Answer:
0.99%
Step-by-step explanation:
The graph of the function f(x)= x2 − 4x + 6 is shown here. What is its axis of symmetry? A. x = 0 B. x = 2 C. x = 6 D. x = -2
9514 1404 393
Answer:
B. x = 2
Step-by-step explanation:
The graph is symmetrical about the vertical line through its vertex. The x-value of that vertex is 2, so the line of symmetry is ...
x = 2
What is the slope of a roof on a house that has a vertical height of 2.4 feet from the ceiling of the top floor to the top of the pitch and a length of 8.2 feet from the center of the edge of the house?
Answer:
Step-by-step explanation:
It is unclear from the phrasing what dimension 8.2 ft represents.
If 8.2 ft is the direct distance from the edge of the roof to the top of the pitch, then the horizontal distance from the edge to the top is √(8.2²-2.4²) ≅ 7.84 ft, and the slope is 2.4/7.84 ≅ 0.31
If 8.2 ft is the horizontal distance from the edge of the root to the top of the pitch, then the slope is 2.4/8.2 ≅ 0.29
The slope of a roof on a house is 0.2926 and the angle of elevation is 16.31°.
What is slope of a line?
The slope or gradient of a line is a number that describes both the direction X and Y and the steepness of the line. It is the ratio of the vertical change to the horizontal change between any two distinct points on a line.
For the given situation,
The diagram below shows the house with the roof.
The vertical height of roof on a house, rise = 2.4 feet
The horizontal length of a roof on a house, run = 8.2 feet
The slope of a roof can be found as
[tex]Slope = \frac{rise}{run}[/tex]
⇒ [tex]slope = (\frac{2.4}{8.2} )[/tex]
⇒ [tex]slope = 0.2926[/tex]
The angle of the slope of a roof can be found as
[tex]tan \alpha =\frac{vertical height}{horizontal length}[/tex]
⇒ [tex]\alpha =tan^{-1} (\frac{2.4}{8.2} )[/tex]
⇒ [tex]\alpha =tan^{-1} (0.2926)[/tex]
⇒ [tex]\alpha =16.31[/tex]
Hence we can conclude that the slope of a roof on a house is 0.2926 and the angle of elevation is 16.31°.
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20 POINTS! The answer is x=4 and x= -5, how should I word it, saying how he is wrong?
Answer:
The student took the numbers for the factors 5, -4 for the zeros instead of solving the equation
The zeros are -5, 4
Step-by-step explanation:
x^2 +x - 20=0
What 2 number multiply to -20 and add to 1
5*-4 = -20
5+-4 = 1
(x+5)(x-4) =0
Using the zero product property
x+5 = 0 x-4 =0
x=-5 x=4
Answer:
Solution given:
equation is:
x²+x-20=0
doing middle term factorisation
note:we need to get 1 while subtracting factor of the product of constant and coefficient of x².
20*1=20=2*5*2*1
we get 1 while subtracting 5-2*2=5-4
now substitute value 5-4 at coefficient of x
we get
x²+(5-4)x-20=0
now
distribute
x²+5x-4x-20=0
taking common from each two term
x(x+5)-4(x+5)=0
again taking common (x+5) and keeping remaining at another bracket
(x+5)(x-4)=0
either
x+5=0
x=-5
or
x-4=0
x=4
Error is:
x= 4 not -4
x=-5 not 5.
How much more area does a large pizza with a 12 in. diameter have than a small pizza with an 8 in. diameter? Round your answer to the nearest square inch.
Answer: About 63 in²
Step-by-step explanation:
Area of circle = π · r²
r = radius lengthπ ≈ 3.14Area of large pizza:
[tex]\pi *r^{2} =3.14*6^{2} =3.14*36=113.04[/tex]
Area of small pizza:
[tex]\pi *r^{2} =3.14*4^{2} =3.14*16=50.24[/tex]
Difference in area:
[tex]113.04-50.24=62.8[/tex]
match the polynomial with its correct name
Answer
Attach a file for us to see the problem
Step-by-step explanation:
A recipe calls for 4 cups of flour and 6 cups of sugar. How many cups of sugar per cup of flour does the recipe require?
