Answer:
[tex]\displaystyle -\frac{1}{3} < x < 2[/tex]
Step-by-step explanation:
We want to solve the quadratic inequality:
[tex]9x^2-15x<6[/tex]
In order to solve a quadratic inequality, find its zeros. That is, let the inequality sign be an equal sign and solve for x. We do this because it denotes when the graph crosses the x-axis: that is, when it is positive and/or negative. This yields:
[tex]9x^2-15x=6[/tex]
Solve for x:
[tex]\displaystyle \begin{aligned} 9x^2-15x-6 &= 0\\ 3x^2 - 15 -6 &= 0 \\ (3x+1)(x-2) &= 0\end{aligned}[/tex]
By the Zero Product Property:
[tex]\displaystyle 3x + 1 = 0 \text{ or } x - 2 = 0[/tex]
Hence:
[tex]\displaystyle x = -\frac{1}{3}\text{ or } x = 2[/tex]
Now, we can test intervals. The three intervals are: all values less than -1/3, values between -1/3 and 2, and all values greater than 2.
To test the first interval, let x = -1. Substitute this into our original inequality:
[tex]\displaystyle \begin{aligned}9(-1)^2 -15(-1) \, &?\, 6 \\ 9+15 \, &? \, 6 \\ 24&> 6 \xmark \end{aligned}[/tex]
The resulting symbol is "greater than," which is not our desired symbol.
To test the interval between -1/3 and 2, we can let x = 0:
[tex]\displaystyle \begin{aligned} 9(0)^2 - 15(0) \, &? \, 6 \\ (0) - (0) \, &? \, 6 \\ 0 &< 6\, \checkmark\end{aligned}[/tex]
The resulting symbol is indeed less than. So, the interval (-1/3, 2) is a part of our solution.
Finally, to test the third interval, let x = 3. Then:
[tex]\displaystyle \begin{aligned} 9(3)^2 - 15(3) \, &? \, 6 \\ (81) - (45) \, &? \, 6 \\ 36 &> 6\end{aligned}[/tex]
Again, this is not our desired symbol.
In conclusion, our only solution is the interval:
[tex]\displaystyle \left(-\frac{1}{3}, 2\right)[/tex]
Or as an inequality:
[tex]\displaystyle -\frac{1}{3} < x < 2[/tex]
What is the equation of a line with a slope of -3 and a y-intercept of 4?
Answer:
y = -3x+4Step-by-step explanation:
the equation of a line is: y = mx+b
Where:
m is the slope, and
b is the y-intercept
Replace m with -3 and replace b with 4, in the equation y=mx+b.
[tex]m = -3\\b =4\\\\y =mx+b\\\\y =-3x+4[/tex]
-4(x+4)=-2(x+4) i need to know what makes the equation true?
Answer:
x=-1
Step-by-step explanation:
first distibute -> -4x-10=-2x+8
then add the x's and numbers
Here’s the picture for it
Answer:
Option (B)
Step-by-step explanation:
[tex]\begin{bmatrix}4 & 0\\ -1 & 2\\ -3 & -1\end{bmatrix}\times\begin{bmatrix}0 & 1 \\ -3 & 1\end{bmatrix}[/tex]
In the multiplication of two matrices we multiply the column of 1st matrix with the row of the 2nd matrix and add them.
= [tex]\begin{bmatrix}(4\times 0)+0(-3) &(4)1+0(1)\\ (-1)0+2(-3) &(-1)1+2(1)\\ (-3)0+(-1)(-3) &(-3)1+(-1)1 \end{bmatrix}[/tex]
= [tex]\begin{bmatrix}0 &4\\ -6 &1\\ 3 &-4 \end{bmatrix}[/tex]
Therefore, Option (B) will be the answer.
What three forms can acceleration take?
Answer:
positive, negative, and volecity
Step-by-step explanation:
it has something to do with those three things....hope this helps at all
Answer:
a change in velocity, a change in direction, or a change in both velocity and direction.
Step-by-step explanation:
A group of friends were working on a student film that had a budget of $1500. They used $1200 of their budget on costumes. What percentage of their total budget did they spend on costumes?
Answer:
80%
Step-by-step explanation:
1200/1500
12/15 = 0.8
80%
An electric pole, 14 metres high, casts a shadow of 10 metres. Find the height of a tree that casts
a shadow of 15 metres under similar conditions.
As shadow is directly propotional to height, we can say that,
Height/Shadow =k, where k is a constant.
So, in case of electric pole,
1410=k→(1)
In case of tree,
HT15=k→(2), where HT is height of tree
So, from (1) and (2),
1410=HT15
HT=14∗1510=21m
So, height of tree is 21 meters.
hope it helps thank youuuu
What is the measure of ZRVE?
60°
7
8
mer
R
Answer:
45 degrees
Step-by-step explanation:
180 - 60 - 75 = 45
Angle RVE is the same as angle LVA
Answer:
this might help you....
A student who is interested in architecture and construction is taking a personal assessment. Which portions of a personal assessment could belong to this student? Select all that could apply. A 3-column table with 1 row. Column 1 is labeled Activities that describe what I like to do with entries 1, read and follow blueprints and or instructions; 2, picture in my mind what a finished product looks like; 3, work with my hands; 4, perform work that requires precise results; 5, solve technical problem; 6, visit and learn from beautiful, historic, or interesting buildings; 7, follow logical, step-by-step procedures. Column 2 is labeled Personal qualities that describe me with entries 1, curious, 2, good at following directions, 3, pay attention to detail, 4, good at visualizing possibilities, 5, patient and persistent. Column 3 is labeled School subjects that I like with entries 1, Math; 2, Drafting; 3,Physical sciences; 4, Construction trades; 5, Electric trades, Heating, Air conditioning, Refrigeration, and Technology Education. A 3-column table with 1 row. Column 1 is labeled Activities that describe what I like to do with entries 1, interpret formulas; 2, find answers to questions; 3, work in a laboratory; 4, figure out how things work and investigate new things; 5, explore new technology; 6, experiment to find the best way to do something; 7, pay attention to details and help things precise. Column 2 is labeled Personal qualities that describe me with entries 1, detail oriented; 2, inquisitive; 3, objective; 4, methodical; 5, mechanically inclined. Column 3 is labeled School subjects that I like with entries 1, Math; 2, Science; 3, Drafting, Computer aided drafting; 4, Electronics, Computer Networking; 5, Technical classes, Technology Education. A 3-column table with 1 row. Column 1 is labeled Activities that describe what I like to do with entries 1, work with my hands and learn that way; 2, do routine, organized, and accurate work; 3, perform activities that produce tangible results; 4, apply math to work out solutions; 5, use hand and power tools and operate equipment and machinery; 6, visualize objects in three dimensions from flat drawings. Column 2 is labeled Personal qualities that describe me with entries 1, practical; 2, observant; 3, physically active; 4, step-by-step thinker; 5, coordinated. Column 3 is labeled School subjects that I like with entries 1, Math and Geometry; 2, Chemistry; 3, Trade and Industry courses; 4, Physics; 5, Language Arts. A 3-column table with 1 row. Column 1 is labeled Activities that describe what I like to do with entries 1, work with computers; 2, reason clearly and logically to solve complex problems; 3, use machines, techniques, and processes; 4, read technical materials, and diagrams, and solve technical problems; 5, adapt to change; 6, play video games and figure out how they work; 7, concentrate for long periods without being distracted. Column 2 is labeled Personal qualities that describe me with entries 1, logical and analytical thinker; 2, see details in the big picture; 3, persistent; 4, good concentration skills; 5, precise and accurate. Column 3 is labeled School subjects that I like with entries 1, Math; 2, Science; 3, Computer tech and Applications; 4, Communications; 5, Graphic design. A 3-column table with 1 row. Column 1 is labeled Activities that describe what I like to do with entries 1, be involved in politics; 2, negotiate, defend, and debate ideas and topics; 3, plan activities and work cooperatively with others; 4, work with details; 5, perform a variety of duties that may change often; 6, analyze information and interpret it to other. Column 2 is labeled Personal qualities that describe me with entries 1, good communicator, competitive, service-minded, well organized, problem solver. Column 3 is labeled School subjects that I like with entries 1, Government; 2, Language Arts; 3, History; 4, Math; 5, Foreign Language.
Answer:
1 and 3
Step-by-step explanation:
Answer:
1 and 3
Step-by-step explanation:
took the quiz!!
Order each set of numbers from least to greatest. 41 3 2 9 0.6 3' V 16' 9.
Can somebody solve this?
9-3 divided by 1/3 +1
Answer:
Hey there!
GIVE THE OTHER PERSON BRAINLIEST, NOT ME.
Dividing by 1/3 is multiplying by 3.
9-3=6
6 times 3 = 18
18+1=19
Hope this helps :)
What is the solution to the equation 3(4x+5) = 3x+12?
Answer:
-3
Step-by-step explanation:
12x+15=3x+12
12x-3x=-15+12
9x =-3
9÷-3
x=-3
Answer:
X= - 1/3Step-by-step explanation:
3(4x+5) = 3x+1212x + 15 = 3x + 1212x - 3x = 12 - 159x = - 3X = -3/9 = - 1/3Hope this helps..Use the order of operations to evaluate each expression.
5) 3+ (4)(5) +6+3
Answer:
44
Step-by-step explanation:
1 3/8 multiplied by 4????????????????????
Answer:
5.5 or 5 1/2
I didn't know if you need decimal answer or fraction so I put both!
Tito is installing a new kitchen floor. The kitchen is square in shape and has an area of 441 sq ft. What is the length of one side of Tito’s. Pls help me with this!
Answer:
21 feet
Step-by-step explanation:
The square root of 441 is 21 and since the room is a square, all sides are even.
What is a scale factor because i'm new to 7th grade and i'm clueless.
Answer:
A scale factor is a number which scales, or multiplies, some quantity.
Step-by-step explanation:
i.e: this shape multiplied by a scale factor of 2. Usually solved by a ratio
Choose all the sets containing the number pie
Answer:
The set of Real Numbers.
The set of Irrational Numbers.
The set of transcendental numbers.
Step-by-step explanation:
7. Bruno noticed today's gasoline price at the local convenience store was advertised as $3.40 per gallon. This price is 15% above last year's price. Calculate last year's price. $ 3.55 O $ 3.25 O $ 2.96 O $ 2.40
Answer:
I'm pretty sure it $2.96
Answer:
option c) $ 2.96
Step-by-step explanation:
15% = 15 /100 = 0.15
Let last year's price = $ x
x + 15% of x = $ 3.40
x + 0.15*x = 3.40
x + 0.15x = 3.40 {Add like terms}
1.15x = 3.40 {Divide both sides by 1.15}
1.15x/1.15=3.40/1.15
x = 2.956
Last year's price = $ 2.96
i need some help lol u get 100 for answering
Answer:
see below
Step-by-step explanation:
-6.75 is a rational real number
since it is not a whole number or a counting number
sqrt(175) = 5 sqrt(7) = irrational real number
since sqrt(7) is irrational
5 pi = irrational real number
since pi is irrational
30/3 = 10 = natural , whole, integer, rational, real number
since this is a counting number
- sqrt(9) = -3 integer, rational, real number
since this is negative
Answer:
see attached
Step-by-step explanation:
Can someone tell me how to do this -3(6+h)
Answer:
[tex]-18-3h[/tex]
Step-by-step explanation:
[tex]-3(6+h)\\\\\text{Distribute:} \left \{ {{-3*6=-18} \atop {-3*h=-3h}} \right.\\\\\boxed{-18-3h}[/tex]
The answer can also be expressed as: [tex]-3h+18[/tex]
Hope this helps.
.¿Cuál de las siguientes alternativas no corresponde a una transformación isométrica? A)Traslación B) Simetría C) Rotación D) Isometría C) Teselación
Answer:
D) Isometría
Step-by-step explanation:
Hola, D es la respuesta correcta porque la isometría no es una transformación isométrica, veamos por qué.
Una Transformación Isométrica es el cambio de forma, pero no por tamaño ni forma de la figura.
A. La traslación es una transformación isométrica porque desliza la figura a otro lugar, sin afectar su forma o tamaño.
B. La simetría es una transformación isométrica porque técnicamente es un reflejo, una vez más no afecta el tamaño o la forma de la figura.
C. La rotación es una transformación isométrica porque gira la figura, sin afectar el tamaño o la forma de la figura.
E. La teselación es una transformación isométrica porque une la misma forma, sin afectar el tamaño o la forma de la figura.
Dejándonos con D.
write the set of all even prime number
Answer:
{2}Step-by-step explanation:
The only even prime number is 2
Answer:
The even prime number is 2.
janie bought 4 apples and 4 bananas .each apple costs 0.40 and each banana cost 0.40 enter an expression representing the total cost
A box measuring 11 inches by 10 inches by 7 inches is filled with solid wooden cubical blocks, each measuring 3 inches per side. How many wooden blocks can fit into the box
Answer:
28
Step-by-step explanation:
[tex]number \: of \: wooden \: blocks \\ = \frac{volume \: of \: box}{volume \: of \: one \: wooden \: block} \\ = \frac{11 \times 10 \times 7}{3 \times 3 \times 3} \\ = \frac{770}{27} \\ = 28.51 \\ [/tex]
Thus, there would be 28 full wooden blocks in the box.
Answer: 28 wooden blocks
Step-by-step explanation: First you must find the volume of the box with the formula: L × W × H so, 10 × 11 × 7 = 770 inches³. Second you must find the volume of the wooden blocks with the formula: x³ ( 'x' is the value of the side of the cube ) so, 3 × 3 × 3 = 27 inches³. Now you can divide the volume of the box by the volume of the wooden block = 770 ÷ 27 = 28.518...*
* Always only count the whole numbers.
A jacket that normally sells for $45 is on sale with 20% off. What is the sale price? in dollars
Answer:
Step-by-step explanation:
The sales price would be $36.00
How I got this answer:
Discount: (45 x 20)/100 = $9.00 the nine dollars is your discount.
Final pricing:
45 - 9.00 = $36.00 when you subtract the cost with the discount you should get thirty-six dollars.
What value of x is in the solution set of 2(3x – 1) ≥ 4x – 6?
–10
–5
–3
–1
Answer: -1
Step-by-step explanation:
Given by your question
2(3x-1)≥4x-6
Distributive property to take off the parentheses
2×3x-2×1≥4x-6
6x-2≥4x-6
Subtract 4x on both sides (Subtractive property of equality)
6x-2-4x≥4x-6-4x
2x-2≥-6
Add 2 on both sides (Addition property of equality)
2x-2+2≥-6+2
2x≥-4
Divide 2 on both sides (Division property of equality)
2/2 x≥-4/2
x≥-2
----------------------------------------------------------------------------
Looking at the options you've provided.
-10 INCORRECT, it is not greater or equal to -2
-5 INCORRECT, it is not greater or equal to -2
-3 INCORRECT, it is not greater or equal to -2
-1 CORRECT, it is greater than -2
Hope this helps!! :)
Please let me know if you have any question
x = - 1
Step-by-step explanation:2(3x – 1) ≥ 4x – 6
6x - 2 ≥ 4x - 6
6x - 4x ≥ 2 - 6
2x ≥ - 4
x ≥ - 2
x ∈ [ - 2 ; + oo )
x = - 1
a farmer plants seven eggplants plants per 0.6m². how many eggplants can be plant in an area of 84m²?
Answer:
980 eggplants
Step-by-step explanation:
If a farmer plants 7 eggplants per 0.6 m², then
Eggplants in an area of 84 m²:
7/0.6*84 = 980Answer is 980
A baby carriage that is carrying twins is sitting at the top of a hill that is 21 m high. The carriage with the babies has a mass of 48 kg. What is the potential energy of the twins and the carriage?
Answer:
1,008 kg
Step-by-step explanation:
9,888 Joules
hope it help
thank you .....
Find the Product: (x+9i)^2
Answer:
x² + 18xi - 81
Step-by-step explanation:
FOIL - First, Outside, Inside, Last
Step 1: Write out expression
(x + 9i)²
Step 2: Expand
(x + 9i)(x + 9i)
Step 3: FOIL
F - x²
O - 9xi
I - 9xi
L - 81i²
Step 4: Combine
x² + 18xi + 81i²
Step 5: Simplify
i² = -1
x² + 18xi + 81(-1)
x² + 18xi - 81
A woman has a total of
$
15,000
to invest. She invests part of the money in an account that pays
10
%
per year and the rest in an account that pays
12
%
per year. If the interest earned in the first year is
$
1720
, how much did she invest in each account?
$4,000 in the 10% per year account
$11,000 in the 12% per year account
Answer:
4000 for 10% a year
11000 for 12% a year
A circular room has a floor of diameter 590cm. Estimate the 92.2 perimeter of the room in metres
Answer:
18.5 m
Step-by-step explanation:
The diameter in meters is 5.90, so the circumference of the room is ...
C = πd = 5.90π m ≈ 18.5 m
The perimeter of the room is about 18.5 m.