Jake has a rectangular garden that measures 12 feet by 14 feet. He wants to increase the area by 50% and plans to increase each dimension by equal lengths, x. Which equation could be used to determine the value of x?
In order to increase the area of a rectangular garden that measures 12 feet by 14 feet by 50% Jake must increase each dimension by equal lengths, x:
[tex]x\approx 2.9ft[/tex]
Explanation:First of all, let's calculate the area of the original rectangular garden:
[tex]A=b\times h \\ \\ b:base \\ \\ h:height \\ \\ \\ b=12ft \\ \\ h=14ft \\ \\ \\ A=12(14) \\ \\ A=168ft^2[/tex]
Jake wants to increase the area by 50%, so the new area would be:
[tex]A'=168(1.5) \\ \\ A'=252ft^2[/tex]
He wants to increase the area by 50% and plans to increase each dimension by equal lengths, x, so this is represented by the figure below, therefore:
[tex](12+x)(14+x)=252 \\ \\ 168+12x+14x+x^2-252=0 \\ \\ x^2+26x-84=0 \\ \\ \\ Using \ quadratic \ formula: \\ \\ x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ a=1 \\ \\ b=26 \\ \\ c=-84 \\ \\ \\ x=\frac{-26 \pm \sqrt{26^2-4(1)(-84)}}{2(1)} \\ \\ x=\frac{-26 \pm \sqrt{1012}}{2} \\ \\ \\ Two \ solutions: \\ \\ x_{1}=-13+\sqrt{253} \approx 2.9\\ \\ x_{2}=-13-\sqrt{253} \approx -28.9 \\ \\ x_{2} \ is \ discarded \ because \ it \ can't \ be \ negatives[/tex]
Finally:
In order to increase the area of a rectangular garden that measures 12 feet by 14 feet by 50% Jake must increase each dimension by equal lengths, x:
[tex]x\approx 2.9ft[/tex]
Learn more:Dilation: https://brainly.com/question/10945890
#LearnWithBrainly
the veterinarian ways jims to dogs his collie weighs 37 pounds is terrier weighs 240 Oz is what is the total weight of Jim's dogs?
Answer:
52
Step-by-step explanation:
240 ÷ 16 = 15
37 + 15 = 52
Three vertices of parallelogram WXYZ are X(–2,–3), Y(0, 5), and Z(7, 7). Find the coordinates of vertex W
Final answer:
The coordinates of vertex W of parallelogram WXYZ, given vertices X(-2,-3), Y(0, 5), and Z(7, 7), are W(9, 15). This is found by calculating vector ZW as equal to vector XY and adding ZW to the coordinates of Z.
Explanation:
The coordinates of vertex W of parallelogram WXYZ can be found by using the properties of parallelograms. In a parallelogram, opposite sides are equal in length and parallel. Given vertices X(-2,-3), Y(0, 5), and Z(7, 7), we can first find the vector representation from X to Y and from Y to Z:
XY = Y - X = (0 - (-2), 5 - (-3)) = (2, 8)YZ = Z - Y = (7 - 0, 7 - 5) = (7, 2)To find the vector from Z to W, which we'll call ZW, we use the fact that ZW must be parallel and equal in length to vector XY. Therefore:
ZW = XY = (2, 8)Now we add vector ZW to the coordinates of Z to find W:
W = Z + ZW = (7, 7) + (2, 8) = (9, 15)Thus, the coordinates of vertex W are (9, 15).
What are the zeros of the quadratic equation y=5(2x-1)(x+3)
Answer:
x = 1/2 or -3
Step-by-step explanation:
to find the zeros, we need to find the values of x which would cause y to become zero,
i.e solve x for :
5(2x-1)(x+3) = 0 (divide both sides by 5)
(2x-1)(x+3) = 0
hence either
2x-1 = 0 (add 1 to both sides)
2x = 1 (divide both sides by 2)
x = 1/2 --> first zero
or
x+3 = 0 (subtract 3 from both sides)
x = -3 ----> 2nd zero
0.05 is 1/10 the value of
A. 5
B. 0.005
C. 0.5
D. 50
Answer:
C.
Step-by-step explanation:
as 0.05 is 1/10 of a number, multiplying 0.05 by 10 will give you the number that when divided by 10 will give you 0.05. Hence just multiply 0.05 by 10 and you get 0.5.
