Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given a quadratic equation in standard form
ax² + bx + c = 0 , then the sum of the roots is
α + β = - [tex]\frac{b}{a}[/tex]
Here 2x² - x - 3 = 0 is in standard form
with a = 2 and b = - 1 , then
sum of roots = - [tex]\frac{-1}{2}[/tex] = [tex]\frac{1}{2}[/tex]
Please help me i need the answer right now. The lesson is Rational Root Theorem.
Step-by-step explanation:
1. The length is one more thrice it's width. The height is 4 more than it width. We can represent the
x+4.(3x+1)(x)The volume is 720.Volume of Rectangular prism is LxWXH. So the volume is equal to the terms all multiplied. which is[tex](3x + 1)(x + 4)[/tex]
[tex](3 {x}^{2} + 13x + 4)x = 720[/tex]
Multiply it by x.
[tex]3 {x}^{3} + 13 {x}^{2} + 4x = 720[/tex]
[tex] 3{x}^{3} + 13 {x}^{2} + 4 x - 720[/tex]
The possible roots
The possible roots are plus or minus is1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, and 720. By a long list of substitution, 5 is a root. So this means that x=5. So the width has to be
[tex]x = 5[/tex]
2. First. we apply the Rational Root Theorem so the possible roots are plus or minus 1,2,3,6.
Let check via synethic division to see which are roots.
Let try 1 and -1 first. If we plug 1 into the equation, we get
[tex]1 - 2 - 5 + 6 = 0[/tex]
So 1 or (x-1) is a solution. Since it's a solution we can divide this into our original polynomial to get us a new polynomial that is more simplified. If we apply synthetic division, we get a new polynomial in
[tex] {x}^{2} - x - 6[/tex]
We can then factor this into
[tex](x - 3)(x + 2)[/tex]
So our roots or factors is
[tex](x - 1)(x - 3)(x + 2)[/tex]
what is a = with a ~ thing on top?
There are 5 seats in a bus. In how many different ways if there are 5 children. How many different ways are there if there are 4 children, and how many different ways are there if there are 3 children.
Answer:
5=1
4=5
i don't really know for the third one sorry but it's more than 11
Step-by-step explanation:
18 Ib. Then her dog loses another 1 lb. Finally, it
Cece dog
gains lb. What is the total change in her dog's weight? how your work. Pleasss help
Answer:
17 lb I guess 8 don't think the question is full
Step-by-step explanation:
the question is half
Grant is a member of a book club. He pays a $10 yearly membership fee and can purchase books through the club for $2.75 each. His total annual cost is a function of the number of books that he purchases in a year. Let b represent the number of books he purchases in a year. Which function, C(b), represents his yearly cost
The lengths of the sides of a triangle are 3, 4, 5. Can the triangle be a right triangle?
Answer:
Yes it can
Step-by-step explanation:
To check wether it's a right angle triangle we need to apply the Pythagoras theorem
h^2= a^2 +b^2
Hypotenuse is always the longest side so
5^2 = 3^2 + 4^2
This is correct, so the triangle is a right angle triangle
Answer from Gauthmath
Use a calculator to determine the unknown angle, to the nearest degree, in each of the following expressions.
tan A = 5/4
cos G = 0.88
Answer:
Using a calculator;
A is approximately 51.34°
G is approximately 28.36°
Step-by-step explanation:
Part 1
The given trigonometric ratio is presented as follows;
tan A = 5/4
Therefore, the angle, A = arctan(5/4)
Using a calculator, the value of A is found as follows;
1. Ensure the angle mode of the calculator is set to the correct value (the selected mode here is degrees)
2. Entering 5/4 into the calculator, using the keypad
3 . Selecting the arctan button to give, A ≈ 51.34°
Part 2
The given trigonometric ratio is cos G = 0.88
Therefore, G = arccos(0.88)
1. Ensure the angle mode of the calculator is set to the correct value (the selected mode here is degrees)
2. Enter 0.88 into the calculator by typing
3. Select arccos from the function menu, to give
arcos(0.88) = G ≈ 28.36°.
Make six prime numbers using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 once each.
~can you plz explain?!
Answer:
2, 3, 5, 7, 11, 13.
Step-by-step explanation:
A prime number is a number that you don't get a whole number when divided by 2 but you do get a whole number when divided by prime numbers such as 3,5,7,11... Basically a number with two factors, it can only be divided by 1 or themselves. for example:
9/2 = 4.5 (this is not a whole number so it might be a prime.
9/3 = 3 (it works when divided by a prime number.
another:
8/2 = 4 (it gives a whole number when divided by 2 therefor, it can't be a prime number.
Answering:
There are 6 prime numbers at the top^^^^.
One possible answer is 2, 3, 5, 41, 67, 89
Another possible answer is 2, 3, 5, 47, 61, 89
Other answers may be possible.
=============================================================
Explanation:
This is a trial and error type of problem. Though with practice it's not as blind of randomly guessing.
We have 9 values here. If we paired them up, then we can form at most 4 pairs (since 9/2 = 4.5 rounds down to 4). That means we won't be able to form six two-digit primes. Some of the primes must be single digits.
We can have 3 single digit primes and 3 two-digit primes since 3+2*3 = 9.
The single digit primes are: 2, 3, 5, 7
Let's say 2 and 5 are definitely locked down to be the single digit group. I'm doing this since we can't have 2 or 5 as the units digit. If the units digit is 2, then 2 is a factor and it's not prime. Similarly, if 5 is the units digit, then 5 is a factor and that two digit value is not prime.
For good measure, we'll throw 3 in there as well and see what happens.
------------------
The digits we have left are: 1, 4, 6, 7, 8, 9
The number 14 isn't prime, but 41 is prime
67 is prime so that's another two values off the list
lastly, 89 is prime so that works as well.
So one possible sequence is 2, 3, 5, 41, 67, 89
Notice how we can swap the 1 and 7 to go from 41,67 to 47,61; this gets us two other primes. So another possible answer is 2, 3, 5, 47, 61, 89
------------------
Side note: having the list of primes on a reference sheet is a handy recommendation. You only need to go up as high as 97 which is the largest two digit prime.
Which statement about the function
true?
The graph of the function f(x) = 4(x + 3)(x - 1) is shown
below.
O The function is positive for all real values of x where
x < -1.
y
6
NA
The function is negative for all real values of x where
x <-3 and where x > 1.
O The function is positive for all real values of x where
x > 0.
O The function is negative for all real values of x where
X<-3 or x>-1.
2
-6
4
2.
4
6
х
-2
-2
4
6
The function is negative for all real values of x where x < -3 or x > -1 and the domain of the function is -∝ < x < ∝
What are domain and range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = - ( x + 3 ) ( x - 1 ) be equation (1)
Now , the values of x which makes the function negative are
when x < -3
f ( x ) = - ( -ve ) ( -ve ) = -ve
when x > 1
f ( x ) = - ( +ve ) ( +ve ) = -ve
So , the domain of the function is all real numbers and -∝ < x < ∝
Hence , the function is solved
To learn more about domain and range click :
https://brainly.com/question/28135761
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I need help what’s the answer?
Answer:
30 words per minute
Step-by-step explanation:
Take the number of words and divide by the number of minutes
150/5 = 30
300/10 =30
450/15 = 30
600/20 = 30
30 words per minute
Answer:
janae types 30 words each minutes.
Step-by-step explanation:
if 5minutes = 150 words
[tex]1 \: minute = \frac{150words}{5minutes} [/tex]
[tex] = \: 30words[/tex]
Write the y-intercept of the line
Answer: -2. Bc if you look on the graph of the y axis you'll see its located at -2.
Hope this helps :)
Step-by-step explanation:
Can somebody help me Answer to this ??
X=7
c is the answer:
[tex]3x + 50 = 10x + 1 \\ 10x - 3x = 50 - 1 \\ 7x = 49 \\ x = \frac{49}{7} \\ x = 7[/tex]
If a zero is
, then the graph of its function only touches the x–axis at that zero.
Answer:
Step-by-step explanation:
Yes. The zeroes of a graph are the values of x where the graph touches (or crosses) the x-axis.
can i get some help? i tried figuring it out myself already but i must have done something wrong. please help!
First, we'll set up two equations. One for the amount of each coin and another for the value of the coins.
N will represent nickels
D will represent dimes
N + D = 30
---The problem tells us that there are 30 total coins
0.05N + 0.10D = 2.95
---Nickels are worth 5 cents and dimes are worth 10 cents, and the total value of the coins is 2.95
Now that we have our equations, we need to solve for one of the variables in the first equation. I will solve for N.
N + D = 30
N = 30 - D
Then, we take that equation and substitute our new value for N into the second equation (value) and solve for D.
0.05(30 - D) + 0.10D = 2.95
1.5 - 0.05D + 0.10D = 2.95
1.5 + 0.05D = 2.95
0.05D = 1.45
D = 29
Now that we know how many dimes there are, we can plug that value into our equation for N and solve for N.
N = 30 - D
N = 30 - 29
N = 1
Therefore, there are 29 dimes and 1 nickel.
Hope this helps!
what are the points for the equation y +2 = - 3/4 (x+4)
Answer:A(1,-5)
B(6,-8)
Step-by-step explanation:
3.)The lateral surface area of a right circular cylinder is 120cm² and the circumference of the bases is 12cm.Find the altitude of the cylinder
Answer:
Lateral surface area= circumference*height
120=12*h
h=10cm
Answer:
h=10 cm
Step-by-step explanation:
cicumference of a circle C=2πr=12
lateral surface area of cylinder=2πrh
120=12h
h=120/12=10 cm
solve the equation 4+2|3x+4|=-4
“Absolute Value Equations and Inequalities”
the solutions are what?
please give an explanation if possible!
Answer:
Value of given expression x is -4
Step-by-step explanation:
Given equation in question;
4 + 2|3x + 4| = -4
Find:
Value of given expression
Computation:
4 + 2|3x + 4| = -4
Using BODMAS rule;
⇒ 4 + 2|3x + 4| = -4
⇒ 2|3x + 4| = - 4 - 4
⇒ 2|3x + 4| = - 8
⇒ |3x + 4| = - 8 / 2
⇒ |3x + 4| = - 4
⇒ 3x + 4 = - 8
⇒ 3x = -8 - 4
⇒ 3x = -12
⇒ x = -12 / 3
⇒ x = -4
Value of given expression x is -4
Solve the equation 5x + 2(2x -23) = -154
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
5x+2(2x-23)=-1545x+4x-46=-1549x-46=-1549x=-154+469x=-108x=[tex]\sf{\dfrac{-108}{9} }[/tex] x=-12Answer:
x = -12
Step-by-step explanation:
5x + 2(2x - 23) = -154
Distribute;
5x + 4x - 46 = -154
Collect like terms
9x - 46 = -154
Add 46 to both sides;
9x = -108
Divide both sides by 9
x = -12
mA = (4x - 2) and mzB = (11x + 17)°. Find x if the angles are
supplementary
A.) 165
B.) 180
C.) 15
D.) 11
Help me pls‼️‼️‼️❤️❤️
Answer:
= 50%
Step-by-step explanation:
There is one point, random number = 1
There are two circles, sample space = 2
[tex]{ \tt{probability = \frac{1}{2} }} \\ { \tt{percentage = \frac{1}{2} \times 100\% }} \\ = 50\%[/tex]
Answer:
25%
Step-by-step explanation:
1. Find the area of both Circles: [tex]A = \pi r^{2}[/tex] [tex]A = \pi 2^{2}[/tex] = [tex]4\pi[/tex] [tex]A = \pi 1^{2} = \pi[/tex]
2. [tex]\frac{\pi }{4\pi }[/tex] to find the percentage
3. 0.25 = 25%
Which of the following accurately describes the median of a set of data? Multiple choice question. The midpoint of the data when it is arranged in order. The difference in the largest and smallest values. The most numerous observation in a set of data. The arithmetic average of the values in the set.
Answer:
The midpoint of the data when it is arranged in order.
Step-by-step explanation:
Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order
For example, the median of the following set of numbers is 5
1, 2, 5, 10, 20
Range is the difference between the highest and lowest values of a set of observations
Range = highest value - lowest value
Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number
Mean = sum of the numbers / total number
If a pine tree grows 3 inches per year,how long will it take for the tree to reach a height of 8 feet
Answer:
32 years
Step-by-step explanation:
8x12 because there are 12 inches in a foot
8x12=96
96/3
96/3=32
Answer:
32 years
Step-by-step explanation:
y = years
1 foot = 12 inches
12 × 8 = 96
Now, plug in random numbers into the expression below to find how long it takes for the tree to grow 8 feet.
3y
3 × 10 = 30
3 × 20 = 60
3 × 30 = 90
3 × 31 = 93
3 × 32 = 96
It will take the pine tree 32 years to grow 8 feet, or 96 inches.
{(5,2), (-2,4), (2, -7)}
Domain:
Range:
Answer:
Step-by-step explanation:
The domain are all the x values in order, no repeats allowed:
D = {-2, 2, 5}
Same thing for the range, except these are the y values:
R = {-7, 2, 4}
The coordinates stated this way don't match up to what they are in coordinate form, but they don't have to.
Answer:
Domain : {-2,2,5}
Range:{ -7,2,4}
Step-by-step explanation:
The domain is the inputs
Domain : {-2,2,5}
The range is the outputs
Range:{ -7,2,4}
Given JIH~ LMN. what is the value of LN?
Answer:
7 units
Step-by-step explanation:
In similar triangles, corresponding sides are same ratio.
[tex]\frac{LN}{JH}=\frac{LM}{JI}\\\\\frac{LN}{14}=\frac{5}{10}\\\\LN=\frac{5}{10}*14\\\\LN=7[/tex]
Find the value x ……….
Answer: 6 because it more than thd base and less than the other triangles leg
Step-by-step explanation:
Answer:
[tex]4\sqrt{5}[/tex]
Step-by-step explanation:
[tex]x^2 = y^2 + 25[/tex]
[tex]\frac{y}{11} = \frac{5}{y}[/tex]
[tex]y^2 = 55[/tex]
[tex]x^2 = 80\\x = \sqrt{80} \\x= 4\sqrt{5}[/tex]
Evaluate w+(-x) - 2/3 where w = -5/9 and x = 4/3
Answer:
-23/9 or -2 5/9
Step-by-step explanation:
w+(-x) - 2/3
Let w = -5/9 and x = 4/3
-5/9+(- 4/3) - 2/3
Get a common denominator of 9
-5/9 - 4/3 *3/3 - 2/3 *3/3
-5/9 - 12/9 - 6/9
-23/9
-2 5/9
Answer:
-2 5/9
Step-by-step explanation:
Solve the system of equations using substitution.
y = x + 6
y = –2x – 3
Answer:
x = -3
y= 3
Step-by-step explanation:
y = x + 6 -----------------------(I)
y = -2x - 3 ---------------------(II)
Substitute y =x +6 in equation (II)
x + 6 = -2x - 3
Add 2x to both sides
x + 2x +6 = -3
Combine like terms
3x + 6 = - 3
Subtract 6 from both sides
3x = - 3 - 6
3x = -9
Divide both sides by 3
x = -9/3
x = -3
Plug in s = -3 in equation (I)
y = -3 + 6
y = 3
A truck was carrying 10 bags of sugar. Each bag weighed 50kg. Calculate the total mass of sugar on the truck. Write your answer in grams.
Answer:
1beg-------------50kg
10beg------------x
x=500kg to grames 500×1000=500000grams
Answer:
500000g
Step-by-step explanation:
first of you multiply the 50kg with the 10 bags
which gives 500kg
then you convert 500kg to grams
which is 500kg/1×1000g/1kg
when you cancel out the kg what is left is to multiply both sides and then you get 50000g.
Which system is equivalent to y=-2x^2 y=x-2
a) y=-2y^2 x=y-2
b) y=-2y^2+2 x=y+2
c) y=-2y^2-8y-8 x=y+2
d) y=-2y^2+8y-8 x=y-2
Answer:
answer C
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y&=&-2x^2\\y&=&x-2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x&=&y-2\\y&=&-2(y-2)^2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x&=&y-2\\y&=&-2y^2-8y-8\\\end{array}\right.\\\\[/tex]
find the missing length indicated
Answer:
119?
Step-by-step explanation:
