Answer:
(x - 4)(2x + 3)
Step-by-step explanation:
Given
2x² - 5x - 12
Consider the factors of the product of the coefficient of the x² term and the constant which sum to give the coefficient of the x- term.
product = 2 × - 12 = - 24 and sum = - 5
The factors are - 8 and + 3
Use these factors to split the x- term
2x² - 8x + 3x - 12 ( factor the first/second and third/fourth terms )
= 2x(x - 4) + 3(x - 4) ← factor out (x - 4) from each term
= (x - 4)(2x + 3) ← in factored form
The factors are (x - 4) and (2x + 3)
A semicircle is drawn onto one of the shorter sides of a rectangle. The shorter side of the rectangle measures 4 centimeters. The area of the figure is 41.4 square centimeters.
What is the length of the longer side of the rectangle?
Use 3.14 for π.
Enter your answer as decimal in the box.
We are given that :
A semicircle is drawn onto the shorter side of rectangle.Shorter side of rectangle measures 4cm. i.e; the diameter of the circle is 4cmArea of the figure is 41.4 cm²Using Formulas:
Area of rectangle:
[tex] \quad\hookrightarrow\quad{\pmb{ \mathfrak {length\times breadth }}}[/tex]
Area of semicircle:
[tex] \quad\hookrightarrow\quad{\pmb{ \mathfrak{ \dfrac{\pi r^2 }{2}}}}[/tex]
We have to find the length of longer side of rectangle!Here, we can know that the figure is composed of one rectangle and one semicircle. Therefore by combining the areas of rectangle and circle and taking the length of rectangle as a variable , we will finds its value ;
[tex] \quad\dashrightarrow\quad \sf {Area_{\tiny { total}} = Area_{\tiny {rectangle}}+ Area_{\tiny {semicircle}}}[/tex]
[tex] \quad\dashrightarrow\quad \sf {A = ( l \times b ) + \dfrac{\pi r^2 }{2} }[/tex]
[tex] \quad\dashrightarrow\quad \sf {41.4 = ( l \times 4 ) +\dfrac{3.14\times 2^2}{2} }[/tex]
[tex] \quad\dashrightarrow\quad \sf { 41.4= ( l \times 4 )+ \dfrac{ 3.14\times 4}{2}}[/tex]
[tex] \quad\dashrightarrow\quad \sf { 41.4=( l \times 4 )+ \dfrac{12.56}{2}}[/tex]
[tex] \quad\dashrightarrow\quad \sf { 41.4= (l \times 4 )+ 6.28}[/tex]
[tex] \quad\dashrightarrow\quad \sf {l \times 4 = 41.4-6.28 }[/tex]
[tex] \quad\dashrightarrow\quad \sf { l\times 4 = 35.12}[/tex]
[tex] \quad\dashrightarrow\quad \sf { l =\dfrac{35.12}{4}}[/tex]
[tex] \quad\dashrightarrow\quad \underline{\underline{\pmb{\sf {l = 8.78\:cm}}} }[/tex]
The length of the longer side of the rectangle will be 8.78 cm.
What is the area?The area of a two - dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.
On one of a rectangle's shorter sides, a semicircle is drawn. The rectangle's shorter side is 4 cm long. The figure has a surface area of 41.4 square centimeters.
Then the length of the rectangle is calculated as,
A = πr² / 2 + l × b
41.4 = (3.14 / 2) × (4/2)² + 4l
41.4 = 6.28 + 4
l = 8.78 cm
The length of the longer side of the rectangle will be 8.78 cm.
More about the area link is given below.
https://brainly.com/question/27683633
#SPJ3
4. If the area of a rectangle is 6 m2, then the dimensions must be 2 meters by 3 meters. oh
Answer:
False.
Step-by-step explanation:
The formula that is used to find the area of a rectangle is given by :
A = l×b
Where,
l is length and b is breadth
If area of a rectangle is 6m², it means we need to find the factors of 6. The factors of 6 are 2 and 3. If we multiply 2 and 3, we get 6.
Other possibility can be 1 m by 6 m because if we muliply 1 m and 6 m, we get 6m².
It means there are more than one possibiliy about the length and breadth of the rectangle.
Hence, the given statement is not true.
The table shows the height y (in thousands of feet) of an unmanned aerial vehicle (UAV) x minutes after it begins its descent from cruising altitude.
Write a linear function that relates y to x . Interpret the slope and y-intercept. y = ___
The slope indicates that the height ___ feet per minute. The y-intercept indicates that the descent ____ at a cruising altitude of ___ feet.
1)
[tex]m = \frac{y - y}{x - x} = \frac{55 - 59}{10 - 0} = \frac{ - 4}{10} = - \frac{2}{5} [/tex]
[tex]y = - \frac{2}{5} x + b[/tex]
Since the line passes through the point (0,59), the coordinates of this point satisfies the equation of y;
[tex]59 = - \frac{2}{5} (0) + b[/tex]
[tex]b = 59[/tex]
Final answer:
[tex]y = - \frac{2}{5} x + 59[/tex]
can someone help me do this??? Thank youuuu!!!!
Answer:
See below.
Step-by-step explanation:
a) Complementary angles (= 90°)
∠DCM and ∠DMC∠FGM and ∠GMFb) ∠FMG, ∠GMC, and ∠DMC
#1 -8=3y-2
#2 5(x+3) = 25
Answer:
-2
Step-by-step explanation:
-8 + 2 = -6; -6=3y; then -6 divided by 3 = -2
What is (184730248764874252034*9748242241036484916485)\(9489258234569786578024628435672046*72386438952467922592641964870)+(892187341935496495*2873937610)+(903781)?
i cant tell if thats a real question or not but ahhhhh thats a big number
Who ever is reading this:
I love u.
U matter.
The world needs u
hang in there ik it may be bad but u deserve the world <3
ur beautiful for who u r, not wht u look like. no matter ur shape, size, color, gender.. anything
don't give up bby i need u to live.
i wish i could take everyones problems so yall wouldn't have to have em but i cant so just know ily and if anyone needs to talk u can talk to me
Pls pass this on. Everyone deserves to know this. ♥️♥️
just copy and paste its not hard pls this could save someones life
Answer:
it 40 super easy
Step-by-step explanation:
Simplify by comibining like terms for x + 10y - 4y + 4x
Answer:
5x + 6y
Hope it helps!
what fraction is equal to 1.5?
Answer:3/2
Step-by-step explanation:
given g(x)=5x+4, solve for x when g(x)=9
Answer:
The value of x is equal to 1, written as x = 1.
General Formulas and Concepts:
Algebra I
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityTerms/Coefficients
Functions
Function NotationStep-by-step explanation:
Step 1: Define
g(x) = 5x + 4
g(x) = 9
Step 2: Solve for x
Substitute in function value: 9 = 5x + 4[Subtraction Property of Equality] Subtract 4 on both sides: 5 = 5x[Division Property of Equality] Divide 5 on both sides: 1 = xRewrite: x = 1∴ when the function g(x) equals 9, the value of x that makes the function true would be x = 1.
---
Topic: Algebra I
The hipotenuse of a right angle, isosceles triangle is 5√2 cm. Find the area of the triangle.
Answer: 12.5 square centimeters
Step-by-step explanation:
what's the answer to: |x+6|+10=13
x=_ or x=_
Answer:
X= -3 or X=-9
Step-by-step explanation:
Answer: x = -3, x = -9
Step-by-step explanation: |x + 6| + 10 = 13
Firstly, subtract 10 from both sides:
|x + 6| = 3
Since it is an absolute value, separate it into two equations with either outcome:
x + 6 = 3
x + 6 = -3
Solve for x now.
x + 6 = 3
Subtract 6 from both sides:
x = -3
x + 6 = -3
Subtract 6 from both sides:
x = -9
Voila! Hope this helps.
Ms. Waters, the manager of Paradise Lake, just ordered a duck and goose food dispenser. She plans to use a paper cone to hold the pellets. The machine is set to dispense no more than 350 cm3 of food for each token. The cones are 12 cm. in diameter. How tall must the cone be to hold the food
Step-by-step explanation:
Equation for the volume of a cone is
V = (pi(r^2)h)/2
Plug in the known values to get
350 = (pi(6^2)h)/2
To find h, just isolate it by first dividing both sides by 2 and squaring 6 to get
175 = pi(36)h
Then, divide both sides by pi36 to get
h = 175/pi(36)
While reviewing last month's finances, Oscar noticed that he had spent $200 on a wedding cake and deposited $500 that he had earned from selling books to a used bookstore. Then, he again spent $127 to buy some new books. Which integer represents the change in Oscar's savings?
Answer:
$173
Step-by-step explanation:
Given the following :
Amount spent on wedding cake = $200
Amount deposited = $500
Amount spent on new books = $127
Change in savings :
Amount deposited - total amount spent
Total amount spent = ($200 + $127).= $327
Hence,
Change in saving = $500 - $327
= $173
Can you solve this inequality: 5 > -x - 7
Answer:
-12 < x
or:
x > -12
Step-by-step explanation:
[tex]5 > -x-7[/tex]
[tex]5+7 > -x[/tex]
[tex]12 > -x[/tex]
[tex]12(-1) > -x(-1)[/tex]
[tex]-12 < x[/tex]
Hope this helps
х
у
-11
-3
-1
-3
0
9
un lwin
13
21
Which function best represents the relationship shown in the graph? 8.51
А
1
y -x + 1
B
y = 4x - 1
C y = x + 4
Dy = 4x + 1
Complete the two-column proof using the figure below.
Given:∠1 ≅ ∠2, l ⊥ n
Prove:l ⊥ p
*IGNORE THE BLANKS FILLED IN I NEED THE ANSWER FOR THOSE OR FOR SOMEONE TO TELL ME IM RIGHT*
Answer:
Step-by-step explanation:
Converse of alternate interior angles theorem:
This theorem states that if two lines are intersected by a transversal and the alternate interior angles are congruent, lines will be parallel.
Therefore, p║n.
Perpendicular transversal theorem:
By this theorem,
In a plane, if a line is perpendicular to one of two parallel lines, then it will be perpendicular to the other line.
Therefore, l ⊥ p.
Options selected in the blank spaces are correct.
2) () = 2 + 4 − 40 is the total daily cost to produce for x bracelets. The bracelets sell for $8 each. (I kept the numbers in the problem small to make the math easier) a) Create a revenue function b) Create a profit function c) Determine the number of bracelets the company should produce and sell to maximize profit. d) What is the maximum profit?
Answer:
The answer is below
Step-by-step explanation:
Given the cost as C(x) = x² + 4x - 40
a) Since the bracelets sell for $8 each, the revenue from x bracelets is given as:
Revenue = price for each bracelet × number of bracelet
Revenue = 8 × x = 8x
b) Profit (P) = Revenue - Cost
P(x) = 8x - [x² + 4x - 40]
P(x) = 8x - x² - 4x + 40
P(x) = -x² + 4x + 40
c) To maximize profit, the derivative of profit is equal to 0
Hence P'(x) = 0
-2x + 4 =0
2x = 4
x = 2
To maximize profit, the company should produce 2 bracelets
d) The maximum profit is:
P(2) = -(2²) + 4(2) + 40 = -4 + 8 + 40
P(2) = $44
The maximum profit is $44
14. The referee at a college football game is standing 12 yards behind the ball. The
back judge is standing 22 yards in front of the ball. The field judge is standing
exactly halfway between them. Using coordinates to model the situation, find
how far in front of the ball the field judge is. Explain.
Using coordinates, the field judge is exactly 5 yards in front of the ball.
What are coordinates?These are values that show the position of an object, these values often include a number for the x-axis (horizontal axis) and one for the y-axis (vertical axis).
What are the positions of the referee, the back judge, and the field judge?If we consider the ball as 0 or the starting point the coordinates are:
Referee (12, 0)Back judge (-22,0)Field judge y-axis = 0 because all of them are at the ground levelx- axis = 12 + 22 = 34/2 = 17x- axis =-22+17= -5=x-axis= -5 or 5 yards in front of the ball.Learn more about coordinates in: https://brainly.com/question/13140132
Find the sum of the measures of the interior
angles of a convex 70-gon.
The average number of customers that visited a particular store during the past year is 200 per day and a standard deviation of 25 customers per day. The probability that x>200 is:
Answer:
0.5
Step-by-step explanation:
Considering we are given a mean and standard deviation, the distribution of the data is likely to be a normal or Gaussian distribution, i.e. a symmetrical, bell-shaped distribution of probability density, peaked at the mean;
Such a distribution has 0.5 probability each side of the mean;
So, if the mean is 200 then, the probability that the number of customers is greater than 200 (x > 200), according to this mean, is 0.5;
As a normal distribution is symmetrical, this is also the probability of a number of customers less than 200.
Molly pracices her multiplication tables every 3 days, her division facts every 5 days, and fractions every 6 days. If she practiced all three skills today, in how many days will she practice all three skills again?
Answer: 30 days.
Step-by-step explanation: Figure out the least common multiple for each number.
Question:
The variables x and y are directly proportional, and y = 4 whenx = 3. What is the value of y whenx = 15?
A shipping box should weigh 2.0 pound. If there is a 5% error on the weight, what is the range of acceptable weight? Question 2 options: 0.1 pound to 0.9 pound 1.1 pounds to 2.2 pounds 1.9 pounds to 2.1 pounds 2.0 pounds to 2.1 pounds
Answer:
2
lb
,
0.05
a
,
2
,
0.1
lb
,
0.99
lb
2
,
4.18
lb
2
,
4.2
lb
2
,
2.1
lb
Step-by-step explanation:
The formula below relates distance, rates, and time.
d = rt
Solve this formula for t
d = rt
d/r rt/r
d/r = t
1/5 plus 3/10 in the most simple form
Hey there!
1/5 + 3/10
= 2/10 + 3/10
= 2 + 3/10 - 0
= 5/10
= 5 ÷ 5 / 10 ÷ 5
= 1 / 2
Therefore, your answer is: 1/2
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
And orange contains 100 mg of vitamin C. It is recommended for a person to eat up to 2000 mg of vitamin C in a day. If you eat seven or just throughout the day what percent of your daily intake of vitamin C did you eat. Round to the nearest whole percent
A. 17%
B.35%
C.49%
D.5%
Answer:
[tex]\sf 35 \%[/tex]
explanation:
[tex]\hookrightarrow \sf \dfrac{orange \ juice \ intake}{recommended \ mg} * 100[/tex]
[tex]\hookrightarrow \sf \dfrac{7*100}{2000} *100[/tex]
[tex]\hookrightarrow \sf 35 \%[/tex]
Answer:
B.35%Step-by-step explanation:
100x7=700
So you ate 700mg of Vitamin C by eating oranges 7 times in that day.
Now, lets figure out the percent part
700 n/100x2000
=35%
We didn't even have to round.
So hence, your answer is B.35%
Thanks!
Mark me brainliest!
Can someone help me with this please 1/4(5x+16/3)-2/4(3/4x+1/2)=-5.
Please help (explain it)
Answer:
The y-intercept is 2 because it is on the y-axis. The y-intercept is located on the y-axis.
Write the equation of the line that passes through (2, 0) and (0, 3).
Answer:
Y= -1.5x+3
Step-by-step explanation:
(Y-Y1)=m(x-x1)
0-3=m(2-0)
m= -1.5
Y= -1.5x+B
when y=3 and x=0 b=3
a toy manufacturer estimates that 16% of its products are defective. if it produces 550 toys in one day, how many will be defective?
Answer:
88 toys
Step-by-step explanation:
If 16 percent of them are defective we want to multiply 550 by .16. This gets you 88.