Find the equation of the axis of symmetry for the parabola y = x² + 4x + 5. Simplify any numbers and write them as proper fractions, improper fractions, or integers.
the equation's squared variable is the "x", namely x², so we're looking at a vertical parabola, and thus its axis of symmetry will be a vertical line that runs through its vertex, so
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+4}x\stackrel{\stackrel{c}{\downarrow }}{+5} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\left(-\cfrac{ 4}{2(1)}~~~~ ,~~~~ 5-\cfrac{ (4)^2}{4(1)}\right) \implies \left( - \cfrac{ 4 }{ 2 }~~,~~5 - \cfrac{ 16 }{ 4 } \right)\implies (\stackrel{x}{-2}~~,~~1) \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{axis of symmetry}}{x=-2}~\hfill[/tex]
Check the picture below.
Ricky takes 2 coins at random from 3 quarters, 5 dimes, and two nickels in his pocket.
1) What is the P(nickel; then a quarter), with replacement
[tex]|\Omega|=10^2=100\\|A|=2\cdot3=6\\\\P(A)=\dfrac{6}{100}=6\%[/tex]
3 less than the square of a number
Answer:
n² -3
Step-by-step explanation:
The square of a number is found by multiplying it by itself. The square of a number in an algebraic expression is shown using an exponent of 2. For a number represented by n, the square of the number is n².
3 less than a number is found by subtracting 3 from the number. Equivalently, it is found by adding -3 to the number. The addition can be done in any order. For a number represented by n, 3 less than the number is either of ...
-3 +n
n -3
__
given expressionThe expression for "3 less than the square of a number" is ...
n² -3 . . . . . where n represents the number
It can also be written ...
-3 +n²
We generally prefer the first form, with variable exponents decreasing left-to-right.
Is this relation a function? Explain.
(-2, -1), (4, 2), (-8, -4), (6, 3)
Yes
Step-by-step explanation:Functions are relations that express a rule between the x-values and the y-values.
What Makes a Function
Functions are types of relations, specifically, where the x-values do not repeat. This means that each x-value has exactly one y-value. So, if the x-values do not repeat in a relation, then it must be a function.
How To Find a Function From Coordinates
In the question, we are given 4 different coordinate points. The points have 4 x-values, none of which repeat. This means that the relationship must be a function.
To find a function from points, all you need to do is check that the x-values do not repeat.
How To Find a Function From a Graph
If you are given a continuous graph, another way to figure out if it is the vertical line test. The vertical line test is when you draw vertical lines across the graph. If you are able to draw a vertical line everywhere on the graph without the line intersecting with the graph more than once, then it is a function. However, if the line intersects with the graph more than once at any point, then it is not a function.
Using the Vertical Line Test
Which graph does not represent a function?
Using the Vertical Line Test, the graph does not represent a function is ellipse, the third graph.
What is vertical line test?The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function. It is done by visually examining the number of intersections of the curve with vertical lines.
Any vertical line in the x y plane must intersect the graph of a function at most once.
In the given graphs, the graph of a function intersects the y axis twice. So, it is not a function.
From the given graphs, the third graph which is of ellipse crosses the vertical line twice.
Thus, the graph does not represent a function is ellipse.
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which ordered pair is a solution of y= 2x + 5?
Answer: (-2, 1)
Step-by-step explanation:
The 1st value in a pair is x, the 2nd is y.
▪︎ (-2, 1)
1 = 2(-2)+5
1 = -4+5
1 = 1 ✅
▪︎ (-1, 4)
4 = 2(-1)+5
4 = -2 + 5
4 = 3❌
▪︎ (1, 6)
6 = 2*1+5
6 = 2 + 5
6 = 7❌
▪︎ (3, 10)
10 = 2*3+5
10 = 6 + 5
10 = 11❌
help please i need answers fast if you help or try to help tysm *hearts*
Answer:
C. 3rd one Fraction 10/24
Step-by-step explanation:
3/4 - 2/6 = 0.41 or = 10/24 or it could be equal to 5/12 are 10/24, 15/36, 20/48 and 25/60 or as Decimal 0.41
Step-by-step explanation:
Hope This Helped
A bag contains 42 red, 45 green, 20 yellow, and 32 pirple candies. You pick one camdy at random. Find the probability that it is green.
Answer:
[tex]\text{P(green)} =\frac{45}{139}[/tex]
Step-by-step explanation:
The total number of candies is :
= 42+45+20+32
= 139
Then
we have 45 green out of 139 candies.
Then
[tex]\text{P(green)} =\frac{45}{139}[/tex]
Note : 45/139 is already simplified.
a circle has a circumference of 28 centimeters. if an arc subtends a central angle of 55 degrees, what is the arc length?
Arc length = 4.28 cm.
What is arc length?Arc length is the distance between two points along a section of a curve.
circumference of a circle of radius r is C = 2πr,
and central angle = 360 degrees.
circumference = 28 cm.
28 cm =2πr
28= 2*3.14*r
28= 6.28*r
r= 4.46 cm.
Arc length, s = r[tex]\theta[/tex]
[tex]\theta[/tex] =55 degrees,
s = 4.28 cm.
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Solve for x...........................................................
Answer:
x = 2 or -2
Step-by-step explanation:
This is a regular hexagon
To find the value of x we will have to find the sum of interior angles first and to do that:
(n-2)*180 (n is the number of angles)
(6-2)*180 = 720 is the sum of all six angles
since this is a regular hexagon, all angles has equal measures so
720/6 = 120 now
30x^2 = 120 divide both sides by 30
x^2 = 4 find the root of both sides
x = 2 or -2
Which of the following is most likely the next step in the series?
Answer:
C
Step-by-step explanation:
Option C is correct, the polygon in c option is the next step in the series
What is Polygon?A polygon is a plane figure made up of line segments connected to form a closed polygonal chain.
In the first step we can see a triangle
The triangle has three sides
In the second step there is a rectangle which has four sides
The third step has pentagon which has five sides
So in next step the polygon should have six sides
Hexagon is the next step in the series
Hence, option C is correct, the polygon in c option is the next step in the series
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Write the square or cube for each number.
1) 19³=
2) 16² =
3) 15³ =
4) 20² =____
5) 10³ =_
Answer:
1) 19³=6859
2) 16² =256
3) 15³ =3375
4) 20² =400
5) 10³ =1000
Step-by-step explanation:
using your calculator to (square = number times itself) or (cube = number times itself times itself again)
Pls help asap and show ur steps pls !!! I’ll give brainliest
Harry works in a local computer store and he kept a record of the number of computers sold each month for the past year. How many more computers were sold in the month of February than in the month of September? A. 20
B. 17
C. 15
D. 10
Answer:
A.) 20
Step-by-step explanation:
According to the bar graph, in February, the store sold 50 computers. In September, it seems like the store sold 30 computers. Therefore, if 50 - 30 = 20, the store sold 20 more computers in February than in September.
Answer:
A) 20
Step-by-step explanation:
Computers sold in Feb: 50
Computers sold in Sept: 30
50 - 30 = 20
Can someone help me with geometry
Applying the circle theorems, we have:
4. y = 120°
x = 45°
5. x = 90°
y = 32°
6. x = 40°
y = 20°
7. x = 116°
y = 98°
8. x = 100°
y = 60°
9. x = 54°
y = 75°
What is the Angle of Intersecting Secants Theorem?The angle formed outside a circle by the intersection of two secants equals half the positive difference of the measures of the intercepted arcs, based on the angle of intersecting secants theorem.
What is the Angle of Intersecting Chords Theorem?The angle formed when two chords of a circle intersect, equals the half the sum of the measures of the intercepted arcs, based on the angle of intersecting chords theorem.
4. y = 360 - 95 - 30 - 115 = 120°
x = 1/2(120 - 30) [angle of intersecting secants theorem]
x = 45°
5. x = 90° [based on the tangent theorem]
y = 180 - 90 - 58 [triangle sum theorem]
y = 32°
6. x = 360 - 160 - 160 [central angle theorem]
x = 40°
y = 1/2(40) [inscribed angle theorem]
y = 20°
7. x = 180 - 2(32)
x = 116°
y = 1/2[132 + 2(32)] [angle of intersecting chords theorem]
y = 98°
8. x = 180 - 80 [opposite angles of an inscribed quadrilateral are supplementary]
x = 100°
y = 1/2[(2(80) - 90) + 50] [inscribed angle theorem]
y = 1/2[70 + 50]
y = 60°
9. 40 = 1/2(134 - x) [angle of intersecting secants theorem]
2(40) = 134 - x
80 = 134 - x
80 - 134 = - x
-54 = -x
x = 54°
y = 360 - 134 - 54 - 97
y = 75°
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PLEASE HELP WILL GIVE BRAINIEST
2.8 devided by 7.2 as a decimal
Answer: 0.388
8 continuing so draw a line over the eights.
Rational number of 2.3
[tex]Rational \: numbers \: can \: be \: written \: in \: the \: form \: of \: \frac{a}{b} \\ 2.3 = \frac{23}{10} = > answer[/tex]
Hope this helps :)
a= 5.2 B=70
Work out the area of the triangle. Round your answer to 1 DP
Answer:
8.7
Step-by-step explanation:
Calculate the area of the triangle by using sine.
Area of Triangle
[tex]A = \frac{1}{2} \times \text{side} \times \text{side} \times \sin{\theta}[/tex]
θ ... included angle between the two sides
We already have two sides a and another side which is congruent to a, making it isosceles triangle. But we don't have the included angle. The angle we need is the vertex angle of the isosceles triangle. Angle B is one of the base angles (two base angles are congruent) and it measures 70°.
Recall that angles in any triangle add up to 180°.
base angle + base angle + vertex angle = 180°
70° + 70° + vertex angle = 180°
vertex angle = 40°
Now we have all the information to use the formula!
[tex]A = \frac{1}{2} \times \text{side} \times \text{side} \times \sin{\theta}[/tex]
[tex]A = \frac{1}{2} \times 5.2 \text{ cm} \times 5.2 \text{ cm} \times \sin{40^\circ}[/tex]
[tex]A = 13.52 \text{ cm}^2 \times \sin{40^\circ}[/tex]
[tex]A \approx 8.6904 \text{ cm}^2[/tex]
Rounded to 1 DP:
[tex]A = 8.7 \text{ cm}^2[/tex]
Find the product of –1.5x and –0.25x.
Answer:
0.375x^2
Step-by-step explanation:
(-1.5x)(-0.25x)
= (-1.5)(0.25)(x)(x)
= 0.375x^2
What is the range of the function graphed below?
On a coordinate plane, a graph shows a curve with two points. A solid point is at (1, 3) and an open point is at (4, negative 3).
1 less-than-or-equal-to y less-than 4
Negative 3 less-than y less-than-or-equal-to 3
Negative 2 less-than-or-equal-to y less-than-or-equal-to 3
Negative 3 less-than-or-equal-to y less-than 4
Answer:
Negative 3 less-than y less-than-or-equal-to 3
Step-by-step explanation:
By looking at a coordinate plane, we can easily see the range
remember, a closed dot means includes , and an open dot means does not include
[closed dot]
(open dot)
the range is all possible y-values. so, all y values shown are
3 which it includes
to -3 which it excludes / does not include
so, all y values are greater than -3 and less than or equal to 3
What are the coefficients for the binomial expansion of (p q)6? 1, 8, 28, 56, 70, 56, 28, 8, 1 1, 6, 15, 20, 15, 6, 1 1, 5, 10, 10, 5, 1 1, 4, 6, 4, 1
An expression is defined as a set of numbers, variables, and mathematical operations. The coefficients for the binomial expansion of (p+q)⁶ are 1, 6, 15, and 20.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The expansion of the given binomial (p+q)⁶ can be done as shown below,
(p+q)⁶ = p⁶ + 6p⁵q + 15p⁴q² + 20p³q³ + 15p²q⁴ + 6pq⁵ + q⁶
Hence, the coefficients for the binomial expansion of (p+q)⁶ is 1, 6, 15, and 20.
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What is the area of this rectangle? 10units 20units 24units 48 units
Answer:
24 units ^2
Step-by-step explanation:
The base runs from 3 to 7 so the base is 7-3 = 4 units
The height runs from 2 to 8 so the height is 8-2 = 6 units
The area is
A = bh
= 6*4 = 24 units ^2
Jacob sells stools with round seats. if
the radius of a seat is 34.2 cm, find the
surface area of the stool
The surface area of the stool is 3629.84 square cm
How to determine the surface area?The radius is given as:
r = 34.2
The surface area is calculated using:
A = πr^2
So, we have:
A = 3.14 * 34^2
Evaluate
A = 3629.84
Hence, the surface area of the stool is 3629.84 square cm
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0.510 (3+0.2) x -1.6
-
Answer:
-2.6112
Step-by-step explanation:
= 0.510 (3+0.2) x -1.6
= 0.510 x 3.2 x -1.6
= -2.6112
hence answer is -2.6112.
If f(x) = −5x − 4 and g(x) = -3x - 2, find (f+ g)(x).
Answer:
[tex](f+g)(x) = -8x-6[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]\displaystyle f(x) = -5x - 4 \text{ and } g(x) = -3x - 2[/tex]
And we want to find:
[tex](f+g)(x)[/tex]
Recall that this is equivalent to:
[tex]\displaystyle (f+g)(x) = f(x) + g(x)[/tex]
Substitute and simplify:
[tex]\displaystyle \begin{aligned} (f+g)(x) &= (-5x-4)+(-3x-2) \\ \\ &= -8x-6 \end{aligned}[/tex]
In conclusion:
[tex](f+g)(x) = -8x-6[/tex]
Which expression is equivalent to 6(4
+ 9)?
Answer: 78
Step-by-step explanation:
6(4+9)
use foil to distribute the 6 to the 4 and 9
6×4 + 6×9
24 + 54
⇒ 78
Lee la información, analiza los datos y contesta en tu cuaderno.
La tabla contiene las temperaturas máxima y mínima por mes en la ciudad de Moscú,
Rusia, en grados Celsius.
Mes
Ene. Feb. Mar. Abr. May. Jun. Jul. Ago. Sep. Oct. Nov. Dic.
Máx. (°C) -6 -4
9
7
21
22 20
14
7
0
-4
Min. (°C) -12 -11 -6
1
-7
11
13
11
6
1
-4
-9
.
¿Cuál fue la temperatura máxima que se registró en el año?
.
¿Y cuál fue la mínima?
¿Hace más frío cuando la temperatura es -7 °C o cuando es 7 °C?
¿Qué temperaturas de la tabla se encuentran entre -7 °C y 7 °C?
●
Ubica en una recta numérica las temperaturas que se muestran en la tabla y verifica
tus respuestas.
Based on the given table, the maximum temperature in the year was 22°C and the minimum was -12°C. It is colder when the temperature is -7°C.
The temperatures between -7°C and 7 °C are :-6, -4, 0, 1, and 6.
What does the table show about temperatures?During the year, the highest recorded temperature was 22°C in the month of July. The lowest temperature was -12°C in the month of Janaury.
The lower the temperature, the colder it is. This is why -7°C is colder than 7°C.
The temperatures between -7°C and 7°C are temperatures that are higher than -7°C but lower than 7°C. These are:
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The owner adds a chemical to the tank to keep the water clear. the instructions say to add 5 cubic centimeters of chemical for every 80,000 cubic centimeters of water. how much chemical will need to be added? round your answer to the nearest tenth if necessary.
The chemical need to be added to the tank is 16000 cubic cm
What is volume?The volume is the total capacity of a container.
Total volume of tank = 80,000 cubic centimeters of water
Chemical volume = 5 cubic centimeters
Chemical needed = = 80,000 /5 = 16000 cubic cm is needed.
Thus, 16000 cubic cm chemical is needed.
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began doing his homework at 3:30 p.m. to stop at 4 p.m. how many degrees does the minute hand turn during rick's walk.explain how you found your answer
At 3:30 pm
the minute hand was at 6 and hour hand was in between 3 and 4
At 4 pm
the minute hand is at 12 and hour hand is at 4
Total numbers travelled by minute hand
12-66Total degrees turn
6(30)180° clockwise turn