Answer:
n = 5
n = 8
Step-by-step explanation:
n^2 - 13n = -40
Equate everything to zero
n^2 - 13n + 40 = 0
Factorise
(n - 5)(n - 8) = 0
Either
n - 5 = 0
Add 5 to both sides
n - 5 + 5 = 0 + 5
n = 5
Or
n - 8 = 0
Add 8 to both sides
n - 8 + 8 = 0 + 8
n = 8
n = 5 or
n = 8
It has two real solutions
Explain how you can use a number line to find the sum
Let's say you wanted to add 2 and 7
One way is you start at 2 on the number line, then move 7 units to the right until you land on 9. This visually shows 2+7 = 9.
Or you could start at 7 and move 2 units to the right, and you'll end up at 9 as well. You can think of it like 2+7 and 7+2 are the same thing.
A circle has a circumference of 12. It has an arc of length 8/5. what is the central angle of the arc, in degrees?
360⁰......12
x.............8/5=1.6
Thus:
x=1.6×360/12=1.6×30=48⁰
Answer: x=48⁰
Answer: The central angle of the arc is 48 degrees.
Step-by-step explanation: The question has provided the first clue, which is the circumference of the circle, given as 12 units. Also the length of an arc along the same circumference has been given as 8/5 units. The circumference of a circle is calculated as
Circumference = 2Pi x radius
Also the length of an arc is calculated as
Length of an arc = (X/360) x 2Pi x radius (where ‘X’ is the angle subtended by the arc).
Having known the answer to 2Pi x radius which is 12, and the length of the arc which is 8/5, we can now express the length of an arc as
Length of an arc = (X/360) x 2Pi x radius
8/5 = (X/360) x 12
By cross multiplication we now have
(8 x 360)/ (5 x 12) = X
2880/60 = X
48 = X
Therefore the central angle of the arc is 48 degrees.
Find f(6) if f(x) = x2 ÷ 3 + x.
Answer:
f(6) = 18
Step-by-step explanation:
So we are given that f(x) = x² ÷ 3 + x, and we are trying to find f(6).
To find f(n) for a function f(x), we plug in n for x into f(x).
To find (6) for f(x) = x² ÷ 3 + x, we plug in 6 for x into f(x).
f(6) = (6)² ÷ 3 + (6) = 36 ÷ 3 + 6 = 12 + 6 = 18
f(6) would equal 18.
f(6) = 18
I hope this helps. :)
Answer:
18
Step-by-step explanation:
Hope this helps :)
is 5361 divisible by three how do you know just by looking at it
Answer and explanation
You add all of the digits together a see if it is divisible by 3 sooooo...........
5+3+6+1=15/3=5
What is Six less than y
Answer:
y-6
Step-by-step explanation:
Y minus six
Step-by-step explanation:
Xavier runs 21 miles in three hours what is his unit rate for the average distance he ran after one hour
Answer:
7 mph
Step-by-step explanation:
21/3 = 7 so Xavier runs 7 miles per hour
On the number line, a bug A is moving in the positive direction from the point 0, and a bug Bis moving in the negative direction from the point 0. The speeds of both bugs are constant. Both leave 0 at the same time, and three seconds later A has reached 18 and B has reached –15.
When will A and B be 220 units apart?
Answer:
20 seconds
Step-by-step explanation:
The speed of A is:
sA = 18 units / 3 seconds = 6 units/second
The speed of B is:
sB = -15 units / 3 seconds = -5 units/second
The relative speed is:
s = sA − sB
s = 6 units/second − (-5 units/second)
s = 11 units/second
The time for the distance between them to be 220 units is:
220 units = 11 units/second × t
t = 20 seconds
Peter is saving for a down payment of $50,000 for a new home. Yesterday, he created an equation that models his current savings plan to
determine how long it will take him reach his goal. In his model, y represents the total amount saved and x represents the number of months
since yesterday. Which statement is true?
Step 1:
Step 2:
30,000
Step 3:
y= 30,000 + 2,000x
y - 30,000 = 30,000 + 2,000x-
y - 30.000 = 2,000x
y - 90,000 2,000
2,000 = 2,000
Step 4:
y
- 30,000
Step 5:
2,000 = x
50,000 - 30,000
=x
2,000
Step 6:
Step 7:
10 = x
O A.
Peter used the division property of equality in step 4.
OB.
Peter used the substitution property in step 5.
C.
