The expression for the cost of Taxi B is 0.40x + 2. The expression for the cost of Taxi A is 0.20x + 4. The inequality asks for when the cost of Taxi B will be greater than Taxi A, so you write it as 0.40x + 2 > 0.20x + 4, or 0.20x + 4 < 0.40x + 2.
The answer is B) 0.20x + 4 < 0.40x + 2.
Answer: B. [tex]0.20x+4<0.40x+2[/tex]
Step-by-step explanation:
let x denotes the number of mile taxi runs.
Given : Taxi A charges $0.20 per mile and an initial fee of $4.
i.e. the expression to show total charge by Taxi A will be :[tex]0.20x+4[/tex]
Taxi B charges $0.40 per mile and an initial fee of $2.
i.e. the expression to show total charge by Taxi B will be :[tex]0.40x+2[/tex]
Now, the inequality that can determine when the cost of Taxi B will be greater than Taxi A will be :-
[tex]0.20x+4<0.40x+2[/tex]
Hence, B is the correct answer.
Simplify the expression. Write the answer using scientific notation.
(9x10^5)(3x10^10)
a. 2.7x10^16
b. 1.2x10^51
c. 1.2x10^16
d. 2.7x10^51
Answer:
2.7 x 1016
Step-by-step explanation:
that's the answer
Given: △KPS
m∠P=105°, m∠S=30°
PS=12
Find: PK.
split ∠ P into a ∠45° and a ∠60° with altitude PO. ΔPOK is isosceles and ΔPOS is 30-60-90. PO=6=KO Pk=6√2
Answer:
PK= 8.5
Step-by-step explanation:
The sum of interior angles in a triangle is 180 degree
[tex]m<k+m<p+m<s=180[/tex]
[tex]m<k+105+30=180[/tex]
[tex]m<k+135=180[/tex]
Subtract 135 from both sides
[tex]m<k=45[/tex]
Now use sine rule
[tex]\frac{sin A}{a} =\frac{sin B}{b}[/tex]
[tex]\frac{sin K}{PS} =\frac{sin S}{PK}[/tex]
[tex]\frac{sin(45)}{12} =\frac{sin(30)}{PK}[/tex]
Cross multiply
[tex]PKsin(45)}=12sin(30)[/tex]
[tex]PK =\frac{12sin(30)}{sin(45)}[/tex]
PK= 8.5
What is the GCF of the expression 4x2 + 3x?
A.x
B.3x
C.4x
D.x2
The greatest factor that will divide into the 2 terms is x.
Its A.
The GCF of the given polynomial expression is the monomial x
What is a polynomial expression?Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is an expression composed of variables, constants, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. For example P(x) = x2-5x+11
Given here: The polynomial expression as 4x²+3x
Greatest Common Factor (GCF) The GCF for a polynomial is the largest monomial that divides (is a factor of) each term of the polynomial.
4x²+3x=x(4x+3)
Thus the greatest polynomial that divides or is a factor the expression is given by x
Hence, The GCF of the given polynomial expression is the monomial x
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How does cot(x)sin(x)=cos^3(x)+cos(x)sin^2(x)?
[tex]\cot(x)\sin(x)=\cos^3(x)+\cos(x)\sin^2(x)[/tex]
[tex]R=\cos(x)[\cos^2(x)+\sin^2(x)]=\cos(x)\cdot1=\cos(x)\\\\L=\dfrac{\cos(x)}{\sin(x)}\cdot\sin(x)=\cos(x)\\\\L=R\\\\\text{used:}\\\\\sin^2x+\cos^2x=1\\\\\cot x=\dfrac{\cos x}{\sin x}[/tex]
A softball team scored 8 runs, 5 runs, 13 runs, 8 runs, and 11 runs in its last five games. What is the range of the number of runs scored in the five games
The range is the difference between the highest number and the lowest number.
The lowest number is 5, the highest number is 13.
The range is 13 - 5 = 8 runs.
The correct answer for the range is: "5 to 13 runs" with a median of 8 and here is why:
The range of a set of numbers is what values could have or could be based on the lowest and highest values. The range is not the same as the average or the median. 5 runs was the least amount of runs that happened during one game and 13 was the most in another.
The average is calculated by adding all of the numbers added together and then divides by how many numbers that you added together.
The median is found by removing the lowest number and then the highest number. You repeat this process until you are left with only one number.
There are other things to find as well, but I think you understand now
Range: 5-13 ; 8
Average: 9
Median: 8
Also here is the definition from Dictionary.com on what range is:
range rānj/Submit
noun
1.the area of variation between upper and lower limits on a particular scale.
ex: "the cost is thought to be in the range of $1-5 million a day"
What is the LCM of xy2 and xz?
xyz
xy2z
x2y2z
x
xy² = x · y · y
xz = x · z
LCM(xy², xz) = x · y · y · z = xy²z
Frances gets 6 paychecks in 1w weeks how many paychecks does she get in 52 weeks
The question says that Frances gets 6 paychecks in 1 week.
To find the number of paychecks that Frances gets paid in 52 weeks we need to know the number of paychecks she gets each week.
She gets 6 paychecks each week,
So that means,
1 w = 6 paychecks
So, in 52 weeks she will get:
[tex]6 \times 52=312[/tex] paychecks.
Over the duration of 52 weeks, Frances gets 312 paychecks.
Leah loves chicken a wings and is comparing the deals at three diffrent restaurants. Buffalo bills has 8 wings for $7 .Buffalo milds wings has 12 wings for $10 .Wingers has 20 wings for $17 .Which restaurant offers the lowest price per wing?
For each, divide the amount by the number of wings
7 divided by 8: 0.875 = $0.88 per wing
10 divided by 12: 0.8333 = $0.83 per wing
17 divided by 20: 0.85 = $0.85 per wing
Looking at each result, the middle one (the $10 for 12 wings) is the best deal
Do 0.3 and 3.0 have the same value? I’m not sure they aren’t but i’m checking
Willie changes the quadratic function f(x)=x2?6x+14 to vertex form f(x)=a(x?h)2+k. If Willie does this correctly, what is the value of k?
Answer:
The value of k is 5.
Step-by-step explanation:
Since we know we can convert function's quadratic form to vertex form by completing the square.
f(x)=x2?6x+14
We will add and subtract 9 to our equation in order to complete the square.
[tex]1(x^{2} ?6x+9)-9+14[/tex]
Upon completing the square and combining like terms we will get,
[tex]1(x?3)^{2} +5[/tex]
Upon comparing Willie's vertex form with our expression we can see that k is 5.
Therefore, the value of k is 5.
Graph 24x+25=−6y+7 .
Use the line tool and select two points on the line.
I just need someone to explain where they would go on a graph
To graph 24x + 25 = -6y + 7, first rearrange it to the form y = mx + b. In our case, y = -4x -3. Plot the y-intercept (0, -3) first, then use the slope (-4) to find a second point (1, -7). Connect these points to form the graph.
Explanation:To graph the equation 24x + 25 = -6y + 7, the first step is to rewrite the equation in slope-intercept form, or y = mx + b, where m is the slope of the line and b is the y-intercept (where the line crosses the y-axis).
Add 6y to both sides of the equation 24x + 25 = -6y + 7 to get 6y = 24x + 25 - 7. Then, rearrange the equations and divide all terms by 6 to get y = -4x - 3.
Now, we can identify the slope and y-intercept. The slope (m) is -4 and the y-intercept (b) is -3. Using these, we can plot two points on a graph. The first point is the y-intercept which is at (0, -3), the point where the line crosses the y-axis.
The slope of -4 means for every step to the right on the x-axis, we go down 4 steps. Therefore, our second point would be at (1, -7). Connect these two points with a straight line, and you have graphed the equation.
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Jenny has $2.40 deducted from her monthly allowanbevery time she forgets to do a chore. If she forgets three times in one month, what will be the charge in jenny's Total allowance
Answer: Charge in Jenny's Total allowance= $7.20
Step-by-step explanation:
Given : Jenny has $2.40 deducted from her monthly allowance every time she forgets to do a chore.
If she forgets three times in one month, then by using the MULTIPLICATION OPERATION the charge in Jenny's Total allowance will be :-
[tex]3\times\$2.40=\$7.20[/tex]
Hence, the charge in Jenny's Total allowance = $7.20
please help me with this .....
