The quadratic equation exists [tex]$x^{2}+3 x+2=0$[/tex].
What is the formula of the quadratic equation?If a quadratic equation exists [tex]$a x^{2}+b x+c=0$[/tex], the utilizing the quadratic equation the solutions for x will be given by
[tex]$x_{1,2}=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$$[/tex]
The solution for x exists
[tex]$x=\frac{-3 \pm \sqrt{3^{2}-4(1)(2)}}{2(1)}[/tex]
Comparing equations (1) and (2) we get, a = 1, b = 3 and c = 2.
Therefore, the quadratic equation exists [tex]$x^{2}+3 x+2=0$[/tex].
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Answer:
One guy said it was B. but I'm going with A.
Step-by-step explanation:
Ramiya is using the quadratic formula to solve a quadratic equation. her equation is x = startfraction negative 3 plus or minus startroot 3 squared minus 4(1)(2) endroot over 2(1) endfraction after substituting the values of a, b, and c into the formula. which is ramiya’s quadratic equation?
Write the first five terms of the recursively defined sequence. a1 = 6, ak 1 = 1 3 ak2
The first five terms of the recursively defined sequence are 6, 12, 48, 768, 196608
For given question,
We have been given the recursive formula of a sequence.
[tex]a_{k+1}=\frac{1}{3}{a_k}^2[/tex]
Also, the first term of the sequence is,
a1 = 6
Substitute k = 1 in given recursive formula.
⇒ [tex]a_{1+1}=\frac{1}{3}{a_1}^2[/tex]
⇒ a2 = 1/3 (6)²
⇒ a2 = (1/3) × 36
⇒ a2 = 12
Substitute k = 2 in given recursive formula.
⇒ [tex]a_{2+1}=\frac{1}{3}{a_2}^2[/tex]
⇒ a3 = (1/3) × (12)²
⇒ a3 = (1/3) × 144
⇒ a3 = 48
Substitute k = 3 in given recursive formula.
⇒ [tex]a_{3+1}=\frac{1}{3}{a_3}^2[/tex]
⇒ a4 = (1/3) × (48)²
⇒ a4 = (1/3) × 2304
⇒ a4 = 768
Substitute k = 4 in given recursive formula.
⇒ [tex]a_{4+1}=\frac{1}{3}{a_4}^2[/tex]
⇒ a5 = (1/3) × (768)²
⇒ a5 = (1/3) × 589824
⇒ a5 = 196608
Therefore, the first five terms of the recursively defined sequence are 6, 12, 48, 768, 196608
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What is the area of this figure?
14 km
8 km
9 km
8 km
5 km
4 km
4 km
4 km
The Area of the composite figure as shown in the image below is: 105.57 km².
What is the Area of a Composite Figure?Referring to the diagram given below, the shape can be decomposed into one rectangle, one square, and one quarter circle.
The area of the composite figure = area of rectangle + area of square + area of quarter circle.
Area of the Rectangle = length × width
Length = 12 km
Width = 7 km
Area of the Rectangle = 12 × 7
Area of the Rectangle = 84 km²
Area of the square = (s)²
s = 3 km
Area of the square = 3²
Area of the Rectangle = 9 km²
Area of the quarter circle = 1/4(πr²)
r = 4 km
Area of the quarter circle = 1/4(π × 4²)
Area of the quarter circle = 12.57 km²
Area of the composite figure = 84 + 9 + 12.57
Area of the composite figure = 105.57 km².
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What steps may be necessary to predict data not included in a data set using a scatter plot and line of best fit? Select all that apply.
Answer:
Step-by-step explanation:
3. A line of best fit can be roughly determined using an eyeball method by drawing a straight line on a scatter plot so that the number of points above the line and below the line is about equal (and the line passes through as many points as possible). This will help me to see weather or not it is positive or negative.3
15 POINTS
Data Analysis and Probability
Constructing a box-and-whisker plot
The box and whisker plot for the data-set is given at the end of the question.
What is a box plot?It is a plot that focuses the interquartile range of the population, which is the difference between the third and the first quartile, but gives a five number summary of the population, composed by these following measures.
The smallest value.The first quartile.The median.The third quartile.The highest value.For this problem, we have that:
The smallest value is of 50, hence the left dot has to be at 50 in your graph.The highest value is of 77, hence the right dot has to be at 50 in your graph.The data-set has an even cardinality, of 17, hence the median is the 9th element, which is of 65, which means that the middle vertical line should be at 65.The first quartile is the median of the first eight elements, hence the mean of the 4th and 5th elements, which are 55 and 57, hence the first quartile is of 56, which means that the left vertical line should be at 56.The third quartile is the median of the first eight elements, hence the mean of the 4th and 5th elements of the second half, which are both 71, hence the third quartile is of 71, which means that the right vertical line should be at 71.The graph at the end gives a vertical version of the box plot.
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Simplify 0.4(5a-3.2b+7)
Step-by-step explanation:
2a -1.28b +2.8 for simplification.
If -3(x+8)= -21, then x = -1.
Step-by-step explanation:
-3(x+8)=-21
open the bracket
-3x-24=-21
-3x=-21+24
-3x=3
x=-3/3
x=-1
Sloane kicked a soccer ball off the ground at a speed of 56 feet per second. the height of the ball can be represented by the function h(t) = −16t2 56t, where t is the time in seconds. how many seconds did the ball travel before returning the ground? t = 56 seconds t = 16 seconds t = 3.5 seconds t = 0.29 seconds
The time in seconds that it took the ball to travel would be = 0.25 seconds.
Calculation of speed timeSpeed can be defined as the distance covered by an object per unit time.
The speed used to kick the soccer off the ground = 56 feet per second.
The height equation= −16t² + 56t
The time= ?
The formula for speed = distance/time
56= −16t² + 56t/t
56t = −16t² + 56t/t
−16t² = -56t + 56t
−16t² = 0
Make t the subject formula,
t = √1/16
t = 0.25 seconds.
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Subtract the given fraction:-
[tex] \frac{3}{5} - \frac{5}{3} = [/tex]
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Match each solid cone to its surface area. Answers are rounded to the nearest square unit.
829 square units
628 square units
444 square units
996 square units
8 units
12 units
525 square units
>
758 square units
Rounded to the nearest square units, the surface area of the cone, is: 524 square units.
How to Find the Surface Area of a Cone?The surface area of a cone = πr(r + l), where:
r is the radius of the cone
l is the length of the cone.
Given the following:
Radius of the cone (r) = 12/2 = 6 units
Slant height of the cone (l) = √(21² + 6²) [Pythagorean theorem]
Slant height of the cone (l) = 21.8 units.
Plug in the values into πr(r + l):
Surface area of the cone = π × 6(6 + 21.8)
Surface area of the cone = 3.14 × 6(27.8)
Surface area of the cone ≈ 525 square units
The surface area of the cone, approximated to the nearest square units, we have: 524 square units.
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HELPPPP WITH ALL OF THE 3 PLSSS
Answer:
See picture.
C is the point that does not move because it is on the line of reflection
Yes, a reflection is a rigid motion. It does not change size. A dilation changes the size.
Step-by-step explanation:
In the picture, you will see that I traced the triangle on tracing paper and then folded (flipped) the drawing over the line of reflection.
Drag the tiles to the boxes to form correct pairs. match each pair of polynomials to their sum. 12x2 3x 6 and −7x2 − 4x − 2 −2x − 2 2x2 − x and −x − 2x2 − 2 2x2 x x2 2 and x2 − 2 − x 2x2 9x − 2 x2 x and x2 8x − 2 5x2 − x 4
The sum of each of the 4 polynomials and their answers are respectively;
12x² + 3x + 6 + (-7x²) – 4x – 2 = 5x² - x + 4
(2x² - x) + (-x – 2x² – 2) = -2x - 2
(x³ + x² + 2) + (x² – 2 - x³) = 2x²
(x² + x) + (x² + 8x - 2) = 2x²+ 9x - 2
How to find the sum of Polynomials?
1) We want to find the sum of the polynomials (12x² + 3x + 6) and (-7x² – 4x – 2). Thus, we have;
12x² + 3x + 6 + (-7x²) – 4x – 2
= 5x² - x + 4
2) We want to find the sum of the polynomials (2x² - x) and (-x – 2x² – 2). Thus, we have;
(2x² - x) + (-x – 2x² – 2)
= -2x - 2
3) We want to find the sum of the polynomials (x³ + x² + 2) and (x² – 2 - x³). Thus, we have;
(x³ + x² + 2) + (x² – 2 - x³)
= 2x²
4) We want to find the sum of the polynomials (x² + x) and (x² + 8x - 2). Thus, we have;
(x² + x) + (x² + 8x - 2) = 2x²+ 9x - 2
The sum of each of the 4 polynomials and their answers are respectively;
12x² + 3x + 6 + (-7x²) – 4x – 2 = 5x² - x + 4
(2x² - x) + (-x – 2x² – 2) = -2x - 2
(x³ + x² + 2) + (x² – 2 - x³) = 2x²
(x² + x) + (x² + 8x - 2) = 2x²+ 9x - 2
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Consider the points (1,7),(-5,-4) what are the domain and range of this function
Answer:
Domain is 1 and 7 and range is -5and -4
Step-by-step explanation:
because domain is a first group element and range is a second element of a set
What is the margin of error for 95% confidence for a sample of size 700 where p = 0.65?
A. 0.0455
B. 0.0303
OC. 0.0651
D. 0.0353
Answer:
D 0.0353
Step-by-step explanation:
a= 0.05. p= 0.65. n=700
S N P = 700 × 065 = 45575
1 n ( 1 - p ) = 700× ( 1 - 0.65 ) = 24575
get the sample is big ,. p~ N ( π. √ π ( 1-π ) p - π
-----------. ------- ~ ( o. 1
n Ñ 1 ~ñ
the margin of error ∆ = Z a
-----. =. √ π ( 1 - π )
2 --------
n
according to the standard normal distribution,
Z d
---. = zo.o25 = 1.96
2
∆=1.96×√p ( 1 - p ). =. 1.96 × √ 0.65× ( 1 - 65)
---------. ---------
π. 700
= 0.0353
Find the area of the trapezoid.
Hint: Use the formula for the area of
a trapezoid given below.
A = (b₁+b2) h
Trapezoid Area
= [?] cm²
b₁ = 6 cm
1h = 7 cm
b₂
=
8 cm please explain answer in full detail
The area of the trapezoid in the given image is: 49 cm².
What is a Trapezoid?A trapezoid can be described as a quadrilateral that has four sides, whereby one pair of opposite sides are parallel to each other.
How to Find the Area of a Trapezoid?The area of a trapezoid is calculated using the formula, Area = 1/2 × (a + b) × h, where:
a and b represents lengths of the parallel sides of the trapezoid
h = height of the trapezoid.
Given the parameters for the trapezoid as:
a = 6 cm
b = 8 cm
h = 7 cm
Plug in the values into Area = 1/2 × (a + b) × h:
Area of trapezoid = 1/2 × (6 + 8) × 7
Area of trapezoid = 1/2 × (14) × 7
Area of trapezoid = 7 × 7
Area of trapezoid = 49 cm²
Thus, the area of the trapezoid in the given image is: 49 cm².
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ABCD is a rhombus. If AB = 2x + 12 , AC = 7x - 3, ∠=12°, and ∠ = (4y - 1)°.m ∠BAC = __ . (FIND BAC NOT CD)
Answer:
Step-by-step explanation:
sketch the graph: y=1/3x+2
The slope of the line is 1/3and the y-intercept is at the (0, 2) as shown in the graph below.
Graph of a linear functionA linear function is a function that has a leading degree of 1. The standard equation for a linear function is expressed as:
y = mx + b
where
m is the slope which is equal to the rate of change of y coordinate to x-coordinates.
b is the y-intercept
Given the following equation
y= 1/3x + 2
The slope of the line is 1/3 and the y-intercept is at the(0,2) as shown in the graph below.
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In the figure below, what is the length of BC?
A) 12
B) 13
C) 17
D) 18
E) 22
B is the answer
i simplified the theorem, but i hope this makes sense!
Answer:
B
Step-by-step explanation:
On saturday evening 5450 people visited india gate. out of these 1265 were men 1150 were woman and rest were children. how many children visited the india gate?
3435 were children visited the India gate.
What is a linear equation in math?
A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line.Given,
men = 1265
women = 1150
Total women and men -
men + women = 2415
= 5450-2415 ⇒ 3435
Therefore, 3435 were children visited the India gate.
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If zeba were younger by 5 years than what she really is then the square of her age would have been 11 more than five times her actually age. What is her age now?
Answer:
I am not 100% confident, but I think that she is 11.
Step-by-step explanation:
Answer:
14 years old
Step-by-step explanation:
Define the variable
Let x be the actual age of Zeba (in years).
Create an equation using the give information and the variable x:
[tex](x - 5)^2=5x+11[/tex]
To find Zeba's age now, solve the equation for x.
Expand the brackets:
[tex]\implies x^2-10x+25=5x+11[/tex]
Subtract 5x from both sides:
[tex]\implies x^2-10x+25-5x=5x+11-5x[/tex]
[tex]\implies x^2-15x+25=11[/tex]
Subtract 11 from both sides:
[tex]\implies x^2-15x+25-11=11-11[/tex]
[tex]\implies x^2-15x+14=0[/tex]
Factor the found quadratic
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex], then rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies x^2-14x-x+14=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x-14)-1(x-14)=0[/tex]
Factor out the common term (x - 14):
[tex]\implies (x-1)(x-14)=0[/tex]
Apply the zero product property:
[tex]\implies (x-1)=0 \implies x=1[/tex]
[tex]\implies (x-14)=0 \implies x=14[/tex]
Therefore, Zeba's age now is either 1 or 14 years.
As the question states "If Zeba were younger by 5 years" then 1 must be an extraneous solution since 1 - 5 = -4 and Zeba cannot be -4 years old.
Therefore, Zeba's age now is 14 years old.
Check
Given the actual age of Zeba is 14 years old.
Therefore, If Zeba were younger by 5 years, she would be 9 years old as: 14 - 5 = 9
The square of 9 is: 9² = 81.
5 times her actual age: 5 × 14 = 70
81 is 11 more than 70, hence verifying that her actual age is 14 years old.
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An apartment building contains 12 units consisting of one- and two-bedroom apartments that rent for $360 and $450 per month, respectively. When all units are rented, the total monthly rental is $4,950. What is the number of two-bedroom apartments?
Answer:
There are 7 two bed bedroom apartments.
Step-by-step explanation:
Solution Given:
let the one bedroom apartment be x and two bedroom apartment be y.
By the question we can make an equation as
x+y=12
or y=12-x............................[1]
Again:
$360x+$450y=$4,950
Now substituting value of y, we get
$360x+$450(12-x)=$4,950
Opening Bracket
$360x+$5400-$450x=$,4,950
solving equation
-90x=-450
dividing both side by -90,we get
x=5
again,
substituting value of x in equation 1,we get
y=12-5=7 two bed bedroom apartments.
Let, x represents the number of one bedrooms and 12 - x represents the number of two bedrooms.
According to the question,
[tex]360x + 450(12 - x) = 4950[/tex]
[tex]360x + 5400 - 450x = 4950[/tex]
[tex]5400 - 4950 = 450x - 360x[/tex]
[tex]450 = 90x[/tex]
[tex] \frac{450}{90} = x[/tex]
[tex]5 = x[/tex]
Therefore, one bedrooms = x = 5
For number of two bedrooms which is equal to 12 - x
= 12 - 5
= 7
So your required answer is 7
Which equation describes the circle having center point (3,7) and radius r = 4
in standard form?
A. (x-3)²+(y-7)² = 4
B. (x+3)² + (y+7)² =4
c. (x-3)²+(y-7)² = 16
D. (x+3)² + (y+7)² = 16
A game involves rolling a fair six-sided die. if the number obtained on the die is a multiple of three, the player wins an amount equal to the number on the die times $20. if the number is not a multiple of three, the player gets nothing. how will you model the simulation for the roll of a die?
The winning probability is 1/3.
What is probability?A probability is a number that represents the likelihood or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.To find the winning probability:
Favorable outcomes to win are 3 and 6.Total outcomes are 6in fair dice.To win $20 × 3 or $20 × 6 favorable outcome is 1 (3 and 6 respectively).The probability is 1 / 6.So, the probability of winning some money = 2/6 = 1/3Therefore, the winning probability is 1/3.
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If the two lines below are perpendicular and the slope of the red line is -
what is the slope of the green line?
O A.
A.
OB. -3
314
O D.
D. -
-10
10
15
Answer:
-(10/7)
Step-by-step explanation:
See attached graphic. The slope of the Green Line is cut off in the problem photo, but can be calculated from the graph to find the slope of the Red Line. The answer options are on drugs; pick the one that looks closest.
Answer:
-4/3
Step-by-step explanation:
PLS HELP IM SO STUCK
3x-2y= 7
Slope intercept form y= mx+b
3x- 2y= 7
- 3x -3x
-2y/-2= 3x/-2 - 7/2
y= 3x/-2 -7/2
Answer:
3x/2 and the second 7/-2y
Step-by-step explanation:
thats how is what i got
What is the approximate total volume of the silo? use 3.14 for π and round the answer to the nearest tenth of a cubic meter. 37.1 m3 71.9 m3 116.5 m3 130.8 m3
The total volume of silo is = 116.5[tex]{~m}^{3}[/tex]
The correct option is C
What are the geometric figures?Any arrangement of points, lines, or planes constitutes a geometric figure. Depending on their dimensions, geometric figures can be categorized as either a space figure, a plane figure, a line, a line segment, a ray, or a point.
Any object's surface area is the space that the object's surface takes up on a specific area or region. Volume, however, refers to how much room a thing has.
Given data:
Radius =4.4/2
=2.2
height of cylinder = 6.2
to find :
total volume of silo = volume of cylinder + volume of hemisphere
[tex]\begin{aligned}&=\pi r^{2} h+\frac{2}{3} \pi r^{3} \\&=\pi r^{2}\left(h+\frac{2}{3} r\right) \\&=\frac{22}{7} \times(2.2)^{2}\left[6.2+\frac{2 \times 2.2}{3}\right]\end{aligned}[/tex]
= 116.5[tex]m^2[/tex]
The total volume of silo is = 116.5[tex]m^2[/tex]
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I understand that the question you are looking for is:
A grain silo is composed of a cylinder and a What is the approximate total volume of the silo? Use hemisphere. The diameter is 4.4 meters. The height of 3.41 for [tex]\pi[/tex] and round the answer to the nearest tenth of its cylindrical portion is 6.2 meters. a cubic meter.
a. 37.1[tex]m^2[/tex]
b. 71.9 [tex]m^2[/tex]
c.116.5 [tex]m^2[/tex]
d. 130.8[tex]m^2[/tex]
A sheet of glass has a density of 2.5 8 What is the density of the glass in k8 ? mi.
Based on the density and the given parameters, the density of the sheet of glass in kg per m cubed is 2500 kg/m cubed
How to determine the density of the sheet of glass in kg per m cubed?The density of the sheet of glass is given as
Density = 2.5g/cm cubed
Start by converting grams (g) to kilogram (kg)
This is done by dividing 2.5 by 1000
So, we have:
Density = 2.5/1000 kg/cm cubed
Evaluate the quotient
Density = 0.0025 kg/cm cubed
Next, we then convert cm cubed (cm^3) to meter cubed (m^3)
This is done by dividing the volume by 1000000
So, we have:
Density = 0.0025 kg/(1/1000000) m cubed
Express as product
Density = 1000000 * 0.0025 kg/m cubed
Evaluate the product
Density = 2500 kg/m cubed
Based on the density and the given parameters, the density of the sheet of glass in kg per m cubed is 2500 kg/m cubed
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Answer:
See below
Step-by-step explanation:
Are you wanting to convert density of gm/ cm^3 to kg/m^3 ??
there are 100 x 100 x 100 cm^3 = 1,000,000 cm^3/ m^3
2.5 gm / cm^3 * 1 000 000 cm^3 / m^3 = 2, 500 000 gm / m^3
now 1 kg is 1000 gm
2, 500 000 gm / m^3 * 1 kg / 1000 gm = 2500 kg / m^3
Write and solve a system of equations. Be sure to label the variables. The sum of two numbers is fourteen. Two times the first number plus three times the second number is nine. What are the two numbers? Show and Explain all work.
Answer:
First number = 33, Second number = -19
Step-by-step explanation:
We can use F to represent the first number and S to represent the second number.
Our two equations then are F + S = 14 and 2F + 3S = 9
We can use substitution:
[tex]F+S = 14\\2F+3S=9\\F=14-S\\2(14-S)+3S=9\\28-2S+3S=9\\28+S=9\\S=-19\\\\F-19=14\\F=33[/tex]
d. If you double a certain number and subtrack 7 you get the same answer as when you add 5 to the number, Determine the number
Answer:
12
Step-by-step explanation:
Let n = the number.
2n - 7 = n + 5
n = 12
Let’s check if we got the right answer by substituting 12 for n into the original equation.
2*12 - 7 = 12 + 5
24 - 7 = 17
17 = 17
pls help right now need pleaseee
Answer:
-1/2
Step-by-step explanation:
The cosine is equal to the x coordinate of the point where the terminal side of the angle intersects the unit circle.
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
The range of the quadratic function y = (2 / 3) · x² - 6 is {- 6, 0, 18, 48}.
What is the range of a quadratic equation?
In this case we have a quadratic equation whose domain is stated. The domain of a function is the set of x-values associated to only an element of the range of the function, that is, the set of y-values of the function. We proceed to evaluate the function at each element of the domain and check if the results are in the choices available.
x = - 9
y = (2 / 3) · (- 9)² - 6
y = 48
x = - 6
y = (2 / 3) · (- 6)² - 6
y = 18
x = - 3
y = (2 / 3) · (- 3)² - 6
y = 0
x = 0
y = (2 / 3) · 0² - 6
y = - 6
x = 3
y = (2 / 3) · 3² - 6
y = 0
x = 6
y = (2 / 3) · 6² - 6
y = 18
x = 9
y = (2 / 3) · 9² - 6
y = 48
The range of the quadratic function y = (2 / 3) · x² - 6 is {- 6, 0, 18, 48}.
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