The length of a rectangle is 8 more than the width. The area is 65 square centimeters. Find the length and width of the rectangle.
Answer: The width of the rectangle is 5 cm and the length is 13 cm
Step-by-step explanation:
Let the width be x cm
Let the length be (x+8) cm
Area = 65cm²
[tex]\Rightarrow x(x+8)=65 \ [\because$ Area of rectangle $=$ length $\times$ width $]$ \\$\Rightarrow x^{2}+8 x-65=0 \Rightarrow x^{2}+13 x-5 x-65=0$ \\$\Rightarrow x(x+13)-5(x+13)=0 \Rightarrow(x+13)(x-5)=0$ \\$\Rightarrow x=-13$ or $x=5$ \\But width car't be negative. so $x=5$ \\[/tex]
Therefore:
Width = 5 cm
Length = 5 + 8 = 13 cm
what are the sin(0) and tan(0) of the picture below? i might have the answers but i want to double check if i did it right :) brainliest for help!
Step-by-step explanation:
sin(0) is opposite over hypotenuse which in this case is 12/15
tan (0) is opposite over adjacent 12/9
you can simplify if you like to 4/5 and 4/3 if you want to.
sinØ
Perpendicular/Hypotenuse12/15tanØ
Perpendicular/Base12/94/3Due NOWW!!! Due right now
Answer: [tex]A=539\pi /16=105.8m^2[/tex]
Step-by-step explanation:
Think of the white circle being on top of a larger shaded circle. You were given the diameter of this larger shaded circle. And, you were also secretly given the diameter of the inner white circle. If you find the area of the white circle, and subtract it from the area of the shaded circle, you will find the area of the shaded region.
Beginning with the area of the shaded circle. The diamater is 21 meters, while the radius is 21/2 meters. Therefore, the area is:
[tex]A=\pi r^2[/tex]
[tex]A=\pi (21/2)^2[/tex]
[tex]A=441\pi /4[/tex]
Moving on to the white circle. The diameter would be 21 meters with 3.5 meters subtracted from it:
[tex]d=21-3.5=17.5=35/2[/tex]
Therefore the radius is:
[tex]r=(35/2)/2=35/4[/tex]
Which means the area would be:
[tex]A=\pi r^2[/tex]
[tex]A=\pi (35/4)^2[/tex]
[tex]A=1225\pi /16[/tex]
Therefore the shaded region is:
[tex]A=441\pi /4-1225\pi /16[/tex]
Get common denominators:
[tex]A=1764\pi /16-1225\pi /16[/tex]
[tex]A=539\pi /16[/tex]
The average distance between the Sun
and Mars is about 228 million km.
What is this distance in standard form?
Give your answer in kilometres (km)
Answer:
2.28 * 10^8 km.
Step-by-step explanation:
228,000,000
= 2.28 * 10^8 km.
If two angles are complementary in a right triangle, then explain how you can find the
value of x if sin 440 = cos x using 2-3 sentences. In the last sentence, give the value of x.
Answer:
46°
Step-by-step explanation:
Points of note
two angles are complementary in a right trianglesin 44° = cos x°Solving
The first thing to understand is "complementary" means that the two angles add up to 90°Therefore, 44 + x = 90x = 46°Answer:
46°
Step-by-step explanation:
Complementary angles
Two angles whose measures sum to 90°
In a right triangle, the angle opposite the hypotenuse is always 90°.
The interior angles of a triangle sum to 180°, therefore the other two angles are complementary angles since their sum is always 90°.
So we can label one angle as [tex]x[/tex] and the other as [tex](90-x)[/tex].
The side opposite angle [tex]x[/tex] is the side adjacent to angle [tex](90-x)[/tex].
Therefore, using trig ratios, we can say that [tex]\sin(x) = \cos(90-x)[/tex]
So, if [tex]x=44[/tex] then:
[tex]\implies \sin(44) = \cos(90-44)=\cos(46)[/tex]
Find the surface area of the rectangular prism using the net
Answer:
170 in²
Step-by-step explanation:
Surface Area
⇒ (2 x Length x Height) + (2 x Width x Height) + (2 x Length x Width)
⇒ (2 x 6 x 5) + (2 x 5 x 5) + (2 x 6 x 5)
⇒ 60 + 50 + 60
⇒ 170 in²
TSA:-
2(LB+BH+LH)2(6×5+5×5+5×6)2(30+25+30)2(85)170in^2Geometry N.6 Properties of parallelograms LLK If AB = 2v - 3 and AD = 6v - 55, find the value of v in parallelogram BCDE. E B А D с V
Answer:
v = 13
Step-by-step explanation:
The diagonals of a parallelogram bisect each other, so AB ≅ AD. This relation gives rise to an equation we can solve for v.
2v -3 = 6v -55
52 = 4v . . . . . . . . . add 55-2v to both sides
13 = v . . . . . . . divide by 4
The value of v is 13 in this parallelogram.
Find the slope of the line 11x + y = -30.
Answer:
slope = -11 or m = -11
Step-by-step explanation:
11x + y = -30
y = -11x - 30
I hope this helps!
Which of the following lines are shown in the drawing?
КА
B
С
D
E
F
F.
G H
1
K
L
OT
OG
Answer:
A, B, DStep-by-step explanation:
According to the drawing we can see the lines
A) LI, yesB) GJ, yesC) CJ, noD) BE, yesE) FA, nosolve for x and find the measure of side CB
Answer:
x=10, CB=24
Step-by-step explanation:
To find x, we know that CD=AB. So first we set up an equation.
5x-18=2x+12
then we solve.
5x-18=2x+12
5x=2x+30
3x=30
x=10
To find CB, plugin x.
3(10)-6
30-6
24
CB=24
16. Lena always keeps her bank account
balance above $50, If she spent $11.60 on
lunch, what was her balance before buying
lunch?
PLEASE HELP
Step-by-step explanation:
so you add the $50 to $11.60 to get your answer
=) A student is taking a standardized test
consisting of multiple choice questions for
which there are five options for each question.
Four points are awarded for each correct
answer, but the student loses 2 points for an
incorrect answer. Questions left blank neither
receive nor lose points. Is it in the student's
best interest to guess?
Answer:
in this problem. Not that the total number of ways of taking one or more alternative out of ...
Step-by-step explanation:
Answer:
No.
Step-by-step explanation:
Well, honestly not sure how to solve this but I'll try.
Each correct answer is giving 4 points but the probability to choose the correct one is 1/5
Each incorrect one gives -2 points and the chance to pick a wrong answer is 4/5.
Obviously, the chance to lose points is more. But is taking the risk and guessing worth it? Well, it depends on how many points the correct answer gives. If it makes up for the possible loss of points, then it is in his interest to guess, otherwise he will end up losing more than they win.
If we sum the two chances to find averagely how many points the student will get, then I guess that would be the correct answer:
4(1/5) + (-2)(4/5) = 4/5 - 8/5 = -4/5
He will get averagely -4/5 points, so I believe it isn't in his interest. It means that the points he gets don't make up for the possible loss of points if you choose answers randomly. (Wow, I'm glad teachers don't do this on tests 0_0)
This is my theory though, not sure how to go for solving this, just thinked logically. I hope this helps, but don't trust me and copy paste my answer on your test or whatever. Think if this is correct first because I'm not sure
Simplify the expression.
(m^-1 m^5/m^-2)^-3
a)- 3m^4/m^2
b)-m^216
c)m^18
d)1/m^18
Answer:
option d
Step-by-step explanation:
[tex]\sf \boxed{a^m*a^n = a^{m+n}\\\\}[/tex]
[tex]\sf \left(\frac{m^{-1}m^{5}}{m^{-2}} \right)^{-3} =\left(\dfrac{m^{-1+5}}{m^{-2}}\right)^{-3}[/tex]
[tex]\sf = \left(\dfrac{m^4}{m^{-2}}\right)^{-3}\\\\[/tex]
[tex]\boxed{\dfrac{a^{m}}{a^{n}}=a^{m+n}}[/tex]
[tex]\sf = \left(m^{4-[-2]}\right)^{-3}\\\\ =\left(m^{4+2}\right)^{-3}\\\\ = \left(m^6\right)^{-3}\\\\[/tex]
[tex]\boxed{(a^{m})^n=a^{m*n}}[/tex]
[tex]\sf= m^{6*(-3)}\\\\ = m^{-18}[/tex]
[tex]\boxed{a^{-m}=\dfrac{1}{a^m}}[/tex]
[tex]\sf=\dfrac{1}{m^{18}}[/tex]
50 POINTS! Please help me! I give Brainliest!
1. Given the following coordinates, complete the listed transformations in sequence, which means you do one after the other.
X(2, 4)
Y(5,-3)
Z(-7, 1)
a) Rotate the points 90 degrees clockwise
b) Dilation by a scaling factor of 2
c) Reflect across the x-axis
d) Translation 2 Up and 5 to the Left
4 PARTS TO THIS QUESTION! ANSWER ALL PLEASE!
Answer:
Step-by-step explanation:
An electrician leans an extension ladder against the outside wall of a house so that it
reaches an electric box 31 feet up. The ladder makes an angle of 78° with the ground.
Find the length of the ladder. Round your answer to the nearest tenth of a foot if
a
necessary.
