The length of a rectangle is 8cm greater than twice its width. Find the dimensions if the area
is 42cm
Answers
Answer:
Length [tex]14\ cm[/tex]
Width [tex]3\ cm[/tex]
Step-by-step explanation:
Let
x-----> the length of rectangle
y ----> the width of rectangle
we know that
The area of rectangle is equal to
[tex]A=xy[/tex]
[tex]A=42\ cm^{2}[/tex]
so
[tex]42=xy[/tex] ----> equation A
[tex]x=2y+8[/tex] ---> equation B
substitute equation B in equation A and solve for y
[tex]42=(2y+8)y\\ \\2y^{2}+8y-42=0[/tex]
Solve the quadratic equation by graphing
The solution is [tex]y=3\ cm[/tex]
see the attached figure
Find the value of x
[tex]x=2(3)+8=14\ cm[/tex]
therefore
Length [tex]14\ cm[/tex]
Width [tex]3\ cm[/tex]
The dimensions of the rectangle are: Width ( W = 3 ) cm and Length ( L = 14 ) cm
We are given that the length L is 8 cm greater than twice its width W. This can be expressed as:
[tex]\[ L = 2W + 8 \][/tex]
The area of the rectangle is given by the formula:
[tex]\[ A = L \times W \][/tex]
Given that the area is 42 cm², we can write:
[tex]\[ 42 = (2W + 8) \times W \][/tex]
Expanding the equation:
[tex]\[ 42 = 2W^2 + 8W \][/tex]
Rearranging the equation in standard quadratic form:
[tex]\[ 2W^2 + 8W - 42 = 0 \][/tex]
Now, let's solve this quadratic equation for ( W ). We can use the quadratic formula:
[tex]\[ W = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]
Where:
- a = 2
- b = 8
- c = -42
Now, let's substitute the values into the quadratic formula:
[tex]\[ W = \frac{{-8 \pm \sqrt{{8^2 - 4 \times 2 \times (-42)}}}}{{2 \times 2}} \]\[ W = \frac{{-8 \pm \sqrt{{64 + 336}}}}{{4}} \]\[ W = \frac{{-8 \pm \sqrt{{400}}}}{{4}} \]\[ W = \frac{{-8 \pm 20}}{{4}} \][/tex]
Now, we have two possible values for \( W \):
[tex]\[ W_1 = \frac{{-8 + 20}}{{4}} = \frac{{12}}{{4}} = 3 \]\[ W_2 = \frac{{-8 - 20}}{{4}} = \frac{{-28}}{{4}} = -7 \][/tex]
Since the width cannot be negative, we discard [tex]\( W_2 = -7 \)[/tex]. Thus, the width of the rectangle is ( W = 3 ) cm.
Now, let's find the length using the equation ( L = 2W + 8 ):
[tex]\[ L = 2 \times 3 + 8 \]\[ L = 6 + 8 \]\[ L = 14 \][/tex]
Related Questions
im very confused on finding y
Answers
Answer:
In this case, you can use the concept of cosine to calculate y, and things are even easier when you have one of the special angles which is a 45° angle.
So we know that: cos45° = √2/2
This fact will always be true. In our case, we have:
cos45° = 7/y
Therefore, we have the equation:
7/y = √2/2
⇔ 14 = y√2
⇔ y = 14/√2
⇔ y = √196/√2 = √(196/2) = √98 = 7√2
So y is equal to 7√2
Answer:
7√2
Step-by-step explanation:
By observation, we can determine that because this is a right angle triangle with one of the internal angles = 45°, that the remaining unknown angle is also 45°, which makes this an isosceles triangle.
This means that x = 7
we can find y by using the Pythagorean equation:
y² = x² + 7²
y² = 7² + 7²
y² = 98
y = √98 = 7√2
[tex] \sqrt{28 } + \sqrt{343} \div 2 \sqrt{63 } [/tex]
Answers
Answer:
Step-by-step explanation:
sqrt(28): sqrt(4*7)
sqrt(4) = 2;
sqrt28)=2*sqrt(7)
sqrt(343): sqrt(7 * 7 * 7) = 7 * sqrt(7)
Note: the rule is if you have 3 equal primes under the root sign, you leave one, you throw one away, and you put one outside the root sign.
2 sqrt(63) = 2 sqrt(3*3*7) The above rule gets modified to throw 1 three away and take the other one outside the root sign.
2sqrt(63) = 2*3 sqrt(7)
Numerator: 2*sqrt(7) + 7sqrt(7) = 9sqrt(7)
9sqrt(7)
======
6 sqrt(7)
3/2
Note without brackets I cannot be certain that I have interpreted this correctly. The division only apply to sqrt(343) / 2 sqrt(63). If this is so please leave a note.
find the multiplicative inverse, or reciprocal, of 5/9?
Answers
The multiplicative inverse (or reciprocal) is the number by which you multiply another to get a product of 1. For any fraction, simply switch the numerator and the denominator. For any whole number, place it under 1.
The reciprocal of 5/9 is 9/5.
Hope this helps!!
Hello There!
To find the reciprocal of a number, just flip the numerator and the denominator so if the numerator is 5 and the denominator is 9, the new numerator would be 9 and the new denominator would be 5.
Our multiplicative inverse of 5/9 is
[tex]\frac{9}{5}[/tex]
Arianne is taking a geometry course and is working with the area of triangles. She knows the area and the height but needs to find the base. Rearrange the following equation for b, where A is the area, b is the base, and h is the height of the triangle.
A = one half b times h
A.b = 2A − h
B.b equals two times A over h
C.b = 2A + h
D.b = 2Ah
Answers
Answer:
B
Step-by-step explanation:
Area of a triangle is given by the formula:
[tex]A=\frac{1}{2}bh[/tex]
Now, we need to solve for b. We multiply the right side, cross multiply, and follow rules of algebra to isolate b. Shown below:
[tex]A=\frac{1}{2}bh\\A=\frac{bh}{2}\\2A=bh\\b=\frac{2A}{h}[/tex]
Thus, b is 2 times A over h, the answer choice B is right.
Answer:
The Answer is B. b equals two times A over h
Hope This Helps!
versity City Geometry 1.2 - CR (9/17)
Equation on a circle
Pre-Test Active
Which equation represents a circle with a center at (-3,-5) and a radius of 6 units?
(x - 3)2 + (-5)2 = 6
(x - 3)2 + (-5)2 = 36
(x + 3)2 + (y + 5)2 = 6
(x+3)2 + (x + 5)2 = 36
Mark this and return
Save and Exit
Next
Answers
Answer:
[tex](x+3)^{2}+(y+5)^{2}=36[/tex]
Step-by-step explanation:
we know that
The equation of a circle in standard form is equal to
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
In this problem we have
[tex](h,k)=(-3,-5)[/tex]
[tex]r= 6\ units[/tex]
substitute
[tex](x+3)^{2}+(y+5)^{2}=6^{2}[/tex]
[tex](x+3)^{2}+(y+5)^{2}=36[/tex]
Tom is riding his bike to the store. After 2
minutes he has traveled 3 blocks, after 6
minutes, he has traveled 9 blocks. Find his
average speed in blocks per minute.
O 1.5 blocks per minute
O 2/3 blocks per minute
O 3.2 blocks per minute
06 blocks per minute
Answers
The answer is:
The correct option is the first option, the average speed in blocks per minute is 1.5 blocks per minute.
[tex]AverageSpeed=1.5\frac{Block}{minute}[/tex]
Why?To calculate the average speed we need to calculate the total distance traveled and the total time taken to cover that distance.
From the statement we know that:
[tex]Distance_{1}=3blocks\\Distance_{2}=9blocks-3blocks=6blocks\\time_{1}=2minutes\\time_{2}=6minutes[/tex]
So, we need to use the following formula in order to calculate the average speed:
[tex]AverageSpeed=\frac{distance_{1}+distance_{2}}{t_{1}+t_{2}}[/tex]
Then, substituting we have:
[tex]AverageSpeed=\frac{3blocks+9blocks}{2minutes+6minutes}[/tex]
[tex]AverageSpeed=\frac{12blocks}{8minutes}=1.5\frac{blocks}{minutes}[/tex]
Hence, we have that the correct option is the first option, the average speed in blocks per minute is 1.5 blocks per minute.
[tex]AverageSpeed=1.5\frac{Block}{minute}[/tex]
Have a nice day!
The slope of a graphed line is -9 and the y-intercept is (0, -2). What is the
slope-intercept equation of the line?
Answers
Answer:
y = -9x - 2Step-by-step explanation:
The slope-intercept form of an equation of a line:
y = mx + b
m - slope
b - y-intercept (0, b)
We have the slope m = -9 and the y-intercept (0, -2) → b = -2.
Substitute:
y = -9x + (-2) = -9x - 2
The slope-intercept equation of a line with a slope of -9 and a y-intercept of (0, -2) is y = -9x - 2.
The slope-intercept equation of a line is in the form y = mx + b, where m is the slope and b is the y-intercept.
Given a slope of -9 and a y-intercept of (0, -2), the slope-intercept equation is y = -9x - 2.
Therefore, the slope-intercept equation of the line is y = -9x - 2.
Solve the equation g2 – 12g = –36
A. g = –6
B. g = 6
C. g = –3, g = 4
D. g = –6, g = 6
Answers
Answer:
g=6
Step-by-step explanation:
[tex]g^{2} -12=-36\\g^{2} -12+36\\ (g-6)(g-6)\\ g-6=0\\ g=6[/tex]
What is the tan of angle B
Answers
Answer:
2.4
Step-by-step explanation:
tanB = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{12}{5}[/tex] = 2.4
Answer: 2.4
Step-by-step explanation:
[tex]tan\theta=\dfrac{opposite}{adjacent}\\\\\\tan\angle B=\dfrac{12}{5}\\\\\\tan\angle B=2.4[/tex]
What is the name of the relationship between ∠1 and ∠8
Answers
Answer: alternate exterior angles
Step-by-step explanation:
If f(–5) = 0, what are all the factors of the function ? Use the Remainder Theorem.
a. (x – 2)(x + 5)(x – 3)
b. (x + 2)(x – 5)(x + 3)
c. (x – 2)(x + 5)
d. (x + 2)(x – 5)
Answers
Answer:
Without any other information the answers could be a and c because they contain the factor x+5
Step-by-step explanation:
f(-5)=0 means that x=-5 is a zero which means x+5 is a factor
Without any other information f can be any of the expressions that have the factor (x+5)
Answer:
A. (x-2)(x+5)(x-3) is the correct answer to this question
Hope it helps!
A number between 49 and 95 that is a multiple of 4,5, and 10?
Answers
Answer: 60 and 80
Step-by-step explanation: Start off with the highest number, which is 10. The numbers between 49 and 95 that can be divided by 10 are 50, 60, 70, 80, and 90. Next, figure out what can be divided by 5. All of them can. Next, find out what numbers can be divided by 4. 50, 70, and 90 can’t because they would end up as a decimals. 60 and 80 can be divided by 4, 5, and 10.
Evaluate 2(x + 1) - 3 when x = 6.
Answers
Evaluate 2(x + 1) - 3 when x = 6.
First, plug in x value.
2(6 + 1) -3 ParenthesisEMDAS
2(7) - 3 PEMultiplyDAS
14 - 3 PEMDASubtract
11 ←
Answer:
11
Step-by-step explanation:
just took test
In Mexico people use pesos for money. There are about 12.8 pesos in 1 dollar. About how much is 1 peso worth in dollars? Show your work, and give your answer to the nearest hundredth of a dollar and a nursing.
Answers
Answer:
$0.08 (rounded to nearest hundredth, 2 decimals)
Step-by-step explanation:
This is very easy if we setup a unitary method ratio.
" If 12.8 pesos equal 1 dollar, 1 peso is HOW MANY (let it be x) dollars?"
We translate the above sentence in ratio and solve for x:
[tex]\frac{Peso}{Dollar}=\frac{12.8}{1}=\frac{1}{x}\\12.8x=1\\x=\frac{1}{12.8}\\x=0.08[/tex]
Thus, it is worth about $0.08
20m to 21m what is the percentage change
Answers
Answer: The correct answer is: " 5% increase " .
_________________________________________
Step-by-step explanation:
_________________________________________
Note: The particular "percentage change" is a "percent increase" ; since we are going from "20" to "21" which is an "increased value of "1" .
_________________________________________
Note the formula for "percent increase" ; as follows:
_________________________________________
Percent increase = [(new value - original value)/original value] * 100 ;
_________________________________________
So; let us "plug in" our known values; to solve for the "percentage change"
→ [i.e. "percent increase" (in this case)] :
_________________________________________
Percent increase = [(21 - 20)/20] * 100 ;
= [1/20] * 100 ;
= [100/20] ;
= 5.
_________________________________________
The correct answer is: " 5 % increase" .
_________________________________________
Hope this helps!
Best wishes to you!
_________________________________________
Find the slope and the y-intercept of the line whose equation is 5x+y = −5.
Answers
Answer:
slope is -5
y-intercept is -5
Step-by-step explanation:
Solve for y to write in y=mx+b
m is slope
b is y-intercept
5x+y=-5
Subtract 5x on both sides
y=-5x-5
slope is -5
y-intercept is -5
Minus 5x to isolate y
Y= -5x - 5
The slope is -5x and y-intercept is -5
Hope this helps!
Please mark me as brainliest if you can. I really appreciate it!
1.00
Given the following functions f(x) and g(x), solve (f + g)(3) and select the correct answer below:
f(x) = 2x + 21
g(x) = x - 24
0-27
0-21
06
48
Answers
Answer:
6
Step-by-step explanation:
Plug in 3 into both expressions
Then add those results
2(3)+21=6+21=27
3-24 =-21
-------
6 is the sum of 27 and -21
| 16+(-4)-7-
[tex]16 + ( - 4) - 7 = [/tex]
Answers
Answer:
Step-by-step explanation:
16+(-4)-7=16 -(4+7)=16-28 = -12
PQ=RQ a=?
Please need help!!
Answers
as 180-140= 40 , 40 x 2 = 80 & 180-80 = 100° = a
Answer:
100 Degrees
Step-by-step explanation:
It's correct for Acellus! :-)
Graph ARST with vertices R(6, 6), S(3, -6), and T(0, 3) and its image after a
reflection over the y-axis.
Answers
Answer:
The answer is the second figure and the vertices of Δ R'S'T' are:
R' = (-6 , 6) , S' = (-3 , -6) , T' = (0 , 3)
Step-by-step explanation:
* Lets revise some transformation
- If point (x , y) reflected across the x-axis
∴ Its image is (x , -y)
- If point (x , y) reflected across the y-axis
∴ Its image is (-x , y)
- If point (x , y) reflected across the line y = x
∴ Its image is (y , x)
- If point (x , y) reflected across the line y = -x
∴ Its image is (-y , -x)
- Now we can solve the problem
∵ R = (6 , 6) , S = (3 , -6) , T = (0 , 3), they are the vertices of ΔRST
- The triangle RST is reflected over the y-axis
- According to the rule above the signs of x-coordinates will change
∵ R = (6 , 6)
∴ Its image is (-6 , 6)
∵ S = (3 , -6)
∴ Its image is (-3 , -6)
∵ T = (0 , 3)
∴ Its image is (0 , 3)
* Now lets look to the figure to find the correct answers
- The image of Δ RST is ΔR'S'T'
∵ The vertices of the image of ΔRST are:
R' = (-6 , 6) , S' = (-3 , -6) , T' = (0 , 3)
* The answer is the second figure
Find the most common ratio 72,12,2, 1/3,1/18
Answers
Answer:
1/6
Step-by-step explanation:
To find the common ratio, you compare a few pairs of consecutive terms, by dividing an element by its predecessor.
12 / 72 = 1/6
2 / 12 = 1 / 6
1/3 / 2 = 1 / 6
The ratio is constant... so that's your common ratio to go from one term to the next.
To go from one term to the next, you have to multiply by 1/6.
What is 1/2 X (6 X 4)+3 + 2 Please show your work
Answers
Answer:
17Step-by-step explanation:
Use PEMDAS:
P Parentheses first
E Exponents (ie Powers and Square Roots, etc.)
MD Multiplication and Division (left-to-right)
AS Addition and Subtraction (left-to-right)
[tex]\dfrac{1}{2}\times\underbrace{(6\times4)}_{1}+3+2\\\\=\underbrace{\dfrac{1}{2}\times24}_{2}+3+2\\\\=12+3+2=17[/tex]
Find the slope of (-2,-5) and (8,-5) And find the slope of the line passing through the points (4,9) and (4,-7)
Answers
Answer:
Part 1) [tex]m=0[/tex]
Part 2) The slope is undefined
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Part 1
we have
[tex]A(-2,-5)\ B(8,-5)[/tex]
Substitute the values
[tex]m=\frac{-5+5}{8+2}[/tex]
[tex]m=\frac{0}{10}[/tex]
[tex]m=0[/tex] ----> is a horizontal line (parallel to x-axis)
Part 2
we have
[tex]A(4,9)\ B(4,-7)[/tex]
Substitute the values
[tex]m=\frac{-7-9}{4-4}[/tex]
[tex]m=\frac{-16}{0}[/tex] ----> is a vertical line (parallel to y-axis)
The slope is undefined
(if f(x)=4x^2 and g(x)=x+1, find (f o g)(x)
Answers
Answer:
f(g(x)) = x² + 2x +1
Step-by-step explanation:
The given functions are:
f(x) = 4x²
g(x) = x+1
f(x) = 4x²
(fog)(x) = f(g(x))
f(g(x)) = 4(x+1)² [f(x) = x² ]
we know that (a+b)² = a² + b² + 2ab
f(g(x)) = 4(x²+1²+2(x)(1))
f(g(x)) = 4(x² + 1 + 2x )
f(g(x)) = 4x² + 8x +4
Viktor picked 4 pounds of cherries. How many containers did he need if he put 2/7 pound of cherries into each container?
Answers
Answer:
13.9 containers or 14 rounded
Step-by-step explanation:
2/7 of a pound is 0.28571429 in decimal form. To solve you have to know how many 2/7 of a pound will go into 4 pounds. So you divide 2/7 of a pound by 4 pounds, and the answer is 14.
Answer:
14
Step-by-step explanation:
He will need 14 containers. 4 times 7/2 is 28/2. You then have to simplify it and will get 14.
What is the product of 6 and n
Answers
Answer:
6n
Step-by-step explanation:
Lesson: ⇒ Algebric Expression
Product: ⇒ multiply
6n is the correct answer.
I hope this helps you, and have a wonderful day!
does 1/3 have a greater unit rate than 2/3
Answers
Answer: No, because 1/3 is smaller than 2/3
Hope this helps :)
Step-by-step explanation:
find the measurement of the indicated angle to the nearest degree
Answers
Answer:
54°
Step-by-step explanation:
Since the triangle is right use the cosine ratio to solve for angle
cos? = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{26}{44}[/tex], hence
? = [tex]cos^{-1}[/tex] ( [tex]\frac{26}{44}[/tex] ) ≈ 54° ( nearest degree )
Which is equivalent
Answers
For this case we must find an expression equivalent to:
[tex](x ^ {\frac {4} {3}} * x ^ {\frac {2} {3}}) ^ {\frac {1} {3}}[/tex]
By definition of power properties we have to:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
So, rewriting the expression we have:
[tex]x ^ {\frac {4} {3 * 3}} * x ^ {\frac {2} {3 * 3}} =[/tex]
[tex]x ^ {\frac {4} {9}} * x ^ {\frac {2} {9}} =[/tex]
By definition of multiplication of powers of the same base, we put the same base and add the exponents:
[tex]x ^ {\frac {4} {9} + \frac {2} {9}} =\\x ^ {\frac {4 + 2} {9}} =\\x ^ {\frac {6} {9}} =\\x ^ {\frac {2} {3}}[/tex]
Answer:
Option B
Answer:
[tex]x^{2/3}[/tex]
Step-by-step explanation:
The question is on rules of rational exponents
Here we apply the formulae for product rule where;
[tex]= a^{n} *a^{t} = a^{n+t} \\\\\\\\=(x^{4/3} *x^{2/3} ) = x^{4/3 + 2/3} = x^{6/3} = x^{2} \\\\\\=(x^2)^{1/3} \\\\\\=\sqrt[3]{x^2}[/tex]
[tex]=x^{2/3}[/tex]
What substitution Should be used to re-write 26(x^3+1)^2-22(x^3+1)-3=0 as a quadratic function?
Answers
Answer:
[tex]x^3+1[/tex]
Step-by-step explanation:
[tex] 26(x^3+1)^2-22(x^3+1)-3=0 [/tex]
Comparing to
[tex] A(u)^2+B(u)+C =0 [/tex]
Where A,B,C are constants
You should see that we need to substitute the [tex]x^3+1[/tex] with u.