Inequalities help us to compare two unequal expressions. The value of x which is the solution set of 9(2x+1)<9x–18 is -4.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
To know which value will satisfy the inequality we need to substitute each of the values into the inequality,
A) x=-4
[tex]9(2x+1) < (9x-18)\\\\9[2(-4)+1] < [9(-4)-18]\\\\9(-8+1) < (-36-18)\\\\9(-7) < -54\\\\-63 < -54[/tex]
Since the inequality is satisfied this is the solution set of the inequality.
Thus, the value of x which is the solution set of 9(2x+1)<9x–18 is -4.
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Answer:
224 ÷ 4 = 56
Step-by-step explanation:
14 × 4 = 56
56 × 4 = 224
224 ÷ 4 = 56
Sara bought 12 pencils for $1.44. What is the cost per pencil?
Answer:
Step-by-step explanation:
each pencil costs $8.33.
12÷$1.44=$8.33.
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Fill in the Blanks:
To factor p^2 - 5p -14 we need to find ___ of ____ that will also add to equal ____.
Answer:
We need to find Factors of 14 that will also add and equal to 5
Step-by-step explanation:
Trinomial factorising
Answer:
see explanation
Step-by-step explanation:
p² - 5p - 14
We need to find the factors of the constant term (- 14) that will also add to give the coefficient of the p- term (- 5)
the factors are - 7 and + 2 , since
- 7 × + 2 = - 14 and - 7 + 2 = - 5
then
p² - 5p - 14 = (p - 7)(p + 2) ← in factored form
HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
[tex]y=-\dfrac 14 x~~....(i)\\\\x+2y = 4~~...(ii)\\\\\text{Substitute}~~ y= -\dfrac 14 x ~~ \text{in equation (ii):}\\ \\ \\x+2\left(-\dfrac 14 x \right) = 4\\\\\implies 4x -2x = 16~~~~;\left[\text{Multiply both sides by 4} \right]\\\\\implies 2x = 16\\\\\implies x =\dfrac{16}2 \\ \\\implies x =8\\\\\text{Substitute x = 8 in equation (i);}\\\\y= -\dfrac 14 \cdot 8 = -2\\\\\text{Hence,}~ (x,y) = (8,-2)[/tex]
Answer:
[tex]y = - \frac{1 }{4} x \\ [/tex]
[tex]x + 2y = 4 \\ [/tex]
[tex]x + 2( - \frac{1}{4} x) = 4 \\ [/tex]
[tex]x + ( - \frac{2}{4} x) = 4 \\ [/tex]
[tex]x - \frac{1}{2} x = 4 \\ [/tex]
[tex] \frac{2x - 1x}{2} = 4 \\ [/tex]
[tex]2x - x = 8[/tex]
[tex]x = 8[/tex]
[tex]x + 2y = 4 \\ [/tex]
[tex]8 + 2y = 4[/tex]
[tex]2y = 4 - 8[/tex]
[tex]2y = - 4[/tex]
[tex]y = - 2[/tex]
The width w is less than 10 inches
Answer:
w - 10
Step-by-step explanation:
Substract 10 from W --> w - 10
Juan's family and Ethan's family go to a food stand.
• Juan's family buys three hot dogs and four drinks for $18.50.
• Ethan's family buys five hot dogs and four drinks for $25.50.
What is the cost of one drink at the food stand?
Answer:
1 hotdog is $3.5.
1 drink is $2.
Step-by-step explanation:
18.50= 3x+4y(times 5)
25.50=5x+4y(times -3)
92.5=15x+20x
-76.5=-15x+-12y
16=-8y
2=y
18.50=3x+4(2)
10.50=3x+8
10.50=3x
3.5=x
i need help with this
i’ll mark Brainliest or whatever it is
Which expression is equivalent to m (n + p)?
O A. m X n + P
Ов. т Хр+п
OC, (m x n) + P
OD. (mx n) + (m xp)
m
O E. (m + n) x (m + p)
Answer:
A
Step-by-step explanation:
m( n+ p)
it's also known as m × n + p
i need help with this
find the mean of 3,2,2,5,1,3,2,0,5
Answer:
2.56
Step-by-step explanation:
(3+2+2+5+1+3+2+0+5)/9=2.55555555556...
what are the angle measures of X and Z?
Answer:
m∠Z=146
m∠X=34
Step-by-step explanation:
Since this is an Isosceles Trapezoid, we can assume that m∠Z=m∠Y, because an isosceles trapezoid has two pairs of congruent angles, therefore m∠Z=146.
Since angle Y and Angle X are same side interior and line ZY║WX, we can assume that m∠X+m∠Y=180. Substitute values:
[tex]146+X=180\\Y=34[/tex]
y (y + 2) = y2 - 6
also
2 [x - (1-3x)] = 3 (x + 1)
Answer:
Step-by-step explanation:
y(y+2)=y²-6
y²+2y=y²-6
2y=-6
y=-3
2[x-(1-3x)]=3(x+1)
2[x-1+3x]=3x+3
2(4x-1)=3x+3
8x-2=3x+3
8x-3x=3+2
5x=5
x=1
y= 2x+5 what is the gradient and y-intercept?
The awse is b) :B...... ur welcum
3. The curve C with equation y=f(x) is such that, dy/dx = 3x^2 + 4x +k
Where k is a constant.
Given that passes through the points (0, -2) and (2, 18).
a. Show that k = 2 and find an equation for C
b. Show that the line with equation y = x-2 is a tangent to C and find the coordinates of the point of contact.
a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have
[tex]\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt[/tex]
Evaluate the integral to solve for y :
[tex]\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt[/tex]
[tex]\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x[/tex]
[tex]\displaystyle y = x^3+2x^2+kx - 2[/tex]
Use the other known value, f(2) = 18, to solve for k :
[tex]18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}[/tex]
Then the curve C has equation
[tex]\boxed{y = x^3 + 2x^2 + 2x - 2}[/tex]
b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:
[tex]\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2[/tex]
The slope of the given tangent line [tex]y=x-2[/tex] is 1. Solve for a :
[tex]3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1[/tex]
so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).
Decide which of these points is correct:
[tex]x - 2 = x^3 + 2x^2 + 2x - 2 \implies x^3 + 2x^2 + x = x(x+1)^2=0 \implies x=0 \text{ or } x = -1[/tex]
So, the point of contact between the tangent line and C is (-1, -3).
Find the lateral area of the prism
Answer: 50, 208 mm²
Step-by-step explanation:
The lateral area is the surface area excluding the bottom, also known as the base. This means we will be solving for two rectangles and two triangles.
[The Rectangles]
They are both congruent, so I will do the following;
A = 2(L * W)
A = 2(7 mm * 24 mm)
A = 2(168 mm)
A = 336 mm²
[The Triangles]
The area of a triangle is [tex]\frac{B * H}{2}[/tex] However, they are both congruent. I will do the following;
A = B * H
A = 24 mm * 2,078 mm
A = 49,872 mm²
[The Total]
Lastly, I will add them together.
336 mm² + 49,872 mm² = 50, 208 mm²
What would be the BEST formula to model the volume of the flower planter shown?
A)
volume of a cone
B)
volume of a cylinder
c
volume of a triangular prism
D
volume of a rectangular prism
Answer:
B
Step-by-step explanation:
if it's one plant it's b, if it means more than one then probably D
Answer:
D) Volume of a rectangular prism
Step-by-step explanation:
If he is choosing one event and one time how many options does he have for his birthday party?
Answer:
6 options
Step-by-step explanation:
hes got 3 event options
and 2 time slots so
3 times 2 is 6
Annual snowfall (in inches):
20, 16, 20, 17.5, 19.5, 18, 23
Mean =
Median =
What is the mean and the median?
Answer:
Mean is all the numbers add up and divide how many number were there. The Median is to line up all in order and the middle on.
Step-by-step explanation:
Answer:
Mean =19.142857142857
Median =19.5
Step-by-step explanation:
Will mark brainlyest!! Please help.
Answer:
The X-coordinates will decrease by 6 units because, anytime you move something to the left on a coordinate plane you are decreasing the x value
Answer:
The x-coordinates will decrease by 6.
Step-by-step explanation:
So when you look at a graph, the left side has smaller numbers than the right side because as you go down it becomes negative and the right means it is going positive. So if you are moving to the left you are getting smaller so you are decreasing. The other options with y-axis is not true because the y-axis is vertical.
What is the sum of the geometric sequence 1, 3, 9, ... if there are 11 terms? (5 points) 29,524 55,987 87,381 88,573
Answer:
S₁₁ = 88573
Step-by-step explanation:
the sum to n terms of a geometric sequence is
[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^{n}-1) }{r-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 1 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{3}{1}[/tex] = 3 , then
S₁₁ = [tex]\frac{1(3^{11}-1) }{3-1}[/tex] = [tex]\frac{1}{2}[/tex] (177147 - 1) = [tex]\frac{1}{2}[/tex] × 177146 = 88573
There are two mechanics who work on cars. For each mechanic, the relationship between x, the number of hours worked, and y, the total cost, in dollars, is described below. • The equation y = 36x represents the total cost charged by Mechanic A for the number of hours worked. The graph shown below represents the total cost charged by Mechanic B for the number of hours worked.
Answer:
B
Step-by-step explanation:
if you divide the 2/88 you should get a price of 44. So Mechanic B charges $44 while Mechanic A charges $36. Subtract 44-36 and get 8. Since Mechanic B charges more, it would give you the answer listed in B.
The equation satisfies option B, Mechanic B charges $8 more per hour then mechanic A.
What is graph?a collection of all points whose coordinates satisfy a given relation (such as a function) a diagram that represents the variation of a variable in comparison to that of one or more other variables, such as a series of one or more points, lines, line segments, curves, or areas
The fundamental subject of graph theory is graphs.
Given the Equation for cost charged by Mechanic A
y = 36x
where y = total cost and x = hours worked
graph shows the total cost charged by Mechanic B
from graph we the coordinates (0, 0) and (2, 88)
when x = 0, y = 0 and when x = 2, y = 88
the equation satisfy the condition is
y = 44x
cost for one hour for Mechanic A
y = 36x (x = 1)
y = $36
cost for one hour for Mechanic B
y = 44x (x = 1)
y = $44
Mechanic B is $8 more than Mechanic A
Hence Mechanic B charges $8 more per hour then mechanic A.
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please help, thank you if you do
Step-by-step explanation:
q3) if the given sequence is 1, 2, 4, 8, 16..., then it is not arithmetic one. The common ratio is 2: 16/8=8/4=4/2=2/1.
q4) if it is given -34; -64; -94; -124; -154..., then it is arithmetic sequence, where the difference is -64--34=-94--64=-124--94=-154--124= -30
PLEASEE HELPPPPPPP!!!!!!!!!!!
Answer:
6
Step-by-step explanation:
[tex]h \sqrt{28 } \\ \sqrt{28} = \sqrt{4 \times 7} \\ \sqrt{28} = \sqrt{4} \times \sqrt{7} \\ 2 \sqrt{7} \\ 8 \sqrt{7} - 2 \sqrt{7} = 6 \sqrt{7} [/tex]
hope this helps :D have a good day
Josh calculated the mean absolute deviation of the points he earned throughout the year in four of his classes: science, math, Spanish, and art. science: MAD of 1.14 math: MAD of 1.6 Spanish: MAD of 1.2 art: MAD of 1.93 In which class were his scores the closest together?
Answer:
science
Step-by-step explanation:
k12 test
What is the trigonometric ratio for cos D ?
Answer:
Here,
H=75P=72B=21We know that cosD= b/h
=21/75
=7/25
Find LJ and mGM if KP=PL and GH=36 ft
find m^gm
Colin put a pie in the oven at 1:35 p. M. He took the pie out at 2:17 p. M. How long was the pie in the oven?
Answer:
42 minutes
Step-by-step explanation:
there are 60 minutes in one hour.
from 12 pm, 1 hour and 35 minutes have passed to get to 1:35 pm
from 12 pm, 2 hours and 17 minutes have passed to get to 2:17 pm
we are trying to figure out the start to end time, or the difference between the times
2 hours and 17 minutes - 1 hour and 35 minutes
1 hour = 60 minutes
if we convert everything to minutes we can get a definitive time in one single unit
2 hours = 1 hour * 2 = 60 minutes * 2 = 120 minutes
1 hour = 60 minutes
plug these in
(120 + 17) minutes - (60 + 35) minutes
= 137 minutes - 95 minutes
= 42 minutes as our answer
Solve the following:
Answer:
-25
Step-by-step explanation:
120
∑ (3n-6)
n=1
Find the sum.
Answer:
21300
Step-by-step explanation:
120∑n=13n−4
Split the summation into smaller summations that fit the summation rules.
120∑n=1 3n−4=3120∑n=1 n+120∑n=1 −4
Evaluate
3120∑n=1 n.
21780
Evaluate
120∑n=1 −4 −480
Add the results of the summations.
21780−480
Subtract 480 from 21780.
21300
(2y^2 – 3y + 1) = (y - 2)
Answer:
see below
Step-by-step explanation:
Move R side to the L side to get
2y^2 -4y +3 = 0
Use quadratic formula to find y = 1 +- i sqrt (2) / 2