Answer:
Option 3: 81 pi cu. in
Step-by-step explanation:
What is the distance, d, between the points(2,7/2) and (5/3,1)?
Enter your answer in the box. Enter your answer in simplest radical form.
\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{\frac{7}{2}})\qquad (\stackrel{x_2}{\frac{5}{3}}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(\frac{5}{3}-2)^2 + (1-\frac{7}{2})^2}\implies d=\sqrt{(\frac{-1}{3})^2 + (-\frac{5}{2})^2} \\\\\\ d=\sqrt{\cfrac{1}{9}~~ + ~~\cfrac{25}{4}}\implies d=\sqrt{\cfrac{229}{36}}\implies d=\cfrac{\sqrt{229}}{\sqrt{36}}\implies d=\cfrac{\sqrt{229}}{6}\)
Bryan invests $6500 in two different accounts. The first account paid 11 %, the second account paid 7 % in interest. At the end of the first year he had earned $519 in interest. How much was in each account?
$ at 11 %
$ at 7 %
Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).
Let's assume that Bryan invested an amount of x dollars in the first account, which earns 11% interest, and (6500 - x) dollars in the second account, which earns 7% interest.
The interest earned from the first account can be calculated as 0.11x, and the interest earned from the second account can be calculated as 0.07(6500 - x).
According to the problem, the total interest earned after one year is $519. So we can set up the equation:
0.11x + 0.07(6500 - x) = 519
Simplifying the equation:
0.11x + 455 - 0.07x = 519
0.04x + 455 = 519
0.04x = 64
x = 64 / 0.04
x = 1600
Therefore, Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).
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i need help figuring out this question
Answer:
I just did the sum and i don't know whether it is correct but the length is 10cm
An office manager has $10,000 to spend on new equipment. He planned to purchase 300 lamps for $72 each. He completed the calculation at the right and concluded that there would be plenty of money left to buy additional equipment. What does the office manager do to support his thinking.
Answer:
he steals more money from the person next door
Step-by-step explanation:
Find the slope of the line passing through the points (-3, -2) and (9,-2).
slope:
Answer:
Step-by-step explanation:
(-2+2)/(9+3)= 0/12= 0
y + 2 = 0(x + 3)
y + 2 = 0
y = -2
Indicate the method you would use to prove the two 's . If no method applies, enter "none".
SSS
ASA
SAS
AAS
None
The method you would use to prove the two triangles are congruent include the following: B. ASA.
What are the properties of similar triangles?In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Additionally, the lengths of corresponding sides are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.
In Mathematics and Geometry, ASA is an abbreviation for Angle-Side- Angle and it states that when two (2) angles and their included side in two (2) triangles are congruent, then the triangles are said to be congruent.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
you did not provide enough information to answer the question
The length of the term is one year. Calculate the principal if the maturity value is $4,500 and the simple interest is $350.
Answer:
Easy! The answer is $4,150
Step-by-step explanation:
The $350 is interest so we will take that away from the maturity value to get 4,150!
mark BRAINLIEST IF YOU THINK I HELPED
Convert 4
3
5
cups to pints.
2 cups = 1 pint PLEASE HELP!
Answer:
4 cups=2 pint
3 cups=1.5 pint
5 cups=2.5 pints
Step-by-step explanation:
Because there are 2 cups in each pint, we can divide the number of cups by two to get the number of pints.
4/2=2
3/2=1.5
5/2=2.5
Let me know if you have any questions!
The volume of a cylinder is 637 cm³. If the radius is 3 cm, what is the height
of the cylinder?
If the radius is 3 cm, the height of the cylinder is approximately 7.06 cm, which is closest to option B, 7 cm. The correct option is B.
The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.
We are given that the volume of the cylinder is 637 cm³ and the radius is 3 cm. Substituting these values into the formula, we get:
637 = π(3²)h
Simplifying:
637 = 9πh
h = 637 / (9π)
h ≈ 7.06
Thus, the height of the cylinder is approximately 7.06 cm, which is closest to option B, 7 cm.
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Which transformation is this an example of?A.reflectionB.rotationC.translationD.None of these
Answer:
I think rotation
Rotation
anyone know the answer?
