we have in this problem
[tex] 3x+1 > 10 [/tex] ------> inequality [tex] 1 [/tex]
[tex] 4x \leq 20 [/tex] ------> inequality [tex] 2 [/tex]
Solve the inequality [tex] 1 [/tex]
[tex] 3x+1 > 10\\ 3x > 10-1\\ 3x > 9\\ x > 3 [/tex]
the solution is the interval------> (3,∞)
Solve the inequality [tex] 2 [/tex]
[tex] 4x \leq 20\\\\ x \leq \frac{20}{4} \\\\ x \leq 5 [/tex]
the solution is the interval------> (-∞,5]
Find the solution for the system
(3,∞) ∩ (-∞,5]--------> (3,5]
therefore
the answer is the option
A. A number line with an open circle on 3, a closed circle on 5, and shading in between.
tom has 6 quarters and 12 dimes in his pocket how many coins does he need to take out his pocket to make sure he has 4 quarters
Henry has 523 baseball cards. He buys 24 each month. What is a explicit rule for the number of baseball cards Henry has in n months?
Answer:
the answer is a_n= 24n+499 just took the test :)
Step-by-step explanation:
Check my answer? Will Upvote!
A scientist counts 35 bacteria present in a culture and finds that the number of bacteria triples each hour. The function y = 35 • 3x models the number of bacteria after x hours. Estimate when there will be about 550 bacteria in the culture.
I think it's about 2.5 hours.
Other answer options:
about 5.5 hours
about 4.5 hours
about 3.5 hours
Answer:
The answer to your question is about 5.5 hours.
Step-by-step explanation:
The equation is y = 35(3x)
Data
# of bacteria = 550 = y
time = ? h
Then 550 = 35(3x) substitution
550 = 105x simplifying
x = 5.23 h.
What is the value of the expression below when r = 2?
9 – 3r
A.12
B.6
C.3
music in 2001, full length cassettes represented 3.4% of total music sales. between 2001 and 2006, the present decreased by about 0.5% per year
A writer charges $5 per word plus a start up fee of $50 per article.
Add.
(5n^2+4n)+(3n^2+6n)
Use the distributive property to create an equivalent expression to 7x 56
Estimate the tip on a $19.65 check using a tip rate of 15%
in the diagram below Bd is parallel to XY . what is the value of x
Answer: The correct option is (B) 60.
Step-by-step explanation: Given that the line BD is parallel ti the line XY.
We are to find the value of x.
We know that
if two parallel lines are cut by a transversal, then the measures of the alternate interior angles are equal.
In the given figure, BD is parallel to XY and they are cut by a transversal.
So, the angles with measures x° and 60° are alternate interior angles.
Therefore, we must have
[tex]x^\circ=60^\circ\\\\\Rightarrow x=60.[/tex]
Thus, the value of x is 60.
Option (B) is CORRECT.
Subtract -34.7 from -7.85
A laptop computer sells for $850. the sales tax is 7%. what is the total cost of the laptop?
Answer:
$909.50
Step-by-step explanation:
$850 x 7% = $59.50 (tax amount)
850 x (1+ 0.07) = $909.50
Write the expression in standard form.
five divided by quantity three minus fifteen i.
Answer:
[tex]\frac{4}{229}+\frac{30i}{229}[/tex]
Step-by-step explanation:
Which statement best describes how to determine whether f(x) = 9 – 4x^2 is an odd function?
Determine whether 9 – 4(–x)^2 is equivalent to 9 – 4x^2.
Determine whether 9 – 4(–x^2) is equivalent to 9 + 4x^2.
Determine whether 9 – 4(–x)^2 is equivalent to –(9 – 4x^2).
Determine whether 9 – 4(–x^2) is equivalent to –(9 + 4x^2).
Answer:
Its CCCCCCCCCCCCCCC aka 3 aka third option
on dredful edge im going nuts
Step-by-step explanation:
a surveyor standing 64 meters from the base of a building measures the angle to the top of building and finds it to be 39 degrees . the surveyor then measures the angle to the top of the radio tower on the building and finds that it is 48 degrees. how tall is the radio tower?
To calculate the height of the radio tower, trigonometry is used to first determine the building height and then the total height including the tower. Subtracting the building height from the total height gives the height of just the radio tower.
Explanation:To determine the height of the radio tower, we must first use trigonometry to find the height of the building. We use the tangent of the angle and the distance from the surveyor to the building:
Tan(39°) = Height of Building / 64 metersHeight of Building = 64 meters * Tan(39°)After calculating the height of the building, we use the same approach to find the total height to the top of the radio tower:
Tan(48°) = Total Height / 64 metersTotal Height = 64 meters * Tan(48°)Finally, to find the height of the radio tower alone, we subtract the height of the building from the total height.
Height of Radio Tower = Total Height - Height of Building
By following these steps, we can calculate the height of the radio tower.
Pablo deposited 57 into a savings account for which interest is compounded quarterly according to the rule 72 what interest rate will cause his money to double is approximately 44 years
To find the interest rate that will cause Pablo's money to double in approximately 44 years, we can use the rule of 72. The interest rate is approximately 1.64%.
Explanation:To find the interest rate that will cause Pablo's money to double in approximately 44 years, we can use the rule of 72. The rule of 72 states that dividing 72 by the interest rate will give you the approximate number of years it takes for money to double. In this case, we need to find the interest rate that makes the money double in 44 years. So, we divide 72 by 44 to get the interest rate.
Interest rate = 72 / 44 ≈ 1.6363636363636363
Therefore, the interest rate that will cause Pablo's money to double in approximately 44 years is approximately 1.64%.
lyn has as much money as jo. together they have $63.how much money does each have
take 63 and divide it by 2.
63÷2= 31.5
so they each had $31.5
Factor completely: 2x3 + 10x2 + 4x + 20
Prime
(2x + 10)(x2 + 2)
2[(x + 5)(x2 + 2)]
(x + 5)(2x2 + 4) ...?
Answer:
B) 2[(x + 5)(x2 + 2)]
Step-by-step explanation:
Given: 2x^3 + 10x^2 + 4x + 20
Here 2 is a common factor, so we take it out and write the remaining terms in the parenthesis.
2(x^3 + 5x^2 + 2x + 10)
Now let's take (X^3 + 5x^2 +2x + 10), we group and factor them as follows:
(x^3 + 5x^2 + 2x + 10) = x^2(x+5) + 2(x + 5) = (x+5)(x^2 +2)
When we combine them, we get
2x^3 + 10x^2 + 4x + 20 = 2(x+5)(x^2 +2)
Therefore, the answer is B) 2[(x + 5)(x2 + 2)]
Hope this will helpful.
Thank you.
From 2000-2010 a city had a 2.5% annual decrease in population. If the city had 2,950,000 people in 2000, determine the city's population in 2008.
The population of the city in the year 2008 is 2409122.
Important information:
Initial population in 2000 is 2,950,000.Decreasing rate is 2.5%.Exponential formula:According to the exponential decay formula:
[tex]f(t)=a(1-r)^t[/tex]
Where a is the initial value, r is the decay rate and t is the time period.
The difference between 2008 and 2000 is 8.
Substitute [tex]a=2950000, r=0.025, t=8[/tex] in the above formula.
[tex]f(8)=2950000(1-0.025)^8[/tex]
[tex]f(8)=2950000(0.975)^8[/tex]
[tex]f(8)=2409122.8208[/tex]
Round the value to the previous integer.
[tex]f(8)\approx 2409122[/tex]
Therefore, the population of the city in 2008 is 2409122.
Find out more about 'Exponential formula' here:
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Simplify the expression: √18x^4y^3
Answer:
[tex]3x^2y\sqrt{2\cdot y}[/tex]
Step-by-step explanation:
We have been given an radical expression. We are asked to simplify our given expression.
[tex]\sqrt{18x^4y^3}[/tex]
We can rewrite terms of our given function as:
[tex]\sqrt{18\cdot x^4\cdot y^3}[/tex]
[tex]\sqrt{2\cdot 9\cdot x^4}\cdot y^2\cdot y}[/tex]
[tex]\sqrt{2\cdot 3^2\cdot (x^2)^2\cdot y^2\cdot y}[/tex]
Using radical rule [tex]\sqrt[n]{a^n}=a[/tex], we will get:
[tex]3x^2y\sqrt{2\cdot y}[/tex]
Therefore, the simplified form of our given expression would be [tex]3x^2y\sqrt{2\cdot y}[/tex].
What is (are) the apparent x-intercept(s) of the function graphed above?
–4, –2, and 6
115 and –9
–3 and 3
50
For this case what we must do is observe the cut points of the function with the x axis.
The cut points with the horizontal axis are:
(-4, 0)
(-2, 0)
(6, 0)
Therefore, the intersections with the axis are:
x = -4
x = -2
x = 6
Answer:
The apparent x-intercept (s) of the function graphed are:
-4, -2, and 6
A curve passes through the point (0, 5) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve? (Use x as the independent variable.) ...?
Which of the following represents this function written in intercept form?
y=x^2-8x+12
a. y=-(x+2)(x+6)
b. y=(x-2)(x-6)
c. y=(-x+3)(x-4)
d. y=-(x+2)(x-6) Which of the following represents this function written in intercept form?
y=x^2-8x+12
a. y=-(x+2)(x+6)
b. y=(x-2)(x-6)
c. y=(-x+3)(x-4)
d. y=-(x+2)(x-6)
Answer:
B. y = (x-2)(x-6)
Step-by-step explanation:
The quadratic function y = x²- 8x + 12 can be factored into intercept form as y = (x - 2)(x - 6), which corresponds to option (b).
The function given is y = x² - 8x + 12. To write this function in intercept form, we need to factor it as the product of two binomials, each representing its intersections with the x-axis where y=0.
To do this, we look for two numbers that multiply to give the constant term (12) and add up to give the coefficient of the middle term (-8). These two numbers are -2 and -6.
Thus, the factored intercept form is y = (x - 2)(x - 6). This corresponds to answer choice (b).
Explain why the square root of a number is defined to be equal to that number to the 1/2 power.
Answer:
Sample Response: Squaring and square root are inverses, so one should "undo" the other. That is, squaring the square root of a number results in the number. Using the power of a power rule, you multiply the exponents. Since a number to the first power is itself, the product of the exponents must equal 1. This means that the power of the square root must be the reciprocal of 2, or one half.
x= 1, 2, 3, 4, 5. y=11\4, 25\4, 39\4, 53\4, 67\4. what equation relates y to x in the values x and y?
Bob has a tree house at a height of 20 ft. When he's feeling adventurous he uses a rope to climb the tree house instead of the ladder. If the weight of the rope is 32 lb, then how much work must Bob do to pull the rope up once he has entered the house? ...?
Justine enrolls in a music program. The cost of the program includes a one-time registration fee of $45 and a fee of $9 per lesson. If the average cost per music lesson is $12 and Justine has taken x classes, which equation represents this scenario?
A.12=54/x
B.12=45+9/x
C.12=45+9x/x
D.12=45x+9/x
If Justine has taken x classes of $9 per lesson, then the total fee for these lessons is $9x.
The cost of the program includes a one-time registration fee of $45 and a fee of $9 per lesson. This means that the total cost of the program in terms of x is
$45 + $9x = $(45 + 9x).
If the average cost per music lesson is $12 (includes a registration fee), then the cost of the program is $12x.
Therefore,
12x = 45 + 9x.
Divide this equation by x:
[tex]12=\dfrac{45+9x}{x}.[/tex]
Answer: correct option is C
The correct option is C) [tex]\[12 = \frac{45 + 9x}{x}\][/tex]. The equation that represents this scenario is [tex]\[12 = \frac{45 + 9x}{x}\][/tex].
To understand why option D is correct, let's break down the costs associated with Justine's music program.
1. The registration fee is a one-time cost of $45. This is a fixed amount and does not depend on the number of classes taken.
2. The cost per lesson is $9, and Justine has taken x classes. Therefore, the total cost for the lessons alone is 9x.
3. The average cost per music lesson, including the registration fee, is $12. This average cost is calculated by taking the total cost (registration fee plus the cost of x lessons) and dividing by the number of classes x.
4. The total cost for x classes, including the registration fee, is the sum of the registration fee and the cost of the lessons, which is [tex]\(45 + 9x\)[/tex].
5. To find the average cost per lesson, we divide the total cost by the number of classes x. This gives us the equation [tex]\(\frac{45 + 9x}{x}\)[/tex].
6. We know that the average cost per lesson is $12, so we set the equation equal to 12: [tex]\(12 = \frac{45 + 9x}{x}\).[/tex]
Therefore, the equation that correctly represents the scenario is: c)
[tex]\[12 = \frac{45 + 9x}{x}\][/tex].
some of the fastest growing occupations in the United States are in which field
a. retail
b. agriculture
c. health care
d. manufacturing
Which best explains why all equilateral triangles are similar?
A. All equilateral triangles can be mapped onto each other using dilations.
B. All equilateral triangles can be mapped onto each other using rigid transformations.
C. All equilateral triangles can be mapped onto each other using combinations of dilations and rigid transformations.
D. All equilateral triangles are congruent and therefore similar, with side lengths in a 1:1 ratio.
Answer: A. All equilateral triangles can be mapped onto each other using dilations.
Step-by-step explanation:
We know that all equilateral triangles are similar to each but not congruent because they all have same measure of corresponding angles 60° but do not have same side-lengths.
So, equilateral triangles can be mapped onto each other using dilation because they maps similar shapes (sometimes congruent) where as rigid transformations always map congruent shapes so we cannot map all equilateral triangles by using rigid transformations.
The ratio of boys to girls in Mrs. Ronilo's math class is 3 to 1. What PERCENT of the class is girls?
Answer:25 %
Step-by-step explanation: there are 4 parts and 1 of those is girls 1 divided by 4 is 0.25, which is 25%
The percent of the class that is girls is 75%
Ratios and proportionGiven the ratio of boys to girls in Mrs. Ronilo's math class is 3 to 1, the total ratio will be:
Total ratio = 3 + 1Total ratio = 4The percent of the class that is girls = 3/4 * 100
The percent of the class that is girls = 75%
Hence the percent of the class that is girls is 75%
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