Answer:
[tex]Area=25\,\,in^2[/tex]
Step-by-step explanation:
The length of the rectangle is unknown and is defined with the letter "x". Notice that the width of the rectangle is also unknown, so we can name it 'y".
Recall the formula for the area of a rectangle (length times width), and notice that it is this quantity the one we need to maximize (find the maximum possible value).
We use the other information provided to represent the rectangle's with (y) in terms of "x" :
length + width = 10 inches
x + y = 10
Therefore, y = 10 - x
Now we use this expression for "y" in the product for the area;
[tex]Area= x\,*\,y\\Area=x\,(10-x)\\Area=10x-x^2\\Area=-x^2+10x[/tex]
Notice that this quadratic expression corresponds to a parabola with branches pointing down (negative leading term), so its maximum value would be given at the vertex of the parabola.
Now recall that the formula for the x-value of a parabola's vertex when its function is of the form [tex]f(x)=ax^2+bx+c[/tex]
is given by:
[tex]x_{vertex}=-\frac{b}{2a}[/tex]
which in our case where "a" = -1 and "b" = +10, gives:
[tex]x_{vertex}=-\frac{b}{2a}\\x_{vertex}=\frac{-10}{2(-1)}\\x_{vertex}=\frac{-10}{-2}\\x_{vertex}=5[/tex]
Then the maximum value for the Area can be obtained by replacing "x" with "5" in the area formula:
[tex]Area=-x^2+10x\\Area=-(5)^2+10\,(5)\\Area=-25+50\\Area=25\,\,in^2[/tex]
Therefore, the area of the rectangle is [tex]25\,\,in^2[/tex]
Jane is going to fence in her backyard. She has purchased 150 feet of fencing
and knows that she wants to fence in a rectangular area where one side will
be the back of her house. She knows her huse is 40 feet across the back.
Which of the following is the equation that Jane can use to figure out how far
back from the house she can fence in?
Answer:
Two sides of the rectangle will extend from the wall of the house, one side of the rectangle will run parallel to the house 40 ft..
Step-by-step explanation:
2x + 40 = 150
or
x + x + 40 = 150
Mountain climber Joe climbed to a mountain peak that was1200 feet above its base and 1500 feet east of its base. Mountain climber Bob climbed to a mountain peak that was 900 feet above its base and 1000 feet east of its base.
Who climbed a steeper mountain? Explain.
Answer:
Joe’s mountain had a rise of 1200 and a run of 1500, making the slope of the mountain 4/5. Bob’s mountain had a rise of 900 and a run of 1000, making the slope of the mountain 9/10. Since 9/10 is larger than 4/5, the slope of Bob’s mountain is steeper than the slope of Joe’s mountain.
Step-by-step explanation:
edge 2020
Answer:
Sample Answer: Joe’s mountain had a rise of 1200 and a run of 1500, making the slope of the mountain 4/5. Bob’s mountain had a rise of 900 and a run of 1000, making the slope of the mountain 9/10. Since 9/10 is larger than 4/5, the slope of Bob’s mountain is steeper than the slope of Joe’s mountain.
Step-by-step explanation:
A beaker is completely filled with water
A ball in the shape of a sphere with radius 4 centimeters is placed in the beaker and is completely submerged, causing the volume of water equal to the ball’s volume to overflow.
All of the water that overflows is collected in a funnel in the shape of a cone.
When the funnel is held vertically, the surface of the water collected forms a circle of radius 4 centimeters.
What is the height of the cone formed by the water in the funnel?
Round your answer to the nearest inch.
Answer:6.3 in.
Step-by-step explanation:
Given
Radius of sphere [tex]r=4\ cm[/tex]
When ball is immersed in beaker, it causes the water to flowout of beaker which is collected in the conical vessel
Such that amount of water equivalent to sphere volume is collected in it.
volume of ball
[tex]V_s=\frac{4\pi }{3}r^3[/tex]
[tex]V_s=\frac{4\pi }{3}\times 4^3[/tex]
[tex]V_s=\frac{256\pi }{3}\ cm^3[/tex]
Now volume of water collected is in shape of cone then volume of cone
[tex]V_c=\frac{\pi }{3}r^2h[/tex]
and [tex]V_s=V_c[/tex]
[tex]\frac{256\pi }{3}=\frac{\pi }{3}(4)^2\times h\ quad [\text{h=height of cone formed}][/tex]
[tex]h=4^2=16\ cm\approx 6.29\approx 6.3\ in.[/tex]
1. Calculate the volume of a cube with the following measurements. Length = 5 cm Height = 10 cm Width = 16 cm 800 cubic cm 400 cubic cm 31 cubic cm 50 cubic cm
Answer:
800
Step-by-step explanation:
lol ain't even a cube das a rectangle
The age of father is three times the age of son. If the age of son is 15 years old, then the age of father is:
50 years
55 years
45 years
40 years
What is the radius of a circle whose equation is x2+y2+8x−6y+21=0? Please just copy and paste this into brainly, I ran out of skips
Answer: 2
Step-by-step explanation:
Answer:
The Radius of the circle of center (-4, 3) is 2.
Radius = 2
Step-by-step explanation:
This is the general form:
[tex]x^2+y^2+8x-6y+21=0[/tex]
Let's convert this to standard form:
[tex]x^2+y^2+8x-6y+21=0[/tex]
[tex]x^2+y^2+8x-6y=-21[/tex]
Group/organize [tex]x[/tex] and [tex]y[/tex] terms:
[tex]x^2+8x+y^2-6y=-21[/tex]
[tex](x^2+8x)+(y^2-6y)=-21[/tex]
Now, let's begin the process to complete the square in both parentheses.
[tex](x^2+8x+16)+(y^2-6y+9)=-21+16+9[/tex]
[tex](x+4)^2+(y-3)^2=4[/tex]
What is the definition of “slope of a ramp using trigonometry ?”
Answer:
Step-by-step explanation:
it is the tangent of the angle slope makes with the horizontal.
I don’t need you to explain just answer.
Answer:
-4 <x< -2
Step-by-step explanation:
you need to plot the line between -4 and -2
There are 42 citizens called for jury duty. Eleven are randomly chosen to for the interview phase. How many different ways can the group of interviewees be made?
The quick way to get the answer is just type "42 choose 11" into Google.
Or if you want to figure it out yourself, you have 42 choices for the first potential juror, 41 choices for the second potential juror, etc.
Now before you stop there, you only care about the combination of the 11 people chosen, not what order they are selected, so you need to divide by the ways to arrange 11 people.
Final expression:
C(42,11) = (42 * 41 * 40 * 39 * 38 * 37 * 36 * 35 * 34 * 33 * 32) / (11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)
Answers:
4,280,561,376 ways
Answer:
42,11
Step-by-step explanation:
Solve 7x - 1 = 20 help
furniture maker used 1/2 of a can of paint to paint some chairs. She used 1/6 of a can of paint for each chair. How many chairs did she paint?
Answer:
3 chairs
Step-by-step explanation:
1/2 is the same as 3/6
There are three 1/6 in 3/6.
(3/6) ÷ (1/6) = 3
The requried, she painted 3 chairs as of the given proportion.
What is proportionality?Proportionality is the relationship between two or more sets of values, and it describes how these values are related to each other.
Here,
Let's assume that the number of chairs she painted is represented by the variable 'c'.
We know that she used 1/6 of a can of paint for each chair. So, the total amount of paint used for all the chairs can be expressed as:
1/6 x c = c/6
We also know that she used 1/2 of a can of paint in total. So we can set up the equation:
c/6 = 1/2
To solve for 'c', we can multiply both sides of the equation by 6:
c = 3
Therefore, she painted 3 chairs.
Learn more about proportionality here: https://brainly.com/question/22620356
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HELP ASAP I WILL GIVE U BRAINLIEST
Answer:
The final answer is [tex]\frac{8}{27}[/tex] .
Step-by-step explanation:
Solve the following equation:
[tex](2^{2} \cdot 3^{-1} \cdot 4^{-1})^{-1} \over 2^{-3} \cdot 3^{4}[/tex]
-Simplify [tex]2^{2}[/tex] :
[tex](2^{2} \cdot 3^{-1} \cdot 4^{-1})^{-1} \over 2^{-3} \cdot 3^{4}[/tex]
[tex](4 \times 3^{-1} \times 4^{-1})^{-1} \over 2^{-3} \times 3^{4}[/tex]
-Simplify [tex]3^{-1}[/tex] :
[tex](4 \times 3^{-1} \times 4^{-1})^{-1} \over 2^{-3} \times 3^{4}[/tex]
[tex](4 \times( \frac{1}{3}) \times 4^{-1})^{-1} \over 2^{-3} \times 3^{4}[/tex]
-Multiply both [tex]4[/tex] and [tex]\frac{1}{3}[/tex] :
[tex](4 \times( \frac{1}{3}) \times 4^{-1})^{-1} \over 2^{-3} \times 3^{4}[/tex]
[tex](\frac{4}{3} \times 4^{-1})^{-1} \over 2^{-3} \times 3^{4}[/tex]
-Simplify [tex]4^{-1}[/tex] :
[tex](\frac{4}{3} \times 4^{-1})^{-1} \over 2^{-3} \times 3^{4}[/tex]
[tex](\frac{4}{3} \times (\frac{1}{4}) )^{-1} \over 2^{-3} \times 3^{4}[/tex]
-Multiply both [tex]\frac{4}{3}[/tex] and [tex]\frac{1}{4}[/tex] together:
[tex](\frac{4}{3} \times (\frac{1}{4}) )^{-1} \over 2^{-3} \times 3^{4}[/tex]
[tex](\frac{1}{3})^{-1} \over 2^{-3} \times 3^{4}[/tex]
-Simplify [tex]\frac{1}{3}^{-1}[/tex] :
[tex](\frac{1}{3})^{-1} \over 2^{-3} \times 3^{4}[/tex]
[tex]3 \over 2^{-3} \times 3^{4}[/tex]
-Then, on the denominator, simplify [tex]2^{-3}[/tex] :
[tex]3 \over 2^{-3} \times 3^{4}[/tex]
[tex]3 \over \frac{1}{8} \times 3^{4}[/tex]
Simplify [tex]3^{4}[/tex] :
[tex]3 \over \frac{1}{8} \times 3^{4}[/tex]
[tex]3 \over \frac{1}{8} \times 81[/tex]
Multiply both [tex]\frac{1}{8}[/tex] and [tex]81[/tex] together:
[tex]3 \over \frac{1}{8} \times 81[/tex]
[tex]3 \over \frac{81}{8}[/tex]
Divide [tex]3[/tex] and [tex]\frac{81}{8}[/tex] by multiplying [tex]3[/tex] by the reciprocal of [tex]\frac{81}{8}[/tex] :
[tex]3 \over \frac{81}{8}[/tex]
[tex]3 \times (\frac{81}{8})[/tex]
-And you multiply [tex]3[/tex] and [tex]\frac{81}{8}[/tex] together:
[tex]3 \times (\frac{81}{8})[/tex]
[tex]\frac{8}{27}[/tex]
So, the final answer would be [tex]\frac{8}{27}[/tex] .
Please help as quickly as possible
Answer:
The next fraction in the sequence is:
4/27Step-by-step explanation:
How you can see, the fractions are decreasing as the sequence advance, to identify the proportion in which it decreases, we will divide the first and the second fractions:
3/4 / 1/2 = 3/2 or 1.5Now, we just need to divide all the fractions in 3/2 to identify the next fraction, as I show below:
3/4 / 3/2 = 1/2 1/2 / 3/2 = 1/3 1/3 / 3/2 = 2/9 2/9 / 3/2 = 4/27As you can see, all the results own to the sequence given, for this reason, the last result 4/27 is the correct fraction next to 2/9.
The box plots show the weights, in pounds, of the dogs in two different animal shelters.
Weights of Dogs in Shelter A
Weights of Dogs in Shelter B
Which is true of the data in the box plots? Select three choices.
The median weight for shelter A is greater than that for shelter B.
The median weight for shelter B is greater than that for shelter A.
The data for shelter A are a symmetric data set.
The data for shelter B are a symmetric data set.
The interquartile range of shelter A is greater than the interquartile range of shelter B.
Answer:
The median weight for shelter A is greater than that for shelter B.
The data for shelter B are a symmetric data set.
The interquartile range of shelter A is greater than the interquartile range of shelter B.
What is the area of this triangle?
Answer:
8 units^2
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh
A = 1/2 (7-3) * (4-0)
= 1/2 4*4
= 8
ASAP What is the slope of the line y= 3?
Answer:
the slope is zero because
Step-by-step explanation:
this is a perfect horizontal line passing through y=-3
I've been thought
hope it helps
Answer:
Slope = 0
This is because the line does not go up or down. And the line is horizontal leading to the factor of the slope being 0.
algebra applications
Answer:
X=55°
Y=30°
Step-by-step explanation:
2y=x+5
Y=1/2x+2.5
3y+30=4x-100
3(0.5x+2.5)+30=4x-100
1.5x+7.5+30=4x-100
4x-1.5x=137.5
2.5x=137.5
X=55°
Y=30°
Answer:
[tex]x = 55\\y = 30\\[/tex]
Step-by-step explanation:
Finding x:
4x - 100 + x + 5 = 180 (Angles on a straight line)
5x - 95 = 180
5x = 180 + 95
5x = 275
Dividing both sides by 5
x = 55
Finding y:
2y + 3y +30 = 180 (Angles on a straight line)
5y = 180-30
5y = 150
Dividing both sides by 5
y = 30
Select the polynomial that is a perfect square trinomial. 9x2 + 9x + 1 36b2 − 24b + 8 16x2 + 24x + 9 4a2 − 10a + 25
Answer:
16x² + 24x + 9
Step-by-step explanation:
16x² + 24x + 9 =(4x)²+2*4x*3 + 3² = (4x +3)²
For every 4 hours of babysitting, Sam charges $30. If last month she earned $75, how many hours did she babysit ?
Answer:
10
Step-by-step explanation:
Which statement is true about the end behavior of the
graphed function?
A: As the x-values go to positive infinity, the function's
values go to negative infinity.
B: As the x-values go to zero, the function's values go to
positive infinity
C: As the x-values go to negative infinity, the function's
values are equal to zero.
D: As the x-values go to positive infinity, the function's
values go to positive infinity.
Answer:
Option A.
Step-by-step explanation:
Let the given graph represent the function f(x).
From the given that given graph it is clear that the end behavior of the function f(x):
1. As the x-values go to positive infinity, the function's values go to negative infinity.
[tex]\lim\limits_{x\to \infty}f(x)=-\infty[/tex]
2. As the x-values go to negative infinity, the function's values go to positive infinity.
[tex]\lim\limits_{x\to -\infty}f(x)=\infty[/tex]
Therefore, the correct option is A.
What is the domain of the following function: f ( x ) = √ x + 4/ x − 2
Answer:
(-∞,+∞) interval notation
it is not clear if the square root on the x only or the four too.
the answer above is if the equation is :
√x +4/x -2
PLS HELP my homework is due tomorrow
Answer:
for 1 its -0.25 and 1.25
for 2 its -0.5. and 1.5
Step-by-step explanation:
idk if there is, but just use the graph + common sense.
you don't need to solve it in any way
At 7pm, the temperature outside was -5 degree celsius. What does |-5| represent in this situation?
The number of degrees between 0 and -5 C
Step-by-step explanation:
Hi! It is not 1-5 is is the absolute value of -5. This would be 5 which is the number of degrees between 0 and -5.
Step-by-step explanation:
|-5| who’s absolute value is 5 is representing temp form 0 to -5
What is Temperature ?Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius
What is modulus?The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign. For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5.
According to question
At 7pm, the temperature outside was -5
And |-5| = 5 (which is absolute value)
And represent count of temp from 0 to -5 .
Hence, |-5| who’s absolute value is 5 is representing temp form 0 to -5
To know more about modulus here :
https://brainly.com/question/10737199
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Chris plotted 3 points on the graph of the equation y=2x. Which coordinates name the points on Chris’s graph?
Answer:
(0,0) (2,4) (-2,-4)
Step-by-step explanation:
What is the value of x in the equation 8 + 4 = 2 (x minus 1)? 5 StartFraction 11 Over 2 EndFraction StartFraction 13 Over 2 EndFraction 7
Answer:
7
Step-by-step explanation:
We can simplify the equation to
12 = 2x - 2
Add 2 to both sides
14 = 2x
Divide by 2
x = 7
Answer:
7
Step-by-step explanation:
A shipping container is in the shape of a right rectangular prism with a length of 13 feet, a width of 4.5 feet, and a height of 6 feet. The container is completely filled with contents that weigh, on average, 0.78 pound per cubic foot. What is the weight of the contents in the container, to the nearest pound?
Answer:
The volume of the right rectangular prism is 12* 8.5 * 4 = 408 content density is 0.25 pounds
Step-by-step explanation:
The rise is the
change in a line. The run is the
change in a line.
horizontal
vertical
Answer:
Horizontal
Step-by-step explanation:
Answer:
1- vertical
2-horizontal
Step-by-step explanation:
Read the defitions! Hope this helped!
Find the mystery number from the following clues. • It is a two-digit number. • It is a factor of 48. • It is a multiple of 6. • The sum of the digits is 3.
Answer:
It might be 24 but probaly not.
Step-by-step explanation:
It is the first 3 , but am not sure about the last one.
Your history teacher is going to give you a 92 point assessment. There are 2 point questions and 3 point questions. If there is a total of 40 questions on the assessment, how many questions are worth 2 points?
Solve the following equation : 2x+3x= 40
then, multiply the value of "x" by 2.
Hope it helps
does anyone know this?
Answer:
Step-by-step explanation:
5•-4= -20
5•-3x= -15x
-6x•-4= 24x
-6x•-3x= 18x^2
Answer:
20 : 15x
:
: : : : :
24x : 18x
:
Step-by-step explanation:
5×-4=20
5×-3x=-15x
-6x×-4=24x
-6x×-3x=18x
// have a great day //
