Answer:
(- 1, 2)
Step-by-step explanation:
Given a quadratic in standard form y = ax² + bx + c : a ≠ 0
Then the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
f(x) = x² + 2x + 3 ← is in standard form
with a = 1 and b = 2, hence
[tex]x_{vertex}[/tex] = - [tex]\frac{2}{2}[/tex] = - 1
Substitute x = - 1 into f(x) for corresponding value of y
f(- 1) = (- 1)² + 2(- 1) + 3 = 1 - 2 + 3 = 2
vertex = (- 1, 2 )
Ohm's Law is given by the equation V = IR where V is voltage in watts, I is current in amperes, and R is resistance in Ohms.
A lamp needs 0.5 amperes.
Which equation can be used to determine the voltage for a given amount of resistance?
V=0.5R
V=R0.5
V = 0.5R
V = 2R
You start with the equation V = IR, plug the value 0.5 for I and you have
V = 0.5*R
So, the first three options are equivalent and correct.
V=IR
And current, Ampere is given as 0.5 so substituting it back in the main equation gives V = 0.5R
What is the median of this data set?
24, 28, 51, 54, 67, 70
Answer:
I'm guessing you need this now, So I'm just going to give the answer without the explanation
Step-by-step explanation:
52.5
Someone plz help me with this
Answer:
[tex]5y^{6}\sqrt{2}[/tex]
Step-by-step explanation:
We want to simplify:
[tex]\sqrt{50y^{12}}[/tex]
We rewrite as:
[tex]\sqrt{2\times25 \times (y^{6})^2}[/tex]
We split the radical sign to obtain:
[tex]\sqrt{25} \times \sqrt{(y^{6})^2} \times \sqrt{2}[/tex]
Simplify the square root for the perfect squares to get:
[tex]5y^{6}\sqrt{2}[/tex]
Therefore the simplified form is: [tex]5y^{6}\sqrt{2}[/tex]
A car goes 15 miles on a gallon of gas when it is driven at 50 miles per hour. When the car is driven at 60 miles per hour it only goes 80% as far. How many gallons of gas will it take to travel 120 miles driving at 60 miles per hour?
Answer:
2 gallons per mile
Miles plans on leasing a new car and has been researching options from different dealerships. For the particular model he wants, Miles compiled the information from two dealerships in the table below.
Dealerships\ Downpayment \monthly lease rate
Cool cars/ 1,999. $ 179
Awesome autos/ $ 0/ $249
Create a system of linear equations that describes the total amount, y, paid towards the lease after x months. Write the slope-intercept form of the equation for cool cars followed by the slope-intercept form of the equation for awesome autos. Do not include dollar signs in the equations.
Answer:
y = 179x +1999
y = 249x
Step-by-step explanation:
Given:
down payment of cool cars= $1999
monthly lease rate of cool cars= $179
down payment of awesome autos= $0
monthly lease rate of awesome autos= $249
Number of months=x
total amount paid towards the lease after x months=y
Now creating a system of linear equations that describes the total amount, y, paid towards the lease after x months:
the slope intercept form of any linear function is given as y=mx +b
where m= slope of function and b=y-intercept
In given case, slope m gives the monthly lease rate and y-intercept b gives the down payment.
So the equations for the two linear functions will be:
cool cars:
Putting the values of m=179 and b=1999, we get
y = 179x +1999
awesome autos:
Putting the values of m=249 and b=0, we get
y = 249x !
how is 5.76 written in words
C. 5 and seventy-six hundredths sorry If I'm wrong, but I'm pretty sure I'm right
please rate my answer
Answer:
Five and seventy six hundredths
Your Welcome :3
A cooler contains 7 cans of lemonade, 4 cans of apple juice, and 9 cans of iced tea.
Without looking, Alina selects a can, hands it to her friend, and then selects another can.
What is the probability that Alina selected 2 cans of lemonade?
Enter your answer in the box. Round to the nearest tenth of a percent.
Answer:
What you have to do is add all of the sums up and put 2 over it. it is 2/20 which is 1/10.
Step-by-step explanation:
in a percent it is 0.1
Can I get brainiest
The probability that Alina selects 2 cans of lemonade is
How to calculate probability?
The given question has concept of conditional probability.
Conditional probability is applied when we have to find the possibility of an event given the another event already occurred.
Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.
Here, the first event is selecting the lemonade can and second event is also selecting lemonade can given one lemonade is already selected.
The probability to select 1st lemonade= 7/20
The probability to select 2nd lemonade=6/19
Multiplying them we get:
Probability:7*6/20*19=21/190
Therefore, the probability to select two lemonades is 21/190.
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what are the roots of the equation? 3x^2+15x=0
The solution of quadratic equation [tex]3x^2 + 15x=0[/tex] is x =0 or -5.
Given Equation: [tex]3x^2 + 15x=0[/tex]
Now, factories each term as
3x² = 3 × x × x
15x = 3 × 5 × x
Now, taking the common term 3x as
[tex]3x^2 + 15x=0[/tex]
3 × x × x+ 3 × 5 × x =0
3x (x + 5)= 0
Now, equate each factor to 0 as
3x =0
x= 0/3
x= 0
or, x + 5= 0
x = -5
Thus, the value of x is -5 or 0.
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Vicky's checking account charges a $12.25 monthly service fee and a $0.26
per-check fee. If Vicky writes 16 checks per month, should she switch to a checking account that charges a $16.50 monthly service fee and no per-check fee?
Answer:
No
Step-by-step explanation:
0.26*16 + 12.25 = 16.41
16.41 < 16.50
Answer:
No, Vicky should not switch.
Step-by-step explanation:
Vicky's checking account charges a monthly service fee = $12.25
Account also charges per-check fee = $0.26
Vicky writes checks per month = 16
His total monthly charges = 12.25+( 16 ×0.26 )
= 12.25 + 4.16
= $16.41
Another account that charges a $16.50 monthly service fee and no per-check fee.
Comparison between account = 16.50 > 16.41
So Vicky should not switch to another account because it charges more than her current account.
Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial.
x - 3; 2x^2 - 4x + 30
Answer:
Not a factor
Step-by-step explanation:
If (x - 3) is a factor then f(3) = 0
f(x) = x² - 4x + 30
f(3) = 2(3)² - 4(3) + 30 = 18 - 12 + 30 = 36 ≠ 0
Since f(3) ≠ 0 then (x - 3) is not a factor of f(x)
( x - 3 ) is not a factor of the polynomial 2x² - 4x + 30
What is Factor Theorem?
The Factor Theorem states that if f(x) is a polynomial of degree n greater than or equal to 1, and 'a' is any real number, then ( x - a ) is a factor of f ( x ) if f ( a ) = 0
Given data ,
f ( x ) = 2x² - 4x + 30
If ( x - 3 ) is a factor of f ( x ) , then by factor theorem f ( x ) = f ( 3 ) = 0
And , f ( 3 ) = 2 x 3 x 3 - 4 x 3 + 30
= 18 - 12 + 30
= 36
Therefore , f ( 3 ) ≠ 0 , so ( x - 3 ) is not a factor of 2x² - 4x + 30
Hence , ( x - 3 ) is not a factor of the polynomial 2x² - 4x + 30
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Find a segment length indicated. Assume that lines which appear to be tangent are tangent.
Answer:
17.872, 8
Step-by-step explanation:
Chords that pass through the center are the diameter, and lines that are tangent to the circle are perpendicular to the diameter at that point.
Therefore, what we are looking at are right triangles, and we can find the distance using Pythagorean theorem.
c² = a² + b²
(19.5)² = (7.8)² + b²
b ≈ 17.872
c² = a² + b²
(10)² = (6)² + b²
b = 8
A triangle has a perimeter of 56 cm. Each of the two longer sides of the triangle is three times as long as the shortest side. What is the length of each side of the triangle?
The lenght of each side is 24cm, 24cm, and 8cm.
In order to solve this problem, we know that the perimeter of a triangle equation is P = a + b + c, where a, b, and c are the sides of the triangle.
The perimeter is 56cm, we can write the equation as follow:
a + b + c = 56cm (1)
If each of the two longer sides of the triangles is three times as long as the shortest side, we can assume:
c = shortest side = x
a = b = longer sides = 3x
Substituting the values in the equation (1):
3x + 3x + x = 56cm
7x = 56cm
x = 56cm/7 = 8cm
c = shortest side = 8cm
a = b = longer sides = 3(8cm) = 24cm
24. Solve for x and y.
Answer:
x = 10√3 and y = 10Step-by-step explanation:
We have the triangle 30° - 60° - 90°. The sides are in ratio 1 : √3 : 2.
(look at the picture).
We have 2a = 20. Therefore a = y = 20 : 2 = 10 and a√3 = x = 10√3
select the correct statement about the function represented by the table.
The correct statement about the function represented by the table is:
D. It is a linear function because the y-value increase by an equal difference over equal intervals of x-values.
Step-by-step explanation:The table of values are given as follows:
x y
1 26
2 44
3 62
4 80
5 98
We know that the function is said to be linear if the rate of change is constant.Here with the x-value is increasing by each 1.
Hence, we will check whether the difference in y-value is equal or not.
( Since, the rate of change is the ratio of the change in y-value to the change in x-value)
Hence,
44-26=18
62-44=18
80-62=18
and 98-80=18
Hence, we get that the change in y-value is equal .
Hence, we get that the slope or rate of change of the function is constant.
Hence, the function is linear.
Find the value of x.
pls help! tysm
Answer:
x = 30.
Step-by-step explanation:
The angle next to the 60 degree angle = 180 - 60 = 120 degrees (adjacent angles are supplementary).
Let the angle just above 3x be y. The sum of 3x and y = 120 degrees (as opposite angles of a parallelogram are equal).
We have the following equations.
3x + y = 120............(1)
2x + 90 + y = 180
2x + y = 90.............(2)
Subtracting, (1) - (2):
x = 30.
Write the equation for an exponential function, in the form y=a•b^x, whose graph passes through the coordinate points (1,7.5) and (3,16.875)
[tex]\bf (\stackrel{x}{1}~~,~~\stackrel{y}{7.5})\implies 7.5=ab^1\implies \boxed{7.5=ab} \\\\\\ (\stackrel{x}{3}~~,~~\stackrel{y}{16.875})\implies 16.875=ab^3\implies 16.875=ab^{1+2}\implies 16.875=abb^2 \\\\\\ 16.875=\boxed{7.5}b^2\implies \cfrac{16.875}{7.5}=b^2\implies 2.25=b^2 \\\\\\ \sqrt{2.25}=b\implies \blacktriangleright 1.5=b \blacktriangleleft \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf 7.5=ab\implies \cfrac{7.5}{b}=a\implies \cfrac{7.5}{1.5}=a\implies \blacktriangleright 5=a \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=5(1.5)^x~\hfill[/tex]
Can someone please help me
Answer:
11.2
Step-by-step explanation:
Calculate the length using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = B(4, 7) and (x₂, y₂ ) = C(2, - 4)
d = [tex]\sqrt{(2-4)^2+(-4-7)^2}[/tex]
= [tex]\sqrt{(-2)^2+(-11)^2}[/tex]
= [tex]\sqrt{4+121}[/tex]
= [tex]\sqrt{125}[/tex] ≈ 11.2
ASAP WILL GIVE BRAINLY
A card was selected at random from a standard deck of cards. The suit of the card was recorded, and then the card was put back in the deck. The table shows the results after 40 trials.What is the relative frequency of selecting a heart? 15% 25% 27% 35% outcome 8 12 14 6
Answer:
Step-by-step explanation:
C.35%
If you divide the number of hearts drawn by the number of total draws you get your answer.
14/20=0.35
Can you please help and need the work to show how you go it.
Answer:
Point Q is (3 , 4)
Step-by-step explanation:
* Lets revise the rule of the point which divides of a line segment in
a ratio
- If point (x , y) divides the line segment AB, where A is (x1 , y1) and
B is (x2 , y2) in the ratio m1 : m2
∴ x = [m2(x1) + m1(x2)]/(m1 + m2)
∴ y = [m2(y1) + m1(y2)]/(m1 + m2)
* Now lets solve the problem
- Point Q divides ST in the ratio 5 : 2 where S (-2 , -6) and T (5 , 8)
- To find the coordinates of point Q use the same rule above
# Q is (x , y)
# S is (x1 , y1) and T is (x2 , y2)
# m1 : m2 is 5 : 2
∵ x1 = -2 and y1 = -6
∵ x2 = 5 and y2 = 8
∵ m1 = 5 and m2 = 2
- Substitute these values in the rule
∵ x = [m2(x1) + m1(x2)]/(m1 + m2)
∴ x = [2(-2) + 5(5)]/(5 + 2) ⇒ multiply the numbers
∴ x = [-4 + 25]/7 ⇒ add
∴ x = [21]/7 ⇒ Divide
∴ x = 3
* The x-coordinate of Q is 3
∵ y = [m2(y1) + m1(y2)]/(m1 + m2)
∴ y = [2(-6) + 5(8)]/(5 + 2) ⇒ multiply the numbers
∴ y = [-12 + 40]/7 ⇒ add
∴ y = [28]/7 ⇒ Divide
∴ y = 4
* The y-coordinate of point Q is 4
∴ Point Q is (3 , 4)
The table below shows the number of tickets sold, t, at a high school basketball game, and the amount of money collected, m.
Tickets Sold (t) Money Collected (m)
25 $62.50
35 $87.50
40 $100
Which equation will calculate the amount of money collected after t tickets are sold?
Answer:
t x 2.5 =m
Step-by-step explanation:
Find the distance between the points given. (0, 5) and (-5, 0) 5 5√2 10
Answer:
5√2
Step-by-step explanation:
The question is on geometry
The formula for distance between two points is;
[tex]d= \sqrt{(X2-X1)^2 + (Y2-Y1)^2}[/tex]
where d is distance.
Given points;
(0,5) and (-5,0) ;
X1=0 ,X2= -5 , Y1= 5, Y2= 0
X2-X1 = -5 - 0= -5
Y2-Y1= 0-5= -5
[tex]d= \sqrt{(-5)^2 + (-5)^2}[/tex]
[tex]d=\sqrt{25+25}[/tex]
[tex]d=\sqrt{50}[/tex]
[tex]d=\sqrt{2*25} =\sqrt{2} *\sqrt{25} =\sqrt{2} *5\\\\\\\\d=5\sqrt{2}[/tex]
Answer:
[tex]d=5\sqrt{2}[/tex]
Step-by-step explanation:
Given : (0, 5) and (-5, 0)
To Find : Distance between the given points
Solution:
We will use distance formula :
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex](x_1,y_1)=(0,5)[/tex]
[tex](x_2,y_2)=(-5,0)[/tex]
Substitute the values in the formula .
[tex]d=\sqrt{(-5-0)^2+(0-5)^2}[/tex]
[tex]d=\sqrt{(-5)^2+(-5)^2}[/tex]
[tex]d=\sqrt{25+25}[/tex]
[tex]d=\sqrt{50}[/tex]
[tex]d=5\sqrt{2}[/tex]
Hence the distance between the given points is 5√2 units
What’s the largest?
823 ppm
378 ppm
2.4 meters
Answer:
Step-by-step explanation:
I think its 823 ppm?
I'm not sure
A moving truck rental company charges $35.95 to rent a truck, plus $0.98 per mile. Suppose the function C(d) gives the total cost of renting the truck for one day if you drive 24 miles.
Give the total rental cost if you drive the truck 24 miles. Give the function notation in the first box, the answer in the second box, and choose the correct units from the third box.
Answer:
0.98x24=23.52+35.95=59.47 hope im right
Step-by-step explanation:
The total cost of renting the truck for one day if you drive 24 miles is $58.47.
Explanation:The function notation for the total cost of renting the truck for one day if you drive 24 miles is C(24). The total rental cost can be calculated by multiplying the cost per mile ($0.98) by the number of miles driven (24) and adding the base cost ($35.95). So, the total rental cost would be $35.95 + ($0.98 x 24) = $58.47.
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If the area of a square is 64 inches squared.what is the length of one side
Answer:
8 in
Step-by-step explanation:
Area of a square is given by
A = s^2 where s is the side length
64 in^2 = s^2
Taking the square root of each side
sqrt(64 in^2) = sqrt(s^2)
8 in =s
Answer:
8 inStep-by-step explanation:
The formula of an area of a square:
[tex]A=s^2[/tex]
s - side length
We have the area
[tex]A=64\ in^2[/tex]
Substitute:
[tex]s^2=64\to s=\sqrt{64}\\\\s=8\ in[/tex]
[tex]\sqrt{64}=8[/tex] because [tex]8^2=64[/tex]
The angles of a pentagon are x, x − 5 0 , x + 100 , 2x + 150and 2x + 300 . Find all the angles.
Answer:
The interior angles are 70°,65°,80°,155° and 170°
Step-by-step explanation:
step 1
Find the sum of the interior angles of the pentagon
The sum is equal to
S=(n-2)*180°
where
n is the number of sides of polygon
n=5 (pentagon)
substitute
S=(5-2)*180°=540°
step 2
Find the value of x
Sum the given angles and equate to 540
x+(x-5)+(x+10)+(2x+15)+(2x+30)=540°
7x+50=540°
7x=490°
x=70°
step 3
Find all the angles
x=70°
(x-5)=(70-5)=65°
(x+10)=(70+10)=80°
(2x+15)=(2*70+15)=155°
(2x+30)=(2*70+30)=170°
What is the slope?
(1,4) (3,2)
For this case we have that by definition, the slope of a line is given by:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
We need two points through which the line passes.
[tex](x_ {1}, y_ {1}) :( 1,4)\\(x_ {2}, y_ {2}) :( 3,2)[/tex]
Substituting:
[tex]m = \frac {2-4} {3-1} = \frac {-2} {2} = - 1[/tex]
Answer:
[tex]m = -1[/tex]
Simplify each of the following powers of i. i^32
Answer:
the answer is 1. the trick here is to divide the exponent to 4.
Step-by-step explanation:
i^32 32÷4=8
i
-1
-i
1
Answer: The required value of the given power of i is 1.
Step-by-step explanation: We are given to simplify the following power of i :
[tex]P=i^{32}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
the value of the imaginary number i(iota) is given by
[tex]i=\sqrt{-1}~~~~~\Rightarrow i^2=-1.[/tex]
From expression (i), we get
[tex]P\\\\=i^{32}\\\\=(i^2)^{16}\\\\=(-1)^{16}\\\\=(1)^8\\\\=1.[/tex]
Thus, the required value of the given power of i is 1.
The length of a room is 22feet by 12 feet. What is the ratio of the length of the room to its area ?
The ratio of the room's length to its area is 1:12, derived from length (22 feet) divided by area (264 square feet).
let's break it down step by step.
Step 1: Calculate the area of the room.
To find the area of a rectangle, you multiply its length by its width.
So, Area = Length × Width
Area = 22 feet × 12 feet
Area = 264 square feet
Step 2: Calculate the ratio of the length of the room to its area.
The ratio of length to area is:
[tex]\[ \text{Ratio} = \frac{\text{Length}}{\text{Area}} \][/tex]
Substituting the values:
[tex]\[ \text{Ratio} = \frac{22 \, \text{feet}}{264 \, \text{square feet}} \][/tex]
Step 3: Simplify the ratio.
[tex]\[ \text{Ratio} = \frac{22}{264} \][/tex]
Step 4: Simplify the fraction.
[tex]\[ \text{Ratio} = \frac{1}{12} \][/tex]
So, the ratio of the length of the room to its area is [tex]\( \frac{1}{12} \)[/tex].
Which is the same function as -3x + 7 = y?
a)f(x) = -3x + 7
b)f(-3x) = 7
c)f(7) = -3x
d)f(x) = -3 + 7
Answer:
A) f(x) = -3x+7
Step-by-step explanation:
f(x) is interchangeable with y when writing a function, so the functions are the same.
The function that corresponds to the equation -3x + 7 = y is f(x) = -3x + 7, which maintains the same relationship between x and y as the given equation.
Explanation:The equation -3x + 7 = y can be rewritten in function notation, which typically uses the format f(x) = some expression involving x. The correct corresponding function is one that maintains the relationship between x and y as displayed in the original equation. Therefore, among the options provided:
a) f(x) = -3x + 7 is the correct answer because it is exactly the original equation -3x + 7 = y written in function notation.b) f(-3x) = 7 incorrectly suggests that -3x is the variable and not just x.c) f(7) = -3x suggests that 7 is the variable, which is incorrect.d) f(x) = -3 + 7 is simply the sum of two numbers and does not involve the variable x in a way that matches the original equation.The correct answer indicates that the function of x (f(x)) is given by the linear equation -3x + 7.
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Look at the following sequence. 21, 42, 126, 504, If it is geometric sequence, choose the common ratio. If it is not geometric sequence, choose “ not geometric “
Answer:
not geometric
Step-by-step explanation:
If the sequence is geometric then the common ratio r between consecutive terms should be equal
[tex]\frac{42}{21}[/tex] = 2
[tex]\frac{126}{42}[/tex] = 3
[tex]\frac{504}{126}[/tex] = 4
There is no common ratio between consecutive terms
Hence the sequence is not geometric