Answer:
-8 ≤ x < 4Step-by-step explanation:
5x + 6 ≥ -34 subtract 6 from both sides
5x + 6 - 6 ≥ -34 - 6
5x ≥ -40 divide both sides by 5
x ≥ -8
and
-2x - 2 > -10 add 2 to both sides
-2x - 2 + 2 > - 10 + 2
-2x > -8 change the signs
2x < 8 divide both sides by 2
x < 4
We have x ≥ -8 and x < 4 ⇒ -8 ≤ x < 4
Find the slope of a line perpendicular to y=3x+7.
Answer:
m=3
Step-by-step explanation:
Formula for m is m=-1/m
m=-1/3
According to the rational root theorem which is a factor of the polynomial f(x)=3x^3-5x^2-12x+20
Answer:
[tex]f(x)=3(x+2)(x-2)(x-\frac{5}{3})[/tex]
Step-by-step explanation:
The rational roots theorem tells you that given a polynomial function with integer or whole number coefficients, a list of possible solutions can be found by listing the factors of the constant, or last term, over the factors of the coefficient of the leading term.
In your case, for the polynomial [tex]f(x)=3x^3-5x^2-12x+20:[/tex]
the last term is 20;the leading coeeficient is 3.So, possible rational roots can be among:
[tex]\pm1,\pm2,\pm4,\pm5,\pm10,\pm20,\pm\dfrac{1}{3},\pm\dfrac{2}{3},\pm\dfrac{4}{3},\pm\dfrac{5}{3},\pm\dfrac{10}{3},\pm\dfrac{20}{3}.[/tex]
Note that
[tex]f(-2)=3\cdot (-2)^3-5\cdot (-2)^2-12\cdot (-2)+20=-24-20+24+20=0.[/tex]
This means that [tex]x=-2[/tex] is a root of the polynomial and [tex]x-(-2)=x+2[/tex] is the factor. Also
[tex]f(2)=3\cdot 2^3-5\cdot 2^2-12\cdot 2+20=24-20-24+20=0.[/tex]
This means that [tex]x=2[/tex] is a root of the polynomial and [tex]x-2[/tex] is the factor. Also
[tex]f(\frac{5}{3})=3\cdot (\frac{5}{3})^3-5\cdot (\frac{5}{3})^2-12\cdot \frac{5}{3}+20=\frac{125}{9}-\frac{125}{9}-20+20=0.[/tex]
This means that [tex]x=\frac{5}{3}[/tex] is a root of the polynomial and [tex]x-\frac{5}{3}[/tex] is the factor.
Then
[tex]f(x)=3(x+2)(x-2)(x-\frac{5}{3}).[/tex]
In the figure below, angle y and angle x form vertical angles. Angle x forms a straight line with the 50° angle and the 40° angle. Right and solving equations to determine the measure of angle Y.
Answer:
angle Y = 90 degrees
Step-by-step explanation:
Since it is stated that angle x forms a straight line with the 50 and 50 degree angles, and that angle x is vertical to angle y, we can do 40+50+y=180 to find angle Y.
Larry spends 3/4 hour twice a day walking and playing with his dog. He also spends 1/6 hour twice a day feeding his dog. How much time does Larry spend on his dog each day?
Answer:
1hr 40min.
Step-by-step explanation:
45+45=90+10=100
write a function rule for the table.
Answer:
the correct answer would be C sorry if I'm wrong but that's how I know how to do it
A train was traveling at a constant speed.the table below shows the distance,in miles the train traveled for the first 4 hours.Write an equation to represent the relationship between t,the time,and d,the total distance traveled by the train
Answer:
1 hour 95 min. 2 hour 190 min. third hour 285 min. fourth hour 380 min.
Step-by-step explanation:
What is the measure of PRQ?
Answer:
It makes sense for the answer to be 86 degrees since it's almost a right angle.
Answer:
The correct answer is option C. 86°
Step-by-step explanation:
From the figure we can see a circle.
To find the measure of <PRQ
Consider the triangle PQR,
<PRQ = <PTR + <RPT
From the figure we get,
<PTR = 102/2 = 51
<RPT = 70/2 = 35
<PRQ = <PTR + <RPT
51 + 35 = 86°
Therefore the correct answer is option C. 86°
b) Are the black triangles above congruent or similar? Explain. (1 point)
Congruent because it contains the same angle measures and shape.
Answer:
congruent
Step-by-step explanation:
How to solve for x/ extraneous solutions
Answer:
x = 8Step-by-step explanation:
[tex]\log_ab=c\iff a^c=b\\\\===================\\\\Domain:\ 8x>0\to x>0\\\\\log_4(8x)=3\iff4^3=8x\\\\8x=64\qquad\text{divide both sides by 8}\\\\x=8\in D[/tex]
Number 8 answers? I need help ASAP
Answer: C
Since all the answers have (-6), it means that you multiply the whole equation on both sides by 6, which makes a (2/3)x become a 4x and a (1/2) become 3
Answer:
C
Step-by-step explanation:
Start by multiplying through by 3. That is the first of 2 possible steps.
3[2/3 x - 1 = 1/2]
2x - 3 = 3/2
Now multiply by 2
2 [ 2x - 3 = 3/2]
4x - 6 = 3
That makes C the only possible answer.
Which quantity is proportional to 90⁄2? Check all that are true. 45⁄1 15⁄3 180⁄3 180⁄4 270⁄8
Answer:
45/1 and 180/4
Step-by-step explanation:
1. True
[tex]\dfrac{90}{2}=\dfrac{45\cdot 2}{1\cdot 2}=\dfrac{45}{1}[/tex]
2. False
[tex]\dfrac{15}{3}=\dfrac{3\cdot 5}{3\cdot 1}=\dfrac{5}{1}\neq \dfrac{45}{1}[/tex]
3. False
[tex]\dfrac{180}{3}=\dfrac{60\cdot 3}{3\cdot 1}=\dfrac{60}{1}\neq \dfrac{45}{1}[/tex]
4. True
[tex]\dfrac{180}{4}=\dfrac{45\cdot 4}{1\cdot 4}=\dfrac{45}{1}[/tex]
5. False
[tex]\dfrac{270}{8}=\dfrac{135\cdot 2}{4\cdot 2}=\dfrac{135}{4}\neq \dfrac{45}{1}[/tex]
Which is the solution set of the inequality 15y-9<36?
Answer:
y < 3
Step-by-step explanation:
Given
15y - 9 < 36 ( Isolate 15y by adding 9 to both sides )
15y < 45 ( divide both sides by 15 )
y < 3
Answer:
y < 3
Step-by-step explanation:
on edge 2020
Need help
Divide
(x^2+5x+4)÷(x+2)
^= to the second
Step-by-step explanation:
[tex](x^2+5x+4)\div(x+2)^2=(x^2+4x+4+x)\div(x+2)^2\\\\=(x^2+2(x)(2)+2^2+x)\div(x+2)^2\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\=\bigg((x+2)^2+x\bigg)\div(x+2)^2=\dfrac{(x+2)^2+x}{(x+2)^2}=\dfrac{(x+2)^2}{(x+2)^2}+\dfrac{x}{(x+2)^2}\\\\=1+\dfrac{x}{(x+2)^2}[/tex]
Write an expression to represent the perimeter of the figure.
Answer:
5x + 2y + z
Step-by-step explanation:
The perimeter of a polygon is the sum of the lengths of all the sides of the polygon. This polygons has 8 sides. Their lengths are:
x, x, x, x, x, y, y, z
The perimeter of the polygon is the sum of the lengths shown above.
perimeter = x + x + x + x + x + y + y + z
The expression above can be simplified by combining like terms.
perimeter = 5x + 2y + z
Which of the following best represents the slope of the line? A. -3 B. - 1 3 C. 1 3 D. 3
Answer: - 1/3 I just saw the other answer and got it wrong so I decided to give u guys the right answer !! :)
Solve for x: x − 2 > 2x + 12. x > 14 x < 14 x > −14 x < −14
For this case we must solve the following inequality:
[tex]x-2> 2x + 12[/tex]
We follow the steps below:
We subtract 2x on both sides of the inequality:
[tex]x-2-2x> 2x + 12-2x\\-x-2> 12[/tex]
We add 2 to both sides of the inequality:
[tex]-x> 14[/tex]
We multiply by -1 on both sides of the inequality, taking into account that the sense of inequality changes:
[tex]x <14[/tex]
Answer:
[tex]x <14[/tex]
Answer:
The guys above is wrong because it should be x < -14 because you have to balance out both sides of the equation, you can't just do something to one side of the equation and not do it to the other.
Step-by-step explanation:
Find the experimental probability that the first three students to arrive at school are boys
Answer:
that depends
Step-by-step explanation:
how many students are in the school all together, see you would do the 3 boys over the number of people (or students) in the school
hoped this helped a little
Marilyn lives 3.5 block from the library. She leaves the library and walks 3.5
blocks before realizing she is walking in the opposite direction from her house.
After walking 3.5 blocks back, how far does Marilyn have to walk?
Answer:
3.5 blocks.
Step-by-step explanation:
After walking 3.5 blocks back she is back at her starting point.
Marilyn has walked 7 blocks in total, going the wrong direction and back to the library. She still needs to walk another 3.5 blocks to reach her house.
Explanation:Marilyn has already walked 7 blocks (3.5 blocks in the wrong direction and 3.5 blocks back to the library). As her house is 3.5 blocks from the library, she has another 3.5 blocks to walk.
Learn more about Distance Calculation here:https://brainly.com/question/34212393
#SPJ3
PLEASSE HELP!! WILL MAKR BRAINLIEST IF CORRECT!!!
Answer:
b. 26cm
oop I didn't realize this was in 2019:-:
What is the median of this data set? 100,102,103,106,109
The answer is 103 because it’s in the “middle”
Median means the middle number.
The answer : 103
What is the volume of the prism?
Enter your answer in the box as a mixed number in simplest form.
___ cm³
A rectangular prism with the width as five centimeters, the length as three and a half centimeters and the height as four and a half centimeters.
PLS HELP ASAP!!!
Answer:
78.75 cm³
Step-by-step explanation:
Volume = Width × Height × Length
V = 5 × 4.5 × 3.5
V = 78.75 cm³
Is my solution correct?
Answer:
The area of the shaded sector is [tex]51.2\pi \ units^{2}[/tex]
Step-by-step explanation:
I assume that the problem is
Find the area of the shaded sector of the circle with radius equal to 16 units
step 1
Find the value of x
we know that
[tex]8x+2x=360\°[/tex]-----> by complete circle
[tex]10x=360\°[/tex]
[tex]x=36\°[/tex]
The central angle of the shaded sector is 2x
[tex]2(36\°)=72\°[/tex]
step 2
Find the area of the circle
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=16\ units[/tex]
substitute
[tex]A=\pi (16)^{2}[/tex]
[tex]A=256\pi\ units^{2}[/tex]
step 3
Find the area of the shaded sector
we know that
A central angle of 360 degrees subtends an area of circle equal to [tex]256\pi\ units^{2}[/tex]
so
by proportion
Find the area of the shaded sector by a central angle of 72 degrees
[tex]\frac{256\pi}{360}=\frac{x}{72} \\ \\ x=256\pi *(72)/360\\ \\x=51.2\pi \ units^{2}[/tex]
Which of the following expressions can be? factored to (3x^2+1)(4x-3)
Answer:
I think it's C, sorry if I'm wrong
Answer:
Step-by-step explanation:
(3x²+1)(4x-3) = 12x^3-9x²+4x-3.....answer 1
How many floors does she travel?
Answer:
15 floors
Step-by-step explanation:
She parks on the third floor below ground +3
She goes up to the twelfth floor +12
3+12=15
What is the volume of four cubes with a side length of fraction 1 over 4 foot? V = s3, where s is the side length.
A. fraction 1 over 4 ft3
B. fraction 1 over 3 ft3
C. fraction 1 over 12 ft3
D. fraction 1 over 16 ft3
Answer:
D. fraction 1 over 16 ft³Step-by-step explanation:
The formula of a volume of a cube:
V = s³
s - side length
We have s = 1/4 ft. Substitute:
V = (1/4)³ = 1/64 ft³
We have four cubes.
4V = 4 · 1/64 = 1/16 ft³
How to find the diameter?
I'm confused with where to start with this problem
Answer:
From the information, we know that the plate will hold 3 pieces of sushi, each with a diameter of 1 1/2 inches, and there be 1/2 inch space from the edge of the of the suchi to the edge of the plate.
The diamter of the suchi plates we need to puchase should be the sum of the diameter of the sushi and the the space between them and the edge of the plate:
(3 . 1 1/2) + (2 . 1/2)
= (3 . 3/2) + 1
= 9/2 + 1
= 9/2 + 2/2
= 11/2 = 5.5 (inches)
Answer:
From the information, we know that the plate will hold 3 pieces of sushi, each with a diameter of 1 1/2 inches, and there be 1/2 inch space from the edge of the of the suchi to the edge of the plate.
The diamter of the suchi plates we need to puchase should be the sum of the diameter of the sushi and the the space between them and the edge of the plate:
(3 . 1 1/2) + (2 . 1/2)
= (3 . 3/2) + 1
= 9/2 + 1
= 9/2 + 2/2
= 11/2 = 5.5 (inches)
Patti's Pet Palace has a 100-gallon fish tank. When it needs to be cleaned, it can be drained at a rate of 5 gallons per minute. Assuming the tank was full, and x represents the number of minutes the tank has been draining, which of the following equations represents the amount of water in the tank after x minutes?
A. y = 5x - 100
B. y = 5x + 100
C. y = 100 - 5x
D. y = 100x - 5
____________________________________________________
Answer:
Your answer would be C). y = 100 - 5x
____________________________________________________
Step-by-step explanation:
Let's break down the question so it would be more easier to figure out the answer.
We would be making a y = mx + b equation
Important information:
100-gallon."Drained" at a rate of 5 gallons PER minute.x represents the number of minutes the tank has been draining.With the information above, we can use that to make our equations.
We know that the place has a 100 gallon fish tank. in the question, it says that for the equation, the tank was full, so that would be our "beginning point" or "starting value. From the equation, it would represent our "B" value.
Our equation should look like this now:
y = mx + 100
Now we need to find the rate of change.
In the question, it says that the tank DRAINS at around 5 gallons per minute, meaning that we would have to subtract 5 (-5). That would represent your "m" value on the equation. Your equations should now look like this:
y = -5x + 100
F.Y.I: y = 100 - 5x is the same that as -5x + 100, it's just flipped, and y = 100 - 5x is the answer choice that looks close to the one we made.
Answer choice C). y = 100 - 5x would be your FINAL answer.
____________________________________________________
The equation that describes the situation where a 100-gallon tank is drained at a rate of 5 gallons per minute is y = 100 - 5x. This because each minute, the volume decreases by 5 gallons from the starting amount of 100 gallons.
Explanation:The question is about how to represent a process which decreases at a constant rate in terms of mathematical expression. In this case, Patti's Pet Palace is draining a 100-gallon fish tank at a rate of 5 gallons per minute. The total amount of water in the tank decreases as time progresses and the tank drains.
This process can be represented using a negative slope linear equation. If y represents the amount of water in the tank after x minutes, the initial amount is 100 gallons and it decreases by 5 gallons each minute.
Therefore, the equation to represent this process is y = 100 - 5x. That means option C is the correct answer. For each minute that passes (represented as 'x'), 5 gallons are subtracted from the initial 100 gallons.
Learn more about Linear Equation here:https://brainly.com/question/32634451
#SPJ3
Factor this expression
Answer:
x^2+6x+9
(x+3)^2
Step-by-step explanation:
what's 22 * 19 + area model
Answer:
(20+2)(10+9)
Step-by-step explanation:
The area model is written as (a+b)(c+d). To write a multiplication problem into an area model, split it into numbers which add to it. Multiples of 10 are most commonly used.
For example 22*19 becomes (20+2)(10+9).
Helppleaseee!!! It's due tomorrow??!!
Answer:
Part a) The total length of the circular portions is [tex]12\pi\ in[/tex]
Part b) The total length of wire needed is tex]53.7\ in[/tex]
Part c) The total weight of the ornament is [tex]97\ g[/tex]
Step-by-step explanation:
Part a) Find the total length of the circular portions in terms of pi
we know that
The diameter of the circle is equal to the length side of the square
[tex]D=4\ in[/tex]
The total length of the circular portions is equal to the circumference of three complete circle
Because each circular portion is equal to 3/4 of circle
so
[tex](3/4)*4=3[/tex]
The circumference of four three quarter circles is equal to
[tex]C=3(\pi D)[/tex]
substitute the diameter
[tex]C=3(\pi (4))[/tex]
[tex]C=12\pi\ in[/tex]
Part b) Find the total length of wire needed
The total length of the circular portions is [tex]12\pi\ in[/tex]
assume
[tex]\pi =3.14[/tex]
[tex]12(3.14)=37.68\ in[/tex]
The total length of the square portion is equal to
[tex]4b=4(4)=16\ in[/tex] -----> perimeter of a square
Adds the lengths
[tex]37.68+16=53.68\ in[/tex]
Round to the nearest tenth
[tex]53.68=53.7\ in[/tex]
Part c) Find the total weight of the ornament
we know that the ornament weights 1.8 grams per inch
so
Multiply the total length by 1.8 to obtain the total weight
[tex]53.7(1.8)=96.66\ g[/tex]
Round to the nearest gram
[tex]96.66=97\ g[/tex]