Using the Factor Theorem, the quadratic equation is given by:
[tex]f(x) = 6(x^2 + 10x + 24)[/tex]
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
In this problem, we have a quadratic function, meaning that it has two roots, and it passes through (-6,0) and (-4,0), hence the roots are [tex]x_1 = -4, x_2 = -6[/tex], thus:
[tex]f(x) = a(x + 4)(x + 6)[/tex]
[tex]f(x) = a(x^2 + 10x + 24)[/tex]
Considering that it passes through (-3, -18), we can find a, hence:
[tex]18 = a[(-3)^2 + 10(-3) + 24][/tex]
[tex]3a = 18[/tex]
[tex]a = 6[/tex]
Hence the equation is:
[tex]f(x) = 6(x^2 + 10x + 24)[/tex]
More can be learned about the Factor Theorem at https://brainly.com/question/24380382
Please help solve
[tex]\left \{ {{y=-2x+6} \atop {y= x-3}} \right.[/tex]
[tex]\left \{ {{y=5x-4} \atop {y=4x+12}} \right.[/tex]
[tex]\left \{ {{y=\frac{2}{3}x-4 } \atop {y=-\frac{4}{3}+9 }} \right.[/tex]
[tex]\left \{ {{4y+7x=6} \atop {4y+7x =-5}} \right.[/tex]
[tex]\left \{ {{y=0.24x} \atop {y=20.18x+0.9} \right.[/tex]
[tex]\left \{ {{y=4.5x+15} \atop {y=5x+1.25}} \right.[/tex]
[tex]\left \{ {{y=3x} \atop {x+y=52} \right.[/tex]
help me with this please (2)
Answer:
Step-by-step explanation:
surface are of triangular prism =(a+b+c)h+bh
=(5+5+4)11+4*6
=14*11+24
=154+24
=178 yd^2
out of the total 225 students surveyed, what is the probability that a randomly selected student who is enrolled in spanish will also be taking math?
Answer:
5 ÷ 5 = 1
125 5 25
Step-by-step explanation:
The number between the two it's the number of people who does both
what is 713.49 written as a standard form
What is the greatest common factor of 20, 12, and 36?
Answer:
The answer is 4
Step-by-step explanation:
Use Pythagorean theorem to solve the following right triangles, put your answer in simplest radical form:
Answer:
x = 10
Step-by-step explanation:
[tex]x^2 = 8^2 + 6^2\\x^2 = 64 + 36 = 100\\x = \sqrt{100} = 10[/tex]
On a set of blueprints for a new home, the contractor has established a scale that states ½ inch = 10 feet.
If the den has dimensions of 0.6 inch by 0.75 inch on the blueprints, what will be the dimensions of the actual den after the house is built?
*For this answer PLEASE answer with the number of feet by the number of feet
*Example: 16 feet by 20 feet OR 16 ft by 20 ft. You can use a decimal if it terminates
Answer:
12 ft by 15 ft
Step-by-step explanation:
set up a proportion of inches over feet equals inches over feet:
.5/10 = .6/x
cross-multiply to get:
.5x = 6
x = 12
.5/10 = .75/y
cross-multiply to get:
.5y = 7.5
y = 15
please answer In(5x-3)=4
Answer:
[tex]\huge\boxed{Answer\hookleftarrow}[/tex]
[tex](5x - 3) = 4 \\ 5x - 3 = 4 \\ 5x = 4 + 3 \\ 5x = 7 \\ x = \frac{7}{5} \\ x = 1.4[/tex]
⎆ The answer will be, x = 7/5 (in fraction form) & x = 1.4 (in standard form).# ꧁❣ RainbowSalt2²2² ࿐
need help again pls and ty
Answer:
22 square units
Step-by-step explanation:
Area of a triangle formula:
A = 0.5bh
Given:
b = 11
h = 4
Work:
A = 0.5bh
A = 0.5(11)(4)
A = 5.5(4)
A = 22
S = {x | x is a multiple of 4 and 9 ≤ x < 37}
Which set is equivalent to S?
A) {8, 12, 16, 20, ...}
B) {8, 12, 16, ..., 36}
C) {9, 12, 16, ..., 37}
D) {12, 16, 20, 24, ...}
E) {12, 16, 20, ..., 36}
PLEASE HELP RNNNN
Answer: the answer is either e or d but I guessed d
Step-by-step explanation:
The equivalent set to set S will be {12, 16, 20, ..., 36} thus, option (E) is correct.
What is a set?A set is a collection of distinct values where each variable's meaning must be the same.
For instance, the set of natural numbers 1, 2, 3, 4, 5, and 6 is made up of variables that each represent a different natural number.
As per the given,
x is the multiple of 4,
4,8,12..
But is it restricted in the domain as, 9 ≤ x < 37
Thus, {12, 16, 20, ..., 36} will be correct.
Hence "The equivalent set to set S will be {12, 16, 20, ..., 36}".
To learn more about the sets,
brainly.com/question/8053622
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if you put $300 into a savings account and the bank account has a 4% annual compound interest-rate, find how much money will be in your savings account after 10 years if you don’t take any money out or put any more in.
32 7/12 ÷3 3/10 but an estimate
Answer:
20.740
Step-by-step explanation:
This is right.
Help me find the mean mode range median
Answer:
Mean=2.53
median=2
mode=2
range=3
Step-by-step explanation:
1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4
MEAN
Add up all data values to get the sum
Count the number of values in your data set
Divide the sum by the count
38/15=2.53
MEDIAN
Arrange data values from lowest to the highest value
The median is the data value in the middle of the set
If there are 2 data values in the middle the median is the mean of those 2 values.
MODE
Mode is the value or values in the data set that occur most frequently.
RANGE
18-15=3
Find the surface area of the pyramid. The faces of the triangular pyramid are equilateral triangles 34.6 mm 40 mm 40 mm The surface area is?
Answer:
would you still like me to help you with this problem?
find the value of x help ASAP
3x - 6 = 90
3x - 6 + 6 90 + 6
3x = 96
3x ÷ 3 = 96 ÷ 3
x = 32
Kai cuts out all the page numbers of a b\ook. He takes each number and cuts the numbers into separate digits (single digit numbers are already separate). Given that the book has 999 pages numbered 1 through 999, how many separate digits does Kai have when he is finished
Answer:
2,889 digits
Step-by-step explanation:
Total pages of the book = 999 pages
Page 1 - 9 cut separately = 9 digits
Page 10 - 99 = 90 pages
Total digits = 2(90)
= 180 digits cut separately
Page 100 - 999 = 900 pages
Total digits = 3(900)
= 2,700 digits cut separately
how many separate digits does Kai have when he is finished
Total separate digits Kai have when he is finished = 9 digits + 180 digits + 2700 digits
= 2,889 digits
Total separate digits Kai have when he is finished = 2,889 digits
Which coordinate grid shows M plotted at (4,3)
Answer:
B
Step-by-step explanation:
4,3 is x 4 y 3
Answer:
B
Step-by-step explanation:
graphs are put like this (x,y) your coordinate is (4,3) 4 is the x-axis meaning go right 4 times, 3 is your y so go up 3 times
can someone tell me if i'm correct or not
you are correct
Step-by-step explanation:
mark me as a brainlist
Which trigonometric function(s) have a value of sqrt 3 / 2 ?
a sin pi/3
b sin 5pi / 6
c cos 5pi / 3
d cons pi / 6
Answer:
sin (π/3)= √3/2
cos (π/6) =√3/2
Five and one half of 2 and one third is what number?
Given:
Five and one half of 2 and one third.
To find:
The number for the given statement.
Solution:
Five and one half = [tex]5\dfrac{1}{2}[/tex]
2 and one third = [tex]2\dfrac{1}{3}[/tex]
The given statement is five and one half of 2 and one third.
Here, the word "of" is used for multiplication.
So, the expression for the given statement is:
[tex]5\dfrac{1}{2}\times 2\dfrac{1}{3}[/tex]
[tex]=\dfrac{10+1}{2}\times \dfrac{6+1}{3}[/tex]
[tex]=\dfrac{11}{2}\times \dfrac{7}{3}[/tex]
[tex]=\dfrac{77}{6}[/tex]
Therefore, the required number is [tex]\dfrac{77}{6}[/tex].
12) Two hexagonal pyramids are similar. The perimeters of the pyramids are 36 inches and 30
inches. If the volume of the larger pyramid is 64873 in what is the volume of the smaller
pyramid?
Please help me:)
Answer:
54061 in³
Step-by-step explanation:
Using proportion
Perimeter of smaller pyramid/ Perimeter of Larger pyramid = volume of smaller pyramid/ volume of Larger pyramid
30/36 = x/64873
Cross Mulitiply
36 × x = 64873 × 30
x = 64873 × 30/36
x = 54060.833333 in³
Approximately = 54061 in³
Therefore, the volume of the smaller pyramid is 54061 in³
What is 6.27 in expanded form?
Answer:
6+0.2+0.07
hope this helps
have a good day :)
Step-by-step explanation:
the price of a photography machine in RS60000.find the price after inculding13%tax
Answer:
Rs. 67800
Step-by-step explanation:
Price of photograph = 60000 = 100%
Tax = x dollars = 13% of 60000
100% + 13% = 113% = 1.13
Multiply
1.13(60000) = 67800
To check, lets find 13% of 60000 and add to 60000
13% = 0.13
0.13(60000) = 7800
60000 + 7800 = 67800
Units = Rs
Rs. 67800
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
if anyone could just look at my recent question pls its super easy its just simplyfing
Answer: K
Step-by-step explanation:
Ill do it
HELP! ILL MARK YOU BRAINLY OR WHATEVER ITS CALLED
Answer:
For #7, the answer is 30.3 yd
For #8, the answer is 32.34 in
For #9, the answer is 56.26 ft
Explanation: The formula for an area of a parallelogram is ( A=bh)
Hope that helped!!
Round 122.1587 to the nearest hundredth?
Answer:
100
Step-by-step explanation:
H T U
1 2 2
2 is a num below 5 therefore
2=0
what is the measure of this angle? god bless help pls
Answer:
The angle SQR is half the intercepted arc SR which is 43°
solve the equation x - 4 = -3 help yall-
Answer:
x = 1
Step-by-step explanation:
x - 4 = -3
(add 4 to both sides)
x - 4 + 4 = -3 + 4
x = 1
Answer:
x = 1
Step-by-step explanation:
So you have to separate the x from the rest of the equation
so you can add 4 to both sides so x is by itself
so ur left with:
x = -3 + 4
and that is equal to x = 1
Hope that helps :)
PLEASE HELP! I'M GIVING 100 POINTS!
The depth of the deepest part of a body of water is 25,344 inches. Express this depth in scientific notation using an appropriate unit from the given list. What is the most appropriate unit for expressing the depth? What is the depth?
1 centimeter
10 millimeters
1 meter
100 centimeters
1 inch
2.54 centimeters
Select the correct choice below. If necessary, fill in the answer box to complete your choice.
(Use scientific notation. Use the multiplication symbol in the math palette as needed.)
A.
The most appropriate unit is the meter. The depth is
nothing meters.
B.
The most appropriate unit is the millimeter. The depth is
nothing millimeters.
C.
The most appropriate unit is the centimeter. The depth is
nothing centimeters.
D.
The most appropriate unit is the inch. The depth in inches is given.
Answer:
meter probably
Step-by-step explanation:
Reflect the vector (-3,5) across
the line y=x.
Answer:
(5, - 3 )
Step-by-step explanation:
Under a refection in the line y = x
a point x, y ) → (y, x ), then
(- 3, 5 ) → (5, - 3 )
The reflection vector is (5, -3) after reflecting over line y = x the answer is (5, -3).
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
We have:
The vector is (-3, 5)
The reflection line is y = x
The transformation rule:
(x, y) → (y, x)
(-3, 5) → (5, -3)
Thus, the reflection vector is (5, -3) after reflecting over line y = x the answer is (5, -3).
Learn more about the geometric transformation here:
brainly.com/question/16156895
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