Answer:
3 cups of sugar per 2 cups of flour
Step-by-step explanation:
just flip and simplify the fraction
4/6 = 6/4 = 3/2
y = 95°, find the measure of x
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Answer:
x = 100°
y = 95°
Step-by-step explanation:
It is probably easier to find y first. Opposite angles of an inscribed quadrilateral are supplementary, so ...
y = 180° -85° = 95°
The measure of an arc is double the measure of the inscribed angle subtending it. The arc subtended by angle y is ...
90° +x = 2y
x = 190° -90° = 100°
_____
Additional comment
The rule cited above regarding opposite angles of an inscribed quadrilateral comes from the theorem regarding inscribed angles. In the given diagram, the diagonal from the bottom vertex to the top one is a chord that divides the circle into two arcs. Their sum is 360°. The inscribed angle theorem tells you ...
2y +2(85°) = 360°
y + 85° = 180° . . . . . . . divide by 2; opposite angles are supplementary
Someone please help me with this
Answer:
Step-by-step explanation:
Jenny has borrowed K2500from a bank at 9.25% p.a. invested for 185 days. How much will she pay back to the bank?
Answer:
115.625
PRT/100
For the function G defined by G(x) = 5x + 3, find G(2)
G(x)=5x+3
[tex]\\ \sf\longmapsto G(2)[/tex]
[tex]\\ \sf\longmapsto 5(2)+3[/tex]
[tex]\\ \sf\longmapsto 10+3[/tex]
[tex]\\ \sf\longmapsto 13[/tex]
Option c is correct
If we decrease a dimension on a figure, how is the figure’s area affected?
The area decreases.
The area increases.
The area becomes 0.
The area remains the same.
01:15:51 Differential equation of the family of circles touching the y-axis at origin is
Step-by-step explanation:
Correct option is
B
x
2
−y
2
+2xy
dx
dy
=0
The system of circles touching Y axis at origin will have centres on X axis. Let (a,0) be the centre of a circle. Then the radius of the circle should be a units, since the circle should touch Y axis at origin.
Equation of a circle with centre at (a,0) and radius a
(x─a)²+(y─0)²=a²
That is,
x²+y²─2ax=0 ─────► (1)
The above equation represents the family of circles touching Y axis at origin. Here 'a' is an arbitrary constant.
In order to find the differential equation of system of circles touching Y axis at origin, eliminate the the arbitrary constant from equation(1)
Differentiating equation(1) with respect to x,
2x+2ydy/dx─2a=0
or
2a=2(x+ydy/dx)
Replacing '2a' of equation(1) with the above expression, you get
x²+y²─2(x+ydy/dx)(x)=0
That is,
─x²+y²─2xydy/dx=0
or
x²─y²+2xydy/dx=0
6) Frazer cycles the first 20 miles at an average speed of 21mph. The second
part is more uphill, and he only manages 13mph. By what percentage did his
speed decrease?
How to solve
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Answer:
38.1% decrease
Step-by-step explanation:
A percentage change is found from ...
% change = (change)/(original amount) × 100%
= (new value - original amount)/(original amount) × 100%
= (13 -21)/21 × 100% = -8/21 × 100% ≈ -38.1%
Frazer's speed decreased by 38.1% during the second part.
_____
Additional comment
A negative % change represents a decrease; a positive % change represents an increase.
A.Yes, since the slopes are the same and the y-intercepts are the same.
B.No, since the y-intercepts are different.
C.Yes, since the slopes are the same and the y-intercepts are different.
D.No, since the slopes are different.
