step 1
Find the equation of the line First Company
y=100.25x+6,500
where
y is the total charge
x is the number of ton of sugar
Second Company
y=225.75x+4,492
Part a)
Equate both equations
100.25x+6.500=225.75x+4,492
solve for x
225.75x-100.25x=6,500-4,492
125.50x=2,008
x=16
answer part a is 16 tonPart b) For x=16 ton
substitute the value of x in any of the two equations (the result is the same)
y=100.25(16)+6,500
y=$8,104
answer Part b is $8,104Two sides of a triangle have lengths 5 and 4. Which of the following can NOT be the length of the third side?
SOLUTION
From the triangle inequality theorem, the sum of the lengths any two sides must be greater than the length of the third side
So, looking at the options and looking at 4 and 5, it means that 5 is the longest side. So
[tex]\begin{gathered} 4+2=6>5 \\ 4+4=8>5 \\ 4+1=5=5 \\ 4+3=8>5 \end{gathered}[/tex]So since 4 + 1 = 5 and 5 is not greater than 5, hence 1 cannot be the length of the 3rd side.
The answer is option C
I need a little understanding on a one page math assignment
Let h(t)=tan(4x + 8). Then h'(3) is
and h''(3) is
The most appropriate choice for differentiation will be given by
h'(3) = 24.02
h''(3) = [tex]210.48[/tex]
What is differentiation?
Differentiation is the process in which instantaneous rate of change of function can be calculated based on one of its variables.
Here,
h(x) = tan(4x + 8)
h'(x) = [tex]\frac{d}{dx} (tan(4x + 8))[/tex]
= [tex]sec^2(4x + 8)\frac{d}{dx}(4x + 8)[/tex]
= [tex]4sec^2(4x + 8)[/tex]
h'(3) =
[tex]4sec^2(4\times 3 + 8 )\\4sec^220\\24.02[/tex]
h''(x) =
[tex]\frac{d}{dx}(4sec^2(4x + 8))\\4\times 2sec(4x + 8)\times \frac{d}{dx}(sec(4x + 8))\\8sec(4x + 8)sec(4x+8)cosec(4x+8)\times\frac{d}{dx}(4x + 8)\\32sec^2(4x + 8)cosec(4x +8)[/tex]
h''(3) =
[tex]32sec^2(4\times 3+8)cosec(4\times 3+8)\\32sec^220cosec20[/tex]
[tex]210.48[/tex]
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write 2500g in appropriate prefix pls.
Answer: 2.5kg
Step-by-step explanation:
I am assuming you mean to simplify it. So 2.5kg
1g=1000kg
2500/1000=2.5
Complete the sentence. The amount of time it takes to complete a puzzle is most likely to be a function of the .
"The ammount of time it takes to complete a puzzle is most likely to be a function of the number of pieces in the puzzle."
I need help on a part of very hard question cuz it isn't very very very very very very far oh yeah. hear it is 2+2
Given:
The objective is to find the solution of 2+2.
Since the required operation in the given question is addition.
So, the addition of 2 and 2 will be,
[tex]2+2=4[/tex]Hence, the answer is 4.
In a middle school with 300 students, there are 40% boys, 1/3 of the students wear glasses, and 15% of the girls wear glasses. What is the probability (= how many percent is it) that a randomly selected student does not wears glasses? (Round the percentage to the nearest hundredth) *
We know that
• There are 300 students.
,• 40% are boys (this means 60% are girls).
,• 1/3 of the students wear glasses.
If 1/3 of the students wear glasses, then 2/3 of the students don't wear glasses. Let's find 2/3 of 300.
[tex]\frac{2}{3}\cdot300=\frac{600}{3}=200[/tex]Therefore, 200 students don't wear glasses.
Then, we divide to find the probability.
[tex]P=\frac{200}{300}=0.6667[/tex]Then, we multiply by 100.
[tex]0.6667\cdot100=66.67[/tex]Therefore, the probability is 66.67%.help meee pleaseeee pleasee
Answer:
f(4) = (16/7)
f(0) = -12
f(-5) = (-7/11)
Step-by-step explanation:
x + 12
f(x) = -----------
2x - 1
(4) + 12 16
f(4) = ----------- = ---------
2(4) - 1 7
(0) + 12 12
f(0) = ----------- = ------- = -12
2(0) - 1 -1
(-5) + 12 7 -7
f(-5) = ------------ = ----------- = -------
2(-5) - 1 -11 11
I hope this helps!
