If the length of the rectangle is x, then we know the width is x + 1.
The area of a rectangle is length · width, so we can substitute as x · (x + 1)
Now, we now x · (x + 1) = 42
Expand
x² + x = 42
Solve
x² + x - 42 = 0
(x + 7)(x - 6) = 0
So, x = 6
That means the length is 6 meters and the width is 7 meters.
The dimensions of the rectangle are:
Width, W = 7 meters
Length, L = 6 meters
Let's denote:
L = the length of the rectangle
W = the width of the rectangle
Given that the length of the rectangle is 1 meter less than its width, we can write the equation:
L = W - 1
We're also given that the area of the rectangle is 42 square meters. The formula for the area A of a rectangle is:
A = length × width
Substituting the given values, we have:
42 = (W - 1) × W
Now, let's solve this equation for W to find the width of the rectangle.
42 = [tex]W^2[/tex] - W
Rearranging terms, we get a quadratic equation:
[tex]W^2[/tex] - W - 42 = 0
Now, we can solve this quadratic equation by factoring or using the quadratic formula. Factoring seems simpler in this case:
Product = 1 × -42 = -42
Sum = -1
Required numbers: 6 × -7
[tex]W^2[/tex] - W - 42 = 0
[tex]W^2[/tex] + 6W - 7W - 42 = 0
W (W + 6) - 7 (W + 6) = 0
(W - 7) (W + 6) = 0
Setting each factor equal to zero gives us two possible values for W:
W - 7 = 0 or W + 6 = 0
Solving each equation:
W - 7 = 0W = 7
W + 6 = 0W = -6
Since the width of the rectangle cannot be negative, we discard W = -6.
So, the width of the rectangle is W = 7 meters.
Now, to find the length L, we can use the equation L = W - 1:
L = 7 - 1
L = 6
The question is:
The length of a rectangle is 1 meter less than its width. The area of the rectangle is 42 square meters. Find the dimensions of the rectangle.
Andre says 10x + 6 and 5x + 11 are equivalent because they both equal 16 when x is 1. Do you agree with Andre?
Answer:
No, They are not equivalent
Step-by-step explanation:
The two expressions are only said to be equivalent if they are the same regardless of whatever value the variable(s) is.
The variable in this question is x.
To prove this, we equate both expressions:
[tex]10x + 6 = 5x + 11[/tex]
[tex]10x - 5x = 11 - 6\\\\\\5x = 5\\\\\\x = 1[/tex]
This shows that they have the same value ONLY when x is 1.
This is why Andre says that they are equivalent, but they are not.
No, I do not agree with Andre because the two equations 10x + 6 and 5x + 11 are indeed equivalent.
Explanation:No, I do not agree with Andre. Two equations are considered equivalent if they have the same solution for all values of x.
Let's check if 10x + 6 and 5x + 11 are equivalent by substituting x = 1 into both equations:
For 10x + 6: 10(1) + 6 = 10 + 6 = 16
For 5x + 11: 5(1) + 11 = 5 + 11 = 16
We can see that both equations indeed equal 16 when x is 1, so Andre is correct in this case. 10x + 6 and 5x + 11 are equivalent equations.
Find the value of X.
Answer:
x=110 i think
Step-by-step explanation:
x+20+2x-70+x+x+20+x+90
=6x+60
6x+60=720
6x=(720-60)
6x=660
660/6=110
x=110
hope this helps!
Answer:
Step-by-step explanation:
sum of all angles of polygon = (n-2)*180 {n is no of sides}
= (6-2)*180 = 4*180 = 720
90 + 2x-70 + x+20 +x + x+20 + x = 720
Bring like terms together
90 - 70 + 20 + 20 + 2x + x + x + x + x =720
60 + 6x = 720
6x = 720 - 60
6x = 660
x = 660/6
x = 110
A cylinder has a volume of 140 pi cubic meters and a height of 14 meters. What is the area of the base?
10 pi square meters
12 pi square meters
126 pi square meters
1,960 pi square meters
Answer:
10
Step-by-step explanation:
divide 140 by 14 and you get 10
Can someone plz help
You raise $420 during a fundraising event. The amount of money that you raise is 120% of your goal. How much more did you raise than your goal?
9514 1404 393
Answer:
$70
Step-by-step explanation:
The excess amount is 20% of the goal. The given amount is 120% of the goal, so the proportion of the given amount that is excess is ...
(20% of goal)/(120% of goal) = 1/6
Then the excess is (1/6)($420) = $70.
You raised $70 more than the $350 goal.
The original fundraising goal was $350, and since $420 was raised, which is 120% of the goal, $70 more was raised than the goal.
Explanation:To find out how much more was raised than the goal during the fundraising event, start by understanding the percentage given. The $420 raised is 120% of the goal, which means the goal amount represents 100%. To calculate the original goal, you should divide the amount raised by the percentage raised (expressed as a decimal), so you divide 420 by 1.2 (since 120% as a decimal is 1.2).
Now, calculate the goal amount:
420 / 1.2 = $350
Therefore, the original goal was $350. Since the amount raised was $420, we subtract the goal from the amount raised to determine how much more was raised:
420 - 350 = $70.
Thus, the amount raised exceeded the goal by $70.
Complete the steps to find the area of the trapezoid.
Area of rectangle = square units
Area of triangle 1 = square units
Area of triangle 2 = square units
Area of triangle 3 = square units
Area of trapezoid = square units
Answer:
Area of rectangle: 256
Area of triangle 1: 24
Area of triangle 2: 16
Area of triangle 3: 96
Area of trapezoid: 120
Step-by-step explanation:
I just did the question on the thing so Ik I'm right.
-The graph measures by twos. To get the area of the rectangle get the base times height of it. That would be 16x16=256.
-Get base (8) times height (6) of triangle 1 then divide by 2, remember to count the squares by 2 for finding all areas. The formula would be 1/2(b)(h) because dividing by 2 is the same as multiplying times 1/2. Plug it in and (8)(6)=48 then divide by 2 which equals 24.
-Same formula for triangle 2. Plug it in and (8)(4)=32 and divide by 2 and it equals 16.
-Same formula for triangle 3. Plugged in is (12)(16)=192 divide by 2 and it equals 96.
-To find the area of the trapezoid get your rectangle area (256) and subtract all the triangle areas. So 256 - 6 - 16 - 96 = 120.
The area of the given shapes are required.
256 square units
24 square units
16 square units
96 square units
120 square units
Area of the rectangle
[tex]A_r=(20-4)\times(20-4)\\\Rightarrow A_r=256\ \text{square units}[/tex]
The area of a right triangle is given by
[tex]\dfrac{1}{2}bh[/tex]
where
b = Base
h = Height
Every triangle here is a right triangle.
Triangle 1
[tex]b=20-14=6\ \text{units}[/tex]
[tex]h=12-4=8\ \text{units}[/tex]
[tex]A_1=\dfrac{1}{2}\times 6\times 8\\\Rightarrow A_1=24\ \text{square units}[/tex]
Triangle 2
[tex]b=20-16=4\ \text{units}[/tex]
[tex]h=20-12=8\ \text{units}[/tex]
[tex]A_2=\dfrac{1}{2}\times 4\times 8\\\Rightarrow A_2=16\ \text{square units}[/tex]
Triangle 3
[tex]b=20-4=16\ \text{units}[/tex]
[tex]h=16-4=12\ \text{units}[/tex]
[tex]A_3=\dfrac{1}{2}\times 16\times 12\\\Rightarrow A_3=96\ \text{square units}[/tex]
Area of trapezoid is Area of the rectangle minus Area of all the triangles.
[tex]A=A_r-(A_1+A_2+A_3)\\\Rightarrow A=256-(24+16+96)\\\Rightarrow A=120\ \text{square units}[/tex]
Learn more:
https://brainly.com/question/14356835
https://brainly.com/question/16928464
Which shows the most likely side lengths for a parallelogram? A. 9, 4, 9, 4. B. 9, 9, 9, 4 C. 4, 4, 4, 9 or D. 4, 9, 9, 6
Option A(9,4,9,4) shows the most likely side lengths for a parallelogram because opposite sides of parallelogram are always equal.
Hope it will help u...
Explain why a rectangle is a convex quadrilateral
Answer:
this is because of two diagonals which lie in the interior of the rectangle.
James’s four-year-old brother is trying to arrange black and yellow Legos in rows. He has 56 yellow Legos and 120 black Legos. He wants to arrange them in rows so that there are either only yellow or only black Legos in each row, and so that each row has the same number of Legos. What is the least number of rows he can make?
Answer:
22
Step-by-step explanation:
The four-year-old brother can arrange the Legos in rows of 8.
Explanation:To find the least number of rows the four-year-old brother can make with the black and yellow Legos, we need to determine the greatest common divisor (GCD) of 56 and 120. The GCD will represent the number of Legos in each row.
To find the GCD, we can use the Euclidean algorithm. Divide the larger number (120) by the smaller number (56). The remainder is 8. Then, divide the smaller number (56) by the remainder (8). The new remainder is 0.
Therefore, the GCD of 56 and 120 is 8. This means that the four-year-old brother can arrange the Legos in rows of 8, with 7 rows of black Legos and 1 row of yellow Legos, or vice versa.
Dimensions of a building are 345 feet by 295 feet. If 1 inch represents 42 feet, what are the dimensions of the building on the drawing? Answer in terms of decimals. Round to hundredths place.
Answer: 8.21 in by 7.02 in
Step-by-step explanation: You would divide 345 by 42 AND 295 by 42, you would get 8.21 from 345 by dividing with 42 and you would get 7.02 by dividing by 7.02 and before you make your final answer MAKE SURE ITS IN INCHES!!!
I’m having a hard time help me
Answer:
The answer is 2881
Step-by-step explanation:
Look at the attached picture ⤴
I have shown the steps there....
So,Hope it will help u ....:)
✴Have a great day✴
Students measure the length of their feet in inches. The data is shown in the frequency table below. If the data were displayed in a dot plot, which of the measures would not be 11? (Check all that apply.)
Foot Length Tally Frequency
9 || 2
10 ||| 3
11 ||||| 5
12 | 1
range
mode
median
mean
Answer: The correct answer is mean and range.
lung cancer kills about 3,000 people per day. if 90% of the deaths from luung cancer are attributted to smoking, what is the rate of people who die from smoking each day?
Answer:
2700!
Step-by-step explanation:
hope that helped <3
area of rectangle:
Area is 21 square units. The Width of rectangle is 5 less than 4 times the length. Find the Dimension.
Write the formula and answer MUST SHOW ALL WORK!
Answer:
its 7 for width and 3 and length
Step-by-step explanation:
L * W = 21
W= 4L-5
find the factors for 21 which is 21 and 1 or 7 and 3. Plug in which one is valified. 7 and 3 are correct.
A field has 7,363 1/8 square feet. The width of the field is 62 1/4 feet. Estimate the length of this field.
hello:) I need help with this. Thanks!
Answer:
Please see the attached pictures for full solution
Which ratio can be used to solve for y in the triangle below?
sin75/25= sin40/y
sin40/25= sin75/y
sin25/75= siny/40
sin25/40= siny/75
Answer:second one should be correct I took this last year
Step-by-step explanation:
Write an equation of the circle with center (8.-3) and radius 6
Answer:
(x -8)^2 +(y +3)^2 = 36
Step-by-step explanation:
The equation of a circle with center (h, k) and radius r is ...
(x -h)^2 +(y -k)^2 = r2
Putting your numbers into this form gives ...
(x -8)^2 +(y +3)^2 = 36
The probability of rolling a 6 on a biased die is 1/5
Work out the probability of rolling exactly one 6
Answer:
if the probability of a 6 is 1/5, the probability of “not six” is 4/5. The probability of a 6 on the first roll and not on the second is 1/5 x 4/5 = 4/25. The six could come on the second roll so that probability must be doubled. The overall probability of exactly one six is 8/25 or 0.32.
Step-by-step explanation:
Find the x value 2x=6
Answer:
x = 3
Step-by-step explanation:
2x = 6
x = 3 (Because we divide on both sides by 2 so that the x is by itself, 6/2 = 3)
A jar contains three red marbles and five green marbles. A marble is drawn at random and not replaced. A second marble is then drawn from the jar. Find the probability that the first marble is red and the second marble is green.
Answer:
P(red then green) = 5/8 * 3/7 = 15/56
Step-by-step explanation: Since this is a logical "and" case, we have to multiply the separate events' probabilities...thus P(red then green) = 5/8 * 3/7 = 15/56
Answer:
3/28
Step-by-step explanation:
3 red+ 5 green = 8 marbles in the jar
1st marble:
P(red) = number of red/ total = 3/8
We keep the marble
2 red+ 5 green = 7 marbles in the jar
P(green) = number of green/ total = 2/7
P (red,keep,green) = P(red)* P(green) = 3/8*2/7 = 6/56 = 3/28
Find the product.
-7(- a2 )( -b3 )
Answer:
-7a^2 b^3
Step-by-step explanation:
-7(- a^2 )( -b^3 )
-7 * -a^2
A negative times a negative is a positive
7a^2
7a^2 * -b^3
A positive times a negative is a negative
-7a^2 b^3
Using the slope formula for the points (1, 5) and (2, -2), what would the denominator be? 2 - 1 2 - 5 -2 - 5 -2 - 1\
will mark brainliest
Answer:
2-1
Step-by-step explanation:
Given two points we can find the slope using
m =(y2-y1)/(x2-x1)
= (-2 -5)/(2-1)
= -7/1
= -7
The denominator is 2-1
Answer:
2 - 1
Step-by-step explanation:
Slope = (y2 - y1)/(x2 - x1)
= (-2 - 5)/(2 - 1)
= -7
what is the slope indicated in the table below
x 4 6 8 10
y 7 14 21 28
Answer:
3/2
Step-by-step explanation:
So for the x it increases by +2. For the y it increases by +7. We do rise over run which is y over x. So it will be 3/2.
Answer: 3.5 or 7/2
Step-by-step explanation: use the slope formula y2-y1 / x2-x1
I chose 14-7 / 6-4
The volume of a cube is 2,460.375 cubic inches, what is the length of each side of the cube?
[tex]V=a^3[/tex]
[tex]2,460.375=a^3\\a=\sqrt[3]{2,460.375} \\a=13.5[/tex]
Answer: length is equal to 13.5
What is the probability of a die landing on an even number on the first toss, and then an odd number on the second toss?
Dice- 6 sides
Please help
Answer:
i dotn know sorry
Step-by-step explanation:
and this is why brainly is bad
Answer:
1/4 chance
Step-by-step explanation:
Number of even numbers on a die-3
Number of odd numbers on a die-3
a die has 6 sides,
therefore
1/2 of the numbers on a die are even and 1/2 are odd
so a 3/6 chance (1/2 chance (simplify)) of landing on an even number on the first roll
And a 3/6 chance (1/2 chance (simplify)) of landing on an odd number on the second roll
Multiply the two together and a 9/36 chance of this event or simplified to a 1/4 chance of this event
What is the approximate volume of the tube? Round to the
nearest whole cubic centimeter
A cylindrical cardboard tube with a diameter of 8
centimeters and a height of 20 centimeters is used to
package a gift
20 cm
1,005 cm
1,340 cm?
03.351 cm
4,021 cm
8 cm
Answer:
Cylinder Volume = π • r² • height
radius = 4 cm
Volume = π • 4^2 * 20
Volume = PI * 320
Volume = 1,005.3096491487 which rounds to
1,005 cubic centimeters
Actually ALL those answers should say CUBIC CENTIMETERS.
Step-by-step explanation:
What is the area of triangle ABC?
0 2.5 square units
3 square units
3.5 square units
04 square units
Hurry
Answer:
A = 3 units^2
Step-by-step explanation:
The area of a triangle is
A = 1/2 bh where b is the length of the base and h is the height
b = the distance from B to C = 4 units = 2 ( watch the scale)
h = the distance from A to C along the x axis =6 units = 3 (watch the scale)
A = 1/2 (2)(3)
A = 3 units^2
A rectangle has a perimeter of 80 inches. Write an equation to represent the area A in terms of width w.
Do I use the perimeter?
Answer:
[tex]A = 40w-w^2[/tex]
Step-by-step explanation:
We are given the following in the question:
Perimeter of rectangle = 80 inches.
Let l be the length and w be the width of rectangle.
Perimeter of rectangle =
[tex]P= 2(l+w)[/tex]
Putting values, we get,
[tex]80 = 2(l+w)\\40 = l+w\\\Rightarrow l = 40 - w[/tex]
Now, we have to find the area of the rectangle in terms of w.
Area of rectangle =
[tex]A = l\times w[/tex]
Putting values, we get
[tex]A = (40-w)w\\A = 40w-w^2[/tex]
is the required expression of area of rectangle in terms of w.
Yes, the perimeter is used to calculate the length of the rectangle in the term of w.
5^x=62 Giving 20 points!
Algebra 2, Chapter 6-7. Common Logarithms.
The answer key says its 2.5, but I need some help to understand how to get that answer by showing work.
Answer:
x = 2.564 ( to 3 dec. places )
Step-by-step explanation:
Using the rule of logarithms
log[tex]x^{n}[/tex] ⇔ n logx
Given
[tex]5^{x}[/tex] = 62 ( take the ln of both sides )
ln[tex]5^{x}[/tex] = ln 62, that is
x ln5 = ln 62 ( divide both sides by ln 5 )
x = [tex]\frac{ln62}{ln5}[/tex] ≈ 2.564
Answer:
2.5
Step-by-step explanation:
ln(5^x)=ln(62)
[tex]x=\frac{ln62}{ln5}[/tex]
≈2.56433