Answer:
5≤u
Step-by-step explanation:
Put the words and numbers into an equation:
-5u+27≤2
Put all like terms on one side:
27-2≤5u ---> Do you see what I did there? Now you don't have to work with negatives. :)
Simplify:
25≤5u
Solve:
5≤u
:)
Draw an angle for each measurement
in this way ,u can do other as well with the help of protractor...
Change to slope-intercept form. Then find the y-intercept, first point, and second point.
-x+3y>6
(choices in photo)
Answer:
1) [tex]y> \frac{x}{3}+2[/tex] 2) (0,2) 3) The first and second Points must have x coordinate <-6, or y-coordinate y >2 e.g. (-7,2), (-6,3)
Step-by-step explanation:
1) To Rewrite it as Slope-intercept form, is to isolate the y on the left side and on the right side the rest of the inequality.
[tex]-x+3y>6\Rightarrow 3y>x+6 \Rightarrow y> \frac{x+6}{3}\Rightarrow y> \frac{x}{3}+2[/tex]
2) Since this is a linear inequality the y intercept is given by "b" parameter.[tex]y> mx+b \Rightarrow y> \frac{x}{3}+2 \Rightarrow b=2[/tex]
So the y-intercept is y > 2, coordinate point (0,2). In the graph, we have a dashed line over 2.
3) Since there no choices, the points that satisfy this inequality lie within the green area. We know that the points for this inequality must satisfy x < -6 or y> 2:
Testing for (-7,2) for x<-6 ⇒-7 <-6
[tex]-x+3*y>6\\-(-7)+3*2>6\\7+6>6\\13>6\:\\True\\[/tex]
Testing for (-6,3) for y>2 ⇒3>2
[tex]-x+3*y>6\\-(-6)+3*3>6\\6+9>6\\15>6\:True\\[/tex]
The sales tax in your city is 8.8%, point, 8, percent, and an item costs $63$, before tax.
How much tax would you pay on that item?
Round to the nearest hundredth or cent.
You would pay $5.54 on that item.
Step-by-step explanation:
Given,
Cost of item = $63
Sales tax rate = 8.8%
Amount of sales tax = 8.8% of cost of item
Amount of sales tax = [tex]\frac{8.8}{100}*63[/tex]
Amount of sales tax = [tex]\frac{554.4}{100}[/tex]
Amount of sales tax = $5.54
You would pay $5.54 on that item.
Keywords: percentage, division
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Given: ΔABC is a right triangle. AC = 20 BC = 5 Determine the length of the missing side of ΔABC. When applicable, simplify radicals and show all of your work.
Answer:
[tex]AB=5\sqrt{15}\ units[/tex]
Step-by-step explanation:
we know that
In the right triangle ABC
we have
[tex]AC=20\ units[/tex] ----> is the hypotenuse
[tex]BC=5\ units[/tex] ----> is a leg
[tex]AB=?\ units[/tex] ----> is a leg
see the attached figure to better understand the problem
Applying the Pythagorean Theorem
[tex]AC^2=AB^2+BC^2[/tex]
substitute the given values
[tex]20^2=AB^2+5^2[/tex]
solve for AB
[tex]AB^2=20^2-5^2[/tex]
[tex]AB^2=375[/tex]
[tex]AB=\sqrt{375}\ units[/tex]
simplify
we know that
[tex]375=(25)(15)=5^2(15)[/tex]
substitute
[tex]AB=\sqrt{5^2(15)}\ units[/tex]
[tex]AB=5\sqrt{15}\ units[/tex]
MR Arsalan bought a plot of land for rs 108 000 and sold it for a profit of 20% at what price did he sold at
Answer:
The plot of land was sold for rs 129,600
Step-by-step explanation:
The cost of the plot of land = rs 108,000
Profit calculation ( 20% x 108,000) = rs 21,600
Price land was sold = (108,000 + 21,600) = 129,600
The cost y (in dollars) for x ounces of peanuts is
represented by the equation y = 0.23x. The cost y
(in dollars) for x ounces of pecans is represented by
the equation y = 0.45x. Which statement is true?
Select all that apply.
A The cost for peanuts is $0.22 per ounce less than
the cost for pecans.
B The cost for peanuts is greater than the cost
for pecans.
C The cost for 8 ounces of peanuts is $3.60.
D The cost for 8 ounces of pecans is $3.60.
Answer:
Options A and D are correct.
Step-by-step explanation:
The cost y (in dollars) for x ounces of peanuts is represented by the equation
[tex]y=0.23x[/tex] .... (1)
It means the cost of each ounce of peanuts is $0.23.
The cost y (in dollars) for x ounces of pecans is represented by the equation
[tex]y=0.45x[/tex] .... (2)
It means the cost of each ounce of pecans is $0.45.
$0.45 > $0.23
It means the cost for pecans is greater than the cost of peanuts. Option B is incorrect.
[tex]\$0.45-\ $0.23=\$0.22[/tex]
The cost for peanuts is $0.22 per ounce less than the cost for pecans. Option A is correct.
Substitute x=8 in equation (1).
[tex]y=0.23(8)=1.84[/tex]
The cost for 8 ounces of peanuts is $1.84. Option C is incorrect.
Substitute x=8 in equation (2).
[tex]y=0.45(8)=3.6[/tex]
he cost for 8 ounces of pecans is $3.60.. Option D is correct.
What is the solution of square 2x+4=16?
A)x=6
B)x=72
C)x=126
D)no solution
Answer:
Its 126 i think
Step-by-step explanation:
Answer:
C) x=126
Step-by-step explanation:
The top band in the state charges C(x)=55x+15,000, where x is the total number of attendees at the concert. The venue charges $70 per ticket. After how many people buy tickets does the venue break even, and what is the value of the total tickets sold at that point?
The venue will break even after selling 1000 tickets.
The value will be $70,000 at that point.
Step-by-step explanation:
Given,
Charges of band;
C(x) = 55x+15000
Per ticket charges by Venue = $70
V(x) = 70x
For breaking even,
C(x) = V(x)
[tex]55x+15000=70x\\15000=70x-55x\\15000=15x\\15x=15000[/tex]
Dividing both sides by 15
[tex]\frac{15x}{15}=\frac{15000}{15}\\x=1000[/tex]
The venue will break even after selling 1000 tickets.
Putting 1000 in V(x)
[tex]V(1000)=70(1000)\\V(1000)=70000[/tex]
The value will be $70,000 at that point.
Keywords: function, multiplication
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A total of $11,000 is invested in two accounts. Part was invested at 4% and the rest was invested at 7%. If the investments earn $680 peer year, how much was invested at each rate? I=prt
Answer:
The amount invested at 4% was $3,000 and the amount invested at 7% was $8,000
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]I=P(rt)[/tex]
where
I is the Final Interest Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=1\ year\\ P_1=x\\P_2=11,000-x\\I=\$680\\r_1=4\%=4/100=0.04\\r_2=7\%=7/100=0.07[/tex]
substitute in the formula above
[tex]I=P_1(r_1t)+P_2(r_2t)[/tex]
[tex]680=0.04x+(11,000-x)0.07[/tex]
solve for x
[tex]680=0.04x+770-0.07x[/tex]
[tex]0.07x-0.04x=770-680[/tex]
[tex]0.03x=90[/tex]
[tex]x=\$3,000[/tex]
so
[tex]\$11,000-x=\$11,000-\$3,000=\$8,000[/tex]
therefore
The amount invested at 4% was $3,000 and the amount invested at 7% was $8,000
Lines c and d are parallel. The equation of line c is y=−3x−5. What is the equation of line d?
Answer: y = -3x - 5
Step-by-step explanation: since the two lines are parallel, it implies that
m1 = m2. From the equation given,
m1 = -3 , m2 = -3
Substantial for m2 in y = mx + c
We now have
y = -3x - 5 since the new line is not passing through any coordinate.
Answer:
The answer is y=-3x-2
I hope it's not too late;)
Step-by-step explanation:
can someone help me please
A candle manufacturer sells cylindrical candles in sets of three. Each candle in the set is a different size. The smallest candle has a radius of 0.5
Inches and a height of 3 inches. The other two candles are scaled versions of the smallest, with scale factors of 2 and 3. How much wax is
needed to create one set of candles?
OA 27 cubic inches
B.
C.
D.
36 cubic inches
53 cubic inches
86 cubic inches
E.
98
cubic inches
Next
The amount of wax needed to create one set of candles is 84.75 cubic inches.
What is a cylinder?A cylinder is a 3-D figure that has a radius and a height.
The volume of a cylinder is given as πr²h.
Example:
The volume of a cup with a height of 5 cm and a radius of 2 cm is
Volume.
= 3.14 x 2 x 2 x 5
= 62.8 cm³
We have,
Let's calculate the volume of each candle and then add them together to find the total wax needed for one set of candles.
For the smallest candle, the radius is 0.5 inches and the height is 3 inches, so the volume is:
V1 = π x (0.5)² x (3) = 0.75π cubic inches
For the medium-sized candle, the radius is twice as big, or 1 inch, and the height is twice as big, or 6 inches. So the volume is:
V2 = π x (1)² x (6) = 6π cubic inches
For the largest candle, the radius is three times as big, or 1.5 inches, and the height is three times as big, or 9 inches.
V3 = π x (1.5)² x (9) = 20.25π cubic inches
To find the total wax needed for one set of candles, we add up the volumes:
V (total) = V1 + V2 + V3
= 0.75π + 6π + 20.25π
= 27π cubic inches
= 27 x 3.14
= 84.78 cubic inches
Therefore,
The amount of wax needed to create one set of candles is 84.75 cubic inches.
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Devon needs a wood board with an area of 516 square yard to complete a project. If the wood board is 13 yard wide, how long must the board be?
Answer:
[tex]L=\frac{15}{16}\ yd[/tex]
Step-by-step explanation:
The correct question is
Devon needs a wood board with an area of 5/16 square yard to complete a project. If the wood board is 1/3 yard wide, how long must the board be?
we know that
The area of a rectangle is equal to
[tex]A=LW[/tex]
where
L is the length
W is the width
we have
[tex]A=\frac{5}{16}\ yd^2\\\\W=\frac{1}{3}\ yd[/tex]
substitute
[tex]\frac{5}{16}=L(\frac{1}{3})[/tex]
solve for L
[tex]L=\frac{5}{16}(3)[/tex]
[tex]L=\frac{15}{16}\ yd[/tex]
The length of the wood board must be approximately 39.69 yards.
Explanation:To find the length of the board, we need to divide the total area by the width of the board. The area of the board is 516 square yards and the width is 13 yards.
Therefore, the length of the board can be found by dividing 516 by 13.
516 ÷ 13 = 39.69 yards.
So, the board must be approximately 39.69 yards long to complete the project.
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Can someone help me with this problem? I just can't seem to get the answer.
Answer:
[tex]\frac{9}{4}[/tex] or [tex]2\frac{1}{4}[/tex] or [tex]2.25[/tex]
Step-by-step explanation:
1 cm = 25000cm = 1/4 km. 9*1/4=9/4=2 1/4= 2.25
Fred is a server at a restaurant. On average, he can serve 6 tables per hour. Fred earns between $3.08 and $5.23 in gratuity per table. Which is a reasonable amount of gratuity that Fred earned in a 33 hour work week? A. $1,584.00 B. $24.00 C. $792.00 D. $132.00
Answer:
C. $792.00
Step-by-step explanation:
33 hours Fred can serve 33 x 6 = 198 tables
minimum gratuity : 3.08 x 198 = 609.8
maximum : 5.23 x 198 = 1035.5
Therefore $792.00 is a reasonable amount
Negative 3 is twice as large as a number,h
Answer:
negative 6 is the answer
Step-by-step explanation:
Please solve question 75
Good evening ,
Answer:
(C) 36
Step-by-step explanation:
The length of the continuous solid path from P To Q = 3×(Length of the dashed line) = 3×(12) = 36 in.
:)
=========================================
Explanation:
Check out the attached image below. Basically I drew out the given diagram and then I added the variables a,b,c,d,e,f,g. Those variables represent the side lengths of the 7 squares. Each square has a perimeter of 4*s where s is the side length, but we dont consider the side that is running along the dashed line (that connects P directly to Q). So we have 3 sides per square added up.
The first square has us travel a distance of 3*a, then the second square a distance of 3*b and so on. Overall, the total distance traveled is
3a+3b+3c+3d+3e+3f+3g = 3(a+b+c+d+e+f+g)
The goal is to figure out what a+b+c+d+e+f+g is equal to. This is equal to the length of segment PQ since the 7 letters are pieces of segment PQ (i.e., I'm using the segment addition postulate).
In other words,
a+b+c+d+e+f+g = 12
3(a+b+c+d+e+f+g) = 3*12
3(a+b+c+d+e+f+g) = 36
Total distance traveled = 36
3. READING Alejandro read 4 pages in a book in 6
minutes. How long would you expect him to take to
read 6 pages at this rate?
Alejandro read 4 pages in 6 minutes, then it would take him 9 minutes to read 6 pages
Solution:
Given that Alejandro read 4 pages in a book in 6 minutes
Therefore,
4 pages = 6 minutes
Let us find the time taken to read 1 page
time taken to read 1 page = time taken to read 4 pages divided by 4
[tex]\text{ time taken to read 1 page } = \frac{6 minutes}{4} = \frac{3}{2} minutes[/tex]
Thus to read 6 pages at this rate, multiply time taken to read 1 page by 6
[tex]\rightarrow \frac{3}{2} \times 6 = 9[/tex]
Therefore it would take 9 minutes to read 6 pages
which expression represents 4 times as much as 12
Answer:
4x+12
Step-by-step explanation:
An expression is a mathematical sentence that doesn't end in an equal sign. This question is asking for you to find four times as much as 12, but doesn't explain what number or phrase you need to find it for. We would replace the unknown number with the variable X.
I may be confusing this with another subject, so sorry if I am! Hope this helps!
The expression which represents 4 times as much as 12 is, [tex]4x=12[/tex]
Let us consider that number is x.
Since, 4 times of number is equal to 12.
So that, [tex]4*x=12\\\\4x=12[/tex]
Hence, the expression which represents 4 times as much as 12 is, [tex]4x=12[/tex]
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Find the factorization of 180
Answer:
180=2^2×3^2×5
Step-by-step explanation:
We have to obtain the factors of 180 which are prime numbers
A prime number being a number with only 2 factors.That is 1 and the number itself.
For example 5 only has 2 factors 1 and 5⇒5=1×5
Here are the first few prime numbers
2,3,5,7,11,13,.....
A number which is not prime is a composite number. Composite numbers have more than 2 factors. All composite numbers can be expressed as a product of prime factors.
Answer:
5 x 2 x 2 x 3 x 3
Step-by-step explanation:
I basically did the prime factors of 18 which is 1, 2, 3, 6, 9, 18. I broke it down elminated any other numbers not referring to the prime factor. Thats how you get your answer sorry if it's not a good explantion
What is 3(1+6r)=14-12
Answer:
r = 0.055555.....
Step-by-step explanation:
3(1+6r)=14-12 Write out formula.
3+18r=2 Distributive Property Form.
(3-3)+18r=2-3 Subtract 3 to both sides.
(18/18)r=-1/18 Divide both sides by 18
r=0.055555..... or -1/18.
Expand
Your answer should be a polynomial in standard form
(
+1)(2-6)
Answer:
x^2 - 6x + x - 6
= x^2 - 5x - 6
A computer can sort x objects in t seconds, as modeled by the functio
below:
1=0.005x2 + 0.002.x
How many objects are required to keep the computer busy for exactly
seconds?
Round to the nearest whole object.
Question:
A computer can sort x objects in t seconds, as modeled by the function below:
t=0.005x^2+0.002x
How many objects are required to keep the computer busy for exactly 9 seconds?
Round to the nearest whole object.
Answer:
42 objects are required to keep the computer busy for exactly 9 seconds
Solution:
Given function is:
Computer can sort x objects in t seconds, as modeled by the function below:
[tex]t = 0.005x^2+0.002x[/tex]
We have to find number of objects required to keep the computer busy for exactly 9 seconds
Therefore t = 9
Substitute t = 9 in given function
[tex]9 = 0.005x^2+0.002x\\\\0.005x^2+0.002x - 9 = 0[/tex]
Let us solve the above equation by quadratic formula,
[tex]\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
Using the above formula,
[tex]\text{ for } 0.005x^2+0.002x - 9 = 0 , \text{ we have } a = 0.005 ; b = 0.002 ; c = -9[/tex]
Substituting the values of a = 0.005 ; b = 0.002 ; c = -9 in above quadratic formula we get,
[tex]\begin{aligned}&x=\frac{-0.002 \pm \sqrt{0.180004}}{0.01}\\\\&x=\frac{-0.002 \pm 0.4242}{0.01}\\\\&x=\frac{-0.002+0.4242}{0.01} \text { or } x=\frac{-0.002-0.4242}{0.01}\\\\&x=42.22 \text { or } x=-42.62\end{aligned}[/tex]
Ignoring negative value,
x = 42.22 ≈ 42
Thus 42 objects are required to keep the computer busy for exactly 9 seconds
Identify the equation of the linear function through the points (- 2,- 7) and (1,2). Then state the rate of change of the function. What is the equation of the linear function? A. y = 3x - 1 B. y = - 3x - 1 C. y = 3x + 1 D. y = -3x + 1 The rate of change is ( ? ).
Answer:
y = 3x - 1
The rate of change of the function is 3.
Step-by-step explanation:
The equation of the linear function through the points (- 2, - 7)and (1,2) will be given by
[tex]\frac{y - ( - 7)}{- 7 - 2} = \frac{x - (- 2)}{- 2 - 1}[/tex]
⇒ (y + 7) = 3(x + 2)
⇒ y = 3x - 1 (Answer)
Now, the rate of change of the function is the slope of the line i.e. 3. (Answer)
We know the equation of a straight line which passes through the points [tex](x_{1}, y_{1})[/tex] and [tex](x_{2}, y_{2})[/tex] is given by
[tex]\frac{y - y_{1}}{y_{1} - y_{2}} = \frac{x - x_{1}}{x_{1} - x_{2}}[/tex]
The circumference of a circle is 3.2mm.
Find the length of the diameter.
Give your answer rounded to 3 SF.
The diameter of circle is 1.018 mm.
Step-by-step explanation:
Given,
Circumference of circle = 3.2 mm
We know that;
Circumference = 2πr
[tex]3.2=2\pi r\\[/tex]
Putting π=22/7
[tex]3.2=2*\frac{22}{7}*r\\3.2=\frac{44}{7}r[/tex]
Multiplying both sides by 7/44
[tex]\frac{7}{44}*3.2=\frac{7}{44}*\frac{44}{7}r\\\\\frac{22.4}{44}=r\\\\r=0.509[/tex]
Diameter = 2r
Diameter = 2*0.509
Diameter = 1.018 mm
The diameter of circle is 1.018 mm.
Keywords: circle, circumference
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Francis is constructing a line parallel to EF through point G.
What step should be his next step?
With the compass point on G and a wider opening
.than was used to construct the first arc, construct
an arc that intersects GD and EF.
o
With the compass point on G and the same
opening that was used to construct the first arc,
construct an arc that intersects GD on the
opposite side of point A and extends to the right of
point G.
With the compass point on A and the same
opening that was used to construct the first arc,
construct an arc that intersects GD on the same
side of point A as point G and extends to the right
of point G.
With the compass point on G and a wider opening
than was used to construct the first arc, construct
an arc that intersects EF twice
Answer:
Hope I helped!
Step-by-step explanation:
To construct a parallel line, set the compass to the same opening used for the first arc and draw an arc from point G that intersects line GD. This creates a parallel line to line EF through G.
Explanation:To construct a line parallel to EF through point G, Francis should set the compass point on G and adjust the compass to the same opening that was used to construct the first arc. He then needs to create an arc that intersects GD on the opposite side of point A and extends to the right of point G. This step ensures that the line through G will have the same angle with GD as EF does with GD, allowing it to be parallel to EF.
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Solve |12x + 1| = 10
(9/2, 11/2)
(-9/2, 9/2)
(-112.9/2)
|12x + 1| = 10
Remove the absolute value term and make two equations:
12x +1 = 10
12x +1 = -10
Now solve for both x values:
12x +1 = 10
Subtract 1 from both sides:
12x = 9
Divide both sides by 12:
x = 9/12
12x +1 = -10
Subtract 1 from both sides:
12x = -11
Divide both sides by 12:
x = -11/12
The answer would be (-11/12, 912)
If f (x) = 3 x squared and g (x) = 4 x cubed + 1, what is the degree of (f circle g) (x)?If f (x) = 3 x squared and g (x) = 4 x cubed + 1, what is the degree of (f circle g) (x)?
options are
2
3
5
6
Answer:
degree = 6
Step-by-step explanation:
Given [tex]f(x)=3x^2[/tex], and [tex]g(x)=4^3+1[/tex], we can find the composition of functions: [tex]fog(x)[/tex] by applying the definition of composition and performing the needed algebra.
Recall that the composition of functions is defined as: [tex]fog(x)=f(g(x))[/tex], where we use as input for the function f(x) the actual expression in terms of "x" of the function g(x):
[tex]f(g(x))=f(4x^3+1)\\f(g(x))=3(4x^3+1)^2\\f(g(x))=3\,(4x^3+1)\,(4x^3+1)\\f(g(x))=3\,[16x^6+4x^3+4x^3+1]\\f(g(x))=3\,[16x^6+8x^3+1]\\f(g(x))=48x^6+24x^3+3[/tex]
Therefore, the degree of this expression is "6" (the highest power at which the variable "x" appears)
Answer:
the answer is 6
Step-by-step explanation:
don't have one
What is 8,147 ÷ 24 with a remainder
Answer:
339 R11
Step-by-step explanation:
8,147 ÷ 24 = 339 R11
Tarzan loaded 3 trucks in 6 minutes. At that rate, how many trucks would he load in 5 hours?
Answer:
150
Step-by-step explanation:
60 minutes in 1 hour
3x10= 30 in one hour
30x5=150 30 trucks in 5 hours
Tarzan can load 150 trucks in 5 hours.
To calculate how many trucks Tarzan can load in 5 hours based on the rate that he loaded 3 trucks in 6 minutes. First, we convert 5 hours into minutes to match the units of the given rate. There are 60 minutes in 1 hour, so 5 hours is 300 minutes (5 hours x 60 minutes/hour). Next, we need to find out how many 6-minute intervals there are in 300 minutes, which is 300 minutes / 6 minutes/intervals = 50 intervals. Since Tarzan loads 3 trucks per interval, we multiply the number of intervals by the number of trucks per interval to get the total number of trucks loaded in 5 hours: 50 intervals x 3 trucks/interval = 150 trucks.