Answer:
[tex]\sqrt{85}[/tex]
Step-by-step explanation:
Calculate the distance d using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (6, - 2)
d = [tex]\sqrt{(6+1)^2+(-2-4)^2}[/tex]
= [tex]\sqrt{7^2+(-6)^2}[/tex]
= [tex]\sqrt{49+36}[/tex]
= [tex]\sqrt{85}[/tex] ← exact distance
Answer:
he other guy is wrong there is no 85
Step-by-step explanation:
Justin opens a savings account with $4. He saves $2 each week. Does a linear function or a nonlinear function represent this situation? Explain.
Yes , the situation can be represented by a linear function where the equation is A = 2x + 4 where x is the number of weeks
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation be represented as A
Now , the value of A is
The initial amount in Justin's savings account = $ 4
The amount saved by Justin every week = $ 2
Let the number of weeks be = x
So , the amount saved by Justin in x weeks = 2x
Now , the total amount saved by Justin in savings account A = initial amount in Justin's savings account + amount saved by Justin in x weeks
Substituting the values in the equation , we get
A = 4 + 2x
On simplifying the equation , we get
A = 2x + 4
which is of the form of a linear equation of line
Hence , the linear equation is A = 2x + 4 , where x is the number of weeks
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What minus -4 2/3 equals a positive number
Answer:-4 2/3
Step-by-step explanation: negative number minus itself will always be positive.
One batch of cookies requires the following ingredients:
2 1/3 cups of flour
3/4 of a cup of chocolate chips
2/5 of a cup of chopped almonds
1 1/2 cups of brown sugar
3/8 of a cup of white sugar
1/2 of a teaspoon of salt
Eric wishes to triple the recipe. How much of each ingredients should he use? Select all that apply
A) 6 1/3 cups of flour
B) 1/6 of a teaspoon of salt
C) 1 1/8 cups of white sugar
D) 9/12 cup of chocolate chips
E) 6/5 cups of chopped almonds
F) 2 1/2 cups of brown sugar
Answer:
it saids all that apply its A and what ????
Step-by-step explanation:
The correct options are:
(A) 6 (1/3) cup of flour
(E) 6/5 cups of chopped almonds.
Step-by-step explanation:
Given information:
One batch of cookies requires the ingredients:
2 (1/3) cup of flour.
3/4 of a cup of chocolate chips
2/5 of a cup of chopped almonds
1 (1/2) cup of brown sugar
3/8 of a cup of white sugar
1/2 of teaspoon of salt
Now if Eric wishes to triple the recipe, He needs to triple all the ingredients.
So the new list of ingredients will be triple of pervious one.
That will be:
6 (1/3) cup of flour
3 (3/4) cup of chocolate chips
3 (2/5) cup of chopped almonds
3 (1/2) cup of brown sugar
3 (3/8) cup of white sugar
3 (1/2) tea spoon of salt
So the correct options are:
(A) 6 (1/3) cup of flour
(E) 6/5 cups of chopped almonds.
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what are associative on rational numbers
Answer:yo7 can add or multiply numbers regardless how they are grouped
Step-by-step explanation:
sec squared 55 - tan squared 55
Answer:
sec squared 55 – tan squared 55 = 1
Explanation:
Given, sec square 55 – tan squared 55
We know that,
[tex]\sec \Theta=\frac{\text {hypotenuse}}{\text {base}}[/tex]
And,
[tex]\tan \theta=\frac{\text { perpendicular }}{\text { base }}[/tex]
where Ө is the angle
Substituting the values
[tex]\left(\frac{\text {hypotenuse}}{\text {base}}\right)^{2}-\left(\frac{\text { perpendicular }}{\text {base}}\right)^{2}[/tex]
Solving,
[tex]\frac{(\text {hypotenuse})^{2}-(\text {perpendicular})^{2}}{(\text {base}) *(\text {base})}[/tex]
According to Pythagoras theorem,
[tex]\text { (hypotenuse) }^{2}-\text { (perpendicular) }^{2}=(\text { base })^{2}[/tex]
Putting this in the equation;
squared 55 - tan squared 55 =
[tex]\frac{(\text {hypotenuse})^{2}-(\text {perpendicular})^{2}}{(\text {base}) *(\text {base})}=\frac{(\text {base})^{2}}{(\text {base}) *(\text {base})}=1[/tex]
Therefore, sec squared 55 – tan squared 55 = 1
The value is always 1.
To solve the expression sec²(55°) - tan²(55°), we can use a trigonometric identity. Recall the Pythagorean identity for tangent and secant:
sec²(θ) - tan²(θ) = 1
Using this identity, we substitute θ with 55°:
sec²(55°) - tan²(55°) = 1This simplifies our expression immediately, as the value is always 1 regardless of the angle, as long as the identity holds.
So, sec²(55°) - tan²(55°) = 1.
What is the volume of this rectangular prism?
4.8 cm
4.1 cm
15 cm
Answer:
those are the dimentions
Step-by-step explanation:
Three consecutive integers have a sum of 132?
Answer:
43 , 44 ,45
Step-by-step explanation:
X + X + 1 + X + 2 = 132
3X + 3 = 132
3X = 132 - 3
3X = 129
X = 129/3
X = 43
so first number is 43.
second number will be 43 + 1 = 44
third number will be 43 + 2 = 45
What is the equation in point slope form of the line that passes through the point (−1, −3) and has a slope of 4?
y+1=4(x+3)
y−1=4(x−3)
y+3=4(x+1)
y−3=4(x−1)
Answer:
y + 3 = 4(x + 1)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = 4 and (a, b) = (- 1, - 3), thus
y - (- 3) = 4(x - (- 1)), that is
y + 3 = 4(x + 1)
Answer:
its C can i have
Step-by-step explanation:
50 points! A polynomial has been factored below, but some constants are missing. 2x^3 - 8x^2 - 24x = ax (x+b)(x+c) What are the missing values of a, b, and c?
The missing values are [tex]\( a = 2 \), \( b = 0 \), and \( c = -24 \),[/tex] yielding the factored form [tex]\( 2x(x - 24) \).[/tex]
To find the missing values of[tex]\( a \), \( b \), and \( c \)[/tex], we need to expand the polynomial [tex]\( (x+b)(x+c) \)[/tex]and equate it to [tex]\( 2x^3 - 8x^2 - 24x \).[/tex]
Expanding [tex]\( (x+b)(x+c) \),[/tex] we get:
[tex]\[ (x+b)(x+c) = x^2 + (b+c)x + bc \][/tex]
Comparing this to [tex]\( 2x^3 - 8x^2 - 24x \),[/tex]we see that:
[tex]\[ x^2 + (b+c)x + bc = 2x^3 - 8x^2 - 24x \][/tex]
We need to match the coefficients of corresponding terms on both sides of the equation.
From the equation above, we can equate coefficients:
1. Coefficient of [tex]\( x^3 \): \( 2 = 0 \)[/tex] (there is no [tex]\( x^3 \)[/tex] term on the right side).
2. Coefficient of [tex]\( x^2 \): \( 1 = -8 \) (from \( x^2 \) term)[/tex].
3. Coefficient of [tex]\( x \): \( b + c = -24 \) (from \( x \) term).[/tex]
4. Constant term: [tex]\( bc = 0 \)[/tex] (there is no constant term on the right side).
From the last equation, we know that either [tex]\( b \) or \( c \)[/tex]must be zero, or both.
If one of them is zero, then the other must be equal to [tex]\( -24 \)[/tex] for the equation [tex]\( b + c = -24 \)[/tex] to hold true.
