Final answer:
The expression 80 + (-22 4/15) is solved by converting the mixed number to an improper fraction, aligning the fractions by the same denominator, and then adding them to get 58 4/15 as the result.
Explanation:
To solve the expression 80 + (-22 4/15), follow these steps:
First, convert the mixed number -22 4/15 into an improper fraction. To do this, multiply the whole number by the denominator and add the numerator: (-22 × 15) + 4 = -330 + 4 = -326, so the mixed number becomes -326/15.
Next, since 80 is a whole number, we can convert it into a fraction with the same denominator of 15 to make it easier to add to -326/15. To do that, multiply 80 by 15/15, which is the equivalent of 1, to get the fraction 1200/15.
Now, add the two fractions: 1200/15 + (-326/15) = (1200 - 326)/15 = 874/15.
This fraction can be simplified back into a mixed number by dividing the numerator by the denominator: 874 ÷ 15 = 58 with a remainder of 4, so the mixed number is 58 4/15.
Therefore, the solution to the expression 80 + (-22 4/15) is 58 4/15.
Factor completely. x2 + 5x + 6 A. (x - 3)(x + 3) B. (x - 1)(x + 6) C. (x + 3)(x + 2) D. (x + 5)(x + 1)
being [tex]x^{2} +5x+6[/tex] the answer is (x-3)(x-2)
begin [tex]x^{2} -5x+6[/tex] the answer is (x+3)(x+2)
1. [tex]x^{2} +5x+6[/tex]
second grade formala is used
[tex]x= \frac{-b±\sqrt{b^{2} } -4ac}{2a}\\ x=\frac{-5±\sqrt{5^{2} } -4.1.6}{2} \\ x= \frac{-5±1}{2} \\ x_{1} =-3 \\ x_{2} =-2[/tex]
explain how you would find how many 1 1/2 cup servings there are in a pot that contains 22 1/2 cups of soup.
Step-by-step explanation:
multiply the 1 1/2 by 2 to get 3.
find the closest number that is divisible by 3
3*7 is 21.
We now have to multiply 7 by 2 since we did that to our mixed number to get a whole number.
There is still a 1 1/2 left over. Simply add 1 to 14.
Answer:
15 servings
Step-by-step explanation:
Given,
Total number of cups = [tex]22\frac{1}{2}[/tex]
The number of cups required for each serving = [tex]1\frac{1}{2}[/tex]
Thus,
[tex]\text{The number of servings}=\frac{\text{Total cups}}{\text{cups required for each serving}}[/tex]
[tex]=\frac{22\frac{1}{2}}{1\frac{1}{2}}[/tex]
[tex]=\frac{\frac{45}{2}}{\frac{3}{2}}[/tex]
[tex]=\frac{45}{3}[/tex]
= 15
Need help with question 9
Hey!
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Solution:
I would assume that the iron intake is combined between breakfast and lunch. So 8.25mg is too meals worth of iron. So all we have to do is subtract.
15 - 8.25 = 6.75
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Answer:
6.75mg are still needed for his daily intake.
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Hope This Helped! Good Luck!
Round the following numbers to the nearest 100. The numbers they have 324,558,256
Answer:
300, 600, 300.
Step-by-step explanation:
324: The tens digit is 2 so we do nothing to the hundreds digit so its 300.
558: The tens digit is 5 so we round up the 5 . So it is 600.
In a similar way 256 becomes 300.
Answer:
300, 600, 300
Step-by-step explanation:
When you round a number up by the nearest 100. The digit in the tens place must be equal to or more than 5.
For example: 250 is rounded up to 300, but 240 can not be rounded up to 300.
When you have a number like 240, it can only be rounded down to 200
324 is rounded down to 300 because the tens place digit is less than 5
558 is rounded up to 600 because the tens place digit is higher than 5.
256 is rounded up to 300 because the tens place digit is 5.
A suitcase is a rectangular prism whose dimensions are 1 3/4 feet by 1 3/4 feet by 2 1/4 feet. Find the volume of the suitcase. Enter the answer as a mixed number in simplest form.
The volume of a rectangular prism is found by multiplying its length, width, and height. Given the dimensions as 1 3/4 ft by 1 3/4 ft by 2 1/4 ft, when converted to improper fractions and multiplied together, we find that the volume of the suitcase is 220.5 cubic feet.
