Answer:
Given two events A and B of a sample set :-
P[A] = 0.20
P[not B]=0.40
[tex]P[B/A]=0.25[/tex]
To find P[A or B]:
[tex]P[A or B] = P[A] + P[B] - P[A \cap B][/tex] ......[1]
Calculate for [tex]P[B][/tex] and [tex]P[A \cap B][/tex]
P[B] = 1- P[not B]
Substitute the value P[not B] we get;
P[B] = 1-0.40 = 0.60
[tex]P[A \cap B] = P[B/A] \cdot P[A][/tex]
Substitute the given values we get;
[tex]P[A \cap B] = 0.25 \cdot 0.20 = 0.05[/tex]
Then;
[tex]P[A or B] = 0.20+0.60-0.05 = 0.80-0.05 =0.75[/tex]
Therefore, the value of P[A or B] is, 0.75.
The probability of P(A∪B) is 0.35.
ProbabilityProbability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
Given
P(A) = 0.20
P(B) = 0.40
P(A∩B) = 0.25
To findThe probability of P(A∪B).
How to find the probability of P(A∪B)?We know the formula
P(A∪B) = P(A) + P(B) - (A∩B)
P(A∪B) = 0.20 + 0.40 - 0.25
P(A∪B) = 0.60 - 0.25
P(A∪B) = 0.35
Thus the probability of P(A∪B) is 0.35.
More about the probability link is given below.
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A kite is 37 feet in the air and string forms an angle of 62 degrees with the ground how long is the string
Answer:
The length of the string is 32.56 feet (Approx) .
Step-by-step explanation:
As given
A kite is 37 feet in the air and string forms an angle of 62 degrees .
Now by using the trignometric identity.
[tex]sin\theta = \frac{Perpendicular}{Hypotenuse}[/tex]
As shown in the figure given below.
[tex]\theta = 62^{\circ}[/tex]
Perpendicular = AB
Hypotenuse = AC = 37 feet
Put in the identity .
[tex]sin\ 62^{\circ} = \frac{AB}{AC}[/tex]
[tex]sin\ 62^{\circ} = \frac{AB}{37}[/tex]
[tex]sin\ 62^{\circ} = 0.88\ (Approx)[/tex]
Put in the identity
[tex]0.88 = \frac{AB}{37}[/tex]
AB = 0.88 × 37
AB = 32.56 feet (Approx)
Therefore the length of the string is 32.56 feet (Approx) .
To determine whether there is a relationship between the type of school attended and verbal reasoning scores for Irish students, three samples with 25 students, in each group, were randomly selected from data used by Raferty and Hout (1985). One group of students attended secondary school, the second group of students attended vocational school, and the third group consisted of students who attended only primary school.
Select one answer.
If we let μ1, μ 2, and μ 3 be the mean verbal reasoning scores for students who attended secondary school, vocational school, and primary school only, respectively, the appropriate hypotheses in this case are:
a. H0: μ1 = μ2 = μ3
Ha: μ1, μ2, μ3, are not all equal
b. H0: μ1, μ2, μ3, are not all equal
Ha: μ1 = μ2 = μ3
c. H0: μ1 = μ2 = μ3
Ha: μ1 μ μ2 μ μ3
d. H0: μ1 μ μ2 μ μ3
Ha: μ1 = μ2 = μ3
e. None of the above are correct.
The correct hypotheses are:
b. [tex]\(H_0: \mu_1 = \mu_2 = \mu_3\) and \(H_a: \mu_1, \mu_2, \mu_3\) are not all equal.[/tex]
To determine the appropriate hypotheses for testing the relationship between the type of school attended and verbal reasoning scores for Irish students, we first need to understand the nature of the comparison being made.
We have three groups of students: those who attended secondary school, vocational school, and primary school only. We want to investigate if there is a difference in the mean verbal reasoning scores among these groups.
The null hypothesis [tex](\(H_0\)) states that there is no difference in the mean verbal reasoning scores among the three types of schools, expressed as \( \mu_1 = \mu_2 = \mu_3 \), where \( \mu_1 \), \( \mu_2 \), and \( \mu_3 \)[/tex] are the population means for students attending secondary school, vocational school, and primary school only, respectively.
The alternative hypothesis [tex](\(H_a\)) suggests that at least one of the population means is different from the others, expressed as \( \mu_1, \mu_2, \mu_3 \)[/tex] are not all equal.
Option b correctly represents these hypotheses:
[tex]\(H_0: \mu_1 = \mu_2 = \mu_3\) \(H_a: \mu_1, \mu_2, \mu_3\) are not all equal.[/tex]
This formulation allows for the testing of differences in mean verbal reasoning scores across the three types of schools. The null hypothesis assumes equality among the means, while the alternative hypothesis considers the possibility of inequality.
Please help! Urgent!
A blue circular target is tacked onto a square corkboard. The area of the target is 75 square units. What is the area of the corkboard that is not covered by the target?
A) 25 square units
B) 65 square units
C) 75 square units
D) 100 square units
Answer:
The Correct Answer Is A.) 25 Square Units
Step-by-step explanation:
The area of the corkboard that is not covered by the target is 25 sq. units.
(Option A).
What is the area of the corkboard that is not covered by the target?The area of the corkboard that is not covered by the target is calculated from the difference between the area of the square and area of the target.
Area of the square is calculated as;
A = L²
A = ( 5 + 5)²
A = 100 sq units
The area of the target is 75 sq. units, so we wil use this value
The area of the corkboard that is not covered by the target is calculated as;
A = 100 - 75
A = 25 sq. units.
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PLEASE HELP FOR BRAINLIEST!!
Write a function rule for the data in the table. Determine if it's a direct variation, inverse variation or neither. Last, determine the value of x if y=10.
Answer: [tex]\bold{y=\dfrac{24}{x}}[/tex] ; indirect variation ; x = 2.4
Step-by-step explanation:
direct variation is when: [tex]\dfrac{y}{x}=k[/tex] ; where k is the constant rate
indirect variation is when: xy = k ; where k is the constant rate
In the table provide: x * y = 24 for each coordinate provided, so this is indirect variation, with equation: [tex]y = \dfrac{24}{x}[/tex]
since k = 24, then input y = 10 and k = 24 into the equation above:
[tex]10 = \dfrac{24}{x}[/tex]
[tex]10x = 24[/tex]
[tex]x = \dfrac{24}{10}[/tex]
x = 2.4
Tricia made a 56% on her science test. If she got 14 problems correct, how many questions were on the test?
Answer:
25
Step-by-step explanation:
let x questions on the text, so we get:
56/100=14/x, 4/100=1/x,
x=25
bobby’s christmas list had 3 more than twice as many items on it than johnny’s list. johnny asked for 8 fewer items than bobby. how many items were on johnny’s (x) and bobby’s (y) christmas lists?
Answer:
Johnny had 5 items and Bobby had 13 items.
Step-by-step explanation:
Let us assume that Johnny has x items and Bobby has y items in their list.
Bobby had 3 more than twice as many items on it than Johnny. So,
[tex]\Rightarrow y=3+2x[/tex] ----------1
Johnny asked for 8 fewer items than bobby. So,
[tex]\Rightarrow y-8=x[/tex] -----------2
Putting the value of x from equation 2 in equation 1, we get
[tex]\Rightarrow y=3+2(y-8)[/tex]
[tex]\Rightarrow y=3+2y-16[/tex]
[tex]\Rightarrow 2y-y=16-3[/tex]
[tex]\Rightarrow y=13[/tex]
Putting the value of y in equation 2,
[tex]\Rightarrow 13-8=x[/tex]
[tex]\Rightarrow x=5[/tex]
So, Johnny had 5 items and Bobby had 13 items.
Alicia was rock climbing. She climbed to a height of 30 ft. Next , she climbed down 18 ft. Finally she climbed up another 55 ft. Write an addition expression to describe this situation then find the sum of your addition expression to determine Alicia's elevation.
Answer:
Step-by-step explanation:
Alicia was rock climbing. She climbed to a height of 30 ft. Next , she climbed down 18 ft. Finally she climbed up another 55 ft. Write an addition expression to describe this situation then find the sum of your addition expression to determine Alicia's elevation.
Brainliest promised!
What is the name of an interior angle of a triangle that is not adjacent to a given exterior angle of the triangle?
A) exterior angle
B) adjacent interior angle
C) remote interior angle
D) alternate interior angle
Answer:
The answer is C) Remote Interior Angle
Step-by-step explanation:
The name of an interior angle of a triangle that is not adjacent to a given exterior angle of the triangle is the remote interior angle. Getting the values of each sides help you come up with the remote interior and exterior angles.
HELPP! Calculate S22 for the arithmetic sequence in which a12=2.4 and the common difference is d=3.4
Answer:
S22 for the arithmetic sequence is:
First option: 15.4
Step-by-step explanation:
a12=2.4
d=3.4
S22=?
Sn=(a1+an)n/2
n=22
S22=(a1+a22)22/2
S22=(a1+a22)11
ak=aj+(k-j)d
a12=a1+(12-1)d
2.4=a1+11(3.4)
2.4=a1+37.4
Solving for a1: Subtracting 37.4 both sides of the equation:
2.4-37.4=a1+37.4-37.4
Subtracting:
-35=a1
a1=-35
a22=a12+(22-12)d
a22=2.4+10(3.4)
a22=2.4+34
a22=36.4
S22=(a1+a22)11
S22=(-35+36.4)11
S22=(1.4)11
S22=15.4
Can someone please take some time to help me? I would really appreciate it. Thank you very much.
Adia plans to wallpaper her bedroom. The measurements are 10’ by 12’ with 8’ ceilings.
Part 2: If each single roll of wallpaper covers 72 square feet, how many single rolls of wallpaper will Adia need for her project?
Answer: _ single rolls (type the number only)
-------------------------------------------------------------------------------------
Adia plans to wallpaper her bedroom. The measurements are 10’ by 12’ with 8’ ceilings.
Part 3: If each single roll of wallpaper covers 72 square feet, how many double rolls of wallpaper will Adia need for her project?
Answer: _ double rolls (type the number only)
Answer:
5 single rolls or 3 double rolls.
Step-by-step explanation:
Ignoring doors and windows, we need to find the lateral surface ares. We are not papering the ceiling or floor.
The lateral surface areas = P*h
= 2(l+w) * h
= 2(10+12) * 8
= 2(22)*8
=352 ft^2
A single roll covers 72 ft^2 so we divide the number of ft^2 that we need (352^2) by the amount of a single roll
352/72 =4.88888(repeating)
Rounding up since we need to buy in full rolls.
We will need 5 rolls
Assuming a double roll will cover twice that of a single roll
2*72 = 144 ft^2
Take 572/144 =2.4444444
Rounding up since we need to buy in full rolls.
We will need to buy 3 double rolls
Adia will need 5 single rolls or 3 double rolls of wallpaper to cover her 10' by 12' bedroom with 8' ceilings.
Adia needs to calculate the amount of wallpaper needed to cover the walls of her bedroom. To find the total wall area, we calculate the perimeter of the room and multiply it by the ceiling height. The perimeter is two times the length (12 feet) plus two times the width (10 feet), giving us 44 feet. Multiplying the perimeter by the ceiling height (8 feet) gives us the total wall area: 44 feet × 8 feet = 352 square feet.