Peter used the subtraction property of equality in step 5.
OD. Peter used the associative property in step 6.
Answer:
Step-by-step explanation:
step 1 y = 30000 + 2000x
step 2 y - 30000 = 30000 + 2000x - 30000
step 3 y - 30000 = 2000x
step 4 y-30000/2000 = 2000x/2000
step 5 y - 30000/2000 = x
step 6 50000 - 30000/2000 = x
step 7 10 = x
therefore the correct option should be
Peter used the division property of equality in step 4.
Peter used the subtraction property of equality in Step 5 of his savings plan equation to determine how much more he needs to save. He subtracted his current savings from his goal to get the remaining amount that has to be saved.
Explanation:The statement that is true based on the steps provided is C. Peter used the subtraction property of equality in step 5. To explain, in step 5, Peter was using the subtraction property of equality when he subtracted $30,000 from his goal of $50,000. The subtraction property of equality states that if you subtract an equal amount from both sides of an equality, it still remains equal. In this case, he subtracted his current savings (i.e., $30,000) from his target amount (i.e., $50,000) to determine how much more money he has to save.
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The midpoint M of CD¯ has coordinates (−1, 3). Point C has coordinates (−5, 6). What are the coordinates of point D?
Answer:
The Co-ordinates of D are (3,0)
Step-by-step explanation:
x= x₁ +x₂ / 2 , y= y₁+y₂ /2
-1 = -5 + x₂ /2 , 3 = 6+y₂ /2
Solve them and u ll get the ans
For -3+2y=11 would I add -3 to 11 to find Y, or would I subtract -3 from 11?
(x - 8) + 33 = 180
how would i find x ?
Answer:
X = 155
Step-by-step explanation:
You subtract 180 and 33 to get 147 and add 8 to that and you get 155 as your answer
Answer:
x = 155
Step-by-step explanation:
Step 1: Distribute
x - 8 + 33 = 180
Step 2: Combine like terms
x + 25 - 25 = 180 - 25
x = 155
Answer: x = 155
Solve for a
- 4a = 20
Answer:
-5
Step-by-step explanation:
-4a - 20 = -4 • (a + 5)
Solve : -4 = 0
Solve : a+5 = 0
a = -5
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× + 20 + 2× = 10 - 2× - 15
Answer:
The answer is -5
Step-by-step explanation:
[tex]\mathrm{Group\:like\:terms}\\x+2x+20=10-2x-15[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:x+2x=3x\\3x+20=10-2x-15[/tex]
[tex]\mathrm{Group\:like\:terms}\\3x+20=-2x+10-15[/tex]
[tex]\mathrm{Add/Subtract\:the\:numbers:}\:10-15=-5\\3x+20=-2x-5[/tex]
[tex]\mathrm{Subtract\:}20\mathrm{\:from\:both\:sides}\\3x+20-20=-2x-5-20[/tex]
[tex]\mathrm{Simplify}\\3x=-2x-25[/tex]
[tex]\mathrm{Add\:}2x\mathrm{\:to\:both\:sides}\\3x+2x=-2x-25+2x[/tex]
[tex]\mathrm{Simplify}\\5x=-25[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}5\\\frac{5x}{5}=\frac{-25}{5}[/tex]
[tex]\mathrm{Simplify}\\x=-5[/tex]
Hope this helps you greatly!
Have a great afternoon!
10. For the equation 3x – 4 = 8, which
number makes the equation true:
x = 2, x= 3, X= 4, or x = 5?
Answer:
x = 4
Step-by-step explanation:
We can find the answer to this by solving the equation:
3x - 4 = 8
3x - 4 + 4 = 8 + 4
3x = 12
x = 4
The post hoc test that is calculated by dividing the desired a level by the number of comprehensions is the
A. Bonferroni correction.
B. Duncan test.
C. Scheffe test
D. Tukeys HSD
The Bonferroni correction is the post hoc test calculated by dividing the desired level of significance by the number of comparisons. This test is used to control the Familywise Error Rate, thereby reducing the likelihood of a Type I error.
Explanation:The post hoc test that is calculated by dividing the desired level of significance, commonly denoted as 'a', by the number of comparisons being made is known as the Bonferroni correction. This adjustment method is designed to control the Familywise Error Rate (FWER), this is, the probability of making one or more Type I errors (rejecting the null hypothesis when it is true) in a set of hypotheses.
For example, if you set your 'desired a level' (also known as the level of significance of the test) at 0.05 and you were making five comparisons, the Bonferroni correction would deflate your 'a level' to 0.05/5 = 0.01.
Therefore, you would only reject a null hypothesis if the p-value for that comparison was less than 0.01, rather than the 0.05 that you originally specified. The effect of this correction is that it makes it harder to reject individual null hypotheses, making the test more conservative and reducing the likelihood of a Type I error.
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A store is having a sale on jelly beans and trail mix. For 6 pounds of jelly beans and 2 pounds of trail mix, the total cost is $20. For 3 pounds of jelly beans and 5 pounds of trail mix, the total cost is $23. Find the cost for each pound of jelly beans and each pound of trail mix.
Answer:
Jelly beans are $2.25/pound, trail mix $3,25/pound
Step-by-step explanation:
Let’s say that the cost of a pound of jelly beans is x, and that the cost of a pound of trail mix is y.
We can then say that 6 pounds of jelly beans + 2 pounds of trail mix, or 6x+2y, equals 20.
Next, 3x+5y=23, and we have
6x+2y=20
3x+5y=23
We can multiply the whole second equation by -2 and add it to the first one to get rid of the x, so -8y=-26. Divide both sides by -8, and a pound of trail mix, or y, is 26/8, or $3.25. Plugging this back into the first equation, we get that
6x+2(26/8)=20, so (20-2(26/8))/6=x=2.25, or the cost of one pound of jelly beans
To solve for the cost per pound of jelly beans and trail mix, create and solve a system of algebraic equations using the provided information. Multiply and subtract equations as needed to eliminate one variable and solve for the other, then back-substitute to find the second value.
Explanation:The question involves a system of two equations based on the prices of jelly beans and trail mix. We can use algebra to solve for the cost per pound of each. Let's denote the cost per pound of jelly beans as j and the cost per pound of trail mix as t.
The two equations based on the given information are:
6j + 2t = $203j + 5t = $23To solve these equations, we can use either substitution or elimination. Let's use the elimination method:
Multiply the first equation by 3 and the second by 2.This gives us 18j + 6t = $60 and 6j + 10t = $46.Subtracting the second equation from the first gives us 12j - 4t = $14.Multiply the second original equation by 2, yielding 6j + 10t = $46.Now take the modified first equation (12j - 4t = $14) and divide by 2 to simplify, getting 6j - 2t = $7.Adding this to the modified second equation results in 12j + 8t = $53.We can now solve for one variable. For instance, from 6j - 2t = $7, we can express t as (6j - $7)/2.Substitute this expression for t in one of the original equations to find j.Once j is found, use it to calculate t from either equation.After solving, we will find the costs per pound for jelly beans and trail mix.
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A quiz has four multiple-choice questions; each question is either true or false. How many different solution keys are possible?
Answer: 2 solution keys
Step-by-step explanation:
Although question has True or False as solution, while the multiple questions are four, solution keys still equals 2, since True in an option in the four questions, false is another option in the four questions.
I hope this helps.
Point S is located at (9,-3). Point T is located at (4,-3). What is the distance from point SSS to point T?
Answer:
5
Step-by-step explanation:
I think this is your corrected question:
Point S is located at (9,-3). Point T is located at (4,-3). What is the distance from point S to point T?
Here is my answer:
S (9. -3) <=> x1 = 9, y1 = -3
T (4, -3) <=> x2= 4, y2 = -3
As we can see, the two coordinates are located in the same line y =-3 so the distance between two points: x1 -x2 = 9-4=5 horizontally.
Dylan is going to the fair and has $35. He is going to use $5 for food. The admission is $7, and rides are $1.85 each.
Which of the following equations could you use to find how many rides Dylan can go on?
