Complete the square to write each equation in vertex form. Then, state whether the vertex is a minimum or a maximum and give its coordinates.
Answer:
vertex form: y = (x + 3)² + 1 the vertex is minimum coordinates of the vertex: (-3, 1)Step-by-step explanation:
[tex]y=x^2+6x+10\\\\y=x^2+6x+9-9+10\\\\\bold{y=(x+3)^2+1}[/tex]
a = 1 > 0 ← it means the parabla opens up, so, the vertex is minimum
The vertex form is y = a(x - h)² + k, where (h, k) is the vertex
So, from y = (x + 3)² + 1 the vertex is: (-3, 1)
If a supermarket sells 5 bags of grapes for Rs. 16.60, what is the unit price of a bag of grapes?
A. 3.32
B. 4.32
C. 5.32
D. 2.32
Answer:
It's A
Step-by-step explanation:
Surface Area of Composite Figure
Solve for d: c=πd what is the answer
Answer:c/π=d
Step-by-step explanation: the d and π was multiply with the d and if we want separate with it, we need to use the opposite way to get it.
OMG PLEASE HELP FAST, Write the equation of the line in fully simplified slope-intercept form.
The equation of the line in the attached graph in slope intercept form is written as
y = -6x + 2How to write the equation of the lineThe slope, m of the linear function is calculated using the points on the graph (1, -4) and (2, -10)
m = (y₀ - y₁) / (x₀ - x₁)
plugging in the values and evaluating
m = (-10 + 4) / (2 - 1)
m = (-6) / (1)
m = -6
equation passing through point (2, -10), using the point slope formula
(y - y₁) = m (x - x₁)
y - (-10) = -6(x - 2)
y + 10 = -6x + 12
rearranging the equation
y = -6x + 12 - 10
y = -6x + 2
The equation of the line in slope intercept form is written as y = -6x + 2
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The lines given by the equations y = 2x and y = 2x + 1 are
A. parallel
B. perpendicular
C. neither perpendicular nor parallel
Answer:
A. parallel
Step-by-step explanation:
when the slopes are the same it's parallel
when slopes are multiplied and they equal -1 it's perpendicular
helppppppppppppppppp
Answer:
The common difference is 6
Step-by-step explanation:
14 - 6 = 8
8 - 6 = 2
Mr. Spears was purchasing supplies for his math classroom. He had $25 to spend. Mechanical pencils and erasers come in bundles of 10. Each eraser costs $0.50. Fill in the missing place in the equation to compute the cost of each mechanical pencil.
x+y=10 and ax+0.50y=25 are the system of equations to compute the cost of each mechanical pencil.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Mr. Spears was purchasing supplies for his math classroom.
He had $25 to spend.
Mechanical pencils and erasers come in bundles of 10
Let x represents the Mechanical pencils
y represents the erasers
x+y=10
y=10-x
Each eraser costs $0.50
ax+0.50y=25
a is the cost of the each mechanical pencil.
Hence, x+y=10 and ax+0.50y=25 are the system of equations to compute the cost of each mechanical pencil.
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Before taking his last test in a class, the arithmetic mean of Brian's test scores is 91. He has determined that if he scores 98 on his last test, the arithmetic mean of all his test scores will be exactly 92. How many tests, including the last test, does Brian take for this class
On solving the provided question, we can say that the mean that 6 tests including the last test brian took.
What is mean?A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency. Simply dividing the dataset's total number of values by the sum of all of those values yields this result. Both raw data and data that have been combined into frequency tables can be used for calculations. Average refers to a number's average. It is straightforward to calculate: Divide by how many digits there are after adding up all the digits. the total divided by the count.
(91n + 98) / (n + 1) = 92
91n + 98 = 92(n + 1)
91n + 98 = 92n + 92
98 = n + 92
6 = n
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Can someone please help me with this algebra
Find the EXACT values of ALL SIX trigonometric functions of θ(sin, cos, tan, cot, sec, csc) from the information given. (a) cosθ=7/12, sinθ<0 (b) tanθ=4/3, θ in Quadrant III
(a) Since cosθ = 7/12 and sinθ < 0, we can find the other four trigonometric functions as follows:
sinθ = √(1 - cos²θ) = √(1 - (7/12)²) = √(1 - 49/144) = -√(95/144)
tanθ = sinθ / cosθ = (-√(95/144)) / (7/12) = -4√(5/18)
cotθ = 1 / tanθ = -1 / (-4√(5/18)) = 1/(4√(5/18))
secθ = 1 / cosθ = 1 / (7/12) = 12/7
cscθ = 1 / sinθ = -1 / (-√(95/144)) = √(95/144)
(b) Since tanθ = 4/3 and θ is in Quadrant III, we can find the other five trigonometric functions as follows:
cosθ = √(1 / (tan²θ + 1)) = √(1 / (16/9 + 1)) = √(9 / 25) = 3/5
sinθ = cosθ * tanθ = (3/5) * (4/3) = 4/5
cotθ = 1 / tanθ = 1 / (4/3) = 3/4
secθ = 1 / cosθ = 1 / (3/5) = 5/3
cscθ = 1 / sinθ = 1 / (4/5) = 5/4
What is trigonometric functions?Trigonometric functions are a set of functions that relate the angles of a right triangle to the ratios of the sides of the triangle. The six most commonly used trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).
The sine function, represented by sin, gives the ratio of the side opposite the angle to the hypotenuse. The cosine function, represented by cos, gives the ratio of the adjacent side to the hypotenuse. The tangent function, represented by tan, gives the ratio of the opposite side to the adjacent side.
The cotangent function, represented by cot, gives the ratio of the adjacent side to the opposite side. The secant function, represented by sec, gives the ratio of the hypotenuse to the adjacent side, and the cosecant function, represented by csc, gives the ratio of the hypotenuse to the opposite side.
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Find the volume of the sphere with 1 inch radius. Round your answer to the nearest tenth. Use 3.14 for Pi.
The volume of the sphere is about______in³.
Answer:
4.16 in^3
Step-by-step explanation:
Given data
Volume of sphere= 4/3πr^3
Radius= 1 inch radius
Substitute
Volume of sphere= 4/3*3.14*1^3
Volume of sphere= 4/3*3.14*1
Volume of sphere= 4*1.04
Volume of sphere= 4.16 in^3
Which quadratic function is represented by the graph?
f(x) = 0.5(x + 3)(x − 1)
f(x) = 0.5(x − 3)(x + 1)
f(x) = 2(x + 3)(x − 1)
f(x) = 2 (x − 3)(x + 1)
Answer:
f(x) = 0.5(x + 3)(x − 1)----------------------------------
hope it helps..
have a great day!!
Answer:
[tex]f(x) = 0.5(x+3)(x-1)[/tex]
Step-by-step explanation:
GIVEN :-
A quadratic function is represented by the graph in which :-
Vertex of the parabola = (-1 , -2)The function intersects x-axis at (-3 , 0) and (1 , 0)Y-intercept of the function = -1.5TO FIND :-
The quadratic functionGENERAL CONCEPT USED IN THIS QUESTION :-
A quadratic function has 2 forms :-
General form → f(x) = ax² + bx + cStandard form → f(x) = a(x - h)² + k [∵ where h = x-coordinate of the vertex of the function & k = y-coordinate of the vertex of the function.]SOLUTION :-
The quadratic function in the graph intersects x-axis at two points (-3 , 0) & (1 , 0). But there are infinite parabolas which also intersect the same two points. And those parabolas have their unique quadratic function.
Method 1 (System of equations method) -To find the unique quadratic function , you need to use three points on the
curve so that you can form 3 equations & solve them.
Using the General form of quadratic function , substitute the known values for x & y.
Let the three points be -
(-3 , 0)(1 , 0)(0 , -1.5)Substitute (-3 , 0) in general form of function -
[tex]0 = a(-3)^2 + b(-3) + c[/tex]
[tex]=> 9a-3b+c = 0[/tex] (eqn.1)
Substitute (1 , 0) in general form of function -
[tex]0 = a(1)^2 + b(1) + c[/tex]
[tex]=> a + b +c =0[/tex] (eqn.2)
Substitute (0 , -1.5) in general form of function -
[tex]-1.5 = a(0)^2 + b(0) + c[/tex]
[tex]=> c = -1.5[/tex]
Substitute c = -1.5 in -
1) eqn.1 → [tex]9a - 3b - 1.5 = 0[/tex]
[tex]=> 9a - 3b = 1.5[/tex]
[tex]=> 3(3a-b) = 1.5[/tex]
[tex]=> 3a-b = 0.5[/tex] (eqn.4)
2) eqn.2 → [tex]a+b-1.5=0[/tex]
[tex]=> a+b=1.5[/tex] (eqn.5)
Add eqn.4 & eqn.5 to get the value of 'a'.
[tex](3a-b)+(a+b) = 0.5+1.5[/tex]
[tex]=> 4a = 2[/tex]
[tex]=> a = \frac{2}{4} = \frac{1}{2} = 0.5[/tex]
Substitute a = 0.5 in eqn.5 -
[tex]0.5 + b = 1.5[/tex]
[tex]=> b = 1.5 - 0.5 = 1[/tex]
Now, rewrite the function in general form by putting the values of 'a' , 'b' & 'c'.
[tex]f(x) = (0.5)x^2 + (1)x - 1.5[/tex]
[tex]=> f(x) = 0.5(x^2 + 2x - 3)[/tex]
Factorise the quadratic polynomial.
[tex]=> f(x) = 0.5(x^2 + 3x - x - 3)[/tex]
[tex]=> f(x) = 0.5[x(x+3)-1(x+3)][/tex]
∴ [tex]f(x) = 0.5(x+3)(x-1)[/tex]
Method 2 (Vertex method) -Another way to find the function is by taking any point on the curve & using the vertex of the parabola ; substitute the known values for x , y , h & k in the Standard form of the function.
Let that point on the curve be (-3 , 0)
Vertex = (-1 , -2)
Substitute the values of x , y , h & k in Standard form of function.
[tex]0 = a[-3 - (-1)]^2 + (-2)[/tex]
[tex]=> 0 = 4a-2[/tex]
[tex]=> 4a = 2[/tex]
[tex]=> a = \frac{2}{4} = 0.5[/tex]
Now rewrite the Standard form of the function by putting the values of h , k & a.
[tex]f(x) = 0.5(x+1)^2-2[/tex]
Expand it.
[tex]=> f(x) = 0.5(x^2+2x+1)-2[/tex]
[tex]=> f(x) = 0.5x^2+x+0.5-2[/tex]
[tex]=>f(x) = 0.5x^2 + x- 1.5[/tex]
[tex]=>f(x) = 0.5(x^2 + 2x - 3)[/tex]
Factorising it will give the final answer.
∴ [tex]f(x) = 0.5(x+3)(x-1)[/tex]
Given csc0=178, determine the values for "a" and "b" in cos0=ab
The value of a and b are respectively 15 and 17 respectively.
What are trigonometry ratios?
The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
Given that csc θ = 17/8 and cos θ = a/b.
The reciprocal of sin θ is csc θ.
Therefore,
1/sinθ = 17/8
or, sin θ = 8 /17
Applying the trigonometry identity cos²θ = 1- sin²θ
cos²θ = 1- (8/17)²
cos²θ = 1- 64/289
cos²θ = 225/289
cos θ = 15/17
The value of a is 15 and the value of b is 17.
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In the adjoining figure, the area of the rectangular surfaces of the prism is 720 sq. Cm, XX' 20 cm and XY : XZ: YZ = 5:3 : 4, find the length of XY
The length of XY, with the area of the rectangular surface of the prism 720 sq.cm, XX' 20 cm and XY : XZ: YZ = 5:3:4, is 12 cm.
Area of the rectangular surface of the prism = 720 sq. cm
XX' = 20 cm
XY : XZ: YZ = 5:3:4
As we know, area of prism = 3 × area of rectangle
⇒720 = 3 × area of rectangle
⇒area of rectangle = 720/3
⇒XY × XX' = 240
⇒XY × 20 = 240
⇒XY = 240/20
⇒XY = 12 cm
Thus, the length of the XY is 12 cm.
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Look down below for the question
Answer:
1.centre
2.chord
3.chord
4.radius
5.diameter
BRAINLY ME PLEASE IF HELPFUL!!!
If m= 2, n=3, and p= -1, then find the value of : 2mn4 – 15m2n + p
In Full Details!! As Soon As Possible
Answer:
-131
Step-by-step explanation:
2×2×3×4-15×2×2×3+-1
48-179
=-131
Which quotient does not belong with the other three? Explain your reasoning.
Answer:
The third from the top does not belong with the others.
Step-by-step explanation:
With the exception of the 3rd quotient, the expressions all involve powers of the same base. There is an exponent property that can be used in such a situation:
[tex]\frac{a^m}{a^n}=a^{m-n}[/tex]
but the base, a, must be the same in both parts of the quotient!
Solve x^2+2x>15 algebraically and graphically, brainliest to the best detailed answer, including the steps.
The algebraic solutions are x < -5 and x > 3.
The graph is given below.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
x² + 2x > 15
x² + 2x - 15 > 0
x² + (5 - 3)x - 15 > 0
x² + 5x - 3x - 15 > 0
x(x + 5) - 3(x + 5) > 0
(x - 3)(x + 5) > 0
x + 5 > 0 and x - 3 > 0
x < -5 and x > 3
The graph is given below.
Thus,
x < -5 and x > 3 is the solution.
The graph is given below.
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Can you help me with this
Answer: 1/4
Step-by-step explanation:
Method 1
this method only works when there is a visual graph, but you can oick 2 points. then go to the point farthest to the left ide of the graph. then count up to be on the same y coordinate as the other point. then count over to be on the same x point, hence 1/4 (up 1 over 4)
Method 2
You can also pick 2 points, and put them into this formula to find slope ([tex]\frac{x2-x1}{y2-y1} }[/tex] then you plug in so the point farthest left would be x1 and y1 and the other point would be y1 and y2 so when you plug in and solve you get 1/4
Answer:
Step-by-step explanation:
rise/run
=1/4
Help im stuck Please help
Answer:
x = 6
Step-by-step explanation:
The three angles form a straight line, which is 180 degrees
5x+ (x+54) +90= 180
Combine like terms
6x+144 = 180
Subtract 144 from each side
6x+144-144 =180-144
6x =36
Divide each side by 6
6x/6 = 36/6
x = 6
James purchased a gaming computer for $2,499. He anticipates each year it will decrease in value by 7.9% from the previous year. Write an exponential function that models the value in dollars of the computer x years after James's purchase.
Answer:
f(x)=2499(0.079)
Step-by-step explanation:
What is a algebraic expression for 1,10,19
The algebraic expression for the sequence 1, 10, 19, is given as a(n) = 1 + (n-1) 9.
What is algebraic expression?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression.
For the given sequence the common difference between two consecutive terms is 19 - 10 = 9.
The general form of the nth term of an arithmetic sequence is given as:
a(n) = a + (n-1) d
Since, the value of a = 1 and the common difference d =9, the resulting expression is:
a(n) = 1 + (n - 1) 9
Hence, the algebraic expression for the given sequence is a(n) = 1 + (n - 1) 9.
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HELP DUE IN 10 MINS!
Given that QUAD is a rectangle, find the values of the variables.
1. x = ?? degrees
2. ° y =?? degrees
3. ° z =?? degrees
Answer:
x= 55°
y=70°
z= 35°
Step-by-step explanation:
.................
Answer:
x = 45°
y = 70°
z = 25°
Hope this helps!
What is the inverse of the logarithmic function f x log9x?
The inverse of the logarithmic function f x log9x is f-1(x)=9^x.
The inverse of a logarithmic function is the exponential function. To find the inverse of the logarithmic function f x log9x, we can use the following equation: f-1(x)=9^x. This equation states that the inverse of the logarithmic function f x log9x is the exponential function f-1(x)=9^x.
The inverse of the logarithmic function f x log9x is f-1(x)=9^x, which is the exponential function.This means that for any value of x, the inverse of the logarithmic function f x log9x is equal to 9 raised to the power of x. For example, if x=2, then the inverse of the logarithmic function f x log9x is 9^2, or 81. Similarly, if x=3, then the inverse of the logarithmic function f x log9x is 9^3, or 729. In general, the inverse of the logarithmic function f x log9x is 9 raised to the power of x, for any value of x.
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Answer: f –1(x) = 9x
Step-by-step explanation:
Find a polynomial which when added to the polynomial 3x^2+3x-1, is equaivelant to the following expressions: 1
The polynomials which, when added to the polynomial 3x²+3x-1, is equivalent to the following expressions: 1, 2x²-3, and x+5 include the following below:
P = 2 - 3x² -3x.P = -2 -x² -3xP = 6 -2x -3x².What is a Polynomial?This is referred to as algebraic expressions that consist of variables and coefficients.
For 1; it is calculated as:
3x²+3x-1 + P = 1.
P = 2 - 3x² -3x.
For 2x²-3, it is calculated as:
3x²+3x-1 + P = 2x²-3
P = -2 -x² -3x
For x +5; it is calculated as:
3x²+3x-1 + P = x +5
P = 6 -2x -3x².
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The full question is:
Find a polynomial which, when added to the polynomial 3x^2+3x-1, is equivalent to the following expressions: 1, 2x^2-3, and x+5
what is 2x=16 i to explan it
Answer:
2x=16
/2 /2
x=8
Step-by-step explanation:
just need to isolate the x, by dividing by two on both sides.
hope this helps :)
Answer:
x=8
Step-by-step explanation:
2x=16
Isolate the variable by diving by 2 on both sides
2x=16
÷2 ÷2
so, x=8
That, given an array a of n integers, returns the smallest positive integer (greater than 0) that does not occur in a. For example, given a = [1, 3, 6, 4, 1, 2], the function should return 5
There is one way to implement a function in Python that takes in an array of integers and returns the smallest positive integer that does not occur in the array.
def smallest_missing_positive(a):
#Create a set to store the unique elements in the array
unique_set = set(a)
#Iterate through the positive integers starting from 1
for i in range(1, len(a) + 2):
#If the current integer is not in the set, return it
if i not in unique_set:
return i
This function first converts the input array into a set, which removes any duplicate elements. It then iterates through the positive integers starting from 1 up to the length of the array plus 2. For each integer, it checks whether it is in the set of unique elements from the input array. If it is not, the function returns that integer as it is the smallest positive integer that does not occur in the array.
For example, when the function is called with the input array [1, 3, 6, 4, 1, 2], it will return 5 as it is the first missing positive number.
You can also use a set and difference() method of set to check the missing elements from 1 to maximum element of array+1 and find the missing first one, this method is more efficient than the above one when the array is large.
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choose vertical or adjacent to tell how each pair of angles is related
Answer:
1 and 2 is adjacent. 1 and 3 are vertical. 3 and 4 are adjacent. 2 and 4 are vertical angles.
Angles ∠1 and ∠2 as well as angles ∠3 and ∠4 are linear and supplementary angles. And angles ∠2 and ∠4 as well as ∠1 and ∠3 are vertically opposite angles.
What is an angle?Angle is the space between the line or the surface that meets. And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Vertically opposite angle - When two lines intersect, then their opposite angles are equal.
Linear angle - If the total of two angles is 180 degrees, they are said to be linear angles.
Angles ∠1 and ∠2 are linear and supplementary angles.
Angles ∠1 and ∠3 are vertically opposite angles.
Angles ∠3 and ∠4 are linear and supplementary angles.
Angles ∠2 and ∠4 are vertically opposite angles.
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Solve the word problem using the RDW strategy. Show all of your work in your journal. Cheryl bought a sandwich for 5 1/2 dollars and a drink for $2. 60. If she paid for her meal with a $10 bill, how much money did she have left? Select the answer as a fraction and in dollars and cents. *
The amount that Cheryl left with is $ 1.9 or 1 dollar and 90 cents.
RDW strategy:1. READ and reread the problem first
2. DRAW an image to illustrate the information. Ask your self Can I infer anything from this information during this step? What could I doodle? Which model will best convey the information? What inferences may I draw from the illustration?
3. WRITE the drawings as a basis for your conclusions. This can be expressed as a mathematical expression, an equation, or a statement.
Given that
Cheryl bought a sandwich for 5 1/2 dollars and a drink for $2. 60
Here 5 1/2 = 11/2 = 5.5 dollars
Then the total cost of the sandwich and drink = $ 5.5 + $ 2.60 = $ 8.1
Given that Cheryl gave $ 10
The amount that Cheryl left with = $ 10 - $ 8.1 = $ 1.9
Here is $ 1.9 = 1 dollar and 90 cents
Therefore,
The amount that Cheryl left with is $ 1.9 or 1 dollar and 90 cents.
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