Final answer:
To find the width of a rectangle when the length is 2 units more than the width and the area is known to be 48 units, you can use algebraic equations to determine the width. In this case, the width of the rectangle is 6 units.
Explanation:
To find the width of the rectangle:
Let x be the width of the rectangle.
Since the length is 2 units more than the width, the length is x + 2.
Given that the area is 48 units, use the formula for the area of a rectangle: width x length = area. Therefore, x(x + 2) = 48.
Solve for x by setting up the equation: x^2 + 2x - 48 = 0.
Factor the quadratic equation: (x + 8)(x - 6) = 0.
Since the width cannot be negative, the width of the rectangle is 6 units.
The width of the rectangle is 6 units.
According to the question, the length is 2 units more than the width, so we can express the length as ( w + 2 ) units.
The area of a rectangle is given by the product of its length and width. Therefore, we can set up the following equation to represent the area of the rectangle:
[tex]\[ \text{Area} = \text{length} \times \text{width} \] \[ 48 = (w + 2) \times w \][/tex]
Expanding the right side of the equation, we get:
[tex]\[ 48 = w^2 + 2w \][/tex]
To find the value of w, we need to solve the quadratic equation. Let's rearrange the equation to set it equal to zero:
[tex]\[ w^2 + 2w - 48 = 0 \][/tex]
Now, we can factor this quadratic equation:
[tex]\[ (w + 8)(w - 6) = 0 \][/tex]
Setting each factor equal to zero gives us two possible solutions for w:
[tex]\[ w + 8 = 0 \quad \text{or} \quad w - 6 = 0 \][/tex]
Solving for w, we get:
[tex]\[ w = -8 \quad \text{or} \quad w = 6 \][/tex]
Since the width of a rectangle cannot be negative, we discard the negative solution. Therefore, the width of the rectangle is:
[tex]\[ w = 6 \text{ units} \][/tex]
7) Find the solutions to the following polynomial: 5x* +5x2 – 10 = 0
Answer:
[tex]x = - 2 \: o r\: 1[/tex]
Step-by-step explanation:
We want to solve the quadratic equation:
[tex]5x + 5{x}^{2} - 10 = 0[/tex]
Rewrite in standard form to get:
[tex]5 {x}^{2} + 5x - 10 = 0[/tex]
Divide through by 5 to get;
[tex]{x}^{2} + x - 2 = 0[/tex]
Factor to get;
[tex](x + 2)(x - 1) = 0[/tex]
Apply zero product property to get:
[tex]x + 2 = 0 \: or \: x - 1 = 0[/tex]
The solutions are:
[tex]x = - 2 \: or \: x = 1[/tex]
need help with how to do this 3x2+12x+6=0
Answer:
-2 + sqrt(2)
-2 - sqrt(2)
Step-by-step explanation:
3x² + 12x + 6 = 0
x² + 4x + 2 = 0
Use the quadratic formula:
[-4 + sqrt(4² - 4(1)(2))]/2
-2 + sqrt(2)
[-4 + sqrt(4² - 4(1)(2))]/2
-2 - sqrt(2)
sqrt: square root
The elevation we call sea level is actually the average level of the sea. This means that at average sea level, the elevation is zero. In reality, the level of the sea rises and falls in what are called tides. Low tide is the point of lowest sea level in a tidal period. High tide is the point of highest sea level in a tidal period. The height above or below average sea level is called elevation. An elevation below sea level is considered a negative value, while an elevation above sea level is positive.
Winston lives near the ocean. He regularly brings an altimeter to the beach to measure the elevation of the ocean’s surface. You will use the data Winston gathered to complete tasks about the rising and falling of the ocean’s surface. When necessary, sketch a diagram of the situation on a separate sheet of paper to assist you.
On Monday at 1 p.m., when the ocean’s surface was at an elevation of 2.2 feet, Winston went to a surf shop that was 8.2 feet above the ocean’s surface. At 7 p.m. when the ocean’s surface was at an elevation of -2.4 feet, Winston ate dinner at a restaurant whose deck was 10 feet above the ocean’s surface.
Part A
What was the net change in the elevation of the ocean’s surface from 1 p.m. to 7 p.m.?
At 1 pm the ocean was at a hight tide but at 7pm it was at a low tide this means the tide has been decreasex by 2.6 feet
Step-by-step explanation:
Which expressions are equivalent to 5 x minus 15? Select three options.
5 (x + 15)
5 (x minus 3)
4 x + 3 y minus 15 minus 3 y + x
Negative 7 y minus 6 x minus 8 y + x
Negative 20 minus 3 x + 5 + 8
Answer:
Step-by-step explanation:
The second expression 5 (x minus 3) the third 4 x + 3 y minus 15 minus 3 y + x
and there is no more
Answer:
5(x+3) 5 (x+15) Those are 2 Your welcome.! (:
Step-by-step explanation:
a jeep finishes a journey in 9 hours at a speed of 60 km her hour. by how much speed should its speed be increased do that it may only take 6 hours to finish the journey??
Answer:
90 km / hour.
Step-by-step explanation:
Speed = distance / time
So Distance = speed * time.
The distance is the same in both scenarios so
60 * 9 = s * 6 where s is the required speed.
540 = 6s
s = 540 / 6
s = 90 km / hour.
Answer:
90 km/h
Step-by-step explanation:
If the jeep finished the journey in 9 hours and 60 km/h, then we know that the journey is 9 * 60 kilometers long, or 540 kilometers.
540 kilometers / 6 hours = 90 km/h
whats the simplest form for 56:32
Answer: 7:4
Step-by-step explanation:
To take this ratio to its simplest form, we have to divide by a value divisible by both sides of the ratio.
8 is a divisible value, therefore,
56/8 = 56 ÷ 8 = 7
32 ÷ 8 = 4
Thus, 56:32 in its simplest form= 7:4
I hope this helps.
In the figure below, PDW and WTC are right triangles. The measure of WPD is 30°, the measure of WC is 6 units, the measure of WT is 3 units, and the measure of WD is 12 units. Determine the measure of PD .
Answer:
PD = 12[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the tangent ratio in right Δ PDW and the exact value
tan30° = [tex]\frac{1}{\sqrt{3} }[/tex], then
tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{WD}{PD}[/tex] = [tex]\frac{12}{PD}[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )
PD = 12[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using similarity it can be solved as:
[tex] In\:\triangle PDW\: \& \: \triangle CTW\\\\
\angle PDW \cong \angle CTW.... (each\:90 °) \\\\
\angle PWD \cong \angle CWT... (Vertical\:\angle s) \\\\
\therefore \triangle PDW\: \sim\: \triangle CTW\\
(by \:AA\: criterion \: of\: similarity) \\\\
\therefore \frac{PW}{CW} =\frac{WD}{WT}.. (csst) \\\\
\therefore \frac{PW}{6} =\frac{12}{3}\\\\
\therefore \frac{PW}{6} =4\\\\
\therefore PW=4\times 6\\\\
\huge \red {\boxed {\therefore PW=24}} \\\\
In\:\triangle PDW\:, \angle PWD = 60°\\\\
\therefore PD =\frac {\sqrt 3}{2} \times PW\\\\
\therefore PD =\frac {\sqrt 3}{2} \times 24\\\\
\huge \orange {\boxed {\therefore PD = 12\sqrt 3\: units}} [/tex]
how to find the area of a circle
Answer:
A=~r
Step-by-step explanation:
Answer:
To find the area of a circle use the formula: A = π * r^2
r is the radius that is given.
Example: Find the area of a 5 in radius circle
A = π * (5)^2
A = 25π
A = 78.54
Hope this helps :)
What number is 105% of 752
Answer:
789.6
You can do it on a calculator
105% of 752 is 789.6.
Explanation:To find what number is 105% of 752, we first need to calculate 105% of 752.
105% of 752 can be found by multiplying 752 by 105% (or 1.05).
The calculation is: 752 * 1.05 = 789.6
Therefore, 105% of 752 is 789.6.
Maria find a local gym that advertises 86 training sessions for $2015 find the cost of 167 training sessions
Answer:$3912.81
Step-by-step explanation:
You can calculate this by finding the cost ofn1 training session and then multiplying by the 167 training sessions
If 86 training sessions =$2015
Then 1training session=2015/86 =$23.43
167 training sessions =$23.43×167= $3912.81
Dan had 249 dollars to spend on 7 books. After buying them he had 18 dollars. How much did each book cost?
First, lets subtract the amount he has after the transaction and the amount he had before the transaction.
249 - 18 = 231
Second, divide by the amount of books Dan bought.
231 / 7 = $33 per book.
Best of Luck!
Temperature in degrees Fahrenheit can be converted into degrees Celsius using the formula C=5(F-32)/9
Make F the subject of formula
Give your answer in the form aC + b/c where a,b and c are all positive integers.
Answer:
F= (9C+160)/5
Step-by-step explanation:
C=5(F-32)/9
make F the subject of the formula= isolate F
5(F-32)=9C
5F-160=9C
5F=9C+160
F= (9C+160)/5
check: a, b, c are all positive integers (a=9, b=160, c=5)
Answer:
9c+160/5
Step-by-step explanation:
PLEASE ANSWERRRRRRRRRR
If two charges attract to each other, then which of the following is true?
A. Both charges must be negative.
B. Both charges must be equal in value.
C. Both charges must be positive.
D. Both charges must be different.
Step-by-step explanation:
D. Both charges must be different.
Because, like charges repel each other and different charges attract each other.
Camden‘s grandparents open a savings account for his on his fifth birthday. They deposited money sign five grand in account that had simple interest rate of 6%. Camden leaves his money in the count for 18 years. What formula would you use to solve this problem?
Step-by-step explanation:
The money deposited in the bank = 5000
Rate of interest = 6%
Number of years = 18
By simple interest Formula,
Interest = PNR / 100
Where P is the principal amount = 5000
N = no of years = 18
R =rate of interest = 6
Substituting the values in the equation, we get
Interest = (5000 * 18 * 6) / 100
Interest = 5400
total amount present = principal + interest
= 5000 + 5400 = 10400
A local park is in the shape of a square. A map of the local park is made with the scale 1 inch to 200 feet.
If the park is shown as a square on the map, each side of which is 12 inches long, how long is each side of the square park?
The length of each side is 50 inch/ 600 ft
Step-by-step explanation:
Given,
The perimeter of the square park = 12 inches
1 inch = 200 ft
12 inches = 12×200 ft = 2400 ft
To find each side of the park.
Let, each side be 'a' inches
Formula
The perimeter of a square = 4a
According to the problem,
4a = 2400
or, a = 600 ft
= 50 inch
Answer:
2400 feet
Step-by-step explanation:
1 : 200
12 : X
X = 12 × 200 = 2400 feet
The figure below shows concentric circles, both centered at 0.0
• Chord XY is tangent to the smaller circle
• The radius of the larger circle is 15cm
• The radius of the smaller circle is 12cm.
What is the length of chord XY?
A. 27 cm
B. 24cm
C. 18cm
D. 10cm
Answer:
C. 18 cm
Step-by-step explanation:
The ratio of the sides of the triangle shown is 12 : 15 = 4 : 5. We know it is a right triangle, so we know the missing side length completes the ratio
3 : 4 : 5 = 9 : 12 : 15
Half of XY is 9 cm, so the length of the entire chord is 18 cm.
_____
The chord is tangent to the inner circle, so makes a 90° angle with the radius to that tangent point. This tells you that the triangle shown is a right triangle. It also tells you that the short radius bisects the chord. The Pythagorean theorem can be used to find the length of the side not shown (half the chord length).
The unknown side (a) can be found from ...
15² = 12² +a²
225 -144 = a² . . . . . . subtract 12²
81 = a² . . . . . . . . . . . simplify
9 = a . . . . . . . . . . . . . take the square root
The chord length is 2a, so is ...
2(9 cm) = 18 cm . . . . length of chord XY
Evaluate -4a+8z if a=8 and z=3
Answer:
- 8
Step-by-step explanation:
Given
= 4a + 8z ← substitute a = 8 and z = 3 into the expression
= - 4(8) + 8(3)
= - 32 + 24
= - 8
Answer:
-8
Step-by-step explanation:
a = 8
z = 3
-4(8) + 8(3) = -32 + 24 = -8
What’s 8 divide by 12.48
Answer:25/39
Step-by-step explanation:
what do you add to 2 1/8 to make 4
Final answer:
To make a total of 4 starting with 2 1/8, you need to add 1 7/8, which is the difference between 4 written as a fraction (32/8) and 2 1/8 (17/8).
Explanation:
To find what you need to add to 2 1/8 to make 4, you follow these steps:
First, you need to write the number 4 as a fraction with the same denominator as 2 1/8. Since 1/8 is the fractional part of 2 1/8, you can write 4 as 32/8 (because 4 × 8 = 32).
Next, you subtract the fraction 2 1/8 from 32/8. The whole number 2 is the same as 16/8 (because 2 × 8 = 16). So 2 1/8 is the same as 17/8 (because 16 + 1 = 17).
Now, subtract 17/8 from 32/8 to get the difference. 32/8 - 17/8 = 15/8.
The fraction 15/8 can also be written as 1 7/8 (because 15 ÷ 8 = 1 with a remainder of 7).
Therefore, you need to add 1 7/8 to 2 1/8 to make 4.
z varies directly with x and inversely with y2.
When x = 2 and y = 5, z = 8.
What is the value of z when x = 4 and y = 9?
Solution:
Given that,
z varies directly with x and inversely with [tex]y^2[/tex]
Which means,
[tex]z \propto \frac{x}{y^2}\\\\z = k \times \frac{x}{y^2}[/tex]
Where, "k" is constant of proportionality
Substitute x = 2 and y = 5, z = 8 in above
[tex]8 = k \times \frac{2}{5^2}\\\\8 = \frac{2k}{25}\\\\k = 25 \times 4\\\\k = 100[/tex]
What is the value of z when x = 4 and y = 9?
Substitute k = 100 , x = 4 and y = 9 in above
[tex]z = 100 \times \frac{4}{9^2}\\\\z = 100 \times \frac{4}{81}\\\\z = 4.938[/tex]
Thus value of z is 4.938
2x + 5
rewrite each expression as the product of a constant and a sum of terms
Answer:
= 2(x+[tex]\frac{5}{2}[/tex] )
Step-by-step explanation:
2x + 5
= 2(x+[tex]\frac{5}{2}[/tex] )
When:
2 is the constant
(x+[tex]\frac{5}{2}[/tex] ) is a sum of terms
Hope it will find you well.
The expression 2x + 5 can be written as the product of 1 and the sum 2x + 5. Therefore, it's 1(2x + 5).
Step 1:
Factor out the greatest common factor.
In the expression 2x + 5, there is no common factor other than 1 since both terms do not share any common factors.
Step 2:
Rewrite as the product of a constant and a sum of terms.
We rewrite 2x + 5 as the product of 1 and the sum of 2x and 5: [tex]\(1 \times (2x + 5)\).[/tex]
Step 3:
Perform the multiplication.
Multiplying 1 by the sum (2x + 5) gives us [tex]\(1 \times (2x + 5) = 2x + 5\)[/tex].
Step 4:
Interpret the result.
The expression [tex]\(2x + 5\)[/tex] represents the original expression 2x + 5 as the product of the constant 1 and the sum of terms 2x and 5. This expression is now in the form requested.
The equations X-2y = 1.3x-y=-1. X+ 2y =-1, and 3x+y= 1 are shown on the graph below. Which system of equations has a solution of approximately (0.6,-0.8)?
Answer:
x+2y=-1 3x+y=1
Step-by-step explanation:
look photo
Answer: x + 2y = -1 and 3x + y = 1
Step-by-step explanation:
A tree casts 30 ft shadow at the time of day when a 2 ft stake casts a 7ft shadow what is the height of the tree
Check the picture below.
how do you rewrite -8x+4+(-3)
Answer:
-8×+1
Step-by-step explanation:
you CLT the 4 + (-3)
Answer:
-8x + 1
Step-by-step explanation:
(Not sure what you wanted it rewritten as. This is the equation in standard form).
Derek sees that a 24 foot flagpole casts a 10 foot shadow. At the same time of day, if a nearby tree casts
25 foot shadow, about how tall is the tree?
Answer:
60 ft.
Step-by-step explanation:
We can solve this problem with a simple proportion:
24 / 10 = h / 25
10h = 24 * 25
600 = 10h
60 ft. = h
The height of the tree would be 60 feet when its shadow 25-foot.
What is the proportion?A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.
We have been given that Derek sees that a 24-foot flag pole casts a 10-foot shadow.
Let the height of the tree would be h when its shadow 25-foot.
According to the given question, we can write the proportion as:
24 : 10 = h : 25
⇒ 24 / 10 = h / 25
⇒ 10h = 24 × 25
⇒ 600 = 10h
⇒ 60 = h
⇒ h = 60
Therefore, the height of the tree would be 60 feet when its shadow 25-foot.
Learn more about the proportion here:
brainly.com/question/1504221
#SPJ5
1. In the figure below, AX'Y'Z' is a dilation of AXYZ. Find
the scale factor of the dilation, and classify it as an
enlargement or a reduction. (1 pt for scale factor, 1 pt for
work shown, lpt for classification.)
Answer:
Enlargement
Factor 2
Step-by-step explanation:
X'Y'/XY = 10/5 = 2
what is -8x-8+3(x-2)=-3x+2
Answer:
x=-8
Step-by-step explanation:
-8x - 8 + 3(x-2) = -3x + 2 Multiply the parentheses by 3
-8x - 8 + 3x -6= -3x +2 Collect all like terms and Calculate
-5x - 14= -3x + 2 Move the terms
-5x + 3x = 2 + 14 Collect all the like terms and Calculate the sum
-2x = 16 Divide both of the sides by -2
x = -8
I hope this is what you were looking for and helps you out.
Answer:
[tex]x=-8[/tex]
Step-by-step explanation:
Given Equation:
[tex]-8x-8+3(x-2)=-3x+2[/tex]
Solving for 'x' by taking the terms of 'x' to one side and constants to the other side:
[tex]-8x-8+3(x)-3(2)=-3x+2\\[/tex]
[tex]-8x-8+3x-6=-3x+2[/tex]
Adding the like terms:
[tex]-5x-14=-3x+2[/tex]
Adding '[tex]3x[/tex]' both sides:
[tex]-5x+3x-14=-3x+3x+2[/tex]
[tex]-5x+3x-14=2\\\\-2x-14=2[/tex]
Adding '[tex]14[/tex]' both sides:
[tex]-2x-14+14=2+14\\\\-2x=16\\\\x=\frac{16}{-2}[/tex]
[tex]x=-8[/tex]
A(n)=3/2(-2)^(n-1). What is the 3rd term in the sequence?
Answer:
6
Step-by-step explanation:
Substitute n for 3
A(n) = 3/2(-2)^(n-1)
A(3) = 3/2(-2)^(3-1)
A(3) = 3/2(-2)²
A(3) = 3/2(4)
A(3) = 12/2
A(3) = 6
Answer:
6 is the right answer i pretty sure
Step-by-step explanation:
3/2(-2)^(n-1)
3/2(-2)^(3-1)
3/2(-2)²
3/2(4)
12/2
which then if we simplify we get
12/2=6
Find the value of x to the nearest tenth.
For this case we have that, by definition of trigonometric relationships of rectangular triangles, the cosine of an angle is given by the division of the leg adjacent to the angle on the hypotenuse of the triangle. According to the figure we have:
[tex]Cosine (50) = \frac {6} {x}\\x = \frac {6} {cosine (50)}\\x = 9.3343[/tex]
Thus, the value of x is 9.3
Answer:
[tex]x = 9.3[/tex]
worksheet 5.9 scale drawings and scale models
Answers:
1. 1/12
2. 1/15
3. 16 feet
4. 222 inches
5. 27 feet
hope it helps :0