Since each single roll covers 72 square feet, dividing the total wall area by the coverage of one roll gives us the number of rolls needed: 352 square feet / 72 square feet/roll = 4.89, which means Adia will need 5 single rolls of wallpaper.
For double rolls, we need to consider that each double roll is equivalent to two single rolls.
Therefore, we divide the number of single rolls needed by 2 to get the number of double rolls: 5 single rolls / 2 = 2.5, which means Adia will need 3 double rolls (since she can't purchase half a roll, she'll have to round up).
A tiger can eat food that weighs up to 15% of its body weight if a tiger can I eat 75 lb of food how much does a Tiger Way
EARN 50 POINTS, WILL MARK BRAINLIEST , PLEASE HELP
Name the property that justifies each statement.
if UV = KL and KL = 6 Then UV = 6
If measure angle 1 + measure angle 2 = measure angle 4 + measure angle 2 then measure angle 1 = measure angle 4
angle ABC is congruent to ABC
If 1/2 measure angle D = 45, then measure angle D = 90
If angle DEF is congruent to angle HJK, then angle HJK is congruent to angle DEF
Answer:
Use desmos it is really helpful
[tex]The\:Answers\:Are:[/tex]
[tex]A.\:If\:\:UV=KL \:\:And\:\:KL=6,\:Then\:\:UV = 6,\:True[/tex]
[tex]C.\:Angle\:ABC\:Is\:Congruent\:To\:ABC,\:True[/tex]
[tex]\mathrm{E.\:If\:Angle\:DE F\:Is\:Congruent\:To\:Angle\:HJK,\:Then\:Angle\:HJK\:Is\:Congruent\:To\:Angle\:DE F},\:True[/tex]
[tex]The\:Questions\:B\:And\:C\:Are\:False[/tex]
[tex]\mathrm{Hope\:This\:Helps!!!}[/tex]
[tex]\mathrm{Please\:Mark\:Brainliest!!!}[/tex]
[tex]\mathrm{-Austint1414}[/tex]
the sum of 2x+7 and −x+12 is equal to 14 what is x?
Answer:-5
Step-by-step explanation:
2x+7-x+12=14
x+19=14
x=-5
Answer:
x=-5
Step-by-step explanation:
Ok so, (2x+7)+(-x+12)=14
solve the equation, by opening the parantheses.
2x+7+-x+12=14
x= -5
Thirty-six of the students in the school choir like to sing solos. These 36 students make up 24% of the choir. How many students are in the choir?
Answer:
150
Step-by-step explanation:
We can write a proportion to find the total amount in the choir using the information given. A proportion is two equivalent ratios set equal to each other.
[tex]\frac{24}{100}=\frac{36}{y}[/tex]
We will cross multiply the numerator of one ratio with denominator of the other. And then solve for y.
24y=100(36)
24y=3600
y=150.
There are 150 students in the choir.
the power in an electrical circuit is given by the equation p= /2 r, where / is the current flowing through the circuit. what is the current in a circuit that has resistance of 100 ohms and a power of 15 watts?
A. 0.15 amps
B. 0.39 amps
C. 6.7 amps
D.2.6 amps
Answer:
Actually, the equation is
power (in Watts) = I² * r
I - current in amps and r - resistance in watts
Solving this for the current (I)
I = square root (power / resistance)
I = square root (15 / 100)
I = square root (.15)
I = 0.3872983346 amps
answer is B
Step-by-step explanation:
The current in the circuit is approximately 0.39 amperes, which is option B.
The power in an electrical circuit can be calculated using the formula:
P = I^2 * R
Where:
P = Power (in watts)
I = Current (in amperes)
R = Resistance (in ohms)
In your case, you have:
P = 15 watts
R = 100 ohms
You want to find the current (I), so rearrange the formula to solve for I:
I = sqrt(P / R)
I = sqrt(15 watts / 100 ohms)
I = sqrt(0.15 A^2)
I = 0.39 A (approximately)
So, the current in the circuit is approximately 0.39 amperes, which is option B.
for such more question on electrical circuit
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When you roll a standard number cube once, what is the probability of rolling a number divisible by 3?
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
On a standard cube there are the numbers 1, 2, 3, 4, 5, 6
Only 2 are divisible by 3, that is 3 and 6, hence
P(divisible by 3 ) = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]
Write an explicit formula for the sequence... then find a17
Answer:
The correct answer option is: [tex]a_n=\frac{5}{2} n-\frac{11}{2}, 37[/tex].
Step-by-step explanation:
We are given the following arithmetic sequence and we are to write an explicit formula for it and the find the 17th term of the sequence:
{[tex]a_n[/tex]}={[tex]-3, -\frac{1}{2} ,2,\frac{9}{2} ,7[/tex]}
From the given options, we can put in the values of n and check if it proves to be true.
For [tex]a_n=\frac{5}{2} n-\frac{11}{2}[/tex], put values of [tex]n[/tex] from 1 to 5 which the number of the term.
[tex]a_1=\frac{5}{2} (1)-\frac{11}{2}\\\\a_1=-3[/tex]
[tex]a_2=\frac{5}{2} (2)-\frac{11}{2}\\\\a_2=-\frac{1}{2}[/tex]
[tex]a_3=\frac{5}{2} (3)-\frac{11}{2}\\\\a_3=2[/tex]
[tex]a_4=\frac{5}{2} (4)-\frac{11}{2}\\\\a_4=\frac{9}{2}[/tex]
[tex]a_5=\frac{5}{2} (5)-\frac{11}{2}\\\\a_5=7[/tex]
Therefore, the formula for the given sequence is [tex]a_n=\frac{5}{2} n-\frac{11}{2}[/tex].
Also, [tex]a_{17}=\frac{5}{2} (17)-\frac{11}{2}=37[/tex]
Answer: The correct one is an=5/2n-11/2,37 so A :)
The width of Florida is 4/5 of its length if the length of Florida is about 450 miles what is the approximate width
Answer:
4/5 of 450 is 360
Step-by-step explanation:
The slope of the line below is-1/7Write a point-slope equation of the line using the coordinates of the labeled point.
The point slope formula is
y-y1=m(x-x1)
M represents slope and (y1, x1) are the coordinates to your point.
From this question we know the slope is -1/7 so you plug that in to the formula which will give you
Y-y1=-1/7(x-x1)
There isn’t a point attached to this question so let’s make up a point and say it’s (1,7). You plug this into the equation to get
Y-7=-1/7(x-1)
This is your equation.
Plz Help!
What is the effect on the graph of the function f(x) = x when f(x) is replaced with −1/2f(x)?
A) vertical reflection over x-axis and vertical stretch
B) vertical reflection over x-axis and vertical compression
C) horizontal reflection over y-axis and horizontal stretch
D) horizontal reflection over y-axis and horizontal compression
When the function f(x) is replaced with -1/2f(x), it results in vertical reflection over x-axis and vertical compression of the graph.
Explanation:When the function f(x) is replaced with -1/2f(x), it means that the values of the original function are multiplied by -1/2. This has two effects on the graph of the function:
Vertical reflection over the x-axis: The positive values of f(x) become negative and vice versa. This flips the graph of the function vertically.Vertical stretch: The values of f(x) are multiplied by -1/2, which compresses the graph vertically. The new graph will be half as tall as the original graph.Therefore, the correct answer is B) vertical reflection over x-axis and vertical compression.
A traveling circus brings along everything it needs for its shows in big trucks.
a. the circus audience sits in rows around the performing ring. there are 9 seats in each row. how many rows will need to be set up if 513 people are expected to attend the show? can the rows be divided into a number of equal sections? explain how you find your answer.
b. circus horses eat about 250 pounds of horse food per week. about how many pounds of food does a circus horse eat each day? explain. (hint: 1 week = 7 days)
Answer :
(a) The number of rows need will be, 57 rows.
(b) The amount in pounds of food a circus horse eat each day is, 35.71 pounds.
Step-by-step explanation :
Part A:
As we are given that the there are 9 seats in each row that means 9 people can sit in each row.
Now we have to determine the number of rows will need to be set up if 513 people are expected to attend the show.
As, 9 people can sit in 1 row
So, 513 people can sit in [tex]\frac{513}{9}=57[/tex] row
Thus, the number of rows need will be, 57 rows.
Yes, the rows be divided into a number of equal sections as, 3 rows would be 19 sections or, 19 rows would be 3 sections.
Part B:
As we are given that circus horses eat about 250 pounds of horse food per week. Now we have to determine the amount in pounds of food does a circus horse eat each day.
Given : 1 week = 7 days
As, in 1 week the circus horses eat about 250 pounds of horse food
or, in 7 days the circus horses eat about 250 pounds of horse food
So, in 1 day the circus horses eat about [tex]\frac{1day}{7day}{\times 250=35.71[/tex] pounds of horse food
Thus, the amount in pounds of food a circus horse eat each day is, 35.71 pounds.
A total of 56 students signed up to play in a flag football league. If each team has 10 students, how many more students will need to sign up so all of the students can be on a team?
Final answer:
A total of 4 more students need to sign up for all 56 students to be placed on teams of 10 in the flag football league.
Explanation:
The question is asking how many additional students will need to sign up to ensure that all students can participate in a flag football league, with the stipulation that each team is made up of 10 students. With 56 students currently signed up, we can divide this number by the team size to see how many complete teams can be formed:
56 students ÷ 10 students per team = 5 teams with 6 students left over.
To have a complete additional team, 10 students are needed. Since there are already 6 students without a team, the number of additional students required is:
10 students needed for a complete team - 6 students already signed up but not placed on a team = 4 additional students needed.
Please answer thank you
Answer:
45°Step-by-step explanation:
they are opposite angles, same value of 45°
Can someone please help me with this question? Thank you!
Answer: A
Step-by-step explanation:
[tex]\stackrel\frown{XY}[/tex] ≅ [tex]\stackrel\frown{YZ}[/tex]
⇒ ∠XOY ≅ ∠ZOY
[tex]\overline{XO}[/tex] ≅ [tex]\overline{ZO}[/tex] since they are both a radius
[tex]\overline{OY}[/tex] ≅ [tex]\overline{OY}[/tex] based on reflexive property
∴ ΔXOY ≅ ΔZOY by SAS
So, [tex]\overline{XY}[/tex] ≅ [tex]\overline{ZY}[/tex] by CPCTC
ZY = 10.2 is given
so, XY = 10.2 by substitution property
A line crosses the y-axis at (0,4) and has a slope of -2. Find an equation for this line. A) y = 2x + 4 Eliminate B) y = -2x + 4 C) y = -2x - 4 D) y = -4x + 2
Answer:
We have the equation y - 4 = (-2)( x - 0 );
Then, y - 4 = -2x;
Finally, y = -2x + 4;
The correct answer is B) y = -2x + 4;
Step-by-step explanation:
The equation for the line with a slope of -2 and crossing the y-axis at (0,4) is y = -2x + 4.
To find an equation for a line that crosses the y-axis at (0,4) with a slope of -2, we can use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. Since we are given that the slope (m) is -2 and the y-intercept (b) is 4, the equation of the line is y = -2x + 4.
Identify the domain of the graphed function.
Answer:
(-4,-2) U (-2,4]
Step-by-step explanation:
Domain is the set of x values for which the function is defined.
We look at the x values on the graph
the graph starts at -4 and we have a hole at x=-4
For a hole we use parenthesis
Graph starts at -4 and ends at -2. Both -4 and -2 have hole, so we use parenthesis.
So interval is (-4,-2)
From -2 to 4 , there is no hole or break in between. the graph is continuous from -2 to 4
so interval is (-2, 4]
combine both intervals
(-4,-2) U (-2,4]
Answer:
B. (-4,-2) (-2,4)
Given: ∆AKL, AK = 9 m∠K = 90° m∠A = 60° Find: P∆AKL The area of ∆AKL
The perimeter (P∆AKL) of triangle AKL is 21.294 m, and the area is 20.25 m². Triangle AKL is a 30-60-90 triangle, with sides in the ratio 1:√3:2, allowing for straightforward calculations of the perimeter and area using the given side lengths and right triangle properties.
Explanation:To find the perimeter (P∆AKL) and the area of triangle AKL (∆AKL), we can use the properties of a right triangle. Since we have one angle of 60°, and the right angle 90°, the remaining angle must be 30°. With this information, we recognize that triangle AKL is a 30-60-90 special right triangle.
For a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. Knowing one side, AK (the side opposite the 60° angle), is 9 m, we determine the side opposite the 30° angle (AL) is half that length, so AL = 9m / 2 = 4.5 m. The side opposite the 90° angle (KL) is √3 times the side opposite the 30° angle, so KL = 4.5m * √3 = 7.794 m.
Now we can find the perimeter (P) by adding all the sides:
AK + AL + KL = 9m + 4.5m + 7.794m = 21.294 mThe area (A) of a right triangle is (½)*base*height.
A = (½) * AK * AL = (½) * 9m * 4.5m = 20.25 m²Find the tan(Θ) of an angle in standard position if the terminal side passes through the point (4, -8).
See the attached explanation and diagram.
Find the zeros of the function f(x) = x2 + 5x + 6. A) y = 6 because the graph crosses the y-axis at 6. B) y = -0.25 because that is the minimum value of the graph. C) x = 2 and x= 3 because the graph crosses the x-axis at 2 and 3. D) x = -3 and x = -2 because the graph crosses the x-axis at -3 and -2.
Answer:
D.)
Step-by-step explanation:
The zero's are referencing when y=0, note that when y=0 they are talking about the x-intercepts. You can graph the function and see when the graph crosses the x-axis or solve for the x-values. I will solve it via factoring and so:
[tex]f(x)=x^2+5x+6[/tex]
Multiply the outer coefficients, in this case 1 and 6, and 1×6=6. Now let's think about all the factors of 6 we have: 6×1 and 2×3. Now is there a way that if we use any of these factors and add/subtract them they will return the middle term 5? Actually we can say 6-1=5 and 2+3=5. Let's try both.
First let's use 6 and -1 and so:
[tex]x^2+5x+6\\\\x^2+6x-x+6\\\\x(x+6)-1(x-6)[/tex]
Notice how we have (x+6) and (x-6), these factors do not match so this is incorrect.
Now let's try 2 and 3 and so:
[tex]x^2+5x+6\\\\x^2+3x+2x+6\\\\x(x+3)+2(x+3)\\\\(x+2)(x+3)[/tex]
Notice how the factors (x+3) matched up so this is a factor and so is (x+2), now to solve for the zero's let's make f(x)=0 and solve each factor separately:
Case 1:
[tex]f(x)=x+2\\\\0=x+2\\\\x=-2[/tex]
Case 2:
[tex]f(x)=x+3\\\\0=x+3\\\\x=-3[/tex]
So your zero's are when x=-2 and x=-3.
D.) x=-3 and x=-2 because the graph crosses the x-axis at -3 and -2.
~~~Brainliest Appreciated~~~
Banu is 20 years older than binu. In 5 years, Banu will be twice as old as binu. Find their present age.
Answer:
i think Banu is 40 and Binu is 20
Step-by-step explanation:
if Banu was 35 and Binu was 15, 5 years go by Banu is 40 so still 20 years older and Binu is 20, Binu is half the age of Banu.