Answers
Answer:
x ≥ 2
Step-by-step explanation:
Given inequality:
[tex]-\dfrac{4(x+3)}{5} \leq 4x-12[/tex]
Values of x less than 2
Substitute two values where x < 2 into the inequality:
[tex]\begin{aligned}x=1 \implies -\dfrac{4(1+3)}{5} & \leq 4(1)-12\\\\ -\dfrac{4(4)}{5} & \leq 4-12\\\\ -\dfrac{16}{5} & \leq -8 \quad \Rightarrow \textsf{Not a solution}\end{aligned}[/tex]
[tex]\begin{aligned}x=0 \implies -\dfrac{4(0+3)}{5} & \leq 4(0)-12\\\\ -\dfrac{4(3)}{5} & \leq 0-12\\\\ -\dfrac{12}{5} & \leq -12 \quad \Rightarrow \textsf{Not a solution}\end{aligned}[/tex]
The values of x < 2 are not solutions to the inequality.
--------------------------------------------------------------------------------
Substitute the value of x = 2 into the inequality:
[tex]\begin{aligned}x=0 \implies -\dfrac{4(2+3)}{5} & \leq 4(2)-12\\\\ -\dfrac{4(5)}{5} & \leq 8-12\\\\ -\dfrac{20}{5} & \leq -4\\\\ -4 & \leq -4 \quad \Rightarrow \textsf{Yes, a solution}\end{aligned}[/tex]
The value of x = 2 is a solution to the inequality.
--------------------------------------------------------------------------------
Values of x more than 2
Substitute two values where x > 2 into the inequality:
[tex]\begin{aligned}x=3 \implies -\dfrac{4(3+3)}{5} & \leq 4(3)-12\\\\ -\dfrac{4(6)}{5} & \leq 12-12\\\\ -\dfrac{24}{5} & \leq 0 \quad \Rightarrow \textsf{Yes, a solution}\end{aligned}[/tex]
[tex]\begin{aligned}x=4 \implies -\dfrac{4(4+3)}{5} & \leq 4(4)-12\\\\ -\dfrac{4(7)}{5} & \leq 16-12\\\\ -\dfrac{28}{5} & \leq 4 \quad \Rightarrow \textsf{Yes, a solution}\end{aligned}[/tex]
The values of x > 2 are solutions to the inequality.
--------------------------------------------------------------------------------
Therefore, the solution to the inequality appears to be x ≥ 2.
To check, solve the inequality:
[tex]\begin{aligned} \implies -\dfrac{4(x+3)}{5} &\leq 4x-12\\-4(x+3) &\leq 5(4x-12)\\-4x-12 &\leq 20x-60\\ -24x & \leq-48\\x & \geq 2\end{aligned}[/tex]
When graphing inequalities on a number line:
< or > : open circle.≤ or ≥ : closed circle.< or ≤ : shade to the left of the circle.> or ≥ : shade to the right of the circle.To graph the solution to the inequality on number line, place a closed circle at x = 2 and shade to the right. (See attachment).
Related Questions
When using a counterexample to prove a conditional statement false, which must be true about the counterexample?
There must be infinite counterexamples.
The counterexample must satisfy the hypothesis of the conditional statement.
There must be at least one example under which the conditional statement is true.
The counterexample must satisfy the conclusion of the conditional statement.
Answers
The counterexample must satisfy the hypothesis of the conditional statement which is the correct answer would be option (B).
What is a Counterexample?A counterexample is an example in which the hypothesis is correct but the conclusion is incorrect.
Since A counterexample is used to show that a conditional assertion is untrue.
So, just one counterexample is required to prove a statement untrue.
Also, when employing a counterexample to prove a conditional assertion untrue.
The counterexample must then meet the hypothesis of the conditional statement.
As a result, the correct statement concerning the counterexample is;
The conditional statement's hypothesis must be satisfied by the counterexample.
Hence, the correct answer would be option (B).
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the amount of water a washing machine uses varies directly with the number of loads of laundry washed. if a machine uses 65 gallons of water to wash 5 loads, how much water will be used to was 8 loads?
Answers
Let g represent gallons of water and let L represent loads.
Here, the gallons of water varies directly with the number of loads, thus we have:
g ∝ L
Now introduce a constant k:
g = kL
65 gallons is used to wash 5 loads, thus we have:
65 = k * 5
Let's solve for k:
65 = 5k
Divide both sides by 5:
[tex]\begin{gathered} \frac{65}{5}=\frac{5k}{5} \\ \\ 13=k \end{gathered}[/tex]To find the amount of water that will be used to wash 8 loads, we have:
g = kl
We are to find g, substitute 13 for k and 8 for l:
g = 13 x 8
g = 104
Therefore, to wash 8 loads, 104 gallons of water is needed.
ANSWER:
104
Graph the solution set of the second linear any quality
Answers
Solution
- The inequality is:
[tex]7y\ge6x+21[/tex]- The graph of the inequality is graphed using a graphing calculator as follows:
Mrs. Escalate was riding a bicycle on a bike path. After riding 2/3 of a mile, she discovered that she still needed to travel 3/4 of a mile to reach the end of the path. How long is the bike path?
Answers
Answer:
17/12
1 5/12
Step-by-step explanation:
If we make the fractions have common denominators, this problem is a piece of cake.
First, since the closest multiple of 3 and 4 is 12, put 12 instead of the 3 and 4.
Since 3x4=12, multiply 2x4.
2x4=8.
So the first fraction would be 8/12
Next, since the 4 turned into a 12, multiply 3 by 3.
3x3=9
So the second fraction would be 9/12.
Now, add 9/12 and 8/12 together.
9/12+8/12=
17/12
1 5/12
(d) Find the domain of function R. Choose the correct domain below.
Answers
Answer:
d
Step-by-step explanation:
The number of years must be non-negative.
This eliminates all of the options except for d.
gure 727 particles) are being deflected by yold market ere plete the following: Find the intercepts and domain and perform the symmetry test on each of the following hyperbolas, (c) 25x2 - 4y2 = 100 e) --- + y2 = 1 g) - 9x2 + raph the vertices, foci, endpoints of the conjugate axis, fundamental rectangle, and asymptotes, en draw the hyperbola for each equation in problem 1. is a chord of the partial hyperbola with equation f(x)=b Jax? - G? les for a, b, A (x, y) and B (x, y) from: 16y2 = 144 (a) 9x2 (b) 9x² - y2 = 9 (d) 25x2 - 36y2 = 900 -25x² + 4y2 = 100 (h) x2 + 4y = 16 Find the lenoth ne Dino
Answers
Find the intercepts and domain and perform the symmetry test on each of the following hyperbola
9x² - 16y² = 144
Domain (-inf, -4] and [4, inf)
Symetry around y-axis
There is no y intercepts
X-intercepts at x = -4 and x = 4
Focus at (-4, 0) and (4, 0)
You are an executive with the Varsity Corporation in Atlanta, Georgia. The company president was scheduled to make an important sales presentation tomorrow afternoon in Seattle, Washington, but he has now asked you to take his place.
The trip consists of a 2 1/4 hour flight from Atlanta to Dallas, a 1 1/2 hour layover in Dallas, and then a 3 1/2 hour flight to Portland. There is a 1 3/4 hour layover in Portland and then a 3/4 hour flight to Seattle. Seattle is on Pacific Time, which is 3 hours earlier than Eastern Time in Atlanta.
a) If you depart Atlanta tonight at 9:30 p.m. and all flights are on schedule, what time will you arrive in Seattle?
b) If your return flight is scheduled to leave Seattle at 9:10 p.m. tomorrow night, with the same flight times and layovers in reverse, what time are you scheduled to arrive in Atlanta?
c) If the leg from Dallas back to Atlanta is 2/3 of an hour longer than scheduled due to headwinds, what time will you actually arrive?
Answers
Using operations with mixed numbers and relations between hours and minutes, it is found that:
a) You will arrive in Seattle at 4:15 am.
b) You will arrive in Atlanta at 9:50 a.m.
c) You will arrive in Atlanta at 10:30 a.m.
How to convert a mixed number to decimal?A mixed number is represented as follows:
a b/c.
In which:
a is the integer part of the number.b/c is the fractional part of the number.As a decimal, the number is given as follows:
a + (b/c).
For item a, it is found that the time it takes to arrive in Seattle from Atlanta is given by the addition of these following numbers:
2.25 hours. (Atlanta to Dallas)1.5 hours. (Layover).3.5 hours (Dallas to Portland).1.75 hours (Layover).0.75 hours (Portland to Seattle).Hence the time in hours is:
2.25 + 1.5 + 3.5 + 1.75 + 0.75 = 9.75 hours = 9 hours and 45 minutes.
Seattle is 3 hours behind Atlanta, hence the time you arrive there is:
6:30 pm + 9 hours and 45 minutes = 4:15 am, as:
6:30 pm is the time in Seattle when you depart Atlanta.30 minutes + 45 minutes = 75 minutes = 1 hour and 15 minutes.9 hours and 45 minutes after 6:30 p.m. is of 4:15 a.m.For item b, we have that:
When the plane leaves Seattle, it is 0:10 am in Atlanta, as it is 3 hours ahead.9 hours and 45 minutes of flight, hence you should arrive in Atlanta at 9:50 a.m.For item c, 2/3 of an hour is 40 minutes, 40 minutes after 9:50 am is 10:30 a.m., which is the time you would arrive.
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Find the equation for the line that passes through the points (-2,-6) and (6,5). Give your answer in point-slope form. You do not need to simplify
Answers
The point-slope form of the equation of a line is given by the following expression:
y - y1 = m(x - x1)
Where m is the slope of the line and (x1, y1) is a point where the line passes through.
The slope of the line can be determined with the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where (x1, y1) and (x2, y2) are two points where the line passes through. In this case we are told that the line passes through the points (-2,-6) and (6,5). By replacing the x and y coordinates of these points into the formula of the slope, taking x1 as -2, x2 as 6, y1 as -6 and y2 as 5, we get:
[tex]m=\frac{5-(-6)}{6-(-2)}=\frac{5+6}{6+2}=\frac{11}{8}[/tex]Then, the slope of the line equals 11/8, by replacing 11/8 for m into the slope-point form, we get:
y - y1 = 11/8(x - x1)
By taking one of the points, for example (-2,-6), we replace the x and y-coordinates that appear in the equation of the line, to get:
y - (-6) = 11/8(x - (-2))
y + 6 = 11/8 (x + 2)
Then, the equation of the line in slope-point form is y + 6 = 11/8 (x + 2)
-45g – 9g
Factor the algebraic expression
Answers
Answer:
-54g or -9g(5+1)
Step-by-step explanation:
-45g - 9g
-9g(5+1)
I'm not sure which form you want it in lol. -9g(6)
:]
Answer:
-9g ( 5 + 1 )
Step-by-step explanation:
-45g - 9g
-(45g - 9g)
common factor or less number = 9
-9g (5 + 1)
What in the equation of part (d) makes its graph different?(PART D IS THE LOOP ONE)a.) y = 2x + 7, b.) y = 3/5x + 1, c.) 3x + 2y = 6, and of course d (the last one), y = x (to the power of 2)
Answers
Given:
The equations are:
a.) y = 2x + 7, b.) y = 3/5x + 1, c.) 3x + 2y = 6, d.) y = x^2
To determine what in the equation of part (d) makes its different, we first note that the graph for part (d) is a parabola, which is a curve with an upward opening. In addition, we also note that the power of x in the equation of part (d) is 2, while the other three graphs have a power of 1.
Therefore, the answer is:
The power of x in the equation of part (d) makes its graph different.
∠A=6x−18 ∘ start color #11accd, angle, A, end color #11accd, equals, start color #11accd, 6, x, minus, 18, degrees, end color #11accd \qquad \green{\angle B} = \green{14x +38^\circ}∠B=14x+38 ∘ start color #28ae7b, angle, B, end color #28ae7b, equals, start color #28ae7b, 14, x, plus, 38, degrees, end color #28ae7b Solve for xxx and then find the measure of \blueD{\angle A}∠Astart color #11accd, angle, A, end color #11accd:
Answers
Using the properties of alternate angles, the value of x = 8 and ∠ A = 30
What are Alternate Angles?A transversal that crosses two parallel lines produces alternate exterior angles. They form two pairs (four total angles) of alternate outside angles since they are situated "outside" the two parallel lines but on different sides of the transversal.
For the given question,
∠A=6x−18
∠B=14x+38
As, both parallel lines are intersected by a transversal,
the value of angle ∠A and ∠180 - B is same as they are alternate angles,
⇒ 6x−18 = 180 - 14x - 38
⇒ 6x + 14x = 142 + 18
⇒ 20x = 160
⇒ x = 8
∠A = 6x−18
⇒ ∠ A = 30
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Correct question -
Assume a normal distribution and that the average phone call in a certain town lasted 9 minutes, with a standard deviation of 2 minutes. What percentage of the calls lasted less than 5 minutes?
Answers
Given the sample mean of the distribution as 9 minutes.
Also, the sample deviation as 2 minutes;
Given the z-score formula;
[tex]z=\frac{x-\mu}{\sigma}[/tex]Where;
[tex]x=5,\text{ }\mu=9\text{ and }\sigma=2[/tex][tex]\begin{gathered} z=\frac{5-9}{2} \\ z=-\frac{4}{2} \\ z=-2 \end{gathered}[/tex]Now, from the Z-table;
[tex]P(x<-2)=0.02275[/tex]Thus, the percentage of the calls lasted less than 5 minutes is 2.3%
Julia received an 88, 90, 94, 89 on her first four English quizzes. What must she get on her fifth in order to have a 92 average?
Answers
Answer:
99
Step-by-step explanation:
You can set up a proportion, and solve for the variable (missing grade in this case):
[tex]\frac{88+90+94+89+x}{5} =92[/tex]
Each grade is already in the database, so it can serve as the constant, and five is the denominator because to get a mean average, you must divide all the values by the number of values that exist. So, in this case, it would be 5, 4 including the missing grade, making it 5. Set the equation equal to 92, because that's her desired average, then just solve for x.
Multiply the 5 on both sides.
-> 5 cancels on left, and 5 multiplies with 92 to get 460.
[tex](5)\frac{88+90+94+89+x}{5} = 92(5)[/tex]
Add all constants on the left side of the equation.
-> 88+90+94+89=361
[tex]361+x = 460[/tex]
Subtract that new constant (361) from the 460, and you get x=92.
-> 460-361=99
[tex]x=99[/tex]
Hope this helped. :)
Without using a calculator, order the following numbers from least to greatest.
15
14
√200
Answers
Answer:
14, 200 squared, 15
Step-by-step explanation:
2.
Tom receives $18 from his father in a week. The ratio of the amount of
money he spends to the amount of money he saves in a week is 5 : 4.
(a) What is the difference between the amount of money spent and the
amount of money saved in a week?
B) How much does Tom save in a week?
Answers
Answer:
a= 2 and b= 8
Step-by-step explanation:
a=5/9×18=10
b=4/9×18=8, then a-b=10-8=2
b=4/9×18=8
What is the midpoint of line segment MN with endpoints M(2.7, –1.2) and N(4.1, 7.2)?
(–0.7, –4.2)
(0.75, 5.65)
(3.4, 3)
(3.9, 3.1)
Answers
Answer:
(3.4,3)
Step-by-step explanation:
(2.7+4.1÷2, -1.2+7.2÷2)
=(6.8÷2, 6÷2)
=(3.4,3)
Show all steps. Let a= -1, b = 2, x = -5, y = 4, and w = -10.
Answers
5. Given
[tex]a^2-bw[/tex]You know that:
a=-1
b=2
w=-10
Replace these values into the expression:
[tex](-1)^2-2\cdot(-10)[/tex]Following the order of operations, first, you have to solve the exponent and the multiplication:
[tex]1-(-20)[/tex]Both minus signs form a "double negative" when this happens, the signs cancel each other and turn into a plus sign, so that:
[tex]1+20[/tex]Next, solve the addition
[tex]1+20=21[/tex]The result of this operation is 21.
What are the coordinates of point Q?
O (-3,0)
O (0, -3)
O (0, 3)
O (3, 0)
Answers
What is the domain of the square root function graphed below?
On a coordinate plane, a curve opens down to the right in quadrant 1. The curve starts at (3, 1) and goes through (4, 2) and (7, 3).
Answers
Answer:
3 ≤ x < ∞
Step-by-step explanation:
You want the domain of a square root function shifted right 3 units and up 1 unit. It goes through points (3, 1), (4, 2) and (7, 3).
DomainThe domain of a function is the set of values of the independent variable for which the function is defined. It is the horizontal extent of the graph.
The graph of the given square root function extends to the right from x=3.
The domain is 3 ≤ x < ∞. In interval notation, it is [3, ∞).
A line that describes a proportional relationship between x and y is graphed on a coordinate grid. The line passes through (6, 2). Through what other point must the line pass?
Answers
The other point through which a line that describes a proportional relationship must pass is the point (0, 0)
What is a proportional relationship?A proportional relationship is one in which each the ratio of the x and y–values of each point on the line of the function is a constant.
The given relationship described by the line = A proportional relationship
The given point on the line = (6, 2)
Required; The other point through which the line must pass.
Given that the relationship described by the line, the ratio of all points on the line is a constant and each point (x, y) can be expressed in the form;
y = K•x
Which gives;
[tex] \displaystyle{ K = \frac{y}{x} }[/tex]
Where, K is a constant which is not equal to zero.
From the zero product property, which states that the product of all numbers and zero is also zero, we have;
When x = 0, k × 0 = 0 = y
A point through the line must pass is therefore; (0, 0)
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sent help please urgent
Answers
they’re asking what help
what is the lowest common denominator of 3/4, 1/8, 7/16, and 3/32
Answers
Answer: im pretty sure its 4 from 3/4
Step-by-step explanation:
Solve the equation. Write your answer as a decimal.
−4.8f+6.4=−8.48
Answers
Isolate the variable
Divide by factors that don’t contain the variable
BEST answer gets 69 points
Find the sum of (9.4 x 10^6) and (3.5 x 10^5). Write the final answer in scientific notation.
a. 1.29 x 10^10 b. 12.9 x 10^11 c. 9.75 x 10^5 d. 9.75 x 10^6
Answers
Answer:
D: 9.75 * 10^6
Step-by-step explanation:
You can make it easy for yourself if you write both answers in the same form:
(9.4 * 10^6) = (9.4 *10 * 10^5 = 94*10^5) and (3.5 * 10^5) stays the same.
We can now add those numbers up easier:
(94*10^5) + (3.5*10^5) = ( 94 + 3.5 ) * 10^5 = ( 97.5 * 10^5 )
but this answer is not in the option list. We have to perform the same trick as in the beginning, but than the other way around:
(97.5 * 10^5) = (9.75 * 10) * 10^5 = 9.75 * 10^6,
which is exactly option D
Which number can you add to 14 to get a sum of 0?
Answers
Inverse operation
14 + (-14) =0
Answer:
The number is -14.
Step-by-step explanation:
Up to now, you've been working with whole numbers. These are the positive numbers, those numbers you usually count with your fingers (1, 2, 3, ...), and 0. You've been working with these numbers ever since elementary school, where you would do computation with them, like adding, subtracting, and multiplying them. And, on a number line, they go from left to right, starting at 0.
But what happens when you go to the left on the number line? That is, what's before 0? We actually find negative numbers. The normal numbers that we usually work with, that being the positive numbers, now look like this:
(-1, -2, -3, ...)
A good thing to come from this is that now, we can define an additive inverse. An additive inverse is the negative, or opposite, of a whole number. The sum of a number and its additive inverse is 0.
So, for example, the additive inverse of 1 is -1, and 1 + (-1) = 0.
So clearly, we can see that the additive inverse of 14 is -14, since
14 + (-14) = 0.
(In case you wanted to know, the additive inverse of 0 is 0 because 0 is neither negative nor positive. So, 0 + 0 = 0.)
Lincoln high wants to estimate the number of students who drive to school. Answer the following
Answers
GIVEN:
We are told that a school wants to estimate the number of students who drive to school.
Required:
To determine which survey would best represent the entire student population..
Step-by-sep solution;
Taking a sample of 11th graders would not correctly represent the entire student population. The result from this survey would at best represent the preference of 11th grade students and not other grades. The same thing applies to a survey of the science club. The science club cannot accurately represent all students (including other clubs).
However, a survey of 25 students from the school would best represent the entire student population since there is a probability of every category of student being represented.
Therefore,
25 students are randomly selected from the school; 4 drive to school.
Part (B):
There are 1750 students at Lincoln High. Use the answer above to estimate the number of students who drive to school.
If the sample of 25 students has 4 students who drive to school, then to estimate the entire population based on this;
[tex]\begin{gathered} Sample\text{ }proportion=\frac{4}{25} \\ \\ Population\text{ }proportion=\frac{4}{25}\times1750 \\ \\ Population\text{ }proportion=280 \end{gathered}[/tex]Therefore, we now have;
ANSWER:
[tex]\begin{gathered} (a)\text{ 25 students are randomly selected from the school; 4 drive to school.} \\ \\ (b)\text{ }280\text{ }students \end{gathered}[/tex]The graph below represents the number of siblings each student in a class has.
Answers
Given;
There are given that the graph represents the number of siblings.
Explanation:
According to the given graph:
The frequency of the number of siblings is:
[tex]6,7,4,4,3,2[/tex]Now,
We need to find the value of the range:
So,
From the concept of range:
The value of the difference between the highest data and lowest data will be representing the value of the range:
So,
The highest number is 7 and the lowest data is 2:
So,
[tex]\begin{gathered} Range=7-2 \\ =5 \end{gathered}[/tex]Final answer:
Hence, the value of the range is 5.
if x - 7/10=y and y=2 what is the value of x
Answers
Answer:
x=27/10
Step-by-step explanation:
move all the terms not containing x to the right side of the equation
Han made some hot chocolate by mixing 4 cups of milk with 6 tablespoons of cocoa.
How many tablespoons of cocoa per cup of milk is that?
tbsps
How many cups of milk per tablespoon of cocoa is that?
cups
Answers
In one cup of milk there is 1.5 tablespoons of cocoa and one tablespoon of cocoa is mixed in 0.67 cups of milk.
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the value of single unit according to the needs.
Given is Han who made some hot chocolate by mixing 4 cups of milk with 6 tablespoons of cocoa.
There are 6 tablespoons of cocoa in 4 cups of milk.
Then, in one cup of milk there will be (6/4) tablespoons of cocoa or 1.5 tablespoons of cocoa.
Similarly, 6 tablespoons of cocoa are mixed in 4 cups of milk.
1 tablespoon of cocoa will be mixed in (4/6) cups of milk or 0.67 cups of milk.
So, in one cup of milk there is 1.5 tablespoons of cocoa and one tablespoon of cocoa is mixed in 0.67 cups of milk.
Therefore, in one cup of milk there is 1.5 tablespoons of cocoa and one tablespoon of cocoa is mixed in 0.67 cups of milk.
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a person's blood type is denoted with the letters a, b, and O, and symbols + and - The blood type A+ is read as A positive blood type B- is read as B negative. Use the data to write a ratio for the comparison and three different ways. O+ donors to B+ Donors.the ratio using the word "to" is [] to []
Answers
Answer:
The ratio using the word "to" is;
[tex]100\text{ to 2}9[/tex]Explanation:
Given on the table;
Number of O+ donors = 100
Number of B+ donors = 29
The ratio of the O+ donors to B+ Donors is:
Number of O+ to Number of B+
Which gives;
The ratio using the word "to" is;
[tex]100\text{ to 2}9[/tex]