Answer:
it would take 9,000 min.
Step-by-step explanation:
multiply the 5 by the 3600
then divide by 2 and you get 9,000 min.
Find the area of this trapezoid:
Answer:
Pls add the image
Step-by-step explanation:
PLEASE HELP!!! Solve 5sin(π/3x)=3 for the four smallest positive solutions
This one's a special case of a right angled triangle with sides (3, 4, and 5 units)
Back to the problem :\(\qquad\displaystyle \tt \dashrightarrow \: 5 \sin \bigg( \frac{ \pi}{3} x \bigg) = 3\)
\(\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \frac{3}{5} \)
Now, check the triangle, sin 37° = 3/5
therefore,
\(\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \sin(37 \degree) \)
[ convert degrees on right side to radians ]
\(\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \sin \bigg(37 \degree \times \frac{ \pi}{180 \degree} \bigg ) \)
There are three more possible values as :
\(\qquad\displaystyle \tt \dashrightarrow \: \sin( \theta) = \sin(\pi - \theta) \)
\(\qquad\displaystyle \tt \dashrightarrow \: sin( \theta) = \sin \bigg( { 2\pi}{} + \theta \bigg) \)
\(\qquad\displaystyle \tt \dashrightarrow \: sin( \theta) = \sin \bigg( \frac{ 3\pi}{} - \theta\bigg) \)
Equating both, we get : First value :\(\qquad\displaystyle \tt \dashrightarrow \: \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} \)
\(\qquad\displaystyle \tt \dashrightarrow \: x = 37 \times \frac{ \cancel \pi}{180} \times \frac{3}{ \cancel \pi} \)
\(\qquad\displaystyle \tt \dashrightarrow \: x = \frac{37}{60} \)
or in decimals :
\(\qquad\displaystyle \tt \dashrightarrow \: x = 0.616666... = 0.6167\)
[ 6 repeats at third place after decimal, till four decimal places it would be 0.6167 after rounding off ]
similarly,
Second value :\(\qquad\displaystyle \tt \dashrightarrow \: \pi - \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} \)
\(\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(1 - \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} \)
\(\qquad\displaystyle \tt \dashrightarrow \: 1 - \frac{x}{3} = \frac{37}{180} \)
\(\qquad\displaystyle \tt \dashrightarrow \: - \frac{x}{3} = 0.205 - 1\)
\(\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 0.795\)
\(\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times 0.795\)
\(\qquad\displaystyle \tt \dashrightarrow \: x = 2.385\)
Third value :\(\qquad\displaystyle \tt \dashrightarrow \: 2\pi + \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} \)
\(\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(2 + \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} \)
\(\qquad\displaystyle \tt \dashrightarrow \: 2 + \frac{x}{3} = \frac{37}{180} \)
\(\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 0.205 - 2\)
\(\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = - 1.795\)
\(\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times -1 .795\)
\(\qquad\displaystyle \tt \dashrightarrow \: x = -5.385\)
Fourth value :\(\qquad\displaystyle \tt \dashrightarrow \: 3 \pi - \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} \)
\(\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(3 - \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} \)
\(\qquad\displaystyle \tt \dashrightarrow \: 3 - \frac{x}{3} = \frac{37}{180} \)
\(\qquad\displaystyle \tt \dashrightarrow \: - \frac{x}{3} = 0.205 - 3\)
\(\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 2.795\)
\(\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times 2.795\)
\(\qquad\displaystyle \tt \dashrightarrow \: x = 8.385\)
" x can have infinite number of values here with the same result, here are the four values as you requested "
I hope it was helpful ~
SOMEONE PLEASE HELPP MEE
The end-points of the line segment will be negative 1.25 and 0.25.
What is a number line?A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.
The length of the line segment is 1.50 units and the midpoint of the line segment is negative 0.50. Then the end-points of the line segment are given as,
⇒ - 0.50 ± (1.50) / 2
Simplify the expression, then we have
⇒ - 0.50 ± (1.50) / 2
⇒ - 0.50 - (1.50) / 2, - 0.50 + (1.50) / 2
⇒ - 0.50 - 0.75, - 0.50 + 0.75
⇒ - 1.25, 0.25
The end-points of the line fragment will be negative 1.25 and 0.25.
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Triangles are similar by :
A) AA similarity postulate.
B) SSS similarity theorem.
C) SAS similarity theorem.
D) The triangles are not similar.
triangles ABC and AMN are similar by the Side-Angle-Side (SAS) similarity theorem.
How to prove similarity?
To show that triangles ABC and AMN are similar, we need to show that their corresponding angles are equal and their corresponding sides are in proportion.
We can start by looking at the angles.
Angle MNA is opposite to side BC, so it is equal to angle BAC in triangle ABC.
Angle MAN is opposite to side BC in triangle AMN, so it is equal to angle ACB in triangle ABC.
Therefore, we have two pairs of corresponding angles that are equal:
angle BAC in triangle ABC and angle MNA in triangle AMN
angle ACB in triangle ABC and angle MAN in triangle AMN
Now let's look at the sides.
We can use the ratios of the corresponding sides to see if they are in proportion.
In triangle ABC, we have:
AB/BC = 21/15 (since AB = AM + MB = 21 + 9 = 30, and BC = BN + NC = 9 + 6 = 15)
In triangle AMN, we have:
AM/MN = 21/x (where x is the length of side MN)
AN/NM = 14/x (since AN + NM = AM = 21)
We can use the fact that MN = BC to substitute for x:
AM/MN = 21/15
AN/NM = 14/15
Therefore, the corresponding sides are in proportion, and we have:
AB/BC = AM/MN = 21/15
AC/BC = AN/NM = 14/15
This shows that triangles ABC and AMN are similar by the Side-Angle-Side (SAS) similarity theorem.
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What is the slope of a line graphed below?
Answer:
Undefined
Step-by-step explanation:
The slope of a horizontal line is zero. The slope of a vertical line is undefined.
1.1x + 1.2x - 5.4 = -10
Answer: x=-2
Step-by-step explanation:
1.1x+1.2x=2.3x
2.3x-5.4=-10
-10+5.4=-4.6
2.3x=-4.6
-4.6/2.3=-2
x=-2
The water usage at a car wash is modeled by the equation W(x) = 5x3 + 9x2 − 14x + 9, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours. Write a function, C(x), to model the water used by the car wash on a shorter day. C(x) = 5x3 + 7x2 − 14x − 6 C(x) = 4x3 + 7x2 − 14x + 6 C(x) = 4x3 + 7x2 − 14x − 6 C(x) = 5x3 + 7x2 − 14x + 6
Find the quotient of z₁ by z2. Express your answer in
trigonometric
form.
² - 3 (0 (4) + (*))
Z₁ cos
+/sin
Z₂
²2 = 7 (cos(377)+
COS
8
O A. 7 (cos (577) + i sin (5/77))
8
B.
21(cos(577)+isin (577))
8
OC. 21 cos
21(cos(-7)+ i sin(-77))
O D. 7 (cos(-7) + + sin(-7))
i
+/sin
37T
8
The quotient of z₁ by z₂ in trigonometric form is:
7/21 * (cos(584°) + i sin(584°))
To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.
Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.
We have:
z₁ = 7(cos(577°) + i sin(577°))
Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.
From the given information, we have:
z₂ = 21(cos(-7°) + i sin(-77°))
To find the quotient, we divide z₁ by z₂:
z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]
Substituting the given values, we have:
z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]
= (7/21) * [cos(584°) + i sin(584°)]
The quotient of z₁ by z₂ in trigonometric form is:
7/21 * (cos(584°) + i sin(584°))
Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.
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Some people advise that in very cold weather, you should keep the gas tank in your car more than half full. Irene's car had 6.2 gallons in the 15-gallon tank on the coldest day of the year. Irene filled the tank with gas that cost $3.50 per gallon. How much did Irene spend on gas?
Answer:
She spend $21,70 on gas
Step-by-step explanation:
6.350=2100
$21,00 for 6 gallons
350:10=35
0,35
035.2=070
0,70
2100+70=2170
X,(x-36) What is the value of x
The value of x is 63
How to determine the valueTo determine the value of the variable, we have that;
Angles at a point is equal to 360 degreesComplementary angles are defined as angles that sum up to 90 degreesSupplementary angles are defined as angles that sum up to 180 degreesAngles on a straight line is equal to 180 degreesFrom the information given, we have that;
x and x - 36 are complementary angles
Now, equate the angles to 90 degrees, we have;
x + x - 36= 90
collect the like terms, we get;
2x = 90 + 36
add the terms
2x =1 26
Divide by the coefficient
x = 63
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Complete question:
The angles X,(x-36) are complementary. What is the value of x
What is the radius of a hemisphere with a volume of 6496 (cm to the third power) to the nearest tenth of a centimeter?
Answer:
14.6cm
Step-by-step explanation:
The volume of a hemisphere is 2/3 × π × r³ → 6496 = 2/3 × π × r³. You can divide both sides by 2/3π to get r³ on its own → 3103.611531 = r³. To find r, cube root both sides → r = ∛3103.611531 = 14.5835... ≈ 14.6cm.
Hope this helps!
The radius of a hemisphere with a volume of 6496 is 14.5 cm
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The volume of a hemisphere is given by the formula V = (2/3)πrr³.
Since we are given the volume of the hemisphere, we can solve for the radius as follows:
V = (2/3)πr³
6496 = (2/3)πr³
Multiplying both sides by 3/2π, we get:
r³ = 6496 × (3/2π)
=6496×3/2×3.14
=19488/6.28
=3103.1
=∛3103.1
radius=14.5
Hence, the radius of a hemisphere with a volume of 6496 is 14.5 cm
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The difference of two supplementary angles is 70 degrees. Find the measures of the angles.
Answer:
DUEDY A. 32 degrees
Step-by-step explanation:
PATROLLING WEE WOOO
Xd
Answer:
55 125
Step-by-step explanation:
Let the smaller angle = x
Let the larger angle = x + 70
They are supplementary so the total of the two angles, by definition must be 180 degrees. Note that you should understand that any number of angles can but supplementary as long as they all add up to 180 degrees.
x + x + 70 = 180
2x + 70 = 180
2x + 70 - 70 = 180 - 70
2x = 110
2x/2 = 110/2
x = 55
the smaller angle = 55 degrees
The larger angle = 55 + 70 = 125
Write an equation in slope-intercept form that goes through (12, 4) and (20,8).
Answer:
Equation in slope-intercept form that goes through (12, 4) and (20,8) is: \(y = \frac{1}{2}x-2\)
Step-by-step explanation:
Given two points are:
\((x_1,y_1) = (12,4)\\(x_2,y_2) = (20,8)\)
Slope intercept form of line is given as:
\(y = mx+b\)
Here m is the slope of the line and b is the y-intercept.
Slope of a line is calculated by the formula:
\(m = \frac{y_2-y_1}{x_2-x_1}\)
Putting the values
\(m = \frac{8-4}{20-12}\\m = \frac{4}{8}\\m=\frac{1}{2}\)
Putting the value of slope in slope-intercept form we get
\(y = \frac{1}{2}x+b\)
To find the value of b, any one point will be put in the equation
Putting the first point (12,4) in the equation
\(4 = \frac{1}{2}(12) + b\\4 = 6+b\\b = 4-6\\b = -2\)
Putting the value of b
\(y = \frac{1}{2}x-2\)
Hence,
Equation in slope-intercept form that goes through (12, 4) and (20,8) is: \(y = \frac{1}{2}x-2\)
Duane begins paying a $5,000
student loan with an annual interest rate of 6.5%
compounded monthly. He schedules monthly payments of $118.57
for 4
years.
The following table shows the first payment in the amortization schedule.
Payment
Number Loan
Amount Payment Interest Principal Remaining
Balance
1
$5,000.00
$118.57
?
What amount of Duane's first payment goes to interest?
Responses
The amount of Duane's first payment that goes to interest is approximately $26.47.
To determine the amount of Duane's first payment that goes to interest, we need to use the amortization formula for a loan.
The formula to calculate the interest portion of a loan payment is:
Interest = Remaining Balance * Monthly Interest Rate.
Let's calculate the interest for the first payment using the given information:
Loan Amount = $5,000.00
Monthly Payment = $118.57
First, we need to calculate the monthly interest rate:
Monthly Interest Rate = Annual Interest Rate / 12
= 6.5% / 12
= 0.00542
Next, we need to calculate the remaining balance after the first payment:
Remaining Balance = Loan Amount - Principal Paid
= $5,000.00 - $118.57
= $4,881.43
Finally, we can calculate the interest portion of the first payment:
Interest = Remaining Balance * Monthly Interest Rate
= $4,881.43 * 0.00542
= $26.47
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8.
The easily accessible part of an emergency fund is _____.
savings
CDs
cash
credit cards
Answer:
Savings
Step-by-step explanation:
If you don't have a lot of money in general and an emergency occurs savings is the easiest way to go because you money money saved up for issues like these. But if u don't even have a savings account credit cards might be the way to go but it will damage your credit score pretty badly. So Savings is my final answer.
Evaluate the algebraic expression 2x + y- z when w = 12, x = 10, 5 and z = 9
Answer:
a
Step-by-step explanation:
Answer:
A/8
Step-by-step explanation:
b) In a group of 1,100 youths, each uses smart phones, either I-phone or Samsung or both or neither, 150 of them use only I-phone, 770 of them use Samsung and 900 use only one of these two smart phones. (i) Find the number of youths who use both of these smart phones. (ii) Find the number of youths who use neither of these smart phones.
b) The university gym opens at 9 am on Saturday mornings. One Saturday morning at 8:55 am there are 15 students outside the gym waiting for it to open. Should you use the same approach from part (a) to calculate the expected number of smokers among these 15 students
Answer:
The complete question is:
At a university, 13% of students smoke.
a) Calculate the expected number of smokers in a random sample of 100 students from this university:
b) The university gym opens at 9 am on Saturday mornings. One Saturday morning at 8:55 am there are 27 students outside the gym waiting for it to open. Should you use the same approach from part (a) to calculate the expected number of smokers among these 27 students?
Part a is easy, because is a random sample, we can expect that just 13% of these 100 students to be smokers, and 13% of 100 is 13, so we can expect 13 of those 100 students to be smokers.
b) This time we do not have a random sample, our sample is a sample of 15 students who go to the gym in the early morning, so our sample is biased. (And we do not know if this bias is related to smoking or not, and how that relationship is), so we can't use the same approach that we used in the previous part.
Basic statistics for business
a) 68% of the widget weights lie between 33 ounces and 51 ounces.
b) The percentage of widget weights between 24 and 51 ounces is of: 81.5%.
c) The percentage of weights above 15 is of: 99.85%.
What is defined by the Empirical Rule?These approximate percentages are defined by the Empirical Rule, for a normally distributed variable:
68% of the measures within one standard deviation of the mean.95% of the measures within two standard deviation of the mean.99.7% of the measures within three standard deviation of the mean.Hence the bounds of the interval containing the middle 68% of the values are given as follows:
42 - 9 = 33.42 + 9 = 51.The normal distribution is symmetric, meaning that 50% of the measures are below the mean and 50% are above.
Hence the interval between 24 and 51 ounces is given as follows:
Between 24 and 42: 95% of 50%.Between 42 and 51: 68% of 50%.Hence the percentage is of:
0.95 x 50 + 0.68 x 50 = 81.5%.
The percentage above 15 is given as follows:
Between 15 and 42: 99.7% of 50%.Above 42: 50%.Hence:
0.997 x 50 + 50 = 99.85%.
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Which of the following matches a quadrilateral with the listed characteristics below?
1. All four sides congruent
2. Both pairs of opposite sides parallel
3. Diagonals are perpendicular
A.
Rhombus
B.
Parallelogram
C.
Rectangle
D.
Trapezoid
Answer:
Option (A)
Step-by-step explanation:
By the characteristics of a quadrilateral given in the question,
1). All four sides are congruent.
It may be Square, Rhombus
2). Both the pairs of opposite sides are parallel.
It may be Parallelogram, Rhombus.
3). Diagonals are perpendicular.
It may be Rhombus, Rectangle, Square.
Since all three characteristics define the properties of a Rhombus,
The given quadrilateral matches with a rhombus.
Therefore, Option (A) will be the answer.
A computer normally sells for $520. During a sale the computer is marked down 15 percent. How much will it cost to buy the computer during the sale
Answer:
$598
Step-by-step explanation:
520=100%
115% =
520×115%÷100%=598
Ans = $598
can u slove ASAP please
Answer:
B) 352
Step-by-step explanation:
45% = 0.45
640 x 0.45= 288
288 is how many students walked to school
So to find how many took the bus to school
640- 288= 352
Solve (x + 1 < 4) ∩ (x - 8 > -7).
Answer:
\(1<x<3\)
Step-by-step explanation:
Let simplify each of these inequalities individually and then look at where they intersect afterwards
\(x+1<4\\\\x<3\)
And
\(x-8>-7\\\\x>1\)
This means that for these two inequalities to intersect, x must be greater than 1, but less than 3.
This can be represented by the following inequality \(1<x<3\)
(39-7) divided by 4^2 = ?
Answer:
Its 2
Step-by-step explanation:
(39-7) / 4^2
32 / 4^2
32 / 2^4
2^5 / 2^4 divide which gets you
2
PLEASE HELP!!!!!!!!! I NEED IT
The angle of elevation from a point on the ground to the top of a tower is 18°. The base of the tower is 100 feet from the point on the ground. Find the height of the tower. Round to the nearest tenth of a foot.
Answer:
32.5 feet
Step-by-step explanation:
This situation forms a right triangle. We are given the distance from the base of the tower (long leg of the triangle) and are asked to find the height (short leg of the triangle).
With this information, we can use the tan ratio, opposite over adjacent, to find the height of the tower.
tan 18 = \(\frac{x}{100}\)
Multiply each side by 100:
(100) tan 18 = x
Simplify and round to the nearest tenth:
32.49 = x
32.5 = x
So, the height of the tower is approximately 32.5 feet
A cereal company makes a cereal from two ingredients: wheat and oats. Each ingredient provides two essential nutrients: vitamin A and vitamin B. The company wants to know how many ounces of wheat and oats to include in each box of cereal so that the minimum requirements of 48 milligrams of vitamin A and 20 milligrams of vitamin B are satisfied. An ounce of wheat provides 10.5 milligrams of vitamin A and 2.4 milligrams of vitamin B. An ounce of oats provides 6 milligrams of vitamin A and 1.8 milligram of vitamin B. An ounce of wheat costs $0.05 and an ounce of oats costs $0.10. The company wants to minimize the total cost of production.
Find the solution to this problem using the Simplex method.
Answer:
z (min ) = 0.4167 $
x = 8,33 oz
y = 0
Step-by-step explanation:
Table:
Vitamin A Vitamin B Cost $/oz
Wheat (x) 10.5 2.4 0.05
Oats (y) 6 1.8 0.10
Requirements 48 (mg) 20 (mg)
Requirements 1,693 (oz) 0,7054 (oz)
The problem is minimized z subject to two constraint
z = 0.05*x + 0.1*y to minimize
Subject to:
Requirement of Vitamin A
10.5*x + 6 * y ≥ 48
Requirement of Vitamin B
2.4*x + 1.8*y ≥ 20
x≥0 y≥0
Using the on-line solver AtomZmaths and after 3 iterations the solution is:
z (min ) = 0.4167 $
x = 8,33 oz
y = 0
Would the answer be 14%?
6) Carmen has several spools of embroidery floss in different colors that she uses to make
bracelets and necklaces. Suppose she selects a spool at random to make a friendship bracele
How much greater is the probability that she selects blue floss than orange floss? Express you
answer as a percent.
Color and number of spools
black. 8
brown 5
red. 7
blue. 10
orange 3
purple 6
pink. 4
yellow. 7
The probability that Carmen selects blue floss greater than the probability that orange floss is selected is 14%.
How to find the probability ?There are a total of 8 + 5 + 7 + 10 + 3 + 6 + 4 + 7 = 50 spools of floss.
The probability of selecting a blue floss is 10/50 = 1/5.
The probability of selecting an orange floss is 3/50.
Therefore, the probability of selecting blue over orange is (1/5 - 3/50) = (10/50 - 3/50) = 7/50.
To express this as a percentage, we can multiply by 100:
7/50 × 100% = 14%.
So the probability of selecting blue floss over orange floss is 14%.
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44. Which part of the survey described in Exercise 32 represents the descriptive branch of statistics? Make an inference based on the results of the survey.
This is what question 32 said
32. A survey of 961 major-appliance shoppers found that 23% bought extended warranties
Answer:
The descriptive statistics here is, p = 0.23 or 23%.
Step-by-step explanation:
Descriptive statistics are short term descriptive coefficients that condenses a given dataset, which can be a demonstration of the whole or a sample of a whole population.
The different types descriptive statistics are:
Measures of frequency: proportion, frequencyMeasures of Central tendency: mean, median, modeMeasure of dispersion: variance, standard deviation, rangeIt is provided that a survey of 961 major-appliance shoppers found that 23% bought extended warranties.
The descriptive statistics here is, p = 0.23 or 23%.
The proportion 0.23 describes the percentage of major-appliance shoppers who bought extended warranties.
to simplify -36 / by (2)(3)^2 + 5 we first
It’s not c I got it wrong
Answer:
A
Step-by-step explanation:
First I thought it was C, but you got it wrong. Writing (2)(3) is the same as 2*3 so if you just imagine taking those parenthesis away, you square the 3.
Simplify (x+1)(x-3)=
Answer: x−²-2x−3
If I Helped, Please Mark Me As Brainliest, Have A Great Day :D
Btw I Will Be Heading Off Now, SO Goodbye