The length of a rectangle is 4 inches less than twice its width. If the area of the rectangle is 70 square inches, what are its demensions
Answers
A = w * l
Where,
w: width
l: long
Substituting values we have:
70 = w * (2w-4)
Rewriting we have:
70 = 2w ^ 2-4w
2w ^ 2 - 4w - 70 = 0
Solving the polynomial we have:
w1 = -5
w2 = 7
We take the positive root because it is a dimension.
w = 7 inches
Then, the length will be:
l = 2w-4
l = 2 (7) -4
l = 14-4
l = 10 inches
Answer:
its demensions are:
w = 7 inches
l = 10 inches
x-----------> the length side of rectangle
y----------> the width side of rectangle
we know that
70=x*y--------> x=70/y-----------> equation 1
x-4=2y--------> equation 2
substitute equation 1 in equation 2
[70/y]-4=2y--------> multiply by y------> 70-4y=2y²----> 2y²+4y-70=0
using a graph tool ----> to resolve the second order equation
see the attached figure
the solution is
y=5
x=70/y--------> x=70/5=14
the answer is
the dimensions are
length=14 in
width=5 in
Related Questions
Deon worked 16 hours last week at the grocery store and earned $124.00. If he continues to earn the same hourly pay, how many additional hours must he work to earn another $186.00? A. 20 hours B. 24 hours C. 32 hours D. 62 hours
Answers
The equation of a circle is (x+9)2+(y+6)2=225 .
What is the center of the circle?
Enter your answer in the boxes.
(
,
)
Answers
Answer:
[tex](-9,-6)[/tex]
Step-by-step explanation:
We have been given an equation of a circle [tex](x+9)^2+(y+6)^2=225[/tex]. We are asked to find the coordinates of the center of the given circle.
We know that center-radius form of a circle is in format: [tex](x-h)^2+(y-k)^2=r^2[/tex], where,
[tex](h,k)=\text{Center of circle}[/tex],
[tex]r=\text{Radius of circle}[/tex]
Upon comparing our given equation with center-radius form of a circle we will get,
[tex](x-(-9))^2+(y-(-6))^2=15^2[/tex]
Therefore, the center of our given circle is at point [tex](-9,-6)[/tex].
WILL GIVE BRAINLIEST
solve for x
A. 70/6
B. 60/16
C. 6
D. 11
Answers
Since it gave you options, the easiest way would be to plug it in (plug and chug)
the answer is 11
first what I did was plug 12 into 5x+10 and then found the answer and then added 58°
the answer of that subtracted from 180
with that I then plugged in 11 for x for 11x+2 = 123
180 - 123 = 57 which is the same answer for the missing angle within the triangle
One ounce is equal to 28.35 grams. convert 16 ounces to grams round your answe to the nearest tenth
Answers
The amount 16 ounce into grams using the conversion factor 1 ounce = 28.35 grams is 454.2 grams.
To convert ounces to grams, you can use the conversion factor:
1 ounce = 28.35 grams
Now, to convert 16 ounces to grams:
= 16 ounces * 28.35 grams/ounce
= 454.16 grams
Rounding to the nearest tenth:
454.16 grams rounded to the nearest tenth is 454.2 grams.
Therefore, the required quantity is 454.2 grams.
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To convert 16 ounces to grams, we multiply 16 by the conversion factor of 1 ounce to grams (28.35). This gives us 453.6 grams, when rounded to the nearest tenth.
Explanation:To convert ounces to grams, we use the conversion factor 1 oz = 28.35 g. Given that we are converting 16 ounces to grams, we multiply the number of ounces by the conversion factor.
So, 16 oz * 28.35 g/oz = 453.6 g. Rounding to the nearest tenth, the result is 453.6 g.
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When you have two shapes to compare on a coordinate plane, you can determine the scale factor, knowing that the transformation was a dilation. Generate instructions you would give another student to determine the scale factor.
Answers
The dilation is therefore:
(x,y) ............> (x',y')
Now, let's assume that the dilation factor is k.
Therefore:
x' = kx
y' = ky
Based on the above, all the student has to do is get the initial coordinates and the final ones and then substitute in any of the above two equations to get the value of k.
Example:
Assume an original point at (2,4) is dilated to coordinates (4,8). Find the dilation factor.
Assume the dilation coefficient is k.
(x,y) are (2,4) and (x',y') are (4,8)
Therefore:
x' = kx .........> 4 = k*2 ..........> k = 2
or:
y' = ky ..........> 8 = k*4 .........> k = 2
Based on the above, the dilation coefficient would be 2.
Hope this helps :)
Sample Response: Locate two corresponding ordered pairs of the two shapes. Calculate how much the pre-image values were multiplied by to obtain the image values. This is your scale factor. You can calculate this by dividing the coordinates of the mage by the corresponding coordinates of the pre-image.
The data set represents a month-to-month progression of gasoline prices over the course of several months in an unspecified city. Use a graphing calculator to determine the quadratic regression equation for this data set.
Answers
Answer:
The correct option is a.
Step-by-step explanation:
The general form of a quadratic regression equation is
[tex]y=ax^2+bx+c[/tex] ..... (1)
Using graphing calculator we get
[tex]a=-0.143393\approx -0.143[/tex]
[tex]b=0.59525\approx 0.595[/tex]
[tex]c=2.82964\approx 2.830[/tex]
Substitute these values in equation (1) to find the quadratic regression equation for this data set.
[tex]y=-0.143x^2+0.595x+2.830[/tex]
Therefore the correct option is a.
Find the volume of the pyramid with height 15 and rectangular base with dimensions 3 and 7.
Answers
How do I solve for X?
Answers
tangent distance = 6
External portion of the secant = 3
Full length of the secant = x + 3
6^2 = 3*(x + 3) Remove the brackets.
36 = 3x + 9 Subtract 9 from both sides.
36 - 9 = 3x
27 = 3x Divide by 3
x = 9 <<<<<<<Answer.
A bag contains 10 res marbles, 15 yellow marbles, 5 green marbles, and 20 blue marbles. Five marbles are drawn from the bag. what is the approximate probability that exactly two of the five are blue
Answers
I don't know how to do this question, help!!
Answers
3.5 - 2.75 = 0.75 hours
0.75 hours / 15 meters = 0.05 hours per meter
Celeste wants to have her hair cut and permed and also go to lunch she knows she will need $95. the perm costs twice as much as her haircut and she needs 5$ for lunch. how much does the perm cost
Answers
now here's the solution:
x + 2x + 5 = 95
3x = 90
x = 30 (haircut)
so 2x = 60 (which is the cost of the perm)
Hope this helps!
PLEASE HELP !!
2. A cube-shaped aquarium has edges that are 3 ft long. The aquarium is filled with water that has a density of 62 lb/ft³.
(a) Should the aquarium be placed on a table that can support a maximum weight of 200 lb? Explain why or why not.
(b) Would the density of the water change if the aquarium was only half full? Explain.
Answers
Let's find the volume of the tank.
Volume of a rectangular prism = length*width*height
V = L*W*H
V = 3*3*3
V = 27 cubic feet
There is 27 cubic feet of water in the tank if the tank is completely full. Use the fact that
1 cubic foot of water = 62 pounds
so we can convert from volume to weight
(27 cubic feet)*(62 pounds/1 cubic foot) = 27*62 = 1674 pounds
If the tank is completely full, then the water weighs 1674 pounds, which is far greater than the 200 lb max weight limit for the table. The table will fall apart if you place a full aquarium on top of it. Note: this is not including anything else that would go inside the tank such as rocks, plant matter, fish, the glass of the tank itself, etc
In short, the aquarium should not be placed on the table as it exceeds the table's weight limit.
---------------------------------------------------------------------------
Part (b)
The density will not change because the density is how packed in a substance is for any cubic unit of volume. Saying "the density of water is 62 pounds per cubic foot" means that for a cubic foot, water naturally weighs 62 pounds .We can scale this to any size we want and the density will stay the same.
It's like saying that the fractions 1/2 and 2/4 are the same. The 2/4 is the scaled version of 1/2. So back to the water example, if we had 2 cubic feet of water then it would weigh 2*62 = 124 pounds. So the ratio
2 cubic feet: 124 pounds
simplifies back to
1 cubic foot: 62 pounds
note: the larger the density, the heavier the object is assuming the volume is held constant
The weight of the water in the cube-shaped aquarium will be 1674 lb, which is much greater than the table's maximum weight capacity of 200 lb. Therefore, the aquarium should not be placed on the table. The density of the water remains constant at 62 lb/ft³ regardless of how much the aquarium is filled.
To determine if the aquarium can be placed on a table with a weight limit of 200 lb, we must first calculate the weight of the water the aquarium will hold. We calculate the volume of the aquarium, then multiply it by the density of water, as the density is given as weight per unit volume (specifically 62 lb/ft³).
The volume (V) of a cube is given by V = side³, so for our aquarium with 3 ft long edges, V = 3³ = 27 ft³. The weight of the water (W) is therefore W = density x volume = 62 lb/ft³ x 27 ft³ = 1674 lb. Since 1674 lb exceeds the table's maximum weight capacity of 200 lb, the aquarium should not be placed on the table.
As for part (b), the density of the water does not change whether the aquarium is full or half full. Density is an intensive property meaning it's independent of the quantity of the substance present. Therefore, whether the aquarium is filled or only half filled, the density of the water remains at 62 lb/ft³.
realtor makes 3% commission. What is the commission on a $200,000 house?
Answers
multiply 200,000 with 0.03
200000 x 0.03 = 6000
$6000 is the commission on a $200,000 house, with the total cost becoming $206,000
hope this helps
shadesha invests $24,000 at age 27. at the age 31 jerome invests $2000 annually until retirement both invest at 7% compounded annually to plan to retire at 65 who has more money for retirement
Answers
Applying annuity formula, Jerome will earn [tex]FV_{34}=2000( \frac{(1+0.07)^{34}-1 }{0.07}) = $256,517. 529629 [/tex]
Shadesha will have more money
what is the sum of 2 2/3 and 1 5/6?
Answers
2 2/3 = 8/3
1 5/6 = 11/6
Next, make the fractions have same denominators. Note, that what you do to the denominator, you do to the numerator.
8/3(2/2) = 16/6
Add
16/6 + 11/6 = 27/6
27/6 = 4 3/6 = 4 1/2
4 1/2 is your simplified answer
hope this helps
What is tan (x)?
20/21
20/29
29/21
29/20
Answers
The first step is to use the pythagorean theorem a^2+b^2 = c^2 to find the missing side to be 21. Once you know this, you find the ratio of the opposite and adajcent sides. The opposite side is the leg furthest from the angle x (the side labeled 20). The adjacent side is the leg closest to or touching the angle x (the side labeled 21 which was found earlier).
So, tan(x) = opposite/adjacent = 20/21
Solve 7 + x - 15 = -2
5 1/3
6 1/3
10 2/3
20 2/3
Since the mod decided to delete my question because of a mistake. Please answer. Need it ASAP
Answers
Combine like terms
(7-15)+x=-2
-8+x=-2
+8 +8
x=6
6 is your answer.
Check :
7+6-15=-2
13-15=-2
-2=-2
Correct!
Hoped I helped!
) the supplement of an angle is thirty more than twice the angle. find the measure of the angle and its supplement. answer
Answers
50 x 2 = 100
100 + 30 = 130
130 + 50 = 180
The other angle would be 130 degrees. And the original angle would be 50.
Please help math question
Answers
___
A spreadsheet is useful for figuring the result of payments on loans.
How do you find the base of this triangle? (Picture should be able to be seen)
Answers
since all three are similar, we can use the proportions on the corresponding sides, as you see in the picture, the base of the triangle then will just be x + y.
There are 750 toothpicks in a regular sized box. If a jumbo box is made by doubling all the dimensions of the regular sized box, how many toothpicks will the jumbo box hold? (With work pls)
Answers
To answer this, let the 3 sides of the regular sized rectangular box be x, y, and z.
When we double all the sides, the new sides have lengths 2x, 2y, and 2z, respectively.
Since the regular box (with dimensions x,y, and z) have 750 toothpicks, we can write
[tex]xyz=750[/tex]
Similarly we can write for the jumbo box as,
[tex](2x)(2y)(2z)[/tex]
which is equal to [tex]8(xyz)[/tex]
So this is 8 times the original of [tex]xyz[/tex]. Hence the jumbo box will have 8 times 750 number of toothpicks.
ANSWER: [tex]8*750=6000[/tex] toothpicks
Answer:
6000
Step-by-step explanation:
How many eggs are needed to make 1 dozen waffles, assuming you have enough of all other ingredients? given: 2 cups flour + 3 eggs + 1 tbs oil → 4 waffles
a. 12
b. 48
c. none of these choices is correct
d. 9
e. 16?
Answers
We have been given that
2 cups flour + 3 eggs + 1 tbs oil → 4 waffles
In order to make 4 waffles we need 3 eggs.
Thus, to make 1 waffle we need 3/4 eggs.
Now, in 1 dozen there are 12 waffles. Hence, to make 12 waffles we need
[tex]\frac{3}{4} \times 12\\ \\ =3 \times 3\\ =9[/tex]
Therefore, 9 eggs are needed to make 1 dozen waffles.
D is the correct option.
Final answer:
The correct option is (d) 9. Using the given recipe, we can determine that 9 eggs are needed to make 1 dozen waffles by setting up a proportion and solving for the number of eggs.
Explanation:
The original recipe provided states that 2 cups of flour, 3 eggs, and 1 tablespoon of oil will yield 4 waffles. To find out how many eggs are needed to make 1 dozen (12) waffles, we need to set up a proportion based on the given recipe.
Since 4 waffles require 3 eggs, we can set up the following equation: 4 waffles / 3 eggs = 12 waffles / x eggs. Cross-multiplying gives us 4x = 36, and dividing both sides by 4 gives us x = 9. Therefore, 9 eggs are required to make 1 dozen waffles.
Find the volume of a cylinder that has the following dimensions. Do not round your answer. (Use 3.14 for π.)
CONVERT M INTO CM
Answers
The volume of cylinder is 1962.5 [tex]cm^{2}[/tex].
To find the volume of a cylinder.
What is mensuration?The part of geometry concerned with ascertaining lengths, areas, and volumes. Mensuration deals with the size, region, and density of different forms both 2D and 3D.
Given that:
Radius= 5 cm
Height= 0.25 m=25 cm
π=3.14
By the formula of volume of cylinder
Volume=π[tex]r^{2} h[/tex]
TO put the value,
Volume=3.14*5*5*25
Volume=1962.5 [tex]cm^{2}[/tex]
So, the volume of cylinder is 1962.5 [tex]cm^{2}[/tex].
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Which equation shows 2x – y = 6 converted to slope-intercept form? y = x – 3 y = 2x – 6 y = –2x + 6
Answers
so you would subtract the 2x over to get -y=-2x+6 then you would divide by -1 to get y=2x-6
so y=2x-6 is the answer
p(x)= x^3+4x^2-8x-6
a= -2
Answers
If that's the case, then
P(-2) = (-2)^3 + 4(-2)^2 - 8(-2) - 6. This simplifies to:
= -8 + 16 + 16 - 6 = 18 (answer)
The longest side of an obtuse triangle measure 20 cm. the two shorter sides measure x cm.and 3x sm round to the nearest tenth,what is the greatedt possible value of x
Answers
22cm is the greatest
It should be greater than17(20-3)
and smaller than 23(20+3)
The side of a square measures 2x^2y^3 what is the area of the square if x=-2 and y=2
Answers
The area of the square is -128.
Help
How much will $5,000 invested at 6% compounded annually amount to after 10 years?
Answers
5000 + 0.06(5000)
For 10 years:
5000 + 10(0.06(5000))
Multiply:
5000 + 0.6(5000)
We can make it smaller:
1.6(5000) = 8000
You can make $8000
A wheelchair ramp has a slope of 1 10 . if its rise is 1 5 2 feet, what is its run?
Answers
[tex]slope = \frac{rise}{run} \\ 110 = \frac{152}{run} \\ run \times 110 = 152 \\ run = \frac{152}{110} \\ run = \frac{76}{55} \: \: \: \: or \: \: \: 1.38[/tex]
1) If the endpoints of the diameter of a circle are (9, 4) and (5, 2), what is the standard form equation of the circle?
Answers
Midpoint = [tex]( \frac{X1+X2}{2} , \frac{Y1+Y2}{2} )[/tex]
where X1 is the x-coordinate of the first ordered pair and Y1 is the y-coordinate of the first ordered pair. Same applies to X2 and Y2. So now we plug in.
Mdpt = [tex]( \frac{9+5}{2} , \frac{4+2}{2} )[/tex]
= [tex]( \frac{14}{2} , \frac{6}{2} )[/tex]
Your midpoint is at (7, 3).
This gives you the beginning of the equation. The equation of a circle is:
(x - h)² + (y - k)² = radius²
where (h, k) is the center.
Your equation is:
(x - 7)² + (y - 3)² = radius²
To find the radius, we do either the distance formula from the center to either of the endpoints. Or the distance between the two endpoints divided by two. Depends on which one you want to do. I choose the latter, but it's all personal preference.
Distance formula = √((X2 - X1)² + (Y2 - Y1)²)
So we plug in:
D = √((5 - 9)² + (2 - 4)²)
D = √((- 4)² + (- 2)²)
D = √(16 + 4)
D = √20
Distance of the diameter = 2√5
Now divide that by 2, your radius is √5
Now we plug in to the equation:
(x - 7)² + (y - 3)² = (√5)²
Your final equation is:
(x - 7)² + (y - 3)² = 5