Given:
15.870 + 6.77
We are required to round each number to the nearest tenth before performing the addition.
The tenth digit is the number first number after the decimal point.
First step:
Round to the nearest tenth
15.870 ==> 15.9
6.77 ==> 6.8
Second step:
Add both numbers after rounding to the nearest tenth
15.9 + 6.8 = 22.7
ANSWER:
22.7
Corie buys dog food in a 34-pound bag. Her dog eats about 1 pound a day. Corie buys cat
food in a 16-pound bag. Her cat eats about 1/4 pound a day. Assume she buys new bags of pet
food on the same day. On which day will the two bags have the same weight? Show how you
figured it out.
The day the two bags will have the same weight is the 24th day.
On which day will the two bags have the same weight?The linear equation that can be used to determine the pound of dog food left is:
Amount of dog food left = capacity of the bag - (number of days x amount the dog eats per day)
Amount of dog food left = 34 - (1 x p)
Amount of dog food left = 34 - 1p
The linear equation that can be used to determine the pound of cat food left is:
Amount of cat food left = capacity of the bag - (number of days x amount the cat eats per day)
Amount of cat food left = 16 - (1/4 x p)
Amount of cat food left = 16 - 1/4p
On the day the two bags will have the same weight, the two above equations would be equal:
16 - 1/4p = 34 - 1p
p - 1/4p = 34 - 16
3/4p = 18
p = (18 x 4) / 3
p = 24 days
To learn more about linear equations, please check: https://brainly.com/question/25711114
#SPJ1
Label the missing side length of the figure below. Click each dot on the image to select an answer. A sculpture made up of 2 rectangular prisms. Color is used to show the rectangular prisms that make up the figure. The first rectangular prism is green and has dimensions of an unknown length of 2 meters width by 3 meters height. The second rectangular prism is purple and has dimensions of 10 meters in length by 4 meters in width by 7 meters in height. Find the volume of the entire figure by adding the importance of the separate figures. \text{Volume}=Volume=start text, V, o, l, u, m, e, end text, equals {}+ \purpleD{280}=+280=plus, start color #7854ab, 280, end color #7854ab, equals \text{ cubic meters} cubic meters create text, space, c, u, b, i, c, space, m, e, t, e, r, s, end text
Answer:
Your answer is A now.
Step-by-step explanation:
I need the answer ASAP!!
The centrifugal force of an object moving in a circle varies jointly with the radius of the circular path and the mass of the object and inversely as the square of the time, it takes to move about one full circle. A 6-gram object moving in a circle with a radius of 75 centimeters at a rate of 1 revolution every 3 seconds has a centrifugal force of 5000 dynes. Find the centrifugal force of a 20-gram object moving in a circle with radius of 155 centimeters at a rate of 1 revolution every 5 seconds.
Write down the equation.
Answer: 12,500
Formula for centrifugal force = [tex]\frac{k r m}{t^{2} }[/tex]
In the first case,
The mass of an object moving in a circle as 'm1' and radius as 'r1', 'k' as constant, and time as 't1'. 'f1' is centrifugal force.
centrifugal force is f1 = [tex]\frac{kr1m1}{t1^{2} }[/tex]
In the second case,
The mass of an object moving in a circle as 'm2' and radius as 'r2', 'k' as constant, and time as 't2'. 'f2' is centrifugal force.
m1 = 6 gram , r1 = 75 cm , t1 = 3 sec, f1 = 5000 dynes
as per equation, 5000 = [tex]\frac{ k * 75 * 6}{3^{2} }[/tex] , after calculation the value of k = 100
in the second case use the same equation and find centrifugal force (f2)
f2 = [tex]\frac{k * r2 * m2}{t2^{2} }[/tex] ,m2 = 20 gram , r1 = 155cm , t1 = 5 sec, k= 100
f2 = [tex]\frac{100 * 155 * 20}{5^{2} }[/tex] after calculation f2 = 12,400.
so, the final centrifugal force is 12,400 dynes.
To learn more about Centrifugal Force
https://brainly.com/question/545816
13) Solve the following quadratic equations by completing the square: X^2 + 16x + 5 = 0
We want to solve the following equation
x² + 16x + 5 = 0
↓
x² + 16x = 5
We want to rewrite the equation so its left side is
(x + a)²
We know that
(x + a)² = x² + 2ax + a²
where a is a number, then, we want that the left side look something like
x² + 2ax + a²
Then we first want to find which must be the number a in this case.
Finding aSince 2 · 8 = 16, then the left side is
x² + 16x = x² + 2 · 8x
then, in this case a would be 8
a = 8
Completing the square with a²We want that the left side of our equation looks like:
x² + 2ax + a²
Since it has the first two terms
x² + 16x = 5
we have to add a² = 8² = 64
We add it both sides of the equation:
x² + 16x + 8² = 5 + 64
x² + 2 · 8x + 8² = 69
Now, we can write it as (x + a)²
x² + 2 · 8x + 8² = 69
↓ since (x + a)² = x² + 2ax + a²
(x + 8)² = 69
Solving the equationIn order to solve the equation, we want to "leave x alone" on the left side:
(x + 8)² = 69
↓ squaring root both sides
(x + 8) = ±√69
x + 8 = ±√69
↓ taking 8 to the right side
x = - 8 ±√69
SolutionsWe have two solutions:
x₁ = - 8 -√69
x₂ = - 8 + √69
Since
How do you find the distance between the points shown
Answer:
A. Subtract the distance between each point and the x-axis.
Step-by-step explanation:
The points shown are horizontally distanced. Because of this, you need to subtract their x values. In coordinate planes, the variable "x" represents how far a point is or is not from the origin. Given this information, you need to subtract the x values to get the distance they are apart. Note: Distance on a number line or graph is always given in absolute value. Absolute value is the term for when a number is converted to its positive form. For instance, |-1| has these brackets around it representing absolute value. Whenever a number in absolute value is a negative number or is greater than 0, it will become its positive form. |-1| = 1
Hope this helps!
Option A is correct, By subtracting the distance between each point and the x axis we find the distance between the points shown
What is Distance?The length along a line or line segment between two points on the line or line segment.
Distance=√(x₂-x₁)²+(y₂-y₁)²
The given two points in the given graph are A(-8, -4) and B(2,-4)
Now let us plug in these points in the formula.
x₂= 2, x₁ = -8, y₂=-4, y₁=-4
Distance=√(x₂-x₁)²+(y₂-y₁)²
=√(2+8)²+(-4+4)²
=√(10)²
=10 units.
By subtracting the distance between each point and the x axis we can find the distance.
Hence, Option A is correct, By subtracting the distance between each point and the x axis we find the distance between the points shown
To learn more on Distance click:
https://brainly.com/question/15172156
#SPJ2
help meeeeeeeeee pleasee
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2=1503\\\\t^2 =\frac{1503}{16}\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
Find the slope of the line that contains the following points: (17, -12) and (7, 8)
Answer: -2
Step-by-step explanation:
To find the slope of a line, we use the formula [tex]\frac{y(2)-y(1)}{x(2)-x(1)}[/tex]
{x(2),y(2)} coordinates of second points in line
{x(1),y(1)} coordinates of first points in line
So to solve, you take any set of your coordinates given and you chose one to be your second set and your first set. Then you take the y from your 1st set, and you subtract it from the y from your 2nd set. Then you take that and you put it over from what you get when you take the x from the 1st set, and you subtract that from the x in your 2nd set.
So when I solve using this the coordinates given, I get -12-8/17-7
This equals to -20/10, and that equals to -2.
So you find the slope of the line as -2
Solve for x: 2x²-2x-1=0
We can use the quadratic formula to solve this question. The quadratic formula is given below.
[tex]\begin{gathered} ax^2+bx+c=0 \\ \Rightarrow x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]In our case,
[tex]\begin{gathered} a=2,b=-2,c=-1 \\ \Rightarrow x=\frac{-(-2)\pm\sqrt[]{(-2)^2-4\cdot2\cdot-1}}{2\cdot2}=\frac{2\pm\sqrt[]{4+8}}{4}=\frac{2\pm\sqrt[]{12}}{4}=\frac{2\pm2\sqrt[]{3}}{4} \\ \Rightarrow x=\frac{1}{2}\pm\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]Then, the solutions are
[tex]x_1=\frac{1}{2}+\frac{\sqrt[]{3}}{2},x_2=\frac{1}{2}-\frac{\sqrt[]{3}}{2}[/tex]The solutions are 1/2+sqrt(3)/2 and 1/2-sqrt(3)/2
Hello! Please see the picture to see the question, Thank you!
7)
The given function is
[tex]f(x)=2x^2+4x^3+3x+5[/tex]Recall that the degree of the polynomial is the highest power of the variable.
The degree of the given polynomial function is 3.
we know that a cubic function is a polynomial function with degree 3.
Hence the given function is a cubic function.
Option D is correct.
what is the product of 2 2/3 and 1 1/6
Answer:
Step-by-step explanation: you can rewrite 2/3 plus 1/6 as: 2 3 + 1 6 To add fractions you need to have a common denominator (the bottom half of the fraction). In this case 6 is a common denominator.
When connected of Wi-fi, Julian's smart phone downloaded 32 songs in 4 minutes. How many songs can bedownloaded per minute
8 songs
Explanation:number of songs = 32
time = 4minutes
let the number of song per minute = y
32 songs = 4 minute
y = 1 minute
Cross multiply:
32(1) = 4(y)
32 = 4y
32/4 = 4y/4
y = 8
This means the number of songs that can be downloaded per minute is 8yna
Alicia watched a drone take off from a bridge. The height of the drone (in meters above the ground)minutes after takeoff is modeled byh(t) = −3+^2 + 12t +96Alicia wants to know when the drone will land on the ground.1) Rewrite the function in a different form (factored or vertex) where the answer appears as a number inthe equation.h(t) =2) How many minutes after takeoff does the drone land on the ground?
a.
Function:
[tex]h(t)=-3t^2+12t+96[/tex]Factoring -3, we have:
[tex]\begin{gathered} h(t)=-3t^2+12t+96 \\ h(t)=-3(t^2-4t-32) \end{gathered}[/tex]Middle term facotizing the term inside parenthesis:
[tex]\begin{gathered} h(t)=-3(t^2-4t-32) \\ h(t)=-3(t-8)(t+4) \end{gathered}[/tex]This is the factored form.
b.
h(t) is the height.
When it lands on the ground, the height (h(t)) is 0, so we have:
[tex]\begin{gathered} h(t)=-3(t-8)(t+4) \\ 0=-3(t-8)(t+4) \end{gathered}[/tex]If we solve this equation for t, we get the line drone lands on the ground.
Let's do this:
[tex]\begin{gathered} -3(t-8)(t+4)=0 \\ t=8,-4 \end{gathered}[/tex]Time can't be negative, so the solution is t = 8 seconds.
Answer:
h(t) = -3(t-8)(t+4) and 8 minutes
Step-by-step explanation:
Enjoy ur answer have a great day please mark as brainliest :D !!!
what is the scale factor of Triangle ABC to Triangle DEF?A. 3 B. 1/2C. 2D. 1/3
If we have the triangle ABC and we want to obtain the triangle DEF, we need to multiply every side of the triangle ABC by 3 as:
5 * 3 = 15
4 * 3 = 12
3 * 3 = 9
So, the scale factor of triangle ABC to triangle DEF is 3
Answer: 3
Ginny has a catering buisness. There is a proportional relationship between the number of people and the amount of meat she uses for an event. For 10 people she uses 4 pounds of meat. Find the amount of meat needed for 20, 30, 40, 50, and 75 people.
Explanation:
Let x be the number of people and y be the amount of meat.
They have a proportional relationship:
[tex]y=kx[/tex]To find the constant of proportionality k we use the initial information that for 10 people she uses 4 pounds of meat.
x=10 and y=4:
[tex]\begin{gathered} 4=k\times10 \\ k=\frac{4}{10}=\frac{2}{5} \end{gathered}[/tex]The relationship is:
[tex]y=\frac{2}{5}x[/tex]Now we just have to replace x by 20, 30, 40, 50 and 75 in this relationship and find y
Answer:
Number of people Amount of meat
20 8
30 12
40 16
50 20
75 30
1. On a clearance rack, t-shirts cost $5 and shorts cost $9. You have $35 to spend. Write an equation
that models the possible combinations of t-shirts, t, and shorts, s, you can buy.
The inequality that represents the situation is [5x + 9y ≤ 35] where x and y are the number of t-shirts and shorts purchased.
What is inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.
The majority of the time, size comparisons between two numbers on the number line are made.
So, we know that:
The T-shirts cost $5.
The shorts cost $9.
The total budget is $35.
Then, the inequality can be:
5x + 9y ≤ 35
Where x and y are the number of t-shirts and shorts purchased.
5(3) + 9(2) ≤ 35
15 + 18 ≤ 35
33 < 35
Therefore, the inequality that represents the situation is [5x + 9y ≤ 35] where x and y are the number of t-shirts and shorts purchased.
Know more about inequality here:
https://brainly.com/question/28964520
#SPJ1
Correct question:
On a clearance rack, t-shirts cost $5 and shorts cost $9. You have $35 to spend. Write a correct inequality that models the possible combinations of t-shirts, t, and shorts, s, you can buy.
I've always wondered why we put the dollar sign ($) before a number, when, when we say an amount of money we say the number first then dollars; like $12, but I think it really should be 12$, cause we don't go and say "dollar twelve", we say "twelve dollars". I don't know if this makes sense, but this always confused me; please share your thoughts.
Answer: I believe it's just custom. Some nations follow the quantity with a currency symbol, such as the dollar sign.
According to one hypothesis I've heard, the currency symbol was added before the quantity to stop individuals from modifying handwritten amounts, like changing 25.00 into 125.00, for example. It might be accurate, however I believe that the amount is always spelled out in words in the majority of situations when such fraud would be conceivable, such as on checks.
Step-by-step explanation:
What is the sum of these numbers?
+7+(-4)=
Answer:
3
Step-by-step explanation:
Since + × - = -
The - sign will change
+7 - 4 = 3
-12 + 8x less than or greater than -44
Could be the two
For example for less than we will obtain -12+8x<-44
For the greater than -12+8x>-44
Find the value of x in the triangle show below
Answer:
A
Step-by-step explanation:
a^2 + b^2 = c^2
2^2 + x^2 = 4^2
4 + x^2 = 16
x^2 = 12
x = √12
Examine the table, which represents a linear function. Input (C) output (y) 8 -40 -49 -58 What is the rate of change of the function? Enter your answer as a number, like this: 42(from MATH workbook 8A)
Answer:
-3
Explanation:
To calculate the rate of change of the function, we pick two pairs of points.
(8, -40) and (17,-67)
We use the formula below:
[tex]\begin{gathered} \text{Rate of change}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{-67-(-40)}{17-8} \\ =\frac{-67+40}{17-8} \\ =\frac{-27}{9} \\ =-3 \end{gathered}[/tex]The rate of change of the function is -3.
The emission veat of local zoo was $1.50 for children and $4.00 for adults, on a certain day 3000 people enter the zoo in $9250 is collected how many children adults attended?
1100 children and 1900 adults attended the local zoo on that day.
A system of equations or an equation system is a finite set of equations for which common solutions are sought.
Given:
A local zoo's admission fee is $1.50 for children and $4.00 for adults.
On a certain day, 3000 people enter the zoo and $9250.00 is collected.
We have to determine how many children and how many adults attended?
Solution:
Let number of children enter the zoo = x
Then number of adults enter the zoo = 3000-x
Total collection = $9250
Collection from children + Collection from adults = 9250
1.50 × x + 4(3000-x) = 9250
1.5x + 12000 – 4x = 9250
1.5x - 4x = 9250 - 12000
-2.5x = -2750
2.5x = 2750
X =2750/2.5
X = 1100
Number of children enter the zoo = x = 1100
Number of adults enter the zoo = 3000 - x = 3000 - 1100 = 1900
Therefore 1100 children and 1900 adults attended the local zoo on that day.
To learn more about the system of equations visit
https://brainly.com/question/24065247
#SPJ1
find the area and perimeter
Area: (4 * 2) + (4 *2) = 16cm^2
Perimeter: (4 + 2 )+ 6 + (2 + 2 + 4) = 20
Z.5 Graph solutions to one-step inequalities TMX DIN 4) Solve the inequality and graph the solution. ≥ 2 Language arts 0 Submit To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it. 1 2 3 Science 4 5 7 8 Recommendations 9 10
The solution of the inequality is d≥ 4. The graph is attached with the answer below.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.
A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
The solution to inequality is,
d/2 ≥ 2
d ≥ 2 x 2
d ≥ 4
The graph states that all the values of "d" are greater than or equal to 4.
Therefore, the solution to the inequality is d≥ 4. The graph is attached with the answer below.
To know more about inequality follow
https://brainly.com/question/24372553
#SPJ1
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 19.6 feet
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]
Solve the compound inequality, graph the solution set, and write in interval notation. SHOW ALL STEPS! 6x - 3x + 12 or 5x – 6 > 3x + 2
Answer
- The solution of this compound inequality is x < 3 OR x ≥ 4
- The graph of this solution is attached below
- The interval notation is (-∞, 3) OR [4, ∞)
Explanation
The compound inequality to be solved is
6x - 3 < x + 12 OR 5x - 6 ≥ 3x + 2
To solve this, we solve each of the pair one at a time for the two-part solution
6x - 3 < x + 12
6x - x < 12 + 3
5x < 15
Divide both sides by 5
(5x/5) < (15/5)
x < 3
OR
5x - 6 ≥ 3x + 2
5x - 3x ≥ 6 + 2
2x ≥ 8
Divide both sides by 2
(2x/2) ≥ (8/2)
x ≥ 4
So, the solution is
x < 3 OR x ≥ 4
So, this solution says that x is less than 3, but greater than or equal to 4.
For the graph, Note that
In graphing inequality equations, the first thing to note is that whenever the equation to be graphed has (< or >), the circle at the beginning of the arrow is usually unshaded.
But whenever the inequality has either (≤ or ≥), the circle at the beginning of the arrow will be shaded.
This solution tells us that the wanted parts are numbers less than 3 and numbers greater than 4.
Also, in writing inequalities as interval, the signs (< or >) indicate an open interval and is written with the bracket () while the signs [≤ or ≥] denote a closed interval which is denoted by the brackets [].
x < 3, that is, x ranges from negative infinity to just before 3.
x < 3 is (-∞, 3)
x ≥ 4, that is, x ranges from 4 to infinity
x ≥ 4 is [4, ∞)
Hope this Helps!!!
How are the least common multiple and the least common denominator related?
Least common denominator is the lowest number to which all the fractions can be expanded, so it is the Least common multiple of all denominators.
Given that,
We have to find the difference of LCD and LCM.
What is LCM?The least common multiple, or LCM, is the smallest common multiple of any two or more numbers. What does "common" mean? In this context, the word "common" refers to something that is shared by two or more people.
What is LCD?The LCD, or least common denominator, is the least common multiple of two or more denominators. In this instance, the denominator, or bottom number, of a fraction contains the common multiple. When arithmetically adding or subtracting fractions, the LCD must be computed. When dividing or multiplying fractions, the LCD is not required.
For example,
Let's check the following fractions:
(1/2,2/3,5/6)
To find the Least common denominator of the fractions we have to find the Least common multiple of the fractions' denominators:
lcd(1/2,2/3,5/6)=lcm(2,3,6)
To calculate the Least common multiple we have to find the lowest number which can be obtained by multiplying those numbers.
This number is 6 because we can multiply 2×3 and 3×2 to get 6.
Therefore, Least common denominator is the lowest number to which all the fractions can be expanded, so it is the Least common multiple of all denominators.
To learn more about multiple visit: https://brainly.com/question/5992872
#SPJ1
the question is in the pic! it must be simplified, decimalized, and percentaged
Answer
Explanation
Probability of an event is calculated as the number of elements in an event divided by the total number of elements in the sample space.
P(quarter)
Number of quarters = 4
Total number of coins in the jar = 6 + 14 + 16 + 4 =
whats b squared + c squared
Answer:
x+1/x-1 + 1-x/x+1 + 4x/1+x^2
What i the equation of a line that pae through the point (4,−17) and i perpendicular to y=x/7−3? Enter your anwer in the box
The equation of the line that is passing through the point (4,−17) and is perpendicular to y=x/7−3 is 7x -y = -30.
The line is passing through the point (4,-17) and is perpendicular to the line y = x/7-3
Now, the slope of the given line y = x/7-3 is,
M = 1/7
If the other line is perpendicular to it and has slope m, then the, we can write,
Mm = -1
So, putting values,
(1/7)m = -1
m = -7
Now, we have the slope m = -7 of the line and the point (4,-17) of the line,
So, the equation of the line will be,
m = [y-(-17)]/[x-4]
-7 = y+17/x-4
7x+47 = y+17
7x -y = -30
So, the equation of line is 7x -y = -30.
To know more about equation of line, visit,
https://brainly.com/question/18831322
#SPJ4
I need help its due today at 11:59 PM!!
Answer:
attached at point A; forms a right angle; attached at point B; forms a right angle; same; yes
Step-by-step explanation: