What is the distance between points S and U?
Round to the nearest tenth of a unit.
3.3 units
6.4 units
8.1 units
12.0 units
Answers
sqrt(16 +49)
sqrt(65)
8.06
round to 8.1 units
The correct answer is C.
[tex] |SU| = 8.1units[/tex]
EXPLANATION
The given points are,
[tex]S(2,1) \: \: and \: \: U(6,8).[/tex]
We use the distance formula to determine the distance between the two points.
[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} [/tex]
We substitute the points to obtain,
[tex] |SU| = \sqrt{(6- 2) ^{2} + (8 - 1) ^{2} } [/tex]
We simplify to obtain,
[tex] |SU| = \sqrt{(4) ^{2} + (7) ^{2} } [/tex]
We further simplify this to obtain,
[tex] |SU| = \sqrt{16 + 49} [/tex]
[tex] |SU| = \sqrt{65} [/tex]
This evaluates to,
[tex] |SU| = 8.062[/tex]
We round to the nearest tenth to get,
[tex] |SU| = 8.1units[/tex]
Related Questions
You plan on financing a home theater system for $1,752. The audio shop offers a 15% APR for a 25 month loan. Use this information, and the table above, to determine the monthly payments. Round your answer to the nearest cent.
a.
$29.89
c.
$82.04
b.
$70.08
d.
$85.32
Answers
Final answer:
To calculate the monthly payments for a $1,752 home theater system at 15% APR over 25 months, convert APR to a monthly rate and apply the loan payment formula, yielding an estimated payment not precisely matching the provided options. This suggests a potential discrepancy in calculation or provided options.
Explanation:
To determine the monthly payments for financing a home theater system at a 15% APR for a 25-month loan costing $1,752, we use the formula for calculating the monthly payment on an amortizing loan. First, convert the annual interest rate to a monthly rate by dividing by 12. In this case, 15% annually becomes 1.25% per month. Then, apply the formula: Monthly Payment = P * (r(1+r)^n) / ((1+r)^n - 1), where P=principal amount ($1,752), r=monthly interest rate (0.0125), and n=number of payments (25).
Plugging into the formula gives us: Monthly Payment = 1,752 * (0.0125(1+0.0125)^25) / ((1+0.0125)^25 - 1), which calculates to approximately $76.55.
However, since the provided options do not include this exact figure, it's essential to note that either there's been a miscalculation or a misunderstanding in the method or given options. The closest provided option is $70.08.
Rose bought some spinach. She used 3/5 of the spinach on a pan of spinach pie for a party and 3/4 of the remaining spinach for a pan for her family. She used the rest of the spinach to make a salad.
What fraction of the spinach did she use ti make the salad?
b. If Rose used 3 pounds of spinach to make the pan of spinach pie for the party , how many pounds of spinach did Rose use to make salad?
Answers
Quantity used on the pan of spinach pie for the party: (3/5)x
Remaining spinach: x-(3/5)x=(1-3/5)x=(5/5-3/5)x=[(5-3)/5]x=(2/5)x
Quantity used on a pan for her family: (3/4)(2/5)x=[(3*2)/(4*5)]=(6/20)x
Quantity used on a pan for her family:(3/10)x
Quantity use to make the salad: x-(3/5)x-(3/10)x=(1-3/5-3/10)x
Quantity use to make the salad: [(10*1-2*3-1*3)/10]x=[(10-6-3)/10]x
Quantity use to make the salad: (1/10)x
a. What fraction of the spinach did she use to make the salad?
She used 1/10 of the spinach to make the salad.
b. If Rose used 3 pounds of spinach to make the pan of spinach pie for the party , how many pounds of spinach did Rose use to make salad?
Quantity used on the pan of spinach pie for the party: (3/5)x= 3 pounds
Quantity used to make the salad: (1/10)x=?
We need to find x. Solving for x in the quantity used on the pan of spinach pie for the party:
(3/5)x=3 pounds
(5/3)(3/5)x=(5/3)(3 pounds)
x=15/3 pounds
x= 5 pounds
Quantity of spinach that Rose bought: x= 5 pounds
Now we can find the quantity used to make the salad:
(1/10)x=(1/10)(5 pounds)=(5/10) pounds=(1/2) pound = 0.5 pound
Answer: Quantity used to make the salad is 1/2=0.5 pound
it cost $35 for one adult and two children to attend a show. It cost $60 for two adults and three children to attend the same show. How much does it cost one adult to attend the show?
Answers
adult = x
child = y
x+2y = 35 (1st equation)
2x+3y = 60 (2nd equation)
x = 35-2y (3rd equation)
Substitute 3 into 2 :
2(35-2y) + 3y =60
70-4y +3y = 60
y = 10
x+2y = 35
x+2(10) =35
x +20 =35
x = 15
One adult = $15
rob works part time at the fallbrook riding stable. He makes $5 an hour exercising horses and $10 hour cleaning stalls. Because Rob is a full time student he can work no more than 12 hours per week. however he must make $60 per week. write a system of inequalitites
Answers
Let y be the number of hours cleaning stalls.
x + y <= 12
5x + 10y >= 60
x + 2y >= 12
At this point you might do well to graph this set of equations on Wolframalpha.com
In the meantime solve this system this way.
12 - x > y > 6 - x/2
When y =0 the x = 12.
Answer: 5x + 10y ≥ 60 ⇒ x+2y ≥ 12 .................. (i)
x + y ≤ 12 ................. (ii)
Step-by-step explanation:
Let the hours spent on exercising horse be x
Let the hours spent on cleaning stalls be y
According to question:
Rob can't work more than 12 hours. So eq. (i) will be x + y ≤ 12
Rob earns $5 an hour by exercising horses and $10 an hour cleaning stalls and he must make $60 . So eq. (ii) will be 5x + 10y ≥ 60.
Dividing eq. (ii) by 5, it will become x + 2y ≥ 12.
∴ system of inequalities are x + y ≤ 12 and x + 2y ≥ 12.
what is the value 1/2 ×3+5.2y when x=2 and y=3
Answers
Fred pays 2/5 of his annual salary in federal, state, and local taxes. His annual salary is 102,000. How much of his salary does he get to keep after taxes are paid? 1) $61,000 2) $72,300 3) $61,200 4) $94,900
Answers
What is the surface area in square feet of a rectangular prism with dimensions of 2 feet by 3 feet by 4 feet as shown in the net?
Answers
Answer: 52 square feet
Step-by-step explanation:
The surface area of a rectangular prism is given by :-
[tex]S.A.=2(lw+wh+hl)[/tex], where l is length , w is width and h is height of then prism.
Given: Dimensions of the rectangular prism : [tex]l\times w\times h=[/tex] 2 feet by 3 feet by 4 feet
Then , the surface area of a rectangular prism will be:-
[tex]S.A.=2(2(3)+(3)(4)+(2)(4))\\\\\Rightarrow\ S.A.=52\text{ inches}^2[/tex]
Hence, the surface area of a rectangular prism= 52 square feet
The drama club members buy 864 bags of popcorn to serve during the intermission of their play. Popcorn comes in cases of 24 bags, and they pay $18 for each case. How much did they pay for all of the popcorn
Answers
Hope this helps
Final answer:
The drama club purchased 36 cases of popcorn at $18 per case, resulting in a total cost of $648 for all the popcorn.
Explanation:
The question involves calculating the total amount spent on popcorn by the drama club, which requires some basic arithmetic and understanding of multiplication and division. To find the total cost, we first need to determine how many cases of popcorn the club bought and then multiply that number by the cost per case.
Step-by-Step Calculation
Determine the number of cases: Divide the total number of bags of popcorn (864) by the number of bags per case (24).
Calculate the total cost: Multiply the number of cases by the cost per case ($18).
Now, let's perform these steps:
Number of cases = 864 bags ÷ 24 bags/case = 36 cases
Total cost = 36 cases × $18/case = $648
Therefore, the drama club paid $648 for all the popcorn.
Simon's water cooler can hold up to 4.2 gallons of water in it. Simons fills the cooler so that there is water in all but 25% of the cooler. How much more water would Simon need to add to fill the entire 100% of the cooler?
A 1.05 gallons
B 3.95 gallons
C 3.15 gallons
D 1.7 gallons
Answers
25% of 4.2 is equal to .25*4.2 which equals 1.05.
So in this scenario, the correct answer would be A.
A picture is 5 inches wide and 8 inches tall:
A rectangle is shown. The length of the rectangle is labeled 5 inches. The width of the rectangle is labeled 8 inches.
A photographer wants to use a scale factor of 2.5 to enlarge a picture. What will the area of the picture be after it is enlarged? (5 points)
40 in2
250 in2
100 in2
81.9 in2
Answers
Final answer:
The area of the enlarged picture will be 250 square inches, calculated by multiplying the new width and height which are scaled up by the factor of 2.5 from the original dimensions.
Explanation:
To find the area of the enlarged picture, we begin by scaling up the dimensions of the original picture using the given scale factor. The original width is 5 inches, and the original height is 8 inches. Applying a scale factor of 2.5 to both dimensions, we calculate the new dimensions as follows:
New width = 5 inches × 2.5 = 12.5 inchesNew height = 8 inches × 2.5 = 20 inchesNow, to find the area of the enlarged picture, we multiply the width by the height:
New area = New width × New height = 12.5 inches × 20 inches = 250 square inches
Therefore, the area of the picture after it is enlarged will be 250 square inches.
What is the volume of this pyramid?
7560 cm³
5040 cm³
2520 cm³
1728 cm³
Answers
1/3 x (1/2 x 18 x 24) x 35
=2520cm3
the answer is C
Answer:
C) 2520 cm^3
Step-by-step explanation:
The given pyramid is a triangle base pyramid.
Volume of a pyramid = 1/3(base area* height)
Here the base is a right triangle with base 24 cm and height 18.
The height of the pyramid is 35 cm.
Plug in the given values in the formula, we get
V = 1/3 (1/2*24*18)*35
= 1/3(216)(35)
= 72*35
V= 2520 cm^3
The volume of the given pyramid is C) 2520 cm^3
Hope this will helpful.
Thank you.
name the quadrilateral with exactly one pair of parallel sides?
A. Kite
B. Parallelogram
C. Rhombus
D. Trapezoid
Answers
B. parallelogram
hope this helps<3
Reasoning:
A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
I hope this helps!
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which expression does not give the area of the shaded figure?
Answers
what is the probability of spinning a 2 and flipping tails
Answers
4/6 or 2/3
Javier bought 47 sports cards. 3/8 of them were baseball cards. How many baseball were baseball cards?
Answers
In math, "of" usually means "times."
3/8 of 48 = 3/8 * 48 = 3/8 * 48/1 = (3 * 48)/(8 * 1) = 144/8 = 18
Answer: 18 cards
Which is one way to check 102 ÷ 6 = 17?
A. 105 ÷ 5 = 21
B. 105 ÷ 10 = 10.5
C. 100 ÷ 5 = 20
D. 102 ÷ 10 = 10.2
I have no idea why the answer choices have different numbers from the question. Please explain your answer to me to understand. I don't want just an answer
Answers
Solution:
102 ÷ 6 = 17
As you can see , 102 has unit digit of 2 ,it means it is divisible by 2
Sum of digits of (102) = 1 + 2 =3, it means it is divisible by 3 also.
So , if a number is divisible by 2 and 3 it means it is divisible by 6 also.
Option (A) and Option (C) are true options which are
105 ÷ 5 = 21, and 100÷5 =20
The reason being if you will look at the unit digit of 105 and 100 , it is 5 and 0. So if a number have unit digit either 5 or 0 it is divisible by 5.
The length of a rectangle is 6 cm longer than the width. If the length is increased by 9 cm and the width by 5 cm, the perimeter will be 160 cm. Find the dimensions of the ORIGINAL rectangle.
Answers
2(w+5) + 2(w+ 6 + 9) = 160
We can add in the parenthesis.
2(w+5) + 2(w+15)
Distribute.
2w+10+2w+30=160
Add like terms.
4w+ 40 = 160
4w=120
w=30
The width is 30 cm and the length is 36 cm.
Let's check by making the rectangle again.
2(45) + 2(35)=160
90+ 70 = 160
Is the domain {1.8,3.4,9,9.8}
{3.2,3.9,5.8,8.4,9.1}
{2.4,4.8,6.3,8.8,10.1}
{3,4.6,6.7,8.9,10.8}
Answers
.. y = 7x -2.7
.. y +2.7 = 7x
.. x = (y +2.7)/7
You are given y values of {14.1, 30.9, 41.4, 58.9, 68}. The corresponding x values are {2.4, 4.8, 6.3, 8.8, 10.1}, corresponding to selection C.
_____
Since the first number in each choice is different, you only need to evaluate f(x) for those numbers to see which gives the correct result. Only the 3rd one (2.4) give f(2.4) = 14.1, the correct answer.
A computer was on sale for 2/3 of the original price. If the original price was $900 what was the sale price? show work please.
Answers
So first you divide 900 by 3, which gives you 300,right? 300 is only one third of the 900, so you need to get to two thirds, which is why you would add another 300, which brings you to $600.
For the end-of-year party, Mt.Rise Middle School ordered 112 pizzas. There were eight fewer veggie pizzas than there were pepperoni pizzas. There were three times as many combo pizzas as pepperoni pizzas. Use the 5-D process to define a variable and write an equation for this situation. Then determine how many of each kind of pizza were ordered.
Answers
pepperoni = x
veggie = x - 8 [There were eight fewer veggie than pepperoni]
combo = 3x [There were three times as many combo as pepperoni]
Given that the total Pizza: 112
x + x - 8 + 3x = 112
5x - 8 = 112
5x = 112 + 8
5x = 120
x = 24
x= 24
x - 8 = 16
3x = 72
So there were 24 pepperoni pizza, 16 veggie pizza and 72 combo pizza
Which number is written in scientific notation? 7.8 x 10−5 0.84 x 106 3.4 x 1002 −5 x 10−12
Answers
First off what is scientific notation?
Scientific Notation is the way that scientist handle very large or very small numbers..
for example, instead of writing 0.0000000056 we write 5.6x10 (exponent -9)
So, now we got that out the way lets look up here at the choices....
I would say that 7.8x10 (exponent -5) would be the answer! :)
I hoped this helped!!!! :)))
God bless you.
a) A square has an area of 121 cm^2. What is the length of each side?
b) A square has a perimeter of 28m . What is the length of each side?
Answers
x*x=121
x^2=121
x=11
The length of each side is 11
A square has equal sides. To find the perimeter, you add all the sides together.
x+x+x+x=28
4x=28
x=7
The length of each side is 7
In Mr.Martinez's sixth period class, there are 8 boys and 12 girls. what is the probability of randomly selecting a girl?
Answers
Boys=8
Total students=8+12=20
Probability of girls=number of girls/total number of students=12/20=6/10=60%
Answer=60%
1/2m-4=5
What is the variable 'M' equal to.
Answers
1/2m-4=5
Add 4 on both sides.
1/2m=9
Divide both sides by 1/2.
m=18
I hope this helps!
~kaikers
We should add 4 on either side as our first step, in order to find the value of the variable
[tex] \frac{1}{2} [/tex]m - 4 ( + 4 ) = 5 ( + 4 )
- 4 and + 4 cancels out in the left hand side
We are left with
[tex] \frac{1}{2} [/tex]m = 9
To find the value of m, we should divide each side by [tex] \frac{1}{2} [/tex]
(diving by a fraction can also be done by multiplying the reciprocal)
[tex] \frac{1}{2} [/tex]m = 9 ÷ [tex] \frac{1}{2} [/tex]
[tex] \frac{1}{2} and \frac{1}{2} [/tex] cancels out
m = 18
Don wrote the expression 8 less than the product of m and 10. What algebraic expression did he write? What is the value of the expression for m = 7?
Answers
10m-8
if m=7
70-8=62
if m=7
70-8=62
hope this helps
a tyrannosaurus rex weighed about 1.4 tons more than one tenth the weight of a Patagotitan mayorum. About how much did the tyrannosaurus rex weigh?
A Patagonian mayorum was a tyrannosaur that weighed about 76 tons
Answers
You have two dinosaurs. Let's just label them as Dinasour A (the Tyrannosaurus Rex), and Dinosaur B (the Patagonian Mayorum)
Dinasoar A weighs in at 1.4 tons more than a TENTH of Dinasoar B's weight
We know that Dinosaur B weighs in at 76 tons.
A tenth means exactly what it sounds like, 10/100. If it helps, you can think of it in terms of money, where a single Dime is a TENTH of a Dollar, because it takes 10 total Dimes to make $1
So, to fine a tenth of anything, you have to divide it by 10!
76/10=7.6
7.6 is the tenth of the weight of Dino B. However, the question states that dino A weighs in at 1.4 tons MORE than a tenth, meaning addition.
So, 7.6+1.4=9
Dinosaur A, AKA the Tyrannosaurus Rex, weighs in at 9 Tons.
~Hope this helps!
The Tyrannosaurus rex weighed approximately 9 tons.
Explanation:To determine the weight of the Tyrannosaurus rex, we need to find one tenth the weight of Patagotitan mayorum, which is 76 tons. One tenth of 76 tons is 7.6 tons. We then add 1.4 tons to this, as the Tyrannosaurus rex weighs about 1.4 tons more than one tenth the weight of Patagotitan mayorum. Therefore, the weight of the Tyrannosaurus rex is approximately 9 tons.
Stacey worked 12 hours and Amy worked 6 hours. They made the same amount of money per hour. If they made a total of $90 how much did they make per hour
Answers
[tex]Amy { \to 6hours} [/tex]
[tex]12 x 5 = 30 6 x 5 = 30 60 + 30 = 90 [/tex]
They made $5 an hour.
need help with question 20
Answers
[tex] \frac{PV}{nt} = r_{1} +r_{2}[/tex]
Then, I would subtract the unwanted variable from the sum.
[tex] \frac{PV}{nt} -r_{2} = r_{1}[/tex]
Compare the dimensions of the prisims. How many time greather is the surface area of the red prism than the surface area of the blue prism
Answers
Answer:
The dimensions of the red prism are 1.5
times the dimensions of the blue prism.
The surface area of the red prism is 2.25
times the surface area of the blue prism.
Step-by-step explanation:
Final answer:
To compare the surface areas of the red and blue prisms, divide the surface area of the red prism by the surface area of the blue prism. In this case, the surface area of the red prism is 2 times greater than the surface area of the blue prism.
Explanation:
To compare the surface areas of the red and blue prisms, we need to find the surface area of each prism. The surface area of a prism is found by adding the areas of all of its faces.
Let's say the surface area of the red prism is 100 square units and the surface area of the blue prism is 50 square units. To find out how many times greater the surface area of the red prism is than the blue prism, we can divide the surface area of the red prism by the surface area of the blue prism: 100/50 = 2.
Therefore, the surface area of the red prism is 2 times greater than the surface area of the blue prism.
X is 85% of 13, 60% of 4.5 is Y
Answers
x=11.05
y=60/100 * 4.5
y=2.7