The answers are presented below:
The equation is a quadratic - TRUEThe graph is linear. the vertex is (7,4) - FALSEThe axis of symmetry is x= -7 - TRUEThe y-intercept is (0,4) - FALSE The graph has a relative maximum. - TRUEThe equation has no real solutions. - FALSEQuadratic function
The quadratic function can be represented by a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.
The vertex of an up-down facing parabola of the form ax²+bx+c is [tex]x_v=\frac{-b}{2a}[/tex] . Knowing the x-coordinate of vertex, you can find the y-coordinate of vertex. When a vertical line passes through the vertex of the parabola, it is called the axis of symmetry.
The y-intercept is the point where the function crosses the y-axis. And, the x-intercept is the point where the function crosses the x-axis, in other words, when y=0.
First, you should convert the given equation to Standard form.
f(x) = -(c+7)² + 4
f(x)= - (c²+14c+49)+4
f(x)= -c²-14c-49+4
f(x)= -c²-14c-49+4
f(x)= -c²-14c-45
After that, you should check each option of the question.
The equation is a quadraticCorrect because present a degree 2 -- f(x)= -c²-14c-45
The graph is linearIncorrect because it is a quadratic function and this function is represented by a parabola.
The vertex is (7,4)The coefficients are: a=-1, b=-14, c=-45. Therefore,
[tex]c_v=\frac{-b}{2a}=-\frac{-14}{2*(-1)} =-\frac{-14}{-2}=-(7)=-7[/tex]
Incorrect because x-coordinate of vertex is -7
The axis of symmetry is x= -7.Correct because [tex]c_v=\frac{-b}{2a}=-\frac{-14}{2*(-1)} =-\frac{-14}{-2}=-(7)=-7[/tex]
The y-intercept is (0,4)You can find the y-intercept using c=0, then f(x)= -c²-14c-45 will be:
f(x)=-45.
Incorrect because the y-intercept is (0,-45).
The graph has a relative maximum.The coefficient a of a quadratic function is negative, thus the function has a point maximum. A relative maximum point is defined as the point where the function changes your direction. In other words, the values of the function increase before the relative maximum and the values decrease after the relative maximum.
Correct, see the attached image.
The equation has no real solutions.It is possible to find the number of roots or solutions from discriminant.
For quadratic equation the discriminant is determined by D=b²-4ac, where: a, b and c are coefficients.
If D > 0 - the function will have two real solutions;
If D = 0 - the function will have one real solution;
If D < 0 - the function will have imaginary solutions;
For given equation, the coefficients are: a=-1, b=-14, c=-45. Thus, D=(-14)²-4*(-1)*(-45)
D=196-180=16
D=16 thus D > 0
Incorrect because the D>0.
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a motorboat travels a distance of one pier to another pier in 4 hrs and the way back in 5 hrs. What is the speed of the boat in still water if it travels 70 km with the current in 3.5 hrs?
let's recall that d = rt, namely distance = rate * time.
d = distance from one pier to another
c = speed of the current
b = speed of the boat
now, let's notice something, on the way over the boat travelled "d" kilometers in 4 hrs, and back the same "d" kilometers in 5 hours.
when going with the current, the boat is not really going at "b" km/s, is really going faster, at "b + c" km/s, because the current is adding to it.
now, when going against the current, the boat is not really going "b" fast, is really going slower, at "b - c", because the current is subtracting from it.
from the above, we can conclude that the 4hrs trip was with the current, since it took less time, and the 5hrs trip was against the current, and we also know that the boat does 70 km with the current in 3.5 hrs, ok hmmm let's put all that in a table.
[tex]\begin{array}{lcccl} &\stackrel{km}{distance}&\stackrel{km/h}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{on the way over}&d&b+c&4\\ \textit{on the way back}&d&b-c&5\\\cline{1-4} \textit{we also know}&70&b+c&3.5 \end{array}~\hfill \begin{cases} d=(b+c)4\\\\ d = (b-c)5 \end{cases} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{(b+c)4~~ = ~~(b-c)5}\implies 4b+4c=5b-5c \\\\\\ 4c=b-5c\implies \boxed{9c=b} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{we know that}}{70~~ = ~~(b+c)3.5}\implies 70=(b+c)\cfrac{7}{2}\implies \stackrel{\textit{substituting "b"}}{70=(9c+c)\cfrac{7}{2}} \\\\\\ 70=10c\cdot \cfrac{7}{2}\implies 70=\cfrac{70c}{2}\implies 140=70c\implies \cfrac{140}{70}=c\implies \blacktriangleright 2=c \blacktriangleleft \\\\\\ \stackrel{\textit{the speed of the boat in still water is then}}{9c=b\implies 9(2)=b}\implies \blacktriangleright 18=b\blacktriangleleft[/tex]
Can someone please help me. ILL GIVE BRAINLIEST TO THE RIGHT ANSWER!!
Adam wishes to have $19,000 available in 18 years to purchase a new car for his son as a gift for his high school graduation. To accomplish this goal, how much should Adam invest now in a CD that pays 1.92% interest compounded semiannually? Adam should invest $ NOW. (Round to the nearest cent as needed.)
The amount of money Adam should save now in order to accomplish his goal is $13,470.30.
How much should Adam save now?In order to determine the amount Adam should save now, the present valaue of $19,000 has to be determined. Present value is the sum of discounted cash flows.
Present value = future value / (1 + interest)^time
Interest = 1.92/2 = 0.96%
Time = 18 x 2 = 36
$19,000 / (1.0096^36) = $13,470.30
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Which of the following expressions is equal to =
Answer:
4th option
Step-by-step explanation:
Remember the Quotient Rule:
[tex]\frac{x^{m} }{x^{n} } =x^{m-n}[/tex]
6-2 = 4
So it is the last option
A science test was given to boys and girls from three different schools. Rudolph, a junior researcher, wants to analyze the difference in the variability of the mean scores among the three schools. The appropriate statistical test would be the
The appropraite statistical test that would be used to measure the difference in the variability of the mean scores among the three schools is mean absolute deviation.
What is the mean absolute deviation?
Mean absolute deviation is the average of the absolute difference between the data set and its mean. Mean absolute deviation is used to measure spread.
MAD = [tex]\frac{1}{n}[/tex]∑ l x - m(x) l
Where:
x = data set m = meanTo learn more about mean absolute deviation, please check: https://brainly.com/question/27365177
Hitung nilai x bagi persamaan
Calculate the value of x for the equation
Answer:
2
Step-by-step explanation:
2⁹ ÷ (4^x) = 32^x × 32^(-1)
2⁹ ÷ 32^(-1) = 32^x × 4^x
16384 = 128^x
Kalau kamu dah belajar logaritma,
[tex]x = log_{128}(16384) \\ x = 2[/tex]
Jika belum,
2¹⁴ = 2^(7x)
Bandingkan kuasa persamaan tersebut,
7x = 14
x = 2
What is the period of rotation of the wheel for which the height of a rider (in feet) above the ground after riding the wheel for t seconds dunce passing the farthest right position on the wheel given by h(t)=60+45 sin (30t)?
According to the given sine function, it is found that the period of rotation is of 0.21 seconds.
What is the period of a sine function?Suppose a sine function modeled by:
[tex]y = A\sin{[B(x + c)]}[/tex]
The period is given by:
[tex]P = \frac{2\pi}{B}[/tex].
In this problem, the function is:
h(t)=60+45 sin (30t).
The vertical shift and the amplitude do not interfer in the period, hence B = 30 and:
[tex]P = \frac{2\pi}{30} = 0.21[/tex]
The period of rotation is of 0.21 seconds.
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HELPPPPPPPPPPP
NO LINKS
Answer:
Point W is [tex](-5,-4)[/tex]
Point Z is [tex](-5,6)[/tex]
Hope This Helps! :) Please Give Brainliest if you can!
Answer: Point W is (5, -4 Point Z is (-5,6)
describe how to simplify the he expression 3^-6/3^-4
Answer:
by using bodmas rule
to solve this problem
Step-by-step explanation:
=3^-6/3^-4
=3-2-4
=-3
Please help me.
2 ^ (2x - 3) * .5 ^ (x - 1) = 200
Answer:
x = 3
Step-by-step explanation:
[tex] {2}^{(2x - 3)} \ast {5}^{(x - 1)} = 200 \\ \\ \implies \: {2}^{(2x - 3)} \ast {5}^{(x - 1)} =8 \ast \: 25 \\ \\\implies \: {2}^{(2x - 3)} \ast {5}^{(x - 1)} = {2}^{3} \ast {5}^{2} [/tex]
Comparing like terms on both sides, we find:
[tex]{2}^{(2x - 3)}= {2}^{3}\: \: or \:\:{5}^{(x - 1)} = {5}^{2} [/tex]
[tex]\implies \:2x - 3 = 3 \: \: or \: \:x - 1 = 2 \\ \\ \implies \:2x = 3 + 3 \: \: or \: \: x = 1 + 2\\ \\ \implies \:2x = 6 \: \: or \: \: x = 3 \\ \\ \implies \:x = \frac{6}{3} \: \: or \: \: x = 3 \\ \\ \implies \:x = 3 \: \: or \: \: x = 3 \\ \\ \implies \huge \:x = 3 [/tex]
5. A bottle contains 2 liters of juice. How many milliliters of juice is that?
Answer:
The answer would be 2000
Step-by-step explanation:
Knowing that there are 1000 milliliters in 1 liter, you can multiply that by 2 to get 2000. I hope this helps! :)
One of the legs of a right triangle measures 13 cm and its hypotenuse measures 17 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
To find the lengths of a right triangle, we can use what is called Pythagorean Theorem: a^2 + b^2 = c^2, where a and b are the legs of the triangle and c is the hypotenuse.
13^2 + b^2 = 17^2
169 + b^2 = 289
b^2 = 120
b = 11.0 cm
The length of the other leg of the triangle is 11.0 cm (rounded).
Hope this helps!
The length of the other leg of the triangle is 11.0 cm rounded to the nearest tenth.
What is the Pythagoras theorem?The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
[tex]a^2 + b^2 = c^2[/tex]
Given that One of the legs of a right triangle measures 13 cm and its hypotenuse measures 17 cm.
To find the lengths of a right triangle, we can use Pythagorean Theorem:
[tex]a^2 + b^2 = c^2[/tex],
where; a and b are the legs of the triangle and c is the hypotenuse.
[tex]13^2 + b^2 = 17^2\\169 + b^2 = 289\\b^2 = 120[/tex]
b = 11.0 cm
Therefore, The length of the other leg of the triangle is 11.0 cm rounded to the nearest tenth.
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1.What is the theoretical probability of popping a striped balloon?
2.What is the experimental probability of not popping a polka dot balloon?
18 solid balloons, 5 polka dot balloons and 17 striped balloons
The probability of popping a balloon is the likelihood of the balloon
The theoretical probability of popping a stripped balloon is 1/3The experimental probability of not popping a polka dot is 0.875How to determine the probability?The given parameters are:
Solid balloons = 18Polka dots = 5Stripped balloons = 17There are three balloons.
So, the theoretical probability of popping a stripped balloon is:
P = 1/3
The experimental probability of not popping a polka dot is calculated as:
P = 1 - P(Polka dot)
This gives
P = 1 - 5/40
Evaluate
P = 0.875
Hence, the experimental probability of not popping a polka dot is 0.875
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PLEASE HELP 20 POINTS!
which statement is true of this graphed function?
A. this function is an even function because it is symmetric about the Y axis
B. this function is an even function because it is symmetric about the origin
C. dysfunction is an odd function because it is symmetric about the origin
D. dysfunction is an odd function because it is symmetric about the Y axis
Answer:
OPTION C
Step-by-step explanation:
This function is odd function because it is symmetric about the origin
Note:This graph also represents the graph of tanx
I hope it helped you
Answer:
Step-by-step explanation:
What should be done to solve the following equation?
=
C-730
7
What should be done to solve the following equations?
C - 7 and 3/4= 0
A) add 7 and 3/4 to both sides of the equation
B)Add O to both sides of the equation.
C)Subtract from both sides of the equation
D) Subtract 7 from both sides of the equation
The equation C -7 - 3/4 = 0 is an algebraic equation
To solve the equation we (a) add 7 and 3/4 to both sides of the equation
How to determine the action on the equation?The equation is given as:
C -7 - 3/4 = 0
Make C the subject of formula by adding 7 and 3/4 to both sides of equation
C = 7 + 3/4
Now, we can solve for C
Hence, to solve the equation we (a) add 7 and 3/4 to both sides of the equation
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Tim drew a triangle with one angle of measure 40 degrees and the other 70 degrees. Which triangle did Tim draw?
Answer:
Isocoles (I can't spell)
Step-by-step explanation:
180-70=110. 110-40=70.
Two angles are 70
Time drew the isosceles triangle because the two angles are equal.
Given that,
Tim drew a triangle with one angle of measure 40 degrees and the other 70 degrees. which triangle Tim drew is to be determined.
A triangle with two sides and two congruent angles is called an isosceles triangle.
Here,
Let one of the angles be x
Sum of angles = 180
40 + 70 + x = 180
x = 70
As two of the angle become equal the triangle becomes an isosceles triangle.
Thus, Time drew the isosceles triangle because the two angles are equal.
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The population of a town is expected to grow by 6% each year.
In 2017 the population was 27,000.
What will the be population in 2018?
Answer:
28620
Step-by-step explanation:
→ Find the multiplier
( 100 + 6 ) ÷ 100 = 1.06
→ Multiply by the original amount
27000 × 1.06 = 28620
The measure of the complement of an angle is 40 less than the measure of the supplement of the angle. Find the measure of the angle.
Step-by-step explanation:
x is the angle.
complementary angles are adding up to 90°.
supplementary angles are adding up to 180°.
so,
90 - x = (180 - x) - 40 = 140 - x
0 = 50 ? no
there is something wrong here. this cannot work out, there is no solution. there cannot be a solution.
because due to the definitions, the supplementary measure of an angle must always be 90° larger than the complementary measure of the same angle. that is by default the difference in their definition.
so, if an angle is only 40° less than the supplementary angle, then it cannot be the complementary angle.
so, either there was a mistake in the question, or this is a trick question.
under the given circumstances, there is no solution possible.
PLS HELP In circle A, secant EC and tangent BC intersect at point C. mЕВ = 171° and mBD 83°. What is mBCD?
Enter your answer in the box.
Answer:
∠ BCD = 44°
Step-by-step explanation:
the secant- tangent angle BCD is half the difference of the intercepted arcs, so
∠ BCD = [tex]\frac{1}{2}[/tex] (EB - BD) = [tex]\frac{1}{2}[/tex] (171 - 83)° = [tex]\frac{1}{2}[/tex] × 88° = 44°
Which quantity is proportional to 40⁄8?
Check all that are true.
10⁄5
120⁄36
20⁄4
5⁄1
120⁄24
Answer:
Step-by-step explanation:
10/5: not part of the answer. This gives 2. The original ratio gives 5.
120 / 36 is not part of the answer. This gives 3 1/3 which is not 5
20/4 true This gives 55/1 true. This gives 5120/24 true. This gives 5The last 3 are the only ones you should choose.
NEED HELP ASAPPP !!!
Answer:
I believe D is the correct answer
pls answer its important
Answer:
i dunno'
Step-by-step explanatio i dont know how to explain diss this
Does the graph shows a proportional relationship
Answer:
no
Step-by-step explanation:
a proportional relationship when graphed always is a straight line that goes through the origin (0,0)
The graph shown, shows a straight line but the line doesn't go through the origin therefore the graph does not show a proportional relationship.
Note that the origin is where the x and y axis cross , or the bottom right corner of the graph in this case
WILL GIVE BRAINLIEST, THANKS, AND 5 STARS! PLEASE HELP EXPLAIN TO ME IN WORDS!
QUESTION IN SCREENSHOT!
Also: hows your day going, how are you feeling?
Answer:
So, we can check step by step.
2x^2-7x+5=0
So, 2x^2-2x-5x+5=0 is correct
2x(x-1)=2x^2-2x, 5(x-1)=-5x + 5= 0, that step is correct
(I'll skip the next step)
2x-5=0,
2x=5
x=5/2, NOT 2/5
The other one is correct
Sorry if this seems a bit vague!
[tex]\\ \rm\Rrightarrow 2x^2-7x+5=0[/tex]
Split the middle term[tex]\\ \rm\Rrightarrow 2x^2-2x-5x+5=0[/tex]
Take common[tex]\\ \rm\Rrightarrow 2x(x-1)-5(x-1)=0[/tex]
Factor up[tex]\\ \rm\Rrightarrow (2x-5)(x-1)=0[/tex]
Find x[tex]\\ \rm\Rrightarrow x=5/2,1[/tex]
Lauren written 2/5 instead of 5/2
Let's verify once more
2x-5=02x=5x=5/2Given point a = -7 and point b = 15, find the distance from point a to b. *
a. 8
b. -22
c. 22
and the solution would be appreciated
Answer:
c
Step-by-step explanation:
the distance between a to b is
| 15 - (- 7) | = | 15 + 7 | = | 22 | = 22
or
| - 7 - 15 | = | - 22 | = 22
f(x)=-3x-23
g(x)=3x+25
I need points X and y
I will give brainly
Answer:
refer to this image here:
hope this helps :)
We will use graphical way to solve it
y=-3x-23y=3x+25Graph it
Solution is
(-8,1)Performing a Rotation in the Coordinate Plane
Fill in the missing numbers to make each rotation true
Figure WXYZ is rotated 90° clockwise around the
origin to form figure W'X'Y'Z'.
Answer:
W: (-4,5) W' -> (5,4)
X: (-1,4) X' -> (4,1)
Y: (-6,1) Y' -> (1,6)
Z: (-8,3) Z' -> (3,8)
Step-by-step explanation:
Let me give you a quick brief of how to master rotations!!
You need to understand the formula and positioning rules
The formulas shall be given by teachers or looked up!
*** BUT THE SHAPE POSITIONING RULES MATTER!!
-If the shape was in quadrant 2 which is where it is right now then a 90 degree turn clockwise would result in the shape being on quadrant 1, 180 quad 4, 270: quad 3, and 360 would be the original quad which is 2.
The formula for clockwise for this one is that you need to flip the (x,y) to (y,x)
The shape should be on quadrant 1 which is the one on the top right of the coordinate plane!
They want you to graph it by W'X'Y'Z
The ' is prime which is the new position/coordinate
W: (-4,5) W' -> (5,4)
X: (-1,4) X' -> (4,1)
Y: (-6,1) Y' -> (1,6)
Z: (-8,3) Z' -> (3,8)
That is the rotation 90 degrees clockwise coordinates!!
***REMEMBER EACH ROTATION RULE HAS A DIFFERENT FORMULA!!**
Counterclockwise is pretty similar but the opposite direction with different rules!
**POSITION OF THE SHAPE IS THE MOST IMPORTANT!!!**
please help!!! I will make you brainliest I need this and I also don't understand
Which fraction does this line plot represent?
5/8
6/8
5/9
3/8
Answer:
5/8
Step-by-step explanation:
Just gonna fill up the required space here lol
6 times the sum of a number and 2
Answer:
6 times means 6 multiplied by
The sum of a number and 2 means x + 2
x = number
(2+x) × 6
