The factorization of the expression by grouping is [tex]P(x) = (x - 3)(x + 3)(x +4)[/tex]
The polynomial function is given as:
[tex]P(x) = x^3 + 4x^2 - 9x - 36[/tex]
Factorize the given expression.
[tex]P(x) = x^2(x + 4) - 9(x +4)[/tex]
Factor out x + 4
[tex]P(x) = (x^2 - 9)(x +4)[/tex]
Express 9 as the square of 3
[tex]P(x) = (x^2 - 3^2)(x +4)[/tex]
Apply the difference of two squares
[tex]P(x) = (x - 3)(x + 3)(x +4)[/tex]
Hence, the factorization of the expression by grouping is [tex]P(x) = (x - 3)(x + 3)(x +4)[/tex]
Read more about factorization at:
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An 8 ounce steak costs $12.80. How much would a 32 ounce steak cost?
Answer:
12.80 divided by 8 = 1.60
1.60 x 32 = 51.20
Step-by-step explanation:
Can you please help me with this question.
Answer:
I have helped you on the other question you asked. It's the same question.
pleeeeeeeeeeeease help :)
ty
Answer:
y = 3x + 16
Step-by-step explanation:
If it is parallel to y = 3x + 8, then it has the same slope of 3.
y = 3x + b. Substitute the x and y values into the equation to solve for b.
7 = 3(-3) + b
7 = -9 + b
16 = b
y = 3x + 16
2) A right isosceles triangle has legs that are each 10 mm. What is the length of its hypotenuse?
round to the nearest whole number
[tex](b) ^{2} + {(h)}^{2} = {(x)}^{2} \: \: \: ( by \: \: \: pythagoras \: \: \: theorem)\\ = > {(10)}^{2} + {(10)}^{2} = {(x)}^{2} \\ = > 100 + 100 = {x}^{2} \\ = > 200 = {x}^{2} \\ = > x = \sqrt{200} mm \\ = > x = \sqrt{2 \times 2 \times 2 \times 5 \times 5}mm \\ = > x = 2 \times 5 \sqrt{2} mm \\ = > x = 10 \sqrt{2} mm[/tex]
So, the length of the hypotenuse is 10√2 mm.Answer:
10√2 mm.
Hope you could get an idea from here.
Doubt clarification - use comment section.
In this diagram shown,
PQRS is a rectangle
Answer:
In the figure, PQRS is a rectangle. If the shaded area is 72 sq. cm,...In the figure, PQRS is a rectangle. If the shaded area is 72 sq. cm, find h
EXPLANATION
From the diagram, PQRS is a rectangle
Area of shaded part = 72sq.cm
But 72 = 3h - 4 + 6h - 4 + 4h
= 72 - 16h - 8
= 16h - 72 + 8
=16h = 80
h = 80/16
= 5cm
e. Find the slope of the line that passes through the points (1, 3) and (9,7),
Answer:
0.5
Step-by-step explanation:
→ Find the difference in y
7 - 3 = 4
→ Find the difference in x
9 - 1 = 8
→ Divide the results
4 ÷ 8 = 0.5
Answer:
The slope is 1/2 (m=1/2)
Step-by-step explanation:
Use the slope formula: [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] to solve for the slope. y2 is 7, y1 is 3, x2 is 1, x1 is 9. [tex]\frac{7-3}{9-1}=\frac{4}{8} = \frac{1}{2}[/tex]
Two identical squares of sides 17 cm overlap to form a rectangle as shown below. The shaded part is the overlapping region
To start with, we are told that the two shapes are squares. This means that they have the same length and breadth. From the diagram, we can see that one of the sides of the squares is 17 cm. This means that the squares are a square of 17cm in length.
If the original length is 17, and the overlapped length of the figure we have is 30 cm. Then we can say that since there exist 2 squares, 30/2 = 15 cm. If the overlapped length is 15 cm, this means that the part that is shaded is 2 cm in length.
Applying area of a rectangle formula
length * breadth = 17 * 2 = 24 cm²to learn more about area of shaded regions, see here https://brainly.com/question/10090807
answer???? i need help asap
Answer:
what kind?
Step-by-step explanation:
Answer:55
Step-by-step explanation:
55
A palm tree is 30 feet tall and casts a 48 foot shadow. The woman standing next to the palm tree casts a shadow similar to that of the palm tree. How tall is the woman if she casts an 8 foot shadow?
Answer:
48 feet foot I took the testttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt oh yeah yeah yeah
Step-by-step explanation:
64 divided by 1184 worked out
Answer: 18.5
Step-by-step explanation: 1184/64= 18.5
A skyscraper is 396 meters tall. At a certain time of day, it casts a shadow that is 332 meters long. At what angle is the sun above the horizon at that time?
Step-by-step explanation:
there is a right-angled triangle.
its legs (enclosing the 90° angle) are the height of the skyscraper (396 m) and the shadow (332 m).
so, we know the third side (the Hypotenuse, which is the line of sight between the end of the shadow and the top of the skyscraper) too by using Pythagoras :
c² = a² + b²
line² = 396² + 332² = 156816 + 110224 = 267040
line = sqrt(267040) = 516.7591315... m
and we know 1 angle : the 90° angle between the legs.
the other angles we can now get by using the law of the sines :
a/sin(A) = b/sin(B) = c/sin(C)
where the angles are opposite of the lines.
the line of sight is opposite of the 90° angle.
and the height of the skyscraper is opposite of the angle between the line of sight and the shadow. this angle is also the angle of the sun above the horizon, as the extended line of sight would lead directly to the sun.
so, we have
516.7591315.../sin(90) = 396/sin(angle)
as sin(90) = 1
516.7591315... = 396/sin(angle)
sin(angle) = 396 / 516.7591315... = 0.76631447...
angle = 50.02407526...°
There are 222 red marbles in a box. Amit takes out 6 red marbles and replaces them with 12 blue
marbles. He continues doing this till all the red marbles are replaced with blue marbles.
Which of the following expressions gives the total number of blue marbles he put in the box?
A (222 + 6) = 12 B (222 - 6) + 12 C (222 - 6) + 12 D (222 + 6) x 12
Answer:
(222 - 6) + 12
Step-by-step explanation:
You put B and C as the same thing but the correct option is this because first you take away 6 (subtract 6) from the 222 marbles then you replace them with 12 (add 12).
Find the gradient of the line segment between the points (-3,1) and (2,5). Give your answer in its simplest form.
Answer:
[tex]\displaystyle m = \frac{4}{5}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinate Planes
Coordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Step-by-step explanation:
Step 1: Define
Identify points.
Point (-3, 1)
Point (2, 5)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m.
Substitute in points [Slope Formula]: [tex]\displaystyle m = \frac{5 - 1}{2 - -3}[/tex][Order of Operations] Evaluate: [tex]\displaystyle m = \frac{4}{5}[/tex]Can someone please tell me the answer
(20 points)
Answer:
the aswer is B
Step-by-step explanation:
Mario started his homework at 3:30 he finished 25 minutes later what time did he finish his homework
Answer:3.55
Step-by-step explanation:
you add the time dude
Point Q is plotted on the coordinate grid. Point P is at (20, −30). Point R is vertically above point Q. It is at the same distance from point Q as point P is from point Q. Which of these shows the coordinates of point R and its distance from point Q?
Point R is at (−40, 30), a distance of 60 units from point Q
Point R is at (−40, −10), a distance of 20 units from point Q
Point R is at (−40, −30), a distance of 60 units from point Q
Point R is at (−40, 10), a distance of 20 units from point Q
Answer:
Point R is at (−40, −30), a distance of 60 units from point Q
Step-by-step explanation:
Correct option is ,
Point R is at (-40, 30) , a distance of 60 units from Point Q.
hope this answer helps you dear take care!
Line ST and point V are shown on the graph. On a coordinate plane, line S T goes through (negative 5, 0) and (5, 2). Point V is at (0, negative 2). Line VW is to be drawn on the graph such that it is perpendicular to line ST. If the coordinates of point W are (â’1, y), what is the value of y? â’7 â’5 2 3.
The value of y in the coordinates of point W is 3
The points are given as:
[tex]S = (-5,0)[/tex]
[tex]T = (5,2)[/tex]
[tex]V = (0,-2)[/tex]
[tex]W = (-1,y)[/tex]
Start by calculating the slope of line ST
[tex]m=\frac{y_2 - y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m=\frac{2- 0}{5--5}[/tex]
[tex]m=\frac{2}{10}[/tex]
[tex]m=\frac{1}{5}[/tex]
Next, calculate the slope of line VW
[tex]m=\frac{y_2 - y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{y --2}{-1-0}[/tex]
[tex]m = \frac{y +2}{-1}[/tex]
[tex]m = -y -2[/tex]
Since both lines are perpendicular, then the product of the slopes is -1.
So, we have:
[tex]\frac 15 \times (-y -2) = -1[/tex]
Divide both sides by -5
[tex]y +2 = 5[/tex]
Subtract 2 from both sides
[tex]y = 3[/tex]
Hence, the value of y in the coordinates of point W is 3
Read more about line coordinates at:
https://brainly.com/question/2037439
Answer:
W=3
Step-by-step explanation:
Find the total surface area of this triangular prism
25 cm
24 cm
10 cm
14 cm
Answer:
Area = (Length * (a + a * (sin(Angle γ) / sin(Angle γ + Angle β)) + a * (sin(Angle β) / sin(Angle γ+Angle β)))) + a * ((a * sin(Angle γ)) / sin(Angle γ + Angle β)) * sin(Angle β)
A t-shirt shop bought a total of 24 t-shirts (t) and hats (h) combined. They bought t-shirts for $12.50 each and hats for $8 each. The store spent a total of $259.50, which system of equations could be used to find the number of hats and t-shirts bought?
Answer:
12.5t + 8h = 259.5
t + h = 24
Step-by-step explanation:
Write one equation to deal with the costs and one equation to deal with the numbers of shirts and hats.
12.5t + 8h = 259.5
t + h = 24
DON'T SEND A LINK AND JUST ANSWER IT PLZ
Answer:
height = 10 , area = 240 units²
Step-by-step explanation:
The diagonal splits the rectangle into 2 right triangles.
Using Pythagoras' identity in the right triangle formed
with hypotenuse h = 26 and legs 24 and height x , then
x² = 26² - 24² = 676 - 576 = 100 ( take square root of both sides )
x = [tex]\sqrt{100}[/tex] = 10
Height = 10 units
area of rectangle = 24 × 10 = 240 units²
What was the percent decrease? 2% 14% 16% 7%
Answer:
Percentage decrease calculator will show the difference and the percent decrease from one quantity to another.
Step-by-step explanation:
Factor
y=x² + 4x + 3
Answer:
[tex]y=(x+3)(x+1)[/tex]
Step-by-step explanation:
[tex]y=x^2+4x+3[/tex] <-- Given
[tex]y=x^2+x+3x+3[/tex] <-- Expand middle term
[tex]y=x(x+1)+3(x+1)[/tex] <-- Factor into two parts
[tex]y=(x+3)(x+1)[/tex] <-- Combine like terms
Write the equation from the table below.
x y
0 -5
1 -2
2 1
3 4
4 7
Answer:
hope this helped
Step-by-step explanation:
y = mx + b
b, the y-intercept, = 3 because when x is 0, y is 3
find m, slope:
(0,3) (2,2)
2 - 3/2 - 0
-1/2
-0.5 or -/2
y = -1/2x + 3
or
y = -0.5x + 3
9. Place the following numbers in descending order: 92, -2.02 , 81%, 1 12
309,303,297 find the 33rd term
Answer:
111
Step-by-step explanation:
multiply 33 by 6 because 6 is being subtracted every time and then subtract 198 from 309
Answer:
117
Step-by-step explanation:
Hope this helps!
Solve the inequality T > l+d/B for D
Answer:
Second option = TB - L > D
Step-by-step explanation:
[Given] T > [tex]\frac{L +D}{B}[/tex]
[Multiply both sides by B] TB > L + D
[Subtract L from both sides] TB - L > D
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
FOR BRAINLIEST
А is equivalent to 0.001 grams.
milligram
kilogram
decigram
Answer:
one milligram
Step-by-step explanation:
Answer:
milligram
Step-by-step explanation:
1,000 mg = 1 g
1 mg = .001 g
Write an equation of the line that passes through the point (3,-5) and has the slope of 2
Answer:
Y-Y1=M(x-x1)
that's the formula then fixing in your values we have
y + 5 =2(x-3)
y+5 =2x-6
Crossing over we have
y-2x=-6-5
equation of the line equals
y-2x-11 =0
Suppose TD=SG and what additional information is needed to prove the two triangles congruent SAS
a)
PLEASE HELP
Answer:c
Step-by-step explanation:
Answer:
If TD = SG and MD = SL, then angle D would have to equal angle S in order to prove the triangles congruent by SAS.
Step-by-step explanation: C
what is parallelogram?
Answer:
A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. Also, the interior angles on the same side of the transversal are supplementary. Sum of all the interior angles equals 360 degrees.
Step-by-step explanation: