Answer:
It didn't saying anything about rounding but the the dimensions in there exact form are:
[tex]L=\frac{-5+\sqrt{249}}{2} \text{ cm}[/tex]
and
[tex]W=\frac{5 + \sqrt{249}}{4} \text{ cm }[/tex].
Now if they said to round to the nearest hundredths the dimensions in this rounded form would be:
L=5.39 cm and W=5.19 cm
(Check your question again and see if you meant what you have)
Step-by-step explanation:
L is 5 less than twice W
L = 2W-5
Area of rectangle=L*W
Area is 28 means L*W=28.
I'm going to insert L=2W-5 into L*W=28 giving me
(2W-5)*W=28
Distribute
2W^2-5W=28
Subtract 28 on both sides
2W^2-5W-28=0
a=2
b=-5
c=-28
We are going to use the quadratic formula.
Plug in...
[tex]W=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\W=\frac{5 \pm \sqrt{(-5)^2-4(2)(-28)}}{2(2)}\\\\W=\frac{5 \pm \sqrt{25+224}}{4}\\\\W=\frac{5 \pm \sqrt{249}}{4}[/tex]
W needs to be positive so [tex]W=\frac{5 + \sqrt{249}}{4}[/tex]
And [tex]L=2W-5=2(\frac{5 + \sqrt{249}}{4})-5[/tex]
[tex]L=\frac{5+\sqrt{249}}{2}-5[/tex]
[tex]L=\frac{5+\sqrt{249}}{2}-\frac{10}{2}[/tex]
[tex]L=\frac{-5+\sqrt{249}}{2}[/tex]
Does L*W=28?
Let's check.
[tex]L \cdot W=\frac{-5+\sqrt{249}}{2} \cdot \frac{5 + \sqrt{249}}{4}[/tex]
[tex]L \cdot W=\frac{249-25}{8}[/tex]
In the last step, I was able to do a quick multiplication because I was multiplying conjugates. (a+b)(a-b)=a^2-b^2.
[tex]L \cdot W=\frac{ 224}{8}[/tex]
[tex]L \cdot W=28[/tex]
25 points!!
Can postulates always be proven true?
Answer:
The basic answer to your question is that we have to start somewhere.
The essence of mathematics (in the sense the Greeks introduced to the
world) is to take a small set of fundamental "facts," called
postulates or axioms, and build up from them a full understanding of
the objects you are dealing with (whether numbers, shapes, or
something else entirely) using only logical reasoning such that if
anyone accepts the postulates, then they must agree with you on the
rest.
It can sometimes be proven.
If cos(x) = 0.5, then what is x?
Answer:
=60 the second option.
Step-by-step explanation:
Given the trigonometric ratio, we can find the value of the angle by simply finding the inverse of the given ratio.
If for example Cos ∅= a, then ∅=Cos⁻¹a
If Cos (x)= 0.5, then x= Cos⁻¹ 0.5
Cos⁻1 0.5=60°
The angle whose sine is 0.5 is ∅=60°
Answer: second option.
Step-by-step explanation:
You have that:
[tex]cos(x)=0.5[/tex]
Then, to find the value of "x", you need to apply Arccosine ( This is the inverse function of the cosine).
Therefore, applying this in the procedure, you get that the value of "x" is the following:
[tex]cos(x)=0.5\\\\x=Arccos(0.5)\\\\x=60\°[/tex]
You can observe that this matches with the second option.
Is PQR-XYZ? If so, name which similarity postulate or theorem applies.
80°
6
3/80
p5 R
A. Similar - AA
O
O
B. Similar - SSS
O
c. Similar - SAS
D. Cannot be determined
Answer:
D. Cannot be determined
Step-by-step explanation:
there is not enough information for you to answer this question. A picture would be helpful to answer this question, but there isn't one.
The correct option is,
D. Cannot be determined.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Since, We are given that two triangle PQR and XYZ are similar.
AA-Similarity postulate: Two angles of one triangle is equal to its corresponding angles of other triangle. Then, the two triangles are similar by AA postulate.
SSS similar: When three sides of two triangles are in the same ratio.
SAS similar: When two sides of two triangle are in the same ratio and one angle between two proportional sides of two triangles is congruent.
But we have not enough information by which we can determine triangle PQR and triangle XYZ is similar.
Hence, option D is true.
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If you apply the changes below to the absolute value parent function, f(x) = |x|,what is the equation of the new function?
• Shift 4 units to the right.
• Shift 6 units up.
Answer:
Option B [tex]g\left(x\right)=\left|x-4\right|+6[/tex]
Step-by-step explanation:
we have
[tex]f\left(x\right)=\left|x\right|[/tex]
The vertex is the point (0,0)
If to the parent function apply
Shift 4 units to the right and Shift 6 units up
The rule of the translation is
(x,y) ------> (x+4,y+6)
so
The vertex of the new function is (4,6)
therefore
the equation of the new function is
[tex]g\left(x\right)=\left|x-4\right|+6[/tex]
Answer:
just entered the answer and it was |x-4|+6
hope that helps!
Step-by-step explanation:
Which graph best represents the solution to the following pair of equations? y = 2x − 10 y = −x + 18
Answer:(6,12)
Step-by-step explanation:
HELP ME WITH THIS QUESTION ✔
THANKS YOU !!
[tex]\text{Hey there!}[/tex]
[tex]\huge\text{Decimals, fractions, \& negatives are below 0!}[/tex]
[tex]2\dfrac{21}{30}\ = 2\times30+21 \ = 2\times 30 = 60+21= 81\rightarrow \dfrac{81}{30}[/tex]
[tex]2\dfrac{1}{2}\ = 2\times2+1=2\times2=4+1=5\rightarrow\dfrac{5}{2}[/tex]
[tex]-\dfrac{32}{40}=-\dfrac{32}{40}[/tex]
[tex]\boxed{\boxed{\huge\text{Answer:}-\dfrac{32}{40}, \ 2\dfrac{1}{2}, \ 2\dfrac{21}{30}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Write an equation in slope intercept from of the line that passes through the point (3,-2) with slope -2
[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{-2})~\hspace{10em} slope = m\implies -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-2)=-2(x-3) \\\\\\ y+2=-2x+6\implies y=-2x+4[/tex]
The measure of central angle XYZ is 3pi/4 radians. What is the area of the shaded sector?
32pi units2
85 ..
96 ..
256 ..
Answer:
96π units²
Step-by-step explanation:
area of shaded sector (A) = area of circle × fraction of circle
A = πr² × [tex]\frac{\frac{3\pi }{4} }{2\pi }[/tex]
= 16² × [tex]\frac{3\pi }{8}[/tex]
= 256 × [tex]\frac{3\pi }{8}[/tex]
= 32 × 3π
= 96π units²
Answer:
Area of sector : 96 π unit².
Step-by-step explanation:
Given : The measure of central angle XYZ is 3pi/4 radians.
To find : What is the area of the shaded sector?
Solution: We have given central angle XYZ is 3pi/4 radians.
Area of sector : [tex]\frac{1}{2}[/tex] (radius)²* central angle.
Plug the values central angle = [tex]\frac{3\pi }{4}[/tex] , radius = 16 units.
Then ,
Area of sector : [tex]\frac{1}{2}[/tex] (16)²* [tex]\frac{3\pi }{4}[/tex].
Area of sector : [tex]\frac{1}{2}[/tex] * 256 * [tex]\frac{3\pi }{4}[/tex].
Area of sector : 128 * [tex]\frac{3\pi }{4}[/tex].
Area of sector : 32 * 3 π
Area of sector : 96 π unit².
Therefore, Area of sector : 96 π unit².
A wholesaler receives an order for 8000 pounds of produce. If the cost of shipping is $90 per ton, how much will the wholesaler have to pay for this shipment?
Answer:360
Step-by-step explanation:
1 ton = 2000 pounds
8000/2000 =4
4x90= 360.00
Answer is 360.00 for shipping
[tex]\huge{\boxed{\$360}}[/tex]
Each pound contains [tex]2000[/tex] pounds, so divide [tex]8000 \div 2000[/tex] to find the number of tons. [tex]8000 \div 2000=4[/tex]
Now, just multiply [tex]\$90*4=\boxed{\$360}[/tex]
The cosine of 23° is equivalent to the sine of what angle
Answer:
So 67 degrees is one value that we can take the sine of such that is equal to cos(23 degrees).
(There are more values since we can go around the circle from 67 degrees numerous times.)
Step-by-step explanation:
You can use a co-function identity.
The co-function of sine is cosine just like the co-function of cosine is sine.
Notice that cosine is co-(sine).
Anyways co-functions have this identity:
[tex]\cos(90^\circ-x)=\sin(x)[/tex]
or
[tex]\sin(90^\circ-x)=\cos(x)[/tex]
You can prove those drawing a right triangle.
I drew a triangle in my picture just so I can have something to reference proving both of the identities I just wrote:
The sum of the angles is 180.
So 90+x+(missing angle)=180.
Let's solve for the missing angle.
Subtract 90 on both sides:
x+(missing angle)=90
Subtract x on both sides:
(missing angle)=90-x.
So the missing angle has measurement (90-x).
So cos(90-x)=a/c
and sin(x)=a/c.
Since cos(90-x) and sin(x) have the same value of a/c, then one can conclude that cos(90-x)=sin(x).
We can do this also for cos(x) and sin(90-x).
cos(x)=b/c
sin(90-x)=b/c
This means sin(90-x)=cos(x).
So back to the problem:
cos(23)=sin(90-23)
cos(23)=sin(67)
So 67 degrees is one value that we can take the sine of such that is equal to cos(23 degrees).
What is the value of a?
Check the picture below.
notice, on the first 2 lines, we used the quadrilateral conjecture.
on the lines 3 and 4 we used the inscribed angle theorem.
line 5, if we add those 3 arcs, we end up with 427°, mind you that the surplus is arcYW or "b", since it's added twice by XW and YZ.
line 6, if we subtract a full circle from it, we have the surplus.
line 7, we simply subtract YW from XW, leaving the leftover of arc "a".
Please help with this one question ASAP. (show steps if you can)
For this case we have that the area of the figure is given by the area of a rectangle plus the area of a square. By definition, the area of a rectangle is given by:
[tex]A = a * b[/tex]
According to the figure we have:
[tex]a = 9 \sqrt {2}\\b = 8 \sqrt {2} -2 \sqrt {2} = 6 \sqrt {2}[/tex]
So, the area of the rectangle is:
[tex]A = 9 \sqrt {2} * 6 \sqrt {2} = 54 (\sqrt {2}) ^ 2 = 54 * 2 = 108[/tex]
On the other hand, the area of a square is given by:
[tex]A = l ^ 2[/tex]
Where:
l: it is the side of the square
According to the figure we have:
[tex]l = 2 \sqrt {2}[/tex]
So:
[tex]A = (2 \sqrt {2}) ^ 2 = 4 * 2 = 8[/tex]
Finally, the area of the figure is:
[tex]A_ {t} = 108 + 8 = 116[/tex]
Answer:
116
Which expression represents the number rewritten in a+ bi form?
[tex]\bf \textit{recalling that }~\hfill i^4=1~\hfill i^3=-i~\hfill i^2=-1 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 5i^4+2i^3+8i^2+\sqrt{-4}\implies 5(1)+2(-i)+8(-1)+\sqrt{-1\cdot 4} \\\\\\ 5-2i-8+\sqrt{-1}\cdot \sqrt{2^2}\implies -2i-3+i\cdot 2\implies ~~\begin{matrix} -2i \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~-3~~\begin{matrix} +2i \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill -3+0i~\hfill[/tex]
Find the distance across the lake. Assume the triangles are similar
Check the picture below.
The distance across the lake is 210 meters, and this is found using the concept of similar triangles and proportionality.
The correct answer is option B.
To find the distance across the lake, we can use the concept of similar triangles. Given that the triangles are similar, we can set up a proportion to find the missing side length.
