Answer:
(- 3, 0), (2 + [tex]\sqrt{2}[/tex], 0), (2 - [tex]\sqrt{2}[/tex], 0)
Step-by-step explanation:
rearrange the equation equating to zero
x³ - x² - 10x + 6 = 0
note that when x = - 3
(- 3)³ - (- 3)² - 10(- 3) + 6 = - 27 - 9 + 30 + 6 = 0, hence
x = - 3 is a root and (x + 3) is a factor of the polynomial
dividing x³ - x² - 10x + 6 ÷ (x + 3) gives
(x + 3)(x² - 4x + 2) = 0
solve x² - 4x + 2 = 0 using the quadratic formula
with a = 1, b= - 4 and c = 2
x = (4 ± [tex]\sqrt{16-(4(1)(2)}[/tex])/ 2
= (4 ± [tex]\sqrt{8}[/tex]) / 2
= (4 ± 2[tex]\sqrt{2}[/tex]) / 2
= 2 ±[tex]\sqrt{2}[/tex], hence
x = 2 + [tex]\sqrt{2}[/tex], x = 2 - [tex]\sqrt{2}[/tex]
intersect at (- 3, 0), (2 +[tex]\sqrt{2}[/tex], 0), (2 - [tex]\sqrt{2}[/tex], 0)
Answer: [tex]\bold{x=-3,\quad x=2+\sqrt{2}, \quad x=2-\sqrt{2} }}[/tex]
Step-by-step explanation:
First, move all terms to one side with zero on the other side so the Zero Product Property can be applied:
x³ - x² - 10x + 6 = 0 Possible rational roots are: ±{1, 2, 3, 6}
Use synthetic division to find one of the roots. Let's try x = -3
-3 | 1 -1 -10 6
| ↓ -3 12 -6
1 -4 2 0 ← remainder is zero, so x = -3 is a root/intercept
Next, evaluate the reduced polynomial x² - 4x + 2 = 0
This can not be factored so use the quadratic formula to find the remaining roots/intercepts: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
a = 1, b = -4, c = 2
[tex]x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(1)(2)}}{2(1)}[/tex]
[tex]=\dfrac{4\pm\sqrt{16-8}}{2}[/tex]
[tex]=\dfrac{4\pm\sqrt{8}}{2}[/tex]
[tex]=\dfrac{4\pm2\sqrt{2}}{2}[/tex]
[tex]=2\pm\sqrt{2}[/tex]
[tex]x=2+\sqrt{2}\qquad x=2-\sqrt{2}[/tex]
Intercepts are [tex]x=-3,\quad x=2+\sqrt{2}, \quad x=2-\sqrt{2}}[/tex]
Helppppp pleaseeeeee
15) Yes, it is a function.
16)
A f(-4)=2
B F(3)= something around -1.75
C f(-5)=0
D f(-2)=4
E f(0)=0
F) -2
17)2(2a+5)=4a+10
a(a+5)=a^2+5a
18) 1
"Name the property:
a + (b+12) = (a+b) + 12"
Answer:
This property would be the Associative property of addition.
If you vertically stretch the exponential function, f(x)=2^x by a factor of 3, what is the equation of the new function?
A. g(x)=2•3^x
B. g(x)=2^3x
C. g(x)=1/3•2^x
D. g(x)=3•2^x
Answer:
The correct answer is D.
Step-by-step explanation:
just multiply the original function by the factor 3.
What is the slant height of the pyramid to the nearest tenth?
A.) 13.9 mm
B.) 15.5 mm
C.) 12.5 mm
D.) 19.0 mm
check the picture below.
Answer:
(C) 12.5mm
Step-by-step explanation:
It is given that a pyramid having slant height AC is to be determined. From the given information, we get
AB=12mm, BC=3.5mm and we have to find out the value of AC.
Thus, using the Pythagoras theorem, we have
[tex](AC)^2=(AB)^2+(BC)^2[/tex]
Substituting the given values, we have
[tex](AC)^2=(12)^2+(3.5)^2[/tex]
[tex](AC)^2=144+12.25[/tex]
[tex](AC)^2=156.25[/tex]
[tex]AC={\sqrt{156.25}}[/tex]
[tex]AC=12.5mm[/tex]
Therefore, the value of the slant height is 12.5mm.
Hence, option C is correct.
Fourteen seniors were asked how many minutes they spent on doing their homework the previous night. The data is displayed below. Find the median and interpret the value in context. 73 75 87 65 69 62 81 64 68 101 74 71 89 87 a 74 minutes; About half of the students spent less than 74 minutes doing homework and about half spent more than 74 minutes on homework. b 73.5 minutes; About half of the students spent less than 73.5 minutes doing homework and about half spent more than 73.5 minutes on homework. c 73 minutes; About half of the students spent less than 73 minutes doing homework and about half spent more than 73 minutes on homework. d 73.5 minutes; Most of the students spent 73.5 minutes on homework.
Answer:
b
Step-by-step explanation:
We need to find the median of:-
73 75 87 65 69 62 81 64 68 101 74 71 89 87
First, we need to arrange the numbers in ascending order as below:-
62, 64, 65, 68, 69, 71, 73, 74, 75, 81, 87, 87, 89, 101
Since there are a total of 14 numbers, let's split it up into two halves (each of seven numbers)
62, 64, 65, 68, 69, 71, 73 ||| 74, 75, 81, 87, 87, 89, 101
The median would be the mean of the two middle numbers i.e. the mean of 73 and 74
Median = [tex]\frac{73+74}{2}[/tex]
= [tex]\frac{147}{2}[/tex]
= 73.5
So, about half of the students spent less than 73.5 minutes doing homework and about half spent more than 73.5 minutes on homework
Answer:
Option b is the correct choice.
Step-by-step explanation:
We have been given a data set about minutes spent on doing homework the previous night by 14 seniors.
To find the median of data set, first of all we will arrange our data values from least to greatest order.
62, 64, 65, 68, 69, 71, 73, 74, 75, 81, 87, 87, 89, 101.
Since our data set has an even number (14) of data points, therefore, median will be the average of middle two points, that is 7th and 8th term.
[tex]\text{Median}=\frac{\text{7th term + 8th term}}{2}[/tex]
[tex]\text{Median}=\frac{73+74}{2}[/tex]
[tex]\text{Median}=\frac{147}{2}[/tex]
[tex]\text{Median}=73.5[/tex]
Therefore, median of our given data set is 73.5.
Since median of a data set separates the higher half from the lower half of a data sample. So about half of the students spent less than 73.5 minutes doing homework and about half spent more than 73.5 minutes on homework.
Therefore, option b is the correct choice.
|x| – 7 = 8 plz help me
x = –1 or 1
x = 1
x = 15
x = –15 or 15
[tex]|x|- 7 = 8\\\\|x|=15\\\\x=-15 \vee x=15[/tex]
Answer:
x = –15 or 15
Step-by-step explanation:
|x| – 7 = 8
We need to isolate the absolute value.
Add 7 to each side
|x| – 7+7 = 8+7
|x| = 15
Now to get rid of the absolute values, we take what is inside the absolute values and set it equal to the right hand side. Remember we set it equal to the positive amount and the negative amount.
x=+15 and x=-15
how to plot 850 integer and it's opposite on a plot
Final answer:
Plotting the integer 850 and its opposite involves marking the points on a coordinate system. The point 850 is plotted 8.5 units to the right of the origin, and its opposite, -850, is plotted 8.5 units to the left, assuming a scale where each unit represents 100.
Explanation:
To plot an integer and its opposite, let's use the number 850 and its opposite, -850, as an example. A plot in mathematics typically refers to marking points on the coordinate system, which consists of two intersecting lines, usually perpendicular, called axes. The horizontal axis is known as the x-axis, and the vertical axis is the y-axis.
To plot the integer 850, you first need to establish a scale suitable for the values you intend to plot. In this example, if each unit on your plot represents 100, then the point representing 850 would be placed 8.5 units to the right of the origin (0,0). Conversely, to plot the opposite of 850, which is -850, you would move 8.5 units to the left of the origin.
In coordinate form, the point 850 can be represented as (850,0), and its opposite, -850, would be (-850,0). This illustration shows how to plot integers and their opposites on a simple two-dimensional graph.
Which is a solution of y=3x+2?
A) (-1,0)
B) (0,3)
C) (1/3,1)
D) (1,5)
Answer:
D) (1,5)
Step-by-step explanation:
You have to substitute so...
(-1,0):
y = 3x + 2
0 = 3(-1) + 2
0 = -3 +2
0 = -1
(-1,0) is NOT a solution.
(0,3):
y= 3x + 2
3 = 3(0) + 2
3 = 0 +2
3 = 2
(0,3) is NOT a solution.
(1/3,1):
y = 3x + 2
1 = 3(1/3) + 2
1 = 1 + 2
1 = 3
(1/3,1) is NOT a solution.
(1,5):
y = 3x + 2
5 = 3(1) + 2
5 = 3 + 2
5 = 5
(1,5) IS a solution.
Problem Page
A certain drug is made from only two ingredients: compound A and compound B. There are
5 milliliters of compound A used for every
6 milliliters of compound B. If a chemist wants to make
935 milliliters of the drug, how many milliliters of compound A are needed?
Answer:
425 mm
Step-by-step explanation:
The ratio of compound A to compound B is 5 is to 6.
So, we can say that the total ratio is of 11 parts (5+6=11).
If the chemist wants a total of 935 mm of the drug, then each of the 11 parts are worth:
[tex]\frac{935}{11}=85[/tex]
From the ratio, we know that Compound A is 5 parts. So:
[tex]85*5=425[/tex]
425 mm of Compound A is needed.
To make 935 milliliters of the drug using 5 milliliters of compound A for every 6 milliliters of compound B, approximately 429 milliliters of compound A would be needed. This was found by setting up and solving a proportion based on the given ratio.
Explanation:This question refers to a ratio or proportion problem. Given that for every 5 milliliters of compound A you use 6 milliliters of compound B, we can set up a proportion to solve for the amount of compound A needed to make 935 milliliters of the drug.
First, establish the existing ratio. 5ml A is to 6ml B, or in other words, 5/6 = A/B. Having the amount of the entire drug, 935 ml, we can sum up the parts, which means A (the required amount of compound A in ml) plus B (the required amount of compound B in ml) should equal to 935 ml.
Substituting B as 6A/5 in the equation, we get A + 6A/5 = 935. Solving this equation gives A approximately equal to 429 ml. Thus, you would need approximately 429 milliliters of compound A to create 935 milliliters of the drug.
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Which best describes why these two figures are similar or not similar?
A. They are not similar because their corresponding angles are not congruent.
Their angles are not the same.
The 1st triangle is a scalene triangle (a triangle that has 3 unequal sides and angles)
The 2nd triangle is an isosceles triangle (a triangle that has 2 congruent/equal sides and 2 congruent angles)
Answer:
Step-by-step explanation:
Mark is making 10 kites.he uses 5yards of ribbon for each kite.he has already made 2 of the kites.how many yards of ribbon will mark need to make the rest of the kites?
Answer:
40 yards
Step-by-step explanation:
8×5≈40
7x + 3x + 4 = 24 (Given) 10x + 4 = 24 (Simplify) 10x = 20 (?) x = 2 (Division) What is the missing reason for the argument shown?
A)
addition
B)
division
C)
subtraction
D)
multiplication
Answer:
I think it is A or B Hope this helps
Step-by-step explanation:
Answer:
The answer is C.Subtraction im a math teacher so if right mark brainliest
Step-by-step explanation:
the 146.35 cost of a party was shared by 10 people. how much did each person have to play? be sure to round to the nearest cent.
Answer:
$14.64 per person
Step-by-step explanation:
If we are sharing the cost between 10 people, we divide the total cost by 10
$146.35 /10 = $14.635
We round to the nearest cent
$14.64
Each of the 10 people would need to pay $14.64 for the party cost of $146.35, rounded to the nearest cent.
To calculate how much each person would have to pay for the party cost of $146.35 shared by 10 people, you divide the total cost by the number of people.
