Answer:
(3, -16)Step-by-step explanation:
The vertex coordinates of f(x) = ax² + bx + c are: (h, k)
where: [tex]h=\dfrac{-b}{2a}\ ,\qquad k=f(h)[/tex]
f(x) = x² - 6x + 11 ⇒ a = 1 b = -6
So:
[tex]h=\dfrac{-(-6)}{2(1)}=\dfrac6{2}=3\\\\y=f(h)=-(3)^2-6(3)+1=-9-18+11=-16[/tex]
The vertex of quadratic equation is (3, 2)
How to find the vertex of quadratic equation?In order to determine the coordinates of the vertex, if they are not clearly labeled or easily identified from the graph, we will need to know the equation for the parabola. In general, the equation of a parabola has the form
y=ax²+bx+c
where a, b, and c are all real numbers, and a≠0.
This is called a quadratic equation, and this form is called the standard form of a quadratic equation.
The vertex of the parabola is located at a pair of coordinates which we will call (h, k). In order to determine what they are, we can simply use the standard form of the quadratic equation.
To find h, use the formula:h=−b/2a.
To find k, evaluate the quadratic equation when x = h. In other words, plug in the value of h for x, and solve.Given:
y= x² - 6x + 11
Now,
h= -b/2a
h= -(-6)/ 2 * 1
h= 3
Now,
y= f(h)
= 3*3 - 6*3 +11
= 9 -18 +11
= -9 +11
= 2
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Solve the inequality b - 12 > -3
What are the solutions?
Answer:
b>9
Step-by-step explanation:
Answer:
b > 9
Step-by-step explanation:
Inequalities represent the value of a variable in relation to other numbers.
Solving the Inequality
The properties of equality state that if you add or subtract a number from both sides, the statement remains true. This means that we can isolate the variable by using the properties of equality.
To isolate the variable, add 12 to both sidesThis gives the inequality b > 9Understanding the Answer
The answer to the inequality is b > 9. This means that the variable must be greater than 9. So, values such as 10 or 100 could all be solutions. However, remember that 9 itself is not a solution. The inequality only accounts for values greater than 9, not equal to.
Next term in the sequence 6 9 15 24
simplify the equation x= -4 plus or minus the square root of -16 all over 2
Answer:
[tex]x = \frac{ - 4 \frac{ + }{} \sqrt{ - 16} }{2} \\ \\ x = \frac{ - 4}{2} \frac{ + }{} \frac{ \sqrt{ - 16} }{2} \\ \\ x = \frac{ - 4}{2} \frac{ + }{} \frac{ \sqrt{16} \sqrt{ - 1} }{2} \\ \\ x = \frac{ - 4}{2} \frac{ + }{} \frac{4i}{2} \\ \\ x = - 2 \frac{ + }{} 2i[/tex]
x = – 2 + 2i , x = – 2 – 2i
An easy way to simplify fractions
Multiply: (x+4)(x+5)Simplify and write your answer in Standard Form.
Answer:
[tex](x + 4)(x + 5)[/tex]
[tex]x \times x + 5x + 4x + 4 \times 5[/tex]
[tex]x {}^{2} + 5x + 4x + 20[/tex]
[tex]x {}^{2} + 9x + 20[/tex]
The standard form of the expression (x+4)(x+5) is x²+9x+20.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is (x+4)(x+5)
x is the variable in the given expression.
We have to multiply and simplify the expression.
Let split the expression as below.
x(x+5)+4(x+5)
Apply the distributive property
x²+5x+4x+20
Combine the like terms
x²+9x+20
x²+9x+20 is the standard form of the expression (x+4)(x+5)
Hence, the standard form of the expression (x+4)(x+5) is x²+9x+20.
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What is the sum of frothy-three thousand and twenty-one hundreds?
Answer:
My answer would be Frothy-five thousand and one hundred (45,100).
Step-by-step explanation:
1.) if gasoline costs $2.50 per gallon and your car or plane drives 25 miles per gallon, then how many gallons of gasoline will you need for your travels? how much would it cost
Answer:
$581.90
Step-by-step explanation:
5819/25 = 232.76
232.76 x $2.50 = $581.90
In a class of 30 children there are g , girls what fraction of the class are girls
PLS HELP!!
Joshua and Isabella are having a snowball fight. Joshua has a snowball, shaped as a sphere, with a radius of 6 cm. Isabella also has a spherical snowball that is 6 cm across the center of the sphere. Find the volume of each snowball (use 3.14 for pi)
A. Find the volumes of each snowball.
B. The volume of Joshua’s snowball is _______ times larger than the volume of Isabella’s snowball.
Answer:
Its 8
Step-by-step explanation:
Math GR08 ist NW DCA 20-21
18 of 21
47 39 /0130 00
Mr. Jones is using a rope that is 8 feet long to stabilize the tree he planted in his
garden. The rope is tied down with a stake that is placed 6 feet away from the base
of the tree. A right angle is created with the rope and the base of the tree. Using the
diagram below, how far up the tree did Mr. Jones tie the rope? Round your answer to
the nearest tenth.
8 ft
6 ft
5.3 feet
6.9 feet
8.3 feet
Type here to search
EF
O
AD10/12/20
Answer:
Step-by-step explanation:
To get how far up the tree that Mr. Jones tied the rope, we will use the Pythagoras theorem since a right angle is created with the rope and the base of the tree.
The length of the rope will be the hypotenuse
The distance up the tree and away from the base will be the opposite and adjacent.
Given
length of the rope = 8feet
Distance away from the base of the tree = 6ft
According to Pythagoras;
hyp² = opp²+adj²
8² = opp²+6²
opp² = 8²-6²
opp² = 64-36
opp² = 28
opp = 5.3 feet
Hence the Mr Jones tied the rope 5.3feet above the tree. Option C is correct
(-15) ÷ (-1.25) ● 4 ½ - 120 HELP
Answer: I believe the answer you're looking for is -66.
Step-by-step explanation:
(-15) / (-1.25) = 12.
12 x 4 1/2 = 54
54 - 120 = -66.
Hope this helps!
Answer:
( -66 )Step-by-step explanation:
[tex]( - 15) \div ( - 1.25) \: . \: 4 \frac{1}{2} - 120 \\ = \frac{ (- 15)}{( - 1.25)} \: . \: 4 \frac{1}{2} - 120 \\ = \frac{( - 15) \times 100}{( - 1.25) \times 100} \: . \: 4 \frac{1}{2} - 120 \\ = \frac{ - 1500}{ - 125} \: . \: 4 \frac{1}{2} - 120 \\ = 12 \: . \: \frac{9}{2} - 120 \\ = 6 \: . \: 9 - 120 \\ = 54 - 120 \\ = ( - 66) \\ [/tex]
There are 15 ice cream flavors and 3 different cone options. How many different 2 scoop cones can you make? (order doesn't matter and flavors can be repeated ie; chocolate on chocolate counts)
There are 675 different combinations.
How many combinations are there?The number of combinations is given by the product between the numbers of options.
For the first scoop, we have 15 possible options.For the second scoop, we also have 15 possible options.For the cone, we have 3 options.So the total number of different combinations is just given by:
C = 15*15*3 = 675
There are 675 different combinations.
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Help plsss. Solve using ratios and please show your work!!! I’ll give brainlist to the first person who is right!!!!!
Answer:
1) 12 cm
2) 20 cm
Step-by-step explanation:
Those are my guess but it is simple math just take the cm of the flag for the length and width and multiple the cm by the 4 to get the answer hope it helps
If < 5 = 35 what is m < 1
Answer:
m < 1 = 35
Step-by-step explanation:
this is because the lines are parallel therefore m<5=m<1
hello people ~
factorise: y² + 4y - 21
Answer:
[tex](y+7)(y-3)[/tex]
Step-by-step explanation:
To factorize [tex]y^2+4y-21[/tex]
[tex]\textsf{for} \ ax^2+bx+c \ \textsf{find} \ v, w \ \textsf{such that} \ v \cdot w=a \cdot c \ \textsf{and} \ v+w=b\\ \textsf{ and group into} \ (ax^2+vx)+(wx+c)[/tex]
[tex]a \cdot c=1 \cdot -21=-21[/tex]
[tex]b=4[/tex]
Therefore, the 2 numbers that multiply together to give -21 and add together to give 4 are: 7 and -3
[tex]\implies y^2+7y-3y-21[/tex]
[tex]\implies (y^2+7y)+(-3y-21)[/tex]
Factor the parentheses:
[tex]\implies y(y+7)-3(y+7)[/tex]
Factor out the common term [tex](y+7)[/tex]:
[tex]\implies (y+7)(y-3)[/tex]
Describe the transformation
A student group determines the profit, in dollars, from a car wash using the function
f(x) =8(x-2) -20, where x represents the number of cars washed. What is the profit, in dollars, from washing 30 cars?
$?
Answer:
$ 204
Step-by-step explanation:
f(x)=8(x-2)
if i did this right then you would substitute 30 in for x------------8 (30-2) - 20
next you would multiply 8 times 30 and 8 times -2 and you would get 240-16-20
then you would subtract and get....................... 204
hope this helps if not then pls know that i tried
Tom walks 3. 15 km to the park. He then walks a further 350 m to the shop. How many km has Tom walked in total?
Answer:
Step-by-step explanation:
We have to convert m to km and we have to add to find the total distance walked.
1000m = 1 km
350 m = 350 ÷ 1000 = 0.35 km
Total distance = 3.15 + 0.35
= 3.50 km
If g(x) = x2 - 4, find g(5).
06
O 14
O 21
0 29
Answer:
g(5)=6
Step-by-step explanation:
g(5)=(5)(2)-4
g(5)=10-4
g(5)=6
Follow the steps to solve this equation.
3(2x + 6) – 4x = 2(5x – 2) + 6
1. Use the distributive property: 6x + 18 – 4x = 10x – 4 + 6
2. Combine like terms: 2x + 18 = 10x + 2
3. Use the subtraction property of equality: 18 = 8x + 2
4. Use the subtraction property of equality: 16 = 8x
5. Use the division property of equality:
= x
Answer:
2
Step-by-step explanation:
Answer: B or 2
Step-by-step explanation:
please help me to find the easy math problem
Answer:
a. = 30
c. = 29
Step-by-step explanation:
what's better 27 out of 32 or 19 out of 21 and why
Answer:
19/21 is better.
Step-by-step explanation:
To find which is better, you need to divide the numerator by the denominator.
27 divided by 32 is equal to 0.84375
19 divided by 21 is equal to 0.9
0.9 is greater than 0.84375, so 19/21 is better.
PLEASE HELP! 30 POINTS AND WILL MARK BRAINLIEST ALONG WITH A THANKS AND RATE 5.
A pizza place is having a special. If you order a large pizza for a regular price $17, you can order any number of additional pizzas for $8.50 each. Use the recursive rule f(1)=17 and f(n)=f(n-1)+8.5 for each whole number n greater than 1.
Answer:
Step-by-step explanation:
f(1)=17
f(n)=f(n-1)+8.5
n f(n)=f(n-1)+8.5 f(n)
1 f(1)=17 17
2 f(2)=f(1)+8.5 =17+8.5=25.5 25.5
3 f(3)=f(3-1)+8.25=f(2)+8.25=25.50+8.5=34 34
4 f(4)=f(3)+8.25 =34+8.5=42.5 42.5
what is the decimal for 6/7
Answer:
the answer to your question is 0.857
Please help me with this question
Answer: 5
Step-by-step explanation:
1
Write an expression that is equivalent to 1/2a-4
Answer:
2/4a-4
Step-by-step explanation:
dividing 2/4a-4 is =1/2a-4
I don’t understand what to do
Answer: 14cm
Step-by-step explanation:
The diameter of a circle is twice the radius.
Therefore, the diameter = 2*7 cm = 14cm
Answer:
14 cm
r=7
d=2r
d=2×7
d=14
Step-by-step explanation:
please mark me as brainlest
Need help on algebra 1
Slopes step by step
Answer:
1 is y=-1/3x. 3 is y=-3/2x. 5 is y=5/3x
Step-by-step explanation:
Simply count the vertical lengths. Meaning count up or down how ever many. That is your top number. Then count your horizontal lengths, meaning left or right, this your bottom number of the slope. So if point A is at (-1,-1) in example 1, then count down 1, and right 3 spaces. Because you go down, the slope is negative, and you went down 1, so the top number is 1, you went right 3 units, so the bottom number is 3.
Write a Pythagorean triplet whose smallest member is 8
FAST
Answer:
Step-by-step explanation:
2m=8
m=4
m²+1=16+1=17
m²-1=16-1=15
Therefore the Pythagorean triplets are 8,15 and 17. Here 8 is the smallest member.
Answer: 8, 15, 17
This is something you get through trial and error, or you could have memorized this particular triple.
Note how 8^2+15^2 = 17^2
3(4+2)=30
pls help me
Answer:
Isn't it 18?
Step-by-step explanation:
Because you need to add 4 and 2 then multiply it with 3?