Now, we can test some values to satisfy these equations:
1. If [tex]\( b = 0 \)[/tex]
[tex]\[ c = -24 \][/tex]
2. If [tex]\( c = 0 \):[/tex]
[tex]\[ b = -24 \][/tex]
3. If both [tex]\( b \) and \( c \)[/tex]are non-zero:
We can solve the equation [tex]\( b + c = -24 \)[/tex] for various values of [tex]\( b \) and \( c \).[/tex]
Therefore, possible combinations are:
1.[tex]\( a = 2 \), \( b = 0 \), \( c = -24 \)[/tex]
2.[tex]\( a = 2 \), \( b = -24 \), \( c = 0 \)[/tex]
3.[tex]\( a = 2 \), \( b = -12 \), \( c = -12 \)[/tex]
So, the possible missing values are:
1. [tex]\( a = 2 \), \( b = 0 \), \( c = -24 \)[/tex]
2. [tex]\( a = 2 \), \( b = -24 \), \( c = 0 \)[/tex]
3.[tex]\( a = 2 \), \( b = -12 \), \( c = -12 \)[/tex]
Solve the system of linear equations. 2x + 5y = 12 4x − y = 2
Answer:
x=1, y=2. (1, 2).
Step-by-step explanation:
2x+5y=12
4x-y=2
--------------
y=4x-2
2x+5(4x-2)=12
2x+20x-10=12
22x-10=12
22x=12+10
22x=22
x=22/22
x=1
4(1)-y=2
4-y=2
y=4-2=2
y=2
Answer:
x = 1, y = 2 → (1, 2)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}2x+5y=12\\4x-y=2&\text{multiply both sides by 5}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}2x+5y=12\\20x-5y=10\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad22x=22\qquad\text{divide both sides by 22}\\.\qquad x=1\\\\\\\text{Put the value of}\ x\ \text{to the second equation:}\\\\4(1)-y=2\\4-y=2\qquad\text{subtract 4 from both sides}\\-y=-2\qquad\text{change the signs}\\y=2[/tex]
Estimate the size of a crowd walking in a charity fundraising march that occupies a rectangular space with dimensions of 10 feet by 1,200 feet (to the nearest whole number). Assume that 40 people occupy a rectangle measuring 10 feet by 12 feet.
Answer:
4000 is size of a crowd walking in a charity fundraising March.
Step-by-step explanation:
Given:
Dimensions of rectangular space 10 feet by 12000 feet
So we can say that,
Length = 1200 ft
Width = 10 ft
Now we will calculate the area of rectangular space which is given by
Hence Area will be = [tex]length\times width= 10\ ft \times 1200 \ ft= 12000 \ ft^2[/tex]
Now we know that 40 people occupy a rectangle measuring 10 feet by 12 feet.
Length = 12 ft
Width = 10 ft
Area = [tex]length\times width= 10\ ft \times 12 \ ft= 120 \ ft^2[/tex]
It says that 40 people are occupied in 120 [tex]ft^2[/tex]
So how many people will be there in 12000 [tex]ft^2[/tex]
By using unitary method we get,
Number of people = [tex]\frac{40\times 12000 \ ft^2}{120 \ ft^2} = 4000 \ peoples[/tex]
Size of a crowd walking in a charity fundraising March is 4000.
Answer:
4,000 people
Step-by-step explanation:
49 people occupy 120 ft^2
Dimensions of crowd: 10×1,200=12,000
120 ft^2/40 people = 12,000 ft^2/x people
X=4,000
Evaluate n+2x2 when n=3 and x=−2.
Answer:
When n=3 and x=−2 the answer is 11.
Step-by-step explanation:
Given:
Let p (n,x) be the function such that
[tex]p (n,x) = n + 2x^{2}[/tex]
To Find:
p (n,x) = p ( 3, -2) = ?
Solution:
[tex]p (n,x) = n + 2x^{2}[/tex]
Substituting n = 3 and x = -2 we get
[tex]p (3, -2) = 3 + 2(-2)^{2}[/tex]
Negative square gives positive number therefore (-2)²=4
[tex]p (3, -2) = 3 + 2\times 4[/tex]
[tex]p (3, -2) = 3 + 8\\p (3, -2) = 11[/tex]
When n=3 and x=−2 the answer is 11.
