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).
Answers
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❀
Related Questions
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4+2(x–4)=–7(x+7)
....Whats the answer? NEEDED ASAP
Answers
Answer:
-5
Step-by-step explanation:
4+2(x-4) = -7(x+7)
First, work out parenthesis: 4+ 2x-8 = -7x -49
Combine like terms: 2x-4= -7x-49
now isolate x by first adding 49 to each side: 2x+45= -7x
Then subtract 2x from each side: 45= -9x
Last, divide both sides by -9:
x= -5
Answer:
The answer is negative five or -5.
Step-by-step explanation:
First, you need to distribute your equation and at the end, the -4 should be just 2x - 8.
Second, subtract the numbers 4 and -8, which will equal to -4.
Third, rearrange your terms. Those terms would be -4 + 2x, so it should be 2x - 4.
Fourth, distribute again but with -7(x + 7) and you should get -7x - 49.
Fifth, add four to both sides of your equation. It should be like 2x - 4 + 4 = -7x - 49 + 4.
Sixth, add the numbers for the both sides. Therefore, you have 2x = -7x - 45.
Seventh, add 7x to both sides of the equation. You add it to 2x and -7x - 45 + 7x.
Eighth, simplify by combining like terms which you get 9x = -45.
Ninth, divide both of the sides of your equation by the same term. Your number to use when diving is 9.
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pls help pls help pls help pls help
Answers
7 is a prime number
Answer:
The difference is 3 for 4-7, and 39 for 52-91. So basically its a change of 3 for every 4-7 I think this is what you ask for. Let me explain and show results and then pick what you need.
Step-by-step explanation:
So, we know 4 to 7 is 3.
52 to 91 is 39.
So one is a change in 3. the other is a change is 39.
However, could these be the same, just bigger?
Lets divide the 52 to 91 with a change of 39 by 4 to 7 with a change of 3:
52/4 to 91/7 with a change of 39/3 =
13 to 13 with a change of 13.
So this tells us that the 52 to 91 with a chang eof 3 is 13 times bigger than 4 to 7 with a change of 3.
Hope this helps!
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Answer:
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Step-by-step explanation:
Answer:
24cm
Step-by-step explanation:
V= 4/3πr³
or, r³= 3/4π ×V= 3/4π× 18432π= 13824
or, r= (13824)^1/3= 24cm
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Answer:
bro/sis through this solution u can solve ur values
Step-by-step explanation:
To calculate the variance, you first subtract the mean from each number and then square the results to find the squared differences. You then find the average of those squared differences. The result is the variance. The standard deviation is a measure of how spread out the numbers in a distribution are.
I hope this will help you
factor the following
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Answers
Answer:
[tex] \rm\displaystyle( {a}^{2} + {b}^{2} - 22)( {a}^{2} + {b}^{2} + 4)[/tex]
Step-by-step explanation:
we would like to factor the following:
[tex] \rm\displaystyle ( {a}^{2} + {b}^{2} {)}^{2} - 18( {a}^{2} + {b}^{2} ) - 88[/tex]
let a²+b²=x
thus substitute:
[tex] \rm\displaystyle x {}^{2} - 18x- 88[/tex]
rewrite the middle term as 4x-22x:
[tex] \rm\displaystyle x^{2} + 4x - 22x - 88[/tex]
factor out x:
[tex] \rm\displaystyle x( x^{} + 4)- 22x - 88[/tex]
factor out -22:
[tex] \rm\displaystyle x( x^{} + 4)- 22(x + 4)[/tex]
group:
[tex] \rm\displaystyle( x- 22)(x + 4)[/tex]
substitute back:
[tex] \rm\displaystyle( {a}^{2} + {b}^{2} - 22)( {a}^{2} + {b}^{2} + 4)[/tex]
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The surface of an air hockey table has a perimeter of 32 feet its area is 60 ft.what are the dimensions of the air hockey table
Answers
The width of a rectangle is 5 3/4 inches. The length is three times its width. What is the perimeter?
Answers
Answer:
perimeter=46.5 inches
Step-by-step explanation:
[tex]width=2\frac{3}{4}[/tex]
[tex]=\frac{5*4+3}{4}[/tex]
=[tex]=\frac{23}{4}[/tex]
[tex]length=3(\frac{23}{4} )[/tex]
[tex]=\frac{23*3}{4}[/tex]
=[tex]\frac{69}{4}[/tex]
perimeter of rectangle =2(l+b)
[tex]=2(\frac{69}{4} +\frac{24}{4} )[/tex]
[tex]=2(\frac{69+24}{4} )[/tex] (since their denominator are same u can add their numerator)
[tex]=2(\frac{93}{4})[/tex]
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Answers
Answer:
Step-by-step explanation:
3x - 14 = 46
+ 14 +14
3x = 60
3x/3 = 60/3
x = 20
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Answers
Answer:
Step-by-step explanation:
Decreased students = 1050 - 798 = 252
Decreased percentage = (decreased students ÷ number of last year students) * 100
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= 24%
Answer:
24%
Step-by-step explanation:
% change = [tex]\frac{difference}{original amount}[/tex] x 100
; 1050 - 798 = 252
% change = [tex]\frac{252}{1050}[/tex] x 100
% change = 0.24 x 100
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Cedric sends text messages at a constant rate of 5 messages per 1 hour. What equation would be used to represent this situation?
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Answer:
...........................I would be I don't know
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Answers
Answer:
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj/ hyp
cos theta = 8/20
cos theta = 2/5
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cos^-1 (cos theta) = cos ^-1 ( 2/5)
theta =66.42182152
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theta = 66 degrees
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Answers
Answer:
(x+5)(x-2)
Step-by-step explanation:
x^2 +3x-10
What two numbers multiply to -10 and add to 3
5*-2 = -10
5+-2 = 3
(x+5)(x-2)
Find the number from which (– 66) is subtracted to get a difference of 100.
Answers
Answer:
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Step-by-step explanation:
4. Change 5 hours to minutes.
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Answers
Answer:
[tex]{ \tt{1 \: hour = 60 \: minutes}} \\ { \tt{5 \: hours = (5 \times 60) \: minutes}} \\ = 300 \: { \bf{minutes}}[/tex]
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Answers
Answer:
14 : -17 : 2
Step-by-step explanation:
8 + (9 · 2 – 3) : 25 – 4 2 : 2
= 14 : -17 : 2
Answer:
- 12.4
Step-by-step explanation:
[tex]8 + \frac{9 * 2 - 3}{25} - \frac{42}{2}[/tex]
[tex]8 + \frac{18 - 3}{25} - 21[/tex]
[tex]8 + \frac{15}{25} - 21[/tex]
[tex]8 + \frac{3}{5} - 21[/tex]
[tex]8 \frac{3}{5} - 21[/tex]
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The perimeter of a square is 56 cm. What is the Area of the square in square centimeters?
Answers
Answer:
[tex]{ \tt{let \: one \: side \: be \: s}} \\ { \bf{perimeter = 4s}} \\ 56 = 4s \\ s = \frac{56}{4} \\ { \tt{s = 14 \: cm}} \\ \\ { \bf{area = {s}^{2} }} \\ = {14}^{2} \\ { \boxed{ \tt{area = 196 \: {cm}^{2} }}}[/tex]
Answer:
A =196 cm^2
Step-by-step explanation:
The perimeter of a square is
P = 4s where s is the side length
56 = 4s
Divide by 4
56/4 = 4s/4
14 =s
The area is given by
A =s^2
A =14^2
A =196 cm^2
Find the Value of X in this Triangle
Answers
Answer:
x = -6
Step-by-step explanation:
All three angles are equal, so all three sides are equal, making this an equilateral triangle
5x+10 = 2x-8
Subtract 2x from each side
5x-2x +10 = 2x-8-2x
3x+10 = -8
Subtract 10 from each side
3x+10-10 = -8-10
3x = -18
Divide by 3
3x/3 = -18/-3
x = -6
Pls help 28 pts and brainliest
Answers
Answer:
43 units^2
Step-by-step explanation:
Area of a rectangle is
A = l*w
The bottom rectangle is 3 by 11 for an area of 33
The top rectangle is 2 by 5 for an area of 10
Add the areas together
33+10 = 43
find the area of the triangle
Answers
Area of a Triangle is 1/2 base X height
So (b)(h) = 2.1m X 19m=39.9m (210 cm = 2.1 m)
Now that we have the base which is 39.9m
We do the sides which is 1/2*28*19=266m
Now that we have the sides, we add the base which is 39.9m and the Height which is 266m, then we get our answer: 305.9m
I hope this helped you. Goodluck, and please give me a Branliest if available. Thanks. :)
(Correct answers only)
A
B
C
Or D
Answers
Answer:
Division property of equality
Step-by-step explanation:
7q=49
Divide each side by 7
7q/7 = 49/7
q = 7
The given equation is : 7q = 49
In order to solve this equation you have to divide the left side by 7 in order to get the variable my itself. And in turn, you also have to do the same to the right side.
This is what the division property of equality states, that if one side is divided, then the other side must be divided as well.
I just need to know the angle
Answers
Answer: B. DBC
Step-by-step explanation:
Answer: [tex]\angle DBC[/tex] (choice b)
================================================
Explanation:
When naming any angle, you need 3 points. The middle point is the vertex of the angle. The other two points can be in any order as long as they are on the lines or rays that we want.
We go for angle DBC, which we can write as [tex]\angle DBC[/tex], since B is at the vertex and points D and C are on either side of the vertex.
Angle ABD is adjacent to the marked angle, but it's not what we're after.
Angle BDC isn't drawn, so we cross this off the list as well.
Saying [tex]\angle B[/tex] is too vague in this context because it could mean either [tex]\angle ABD[/tex] or it could mean [tex]\angle DBC[/tex] since they both share the same vertex B.
factorise fully p^3 + p^2
Answers
Answer:
[tex]\huge\boxed{p^3+p^2=p^2(p+1)}[/tex]
Step-by-step explanation:
[tex]p^3+p^2\\\\p^3=p^{2+1}=p^2\cdot p\\\\p^3+p^2=p^2\cdot p+p^2\cdot1=p^2(p+1)[/tex]
Used:
[tex]a^n\cdot a^m=a^{n+m}\\\\\text{distributive property}:\ a(b+c)=ab+ac[/tex]
Alex’s paycheck for the last two weeks totaled $239.64. He owes the cell phone company $44.87. How much money does he have left
Answers
Answer:
the answer would be 193.77
Step-by-step explanation:
literally, subtract 45.87 from 239.64.
you get 193.77.
(you put 44 instead of 45, so the sum with 44 would be 194, that is incorrect.)
Graph the solution set to this inequality.
3x – 11 > 7x + 9
Answers
Step-by-step explanation:
Solve the inequality:
[tex]3x - 11 > 7x + 9[/tex]
Rearrange unknown terms to the left side of the equation:
[tex]3x - 7x > 9 + 11[/tex]
Combine like terms:
[tex] - 4x > 9 + 11[/tex]
Calculate the sum or difference:
[tex] - 4x > 20[/tex]
Reduce the greatest common factor for both sides of the inequality:
[tex] - x > 5[/tex]
Divide both sides of the inequality by the coefficient of variable:
[tex]x < - 5[/tex]
2: plot:
[tex]x < - 5[/tex]
Graph on number line:
The solution inequality that represents the solution of the given expression inequality is → x < - 5.
What is inequality? Differentiate between equation and expression? expression inequality : An inequality is used to make unequal comparisons between two expressions or numbers.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is the inequality as follows -
3x – 11 > 7x + 9
The inequality is given as -
3x – 11 > 7x + 9
3x > 7x + 9 + 11
3x - 7x > 9 + 11
- 4x > 20
x < - 5
Therefore, the solution inequality that represents the solution of the given expression inequality is → x < - 5.
To solve more questions on functions, expressions and polynomials, visit the link below -
brainly.com/question/17421223
#SPJ2
Anybody know the answer ?
Answers
Answer:
The final speed after collision of the first ball that weighs 4 kg will be 8.5 m/s.
Step-by-step explanation:
M1 = 4
M2 = 2
V1 = 8
V2 = 6
V2f = 5
V1f = ?
Rep. Situation with Momentum formula:
M1*V1+M2*V2 = M1*V1f+M2*V2f
Rearrange:
((M1*V1+M2*V2)-M2*V2f) / M1 = V1f
Calculate:
((44) - 10) / 4 = V1f
V1f = 8.5
What is the slope of the line 3x -9y =4?
Answers
Answer:
1/3
Step-by-step explanation:
3x -9y =4
To find the slope get the equation in slope intercept form ( y= mx+b where m is the slope and b is the y intercept)
Subtract 3x from each side
-9y = -3x+4
Divide each side by -9
-9y/-9 = -3x/-9 +4/-9
y = 1/3x -4/9
The slope is 1/3 and the y intercept is -4/9
Here,
3x -9y =4
To find the slope get the equation in slope intercept form ( y= mx+b where m is the slope and b is the y intercept)
Subtract 3x from each side
-9y = -3x+4
Divide each side by -9
-9y/-9 = -3x/-9 +4/-9
y = 1/3x -4/9
The slope is 1/3 and the y intercept is -4/9
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