Answer: Hello there!
Let's define x = age of parent 1, and y = age of parent 2, and suppose that y is the oldest one.
we know that:
x + y = 92
x*y = 2107
now we have a system of equations that we need to solve:
the first step is isolate one of the variables in one of the equation, let's isolate x in the first equation:
x = 92 - y
now we can replace it in the second equation and find the value of y.
x*y = 2107
y*(92 - y) = 2107
92y - y^2 = 2107
now we need to solve a cuadratic equation!
-y^2 + 92y - 2107 = 0
using the Bhaskara formula, we get:
[tex]y = \frac{-92 +/- \sqrt{92^{2} -4 *(-1)*(-2107) } }{-2} = \frac{-92 +/- \sqrt{36} }{-2} = \frac{-92 +/- 6}{-2}[/tex]
so we have two solutions:
y = (-92 + 6)/(-3) = 43
y = (-92 - 6)/(-2) = 49
because y is the oldest one, we need to take the biggest solution, this is y = 49.
so the oldest parent has 49 years.
if you want to find the age of the other parent, replace this in the first equation:
y + x = 92
49 + x = 92
x = 92 - 49 = 43
At the end of 2005, the national debt for the U.S. was about 10 trillion dollars, and the population of the U.S. was about 10 to the 8th power. About how much was the per capita (per person) debt?
Final answer:
To find the per capita debt in 2005, divide the national debt of $10 trillion by the U.S. population of 100 million. The per capita debt comes out to be approximately $100,000 per person.
Explanation:
To calculate the per capita debt, we need to divide the national debt by the population of the U.S. The question states that the national debt at the end of 2005 was about $10 trillion, and the population was about 10 to the 8th power (100,000,000). To find the per capita debt, we perform the following calculation:
Per Capita Debt = Total National Debt / Population
= $10,000,000,000,000 / 100,000,000
= $100,000
Thus, the per capita debt was approximately $100,000 per person at the end of 2005.
Water rushes over Niagara Falls at the rate of 180 million cubic feet every 30 mins. How much water goes over the falls in 1 min?
also, please tell me the steps to do it, instead of just the answer
Answer:
20 million cubic feet every 1 mins
Step-by-step explanation:
180÷3=60
60÷3=20
MATH HELP PLEASE WILL GIVE BRAINLIEST!!
Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle A?
Marram spent 3/4 of her allowance at the mall. Of the money spent at the mall1/3 was spent on new earrings. What part of her allowance did Merrimack spent on earrings.
What is the measure of angle x?
Enter your answer in the box.
x = °
Answer:
I also got 43 using the same strategy as the first guy.
Step-by-step explanation:
90*-40*=43*
The map At the right shows ELLies locker,her English class,and the cafeteria.is her locker closer to the English class or the cafeteria?
The locker is closer.
what is 7x6 like 7 rows of 6 collums
Final answer:
To solve 7x6, visualize a table with 7 rows of 6 columns each. Multiplying these numbers means counting all the cells in this table, which equals 42, since 7 times 6 is 42.
Explanation:
To find the product of 7x6, imagine you have 7 rows of a chart and each row has 6 columns. This means you'll fill the chart with numbers so that there are six numbers in each of the seven rows. Multiplying 7 by 6 means you're essentially counting how many numbers you'll have if you filled all the rows and columns.
To find the result, you just need to do a simple multiplication of the two numbers (7 and 6).
Here's how it's done step-by-step:
Understand that 7x6 is the same as adding the number 6 together, 7 times.
6 + 6 + 6 + 6 + 6 + 6 + 6
When you add them up, you get 42.
Therefore, the product of 7x6 is 42, meaning if you had a table with 7 rows and 6 columns, it would contain 42 cells.
Is 11 to 15 correct?
please help! im bad at this!
Rewrite the following equation in slope-intercept form. 17x − 7y = 16 Write your answer using integers, proper fractions, and improper fractions in simplest form.
Angles A, B, and C represent the three angles of triangle ABC. If the measure of angle A is (4x - 8)°, the measure of angle B is (5x+2)°, and the measure of angle C is (6x-9)°, what is the measure of angle B (in degrees)?
The price of a math book is $50, but you have only $35 with you. If you get a discount of 20%, how much money do you need to borrow from a friend so that you can buy the book?
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Segment CO is congruent to segment HZ .
Which congruence statement is true?
CH≅HZO
OZ≅CO
CO≅HZ
CH≅COZ
Answer: CO≅HZ
Step-by-step explanation:
The two chords are congrunt so the intercepted arcs are congruent CO≅HZ
Since segment CO is congruent to segment HZ, a congruence statement that is true include the following: C. CO ≅ HZ.
What are the corresponding parts of two congruent figures?In Mathematics and Euclidean Geometry, two geometric figures are considered to be congruent only when their corresponding side lengths are equal and the magnitude of their angles are congruent.
Since we know that rigid motions preserve both the side length and angle measure, this ultimately implies that congruent segments have the same (equal) length.
In this context, we can reasonably infer and logically deduce that arc CO is congruent with arc HZ because chord CO is congruent to chord HZ;
arc CO ≅ arc HZ (intercepted arcs).
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a triangular pyramid has a volume of 840 cubic inches the triangular base has a base length of 20 inches and a height of 21 inches find the height of the pyramid
The required height of the pyramid is 6 inches.
Given that,
A triangular pyramid has a volume of 840 cubic inches a triangular base has a base length of 20 inches and a height of 21 inches find the height of the pyramid is to be determined.
What is volume?Volume is defined as the ratio of the mass of an object to its density. In other words, the Volume of the object is the product area of the cross-sectional profile and extruded height.
Here,
The base area of the triangle = 20 * 21 = 420 inches².
Volume of the triangular pyramid = 1 / 3 * base area * height
840 = 1 / 3 * 420 * height
840 / 140 = height
height = 6 inch.
Thus, the required height of the pyramid is 6 inches.
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Question 10 please :(
A contest on a game show receives -25 points for each wrong answer what integer represents the change in periods after three wrong answers
A crew of loggers cleared ½ acre of lumber in 4 days. How long will it take the same crew to clear 2 ¾ acres of lumber?
Please help me on this math question pleasee
Sophie bikes at a speed of s miles per hour. Her friend Rana is slower, her biking speed is only r miles per hour. Today the girls went for a 20 miles trip, each girl was biking at her usual speed. How long did Sophie wait for Rana after her own arrival to the finish?
Final answer:
Sophie waits for Rana after finishing a biking trip of 20 miles, accounting for their different speeds. The answer is calculated based on the difference in distances covered by Sophie and Rana.
Explanation:
Sophie bikes at a speed of s miles per hour, and Rana bikes at a speed of r miles per hour. They went for a 20 miles trip each at their usual speeds. After Sophie finishes, Rana still has to cover a distance of 20 - 20*(r/s) miles. Therefore, the time Sophie waits for Rana is (20 - 20*(r/s))/s hours.
Sarah multiplied 4.16 and 1.83, as shown. But she forgot to put a decimal point in the answer. Complete the sentence below.
Answer:
The decimal point should be placed between the digits 7 and 6 because the product should be greater than 4 × 1 and less than 5 × 2.
Step-by-step explanation:
55% decrease followed by a 25% increase
What is the area or perimeter for carpeting a floor?
The area for carpeting a floor is the measurement of the surface that needs to be covered by carpet, while the perimeter refers to the total length around the edges of the floor.
Explanation:The area for carpeting a floor is the measurement of the surface that needs to be covered by carpet. The perimeter, on the other hand, refers to the total length around the edges of the floor. The choice between calculating the area or perimeter for carpeting a floor depends on whether you need to determine how much carpet material is needed (area) or how much carpet edge is required (perimeter).
For example, if you want to calculate the area to determine the amount of carpet needed to cover the floor, you would measure the length and width of the floor and multiply them together. The resulting area would be in square units (such as square feet or square meters).
On the other hand, if you want to calculate the perimeter to determine how much carpet edge needs to be trimmed or finished, you would add up the lengths of all the sides of the floor. The resulting perimeter would be in linear units (such as feet or meters).
540 seconds how many minutes
A. 41 Cu in
B. 83 Cu in
C. 124 Cu in
D. 166 Cu in
WILL GOLD MEDAL
1) Given the data 12, 39, 21, 18, 24, 17, 12, 25:
What is the outlier in the data?
What is the mean with the outlier?
What is the mean without the outlier?
A)12; 21; 18.4
B)12; 18.4; 21
C)39; 21; 18.4
D)39; 18.4; 21
what type of relationship does this pair of angles have?67 degrees and 23 degrees
67° and 23° are complementary angles.
67 + 23 = 90
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
We know that, a ray is a line that continues on forever inn one direction with a point at it's start.
here, we have,
67 degrees and 23 degrees
we know,
67 + 23 = 90
Hence, 67° and 23° are complementary angles.
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The table shows the number of hours two groups of teens spent on science and math homework last week. Each group was made up of 10 teens. 13- to 14-year olds 10 9 11 8 10 10 2 7 8 12 15- to 16-year olds 12 10 8 11 12 12 6 4 4 10 Select from the drop-down menus to correctly complete each statement. The mean hours the groups of teens spent studying is , The range for the two groups of of teens is .
Answer: The mean hours the groups of teens spent studying is little bit greater for 15- to 16-year old teen or about same .
The range range for the two groups of of teens is greater for 13- to 14-year old teens.
Step-by-step explanation:
We know that the mean of a data is given by :-
[tex]\text{Mean}=\dfrac{\text{Sum of all observations}}{\text{Number of observations}}[/tex]
Range = largest observation - least observation
From the given table :
The mean hours spent by 13- to 14-year olds is given by :-
[tex]\text{Mean}=\dfrac{87}{10}=8.7[/tex]
[tex]\text{Range=12-2=10}[/tex]
The mean hours spent by 15- to 16-year olds is given by :-
[tex]\text{Mean}=\dfrac{89}{10}=8.9[/tex]
[tex]\text{Range=12-4=8}[/tex]
The mean hours the groups of teens spent studying is little bit greater for 15- to 16-year old teen or can say about same.
The range range for the two groups of of teens is greater for 13- to 14-year old teens.
Measure of angle a=71 measure of angle b =38. Find measure of angle bcr
Jorge, Lynne, and Crosby meet at the playground. Jorge lives 5/6 mile from the playground. Lynne lives 4/6 mile from the playground. Crosby lives 7/8 mile from the playground. Who lives closer to the playground, Jorge or Lynne? Explain how you know.
In comparing distances, Lynne lives closer to the playground than Jorge. This is determined by comparing the fractions representing their distances from the playground, with Lynne's being smaller.
Explanation:In this situation, we need to compare the distances each person lives from the playground. Jorge lives 5/6 mile from the playground and Lynne lives 4/6 mile from the playground. Since a smaller fraction represents a smaller distance, we can say that Lynne lives closer to the playground than Jorge does.
To understand this better, consider fractions as a way to divide a whole into parts. The larger the denominator, the more parts the whole is divided into and the smaller each part is. But in this case, the denominators are the same (6), so we look at the numerators. The numerators tell us how many of these parts we have. Since 4 is smaller than 5, Lynne who lives 4/6 mile away lives closer than Jorge who lives 5/6 mile away.
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Stretch Your Thinking Ann arranges her marbles in groups, with 8 marbles in each group. She writes the fraction 5/8 to show the fraction of marbles in each group that is red. What equivalent fraction names the fraction of marbles in 6 groups that are Red? Explain.