Consider this expression. -3x2−24x−36 What expression is equivalent to the given expression?
The expression equivalent to the expression -3x²-24x-36 is -3(x+6)(x+2)
What is an expression?An expression in maths, a statement involving at least two different numbers (known or unknown) and at least one operation.
Given an expression, -3x²-24x-36;
Factorizing, we get,
-3x²-24x-36 = -3(x²+8x+12)
= -3(x²+6x+2x+12)
= -3[x(x+6)+2(x+6)]
= -3(x+6)(x+2)
Hence, The expression equivalent to the expression -3x²-24x-36 is -3(x+6)(x+2)
For more references on expression, click;
https://brainly.com/question/14083225
#SPJ1
Based on the graphs of f(x) and gtx), what is (fg)(1)?
NO LINKS!! Help me with the 2-Column Proof Part 5aa
Perpendicular lines intersect at 90° - definition of perpendicular.
Here is the two column proof:
Statement Reason
FH ⊥ NS Givenm∠FHS = 90° Definition of perpendicular lines∠FHS is a right angle Definition of a right angle ProvedQuestion 14(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
In triangle LMN, mL = (4c + 47). If the exterior angle to L measures 69°, determine the value of c.
Oc= 36
Oc=34
Oc=16
Oc=11
The required value of c is 16 which is the correct answer that would be an option (C).
In triangle LMN, m∠L = (4c + 47). If the exterior angle to L measures 69°,
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it.
In the case of triangle LMN, we can use the given information to write the following equation:
⇒ 180 - 69 = (4c + 47)
⇒ 111 = 4c + 47
⇒ 4c = 111- 47
⇒ 4c = 64
⇒ c = 64/4
Apply the division operation, and we get
⇒ c = 16
Thus, the value of c is 16.
Learn more about the exterior angles here :
https://brainly.com/question/28835566
#SPJ1
An algebraic expression is given. Use the expression to answer the following questions,
a) How many terms are there in the algebraic expression?
b) What is the numerical coefficient of the first term?
c) What is the constant term?
d) Does the algebraic expression contain like terms? If so, what are the like terms?
X+ 3+ 7x
The
The number of terms in the algebraic expression is 3 terms.
The numerical coefficient of the first term is 1The constant term of the algebraic expression is 3Yes, the algebraic expression contain like terms; the like terms are x and 7xWhat is an algebra?An algebra is the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.
Coefficient refees to a constant by which an algebraic term is multiplied.
Constant is a quantity that remains at a fixed value throughout a given discussion.
x + 3 + 7x
Thr terms are;
x;
3;
7x
Therefore, the algebraic expression has Coefficient, constant, and like terms.
Read more on algebra:
https://brainly.com/question/4344214
#SPJ1
Irene is buying a new carpet for her living room which is rectangular the room with 18 foot wide and 24 foot long carpet is go by the square yard how many square yards does she need to carpenters
Answer:
18x24=432 so basically 432 should go to the carpenters
Given:-2x+3y=18 . When x has a value of zero, what is the value of y? When y has a value of zero, what is the value of x? What are these solutions called when they are graphed as part of the line -2x+3y=18? Complete your work in the space provided.
Answer:
When x has a value of 0, the equation -2x+3y=18 becomes 0+3y=18. Solving for y, we find that y=6.
When y has a value of 0, the equation -2x+3y=18 becomes -2x+0=18. Solving for x, we find that x=-9.
These solutions are called the x-intercept and the y-intercept, respectively, when they are graphed as part of the line -2x+3y=18. The x-intercept is the point where the line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. In this case, the x-intercept is (-9,0) and the y-intercept is (0,6). These points can be used to graph the line and to understand its slope and direction.
Step-by-step explanation:
Answer: 6, -9, ?
Step-by-step explanation:
When x has a value of zero:
-2x + 3y = 18
Substitute 0 into the value of x:
-2(0) + 3y = 18
We know that anything multiplied by 0 will always be zero, so you get:
3y = 18
Therefore, after dividing both sides by 3 to get y on its own, you get:
y = 6
When y has a value of zero:
-2x + 3y = 18
Substitute 0 into the value of y:
-2x + 3(0) = 18
We know that anything multiplied by 0 will always be zero, so you get:
-2x = 18
To get a positive number from a negative number x needs to be a negative number. Remember - and - makes +.
x = -9
Unfortunately, I am unable to answer the final part of the question, but hopefully what I've already written will spark a memory of something you learnt in class :)
Hoped this helped!
In ΔA B C, C Z, BY and XA are medians - point O is the centroid of the triangle. X A=36$ and O Y=12. Find BO.
12
18
24
36
Answer:
Step-by-step explanation:
line r has a slope of 7/9. line s is perpendicular to r. what is the slope of line s?
Answer:
- 7/9
Step-by-step explanation:
I will give BRAINLIEST 50 POINT Question
What is the expression 4 + 8 (3x − 2) − 7x when simplified? Apply the order of operations and the commutative and distributive properties. Show all your work
Answer:
17x - 12--------------------------------
Given expression:
4 + 8(3x - 2) - 7xSimplify it in below steps:
4 + 8(3x - 2) - 7x = Given4 + 8(3x) + 8(-2) - 7x = Distribute4 + 24x - 16 - 7x = Simplify(24x - 7x) + (4 - 16) = Collect like terms(24 - 7)x + (-12) = Simplify17x - 12 AnswerAnswer:
4+(8×3x)+(8×(-2))-7x
4+24x-16-7x
4-16+24x-7x
-12+17x
or 17x-12
A jet is flying East. When the jet is 5 miles away from the airport, the distance from the jet to the airport is increasing at a rate of 180 miles/hour; the ground or horizontal distance (that is the distance from the projection of the jet onto ground to the airport) equals 4 miles and is increasing at a rate of 150 miles/hour. Find the vertical speed of the jet at this moment in time.
Answer:
90
Step-by-step explanation:
Let's call the initial distance from the jet to the airport $x$. We are told that $x = 5$ miles.
Let's call the initial ground distance from the projection of the jet onto the ground to the airport $y$. We are told that $y = 4$ miles.
Let's call the rate at which the distance from the jet to the airport is increasing $v_x$. We are told that $v_x = 180$ miles/hour.
Let's call the rate at which the ground distance from the projection of the jet to the ground to the airport is increasing $v_y$. We are told that $v_y = 150$ miles/hour.
We want to find the vertical speed of the jet at this moment in time. Let's call this quantity $v_z$.
Since the jet is flying in the eastward direction, we can use the Pythagorean theorem to relate the three sides of the right triangle formed by the jet, the projection of the jet onto the ground, and the airport. Specifically, we have
$$x^2 = y^2 + z^2$$
where $z$ is the vertical distance from the jet to the ground (i.e., the height of the jet above the ground).
Since the distance from the jet to the airport and the ground distance from the projection of the jet to the airport are both increasing, we can take the derivative of both sides of the equation above to find the rate of change of $z$ with respect to time. This gives us
$$2x \frac{dx}{dt} = 2y \frac{dy}{dt} + 2z \frac{dz}{dt}$$
where $t$ is time.
We are given the values of $x$, $y$, $v_x$, and $v_y$, so we can plug these values into the equation above to solve for $v_z$. This gives us
$$2 \cdot 5 \cdot 180 = 2 \cdot 4 \cdot 150 + 2z \frac{dz}{dt}$$
Solving for $\frac{dz}{dt}$, we get
$$\frac{dz}{dt} = \frac{2 \cdot 5 \cdot 180 - 2 \cdot 4 \cdot 150}{2z}$$
We are told that $z = x - y$, so we can plug this into the equation above to find $\frac{dz}{dt}$. This gives us
$$\frac{dz}{dt} = \frac{2 \cdot 5 \cdot 180 - 2 \cdot 4 \cdot 150}{2(x-y)}$$
Substituting the values of the known quantities, we get
$$\frac{dz}{dt} = \frac{2 \cdot 5 \cdot 180 - 2 \cdot 4 \cdot 150}{2(5-4)} = \frac{180}{2} = 90$$
Therefore, the vertical speed of the jet at this moment in time is $v_z = 90$ miles/hour.
The vertical speed of the jet is approximately 300 miles/hour.
What is speed?Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is traveling along a route.
Let's call the distance from the jet to the airport "d" and the height of the jet "h". Then we have two related rates:
d is increasing at a rate of 180 miles/hour.
The horizontal distance is increasing at a rate of 150 miles/hour.
Using the Pythagorean theorem, we can relate these two distances:
d² = h² + 4²
Taking the derivative of both sides with respect to time, we get:
2d(dd/dt) = 2h(dh/dt)
Simplifying, we get:
dd/dt = (h/d)(dh/dt)
We're looking for the vertical speed of the jet, which is dh/dt. We can solve for this by plugging in the given values:
d = 5 miles
dd/dt = 180 miles/hour
h² + 4² = 5² (from the Pythagorean theorem)
dh/dt = ?
Solving for h, we get:
h² = 5² - 4² = 9
h = 3 miles
Now we can plug in all the values and solve for dh/dt:
dh/dt = (dd/dt)(d/h) = (180 miles/hour)(5 miles/3 miles) ≈ 300 miles/hour
To learn more about the speed;
https://brainly.com/question/7359669
#SPJ2
RADICAL FUNCTIONS PROBLEM PLS HELP
Answer:
D) [tex]\frac{\sqrt{14}}{7}[/tex]
Step-by-step explanation:
[tex]\sqrt{\frac{2}{7}}=\frac{\sqrt{2}}{\sqrt{7}}=\frac{\sqrt{14}}{7}[/tex]
50 POINTS ASAP!!!!!!!!!!!!!!!! 50 POINTS ASAP!!!!!50 POINTS ASAP!!!!!
ΔABC is rotated 90° clockwise about the origin.
Answer:
(4,5)
Step-by-step explanation:
Which of the following sets of ordered pairs is a function?
PLS LOOK AT THE PICTURE AND HELP ME !!
Answer: c
Step-by-step explanation:
A function cannot have repeated X value in a set
100 POINTS WILL GIVE BRAINLIEST If businesses lower prices, consumers want more. What is it called when businesses have negative products to provide to demanding consumers?
A. supply surplus
B. consumer surplus
C. producer surplus
D. profit surplus
Answer:consumer surplus
Step-by-step explanation:
Answer:
Its B consumer
Step-by-step explanation:
A) Find the linear approximation to the function f(x) = ln(x) near a = 1.
B) Then use the linear approximation found to estimate ln(0.97).
C) Lastly is the answer you found in b an underestimate or an overestimate?
The linear approximation found to estimate ln(0.97) is 9.1%.
What is linear approximation?The definition of a linear approximation of a function is simply utilising a line to approximate the value of the function at a point. We recall the idea of the tangent line as soon as we see a curve (of a function) and a point on it. The value of the function at any point that is very close to the provided point can be roughly determined using the equation of the tangent line if the equation of the tangent line is found at the supplied point.
The given function is f(x) = ln(x).
We start by finding the equation of the tangent line at x=1 to the graph of y=lnx.
f(1)=ln(1)=0
We know the derivative of f(x) will be f'(x)=1/x
f'(1)=1/1=1
Therefore, the equation of the tangent is:y−y1=m(x−x1)
y−0=1(x−1)
y=x−1
An approximation for ln(1.19) would be y=1.19−1=0.19
The actual value, obtained using a calculator, would be 0.174. This means the percent error is (0.19−0.174)/0.174 ×100
= 9.1%
Therefore, the linear approximation found to estimate ln(0.97) is 9.1%.
To learn more about the linear approximation visit:
https://brainly.com/question/1621850.
#SPJ1
A group of students brought two tanks of water to clean the classroom.Tank A held 5,511 ml of water and Tank B held 7,275 ml of water. The water from both tanks was poured into Tank C which was empty. What was the volume of water in Tank C, rounded to the nearest hundred ml?
The volume of water in Tank C is 12800 ml.
How to calculate the volume?Given that the group of students brought two tanks of water to clean the classroom.Tank A held 5,511 ml of water and Tank B held 7,275 ml of water and the water from both tanks was poured into Tank C which was empty.
It should be noted that the volume on tank C will be the addition of A and B volume. This will be calculated thus:
= Volume of A + Volume of B
= 5511 ml + 7275 ml
= 12786 ml
= 12800 ml to nearest hundred.
The volume is 12800 ml.
Learn more about expressions on:
brainly.com/question/723406
#SPJ1
Fwam and his children went into a bakery and will buy cupcakes and brownies. Eac
cupcake costs $4.50 and each brownie costs $1.75. Fwam has a total of $50 to spenc
on cupcakes and brownies. Write an inequality that would represent the possible
values for the number of cupcakes purchased, c, and the number of brownies
purchased, b.
Therefore , the required inequality expression is 4.50x+1.75y ≤50
What is expression?A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations.. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers.An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
One cupcake costs $4.50,
So, “x” cupcakes cost = 4.50x.
One brownie cost $1.75,
so “y” brownies cost = 1.75y.
thus, the total 4.50x+1.75y must be less or equal to $50.
Therefore , the required inequality expression is 4.50x+1.75y ≤50
To know more about expression , visit
https://brainly.com/question/14083225
#SPJ1
Clinic offers maria 15% discount off her total cost.
(-8,23) and (-9,24) slope
Answer:
the answer for slope is -1
Write the equation of the line described below in slope-intercept form.
Find the equation of the line that is perpendicular to the line y=2 x and passes through the point (10,2).
The equation of the line perpendicular to the line y = 2x and is passes through (10,2) is given by y = (-1/2)x + 7.
As given in the question,
Equation of the line is given by :
y = 2x
Point (x₁ , y₁ ) = (10, 2) through which line passes .
Slope intercept form is given by :
y = mx + c
'm' is the slope of the line.
slope of the line y = 2x is equal to 'm₁' = 2
let 'm₂' be the slope of the line perpendicular to the given line y = 2x.
Relation between the slopes of two perpendicular lines is given by :
m₁ × m₂ = -1
⇒2 × m₂ = -1
Divide both the side by 2 we get,
⇒m₂ = -1/2
Equation of the required line is:
(x₁ , y₁ ) = (10, 2)
y - y₁ = m₂ ( x - x₁ )
⇒ y - 2 = (-1/2) ( x - 10 )
⇒ y =(-1/2)x + 7
Therefore, the equation of the line perpendicular to the given line y =2x is given by y = (-1/ 2)x + 7 .
Learn more about equation here
brainly.com/question/29657992
#SPJ4
Estimate the measure of this angle within 15°.
Answer:
[tex]90^{\circ}[/tex]
Step-by-step explanation:
A right angle measures [tex]90^{\circ}[/tex].
PLEASE PLEASE HELP!! A lot of points!!
Consider the diagram below showing a light ray reflecting off a plane mirror. If angle B were 25°, then the angle of reflection would be?
The 25° angle the light ray makes with the normal, B which is the angle of incidence, according to the laws of reflection, indicates that the angle of reflection, which is the angle the reflected ray makes with the normal, C, is 25°
What are the laws of reflection?The laws of reflection states that (1) The angle of incidence and the angle of reflection have the same value (2) The incident ray, the reflected ray and the normal are coplanar (3) The refracted ray is on the opposite side of the normal with regards to the incident ray.
The law of reflection states that the angle the in of reflection and the angle of incidence are equal; [tex]\theta_i = \theta_r[/tex]
The angle the incident ray makes with the normal of the plain mirror and the angle the reflected ray makes with the normal are the same.
The angle the incident ray in the diagram of the question makes with the normal line segment, B = 25°
The angle the reflected ray makes with the normal line segment = C
Therefore, according the to the laws of reflection, we get;
Angle B = Angle C
Angle B = 25°
Therefore;
Angle C = Angle B = 25° (symmetric property)
The angle of reflection, C = 25°Learn more about the laws of reflection here:
https://brainly.com/question/13101215
#SPJ1
Barry wants to post five parcels, with the
following masses:
2.7 kg
27.3 kg
0.245 kg
Mass of parcel
Less than 1kg
4.16 kg
Use the table below to work out how
much it would cost Barry in total to post
all of his parcels separately.
1kg to 5kg
5kg to 10kg
10kg to 20kg
More than 20kg
16 kg
Cost to post
£2.04
£4.87
£6.15
£9.68
£13.50
Barry will post all of his parcels separately at £17.84
How to find the the cost of posting the five parcelsThe information in the table have the amount to post certain weights of the parcel. This will be used to ascertain how much to send Barry's parcel
Barry's parcel will contains (starting from the least)
weight of parcel cost of posting as from the table
less than 1 kg (1kg to 5kg) £2.04
0.245 kg (1kg to 5kg) £2.04
2.7 kg (1kg to 5kg) £2.04
4.16 kg (1kg to 5kg) £2.04
27.3 kg (More than 20kg) £9.68
addition of the costs
= £2.04 * 4 + £9.68
= £17.84
hence the cost of sending the five parcels is £17.84
Learn more on cost of posting parcel at:
https://brainly.com/question/12796802
#SPJ1
Write an equation
where 45 is the product.
Answer:
Welcome to Brainly! I saw that this was your very first question. I will gladly assist you with your problem. (see explanation)
Step-by-step explanation:
Here are 4 options available to choose from:
1) 45 = 3² x 5 (multiply the sum of 3 times 3 by 5)
2) (3 x 8 )+ (24 x 2) - 3 (multiply 8 times 3 and then 24 times 2 add expressions together then subtract 3 from sum of expressions)
3) (9 x 9)- 36 = 45 (multiply 9 times 9 and subtract 36 from 81)
4) [tex]6^{2}[/tex] -9 (multiply 6 times 6 and subtract 9 from 36)
(Hope this helped you )
Mr. Crane and Ms. Finch are next-door neighbors. They both have beautiful gardens with feeders that attract wildlife. Mr. Crane uses 2 cups of sunflower seeds for every 6 cups of birdseed in his feeders. Ms. Finch uses 3 cups of sunflower seeds for every 5 cups of birdseed in her feeders. Whose feeder has a greater ratio of sunflower seeds to birdseed?
Answer:
Ms finch has the higher ratio
Step-by-step explanation:
Given ratios 2 : 6 and 3 : 5, you want to know which is greater.
ComparisonThere are several ways to compare ratios. You can express them over a common denominator, compare them to a common value, convert them to decimal, subtract one from the other.
Common denominator2 : 6 vs 3 : 5 = 10 : 30 vs 18 : 30
3 : 5 is greater than 2 : 6, so Ms finch has the higher ratio.
Common value2 : 6 vs 3 : 5
We can compare each of these to 1/2.
2 : 6 < 3 : 6 = 1/2
3 : 5 > 2.5 : 5 = 1/2
3 : 5 is greater than 2 : 6, so Ms finch has the higher ratio.
Decimal conversion2 : 6 ≈ 0.333
3 : 5 = 0.600
3 : 5 is greater than 2 : 6, so Ms finch has the higher ratio.
Subtraction2/6 -3/5 = (10 -18)/(30) = -8/30 so the second ratio is higher
3 : 5 is greater than 2 : 6, so Ms finch has the higher ratio.
What term has the y, in the equation 3y + 4 = x
-12 will be the term for y
Let us suppose that x= 0
then we will get
3y + 4 = x
and then it will be
3y+ 4 = 0
Now, we will move 4 to the right hand side and it being positive this side will become negative on right hand side
3y= -4
now,
3y = 1/4
y = 1/[4*3]
y=1/12
y= - 12
Hence the answer will be y= -12
To learn more about equation -
https://brainly.com/question/24262709
terrence plants a garden that has 8 rows of flowers,with 28 flowers in each row.How many flowers did terrence plant?
Answer:
224
Step-by-step explanation:
28x8=224
Answer: 224 flowers
Step-by-step explanation:
8*28=224
through (4,5) and (0,-2)
Answer: y=7/4x-2
Step-by-step explanation:
I find the slope first, using 5--2/4-0. This is 7/4. I then plug it into point-slope form, which is y--2=7/4(x-0). Simplifying get y=7/4x-2.
01 L1 - Perimeter Word Problems
Cooper, Sha Niya
11
1 of
A piece of Plexiglas has a width which is 5 centimeters shorter than its length. What represents the area of the Plexiglas, in terms of its length (L)?
Answer:
The area of the Plexiglas is given by the formula for the area of a rectangle, which is A = L * W, where L is the length and W is the width of the rectangle. In this case, the width is 5 centimeters shorter than the length, so we can represent it as W = L - 5. Substituting this expression for the width into the formula for the area, we get:
A = L * (L - 5)
This expression represents the area of the Plexiglas in terms of its length.