Answer:
87.5 miles
Step-by-step explanation:
Distance between points = 3 1/2 × 25 = 87.5 miles
Which statement is true?
A. The number 31 is prime, but 37 is composite.
B. The number 29 is prime, but 37 is composite.
C. The number 31 is prime, but 33 is composite.
D. The number 33 is prime, but 35 is composite.
Answer:
C
Step-by-step explanation:
A and B are wrong because 37 is prime. 31 is prime and 33 is divisible by 11 and 3 so C
15. This year Lucille weighs 106 lb 13 oz. A
year ago she weighed 101 lb 12 oz. How
much has she gained in the year?
Answer:
5 lbs 1 oz
Step-by-step explanation:
This year Lucille weighs 106 lb 13 oz. A
year ago she weighed 101 lb 12 oz. How
much has she gained in the year?
16oz = 1 lb
13 oz = 13/16 = .8125
12 oz = 12/16 = 3/4 = .75
106.8125 - 101.75
106.8125
-101.7500
---------------
5.0625 =
5.0625 = 5 1/16
1/16 of a pound is 1oz
5 lbs 1 oz
While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on his trip. After returning
to the United States he converts his money back to US dollars. How much of the original 250 US dollars does Phelan
now have? Round to the nearest cent.
1 European euro =
1.3687 US dollars
Answer:
44.70 US dollars
Step-by-step explanation:
euro left=(250/1.3687)-150=32.66(rounded to nearest cents
US dollars=32.66x1.3687
=44.70US dollars
A boat traveled north for 28 miles, then turned x° southwest and traveled for 25 miles before stopping. When it stopped, the boat was 18 miles from its starting point.
A triangle shows the course of a boat. Starting at the dock, it travels 18 miles to the left, then 25 miles up and to the right, and then 28 miles down and back to the dock. The angle between 25 miles and 28 miles is x degrees.
Law of cosines:
By how many degrees did the direction of the boat change when it made its first turn? Round to the nearest degree.
30 degrees
39 degrees
46 degrees
50 degrees
Answer:
Option B :39 degrees is the correct.
The nearest degree is 39°
Step-by-step explanation:
Laws of cosines relates each side with its opposite angle.
Formula for this is :
[tex]c^{2} =a^{2} +b^{2} - 2abcosC[/tex]
[tex]a^{2} = b^{2}+c^{2} - 2bccosA[/tex]
[tex]b^{2} =a^{2}+c^{2} -2accosB[/tex]
in figure a=28
b=18
c=25
Here we have to find angle between a and c that is B
So [tex]18^{2} = 25^{2} +28^{2} -2*25*28cosB[/tex]
324 = 625 + 784 - 1400cosB
1400cosB = 625 + 784 - 324
1400cosB = 1085
cosB = 0.775
∠B = 39.195° ≈ 39°
The boat change 39° when it made its first turn.
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Answer:
B 39 degrees
Step-by-step explanation:
The person above me is correct and I got proof for the people with trust issues. : )
the equation of lime 1 is 3x-2y=5, and the equation of lime 2 is x+2y=7. What is the point of intersection of the two lines?
To find the point of intersection for two lines, we can use substitution to solve for the coordinates.
Solving the QuestionWe're given:
[tex]3x-2y=5[/tex][tex]x+2y=7[/tex]With these two equations, we can:
First isolate x in the second equationUse substitution to input in second equation into the first and solve for yUse the y-coordinate to find the corresponding x-coordinate using substitutionIsolate x in the second equation:
[tex]x+2y=7\\x =7-2y[/tex]
Substitute the second equation into the first:
[tex]3x-2y=5\\3(7-2y)-2y=5\\21-6y-2y=5\\21-8y=5\\21-8y=5[/tex]
Solve for y:
[tex]21-6y-2y=5\\21-8y=5\\-8y=-16\\y=2[/tex]
Solve for x:
[tex]x+2y=7\\x+2(2)=7\\x+4=7\\x=3[/tex]
AnswerThe point of intersection of the lines is (3,2).
