Simplify. 1/3(−32.48−14.02) Enter your answer, as a decimal to tenths, in the box.
Answer: After doing the order of operations and round the decimal to tenths the result is - 15.5
Solution:
1/3(-32.48-14.02)
1. Operations inside the parentheses: Add numbers with the same sign:
1/3(-46.50)
2. Multiplication:
1/3(-46.50/1)=[(1)(-46.50)] / [(3)(1)]=(-46.50)/(3)
3. Dividing:
(-46.50)/(3) = - 15.50
4. Rounding decimal to tenths:
- 15.50 = - 15.5
Prove that the sum of three consecutive positive integers is divisible by 3
[tex]n+n+1+n+2=3n+3=3(n+1)[/tex]
Which statements are true about the ordered pair (−3, 1) and the system of equations?
{x−4y=6
3x+y=−8
Select each correct answer.
The ordered pair (−3, 1) is a solution to the first equation because it makes the first equation true.
The ordered pair (−3, 1) is a solution to the second equation because it makes the second equation true.
The ordered pair (−3, 1) is not a solution to the system because it makes at least one of the equations false.
The ordered pair (−3, 1) is a solution to the system because it makes both equations true.
50 POINTS
Mei draws three pairs of parallel lines that are each intersected by a third line. In each figure, she measures a pair of angles.
What is a reasonable conjecture for Mei to make by recognizing a pattern and using inductive reasoning?
A reasonable conjecture for Mei is the Alternate Interior Angles Theorem, which states if a transversal intersects parallel lines, the alternate interior angles are equal.
Explanation:Based on the scenario, a reasonable conjecture for Mei to make would be, if a transversal intersects parallel lines, then the alternate interior angles are congruent. This statement is known as the Alternate Interior Angles Theorem. In other words, in each of Mei's figures, if the angles she measured are alternate interior angles, they should have the same measurement.
For example, if three pairs of parallel lines are intersected by a third line (called a transversal), a pattern that consistently appears is the equality of the alternate interior angles (angles that are on opposite sides of the transversal and inside the parallel lines). This implies, if the two lines are parallel, then any alternate pair of interior angles are equal.
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Are the following figures similar?
yes or no?
Corresponding angles are congruent
Yes or no?
Corresponding sides are proportional
Simplify (5ab4c)(-abc2). 4b3c -5a2b5c3 -5ab4c2
it will be simplified as [tex]\( -5a^2b^5c^3 \).[/tex]
Sure, let's simplify the expression step by step:
Given expression: [tex]\( (5ab^4c)(-abc^2) \)[/tex]
Step 1: Multiply the coefficients (numbers) together:[tex]\( 5 \times -1 = -5 \)[/tex]
Step 2: Multiply the variables with the same base together and add their exponents. Start with 'a': [tex]\( a \times a = a^{1+1} = a^2 \)[/tex]
Step 3: For 'b', multiply[tex]\( b^4 \) with \( b^1 \) which gives \( b^{4+1} = b^5 \).[/tex]
Step 4: For 'c', multiply[tex]\( c^1 \) with \( c^2 \) which gives \( c^{1+2} = c^3 \).[/tex]
Combine all these results together:[tex]\( -5a^2b^5c^3 \)[/tex]
So, the simplified expression is [tex]\( -5a^2b^5c^3 \).[/tex]
1. Start by multiplying the coefficients (numbers) together. In this case,[tex]\( 5 \times -1 = -5 \).[/tex]
2. Next, multiply the variables with the same base together and add their exponents. For 'a',[tex]\( a^1 \) times \( a^1 \) gives \( a^{1+1} = a^2 \). Similarly, for 'b', \( b^4 \) times \( b^1 \) gives \( b^{4+1} = b^5 \), and for 'c', \( c^1 \) times \( c^2 \) gives \( c^{1+2} = c^3 \).[/tex]
3. Combine all these results together to get [tex]\( -5a^2b^5c^3 \).[/tex]
This process ensures that each term in the expression is simplified according to the rules of exponents and multiplication of coefficients.
complete question
Simplify (5ab4c)(-abc2). 4b3c -5a2b5c3 -5ab4c2
What is the equation of the line in standard form? (-1,-4) (2,2)
If m FDG = 50°, what is m FEG?
75°
50°
100°
25°
Thank you!
What is the value of x in the equation 1/5x – 2/3y = 30, when y = 15? 4 8 80 200
An exterior angle of an isosceles triangle has measure 130°. Find two possible sets of measures for the angles of the triangle.
If the exterior angle of the bases is 130°, then the measure of the angle of each base is
--------degrees° and the measure of the vertex is --------
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Given that an isosceles triangle has an exterior angle of its base angle that is 130°, the two possible sets of angles obtainable in the triangle are:
Base angles: [tex]\mathbf{30^{\circ}}[/tex]Vertex angle: [tex]\mathbf{80^{\circ}}[/tex]Recall:
An isosceles triangle has two equal base angles and two equal sides.Thus:
The isosceles triangle has been given in the image attached below to show the possible angle measures we can get.
In figure 1, we see that when the exterior angle of the bases is 130°, the measure of each of the base angles would be:
[tex]\mathbf{180 - 130 = 50^{\circ}}[/tex]
The vertex angle would be:
[tex]\mathbf{180 - (50 + 50) = 80^{\circ}}[/tex]
Therefore, given that an isosceles triangle has an exterior angle of its base angle that is 130°, the two possible sets of angles obtainable in the triangle are:
Base angles: [tex]\mathbf{30^{\circ}}[/tex]Vertex angle: [tex]\mathbf{80^{\circ}}[/tex]Learn more here:
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You need to buy fertilizer for a circular flower bed with a diameter of 13 feet. If one bag will fertilize 10 square feet, how many bags do you need to buy?
The area of the flower bed is approximately 132.73 square feet. Each bag of fertilizer covers 10 square feet, so we'd need 13.27 bags. Rounding up, we'll need to buy 14 bags.
Explanation:The question involves the calculation of the area of a circular flower bed and determining the amount of fertilizer needed for that area. The area of a circle can be calculated using the formula πr², where 'r' (radius) is half of the diameter. In this case, the diameter of the flower bed is 13 feet, so the radius is 13/2 = 6.5 feet. We then square the radius (6.5²) which gives us 42.25 and multiply by π (approximately 3.14), resulting in an area of approximately 132.73 square feet. Given that each bag of fertilizer covers 10 square feet, we would need 13.27 bags of fertilizer. Since we cannot buy a fraction of a bag, we would need to buy 14 bags to fully cover the flower bed.
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What is the product of all positive divisors of $100$?
The product of all positive divisors of the number 100 is 1,000,000, using the property that the product of an integer's positive divisors is equal to the integer raised to the power of half its total number of divisors.
Explanation:The product of all positive divisors of 100 can be found using a special property. This property states that for any positive integer n, the product of all its positive divisors will be equal to n raised to the power of half its total number of divisors. Now, factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. So, there are 9 divisors, and the product of all positive divisors will be 100^((9/2)). The answer is 1,000,000.
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Francesca typed 496 words in 8 minutes. Which of the following is a correct understanding of this rate?
a. at this rate, it takes 62 minutes for Francesca to type one word
b.at his rate, Fransesca can type 62 words in 8 minutes.
c. at this rate, Fransesca can type 62 words in one minute.
d. at this rate, Fransesca can type 8 words in one minute.
At 2:00 p.m. two cars start toward each other from towns 240 miles apart. If the rate of one car is 10 mph faster than the other, how fast does each car go if they meet at 5:00 p.m.? If 3x represents the distance that the slower car traveled, then which expression represents the distance the faster car traveled?
To find the speed of each car, we set up and solve an equation based on the given information. The slower car's speed is 35 mph and the faster car's speed is 45 mph.
Explanation:To solve this problem, we need to set up an equation based on the given information. Let's assume that the slower car's speed is x mph, so the faster car's speed would be (x + 10) mph. Since they meet at 5:00 p.m. and start at 2:00 p.m., they have been traveling for 3 hours.
Using the formula: speed = distance/time, we can write the equation:
x * 3 + (x + 10) * 3 = 240
Simplifying the equation, we get:
3x + 3(x + 10) = 240
6x + 30 = 240
6x = 210
x = 35
So, the slower car's speed is 35 mph and the faster car's speed is (35 + 10) = 45 mph.
What is the solution to the equation 1.2m − 0.8 = −2.0m?
A.) m= 0.25
B.) m= 0.4
C.) m= 1
D.) m= 4
The measure of DCG is 145°. What is mDCE? 90° 100° 180° 190°
The measure of ∠DCE is 100° so option (B) will be correct.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
In another word, the angle is the measurement of the angular distance for example for linear motion we have a meter inch but for angular rotation, we don't have the measurement so the angle is useful to measure the angular rotation.
Given the angle,
∠DCG = ∠DCE + 20 + 25
145° = ∠DCE + 20 + 25
∠DCE = 100°
Hence "The measure of ∠DCE is 100°
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A stadium has 46,000 seats. Seats sell for $30 in Section A, $24 in Section B, and $18 in Section C. The number of seats in Section A equals the total number of seats in Sections B and C. Suppose the stadium takes in $1,193,400 from each sold-out event. How many seats does each section hold?
A car averages 27 miles per gallon. If gas costs $4.04 per gallon, which of the following is closest to how much the gas would cost for this car to travel 2,727 typical miles? Individual Question $44.44 $109.08 $118.80 $408.04 $444.40
Need help ASAP quick
Mike is 11 years old. jim is twice as old as mike. when jim is 50 years old, how old will mike be? 28
Simplify the expression 2.1(4.5x)
There are 50 cards numbered from 1 to 50. two different cards are chosen at random. what is the probability that one number is twice the other number?
The probability that one number is twice the other number when two different cards are chosen at random is 1/49.
Explanation:To find the probability that one number is twice the other number when two different cards are chosen at random from a set of 50 cards numbered from 1 to 50, we need to determine the number of favorable outcomes and the total number of possible outcomes.
The favorable outcomes occur when one card is twice the value of the other card. Let's consider the smaller number as 'x'. In that case, the larger number would be '2x'. We can see that 'x' can take any value from 1 to 25, since the larger number '2x' should be less than or equal to 50.
So, the number of favorable outcomes is 25. The total number of possible outcomes is the number of ways to choose 2 cards out of 50, which is given by the combination formula: C(50, 2) = 50! / (2! * (50-2)!), which simplifies to 50 * 49 / 2 = 1225.
Therefore, the probability is given by the ratio of the favorable outcomes to the total number of possible outcomes: 25/1225 = 1/49.
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If it takes 5 machines 5 minutes to make 5 widgets, how many minutes does it take 500 machines to make 500 widgets?
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Does 1/1 count as 1 in fractions
The height of a right circular cone is multiplied by 3, but its radius remains fixed. By what factor will the volume of the cone be multiplied?
The volume of the cone will be multiplied by a factor of [tex]\(3^1 = 3\).[/tex]
The volume of a right circular cone is given by the formula:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height of the cone.
Given that the height of the cone is multiplied by 3, the new height [tex](\( h' \))[/tex] becomes 3 times the original height [tex](\( h \))[/tex]:
[tex]\[ h' = 3h \][/tex]
Now, let's find the volume of the new cone with the updated height:
[tex]\[ V' = \frac{1}{3} \pi r^2 (3h) \][/tex]
[tex]\[ V' = \pi r^2 (h) \times 3 \][/tex]
So, the volume of the new cone is three times the original volume.
Now, let's dive into the explanation:
When the height of a cone is multiplied by a factor, the volume of the cone is directly proportional to the cube of that factor. This is because the volume formula contains the height term raised to the power of 3. So, if the height is tripled, the volume will be multiplied by[tex]\(3^3 = 27\).[/tex]
Alternatively, we can calculate it directly:
Original Volume: [tex]\(V = \frac{1}{3} \pi r^2 h\)[/tex]
New Volume:[tex]\(V' = \frac{1}{3} \pi r^2 (3h) = \pi r^2 h \times 3\)[/tex]
Therefore, the volume of the cone will be multiplied by a factor of [tex]\(3^1 = 3\).[/tex]
Complete question:
The height of a right circular cone is multiplied by 3, but its radius remains fixed. By what factor will the volume of the cone be multiplied?
94 POINTS
Ricardo draws three right triangles. In each figure, he measures a pair of angles.
What is a reasonable conjecture for Ricardo to make by recognizing a pattern and using inductive reasoning?
A.) In a right triangle, all of the angles are right angles.
B.) In a right triangle, all of the angles are acute.
C.) In a right triangle, the acute angles are complementary.
D.) In a right triangle, the acute angles are congruent.
Answer:its c
Step-by-step explanation:
cccccccccccccccccccccccccccccccccccccccccccc
The graph of g(x)=(1/2)x is the graph of f(x)=2x reflected over the y-axis. Which graph represents g(x) please help!
Answer:
Step-by-step explanation:
To which graph does the point (−1, 4) belong?
y ≤ −x + 4
y ≤ −x − 2
y ≤ 2x − 3
y ≤ 4x + 1
Answer: First one
Step-by-step explanation:
Due to slope form which is y=mx + b.
-1 = x and y = 4.
It does not show the one because it would be equal to X, but it does show the negative
Wen takes a job with a starting salary of $100,000 for the first year. She earns a 3% increase each year. What does S5 represent?
Final answer:
S5 represents Wen's salary in the fifth year after receiving a 3% annual raise from a starting salary of $100,000. Fifth year salary is $112,550.
Explanation:
The student is asking about an arithmetic sequence or a geometric sequence involving a salary increase. In this case, S5 represents the salary Wen will earn in the fifth year of her employment, assuming a 3% annual salary increase from a starting salary of $100,000. To calculate S5, we use the formula for the sum of a geometric sequence because a constant percentage change implies exponential growth. The first term (a) is her starting salary, the common ratio (r) is 1.03 (reflecting the 3% increase), and the term we want to calculate is the fifth term (n=5).
The formula for the nth term of a geometric sequence is Tn = a × r^(n-1), where Tn is the nth term, a is the first term, and r is the common ratio. Applying the formula:
First Term (a): $100,000Common Ratio (r): 1.03Fifth Term (S5): $100,000 × (1.03)^(5-1)S5 = $100,000 * (1.03)^4 = $100,000 * 1.1255 = $112,550.Therefore, S5 calculates the salary Wen will earn in year five after receiving a 3% raise each year from the starting salary of $100,000 to $112,550.
A magazine has a special offer of 18 issues for $28.44. How much does each issue cost?
Answer:
A magazine has a special offer of 18 issues for $28.44. Each issue costs $1.58. Solution: 28.44 / 18 = 1.58.