51=0 or l−91=0(Set factors equal to 0)
l=51 or l=91
now, lets plug it into one of the equations to find w
51*w=4641
w=91, l=51
or...
91*w=4641
w=51, l=91
Answer:
91 ft × 51 ft
Step-by-step explanation:
while the other answer is basically correct, it makes a to at the beginning of the calculation (but the continues correctly).
and it assumes you can find the right factoring of the expression.
so, I will show you here how to generally solve this, even if you cannot find the right factorization :
l×w = 4,641 ft²
w = 4641/l
2l + 2w = 284
2l + 2(4641/l) = 284
2l + 9282/l = 284
2l² + 9282 = 284l
2l² - 284l + 9282 = 0
to make things easier let's divide everything by 2
l² - 142l + 4641 = 0
the general solution to a squared equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = l
a = 1
b = -142
c = 4641
l = (142 ± sqrt((-142)² - 4×1×4641))/(2×1) =
= (142 ± sqrt(20,164 - 18,564))/2 =
= (142 ± sqrt(1600))/2 = (142 ± 40)/2 = 71 ± 20
l1 = 71 + 20 = 91
l2 = 71 - 20 = 51
w1 = 4641/91 = 51
w2 = 4641/51 = 91
so, they are interchangeable (it does not matter which we call length and which width).
the dimensions are 91 ft × 51 ft
Please help!!!
Triangle ABC is similar to triangle PQR
AB = 4cm
PQ=12cm
RQ= 16.5 cm
AC = xcm
PR= ycm
(a) Calculate the length of BC
(b) Write down an expression for y in terms of x
Check the picture
Answers
Answer:
5.5
3y = x
Step-by-step explanation:
→ Find the scale factor enlargement
12 ÷ 4 = 3
→ Divide 16.5 by 3
5.5
→ Write SF in terms of x and y
3y = x
The Length of BC is 5.5 cm and equation for y in terms of x is y = 3x
What are similarity in triangles?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.
According to question
Triangle ABC ≅ triangle PQR
where,
AB = 4cm
PQ=12cm
RQ= 16.5 cm
AC = xcm
PR= ycm
According to the similarity rule
the same ratio of corresponding sides
therefore,
[tex]\frac{AB}{PQ} = \frac{BC}{QR} = \frac{AC}{PR} \\[/tex]
(a) Calculate the length of BC
[tex]\frac{AB}{PQ} = \frac{BC}{QR}[/tex]
⇒ [tex]\frac{4}{12} = \frac{BC}{16.5}[/tex]
⇒ [tex]\frac{1}{3} = \frac{BC}{16.5}[/tex]
⇒ BC = 5.5 cm
(b) Write down an expression for y in terms of x
we know , [tex]\frac{AB}{PQ} = \frac{AC}{PR} \\[/tex]
⇒ [tex]\frac{4}{12} = \frac{x}{y} \\[/tex]
⇒ [tex]\frac{1}{3} = \frac{x}{y} \\[/tex]
⇒ [tex]y=3x[/tex]
Hence, Length of BC is 5.5 cm and equation for y = 3x
To know more about similarity in triangles here :
https://brainly.com/question/20502441
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