Step-by-step explanation:
The solutions of the related quadratic equation are -1.5 and -3
To summarize, the true statements are:
(b) The function has two roots.
(d) The related quadratic equation has two solutions.
What is a Quadratic equation?ax²+bx+c=0, with a not equal to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
To determine which statements about the quadratic function that passes through (1,0) and (3.5,0) are true, we need to use the fact that the roots (or x-intercepts) of a quadratic function can be found by solving the related quadratic equation, which is obtained by setting the function equal to zero.
Let's start with a statement (a). Plugging in the two points given into the equation y = 2x^2 - 9x + 7, we get:
At x = 1, y = 2(1)^2 - 9(1) + 7 = 0
At x = 3.5, y = 2(3.5)^2 - 9(3.5) + 7 = 0
This confirms that points (1,0) and (3.5,0) are indeed on the graph of the function, but it doesn't tell us whether this is the only function that passes through those points. So statement (a) alone is not sufficient to determine the true statements.
Next, let's consider statement (b). Since the graph passes through (1,0) and (3.5,0), we know that it must cross the x-axis at those two points. Therefore, the function has two roots or x-intercepts. Statement (b) is true.
Moving on to statement (c), we need to find the solutions of the related quadratic equation. Setting y = 2x² - 9x + 7 equal to zero, we get:
2x² - 9x + 7 = 0
Using the quadratic formula, we find that the solutions are:
x = (9 ± √(9² - 4(2)(7))) / (2(2)) ≈ 2.5 and ≈ 1.75
Therefore, statement (c) is false.
Finally, statement (d) asks whether the related quadratic equation has two solutions. We just found that it has two solutions, so statements (b) and (d) are true.
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help please ASAPPPPP
Answer:
the height is 11 units the base is 12 units and the area is (i think) 84
find the length of CD.
I need answer Immediately pls!!!!!!
Answer:
14 players.
Step-by-step explanation:
The bus is a fixed cost, so the unknown “p” comes after the player meals, as that price isn’t fixed and is per player.
993.5 + 74.25p = 2033
74.25p = 1039.5
p = 14
HELP!!!! I WILL MARK BRAINLEST
Answer:
i believe its 3
Step-by-step explanation:
sorry if im wrong
if f,g and h are midpoints of the sides of the triangle jkl, fg=40, kl=52 and gh=26, find each measure
Answer: The measure of JK is 60 and the correct option is d.
Explanation:
It is given that the points F, G, and H are the midpoints of the sides of triangle JKL , FG = 37, KL = 48, and GH = 30.
The point F is midpoint of JK, point G is midpoint of KL and the point H is midpoint of LJ as shown in figure .
According to the midpoint theorem, the line connecting the midpoints of two sides is parallel to the third and its length is half of the third side.
By midpoint theorem,
Therefore the measure of JK is 60 and the correct option is d.
list the planets in order from least to greatest
Only give me an answer if you know the answer please
Answer:
Uranus, Neptune, Saturn, Jupiter
Step-by-step explanation:
l
Mhanifa please help! Solve for the unknown in each triangle. Round to the nearest tenth.
Answer:
(D)
Use the law of sines:
13 / sin x = 12 / sin 67°sin x = 13 sin 67° / 12sin x = 0.997x = arcsin (0.997)x = 85.6°(E)
Find the third angle:
180° - (48° + 61°) = 71°Use the las of sines:
x / sin 61° = 21 / sin 71°x = 21 sin 61° / sin 71°x = 19.4 cm320 divided by 60=
Will give brainliest
Answer:
5.33333 (repeating)
Step-by-step explanation:
Answer:
5.333333 and the 3 is infinite.
Step-by-step explanation:
A teacher wants to find out the average number of weekly reading hours of her students. She noted the number of reading hours of 5 of her students, as shown below:
8, 6, 5, 7, 4
Which measure of central tendency is most appropriate for this situation and what is its value?
Only the median; 6
Only the mean; 5
Either the mean or median; both are 6
Either the mean or median; both are 5
Answer:
The answer is C both the mean and median are 6
Step-by-step explanation:
What is the product (7 times 10 to the power of -5) times (5 times 10 to the power of -8)
Answer:Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10
. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
3.5×10^−12
Step-by-step explanation:
in simple terms 3.5×10^−12 or 3.5 times 10 to the power of -12
how do i find this out?
Answer:
8
Explanation:
A good way to find the area of a figure with diagonal lines is to find the area of the section that has full squares and then add the other parts together and find the area of that. As you can see in the polygon, there are four units in the middle that don't get cut off by the diagonal line. The area of that part of the figure is 1*4 = 4. Now, if you take out that section, and move the other parts together, you can find their area and then add it to 4. The other parts of the polygons are triangles, and when you move them together, they form the same shape as the middle section did, and have an area of 4. The area of the entire figure is the area of one section plus the area of the other. 4 + 4 = 8
I hope that makes sense :)
OMG I NEED HELP PLSSSSSSSSSSS
WHATS 1 + 1?
ILL MAKE U BRAINLIEST IF U ANSWER SO PLS HELP ME
Answer:
2
Step-by-step explanation:
Answer:
1+1 = 2.
If you had one apple, and I gave you one more, you would have 2 apples.
A system of linear equations for the variables x and y is shown.
y=-x-4
3y=cx-18
For what value of c, if any, will this system have no solution? Justify your answer.
Answer: -3
Step-by-step explanation:
Given
Equations of the lines are
[tex]y=-x-4\\3y=cx-18[/tex]
For the system of linear equation [tex]a_1x+b_1y=c_1,a_2x+b_2y=c_2[/tex] has no solution if
[tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq \dfrac{c_1}{c_2}[/tex]
Rewrite the equations
[tex]x+y=-4,\ cx-3y=18[/tex]
Insert the values for the no solution condition
[tex]\Rightarrow \dfrac{1}{c}=\dfrac{1}{-3}\\\\\Rightarrow c=-3[/tex]
Therefore, for c=-3, the system of linear equation ha no solution.
Which letter matches the coordinate (4, -6)?
Helpppp plsss
Answer:The answer is z
Step-by-step explanation:
PLEASE HELP! No random links.
Answer:
B and F are non-statistical questions
Step-by-step explanation:
B is asking how many years until you are 16; this is not statistical because it just a fact. F is pretty much the same because it's just asking a subjective fact-like question.
Statistical questions ask for a collection of varying data. If there is only one data point, it is non-statistical.
Solve 10^(x + 2) = 34
Answer:
-.4685
Step-by-step explanation:
[tex]x^y=z\\y=log_zy\\10^{x+2}=34\\x+2=log_{10}34\\x+2=log34\\x+2=1.531478917\\x=-.468521083[/tex]
Which equation does NOT graph a line?
A)
y = 5
B)
y=-3x3
yox
IN
D)
y=-8x
The Answer is B.
Its a Cubic function and this does not graph a line.
The first option
y=5 (A straight line)
for Y=-8x
Using Y=Mx + c
M is the slope
So it has a slope of -8.
Help need help cause I don’t understand stand
Answer:
A
Step-by-step explanation:
just cut off one side and add it to the other thats how you solve paralellograms
Answer: 6 x 7?
Step-by-step explanation: To find the area of a parallelogram it's base times height.
General formula for
6 ; 8 ; 10 ; 12
Answer:
[tex]an=2n+4[/tex]
Step-by-step explanation:
-2(4w-11)+6(5-2w)
Find the value of the expression if w = -3
Find the perimeter of the triangle in inches.
19 in.
16 in.
23 in.
42 inches
O 74 inches
58 inches
48 inches
O
Answer:
58 inches
Step-by-step explanation:
Perimeter means the sum of length of all sides of a figure.
So, the perimeter of this triangle would also be the sum of the length of its sides.
It has 3 sides.
19 in, 16 in and 23 in.
So, its perimeter equals 19 + 16+ 23
which equals 58 inches!
So, the perimeter would be 58 inches.!
Need some assistance yall look at picture :) Algebra 2 type vibe
Answer:
It is C.
III is saying that the two functions are inverse functions. If two functions, f(x) and g(x) are inverse, then f(g(x)) = x and g(f(x)) = x. Therefore, we see that if III is true, then I and II should also be true. Now, all we have to prove is that f(x) and g(x) are inverse functions. As we said before, if two functions are inverse, then f(g(x)) = x and g(f(x)) = x.
f(g(x)) = 3([tex]\sqrt[3]{\frac{x-2}{3} }[/tex])^3 + 2
f(g(x)) = 3[(x-2)/3]+2
f(g(x)) = x-2 + 2
f(g(x)) = x
Therefore, we have proved that f(g(x)) = x, and so f(x) and g(x) are inverse functions, and so all of I, II, and III are true. Thus, the answer is C.
fyi, we didn't have to do g(f(x)) because if f(g(x)) = x, then so will g(f(x)).
Alonzo worked for 13 hours each day for 6 days then he worked 7 hours how many hours it Alonzo work in all?
Answer:
85 hours
Step-by-step explanation:
Number of hours per day = 13 hours
Number of days = 6
Number of hours worked for 6 days = 6 days × 13 hours
= 78 hours
then he worked 7 hours
Total Number of hours worked = Number of hours worked for 6 days + 7 hours
= 78 hours + 7 hours
= 85 hours
Total Number of hours worked = 85 hours
A triangle has three angles of 36°, 34°, and 110°.
A. equilateral B. obtuse C. acute D. right
Answer:
Obtuse Triangle.
Step-by-step explanation:
An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees. In this case, 110° is more than 90°. So, its an obtuse angle. If one angle of the triangle is obtuse, then the other two angles with always be acute.
Hence, this is an obtuse triangle
The triangle with the given measures is obtuse angle triangle. Therefore, option B is the correct answer.
What is an obtuse angle triangle?An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees. In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°.
Given that, a triangle has three angles of 36°, 34°, and 110°.
Here, one of the angle measure more than 90°, that is 110°.
Sum of remaining two angles is 36°+34°
= 70°
Therefore, option B is the correct answer.
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find the surface area. round to the nearest hundredth when necessary.
Answer:
The area of the shape is 122.30 cm^2
Step-by-step explanation:
To calculate the surface area, we identify the side shapes
We have this as;
a rectangle that measures 11 cm by 3 cm, a rectangle that measures 3 cm by 6 cm, a rectangle that measures 8 cm by 3 cm, 2 triangles ( base and top) that has a height of 4.3 cm and a base of 11 cm
The area of the rectangles is simply the product of the side lengths
The area of the triangles is the product of the base and the height divided by 2; but since we have 2 exact triangles, we can simply multiply the base and the height to serve as the area of both
Thus, we have the area of the shape as follows;
(11 * 3) + (3 * 6) + (8 * 3) + (4.3 * 11)
= 33 + 18 * 24 + 47.3
= 122.30 cm^2
Enter an estimate. Round each mixed number to the nearest whole in your estimate
Answer:
1. 4-2=2
2.2 10/21
Step-by-step explanation:
A grocery chain runs a prize game by giving each customer a ticket that may win a prize when the box is scratched off. Printed on the ticket is a dollar value ($500, $100, $25) or the statement "This ticket is not a winner." Monetary prizes can be redeemed for groceries at the store. Below is the probability distribution of the amount won on a randomly selected ticket. Which of the following are the mean and standard deviation, respectively, of the winnings? * 2 points Captionless Image $156.25 $53.85 $15.00, $2900.00 $15.00, $26.93 $15.00, $53.85 $156.25, $26.93
Answer:
[tex]Mean = \$15[/tex]
[tex]Standard\ Deviation = \$53.85[/tex]
Step-by-step explanation:
Given
See attachment for probability distribution
Required
Determine the mean and the standard deviation
The mean of the distribution is:
[tex]Mean = E(x)[/tex]
and
[tex]E(x) = \sum x * P(x)[/tex]
So, we have:
[tex]Mean = \$500 * 0.01 + \$100 * 0.05 + \$25 * 0.20 + \$0 * 0.74[/tex]
[tex]Mean = \$5 + \$5 + \$5 + \$0[/tex]
[tex]Mean = \$15[/tex]
So:
[tex]E(x) = 15.00[/tex]
The standard deviation of the distribution is:
[tex]S = \sqrt{Var(x)}[/tex]
Where:
[tex]Var(x) = E(x^2) - (E(x))^2[/tex]
[tex]E(x^2) = \sum x^2 * P(x)[/tex]
So, we have:
[tex]E(x^2) = 500^2 * 0.01 + 100^2 * 0.05 + 25^2 * 0.20 +0^2 * 0.74[/tex]
[tex]E(x^2) = 2500 + 500 + 125 +0[/tex]
[tex]E(x^2) = 3125[/tex]
So:
[tex]Var(x) = E(x^2) - (E(x))^2[/tex]
Where
[tex]E(x^2) = 3125[/tex]
[tex]E(x) = 15.00[/tex]
[tex]Var(x) = 3125 - 15^2[/tex]
[tex]Var(x) = 3125 - 225[/tex]
[tex]Var(x) = 2900[/tex]
Recall that:
[tex]S =\sqrt{Var(x)[/tex]
[tex]S =\sqrt{2900[/tex]
[tex]S =53.85[/tex]
30 pts ! The height of the Ferris wheel in feet can be represented by the function 50 cos (π/15(x-10))+52 with time in x seconds. When does the height of 80 feet occur on the interval 0
The time that the height of 80 feet occur on the interval 0 is 4.662 seconds.
Given:
50 cos (π/15(x-10))+52
Height=80 feet
Time= x second
Hence:
height (h)= 50 cos [pie(x - 10 )/15 ] + 52
80 = 50 cos [pie( x - 10 )/15 ]+ 52
Collect like terms
80 - 52 = 50 cos [ pie( x - 10 )/15 ]
28 = 50 cos [ pie( x - 10 )/15 ]
cos [pie( x - 10 )/15 ] = 28/50
cos [ pie( x - 10 )/15 ] =56
cos [pie( x - 10 )/15 ]= cos ( 56 )
cos [ pie( x - 10 )/15 )]= cos ( 0.3111 pie )
Hence:
pie( x - 10 )/15 = 0.3111
( x - 10 )/15 = 0.3111
x - 10 = 15 × 0.3111
x - 10 = 4.662
x = 10 + 4.662
x = 14.662 seconds
Therefore the correct option is C.
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Find the values of x and y in the diagram.
Answer:
x =4 and y =1
Step-by-step explanation:
Triangle ADB is an equilateral triangle that means the side a 3 unit each
so,
y + 2 = 3
y = 1
Triangle DBC is an isosceles triangle that means two legs are equal
So,
y + 2 = x -1
we already know that y+2 = 3
So,
3 = x -1
4 = x
HELP ASAP
I need someone to help please I need to make my mom proud
Answer:
perimeter =52cm
hope it helps.
stay safe healthy and happy.Answer:
52 cm (second opinion)
Step-by-step explanation:
add all the sides