Let's label the sides of the larger triangle as A, B, and C and the sides of the smaller triangle as X, Y, and Z. The given values are:
A = 70 m (the length of the larger triangle)
X = 20 m (the length of the smaller triangle)
Y = 60 m (the width of the smaller triangle)
We want to find side C, which represents the distance across the lake.
We can set up a proportion between the corresponding sides of the two similar triangles:
A / X = B / Y = C / Z
Plugging in the given values:
70 m / 20 m = C / 60 m
Now, solve for C by cross-multiplying:
70 m * 60 m = 20 m * C
4200 m² = 20 m * C
To isolate C, divide both sides by 20 m:
C = 4200 m² / 20 m
C = 210 m
So, the distance across the lake (side C) is 210 meters. This is the solution based on the concept of similar triangles and the given side lengths.
Therefore, from the given options the correct one is B.
For more such information on: distance
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Using the data: 2, 2, 3, 3, 3, 4, 5, 6, 6, 19
What is Q1 and Q3
3.5, 6.5
2, 10
3, 6
2, 5
Answer: Third Option
[tex]Q_1=3[/tex]
[tex]Q_3=6[/tex]
Step-by-step explanation:
Notice that we already have the data sorted from least to greatest.
Now to find Q1 and Q3 we can use the following formulas
For a set of data ordered from least to greatest of the form [tex]X_1, X_2, ..., X_n[/tex]
Where n is the total number of data
[tex]Q_1=X_{\frac{1}{4}(n+1)}[/tex]
In this case [tex]n=10[/tex]
So:
[tex]Q_1=X_{\frac{1}{4}(10+1)}[/tex]
[tex]Q_1=X_{2.75}[/tex]
Round the nearest whole and get:
[tex]Q_1=X_{3}[/tex]
[tex]Q_1=3[/tex]
For [tex]Q_3[/tex] we have:
[tex]Q_3=X_{\frac{3}{4}(n+1)}[/tex]
[tex]Q_3=X_{\frac{3}{4}(10+1)}[/tex]
[tex]Q_3=X_{8.25}[/tex]
Round the nearest whole and get:
[tex]Q_3=X_{8}[/tex]
[tex]Q_3=6[/tex]
find the x and y intercepts for the equation 2x-5y=6
Answer:
X intercepts (3,0) Y (0, -6/5)
Step-by-step explanation:
X intercepts: -6-2x/5=0
5(-6-2/5)=0*5
-6+2x=0
-6+6+2x=0+6
2x=6
2x/2=6/2
x=3
Y intercepts: y=-6-2*0/5
y=6-2*0=6
6-2*0/5
6-0/5
6/5
Answer:
X= 5y/2+3
Step-by-step explanation:
First add 5y to both sides
2x-5y+5y=6+5y
2x=5y+6
Step 2
Divide both sides by 2
2x/2=5y+6/2
X=5y/2+3
factor the expression 6x^2 + 5x + 1
Answer:
The factors are (3x+1)(2x+1)
Step-by-step explanation:
The expression is:
6x^2 + 5x + 1
We have to break the middle term to find its factors. For this first we have to multiply the coefficient of 1st terms with the constant term:
6*1 = 6
Now we have to find any two numbers whose product is 6 and whose sum is the middle term:
3*2=6
3+2=5
Now break the middle term by these two numbers.
6x^2 + 5x + 1
6x^2+3x+2x+1
Group the first two terms and last two terms:
(6x^2+3x)+(2x+1)
Now take out common factor from each term:
3x(2x+1)+1(2x+1)
(3x+1)(2x+1)
Therefore the factors are (3x+1)(2x+1)....
Answer:
(2x + 1)(3x + 1)
Step-by-step explanation:
Given
6x² + 5x + 1
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 6 × 1 = 6 and sum = + 5
The factors are + 3 and + 2
Use these factors to split the x0 term
6x² + 3x + 2x + 1 ( factor the first/second and third/fourth terms )
= 3x(2x + 1) + 1 (2x + 1) ← factor out (2x + 1) from each term
= (2x + 1)(3x + 1) ← in factored form
Problem solving fractions please help!
Problem #1= 7 5/12- 6 1/12= 1 4/12 which is simplified to 1 1/3
The answer to the first problem is 1 1/3 feet.
