The sum of the given expressions will be 6x-18.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The given expression is (2x−6)+4(x−3). The summation will be calculated as
Sum = (2x-6)+4(x-3)
Sum = (2x-6)+4x-12
Then we combine like terms.
Sum = (2x-6)+4x-12
Sum = 6x-6-12
Sum = 6x-18
Therefore, the sum of the given expressions will be 6x-18.
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What if Randy needs an equal number if bowls and cups for his picnic how many packs of each will he need to buy bowls number 1 pack is 6 cups number of pack is 8
To have equal numbers of bowls and cups, Randy should buy 4 packs of bowls and 3 packs of cups, as the least common multiple of 6 (number of bowls per pack) and 8 (number of cups per pack) is 24.
Explanation:If Randy needs an equal number of bowls and cups for his picnic and one pack consists of 6 bowls and another pack consists of 8 cups, the least common multiple (LCM) of 6 and 8 must be found to ensure an equal number of both items. The LCM of 6 and 8 is 24, because 24 is the smallest number that both 6 and 8 can divide evenly into. Therefore, Randy will need to buy 4 packs of bowls (4 packs × 6 bowls per pack = 24 bowls) and 3 packs of cups (3 packs × 8 cups per pack = 24 cups) to have an equal number of each for his picnic.
which set of ordered pairs is a function?
[(-5, 1), (-3, 2), (-1, 3) (1, 4), (3, 5) or
[(-2, 1), (-4, 2), (0,3), (4, 1), (-2,5)]
[(-1, 5), (-1,4), (-1, 3), (-1, 2) (-1, 1)]
[(-6, -4), (-4, -2), (0, 0), (-4, 2) (-6, 4)]
Functions can't have multiple y values have the same x value.
[(-5, 1), (-3, 2), (-1, 3) (1, 4), (3, 5)] ** No repeating x-values.
[(-2, 1), (-4, 2), (0,3), (4, 1), (-2,5)]
[(-1, 5), (-1,4), (-1, 3), (-1, 2) (-1, 1)]
[(-6, -4), (-4, -2), (0, 0), (-4, 2) (-6, 4)]
Answer:
[(-5, 1), (-3, 2), (-1, 3) (1, 4), (3, 5)]
I really need some help with this, it's confusing me something fierce. Could you do a step by step if possible, please.
Choose the correct answer.
Mike Morgan has a $83,098.59 loan. He paid $1,000 in fees and $4,900 in total interest the first year. If the APR is the finance charge (interest plus fees) for one year ÷ amount financed, what was the APR for that year?
A) 7.5
B) 7.1
C) 7.3
Total of fees: 1,000 + 4,900 = 5,900
You are told the APR is the total fees divided by the amount financed, so divide the total fees by the amount financed:
5,900 / 83,098.59 = 0.71
0.71 x 100 = 7.1% APR.
The answer is B.
1.complete the column of proof
given < B=<D, m<b=80
prove <c=100
2.complete the paragraph proof
GIVEN<a a=and <b are complementary and <b and <c are complementary proof <a =<c
The first question probably has a drawing that is not included. Can you please include whatever drawing cam with it?
The Qeustion 2:
starting with writing the complementary angles:
The angles <a and <b being complementary means that
<b = 180 - <a
The angles <b and <c are complementary - that means
<c = 180 - <b
now plug in the first equation for <b to get:
<c = 180 - (180 - <a) = 180-180+<a= <a
so
<c = <a
which was to be proved!
Wolves have good endurance and have been known to travel long distances-up to about 60 miles-in one night.If a wolf trots 18 4/5 miles in 2 1/3 hours,what is its speed?
Answer:
8 2/35 miles per hour
Step-by-step explanation:
We are given distance traveled and the time required. We can use those directly in the relation that gives speed:
speed = distance / time
... = (18 4/5 miles)/(2 1/3 hours)
... = (94/5 miles)/(7/3 hours) . . . . . . converte mixed numbers to improper fractions
... = (94/5×3/7) miles/hour . . . . . . . "invert and multiply"
.. = 282/35 miles/hour . . . . . . . . . . improper fraction result
... = 8 2/35 miles/hour . . . . . . . . . . as a mixed number
Help with this question please!
∠1 and ∠2 are alternate exterior angles where transversal BE crosses parallel lines AC and DF, therefore they are equal. ∠2 and ∠3 are opposite angles of a parallelogram, therefore they are equal.
