Answer:
Yes, the Pie Graph is the right choice.
Step-by-step explanation:
A Pie Graph, or Sector Graph is one of the good options to display, usually relative frequencies, proportionally.
In a Pie Graph the focus is to show the importance of each observation, or category in comparison with the whole.
You need to be careful with the angles, since 180º is equal to 50%, 90º to 25% and 360º is equal to 100% so each "slice" each portion must directly proportional to the angles of one circle.
Since the goal is to show the importance of each work to the whole team, definitely a Pie Graph is one the appropriate one to pick.
Solving Square Roots Worksheet (x - k)^2 : Part 1
1. 2(x + 7)^2 = 16
2. (x - 3)^2 = -12
3. -5(n - 3)^2 = 10
Answer:
1. x = +/- 2[tex]\sqrt{2}[/tex] - 7
2. x = [tex]3[/tex] +/- [tex]2i\sqrt{3}[/tex]
3. n = [tex]2[/tex] +/- [tex]i\sqrt{2}[/tex]
Step-by-step explanation:
1. Divide both sides by 2: (x + 7)^2 = 8
Square root both sides: x + 7 = +/- 2[tex]\sqrt{2}[/tex]
Subtract 7 from both sides: x = +/- 2[tex]\sqrt{2}[/tex] - 7
2. Square root both sides: x - 3 = [tex]\sqrt{-12}[/tex]
Since there is a negative inside the radical, we need to have an imaginary number: [tex]i=\sqrt{-1}[/tex] . So, [tex]\sqrt{-12} =i\sqrt{12} =2i\sqrt{3}[/tex]
Add 3 to both sides: x = [tex]3[/tex] +/- [tex]2i\sqrt{3}[/tex]
3. Divide by -5 from both sides: (n - 2)^2 = -2
Square root both sides: n - 2 = [tex]\sqrt{-2}[/tex]
Again, we have to use i: [tex]n-2=\sqrt{-2} =i\sqrt{2}[/tex]
Add 2 to both sides: n = [tex]2[/tex] +/- [tex]i\sqrt{2}[/tex]
Hope this helps!
Answer:
1. x = 2sqrt(2) - 7, -2sqrt(2) - 7
2. No real solutions
x = 3 + 2sqrt(3) i, 3 - 2sqrt(3) i
3. No real solutions
n = 3 + sqrt(2) i, 3 - sqrt(2) i
Step-by-step explanation:
1. 2(x + 7)² = 16
(x + 7)² = 8
x + 7 = +/- sqrt(8) = +/- 2sqrt(2(
x = 2sqrt(2) - 7, -2sqrt(2) - 7
2. (x - 3)² = -12
A perfect square can never be negative for real values of x
(x - 3) = +/- i × sqrt(12)
x - 3 = +/- i × 2sqrt(3)
x = 3 +/- i × 2sqrt(3)
3. -5(n - 3)² = 10
(n - 3)² = -2
A perfect square can never be negative for real values of x
n - 3 = +/- i × sqrt(2)
n = 3 +/- i × sqrt(2)
help pleases with this question !!!!
Answer: 2.13
Step-by-step explanation:
1.42/2=0.71
1.42+0.71=2.13
Answer:
The answer to your question is £ 2.13
Step-by-step explanation:
Data
Cost of 1 kg or oranges = £1.42
Cost of the oranges in the scales = ?
Process
1.- Determine the weight of the oranges in the scales.
As we can see the weight of the three oranges is 1.5 kg
2.- Use proportions and cross multiplication to find the cost.
1 kg of oranges --------------------- £ 1.42
1.5 kg of oranges ------------------ x
x = (1.5 x 1.42) / 1
x = 2.13 / 1
x = £ 2.13
A tower is 1964 feet tall. The angle of elevation from the base of an office building to the top of the tower is 37degrees. The angle of elevation from the roof of the office building to the top of the tower is 19degrees.
To find the height of the office building and the angle of elevation to the top of the tower, we can use the tangent function and solve two equations simultaneously.
To find the height of the office building and the angle of elevation from the base to the top of the tower, we can use the Tangent function.
Tan(angle) = Opposite/Adjacent
For the first angle (37 degrees), the opposite side is the height of the tower (1964 feet) and the adjacent side is the height of the office building.
So, tan(37) = 1964/Adjacent.
For the second angle (19 degrees), the opposite side is again the height of the tower (1964 feet) and the adjacent side is the height of the office building + the height from the roof to the top of the tower.
So, tan(19) = 1964/(Adjacent + Roof Height).
We can solve these two equations simultaneously to find the height of the office building and the height from the roof to the top of the tower.
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12 rotten tomatoes are usually found in every four boxes.how many rotten tomatoes would likely be found in 14 boxes?
Answer:
42 tomatoes
Step-by-step explanation:
tomatoes/boxes = tomatoes/boxes
12/4 = x/14
4x/4 = 168/4
x=42
Answer:
42 rotten tomatoes would likely be found in 14 boxes
Step-by-step explanation:
1) Find how many rotten tomatoes are normally found in one box by dividing the amount of rotten tomatoes by the number of boxes they are found in. [tex]12/4=3[/tex]
2) So, now you know that 3 rotten tomatoes are normally found in one box, but the question is asking how many tomatoes would likely be found in 14 boxes which means you need to multiply the amount of rotten tomatoes found in one box by the amount of boxes you want to know about. [tex]3*14=42[/tex]
The regular price of a computer is $1200 and the regular price of a printer is $300. The regular price of a computer is 1200 dollars and the regular price of a printer is 300 dollas. An electronics store has a promotion that offers a 40% 40 percent discount on the printer when the computer is purchased at the regular price. What is the total cost of the computer and the printer at the promotional price?
Answer:
$1380
Step-by-step explanation:
The regular price of a computer is $1200The regular price of a printer is $300.The electronics store offers a 40% discount on the printer only when the computer is purchased at the regular price.
Discount on the Printer = 40% of $300 =0.4 X 300 =120
Promotional Price of the Printer = $300-120 =$180
Therefore, the total cost of the computer and the printer at the promotional price
=Regular price of a computer + Promotional Price of the Printer
=1200+180
=$1380
These numbers are either whole numbers ,or negative of whole numbers ,they are called __
Answer:
integers
Step-by-step explanation:
Answer:
Intergers
Step-by-step explanation:
Intergers are a whole number meaning a number that's not a fraction.
Suppose your new business made a profit during the first year of $3000. If the profit increased 12% per year, find the total of all profit earned by the end of the first 5 years.
Answer:
Therefore the total of all profit earned by the end of of the the first 5 years is $19,058.542.
Step-by-step explanation:
To find total profit earned per year, we need to use the compound growth formula.
The compound growth formula:
[tex]A= P(1+r)^t[/tex]
A= Amount after t years
P= initial amount
r= rate of growth
t= time in year.
Given that,
New business made a profit during the first year of $3000.
If the profit increased 12% per year.
Here P= $3,000 and r =12%=0.12 , t=1 years
Plugging all value in the above formula:
[tex]A=3000(1+0.12)^1[/tex]
=3000(1.12)
=$3360
Profit after 2 year is $3,360.
Now, P= $3,000 and r =12%=0.12 , t=3 years
[tex]A=3000(1+0.12)^2[/tex]
=3000(1.12)²
=$3763.2
Similar the profit at 4 year is
[tex]A=3000(1+0.12)^3[/tex]
=3000(1.12)³
=$4214.784
The profit at 5th year is
[tex]A=3000(1+0.12)^4[/tex]
=3000(1.12)⁴
=$4720.558
Therefore the total of all profit earned by the end of of the the first 5 years is=$(3,000+3360+3763.2+4214.784+4720.558)
=$19,058.542
Mrs. Garcia has two kinds of flowers in her garden. The ratio of lilies to daisies in the garden 3:2 if there are 15 lilies, what is the total number of flowers in her garden?
Answer:
The total number of flowers in Mrs. Garcia's garden is 25.
Step-by-step explanation:
The ratio of lilies to daisies is 3:2 and there are 15 lilies. We need to compute the number of daisies first and then add both the number of daisies and lilies to compute the total number of flowers. Using the ratio method:
Lilies : Daisies
3 : 2
15 : x
By cross multiplying we get:
3x = 15*2
3x = 30
x = 10
Hence, the total number of flowers in the garden are:
10 + 15 = 25
The total number of flowers in Mrs. Garcia's garden is 25.
Answer:
25
Step-by-step explanation:
Given that the number of lilies = 15
Given ratio = 3:2
Let the total number of flowers be X
Let the number of daisies be 'a'
3/2 = 15/a
3×a = 2×15
3a = 30
a = 30/3
a = 10
X = number of lilies + number of daisies
X = 15 + 10
X = 25
PLEASE HELP
What is the volume, in cubic m, of a cube with an edge length of 14m?
Answer:
v = 2744 m³
Step-by-step explanation:
Volume of cube
= length³
= l³
= 14³
= 2744 m³
make as the brainliest
Final answer:
The volume of a cube with an edge length of 14m is 2,744 cubic meters (m³), calculated using the formula V = a³, where a is the edge length.
Explanation:
To find the volume of a cube with an edge length of 14m, we use the formula for the volume of a cube, which is V = a³, where a is the length of an edge of the cube. In this case, each edge is 14 meters long. Therefore, the volume of the cube is calculated as follows:
V = 14m × 14m × 14m = 2,744 m³
This means the volume of the cube is 2,744 cubic meters (m³). It's important to remember that the volume measures the amount of space within the cube, and the unit of measure for volume in the International System of Units (SI) is cubic meters (m³).
Each month, Jeremy adds the same number of cards to his baseball card collection. In Jeremy, he had 36. 48 in February. 60 in March. How many baseball cards will Jeremy have in April
Jeremy will have 72 baseball cards in April.
What is a consecutive pattern?A consecutive pattern refers to a sequence or order of numbers, letters, or other objects in which each follows in direct and uninterrupted succession from the one that precedes it.
We have,
To solve this problem, we need to determine the pattern of how many cards Jeremy adds to his collection each month.
To do this, we can find the difference between consecutive months:
February minus January: 48 - 36 = 12
March minus February: 60 - 48 = 12
We can see that Jeremy is adding 12 cards to his collection each month.
So to find out how many cards he will have in April, we can add 12 to the number he had in March:
April
= 60 + 12
= 72
Therefore,
Jeremy will have 72 baseball cards in April.
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Is it A)50 degrees, B) 60 degrees C) 74 degrees or D) 78 degrees
An amusement park charges an admission fee of 20 dollars for each person. Let C be the cost (in dollars) of admission for P people. Write an equation relating to C to P. Then use this equation to find the cost of admission for 17 people.
Answer:
20 x 17 = 340
Step-by-step explanation:
C= cost
P=people
Equation- 20p=c
20 x 17 (people) = cost
:) would appreciate anything
Explain How to find the volume of a cube whose edge length is 1/4 yd. Then find the volume of such a cube
Answer:
[tex]Volume=0.015625\ yd^3[/tex]
Step-by-step explanation:
-A cube is a 3-D object whose height=length=width.
-To find its volume, we multiply its length by width by height dimensions.
#We can calculate the volume of a cube using the formula:
[tex]V=length\times width\times height\\\\=0.25 \ yd\times 0.25\ yd \times 0.25\ yd\\\\=(0.25\ yd)^3\\\\=0.015625\ yd^3[/tex]
Hence, the volume of the cube is [tex]0.015625\ yd^3[/tex]
To find the volume of a cube with an edge length of 1/4 yard, cube the length of the edge. The volume of the cube is 1/64 cubic yards.
Explanation:To find the volume of a cube, you need to cube the length of its edge. In this case, the edge length is 1/4 yard. So, the volume formula becomes (1/4)^3 = 1/4 × 1/4 × 1/4 cubic yards. Simplifying further, we have 1/64 cubic yards as the volume of the cube.
Can someone help solve for X
Answer:
x = 2sqrt(5)
Step-by-step explanation:
We can use the Pythagorean theorem to solve
The legs are x and 8/2 =4
and the hypotenuse is 6
a^2 + b^2 = c^2
x^2 +4^2 = 6^2
x^2 +16 = 36
Subtract 16 from each side
x^2 +16-16=36-16
x^2 = 20
Take the square root of each side
sqrt(x^2) = sqrt(20)
x = sqrt(4*5)
x = sqrt(4) sqrt(5)
x = 2sqrt(5)
Answer:
Step-by-step explanation:
"Benny decided to look at the price of new and used vans. Benny found a used van for $3000. Benny found that he paid 20% of the price of a new van. How much would a new van cost?"
Answer:
$15000
Step-by-step explanation:
We have that the value of the truck is $ 3000 and that this payment is equivalent to 20% of the value of a new truck, therefore the value of the new truck would be:
% of value value
20 3000
100 x
x = 100 * 3000/20
x = 15000
therefore the value of the new truck is $ 15000
Sistemas de ecuaciones no lineales
Answer:
¿que hay de ellos?
Historically, the mean yield of corn in the United States has been 120 bushels per acre with a standard deviation of 12. A survey of 40 farmers this year gives a sample mean yield of 125 bushels per acre . Let p be the mean yield of corn nationally for this year. Supposing that the past standard deviation is still correct, what is the p-value for testing a null hypothesis of mu=120 against an alternative of mu not equal to 20 ? A 0.0041 B 0.0082 C 2.64 D 125
Answer:
[tex]z=\frac{125-120}{\frac{12}{\sqrt{40}}}=2.64[/tex]
P-value
Since is a two sided test the p value would be:
[tex]p_v =2*P(z>2.64)=0.0082[/tex]
And the best answer would be
B 0.0082
Step-by-step explanation:
Data given and notation
[tex]\bar X=125[/tex] represent the mean height for the sample
[tex]\sigma=12[/tex] represent the population standard deviation
[tex]n=40[/tex] sample size
[tex]\mu_o =120[/tex] represent the value that we want to test
[tex]\alpha[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the true mean is 120 or not, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 120[/tex]
Alternative hypothesis:[tex]\mu \neq 120[/tex]
If we analyze the size for the sample is > 30 and we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]z=\frac{125-120}{\frac{12}{\sqrt{40}}}=2.64[/tex]
P-value
Since is a two sided test the p value would be:
[tex]p_v =2*P(z>2.64)=0.0082[/tex]
And the best answer would be
B 0.0082
The table shows employment status for 1600 adults from five countries. Are the events S = "is Swedish" and E = "is employed"
independent? Why or why not?
Answer:
Yes; because P(S & E)= P(E) • P(E).
Step-by-step explanation:
P(S)=530/1600 = 0.33, P(E)= 1523/1600= 0.95, and P(S & E)= 498/1600= 0.31 = (0.33)(0.95)
A circle with radius of 3cm sits inside a circle with radius of 11cm
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
The larger circle is shaded.
Answer:
Circular shapes - They are those planner shapes that represent the locus of all the points that has a constant distance from a fixed point on the plane. This constant distance is termed as the radius of the circle and the fixed point is known as the center of the circle.
The center of the circle is enclosed by all the points on its periphery.
The circumference of the circle is the total length of its periphery around the center.
Concentric circles are two circles that have the same center
Step-by-step explanation:
Zad.1 12 pracowników spytano o liczbę dni wykorzystanego urlopu. Oto odpowiedzi: 2, 5, 14, 3, 6, 5, 8, 2, 5, 4, 6, 8. Podaj dominantę i medianę. Zad. 2 13 pracowników spytano o liczbę dni wykorzystanego urlopu. Oto odpowiedzi: 2, 4, 14, 3, 6, 7, 8, 2, 5, 4, 6, 8, 9. Podaj dominantę i medianę. Zad.3 Oblicz dominantę i medianę a)Odległość zamieszkania w km. b) Liczba pracowników a) b) 0-5 5 5-10 25 10-15 30 15-20 55 20-35 30 25-30 20 30-35 15
Answer:
Taak 1.12
Mediaan is 5 en het gemiddelde is 5,67
Taak 2 13
De mediaan is 6
Het gemiddelde is 6
Standaarddeviatie is 3,32
Variantie is 11
Aantal werknemers is 13
Step-by-step explanation:
Taak.1 12 medewerkers is gevraagd naar het aantal verlofdagen. Hier zijn de antwoorden: 2, 5, 14, 3, 6, 5, 8, 2, 5, 4, 6, 8. Geef de dominante en de mediaan. Taak 2 13 medewerkers is gevraagd naar het aantal vakantiedagen. Hier zijn de antwoorden: 2, 4, 14, 3, 6, 7, 8, 2, 5, 4, 6, 8, 9. Geef de dominante en mediaan. Zad.3 Bereken de dominante en de mediaan a) Verblijfsafstand in km. b) Aantal werknemers a) b) 0-5 5 5-10 25 10-15 30 15-20 55 20-35 30 25-30 20 30-35 15
Taak. 1 12, wordt de mediaan gegeven door
2, 5, 14, 3, 6, 5, 8, 2, 5, 4, 6, 8 herschikken, we krijgen
2, 2, 3, 4, 5, 5, 5, 6, 6, 8, 8, 14
Daarom is de mediaan 5 en het gemiddelde 5,67
Taak 2 13
2, 4, 14, 3, 6, 7, 8, 2, 5, 4, 6, 8, 9 herschikken, we krijgen
2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 14
De mediaan is het zevende nummer in de rij = 6
Het gemiddelde is ook = 6
Standaarddeviatie = 3,32
Variantie = 11
Aantal werknemers = som van frequentie of aantal gegevens = 13.
If the slope of the linear function y=-2x-4 was changed to 3, what would the new equation be? *
A. y=2x-3
B. y=3x-4
C. y=2x+3
D. y=3x+4
Answer:
b
Step-by-step explanation:
-2 is the slope so change -2 to 3
find two numbers that multiply to 17 and add to 18
Answer:
The numbers are 1 and 17
Step-by-step explanation:
The only factors of 17 are 1 and 17 since 17 is a prime number
1*17 =17
1+17 =18
The two numbers that multiply to 17 and add to 18 are 1 and 17.
To find two numbers that satisfy the conditions of multiplying to 17 and adding to 18, we can set up a system of equations based on these criteria.
Let the two numbers be x and y .
1. Set up the equations:
- [tex]\( xy = 17 \)[/tex] (product of the numbers)
- [tex]\( x + y = 18 \)[/tex] (sum of the numbers)
2. Solve the system of equations:
From x + y = 18, express y in terms of x :
[tex]\[ y = 18 - x \][/tex]
Substitute y = 18 - x into [tex]\( xy = 17 \)[/tex]:
[tex]\[ x(18 - x) = 17 \][/tex]
[tex]\[ 18x - x^2 = 17 \][/tex]
[tex]\[ x^2 - 18x + 17 = 0 \][/tex]
3. Find the roots of the quadratic equation:
Use the quadratic formula [tex]\( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)[/tex], where a = 1 , b = -18, and c = 17:
[tex]\[ x = \frac{-(-18) \pm \sqrt{(-18)^2 - 4 \cdot 1 \cdot 17}}{2 \cdot 1} \][/tex]
[tex]\[ x = \frac{18 \pm \sqrt{324 - 68}}{2} \][/tex]
[tex]\[ x = \frac{18 \pm \sqrt{256}}{2} \][/tex]
[tex]\[ x = \frac{18 \pm 16}{2} \][/tex]
So, [tex]\( x = \frac{34}{2} = 17 \)[/tex] or [tex]\( x = \frac{2}{2} = 1 \)[/tex].
4. Determine the corresponding y values:
- If x = 17, then [tex]\( y = 18 - 17 = 1 \)[/tex].
- If x = 1 , then [tex]\( y = 18 - 1 = 17 \)[/tex].
Therefore, the two numbers that multiply to 17 and add to 18 are 1 and 17.
The numbers 1 and 17 satisfy the conditions of multiplying to 17 and adding to 18, providing a clear solution based on the given criteria of the problem.
PLEASE HELP ASAP!Complete the steps to find the area of the trapezoid.
Area of rectangle=
Area of triangle 1=
Area of triangle 2=
Area of triangle 3=
Area of trapezoid=
just put them how u normally wuld 1 is
3 is 6
4 is 5
2 is 8
5 is 13
Answer: area of the rectangle = 256
area of triangle 1 = 24
area of triangle 2 = 16
area of triangle 3 = 96
area of the trapezoid = 120
Which of these equations correctly represents the following scenario: In her prime, 40 million people knew who Britney Spears was, but that number has been decreasing by 10% each year. So, since 90% of people still recognize her each year, how many people still know who Britney is each year?
y = 40,000,000(0.9)x
y = 0.9(40,000,000)x
y = 40,000,000(0.01)x
y = 0.1x + 40,000,000
y = 0.01(40,000,000)x
Answer:
Its the first option
40,000,000(0.9)x.
Step-by-step explanation:
90% recognise her each year so after 1 year so the number (N) is:
N = 40,000,000(0.90)^1 = 36,000,000 recognise her after 1 year.
N = 40,000,000(0.90)^2 = 32,400,000 recognise her after 2 yeas
- and so on.
After x years:
N = 40,000,000(0.90)^x.
Note the x is a power and is best written as ^x.
The correct equation to represent the given scenario is [tex]y = 40,000,000(0.9)^x[/tex]. This equation represents a geometric sequence, with the initial quantity being 40,000,000 and decreasing by 10% each year.
Explanation:The scenario is a geometric sequence, where the number of people who still recognize Britney Spears each year is decreasing by 10%. To represent this situation mathematically, we can use a geometric equation: [tex]y = a \cdot r^x[/tex]where 'a' is the initial quantity, 'r' is the ratio of decrease or increase, and 'x' is the number of time periods.
In this case, 'a' is 40,000,000 (the initial amount of people), 'r' is 0.9 (representing a 10% decrease each year), and 'x' will represent the number of years since her prime. Thus, the correct equation out of the options to represent the scenario is [tex]y = 40,000,000(0.9)^x.[/tex]
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f(x) = x4 + x3 + 2x2 + ax + b,
where a and b are constants.
When f(x) is divided by (x - 1), the remainder is 7
(a) Show that a + b = 3
When f(x) is divided by (x + 2), the remainder is -8
(b) Find the value of a and the value of b
Answer:
see explanation
Step-by-step explanation:
The remainder theorem states that if f(x) is divided by (x - h)
The the remainder is f(h)
(a)
Given f(x) is divided by (x - 1) then remainder is f(1), thus
f(1) = [tex]1^{4}[/tex] + 1³ + 2(1)² + a + b = 7, that is
1 + 1 + 2 + a + b = 7
4 + a + b = 7 ( subtract 4 from both sides )
a + b = 3 ← as required → (1)
(b
Given f(x) is divided by (x + 2) then the remainder is f(- 2), thus
f(- 2) = [tex](-2)^{4}[/tex] + (- 2)³ + 2(- 2)² + 2a + b = - 8, that is
16 - 8 + 8 + 2a + b = - 8
16 + 2a + b = - 8 ( subtract 16 from both sides )
2a + b = - 24 → (2)
Multiply (1) by 2
2a + 2b = 6 → (3)
Add (2) and (3) term by term to eliminate the term in a
3b = - 18 ( divide both sides by 3 )
b = - 6
Substitute b = - 6 into (1)
a - 6 = 3 ( add 6 to both sides )
a = 9
Thus a = 9 and b = - 6
Final answer:
To solve for the constants a and b in the polynomial function f(x), we apply the remainder theorem to the given division scenarios. Setting up and solving a system of linear equations using the remainders allows us to find that a is 9 and b is -6.
Explanation:
The given function is f(x) = x^4 + x^3 + 2x^2 + ax + b, and we need to find the constants a and b given that when f(x) is divided by (x - 1), the remainder is 7, and when divided by (x + 2), the remainder is -8.
To find a + b, we apply the remainder theorem. When a polynomial f(x) is divided by (x - p), the remainder is f(p). Therefore, for (x - 1):
f(1) = 1 + 1 + 2 + a + b = 7
4 + a + b = 7
a + b = 3
Similarly, for (x + 2):
f(-2) = (-2)^4 + (-2)^3 + 2(-2)^2 + a(-2) + b = -8
16 - 8 + 8 - 2a + b = -8
16 - 2a + b = -8
We already know that a + b = 3, so we can set up a system of equations:
a + b = 3
-2a + b = -24
Solving for a and b:
Subtracting the first equation from the second: -3a = -27
Divide by -3: a = 9
Substitute a into the first equation: 9 + b = 3
Solve for b: b = -6
Simplify the algebraic expression
6(-4x-7) -4(x-6)
A -20x-18
B -20x-66
C -28x+66
D -28x-18
6(-4x - 7) - 4(x - 6) Distribute 6 into (-4x - 7) and -4 into (x - 6)
(6)(-4x) + (6)(-7) + (-4)x + (-4)(-6) (two negative signs cancel each other out and become positive)
-24x - 42 - 4x + 24 Combine like terms(terms that have the same variable and power/exponent)
-24x - 4x - 42 + 24 (I rearranged the terms to be next to their like term)
-28x - 18 Your answer is D
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Write 14 as a product of primes.
Answer:
14 = 2*7
Step-by-step explanation:
2 and 7 are prime.
Answer:
14 = 1 x 14 or 2 x 7. Factors of 14: 1, 2, 7, 14. Prime factorization: 14 = 2 x 7
Step-by-step explanation:
PLEASE HELP
factor 12n - 18.
I think the answer is 6(2n-3)
Which point on the graph shows the reflection of point A across the y-axis?
Answer:
point t
Step-by-step explanation:
to reflect over the y-axis, flip the sign of the x coordinate
(6, -4) to (-6, -4)
point t is located at (-6,-4)
For five days, several hikers walk the distance and direction described by the vector
⟨5, –2⟩ each day. The next day, they walk the distance and direction described by the vector ⟨–1, 8⟩. At the end of the six-day trip, what is their bearing from their starting location?
Answer:
94.76°
Step-by-step explanation:
Assuming the coordinates are <E, N>, the total distance from the start is ...
5<5, -2> +<-1, 8> = <5·5 -1, 5(-2) +8> = <24, -2>
These coordinates represent a vector south of east, so the bearing measured clockwise from north will be greater than 90°. The reference angle (with respect to a north-south line) will be ...
arctan(24/2) = 85.24°
The bearing is 180° -85.24° = 94.76°.