Problem #2= 28(3/4)= 84/4= 21
The answer to the second problem is 21 points.
Hope this helps!
21 plus 6p minus two-thirds the sum of 14p and 3q
Step-by-step explanation:
any doubt regarding to answer !Number 10 please I don’t know how to do it and if you could also do 11
Answer:
C) -3Step-by-step explanation:
x = 1, y = 12
x = 2, y = 9
x = 3, y = 6
x = 4, y = 3
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{9-12}{2-1}=\dfrac{-3}{1}=-3[/tex]
Sin x + cos x = cos x/1-tanx + sin x/1-cot x. Verify the identity. Explain each step please!
Answer:
[tex]sinx+cosx=\frac{cosx}{1-tanx}+\frac{sinx}{1-cotx}\\[/tex] proved.
Step-by-step explanation:
[tex]sinx+cosx=\frac{cosx}{1-tanx}+\frac{sinx}{1-cotx}\\[/tex]
Taking R.H.S
[tex]\frac{cosx}{1-tanx}+\frac{sinx}{1-cotx}\\[/tex]
Multiply and divide first term by cos x and second term by sinx
[tex]=\frac{cosx*cosx}{cosx(1-tanx)}+\frac{sinx*sinx}{sinx(1-cotx)}[/tex]
we know tanx = sinx/cosx and cotx = cosx/sinx
[tex]=\frac{cos^2x}{cosx(1-\frac{sinx}{cosx} )}+\frac{sin^2x}{sinx(1-\frac{cosx}{sinx})}\\=\frac{cos^2x}{cosx-sinx}+\frac{sin^2x}{sinx-cosx}[/tex]
Taking minus(-) sign common from second term
[tex]=\frac{cos^2x}{cosx-sinx}-\frac{sin^2x}{cosx-sinx}[/tex]
taking LCM of cosx-sinx and cosx-sinx is cosx-sinx
[tex]=\frac{cos^2x-sin^2x}{cosx-sinx}[/tex]
We know a^2-b^2 = (a+b)(a-b), Applying this formula:
[tex]=\frac{(cosx+sinx)(cosx-sinx)}{cosx-sinx}\\=cosx+sinx\\=L.H.S[/tex]
Hence proved
What is the point slope form of a line that has a slope of 3 and passes through the point (-1,4)
Answer:
y - 4 = 3(x- (-1) ---> y-4 = 3(x+1)
Step-by-step explanation:
y - 4 = 3(x + 1)
y - 4 = 3x + 3
y = 3x + 7
then plug in (-1,4)
4 = 3(-1) + 7
4 = -3 + 7
4 = 4
Point slope form looks like:
y - y₁ = m(x - x₁)
Answer:
Y-4=3[(x-(-1)]
Step-by-step explanation:
This answer is corect i got it right on my questions
b is the midpoint of AC and E is the midpoint of BD if A(-9,-4) C(-1,6) and E(-4,-3) find the coirdinates of D
Answer:
Step-by-step explanation:
[tex]B=(\frac{-9-1}{2},\frac{-4+6}{2} ) (midpoint formula)\\B=(-5,1)\\\\Then using midpoint formula again,\\E=(-4,3)=(\frac{-5+x}{2} =-4,\frac{1+y}{2} =3)\\so \\x=-3\\y=5\\\\D=(-3,5)[/tex]:
