Mr. Anders was three times as old as Kate 5 years ago. Their total age now is 42 years. How old is Kate now?

Answers

Answer 1

We can write this as two equations. Call Mr. Anders' age A and Kate's age K:
[tex]A-5=3(K-5)[/tex]
[tex]A+K=42[/tex]

Then solve for A in the second equation:
[tex]A=42-K[/tex]

Substitute this into the first equation:
[tex](42-K)-5=3(K-5)[/tex]
[tex]-K+37=3K-15[/tex]
[tex]52=4K[/tex]
[tex]K=13[/tex]

Related Questions

Katie has a collection of nickels dimes and quarters with a total value of $4.20 there are 7 more dimes than nickels and six more quarters and nickels how many of each coin does she have

Answers

Katie, Let the number of nickles = N Since there are 7 more dimes than nickles, the number of dimes D = N + 7 Since there are 4 more quarters than nickles, the number of quarters Q = N + 4 Since quarters = $0.25, dimes = $0.10, and nickles = $0.05 and all added together = $4.90 ⇒ 0.25·Q + 0.10·D + 0.05·N = 4.90 Now multiply through by 100 to eliminate the decimal: 25Q + 10D + 5N = 490 Substitute for Q and D 25(N+4) + 10(N+7) + 5N = 490 25N + 10N + 5N +100 +70 = 490 40N + 170 = 490 ⇒ 40N = 320 ⇒ N = 320/40 N = 8, D = N+7 = 15 Q = N+4 = 12 Check: 25(12) + 10(15) + 5(8) = 300 + 150 + 40 = 490

Draw a number line to represent 4 + (-7) = -3?

Answers

Draw a number line and indicate the location of zero (0). From that point, move four units to the right and place a black dot there. Now, from this black dot, move 7 spaces to the left and place a black dot where you en up. It should be at -3.

There are (3^5)^2 ⋅ 30 leaves on a tree. What is the total number of leaves on the tree?

Answers

First you do 3 to the 5th power or 3x3x3x3x3= 243 then multiply it by 2 or
243 x 2 = 486
Last multiply it by 30 which gives you an answer of 14,580 leaves.

I have chosen 4 MYSTERY INTEGERS. At least one is positive and one is negative.
Follow these clues to figure out my integers. BE SURE TO EXPLAIN YOUR REASONING!
1. The sum of the four integers is (-6)
2. When you order the integers from LEAST to GREATEST the difference of the middle two integers is (-4) and the sum is 0
3. The quotient when you divide the LEAST integer by the GREATEST is (-3)
4. The product of the two greatest integers is (+6)

Answers

Let the four numbers be A,B,C,D in ascending order.

The key is in conditions 2 & 3.
B-C=-4, and B+C=0
therefore B=-2, C=2 by solving the two previous equations.

Given that the product of the two greatest numbers is 6, we have C*D=6, or
D=6/C=6/2=3
Now since the sum of all the four numbers is -6, we have
A+B+C+D=-6
A-2+2+3=-6
A=-6+2-2-3=-9
Check: we were told smallest divided by greatest = A/D=-9/3=-3 ok.

So the numbers are
A=-9, B=-2, C=2, D=3.

Graph the lines by finding the points of intersection with the axes (intercepts):
y=4x+8
Answer:
x − intersection is (____ )
. y − intersection is (,____).

Answers

x intersects at -2, and y is 8

the x-intersection is (-2,0)
the y- intersection is (0,8)

az+17=-4z-b solve of z .

Answers

Z=(-b-17)/(a+4)

Az+4z+17z=-b
Az+4z=-b-17
Z(a+4)=-b-17
Z=(-b-17)/(a+4)

plz help...The graph of the equation y = 3x + 4 is shown. Determine the value of y for the point (-1, y).

A)
-2

B)
-1

C)
0

D)
1

Answers

Substitute -1 in for the x in the equation.

y=3x+4
y=3(-1)+4
y=-3+4
y=1

So, the answer is D.

Hope this helps!

I think it's answer D.

What is the product?

(7.1 x 10^4) x (4.8 x 10^3)

A. 3.408 x 10^7
B. 3.408 x 10^8
C. 3.408 x 10^12
D. 3.408 x 10^13

Answers

(7.1 x 10^4) x (4.8 x 10^3) = A. 3.408 x 10^7

To meet building codes, a building must have a roof no taller than 74 feet. An architect is designing a museum with a 14 ½ foot ground floor, and 12 foot 3 inch upper floors (including supports) How many floors, including the ground floor, can the building have?

Answers

Answer:

Building can have 4 floors.

Step-by-step explanation:

Height of the ground floor is 14.5 foot and height of upper floors = 12 foot 3 inches or 12.25 foot per floor

Let there are x floors in the building.

Total height of the building = 74 foot

Therefore, total height of the building = Height of the ground floor + Height of the upper floors

74 = 14.5 + 12.25x

74 - 14.5 = 12.25x

12.25x = 59.5

x = [tex]\frac{59.5}{12.25}[/tex]

x = 4.9 floors

Therefore, the building can have 4 floors.

If 2x^2-5x+7 is subtracted from 4x^2+2x-11, what is the coefficient of x in the result?

Answers

Answer:

-3

Step-by-step explanation:

The coefficient of x in 2x^2 + 7x - 18 is 7.

What is quadratic trinomial?It is a type of polynomial which contains three terms and the power of the polynomial is two.The general form of quadratic trinomial is [tex]ax^{2} +bx+c[/tex], where a, b, c are non zero real numbers and x is variable

For given example,

We have been given two quadratic trinomials (2x^2 - 5x + 7) and (4x^2 + 2x - 11).

If (2x^2 - 5x + 7) is subtracted from (4x^2 + 2x - 11),

= (4x^2 + 2x-11) - (2x^2 - 5x + 7)

= 4x^2 + 2x - 11 - 2x^2 + 5x - 7

= (4 - 2)x^2 + (2 + 5)x - (11 + 7)

= 2x^2 + 7x - 18

Therefore, the coefficient of x is 7.

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The midpoint of AB is M (4,2). If the coordinates of A are ( 6,-4) what are the coordinates of B?

Answers

Final answer:

The coordinates of point B are calculated using the midpoint formula. Substituting given values for points A and M allows us to find B's coordinates, which are (2, 8).

Explanation:

The midpoint of a line segment is calculated using the formula M=(x1 +x2)/2, (y1+y2)/2 where x1 and y1 are the coordinates of the first point and x2, y2 are the coordinates of the second point. Given that the coordinates of point A are (6,-4) and the coordinates of the midpoint M are (4, 2), we can set up the following equations to solve for the coordinates of point B (x2, y2): (6+x2)/2 = 4 and (-4+y2)/2 = 2. Solving for x2 and y2 gives us the coordinates of Point B: (2, 8).

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a grocery Store has small bags of apples for $5 and large bags of apples for $8. If you buy 6 bags and spend $45, how many of each size bag did you buy?

Answers

9 small bags and 5 large bags

Carmen cuts a 60 inch long wire into pieces that are 3/4 inch long. How many pieces does she have?

Answers

Basically, she is dividing a 60 inch long wire into 3/4 pieces. So, what we have to do here is divide 60 by 3/4.

= 60 ÷ 3/4

Keep the first number, change the sign, and flip the fraction.

= 60 × 4/3

You can reduce the numbers by the GCF (greatest common factor) of 3.

= 20 × 4/1

After reducing 60 to 20 and 3 to 1, you are left with 20 × 4/1 or simply 20 × 4.

Multiply the numbers as usual, and you will get your product of 80.

Carmen has 80 pieces.

Answer:

Step-by-step explanation:

Aubrey and Charlie are driving to a city that is 120 mi from their house. They have already traveled 20 mi, and they are driving at a constant rate of 50 mi/h. Complete the function that models the distance they drive as a function of time. Then complete a reasonable domain for this situation.

Answers

1. The total distance will be equal to 20 miles plus the remaining distance which would be obtained when you multiply the speed to time t. The equation would be written as follows:

120 = 20 + 50t

2. The minimum time would be 0 hours. The maximum time is when the total distance of 120 is fully covered.

t ≤ (120 - 20)/50
t ≤ 2 hours

Thus, the domain would be 0 < t ≤ 2.

The function that models the distance they drive as a function of time is 120 = 20 + 50t

The required domain must be within the range of 0 and 2 i.e. 0≤t≤2

The formula for calculating distance travelled is expressed as:

Distance = Speed × time

Given the following

Total distance = 120 miles

Distance already travelled = 20miles

If they are trying at a constant rate of 50mi/hr, the distance travelled at the time "t", this period will be 50t.

The required function that models the distance is expressed as;

120 = 20 + 50t

Hence the function that models the distance they drive as a function of time is 120 = 20 + 50t

To get a reasonable domain, we need to get the value of t as shown;

120 = 20 + 50t

120 - 20 = 50t

100 = 50t

t = 100/50

t = 2sec

Hence the required domain must be within the range of 0 and 2 i.e. 0≤t≤2

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the summer solstice can occur on any day of the week, with each day being equally likely. what is the propability the summer solstice will occur on a weekday

Answers

There are seven days in the week. Out of those seven days, five are weekdays and two are weekends. The probability of the summer solstice occurring on a weekday is a ratio for the # of weekdays/the # of days in a week: 5/7.

Whiteboard markers cost $4.75 per set at an office supply store. Which equation can be used to determine the price, P, of n sets of these markers? P = 4.75n, n = 4.75P, P equals 4.75 over n, n equals 4.75 over P

Answers

The expression which represents the price of the n number of the set is p = 4.75n. The correct option is A.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Whiteboard markers cost $4.75 per set at an office supply store. There is n number of Whiteboard markers.

The expression for the cost of n numbers of the Whiteboard markers is,

P = $4.75 x n

Therefore, the expression which represents the price of the n number of the set is p = 4.75n. The correct option is A.

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In a different sixth grade class the ratio of boys to girls is 3:2.how many boys and how many girls could there be in this class?is there more than one possible answer?explain

Answers

There could be 12 boys and 8 girls. yes. bc that ration is in simplest form so if u make it bogger theres more than one possible awnser to c how many boys than girls there are

Jen bought a 5.00 footling. Sales tax is 8%. How much was sales tax

Answers

500 : 100 * 8 =

0.4 $

To convert a repeating decimal to a fraction, your goal is to:

A Get all the numbers to be the same

B Get the numbers to the left of the decimal point to be the same

C Get the numbers to the right of the decimal point to be the same

D It's impossible to convert a repeating decimal to a fraction

Answers

To convert a repeating decimal to a fraction, your goal is to get the numbers to the left of the decimal point to be the same

How does the method for solving equations with fractional or decimal coefficients and constants compare with the method for solving equations with integer coefficients and constants?

Answers

Sorry I'm not good at math!

All social science theories of child socialization emphasize:

Answers

All social science theories of child socialization emphasize different aspects of socialization.
Remember to put me in the brain list answer ;)

write 7,800 in expanded form

Answers

7,800 in expanded form would be 7,000 + 800.
Hope this helps!

Expanded Notation Form
7,000
+ 800
+ 0
+ 0
Expanded Factors Form
7 x 1,000
+ 8 x 100
+ 0 x 10
+ 0 x 1
Expanded Exponential Form
7 x 10^3
+ 8 x 10^2
+ 0 x 10^1
+ 0 x 10^0
Word Form
seven thousand, eight hundred
Hope this helps! Let me know if you need any further assistance!

Solve on the interval [0,2pi) : 2 csc x -3 = -5 a- pi/6, 5pi/6 b- 3pi/2 c- 2pi/3, 4pi/3 d- 7pi/6, 11pi/6

Answers

[tex]\mathsf{2\cdot csc~x-3=-5}\\ \\ \mathsf{2\cdot csc~x=-5+3}\\ \\ \mathsf{2\cdot csc~x=-2}\\ \\ \mathsf{csc~x=\frac{-2}{2}}\\ \\ \mathsf{csc~x=-1}\\ \\ \mathsf{csc~x=\frac{1}{sen~x}}\\ \\ \mathsf{sen~270\°=-1}\\ \\ \boxed{\mathsf{x=\frac{3\pi}{2}}}[/tex]

shade the grid to represent the ratio 23\50. Then find the missing number

23\50=__\100

Answers

Missing number is 46

Match the inequality to the graph of its solution.
a. n/4 ≤ -1
b. -10 ≥ -100
c. 5x ≥ 20

Answers

a. n/4 ≤ -1

Multiply both sides by 4 => n ≤ - 4, which is all the real numbers less or equal than - 4.

That in the real number line is all the numbers to the left of - 4 (including -4)

The matching graph is the B.

b. -10n ≥ -100

Divide both sides by - 10 => n ≤ 10

That is all the real numbers less or equal than 10.

In the real number line it is all the numbers to the left of 10, including 10.

So, the matching graph is the A.

c. 5x ≥ 20

Divide both sides by 5 => x ≥ 4

That is all the real numbers greater or equal to 4.

In the real number line it is all the numbers to the right of 4, including 4.

The matching graph is C.

(-7a^4bc^3)(5ab^4c^2)

Answers

-35a^5b^5c^5 is the answer

You have $25 to spend at the movie you spent $18.75 on ticket you want to go buy a bag of popcorn with the rest of the money how many bags can you buy in one bag cost $2.50 use the inequality 2.50b + 18.75 <25 where b represents the number of bag of popcorn

Answers

you could buy 2 bags

2.50b+18.75< 25
- 18.75 -18.75
2.50b< 6.25
––––––––––
2.50 2.50
b= 2.5
Round to 2 bags

Round 95,234 to the nearest ten thousand

Answers

The ten thousand digit is 9, so to round you look at the digit before it. We know if the digit we are looking at is 5 or more, we round up. So, the answer is 100,000. Even though this is in the hundred thousands, it still works because it can be considered as 10 ten thousands.

The answer is 100,000

Find one terminating decimal and one repeating decimal between -1/2 and -1/3

Answers

Terminating decimal:
-0.45
Repeating decimal:
-2/9 = -0.22222222... or -0.2 with an overline over the 2(that's how you notate a repeating decimal)

Gina and Danny are playing an addition card game. In the card game, each player takes turns pulling two cards, one at a time, from a deck of cards. If the first card plus the second card is positive, the player keeps those cards. If the answer is zero or negative, the player loses those cards, and the cards go back in the deck.
There are only 10 cards in the deck, which have the following numbers:

(a) If a player gets a first card that is a positive number, what must the second card be in order for the player to keep the cards? Explain your reasoning.

(b) Gina pulls as her first card. What must her second card be in order for her to have a positive answer? List all correct answers and explain why or show your work.

(c) Danny also pulls a as his first card. He pulls a second card and says he has to put the cards back in the deck because he got a negative answer. What card could Danny have pulled? List all correct ans

Answers

what are the numbers tho, cant answer without the numbers

numbers...

1 2 3 4 5

-1 -2 -3 -4 -5

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