Answer:
50.41 feet
Step-by-step explanation:
Hypotenuse = length of ladder
31 = opposite side of angle
sin(angle) = (opposite)/(hypotenuse)
sin(78) = (36)/(hypotenuse)
hypotenuse = sin(78)/ (36)
hypotenuse = 50.41 feet
length of ladder = 50.41 feet
Calculate the rise and run to and the slope of each line. someone help me
Rise: -4
Run: 3
Solution:The rise is how many units we move up or down.The run is how many units we move left or right.We move down 4 units, so the rise is -4.Then, we "run" 3 units, so the run is 3.Hope it helps.
Do comment if you have any query.
If limx-b f(x)=2 and limx-b f(x)=10, then limx-b [3f(x)-4g(x)]=-34
true or false?
Answer:
True
Step-by-step explanation:
limx→b [3f(x)-4g(x)]
limx→b [3f(x)-4g(x)]= limx→b [3f(x)] - limx→b [4g(x)]
= 3[limx→b f(x)] - 4[limx→b g(x)]
Since limx→b f(x) = 2 and limx→b g(x) = 10,
= 3(2)-4(10)
= -34
Please help me with this question im really confused on it (please show work)
Answer:
SA = 434 ft^2
Step-by-step explanation:
We are going to exclude the floor since we are assuming he won't paint the floor. The shed has 5 sides since we aren't going to consider the floor.
length - L
width - W
height - H
surface area - SA
H = 8 ft
L = 14 ft
W = 7 ft
To calculate the area of each side or surface of the shed,
since there are two sides/ surfaces with the same are except for the roof, we will multiply the areas by 2.
Surface area:
SA = 2 × (W×H + L×H) + L×W
SA = 2 × (7×8 + 14×8) + 14×7
SA = 434 ft^2
there are 36 pupils in a class.the number of boys is twice the number of girls.how many are girls?
Answer:
12 girls
Step-by-step explanation:
Boys to girls ratio= 1:2
Thats means there are (1+2) 3 total parts.
So [tex]\frac{36}{3}[/tex]=12
Each part is 12 so
boys is 12*2= 24 boys
Girls id 12*1= 12 girls
Answer:
12
Step-by-step explanation:
Total number of students in class ⇒ 36
Given that,
The number of boys is twice the number of girls.
First, let us make an expression to find the number of girls.
For that, let the number of girls be x.
Number of girls ⇒ x
Number of boys ⇒ 2x
Total number of pupils ⇒ x + 2x
So,
x + 2x = 36
3x = 36
Divide both sides by 3.
x = 12
Therefore, there are 12 girls and 24 boys in the class.
100 apples in total, 65% are green, and 21% of the green apples have worms. how many apples have worms?
Answer:
14 apples are green with worms.
Step-by-step explanation:
100 apples right
65% are green
21% are green with worms
Imma pretend the first time you meant red ok....
sooo to solve this
.65*100=65 are red
.21*65=13.65 are green with worms
I NEED HALP PWEASE AND PWEASE DONT IGNORE ME EVERONE DOES THAT WHEN I PUT A QUESTION UP IM GIVING BRAINLYS OUT
Answer:
The order goes:
B
A
D
C
Step-by-step explanation:
Based on the clues joe has the least so he would be B
Terrell has the most so his would be A
Jimmy has half so he would be D
and Justin is C last option
Answer:
Clue 1: 1,4 = B
Clue 2: 1,6 = A
Clue 3: 2,4 = C
Clue 4 : 4,5 = D
ASKING AGAINN COMONN YALL
Answer:
20 units
Step-by-step explanation:
The y axis is 2-6 so subtract 6 and 2 which is 4
the x axis is 3-9 so subtract 9 and 3 which is 6
The other sides are the same
4+4+6+6= 20
PLEASE HELP FOR BRAINLIEST ;-;
Find the area of this parallelogram. Be sure to include the CORRECT UNIT in your answer.
Answer:
182ft^2
pls give brainlyist
Step-by-step explanation:
area of a parallelogram is base * hight
13ft* 14ft
182ft^2
Students were asked to simplify the expression the quantity cosecant theta minus sine theta end quantity over cosecant period Two students' work is given. (In image below)
Part A: Which student simplified the expression incorrectly? Explain the errors that were made or the formulas that were misused. (5 points)
Part B: Complete the student's solution correctly, beginning with the location of the error. (5 points)
Answer:
A. student A is correct; student B was confused by the division
B. 3: cos²(θ)/(sin(θ)csc(θ)); 4: cos²(θ)
Step-by-step explanation:
Each student correctly made use of the trig identities ...
csc(θ) = 1/sin(θ)
1 -sin²(θ) = cos²(θ)
__
A.Student A's work is correct.
Student B apparently got confused by the two denominators in Step 2, and incorrectly replaced them with their quotient instead of their product.
__
B.The transition from Step 2 can look like ...
[tex]\textsf{Step 3: }\ \dfrac{\left(\dfrac{1-\sin^2\theta}{\sin\theta}\right)}{\csc\theta}=\dfrac{1-\sin^2\theta}{\sin\theta}\cdot\dfrac{1}{\csc\theta}=\dfrac{\cos^2\theta}{(\sin\theta)(\csc\theta)}\\\\\textsf{Step 4: }\ \cos^2\theta[/tex]
What is the limit on the number of members in a limited liability company? There is no limit to the number of members in a limited liability company.
If the labor force is 300,000 workers,
but 24,000 are unemployed, what is the
unemployment percentage?
A. 3%
B. 8%
C. 18%
D. 24%
Answer:
8%
Step-by step explanation:
We are given:
Total workers: 300,000Unemployed workers: 24,000The formula to determine the percentage of unemployed workers in the total workers, we need to divide the number of unemployed works by the total workers in the labor force. Then, multiply the quotient by 100 to obtain the percentage of unemployed workers.
Formula:
[tex]\dfrac{\text{Unemployed workers}}{\text{Total workers} } \times 100 = \text{Percentage of unemployed workers}[/tex]
Substitute the given values into the formula to determine the percentage of unemployed workers in the labor force.
[tex]\implies \dfrac{\text{24,000}}{\text{300,000} } \times 100 = \text{Percentage of unemployed workers}[/tex]
Now, simplify the equation. The easiest way to simplify the equation is to temporially ignore the "100".
[tex]\implies \dfrac{\text{24,000}}{\text{300,000} } = \text{Percentage of unemployed workers}[/tex]
Then, cancel the "0's" on the L.H.S. This is a good way to simplify the equation on the L.H.S
[tex]\implies \dfrac{\text{24}}{\text{300} } = \text{Percentage of unemployed workers}[/tex]
Don't forget to multiply the result by 100 as it was temporaily hidden.
[tex]\implies \dfrac{\text{24}}{\text{300} } \times 100= \text{Percentage of unemployed workers}[/tex]
Let 100 be 100/1. Thus, our equation will be:
[tex]\implies \dfrac{\text{24}}{\text{300} } \times \dfrac{100}{1} = \text{Percentage of unemployed workers}[/tex]
Multiply the numerator with the numerator and the denominator with the denominator.
[tex]\implies \dfrac{24 \times 100}{\text{300} \times 1} } = \text{Percentage of unemployed workers}[/tex]
[tex]\implies \dfrac{2400}{\text{300} } = \text{Percentage of unemployed workers}[/tex]
Cancel the "0's" on the L.H.S to make it easier to simplify.
[tex]\implies \dfrac{2400}{\text{300} } = \text{Percentage of unemployed workers}[/tex]
[tex]\implies \dfrac{24}{\text{3} } = \text{Percentage of unemployed workers}[/tex]
[tex]\implies 8 = \text{Percentage of unemployed workers}[/tex]
Thus, 8% of the workers are unemployed workers.
the point inside a circle that is the same distance from all the points on the circle
Answer:
the center
Step-by-step explanation:
The only point in the circle that is equidistant from the border is the center, and the lines that connect the center to the points on the circle is called the radius. All radii in a circle are congruent.
Type your answer in the box. You may use numbers, a decimal point (.), and/or a negative sign (-) in
your answer.
In one design being considered for the container shaped like a cylinder, the container will have a height
of 12 inches. What will be the radius of the container, to the nearest tenth of an inch?
Please answer the question in the picture for brainliest
Answer:
26
Step-by-step explanation:
simply count the number of times the team scored more than 50 points by looking at the graph.
the team scored 51-60 points 11 times, 61-70 points 12 times and 71-80 points 3 times.
so the team scored more than 5 points a total of 11 + 12 + 3 = 26 times
Answer:
26
Step-by-step explanation:
Game scores above 50 points can be represented by the last three boxes to the left. To find the total number of times this happened, add up the values measured by the y-axis:
51-60 = 11 games
61-70 = 12 games
71-80 = 3 games
11 + 12 + 3 = 26
I hope this helps!
Randy has 1.5 gallons of sprite and 2.25 gallons of coke in his fridge. Andy has 1.15 gallons of sprite and 0.62 gallons of coke. How much more soda does Randy have than Andy?
Answer:
1.98Gal
Step-by-step explanation:
Randy soda total is 1.5 gal + 2.25 Gal = 3.75 Gal
Andy soda total is 1.15 + 0.62 Gal = 1.77 Gal
3.75-1.77=1.98Gal
1.98
Step-by-step explanation:
1.5+2.25=3.75
1.15+0.62=1.77
3.75-1.77=1.98