Solve the inequality
-5x + 3 > (-7x) - 12
We want to move the variables to the left side and the numbers to the right side. The (-7x) can be eliminated from the right side by adding 7x on both sides.
Add 7x to both sides:
-5x + 3 + 7x > -12
We need to move the 3 from the left to the right side. So we subtract 3
Subtract 3 to both sides:
-5x + 7x > -12 - 3
Joining like terms:
2x > -15
Solving:
x > -15/2
The solution is every real number greater than -15/2
In interval notation, it can be written as:
[tex]\mleft(-15/2,+\infty\mright)[/tex]The left parentheses are used because the endpoint is not included in the solution
If the endpoint was included, we'd use a bracket [
The expression 81√ ⋅ 100√ represents the number of feet between home plate and first base. What is the distance, in feet, between home plate and first base?
Using perfect squares to solve the expression √81-√100 the distance between home plate and first base is 1 feet
Which numbers are perfect square?The perfect square is the number which can be written as the square of some integer.
A number x is a perfect square if x=y² for some y. or y =√x
Given:
The number of feet between home plate and first base = |√81-√100|
|x| absolute function is put because number of feet need to be a positive number
81 is a perfect square ∵ 81 = 9×9 = 9²
As 81 = 9²
⇒ √81 = √9² = 9
100 is also a perfect square ∵ 100= 10×10 =10²
As 100=10²
⇒ √100= √10² = 10
The expression √81-√100 = 9-10 = -1
The distance between home plate and first base = Number of feet between home plate and first base = |√81-√100| = |-1| = 1 feet
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The complete question is given below:
The expression √81-√100 represents the number of feet between home plate and first base. What is the distance, in feet, between home plate and first base?
which system of linear equations has the ordered pair (-4,-12)as it's solution?
In order to find which system has the ordered pair (-4, -12) as a solution, let's check this pair in each system.
We can see that the first two options have the function x = (1/3)y and the last two have the function y = (1/3)x.
Looking at the ordered pair, we have that x is 3 times smaller than y, therefore the correct equation is x = (1/3)y.
Then, the second equation has a constant value for the sum "x + y".
Calculating x + y using the coordinates of the ordered pair, we have a value of -16.
Therefore the correct equation is x + y = -16.
So the option that has the correct system is the second one.
chords AB and CD intersect as shown nelow find the length of CD
We are asked to determine the length of CD, to do that we will use the following relationship:
[tex]\begin{gathered} CD=21+x+1 \\ CD=22+x \end{gathered}[/tex]Therefore, we need to determine the value of "x". To do that we will use the intersecting chords theorem, that is:
[tex](21)(x+1)=(9)(3x-9)[/tex]Now we solve for "x" first by applying the distributive law:
[tex]21x+21=27x-81[/tex]Now we will subtract 21 to both sides:
[tex]\begin{gathered} 21x=27x-81-21 \\ 21x=27x-102 \end{gathered}[/tex]Now we will subtract 27x to both sides:
[tex]\begin{gathered} 21x-27x=-102 \\ -6x=-102 \end{gathered}[/tex]Dividing both sides by -6:
[tex]x=-\frac{102}{-6}=17[/tex]Now we replace the value of "x" in the expression for segment CD:
[tex]\begin{gathered} CD=22+17 \\ CD=39 \end{gathered}[/tex]Therefore, the length of CD is 39.
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
2x - 3y = 18
Answer:
y = (2/3)x - 6Step-by-step explanation:
Slope-intercept form is:
y = mx + bConvert the given equation as following:
2x - 3y = 18 Isolate the term with y3y = 2x - 18 Divide all terms by 3y = (2/3)x - 6Jackson is donating some of his old games to the community center. He uses a frequency chart to record the number of pieces in each game.
If 1/8 of the chess pieces are knights, how many knights are there?
Answer:
4 knights
Step-by-step explanation:
32÷8=4
32 chess pieces divided by 8 is. 4 will represent 1/8 of the total of the amount of chess pieces. So, there are 4 chess pieces.
Need ASAP please and thank you! :)
Answer:
B. [tex]\dfrac{x^2+3}{\left(x-1\right)\left(x-3\right)}[/tex]
Step-by-step explanation:
Will provide explanation later since you are in a hurry
1. Find the LCM of the two denominators: x-1 and x -3
This is (x-1)(x-3)
2. Multiply each numerator by the same amount needed to multiply itscorresponding denominator to turn it into the LCM (x−1)(x−3)
[tex]\mathrm{For}\:\dfrac{x-3}{x-1}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:x-3[/tex]
[tex]\dfrac{x-3}{x-1} = \dfrac{\left(x-3\right)\left(x-3\right)}{\left(x-1\right)\left(x-3\right)} = \dfrac{\left(x-3\right)^2}{\left(x-1\right)\left(x-3\right)}[/tex]
[tex]\mathrm{For}\:\dfrac{6}{x-3}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:x-1[/tex]
[tex]\dfrac{6}{x-3} = \dfrac{6\left(x-1\right)}{\left(x-3\right)\left(x-1\right)} = \dfrac{6\left(x-1\right)}{\left(x-1\right)\left(x-3\right)}[/tex]
[tex]2. \mathrm{Simplify\:}\left(x-3\right)^2+6\left(x-1\right)[/tex]
[tex]\left(x-3\right)^2 = x^2 - 6x + 9\\\\\\3. \; \text{Expand }6\left(x-1\right)\;6\left(x-1\right) = 6x-6\\\\[/tex]
4. Since the denominators are the same in both terms, we can add the numerators and use the common denominator as the denominator for the result
Adding numerators derived from steps 2 and 3 above we getAnswer:
While adding two Fractions first we find the LCM of Denominators,
The LCM of x-1 and x-3 is (x-1)(x-3)
now, we perform the calculation as ,
[tex]{\frac{x-3}{x-1}} + {\frac{6}{x-3}}[/tex]
[tex]{\frac{(x-3)²+6(x-1)}{(x-1)(x-3)}}[/tex]
[tex]{\frac{x²+9-6x +6x-6}{(x-1)(x-3)}}[/tex]
[tex]{\frac{x²+3}{(x-1)(x-3)}}[/tex]
Hence option B is the answer
Write the equation of the circle given the following information
Given;
There are given that points are:
[tex](1,13)\text{ and \lparen-3,-9\rparen}[/tex]Explanation:
From the standard form of the circle:
[tex](x-a)^2+(y-b)^2=r^2[/tex]Where
a and b represent the center.
Now,
To establish the equation, we require to know it is center and radius.
Since we are given the endpoints of the diameter
Then,
The center will be at the midpoint and the radius will be the distance from the center to either of the two given points.
Then,
From the formula of midpoint to calculate the midpoint:
[tex](x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Then,
From the given two points:
[tex]\begin{gathered} (x,y)=(\frac{1-3}{2},\frac{13-9}{2}) \\ (x,y)=(-\frac{2}{2},\frac{4}{2}) \\ (x,y)=(-1,2) \end{gathered}[/tex]The midpoint is ( -1, 2).
Now,
We need to find the value of the radius.
So,
To calculate the radius, we need to use the distance formula:
Then,
From the formula of distance, here we will use the points: (-1, 2) and (1, 13)
[tex]\begin{gathered} r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ r=\sqrt{\left(1+1\right)^2+\left(13-2\right)^2} \\ r=\sqrt{4+121} \\ r=\sqrt{125} \end{gathered}[/tex]Now,
We have the value of radius and the point of center.
Then,
Put the value of radius and point of the center into the standard form of the circle:
So,
From the standard form of the circle:
[tex]\begin{gathered} (x-a)^{2}+(y-b)^{2}=r^{2} \\ (x-\left(-1\right))^2+(y-2)^2=\lparen\sqrt{125}^)^2 \\ (x+1)^2+(y-2)^2=125 \end{gathered}[/tex]Final answer:
Hence, the equation of the circle is shown below;
[tex](x+1)^{2}+(y-2)^{2}=125[/tex]What is the value of x?
4x=5x–12
Answer:
x=12
Step-by-step explanation:
I just know
Answer: 12
Step-by-step explanation: The value of x is 12
1. subtract 5 from both sides, 4x-5 and 5x-5
2. combine like terms
3. divided by -1
4. you get 12
Suppose contact lenses cost $300 for a year’s supply or $30 for a month’s supply. Which is less expensive to order per year, paying for 12 months at one time or paying for 1 month at a time?
The cost that is less expensive is paying for 12 months at one time for $300.
How to calculate the value?From the information, contact lenses cost $300 for a year’s supply or $30 for a month’s supply.
In this case, for the $30 for a month’s supply, the amount that will be paid yearly will be:
= $30 × 12
= $360
In this case, the one time payment for $300 is cheaper.
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I tried to do this on my own and I got nine and they said it was incorrect so please help
Answer:
9u
Explanation:
Given the expression:
[tex]3u(3)[/tex]First, replace the parenthesis with a multiplication sign.
[tex]\begin{gathered} =3u\times3 \\ =3\times u\times3 \end{gathered}[/tex]Next, reorder to bring the numbers together.
[tex]\begin{gathered} =3\times3\times u \\ =9u \end{gathered}[/tex]The simplified form of the expression is 9u.
If 12 + _ = 0 + 12, then _ must equal:A: 120B: 12C: 1D: 10E: 0
1) Examining this equality 12 + _ = 0 + 12 we can see that this the 0 is the neutral element then applying the Commutative Property we can state that:
12 +0 = 0+12
2) Because the order of the addends does not alter the sum.
E
Multiply. State any excluded values. Simplify your answer. Type your answer in factored form.
Multiplication:
[tex]\frac{f(x)}{g(x)}\cdot\frac{h(x)}{j(x)}=\frac{f(x)h(x)}{g(x)j(x)}[/tex]For the given functions:
[tex]\begin{gathered} \frac{x}{x-7}\cdot\frac{x-2}{x-3}=\frac{x(x-2)}{(x-7)(x-3)} \\ \end{gathered}[/tex]The expression cannot be simplified and is already written in factored form.
The exclude values are those that make the denominator be equal to zero: 7,3
[tex]\begin{gathered} (x-7)(x-3)=0 \\ \\ x-7=0 \\ z=7 \\ \\ x-3=0 \\ x=3 \end{gathered}[/tex]Which set of ordered pairs (x,y) could represent a linear function?A. {(-7,3), (-2,1), (3,-1), (8,-3)}B. {(-2,8), (-1,4), (1,0), (3,-4)}C. {(-3,-6), (0,-5), (3,-3) (6,-2)}D. {(0,-8), (3,-5), (5,-2), (8,1)}
Answer:
A. {(-7,3), (-2,1), (3,-1), (8,-3)}
Explanation:
A linear function has a constant slope.
To determine the set of ordered pairs (x,y) that could represent a linear function, we find the slope for two pairs of points.
[tex]\text{Slope}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}[/tex]Option A
Using points (-7,3) and (-2,1).
[tex]\text{Slope}=\frac{3-1}{-7-(-2)}=\frac{2}{-7+2}=-\frac{2}{5}[/tex]Using points (-7,3) and (3,-1).
[tex]\text{Slope}=\frac{3-(-1)}{-7-3}=\frac{4}{-10}=-\frac{2}{5}[/tex]We see that the slopes are the same.
Therefore, the set of ordered pairs in Option A represent a linear function.
Identify the values of the variables that complete the table to show the equivalent fractions, decimals, and percents.
1.2 as a fraction is computed as follows:
[tex]1.2=1.2\cdot\frac{10}{10}=\frac{1.2\cdot10}{10}=\frac{12}{10}=\frac{6}{5}=a[/tex]Computing 1 divided by 9, we get:
[tex]\frac{1}{9}=0.11111\ldots=b[/tex]To convert 5/3 to percent, we have to multiply it by 100, as follows:
[tex]\frac{5}{3}\cdot100=\frac{500}{3}=166\frac{2}{3}\text{ \% = c}[/tex]Name three points in the diagram that are not collinear.
Select all that apply.
A. F, N, R
B. F, N, C
C. F, R, V
D. F, C, V
E. F, N, V
F. C, F, R
Answer: B, D, and F
Step-by-step explanation:
When points are collinear, it means they are all on a single line.
View the attachments for all my work. I can only add up to five, but answer option E is similar to A and C.
Which of the following symbol will make a true sentence when inserted in the blank?
5/7___0.6
a. <
b. >
C. =
Answer:
b: >
Step-by-step explanation:
We know that 4/6 = 2/3 = 0.6667
This is bigger than 0.6.
Since 5/7 > 4/6, we directly see that 5/7 > 0.6
In fact, 5/7 is approximately 0.714 which tells us that we have found the correct answer
Added: A better method might be: 5/7 = 10*5 / (7 * 10) = 50/70,
where 0.6 = 6/10 = 6*7/(10*7) = 42 / 70.
Since 50/70 > 42/70, it follows that 5/7 > 0.6 so B is the right answer
What is the equation of the following line written in slope-intercept form.
y = 2 /3 x + 9 /2
y = 3 /2 x - 9 / 2
y = - 3 /2 x - 3 / 2
Answer:
y = -3/2x - 9/2
Step-by-step explanation:
The general form of a line in slope-intecept form is given by:
y = mx + c
where: m = slope, c = intercept.
from the graph, slope is calculated as:
m = (-3 - 0)/(-1 -(-3))
m = -3/2
To obtain c, choose any value of x, and corresponding y value.
we choose: (-3, 0)
using y = mx + c
0 = -3/2(-3) + c
simplify
c = -9/2
Therefore, y = -3/2x - 9/2
Need help with #9 please it’s due today
9. The equation of the line parallel to y = 2x+4 and passing through the point (-4, -1) is y = 2 x +7
Given:
line = y = 2x+4
point = (x, y)= (-4,-1)
The given equation is of the form,
y = mx+ c ---- (1)
slope= m = 2
The line parallel to this line will have the same slope,
m = 2
The new line is of the form,
y = 2 x+ c ----(2)
Substituting the given point (-4, -1) in (2)
- 1= 2(-4) + c
c = 7
Substituting c in (2)
y = 2 x +7 is the parallel line equation.
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Given the graph of f (x), determine the domain of f –1(x).
Radical function f of x that increases from the point negative 3 comma negative 2 and passes through the points 1 comma 0 and 6 comma 1
The domain of the inverse function f-1(x) is [-2, oo)
How to determine the representation of the domain of the inverse function ?The graph represents the given parameter
On the graph, we can see that:
The y values starts from y = -2 and it extends upwards to the positive axis
This means that the range of the function is
Range = [-2, oo)
When the function is inverted, the range becomes the domain
This implies that
Domain of the inverse function = Range of the function = [-2, oo)
Hence, the inverse function has a domain of [-2, oo)
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hat is the value of ?The solution is
l5l - l-5l - (-5)
the absolute value of l5l and l-5l is 5
5 - 5 - (-5)
Subtracting a negative number is the same as adding that number
5 - 5 + 5
5
Answer = 5
What’s the Missing angle
Answer: 60
Step-by-step explanation: All angles are equal in a triangle if one angle is 60 degrees because 60x3=180
Which rectangles have an area of 36 square feet? Choose all that are correct. 10 ft 8 ft 9 ft 4 ft 6 ft 6 ft 11 ft 7 ft 12 ft 3 ft
The area of a rectangle is given by the formula below.
[tex]A=bh[/tex]Then, from top to bottom, the areas of the rectangles are
[tex]\begin{gathered} A_1=10\cdot8=80 \\ A_2=9\cdot4=36 \\ A_3=6\cdot6=36 \\ A_4=7\cdot11=77 \\ A_5=3\cdot12=36_{} \end{gathered}[/tex]Therefore, the answers are (top to bottom) the second, third, and fifth rectangle.
In a newspaper, it was reported that yearly robberies in Springfield were down 40% to 126 in 2013 from 2012. How many robberies were there in Springfield in 2012?
Answer:
210
Step-by-step explanation:
210-40% is 126
Jerry, Jack and Sophie are all hoping to save money! Jerry thinks saving money in a shoe box in his closet every month is a good idea. He decides to start with $125, and then save $50 each month. Jack was given $3520 from his Grandma, and decides to put the money into an account that has a 6.5% interest rate that is compounded annually. Sophie has earned $3500 working at the movie theater decides to put her money in the bank in an account that has a 7.05% interest rate that is compounded continuously Part 3: Describe the type of equation that models Sophie’s situation. Create that equation of Sophie’s situation. Using the equation you created, how much money will be in Sophie’s account after 3 years? 10 years?
Sophie
- The formula for continuously compounded interest is given by:
[tex]A=Pe^{rt}[/tex]Where:
A is the amount after t years.
P is the principal.
r is the annual interest rate.
Therefore the equation is:
P = $3500
r = 7.05% = 0.0705
[tex]A=3500e^{0.0705t}[/tex]- Money in Sophie’s account after 3 years:
t = 3
[tex]A=3500e^{0.0705(3)}=3500e^{0.2115}=4324.35[/tex]This is $4324.35
- Money in Sophie’s account after 10 years:
t = 10
[tex]A=3500e^{0.0705(10)}=3500e^{0.705}=7083.46[/tex]This is $7083.46
Answer
Describe the type of equation that models Sophie’s situation: exponential growth model.
Create that equation of Sophie’s situation:
[tex]A=3500e^{0.0705t}[/tex]Money will be in Sophie’s account after 3 years: $4324.35
Money will be in Sophie´s account after 10 years: $7083.46
Refer to the photo that I have posted to much to type
The total cost of the chocolate cookies is $300
The markup cost on cookies is $135
The total selling price of cookies is $435
The percentage of defective cookies is 15%.
The number of sellable cookies after removing the defective cookie is 170
The price of each cookie is $2.56
What is the total cost?The total cost of the chocolate cookies is the product of the cost per cookie and the number of cookies produced.
Total cost = cost per cookie x total cookies produced
$1.50 x 200 = $300
The markup cost on cookies can be determined by multiplying the percentage markup by the total cost of cookies
Markup = percentage markup x total cost of cookies
45% x $300
0.45 x $300 = $135
The total selling price of cookies is the sum of the markup on cost and the total cost of producing the cookies
Total selling price = $135 + $300 = $435
Number of sellable cookies after removing the defective cookies = (1 - percentage of defective cookies) x number of cookies produced
200 x (1 - 0.15)
200 x 0.85 = 170
Price of each cookie = total cost after markup / total number of sellable cookies
435 / 170 = $2.56
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Using a trigonometric ratio to find an angle measure in a right
ANSWER :
x = 33.6 degrees
EXPLANATION :
Recall that the cosine function is :
[tex]\cos\theta=\frac{\text{ adjacent}}{\text{ hypotenuse}}[/tex]From the problem, the adjacent to the angle x is 15 and the hypotenuse is 18.
Using the formula above :
[tex]\begin{gathered} \cos x=\frac{15}{18} \\ \\ \text{ take the arccos :} \\ x=\arccos(\frac{15}{18}) \\ \\ x=33.56\sim33.6 \end{gathered}[/tex]Determine the x-intercepts of the graph represented by the following quadratic function. Recall that y = f(x).f(x) = x2 − 4x − 21(x, y) = (smaller x-value)(x,y)= (larger x-value)
For this problem, we are given the expression for a quadratic equation and we need to determine the x-intercepts of its graph.
The x-intercepts coincide with the zeros of the equation, which are obtained when f(x) = 0. So we have:
[tex]x^2-4x-21=0[/tex]We need to determine the roots of the equation above.
[tex]\begin{gathered} x_{1,2}=\frac{-(-4)\pm\sqrt{(-4)^2-4\cdot1\cdot(-21)}}{2\cdot1}\\ \\ x_{1,2}=\frac{4\pm\sqrt{16+84}}{2}=\frac{4\pm\sqrt{100}}{2}=\frac{4\pm10}{2}\\ \\ x_1=\frac{4+10}{2}=\frac{14}{2}=7\\ \\ x_2=\frac{4-10}{2}=\frac{-6}{2}=-3 \end{gathered}[/tex]The intercepts are: (-3,0) and (7,0).
Estimate by using the table of percent-fraction equivalents: 34% of 18 = _____table PercentFraction25% 1/433-1/3%1/350% 1/266-2/3%2/375% 3/4
34 % of 18
Using the table
the 33% of any value is 1/3 of the value, as follows
[tex]18*\frac{1}{3}=6[/tex]then 33% of 18 is 6
then
34% of 18 is equivalent to 6
sales tax is caculated as a percantage of the sales price . if sales tax 5% what is the sales tax on clothing that cost 170
triangle p undergoes a sequence of tranformations resultig in triangle Q which sequence of transformations could be used to show that triangle Q is similar but not congruent to triangle p
The most appropriate choice for Similar and congruent triangles will be given by
Third Option dilation is correct.
What are Similar and congruent triangles?
Two triangles are similar if their angles are equal but their sides are proportional
The different axioms of similarity are SAS, SSS, AA
Two triangles are congruent if their sides and angles are both equal
The different axioms of congruency are ASA, SAS, AAS, RHS, SSS
Here, A stands for angle, S stands for side R stands for right angle, H stands for hypotenuse.
Here,
Two Similar triangle means corrosponding sides are proportional and two congruent triangle means corrosponding sides and angles and angles are same
The triangle after rotation and reflection do not change any length of side or angle. So the triangles will be same after reflection or rotation. So congruency will not be disturbed here.
Now, in case of dilation, length of each side will change but in same proportion.
So dilation can make two similar triangles but not congruent triangles
So third option is correct.
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Complete Question
Triangle P undergoes a sequence of tranformations resultig in triangle Q which sequence of transformations could be used to show that triangle Q is similar but not congruent to triangle P
a) Rotation
b) Reflection
c) Dilation
d) Any of these could be the transformation