Answer:
[tex]\huge \boxed{\sf \ \ x=-\dfrac{1}{2} \ \ }[/tex]
Step-by-step explanation:
Hello,
We need to express this parabola using this kind of expression
[tex]y=a(x-b)^2+c[/tex]
and then, the line of symmetry will be the line x = b
Let's do it !
[tex]\text{*** Complete the square ***} \\ \\ x^2+x=x+2\cdot \dfrac{1}{2}\cdot x=(x+\dfrac{1}{2})^2-\dfrac{1^2}{2^2}=(x+\dfrac{1}{2})^2-\dfrac{1^2}{4} \\ \\ \text{*** Apply it to our parabola } \\ \\y=-x^2-x+2=-(x^2+x)+2=-[(x+\dfrac{1}{2})^2-\dfrac{1}{4}]+2 = -(x+\dfrac{1}{2})^2+\dfrac{1+2*4}{4}= -(x+\dfrac{1}{2})^2+\dfrac{9}{4} \\ \\ \text{*** It comes ***} \\ \\ \Large \boxed{\sf \ \ y=-(x+\dfrac{1}{2})^2+\dfrac{9}{4} \ \ }[/tex]
So the line of symmetry is
[tex]\huge \boxed{\sf \ \ x=-\dfrac{1}{2} \ \ }[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
please help.
create five word expressions that will need to be translated into an algebraic expression also provide a value for the variable mentioned in the expression.
Answer:
The answers are as follows.
Step-by-step explanation:
Expressions:
Product of 2 and x is 146 added with a number gives 14The product of six and a gives 1212 divided by y gives 26 subtract with a number and get 12Computation:
Product of 2 and x is 14
2(x) = 14
x = 7
6 added with a number gives 14
6+x = 14
x = 8
The product of six and a gives 12
6(a) = 12
a = 2
12 divided by y gives 2
12 / y = 2
y = 6
6 subtract from a number and get 12
x - 6 = 14
x = 20
Suppose you deposit a principal amount of p dollars in a bank account that pays
compound interest. If the annual interest rate r (expressed as a decimal) and the bank
makes interest payments n times every year, the amount of money A you would have
after t years is given by:
A = P[1+ (r/n)]"
Find the account balance after 20 years if you started with a deposit of $1000, and the
bank was paying 4% interest compounded quarterly (4 times a year). Round your
answer to the nearest cent.
Answer:
Answer:
$2216.72
Step-by-step explanation:
Simply plug in your known variables into the formula:
a = 1000
r = 0.04 (4%)
n = 4
t = 20
A = 1000(1 + 0.04/4)⁴⁽²⁰⁾
A = 1000(1 + 0.01)⁸⁰
A = 1000(1.01)⁸⁰
A = 1000(2.21672)
A = 2216.72
If x2 + 6x + 8 = 0 , then x could equal which of the following?
Answer:
x = -4 , -2
Step-by-step explanation:
I am assuming "x2" is x^2. If the equation is x^2 + 6x + 8 = 0, then you first have to factor the equation x^2 + 6 + 8.
In order to do that, you would have to find the multiples of 1 (from x) and 8.
We can see that 1 * 1 is 1, so that is the only pair that would work for the problem. 4 * 2 is 8, but 8 * 1 is also 8. So, which set of numbers do we have to choose? It's actually really simple. You multiply the first set of numbers (1 and 1) with one of the sets from 8 ( 4 and 2 or 8 and 1). Then when you are finished multiplying them together, you add them together to see if they equal to the number in the middle (6x). So 1(x) * 4 is 4x, and 1(x) * 2 is 2x, and when we add the numbers together, we get 6x, which is the middle number, so therefore, 4 and 2 is the correct set of numbers, not 8 and 1, because if we multiply and add those together, we get 7x, not 6x.
After doing that, you have to put them like this:
(x + 4)(x + 2)
This is so when you multiply them together, you get the starting equation. But we have to solve for x. In order to do that, we have to plug that into the equation we started off with.
(x + 4)(x + 2)=0
Now we have to make x + 4 and x + 2 equal to 0, so x is -4 and -2. There are two correct answers. Hope this helps :)
Answer:
x is -2 and -4
what is 149 scaled down by a factor of 1/10
Answer:
14.9
Step-by-step explanation:
Given
149
Required
Scale factor of ⅒
The result of a scale factor is the product of an expression by its scale factor.
The result of 149 scale factor of 10 is the product of 149 by 10
In other words;
149 * ⅒
= (149 * 1)/10
= (149)/10
Remove bracket
= 149/10
= 14.9
Hence, 149 scaled down by a factor of ⅒ is 14.9
The first entry of the resulting matrix is:
Answer:
[tex]\boxed{1}[/tex]
Step-by-step explanation:
[tex]\left[\begin{array}{ccc}1 \times 1&2 \times 1\\3 \times 5&4 \times 5 \end{array}\right][/tex]
15 POINTS!!!!! How is a linear function affected when a constant is multiplied by y?
Answer:
a constant multiplied by y can affect the linear, because it determines a dependent variables.
Step-by-step explanation:
a linear relationship is a statistical term used to described a straight line relationship between two variables.
Which algebraic expression is a polynomial with a degree of 2? 4x3 − 2x 10x2 − StartRoot x EndRoot 8x3+ StartFraction 5 Over x EndFraction + 3 6x2 − 6x + 5
Answer:
[tex]6x^2 - 6x + 5[/tex]
Step-by-step explanation:
Given
List of Options
Required
Which of the options has a degree of 2
The general format of a polynomial is
[tex]ax^n + bx^{n-1} + ..... + cx^{n-n}[/tex]
Where n represents the degree
In this case;
n = 2
Substitute 2 for n in expression above;
[tex]ax^n + bx^{n-1} + ..... + cx^{n-n}[/tex]
[tex]ax^2 + bx^{2-1} + ..... + cx^{2-2}[/tex]
[tex]ax^2 + bx^{1} + ..... + cx^{0}[/tex]
[tex]ax^2 + bx + c *1[/tex]
[tex]ax^2 + bx + c[/tex]
Comparing this format to the list of given options; the option with the same format is: [tex]6x^2 - 6x + 5[/tex]
Where [tex]a = 6[/tex]; [tex]b = -6[/tex] and [tex]c = 5[/tex]
Hence, the polynomial with a degree of 2 is [tex]6x^2 - 6x + 5[/tex]
Answer:
6x^2-6x+5
Step-by-step explanation:
1. A man decided to buy new furniture from Futuristie Purniture for $2600, Futuriste Vurniture
gave the man two choices pay the entire amount in one payment with cash, or pay $1000 as a dews
payment and 1120 per month for two full years in the finanong plan. If the man chooses the
financing plan, how much more would he payl
Answer:
Also, there seem to be many typos in this question, I am trying my best to decipher them all :) next time maybe double check the wording thx!
Step-by-step explanation:
the question doesn't make sense because if you were to pay $1120 per month, for 2 years, you would go over the amount that you bought. I also am not sure what a dews payment is. Try wording it differently/check you spelling.
im badd i kinda understand but not really understanding it
Answer:
40
Step-by-step explanation:
if you add all the numbers up it becomes 96 and 96 goes Into. 480 5 times so you multiply 5 times the number of giant swallow tails
Answer:
If they are proportional we can expect 40
lol iready
a food truck did a daily survey of customers to find their food preferences. The data is partially entered in the frequency table. complete the table to analyze the data and anser the questions
Answer:
That right, no picture, no answer
Step-by-step explanation:
The formula for any geometric sequence is an = a1 · rn - 1, where an represents the value of the nth term, a1 represents the value of the first term, r represents the common ratio, and n represents the term number. What is the formula for the geometric sequence 1, -2, 4, -8, ...? an = 1 · (-2)n - 1 an = -2 · 1n - 1 an = -8 · (-2)n - 1 an = 1 · 2n - 1
Answer:
[tex]\huge\boxed{a_n=1\cdot(-2)^{n-1}}[/tex]
Step-by-step explanation:
[tex]a_n=a_1r^{n-1}[/tex]
We have the geometric sequence: 1, -2, 4, -8, ...
Find the common ratio:
[tex]r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}[/tex]
[tex]a_1=1,\ a_2=-2[/tex]
substitute:
[tex]r=\dfrac{-2}{1}=-2[/tex]
Substitute
[tex]a_1=1;\ r=-1[/tex]
to
[tex]a_n=a_1r^{n-1}[/tex]
[tex]a_n=1\cdot(-2)^{n-1}[/tex]
Answer:
[tex]a_{n}=1 (-2)^{n-1}[/tex]
Step-by-step explanation:
Hi there!
Let's do it,
1)[tex]1,-2,4,-8[/tex]
First let's find the q, the common ratio by dividing the second term by the anterior one.
-2:1 =-2
4:-2=-2
So the common ratio is -2. Plugging in on the General formula:
[tex]a_{n}=a_{1}q^{n-1}[/tex]
[tex]a_{n}=1 (-2)^{n-1}[/tex]
FIRST GETS BRAINLLEST If the rectangle below is enlarged by a scale factor of 1.2, what will be the area of the new rectangle? 62 square units 66 square units 72 square units 76 square units
Answer:
72 square units.
Step-by-step explanation: You have to multiply both sides by the scale factor. 5 times 1.2 is 6, and 10 times 1.2 is 12. Then, multiply 6 by 12 to get your area of 66 square units.
795.800.913.789
seven hundred ninety-five billions eight hundred sixty millions, nine hundred thirteen thousands, seven hundred
eighty-nine
seven hundred and ninety-five billion, eight hundred and sixty million, nine hundred and thirteen thousand, seven
hundred and eighty-nine
seven hundred ninety-five billion eight hundred sixty million nine hundred thirteen thousand, seven hundred eighty.
nine
seven hundred ninety-five billion eight hundred six million nine hundred thirteen thousand, seven hundred eighty-nine
Submit
Reset
Answer:
seven hundred ninety-five billion eight hundred million nine hundred thirteen thousand seven hundred eighty-nine
can someone please help? i don’t know how to solve this.
Answer:
Hey there!
We have the absolute value of x is greater than two.
Thus, to solve absolute value inequalities, we want to break the inequality down.
We break this down to
x>2
x<-2
Thus, we don't need to simplify this any further, and have our answer.
Hope this helps :)
Answer:
x >= 2 or x <= -2
Step-by-step explanation:
|x|>= 2
Means the absolute value of x is greater than or equal to two.
When we deal with absolute value, we can equivalently break into two cases
+x >= 2 => x >= 2
-x >= 2 => x <= -2
On the number line it looks like what is shown in the attached figure.
help me i want to get this correct
Answer:
1/8
Step-by-step explanation:
Well there is a .5 chance you get each side so in order for them all to land on the same side you do .5^3 which is .125 or 1/8
Mr. Weaver invested part of his $6000 inheritance in an account that earns 4%
simple interest and the other part in an account that earns 7% simple interest.
How much did he invest in each account if the two accounts earned $360 after
the first year?
Answer:
Mr. Weaver invested $ 2,000 in the 4% simple interest account and $ 4,000 in the 7% simple interest account.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Amount of the inheritance = $ 6,000
Interest rate of the first part = 4% simple
Interest rate of the second part = 7% simple
Interest of the accounts after the first year = $ 360
2. How much did he invest in each account?
For answering the question, we will use the following equation:
x = Amount invested in the first account
6,000 - x = Amount invested in the second account
0.04x + 0.07 * (6,000 - x) = 360
0.04x + 420 - 0.07x = 360
-0.03x = 360 - 420 (Subtracting 420 at both sides)
-0.03x = -60
x = -60/-0.03
x = 2,000 ⇒ 6,000 - x = 4,000
Mr. Weaver invested $ 2,000 in the 4% simple interest account and $ 4,000 in the 7% simple interest account.
When you simplify,
10!/(10 - 3)!-3
is equal to:?
Answer:
120
Step-by-step explanation:
expand and calculate
10x9x8x7!/(10-3)!x3!
10x9x8x7!/7!x3!
reduce
10x9x8x7!/7!x3!
10x9x8/3!
Calculate the product
10x9x8/3!
Now Cacluate the factorial
720/3!
720/6
reduce
120
Answer: 120
Step-by-step explanation:
Can you guys please help me with this? It’s for tomorrow
IM TIMED Find an ordered pair that represents the vector from (-3.7,2) to (-4, -5).
a.
(-7.7,-3)
c.
(1.3,7)
b.
(-0.3,-7)
d.
(7.7,3)
Answer:
<-0.3, -7>
Step-by-step explanation:
Re: a vector from (-3.7,2) to (-4, -5).
This has two components: a horizontal one and a vertical one.
The horizontal component is -4 - (-3.7) = -0.3.
The vertical component is -5 - 2 = -7
Thus, the desired vector is <-0.3, -7>
Answer:
B on edge
Step-by-step explanation:
got it right (2021)
7 movie tickets cost $35
Unit rate
Answer:
$5 per ticket
Step-by-step explanation:
If you put it into a ratio of movie tickets to cost it will be 7 : 35
When you simplify it the ration will be 1 : 5
Answer:
$5 per ticket . # Unit rate.
Step-by-step explanation:
7 tickets costs =$35
therefore, 1 ticket cost = $35÷ 7
= $5
I wish to have $10,000 at the end of 8 years in a bank offering a simple interest rate of 7.5% per year. How much should I deposit in the bank? Please ANSWER CORRECTLY! I will give brainliest for CORRECT answer
Answer:
$6250
Step-by-step explanation:
6250x.075x8=3750
6250+3750=10,000
HELP ME PLZ NEED ANSWER Which relation is a function? A coordinate grid containing a U shape with arrows on both ends that opens to the right. The bottom portion of the U passes through the origin. A coordinate grid with the graph of a circle centered at the origin and passing through the point begin ordered pair 2 comma 1 end ordered pair. A coordinate grid containing a U shaped graph with arrows on its ends. The U shape opens upwards and the bottom of the U shape is located at the origin. Coordinate grid with graph of a vertical line at x equals 3.
Answer:
A function is a relation in which each input has only one output.
Step-by-step explanation: In the relation , y is a function of x, because for each input x (1, 2, 3, or 0), there is only one output y. x is not a function of y, because the input y = 3 has multiple outputs: x = 1 and x = 2.
A function is a coordinate grid containing a U-shape with arrows on both ends that open to the right, and in which the bottom portion of the U passes through the origin which is the correct answer would be an option (A).
What is a function?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
A function is a coordinate grid with a U-shaped pattern, arrows on both ends that open to the right, and the origin at the bottom of the U.
Because there is only one output of the relation, y, for any input x (1, 2, 3, or 0), is a function of x. Because the input y = 3 contains multiple outputs, including x = 1 and x = 2, x is not a function of y.
Therefore, the function is a coordinate grid containing a U-shape with arrows on both ends that open to the right, and in which the bottom portion of the U passes through the origin.
Hence, the correct answer would be option (A).
Learn more about the functions here:
brainly.com/question/12431044
#SPJ2
PLEASE HELP!!!! I WILL GIVE BRAINLIEST AND LOTS OF POINTS!!! Please provide an explanation and answer only if you know the answer for sure. In the following diagram, BC is parallel to DE. What is the measure of angle х? **Angles are not necessarily drawn to scale.**
Answer:
x = 29
Step-by-step explanation:
If the lines are parallel
< CBA = < DAB due to the fact that they are alternate interior angles
42 = DAB
We also know that
DAB + BAC + CAE = 180 since they form a straight line
Substituting the given values
42+ 109 + x = 180
Combine like terms
151 + x = 180
151+x-151 = 180-151
x = 29
Find the measure of b.
The lines around the angle is saying that they are corresponding. so the angle of b is 25
Answer:
[tex]\boxed{<b = 25}[/tex]
Step-by-step explanation:
Two angles in the same sector/segment have congruent measures.
So, <b = 25 (These are the two angles in the same segment).
Solve |3x + 9| + 6 = 6 Question 5 options: A) x = 3 B) x = 3 or x = –3 C) No solutions D) x = –3
Answer:
Hey there!
We have |3x + 9| + 6 = 6. Subtracting 6 from both sides gives us |3x + 9| = 0.
3x+9=0
3x=-9
x=-3
Hope this helps :)
Answer:
-3
Step-by-step explanation:
Subtracting 6 from both sides yields |3x + 9| = 0. For this to be true, 3x + 9 must be 0, and so x must be -3.
thanks for helping me out y’all if anyone of y’all play roblox mine is ( colIapsinq ) the second L is a capital ( i )
Answer:
1. 5
2. 6
3. 8
4. 200
Step-by-step explanation:
I said the answer already
first 5
next 6
then 8
lastly 200 my accounts (try both of them) king1ev15 and/or king1ev151
From the set {20, 30, 35}, use substitution to determine which value of x makes the inequality true. x - 5 > 25 A. 30 B. 20 C. none of these D. 35
Answer:
D. 35
Step-by-step explanation:
20-5>25 = 20>25 incorrect
30-5>25 = 25>25 incorrect
35-5>25 = 20>25 correct
suppose that all of the points on the circular dartboard shown are equally likely to be hit by a dart. If the radius of the shaded center circle is 2 and the radius of the entire dartboard is 4, what is the probability of throwing a dart and hitting the white part of the board? Round your answer to the nearest whole number.
Answer:
P(white region) = 0.75 or 75%
Step-by-step explanation:
Find the area of the shaded region:
A = πr²
A = π(2)²
A = 12.56
Find the area of the entire dartboard:
A = πr²
A = π(4)²
A = 50.24
Find the probability that the dart hits the blue region:
P(blue region) = Area of blue region/ Total Area
P(blue region) = 12.56 / 50.24
P(blue region) = 0.25
As total probability is equal to 1, find the probability of throwing a dart that hits the white part of the board by substracting 0.25 from 1
P(white region) = 1 - P(blue region)
P(white region) = 1 - 0.25
P(white region) = 0.75
(20 POINTS!!!) Richie and his brother have a paper route. Together they can deliver all of the papers in 40 minutes, and Richie can do it alone in 90 minutes. Richie’s brother slept in one day, leaving Richie to deliver alone for 30 minutes. How long must the two of them work together to finish delivering the newspapers?
Simplify equation: 14 - 7y + 5 = 1 + 3y + 24
simplify again: 19 - 7y = 25 + 3y
add -25 and 7y to both sides: -6 = 10y
y = -6/10 or -0.6
2. After 30 minutes, richie has delivered 1/3 of the papers, so they have to deliver the remaining 2/3. Since they can deliver them all in 40 minutes, would the answer be 2/3 of 40? I'm not sure about this.
What is the slope of the line ?
Answer:
The slope is 1
Step-by-step explanation:
there's actually a trick you can do to find the slope. if you go from where the y-intercept is and go over to the x- intercept it will give you the slope hope this helps you