Answer:
C
Step-by-step explanation:
one line is
y = 3x/7 + 11
its slope is 3/7
the y-intercept is, of course, when x=0. there y=11
the other is
-3x + 7y = 13
7y = 3x + 13
y = 3x/7 + 13/7
its slope is 3/7 (the same as the other line)
the y-intercept (x=0) is y = 13/7 (different to the other line)
Answer:
C. Yes, since the slopes are the same and the y-intercepts are different.
Step-by-step explanation:
[tex]y=\frac{3}{7} x+11[/tex] and [tex]-3x+7y=13[/tex]
→ Rearrange the second equation to make y the subject
7y = 3x + 13
→ Divide everything by 7
[tex]y=\frac{3}{7} x+\frac{13}{7}[/tex]
What is the derivative of (x + 1) sin x?
Answer:
By the Sum Rule, the derivative of 1−sin(x) 1 - sin ( x ) with respect to x x is ddx[1]+ddx[−sin(x)] d d x [ 1 ] + d d x [ - sin ( x ) ] .
"The fitted regression line will always run through the mean of the observed data. In other words, the point (x with bar on top, y with bar on top) will always lie on the estimated (fitted) regression line. Is it true or false?"
Which expressions are equivalent to 6 + 12x?
A.
5(1 + 2x) + 1 + 2x
B.
7(1 + 2x) + 2x - 1
C.
3(2 + 6x) + 2x
D.
7(1 + 2x) - 2x - 1
E.
3(2 + 4x)
Answer:
A. 5(1 + 2x) + 1 + 2x
D. 7(1 + 2x) - 2x - 1
E. 3(2 + 4x)
y you work from 7 a.m. to 4 p.m. The state you live in requires that you take a 30-minute break during any shift longer than 6 hours. This break does not count towards your hours. How many hours did you work today? Remember 30 minutes is equal .5 hours
Answer:
You’ve worked 7 hours and 30 minutes
Step-by-step explanation:
find x on this special right triangle, 45 is not an option!!!!
let the line between 2 tria be y
sin 60/8√2 = sin 90/y
y=13.06
sin 45/13.06 = sin 90/x
x=18.46
Answer:
First, find the hypotenuse of the right triangle with the 60° & 30°.
Hypotenuse = hsin(x) = opposite side/hypotenuse[tex]sin(60) = \frac{8\sqrt{2}}{h} \\\\sin(60)h=8\sqrt{2}\\\\\frac{\sqrt{3}}{2} h=8\sqrt{2}\\\\h=\frac{8\sqrt{2}}{\frac{\sqrt{3}}{2}}=8\sqrt{2}*\frac{2}{\sqrt{3}} =\frac{16\sqrt{2} }{\sqrt{3}} =\frac{16\sqrt{2}(\sqrt{3}) }{\sqrt{3}(\sqrt{3})} =\frac{16\sqrt{6} }{3}[/tex]
Use that side length to find x.
sin(x) = opposite side/hypotenuse[tex]sin(45)=\frac{\frac{16\sqrt{6}}{3}}{x}\\\\sin(45)x=\frac{16\sqrt{6}}{3} \\\\\frac{\sqrt{2}}{2}x=\frac{16\sqrt{6}}{3} \\\\x=\frac{\frac{16\sqrt{6}}{3}}{\frac{\sqrt{2}}{2}}=\frac{16\sqrt{6}}{3}*\frac{2}{\sqrt{2}}=\frac{16\sqrt{2}\sqrt{3}(2)}{3\sqrt{2} }=\frac{32\sqrt{3} }{3}[/tex]
An oil company is going to issue new ID codes to its employees. Each code will have one letter, followed by one digit, followed by three letters. The letters w, x, y, and z will not be used. So, there are 22 letters and 10 digits that will be used. Assume that the letters can be repeated. How many employee ID codes can be generated?
Answer:
2342560 combos
Step-by-step explanation:
so its 1 letter*1number*1 letter*1 letter*1 letter, or 22x10x22x22x22 which should equate to 2342560 possible ID codes, hope this helps :)
Write each percent as a fraction in simple form 15 3/5%
Answer:
39/250
Step-by-step explanation:
15 3/5 = 78/5 and percent means per 100, so
(78/5)/100 = (78/5)(1/100)
=78/500 = 39/250
Hello! Please help thanks
Answer:
A. [tex]\frac{5}{13}[/tex]
Step-by-step explanation:
Hi there!
We are given right triangle PQR, with PR=5, RQ=12, and PQ=13
We want to find the value of sin(Q)
Let's first recall that sine is [tex]\frac{opposite}{hypotenuse}[/tex]
In reference to angle Q, PR is the opposite side, RQ is the adjacent side, and PQ is the hypotenuse
So that means that sin(Q) would be [tex]\frac{PR}{PQ}[/tex]
Substituting the values of PR and PQ gives sin(Q) as [tex]\frac{5}{13}[/tex], which is A
Hope this helps!
The diagram shows a wooden prism of height 5cm.
The cross section of the prism is a sector of a circle with sector angle 25º.
The radius of the sector is 15 cm.
Calculate the total surface area of the prism.
Answer:
280.8997
Step-by-step explanation:
cross section = 2*15*5+2*(25/360)*15*15*pi+5*(25/360)*2*pi*15
= 280.8997
Total surface area of prism is 280.890cm²
What is surface area?A solid object's surface area is a measurement of the overall space that the object's surface takes up, and it is always expressed in square units.
The term "surface area" is sometimes used to refer to "total surface area".
Find the sector angle in radians
α = 25× (π/180)
α = (25π)/(180) rad
Find the area of the prism:
A = 2×15×5 + 15×15×α + 5×15×α
A = 150 + 15×15×(25π)/(180) + 5×15×(25π)/(180)
A = 280.890cm²
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A sample of 4 children was drawn from a population of rural Indian children aged 12 to 60 months. The sample mean of mid-upper arm circumference was 150 mm with a standard deviation of 6.73. What is a 95% confidence interval for the mean of mid-upper arm circumference based on your sample
Answer:
The 95% confidence interval for the mean of mid-upper arm circumference based on your sample is between 139.29 mm and 160.71 mm.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So
df = 4 - 1 = 3
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 3 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 3.1824
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 3.1824\frac{6.73}{\sqrt{4}} = 10.71[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 150 - 10.71 = 139.29 mm
The upper end of the interval is the sample mean added to M. So it is 150 + 10.71 = 160.71 mm
The 95% confidence interval for the mean of mid-upper arm circumference based on your sample is between 139.29 mm and 160.71 mm.
find all the missing measurement
Answer:
Hello,
|FD|=15
Step-by-step explanation:
Since the triangles are similar, the bissects are also.
k*35=21 ==> k=21/35
k*25=|FD|
|FD|=(21/35)*25=15
A polynomial function has real coefficients, a leading coefficient of 1, and the zeros -6, 1, and 1. Write a polynomial function of least degree in standard form.
Answer:
[tex]{ \sf{ \underline{ {x}^{2} + 5x - 6 }}}[/tex]
Step-by-step explanation:
[tex](x + 6)(x - 1) \\ = {x}^{2} - x + 6x - 6 \\ = {x}^{2} + 5x - 6[/tex]
Operations and scientific notation math project need to know how to find the scientific notation
Answer:
how did not orderstan that
A four digit password is a number that begins with a 3. If digits can be repeated how many possible passwords are there? show and explain your work
Answer:
The answer is 1,000
SInce the beginning number is 3 and there are ten possible numbers to put in the remaining three slots, there are exactly 1,000 possible combinations for a 3-digit code. The answer is 1,000. There are 3 rows of 10 digits. The number of combinations 10 to the thid power which is 1000 (10 * 10 * 10)
Which side of the pentagon on the right corresponds to
side KJ on the pentagon on the left.
Answer:
side st.Step-by-step explanation:
st corresponds to kj since a it has five sides.How many ways are there to rearrange the letters of the word: COMBINATION?
Answer: 4,989,600 different ways
Step-by-step explanation:
