besties this is 100 points & i'll give brainliest istg i need to know this
Find the unknown values of b and c in the equation y = -x² + bx + c given its vertex is (-7, -5).
Answer:
[tex] \displaystyle b = - 14[/tex]
[tex] \displaystyle c = - 54[/tex]
Step-by-step explanation:
to figure out b we can consider the following formula:
[tex] \displaystyle \frac{ - b}{2a} = h[/tex]
the form of vertex coordinate given by
[tex] \displaystyle (h,k)[/tex]
so according to the question
[tex] \displaystyle (h,k) = ( - 7, - 5)[/tex]
by order pair we obtain:
[tex] \displaystyle h = - 7, k = - 5[/tex]
now substitute the value of h and a to the formula:
[tex] \displaystyle \frac{ - b}{2(- 1)} = - 7[/tex]
simplify multiplication:
[tex] \displaystyle \frac{ - b}{ - 2} = - 7[/tex]
cross multiplication:
[tex] \displaystyle - b = 14[/tex]
divide both sides by -1:
[tex] \displaystyle b = - 14[/tex]
now we need to figure out C to do so substitute -7 for x and -5 for y which yields:
[tex] \displaystyle - {7}^{2} - 14( - 7) + c = - 5[/tex]
simplify square:
[tex] \displaystyle -49 - 14( - 7) + c = - 5[/tex]
simplify multiplication:
[tex] \displaystyle -49 + 98+ c = - 5[/tex]
simplify addition:
[tex] \displaystyle 49+ c = - 5[/tex]
cancel 49 from both sides:
[tex] \displaystyle c = - 54[/tex]
hence,
b=-14C=-54___________________________________
Problem:Find the unknown values of b and c in the equation y = -x² + bx + c given its vertex is (-7, -5).Let's Solve it!This is a problem where you want to able to ake use of tue Vertex Form in order to get the values of b and c fir the standard form of the parabola. Vertex (-7,-5) or (h,k) in the standard form. These are the x and y coordinates of the vertex. Note the standard form is:[tex]\quad\quad\quad\quad\tt{ a{x}^{2} + bx + c}[/tex]
Since we have the given of:[tex]\quad\quad\quad\quad\tt{ a \: = - 1}[/tex]
[tex]\quad\quad\quad\quad\tt{ h = - 7}[/tex]
[tex]\quad\quad\quad\quad\tt{ k \: = - 5}[/tex]
Note the vertex form is:[tex]\quad\quad\quad\quad\tt{y = a(x - h {)}^{2} } + k[/tex]
[tex]\quad\quad\quad\quad\tt{y = - 1(x - ( - 7) {)}^{2} } + ( - 5)[/tex]
[tex]\quad\quad\quad\quad\tt{y = - 1(x + 7 {)}^{2} } - 5[/tex]
[tex]\quad\quad\quad\quad\tt{ \boxed{y = - {x}^{2} - 14x - 54}}[/tex]
Hence, The answer for b and c is:[tex]\quad\quad\quad\quad\tt{ \boxed{ \boxed{ \color{magenta}{b = - 14}}}}[/tex]
[tex]\quad\quad\quad\quad\tt{ \boxed{ \boxed{ \color{magenta}{c = - 54}}}}[/tex]
Let's confirm it :You can use x coordinate of the vertex like this,[tex]\quad\quad\quad\quad\tt{ - 7 = \frac{b}{2(a)} }[/tex]
[tex]\quad\quad\quad\quad\tt{ - 7 = \frac{b}{2(-1)} }[/tex]
[tex]\quad\quad\quad\quad\tt{ - 7 = \frac{b}{-2} }[/tex]
[tex]\quad\quad\quad\quad\tt{ (- 2)( - 7) = - b }[/tex]
[tex]\quad\quad\quad\quad\tt{ \frac{ (- 2)( - 7)}{ - 1} = b }[/tex]
[tex]\quad\quad\quad\quad\tt{ \frac{ 14}{ - 1} = b }[/tex]
[tex]\quad\quad\quad\quad\tt{ \boxed{ - 14 = b }}[/tex]
You can also confirm the y coordinate of the vertex in the standard form by plugging the x coordinate.[tex]\quad\quad\quad\quad\tt{y = - {(-7)}^{2} - 14(-7) - 54}[/tex]
[tex]\quad\quad\quad\quad\tt{y = - 49 +98 - 54}[/tex]
[tex]\quad\quad\quad\quad\tt{y = - 49 +98 - 54}[/tex]
[tex]\quad\quad\quad\quad\tt{y = 49 - 54}[/tex]
[tex]\quad\quad\quad\quad\tt{ \boxed{y = - 5}}[/tex]
So, the final answer for b and c is:[tex]\quad\quad\quad\quad\tt\huge{ \boxed{ \boxed{ \color{magenta}{b = - 14}}}}[/tex]
[tex]\quad\quad\quad\quad\tt\huge{ \boxed{ \boxed{ \color{magenta}{c = - 54}}}}[/tex]
___________________________________
#CarryOnLearning
✍︎ C.Rose❀
A parabola intersects the x- axis at x=3 and x=9
Step-by-step explanation:
To find the equation of a parabola we need to have 3 points. The intercept of the X axis is the X intercept. The definition of an intercept is when the other value is equal to zero. (3,0) and (9,0)
There appears to not be enough points to answer your question. we also need a vertex
Select the correct answer.
In which quadrant are the x-coordinate and the y-coordinate of a point both negative?
A.
quadrant I
B.
quadrant II
C.
quadrant III
D.
quadrant IV
Answer: c
Step-by-step explanation:
I am doing a connexus geometry unit test. please send assistance!
Answer:
x=37
Step-by-step explanation:
50+24=74
74/2=37
The chart below represents the number of marbles in a jar. What is the probability of picking blue?
P(blue) =
Answer:
yes
Step-by-step explanation:
A person rides a bike from home to a restaurant, eats a meal, and then rides home.
Which graph could represent this situation?
A.
Step-by-step explanation:
It is A because the person left, which would cause the distance to become greater, then ate a meal which would cause them to stop. Finally, the person went back home, which would cause the distance to decrease.
Answer:
a
Step-by-step explanation:
-2x-2y=-8
-4x-8y=-20
Answer:
-2x-2y=-8
-4x-8y=-20
From the 1st eqn
Dividing through by 2
you have
-x-y=-4
Multiply through by -(minus)
x+y=4
x=4-y
Substitute into eqn 2
-4x-8y=-20
-4(4-y)-8y=-20
-16 + 4y - 8y = -20
-4y = -20 +16
-4y = -4
y= 1
Substitute into any of the other eqn's to get x
x= 4-y
x= 4-1
x=3
Find the sum of this series \displaystyle \log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right)log( 2 1 )+log( 3 2 )+log( 4 3 )+log( 5 4 )+...+log( 99 98 )+log( 100 99 )
Answer:
[tex]\log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right) = \log(\frac{1}{100})[/tex]
Step-by-step explanation:
Given
[tex]\log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right)[/tex]
Required
The sum
Using the laws of logarithm, we have:
[tex]\log(a) + \log(b) = \log(ab)[/tex]
Take the first two terms of the series
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3}) = \log(\frac{1}{2} * \frac{2}{3})[/tex]
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3}) = \log(\frac{1}{3})[/tex]
Include the third term
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) = \log(\frac{1}{3} * \frac{3}{4})[/tex]
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) = \log(\frac{1}{4})[/tex]
Include the fourth term
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) + \log(\frac{4}{5}) = \log(\frac{1}{4} *\frac{4}{5})[/tex]
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) + \log(\frac{4}{5}) = \log(\frac{1}{5})[/tex]
Notice the following pattern
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3}) = \log(\frac{1}{3})[/tex] ---------------- n =2
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) = \log(\frac{1}{4})[/tex] -------------- n = 3
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) + \log(\frac{4}{5}) = \log(\frac{1}{5})[/tex] ----------- n = 4
So the sum of n series is:
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ ............ + \log(\frac{n}{n+1}) = \log(\frac{1}{n+1})[/tex]
So, the sum of the series is:
[tex]\log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right)[/tex]
[tex]\log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right) = \log(\frac{1}{99+1})[/tex]
[tex]\log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right) = \log(\frac{1}{100})[/tex]
what set of numbers are shaded on the hundred chart.
A: only all the factors of 36
B: only the multiples of 36
C: only all the factors of 72
D: only all the multiples of 72
I need help solving these problems
Answer:
question one:
x = 6.018150231520483
adjacent angle = 7.986355100472928
Step-by-step explanation:
i have no links, but try to search triginometry calculator and pick carbide calculator for fast trigonometry calculations
it automaticly does sin, cos, and tan for you.
Which ordered pair makes the equation true? 2x – 5y = –10
(5, 4)
(2, 5)
(20, 4)
(–10, 4)
120÷[17-{15-3(8-2)}]
Answer:
the ans has to be 6.........
1 point
28. Malcolm is tiling his kitchen wall. The kitchen wall is
rectangular in shape measuring 700cm by 200cm. Each tile
is 50 cm by 50 cm. How many tiles does he need to tile the
kitchen wall?
Answer:
i think its 110
Step-by-step explanation:
hope it helps
What is the perimeter in terms of x, of the rectangle shown here (x^2+7x-9) (3x^2-2x)
Given:
Consider the dimensions of the rectangle are [tex](x^2+7x-9)[/tex] and [tex](3x^2-2x)[/tex].
To find:
The perimeter in terms of x, of the rectangle.
Solution:
Let the length of the rectangle be [tex](x^2+7x-9)[/tex] and the width of the rectangle is [tex](3x^2-2x)[/tex] units.
The perimeter of a rectangle is:
[tex]P=2(l+w)[/tex]
Where, l is the length and w is the width of the rectangle.
Substituting [tex]l=(x^2+7x-9)[/tex] and [tex]w=(3x^2-2x)[/tex] in the above formula, we get
[tex]P=2((x^2+7x-9)+(3x^2-2x))[/tex]
[tex]P=2(4x^2+5x-9)[/tex]
[tex]P=2(4x^2)+2(5x)+2(-9)[/tex]
[tex]P=8x^2+10x-18[/tex]
Therefore, the perimeter of the rectangle is [tex]8x^2+10x-18[/tex] units.
Fatuma invests a total of $14,000 in two accounts. The first account earned an annual interest rate of 15% and the second account earned an annual interest of 12%. At the end of one year, the total amount of money gained was $1,815.00. How much was invested into each account? $ was invested in the account that earned 15% and $ was invested in the account that earned 12%.
Answer: that’s 5
Step-by-step explanation:
Renee has dimes and quarters in her wallet that total $1.60. She has 2 more dimes than quarters.
How many of each coin does Renee have?
Given:
Renee has dimes and quarters in her wallet that total $1.60.
She has 2 more dimes than quarters.
To find:
The number of each type of coins.
Solution:
Let x be the number of dimes and y be the number of quarters.
She has 2 more dimes than quarters. So,
[tex]x=y+2[/tex] ...(i)
We know that,
1 dime = $0.10
1 quarter = $0.25
Renee has dimes and quarters in her wallet that total $1.60. So,
[tex]0.10x+0.25y=1.60[/tex] ...(ii)
From (i) and (ii), we get
[tex]0.10(y+2)+0.25y=1.60[/tex]
[tex]0.10y+0.20+0.25y=1.60[/tex]
[tex]0.35y=1.60-0.20[/tex]
[tex]0.35y=1.40[/tex]
Divide both sides by 0.35.
[tex]y=\dfrac{1.40}{0.35}[/tex]
[tex]y=4[/tex]
Substituting [tex]y=4[/tex] in (i), we get
[tex]x=4+2[/tex]
[tex]x=6[/tex]
Therefore, the number of dimes is 6 and the number of quarters is 4.
Help, Help, Help, Help, Help,
Step-by-step explanation:
answer is in photo above
Answer:
0.25
Step-by-step explanation:
f(1)=(1/4)^1
0.25
Find the next three terms in the arithmetic sequence: 25, 34, 43, 52, ...
Answer:
61,70,79
Step-by-step explanation:
common difference=9
It is an arithmetic progression.
therefore next 3 terms of the sequence is 61,70,79
Answer:
61, 70,79
Step-by-step explanation:
34 - 25 = 9
43 - 34 = 9
52 - 43 = 9
52 + 9 =61
the pattern is plus 9
During a baseball game, Jeff hit the ball 2 out of 3 times at bat, Brad hit the ball 3 out of 5 times at bat, and Zackary hit the ball 2 out of 4 times at bat. Who had the greatest ratio of hits?
Answer:
Jeff
Step-by-step explanation:
Answer:
Jeff had the greatest ratio
Step-by-step explanation:
First you would find the common denominator, which is 60.
Jeff - 40/60
Brad - 36/60
Zackary - 30/60
Jeff has the highest ratio and Zackary has the lowest.
this is homework. please help with the answer for both 11a and 11b :))
Can someone help me? It's urgent and thank you!
Answer:
B. [tex]\frac{x + 6}{10x}[/tex]
Brian and Hayden go out for dinner and the bill comes to $120.00. Hayden usually tips more than 20% of the bill and Brian usually tips at most 25% of the bill. Given Brian and Hayden's tipping habits, what graph below best represents the range for a tip (d) that the server should expect to see?
Answer:
There are no graphs
Step-by-step explanation:
"what graph below best represents the range for a tip "
Brian
120 * .2 = 24
24 < d
Hayden
120 * .25 = 30
d ≤ 30
24 < d ≤ 30
If you dont know the answer to my question then dont say anything!
True or false: You can rely slowly upon induction to prove that your conclusion is correct.
Answer:
False
Step-by-step explanation:
You can't rely slowly upon induction to prove that your conclusion us correct.
Answer:
False
Explanation:
This is a false statement because it is the deductive reasoning where you can prove a specific conclusion with the help of many generalized principles that are known to be true.
Combine these radicals.
–66
–54
Answer:
-100
Step-by-step explanation:
No dia da festança, bianca comprou dos pasteis por $5,20, duas maçãs do amor por $ 3,40 e dois refrigerantes por $7,60. Quanto bianca gastou?
Responder:
$ 16,2
Explicação passo a passo:
No dia da festa, Bianca comprou os pastéis por US $ 5,20, duas maçãs do amor por US $ 3,40 e dois refrigerantes por US $ 7,60. Quanto bianca você gastou?
O valor gasto por Bianca é a soma de todos os itens que ela comprou:
Pastelaria = $ 5,20
Maçãs do amor = $ 3,40
Refrigerantes = $ 7,60
A soma da soma dá o valor gasto de Bianca:
Doces + Maçãs do Amor + Refrigerante
$ (5,20 + 3,40 + 7,60)
= $ 16,2
9. Griffin ordered a pair of sneakers online. He had a $16 credit that he applied
toward the purchase, and then he used a credit card to pay for the rest of the
cost. If the shoes cost $80, how much did Griffin charge to his credit card when
he bought the sneakers?
Plz help
Answer: 79 more
Step-by-step explanation:
Mrs. Jones is planning a field trip to the state capitol building for all of the sixth graders at her school. She needs $3.75 to cover the cost of each student's lunch. There are 327 students attending the field trip. How much money does Mrs. Jones need to cover the cost of all of the students' lunches?
Answer:
= $1226.25
Step-by-step explanation:
There are 327 students
Each student lunch is $3.75
She needs 327 of these $3.75 lunches
So 327 times $3.75
= $1226.25
A company sold 123 mobile phones for ₹ 8000 each. With the same money, 48 music systems were bought. Find the cost of one music system.
Answer:
Step-by-step explanation:
123 X 8000 = 984000
984000/48 = 20500(PUT EURO SIGN)
use the function below to find F(3).
F(x) = 4(1/3)^x
Answer:
4/27
Step-by-step explanation:
F(x) = 4(1/3)^x
Let x =3
F(3) = 4(1/3)^3
Exponents first
F(3) = 4 * 1/27
Then multiply
f(3) = 4/27
Answer:
4/27
Step-by-step explanation:
f(x) = 4(1/3)^x
f(3) = 4(1/3)^3
f(3) = 4(1/27)
f(3) = 4/27
hope that helps
Help Me with this math work.
Step-by-step explanation:
-2-2