... ∠1 = ∠2
... 3x -5 = 2x +15 . . . . substitute the given values
... x = 20 . . . . . . . . . . . add 5-2x
The measures of angles 1, 2, and 3 are 2·20+15 = 55 . . . degrees.
Graph x <17/5+7/20 on number line
The open circle at 3.75 and the arrow pointing left represents the values of x that are less than 3.75.
To graph [tex]\(x < \frac{17}{5} + \frac{7}{20}\)[/tex] on a number line, we'll first simplify the expression:
[tex]\(\frac{17}{5} + \frac{7}{20}\)[/tex]
To add these fractions, find a common denominator, which in this case is 20:
[tex]\(\frac{17}{5} = \frac{17 \times 4}{5 \times 4} = \frac{68}{20}\)[/tex]
Now, add the fractions:
[tex]\(\frac{68}{20} + \frac{7}{20} = \frac{75}{20}\)[/tex]
So, the expression simplifies to [tex]\(x < \frac{75}{20}\)[/tex].
To simplify [tex]\(\frac{75}{20}\)[/tex]:
[tex]\(75 \div 20 = 3.75\)[/tex]
This means the inequality is [tex]\(x < 3.75\)[/tex].
Now, to graph this on a number line, mark a point at 3.75, but as it is "less than" <, make sure to have an open circle at 3.75, indicating that it does not include the value itself. Then, draw an arrow to the left, signifying all values less than 3.75.
```
0-------------------o-------------------3.75------------------->
```
Here, the open circle at 3.75 and the arrow pointing left represents the values of x that are less than 3.75.
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What system of linear inequalities is shown in the graph?
Enter your answers in the boxes.
two boxes
Try this option:
1) to difine the equations of the lines given in the picture. They are: y= -0.5x+2 (for the left line, see the attached picture) and y=2x-3 (for the right line).
2) according to the condition (dark area and type of the line) the 1st inequation is y≥ -0.5x+2, the 2d inequation is y>2x-3.
3) the required system is
[tex]\left \{ {{y>2x-3} \atop {y\geq -0.5x+2}} \right.[/tex]
find the distance CD rounded to the nearest tenth C=(7,-4) D=(-8,-5)
15.0 ( to the nearest tenth )
calculate the distance (d) using the distance formula
d = √(x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (7, - 4 ) and (x₂, y₂ ) = (- 8, - 5 )
d = √(-8 - 7 )² + (- 5 + 4 )² = √(225 + 1 ) = √226 ≈ 15.0
A student has passed 60 percent of the 20 quizzes he has written so far successfully. If the student writes 50 quizzes during the year and passes 80 percent of the remaining quizzes successfully, what is the percent of all successful quizzes for the entire year?
PLS HELP QUICK
The student’s total percent of all successful quizzes for the entire year is 72%.
To determine the percent of all successful quizzes for the entire year, we need to follow these steps:
Calculate the number of quizzes passed so far: The student has passed 60% of 20 quizzes. This is calculated as follows:
0.60 x 20 = 12 quizzes passed.
Determine the number of quizzes remaining: The student needs to write 50 quizzes in total, so the remaining quizzes are 50 - 20 = 30 quizzes.
Calculate the number of additional quizzes passed: The student is expected to pass 80% of the remaining quizzes.
0.80 x 30 = 24 quizzes passed.
Calculate the total number of quizzes passed: Add the quizzes passed so far to the additional quizzes passed.
12 + 24 = 36 quizzes passed in total.
Determine the percentage of successful quizzes for the entire year: Divide the total number of successful quizzes by the total number of quizzes.
(36 / 50) x 100 = 72% successful quizzes.
Thus, the student’s total percent of all successful quizzes for the entire year is 72%.
A circle has an area of 324π cm2. What is the radius?
Final answer:
To find the radius of a circle, use the formula A = πr² and solve for r by dividing the area by π and then taking the square root of the result.
Explanation:
The radius of a circle can be found using the formula for the area of a circle, A = πr².
Given A = 324π cm², substitute this value into the formula: 324π = πr².
Solve for r by dividing both sides by π: r² = 324, r = √324, r = 18 cm.
One ordered pair (a,b) satisfies the two equations ab^4 = 12 and a^5 b^5 = 7776. What is the value of 'a' in this ordered pair?
Answer:
a = 4.762203156
Step-by-step explanation:
Given:
ab^4 = 12 and a^5b^5 = 7776
Making the equations a subject of a;
a = 12/b^4 and a^5 = 7776/b^5
Finding fifth root on both sides of equation two;
a = [tex]\sqrt[5]{7776}[/tex]/b
You will get a = 6/b
Equating the two equations;
12/b^4 = 6/b
Multiplying both sides by b^4 gives:
b = [tex]\sqrt[3]{2}[/tex] = 1.25992105
We had that a = 12/b^4 so;
a = 12/1.25992105^4 = 12/2.5198421 = 4.762203156
Terri wants to make a triangle on her driveway with one side 8ft, one side 17 ft, and one side 8ft. Write an indirect proof to show that Terri’s design is not possible.
The third side of a triangle must always be less than the sum of the other 2 sides
here 8 + 8 = 16 and 17 ( the third side ) 17 > 16
Hence this is not a valid triangle
one type of insect is 0.0052 meter long. what is the length in scientific notation.
Here, we need to write the length of the insect in scientific notation.
The given length of the insect is 0.0052 meter
Now, to write 0.0052 meter in scientific notation we need to follow this:
Scientific notation always start with non-zero digit followed by a decimal point.
Since in our number the decimal is needed to be moved three places to the right to get the first non-zero digit.
The exponent of the 10 is [tex]-3[/tex].
[tex]10^{-3}=\frac{1}{1000} =0.001[/tex]
Therefore, our number 0.0052 can be written as:
[tex]5.2 \times 10^{-3}[/tex]
Hence, the require scientific notation is [tex]5.2 \times 10^{-3}[/tex].
Help me with this pls!
The third angle of the triangle will be the supplement of the sum of the given angles. In order for the triangle to be isosceles, two of the three angles must have the same value.
a) 180 -40 -75 = 65 . . . not isosceles
b) 180 -30 -100 = 50 . . . not isosceles
c) 180 -35 -70 = 75 . . . not isosceles
d) 180 -50 -80 = 50 . . . matches one of the other angles. This triangle is isosceles.
The appropriate choice is ...
... 50 and 80
Convert the following repeating decimal to a fraction.
0.37 repeating
[tex]x=0.\overline{37}\\\\100x=37.\overline{37}\\\\100x-x=37.\overline{37}-0.\overline{37}\\\\99x=37\\\\x=\dfrac{37}{99}[/tex]
Ethan and Leo start riding their bikes at the opposite ends of a 65-mile bike path. After Ethan has ridden 1.5 hours and Leo has ridden 2 hours, they meet on the path. Ethan’s speed is 6 miles per hour faster than Leo’s speed. Find the speed of the two bikers
let Leo's speed = x mile/hr
so Ethan speed = (x + 6) miles per hour
Distance = Speed × Time
so distance traveled by Leo in 2 hours = x × 2 = 2x
and distance traveled by Ethan in 1.5 hours = 1.5( x + 6 ) = 1.5x + 9
since they meet on the path , After Ethan has ridden 1.5 hours and Leo has ridden 2 hours , so together the have traveled on complete path that is 65 miles.
⇒ distance traveled by leo in 2 hours + distance traveled by Ethan in 1.5 hours = 65
⇒ 2x + 1.5x + 9 = 65
⇒ 3.5x = 56
⇒ x = 16
Hence Leo's speed = x miles/hr = 16 miles/hour
and Ethan's speed = (x + 6) miles/hr = 16 +6 = 22 mile/hour
Answer:
Leo's Speed = 16
Ethan's Speed = 22
Step-by-step explanation:
Jacob has a mean score of 78 after his first four math tests. He wants to make a B, or an average of 80, in math. What does he need to score on the fifth test to have a mean score of 80?
A.
82
B.
88
C.
94
D.
108
I also have another one.
Which of the following is a valid conclusion from the pie chart?
A.
If 60 students read four books, then 15 students read five or more books.
B.
More than half the students read fewer than 3 books.
C.
If 60 students read four books, then 120 students read two books.
D.
Twenty-two percent of the students read four or more books.
Answer:
1) B. 88
2) C. If 60 students read four books, then 120 students read two books.
Step-by-step explanation:
1) Solution
Step 1: Let "x" be the 5th test score.
Scores upto the 4th tests = 4*78 = 312
Step 2: Mean of the five tests = 80
(x + 312)/5 = 80
x + 312 = 80*5
x + 312 = 400
Step 3: Now find the value of x.
x = 400 - 312
x = 88
Therefore, Jacob scored 88 in the 5th test.
2) Solution
Step 1: 60 students read four books.
Now find the number of students.
Percentage of students read four books = 12% = 0.12
Total number of students = 60/0.12 = 500
Percentage of students reads two books = 24% = 24/100 = 0.24
Number of students read two books = 0.24*500
= 120
Hope you will understand the concept.
Thank you.
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Classify the following triangle. Check all that apply.
Step-by-step explanation:
A triangle can be of many types like right angled triangle, isosceles triangle, scalene triangle, obtuse, acute etc.
A right angle can be defined as the triangle in which one of the angle is 90 degrees.
An obtuse angle is that type of triangle in which the the angle is more than 90 degrees and less than 180 degrees.
An isosceles triangle is one in which two sides are equal.
An acute angle is the triangle in which the angle is less than 90 degrees.
The attached triangle is :
1. Right angle triangle
2. Isosceles triangle
Does anyone know these?
You seem to generally have the right idea, and you seem to be able to solve the equations you write. However, your choice of equations for the problem sometimes needs a little work.
12.Given∠DBC = (12x -3)°∠DBE = (5x +12)°∠EBC = (3x +13)°∠DBC = ∠DBE + ∠EBCFind∠EBCSolution∠DBC = ∠DBE + ∠EBC
(12x -3) = (5x +12) + (3x +13) . . . . . substitute given values
12x -3 = 8x +25 . . . . . . . . . collect terms
4x = 28 . . . . . . . . . . . . . . . add 3-8x
x = 7 . . . . . . . . . . . . . . . . . . divide by 4
3x +13 = 3·7 +13 = 34
∠EBC = 34°
__________
13.Given∠FBC = (10x -9)°∠CBE = (4x +15)°∠FBC = ∠CBE = (1/2)∠FBEFind∠FBESolution∠FBC = ∠CBE
10x -9 = 4x +15 . . . . . substitute given values
6x = 24 . . . . . . . . . . . .add 9-4x
x = 4 . . . . . . . . . . . . . . divide by 4
∠FBC = (10·4 -9)° = 31°
∠FBE = 2·∠FBC = 2·31°
∠FBE = 62°
__________
14.Given∠1 = (7x -19)°∠2 = (x +5)°∠1 + ∠2 = 90°Find∠2Solution∠1 +∠2 = 90°
(7x -19) +(x +5) = 90 . . . . . . substitute the given values
8x -14 = 90 . . . . . . . . . . . . . collect terms
8x = 104 . . . . . . . . . . . . . . . add 14
x = 13 . . . . . . . . . . . . . . . . . . divide by 8
∠2 = (13 +5)°
∠2 = 18°
__________
15.Given∠1 = (6x +25)°∠4 = (10x -11)°∠1 = ∠4 . . . . . . they are vertical anglesFind∠1Solution∠1 = ∠4
6x +25 = 10x -11 . . . . substitute the given values
36 = 4x . . . . . . . . . . . add 11-6x
9 = x . . . . . . . . . . . . . .divide by 4
∠1 = (6·9 +25)°
∠1 = 79° . . . . . . matches your answer
Vanessa wants to buy a new iPod that costs $239.25. She earns $7.25 per hour at work.
Answer:
She would have to work for 33 hours.
Step-by-step explanation:
239.25/7.25=33. Since we are going with hours, this would be 33.
Write a ratio for each situation 310 beats per minute
The obvious one is (310 beats)/(1 minute).
Which of the following describes how to translate the graph y = |x| to obtain the graph of y = |x - 1| - 1? 1 unit left and 1 unit down 1 unit left and 1 unit up 1 unit right and 1 unit down 1 unit right and 1 unit up
Answer:
1 unit right and 1 unit down
Step-by-step explanation:
When you replace x with x - h, you translate the graph h units horizontally.
When you replace y with y - k, you translate the graph k units vertically.
y = |x - 1| - 1
y + 1 = |x - 1|
y - (-1) = |x - 1|
Compare the last equation above with y = |x|. x was replaced by x - 1, so h = 1, and the translation is 1 unit horizontally. Since 1 is positive, it is a 1 unit translation to the right. y was replaced by y - (-1), so k = -1, and the vertical translation is 1 unit down.
Answer:
1 unit right and one unit down
Step-by-step explanation:
A large balloon holds 3 cubic feet of helium gas. How many balloons can be filled with 2,301 cubic feet of helium gas? A) 747 B) 757 C) 767 D) 777
i think it will be c not really 100 percent sure
Answer:
C 767
Step-by-step explanation:
2031 ÷ 3 = 767
and took test
At the bank, Sheila made 5 deposits, each in the same amount. Her sister Sherri made 4 deposits, each in the same amount. Each of Sherri's deposits was $15 more than each deposit Sheila made. Both sisters deposited the same amount in the end. How much did each sister deposit each time?
- Write an equation. Let x represent the amount of one of Sheila’s deposits.
- Solve the equation. Show your work.
- Check your solution. Show your work.
- State the solution in complete sentences.
The equation would be 4y=5x 4(x+15)=5x x+15=y
let x be the amount that Shelia deposits each time
let y represent the amount that Sherri deposits each time
4(x+15)=5x
4x+60=5x
-4x -4x
60=x
Check:
x+15=y 60+15=y y=75
4(75)=5(60)
300=300
Shelia deposits $60 each time.
DERIVAR :
(2x – 1) / √ x2 + 1
Compare 9.36 and 9.359
Try this option (this is not the only way!):
1. the rule: if 'number_1' - 'number_2' > 0, then number_1>number_2. If 'number_1'-'number_2'<0, then number_2>number_1.
2. according to the rule above: 9.36-9.359=0.001. 0.001>0, it means, 9.36>9.359.
Volume of triangular prism
Answer:
216
Step-by-step explanation:
9 * 6 = 54
54 * 8 = 432
432/2 = 216 is the answer
The volume of a triangular prism is the area of the base multiplied by the height. This can be represented as volume = base × height
Let's first identify our values:
9 m = height of the prism
6 m = base of the triangle
8 m = height of the triangle
First, we need to calculate the area of the triangle. To calculate the area of a triangle, the formula is base × height ÷ 2.
The base of the triangle is 6 and the height of the triangle is 8 so 6 multiplied by 8 will give us a product of 48. Next, we need to divide 48 by 2 and we will get a quotient of 24.
Finally, we need to multiply the area of the triangle by the height of the prism.
24 × 9 = 216
Therefore, the volume of the triangular prism is 216[tex]m^{3}[/tex]
Write an equation of the line passing through each of the following pairs of points. c (4, 0), (−2, 8)
Moving from -2 to 4 is a gain of 6 in the x-direction and a drop of 8 in the y-direction. Thus, the slope of this line is m = -8/6, or m = -4/3.
Then, using the point-slope formula, y - 0 = (-4/3)(x-4), or y = (-4/3)x + 16/3
y=-1 1/3x+5 1/3
I hope this helps
Free Brainliest! **PLEASE HELP**
Use the equation to find the length of the missing leg measure.
a^2 + 16^2 = 20^2
1. Evaluate Powers: A^2 + 256 = 400
2. Undo addition: a^2 = 144
3. Undo The square: a= 144 ( Square root )
What is the length of the missing leg measure?
a = ________ units
[tex] a^2+16^2=20^2[/tex]
[tex] a^2+256=400[/tex]
Subtracting 256 from both sides
[tex] a^2=144[/tex]
Taking squareroot both sides
[tex] a= \sqrt144[/tex]
[tex] a = \sqrt2.2.3.2.2.3[/tex]
[tex] a=12[/tex]
Therefore length of missing leg is
[tex] a = 12 units[/tex]
a^2+16^2=20^2
a^2+256=400
Subtracting 256 from both sides
a^2=144
Taking squareroot both sides
a= \sqrt144
a = \sqrt2.2.3.2.2.3
a=12
Therefore length of missing leg is
a = 12 units
Need help ASAP please!
x | - 8 - 4 0 4 8
y | 28 16 4 - 8 - 20
to calculate the values of y, substitute the given values of x into the equation
x = - 8 : y = (- 3 × - 8 ) + 4 = 24 + 4 = 28
x = - 4 : y = (- 3 × - 4 )+ 4 = 12 + 4 = 16
x = 0 : y = (- 3 × 0 ) + 4
0 + 4 = 4
x = 4 : y = (- 3 × 4 ) + 4 = - 12 + 4 = - 8
x = 8 : y = (- 3 × 8 ) + 4 = - 24 + 4 = - 20