The correct representation of the inequality is x > 5 or –6x + 15 < 10 – 5x.
How to solve inequality?The inequality can be best represented as follows;
–3(2x – 5) < 5(2 – x)
An inequality is a mathematical expression that has the signs <, >, ≤ and ≥.
Therefore,
–3(2x – 5) < 5(2 – x)
open the brackets
- 6x + 15 < 10 - 5x
Lets solve further by subtracting 15 from both sides of the inequality.
- 6x + 15 < 10 - 5x
- 6x + 15 - 15 < 10 - 15 - 5x
- 6x < - 5 - 5x
add 5x to both sides of the inequality.
- 6x < - 5 - 5x
- 6x + 5x < - 5 - 5x + 5x
-x < - 5
divide both sides by -1
Therefore,
x > 5
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The solution of the given inequality is x > 5 which is the correct representation of x > 5 or –6x + 15 < 10 – 5x.
The inequality is given in the question as
–3(2x – 5) < 5(2 – x)
Open the parenthesis and apply the distributive property of multiplication,
⇒ - 6x + 15 < 10 - 5x
Subtract 15 from both sides of the above inequality,
⇒ - 6x + 15 - 15 < 10 - 15 - 5x
⇒ - 6x < - 5 - 5x
Add 5x to both sides of the inequality,
⇒ - 6x + 5x < - 5 - 5x + 5x
⇒ -x < - 5
Multiply both sides by -1 and flip the sign of inequality
⇒ x > 5
Therefore, the solution of the given inequality is x > 5.
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Given m ||n, find the value of x and y.
Answer: The correct answer is x=18 and y=59
Step-by-step explanation:
Opposite angles are congruent:
(6x+13) = (7x-5)
Solve for x:
6x+13−7x=7x−5−7x
−x+13−13=−5−13
−x=−18
x=18
Plug x value in for y:
Y=180-(7x-5)
Y=180-(126-5)
Y=180-121
Y=59
Given f(x)=x+2 and g(x)=4-x^2 find the following (g o f)(x)
Given functions are
[tex]\begin{gathered} f(x)=x+2 \\ g(x)=4-x^2 \end{gathered}[/tex]Then,
[tex]\begin{gathered} (g\circ f)(x)=g(f(x)) \\ =g(x+2) \\ =4-(x+2)^2 \\ =4-(x^2+4x+4) \\ =4-x^2-4x-4 \\ =-(x^2+4x) \end{gathered}[/tex]Thus,
[tex](g\circ f)(x)=-(x^2+4x)[/tex]Please help me, it is sooooo important
Answer:
1: figures a and b
2: figures a and b
3: figure a
Step-by-step explanation:
2 & 3:
all squares are rectangles, but not all rectangles are squares
Hope this helps!
Solve for X round to nearest tenth
Answer:
the answer for this question is 35.0
A class measured the radius r, circumference C, and area A of various circular objects. The results are recorded in thistable. b. Does the equation A=1/2*r* C describe the relationships in the table? Explain your reasoning.YesNor (cm) C (cm) A (cm)42550
Equation:
A =1/2 * r * C
Replace with the values from the table and check the equation:
First row:
50 = 1/2*4*25
50= 50 TRUE
Second row:
78.5= 1/2*5*31.5
78.5= 78.75 FALSE
Since one equality is false, the equation Doesn't describe the relationship-
Answer : NO
What is the answer to this ive been doing this all day and still cant figure it out
The proof explained below shows that the triangles are congruent by the AAS congruence theorem.
What is the AAS Congruence Theorem?The AAS congruence theorem states that two triangles can be proven to be congruent to each other if the two angles and a non-included side in one triangle is equal or congruent to two corresponding angles and a corresponding non-included sides in the other triangle.
This implies that, once the criteria needed prove that two triangles are congruent by the AAS congruence theorem are two pairs of congruent angles and a pair of non-included congruent sides.
Using the AAS congruence theorem, the two-column proof that shows each statement and the reason are explained below.
Statement Reason
1. CA bisects angle BAD 1. Given
angle B ≅ angle D
2. Angle CAB ≅ angle CAD 2. Congruent angles formed from bisection
3. Side AC ≅ side CA 3. Reflexive property
4. Triangle ABC ≅ triangle ADC 4. AAS congruence theorem
Thus, the above reasons and statements shows that the two triangles, triangle ABC and triangle ADC, are congruent by the AAS congruence theorem.
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suppose 52% of the students in a university are baseball players. if a sample of 436 students is selected, what is the probability that the sample proportion of baseball players will be greater than 45%? round your answer to four decimal places.
Probability of proportion will be greater than 3.18
What is meant by Probability of Proportion?Probability of Proportion: Probability represents the chances of some event happening. It is theoretical. Proportion summarizes how frequently some event actually happened
Population Proportion, p=0.52
sample proportion p'=0.45
sample size be n =436
probability of proportion will be greater than 52%
[tex]p(p' > 0.45)=p(p'-p\sqrt{p(1-p)/n} )[/tex]
[tex]=-p(z > (0.45-0.52)/\sqrt{0.52((1-0.52)/436}[/tex]
=P(z>-3.18)
probability of proportion will be greater than 3.18
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Which IRS form is provided at the end of the year by employers, so employees can use it to file taxes?
The IRS form is provided at the end of the year by employers, so employees can use it to file taxes is Form W-2.
What is Form W-2?Form W-2 can be described as the form that is been offered from the Internal Revenue Service which can be considered as the (IRS) tax form .
It should be noted that this form is been used in the United States so that the wages that is been paid to employees as well as their taxes can be reported. withheld from them
It should be noted that the form is been provided when the year is coming to an end by employers.
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which pair of equations is a set of parallel lines ? a. y = x + 2 and y = 2 b. x = 2 and y = 4
Neither of the pairs of linear equations has the same slope in both lines, so we don't have parallel lines.
Which pair of equations is a set of parallel lines?A general linear equation is of the form:
y = m*x + b
Where m is the slope and b is the y-intercept.
Two linear equations are parallel only if both lines have the same slope and a different y-intercept.
In this case, the lines given are:
y = x + 2 and y = 2.
x = 2 and y = 4
Neither of these are particularly parallel lines (because in both pairs we have different slopes), so we conclude that there is no correct option.
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(10-x)+(12-x) HELPPPPPPPPPPPPPPPPPP
Answer:
x=-11
Step-by-step explanation:
Steps are in the attachment, but I couldn't include the last step.
The last step is to divide by -2 on both sides.
The final answer then will be x=-11
y=3/5x+3 graph the line
We want to graph the line:
[tex]y=\frac{3}{5}x+3[/tex]For doing so, we will choose two different x-values, and we will find its correspondent y-values. This gives us two different points, and when we trace the line that passes through those points, we will have the line we wanted.
In this exercise, we will choose x=0, and x=5.
For x = 0
[tex]y=\frac{3}{5}(0)+3=0+3=3[/tex]This gives us the point (0,3).
For x = 5
[tex]y=\frac{3}{5}(5)+3=\frac{15}{5}+3=3+3=6[/tex]This gives us the second point: (5,6).
Now, graphing the points on a cartesian plane, and drawing the line between them, we obtain:
n is an integer. What are the possible values of n? A -2, -1, 0, 1, 2, 3, 4, 5, 6 B BUDE -2 < n ≤ 6 C -1, 1, 2, 3, 4, 5, 6 -2, -1, 0, 1, 2, 3, 4, 5 -2, -1, 0, 1, 2, 3, 4, 5, 6, 7 E -1, 0, 1, 2, 3, 4, 5, 6
Answer: Choice E
Explanation:
The given inequality means n is between -2 and 6. We exclude -2 itself, but include 6.
The set of integer values is -1, 0, 1, 2, ..., all the way up to 6.
[tex]x^{2} + 2x _5=0[/tex]
Step-by-step explanation:
Substitute the values
a
=
1
,
b
=
−
2
, and
c
=
−
5
into the quadratic formula and solve for
x
.
2
±
√
(
−
2
)
2
−
4
⋅
(
1
⋅
−
5
)
2
⋅
1
Simplify.
x
=
1
±
√
6
Simplify the expression to solve for the
+
portion of the
±
.
x
=
1
+
√
6
Simplify the expression to solve for the
−
portion of the
±
.
1. What is the value of 18 + (-7) – (-5)
Answer:
16
Step-by-step explanation:
Two negatives make a positive:
18-7+5
Solve the problem left to right:
18-7=11
11+5=16
-3/2 = -2/3w - 4/5 solve for w and simplify your answer as much as possible
Hello!
Here are all three solutions to the given equation.
Exact Form:
[tex]w=\frac{21}{20}[/tex]
Decimal Form:
[tex]w=1.05[/tex]
Mixed Number Form:
[tex]w=1\frac{1}{20}[/tex]
Hope this helps!
Alexa buys an oil painting online for $941.20. If shipping and handling are an additional 20% of the price, how much shipping and handling will Alexa pay?
What's a corner of a square? Two lines where they meet
Answer: A square is a shape with four equal-length sides and four corners that are all right angles.
2
Select the correct answer.
Each statement describes a transformation of the graph of y = x. Which statement correctly describes the graph of y = x − 8?
A.
It is the graph of y = x where the slope is decreased by 8.
B.
It is the graph of y = x translated 8 units up.
C.
It is the graph of y = x translated 8 units to the left.
D.
It is the graph of y = x translated 8 units down.
Answer:
the answer of a question is option A
10 miles per hour equal feet per second
Let's recalll that:
• 1 mile per hour = 1.46667 feet per second
Therefore:
• 10 miles per hour = 1.46667 * 10 feet per second
,• 10 miles per hour = 14.6667 feet per second, Khalil!
If y= 4 1/4 when x= 3/4, find y when x= 4 1/2
when y = 17/4, x= 3/4
then assume y varies directly as x
then y =kx
k = y/x
k= 17/4× 4/3
k= 17/3
when x= 3/4, y = 27/34
What is variation?A variation is a relation between a set of values of one component and a set of values of other component.
Direct variation is a type of variation in which two variables go line in line with their values
y= kx where k is the proportionality constant
k = 17/3 when y = 17/4 and x= 3/4
using thesame value of k in the expression k=y/x
and x = 3/4, then
y= 27/34
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What is DA equal to? Brainiest if correct and please show your answer.
Answer:
DA is equal to 25 or BAStep-by-step explanation:
ABC
ADC
Since we know that line CA is equal to line CA because of reflexive propertyAngle BAC and DAC are equal because of definition of an angle bisectorAngle ABC and ADC are equal because of definition of an angle bisectorThis will give us ASA, proving to us that all sides and angles are congruent (this was already given to us)So, if BA is 25, and we know that BA is congruent to DA, this tells us that DA is 25Marques works in a department store selling clothing. He makes a guaranteed salary of $200 per week, but is paid a commision on top of his base salary equal to 10% of his total sales for the week. How much would Marques make in a week in which he made $750 in sales? How much would Marques make in a week if he made x dollars in sales?
The most appropriate choice for percentage will be given by -
Total salary of Marques in a week = $825
If Marques makes $x in sales, his total salary in a week = $([tex]750 + \frac{x}{10}[/tex])
What is Percentage?
Suppose there is a number and that number has to be expressed as a fraction of 100. The fraction is called percentage. For example 2% means [tex]\frac{2}{100}[/tex]
Here,
Guarantee salary of Marques = $200
Sales made by Marques in a week= $750
Percentage commission on total sales = 10 %
Commission received by Marques = [tex]\frac{10}{100} \times 750\\[/tex]
= $75
Total salary of Marques in a week = $(750 + 75)
= $825
If Marques makes $x in sales, his total salary in a week = $([tex]750 + \frac{10}{100}\times x[/tex])
= $([tex]750[/tex] + [tex]\frac{x}{10}[/tex])
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what is the first step that contains an error
7+8x=0
first step -Subtract 7 from both sides.
7+8x-7=0-7
Step 2
8x=-7
Step 3
Divide both side by 8
[tex]\frac{8x}{8}=\frac{-7}{8}[/tex]Instead of dividing the right hand side of equation in step 2 by 8, the right hand side is multiplied by 8 in step 3.
So, the error is in step 3.
Miguel is going to see a movie and is taking his 5 kids. Each movie
ticket costs $12 and there are an assortment of snacks available to
purchase for $5 each. How much total money would Miguel have to
pay for his family if he were to buy 5 snacks for everybody to share?
How much would Miguel have to pay if he bought a snacks for
everybody to share?
Total cost with 5 snacks:
Total cost with a snacks:
a report on high school graduation stated that 85 percent of high school students graduate. suppose 3 high school students are randomly selected from different schools. what is the probability that none will graduate?
The probability that exactly none will graduate is [tex]0.003375[/tex].
What is probability?
Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes.
Step-by-step explanation:
Let [tex]X[/tex] be the random variable for the number of students who graduate.
Binomial distribution theorem tells that, [tex]P(X=x)=C(n , x)p^xq^{n-x}[/tex].
Here [tex]p=[/tex]probability of success on a single trial, [tex]q=[/tex]probability of failure on a single trial, [tex]n=[/tex] number of trials.
Given that [tex]p=0.85, q=1-p=1-0.85=0.15[/tex] and [tex]n=3.[/tex]
[tex]P(X=x)=C(3 , x)0.85^x0.15^{3-x}[/tex]
When [tex]3[/tex] students are randomly selected the probability that exactly none will graduate is given by,
[tex]P(X=0)=C(3 , 0)0.85^00.15^{3-0}[/tex]
[tex]P(X=0)=\frac{3!}{0!(3-0)!} 0.15^{3}[/tex]
[tex]P(X=0)=0.15^{3}[/tex]
[tex]P(X=0)=0.003375[/tex]
Hence the probability that exactly none will graduate is [tex]0.003375[/tex].
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high school seniors in a small town are asked a series of questions to measure the frequency of their drinking and driving. the students give consistent answers to the series of questions, but police records indicate that drinking and driving is much more common than indicated by the students' responses. this suggests that the measure of frequency of drinking and driving is:
When a study's findings are highly valid, it means that they accurately reflect the genuine features, traits, and variations in the physical or social reality. The measure of frequency of drinking and driving is: reliable but not valid.
What are the measure of frequency of drinking and driving?This option contends that although the survey's measure was not valid, it was dependable. This happens when research is constructed in a consistent but ineffective manner. In this instance, a sample of young people from a small town was taken into account; however, despite its consistency and reliability, it does not accurately reflect the findings of data from police records.
How well a method measures what it is supposed to measure is known as its validity. When a study's findings exists highly valid, it indicates that they accurately reflect the genuine features, traits, and variations in the physical or social reality. High dependability exists one sign of a valid measurement.
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the length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of 8 cm/s. when the length is 7 cm and the width is 4 cm, how fast is the area of the rectangle increasing (in cm2/s)?
The rate at which the area is increasing is 95cm/sec² .
Let us take the variable a to be the length of the rectangle and take the variable to b be the width of the rectangle.
We know that the area of the rectangle is given by A=a × b
Now differentiating with respect to t we get :
[tex]\frac{dA}{dt} = w\times\frac{da}{dt} +l\times\frac{db}{dt}[/tex]
Substituting the values we get that the rate of increase in the area is :
Rate of increase = (32 + 63) cm/sec² = 95 cm/sec²
A constant function is also regarded as linear in this sense because it is a polynomial of degree zero, or the zero polynomial.
A line segment represents the graph of a single variable.In this context, a function that is also a linearly map may be referred to as a homogeneous linear function or a linear form (the other meaning). In the context of linear algebra, the scalar-valued affine mappings are functions of degree 0 or 1.To learn more about area visit:
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Using the formula °F = 1.8°C +32°, find the temperature in
Degrees Celsius of an oven that is 500°F.
Using the formula °F = 1.8°C +32°, The temperature in Degrees Celsius of an oven that is 500°F is 260°C.
What is Fahrenheit?For everyday purposes, Fahrenheit is used in the United States, its territories, and related states (all of which are covered by the U.S. National Weather Service), as well as in Liberia, the Cayman Islands, and other places. For instance, temperatures for freezing, cooking, and other conditions are typically given in degrees Fahrenheit in the United States.
What is Celsius?On the Celsius scale, one of the two temperature scales used in the International System of Units along with the Kelvin scale, the unit of temperature is the degree Celsius. The term "degree Celsius" can be used to describe either a specific temperature on the Celsius scale or a measurement of the difference between two temperatures.
Here,
°F=1.8°C+32°
500°F=1.8°C+32°
1.8°C=468°F
°C=468/1.8
°C=260°C
The temperature in Degrees Celsius of an oven that is 500°F is 260°C by using the formula °F = 1.8°C +32°.
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2. How much heat in kilojoules has to be removed from 225g of water to lower its temperature from 25.0oC to 10.0oC?
Answer:
-14.1 kJ
Step-by-step explanation:
We need the specific heat of water, which is 4.184 J/g-K. It means that 4.184 Joules of energy will raise 1 gram of water by 1 degree Kelvin. It also means that removing 4.184 Joules of energy will lower the temperature of 1 gram of water by 1 degree Kelvin.
We want to lower the temperature by 15 degrees C (-15C). That is also -15K. We have 225 grams of water.
This can be used in the equation q = mc(T2 - T1),
where q is the heat, or energy, m is the mass, c is the specific heat, and (T2-T1) is the temperature change, in Kelvin.
q = mc(T2 - T1)
q = (225g)(4.184 J/g-K)(10K - 25K)
q = (225g)(4.184 J/g-K)(-15K)
q = -14121 J or -14.1 kJ
It is negative because heat is leaving the system.
What is the value of x?
Answer:
5
Step-by-step explanation: