Answer:
C. 0.000743 LStep-by-step explanation:
[tex]1\ L=1,000\ mL\Rightarrow1\ mL=\dfrac{1}{1,000}\ L=0.001\ L\\\\0.743\ mL=0.743\cdot0.001\ L=0.000743\ L[/tex]
Jason and Jeremy work together at a juggling-ball factory. Jason lives 25 miles away from the factory and drives at 60 miles per hour. Jeremy lives 35 miles away from the factory and drives at 70 miles per hour.
If they leave their houses at the same time, then
(a) who arrives at the factory first ?, and
(b) how long is it until the other person arrives?
(a) Jason arrives at the factory first
(b) It takes 5 minutes until the other person arrives
Step-by-step explanation:
Jason and Jeremy work together at a juggling-ball factory
Jason lives 25 miles away from the factory and drives at 60 miles per hourJeremy lives 35 miles away from the factory and drives at 70 miles per hourThey leave their houses at the same timeWe need to know who arrives at the factory first and how long it is until the other person arrives
Time = Distance ÷ speed
∵ Jason lives 25 miles away from the factory
∴ The distance = 25 miles
∵ He drives at 60 miles per hour
∴ The speed = 60 miles per hour
- Use the rule above to find the time
∵ Time = 25 ÷ 60 = [tex]\frac{5}{12}[/tex] hour
∵ 1 hour = 60 minutes
∴ [tex]\frac{5}{12}[/tex] hour =
∴ Jason arrives to the factory in 25 minutes
∵ Jeremy lives 35 miles away from the factory
∴ The distance = 35 miles
∵ He drives at 70 miles per hour
∴ The speed = 60 miles per hour
- Use the rule above to find the time
∵ Time = 35 ÷ 70 = [tex]\frac{1}{2}[/tex] hour
∵ [tex]\frac{1}{2}[/tex] hour =
∴ Jeremy arrives to the factory in 30 minutes
∵ They leave their houses at the same time
∵ 25 minutes < 30 minutes
∴ Jason arrives first
(a) Jason arrives at the factory first
∵ Jason arrives to the factory in 25 minutes
∵ Jeremy arrives to the factory in 30 minutes
∵ 30 - 25 = 5 minutes
∴ Jeremy arrives after Jason by 5 minutes
(b) It takes 5 minutes until the other person arrives
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Final answer:
Jason arrives at the factory first, taking approximately 25 minutes, while Jeremy arrives 5 minutes later, taking around 30 minutes to reach.
Explanation:
The question involves calculating time taken for different scenarios involving motion and relative speed. In the given scenario, Jason lives 25 miles away from the factory and drives at 60 miles per hour, while Jeremy lives 35 miles away and drives at 70 miles per hour. To find out who arrives at the factory first, we calculate the time each person takes to reach the factory.
For Jason: Time = Distance / Speed = 25 miles / 60 mph = 0.4167 hours.
For Jeremy: Time = Distance / Speed = 35 miles / 70 mph = 0.5 hours.
Clearly, Jason will arrive first.
The difference in arrival time between Jeremy and Jason is:
Jeremy's time - Jason's time = 0.5 hours - 0.4167 hours = 0.0833 hours, which is 5 minutes.
Jason arrives at the factory first, and Jeremy arrives 5 minutes later.
Jeff has ten packages that he wants to mail. Nine identical packages that weigh 2 7/8 pounds each. A tenth package weighs two times as much of one the nine packages. How many ponds do all packages weigh?
Answer:
31 5/8 pounds
Step-by-step explanation:
The total weight is ...
9(2 7/8 lb) + 2(2 7/8 lb) = (2 7/8 lb)(9 +1) = (23/8 lb)(11) = 253/8 lb
= 31 5/8 lb
The total of package weights is 31 5/8 pounds.
Final answer:
The total weight of all ten packages that Jeff wants to mail is 31 5/8 pounds.
Explanation:
Jeff has ten packages to mail, with nine identical packages weighing 2 7/8 pounds each and one package weighing double the weight of one of the nine.
To find the total weight of all the packages, we first calculate the weight of the nine identical packages by multiplying their weight by the number of packages, which is:
2 7/8 pounds/package × 9 packages = 25 7/8 pounds
Next, we determine the weight of the tenth package:
2 × 2 7/8 pounds = 5 6/8 pounds, which simplifies to 5 3/4 pounds.
Finally, we add the total weight of the nine packages to the weight of the tenth package:
25 7/8 pounds + 5 3/4 pounds = 31 5/8 pounds.
Therefore, the total weight of all ten packages is 31 5/8 pounds.
where do y=2x+4 and y=2.50x+2 intersect
Answer:
(4, 12)
Step-by-step explanation:
When the two lines intersect on a graph, it is when you can put the same value for "x" into both equations, and the same value for "y" into both equations.
Because they both equal "y", and y = y, you can equate the expressions together.
y = y
2x + 4 = 2.50x + 2
Now the goal is to move all the numbers with "x" to the left. Move the the numbers to the right side. (This is called isolating "x" because it will be alone).
2x + 4 - 4 = 2.50x + 2 - 4 Subtract 4 from both sides
2x = 2.50x - 2
2x - 2.50x = 2.50x - 2.50x - 2 Subtract 2.50x from both sides
-0.50x = -2
-0.50x/-0.50 = -2/-0.50 Divide both sides by -0.50
x = 4 Found "x" coordinate
Choose one of the original equations. Change "x" to 4 (called substitution).
y = 2x + 4
y = 2(4) + 4 Multiply first
y = 8 + 4 Add
y = 12 Found "y" coordinate
Now write the coordinates like an ordered pair (x, y).
The lines intersect at (4, 12).
If the length of each side of a triangle is cut to 1/3 of its original size, what happens to the area of the triangle?
Answer:
The new area of the triangle is (1 / 9) th of the original area.
That is to say the original area of the triangle is decreased to (1/9) th of its value.
Step-by-step explanation:
The area of a triangle is given by, Area = 1/2 [tex]\times[/tex] base [tex]\times[/tex] height
If each side of a triangle is cut to 1/3 of its original size then the base will also become one third and the height will also become one third.
Therefore the new area will be given by = 1/2 [tex]\times[/tex] (1/3 [tex]\times[/tex] base) [tex]\times[/tex] (1/3 [tex]\times[/tex] height)
= 1/9 [tex]\times[/tex] 1/2 [tex]\times[/tex] base [tex]\times[/tex] height
= 1/9 [tex]\times[/tex] Area.
The new area of the triangle is 1 / 9 th of the original area.
When the sides of a triangle are reduced to 1/3 of their original size, the area of the triangle becomes 1/9 of its original area.
When the length of each side of a triangle is cut to 1/3 of its original size, the area of the triangle is affected by the square of the scale factor applied to the sides.
Let's use some mathematics to understand why this happens. The area of a triangle is given by the formula:
A = 1/2 * base * height, where 'base' represents the base of the triangle and 'height' represents the height of the triangle.
If each side of the triangle is reduced to 1/3 of its original size, both the base and the height will become 1/3 of their respective original sizes.
The new area (A') can be calculated as follows:
New base = 1/3 of original baseNew height = 1/3 of original heightA' = 1/2 * (1/3 * base) * (1/3 * height)Simplifying this:
A' = 1/2 * (base * height) * (1/3 * 1/3)
A' = 1/2 * base * height * 1/9
A' = (1/2 * base * height) * 1/9
A' = A * 1/9
Therefore, the area of the triangle becomes 1/9 of its original area.
Can you simplify 5x+2(x-y)
Answer:
5x+2x-2y
7x-2y
Step-by-step explanation:
Answer:
7x-2y
Step-by-step explanation:
distribute the 2 to the numbers in the parenthesis then combine like terms
Thinking Dan drew the trapezoid at the right.
The top is 3 inches long. The bottom is twice as long as the
top. The length of a side is 5 inches. How can you find the
perimeter of the trapezoid? Label the lengths of the sides.
Answer:3x6x5
Step-by-step explanation:
Find the value of the expression: 2xy+2x^2 for x=−2.5 and y=−7.5
Answer:
Expression = 25
Step-by-step explanation:
2xy+2x^2 = ?
2(-2.5)(-7.5)+2(-2.5)^2 = ?
37.5 + (-12.5) = ?
= 25
Final answer:
The value of the expression 2xy + 2x² for x=-2.5 and y=-7.5 is 50.
Explanation:
To find the value of the expression 2xy + 2x² for x=-2.5 and y=-7.5, we substitute these values into the expression:
2(-2.5)(-7.5) + 2(-2.5)²
Simplifying this expression, we get:
(7.5) + 2(6.25)
= 37.5 + 12.5
= 50
Therefore, the value of the expression 2xy + 2x² for x=-2.5 and y=-7.5 is 50.
The base of a triangle is 5 times the height. If the area is 490 square feet, then what is the height of the triangle, in feet?
Answer: 14 feet
Step-by-step explanation:
The formula for finding the area of a triangle is given as :
Area = [tex]\frac{1}{2}[/tex] x base x height
Let the height be h , then the base is 5 times the height , that is the base is 5h.
