By solving the quadratic equation using completing the square method we got that Penelope should have added 4 to both sides instead of adding 1.
What is quadratic equation ?Any equation of the form [tex]ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called quadratic equation .
Given work of Penelope is
[tex]$$\begin{aligned}&f(x)=4 x^{2}+8 x+1 \\&-1=4 x^{2}+8 x \\&-1=4\left(x^{2}+2 x\right) \\&-1+1=4\left(x^{2}+2 x+1\right) \\&0=4(x+2)^{2} \\&0=(x+2)^{2} \\&0=x+2 \\&-2=x\end{aligned}$$[/tex]
Now we can see that Penelope determined the solutions of the quadratic function by completing the square. so he must have been done as following
[tex]$$\begin{aligned}&f(x)=4 x^{2}+8 x+1 \\&-1=4 x^{2}+8 x \\&-1=4\left(x^{2}+2 x\right) \\&-1+4=4\left(x^{2}+2 x+1\right) \\&3=4(x+2)^{2} \\&\frac{3}{4} =x+2)^{2} \\&\frac{\pm\sqrt3}{2} =x+2 \\&\frac{-2\pm\sqrt3}{2} =x\end{aligned}$$[/tex]
By solving the quadratic equation using completing the square method we got that Penelope should have added 4 to both sides instead of adding 1.
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Answer:
C) Penelope should have added 4 to both sides instead of adding 1.
Step-by-step explanation:
Got it right on edge! Good Luck <3
Find the midpoint of the line segment with end coordinates of:
(
−
3
,
−
1
)
and
(
4
,
−
5
)
Give coordinates as decimals where appropriate.
Answer:
(0.5, -3)
Step-by-step explanation:
(-3, -1) (4, -5)
midpoint formula
(x1 + x2) /2, (y1 + y2) /2
-3 + 4 = 1 / 2 = 0.5
-1 + -5 = -6 / 2 = -3
Find the measurement of angle ( A ) round to the nearest hundred
Answer:
all you have to do is round to the nearest.
Step-by-step explanation:
just do it .
The weight that a horizontal beam can support varies inversely as the length of the beam. Suppose that a 2-m beam can support 310 kg. How many kilograms can a 10-m beam support? a. 0. 0161 kg b. 62 kg c. 15. 5 kg d. 0. 0645 kg.
A beam of length 10m can support a weight of 62kg.
It is given that
Weight W ∝ 1/ Length L
W ∝ 1/L
W = k/L...........eq1
where k is constant of proportionality
What is the constant of proportionality?The constant of proportionality is the ratio that relates two given values.
It is given that when L= 2m, W = 310kg
310 = k/2
k = 620
So put the k value in eq1,
eq1 becomes,
W = 620/L
when L = 10
W = 620/10
W =62kg
Therefore, a beam of length 10m can support a weight of 62kg.
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What is the value of x? (5 points)
Let x, y, and z represent three rational numbers, such that y is 512 times x and z is 50.25 more than x. If y=15.5, what is the value of z?
The value of z is equal to 50.28.
System of Linear EquationsSystem of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.
Rational NumbersThese numbers are represented by a ratio between two integers numbers ([tex]\frac{a}{b}[/tex]), where b[tex]\neq[/tex]0. Besides, this ratio can be simplified in decimal form.
For solving this equation, firstly, rewrite the information given:
[tex]y=512x \;(1)\\ \\ z=50.25+x \;(2)\\ \\ y=15.5 \;(3)[/tex]
As the question gives the values for y, you can find x.
[tex]y=512x\\ \\ 15.5=512x\\ \\ x=\frac{15.5}{512} =0.03[/tex]
Applying x=0.03 in the equation (3), you can find z.
[tex]z=50.25+x \\ \\ z=50.25+0.03\\ \\ z=50.28[/tex]
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i need help asap pls
Step-by-step explanation:
[tex]m + 148 = 3m + 10[/tex]
[tex]148 - 10 = 3m - m[/tex]
therefore
3m = 138
m = 138/3
m = 46°
pls give brainliest
Colin is c years old. His 14 year old sister, Katie, is 4 years younger than Colin. write an expression
Answer: C - 4 = 14
Step-by-step explanation: In the expression, "c" is colin's age so, if you subtract 4 years for his age, you get Katie's age, which is 14.
Also 5 3/7 x 3 1/2 Thanks
What decimal best represents 1/4
Answer:
.25
Step-by-step explanation:
.25 or 1/4 is one-fourth of 1
You can divide 1 by 4 to get .25
PLEASE HELP FAST URGENT!!!
Answer:
A= Origen C= q1 B=Q2
Step-by-step explanation
your left-hand side is quadrant TWO Your top right-hand corner is Quadrant ONE and your second to the last one is left-hand side down Is Quadrant THREE last but not least is Quadrant FOUR. And the zero in the middle means ORIGEN.
Please please help me please
Answer:
A
Step-by-step explanation:
It could just be it was dilated (I think thats the word) by 3. 6×3=18, 8×3=24
PLEASE HELP ANSWER THESE FAST, will give brainliest and 100 points
Step-by-step explanation:
11.
x is sin(60) in a circle with radius of 8.
x = sin(60)×8 = 6.92820323... ≈ 6.9
12.
x is sin(30) in a circle with radius "diagonal length".
6 is cos(30) in the same circle.
6 = cos(30)×r
r = 6/cos(30) = 6.92820323...
x = sin(30)×r = 3.464101615... ≈ 3.5
13.
similar to 12.
but we refer to the angle at the bottom right vertex.
remember, the sum of all angles in a triangle is always 180°.
so, the angle over there at the right is
180 - 90 - 68 = 22°
x = sin(22)×r
25 = cos(22)×r
r = 25/cos(22) = 26.96336857...
x = sin(22)×r = 10.10065565... ≈ 10.1
14.
9 is the sine of the complementary angle of 49 in a circle with radius x.
the complementary angle is the angle that adds up with the original angle to 90° and is therefore
90 - 49 = 41°
9 = sin(41)×x
x = 9/sin(41) = 13.71827778... ≈ 13.7
18.
we use the extended Pythagoras :
c² = a² + b² - 2ab×cos(C)
with c being the side opposite of the angle C.
so we have
LK² = 16² + 24² - 2×16×24×cos(29) =
= 256 + 576 - 768×cos(29) =
= 832 - 671.7079351... = 160.2920649...
LK = 12.66065026... ≈ 12.7
19.
law of sine
a/sin(A) = b/sin(B) = c/sin(C)
with the sides being always opposite to the corresponding angles.
to find the angle at H we need to find the angle at G first, because we don't know GF yet.
so,
28/sin(76) = 18/sin(G)
sin(G) = 18×sin(76)/28 = 0.623761538...
G = 38.59134528...°
remember the 180° rule in triangles.
H = 180 - 76 - G = 65.40865472...° ≈ 65.4°
20.
GF is now calculated using the law of sine again.
28/sin(76) = GF/sin(H)
GF = 28×sin(H)/sin(76) = 26.23980579... ≈ 26.2
hey so im also looking for the first answer and the choices were “ is not “ and “ is “
so the investigator found the skid marks were 75 feet long hmmm what speed will that be?
[tex]s=\sqrt{30fd}~~ \begin{cases} f=\stackrel{friction}{factor}\\ d=\stackrel{skid}{feet}\\[-0.5em] \hrulefill\\ f=\stackrel{dry~day}{0.7}\\ d=75 \end{cases}\implies s=\sqrt{30(0.7)(75)}\implies s\approx 39.69~\frac{m}{h}[/tex]
nope, the analysis shows that Charlie was going faster than 35 m/h.
now, assuming Charlie was indeed going at 35 m/h, then his skid marks would have been
[tex]s=\sqrt{30fd}~~ \begin{cases} f=\stackrel{friction}{factor}\\ d=\stackrel{skid}{feet}\\[-0.5em] \hrulefill\\ f=\stackrel{dry~day}{0.7}\\ s=35 \end{cases}\implies 35=\sqrt{30(0.7)d} \\\\\\ 35^2=30(0.7)d\implies \cfrac{35^2}{30(0.7)}=d\implies 58~ft\approx d[/tex]
Determine is (x-3) is a factor of
x^3 - 5x^2 - 4x + 6 using the remainder
theorem:
Answer:
(x - 3) is not a factor
Step-by-step explanation:
If (x - h) is a factor of f(x) then f(h) = 0
here
f(x) = x³ - 5x² - 4x + 6 , then
f(3) = 3³ - 5(3)² - 4(3) + 6 = 27 - 5(9) - 12 + 6 = 27 - 45 - 6 = - 24
since f(x) ≠ 0 then (x - 3) is not a factor of f(x)
After spending $6.75 on a meal and $1.25 on drinks, Maria had $12 left.
What percent of her money did Maria spend?
Answer:
40%
Step-by-step explanation:
6.75 + 1.25 = 8 (Total she just spent)
8 (Total she just spent) + 12 (Total she had left) = 20 (Total she started with)
8/20 = 0.4 = 40%
(Total spent / total she started with = 40%)
Instructions: Find the length of the missing sides.
I WILL GIVE A BRAINIST !!
please explain how to do this
Answer:
y = 8sqr3,
x = 4sqr3
Step-by-step explanation:
Use SOH CAH TOA, to solve this.
Here I know the opposite, so I could use either SOH either TOA or both to find the 2 unknowns.
To find y, I would use SOH, which is Sin(angle) = opposite/hypotenuse.
When I rearrange it, I get opposite/Sin(angle) = hypotenuse.
Now let's fill in with the values to give:
12/sin(60) = 8sqr3
And then to find x, let's use TOA, which is Tan(angle) = opposite/adjacent.
Rearrange it to get opposite/Tan(angle) = adjacent. This gives us a side x with a value of:
12/tan(60) = 4sqr3
A triangle has two sides of length 17 and 2. What is the smallest possible whole-number length for the third side?
Answer: 16
Step-by-step explanation:
A rectangular prism has a length of 3 meters, a height of 7 meters, and a width of 7 meters. What is its volume, in cubic meters?
tell me how to decompose 792
Answer:
break it down to prime factorization
so the ans will be 2^3 * 3^2 *11
A lil help would be nice
(Explained answer will get brainlyist)
Answer:
10 cm
Step-by-step explanation:
Out of that [tex]160 cm^2[/tex], part of it is given by the surface of the top and bottom faces, which have area [tex]2\times 5 cm^2 = 10 cm^2[/tex] each, for a total of [tex]20 cm^2[/tex] . We are then left with [tex]140 cm^2[/tex] of surface from the side area. That area you can imagine as a rectangle of height h (which we need to know) and base [tex]5+2+5+2 cm = 14 cm[/tex] (imagine it as a box opened on a flat surface)
At this point we have [tex]140cm^2 = 14 cm \times h \rightarrow h= 10 cm[/tex]
look at the attachment
Simplified it too
pls take it seriously
[tex]\\ \rm\rightarrowtail \dfrac{sin(180+A)+2cos(180+A).cos(A-180)}{2cos^2(360+A)-cos(-A)}[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{-sinA+2(cos^2A-sin^2A)}{2cos^2A-cosA}[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{-sinA+2cos^2A-2sin^2A}{cosA(2cosA-1)}[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{-sinA+2-2sin^2A-2sin^2A}{cosA(2cosA-1)}[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{-sinA-4sin^2A}{cosA(2cosA-1)}[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{-sinA(4sinA-1)}{cosA(2cosA-1)}[/tex]
[tex]\\ \rm\rightarrowtail -tanA\left(\dfrac{4sinA-1}{2cosA-1}\right)[/tex]
Laura is building a fence around a circular pond. The pond has a diameter of 30 feet. What is the minimum amount of fencing Laura will need?
Answer:
Step-by-step explanation:
Minimum Amount = circumference of the pond.
Formulas
C = pi * d
Givens
pi = 3.14
d = 30 feet
Solution
C = pi*d Substitute for the givens.
C = 3.14 * 30 Multiply
C = 94.2
The function f(x)= -45x + 270 represents the total distance, in miles, a traveler is from home x hours after beginning the trip home. What is the average rate of change over the interval from x = 1 to x = 3, in miles per hour?
[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Given :- We have given one function f(x) = -45x + 270 The given function represents the total distance in miles. The initial interval was x = 1 and final interval was x = 3 To Find :- We have to find the rate of change over the given interval Let's Begin :-Here, We have
Function = f(x) = -45x + 270The given function represents the total distance in miles covered by the traveller.
Therefore,
For initial interval that is x = 1 , Distance covered by the traveller
[tex]\sf{ f(x) = -45x + 270 }[/tex]
[tex]\sf{ f(1) = - 45(1) + 270 }[/tex]
[tex]\sf{ f(1) = - 45 + 270 }[/tex]
[tex]\sf{ f(1) = 225 }[/tex]
For final interval that is x = 3, Distance covered by the traveller
[tex]\sf{ f(x) = - 45x + 270 }[/tex]
[tex]\sf{ f(1) = - 45(3) + 270 }[/tex]
[tex]\sf{ f(1) = - 135 + 270 }[/tex]
Now,We have to find the average rate of change over the given time interval
Therefore,Average rate of change in the given time interval
[tex]\sf{ = }{\sf{\dfrac{ f(1) + f(3) }{3 - 1}}}[/tex]
[tex]\sf{ = }{\sf{\dfrac{ 225 + ( -135) }{ 2}}}[/tex]
[tex]\sf{ = }{\sf{\dfrac{ 225 - 135 }{ 2}}}[/tex]
[tex]\sf{ = }{\sf{\dfrac{ 90 }{ 2}}}[/tex]
[tex]\sf{ = 45 }[/tex]
Hence, The average rate of change over the given interval is 45 miles per hour.
100!!! Points
Select the correct answer.
What is the range of the function shown in the graph?
So
The range is
(-oo,0)U(oo,5)So
-oo<y<5Option D is correct
Shelley drew a scale drawing of the high school. She used the scale 5 millimeters: 3 meters.
If the actual width of the parking lot is 42 meters, how wide is the parking lot in the drawing?
Answer:
70 meters
Step-by-step explanation:
Based on the given conditions, formulate:: 45x5/3
Cross out the common factor: 14x5
Calculate the product or quotient: 70
The width of the parking lot in the drawing is, 70 milliliters.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
She used the scale 5 millimeters: 3 meters.
And, The actual width of the parking lot is 42 meters.
Hence, We can formulate;
The width of the parking lot in the drawing = 42 × 5 / 3
= 70 milliliters
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PLEASE HELP ME ITS URGENT!!!!
A rectangular garden has a walkway around it. The area of the garden is 4(5.5x + 1.5). The combined
area of the garden and the walkway is 4.5(8x + 4). Find the area of the walkway around the garden as
the sum of two terms.
CD
The area of the walkway around the garden is 1
(Simplify your answer. Use integers or decimals for any numbers in the expression.)
We're given:
Area (garden) = 4(5.5x + 1.5)Area (garden + walkway) = 4.5(8x + 4)To find the area of the garden alone, we can subtract the area of the garden from the combined area of the garden and walkway:
[tex]4.5(8x + 4)-4(5.5x + 1.5)[/tex]
Open up the parentheses:
[tex]= 36x +18 -22x - 6[/tex]
Combine like terms:
[tex]= 36x +18 -22x - 6\\= 14x +18 - 6\\= 14x +12[/tex]
AnswerThe area of the walkway around the garden is 14x + 12.
A model of a skyscraper is made using a scale of 1 inch: 75 feet. What is the height of the actual building if the height of the model is 19 2/5 inches?
What is the value of v?
Answer: 43
Step-by-step explanation:
Which number line shows the solution of –5x + 10 > –15?
Answer:
B.
Step-by-step explanation:
-5x + 10 > -15
-5x + 10 - 10 > -15 - 10
-5x > -25
-5x / -5 > -25/(-5)
x < 5
Ratio volume of 2 cylinders is 125:343
Answer:
5145cm²
125/343=1875/x
x=1875×343÷125=5145