3(x-1)≤ ½(x+1) -6. Topic is Linear inequalities
Answer:
[tex]x\le \:-1[/tex]
Step-by-step explanation:
[tex]3\left(x-1\right)\le \frac{1}{2}\left(x+1\right)-6[/tex]
[tex]3x-3\le \:-\frac{11}{2}+\frac{1}{2}x[/tex]
[tex]3x\le \:-\frac{5}{2}+\frac{1}{2}x\\[/tex]
[tex]\frac{5}{2}x\le \:-\frac{5}{2}[/tex]
[tex]5x\le \:-5[/tex]
[tex]x\le \:-1[/tex]
x = -1
3(-2) ≤ ½(0) - 6
-6 ≤ 0 - 6
-6 ≤ -6
This is true.
x = -2
3(-3) ≤ ½(-1) - 6
-9 ≤ -½ - 6
-9 ≤ [tex]-\frac{13}{2}[/tex]
This is also true.
Therefore, x ≤ -1.
In triangle ABC, b = 600, ∠B = 11°, and ∠C = 75°. Find a.
Answer:
Step-by-step explanation:
We could use the Law of Sines if we only knew what angle A was. It just so happens that by the Triangle Angle-Sum Theorem, angle A is equal to
180 - B - C. Therefore,
angle A = 180 - 11 - 75 so
angle A = 94. And the Law of Sines is
[tex]\frac{sin94}{a}=\frac{sin11}{600}[/tex] and cross multiply to get
600sin94 = asin11 and solve for a:
[tex]a=\frac{600sin94}{sin11}[/tex] gives you that
a = 3136.85
A timer is started as a ball is dropped from a certain height and its velocity measured. After 0 seconds, the ball is falling at 0 feet per second. After 2 seconds, the ball is falling at 64 feet. After 3 seconds, the ball is traveling at 96 feet and after 4 second the ball is traveling 128. Is this a proportional relationship?
Answer:
yes
because the descent of the ball is 32m per second
Step-by-step explanation:
To determine if the relationship is proportional, determine the descent of the ball per second
after 2 seconds = 64 / 2 = 32
after3 seconds = 96/3 = 32
after 4 seconds = 128 / 4 = 32
the relationship is proportional
What is another word for zeros?
Answer:
nothing
Step-by-step explanation:
Zero is a number without a value so nothing could be another word for it
Given that y is directly proportional to x. If y = 30 and x= 5, write an equation that connects y with x.
Answer: y = 6x
Step-by-step explanation:
Since this is a direct proportion, we will introduce the constant of proportionality here and this will be:
y = kx
Since y = 30 and x= 5,
30 = 5 × k
30 = 5k
k = 30/5
k = 6
Therefore, the equation that connects y to x will be:
y = kx
y = 6x
The equation that connects y to x is y = 6x.
Sienna is determining the solution 6b + 12 = 102 A:15 B:17 C:90 D:102
A car travels at a speed of s miles per hour. It covers 126 miles in 3 hours.
The equation that can be used to find the value of s is
× s = ??
The speed of the car is ??
miles per hour.
PLEASE HELP (also thanks for the answers on the last couple of questions yall)
Answer:
Step-by-step explanation:
This is a distance = rate times time problem where you are calling the rate "speed" instead. So our formula for distance then is distance = speed times time which is
d = st
The distance traveled in 126 miles and the time it took to do this was 3 hours. Filling in those values gives us
126 = s3 or
126 = 3s since multiplication is commutative. Solve for s by dividing both sides by 3 to get
s = 126/3 which is
s = 42 miles per hour
Draw the two lines y = 2x + 2/3, and y = 2x + 1/3. They are parallel a
Answer:
Two line are perpendicular when they are at right angles to each other.
The red line is perpendicular to the blue line in each of these examples:
Perpendicular Example
Step-by-step ex;planation:
A ride-share company has a fee that includes a fixed cost and a cost that depends on both the time spent travelling, in minutes, and the distance travelled, in kilometres. The fixed cost of a ride is $2.55 Judy's ride costs $16.75 and took eight minutes. The distance travelled was 10 km. Pat's ride cost $30.35 and took 20 minutes. The distance travelled was 18 km. Roy's ride took 10 minutes. The distance travelled was 15 km. Find the cost of Roy's ride.
Answer:
the cost of Roy's ride is $23.05
Step-by-step explanation:
According to the Question,
Let, Cost of per minute charge is 'x' & Cost Of Per Kilometre charge is y .
Given, A ride-share company has a fee of the fixed cost of a ride is $2.55 .And, The Total cost of the Ride depends on both the time spent on travelling(in minutes), and the distance travelled(in kilometres) .⇒ Judy's ride costs $16.75 . but the actual cost after deducting the fixed charge is 16.75-2.55 = $14.20, took 8 minutes & The distance travelled was 10 km. Thus, the equation for the journey is 8x+10y=14.20 ⇒ Equ. 1
⇒ Pat's ride costs $30.35 . but the actual cost after deducting the fixed charge is 30.35-2.55 = $27.80, took 20 minutes & The distance travelled was 18 km. Thus, the equation for the journey is 20x+18y=27.80 ⇒ Equ. 2
Now, on Solving Equation 1 & 2, We get
x=0.4(Cost of per minute charge) & y=1.1(Cost Of Per Kilometre charge)
Now, Roy's ride took 10 minutes & The distance travelled was 15 km . Thus, the cost of Roy's Ride is 10x+15y ⇔ 10×0.4 + 15×1.1 ⇔ $20.5
Hence, the total cost of Roy's ride is 20.5 + 2.55(fixed cost) = $23.05
if you apply the changes below to the linear parent, f(X)=x, what is the equation of the new function vertically stretch by multiplying by 3. flip over the x-axis
Answer:
f(x) = -3x
Step-by-step explanation:
f(x) = -3x
What type of polynomial is: 2x - 4x^3 - 7 + 6x^2
A. quadratic
B. linear
C. quartic
D. cubic
Answer:
Option D
Step-by-step explanation:
Given polynomial :-
=> 2x - 4x³ -7 + 6x²
Here the highest degree of variable is 3 ,
Therefore it is a cubic polynomial .
find the compound ratio of the following
a) 2/15 : 3/7 and 5/8 : 14/27
please help me
give in step by step
Answer:
1/12 : 2/9Step-by-step explanation:
Compound ratio is the multiplication of the ratios:
2/15 : 3/7 and 5/8 : 14/27Multiply to get:
(2/15*5/8) : (3/7*14/27) = 1/12 : 2/9Given ratios,
2/15 : 3/7 and 5/8 : 14/27
Then to find the compound ratio,
We have to multiply,
→ (2/15 × 5/8) : (3/7 × 14/27)
→ 10/120 : 42/189
Now simplify the ratio,
→ 1/12 : 2/9
Thus, required ratio is 1/12 : 2/9.
Question 2 of 10
A rectangle's width is 5 feet less than its length. Write a quadratic function
that expresses the rectangle's area in terms of its length.
O A. A(1) = lw
B. A(1)=12 + 51
C. All) = w(w+5)
O D. All) = 12 - 51
A rectangle's width is 5 feet less than its length. Write a quadratic function
that expresses the rectangle's area in terms of its length.
O A. A(1) = lw
B. A(1)=12 + 51
C. All) = w(w+5)
O D. All) = 12 - 51
part ion even know of the hardest test
Given:
The equation of a line is:
[tex]y=-\dfrac{5}{7}x+2[/tex]
A line passes through the point (-5,-3) and perpendicular to the given line.
To find:
The equation of the line.
Solution:
Slope intercept form of a line is:
[tex]y=mx+b[/tex] ...(i)
Where, m is the slope and b is the y-intercept.
We have,
[tex]y=-\dfrac{5}{7}x+2[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]m=-\dfrac{5}{7}[/tex]
We know that the product of slopes of two perpendicular lines is always -1.
[tex]m_1\times m_2=-1[/tex]
[tex]-\dfrac{5}{7}\times m_2=-1[/tex]
[tex]m_2=\dfrac{7}{5}[/tex]
Slope of the required line is [tex]\dfrac{7}{5}[/tex] and it passes through the point (-5,-3). So, the equation of the line is:
[tex]y-y_1=m_2(x-x_1)[/tex]
[tex]y-(-3)=\dfrac{7}{5}(x-(-5))[/tex]
[tex]y+3=\dfrac{7}{5}(x+5)[/tex]
Using distributive property, we get
[tex]y+3=\dfrac{7}{5}(x)+\dfrac{7}{5}(5)[/tex]
[tex]y+3=\dfrac{7}{5}x+7[/tex]
[tex]y=\dfrac{7}{5}x+7-3[/tex]
[tex]y=\dfrac{7}{5}x+4[/tex]
Therefore, the equation of the line is [tex]y=\dfrac{7}{5}x+4[/tex]. Hence, option A is correct.
How do I solve this? (3^0y)^2x2(xy)^0
Answer:
(y ^2 ) (x ^2)
Step-by-step explanation:
plz any one here to follow me plz tellme any one ?
(2x6)3/4 using rational exponents
Answer:
the answer is 9 divided by 1
Given one of the roots of the quadratic equation px2- 4x + 3p -8 =0 is 1 . Calculate the value of p
Answer:
Value of p is 3
Step-by-step explanation:
One of the root is 1.
So, putting 1 in the place of x in the given equation,
px²-4x+3p-8=0
or, p-4+3p-8=0
or, 4p-12=0
or, 4p=12
or, p=3
Answered by GAUTHMATH
75 mm
a
60 mm
What is the length of the missing leg?
Answer:
a = 45 millimeters
Step-by-step explanation:
In order to solve this, we need to know that for right-angled triangles the following is true:
[tex]c^{2} = a^{2} + b^{2}[/tex] (where c is the hypotenuse and "a" and "b" are the legs)
From the formula above we can conlude that...
[tex]a = \sqrt{c^{2} - b^{2} }[/tex]
Now we just substitute the variable that we know and get that...
[tex]a = \sqrt{c^{2} - b^{2} }\\a = \sqrt{75^{2} - 60^{2} } \\a = \sqrt{5,625 - 3600} \\a = \sqrt{2025} \\a = 45[/tex]
Therefore a = 45millimeters.
A student multiplied 4986 by 45 instead of multiplying by 54. By how much was his answer greater than the correct answer? Mention the property used.
Answer:
So, the difference is 44874.
Step-by-step explanation:
Multiplication of 4986 by 45
= 4986 x 45 = 224370
Multiplication of 4986 by 54
= 4986 x 54 = 269244
So, the difference in results is
= 269244 - 224370 = 44874
Which one could NOT be the probability of an event occuring?
A. 23
B. 3/4
C. 2.3
D. 0
Please help !!!
Answer:
D
Step-by-step explanation:
there is zero chance of it happening
2. A carpenter wants to cut a wood board that is feet long
d on
5
into pieces that are feet long. How many whole pieces
can be cut from the board? How much wood is left over
16
Answer:
2 whole pieces
5/24 feet left
Step-by-step explanation:
divide 5/6 by 5/16 = 2 2/3 pieces
so there are 2 whole pieces and 2/3 small piece.
The 2/3 small short equals to 5/16 x 2/3 = 5/24 ft
Determine the value of a so that x1-3x3=-3 2x1+ax2-x3=-2 (i)unique solution(ii)no solution(iii)many solutions
Answer:
(i)unique solution
Explanation:
We solve for x1 thus in the first equation:
x1-3x3=-3
x1-9=-3
x1=-3+9
x1= 6
We solve for a thus in the second equation:
2x1+ax2-x3=-2
2+a2-x3=-2
a2-x3=-4
a2=-4+x3
Someone pls pls pls solve this!!!!!!! And pls explain how u solved it. I need this due rn ASAP!!!
35°..
can also be 145° but not in this case since the angle is less than 90°
On the image below, which is the correct answer?
Answer:
d
Step-by-step explanation:
its the correct answer
Hope this helps:)
Keegan deposited $700 into his bank account. After one year, his bank account balance was $761.60. What interest rate did he earn?
Answer:
8.8%
Step-by-step explanation:
We first divide the new amount by the original and close it with brackets.
Our one year will be shown as 1/1 as an indices
(761.60/700)^1/1
= 1.088
We then convert it to 0.088 and times it by 100.
0.088×100= 8.8% Compound interest rate.
This is correct as:
700×1.088= 761.6
Have a nice day! :)
4g+1 5 − G−7 4 = 2g−5 10
Brenya Estate produces a high quality tea branded Super by blending three types of tea coded A, B and C in the ration 1: 5:1. Originally Type A tea costs GHS 1,600 type B costs GHS 800 and type C costs GHS 1,700 per kg to produce. Brenya Tea Estate packs Super tea in packets of 825g each. Blending and packing costs are 40 per kg. Determine the production cost for a packet of Super tea,
Solution :
Cost of 1 kg super tea mixture
[tex]$=\frac{1(1600)+5(800)+1(1700)}{1+5+1}$[/tex]
[tex]$=\frac{1600+4000+1700}{7}$[/tex]
[tex]$=\frac{7300}{7}$[/tex]
= 1042.8
≈ 1043
Include of cost blending and packaging.
So, cost of 1 kg is 1043 + 40 = 1083
Cost of packaging of 825 gram super tea = [tex]$\frac{825}{1000} \times 1083$[/tex]
= 893.47
Find x in circle O. Figure is not drawn to scale. HURRY PLEASE
Answer:
B. 23,5
Step-by-step explanation:
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Find the Lowest Common Multiple of 3, 5 and 6.