One of the roots of the quadratic equation x^2−5mx+6m^2=0 is 36. Find the greatest possible value of the second root.
Answer:
The greatest possible value of the second root will be 54.
Step-by-step explanation:
The given quadratic equation is x² - 5mx + 6m² = 0
So, we have to find the values of variable x.
Now, x² - 5mx + 6m² = 0
⇒ x² - 3mx - 2mx + 6m² = 0
⇒ x(x - 3m) - 2m(x - 3m) = 0
⇒ (x - 3m)(x - 2m) = 0
So, x = 3m and 2m.
Now, if 3m = 36
Then, m = 12 and the other root will be x = 2m = 24.
Again, if 2m = 36
Then, m = 18 and the other root will be x = 3m = 54.
So, if one root of the equation is 36 then, the greatest possible value of the second root will be 54. (Answer)
Mary took out a student loan for $15000 at 4% simple interest. How much interest will she pay in 10 years? suppose she paid it off in 8 years instead of 10 years. how much would she save in interest? :)
Simple interest formula:
Total = principal x (1 + rate x years)
10 years:
Total = 15,000(1+0.04x10)
Total = $21,000
8 years:
Total = 15000(1+0.04x8)
Total = $19,800
Savings = 21,000 - 19,800 = $1,200
Does the following table represent a proportional relationship, and if so what is the proportion of the cost for a box of cereal to the size of the box?
Cost for a box of cereal $2.20 $2.64 $3.30 $4.84
Size of box (in ounces) 10 12 15 22
yes, $0.22 per ounce
yes, $4.55 per ounce
yes, $0.44 per ounce
no it is not proportional
Answer:
A
Step-by-step explanation:
I'm not entirely sure but please let me know if I'm right
Answer: yes
Step-by-step explanation: 2.20 divided by 10 is .22, so one ounce is 22 cents. 2.64 divided by 12 is .22, 3.30 divided by 15 is .22, and 4.84 divided by 10 is .22. All the costs are the same per ounce, so it is a proportional relationship of .22.
Kim drew a map of the Mississippi River. The scale was 3 centimeters represents 120 miles. The actual length of the Mississippi River is 2,320 miles. What is the river on the map
To represent the actual length of the Mississippi River, which is 2,320 miles, on a map with a scale of 3 cm per 120 miles, the river would be 58 cm long on the map.
Explanation:The question concerns calculating the scale representation of the actual length of the Mississippi River on a map. According to the given scale, 3 centimeters on the map represents 120 miles in reality. The actual length of the Mississippi River is 2,320 miles. To find the length of the Mississippi River on the map, we use the scale ratio to set up a proportion.
First, we calculate the scale ratio which is 3 cm to 120 miles. This means 1 cm represents 40 miles (120 miles ÷ 3 cm). To find how many centimeters represent 2,320 miles, we divide the actual miles by the miles each centimeter represents. Therefore, 2,320 miles ÷ 40 miles/cm equals 58 cm. Thus, the Mississippi River would be represented as 58 cm long on Kim's map.
Write each in ax^b form where n can be either positive or negative integer
Answer:
a. [tex]$ x^{-5} $[/tex]
b. [tex]$ 3x^{-2} $[/tex]
c. [tex]$ \frac{4}{3}x^4 $[/tex]
Step-by-step explanation:
We have to know the two results to compute the problems.
1. [tex]$ x^a . x^b = x^{a + b} $[/tex]
2. [tex]$ \frac{x^c}{x^d} = x^c . x^{-d} = x^{c - d} $[/tex]
a. [tex]$ \frac{x^3}{x^8} $[/tex]
Using (2), we get: [tex]$ \frac{x^3}{x^8} = x^{3 - 8}[/tex]
[tex]$ \textbf{= x}^{\textbf{5}} $[/tex]
b. [tex]$ \frac{6x}{2x^3} $[/tex]
[tex]$ = 3\frac{x}{x^3} $[/tex]
[tex]\textbf{= 3x}^{\textbf{-2}} $[/tex]
c. [tex]$ \frac{28x^6}{21x^2} $[/tex]
[tex]$ = \frac{4}{3}x^{6 - 2} $[/tex]
[tex]$ = \frac{\textbf{4}}{\textbf{3}}\textbf{x}^{\textbf{4}} $[/tex]
Hence, the answer.
Tipeni bought 100 shares in a bank for $35.60 each. He sold them two years later for $48.90 each and paid a brokerage fee of $32.95.
a) what is the profit made on these shares?
I need help with a please I’m dying
Yo sup??
no of shares=100
cost price=35.60
selling price=48.90
profit=(SP-CP)*100
=(48.9-35.6)*100
=1330
But since he loses 32.95 to the broker therefore net profit obtained is
=1330-32.95
=1297.05
Hope this helps
Final answer:
To calculate Tipeni's profit on selling the shares, subtract the total buying cost and brokerage fee from the total selling price. The profit made on these shares is $1297.05.
Explanation:
To calculate the profit Tipeni made on selling the shares, we need to find the total selling price of the shares, subtract the total buying price of the shares, and also account for the brokerage fee.
Calculate total buying cost: 100 shares × $35.60 per share = $3560.00
Calculate total selling price: 100 shares × $48.90 per share = $4890.00
Subtract the brokerage fee from the total selling price: $4890.00 - $32.95 = $4857.05
Subtract the total buying cost from the adjusted total selling price to get the profit: $4857.05 - $3560.00 = $1297.05
The profit made on these shares is $1297.05.
Simplify 12 × 10 ^8/ 4 × 10^5 and leave in ordinary form
Answer:
3 x 10^3
Step-by-step explanation:
The first is to identify the operation to be performed, it is a quotient between two potency.
Being two potency of the same base number (10), the property says that the quotient of two potency of the same base subtracts its exponent, and the base remains the same.
The corresponding exponents are 8 and 5.
The subtraction is 8-5 = 3.
The whole number that accompanies the base is divided in a current way, that is 12/4. Therefore, the result is 3.
Lucia's back hurts! She figured out that the books in her backpack are 5 times heavier than the backpack itself. By what percent heavier is the backpack with the books inside, than the books by themselves?
Answer:
120%
Step-by-step explanation:
If the books in the bag are 5 times heavier than the bag itself then the books and the backpack together are 6 times heavier than the backpack itself, so the backpack with the books is (6 ÷ 5) × 100% = 120% heavier than the book by themselves.
Yo sup??
Let the weight of the backpack be y
and weight of books be x, then
x=5y
percentage heavier=((x+y)/x)*100
=6y/5y*100
=120%
Hope this helps.
What is 20 plus -14?
Answer:
6
Step-by-step explanation:
the ratio of roses to lilies in a flower arrangement is 3 to 5. how many roses would there be if there were 24 total flowers in the arrangement?
Answer:
There would be 9 roses.
Step-by-step explanation:
The ratio began as 3 to 5 so in all there were 8 flowers.
If there are 24 , being that 8 x 3 = 24, then all you have to is multiply both sides of the ratio by 3.
3 x 3 = 9
5 x 3 = 15
9 + 15 = 24
New ratio is 9 to 15
calculate correct to three significant figures length of Arc with subtend an angle of 70 degrees at the centre of circle of radius 4 cm
Answer:
4.89 cm
Step-by-step explanation:
Formula for arc length = (angle/360)×2×pi×r
(70/360)×2×pi×4 = 4.89cm
what is the fifth term of the geometric sequence? 5, 15 , 45, ...
The geometry sequence has the equation [tex]a(n)=5(3^{n-1})[/tex].
The 5 represents the first number of the sequence and the 3 represents the common ratio.
a(5) = [tex]5(3^{5-1})=5(3^{4})=5(81)=405[/tex]
answer: 405
Answer:
It is 405.
It is 405.
Use the order of operations and the digits 2, 4, 6, and 8 to create an expression with a value 2.
By using the expression 8 ÷ (4 + (6 - 2)), we can follow the order of operations with the digits 2, 4, 6, and 8 to achieve a result of 2.
Explanation:Tocreate an expression with a value of 2 using the digits 2, 4, 6, and 8, and following the order of operations, one possible solution involves basic arithmetic operations and a thoughtful approach to number manipulation. An example of such an expression is 8 ÷ (4 + (6 - 2)).
Here is the step-by-step explanation:
Start with the operation inside the innermost parentheses: 6 - 2 equals 4.Add this result to 4 (the next number outside the parentheses), which equals 8.Finally, divide 8 (the leftmost number) by the result from step 2, which also equals 2.This method strictly adheres to the order of operations, ensuring that operations within parentheses are done first, followed by division, to achieve the desired result.
Final answer:
An expression using the digits 2, 4, 6, and 8 to equal the value 2 is 16 / 8, achieved by manipulating the operations and order of the digits according to precedence rules and simplifying.
Explanation:
The question requires us to use the digits 2, 4, 6, and 8, along with the correct order of operations, to create an expression that equals 2.
One way to do this is to take advantage of the properties of division and multiplication, which have the same precedence level but are performed from left to right. Using these operations, we can come up with an expression such as 8 / (4 * (6 - 2)), which equals 2. Here's the step-by-step breakdown of the expression:
First, perform the operation within the innermost parentheses (6 - 2) = 4.Next, perform the multiplication operation within the outer parentheses using the result from the first step: 4 * 4 = 16.Finally, divide the number 8 by the result from the second step: 8 / 16 = 0.5.To reach the desired value of 2, flip the fraction to get the reciprocal which leads to 16 / 8 = 2.Thus, the expression that uses the digits 2, 4, 6, and 8 to yield a value of 2 is 16 / 8, after simplification.
0.56 rounded to the nearest tenth
Answer:
60
Step-by-step explanation:
because there is a 6 in the one place five or greater add one more
Solve for x: 3(x + 1) = 2(x - 1)
Answer:
x = -5
Step-by-step explanation:
3(x + 1) = 2(x - 1)
Distribute on both sides.
3x + 3 = 2x - 2
Subtract 2x from both sides.
x + 3 = -2
Subtract 3 from both sides.
x = -5
Answer:
The answer you are looking for is x = -5.
Step-by-step explanation:
First, start by distributing the 3 and 2. This will remove the parentheses. The way you do this is by multiplying each number or variable inside the parentheses by the number outside the parentheses.
3x + 3 = 2x - 2
Next, get the variable to one side. One way to accomplish this is by subtracting 2x from each side.
x + 3 = -2
Lastly, move the numbers to one side. Do this by subtracting 3 from both sides.
x = -5
There you go. Your answer is now in the simplest form. Confirm the answer is as simple as plugging in -5 for x in the original equation.
Please explain and show me how to do question 8 please, I’m dying and I have a test!
Answer:
So linear means equal so you’ll put x on one side and 750 plus 10% on one side and add an equal sign in the middle
I’m really terrible at explaining things but I hope this helped
6. Jefferson purchased a jacket originally priced at $129 on sale for $90.30. What
was the percent of discount?
A. 70%
B. 30%
C. 50%
D. 39%
Final answer:
To find the percent of discount, subtract the sale price from the original price, divide by the original price, and multiply by 100. The percent of discount is 30%.
Explanation:
To find the percent of discount, we need to calculate the difference between the original price and the sale price, and then divide it by the original price and multiply by 100.
Original price - Sale price = $129 - $90.30 = $38.70
Percent of discount = ($38.70 / $129) * 100 = 30%
Therefore, the percent of discount is 30%, which is option B.
Find the missing side round to the nearest tenth
Answer: X = 13.2 (Approximated to the nearest tenth)
Step-by-step explanation: This is a right angled triangle, with one side given, and one angle given. We can calculate the other two sides provided the reference angles are known, and in this question, all angles are known. One is 90°, the second is 47° while the third is 43° (that is 180° - {90° + 47°} )
We shall use angle 47 as the reference angle, and note that the line that lies between the reference angle and the right angle is the adjacent. Note also that the unknown side is the hypotenuse, (the side facing the right angle).
Now that we have established two sides of the triangle, the adjacent (9 units) and the hypotenuse (X), we can calculate the unknown side by using the trigonometrical ratio of cosine.
Cos 47 = adjacent/hypotenuse
Cos 47 = 9/X
By cross multiplication we now have
X/1 = 9/Cos 47
By checking your table of values or by use of your calculator, cos 47 is equal to 0.6819
Therefore
X = 9/0.6819
X = 13.19 units
However, by rounding up to the nearest tenth,
X = 13.2 units
Joaquin reshaped the dough into another three dimensional shape that could have a circular cross section.What is one shape Juaquin could have made?
Answer:
Sphere
Step-by-step explanation:
What is the measure of AC ?
Answer:
Therefore the measure of[tex]\widehat{AC}[/tex] is [tex]39^\circ[/tex].
Step-by-step explanation:
Arc measure : In a circle the degree measure of an arc is equal to the measure of the central angle.
Here the value of central angle is [tex]39^\circ[/tex]
Therefore the measure of[tex]\widehat{AC}[/tex] is [tex]39^\circ[/tex].
Rashid is standing 15 feet away from a tree. The height of the tree is 15 feet. What is the measure of ∠θ, which is the angle of elevation from Rashid's feet to the top of the tree?
You apply the formula of tan^-1(15÷15) wich gives you 45 degrees
A teacher's cabinet has 56 black dry erase markers and 14 red dry erase markers. Which proportion can be used to determine P the percent of dry erase markers that are red?
A=p\100 = 14\56
B=70 / 14 = 100 / p
C=p\14 = 56\100
D=70 / 56 = p\100
Answer:
D. 3b2 + 2b ≥ 56
Step-by-step explanation:
I just did the test too
The correct proportion to determine the percentage of red dry erase markers is 'p/100 = 14/56'. By cross-multiplying and simplifying, we find that 25% of the markers are red.
Explanation:In order to find the percent of dry erase markers that are red, it would be correct to use the proportion 'p/100 = 14/56'. This proportion represents 'p', the percent of red markers out of a total of 100, equal to the actual number of red markers (14) out of the total number of markers (56). Therefore, option A is correct. For example, if you cross-multiply and simplify, you can find the value of 'p' and hence the percentage ratio of red markers. Multiply 14 by 100 to obtain 1400 and then divide 1400 by 56 to obtain 25. Therefore, 25% of the dry erase markers are red.
Learn more about Proportions here:https://brainly.com/question/34018947
#SPJ2
Macon has 32 rocks in his collection. He has 4 times as many rocks as his brother. How many rocks does Macon’s brother have?
Answer:
8
Step-by-step explanation:
macon has 4 TIMES as many as his bro, so just divide 4.
32 / 4 = 8
Does anyone know this??
Answer:
The measure of an interior angle is
180° - 24° = 156°.
This polygon has 360°/24° = 15 sides.
The regular polygon has 24 sides, and each interior angle measures 165°.
The measure of an exterior angle of a regular polygon can be found using the formula: 360° divided by the number of sides.
For a polygon with 24 sides, each exterior angle measures (360° / 24) = 15°.
To find the measure of an interior angle in a regular polygon, we use the fact that the sum of exterior angles in any polygon is always 360°.
Since each exterior angle measures 15°, the corresponding interior angle measures (180° - 15°) = 165°.
The number of sides in a regular polygon can be calculated by dividing 360° by the measure of one exterior angle.
In this case, since each exterior angle measures 15°, the number of sides in the polygon is (360° / 15°) = 24.
Therefore, the regular polygon has 24 sides, and each interior angle measures 165°.
The probable question may be:
The measure of an exterior angle of a regular polygon is given below Find the measure of an exterior angle. The find the number of sides
24
What is the measure of an interior angle?
How many side does the polygon have?
Round to the nearest tenth, if necessary. Question: z2 = 361
options:
A.) 18, –18
B.) 180.5, –180.5
C.) 19, –19
D.) 19
The answer is option C) 19,-19
Step-by-step explanation:
Given, z² = 361
To eliminate the square of z, take square root on both sides
z = √361
The factor of 361 could not be an even number, since the last digit of 361 is odd. So, eliminate option A)The option B) is a larger number and it cannot be the answer. So, eliminate it.Try option C) works or not. (19)² = 19[tex]\times[/tex]19 = 361 and (-19)² = -19[tex]\times[/tex]-19 = 361.Therefore, z = √361 = ±19. option C) is the correct answer.[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{z^2 = 361}\\\\\large\text{Take the square root of the number 361}\\\\\mathsf{z = \pm \sqrt{361}}\\\\\large\text{Simplify it}\\\\\mathsf{z = -19\ or\ z = 19}\\\\\\\huge\text{Therefore your answer should be:}\\\huge\boxed{\mathsf{z = 19\ or\ z = -19 \ (Option\ C.)}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]