05.05 HC) Figure ABCD has vertices A(−2, 3), B(4, 3), C(4, −2), and D(−2, 0). What is the area of Figure ABCD?
Answer:
The area of ABCD is 24 units²
Step-by-step explanation:
* Lets explain how to solve the problem
- All the point in a vertical line have the same x-coordinates
- The length of the vertical line is y2 - y1
- All the point in a horizontal line have the same y-coordinates
- The length of the horizontal line is x2 - x1
- The horizontal and the vertical lines are perpendicular to each other
- The trapezoid has two parallel bases not equal in length and the other
two sides are nonparallel sides
- The area of the trapezoid = 1/2 (sum of the two // bases) × height
* Lets solve the problem
∵ ABCD is a quadrilateral
∵ A = (-2 , 3) , B = (4 , 3) , C = (4 , -2) , D = (-2 , 0)
∵ Side AD has same x-coordinates in A and D (-2)
∴ AD is vertical side
∴ AD = 3 - 0 = 3
∵ Side BC has same x-coordinates in B and C (4)
∴ BC is vertical side
∴ BC = 3 - (-2) = 3 + 2 = 5
∵ AD and BC are vertical lines
∴ AD // BC
∵ Side AB has same y-coordinates in A and B (3)
∴ AB is horizontal side
∴ AB = 4 - (-2) = 4 + 2 = 6
∵ The horizontal and the vertical lines are perpendicular to each other
∴ AB is perpendicular on AD and BC
∵ The side CD is not vertical or horizontal
∴ ABCD has only two parallel sides AD and BC
∵ AD ≠ BC
∴ ABCD is a trapezoid
∵ The two parallel bases are AD and BC
∵ Its height is AB
∵ AD = 3 , BC = 5 , AB = 6
∴ Its area = 1/2 (3 + 5) × 6 = 1/2 (8) × 6 = 4 × 6 = 24 units²
* The area of ABCD is 24 units²
Answer:
24 square units
i did the test
Step-by-step explanation:
misty's surgery lasted 2 1 hr. convert time to seconds?
For this case we must convert 21 hours to seconds!
We have that by definition, 1 hour equals 3600 seconds. Then, making a rule of three we have:
1h ------------> 3600s
21h ----------> x
Where "x" represents the number of seconds equivalent to 21 hours.
[tex]x = \frac {21 * 3600} {1} = 75600[/tex]
Thus, 21 hours represent 75600 seconds.
Answer:
75600 seconds.
Examine the following system of inequalities.
{y <−1/4x+4 and y>(x+4)^2
Which option shows the graph of the system?
Dotted linear inequality shaded above passes through (0, 4) & (4,5). Dotted parabolic inequality shaded below passes through (negative 6,4), (negative 4, 0) & (negative 2, 4).
Dotted linear inequality shaded below passes through (0, 4) & (4,3). Dotted parabolic inequality shaded above passes through points (negative 6,4), (negative 4, 0) & (negative 2, 4).
Dotted linear inequality shaded below passes through (0, 4) & (4,5). Dotted parabolic inequality shaded above passes through points (negative 6,4), (negative 4, 0) & (negative 2, 4).
Dotted linear inequality shaded above passes through (0, 4) & (4,3). Dotted parabolic inequality shaded below passes through (negative 6,4), (negative 4, 0) & (negative 2, 4).
Dotted linear inequality shaded below passes through (0, 4) & (4,3). Dotted parabolic inequality shaded above passes through points (negative 6,4), (negative 4, 0) & (negative 2, 4).
Step-by-step explanation:Hello! Let me help you to find the correct option to this problem. First of all, we have the following system of inequalities:
[tex]\left\{ \begin{array}{c}y< -\frac{1}{4}x+4\\y>(x+4)^{2}\end{array}\right.[/tex]
To solve this, let's write the following equations:
FIRST:[tex]y=-\frac{1}{4}x+4[/tex]
This is a linear function written in slope-intercept form as [tex]y=mx+b[/tex]. So, the slope [tex]m=-\frac{1}{4}[/tex] and the y-intercept is [tex]b=4[/tex]. Since in the inequality we have the symbol < then the graph of the line must be dotted. To get the shaded region, let's take a point, say, [tex](0, 0)[/tex] and let's test whether the region is above or below the graph. So:
[tex]y< -\frac{1}{4}x+4 \\ \\ Let \ x=y=0 \\ \\ 0<-\frac{1}{4}(0)+4 \\ \\ 0<4 \ True![/tex]
Since the expression is true, then the region is the one including point [tex](0, 0)[/tex], that is, it's shaded below.