Step-by-step calculation:
Find the total cost of the party: $146.35.Divide the total cost by the number of people sharing the cost, which is 10.The calculation would be: $146.35 / 10 = $14.635.Round the amount to the nearest cent: $14.64.Therefore, each person would have to pay $14.64.
Thank you :) I appreciate it
Answer:
Question 7: I am not very good at recursive rules, so I cannot figure it out, sorry.
Question 8: 1/3
Question 9 a: 75 = How much money per paycheck
Question 9 b: 300 = How much money he started with
Question 10 a: 0,328 = initial amount
Question 10 b: 1.013 = percent increase
Question 11-12: Please submit another picture/question with the full graph.
Step-by-step explanation:
Question 8:
To find the common ratio you take one term divided by one term: 3/1 = 3
Since it is getting smaller every time, fraction: 1/3, because 3 * 1/3 = 1. 1 * 1/3 = 1/3, and it continues in that pattern.
Question 9 a:
f(p) = 75p + 300
Since p = paychecks, 75 appears to be how much money he makes per paycheck.
Question 9 b:
Since you are adding 300 to his current makings, it appears that 300 is the amount of money he already has.
Question 10 a:
Since t = weeks after beginning, 1.013 appears to be the percent increase, and since original amount times percent increase equals total, 10,328 appears to be the initial amount.
Question 10 b:
Since t = weeks after beginning, you would times the percent increase in order to calculate the increase, therefore 1.013 is the percent increase.
Question 11-12: Please submit another picture/question with the full graph.
What is the gcf of 42 and 56
[tex]42=2\cdot21=\boxed2\cdot3\cdot\boxed7\\\\56=2\cdot28=2\cdot2\cdot14=\boxed2\cdot2\cdot2\cdot\boxed7\\\\Answer:\ GCF(42,\ 56)=\boxed2\cdot\boxed7=14[/tex]
Solve for d. 20d − 19d + 3d + 4d + 2d = 20
What is the slope of a line perpendicular to line B
Answer:
Step-by-step explanation:
Where is line B?
the number of chocolate chips in an 18- ounce bag of Chips Ahoy! chocolate chip cookies is approximately normally distributed with a mean of 1262 chips and a standard deviationof 118 chips, according to a study by cadets of the U.S. Air Force Academy.
Answer: the answer is (A)
Step-by-step explanation:
A pilot whale is swimming at 20 feet below sea level. He dives to a depth of 3290 feet in 15 minutes. What is the change in depth per minute?
Answer:
218 feet per minute
Step-by-step explanation:
To find this, first subtract the initial amount (20) from the depth he soon reaches (3290). This will leave you with the amount of 3270 which is the distance the pilot whale went.
To find the feet per minute, divide by new depth by 15 in order to get the final answer of 218 feet per minute.
Hope this helps!
plz help I don't understand
thank you
Answer:
A. you take 3 ft and divide it in fourths which is 9 inches.
B. side length is 9 inches and the equation is 3ft ÷ .25
Step-by-step explanation:
I explained it in the answer however I will say that a square is the same length all around so I chose to use 3ft instead of 4.5 because its easier but you cannot do this with rectangles.
Solve the equation 9x = 7(x + 2).
A) -7
B) -1
C) 1
D) 7
Answer:
The solution of the equation 9x=7(x+2) is:
Option D) 7
Step-by-step explanation:
9x=7(x+2)
Eliminating the parentheses applying distributive property:
9x=7(x)+7(2)
Multiplying:
9x=7x+14
Grouping the x's on the left side of the equation: Subtracting 7x both sides of the equation:
9x-7x=7x+14-7x
Subtracting:
2x=14
Solving for x: Dividing both sides of the equation by 2:
2x/2=14/2
Dividing:
x=7
Solution: x=7 (option D)
A roller coaster can give rides to 50 more people. Each car can hold 5 people. What is the best way to interpret the remainder of 50 / 5 so that everyone gets a ride?
A. Write the remainder as a fraction
B. Use the remainder as the answer
C. Use only the quotient
D. Add 1 to the quotient
Solve the inequality
-5(3m-2)>30
Answer:
m < −4/3
Step-by-step explanation:
−5(3m−2)>30
Simplify both sides of the inequality.
−15m+10>30
Subtract 10 from both sides.
−15m+10−10>30−10
−15m>20
Divide both sides by -15.
−15m/−15 > 20/−15
m<−4/3
[tex]-5(3m-2)>30\qquad\text{use distributive property}\\\\(-5)(3m)+(-5)(-2)>30\\\\-15m+10>30\qquad\text{subtract 10 from both sides}\\\\-15m>20\qquad\text{change the signs}\\\\15m<-20\qquad\text{divide both sides by 15}\\\\m<-\dfrac{20}{15}\qquad\text{simplify}\\\\m<-\dfrac{20:5}{15:5}\\\\\boxed{m<-\dfrac{4}{3}}[/tex]
It cost Marc $29.75 a week to feed his dog .About how much does it cost him to feed his dog for 3 weeks?
Answer:
$89.25
Step-by-step explanation:
If one week is 29.75, then you can infer that each week separately would be the same amount. With this information, you can form this equation:
y = 29.75x
X would be the number of weeks while y would be the final amount based off the number of weeks.
If you substitute x with 3, then you should get the final answer of 89.25.
Hope this helps!
5(a+3)=8a
How can I solve this?
Simplify the left side of the equation using the distributive property.
5(a+3) = 5*a + 5*3 = 5a + 15
Now the equation looks like this: 5a + 15 = 8a
Next we want to put all the variables on the same side.
In this case, the easiest way to do this is subtract 5a from both sides.
5a + 15 - 5a = 8a - 5a
15 = 3a
In order to isolate a, divide both sides by 3
15/3 = 3a/3
5 = a
Answer: a = 52−1/2n=3n+16 what is n
Answer:
n = -4
Step-by-step explanation:
2 - 1/2n = 3n + 16
First isolate n
2 - 16 = 3n + 1/2n
-14 = 3 1/2n
n = -4
Answer:
n=-4
Step-by-step explanation:
2-.5n=3n+16 REWRITTEN
2=3.5n+16 ADDITION PROPERTY OF EQUALITY
-14=3.5n SUBTRACTION PROPERTY OF EQUALITY
n=-4 DIVISION PROPERTY OF EQUALITY
Lines g, h, and I are parallel and
m< 2= 115°.
BRAINLIEST ASAP!!!
what is m<11?
A. 35°
B. 65°
C. 115°
D. 145°
♥️♥️♥️♥️
Answer: Choice C) 115 degrees
Focus on the parallel lines G and L, which are the top and bottom most horizontal lines. Notice that the transversal cut forms the alternate exterior angles 2 and 11. The angles are on the outside or exterior of the "train tracks" of the parallel lines. Also, they are on opposite sides of the transversal line. So that is how we can consider them to be alternate exterior angles.
Similar to alternate interior angles, alternate exterior angles are congruent if we have a transversal cutting a pair of parallel lines.
So in short, angle 2 and angle 11 are congruent. We are given angle 2 to be 115 degrees. Angle 11 is also 115 degrees.
Can someone plz help me ♀️
Answer: (D) 4
Step-by-step explanation:
Average rate of change means slope (m) from point a to point b.
when x = 5, y = -2 → coordinate (5, -2)
when x = 7, y = 6 → coordinate (7, 6)
slope (m) = [tex]\dfrac{6-(-2)}{7-5} = \dfrac{8}{2}=4[/tex]
state if each triangle is a right triangle
Answer:
both 17 and 19 are right triangles because they both have a right angle
Step-by-step explanation:
find the radius of a circle with a circumference of 45pi centimeters
Answer: 7.16cm
Step-by-step explanation:
R=C/2pi
R=45/pi2
R=45/2 = 22.5pi
The radius of a circle with a circumference of 45pi centimeters is 22.5 centimeters.
Explanation:To find the radius of a circle with a circumference of 45pi centimeters, we can use the formula for circumference:
C = 2(pi)r
Given that the circumference is 45pi, we can substitute this value into the formula:
45pi = 2(pi)r
Now, we can solve for r:
r = 45/2 = 22.5 centimeters
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