The time that it will take Joe to catch up with Mary is; 8 hours
How to solve Algebra Word Problems?We are told that;
Time Mary leaves the house = 12 pm
Time that Joe leaves the house = 2 pm
Speed of Mary = 45 mi/hr
Speed of Joe = 60 mi/hr
This means that Mary had a 2 hour time lead over Joe.
Thus;
Distance is calculated from the formula;
Distance = Speed * time
Thus;
Distance covered by Mary in the 2 hours lead is;
Distance = 45 * 2 = 90 miles
Thus, time that it will take Joe to catch up with mary is;
t = 2 + (90/(60 - 45))
t = 2 + 6
t = 8 hours
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Sum and Product of Two Numbers Find two numbers whose sum is 20 and whose product is the maximum possible value. (Hint: Let x be one number. Then 20 - x is the other number. Form a quadratic function by multiplying them, and then find the maximum value of the function.)
Answer:
The numbers are 10 and 10Step-by-step explanation:
As described in the hint:
the numbers are x and 20 - x, their product is maximum possible value.The product is:
x(20 - x) = - x² + 20xThis is a quadratic expression ax² + bx + c with the leading coefficient of a = - 1, b = 20 and c = 0.
It has a maximum and no minimum value since a < 0.
The x-coordinate of the maximum is the vertex which is x = - b/2a.
The x- coordinate of the vertex is:
x = - 20/-2 = 10The maximum value itself is:
- 10² + 20*10 = - 100 + 200 =100Answer:
10 and 10.
[tex]f(x)=-x^2+20x[/tex]
Maximum value of the function is 100.
Step-by-step explanation:
Two numbers whose sum is a positive integer, and whose product is the maximum possible value have to be two positive integers.
Pairs of positive integers whose sum is 20:
1 and 192 and 183 and 174 and 165 and 156 and 147 and 138 and 129 and 1110 and 10The pair of numbers whose product is the maximum possible value is the pair of numbers that are closest to each other.
Therefore the pair of numbers is 10 and 10:
[tex]\implies x = 10[/tex]
[tex]\implies 20 - x = 10[/tex]
Form a quadratic function by multiplying:
[tex]\implies f(x)=x(20-x)[/tex]
[tex]\implies f(x)=20x-x^2[/tex]
[tex]\implies f(x)=-x^2+20x[/tex]
The maximum value of the function is the y-value of its vertex.
[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
To convert the function to vertex form, complete the square.
Factor out negative 1:
[tex]\implies f(x)=-(x^2-20x)[/tex]
Add and subtract the square of half the coefficient of the term in x:
[tex]\implies f(x)=-\left(x^2-20x+\left(\dfrac{-20}{2}\right)^2-\left(\dfrac{-20}{2}\right)^2\right)[/tex]
[tex]\implies f(x)=-(x^2-20x+100-100)[/tex]
[tex]\implies f(x)=-(x^2-20x+100)+100[/tex]
Factor the perfect square trinomial:
[tex]\implies f(x)=-(x-10)^2+100[/tex]
Therefore, the vertex of the function is (10, 100), and so the maximum value of the function is 100.
which statistics about older workers are true?
Answer:Older workers are staying in the workforce longer.
Step-by-step explanation: I had the same question as you it should be right.
Help please <3 end of quarter is soon!
Answer:
x = 2
Step-by-step explanation:
8x - 21 - 5x = - 15 ( collect like terms on left side )
3x - 21 = - 15 ( add 21 to both sides so numeric values on right side )
3x = 6 ( isolate x by dividing both sides by 3 )
x = 2
Express using exponents and simplify any numerical coefficients: w · w · w
Answer:
w to the power of 3 or w^3
Step-by-step explanation:
For example, plug in a number for the variable given, and in this case, I used the number 2. When using the number 2, the question would become 2 * 2 * 2. It would be simplified as 2 to the power of 2 to the power of 3. That's how I got the answer of w to the power of 3.
HELP ME ASPPP PLEASE SHOW UR WORK PLEASE
Answer: -9
Step-by-step explanation:
Below, the two-way table is given for a class
of students.
Sophomore
Male
Female
Total
Freshmen
4
3
6
4
Juniors
2
6
Seniors Total
2
3
If a female student is selected at random, find the
probability that the student is a senior.
P(Senior | Female ) = [ ? ]%
Round to the nearest whole number.
Answer:
19%
Step-by-step explanation:
You want the probability a student is a senior, given that they are female.
TableThe table indicates that 3 +4 +6 +3 = 16 students are female. Of those, 3 are seniors. The desired probability is ...
P(senior | female) = N(senior & female)/N(senior) = 3/16 = 0.1875
The probability that a female student is a senior is about 19%.
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jack and bob leave their houses at 10:00 am walking toward each other. they meet at 10:30 am. if their houses are 7km apart, and jack is walking at 8 km/h , find bobs rate
URGENT
Bob is walking at the rate of 6 kilometer per hours
Jack and Bob leave their houses at 10:00 am walking toward each other and they meet at 10.30 am.
The distance between two houses = 7 kilometer
The speed of the Jack = 8 kilometer per hour
The distance traveled by Jack in 30 minutes = 8 / 2
= 4 kilometer
The remaining distance = 7 - 4
= 3 kilometer
Bob traveled 3 kilometers in 30 minutes
Then the speed of the Bob = 3 × 2
= 6 kilometer per hour
Hence, the Bob is walking at the rate of 6 kilometer per hours
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A rival company offers you an annual salary of $36,000.Except for the pay, everything is identical between the companies. Do you accept or reject the rival company's offer, and why?
I will have to reject the offer of the rival company since it's lesser than $40560.
How to calculate the amountFrom the information, the person works a basic week of 40 hours and the basic rate is $19.50 per hour. It should be noted that there are 52 weeks in a year. The total amount will be:
= 40 × 19.50 × 52
= $40560
The rival company offers you an annual salary is $36000.
I'll reject the rival company's offer since it's lower.
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Complete question
You work a basic week of 40 hours and your basic rate is $19.50 per hour. A rival company offers you an annual salary is $36.000. Except for the pay, everything is identical between the conpanies. Do you accept or reject the rival company's offer, and why?
BobbyLou's cell company charges $27 a month for voice service plus $0.43 for each text message. Write the equation that would give you the amount each month, given a certain number of text messages.
The equation that would give the amount each month, given a certain number of text messages is 27 + 0.43t.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let the number of text messages be represented as t.
Since BobbyLou's cell company charges $27 a month for voice service plus $0.43 for each text message. The amount will be:
= 27 + (0.43 × t)
= 27 + 0.43t
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Bria and April were comparing text messages during lunch. April sent 20 messages today. April sent one fourth the amount of text messages sent by Bria. write a equation to determine how many text messages Bria sent.
answer:
0.25 (or 1/4) x 20 = 5
step-by-step explanation:
math. 0.25x20 = 5
HELP NOW
The function f(x)=(1-x)^2-4 is decreasing only throughout the interval:
The function f(x)=(1-x)^2-4 is decreasing only throughout the interval is
-∞ < x < 1.
Given function:
f(x)=(1-x)^2-4
= 1 + x^2 - 2x - 4
= x^2 - 2x - 3
for decreasing:
f'(x) ≤ 0
2x - 2 - 0 ≤ 0
2x -2 ≤ 0
2x ≤ 2
x ≤ 1
-∞ < x < 1.
Therefore The function f(x)=(1-x)^2-4 is decreasing only throughout the interval is -∞ < x < 1.
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Simplifying Square Roots of Negative numbers
Answer:
10i
Step-by-step explanation:
using the fact that [tex]\sqrt{-1}[/tex] = i , then
[tex]\sqrt{-100}[/tex]
= [tex]\sqrt{100(-1)}[/tex]
= [tex]\sqrt{100}[/tex] × [tex]\sqrt{-1}[/tex]
= 10 × i
= 10i
= 0 + 10i ← in standard form
how much of brand A fruit punch (20% fruit juice) must be mixed with 9 L of brand b fruit punch (40% fruit juice) to create a mixture contains 32% fruit juice ?
6 liters of brand A fruit punch must be mixed with 9 L of brand b fruit punch.
Let x=liters of Brand A fruit punch to be mixed with 9 liters of Brand B fruit punch.
x + 9 = liters of mixture.
20%(x) + 9*40% = 32%(x+9)
20/100 x + 9*40/100 = 32/100 (x+9)
0.2x + 360/100 = 0.32x + 9*0.32
0.2x + 3.6 = 0.32x + 2.88
0.12x = 3.6 - 2.88
0.12x = 0.72
divide by 0.12 on both sides
x = 0.72/0.12
= 72/100/12/100
= 72/12
= 6 liters.
Therefore 6 liters of brand A fruit punch must be mixed with 9 L of brand b fruit punch.
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FLOWERS The number of tulips in Paula's garden is 8 less than the number of marigolds. If there are 16 tulips, write and solve an equation to determine the number of marigolds m.
The number of marigold in the garden of Paula is 24.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let the number of marigold be m.
In this case, the number of tulips in Paula's garden is 8 less than the number of marigolds. The number of marigold will be:
m - 8 = 16
m = 16 + 8.
m = 24
The number of marigold is 24.
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Choose the graph of y=2|x|+5
Answer:
2nd one
Step-by-step explanation:
You can see that at the end, it is +5. That means it is to the left, NOT the right. So the second one is correct.
A family buys a studio apartment for 150,000. They pay a down payment of $22,500. a)Their down payment is what percent of the purchase price? b) What percent of the purchase price would a $7500 down payment be?
Answer:
15% and 40%
Step-by-step explanation:
22500/150000 is 15/100 or 15%
60000/150000 is 40/100 or 40%
The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
2, 8, 14, ...
Find the 42nd term.
The 42nd term of the sequence is 248
What is Arithmetic Progression?
Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value.
The furmula is [tex]a_{n}[/tex]=a + (n - 1 )d
where a = The first form of A.P
n = Number of terms given to find
d = Common difference between each terms
Given,
a = 2
n = 42
d = 6
Now,
[tex]a_{42\\[/tex] = 2 + (42 - 1)6
[tex]a_{42}[/tex] = 2 + (41)6
[tex]a_{42}[/tex] = 2+ 246
Therefore, for 42nd term
[tex]a_{42}[/tex] = 248
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The numbers 2.8888..... and 2.99999...... are both rational numbers. What is an irrational number that is between the two rational numbers?
Answer:Anything between the square root of 8.36 and 8.99
Step-by-step explanation:
Any of the square roots of the number above are between 2.8 repeating and 2.9 repeating.
What kind of transformation is illustrated in this figure?
O rotation
O dilation
O translation
O reflection
Answer:
dilation (sorry if i got it wrong im trying my best)
Answer:
Rotation
Step-by-step explanation:
It is rotated 180° at a point (which u could draw line of each object with its respective image to find the rotation point)
In the first week of July,1,020 a record people went to the local swimming pool. In the second week, 125 fewer people went to the pool than in the first week. In the third week, 145 more people went to the pool than in the second week. In the fourth week, 175 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
The percent decrease in the number of people who went to the pool over these four weeks is 15.2%.
How to calculate the percentage?The change regarding the people at the swimming pool for the number of weeks will be:
= 1020 - 125 + 145 - 175
= 865
The initial number of people is 1020.
Therefore, the percentage decrease will be:
= Decrease in number / Initial number × 100
= (1020 - 865) / 1020 × 100
= 155/1020 × 100
= 15.2%
The Percentage is 15.2%.
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Dilate the figure by the scale factor. Then enter the new coordinates
K=10
A'(0,20)
B'([?],[])
C'([ ][ ])
The will be A'(0, 20), B'(20, 10) and '(-10, 0). Transformation is the of a point from its to a. Types of transformation are reflection, translation, rotation and dilation.
What is transformation?
When a function is transformed, the graph's curve either "moves to the left/right/up/down," "expands or compresses," or "reflects." For instance, by simply moving the graph of the function g(x) = x2 up by 3 units, the graph of the function f(x) = x2 + 3 is obtained. Function transformations are very useful for graphing functions without having to start from scratch because they allow you to move, expand, compress, or reflect the curve. In this article, we will examine the guidelines for function transformations as well as examples of how to transform various function types.
Let ABC be a with coordinates A(0, 2), B(2, 1), C(-1, 0).
The coordinate of points A, B, C will change by below rule
(x, y)↔(10x, 10y)
where 10 is the scale factor.
∴A(0, 2) ↔A'(0, 20)
B(2, 1) ↔B'(20, 10)
C(-1,0) ↔C'(-10, 0)
Hence, will be A'(0, 20) ,B'(20, 10) and C'(-10, 0)
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A furniture maker uses the specification 17.9≤w≤18.1 for the width w in inches of a desk drawer. Write the specification as an absolute value inequality.
The specification as an absolute value inequality is l w - 18 l ≤ 0.1.
Given:
A furniture maker uses the specification 17.9≤w≤18.1 for the width w in inches of a desk drawer.
m = 17.9 + 18.1 / 2
= 36/2
= 18
t = 18.1 - 17.9
= 0.2/2
= 0.1
l w - 18 l ≤ 0.1
Therefore The specification as an absolute value inequality is l w - 18 l ≤ 0.1.
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Help.
What would the graph look like if all of your classmates
points were shown along with yours?
Answer: 5
Step-by-step explanation:
Tell whether the relation, represented by the ordered pairs below, represents a function. Explain.
{ (-2, 4), (-1, 3), (0, 2), (-2, 0), (1, 1)
The relation represented by the ordered pair is not a function
How to determine the relation that is a function?The given parameter is represented as
{(-2, 4), (-1, 3), (0, 2), (-2, 0), (1, 1)}
As a general rule;
For a relation to be considered a function, the following must be true:
One x value must not point to several y values
Using the above as a guide, the ordered pair in the relation are not functions
This is because one x value must not point to several y values
Hence, (d) the ordered pair is not a function
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Find the quotient.
(2x4 – 3x3 – 6x2 + 11x + 8) ÷ (x – 2)
Quotient is 2x³ +x² -4x+3 for (2x⁴ – 3x³ – 6x² + 11x + 8) ÷ (x – 2)
What is Division?A division is a process of splitting a specific amount into equal parts.
(2x⁴ – 3x³ – 6x² + 11x + 8) ÷ (x – 2)
Let f(x)=2x⁴ – 3x³ – 6x² + 11x + 8
and g(x)=x-2
We need to divide the f(x) by g(x),
f(x)=g(x)× (2x³ +x² -4x+3)+16
If we equate the above equation with division algorithm which says,
a=bq+r
f(x)=g(x)q(x)+r(x)
so quotient is 2x³ +x² -4x+3
Hence quotient is 2x³ +x² -4x+3 for (2x⁴ – 3x³ – 6x² + 11x + 8) ÷ (x – 2)
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HELPPPPPPPPPP PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
150 plates
Step-by-step explanation:
if 1 stack = 10 plates then
15 stacks =?
15×10 =150
Answer:
150
Step-by-step explanation:
If 1 stack = 10 plates all you have to do is figure out how 1 changes to 15 ( in this case multiply). You tyen multiply 10 by 15 which equals to 150.
HELP ME OLEASE
The number of integers between 1 and 2022 inclusive that are multiples of 11 but not multiples of 3 is
The number of integers between 1 and 2022 inclusive that are multiples of 11 but not multiples of 3, using arithmetic sequences, is of:
122.
What is an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
The nth term of an arithmetic sequence is given by the rule presented as follows:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term of the arithmetic sequence.
The sequence composed by the integer multiples of 11 between 1 and 2022 are given as follows:
(11, 22, ..., 2013)
The first term and the common ratio of the sequence are given as follows:
[tex]a_1 = 11, d = 11[/tex]
The number of terms is obtained as follows:
2013 = 11 + 11(n - 1)
11n = 2013
n = 2013/11
n = 183.
The sequence composed by terms that are multiples of 11 and of 3 is given by:
(33, 66, ..., 2013).
The first term and the common ratio of the sequence are given as follows:
[tex]a_1 = 33, d = 33[/tex]
The number of terms is obtained as follows:
2013 = 33 + 33(n - 1)
33n = 2013
n = 2013/33
n = 61.
Hence the number of integers that are multiples of 11 but not 3 is given by:
183 - 61 = 122.
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can some pls help me with this
Jeremy has 2 bags with 3 marbles in each bag
Answer:
then he has 6 marbl3s total.
Use the GCF and the distributive property to find the sum of 30+45
The sum using the distributive property is 75
How to determine the GCF sum of the expressions?From the question, we have the following expression
30 + 45
Rewrite the given expression as follows
This is represented using
(30 + 45)
Factor out 5 from the expression
So, we have the following representation
30 + 45 = 5(6 + 9)
The above means that 5 is the GCF of the sum expression 30 + 45
This represents the GCF
Solving further, we have
30 + 45 = 5 * 15
Evaluate
30 + 45 = 75
Hence, the sum is 75
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