Answer:
y-intercept = 1
Step-by-step explanation:
Here 1 grids crossing means increasing or decreasing by 1 grid. Here we are seeing the line crosses 1 grid above 0. So its positive 1. From here we find the y intercept is +1. Line crosses at coordinate ( 0 , 1 )
Answer:
y-intercept = 1Explanation:
The y-intercept of a line is the point of a line that intersects the y-axis. When we look at the line, we can tell that the line is intersecting at (0,1) on the y-axis. When we compare (0,1) to (x,y), we can tell that the intersecting x-coordinate is 0 and the intersecting y-coordinate is 1.
Hence, 1 is the y-intercept.
A football is originally priced at $15. In this state, the sales tax rate is 7%. What was the total price of the football?
Answer:
107%=16.06
Step-by-step explanation:
im pretty sure that's it, if its not please correct me.
How can I factor the following expression by grouping:
a) 4x^3 - 2x^2 + 8x - 4
The factored expression of 4x³ - 2x² + 8x - 4 is (2x² + 4)(2x - 1) by grouping
How to factor the expression by groupingFrom the question, we have the following parameters that can be used in our computation:
4x³ - 2x² + 8x - 4
Group the expression in 2's
So, we have
(4x³ - 2x²) + (8x - 4)
Factorize each group
2x²(2x - 1) + 4(2x - 1)
So, we have
(2x² + 4)(2x - 1)
Hence, the factored expression is (2x² + 4)(2x - 1)
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Drag statements and reasons to each row to show why the slope of the line between R and S is the same as the slope between S and T, given that triangles A and B are similar.
For statement 5/3, the reason is the definition of slope. And for statement (5/3)=(15/9), the reason is triangle A is similar to triangle B.
What is the slope?Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope is also defined as the ratio of the rise to the run.
If the slope of the triangles is equal then triangle A is similar to triangle B.
In the statement when we simplify
(5/3)=(15/9),
(5/3)=(5/3),
Then the reason for this statement is "If the slope of triangles are equal"
And the definition of slope in general is m = y/x.
Therefore, for statement 5/3, the reason is the definition of slope. And for statement (5/3)=(15/9), the reason is triangle A is similar to triangle B.
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Translate the following verbal statement into an algebraic equation and then solve:
Julio bought a refrigerator on sale for $200, which was one-half of the original price. What was the original price of the refrigerator?
The original price of the refrigerator was $400.
The statement "Julio bought a refrigerator on sale for $200 was one-half of the original price" can be translated into an algebraic equation as follows:
1/2x = 200
x represents the original price of the refrigerator.
This equation states that half of the original price is equal to $200 is the sale price that Julio paid.
To solve for x, we can multiply both sides of the equation by 2 gives us:
x = 2 × 200
x = 400
We can check this answer by verifying that half of $400 is indeed equal to $200 was the sale price that Julio paid.
We translated the verbal statement into an algebraic equation and solved for the unknown variable to find that the original price of the refrigerator was $400.
The phrase "Julio bought a refrigerator on sale for $200 was one-half of the original price" may be transformed into the following algebraic equation:
The initial cost of the refrigerator is 1/2x = 200x.
According to this calculation, Julio paid $200 for the item, which is equal to half of the original price.
By multiplying both sides of the equation by 2, we may find the value of x as follows:
x = 2 × 200 x
= 400
By confirming that half of $400 is actually equal to $200, which was the sale price paid by Julio, we can confirm this response.
The spoken statement was converted into an algebraic equation and the unknown variable was solved for in order to determine that the refrigerator's initial cost was $400.
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If you were to track coffee preferences among your co-workers for the next two weeks, which type of statistical study would you be performing? (statistics)
Answer:
Well I would say inferntial because its more testing your hyptohsis between two friends to see which coffe they like more
A bag contains 6 batteries, all of which are the same size and are equally likely to be selected. Each battery is a different brand. If you select 3 batteries at random, use the counting principle to determine how many points will be in the sample space if the batteries are selected
Answer:
there are 120 possible points in the sample space if we select 3 batteries at random from a bag containing 6 batteries of different brands.
Step-by-step explanation:
The counting principle states that if there are n ways to do one thing and m ways to do another, then there are n x m ways to do both.
In this case, we want to determine how many ways we can select 3 batteries out of 6. Using the counting principle, we can break down the selection process into three steps:
Select the first battery. There are 6 choices for the first battery.
Select the second battery. There are 5 choices left for the second battery, since we've already selected one.
Select the third battery. There are 4 choices left for the third battery.
Using the counting principle, we can multiply the number of choices for each step to get the total number of ways to select 3 batteries:
6 x 5 x 4 = 120
Therefore, there are 120 possible points in the sample space if we select 3 batteries at random from a bag containing 6 batteries of different brands.
jalen drew a rectangle with a perimeter of 20 inches. the smaller side measured 3 inches. jalen said the longer side of the rectangle had to be 7 inches. is jalen correct?
Yes, Jalen is correct because the rectangle has a perimeter of 20 inches with the smaller side measuring 3 inches and the longer side of the rectangle had to be 7 inches.
How to calculate the perimeter of a rectangle?In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);
P = 2(L + W)
Where:
P represent the perimeter of a rectangle.W represent the width of a rectangle.L represent the length of a rectangle.By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;
P = 2(3 + 7)
20 = 2(10)
20 = 20 (True).
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5. Jenna is making
bracelets.
She needs 7
inches of string for each
bracelet. She has a spool
with 16 feet of string. How
many bracelets can Jenna
make?
Answer:
Step-by-step explanation:
Each bracelet need 7 inches of string. Jenna has a total of 16 feet of string.
Divide the total amount of string by the number of inches needed for each bracelet.
Step 1: Convert 16 feet into inches. 12 inches = 1 foot
16 feet x (12 inches/1 foot) = 192 inches
This is the total inches of string.
Note that feet and foot units cancel and you are left with inches.
Step 2: Find the number of bracelets that can be made. Use the answer from step 1. Each bracelet needs 7 inches of string.
Total inches of string / 7 inches of string for each bracelet
192 inches / 7 inches = 27.4
Round the answer to 27.
14.32 × 1.2,...........
Answer:
17.18400
Step-by-step explanation:
When rounded to the nearest whole number, it's 17.
Hope this helped :)
JUST LOOK AT THE PICTURE THE QUESTION IS THERE ALREADY JUST GIVE ME THE RIGHT ANSWER PLEASE
Area of rectangle is length times of width. Thomas is painting the wall at a warehouse blue. He painted in 6 hours of area 240 square feet.
What is area of rectangle?Area of rectangle is length times of width.
Area=Length*width.
From the given figure the length is 12 ft and width is 5 ft in 1.5 hrs.
area he covered painting= 12ft*5ft
=60 square feet.
In 1 and half hour he painted 60 square feet.
Now for 6 hours we have to calculate.
4*(1 and half hrs)=6 hrs
So we have to multiply 4 with 60 to get the area in 6 hours.
4*60=240square feet.
Therefore 240 square feet area Thomas painted.
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3X squared plus 5X - 2 =0
Answer: x= -0.3,2
Step-by-step explanation:
Combine your like terms then solve.
Answer:
Step-by-step explanation:
Sum = 5
Product = -6
Factors = (-1) ; 6 {-1+ 6 = 5 & (-1)*6 = -6}
3x² + 5x - 2 = 0
3x² - x + 6x - 2 = 0
x(3x - 1) + 2(3x - 1) = 0
(3x - 1)(x + 2) = 0
Ian's bird feeder holds 1 1/2 cups of birdseed. Ian is filling the bird feeder with a scoop that holds 3/4 of a cup. How many scoops of birdseed will Ian put into the feeder
The required scoops of birdseed Ian will put in the feeder are 2.
What is the Ratio?The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
Ian's bird feeder holds 1 1/2 cups of birdseed.
Ian is filling the bird feeder with a scoop that holds 3/4 of a cup.
So, the ratio of the cup to scoop gives the number of cups,
Number of scoops = 1 1/2 / [3/4]
= 3/2 × 4/3
= 2 scoops
Thus, the required scoops of birdseed Ian will put in the feeder are 2.
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Write an equation of the parabola that passes through the point (62,-490) and has x-intercept-8 and 72. Then find the average rate of change from x =-8 to x=2.
Part 1
The equation is \(y=a(x+8)(x-72)\).
Using the point \((62, -490)\) to solve for \(a\),
\(-490=a(62+8)(62-72) \implies a=\frac{7}{10}\\\\\therefore \boxed{y=\frac{7}{10}(x+8)(x-72)}\)
Part 2
When \(x=-8\), \(y=0\).
When \(x=2\), \(y=-490\).
So, the average rate of change is \(\frac{-490-0}{2-(-8)}=\boxed{-49}\)
The product of two whole numbers is 588 and their sum is 49. What are the two numbers?
Answer:
Here is your answer. HOPE THIS HELPS YOU! STAY BLESSED.
Answer:
28,21
Step-by-step explanation:
let the numbers be x and y
x+y=49
y=49-x
xy=588
x(49-x)=588
49x-x²=588
x²-49x+588=0
\(x=\frac{49 \pm \sqrt{49^2-4*1*588} }{2*1} \\=\frac{49 \pm \sqrt{2401-2352} }{2} \\=\frac{49 \pm\sqrt{49} }{2} \\=\frac{49 \pm 7}{2} \\=\frac{49+7}{2} ,\frac{49-7}{2} \\=28,21\)
Look a tu the picture
The area of the composite figure in this problem is given as follows:
A = 87 ft².
How to obtain the area of the composite figure?When we want to obtain the area of a composite figure, we must add the areas of all the components of the figure.
The figure in this problem is composed as follows:
Rectangle of dimensions 10 ft and 6 ft.Rectangle of dimensions 10 - 4 = 6 ft and 9 - 6 = 3 ft.Right triangle of legs 10 - 4 = 6 ft and 6 - 3 = 3 ft.The areas are calculated as follows:
Rectangle: multiplication of dimensions.Right triangle: half the multiplication of the legs.Hence the area of the composite figure is given as follows:
A = 10 x 6 + 6 x 3 + 0.5 x 6 x 3
A = 87 ft².
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Evaluate: 8+k
when k = -3
\(5.\)
Step-by-step explanation:-
\(8 + k\)
If k = -3. Then,
\(8 + ( - 3)\)
\( = 8 - 3\)
\( = 5.\)
The graph below shows a line of best fit for data collected on the distance drivers traveled as a function of time. Which of the following is the equation of the line of best fit? A. B. C. D.
The equation for the line of best fit is given as follows:
y = 50x/3.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b.
The parameters of the definition of the linear function are given as follows:
m represents the slope of the function, which is by how much the dependent variable y increases(positive) or decreases(negative) when the independent variable x is added by one.b represents the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On the case of the graph, the intercept is given by the value of y at which the graph crosses or touches the y-axis.From the graph, when x = 0, y = 0, hence the intercept b is given as follows:
b = 0.
Hence:
y = mx.
When x = 3, y = 50, hence the slope m is given as follows:
3m = 50
m = 50/3.
Hence the equation is:
y = 50x/3.
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4(3x + 2)
(Box)x+ 8
What number belongs in the box?
A. 3
B. 4
C. 7
D. 12
Answer:
option D 12 is correct..
in second question the student didn't multiply -3 with 4. that's the mistake he did.
hope it helps
Answer:
D. 12
Step-by-step explanation:
4(3x+2)
=(4)(3x+2)
=(4)(3x)+(4)(2)
=12x+8
Rosa is saving money to buy a baseball bat that costs $229. Rosa has$19 and will save $14 each week. How many weeks will it take Rosato save enough money to buy the baseball bat? Write an equation torepresent this situation. Do not simplify the equation. Use w torepresent the number of weeks.
Let w be the number of weeks that Rosa have to work to save enough money. Since she can save 14 dollars per week, and that she started saving money with 19 dollars, then the equation would look like this:
\(14w+19=229\)Solving for w we get:
\(\begin{gathered} 14w+19=229 \\ \Rightarrow14w=229-19=220 \\ \Rightarrow w=\frac{220}{14}=15 \end{gathered}\)Therefore, Rosa has to work 15 weeks to save enough money to buy the baseball bat.