Answer:
[tex]\Large \boxed{(x+4)(x-1)}[/tex]
Step-by-step explanation:
Hello,
[tex]x^2+3x-4\\\\\text{*** The product of the zeroes is -4=-1*4 and their sum is -3=-4+1. ***}\\\\\text{*** So we can factorise. ***}\\\\x^2+3x-4=x^2-x+4x-4=x(x-1)+4(x-1)=\large \boxed{(x+4)(x-1)}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
The factors of given function are (x + 4) and (x - 1)
To undestand more, check below explanation.
Factors of function:The modeled for algebra tiles is given as,
[tex]f(x)=x^{2} +3x-4[/tex]
We have to find the factors of given function.
Factoring means finding expressions that can be multiplied together to give the given equation.
If a quadratic equation can be factored, it is written as a product of linear terms.
[tex]f(x)=x^{2} +3x-4\\\\f(x)=x^{2} +4x-x-4\\\\f(x)=x(x+4)-1(x+4)\\\\f(x)=(x+4)(x-1)[/tex]
Hence, the factors of given function are (x + 4) and (x - 1)
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Sketch the graphs of the equations: y = −3 −x
This is a linear equation in slope-intercept form. We can see that the slope is -1 and the y-intercept is -3 -- the line passes through (0, -3).
To graph this, we can simply plot the point (0, -3) and draw a line with slope negative 1 (this means that for every unit right, we have to move 1 unit down.
I have attached a picture of the graph.
On a trip, a car traveled 80 miles in an hour and a half, then was stopped in traffic for 30 minutes, then traveled 100 miles during the next 2 hours. What was the car's average speed in miles per hour for the 4-hour trip?
Answer:
45 mph
Step-by-step explanation:
HALP PLS 1000 students are arranged in several rows (more than 16). The numbers of students in each row are consecutive positive integers. How many students are there in the first row? (A) 20 (B) 25 (C) 28 (D) 44 (E) 80
Answer:
The correct option is;
(C) 28
Step-by-step explanation:
The information given are that;
The total number of students = 1000
The number of students in each row are consecutive positive numbers
Let the number of students in the first row be x,
Let the number of rows be 17
We have;
The number of students in the last row = x + 16
The number of students in the penultimate row = x + 15, we continue to get;
n×x + n/2×(n-1) = 1000
(The term n/2×(n-1) is from the sum of an arithmetic progression formula)
Which gives;
17×x + 17/2×16 = 1000
17×x = 1000 - 17/2×16 = 1000 - 136 = 864
x = 864/17 = Which is not an integer,
We continue checking till we get to 25 rows which gives;
25×x + 25/2×24 = 1000
25×x + 300 = 1000
25×x = 1000 - 300 = 700
x = 700/25 = 28
The number of student in the first row = 28 students.
A baseball 4 feet off the ground is hit with an upward velocity of 52 feet per second.
The height of the baseball in feet after t seconds is given by the equation
h = – 1672 + 52t + 4. A fan catches the ball 16 feet off the ground when it is coming
down. When does the fan catch the ball?
The fan catches the ball
seconds after it is hit.
(Note: the ball is 16 feet high at one point when it is going up and again when it is
coming down.)
The solution is
Answer: The fan catch the ball after 3 seconds.
Step-by-step explanation:
Given, A baseball 4 feet off the ground is hit with an upward velocity of 52 feet per second.
The height of the baseball in feet after t seconds is given by the equation
[tex]h = - 16t2 + 52t + 4[/tex]
If a fan catches the ball 16 feet off the ground when it is coming down.
then, at that time h= 16 feet
At h= 16
[tex]16=-16t^2+52t+4\\\\\Rightarrow\ 16t^2-52t+12=0\\\\\Rightarrow\ 4t^2-13t+3=0[/tex]
[tex]\Rightarrow\ 4t^2-t-12t+3=0\Rightarrow\ t(4t-1)-3(4t-1)=0\\\\\Rightarrow\ (4t-1)(t-3)=0\\\\\Rightarrow\ t=\dfrac{1}{4},\ t=3[/tex]
From the graph , it can be observe that when ball comes back , for height 16 feet the corresponding time t= 3 sec
So, the fan catch the ball after 3 seconds.
The coordinates of rhombus ABCD are A(–4, –2), B(–2, 6), C(6, 8), and D(4, 0). What is the area of the rhombus? Round to the nearest whole number, if necessary.
Answer:
The rhombus ABCD has an area of 22 square units.
Step-by-step explanation:
The coordinates of rhombus ABCD are shown in the image attached below. The area of the rhombus can be found in terms of their diagonals, which are now calculated by Pythagorean Theorem:
[tex]AC = \sqrt{[6-(-4)]^{2}+[8-(-4)]^{2}}[/tex]
[tex]AC = 15.620[/tex]
[tex]BD = \sqrt{(4-6)^{2}+[0-(-2)]^{2}}[/tex]
[tex]BD \approx 2.828[/tex]
The area of the rhombus is: ([tex]AC = 15.620[/tex] and [tex]BD \approx 2.828[/tex])
[tex]A = \frac{AC\cdot BD}{2}[/tex]
[tex]A = \frac{(15.620)\cdot (2.828)}{2}[/tex]
[tex]A = 22.087[/tex]
The rhombus ABCD has an area of 22 square units.
Answer:
22 units
Step-by-step explanation:
Why is the HCF x*2 ? Please explain thanks for number d
Answer:
x² is HCF (Height common factor)
Step-by-step explanation:
Given:
x² , x³
Find:
HCF (Height common factor)
Computation:
HCF (Height common factor) is uused to find Height common factor from the given numbers.
x² , x³
Takling x² as common
x² (1 , x)
So,
x² is HCF (Height common factor)
What is the remainder in the synthetic division problem below?
-2 1 2 -3 1
O A. 11
O B. 7
O C. 9
O D. 13
Answer:
B
Step-by-step explanation:
-2 / 1 2 -3 1
____-2 _ 0_ _6_____
1 0 -3 7
Write down the first number 1 as it is.
Step 2: Multiply 1 by -2 ( 1*-2 = -2) and write under the next number. Then add
2 +(-2) = 0
Step 3: Now Multiply 0 by -2 ( 0 * -2 =0) and write under the next number ie, -3.
-3 +0 = -3
Step 4: Multiply -3 by -2, ( -3*-2 = 6) and write under the number 1
1 + 6 = 7
7 is the remainder
The remainder in the synthetic division problem given is 7.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
Given a synthetic division problem.
Put the first number straight down.
So 1 is taken down.
Multiplying 1 by -2, we get -2.
2 + (- 2) = 0
Multiplying 0 by -2, we get 0.
-3 + 0 = -3
Multiplying -3 by -2, we get 6.
1 + 6 = 7, is the remainder.
Hence the remainder is 7.
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help asap! <3 The golf scores for the 32 members of the Belmont Country Club were 108, 89, 74, 115, 92, 86, 103, 107, 94, 89, 111, 78, 116, 82, 99, 107, 74, 78, 101, 93, 85, 98, 109, 82, 83, 105, 91, 106, 97, 84, 92, 96. Which histogram correctly shows the frequency distribution of the scores using ten-point intervals?
Answer:
histogram D
Step-by-step explanation:
From left to right, your frequencies (aka height of columns) should be 4, 8, 9, 8, and 3
what are the four different ways to solve a quadratic equation? When would you prefer to use each method?
Answer:
1. Factorization method
2. Formula method
3. Completing the square method
4. Graphical method
Step-by-step explanation:
There are four methods of solving quadratic equation:
1. Factorization method
2. Formula method
3. Completing the square method
4. Graphical method
1. Factorization method: Use factorization method when the quadratic equation can easily be factorize.
Example: x^2 - 4x - 12 = 0
(x-2)(x+6)
2. Formula method: This can be used when factoring the quadratic equation looks difficult or you are given instruction to use formula method
3. Completing the square method: Use completing the square method when you are instructed to do so.
4. Graphical method: This method is used when instructed to find x intercept.
Finding changed average
Answer:
15.
Step-by-step explanation:
The new average will be 11 + 4 = 15.
Answer: The overall average will increase by 4 from 11 to 15
Step-by-step explanation: If each of the six integers is increased by four, that will add 6×4 to the total.
The original average was based on six numbers totaling 66, then divided by 6 to get the average, 11.
So add 66 + 24 = 90
Divide 90/6 = 15. The new average.
That is 4 more than the original 11.
Help please and show work too
Answer:
Below
Step-by-step explanation:
51)
Let n be the first even number.
So the four consecutive even numbers are:
● n
● n+2
● n+4
●n+6
The smallest minus twice the larger is 4
● n-2(n+6)= 4
●n-2n-12 =4
● -n -12 =4
● -12 = 4+n
● -12-4 = n
● -16 = n
so the first even number is -16 and the largest one is -10
● -16+6= -10
■■■■■■■■■■■■■■■■■■■■■■■■■
Let m be the first integer
So the five consecutive integers are:
● m
● m+1
● m+2
● m+3
● m+4
The sum of this terms is 5.5 times the middle(m+2)
● m+m+1+m+2+m+3+m+4 = 5.5(m+2)
● 5m + 10 = 5.5 m +11
● -0.5 m = 1
●-m = 2
● m= -2
So the integers are;
● -2
● -1 (-2+1)
● 0
● 1
● 2
13. Marco took out an unsubsidized student loan for $20,000, which he will start paying in 4
years, after he graduates. If the interest rate is 4.2%, what is the amount he will owe once he
graduates?
Answer:
Marco will owe $ 23,360 once he graduates.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Principal of the loan = 20,000
Time in years = 4
Interest rate = 4.2%
2. What is the amount he will owe once he graduates?
Let's use the formula of the interest simple, this way:
A = P * (1 + r * t)
where P is the principal of the loan, r the interest rate and t, the time in years.
Substituting with the values we know, we have:
A = 20,000 * (1 + 4 * 0.042)
A = 20,000 * 1.168
A = 23,360
Marco will owe $ 23,360 once he graduates.
10 points are placed on a circle. How many triangles is it possible to form, such that their vertices will be the given points?
Answer:
120
Step-by-step explanation:
The total number of triangles that can be made are 120.
We have a circle and 10 points are placed on it.
We have to find how many possible triangles can be made such that their vertices will be the given points.
What is a Combination?A combination can be defined as the number of possible arrangements of elements without taking into consideration the order of selection. The number of possible combinations can be given by -
[tex]\frac{n!}{(n-r)!r!}[/tex]
In the question given to us - we have 10 points on circle. Only three points are needed to make a triangle. The order does not matter here, therefore -
[tex]\frac{10!}{(10-3)!3!}\\\\\frac{10!}{7!\times3!} \\\\\frac{10\times9\times8\times7!}{7!\times3\times2\times1}[/tex]
10 x 3 x 4 = 120
Hence, the total number of triangles that can be made are 120.
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please help me with vivid explanation
Answer:
864 m²
Step-by-step explanation:
First calculate the total area of the rectangular field
The area of a rectangle is given by the product of the length and the width
let A be the total area
A = 100*120
A = 12000 m²
Calculate the area of the small rectangles
Let A' be the total area of the four small rectangles and A" the area of one small rectangle A' = 4 A" A' = 4 [([tex]\frac{120-4}{2}[/tex])*([tex]\frac{100-4}{2}[/tex])] A' = 4*58*48A' = 11136 m² Substract the A' from A to get the area of the roadLet A"' be the area of the road
A"' =A-A'
A"' = 12000-11136
A"' = 864 m²
PLEASE HELP!!! I AM DESPERATE BECAUSE MY CLASS IS IN A FEW MINUTES. Solve using statement reason.
Answer:
Statement 1. P
Reason 1. Theorem: The measure of an external angle of a triangle is equal to the sum of the measures of the remote interior angles.
Statement 2. 132 = 3x + 54
Statement 3. x = 26
The polynomial 24x3 − 54x2 + 44x − 99 is factored by grouping.
24x3 − 54x2 + 44x − 99
24x3 + 44x − 54x2 − 99
4x(____) − 9(____)
What is the common factor that is missing from both sets of parentheses?The polynomial 24x^3 − 54x^2 + 44x − 99 is factored by grouping.
Answer:C
Step-by-step explanation:It’s C on edge
how to convert 3mm into cm
Answer:
0.3 cm
Step-by-step explanation:
1 cm = 10 mm
1) Using proportion:
1 cm ----- 10 mm
x cm ----- 3 mm
x = 1 cm * 3 mm/10 mm = 0.3 cm
2) 3 mm * 1cm/10mm = 0.3 cm
Answer:
3mm = 0.3 cm
Step-by-step explanation:
1 cm = 10 mm
3mm = 3/10 = 0.3cm
FIRST WILL GET BRAINLLEST Each group of students receives a bag that has 8 red cubes, 2 green cubes, and 10 blue cubes. If each group makes 100 pulls and replaces the cube after each pull, how many times would you expect them to draw a green cube?
Answer:
10
Step-by-step explanation:
We can do the ratio of 8:2:10. If we add it all up, we get 20. We do 100/20 and get 5, so each number equals 5. Then we do 2*5.
Sorry if this is wrong.
nth term of this sequence 1, 10, 19, 28
Answer:
The nth term of the sequence is
9n - 8Step-by-step explanation:
The sequence above is an arithmetic sequence
For an nth term in an arithmetic sequence
A(n) = a + ( n - 1)d
where a is the first term
n is the number of terms
d is the common difference
From the question
a = 1
d = 10 - 1 = 9 or 19 - 10 = 9 or 28 - 19 = 9
So the nth term of the sequence is
A(n) = 1 + (n - 1)9
= 1 + 9n - 9
= 9n - 8
A(n) = 9n - 8Hope this helps you
Which expression can be used to find the surface area of the following square pyramid?
Answer:
Step-by-step explanation:
The slant height of one side of this pyramid is 5, and the base of this side is 4. Thus, the area of one slant side is (1/2)(5)(4) = 10 units^2.
There are 4 such sides. Thus, the total slant surface area is 4(10 units^2), or 40 units^2.
If you also want to include the base area, the total would be
40 units^2 + 16 units^2 = 56 units^2.
Glven: F(x) = 2x - 1; G(X) = 3x + 2; H(x) = x2
Find F/G/H(2)
121
27
71
Answer:
3/32
Step-by-step explanation:
One approach to doing this probelm is to evaluate all three functions F, G and H at x = 2:
F(2) = 2(2) - 1 = 3
G(2) = 3(2) + 2 = 8
H(2) = (2)^2 = 4
3/8
Then (F/G)(2) = (3/8), and (F/G/H) = -------- = 3/32
4
Please Help Me Asap Will Give BRAINLIEST What are the solutions to the system of equations? {y = 1/4x^2 − 2 y = −1/2x} Graph the system of equations to solve. (0, 0) and (−4, 2) (2.9, 0) and (−2.9, 0) (−4, 2) and (2, −1) (0, 0) and (0, −2)
Answer:
{y = 1/4x^2 − 2 y = −1/2x}
(0,0)
(-6,3)
Step-by-step explanation:
Rewrite as system of equations
y=-1/2x
1/4x^2-2y=-1/2x
Move expression to left and change its sign
y+1/2=0
1/4x^2-2y+1/2x=0
Multiply both sides of equation by 2
2y+x=0
1/4x^2-2y+1/2x=0
Sum the equation vertically and eliminate variable (2y)
3/2x+1/4x^2=0
Solve the equation
x=0
x=-6
Substitute the value of x into equation
y+1/2*0 = 0
y+1/2*(-6) = 0
Solve equation for y
y=0
y=3
so the solution is
(x1,y1)=(0,0)
(x2,y2)=(-6,3)
Terry bought some gum and candy. The number of packages of chewing gum was one more than the number of mints. The number of mints was three times the number of candy bars. If gum was 6 cents a package, mints were 3 cents each, and candy bars were 10 cents each, how many of each did he get for 80 cents?
Answer:
2 Candy bars
6 Mints
7 Gum
Step-by-step explanation:
Candy bars=x
mints=3x
gum=3x+1
10(x)+3(3x)+6(3x+1)=80
10x+9x+18x+6=80
37x=80-6
37x=74
x=2
SO:
cand bars = x = 2
mints = 3x = 6
gum = 3x+1 = 7
Answer:
2 candy bars, 6 mints, and 7 packages of gumm
Step-by-step explanation:
HELP NOWWWWW Jeanne wrote the numbers 1-100 and placed them in a bag. If she selects a number without looking, what is the probability that the number is odd? Input your answer as a decimal or fraction.
Answer:
P(odd) = 0.5
Step-by-step explanation:
There are 50 odd numbers for whole numbers 1-100, namely
{1,3,5,....97,99}
Therefore the probability that a single chosen number is odd is
P(odd) = 50/100 = 1/2
1/2 is the probability that the number is odd.
What is probability?The probability is defined as the possibility of an event is equal to the ratio of the number of outcomes and the total number of outcomes.
Total number of possibilities = 100
We want to find Probability of selecting odd:
There are 50 odd numbers for whole numbers 1-100, namely
Favourable possibilities are:
{1,3,5,....97,99} (Total 5 possibilities).
Therefore Probability = 50/100 = 1/2 or 50%
P(odd) = 50/100 = 1/2
Hence, 1/2 is the probability that the number is odd.
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Debby pays rent twice a year, buys groceries once every quarter, and buys a transit pass
every month. How should her yearly expenses be represented?
1. O2 + 4y + 122
2. O 2x + 4y + 12z
3. OI +y + 122
4. O 2x + 3y + 12z
Work Shown:
x = amount of rent paid per half year
2x = amount of rent paid annually
y = amount spent on groceries per quarter
4y = amount spent on groceries annually
z = amount spent on a transit pass monthly
12z = amount spent on transit pass annually
2x+4y+12z = total amount of money spent annually
Answer:
2x+4y+12z
Step-by-step explanation:
I just did the test and got it right
Simplify each expression using the proper order of operations. please help thank you so much :)
[tex]\frac{41-3^2}{\sqrt{36}*3-26 }[/tex]= ?
12 +[tex]\sqrt[3]{8}[/tex] *(9-2)= ?
[tex]\frac{28-(7^2+3)}{-13+3*5}[/tex]= ?
[tex]\frac{28}{4}[/tex] -[tex]\sqrt[3]{8}[/tex]*2^3= ?
7^2 - 5* 8+1= ?
(2*[tex]\sqrt{16}[/tex]) -([tex]\sqrt[3]{27}[/tex]*[tex]\sqrt{81}[/tex] ) + 7= ?
Answer:
a) [tex]\boxed{-4}[/tex]
b) [tex]\boxed{26}[/tex]
c) [tex]\boxed{-12}[/tex]
d) [tex]\boxed{-9}[/tex]
e) [tex]\boxed{10}[/tex]
f) [tex]\boxed{-12}[/tex]
Step-by-step explanation:
1) [tex]\frac{41 - 3^2}{\sqrt{36}* 3-26 }[/tex]
=> [tex]\frac{41-9}{6*3-26}[/tex]
=> [tex]\frac{32}{18-26}[/tex]
=> [tex]\frac{32}{-8}[/tex]
=> -4
2) [tex]12+\sqrt[3]{8} * (9-2)[/tex] ∴ [tex]\sqrt[3]{8} = 2[/tex]
=> [tex]12+2*(7)[/tex]
=> 12 + 14
=> 26
3) [tex]\frac{28-(7^2+3)}{-13+3*5}[/tex]
=> [tex]\frac{28-(49+3)}{-13+15}[/tex]
=> [tex]\frac{28-52}{2}[/tex]
=> [tex]\frac{-24}{2}[/tex]
=> -12
4) [tex]\frac{28}{4} - \sqrt[3]{8} * 2^3[/tex]
=> 7 - 2 * 8
=> 7 - 16
=> -9
5) [tex]7^2-5*8+1[/tex]
=> 49 - 40 + 1
=> 9 + 1
=> 10
6) [tex](2 * \sqrt{16} ) - (\sqrt[3]{27} * \sqrt{81} ) + 7[/tex]
∴ [tex]\sqrt{16} = 4, \sqrt[3]{27} = 3 , \sqrt{81} = 9[/tex]
=> (2 * 4) - (3 * 9) + 7
=> 8 - 27 + 7
=> -19 + 7
=> -12
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
Apply order of operations to solve each expression.
[tex]\frac{41-9}{6 \times 3-26}[/tex]
[tex]\frac{41-9}{18-26}[/tex]
[tex]\frac{32}{-8}=-4[/tex]
[tex]12+2\times 7[/tex]
[tex]12+14=26[/tex]
[tex]\frac{28-(49+3)}{-13+15}[/tex]
[tex]\frac{28-52}{2}[/tex]
[tex]\frac{-24}{2} =-12[/tex]
[tex]7-2 \times 8[/tex]
[tex]7-16=-9[/tex]
[tex]49-40+1[/tex]
[tex]=10[/tex]
[tex](2 \times 4)-(3 \times 9) +7[/tex]
[tex]8-27+7[/tex]
[tex]=-12[/tex]
What is the value of this expression when g= -3.57
8- 12g-51
Answer:
-0.16
Step-by-step explanation:
Since it states g is equal to -3.57, we have to plug in -3.57 into the equation wherever it says g.
[tex]8-12(-3.57)-51[/tex]
We can multiply -12 and -3.57 to get 42.84.
[tex]8+42.84-51[/tex]
Now we can add 8 to 42.84 to get 50.84. Then, we subtract 51 from 50.84 to get our answer, -0.16!
Can Negative numbers turn into Scientific Notation?
Answer: Yes, negative numbers can be written in scientific notation
Examples:
-1200 = -1.2 * 10^3
-1,897,000 = -1.897 * 10^6
We simply can ignore the negative at first, then convert to scientific notation (as you normally would with any positive number). Afterward, don't forget to put the negative back in.
Please Help I will mark Brainliest or whatever Match each function formula with the corresponding transformation of the parent function y = (x - 1)∧2 1. y = ( x - 1) 2 - 3 Reflected over the y-axis 2. y = - ( x - 1) 2 Translated up by 1 unit 3. y = ( x + 3) 2 Reflected over the x-axis 4. y = ( x - 2) 2 Translated down by 3 units 5. y = ( x + 1) 2 Translated right by 1 unit 6. y = ( x - 1) 2 + 1 Translated left by 4 units
Answer:
1 -> D
2 -> C
3. -> F
4. -> E
5. -> A
6. -> B
Step-by-step explanation:
Match each function formula with the corresponding transformation of the parent function y = (x - 1)∧2
1. y = ( x - 1) 2 - 3 A. Reflected over the y-axis
2. y = - ( x - 1) 2 B. Translated up by 1 unit
3. y = ( x + 3) 2 C. Reflected over the x-axis
4. y = ( x - 2) 2 D. Translated down by 3 units
5. y = ( x + 1) 2 E. Translated right by 1 unit
6. y = ( x - 1) 2 + 1 F. Translated left by 4 units
Using the standard transformation rules
f(x) -> a*g(bx-h) + k, we can obtain the following results
Answers:
1 -> D
2 -> C
3. -> F
4. -> E
5. -> A
6. -> B
Consider the function f(x) = x^2 +2\sqrt{x}. Evaluate 2f(2) - f(8).
Answer:
-56 + 3 sqrt(2) /2
Step-by-step explanation:
f(x) = x^2 +2/sqrt{x}.
2f(2) - f(8).
First find f(2)
f(2) = 2^2 +2/sqrt{2} = 4 + 2/ sqrt(2)
Then f(8)
f(8) = 8^2 +2/sqrt{8} = 64 + 2 / sqrt(4)sqrt(2) = 64+ 2/2sqrt(2) = 64 + 1/ sqrt(2)
2f(2) - f(8).
2 * (4 + 2/ sqrt(2)) - (64 + 1/ sqrt(2))
8 + 4/ sqrt(2) - 64 - 1/ sqrt(2)
Combine like terms
-56 + 3 / sqrt(2)
Rationalizing the second term
-56 + 3/ sqrt(2) * sqrt(2)/sqrt(2)
-56 + 3 sqrt(2) /2