Final answer:
When evaluating the expression n+2x^2 with n=3 and x=-2, we substitute the values to get 3 + 2(-2)^2, which simplifies to 3 + 8. The final evaluated expression is 11.
Explanation:
To evaluate the expression n+2x² with given values for n and x, we need to substitute the values into the expression and simplify it.
In this case, n = 3 and x = -2. Substituting these values in, we get:
3 + 2(-2)²
First, we calculate the square of -2:
3 + 2(4)
Now, we multiply 2 by 4:
3 + 8
Finally, we add 3 and 8 together:
11
Therefore, the evaluated expression is 11.
P(A) = 8/15
P(B) = 6/15
P(A n B) = 1/5
Find P(AUB)
A. 2/15
B. 11/15
C. 1/15
D. 4/15
Answer:
Step-by-step explanation:
note : P(AUB) = p(A)+p(B) - p(A∩B)
P(AUB) = 8/15+6/15- 1/5 = 8/15+6/15-3/15 = 11/15 answer : B
Probability helps us to know the chances of an event occurring. The correct option is B.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Given that P(A) = 8/15, P(B) = 6/15, and P(A n B) = 1/5. Therefore, the value of P(AUB) will be,
P(AUB) = P(A) + P(B) + P(A n B)
= 8/15 + 6/15 - 1/5
= 11/15
Hence, the correct option is B.
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A rational function is a function whose equation contains a rational
expression.
A. True
B. False
Answer:
True
Step-by-step explanation:
Answer:
true
Step-by-step explanation:
Marco needs $57 to buy new basketball shoes. If Marco earns $3 per day working and already has $12 saved, which equation shows how many days Marco must work before he can afford the shoes?
Answer:
3x+12=57
x= how many days
Step-by-step explanation:
Answer:
[tex]3x+12=57[/tex]
Step-by-step explanation:
Let x represent number of days.
We have been given that Marco earns $3 per day working. So amount earned in x days would be [tex]3x[/tex].
We are also told that Marco already has $12 saved, so total amount saved by Marco in x days would be [tex]3x+12[/tex].
Now we will equate total amount saved by Marco in x days with 57 as Marco needs to save $57 to buy new shoes.
[tex]3x+12=57[/tex]
Therefore, the equation [tex]3x+12=57[/tex] shows the number of days (x) that Marco must work before he can afford the shoes.
1. Two pieces of equipment were purchased for a total of $4000. If one piece cost $850 more fean
the other, find the price of the less expensive piece of equipment. Assume all data ze 2002
to two significant agits unless grezier 20curacy is given
Answer:
$1,575
Step-by-step explanation:
x = the cost of the less expensive piece of equipment
x+850 = the cost of the more expensive piece of equipment
x + (x+850) = 4,000 the. two pieces together cost 4,000, so I added up the cost of the less expensive piece and the more expensive piece, and equaled it to 4,000
solve the equation:
x + (x+850) = 4,000
2x+850=4,000
2x=3,150
÷2
x=1,575
The third angle of a triangle is the same size as the first. The second angle is 4 times the third. Find the measure of angles.
Answer:
1st angle 30°
2nd angle 120°
3rd angle 30°
Step-by-step explanation:
Let's call
A = 1st angle
B = 2nd angle
C = 3rd angle
In every triangle it holds
A + B + C = 180°
Now, if the third angle of the triangle is the same size as the first
A = C
If the second angle is 4 times the third
B = 4C
we have then
C + 4C + C = 180° ===> 6C = 180° ===> C = 30°
If C = 30° then A = 30° and B = 120°
What is the area of the triangle with a base of 5 1/2 cm and a height of 3 1/2 cm?