SECOND:[tex]y=(x+4)^{2}[/tex]
This is a parabola that opens upward and whose vertex is [tex](-4,0)[/tex]. Since in the inequality we have the symbol > then the graph of the parabola must be dotted. Let's take the same point [tex](0, 0)[/tex] to test whether the region is above or below the graph. So:
[tex]y>(x+4)^{2} \\ \\ Let \ x=y=0 \\ \\ 0>(0+4)^2\\ \\ 0>16 \ False![/tex]
Since the expression is false, then the region is the one that doesn't include point [tex](0, 0)[/tex], that is, it's shaded above
____________________
On the other hand, testing points (0, 4) and (4,3) on the linear function:[tex]y=-\frac{1}{4}x+4 \\ \\ \\ \bullet \ (0,4): \\ \\ y=-\frac{1}{4}(0)+4 \therefore y=4 \\ \\ \\ \bullet \ (4,3): \\ \\ y=-\frac{1}{4}(4)+4 \therefore y=3[/tex]
So the line passes through these two points.
Now, testing points (negative 6,4), (negative 4, 0) & (negative 2, 4) on the parabola:[tex]y=(x+4)^2 \\ \\ \\ \bullet \ (-6,4): \\ \\ y=(-6+4)^2 \therefore y=(-2)^2 \therefore y=4 \\ \\ \\ \bullet \ (-4,0): \\ \\ y=(-4+4)^2 \therefore y=0 \\ \\ \\ \bullet \ (-2,4): \\ \\ y=(-2+4)^2 \therefore y=(2)^2 \therefore y=4[/tex]
So the line passes through these three points.
Finally, the shaded region is shown below.
Miranda and Jean are planning a trip together. They want to drive, but they're not sure whose car to take. Jean's car uses gallons of gasoline to travel miles. Miranda's car can go miles on gallons of gasoline. Whose car is more fuel efficient, and what is the car’s fuel efficiency in miles per gallon?
is more fuel efficient. Her car gets miles per gallon.
Jean's car :
(12 1/2) / (5/12) =
(25/2) / (5/12) =
25/2 * 12/5 =
150/5 =
30 miles per gallon
Miranda's car :
(20 5/7) / (5/7) =
(145/7) / (5/7) =
145/7 * 7/5 =
145/5 =
29 miles per gallon
most fuel efficient is Jean's car....it gets 30 miles per gallon
Answer:
most fuel efficient is Jean's car gets 30 miles per gallon
Step-by-step explanation:
what are the x intercepts, vertex and axis of symmetry of y=-(x+1)(x-5)
Answer:
x intercepts: (-1, 0) and (5, 0)
vertex: (2, 9)
axis of symmetry: x = 2
Step-by-step explanation:
The x intercepts are where y = 0.
0 = -(x + 1)(x − 5)
x = -1, x = 5
So the x intercepts are (-1, 0) and (5, 0).
The x coordinate of the vertex is halfway between the x intercepts.
x = (-1 + 5) / 2
x = 2
So the vertex is at (2, 9).
The axis of symmetry passes through the vertex.
x = 2
whihc question is not a good survey question? dont you agree that the financial crisis is essentially over? on average how many hours do you sleep per day?
Answer:
The correct answer would be option A, Don't you agree that the financial crisis is essentially over.
Step-by-step explanation:
A survey questionnaire is a series of question which is set formally to be asked from a specific sample of a population to gather, analyze and interpret the data obtained from the sample population. So the questions in the survey must be structured, to the point, clear, short and straight. Survey questions are desirably closed ones and the ones which do not need much explanation by the person who is doing the survey. So the first question in this question require an explanation, and also the question is not structured, clear and to the point and thus is not a good survey question. Comparatively, the second question is more structured, clear and to the point and such questions are normally desirable in the surveys.
Answer:
See image
Step-by-step explanation:
Plato
What is the prime factorization of 31?
Enter your answer as a product of prime numbers, like 2 x 3, or as a single prime number, like 17.
Answer:
Step-by-step explanation:
31 is prime. It can't be factored. The way I'm reading the directions, you should enter 31.
Answer:
31
Step-by-step explanation:
The prime factorization of 31 is 1 x 31 = 31.
You have to multiply the number by 1 to find its prime factorization.
However, it is usually written as just 31.