If the radius of both of the green circles is 10 cm, find the area of the yellow region (outside of the circles but inside the rectangle)
The area of the yellow region if the radius of each of the circles is 10 cm is calculated as: 171.7 cm².
How to Find the Area of Circles and Rectangles?The formula that is used to find the areas of circles and rectangles are given below:
Area of a circle = πr², where r is the radius.Area of a rectangle = length × width.Given the diagram in the attachment which shows the green circles and the rectangle, we can deduce the following:
Radius of the each of the circles (r) = 10 cm
Length of the rectangle = 4(r) = 4(10) = 40 cm
Width of the rectangle = 2(r) = 2(10) = 20 cm
The area of the yellow region = area of the rectangle - area of the 2 circles
= (length × width) - 2(πr²)
Substitute
The area of the yellow region = (40 × 20) - 2(π × 10²)
= 800 - 628.3
= 800 - 628.3
= 171.7 cm²
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Julia found the equation of the line perpendicular toy = -2x + 2 that passes through (5.-1).Analyze Julia's work. Is she correct? If not, what washer mistake?1 y25= 1/2 (-2) + 6Yes, she is correct,No, she did not use the opposite reciprocal for theslope of the perpendicular line.No, she did not substitute the correct x and yvaluesNo she did not apply inverse operations to solve forthe y-intercept.3+5b=555y=x5.5
The given line is
[tex]y=-2x+2[/tex]The line passes through (5, -1),
Perpendicular lines have opposite slopes, so we use the following equation to find the new slope knowing that the slope of the given line is -2.
[tex]\begin{gathered} m\cdot m_1=-1 \\ m\cdot(-2)=-1 \\ m=\frac{-1}{-2} \\ m=\frac{1}{2} \end{gathered}[/tex]Now, we use the slope, the point, and the point-slope formula to find the equation.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-1)=\frac{1}{2}(x-5) \\ y+1=\frac{1}{2}x-\frac{5}{2} \\ y=\frac{1}{2}x-\frac{5}{2}-1 \\ y=\frac{1}{2}x+\frac{-5-2}{2} \\ y=\frac{1}{2}x-\frac{7}{2} \end{gathered}[/tex]Therefore, the equation of the new perpendicular line is[tex]y=\frac{1}{2}x-\frac{7}{2}[/tex]So, she's not correct, she didn't substitute the correct x and y values.
The right answer is C.Can anyone please help me with this fast? Thank you!
Answer:
Step-by-step explanation:
16. 4/16 1/16 1/16 or 6/16
17. 1/16 1/16 or 2/16
18. 7/16 1/16 2/16 or 10/16
19. 2/16
20 4/16 1/16 1/16 7/16 1/16 2/16 or 16/16=1
Function g can be thought of as a translated (shifted) version of f(x) = x?Y Y6+5+432f7 6 5 4 3 21 2 3 4 5 6 7-2--3+-6-7Write the equation for g(x).
Answer:
g(x) = (x + 5)²
Explanation:
g is the same function f shifted 5 units to the left.
Then, if we have a function h(x) =f(x+c), h(x) is f(x) shifted c units to the left.
So, to translate f 5 units to the left, we need to replace x by (x + 5), to get:
[tex]\begin{gathered} f(x)=x^2 \\ g(x)=f(x+5) \\ g(x)=(x+5)^2 \end{gathered}[/tex]So, the equation for g(x) is:
g(x) = (x + 5)²
Use substitution to solve the system of equations. y = x + 2 4x - 5y = 14 A. (-22,-24) C. (-4,-2)B. (-24, -22) D. (-14, -12)
Solve by substitution;
[tex]\begin{gathered} y=x+2---(1) \\ 4x-5y=14---(2) \\ \text{Substitute for the value of y into equation (2)} \\ 4x-5(x+2)=14 \\ 4x-5x-10=14 \\ \text{Collect like terms} \\ 4x-5x=14+10 \\ -x=24 \\ \text{Divide both sides by -1} \\ x=-24 \\ \text{Substitute for the value of x into equation (1)} \\ y=x+2 \\ y=-24+2 \\ y=-22 \end{gathered}[/tex]Challenge A family wants to rent a car to go on vacation. Company A charges $75.50 and14¢ per mile. Company B charges $30.50 and 9¢ per mile. How much more does Company Acharge for x miles than Company B?For x miles, Company A charges dollars more than Company B.(Simplify your answer. Use integers or decimals for any numbers in the expression.)
Company A charges $75.50 and 14¢ per mile, then for x miles, Company A charges 75.5 + 0.14x dollars
Company B charges $30.50 and 9¢ per mile, then for x miles, Company B charges 30.5 + 0.09x dollars
Subtracting the second equation to the first one,
75.5 + 0.14x
-
30.5 + 0.09x
----------------------
45 + 0.05x
For x miles, Company A charges 45 + 0.05x dollars more than Company B.
Which of the following tests should be administered to see if an experimental medicine lowers blood pressure among hypertensive patients? A. two-tailed test OB. right-tailed test OC. alternative test OD. left-tailed test
We have to select the appropiate test to see if an experimental medicine lowers blood pressure among hypertensive patients.
In this case, we want to test if the mean for the blood pressure after the treatment is significantly lower than the blood pressure mean without treatment.
Then, for the blood pressure to be significantly different it has to be to the left of a critical value.
Then, it is a left-tailed test.
Answer:
7) A math teacher asked 60 randomly selected 7th graders whether they 10 pointsare left handed or right handed. The table below shows the results of thesurveyLeft or Right-Handed?Hand FrequencyLeftRight4218A school has a total of 280 seventh-grade students. Based on the resultsshown in the table above, how manyof those seventh-grade studentswould you expect to be left-handed?A 60B 72C 84D 120
Answer:
C. 84
Explanation:
First, we will calculate the percentage of left-handed students in the group of 60 that the teacher asked.
So, the percentage is equal to:
[tex]\frac{18}{60}\times100\text{ \% = 30\%}[/tex]Therefore, 30% of the randomly selected students are left-handed.
Now, we can use this percentage to estimate the number of left-handed students in the group of 280.
Then, 30% of 280 is equal to:
[tex]30\text{ \% }\times280=\frac{30}{100}\times280=84[/tex]So, the answer is C. 84.
Translate each sentence into an equation. Then find each number.
The sum of six, and a number divided by two is 0.
the possible answers are:
y/2-6=0;y=12
2y+6=0;y=-3
y/2+6=0;y=12
y/2+6=0;y=-12
The sum of six and a number divided by two is zero is translating into an equation is y/2+6 = 0, and the number is y = -12
The given sentence is "The sum of six and a number is divided by two is 0"
Consider the number as y
A number is divided by two = y/2
The sum of 6 and a number divided by two = y/2 + 6
The sum of six and a number is divided by two is 0
y/2 + 6 = 0
We have to solve the equation
Move the 6 to the right hand side of the equation
y/2 = -6
Move the 2 to the right hand side of the equation
y = -6×2
Multiply the numbers
y = -12
Hence, the sum of six and a number divided by two is zero is translating into an equation is y/2+6 = 0, and the number is y = -12
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15 points?Solve for A 5/A = P A = ???? That’s all it saysPlease state what A is.
use and show all conversion factors to convert 352 inches per second to miles per hour. 352 inches divided by 1 second
Okay, here we have this:
We need to convert 352 inches per second to miles per hour. So we obtain the following:
[tex]\begin{gathered} \frac{352in}{1sc}\cdot\frac{1mile}{63360in}\cdot\frac{3600sc}{1h} \\ =\frac{20\text{miles}}{h} \end{gathered}[/tex]Finally we obtain that 352 inches per second 20 are miles per hour.
PLEASE HELP
OFFERING 10 POINTS
Answer: AAS
Step-by-step explanation:
Two sides are congruent, two angles are congruent, and vertical angles are congruent
Round to the nearest thousand to estimate the difference between 7,333 and 4,983
Rounded to the nearest thousand the given numbers are:
[tex]\begin{gathered} 7,333 \\ 3<5\colon Round\text{ by leaving the digit in thousand position} \\ \\ 7,333\approx7,000 \end{gathered}[/tex][tex]\begin{gathered} 4,983 \\ 9>5\colon\text{ Round increasing the digit in thousand position} \\ \\ 4,983\approx5,000 \end{gathered}[/tex]Estimate the difference between 7,000 and 5,000:
[tex]7,000-5,000=2,000[/tex]Estimated difference: 2,000In the diagram below, if the measure of < C = 45 °, and side AB = 6.8, then side BC = _____.
Solution
Since
[tex]\begin{gathered} \tan45=\frac{6.8}{BC} \\ \\ \Rightarrow BC=\frac{6.8}{\tan45}=6.8\text{ since}\tan45=1 \end{gathered}[/tex]The correct option is A.
What is the slope between (2,-1 ) and ( 5,4 )
the slope will be 5/3 because:
[tex]\frac{4-(-1)}{5-2}=\frac{5}{3}[/tex]Write an equation for the linear function f(x) using the given information. ———————————————Using the points 2,0 & 4,3
To find the equation in the form
[tex]y=mx+b[/tex]the slope is defined by:
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ m=\frac{3-0}{4-2} \\ m=\frac{3}{2} \end{gathered}[/tex]To find b you can replace any of the points on the equation an clear for b
(x,y)=(4,3)
[tex]\begin{gathered} y=\frac{3}{2}x+b \\ 3=\frac{3}{2}\cdot4+b \\ 3=6+b \\ 3-6=b \\ b=-3 \end{gathered}[/tex]to check if the answer is correct replace 2 as x in the equation.
[tex]\begin{gathered} y=\frac{3}{2}\cdot2-3 \\ y=3-3 \\ y=0 \end{gathered}[/tex]since the answer was 0 and point was 2,0 the equation is correct.
Solve using substitution.x = -7-8х - бу = 14
The given system of equation :
x = - 7
-8x - 6y = 14
Substitute the value of x = (-7) in the given system :
-8x - 6y = 14
-8(-7) - 6y = 14
Simplify the equation :
56 - 6y = 14
56 - 14 = 6y
6y = 42
y = 42/6
y = 7
y = 7 & x = (-7)
Answ
Answer:
Step-by-step explanation:
What is a rational number between -0.45 and -0.46?
Answer:-0.4545555...,-0.453333...,-0.45222.....
hope i helped
Step-by-step explanation:
12 + 24 =__(__+__)
Find the GCF. The first distributing number should be your GCF
A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, the numbers 12, 20, and 24 share the components 2 and 4.
Therefore, 12 and 24 have the most things in common. Figure 2: LCM = 24 and GCF = 12 for two numbers.
Find the other number if one is 12, then. What does 12 and 24's GCF stand for?
Example of an image for 12 + 24 = ( + ) Locate the GCF. You should distribute your GCF as the first number.
12 is the GCF of 12 and 24. We must factor each number individually in order to determine the highest common factor of 12 and 24 (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 24 = 1, 2, 3,.
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1a. 100 foot-long rope is cut into 3 pieces.The first piece of rope is 3 times as long asthe second piece of rope. The third piece istwice as long as the first piece of rope.What is the length of the longest piece ofrope?
To solve the exercise, it is easier to make a drawing, like this
So, you have
[tex]\begin{gathered} z=3y \\ y=y \\ x=2z \\ z+y+x=100 \end{gathered}[/tex]Now solving
[tex]\begin{gathered} x=2z \\ x=2(3y) \\ x=6y \end{gathered}[/tex][tex]\begin{gathered} z+y+x=100 \\ 3y+y+6y=100 \\ 10y=100 \\ \frac{10y}{10}=\frac{100}{10} \\ y=10\text{ ft} \end{gathered}[/tex][tex]\begin{gathered} x=6y \\ x=6(10) \\ x=60\text{ ft} \end{gathered}[/tex][tex]\begin{gathered} z=3y \\ z=3(10) \\ z=30\text{ ft} \end{gathered}[/tex]Therefore, the length of the longest piece is 60ft.
How to draw A Area Model For 29×56
First, notice that:
[tex]29\text{ x }56=1624[/tex]now, we can write 29 as 20 + 9 and 56 as 50 + 6, so, we can draw the following rectangles:
Then, if we calculate the area of each of the rectangles, we get the following:
then, if we add all the areas together, we get:
[tex]1000+120+450+54=1120+504=1624[/tex]which is the same result as 29 x 56
xin uses 20 yards of fencing to build the walls of a square Chicken Coop which equation and solution represents x, the length, in yards, of each wall of the square coop?A: [tex]x + 4 = 20 \\ x = 16[/tex]b:[tex]x + 4 = 20 \\ x = 24[/tex]c:[tex]4x = 20 \\ x = 80[/tex]d:[tex]4x = 20 \\ x = 5[/tex]
Since the coop is in square shape The fencing is in the shape of a square
So equation is 4x=20, x=5