Answer:
9.63
Step-by-step explanation:
Tommy's Diner offers its clients a choice of regular and diet soda. Last night, the diner served 51 regular sodas and 34 diet sodas. What percentage of the sodas served were regular?
Answer:
60%
Step-by-step explanation:
51+34=85
51/84= 0.60 or 60%
The circumference of a circle is 15 ft. What is the length of the radius? Use 3.14 for π. Round your answer to the nearest tenth of a foot.
Answer:
The radius of the circle is 2.4ft
Step-by-step explanation:
circumference of circle = 2πr
circumference = 15ft
2πr = 15
(2×3.14)r = 15
6.28r = 15
r = 2.4ft (near. tenth)
Answer:
The answer is 2.4 ft.
Step-by-step explanation:
C= 2πr
15= 2(3.14)r
15= 6.28r
15÷6.28= 6.28r÷ 6.28
2.4= r
Mary and Lamar establish a tutoring service at a local mall. They tutor college students in math and English. They charge $40 per hour for tutoring. In the month of January they charged for 200 tutoring hours. The expenses of their business are given in the table below. Expense Amount/Month Rent of Space $4000 Electricity $325 Advertising $375 Using the formula Profit = $40(number of hours) – (expenses) , calculate their profit for the month of January.
The profit is $3300 for the month of January.
Step-by-step explanation:
Per hour charge = $40
Total number of tutoring hours = 200
Rent of space = $4000
Electricity = $325
Advertising = $375
Total expenses = 4000+325+375 = $4700
Profit = $40(number of hours) - (expenses)
[tex]Profit=\$40(200)-4700\\Profit=\$8000-4700\\Profit=\$3300[/tex]
The profit is $3300 for the month of January.
Keywords: profit, addition
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A = {1, 2, 5, 7} B = {3, 4, 6, 7} C = {0, 5, 8, 9} Find A U B U C. A) {0,1,2,3,4,5,6,7,8,9} B) {1,2,3,4,5,6,7} C) {3,4,5,6,7} D) {3,4,7}
A) {0,1,2,3,4,5,6,7,8,9} is the right answer
Step-by-step explanation:
Given
A = {1, 2, 5, 7}
B = {3, 4, 6, 7}
C = {0, 5, 8, 9}
We hvae to find the union of all thre sets. In union, the elements of involved sets are combined. The repating elements are only written once
So,
[tex]AUBUC = \{1, 2, 5, 7\}U\{3, 4, 6, 7\}U\{0, 5, 8, 9\}\\= \{0,1,2,3,4,5,6,7,8,9\}[/tex]
Hence,
A) {0,1,2,3,4,5,6,7,8,9} is the right answer
Keywords: Sets, Union
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How many pounds of ground beef are needed to make 80 hamburger patties if each uncooked patty weighs 4.8 ounces?
A
10.4 pounds
B
24 pounds
C
61.4 pounds
D
96 pounds
The right answer is Option B.
Step-by-step explanation:
Beef per patty = 4.8 ounces
Number of hamburgers = 80
Beef required = Number of hamburgers * beef per patty
Beef required = [tex]80*4.8 = 384 \ ounces[/tex]
As we know,
16 ounces = 1 pound
1 ounce = [tex]\frac{1}{16} \ pounds[/tex]
384 ounces = [tex]\frac{1}{16}*384[/tex]
384 ounces = 24 pounds
24 pounds of beef is required to make 80 hamburger patties.
The right answer is Option B.
Keywords: multiplication, division
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What is the domain of the function shown in the mapping?
Input
Output
{x|x=-5, -3, 1, 2, 6}
{yl y = -9,6, 0, 2, 4}
{x|x = -9, -6, -5, -3,0, 1, 2, 4, 6}
{yly = -9, -6, -5, -3,0, 1, 2, 4, 6}
{x|x=-5, -3, 1, 2, 6} is the domain of the function shown in the mapping?.
Step-by-step explanation:
The function’s domain is the whole group of the possible values for the independent variables. Generally, this definition explains:
A domain is a group of all possible x values that cause a "function work" to perform true y values.
When finding your domain, pay attention to the following:
• The denominator (in bottom) must not be zero
• The number below the square root must be positive in the section.
From the given mapping figure, Domain: {x| x = -5, -3, 1, 2, 6}
In a recent poll, 370 people were asked if they liked dogs, and 7% said they did. Find the margin of error of this poll, at the 90% confidence level. Give your answer to three decimals.
Answer:
[tex] ME=1.64\sqrt{\frac{0.07(1-0.07)}{370}}=0.0218[/tex]
Step-by-step explanation:
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]p[/tex] represent the real population proportion of interest
[tex]\hat p=0.07[/tex] represent the estimated proportion for the sample
n=370 is the sample size required (variable of interest)
[tex]z[/tex] represent the critical value for the margin of error
The population proportion have the following distribution
[tex]p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})[/tex]
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by [tex]\alpha=1-0.90=0.10[/tex] and [tex]\alpha/2 =0.05[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64[/tex]
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
And replacing into formula (a) the values provided we got:
[tex] ME=1.64\sqrt{\frac{0.07(1-0.07)}{370}}=0.0218[/tex]
The margin of error on this case would be ME=0.0218
Select the equation of the line that passes through the point (3, 5) and is
perpendicular to the line x= 4
O 1) y = 5
O2)x= 5
O3) y = 4
O4) x = 3
Answer:
1) y = 5Step-by-step explanation:
x = 4 it's a vertical line.
Perpendicular line to a vertical line is a horizontal line.
A horizontal line has equation y = a.
A horizontal line passes through the point (3, 5) → x = 3 and y = 5.
Therefore the equation is y = 5
Solve the inequality $-4x > -24.$ Give your answer in interval notation.
Final answer:
To solve the inequality -4x > -24, divide both sides by -4 and flip the inequality sign to obtain x < 6. The solution in interval notation is (-∞, 6).
Explanation:
To solve the inequality -4x > -24, we can divide both sides of the inequality by -4. Remember, when dividing or multiplying both sides of an inequality by a negative number, the inequality sign flips. So, the inequality becomes:
x < 6
The solution in interval notation is (-∞, 6).
Final answer:
The solution is x < 6, which is represented as (-∞, 6) in interval notation.
Explanation:
To solve the inequality -4x > -24, we can start by dividing both sides by -4.
Divide both sides of the inequality by -4. Remember that when you multiply or divide both sides of an inequality by a negative number, the direction of the inequality sign changes.
However, when dividing an inequality by a negative number, the direction of the inequality sign must be flipped. So we have x < 6.
Since the inequality sign is less than, the solution set is all values of x that are less than 6. In interval notation, this is represented as (-∞, 6).
for the function below, state the x-coordinate of the x-intercept that is located to the left of the origin
f(x)=4x^3-12x^2 - x + 15
Answer:
The x-coordinate of the x-intercept that is located to the left of the origin is equal to -1
Step-by-step explanation:
we have the function
[tex]f(x)=4x^3-12x^2-x+15[/tex]
we know that
The x-intercepts are the values of x when the value of the function is equal to zero
using a graphing tool
The function has three x-intercepts
The x-intercepts are the points
(-1,0),(1.5,0) and (2,5,0)
see the attached figure
The x-intercept that is located to the left of the origin is the point (-1,0)
therefore
The x-coordinate of the x-intercept that is located to the left of the origin is equal to -1
Answer:
The x-coordinate of the x-intercept is -1.
Step-by-step explanation:
If a figure has been dilated by a scale factor of 1/3, which transformation could be used to prove the figures are similar using the AA similarly postulate?
PLEASE HELP QUICKLY 25 POINTS
What is the common difference,d,of the sequence ?
-92,-74,-54,-38,-20
Enter your answer in the box
D = [ ]
Answer:
+18
Step-by-step explanation: