2 possible solutions.
When width is 4 cm, length is 20 cm; When width is 20 cm, length is 4 cm
Step-by-step explanation:
Step 1: Let the width of the rectangle be x. Perimeter of the rectangle = 48 cm. Find expression for length.Perimeter of the rectangle = 2(length + width)
48 = 2(length + x)
24 = length + x
⇒ Length = 24 - x
Step 2: Find the dimensions if area = 80 cmArea of the rectangle = length × width
80 = x (24 - x)
80 = 24x - x²
x² - 24x + 80 = 0
x² - 20x - 4x + 80 = 0
x(x - 20) - 4(x - 20) = 0
(x - 4)(x - 20) = 0
⇒ x = 4, 20
24 - x = 20, 4
So there are two possible answers.
When width is 4 cm, length is 20 cm
When width is 20 cm, length is 4 cm
CAN SOMEONE PLEASE SOLVE THIS?????????? NEED HELP!!!!!!!!!!!!!!!!!!!
Answer:
x = 9, GH = 21, CD = 17
Step-by-step explanation:
Quadrilateral CDEF is a trapezoid in which G and H are mid points of the sides CF and DE respectively.
In a trapezoid, segment joining the mid points is equal to the half of the sum of the parallel sides.
[tex] \therefore \: GH = \frac{1}{2} (CD + FE) \\ \\ \therefore \:3x - 6 =\frac{1}{2} (2x - 1 + 25) \\ \\ \therefore \:3x - 6 =\frac{1}{2} (2x + 24) \\ \\ \therefore \:3x - 6 =\frac{1}{2} \times 2 (x + 12) \\ \\ \therefore \:3x - 6 = x + 12 \\ \\ \therefore \:3x - x = 12 + 6 \\ \\ \therefore \:2x = 18 \\ \\ \therefore \:x = \frac{18}{2} \\ \\ \huge\red{ \boxed{\therefore \:x = 9}} \\\\ \because \overline{GH} = 3x - 6 \\ \\\therefore \:\overline{GH} =3 \times 9 - 6 \\ \\ \therefore \:\overline{GH} =27 - 6 \\ \\ \huge\purple{ \boxed{\therefore \:\overline{GH} =21}} \\ \\ \because\overline{CD} = 2x - 1 \\\\ \therefore \:\overline{CD} =2 \times 9 - 1 \\ \\ \therefore \:\overline{CD} =18 - 1 \\ \\ \huge\pink{ \boxed{\therefore \:\overline{CD} =17}} \\ \\ [/tex]
The hypotenuse of a right triangle is 10m and the length of one of the legs is 8m , find the length of the other leg of the triangle
Answer:
6 m
Step-by-step explanation:
a squared + b squared = c squared
8 squared plus ? squared = 10 squared
64 + ? = 100
100 - 64 = 36
the square root of 36 is 6
Final answer:
Using the Pythagorean theorem, the length of the other leg of the right triangle is found to be 6 meters.
Explanation:
The student is asking to find the length of the other leg of a right triangle, given the lengths of the hypotenuse (10m) and one leg (8m). To solve this problem, we use the Pythagorean theorem, which relates the lengths of the sides of a right triangle: a² + b² = c², where c is the hypotenuse and a and b are the legs of the triangle. Since the hypotenuse length (c) is 10m and one leg (a) is 8m, we can solve for the length of the other leg (b) using the equation 8² + b² = 10².
First, square the known length of one leg: 8² = 64.
Next, square the hypotenuse: 10² = 100.
Now, subtract the squared length of the known leg from the squared hypotenuse to find b²: 100 - 64 = 36.
Finally, take the square root of 36 to find b: √36 = 6m. So, the length of the other leg is 6 meters.
Given a+b=7 and a–b=3, find:
3^a/3^b
Answer:
A=-2 and B=3
Step-by-step explanation:
Step 1) Solve the first equation for A:
a+3b=7
a+3b-3b=7-3b
a+0=7-3b
a=7-3b
Step 2) Substitute (7-3b) for a in the second equation and solve for b:
2a=b-7 becomes:
2(7-3b)=b-7
(2*7)-(2*3b)=b-7
14-6b=b-7
14+7-6b+6b=b+6b-7+7
21-0=1b+6b-0
21=(1+6)b
21=7b
7b/7=21/7
=3
a=7-3b becomes:
a=7-(3*3)
a=7-9
a=-2
Answer:
27
Step-by-step explanation:
Find numbers that add up to 7.
0, 1, 2, 3, 4, 5, 6, 7
Which of those could subtract to get 3?
5 and 2
5 - 2 = 3
a = 5
b = 2
3^5 = 243
3^2 = 9
243 / 9 = 27
What is the arithmetic mean of the following numbers? 3, 5, 6, 2, 9
Answer:
5
Step-by-step explanation:
3+5+6+2+9=25
25/5=5
Answer:
5
Step-by-step explanation:
The mean of a set of numbers is (sum of numbers)/(number of values)
The sum of the values is 3 + 5 + 6 + 2 + 9 = 25
The number of values is 5
25/5 = 5
4 strips of paneling 40cm long and 4cm wide are arranged to form a square. What is the area of the inner square in cm
The area of the square will be 640 sq cm.
Step-by-step explanation:
Given,
Number of strip = 4
Length (l) of each strip = 40 cm
Width (b) of each strip = 4 cm
To find the area of the inner square.
Formula
The area of rectangle = l×b
If the area of a square is A, each side will be √A
Now,
Area of each strip = 40×4 sq cm = 160 sq cm
Area of 4 strips = 160×4 sq cm = 640 sq cm
Hence,
The area of the square will be 640 sq cm.
how do I simplify this? -4k - 13 + 6k +23
-4k + 6k -13 +23
2k +10
you can even write it like this:
2 ( k+ 5)
Can someone pls help me
Simplify:
[tex] \frac{21x {}^{6} {y}^{5} }{ {14x}^{2} {y}^{9} }[/tex]
Look at the attached picture ⤴
Hope it will help u...
Solve the equation
8 + 10 = 14
Answer:
4
Step-by-step explanation:
8+10
= 18
18-14
=4
Answer:
Step-by-step explanation:
8+10=14? 8-10= 2 2+8=10 8+10=18.....This is what I am think....
I am not sure..
A number is selected at random from the set (2, 3, 4, ... 10). Which eventby definition, covers the entire sample space of this experiment?
A.
The number is greater than 2.
OB.
The number is not divisible by 5.
C.
The number is even or less than 12.
OD. The number is neither prime nor composite.
E.
The square root of the number is less than 3.
Answer:
C
Step-by-step explanation:
A doesn't include the term "2"
B doesn't include "5" or "10"
D doesn't include "10"
SO... it's C
Use a calculator to solve for xin the equation 2e^3x = 400. Round your answer to
three decimals.
To solve the equation 2e^3x = 400, we isolate e^3x and then use the natural logarithm to solve for x, which gives x ≈ 2.995 when rounded to three decimals.
Explanation:The question asks us to solve the equation 2e^3x = 400 for the variable x. First, we isolate e^3x by dividing both sides of the equation by 2. We get: e^3x = 400/2 which is e^3x = 200. Finding x means solving for 'x' in an exponential equation, which involves using the natural logarithm.
So, our equation becomes: x = ln(200)/3. Using a calculator, x ≈ 2.995 when rounded to three decimals.
Learn more about Solving Exponential Equations#SPJ2Joseph opens a checking account with $400. each month he adds $150 to the account wright an equation representing the total amount A in the account at the end of any given month M
Answer:
[tex]A=400+150m[/tex]
Step-by-step explanation:
since 'A' is the final amount it acts as the 'y' value, and if it's 150 per month then you would multiply the number of months (m) by 150 plus the 400 that was already there.
Question 2 and 3, if u just feel like answering one that’s okay
Answer:
[tex]w^{20}[/tex]; [tex]y^7[/tex]
Step-by-step explanation:
[tex](w^4)^5=\\w^{4*5}=\\w^{20}\\\\\frac{y^9}{y^2}=\\ y^{9-2}=\\y^7[/tex]
Answer:
1) =W20
2=Y7
Both 20 and 7 are exponents but i cannot type them in that format since I am on a computer. Hope this helps!
Step-by-step explanation:
Tim's piggy bank contains dimes and nickels worth $5.50. He has 70 coins in all. Use substitution to solve the system of equations to find out how many of each coin Tim has.
Tim has a total of 30 nickels and 40 dimes.
What is Linear Equation?Linear equations are the equations which consist of two or more variables having the exponent of the variable equals 1.
Total number of coins in the Tim's piggy bank = 70 coins
Let d be the number of dime coins and n be the number of nickel coins.
So d + n = 70
Total dollars = $5.50
10 dimes = 1 dollar
1 dime = 1/10 dollar = 0.1 dollar
20 nickels = 1 dollar
1 nickel = 1/20 dollar = 0.05 dollar
0.1 d + 0.05 n = 5.50
So we have two linear equations here : d + n = 70 and 0.1 d + 0.05 n = 5.50.
d + n = 70 ⇒ d = 70 - n
Substituting d = 70 - n in the equation 0.1 d + 0.05 n = 5.50,
0.1 (70 - n) + 0.05 n = 5.50
(0.1 × 70) - 0.1n + 0.05n = 5.50
7 - 0.05n = 5.50
-0.05n = -1.5
n = 30
So d = 70 - n = 70 - 30 = 40
Hence the number of nickel coins is 30 and number of dime coins is 40.
Learn more about Linear Equations here :
https://brainly.com/question/29739212
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Consider the original complex figure and the reduction.
Figures not drawn to scale.
What is the scale factor of the reduction?
1/8
1/5
5
9
Answer:
1/8
Step-by-step explanation:
I'm going to try to explain this as easy as possible. What I did was take the original shape and divide it by the new shape. For this question, I solved it by dividing 32(the original base) by 4(the new base) and got 8. So the scale factor of the reduction was 1/8.
Answer:
1/8
Step-by-step explanation:
The only one that makes sense
In a bag of 18
18
oranges, 12
12
have gone bad.
What is the ratio of good oranges to bad oranges?
Answer:
1 :2
Step-by-step explanation:
18 oranges
12 bad
-------
6 good
good: bad
6 :12
Divide each by 6
6/6 : 12/6
1 :2
The ratio of good oranges to bad oranges is 1:2.
To find the ratio of good oranges to bad oranges in a bag containing 18 oranges, where 12 oranges have gone bad, follow these steps:
Determine the number of good oranges:
Total oranges in the bag: 18Bad oranges: 12Good oranges: 18 - 12 = 6Find the ratio of good oranges to bad oranges:
Good oranges: 6Bad oranges: 12Simplify the ratio:
The ratio of good oranges to bad oranges can be written as 6:12.Simplify this by dividing both numbers by their greatest common divisor (GCD), which is 6.Simplified ratio: 6 ÷ 6 : 12 ÷ 6 = 1:2
May You Please Help Me? :(
In triangle ABC, the length of side AB is 11 inches and the length of side BC is 18 inches. Which of the following could be the length of side AC?
1. 5 inches
2. 31 Inches
3. 34 inches
4. 19 inches
V= u + at
u = 2 a = -5 t = 1/2
Work out the value of v.
Answer:
-0.5
Step-by-step explanation:
2+-5x1/2
-5x1/2=-2.5
2+-2.5=-0.5
Answer:
-1/2
Step-by-step explanation:
u=2
a=-5
t=1/2
Using
v=u+at
v= 2+(-5×1/2)
v=2+(-5/2)
v=2-5/2
v= -1/2
Find the area of each trapezoid.
Does anyone knows how to solve this question??
Answer:
24
Step-by-step explanation:
cos(x) is just a trigonometric function. To find it on a right triangle, you take the "adjacent" side, which should be the side next to the angle x, and divide it by the hypotenuse.
In this case, the adjacent side is 12. We don't know the hypotenuse, but we can figure it out using the Pythagorean Theorem: [tex]\sqrt{9^{2}+12^{2}}[/tex] = [tex]\sqrt{225}[/tex] = 15. So, the hypotenuse is 15.
Thus, cos(x) = 12/15 = 4/5. We want 30 * cos(x), so we get: 30 * (4/5) = 24, and that is our answer.
Answer:
24
Step-by-step explanation:
From the mnemonic SOHCAHTOA you would know that cos x = adjacent/hypotenuse.
Adjacent side is given as 12, but we must calculate the hypotenuse.
For that we use Pythagoras.
hypotenuse = √(9²+12²) = 15
Now you can calculate
30×cos(x) = 30×12/15 = 24
Find the area of the semicircle.
Either enter an exact answer in terms of
or use 3.14 for and enter your answer as a decimal.
units
Answer:
8 pie
Step-by-step explanation:
area of a circle is pie(radius squared)
radius is 4
4 squared is 16
divide by two because its a semi circle
Answer:
8pi
Step-by-step explanation:
A=pi*r^2
A=pi(4^2)
A=16pi
16pi would be the area if the circle was complete, but since this is a semicircle you just have to divide by two which would give us:
A=8pi
A traveler is driving across the country and spots Gateway Arch in St. Louis, Missouri. She has read that the arch is 630 feet tall. Her angle of elevation to the top of the arch is 3º. How far away is Gateway Arch, to the nearest tenth of a mile?
Answer:
d = 12,021.1 ft
The Gateway Arch is 12,021.1 ft away
Step-by-step explanation:
Given;
Angle of elevation = 3°
Height of arch = 630 ft
Tanθ = opposite/adjacent
Opposite = 630 ft
Adjacent = d
Substituting the values;
Tan3 = 630/d
d = 630/tan3
d = 12,021.1 ft
The Gateway Arch is 12,021.1 ft away
Answer:
[tex]x = 12021.1\,ft\,(2.3\,mi)[/tex]
Step-by-step explanation:
The distance is given by the following trigonometric equation:
[tex]x = \frac{y}{\tan \alpha}[/tex]
[tex]x = \frac{630\,ft}{\tan 3^{\textdegree}}[/tex]
[tex]x = 12021.1\,ft\,(2.3\,mi)[/tex]
What is the value of h in the equation 3h-4=15+2?
Answer:
The value of h is 7.
Step-by-step explanation:
3h - 4 = 15 + 2
15 + 2 = 17
3h - 4 = 17
Add 4 to each side
3h = 21
Divide each side by 3
h = 7
How does the risk of needing insurance impact the cost of premiums?
A. In some cases, higher risk results in lower costs.
B. Higher risk always results in lower costs.
C. Higher risk always results in higher costs.
D. In some cases, higher risk results in higher costs.
Answer:
D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
because when you go to get health insurance, they never want to have to pay alot. for instance, when you smoke, do risky activities, etc. that ups the risks, making your health insurance cost much more to cover for the costs of the doctors appointments, screenings, and tests that come along with those risks. this is the answer on PLATO. please make me brainliest !
Order the following from greatest to least -12, 12, -19, 1 1/2(BTW this is a mixed number ;-; ) , 5
PLEASE HELP ME!!!!!
Answer:
12, 5, 1 1/2, -12, -19
Step-by-step explanation:
hope this helped!
In a class of 150 students, 95 are taking Math, 75 are taking Science and 55 are taking both.What is the probability that a student is taking neither Math or science?
Answer:
[tex] \frac{7}{30} [/tex]
Step-by-step explanation:
In a class of 150 students, 95 are taking Math, 75 are taking Science and 55 are taking both.
We want to determine the probability that a student is taking neither Math or science.
The number taking only Math is
[tex] = 95 - 55 = 40[/tex]
The number taking only Science
[tex] = 75 - 55 = 20[/tex]
The number of students taking Math, Science, or both
[tex] = 40 + 55 + 20 = 115[/tex]
The number taking neither Mathematics or Science
[tex] = 150 - 115 = 35[/tex]
The probability that a student is taking neither Math or science
[tex] = \frac{35}{150} [/tex]
[tex] = \frac{7}{30} [/tex]
What is x rounded to the nearest tenth please help
Answer:
8.9
Step-by-step explanation:
!!!!!HURRY!!!!!!
Bethany used the steps below in an attempt to solve for angle B in triangle ABC.
Where is bethanys error?
The measure of angle B in triangle ABC is 63.9°. Hence, Bethany has done a mistake in step 2.
Given that, in the triangle ABC, AC=4.1 cm, AB=4.5 cm and BC=2.7 cm.
We need to find the measure of angle B.
What is the trigonometric function to find the angle in the triangle?The trigonometric function to find the angle in the triangle is b²=a²+c²-2ac cosB.
Now, (4.1)²=(4.5)²+(2.7)²-2×4.5×2.7 cosB.
⇒16.81=20.25+7.29-24.3 cosB
⇒16.81-27.54=-24.3 cos B
⇒cos B=0.44
⇒B=63.9°
The measure of angle B in triangle ABC is 63.9°. Hence, Bethany has done a mistake in step 2.
To learn more about the angles of a triangle visit:
https://brainly.com/question/27682397.
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Answer:
B. Bethany took the square root of each squared term before isolating cosB and solving for B.
Step-by-step explanation:
took the quiz
Please help meh please.
Answer:
d. 84.5
Step-by-step explanation:
You will have to put the numbers in order than cross out one from each side;
70x
80x
83
86
88x
88x
In doing this you have taken out B,E, and F. The answer would have to be somewhere in between 83 and 86, which would be around 84 and 85, so therefore the answer would be 84.5
How many different ways can 9 trumpet players in the marching band line up?
Answer:
362880 ways
Step-by-step explanation:
In this case, the order does matter therefore to know how many ways it can be aligned, we must resort to permutations.
The formula for permutations is:
P = n!
we know that there are 9 trumpet players, therefore:
P = 9!
P = 362880
So there are 362,880 ways to line up
If r is an integer greater than 1, what is the value of (−1)r +1 if: a r is an odd integer
Answer:
The value of the given expresion is zero.
Step-by-step explanation:
I am assuming that, your exprssion is
[tex] {( - 1)}^{r} + 1[/tex]
where r is an integer greater than 1.
Let us see what a negative base 1 to an off exponent give us:
[tex] {( - 1)}^{1} =-1[/tex]
[tex] {( - 1)}^{3} =-1[/tex]
[tex] {( - 1)}^{5} =-1[/tex]
[tex] {( - 1)}^{7} =-1[/tex]
If r is odd, then
[tex] {( - 1)}^{r} = - 1[/tex]
This implies that:
[tex] {( - 1)}^{r} + 1 = - 1 + 1 = 0[/tex]
The value of the given expresion is 0.