5+7=12-35=23
EQUATION. 12+1.85x=35
ANSWER. 12 RIDES
Answer
. 12 RIDES
Step-by-step explanation:
indicate the standard form the equatin of the line passing through the given pints E(-2,2) F(5,1)
Answer:
y = -x/7 + 12/7
Step-by-step explanation:
We are requested to find the standard equation of a line
We are given two points
E and F
E ( -2 , 2)
F ( 5 ,1 )
Step 1: find the slope
m = y_2 - y_1 / x_2 - x_1
x_1 = -2
y_1 =2
x_2 = 5
y_2 = 1
Inserting the values
m = 1 - 2 / 5 - (-2)
m = 1 -2 / 5 + 2
= -1 / 7
Slope = -1/7
Step 2: using the point slope form
y - y_1 = m( x - x_1)
Using point ( 5, 1)
x_1 = 5
y_1 = 1
m = -1/7
Insert the values
y - 1 = -1/7(x - 5)
y - 1 = -1(x - 5)/7
Open the bracket with -1
y - 1 =( -x + 5) / 7
following the equation of a line
y = mx + C
y = (-x + 5)/7 + 1
LCM = 7
y = (-x + 5+ 7) / 7
y = (-x + 12)/7
We can still separate
y = -x/7 + 12/7
The standard equation of a line is
y = -x/7 + 12/7
A $18.00 haircut cost $25.63 after tax and tip. What percent was the tax and tip combined? If needed, round the answer to the nearest tenth
Answer:
42.3 percent was the tax and tip combined.
Step-by-step explanation:
Given : A $18.00 haircut cost $25.63 after tax and tip.
To find : What percent was the tax and tip combined?
Solution :
Using sales tax formula,
[tex]\text{Sales tax}=\text{Rate}\times \text{Original price}[/tex]
Original price = $18
After tax and tip cost is $25.63
Sales tax = After tax and tip cost - Original cost
Sales tax = $25.63 - $18
Sales tax = $7.63
Substitute the values,
[tex]7.63=\text{Rate}\times 18[/tex]
[tex]\text{Rate}=\frac{7.63}{18}[/tex]
[tex]\text{Rate}=0.423[/tex]
Into percentage,
[tex]\%\text{Rate}=0.423\times 100=42.3\%[/tex]
Therefore, 42.3% was the tax and tip combined.
Using the double angle identities, find sin2x given sinx=4/5
Answer:
24/25
Step-by-step explanation:
The usual form of the double-angle identity is for sine is ...
sin(2x) = 2sin(x)cos(x)
The cosine can be found from the sine using the Pythagorean identity ...
sin(x)² + cos(x)² = 1
cos(x) = √(1 -sin(x)²)
__
Filling in the given value for sin(x), we can find the cosine to be ...
cos(x) = √(1 -(4/5)²) = √(9/25) = 3/5 . . . . . . . assuming a first-quadrant angle
Then the desired sine is ...
sin(2x) = 2sin(x)cos(x) = 2(4/5)(3/5)
sin(2x) = 24/25
The scatterplot that represents the monthly values of stock QRS has an r
value of 0.315. Which best describes the correlation of the graph?
O
A. Strong negative correlation
O
B. No correlation
O
C. Strong positive correlation
D. Weak correlation
Answer:
D
Step-by-step explanation:
The correlation coefficient, r value, measures the strength and direction of 2 variables in a scatterplot. It ranges from +1 to -1.
+1 means a perfect positive correlation
-1 means a perfect negative correlation
0 means there is no correlation
Also,
a value close to 0.7 would signify a strong relationship (whether positive or negative)
a value close to 0.5 indicates a moderate relationship
a value close to 0.3 indicates a weak relationship
Now, the question says the r value is 0.315
THis is POSITIVE
Also, this is a "weak" relationship
Thus, we can say:
It has weak correlation, or answer choice D
D is right.
Answer:
Strong negative correlation
Step-by-step explanation:
AP3X
Find the lateral and total surface area of the prism.
lateral SA:_____
Total SA:_____
Lateral surface area of the prism = 920 in²
Total surface area of the prism = 1180 in²
Solution:
Length of the prism = 13 in
Width of the prism = 10 in
Height of the prism = 20 in
Lateral surface area of the prism = 2(l + w)h
= 2(13 + 10) × 20
= 2(23) × 20
= 920 in²
Lateral surface area of the prism = 920 in²
Total surface area of the prism = Lateral area + 2lw
= 920 + 2 × 13 × 10
= 920 + 260
Total surface area of the prism = 1180 in²
Hence Lateral surface area of the prism = 920 in²
Total surface area of the prism = 1180 in²
The lateral surface area of a prism is found by multiplying the perimeter of the base shape by the height of the prism. The total surface area is the lateral surface area plus twice the area of the base shape. The formulas are applied differently depending on the base shape of the prism.
Explanation:To find the lateral surface area (SA) and the total surface area of the prism, we need to apply the correct formulas. The lateral SA for a prism is the perimeter of the base shape times the height. The total SA is the lateral SA plus twice the area of the base shape.
For example, let's use a rectangular prism with dimensions: length (l)=5 cm, width (w)=3 cm, and height (h)=10 cm. The lateral SA = 2*h*(l+w) = 2*10*(5+3) = 160 sq cm. The base shape has area = l*w, so total SA = 2*lw + lateral SA = 2*(5*3) + 160 = 30*2 + 160 = 220 sq cm.
In similar manner, the formula can be adjusted depending upon the base shape of the prism like for a triangular prism, square prism, etc.
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Writing expressions. 3 times the sum of 4 and 8
Answer:
3(4+8)
Step-by-step explanation:
Answer:
3 * (4 + 8)
Step-by-step explanation:
Step 1: Convert words into an expression
3 times the sum of 4 and 8
3 times = 3 *
Sum of 4 and 8 = (4 + 8)
3 * (4 + 8)
Answer: 3 * (4 + 8)
If p || q, solve for x.
The value of x is 8.
Solution:
Given line p is parallel to line q.
If two parallel lines are cut by a transversal, then the corresponding angles are congruent.
(11x - 5)° = (7x + 27)°
11x° - 5° = 7x° + 27°
Add 5° on both sides.
11x° = 7x° + 32°
Subtract 7x° from both sides.
4x° = 32°
Divide by 4 on both sides.
x° = 8°
x = 8
The value of x is 8.
Marcus reads for 30 minutes each night. He wants to determine the total number of minutes he will read over the course of a month. He wrote the equation t=30 d to represent the total amount of the time that he has spent reading, where t represents the total number of minutes read and d represents the number of days that he read during the month. Determine which variable is independent and which is dependent. Then create a table to show how many minutes he read in the first seven days,
Answer:
The time is independent of the months we multiply these minutes as grouping with subject impression or importance. This way within the frequency you can see 263340 represents what score you are looking for importance ie) 20/20 for your book choice. This is 8 days which fits better for a monthly review 8,8,8 and 6. Which would easily be readable in the minute totals.
240= 8 nights 180 minutes = 6 nights. Having a frequency helps determine patterns for book interest and study.
Step-by-step explanation:
Subjects (imp) Minutes (M P/D) F(Frequency)
score 1-3 30 60
4-6 60 300
7-9 60 420
10-12 90 990
Total 26 + 240 ...266 x990 = 263340
Labyrinth Middle School is 363 ft long Tabitha makes a scale model of the skull and the drawing is 33 in Long. What is the scale factor used to create the model PLZZZ HELP ME HURRY THE ANSWERS CHOICES ARE IN THE PICTURE
1 inch on the drawing represents 11 feet in the labyrinth middle school.
Step-by-step explanation:
Step 1:
The labyrinth middle school is much larger than the drawing. For 33 inches on the drawing, it is 363 feet on the actual school.
So 33 inches on the drawing is equal to 363 feet in the labyrinth school.
Step 2:
To calculate the scale factor, we divide the measurement after scaling by the same measurement before scaling.
In this case, the drawing that Tabitha drew is after scaling and the labyrinth middle school is the measurement before scaling
The scale factor [tex]= \frac{33}{363} = \frac{1}{11}.[/tex]
So the scale factor is [tex]\frac{1}{11}[/tex]. This means that 1 inch on the drawing is 11 feet in the actual school.
Write seven hundred eighty-six thousandths as a decimal number
Answer:
0.7860
Step-by-step explanation:
Answer:
0.7860
Step-by-step explanation:
It is because there is no "and." If it were to say: seven hundred and eighty-six thousandths it would be 700.860.
Whenever it ads "ths" at the end it will be a decimal.
Match each word to the appropriate example using the expression 5a + 9b - 4.
is a coefficient
is a constant.
There are
terms in the expression.
Answer:
9 is the coefficient
-4 is the constant
There are 3 terms in the expression.
Step-by-step explanation:
The expression 5a + 9b - 4 consists of three terms: 5a, 9b, and -4. The coefficients are 5 and 9, while the constant is -4.
Explanation:The expression 5a + 9b - 4 consists of three terms. Each term represents a part of the expression that is separated by + or - signs.
In this expression, 5a, 9b, and -4 are the terms.
The coefficient is the number that multiplies the variable. In this expression, the coefficients are 5 and 9.
The constant is a term that does not have a variable attached to it. In this expression, the constant is -4.
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