Use the elimination method to solve the system of equations. Choose the correct ordered pair. 2x – 5y = 2 3x + 2y = –16
A. (–4, –2)
B. (2, –11)
C. (4, –14)
D. (–9, –4)
Answer:
It is -4,-2
Step-by-step explanation:
Answer:
The solution is (-4, -2)
Step-by-step explanation:
Given two equations
[tex]2x-5y=2[/tex] → (1)
[tex]3x+2y=-16[/tex] → (2)
we have to solve the system of equations by elimination method
Multiply (1) by 3 and (2) by 2 and then subtracting we get
[tex]3(2x-5y)-2(3x+2y)=6-(-32)[/tex]
[tex]6x-15y-6x-4y=38[/tex]
[tex]-19y=38[/tex]
[tex]y=-2[/tex]
⇒ [tex]2x=2+5(-2)=2-10=-8[/tex]
[tex]x=-4[/tex]
Hence, the solution is (-4, -2)
Option A is correct
Which exponent makes this statement true? 1/5^9= 5^?
Answer:
The exponent -9 makes the given statement true.
Step-by-step explanation:
We have been given an incomplete mathematical statement and we need to figure out the exponent for 5 on the right hand side to complete the statement.
The given incomplete statement is [tex]\frac{1}{5^{9}}=5^{?}[/tex].
Let us rewrite the left hand side of the expression by moving the exponential term to the numerator using exponent property. As per this property, if we shift an exponential term from denominator to numerator (or vice versa), the sign of exponent changes.
Therefore, we get:
[tex]5^{-9}=5^{?}[/tex]
Now that we have common bases on both the sides, we can equate the exponents. And upon equating the exponents, we can see that the 'question mark' should be replaced by -9 in order for statement to be true.
Therefore, exponent -9 on the right hand side will make the statement true.
Answer:
1/5^9 = 5^-9
Step-by-step explanation:
Graphing Polynomial Functions
Let's assume
'a' , 'b' are zeros
so, we will find total zeros from graph
We can curve touches x-axis
Let's assume it touches at x=b
so, there would be two zeros at x=b
it also crosses origin
so, another zero is at x=0
it crosses x-axis one more time
Let's assume that zeros at x=a
so, we have got four zeros
x=a,0,b,b
now, we can set up function
[tex]f(x)=(x-0)(x-a)(x-b)(x-b)[/tex]
we can also write as
[tex]f(x)=x(x-a)(x-b)^2[/tex].................Answer
Solve the following multiplication and division problems.
a. 3 km 5 hm × 15 =
b. 19 m 44 cm × 32 =
c. 1,140 m ÷ 12 =
d. 3 km 6 hm 7 dam 5 m ÷ 15 =
Answer:
a. 22.5 km
b. 267.52 m
c. 95 m
d. [tex](4.2)(10^{-5})[/tex] km
Step-by-step explanation:
a. You can convert from hectometers to kilometers, and then you can make the multiplication:
[tex]\frac{5hm}{10}=0.5km[/tex]
[tex](3km)(0.5km)(15)=22.5km[/tex]
b. You can convert from centimeters to meters, and then you can make the multiplication:
[tex]\frac{44cm}{100}=0.44m\\(19m)(0.44m)(32)=267.52m[/tex]
c. You only need to divide 1,140 meters by 12:
[tex]\frac{1,140m}{12})=95m[/tex]
d. You can convert from hectometers to kilometers, from decameters to kilometers and from meters to kilometers, and divide this by 15:
[tex]\frac{6hm}{10}=0.6km[/tex]
[tex]\frac{7dam}{100}=0.07km[/tex]
[tex]\frac{5m}{1000}=0.005km[/tex]
[tex]\frac{(3km)(0.6km)(0.07km)(0.005km)}{15}=(4.2)(10^{-5})[/tex] km
A person invests $2,740 in an account that earns 4.3% annual interest. Find when the value of the investment reaches $7,000. If necessary, round to the nearest tenth. the investment will reach $7,000 in approximatelyyears.
So, to set up your equation is the hardest part. If you remember the basic format, you're set.
I(t) = P * (1+r%)^t
t= time and this will be our variable
Initial amount P = $2740
Rate = 4.3% which converts numerically into .043
I(t) = 7000
Before we get to find out how to find how many years it takes to get to $7000, set up the basic equation by plugging in what we know.
I(t) = $2740(1+4.3%)^t
I(t)=2740(1.043)^t
Now plug in for $7000 for I(t)
7000=2740(1.043)^t Divide both sides by 2740
7000/2740 = 2740/2740(1.043)^t
2.55474453=(1.043)^t
Now you can solve for t in two ways. You can either use the natural log or graph it on your graphing calculate and see when the two equations meet.
In your calculator you can set up:
ln(2.55474453)/ln(1.043) = t which is the method I prefer since it's much simpler
t=22.278528
but you can also graph it in your ti-84
with
y1=2.55474453
y2=(1.043)^x
and find where they intersect on the graph.
either way it'll be the same answer
2. At Algorithms Pizza they have the exponential pizza, which is a 24-inch cheese pizzoa that costs $17.50. Each topping for the pizza costs $2.35. If Connor ordered the exponential pizza and was charged $29.25, how many toppings were on his pizza? Justify your answer by using an algebraic equation to solve this problem step by step.
Answer:
Connor ordered 5 toppings on his pizza.
Step-by-step explanation:
17.50 + (2.35 * x) = 29.25
Remove the parentheses
17.50 + 2.35x = 29.25
Subtract 17.50 from both sides
2.35x = 29.25 - 17.50
Subtract
2.35x = 11.75
Divide both sides by 2.35
x = 5
Answer:
29.25 - 17.50 = 11.75
11.75 divided by 2.35 = 5
So that he had 5 toppings on his pizza.
Step-by-step explanation:
Which set of ordered pairs in the form of (x, y) does not represent a function of x?
A. {(1, 1.5), (2, 1.5), (3, 1.5), (4, 1.5)}
B. {(0, 1.5), (3, 2.5), (1, 3.3), (1, 4.5)}
C. {(1, 1.5), (–1, 1.5), (2, 2.5), (–2, 2.5)}
D. {(1, 1.5), (–1, –1.5), (2, 2.5), (–2, 2.5)}
Answer:
Option B
Step-by-step explanation:
For answering this question we must understand what is a function.
A function is different from mapping.
Mapping is just a subset of AxB where A and B are two sets.
But function is constrained to the point that elements of I set will have unique image in second set.
We find From the options
But in option B,, we find that 1 has two images 3.3 and 4.5. i.e. 1 does not have unique image. Hence not a function.
All other options the first element in ordered pair have a unique image.
Hence all other options are functions.
Only option B is not a function.
The actual length of Lake Superior is 350 miles and the width is 160 miles. What's the length and width of the lake on a map if the scale is "1 cm = 25 miles"?
A. length: 6.4 cm, width: 14 cm
B. length: 14 cm, width: 6.4 cm
C. length: 7 cm, width: 3.2 cm
D. length: 3.2 cm, width: 7 cm
The correct option is: B. length: 14 cm, width: 6.4 cm
Explanation
The actual length of Lake Superior is 350 miles and the width is 160 miles.
The scale is given as: 1 cm = 25 miles
Suppose, the length and width of the lake on the map are [tex]x[/tex] cm and [tex]y[/tex] cm respectively.
First, the equation according to the ratio of scaled length to the actual length will be....
[tex]\frac{x}{350}=\frac{1}{25}\\ \\ 25x=350\\ \\ x=\frac{350}{25}=14[/tex]
Now, the equation according to the ratio of scaled width to the actual width will be....
[tex]\frac{y}{160}=\frac{1}{25}\\ \\ 25y=160\\ \\ y=\frac{160}{25}=6.4[/tex]
Thus, the length and width of the lake on the map will be 14 cm and 6.4 cm respectively.
What Number has the dame valué as 12 tens
Select the multiplication sentence that applies the associative property of multiplication to the example. Example: (4 × 5) × 2 = 40 A. 4 × (5 + 2) = 28 B. 4 + (9 × 4) = 40 C. 4 × (5 × 2) = 40 D. (4 + 5) × 2 = 18
C. 4 x (5 x 2) = 40 hope that helps
Answer : option C
A. 4 × (5 + 2) = 28
Associative property of multiplication . Here we have 5+2 so it does not comes under Associative property of multiplication
B. 4 + (9 × 4) = 40
Here we have 4 + . there is a + sign inbetween. so it does not comes under Associative property of multiplication
C. 4 × (5 × 2) = 40
Here we have 4 times 5 times 2. so it comes under Associative property of multiplication
D. (4 + 5) × 2 = 18
Here we have 4 + 5 so it does not comes under Associative property of multiplication
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A bicycle wheel with radius 26" rotates through an arc that measures 80°. What is the length of the arc of the tire that touched the ground?
2.88pi inches
5.78pi inches
11.56pi inches
hang on just a seci think i got it
Answer:
Option C is the correct answer.
Step-by-step explanation:
We have arc length = Radius x Angle in radian
Radius = 26 inches
[tex]\texttt{Angle rotated }= 80^0=80\times \frac{\pi}{180}=\frac{4\pi}{9}[/tex]
Arc length = [tex]l=\frac{4\pi}{9}\times 26=11.56\pi[/tex]
Length of the arc of the tire that touched the ground = 11.56π
Option C is the correct answer.
A student has some $1 and $5 bills in his wallet. He has a total of 19 bills that are worth $55. How many of each type of bill does he have?
To solve the problem, we use a system of linear equations. We find that the student has 14 $1 bills and 5 $5 bills.
Explanation:This problem can be solved using a system of linear equations. Let's define two variables: x represents the number of $1 bills and y represents the number of $5 bills . From the problem, we can set up the following two equations:
x + y = 19 (since the total number of bills is 19) $1x + $5y = $55 (since the total worth of the bills is $55)
Solving these equations simultaneously, we find that x = 14 and y = 5. Thus, the student has 14 $1 bills and 5 $5 bills.
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If x=-2 and y=6 is a solution of equation 3ax+2by=6, then find the value of b
[tex]\text{Substitute the values of x and y to the equation}\\\\x=-2,\ y=6,\ 3ax+2by=6\\\\3a(-2)+2b(6)=6\\\\-6a+12b=6\qquad|\text{add 6a to both sides}\\\\12b=6a+6\qquad|\text{divide both sides by 12}\\\\b=\dfrac{6a}{12}+\dfrac{6}{12}\\\\\boxed{b=\dfrac{1}{2}a+\dfrac{1}{2}}[/tex]
Graph y<1−3x .
Please only answer if you know what you're doing
y < 1 - 3x can alse be written as y < -3x + 1 (which crosses the y-axis at 1 and has a slope of -3 (aka rise over run of: down 3 and to the right 1)
The symbol (<) represents a dashed line that is shaded below.
Answer: A
If manuel deposits 25% of 130 into a savings how much is the amount of his deposit
Which numbers are a distance of 3 units from 12 on a number line? A number line ranging from negative 5 to 17. Select each correct answer.
The distance between A and B is d = |B - A|
We have d = 3 and A = 12.
Substitute:
[tex]|B-12|=3\iffB-12=3\ \vee\ B-12=-3\qquad|\text{add 12 to both sides}\\\\B=15\ \vee\ B=9[/tex]
Answer: 9 and 15.Given sample set A= {1,2,3,4,5} how many items are in the complement of set B if set B= all numbers greater than 2? (30 pts)
Alright, so first we need to establish two things.
First, the compliment of a set is like the extreme opposite; everything that is not in set B will be in the complement.
Second, we need to find out what B is.
Okay, so B is everything that is greater than 2, that's given. That includes 3, 4, and 5. B = {3, 4, 5}. There are three items in this set.
The numbers that aren't included are 1 and 2. The complement of B, let's call this C I guess, is C = {1, 2}. There are 2 items in this set.
The answer, I believe, is two. Hope this helps!
You ask 150 people about their pets. The results show that 925 of the people own a dog. Of the people who own a dog, 16 of them also own a cat. A. What fraction of the people own a dog and a cat? Of the people own a dog and a cat. B. How many people own a dog but not a cat? People own a dog but not a cat.
Let us assume the total number of people surveyed be = 1500
People who own a dog = 925
People who also own a cat along with dog = 16
So, people who own only dog = 925-16 = 909
A.
The fraction of people who own both a dog and a cat are = [tex]\frac{925}{1500}[/tex]
= [tex]\frac{37}{60}[/tex]
B.
Number of people who own a dog and not a cat are = 909
In fraction it will be [tex]\frac{909}{1500}=\frac{303}{500}[/tex]