Answer: x ≤ -14
Step-by-step explanation:
3 - [tex]\frac{1}{2}[/tex]x ≥ 10
1) You want to subtract 3 from both sides of the equation: 3 - [tex]\frac{1}{2}[/tex]x ≥ 10
-3 -3
------------------------
2) Once you subtract 3 from both sides of the equation you'll be able to cancel out 3-3.
3) After, you'll be left with; -[tex]\frac{1}{2}[/tex]x ≥ 7
4) You'll then want to divide both sides by -[tex]\frac{1}{2}[/tex] to isolate x.
5) Divide 7 by -[tex]\frac{1}{2}[/tex]
6) X ≥ -14, but then you'll want to flip the inequality since you divided by a negative.
7) X ≤ -14
What is the length of the short leg in the 30-60-90 triangle shown below?
Answer:
it is D. 5
Step-by-step explanation:
The long side (B) will always be (A root 3) meaning, if you just take away the square root of 3, then you get the short side A
Answer:
[tex]\boxed{Shortest\ Leg = 5}[/tex]
Step-by-step explanation:
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
Where θ = 60 , opposite = [tex]5\sqrt{3}[/tex] and adjacent = shortest leg
=> Tan 60 = [tex]5\sqrt{3}[/tex] / shortest leg (Tan 60 = √3)
=> Shortest Leg = [tex]\frac{5\sqrt{3} }{\sqrt{3} }[/tex]
=> Shortest Leg = 5
In the circle below, O is the center and mĞ= 128° What is the measure of angle HIG?
Answer:
26 degrees.
Step-by-step explanation:
From the figure it is clear that HI is the diameter and [tex]acr(GI)=128^{\circ}[/tex]. So,
[tex]\angle GOI=128^{\circ}[/tex]
[tex]\angle GOI+\angle GOH=180^{\circ}[/tex] (linear pair)
[tex]128^{\circ}+\angle GOH=180^{\circ}[/tex]
[tex]\angle GOH=180^{\circ}-128^{\circ}[/tex]
[tex]\angle GOH=52^{\circ}[/tex]
Using central angle theorem of a circle, we get
[tex]\angle HIG=\dfrac{\angle GOH}{2}[/tex]
[tex]\angle HIG=\dfrac{52^{\circ}}{2}[/tex]
[tex]\angle HIG=26^{\circ}[/tex]
Therefore, the measure of angle HIG is 26 degrees.
I need help doing this can anyone help?
You posted a lot of questions. I'll do the first four problems to get you started.
============================
Problem 1
This sequence is arithmetic because we add the same amount (4) each time to get the next term. The first term is -2. The first five terms are: -2, 2, 6, 10, 14
============================
Problem 2
This sequence is geometric. We multiply each term by 1/4 to get the next term. We start with 8 as the first term. The first five terms are 8, 2, 1/2, 1/8, 1/32.
============================
Problem 3
Similar to problem 1. This time we're adding -19 to each term to get the next one. The starting term is -6. This sequence is arithmetic and the first five terms are -6, -25, -44, -63, -82
============================
Problem 4
Similar to problem 2. This sequence is geometric with common ratio 2/3. First term is 6. The first five terms are 6, 4, 8/3, 16/9, 32/27
Which point is the image of R? Choose one answer: A B C D
Answer:
point D
Step-by-step explanation:
moving 270 degrees clockwise from point R would result in the point being in quadrant I
point D is the only point in quadrant I
in the figure below, BCA ~ STR. Find cos C, sin C, and tan C. Round your answers to the nearest hundredth.
Answer:
[tex]\sin C\approx0.85\\\\\cos C \approx0.52\\\\\tan C\approx1.63[/tex]
Step-by-step explanation:
According to the trigonometric ratios in aright triangle :
[tex]\sin x =\dfrac{\text{Side opposite to x}}{\text{Hypotenuse}}\\\\\cos x =\dfrac{\text{Side adjacent to x}}{\text{Hypotenuse}}\\\\\tan x=\dfrac{\sin x}{\cos x}[/tex]
Given: ΔBCA ~ ΔSTR
Since , corresponding angles of two similar triangles are equal.
So, ∠C = ∠T ...(i) [Middle letter]
In triangle STR
[tex]\sin T=\dfrac{\text{Side opposite to T}}{\text{Hypotenuse}}\\\\=\dfrac{26.4}{30.9}\approx0.85\\\\\cos x =\dfrac{\text{Side adjacent to T}}{\text{Hypotenuse}}\\\\=\dfrac{16.2}{30.9}\approx0.52\\\\\tan T=\dfrac{\sin T}{\cos T}\\\\=\dfrac{0.85}{0.52}\approx1.63[/tex] ...(ii)
From (i) and (ii), we have
[tex]\sin C\approx0.85\\\\\cos C \approx0.52\\\\\tan C\approx1.63[/tex]
In the diagram, AC and PR are vertical lines, while CB is a horizontal line segment. If CR : RB = 2 : 3, what are the coordinates of point Q? A. (-2, -4) B. (-1, -5) C. (-3, -3) D. (0, -6)
Answer:
A. (-2,-4)
Step-by-step explanation:
If CR:RB is 2:3, and C is (-4,-7), then R is (-2,-7)
You can stop here because only A has the x value as -2.
If you want to look at the y value also, -4 is 2/5 of the way between -2 and -7, which has the same 2:3 proportion.
Translate the following into an algebraic expression: A number is 30% of 20% of the number x.
Answer:
.06x
Step-by-step explanation:
So 20 percent of x has to first be represented. So would do .2x. So then we have to find 30% of that number. So we multiply .2x*.3 and we get 0.06x.
I believe this is correct but tell me if I'm wrong
Answer:
0.06x
Step-by-step explanation:
.2x*.3=0.06x
A swim team must be chosen from 12 candidates. What is the greatest number of different 3-person teams that can be chosen?
==========================================
Explanation:
We have 12*11*10 = 1320 permutations possible. This is where order matters. However, order does not matter with swim teams as there are no positions or ranks. All that matters is the group overall (rather than any individual in the group).
Consider the set {A,B,C}. We have 3*2*1 = 6 ways to arrange this set of letters. When considering a permutation, there are 6 permutations but only 1 combination since order doesnt matter and ABC is the same as BAC. Therefore, we divide 1320 over 6 to get the final answer of 1320/6 = 220.
---------
You can use the combination formula with n = 12 and r = 3. Doing so will give the following:
[tex]_n C _r = \frac{n!}{r!*(n-r)!}\\\\_{12} C _3 = \frac{12!}{3!*(12-3)!}\\\\_{12} C _3 = \frac{12!}{3!*9!}\\\\_{12} C _3 = \frac{12*11*10*9!}{3!*9!}\\\\_{12} C _3 = \frac{12*11*10}{3!}\\\\_{12} C _3 = \frac{12*11*10}{3*2*1}\\\\_{12} C _3 = \frac{1320}{6}\\\\_{12} C _3 = 220\\\\[/tex]
As you can see, we get the same result and note how 1320/6 is also present as well.
The greatest number of different 3-person teams that can be chosen is 220.
How many ways k things out of m different things (m ≥ k) can be chosen if order of the chosen things doesn't matter?We can use combinations for this case,
The Total number of distinguishable things is m.
Out of those m things, k things are to be chosen such that their order doesn't matter.
This can be done in total of
[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!} ways.[/tex]
So, total number of choices in that case would be:
[tex]^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}[/tex]
This is called permutation of k items chosen out of m items (all distinct).
Consider the set {A,B,C}.
3*2*1 = 6 ways to arrange this set of letters.
When considering a permutation, there are 6 permutations but only 1 combination since order doesnt matter and ABC is the same as BAC.
We can use the combination formula with n = 12 and r = 3.
[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!} ways.\\\\^{12}C_3= \dfrac{12!}{3! \times (12-3)!} ways.\\\\\\^{12}C_3= \dfrac{12!}{3! \times (9)!} ways.\\\\^{12}C_3= \dfrac{12 \times 11 \times 10 \times 9}{3! \times (9)!} ways.[/tex]
1320/6 = 220
Thus, the greatest number of different 3-person teams that can be chosen is 220.
Learn more about combinations and permutations here:
https://brainly.com/question/16107928
#SPJ2
In the given diagram, find the values of x, y, and z.
Oax = 20°, y = 21°, z = 20°
Ob.x = 64°, y = 21°, z = 64°
Oox = 64°, y = 21°, z = 20°
Odx = 115°, y = 115°, z = 64
Answer:
B) x=64, y=21, z=64
Step-by-step explanation:
X=180-116=64
Y cannot equal 115, and one angle is already 95, and that would put it over 180. The only remaining choice for y=21
z=180-95-21=64
AssAssessment captures blank growth
What is the middle term of the product of (x - 4)(x - 3)?
Answer:
- 7x
Step-by-step explanation:
Given
(x - 4)(x - 3)
Each term in the second factor is multiplied by each term in the first factor, that is
x(x - 3) - 4(x - 3) ← distribute both parenthesis
= x² - 3x - 4x + 12 ← collect like terms
= x² - 7x + 12
with middle term = - 7x
Answer:
Step-by-step explanation:
= x(x-3) - 4(x-3)
= x²-3x - 4x + 12
= x² -7x +12
So -7x is the middle term
Jacqueline. Harry, and Stanley bought a pizza pie to share for dinner. Harry ate
of the pie, and then Jacqueline ate of what was left. After Jacqueline
finished, Stanley ate of what was left of the pic. What fractional part of the
pizza pie was left after Stanley finished eating?
Answer:
1/6
Step-by-step explanation:
Harry 1x1/2=1/2
Jacqueline 1/2x1/2=1/4
Stanley 1/3x1/4=1/12
1-1/2-1/4-1/12=
12/12-6/12-3/12-1/12=
2/12 or 1/6
How to find constant M ? did I do anything wrong here ?
Answer:
M=-1, N=7
Step-by-step explanation:
Something went wrong on the 4th line.
From the third line, it should read
2x^2-x+6Mx-3M+4
=x(2x-1+6M) - 3M+4
Equating with the RHS,
2x-1+6M = 2x-7
6M = -7+1 = -6
M = -1
Therefore
N = -3M+4 = -3(-1)+4 = 7
or
M=-1, N=7
FIRST GETS BRAINLLEST What is the perimeter of the track, in meters? Use π = 3.14 and round to the nearest hundredth of a meter.
Answer:
8110
Step-by-step explanation:
80+80+50+50=260
3.14(50)²=7810
7810+260=8110
Alice is building a caterpillar habitat for some caterpillars she found in her back yard. She plans to cover all sides of the habitat with screen so the caterpillars get plenty of fresh air. What is the total amount of screen that Alice will need for her habitat? Give an exact answer (do not round).
Answer:
SA = 3.04m²
Step-by-step explanation:
SA = 2 x ( Length x Width + Width x Height + Length x Height )
SA = 2 x ( 0.4 x 1 + 0.4 x 0.8 + 1 x 0.8 )
SA = 2 x ( 0.4 + 0.32 +0.8)
SA = 2 x 1.52
SA = 3.04 m²
I wish this could help you !
Answer:
3.04 is the correct answer =)
Step-by-step explanation:
Find the path of the numbers from the upper left corner to the bottom right corner. The sum of the numbers must be equal to the number at the exit arrow. You are allowed to move either down or to the right only.
Answer:
8, 11, 19, 1, 6, 18, 3
Step-by-step explanation:
8+11+19+1+6+18+3=66
A number is no more than five. How would you graph this inequality?
Answer:
X<=5 and you would graph it with a closed dot on five and an arrow going left of it.
Step-by-step explanation:
Answer:
[tex]a<5\\\\a\in R[/tex]
Step-by-step explanation:
In several ways, for example, let:
[tex]a[/tex], an arbitrary constant, where:
[tex]a\in R[/tex]
Besides:
[tex]a< 5[/tex]
Because the number can be greater than five.
Therefore, the graph, would be all number over the interval:
[tex](-\infty, 5)[/tex]
As you can see, all numbers bellow the line [tex]y=5[/tex].
PLEASE HELLLLLLP MEEE
Answer:
None of the above
Step-by-step explanation:
In my opinion, I believe the answer is none of the above because
answer A says it has a peak from 10 to 15 km but the graph goes higher than 15 km
answer B says it has a gap from 25 to 30 km but the graph doesn't go that high.
Hope did helps:)
help please. Find the length of x.
Answer:
x=10
Step-by-step explanation:
The triangles are similar so we can use ratios to solve
6.5 (6.5+6.5)
------ = -----------------------
5 x
6.5 (13)
------ = -----------------------
5 x
Using cross products
6.5x = 65
Divide by 6.5
6.5x/6.5 = 65/6.5
x = 10
An eraser is in the shape of a triangular prism. Its dimensions are shown in the diagram. What is surface area of the
eraser?
50 mm
40 mm
40 mm
30 mm
3,600 square millimeters
4.800 square millimeters
5,400 square millimeters
6,000 square millimeters
Answer:
6000 square millimeters
Step-by-step explanation:
Side length of the slanting side can be calculated using the Pythagorean theorem,
L = sqrt(30^2+40^2) = 50
sufrace area of a triangular prism
= surface area of the end sections + the surface area of the three side faces
= 2*(30*40/2) + 40*(30+40+50)
= 1200 + 4800
= 6000 mm^2
Answer:
D) 6,000 square mm
Step-by-step explanation:
To find the surface area of the triangular prism, find the are of each face.
40 × 30 ÷ 2 = 600 × 2 sides = 120040 × 50 = 200040 × 30 = 120040 × 40 = 1600After adding all the sides' together, you get 6,000 square mm.
Anton bought a picnic cooler. His total bill, with tax, was $7.95.
He paid 6 percent sales tax. How much did he pay for the cooler
alone without the tax?
Answer:
$ 7.50
Step-by-step explanation:
The cost of the picnic cooler would be 100%.
With the 6% sales tax, Anton would pay 106% of the cost if the picnic cooler.
(since 100% +6%= 106%)
106%(picnic cooler)= $7.95
Cost of picnic cooler= 100%(picnic cooler).
Cost of picnic cooler
[tex] = \frac{7.95}{106} \times 100 \\ = 7.50[/tex]
Thus, he paid $7.50 for the cooler alone.
-p + 3/5a -1/10q + 1/9-1/9p+2 1/3p
Step-by-step explanation:
1.) first simplify or combine like terms.[tex]\frac{3a}{5} -p-\frac{p}{9}+\frac{7p}{3} -\frac{q}{10}+\frac{1}{9}[/tex]
2.) then condense. [tex]\frac{3a}{5} +\frac{11p}{9}-\frac{q}{10}+\frac{1}{9}[/tex].
What is the slope of the line shown on the graph? A)3 B)1/3 C)−3 D)−1/3
Answer:
1/3
Step-by-step explanation:
The slope of the line is found by
m = (y2-y1)/(x2-x1)
we have two point ( 0,0) and ( 3,1)
= ( 1-0)/( 3-0)
= 1/3
what is the smallest number by which 2408 should be multiplied to get a perfect cube
Answer:
90601
Step-by-step explanation:
we have to find smallest number by which 2408 should be multiplied to get a perfect cube.
First lets find prime factor of 2408 and power these prime factors have
2408 = 2*1204 = 2*2*602 = 2*2*2*301= 2*2*2*7*43
thus,
2408 = 2^3*7*31
we know that a cube is a number raised to the power three
in 2408
2 has a power of three
but 7 and 31 and there is power of one,
thus we need to make
power of 7 and 31 three by multiplying
7 with 7*7
and 31 with 31*31
thus,
2^3*7*31*7*7*31*31 is the minimum cube value for this number
2^3*7*31*7*7*31*31 = 2^3*7^3*31^3 = 2408 * 7^2*31^2 = 2408*90601
Thus, smallest number which should be multiplied with 2408 to make it a perfect cube is 90601
Amanda is ordering an ice cream dessert. She must order a size, a flavor of ice cream, and a topping. There are 2 sizes, 1 flavor, and 6 toppings to choose from. How many different ice cream desserts could she order?
Answer: 12
Step-by-step explanation:
Order requirement:
Size ; flavor and topping
Available variety:
Size = 2
Flavor = 1
Toppings = 6
Number of different ice-cream desserts which can be ordered :
Since one of each of size, topping and flavor must be selected :
(Number of available flavors * number of Toppings available * number of sizes available)
1 * 6 different Toppings = 6 varieties
6 varieties * 2 different sizes = 12 varieties
Therefore, there are 12 different variety of ice-cream dessert she can order.
Simplify the inequalities and match them with the graphs that represent them. x + 1 15 7x 12 arrowRight arrowRight arrowRight arrowRight Reset Next
Answer:
I dont quite understand the inequalities, I think it might be the way is shows up, bit the first graph represents x equals all numbers less than 6. The second graph is all numbers greater than 6. Third graph is all numbers less than 7. forth graph is all numbers greater than 7.
Step-by-step explanation:
If you want to give me a better representation of the inequalities, I would be more than happy to help you more!! :)
Hope this helps!!
Terry bought some gum and candy. The number of packages of chewing gum was one more than the number of mints. The number of mints was three times the number of candy bars. If gum was 6 cents a package, mints were 3 cents each, and candy bars were 10 cents each, how many of each did he get for 80 cents?
Answer:
2 Candy bars
6 Mints
7 Gum
Step-by-step explanation:
Candy bars=x
mints=3x
gum=3x+1
10(x)+3(3x)+6(3x+1)=80
10x+9x+18x+6=80
37x=80-6
37x=74
x=2
SO:
cand bars = x = 2
mints = 3x = 6
gum = 3x+1 = 7
Answer:
2 candy bars, 6 mints, and 7 packages of gumm
Step-by-step explanation:
Put the steps of storm formation in the correct order.
Ice and water droplets fall
The Sun heats the
Water vapor condenses
Water droplets freeze.
Warm air rises into the
to the surface
surface
upper atmosphere.
Answer:
The Sun heats the surface
Warm air rises into the upper atmosphere
Water Vapors condenses to the surface
Water droplets freeze
Ice and water droplets fall.
Step-by-step explanation:
Clouds are formed when invisible water vapors condenses into air and droplets or ice crystals are formed. Water enters into the air through evaporation process. The are few necessary steps for storm formation. The sun heats the surface of the earth and warm air rises into the upper most atmosphere where temperature is lowered. Water vapors condenses from the surface and rises to the upper atmosphere water droplets freeze in upper atmosphere because of reduce temperature and then ice or water droplets fall.
Answer:
The Sun heats the surface
Warm air rises into the upper atmosphere
Water Vapors condenses to the surface
Water droplets freeze
Step-by-step explanation:
Trust me on this, also can I have brainiest please?
Hope you do well! :D
Mandy works construction. Shes knows that a 5 meter long metal bar has a mass of 40 kg.Mandy wants to figure out the mass (w) of a bar made out of the same metal that is 3 meters long and the same thickness.
Answer:
24 kg
Step-by-step explanation:
40/5 = 8 and 3x8 = 24
Answer:
24 kg
Step-by-step explanation:
[tex]\frac{5}{40} =\frac{3}{w} \\5w=120\\w=\frac{120}{5}=24[/tex]
Line
A.
C.
D.
B.
Defined
Postulates
Theorems
Undefined
Terms
Answer: Undefined
Step-by-step explanation:
In geometry there are three undefined terms that we use to define other terms:
Point → In geometry a point has a location but no dimension.Plane → A plane extends is a 2-dimensional surface that extends infinitely on both sides. Line → A line is a one-dimensional undefined figure that extends infinitely in both the directions. It has length but has no width.Hence, the correct option is "Undefined".