Step-by-step explanation:
the area is
(x² + 17x + 72) m²
it is the result of the usual
length × width
calculation.
length = x + g
width = x + h
length × width = x² + gx + hx + ab = x² + (g+h)x + gh =
= x² + 17x + 72
g + h = 17
gh = 72
just by looking at it that gives us 9 and 8 as g and h.
FYI - formally to calculate them we can say
g = 17 - h
(17 - h)h = 72
17h - h² = 72
h² - 17h + 72 = 0
the solution to such a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = h
a = 1
b = -17
c = 72
h = (17 ± sqrt(17² - 4×1×72))/(2×1) =
= (17 ± sqrt(289 - 288))/2 = (17 ± 1)/2
h1 = (17 + 1)/2 = 18/2 = 9
h2 = (17 - 1)/2 = 16/2 = 8
as we can see
g = 17 - h
if we say h = 9, then g = 8.
if we say h = 8, then g = 9.
so, these are our solutions.
we simply pick that length is longer than width, so, g = 9, h = 8.
the area including the walkway is then
(length + 3)(width + 3) =
= (x + 9 + 3)(x + 8 + 3) = (x + 12)(x + 11) m²
and the dimensions incl. the walkway are
length = x + 9 + 3 = x + 12
width = x + 8 + 3 = x + 11
A graph titled Cost of a Lunch in a School's Cafeteria has Days since school started on the x-axis and cost of lunch (dollars) on the y-axis. A horizontal line is at y = 2.5.
Which is correct about the graph’s slope?
Its slope is positive.
Its slope is negative.
Its slope is zero.
It has no slope.
The true statement about the graph's slope is (c) Its slope is zero.
How to determine the true statement?From the question, we have:
A horizontal line is at y = 2.5.
The horizontal line implies that the cost of lunch do not change
Horizontal lines have a slope of 0
Hence, the true statement about the graph's slope is (c) Its slope is zero.
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Can I Please Get Help I Need The Units With The Answer Too
The rate of change of the the given table is: 3/4soda per dollar.
What is the Rate of Change?Rate of change = change in total cost / change in number of sodas.
Using (24, 18) and (28, 21), we would have:
Rate of change = (21 - 18)/(28 - 24)
Rate of change = 3/4
Therefore, the rate of change is 3/4soda per dollar.
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Suppose that a researcher is interested in estimating the mean systolic blood pressure, , of executives of major corporations. He plans to use the blood pressures of a random sample of executives of major corporations to estimate . Assuming that the standard deviation of the population of systolic blood pressures of executives of major corporations is mm Hg, what is the minimum sample size needed for the researcher to be confident that his estimate is within mm Hg of
The minimum sample size needed in the research of systolic blood pressure is 68.
Given standard deviation=25 mm Hg, confidence level=90%, Estimation =5 mm Hg.
We have to first find the level of alpha which is known as error.
α=(1-0.9)/2
=0.05
Now we have to find z in the z table as such z has a p value of 1-α,that is z with a p value of 1-0.05
=0.95 ,so Z=1.645.
now finding the margin of error, which is as under:
[tex]M=z st/\sqrt{n}[/tex]
in which st is standard deviation and the n is sample size of population.
By assuming the standard deviation of 25 mm Hg we get values as under:
n is sample size.
[tex]M=z* st/\sqrt{n}[/tex]
[tex]5=1.645*25/\sqrt{n}[/tex]
[tex]5\sqrt{n}=1.645*25\\[/tex]
dividing both sides by 5
[tex]\sqrt{n}=1.645*5[/tex]
squaring both sides we get
n=67.65.
Hence the sample size needed by the researcher is 68.
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The given question is incomplete as it should includes :
standard deviation= 25mm Hg
Confidence level=90%
Estimation 5 mm Hg of u.
please can someone help me
Answer: A=48 squared centimeters
Step-by-step explanation: First you need to find the area of the whole rectangle. Area equals length times width (9*8), which is 72. Next you find the area of the white region: 4*6=24. Finally, you subtract the smaller region from the whole: 72-24=48. BOOM: you got the exact right answer :)
Simplify the expression write the answer using scientific notation (8x10^7)(2x10^6)
Answer:
Second option 1.6x10^14
Step-by-step explanation:
What is the equation of a line passing through (-3, 7) and having a slope of 5 ?
Answer:
B
Step-by-step explanation:
since the slope is 5, 1/5x or -1/5x cannot be the slope. since the slope isn't negative it also cancels out -5x. 5x can be your only slope and that is in answer B.
Find the quotient:
15x²-3x
————
-3x
Enter the correct answer.
Answer:
-5x + 1
Step-by-step explanation:
Hello!
We can find the quotient by factoring the numerator, and cancelling common factors.
Simplify[tex]\frac{15x^2 - 3x}{-3x}[/tex][tex]\frac{(-3x)(-5x + 1)}{-3x}[/tex][tex]\frac{\not{(-3x)}(-5x + 1)}{\not{-3x}}[/tex][tex]-5x +1[/tex]The quotient is (-5x + 1).
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathbf{\dfrac{15x^2 - 3x}{-3x}}[/tex]
[tex]\huge\textbf{Simplify the current equation:}[/tex]
[tex]\mathbf{= \dfrac{-3x(-5x + 1)}{-3x}}[/tex]
[tex]\huge\textbf{Cancel out \boxed{\bf -3x} \& simplify it:}[/tex]
[tex]\mathbf{= \dfrac{-15x + 3}{3}}[/tex]
[tex]\huge\textbf{Simplify that above:}[/tex]
[tex]\mathbf{= -5x + 1}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{-5x + 1 }}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
11. Find the slope of the line that passes through the pair of points. (2, 6), (7, 0)
[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]
Find the slope of the line that passes through the pair of points.
[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]
In this problem we have two points given to us, which are...
(2,6)(7,0)... and we should find the slope.
[tex]\bf{We\;will\;use\;the\;Slope-Equation:}\\m=\dfrac{y2-y1}{x2-x1}[/tex]
[tex]\bf{\dfrac{0-6}{7-2}=\dfrac{-6}{5} =-\dfrac{6}{5}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{Slope:}[/tex]
[tex]\bf{=-\dfrac{6}{5}}[/tex]
[tex]\boxed{\bf{aesthetic \not101}}[/tex]
x−10y=12
10x+10y=10 Addition Elimination
Answer:
x = 2 and y = -1
Step-by-step explanation:
that is the solution above
Answer:
x = 2
y == -1
Step-by-step explanation:
Solving linear equations by elimination method:x - 10y = 12 ----------------(I)
10x + 10y = 10 --------------(II)
We can find the value of 'x' by eliminating 'y'. To eliminate 'y', add equations (I) & (II)
(I) x - 10y = 12
(II) 10x + 10y = 10 {Now add the equations}
11x = 22
x = 22 /11
[tex]\sf \boxed{\bf x = 2}[/tex]
Now, Plugin x = 2 in equation (1)
10*2 + 10y = 10
20 + 10y = 10
10y = 10 - 20
10y = -10
y = -10/10
[tex]\sf \boxed{\bf y = -1}[/tex]
Perpendicular bisector: put the following steps in order using what you know about constructing a perpendicular bisector.
In order to draw a perpendicular bisector you must have ruler , compass and a pencil.
Given nothing and we have to show the steps to draw a perpendicular bisector.
Perpendicular bisector is the line which divides the line into two equal parts and makes 90° angle on other line.
If we want to make a perpendicular bisector on a line then we have to follow the following steps:
1) First draw a line with the help of ruler on which we want to make perpendicular bisector.
2) Now take a compass and a pencil.
3) Put the pencil in the compass and strech the compass equal to half or little more of the length of the line.
4) Now put the compass on one end of the line and draw an arc on the line or may be just upward.
5) Now repeat the step 4 from other end.
6) Now draw a line from the point where two arcs intersects on the line.
7) It is the perpendicular bisector of the line.
Hence to draw a perpendicular bisector we require compass, ruler and a pencil.
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In Mr. Romano's class, the ratio of the number of girls to the number of boys is 3:2. A student is selected at random from
the class. The probability that the selected student is a boy is
F. 1/6
G. 1/3
H. 2/5
J. 3/5
K. 2/3
Which of the following options have the same value as 40% percent of 84?
Choose 2 answers
Answer:
The answer in decimal form is 33.6.
The answer in fraction form is [tex]33\frac{3}{5}[/tex].
Step-by-step explanation:
To find 40% of 84, multiply 84 and 0.4.
84 × 0.4 = 33.6
The answer in decimal form is 33.6.
The answer in fraction form is [tex]33\frac{3}{5}[/tex].
Hope this helps!
Please please please help i need help asap im so lost
if x^3 - 7x + 16x - 12 + (x-a) (x-b) (x-c) for all values of x, what is the value of abc?
[tex](x - a)(x - b)(x - c) \\ (x {}^{2} - bx - ax + ab)(x - c) \\ x {}^{3} - bx {}^{2} - ax {}^{2} + abx - cx {}^{2} + cbx + cax - abc[/tex]
[tex]x {}^{3} + ( - a - b - c)x {}^{2} + (ab + cb + ca)x - abc [/tex]
[tex] - a - b - c = - 7 \\ ab + ac + bc = 16 \\ - abc = - 12 \: \: \: \: \: abc = 12[/tex]
( a , b , c ) = ( 2 , 2 , 3 )
The ratio of Anne's height: Ben's height is 7:9.
Anne's height is 1.4m.
Find Ben's height.
Answer:
Ben's height is 1.8 mStep-by-step explanation:
The ratio of Anne's height: Ben's height is 7:9.
Anne's height is 1.4m.
Find Ben's height.
we can solve with an equation
7 : 9 = 1.4 : x
x = 9 * 1.4 : 7
x = 1.8 m
Mackenzie is a waitress at a restaurant. Each day she works, Mackenzie will make a guaranteed wage of $25, however the additional amount that Mackenzie earns from tips depends on the number of tables she waits on that day. From past experience, Mackenzie noticed that she will get about $15 in tips for each table she waits on. How much would Mackenzie expect to earn in a day on which she waits on 13 tables? How much would Mackenzie expect to make in a day when waiting on tt tables?
Answer: If she waits on 13 tables than she should expect to earn $220
Step-by-step explanation:
15*13=195
195+25=220
Question 8 c
A bag of tokens contains 7 red, 9 green, and 6 blue tokens. What is the probability that
a randomly selected token is not red? Enter your answer as a fraction.
Below is the graph of y=b^x. Find b.
b=
Answer: 1
Step-by-step explanation:
When [tex]x=0[/tex], [tex]y=\boxed{1}[/tex]
Which numbers are the means of the proportion shown below?
213
818
3 30
A. 2 and 30
B. 3 and 30
C. 2 and 20
D. 3 and 20
The numbers which are the means of the proportion as given in the task content are in; Choice D; 3 and 20
Which numbers are the means of the proportion shown below?It follows from the task content that the proportion whose mean is to be evaluated in the task content is; 2/3 = 20/30.
On this note, it follows that the numbers 2 and 30 are the lower and upper extremes of the property and hence, 3 and 20 are the mean of the proportion.
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PLEASE HELP ME ASAP!!!!!
HELP PLEASE! will give brainliest
1. The following diagram shows a slide at a park. a. Find the vertical distance from the ground to the top of the slide. b. Find the length of the slide. c. What is the area of the space under the slide. Steps 2 m /70* Slide 40° H
The area of the space under the slide is 2.10 square meters
The vertical distanceThe diagram in the question is added as an attachment
The vertical distance is represented by h.
So, we have:
sin(70) = h/2
Solve for h
h = 2 * sin(70)
Evaluate
h = 1.88 m
Hence, the vertical distance is 1.88 m
The length of the slideThis is calculated using
sin(40) = h/Slide
This gives
sin(40) = 1.88/Slide
Solve for Slide
Slide = 1.88/sin(40)
Evaluate
Slide = 2.92
Hence, the length of the slide is 2.92 m
The area of the space under the slideThis is calculated using:
A = 0.5 * h * slide * sin(∅)
Where
∅ = 90 - 40 = 50
So, we have:
A = 0.5 * 1.88 * 2.92 * sin(50)
Evaluate
A = 2.10
Hence, the area of the space under the slide is 2.10 square meters
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In Washington County, 850 homes were sold in 2017. How many homes were sold in the Southwest region?
A)102
B)1,020
C)1,231
D)588
Option A is correct answer; i.e. 102 homes were sold in 2017.
What is Pie Chart?A pie chart is a type of graph that records data in a circular manner that is further divided into sectors for representing the data of that particular part out of the whole part.
Here,
Total Homes sold in 2017 = 850 homes.
Homes sold in Southwest region = 12 % of the total.
= 0.12 X 850
= 102.
Thus, option A is correct answer; i.e. 102 homes were sold in 2017.
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k – 8 = 12. Pls help
Answer:
k = 20
Step-by-step explanation:
1) Isolate the variable
k - 8 = 12
+8 +8
2) Solve
k = 12+8
k = 20
Work out the volume of the cone, giving your answer
to 3 significant figures.
Answer: 1010
Step-by-step explanation:
[tex]V=\frac{1}{3}(\pi)(8^{2})(15) \approx \boxed{\text{ } 1010 \text{ cm}^{3}}[/tex]
in the rectangle abcd, AC= -6x-2, BP= -4x-3, DP+ -6y-19 find the value of y
is that 2.11 I think so
Step-by-step explanation:
I don't know explain it to you and
Solve the system of equations using elimination: -x+3y=-24− and -4x+2y=4
Answer:
[tex]\begin{cases}x=-6\\y=-10\end[/tex]
Step-by-step explanation:
[tex]\begin{cases}-x+3y=-24 \left(1)\right\\-4x+2y=4 \left(2)\right\end[/tex]
Make x the subject in (1)
[tex]x=3y+24 \left(3)\right[/tex]
Sub into (2)
[tex]-4(3y+24)+2y=4\\\\\implies-12y-96+2y=4\\\\\implies10y=-100\\\\y=-10[/tex]
Sub into (3)
[tex]x=-30+24\\\\x=-6[/tex]
Hence
[tex]\begin{cases}x=-6\\y=-10\end[/tex]
Answer:
[tex]\left \{ {{x=-6} \atop {y=-10}} \right. .[/tex]
Step-by-step explanation:
[tex]\left \{ {{-x+3y=-24\ \ (1)} \atop {-4x+2y=4\ \ \ (2)}} \right. \ \ \ \ \\[/tex]
We multiply equation (1) by -4:
-x+3y=-24 |*(-4)
-x*(-4)+3y*(-4)=-24*-(-4)
4x-12y=96. (3) ⇒
[tex]\left \{ {{4x-12y=96\ \ (3)} \atop {-4x+2y=4\ \ \ (2)}} \right.[/tex]
We summarize equations (2) and (3):
[tex]-10y=100\ |:(-10)\\y=-10.\\Make\ y \ the\ subject\ in\ (1):\\-x+3*(-10)=-24\\-x-30=-24\\-x=-24+30\\-x=6\ |*(-1)\\x=-6.[/tex]
Guys help me with this problem, please. I really need help right now.
Answer:
A
Step-by-step explanation:
So whenever you're finding the difference between two numbers you generally use the equation: |a-b| since a-b may or may not be negative, but |a-b| will always equal |b-a|. Since the only thing that differs is the sign. So when you have: [tex]|-\frac{2}{3}-\frac{5}{3}|[/tex], in this case a=-2/3 and b=5/3 (b is positive since you're subtracting b, so if b appeared positive in the equation, it's actually negative, since the negative sign in |a-b|, which would make the two negatives cancel out). This means A is the correct answer. You could also calculate what the value is. Calculating gives you: [tex]|-\frac{7}{3}| = \frac{7}{3}[/tex]. And as you can see the top one, has two numbers separated by 7 one thirds.
Answer:
A
Step-by-step explanation:
It is absolute value and when it is absolute value, it is positive.
A shopkeeper bought two watches for rs. 400.he sold them to gain 5 percent on one and lose 5 percent on the other .calculate his final gain or loss lercent if the sp of both watches is the same.
The final loss percent is 0.25%.
What is the final loss percent?The gap between the cost price and the selling price is what is referred to as a loss. And the loss percent is the loss as a percentage of the actual cost.
Total CP=Rs. 400
Let the CP of the first watch be Rs. x
So, CP of the second watch=Rs.(400-x)
For the first watch,
Gain Percent=5%
SP = [tex](1+\frac{5}{100})*x[/tex]
SP=105x/100
For the second watch,
Loss Percent=5%
SP=[tex](1-\frac{5}{100})(400-x)[/tex]
SP=95(400-x)/100
As the SP of both the watches is the same.
[tex]\frac{105}{100}x=\frac{95}{100}(400-x)[/tex]
105x=38000-95x
105x+95x=38000
200x=38000
x=38000/200
x=190
CP of the first watch=Rs. 190
CP of the second watch=Rs. (400-190)=Rs. 210
SP of first watch=[tex]\frac{105}{100}*190[/tex] =Rs. 199.50
SP of second watch=[tex]\frac{95}{100}*210[/tex]=Rs. 199.50
Total SP=Rs. 399
Final Loss=Total CP-Total SP
=Rs.(400-399)
=Rs. 1
Final Loss Percent=100/400
=0.25%
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f(x)=6x^3-4, g(x)=2x+2, find (g-f)(x)
The value of (g-f)(X) is 2x - 6x³ +6.
what is Function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given:
f(x)= 6x³-4, g(x)= 2x+2
Now,
(g-f)(x)= g(x)-f(x)
= 2x+2-( 6x³-4)
=2x+2- 6x³+4
=2x - 6x³ +6
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The graph represents a system of linear equations comparing the outside and inside temperatures y, in degrees Fahrenheit, recorded at a school one day x hours after 8:00 a.m.
A coordinate grid showing Daily Temperature with Hours after 8:00 a m on the horizontal, x axis and Temperature in degrees Fahrenheit on the vertical, y, axis. One line labeled Inside passes through (0, 70) and (8, 70). The second line passes through (0, 58) and passes through (8, 70).
After how many hours were the inside and outside temperatures equal?
6 hours
7 hours
8 hours
10 hours
Using linear functions, it is found that the temperatures would be equal after 8 hours.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Two functions are equal when they intersect. In this problem, both lines pass through point (8,70), that is, they have the same temperature(of 70 degrees) after 8 hours.
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