Answer:
a) maximum; the parabola opens downward
b) positive; it must lie above the x-axis
c) x = 1.5
Step-by-step explanation:
The x-intercepts of a function are the points where the graph of the function crosses the x-axis. The y-values there are zero.
The "differences" of a function are related to the average slope between adjacent points. Second differences are related to the rate of change of the slope of the function. When second differences are negative, as here, the slope of the quadratic function is decreasing, becoming more negative. We say the curvature of the function is negatve, and that it opens downward.
__
a, b.If the graph of the parabola opens downward, and it crosses the x-axis, it must have a maximum that is a positive value of y.
__
c.The graph of a parabola is symmetrical about its vertex. That means points on the same horizontal line are the same distance from the line of symmetry, which must go through the vertex. The x-coordinate of the vertex will be the x-coordinate of the midpoint between the two x-intercepts:
x = (-2 +5)/2 = 3/2
The x-coordinate of the vertex is x = 1.5.
______
Additional comment
The attachment shows a table with three evenly-spaced points on the curve. The calculations show first differences (d1) and second differences (d2). You can see that the sign of the second diffference is negative, in agreement with the given conditions.
log7(49)=2 in exponential form
Answer:
49 = 7²
Step-by-step explanation:
A logarithm is an exponent. The base of the logarithm is the base of the exponent. The base to that exponent is the argument of the log function.
__
The logarithm (exponent) is 2. The base is 7. The argument of the log function is 49. In exponential form, this is written ...
7² = 49
how to solve 3x+4y=36
y=-1/2x+8
Answer:
x = 4
y = 6
Step-by-step explanation:
3x + 4y = 36 ⇒ ( 1 )
y = - 1/2x + 8 ⇒ ( 2 )
( 2 ) × 2
2y = -x + 16 ⇒ ( 3 )
2y + x = 16
x = 16 - 2y ⇒ ( 4 )
Let us replace x with ( 16 - 2y ) and the value of y.
For that, let us use the equation (1).
3x + 4y = 36
3 ( 16 - 2y ) + 4y = 36
48 - 6y + 4y = 36
48 - 2y = 36
48 - 36 = 2y
12 = 2y
Divide both sides by 2.
6 = y
Now let us replace y with 6 and find the value of x.
For that let us use equation 4.
x = 16 - 2y
x = 16 - 2 × 6
x = 16 - 12
x = 4
HELPPP PLSSSS THE PYTHAGOREAN THEOREM
Answer:
Step-by-step explanation:
a²+b² = c² c is always the longest line thats opposite to the 90 degree angle
for 1
15² + b² = 17²
b² = 17² - 15²
b = √(17² - 15²)
b= 8
10.A water tank has strps inside it. A monkeyis sitting on topmost floor(i.e.,the first step).The water level is at ninth step. (i) He jumps 3 steps down and then jumps back 2 strps up.In gow many jumps will he reach the water level? Ch-integers class-7
Answer:
7 steps.
Step-by-step explanation:
Since the monkey is sitting on the first step already you can subtract 9 by 1 to find the amount of steps left.
9-1 = 8 steps left
The monkey jumps 3 steps down
8-3= 5 steps
Then jumps 2 steps up
5 + 2 = 7 steps
The monkey has 7 more steps until he reaches the water level.
Suppose you pay back $600 on a $550 loan. You had the loan for 105 days. What was your simple annual interest rate?
well, since we'll be assuming a year has 365 days, well, 105 days is really just 105/365 of a year, and since you paid back 600, that means the interest was 50 bucks, 600 - 550 = 50.
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$50\\ P=\textit{original amount deposited}\dotfill & \$550\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to \frac{105}{365}\dotfill &\frac{21}{73} \end{cases} \\\\\\ 50 = (550)(\frac{r}{100})(\frac{21}{73})\implies 50=\cfrac{11550r}{7300}\implies 50=\cfrac{231r}{146} \\\\\\ 7300=231r\implies \cfrac{7300}{231}=r\implies \stackrel{\%}{31.6}\approx r[/tex]
what is 2pi*4^2 + 2pi*4*4
~giving brainliest!~
Answer:
[tex]64\pi[/tex]
Step-by-step explanation:
[tex]2\pi {(4)}^{2} + 2\pi \: 4 \ast4 \\ \\ = 2\pi \ast16 + 2\pi \ast16 \\ \\ = 32\pi + 32\pi \\ \\ = 64\pi[/tex]
Answer:
64π
Step-by-step explanation:
2π(4²) + 2π(4)(4) <== exponents first
2π(16) + 2π(16) <== multiply
32π + 32π <== add
64π <== final answer
Note: 4 * 4 can also be written as 4²
Hope this helps!
can please someone help me with more of these asap
Answer: 75.36
Step-by-step explanation: Lenght of arc=2nr
=2nx12in
=75.36
lenght of arc of sector=120/360x75.36
=25.12
the dot plot below shows the number of books read during one month by students in the sixth grade at Ledbetter middle school.Each dot plot represents one student
Answer:
Bedwetter middle school? Also where is dot plot
Step-by-step explanation:
Express (x+9)^2 as a trinomial in standard form.
Answer:
x^2 + 18x + 81
Step-by-step explanation:
(x+9) (x+9)
then distributive property
[tex](x+9)^2\\\\=x^2 + 2\cdot 9 \cdot x + 9^2\\\\=x^2 +18x+81[/tex]
How many centimetres are there in 1.6 metres?
Find the circumference.
Use 3.14 for π.
r = 2m
C = [?] m
C=πd
circumference = 12.57m
hope it helps...!!!
un camion se encuentra del lado izquierdo del cero del sistema de referencia, es decir, desde una posicion negativa de -2 km, como el conductor va buscando pasaje se mueve muy lentamente a una velocidad de 10 km/h? escribe la ecuacion horaria.
Veremos que la ecuación que describe el movimiento del camión es:
f(t) = -2km + (10km/h)*t
¿Como encontrar la ecuación de movimiento del camión?Primero debemos recordar la relación:
distancia = velocidad*tiempo.
Entonces, podemos escribir la pocición del camión como:
f(t) = pocición inicial + velocidad*t
Donde t es el tiempo en horas.
Sabemos que:
posición inicial = -2kmvelocidad = 10km/hReemplazando eso obtenemos:
f(t) = -2km + (10km/h)*t
Esta es la ecuación de movimiento del camión.
Sí quieres aprender más sobre ecuaciones de movimiento, puedes leer:
https://brainly.com/question/19365526
3/2 times 6/2 times 2
Answer:
9
Step-by-step explanation:
3/2x6/2=18/2 Simply that and it turns to 9.
Answer:
9
Step-by-step explanation:
3*6*2 = 36
2*2 = 4
36/4 = 9
I multiplied the numerators together and the denominators together.
PLEASE RATE!! I hope this helps!!
What is a[tex]\frac{1}{3}[/tex] As a ratio?
How much pound sterling can be obtained while exchanging NRs250000 paying 2% commission?
(Buying rate: 1 pound=NRs 148.96) (Selling rate: 1 pound=NRs 149.74)
help me help me help me
Answer:
read step by step
Step-by-step explanation:
6 is +4.
19, 23, 27, 31
7 is all perfect square numbers
25, 36, 49, 64
8 is x2.
32, 64, 128, 256
9 is each number multiplied by the next. ex: 1x2=2, 2x3+6, 3x4=12
so the next few would be 30, 42, 56, 72
1) Which fractions are equivalent to 6/12? Choose ALL the correct answers.
12
Answer:
Infinite
Step-by-step explanation:
Most common examples are 1/2 3/6 7/14 4/8 2/4 5/10 8/16 50/100
2 (b) The area of a rectangular window is 6272 cm cm? If the length of the window is 98 cm, what is its width?
Answer:
The width would be 64 cm
Step-by-step explanation:
Because the equation to find area is length times height
Since you have the area and the length, divide the area by the length to find the width
I hope this helps!
solve for a ~
[tex]a {}^{2} - 5a + 6 = 0[/tex]
thankyou ~
Answer:
Hi there!
Given equation :-[tex]\:\mathsf{a^2\:-\:5a\:+\:6\:=\:0}[/tex]
Now=> By splitting the middle term
=> [tex]\:\mathsf{a^2\:-\:2a\:-\:3a\:+\:6\:=\:0}[/tex]
=> [tex]\:\mathsf{a(a\:-\:2)\:-\:3(a\:-\:2)\:=\:0}[/tex]
=> [tex]\:\mathsf{(a\:-\:2)\:-\:(a\:-\:3)\:=\:0}[/tex]
We get ,=> [tex]\:\sf{a\:=\:2\: and\: a\:=\:3}[/tex]
[tex]\:\mathsf{Hope\:this\:helps\:you!\::)}[/tex]
Thank you!
Answer:
[tex]a = 3 \: \: \: and \: \: a = 2[/tex]
Step-by-step explanation:
⬇
[tex]a^{2} - 3a - 2a + 6 = 0[/tex]
⬇
[tex]a \: (a - 3) \: \: (a - 2)[/tex]
⬇
[tex]{}\ a - 3 = 0 \\ a = 2{}[/tex]
The cost of 5 pounds of apples is $12.45. What will be the cost of 12 pounds of apples if the
cost varies directly with the number of pounds purchased.
Edit View Insert Format Tools Table
Answer: 29.88
Step-by-step explanation: if 5 pounds = $12.45,
then 12 pounds = x
Therefore, Cross-multiply
5 x = 12 (12.45)
5x=149.4
x=149.4/5
x=29.88
Answer:
Step-by-step explanation:
Equation
Cost = k*weight
Givens
weight = 5 pounds
Cost = 12.45
12 pounds
Find k
Cost = k*weight
cost = 12.45
weigh = 5 pounds Substitute these values into the equation
12.45 = k * 5 Divide by 5
12.45 /5 = k*5/5
2.49 = k
Solve for 12 pounds
k = 2.49weight = 12 poundsCost = 2.49 * 12
Cost = 29.88
Answer
Cost = 29.88
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In her free time, Isabelle likes to read. She kept track of the number of pages in each book she read last summer. This box plot shows the results.
Book pages
100
150
200
250
300
350
What fraction of the books had 200 or fewer pages?
Using the box plot, it is found that 200 is the median, that is 50% of the books had 200 or fewer pages.
What is a box plot?It is a plot that focuses the interquartile range of the population, that is, it gives:
The first quartile.The median.The third quartile.In this problem, they are given as follows:
The first quartile is of 175.The median is of 200.The third quartile is of 250.Hence, 50% of the books had 200 or fewer pages.
More can be learned about box plots at https://brainly.com/question/14277132
Given that 5 miles is 8 km, convert 17.8 miles to km.
Answer:
[tex]28km[/tex]
Step-by-step explanation:
[tex]5miles = 8km[/tex]
[tex]17.8miles = x[/tex]
[tex] \frac{17.8}{5} \times 8km[/tex]
[tex]x = 28km[/tex]
1) Graph y = f(x) = 3(2)%. Adjust the equation to make the y-intercept (0, -3). Which response is not correct?
A) Replace 3 with -3.
B) Replace x with -x.
C) Add -6 to the right side.
D) Replace x with -x and subtract 6 from the right side.
Using the concept of y-intercept, it is found that the response that is not correct is given by:
B) Replace x with -x.
What is the y-intercept of a function?It is the value of the function when x = 0, hence it is the point (0, f(0)).
In this problem, the function is:
[tex]f(x) = 3(2)^x[/tex]
The y-intercept is given by:
[tex]f(0) = 3(2)^0 = 3[/tex]
If we just replace x with -x, we still have the same expression as above, hence the y-intercept does not change and option B is the answer to this question.
More can be learned about y-intercepts at https://brainly.com/question/24737967
please help me Find the value of x
Answer:
x=3
Step-by-step explanation:
3x+1+15
/2
= 12.5
45th term of an arithmetic sequence having a=3 and d=8 is:
Answer:
a45 = 320
Step-by-step explanation:
The 45th term of the Arithmetic Sequence will be 355.
We have a Arithmetic Sequence with a = 3 and d = 8.
We have to determine the 45th term of this sequence.
What is the formula to calculate the nth term of an Arithmetic Sequence ?The formula to calculate the nth term of an Arithmetic Sequence is -
a(n) = a + (n - 1)d
a - first term of A.P.
d - Common difference of A.P.
n - position of term
According to the question -
a = 3
d = 8
n = 45
Then, using the formula to calculate the nth term, we get -
a(n) = a + (n - 1)d
a(45) = 3 + (45 - 1)8
a(45) = 3 + 44 x 8
a(45) = 3 + 352
a(45) = 355
Hence, the 45th term of the Arithmetic Sequence will be 355.
To solve more questions on Arithmetic Sequences, visit the link below-
https://brainly.com/question/19828148
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a. Use the appropriate formula to find the value of the annuity
b. Find the interest
Rate
Periodic Deposit
$6000 at the end of each year
15.5% compounded annually
Time
10 years
The value of the $6000 annuity given annual compounding is $124,836.12.
What is the value of the annuity?
The value of the annuity can be determining using this formula: amount deposited x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
n = number of years r = interest rate$6000 x [(1.155^10) - 1/0.155] = $124,836.12
To learn more about annuities, please check: https://brainly.com/question/24108530
can i get the answer with work?
Answer:
Step-by-step explanation:
D
Answer: 15
Based on this info they have a probability of 0.6 of winning a game.So for 15 games they should win 0.6*15 = 9 gamesSo prediction for whole season = 6+9 = 15 games.
Step-by-step explanation:
Which point would be a solution to the system of linear inequalities shown below?
Answer: (-4, -6)
Step-by-step explanation:
Solving by graphing
[] See attached
() The only point in the required range is point (-4, -6)
Solving by plugging-in
I will figure out what the correct option is by plug them into the first equation. Since only one of these options is true, I do not need to do the second equation.
[✗] Let's check point (4, 10)
() 10 < (1/4)4 - 4
10 < 1 - 4
10 < -3 is false, so this answer is incorrect
[✗] Let's check point (-4, 5)
() 5 < (1/4)-4 - 4
5 < -1 -4
5 < -5 is false, so this answer is incorrect
[✗] Let's check point (-4, -4)
() -4 < (1/4)-4 - 4
-4 < -1 -4
-4 < -5 is false, so this answer is incorrect
[✓] Let's check point (-4, -6)
() -6 < (1/4)-4 - 4
-6 < -1 - 4
-6 < -5 is true, so this answer is correct
Solve the system of linear equations. separate the x- and y- values with a coma. -5x+6y=33 -18x+4y=-22
Order the integers from greatest to
least: 4, -3, 0, 8, -5.
A 5, 3, 0, 4,8
B 3.-5, 0. 4.8
8, 4.0, 3, 5
D 0, -3, 4, 5,8
Answer:
8, 4, 0, -3, -5
(greatest to least order)
-Answer: C-
Step-by-step explanation:
8 is positive so its greatest
-5 is negative but it is farthest away from 0 so it is least