Explanation:The subject of the student's question is focused on the mathematical concept of volume, specifically the volume of a rectangular prism. To find the volume of the suitcase, we need to multiply the length, width, and height of the suitcase. Given that the suitcase's dimensions are 1 3/4 ft by 1 3/4 ft by 2 1/4 ft, we first convert these mixed numbers into improper fractions (7/4 ft by 7/4 ft by 9/4 ft). Then, we multiply them together:
Volume = Length x Width x Height.
Volume = (7/4 ft) x (7/4 ft) x (9/4 ft) = 220.5 ft³.
The volume of the rectangular prism (suitcase) is 220.5 cubic feet.
Learn more about Volume of Rectangular Prism here:https://brainly.com/question/22023329
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A classroom teacher randomly draws the name of a student. If the teacher has between 20 and 30 students in her class, what is a good estimate of the probability of a specific student's name being drawn?
Answer:2 to 4%
Step-by-step explanation:
your odds are 1/30 then your persentage would be 3 percent so your range of 20 to 30 students would be 2 to 4 percent chances
Final answer:
The estimated probability of a specific student's name being drawn from a class of 20-30 students is 4% or 1 in 25.
Explanation:
The probability of a specific student's name being drawn from a class with a number of students between 20 and 30 can be estimated by taking the inverse of the average of the maximum and minimum possible number of students. We calculate the average by adding 20 (the minimum) to 30 (the maximum) and dividing by 2, resulting in an average class size of 25 students.
To estimate the probability of drawing any one student's name, we take the inverse of 25, which is 1/25 or 0.04. Thus, the estimated probability is 4% that any particular student would be chosen in a random draw from a class size between 20 and 30 students.
PLEASE HELP ME!! I DO NOT UNDERSTAND PLEASE SHOW WORK THANK YOU!!
Answer:
= 10x² + 9x³
Step-by-step explanation:
I'm assuming you mean question 19
3x² + 5x³ + 7x² + 4x³ (rearrange to group like terms)
=3x² + 7x² + 5x³ + 4x³ (factor out common powers)
= (3+7)x² + (5+4)x³
= 10x² + 9x³
How did the railroad facilitate population growth in
the interior of the country? Check all of the boxes
that apply.
The railroad built towns along the railroad.
The railroad bought land from farmers,
ranchers, and business owners.
The railroad recruited settlers to form new
communities along the route.
The railroad encouraged American Indians to
settle along the route.
DONE
Answer:
1. The railroad built towns along the railroad.
and
3. The railroad recruited settlers to form new.
Step-by-step explanation:
I just took it
The railroad facilitate population growth in the interior of the country by The railroad built towns along the railroad, The railroad recruited settlers to form new.
What is the population?A population is a complete set of a group of individualists, whether that group constitutes a nation or a group of groupings with a common characteristic. In data point, a population is the pool of individuals from which a statistical sample is drawn for a study. As we see, different countries have different populations.
The construction of the transcontinental railroad boosted Western economic development and population growth. For both persons and commodities, railroad businesses offered superior transportation. Additionally, they sold the property to settlers, which prompted a Westward migration. New railroads benefited the industry.
Therefore, option (A) is correct
Learn more about populations here:
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Turn 3.45 into a mixed number write in simplest form
Answer:
3 whole number, 9/20
because if you multiply 20 by 3 and add it by 9 you get 69, so when you divide the 69/20, you get 3.45
What is the domain of the function y=2.X-6?
E OF
O
O 05x<
O 35x<<
O 65x<0
Answer:
6 ≤ x < ∞
Step-by-step explanation:
The value of x cannot be less than 6 because that would make the term in the square root part negative. There is no real square root of a negative vale.
4. A square court for playing the game four square has an area of 256 ft?. How long is one
side of the court?
Describe a real world situation that can be represented by the quotient -85\15.
Final answer:
A real world situation that can be represented by the quotient -85/15 is paying off a credit card debt.
Explanation:
A real world situation that can be represented by the quotient -85/15 is the following:
Suppose you owe $85 on your credit card and you make monthly payments of $15. You want to know how many months it will take for you to pay off your debt completely.
To find the answer, you divide the amount you owe ($85) by the monthly payment ($15):
-85/15 = -5.67
This means it will take approximately 5.67 months to pay off your debt.
Simplify (3x2 − 2) + (5x2 + 5x − 1).
Answer: 9
The steps are in the picture
Answer:
8x² + 5x - 3
Step-by-step explanation:
Given
(3x² - 2) + (5x² + 5x - 1)
Since both parenthesis are distributed by 1 just remove them, that is
3x² - 2 + 5x² + 5x - 1 ← collect like terms
= (3x² + 5x²) + 5x + (- 2 - 1)
= 8x² + 5x - 3
A man is paid $9.60 per hour for a 40 hour week and he is paid at a time and a half for overtime he worked when his wage for a certain week was $528.00.
Answer:
50 hours.
Step-by-step explanation:
First I found how how much the man was paid in a week for the base 40 hours which was 384. Then i subtracted that from the wage from the week so i could just have the overpay amount which was 144. I then multiplied 9.6 by 1.5 to get the hourly pay for overtime and god 14.4 dollars an hour. Lastly, i divided 144 by 14.4 and got 10 extra hours which got me to my answer of 50 hours because i added the 40 initial hours.
Final answer:
In this case, the man worked 10 hours of overtime.
Explanation:
The question pertains to calculating the regular and overtime pay of a man who earns $9.60 per hour for a standard 40-hour work week and time and a half for any hours worked beyond that. To find how many hours of overtime he worked when he earned $528.00 in a week, we need to use mathematical equations.
First, we calculate the man's regular weekly pay for 40 hours: 40 hours × $9.60/hour = $384.00. Since his total pay is $528.00, the overtime pay is $528.00 - $384.00 = $144.00.
Overtime pay is time and a half, so the overtime rate is $9.60/hour × 1.5 = $14.40/hour. We then divide the total overtime pay by the overtime rate: $144.00 / $14.40/hour = 10 hours of overtime work.
Thus, the man worked 10 hours overtime in addition to his regular 40 hours to make a total of $528.00.
What is the value of y if 6y -2 = 34
Answer:
y = 6
Step-by-step explanation:
Given
6y - 2 = 34 ( add 2 to both sides )
6y = 36 ( divide both sides by 6 )
y = 6
Answer:
y = 6
Step-by-step explanation:
6y - 2 = 34
+2 +2
6y = 36
--- -----
6 6
y = 6
What is the highest common factor of 24 and 76
Answer:
4 is the highest common factor
Answer:
The highest common factor is 4
Step-by-step explanation:
Factors of 24 are { 1,2,3,4,6,8,12.......}
And factors of 76 are{ 1,2,4,19......)
from the two factors,
common factor ( C. F ) ={1,2,4}
and from the common factors, the highest is 4
Therefore 4 is the highest common factor for 24 and 76.
whats the pattern and the next 2 numbers of this question: -1, 2, 7, 17, _, _ .
Answer:
see explanation
Step-by-step explanation:
Consider the differences in the terms
2 - (- 1) = 2 + 1 = 3
7 - 2 = 5
14 - 7 = 7
The differences are 3, 5, 7 ← increasing in steps of 2
Thus the next 2 differences should be 9 and 11
Then the next 2 terms are
14 + 9 = 23
23 + 11 = 34
Solve y2+22=38 for y.
A
16
B
8
C
32
D
24
What’s the measure of x
Answer:
[tex]\boxed {\sf x=66^o}[/tex]
Step-by-step explanation:
Apply the properties of a triangle:-
Where, the sum of all internal angles of a triangle is always equal to 180°.
[tex]\sf 90^o+x+24^o=180^o[/tex]
Combine like terms.
[tex]\sf x+90+24=180^o[/tex]
Add numbers.
[tex]\sf x+114=180^o[/tex]
Subtract 114 from both sides.
[tex]\sf x+114-114=180-114[/tex]
[tex]\sf x=66^o[/tex]
I need a story for 24-(6+3) I’m super confused cause all the stories here are hard for me to understand
Answer:
Are there any options for this question?
Step-by-step explanation:
I cant answer it without options.
find the coordinates of Z if Y is the midpoint of XZ , X( -10, 9) , and Y( -4,8)
Answer:
The coordinates of Z are (2,7)
Step-by-step explanation:
we know that
The formula to calculate the midpoint between two points is equal to
[tex]Y=(\frac{x1+x2}{2} ,\frac{y1+y2}{2})[/tex]
we have
X(-10,9),Y(-4,8)
Let
(x2,y2) ----> the coordinates of Z
substitute the values
[tex](-4,8)=(\frac{-10+x2}{2} ,\frac{9+y2}{2})[/tex]
Solve for x2
[tex]-4=(-10+x2)/2\\-8=-10+x2\\x2=10-8\\x2=2[/tex]
Solve for y2
[tex]8=(9+y2)/2\\16=9+y2\\y2=16-9\\y2=7[/tex]
therefore
The coordinates of Z are (2,7)
Answer: The required co-ordinates of Z are (2, 7).
Step-by-step explanation: Given that Y is the midpoint of XZ and the co-ordinates of X are (-10, 9) and the of Y are (-4, 8).
We are to find the co-ordinates of Z.
Let (a, b) represents the co-ordinates of the point Z.
We know that
the co-ordinates of the midpoint of a line segment with endpoints (x, y) and (z, w) are given by
[tex]\left(\dfrac{x+z}{2},\dfrac{y+w}{2}\right).[/tex]
So, according to the given information, we have
[tex]\left(\dfrac{-10+a}{2},\dfrac{9+b}{2}\right)=(-4,8)\\\\\\\Rightarrow \dfrac{-10+a}{2}=-4\\\\\Rightarrow -10+a=-8\\\\\Rightarrow a=-8+10\\\\\Rightarrow a=2[/tex]
and
[tex]\dfrac{9+b}{2}=8\\\\\Rightarrow 9+b=16\\\\\Rightarrow b=16-9\\\\\Rightarrow b=7.[/tex]
Thus, the required co-ordinates of Z are (2, 7).
What is 1 4/7 divided by 4 5/7
ANSWER THIS ASAP I ONLY HAVE 57 minutes LEFT PLEASE HURRY!!!!
Answer:
Step-by-step explanation:
[tex]\frac{11}{7} * \frac{7}{33}[/tex]
[tex]\frac{11 * 7}{7 * 33}[/tex]
[tex]\frac{1}{3}[/tex]
[tex]0.333[/tex]
how many grams would be in 10 kilograms?
INEEDHELP!!!!!!
Every kilogram is 1,000 grams, but you want 10 kilograms. You can multiply 1,000 10 times (you can also add 1,000 10 times,) giving you the answer > 10,000.
Hope this helped!
Nate
[tex]\huge\boxed{\text{10,000 grams}}[/tex]
One kilogram is made up of [tex]\text{1,000}[/tex] grams. You can remember this because the Greek root "kilo" means "thousand."
So, just multiply [tex]\text{10} \times \text{1,000}[/tex] to get [tex]\boxed{\text{10,000 grams}}[/tex].
Use the point slope equation to identify the slope and the coordinates of a point
on the line y - 4= (x - 1)
Answer:
[1, 4]; 1 = m
Step-by-step explanation:
According to the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE terms of what they really are, so in this case, the coordinates are [1, 4]. Now, the rate of change [slope] is 1 because an invisible coefficient is always assumed to be 1.
I am joyous to assist you anytime.
Answer:
The slope of the line is 1 and it passes through the point (1,4).
Step-by-step explanation:
If a line passes through a points [tex](x_1,y_1)[/tex] with slope m, then the point slope form of the line is
[tex]y-y_1=m(x-x_1)[/tex] .... (1)
The given equation of line is
[tex]y-4=(x-1)[/tex] .... (2)
We need to find the slope and the coordinates of a point on the given line.
On comparing (1) and (2) we get
[tex]m=1[/tex]
[tex]x_1=1[/tex]
[tex]y_1=4[/tex]
Therefore, the slope of the line is 1 and it passes through the point (1,4).
NUMBER 52:
PLEASE HELP ME HAVE TO TEST ON IT TOMMORROW AND I DO NOT UNDERSTAND PLEASE EXPLAIN THOROUGHLY !!
Answer:
c
Step-by-step explanation:
Its c because 10/3.69=0.369 then you tomes that by twelve and itequals 4.428 round that up and its 4.43.
Solve the formula for the specified variable
A=p+prt solve for r
Answer:
Step-by-step explanation:
The first step is to take p on both sides:
[tex]A - p = p + p*r*t - p[/tex]
On the right hand side, cancel p and -p, since [tex]p-p=0[/tex]. The equation will be:
[tex]A - p = p*r*t[/tex]
Then, divide both sides of the equation by p*t:
[tex]\frac{A-p}{p*t} = \frac{p*r*t}{p*t}[/tex]
On the right hand side, p*t can be cancelled:
[tex]\frac{A-p}{p*t} = r[/tex]
Answer:
r=A-p (the line is the bar so this is a-p over pt)
pt
Step-by-step explanation:
P + Prt = A
P r t=A −P isolate the term which contains r
P rt=A−P
divide pt by each side
- 3/4 (x + 2) = 6
the / is a fraction can someone help
Triangle ABC has a perimeter of 12 units. The vertices of the triangle are A(x,2), B(2,-2), and C(-1,2). Find the value of x.
Answer:
The value of x is 2
Step-by-step explanation:
* Lets explain how to find a distance between 2 points
- If the endpoints of a segment are [tex](x_{1},y_{1})[/tex] and
[tex](x_{2},y_{2})[/tex] is [tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
- Triangle ABC has a perimeter of 12 units
∵ The perimeter of any triangle is the sum of lengths of its sides
∴ P Δ ABC = AB + BC + AC
* Lets find the length of the three sides
∵ A = (x , 2) , B = (2 , -2) , C = (-1 , 2)
∵ [tex]AB=\sqrt{(2-x)^{2}+(-2-2)^{2}}[/tex]
∴ [tex]AB=\sqrt{(2-x)^{2}+(-4)^{2}}[/tex]
∴ [tex]AB=\sqrt{(2-x)^{2}+16}[/tex]
∵ [tex]BC=\sqrt{(-1-2)^{2}+(2--2)^{2}}[/tex]
∴ [tex]BC=\sqrt{(-3)^{2}+(4)^{2}}[/tex]
∴ [tex]BC=\sqrt{9+16}[/tex]
∴ [tex]BC=\sqrt{25}[/tex]
∴ BC = 5
∵ [tex]CA=\sqrt{(x--1)^{2}+(2-2)^{2}}[/tex]
∴ [tex]CA=\sqrt{(x+1)^{2}+(0)^{2}}[/tex]
∴ [tex]CA=\sqrt{(x+1)^{2}}[/tex]
- The √ is canceled by power 2
∴ CA = (x + 1)
∵ AB + BC + CA = 12
∴ [tex]\sqrt{(2-x)^{2}+16}[/tex] + 5 + (x + 1) = 12
- Add 5 and 1
∴ [tex]\sqrt{(2-x)^{2}+16}[/tex] + 6 + x = 12
- subtract 6 and x from both sides
∴ [tex]\sqrt{(2-x)^{2}+16}[/tex] = (6 - x)
- To cancel (√ ) square the two sides
∴ (2 - x)² + 16 = (6 - x)²
- Simplify the two sides
∴ [(2)(2) + (2)(2)(-x) + (-x)(-x)] + 16 = (6)(6) + (2)(6)(-x) + (-x)(-x)
∴ 4 - 4x + x² + 16 = 36 - 12x + x²
- Subtract x² from both sides
∴ 20 - 4x = 36 - 12x
- Add 12x to both sides and subtract 20 from both sides
∴ 12x - 4x = 36 - 20
∴ 8x = 16
- Divide both sides by 8
∴ x = 2
* The value of x is 2
How do you do 185 times 12 in standard algorithm?
the answer is 2,220
you first aline 185 × 12 like so 185
× 12
then you need to multiply everything
Find the perimeter of quadrilateral ABCD. Round your answer to the nearest hundredth.
A(-5, 4)
B(0,3)
C(4,-1)
D(4,-5)
E(2,-3)
F(-2,1)
Answer:
The perimeter of quadrilateral ABCD is 27.48 units
Step-by-step explanation:
we know that
The perimeter of quadrilateral ABCD is the sum of its four length sides
so
[tex]P=AB+BC+CD+AD[/tex]
we have
A(-5, 4),B(0,3),C(4,-1) and D(4,-5)
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Find the distance AB
Substitute in the formula
[tex]d=\sqrt{(3-4)^{2}+(0+5)^{2}}[/tex]
[tex]d=\sqrt{(-1)^{2}+(5)^{2}}[/tex]
[tex]AB=\sqrt{26}\ units[/tex]
Find the distance BC
Substitute in the formula
[tex]d=\sqrt{(-1-3)^{2}+(4-0)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(4)^{2}}[/tex]
[tex]BC=\sqrt{32}\ units[/tex]
Find the distance CD
Substitute in the formula
[tex]d=\sqrt{(-5+1)^{2}+(4-4)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(0)^{2}}[/tex]
[tex]CD=4\ units[/tex]
Find the distance AD
Substitute in the formula
[tex]d=\sqrt{(-5-4)^{2}+(4+5)^{2}}[/tex]
[tex]d=\sqrt{(-9)^{2}+(9)^{2}}[/tex]
[tex]AD=\sqrt{162}\ units[/tex]
Find the perimeter
substitute the values
[tex]P=\sqrt{26}+\sqrt{32}+4+\sqrt{162}=27.48\ units[/tex]
see the attached figure to better understand the problem