Substituting into the formula , we have
490 = [tex]\frac{1}{2}[/tex] x h x 5h
490 = [tex]\frac{1}{2}[/tex] x [tex]5h^{2}[/tex]
multiply through by 2
980 = [tex]5h^{2}[/tex]
divide through by 5
196 = [tex]h^{2}[/tex]
Therefore :
h = 14
Therefore : the height is 14 feet
Which of the following sets of numbers could be the sides of a triangle
6, 8, and 15
9, 13, and 17
2,3, and 6
10, 10, and 20
Answer:
the answer is 10,10and 20
Step-by-step explanation:
becoz 2 sides are equal n the other is not
Answer:
your answer is D.) 10,10 and 20
Step-by-step explanation:
Combine 2y+1x=40 and y=2x using substitution
2(2x) + 1x = 40 or 4x + 1x = 40 is the result of combining by substitution
Solution:
Given that we have to combine 2y + 1x = 40 and y = 2x using substitution method
The substitution method for solving systems of equations involves expressing one variable in terms of another, thus removing one variable from an equation.
Given equations are:
2y + 1x = 40 -------- eqn 1
y = 2x ----------- eqn 2
We can substitute eqn 2 in eqn 1
Which means, substitute y = 2x in place of y in eqn 1
2(2x) + 1x = 40
4x + 1x = 40
5x = 40
x = 8
From eqn 2,
y = 2(8)
y = 16
Thus by combining using substitution method we found the solution
What is the product of -3 and 5?
Answer:
-15
Step-by-step explanation:
3 x 5 = 15
when negative numbers are multiplied by positive numbers the product will be negative.
Final answer:
The product of -3 and 5 is -15, as per the multiplication rules where a negative number multiplied by a positive number results in a negative product.
Explanation:
The product of -3 and 5 is -15. In mathematics, when we talk about the product of two numbers, we are referring to the result of multiplying them. According to multiplication rules, when two numbers have opposite signs, the product has a negative sign. If we multiply a negative number by a positive number, the answer will also have a negative sign.
It's important to remember that multiplication is commutative, meaning that changing the order of the numbers does not change the product. The key concepts are similar to those used when figuring out subtraction and addition of signed numbers. For example, subtracting a negative is the same as adding a positive.
If we apply this to -3 multiplied by 5, we multiply the absolute values (3 and 5) to get 15. Since we have one positive number (5) and one negative number (-3), our final product is -15.
A section of rope 5 inches long represents 20% of the length of the entire rope. How long is the rope?
Answer:
the rope is 25 inches long
1. 20×5=100%
2. 5×5=25 inches
3. 100% of the rope is equal to 25 inches
Final answer:
The entire rope is 25 inches long, as the given 5-inch section is 20% of the whole rope, and multiplying by 5 gives us the full length.
Explanation:
If a section of rope 5 inches long represents 20% of the length of the entire rope, we can find the full length of the rope by setting up a proportion. Considering that 20% is equivalent to the fraction 1/5, we would multiply the length of the shortened rope by 5.
The calculation would be as follows:
5 inches (given length representing 20%) × 5 (since 20% is 1/5 of 100%) = 25 inches.
Thus, the entire length of the rope would be 25 inches.
Someone bought a watermelon pack of napkins and a paper plate the food do not have tags but the non-food items have 5% tax the total cost before tax was $8.25 the tax was $.19 how much was the watermelon
Question:
A shopper bought a watermelon, a pack of napkins, and some paper plates. In his state, there is no tax on food. The tax rate on non-food items is 5%. The total for the three items he bought was $8.25 before tax, and he paid $0.19 in tax. How much did the watermelon cost?
Answer:
Cost of watermelon is $ 4.45
Solution:
From given,
Total amount for three items before tax = $ 8.25
Tax amount = $ 0.19
Tax on non food = 5 %
Here, non food means napkin and paper plates
Let "x" be the cost spent for napkin and paper plates
Then,
5 % = 0.19
100 % = x
This forms a proportion
[tex]5 \times x = 0.19 \times 100\\\\5x = 19\\\\x = 3.8[/tex]
Thus cost spent for napkin and paper plates is $ 3.8
Therefore,
Watermelon cost = total amount before tax - cost spent for napkin and paper plates
Watermelon cost = 8.25 - 3.8 = 4.45
Thus cost of watermelon is $ 4.45
The watermelon cost $4.45, calculated by subtracting the cost of the non-food items ($3.80) taxed at 5% from the total cost before tax ($8.25).
The information provided gives us the total cost before tax ($8.25) and the total tax amount ($0.19). Because only non-food items are taxed, and the tax rate is 5%, we can find the cost of the non-food items by dividing the total tax amount by the tax rate (expressed as a decimal).
Convert tax rate to decimal: 5% = 0.05
Divide the total tax by the tax rate: $0.19 / 0.05 = $3.80
Deduct the cost of the non-food items from the total cost before tax: $8.25 - $3.80 = $4.45
The cost of the watermelon, which is a food item and thus not taxed, is $4.45.
A post it note has an area of A square inches. The width of the post it note is 4 inches.which equation represents X the length of the post it note in inches A X=4/A. B. X=A+2(4) C. X=A/4. D. X=A-2(4)
Answer:
Option C. X=A/4
Step-by-step explanation:
we know that
The area of the rectangular post it note is equal to
[tex]A=LW[/tex]
where
L is the length
W is the width
In this problem we have
[tex]W=4\ in[/tex]
[tex]L=X\ in[/tex]
substitute
[tex]A=4X[/tex]
solve for x
That means ----> isolate the variable x
Divide by 4 both sides
[tex]X=\frac{A}{4}[/tex]
-- Simplify the expression: Show your work. Write the answer in standard form
(15 +6d - (2) + (-502 - 18 + 60)
PLEASE HELP
Answer:
6d - 447
Step-by-step explanation:
(15+6d) - 2 + (-502 - 18 + 60)
(13+6d) + (-460)
6d + 13 - 460
6d - 447
The required answer is 6d - 531
What is simplification?Simplification generally means finding an answer for the complex calculation that may involve numbers on division, multiplication, square roots, cube roots, plus and minus.
Now the given expression is,
(15 +6d - (2) + (-502 - 18 + 60)
Thus,
(15 +6d - (2) + (-502 - 18 + 60)
= 15 + 6d - 2 - 502 + 18 - 60
Rearranging we get,
= 15 + 18 + 6d - 2 - 502 - 60
= 33 + 6d - 564
= 6d - 564 + 33
= 6d - 531
this is the required answer.
Thus, the required answer is 6d - 531.
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what is arctan(1)???
Answer:
0.785398163 rad
Step-by-step explanation:
The value of arctan(1) is equal to π/4 or 45 degrees.
The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.
For the angle whose tangent is 1, we can visualize a right triangle where the length of the side opposite to the angle is 1 and the length of the adjacent side is also 1.
Using the Pythagorean theorem, we can calculate the length of the hypotenuse:
hypotenuse² = opposite² + adjacent²
hypotenuse² = 1² + 1²
hypotenuse² = 1 + 1
hypotenuse² = 2
hypotenuse = √2
Now, we can use the definition of the arctan function to find the angle whose tangent is 1:
arctan(1) = angle whose tangent is 1 = angle whose opposite side is 1 and adjacent side is 1
This angle is a well-known special angle in trigonometry.
It is a 45-degree angle (π/4 radians) or a quarter of a full circle.
Therefore, arctan(1) is equal to π/4 or 45 degrees.
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Help please! Question is in picture
39 ft of carpet
11x3+3x2=39
Pls Answer 30 points
Answer:
84
Step-by-step explanation:
72/x = 6/7
muliply by x on both sides
72 = 6/7x
mulitply by 7 on both sides
504 = 6x
divide by 6 on both sides
84
Answer:84
Step-by-step explanation:
6*12=72
7*12=84
Solve the inequality and graph the solution.
2x + 5 > 22
1 solve it
2 show your work
3 the solution is graphed correctly
The solution of the inequality is 8.5 < x.
Solution:
Given inequality is 2x + 5 > 22.
2x + 5 > 22
Subtract 5 from both sides of the inequality.
2x + 5 – 5 > 22 – 5
2x > 17
Divide by 2 on both sides of the inequality.
[tex]$\frac{2x}{2}>\frac{17}{2}[/tex]
[tex]$x>\frac{17}{2}[/tex]
x > 8.5
8.5 < x
The graph of the solution is attached below.
I need help please and thank you
Answer:
yes
Step-by-step explanation:
can i get brainliest please and thank you.
A seller has a house that is 1900 ft^ 2 . The neighborhood comps show the line of best fit to be y = 0.074x + 50.48 . What is a fair price for this house?
Answer: 191,000
Step-by-step explanation:
Quadratic equation whose roots are 6 and -5
Quadratic equation is x² - x - 30
Step-by-step explanation:
Step 1: Given that the roots of the equation are 6 and -5.⇒ Factors are (x - 6) and (x + 5)
Step 2: Form the quadratic equation using these factors.⇒ (x - 6)(x + 5) = x² + 5x - 6x - 30 = x² - x - 30
Combine the like terms to create an equivalent expression 2a + 6 + 1
Answer:
2a+7
Step-by-step explanation:
Answer:
2a+7
Step-by-step explanation:
2a+6+1=2a+7
what is 33 1/3 of 687
[tex]\(33 \frac{1}{3}\)[/tex] % of 687 is 229.
To find [tex]\(33 \frac{1}{3}\)[/tex] the percent of 687, you can first convert [tex]\(33 \frac{1}{3}\)[/tex]% to a decimal, then multiply by 687.
[tex]\[33 \frac{1}{3}\% = \frac{33\frac{1}{3}}{100} = 0.3333\][/tex]
Now, multiply this decimal by 687:
[tex]\[0.3333 \times 687 = 229\][/tex]
So, [tex]\(33 \frac{1}{3}\)[/tex] % of 687 is 229.
Correct question:
what is [tex]\(33 \frac{1}{3}\)[/tex] of 687?
(3 2/3 + 17 1/5) - ( 11 3/5 + 2 1/3) =
Answer:
6 14/15
Step-by-step explanation:
I would say simplifie the paratensies.
First:
3 2/3+ 17 1/5 =
Common factor of 3 and 5 is 15
3 10/15 + 17 3/15 = 20 13/15
Second:
11 3/5 + 2 1/3 =
Common factor of 3 and 5 is 15
11 9/15 + 2 5/15 = 13 14/15
20 13/15 - 13 14/15 = 7 13/15 - 14/15 = 7 - 1/15 = 6 14/15
Olivia is cutting a 1 1/2 m by 3/4 m piece of rectangular paper into two pieces along its diagonal. Find the area
Answer:
9/16 m.
Step-by-step explanation:
When you cut two pieces along its diagonal it causes it to be two congruent triangular pieces.
You need to multiply the length and the width to find an area:
1 1/2 × 3/4
Now you need to change it into an improper fraction:
1*2+1 = 2+1 = 3; this gives us 3/2:
3/2 × 3/4 = 9/8 = 1 1/8
Dividing it by 2:
9/8 ÷ 2
find the values of x and y. write your answers in simplest form.
I know x=9√3 and y=18 but I don't know why pls pls help ASAP
Step-by-step explanation:
Given triangle is 30°, 60° & 90° angled triangle.
We know that in 30°, 60° & 90° angled triangle. Side opposite to 30° is half of hypotenuse and side opposite to 60° is root 3 upon 2 times of hypotenuse.
[tex] \therefore \: 9 = \frac{1}{2} \times y \:\:\:(side \: opposite \: to \: 30 \degree)\\ \\ \therefore \: 9 \times 2 = y \\ \\ \therefore \:y = 18 \: units \\ \\ next \\ \\ x = \frac{ \sqrt 3}{2} \times y \:\:\: (side \: opposite \: to \: 60 \degree)\\ \\ \therefore \: x = \frac{ \sqrt 3}{2} \times 18 \\ \\\therefore \: x = \sqrt 3 \times 9 \\ \\ \therefore \: x = 9 \sqrt 3 \: units[/tex]
Please help me asap very urgent
The interior angles formed by the sides of a quadrilateral have measures that sum to 360°.
What is the value of x?
Enter your answer in the box.
x =
Answer:
34
Step-by-step explanation:
We know that the sum of angles in a quadrilateral must be 360.
As such, we can sum up all given values for all 4 angles and set it equal to 360
[tex]360=108+88+2x+(3x-6)\\360=190+5x\\170=5x\\x=34\\\\[/tex]
Answer:
x=59
Step-by-step explanation:
the sum is 360 degrees.. Therefor
x + x + 2x + 3 + 2x + 3 = 360
combine alike terms
6x + 6 = 360
6x = 354
x = 59
If a(x) = 3x + 1 and b (x) = StartRoot x minus 4 EndRoot, what is the domain of (b circle a) (x)?
Answer:
The domain is [1,∞)
Step-by-step explanation:
The given functions are:
[tex]a(x)=3x+1[/tex]
and
[tex]b(x) = \sqrt{x - 4} [/tex]
We want to find the domain of
[tex](b\circ a)= \sqrt{3x + 1 - 4} [/tex]
Simplify to get:
[tex](b\circ a)= \sqrt{3x -3} [/tex]
This function is defined when the expression under the radical is greater or equal to zero.
[tex]3x -3 \geqslant 0 \\ x \geqslant 1[/tex]
Answer:
C on Edge 2021
Step-by-step explanation:
Took the test
Check all solutions to the equation. x² =-4
Answer:
x=2i, -2i
Step-by-step explanation:
Answer:
2,-2 or maybe no real solutions but i went with 2,-2
Step-by-step explanation: