The correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9 is,
⇒ - 12 + 20x ≥ - 6x + 9
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
We have to given that;
The inequality is,
⇒ - 4(3 - 5x) ≥ - 6x + 9
Now, We can simplify as;
⇒ - 4(3 - 5x) ≥ - 6x + 9
⇒ - 12 + 20x ≥ - 6x + 9
⇒ 20x + 6x ≥ 12 + 9
⇒ 26x ≥ 21
⇒ x ≥ 21/26
Thus, The correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9 is,
⇒ - 12 + 20x ≥ - 6x + 9
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What is the answer to 2/5 - 1/3?
Work Shown:
2/5 - 1/3
6/15 - 5/15
(6-5)/15
1/15
Here are two ways to check the answer:
Type 2/5 - 1/3 into your calculator to get roughly 0.06667. The 6's actually repeat forever, but of course the calculator rounds at some point. You should notice that 1/15 has the same decimal value. Therefore 2/5 - 1/3 = 1/15Type (2/5-1/3) - (1/15) into your calculator. You should get zero or very close to it. I'm using the fact that if A = B, then A-B = 0.Hi Student!
Looking at the problem statement and them just asking for us to determine the difference between two numbers seems like an easy task. The first thing that we must do is to find a common denominator so we subtract them otherwise we can not since the denominators are different.
The denominators of the fractions are 5 and 3 and we know that they both multiply up to 15 so that can be our common denominator.
Convert to common denominator
[tex]\frac{2}{5}-\frac{1}{3}[/tex][tex]\frac{2*3}{5*3}-\frac{1*5}{3*5}[/tex][tex]\frac{2*3}{15}-\frac{1*5}{15}[/tex][tex]\frac{6}{15}-\frac{5}{15}[/tex]Subtract
[tex]\frac{6}{15}-\frac{5}{15}[/tex][tex]\frac{6-5}{15}[/tex][tex]\frac{1}{15}[/tex]Therefore, the final answer to the question asking the difference between 2/5 and 1/3 would be 1/15.
A tractor costs $20000 and depreciates in value by 15% per year. how much will the tractor be worth after 5 years?
Answer:
$ 8874.11 after 5 years
Step-by-step explanation:
Each year it is worth 85 % of its value
20 000 ( .85)^5 = 8874.11
5. Find the value of x so that lines s and t are parallel.
(7x - 20)°
(4x + 16)
The value of x so that lines s and t are parallel is 12
How to find angles involving parallel lines?The angle are alternate exterior angles.
Therefore, alternate exterior angle theorem states that when two parallel lines are intersected by a transversal, then the exterior angles formed on either side of the transversal are equal.
Hence,
7x - 20 = 4x + 16
7x - 4x= 16 + 20
3x = 36
x = 36 / 3
x = 12
Therefore, the value of x is 12.
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Which equation can be solved by using this system of equations?
StartLayout Enlarged left-brace 1st Row y = 3 x Superscript 5 Baseline minus 5 x cubed + 2 x squared minus 10 x + 4 2nd Row y = 4 x Superscript 4 Baseline + 6 x cubed minus 11 EndLayout
The equation that can be solved using the system of equations is 4x^4 + 6x^3 - 11 = 3x^5 - 5x^3 + 2x^2 - 10x + 4
How to determine the equation?The correct formats of the equations are:
y = 3x^5 - 5x^3 + 2x^2 - 10x + 4
y = 4x^4 + 6x^3 - 11
To determine the equation, we substitute 4x^4 + 6x^3 - 11 for y in the first equation.
So, we have:
4x^4 + 6x^3 - 11 = 3x^5 - 5x^3 + 2x^2 - 10x + 4
Hence, the equation that can be solved using the system of equations is 4x^4 + 6x^3 - 11 = 3x^5 - 5x^3 + 2x^2 - 10x + 4
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Gabby is a makeup artist and carries a lot of makeup around with her. she has 20 cosmetics in her bag, including 4 eye shadows. what is the probability that a randomly selected makeup item from her bag will be an eye shadow? write your answer as a fraction or whole number.
The probability that a randomly selected makeup item from her bag will be an eye shadow is 1/5 or 20%.
The probability of selecting an eye shadow from Gabby's bag can be calculated by dividing the number of eye shadows in the bag by the total number of cosmetics in the bag.
There are 4 eye shadows in Gabby's bag, and a total of 20 cosmetics. Therefore, the probability of selecting an eye shadow is:
P(eye shadow) = 4/20 = 1/5
This means that there is a 1 in 5 chance, or a 20% chance, that a randomly selected makeup item from Gabby's bag will be an eye shadow.
The probability can be expressed as a fraction or a whole number, depending on the context of the problem. In this case, we can express the probability as the fraction 1/5, which means that out of 20 possible cosmetics, only 4 are eye shadows.
We can also express the probability as the whole number 0.2 or 20%, which represents the proportion of eye shadows in Gabby's bag.
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Question 4 of 10
Solve (x-4)²2 = 5.
OA. x=-4± √5
OB. x=5± √√4
OC. x=9 and x = -1
OD. x=4± √5
Step-by-step explanation:
Solve the following equation for x.
10 = 2 – 4(ar – 3)
OA. -
a
OB.
Oc.
OD.
5
a
The equation for the (x-4)²2 is 5. x=4± √5. Hence, option D is correct.
What is a quadratic equation?Due to the fact that they contain two or more algebraic terms, quadratic equations fall within the category of polynomial equations. It must equal 0 in order to solve a quadratic equation. There can be zero, one, or two (true) solutions to a quadratic equation.
To solve the equation (x - 4)² = 5, we can start by taking the square root of both sides:
√[(x - 4)²] = ±√5
This gives us two possible equations:
x - 4 = √5 or x - 4 = -√5
Now it can add 4 to both sides of each equation:
x = 4 + √5 or x = 4 - √5
So the solutions to the equation (x - 4)² = 5 are x = 4 + √5 and x = 4 - √5.
Thus, option D is correct.
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The given equation is wrong, the correct equation is given below-
(x-4)²2 = 5.
Prove (1+tanx)/(1+cotx)=tanx by algebra
[tex]\text{L.H.S}\\\\=\dfrac{1+\tan x}{ 1+ \cot x}\\\\\\=\dfrac{1+ \tan x}{ 1+ \tfrac 1{\tan x}}\\\\\\=\dfrac{1+\tan x}{\tfrac{\tan x+1}{\tan x}}\\\\\\=(1+\tan x) \times \dfrac{\tan x}{1+ \tan x}\\\\=\tan x\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]
Find a number that is 45% greater than 90
Answer:
130.5Step-by-step explanation:
the number that is 45% greater than 90 is :
[tex]90+90\times \frac{45}{100} = 90 + 40.5 = 130.5[/tex]
what is the center of the circle given by the equation (x-2)2+(y+4)2=6
Answer:
(2,-4)
Step-by-step explanation:
Here, h=2 and k=-4, so the center is (2,-4)
Triangle ABC has perimeter 22 cm.
AB = 8 CM
BC = 5cm
By calculation, deduce whether triangle ABC is a right-angled triangle.
Answer:
Triangle ABC is not a Right Triangle
Step-by-step explanation:
The perimeter of a triangle is all of the sides added together so we can model our equation like so:
AB + BC + CA = P
or
8 + 5 + CA = 22
We first combine like terms
13 + CA = 22
Then make the variable have no numbers on its side
13 + CA = 22
-13 -13
CA = 9
So now that we know what CA is, we can determine whether or not its a right triangle
We can use the Pythagorean Theorem for this:
a^2 + b^2 = c^2 (the '^' symbol means 'to the power of')
or
5^2 + 8^2 = 9^2
Now we Solve
5^2 = 25
8^2 = 64
9^2 = 81
25 + 64 =? 81
89 does not equal 81
So Triangle ABC is not a Right Triangle
The coordinates of A,B,C are(6,3),(-3,5),(4,-2) respectively and P(x,y) is any point,prove that∆PBC/∆ABC=x+y-2/7
The solution to the coordinates of A,B,C as (6,3),(-3,5),(4,-2) and the prove that ∆PBC/∆ABC=x+y-2/7 is given in the image attached.
What is coordinates?This is known to be that which is created by two part that are known to give the latitude and longitude position of a person or place.
Therefore, The solution to the coordinates of A,B,C as (6,3),(-3,5),(4,-2) and the prove that ∆PBC/∆ABC=x+y-2/7 is given in the image attached.
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The population of a small town has a decay rate of 0.5% every year. If I had 58,000 people in 2011, how many will they have today.
Answer:
If I am not mistaken the number is 54,810.
Hope I helped.
Where did he even get the 5 and the -1?
Answer:
the arrows and dots show where
Hey there!
Look at your graph… then look at your points (the green dots) and it should be there.
Your x-values are across (just think of its saying “East” and ”West”) & your y-values are up and down (just think of it as “North” and “South”)
So, based on that that information:
ANSWER:
Your x-value would be: -1 because the point landed on it whereas the y-value would be: 5 because the point landed on it.
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Find the measure of
Answer:
h=70°
Step-by-step explanation:
h + 110° = 180° {linear pair angles}
h = 180° - 110°
h = 70°
Answer:
h=70
pa brainliest po kuya/ate
Step-by-step explanation:
pa brainliest po
One angle of a right-angled triangle is 60 grades . Find the other angle in degree.
Answer:
30°
Step-by-step explanation:
This right triangle has :
right angle (90°)One angle of 60°=========================================================
Solving :
We know the angle sum of a triangle is 180°.
⇒ x + 90° + 60° = 180°
⇒ x + 150° = 180°
⇒ x = 30°
We know the angle sum of a triangle is 180° so
x + 90° +60°= 180°
x + 150°= 180°
⇒x = 30°
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Said deposited sh 56 800 in a SACCO, which paid simple interest at the rate of 12% 1 per annum. After sometime he withdrew all his money from the SACCO amounting to sh 62 125. For how long was the money in the sacco?
Answer:
time=t= 9.36 months.........
The money was in the SACCO for a time of 0.78125 years.
What is Simple Interest?Simple interest is defined as the interest obtained over the principal amount on a certain rate.
Given that,
Amount of money deposited or principal amount = 56,800
Rate of interest = 12% = 12/100 = 0.12
Final amount = 62,125
The formula for simple interest is,
A = P(1 + rt), where A is the final amount, P is the principal amount, r is the interest rate and t is the time.
Substituting,
56800 (1 + 0.12t) = 62125
1 + 0.12t = 1.09375
0.12t = 0.09375
t = 0.78125 years
Hence the time that the money kept for is 0.78125 years.
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1.1 How many grams of can of apple pie filling Chantel is going to use in the Apple (2) Cinnamon Cake.
The number of grams of canned apple that Chantel needs for her apple-cinnamon cake is about 1400 grams.
How to calculate the amount of canned apple that Chantel needs?To know the amount of canned apple that Chantel needs for her apple and cinnamon cake recipe, we must review the amount of apple that she needs for the filling of her cake.
According to the basic recipe to make this cake, we need 6 to 8 apples. Taking into account that each apple weighs about 200g, we can infer that Chantel is going to use about 1400g of canned apple as shown below.
On average we need 7 apples.
6 + 8 = 1414 ÷ 2 = 7Each apple weighs 200g, so 7 apples would be 1400g.
7 × 200g = 1400gBased on the above, Chantel needs 1400g of canned apple.
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What is the area of the rhombus in simplest radical form? The figure is not drawn to scale.
0162 √3
0162
081 √6
018 √3
The area of the Rhombus is 162√3 sq.unit , Option A is the correct answer.
What is a Rhombus ?A rhombus is a polygon , which has four equal sides , its diagonal bisect each other at 90 degree.
Let x be the half of the other diagonal.
tan 60 = x / 9
x = 9 tan 60
x = 9√3
Area of the Rhombus = (d1 * d2 /2 )
d1 and d2 are the length of the diagonal.
Area of the Rhombus = (9*2)(2 *9√3)/2
Area of the Rhombus =162√3 sq.unit
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. Construct Arguments Based on the survey data below, a marketing team for an airline concludes that someone between 18 and 24 years of age is more likely never to have flown on a commercial airliner than someone 25 years or older. Do you agree with this conclusion? Justify your answer.
The marketing team conclusion that someone between 18 and 24 years of age is more likely never to have flown on a commercial airliner than someone 25 years or older is true based on the percentage.
How to compute the percentage?The percentage for someone between 18 and 24 years of age to have flown on a commercial airline will be:
= 216/279 × 100.
= 77.4%
The percentage for someone that is 25 years older to have flown will be:
= 2210/2988 × 100
= 74%
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A 210-N mass is suspended from a horizontal beam by two cables that make angles of 29 degrees and 53 degrees with the beam. Find, using vectors, the tension in the cables.
The tension in the cable is given by the newton's first law will be 163.622 N.
What is newton's first law?The summation of the force is equal to zero.
The formula is given as
ΣF = 0
Where m is the mass of the body and a is the acceleration.
A 210-N mass is suspended from a horizontal beam by two cables that make angles of 29 degrees and 53 degrees with the beam.
Then the tension in the cable will be
Let T be the tension in the cable.
T sin 29° + T sin 53° – 210 = 0
On simplifying, we have
T (sin 29° + sin 53°) = 210
T = 163.622 N
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John is buying a new car. The value of one car he is considering is $20,000. The value of the car as it ages can be modeled by the
function v= 20, 000 (0. 84), where t is the number of years from the time of purchase. One of the factors John is using to make his decision is
the value of the car over time until it reaches half its original value. What values of domain are reasonable for the given function in this
context?
O
A. all real numbers greater than or equal to 0 and less than 4
O B. all real numbers greater than or equal to 0
O
C. all real numbers greater than or equal to 10,000 and less than or equal to 20,000
O
D. all real numbers greater than or equal to 0 and less than 2.8
Answer:
all real numbers greater than or equal to 10,000 and less than or equal to 20,000
Step-by-step explanation:
ye
What is the axis of symmetry of h(x) = 5x2 40x 64?
The axis of symmetry of h(x) = 5x2 + 40x + 64 = -4
The formula for calculating the axis of symmetry is expressed as:
Axis of symmetry x = -b/2a
h(x) = 5x^2 + 40x + 64
a = 5 and b = 40
Which expression is equivalent to - 14.6 - (- 5.75) - 8.4
Answer:
-17.25
Step-by-step explanation:
A data set is represented by the box-and-whisker plot below.
A box plot has 5 data descriptions. The correct option is 87 and 132.
How does a boxplot show the data points?A box plot has 5 data descriptions.
The leftmost whisker shows the minimum value in the data.The rightmost whisker shows the maximum value in the data.The leftmost line in the box shows the first quartile.The middle line shows the median, also called the second quartile.The last line of the box shows the third quartile.Since each quartile of the box-and-whisker plot represents 25% of the data. Therefore, values between which there are 3 quartiles present will represent 75% of the data.
Hence, the correct option is 87 and 132.
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Select the correct answer.
Which expression is equivalent to the given expression? Assume the denominator does not equal zero.
12x^9y^4 / 6x^3y^2
[tex]2x^6y^2[/tex]The equivalent expression to the given expression is [tex]2x^6y^2[/tex] (option D)
How to determine the equivalent expression?An expression in mathematics is a fusion of numbers, variables, and operators that embodies a mathematical entity. Expressions possess the ability to symbolize magnitudes, functions, and connections, exhibiting versatility and finesse.
Expressions are used in many different areas of mathematics. They are used to represent quantities, functions, and relationships.
To determine the given expression, lets start:
[tex](12x^9y^4)/(6x^3y^2)[/tex]
= [tex](12/6) x^(^9^-^3^) y^(^4^-^2^)[/tex]
= [tex]2x^6y^2[/tex]
Therefore, the equivalent expression to [tex](12x^9y^4)/(6x^3y^2)[/tex] is [tex]2x^6y^2[/tex]
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10) Eve has a fall job to pick pumpkins at the farm.
She earns $4.00 every 12 minutes that she picks pumpkins.
• She earns $4.40 every 12 minutes that he picks apples.
• She picked pumpkins for an hour and apples for 48 minutes.
How much money did Eve earn?
For pumpkins
Total 12mins sets
1hr/12min60min/12min5earnings
4(5)$20.00For apples
Total 12 mins
48/124Earnings
4(4.40)$17.60Total earnings
20.00+17.60$37.60Answer:
$37.60
Step-by-step explanation:
Eve earns:
$4.00 per 12 minutes spent picking pumpkins$4.40 per 12 minutes spent picking applesMoney earned from picking pumpkins:
1 hour = 60 minutes
[tex]\begin{aligned}\implies \sf Money\:earned & = \sf Salary \times 60\:minutes\\\\& = \sf \$4.00\:per\:12\:minutes \times 60\:minutes\\\\& =\sf \dfrac{\$4.00}{12\:minutes} \times 60\:minutes\\\\ & = \sf \$4.00 \times \dfrac{60\:minutes}{12\:minutes}\\\\ & = \sf \$4.00 \times 5\\\\ & = \sf\$20.00\end{aligned}[/tex]
Money earned from picking apples:
[tex]\begin{aligned}\implies \sf Money\:earned & = \sf Salary \times 48\:minutes\\\\& = \sf \$4.40\:per\:12\:minutes \times 48\:minutes\\\\& =\sf \dfrac{\$4.40}{12\:minutes} \times 48\:minutes\\\\ & = \sf \$4.40 \times \dfrac{48\:minutes}{12\:minutes}\\\\ & = \sf \$4.40 \times 4\\\\ & = \sf\$17.60\end{aligned}[/tex]
Total earned:
= money earned from picking pumpkins + money earned from picking apples
= $20.00 + $17.60
= $37.60
for each sequences, find the first 4 term and the 10th term the sequences are
(a) n^2+3
(b)2n^2
Answer:
see explanation
Step-by-step explanation:
to find the first 4 terms substitute n = 1, 2, 3, 4 into the sequence rule
to find the 10th term substitute n = 10 into the rule
(a)
a₁ = 1² + 3 = 1 + 3 = 4
a₂ = 2² + 3 = 4 + 3 = 7
a₃ = 3² + 3 = 9 + 3 = 12
a₄ = 4² + 3 = 16 + 3 = 19
a₁₀ = 10² + 3 = 100 + 3 = 103
(b)
a₁ = 2(1)² = 2(1) = 2
a₂ = 2(2)² = 2(4) = 8
a₃ = 2(3)² = 2(9) = 18
a₄ = 2(4)² = 2(16) = 32
a₁₀ = 2(10)² = 2(100) = 200
If f(x) = x2 2x 3, what is the average rate of change of f(x) over the interval [-4, 6]?
Answer:
see the attachment photo!
If f(x)=5x-4, what is the value of f(3)?
Answer:
11 hope this helps you and write
write an equation of the line that passes through (-6, 6) and is parallel to the line y = -2x + 2.
Answer:
y = -2x - 6
Step-by-step explanation:
We know that the slopes of the lines are equal when the lines are parallel to each other.
So, the equation of the given line is y = -2x + 2.
Here,
y = mx + c
y = -2x + 2
slope ⇒ m ⇒ -2
Therefore, the slope of the new line will be ( - 2 ).
And now we have to find the y-intercept ( c ).
For that let us use the given coordinate.
( -6 , 6 ) ⇒ ( x , y )
To find the y-intercept we have to make c the subject of the equation y mx + c.
Also, we have to replace m with ( - 2 ) as the slope of the new line is -2.
Let us solve it now.
y = m x + c
6 = -2 × -6 + c
6 = 12 + c
6 - 12 = c
-6 = c
Now we have found that,
m ⇒ - 2
c ⇒ -6
And now let us write the equation of the line.
y = m x + c
y = -2x - 6