Answer:
1) The picture whose width = x and Length = (x + 8) feet
2) Width = 4 feet
Length = 12 feet
Step-by-step explanation:
A rectangle has one side longer than the other.
Area of a rectangle = product of its sides.
= length × width
Width = x feet
Length = (x + 8) feet
Area = 48
∴ x × (x + 8) = 48
x² + 8x = 48
x² + 8x + 4² = 48 + 4²
(x + 4)² = 64
x + 4 = √64
x = ±8 - 4
x = - 12 or x = 4
Since length can not be negative, x = 4
∴ Width = 4 feet
Length =4 + 8 = 12 feet
The dimensions of the rectangle where its area is 48 square feet and length is 8 feet more than width is 4 feet (width) and 12 feet (length). The question is set on algebra, calculation of area and understanding of shapes.
Explanation:This problem falls under the category of algebra and involves understanding the concept of shapes, particularly rectangles, and calculation of their area.
We know, the area of a rectangle is calculated as the product of its length and width. Given that the area is 48 square feet and the length is 8 feet more than the width. Let's denote the width as 'w' and the length as 'w + 8'.
So, we can set up the equation as: w * (w + 8) = 48. Solving this quadratic equation will give us the values for 'w' and 'w + 8' or the dimensions of the rectangle.
If you factor the quadratic equation, you get (w - 4)(w + 12) = 0. Setting these factors to zero, we find that w = 4 or w = -12. Since width cannot be negative, the width is 4 feet. And the length, which is 8 feet more than the width, will be 4 + 8 = 12 feet.
For the picture representation, simply imagine or draw a rectangle. Label the shorter side as 4 feet (width) and longer side (length) as 12 feet.
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Math help pls,, will give brainiest reward! :)
Answer
16
Step by step
The triangles,PRS and PQT are similar.
PS:ST=15:3
=5:1
let PQ=x
PR:RQ
x+4:4
using the PS:ST ratio,
5:1=x+4:4
4×5=1(x+4)
20=x+4
collecting like terms
20-4=x
x=16.
You must show all steps and provide any evidence needed in your solution to receive full credit.
4. The company is building a scale model of the theater’s main show tank for an investor's presentation. Each dimension will be made one eight of the original dimension to accommodate the mock-up in the presentation room. What is the volume of the smaller mock-up tank?
5. Using the information from #4, answer the following question by filling in the blank: The volume of the original main show tank is ____% of the mock-up of the tank.
Answer:
4) Volume model = 1723 ft³
5) The percentage of the original tank is 51200% of the mock-up
Step-by-step explanation:
4) ∵ The volume of the main tank is 882,158 ft³
∵ The dimension of the scale model is 1/8 of the original model
∵ V model/v original = (dimension model/dimension original)³
∴ Volume model/882,158 = (1/8)³
∴ Volume model = (1/512) × 882,158 = 1722.965 = 1723 ft³
5) The percentage of the original tank is
(882158/1722.965) × 100% = 51200%
Final answer:
The volume of the scale model tank is 1/512 of the original tank's volume, which is approximately 0.1953125%. The original tank's volume is 51200% of the scale model's volume.
Explanation:
Step-by-Step Solution for Volume of Scale Model Tank
Let's denote the original dimensions of the theater's main show tank as length L, width W, and height H. Therefore, the original volume V of the tank is V = L \times W \times H.
For the scale model, each linear dimension is scaled down to one eighth of the original. Thus, the dimensions of the model will be L/8, W/8, and H/8.
Now, the volume of the scale model V_{model} can be calculated as:
The volume of the scale model is 1/512 or about 0.1953125% of the original tank's volume.
Percentage Volume of Original Tank to Mock-up Tank
To find out what percentage the original volume is of the mock-up tank, we can set up a proportion.
The original volume is 51200% of the mock-up of the tank.
Ian ran a total of 6 miles around his school track. Each lap around the track is 3/4 mile. What math expression can be used to find the number of laps Ian ran? How many laps did he run?
Answer:
The answer is 8
Step-by-step explanation:
PLZ HELP
Robert makes a monthly budget. His monthly
allowance is $40. He makes $25 each month from
mowing the neighbor’s yard. Robert’s monthly
expenses are $75. How much does he need to earn
from babysitting to balance his budget?
A $75
B $10
C $50
D $35
How many yards long is John's new surfboard if it is 7 feet long
A) 2 1/3
B) 2 2/3
C) 4 yards
D) 21 yards
Answer:
A)
Step-by-step explanation:
An item regularly priced at $80 is on sale for 20% off. There is 3% sales tax. What is the sales price before sales tax?
Answer:
Price before tax is $64
Step-by-step explanation:
It asks for price before sales tax, so ignore sales tax %.
P=original-[original•(20/100)]
=80-80•0.2
=80-16
P=64
Answer:
$64
Step-by-step explanation:
We have been given that an item regularly priced at $80 is on sale for 20% off. There is 3% sales tax. We are asked to find the sales price before sales tax.
The sales price would be 80 minus 20% of 80.
[tex]\text{Sales price}=80-\frac{20}{100}\times 80[/tex]
[tex]\text{Sales price}=80-\frac{1600}{100}[/tex]
[tex]\text{Sales price}=80-16[/tex]
[tex]\text{Sales price}=64[/tex]
Therefore, the sales price before sales tax would be $64.
A store is having a Back To School Sale.The total for a skirt,a pair of shoes,and a pair of socks is $34.95 before tax.The pair of socks costs $3.75.The original prices of the skirt and shoes were the same.What was the sales price of the skirt
Final answer:
The sales price of the skirt was $15.60.
Explanation:
In this problem, we are given that the total cost of the skirt, pair of shoes, and pair of socks is $34.95 before tax. We are also given that the pair of socks costs $3.75. Since the original prices of the skirt and shoes were the same, we can assume they each cost x dollars.
Therefore, the equation we can set up is: x + x + 3.75 = 34.95.
We can solve this equation to find the value of x, which represents the original price of the skirt. Subtracting 3.75 from both sides, we get: 2x = 31.20. Dividing both sides by 2, we find that x = 15.60. Therefore, the sales price of the skirt was $15.60.
The graph shows the cost of one pound of apples at the grocery store. Find the slope of the line??????
i dont understand!!
Answer:
[tex]\large\boxed{The\ slope=\dfrac{3}{2}}[/tex]
Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the graph we have the points (0, 0) and (4, 6) - look at the picture.
Substitute:
[tex]m=\dfrac{6-0}{4-0}=\dfrac{6}{4}=\dfrac{6:2}{4:2}=\dfrac{3}{2}[/tex]
The slope of the line is [tex]\frac{3}{2}[/tex]
What is slope of a line ?
The change in y co-ordinate with respect to the change of x co-ordinate of a line is called the slope of the line.
Slope of a line is denoted by "m"
If two points on the line are [tex](x_{1},y_{1})[/tex] & [tex](x_{2} ,y_{2})[/tex], then m = [tex]\frac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex]
What is the required slope ?From the given graph, We take to points (2, 3) & (4, 6)
Now, Slope (m) = [tex]\frac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex]
= [tex]\frac{6-3}{4-2}[/tex]
= [tex]\frac{3}{2}[/tex]
The slope = [tex]\frac{3}{2}[/tex]
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Alice took out a $15,000 loan for college. She is borrowing money from two banks. Bank A charges an interest rate of 6%, and Bank B charges an interest rate of 7%. After one year, Alice owes $960 in interest. How much money did she borrow from Bank A?
Answer:
Final answer is $9000.
Step-by-step explanation:
Given that Alice took out a $15,000 loan for college. She is borrowing money from two banks. Bank A charges an interest rate of 6%, and Bank B charges an interest rate of 7%. After one year, Alice owes $960 in interest.
Now we need to find out about how much money did she borrow from Bank A.
So let's assume that money borrowed from bank A = x
then money borrowed from bank B = 15000-x
Interest from bank A = 6% of x = 0.06x
Interest from bank B = 7% of (15000-x) = 0.07(15000-x)
Given total interest is $960. So we can write equation:
0.06x+0.07(15000-x)=960
0.06x+1050-0.07x=960
1050-0.01x=960
-0.01x=960-1050
-0.01x=-90
[tex]x=\frac{-90}{-0.01}[/tex]
x=9000
Hence final answer is $9000.
Answer:
The amount borrowed from bank A = $9000
Step-by-step explanation:
Formula:
I = PNR/100
P - Principle amount
N - Number of years
R - Rate of interest
It is given that,Alice took out a $15,000 loan for college. Bank A charges an interest rate of 6%, and Bank B charges an interest rate of 7%. After one year, Alice owes $960 in interest.
Let 'x' be the amount borrowed from Bank A
Then the amount borrowed from Bank B = 15000 - x
To find the value of x
I = PNR/100
Here I = $960
(x*1*6)/100 + (15000 - x)*1*7/100 = 960
6x/100 + (15000*7)/100 - 7x/100 = 960
1050 - x/100 = 960
x/100 = 1050 - 960 = 90
x = 90 * 100 = 9000
Therefore the amount borrowed from bank A = $9000
Please help me with 26
Answer:
Step-by-step explanation:
3x3=9 For the second week
9x3=27 For the Third week
27x3=81 For the Forth week so
3 Min first week
9 Min second week
27 Min third week
81 Min forth week
A living room has a circular rug with a diameter of 8 feet. What is the rug's area? Use 3.14 for .
Answer:
Step-by-step explanation: 50.27 is the area
Final answer:
The area of a circular rug with an 8 feet diameter, using the formula A = π[tex]r^2[/tex] and π approximated as 3.14, is 50.24 square feet.
Explanation:
The question seeks to determine the area of a circular rug with a diameter of 8 feet. To calculate the area of a circle, the formula used is A = π[tex]r^2[/tex], where A is the area and r is the radius of the circle. Since the diameter is twice the radius, we have a radius of 4 feet (8 feet divided by 2).
Using 3.14 for π, the calculation is:
First square the radius: 4² = 16.
Multiply this by π (approximated as 3.14): A = 3.14 × 16.
Complete the multiplication to find the area: A = 3.14 × 16 = 50.24 square feet.
Therefore, the area of the rug is 50.24 square feet.
The button on Monica's shirt has a radius of 1 centimeter. What is the button's diameter?
radius(r)=1cm
answer:-
diameter(d)=2r=2cm
Answer:
diameter = 2cmStep-by-step explanation:
A diameter is two times longer than a radius. Therefore, if the radius r = 1cm, then the diameter d = 2(1cm) = 2cm.
need help asap!!! plzz
What is 75% of 240?
(A)150
(B)60
(C)165
(D)180
Answer:
D) 180
Step-by-step explanation:
Keep in mind to properly use a percent you must set it to a decimal.
To do so simply move the . in 75. over to the left 2 times. Which will go to .75!
Now time to multiply 240 by .45.
240 x .45 =180
Answer:
D 180
Step-by-step explanation:
75/100*240=180
Which transformation will always map a parallelogram onto itself? A. a 90° rotation about its center B. a reflection across one of its diagonals C. a 180° rotation about its center D. a reflection across a line joining the midpoints of opposite sides
Answer:
C. a 180° rotation about its center.
Answer:
The correct answer option is C. a 180° rotation about its center.
Step-by-step explanation:
We are to determine whether which of the transformations will always map a parallelogram onto itself.
We know that a parallelogram has a rotational symmetry of 2 so during a rotaion of 360 degrees, a parallelogram maps onto itself twice, which is at 180^{\circ} and 360^{\circ} about its center.
Therefore, the correct answer option is C. a 180° rotation about its center.
Given the points (3,0) and (-1,-3) which of the statements below is true
What are the statements?
Final answer:
The given statements about the points (3,0) and (-1,-3) are not true. One cannot determine if they are parallel to x-axis or mutually perpendicular without more information or a third point/vector.
Explanation:
The question describes two points, (3,0) and (-1,-3), and asks which statements are true regarding their position. To determine the relationship between these points, we can visualize them on a coordinate system. Point (3,0) lies on the x-axis, while point (-1,-3) does not. The statements provided suggest a scenario where the points either form parallel lines along the x-axis or are mutually perpendicular to each other.
Neither of the given statements is correct since one point lies on the x-axis, and the other does not, which means they cannot be parallel along the x-axis. Additionally, without a third point to form a triangle or a clear reference for perpendicular vectors, we cannot assert that they are mutually perpendicular. Therefore, we need additional information, such as the context for these points or the third reference point/vector, to make a proper determination.
Regarding the information about vectors and coordinates, remember that vectors can be used to define directions and magnitudes from one point to another. In this case, however, we are only given two points without clear instruction on how to interpret them as vectors.
For the statement 'Clearly, the three directions are mutually perpendicular to each other,' note that this applies to three-dimensional coordinate axes or where three vectors are given, which are specifically defined as perpendicular. This situation described with two points does not satisfy the conditions of that statement.
which of the following has two bases?
A. prism
B. pyramid
C. line
D. plane
A. Prism
A prism has two bases
Will give brainly
ABCD =JKLM
What side in the second quadrilateral corresponds to AD?
Jk
Kl
LM
JM
Answer:
JM
Step-by-step explanation:
If it is equal to each other than all you do is look at what it will be like for the other one.
A is at the beginning and D is at the end.
J is at the beginning and M is at the end.
JM is your answer.
Answer:
JM corresponds to AD.
Step-by-step explanation:
Look at their relative positions in the 2 names.
A and D are the first and last letters.
So the answer is JM because they are the first and last letters in JKLM.
Triangle ABC is shown below :
Answer:
try the answer C
Step-by-step explanation:
What is the number????
Step-by-step explanation:
[tex]n-a\ number\\\\3.145<n<3.146\Rightarrow 3.1450<n<3.1460\\\\n\in\{3.1451,3.1452,\ 3.1453,\ 3.1454,\ ...,3.1459\}[/tex]
Find the seventh term of
Answer:
99
Step-by-step explanation:
tell whether the sequence is arithmetic 4,8,16,22,32
Answer:
see explanation
Step-by-step explanation:
If the sequence is arithmetic then there will be a common difference d between consecutive terms, that is
8 - 4 = 4
16 - 8 = 8
22 - 16 = 6
32 - 22 = 10
The difference between terms is not common
Hence this is not an arithmetic sequence
in mrs. wallace class's science class, 1/2 of the students are boys. Of the boys , 1/8 are left- handed. what fraction of the students in Mrs wallace science class are left handed
Answer:
1/16 of the class are left handed boys but we do not know the amount of left handed girls so we cannot be sure.
Step-by-step explanation:
1/2 * 1/8 = 1/16
there is still no way to be sure of how many girls are left handed so you should probably make a note by the problem so the mistake on the test will be realized
By multiplying the fractions, we find that 1/16 of the students in Mrs. Wallace's science class are left-handed boys.
Explanation:To solve this problem, we first need to understand that it involves fraction multiplication. We know that 1/2 of the students in Mrs. Wallace's science class are boys. Out of these boys, we know that 1/8 of them are left-handed.
When you want to find out a certain amount out of a fraction, you multiply fractions. In this case, 1/2 (the number of boys in class) times 1/8 (the fraction of boys who are left-handed) gives us 1/16. Therefore, 1/16 of the students in Mrs. Wallace's science class are left-handed boys.
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can someone help me.
Answer:
[tex]\large\boxed{x=\pm\sqrt{10}}[/tex]
Step-by-step explanation:
[tex]x^2=10\Rightarrow x=\pm\sqrt{10}\\\\\text{because}\ (-\sqrt{10})^2=10\ \text{and}\ (\sqrt{10})^2=10.\\\\\text{used}\ (\sqrt{a})^2=a[/tex]
PLEZ HELP ME ASAP 21.66÷5.7
Answer: 3.8
Step-by-step explanation: See the attached file!
How many committees or three people are possible from a group of 12
I thinks its 4 if that's one of your answers. It says of 3 people from a group of 12. And a 3 and 4 are both factors of 12. 3 x 4 = 12.
The number of possible committees of three people from a group of 12 can be found by using combinations, resulting in 220 possible committees.
The number of committees of three people possible from a group of 12 can be calculated using combinations.
To choose 3 people out of 12, you use the combination formula: C(12,3) = 220.
Therefore, there are 220 possible committees of three people from a group of 12.
Which equations are true?
Choose all answers that apply:
A. − x = −x + x + 0
B. − x = 0 + (−x)
C. None of the above
B 'cause A return value equal to 0
50 POINTS!! HELP ME PLEASE HURRY IM RUNNING OUT OF TIME!!!
Find the volume of each figure to the nearest tenth.
Volume of sphere = 4/3 x PI x r^3
= 4/3 x 3.14 x 6^3
= 904.3 cubic meters
Volume of cone = PI x r^2 x h/3
h = √13^2-5^2 = 12
= 3.14 x 5^2 x 12/3
= 314 cubic meters
A machine uses pieces of tape to seal packages. It cuts the tape into pieces exactly 2.375 inches long. If it uses 4 pieces of tape for a package, how many packages can it seal with a roll of tape of 1,900 inches long?
Answer:
200
Step-by-step explanation:
Which expression gives the measure of ACE in the diagram below
Answer:
B
Step-by-step explanation:
There are 2 secant lines intersecting a circle. We can use far arc - near arc formula to find this.
Let far arc be arc AE, and near arc be arc BD. So the theorem tells us:
Measure of Angle C = half of the difference of far arc - near arc
so we can say:
∠ACE = half of (arc AE - arc BD)
or
∠ACE = [tex]\frac{1}{2}(172-58)[/tex]
Option B is right.
Answer:b
Step-by-step explanation:
!!~~I RAISED THE POINTS AND WILL GIVE BRAINLIEST ITS ALSO MULTIPLE CHOICE~~!!
which describes the type of sequence in 99, 89.9, 78.8, 68.7, . . . . . ?
a) neither geometric nor arithmetic
b) geometric
c) arithmetic
d) both arithmetic and geometric
(pLeAsE TelL mE wHY yOu PIcKeD YoUr AnSwER)
Answer:
a) Neither arithmetic nor Geometric
Explanation:
Since 99-89.9= 9.1, and 89.9 - 78.8 = 11.1, the sequence is not arithmetic.
Like wise 89.9/99=0.908 and 78.8/89.9 = 0.876 makes it not a geomtric sequence
Step-by-step explanation:
Answer: Option 'a' is correct.
Step-by-step explanation:
Since we have given that
99, 89.9, 78.8, 68.7, . . . . .
Here,
[tex]a_1=99\\\\a_2=89.9\\\\a_3=78.8\\\\a_4=68.7[/tex]
But we can see that there is minor difference between the consecutive terms:
So, we will go for common difference whether it is same or not.
[tex]a_2-a_1=89.9-99=-9.1\\\\a_3=a_2=78.8-89.9=-11.1\\\\a_4-a_5=68.7-78.8=-10.1[/tex]
Their difference are not common.
So, It is neither geometric nor arithmetic.
Hence, Option 'a' is correct.