Jack has a rectangular piece of land, the area of which is represented by a1 = 9.5l. His brother has a different rectangular piece of land, the area of which is represented by a2 = l(14 − l). Let a represent the area in square meters and l represent the length in meters of the pieces of land. The two equations plotted on a graph meet at a point as shown in the image.
The area of the brothers’ pieces of land will be the same when the length is ______ meters.
Answer:2
Step-by-step explanation:
Answer: 13
Step-by-step explanation:
please help me...!!!???????????????????????????????????????????
Answer: C
Step-by-step explanation:
(rx+t)/s = w [given]rx+t = sw [multiply both sides by s]rx = sw-t [subract t from both sides]x = (sw-t)/r [divide both sides by r]An equation is formed of two equal expressions. The correct option is C.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The given equation can be solved for x as shown below, Therefore,
[tex]\dfrac{rx+t}{s} = w\\\\[/tex]
Using the multiplication property of equality, multiply s on both the sides of the equation,
rx + t = ws
using the subtraction property of equality, subtract t on both the sides of the equation,
rx = ws - t
[tex]x = \dfrac{sw-t+t}{r}[/tex]
Hence, the correct option is C.
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Find the indicated angle measures:
Answer:
Angle 1: 55 degrees
Angle 2: 55 degrees
Angle 3: 70 degrees
Step-by-step explanation:
Finding angle 1: We know that in a triangle, all three angles must add up to 180 degrees. In the triangle on the left, 2 of the angle measures are already given to us. Therefore, we can simply do 180 - 40 - 85, thus the measure of angle 1 is 55 degrees.
Finding angle 2: We know that opposite angles are congruent. Therefore, angle 2 and angle 1 have the same measure.
Finding angle 3: Using the same thought process as we used when finding the measure of angle 1, we can subtract the other 2 angles. 180 - 55 - 55 is equal to 70.
Answer:
first, we take the first triangle( the right one), since a triangle is equal to 180 we add 85 and 40 which gives us 125, we then subtract 125 with 180 getting 55 so (1) =55
to find (2) we put 55 the same number as no. (1) because of the property VERTICALLY OPPOSITE ANGLES.
then to find (3) we do the same steps as (1), we add 55 and 55 and subtract by 180. 55+55=110
=110 - 180
=70
There u go, please mark me as brainless
Suppose that you borrow $30,000 for four vears at 8% for
the purchase of a car. Find the monthly payments and the
total interest for the loan.
Answer:
$41269.983
rounded:
$41,269.98
Step-by-step explanation:
well you begin with the equation a=p(1+r/n)[tex]^{nt}[/tex]
so 30,000(1+0.08/12)to the power of 4 times 12
when you plug all of that in a calculator your receive $41269.983
pleaseee answer people good at math
Car averages x miles per gallon means that 1 gallon is enough to drive 36 miles.
We are asked to find average miles per gallon (miles/gallon) --> average miles per gallon would be total miles driven divided by total gallons used (miles/gallon).
Total miles driven is 10+50=60.
As a car averages 25 miles per gallon in the city for 10 miles in the city it will use 10/25=0.4 gallons
What is the average value?
A data set, the arithmetic mean, also known as arithmetic average, is a measure of the central tendency of a finite set of numbers: specifically, the sum of the values divided by the number of values.
As a car averages 40 miles per gallon on the highway for 50 miles on the highway it will use
50/40=1.25 gallons;
So average miles per gallon equals to
[tex]=\frac{10+50}{0.4+1.25}\\=36[/tex]
Therefore option D is correct.
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Identify how the two trianiges are congruent. Fill in the blank below the triangles with SSS, SAS, ASA, AAS, or HL. If the two triangles are not
congruent, type not congruent.
A4X4
Blank 1:
Blank 2:
Blank 3:
Blank 4:
Question 2 (1 point)
Answer:
Blank 1 = SAS
Blank 2 = HL
Black 3 = ASA
Blank 4 = SSS
SAS - when two corresponding sides and one corresponding angles are equal HL - in a right angle triangle when corresponding hypotenuse and length are equal ASA - when 2 corresponding angles and one corresponding side are equal when all the sides of triangle is equal to other.Find the compound interest on $4000 for 2 years and 3months at 2% per annum,
compounded annually.
Answer:
CI = $182.25
Step-by-step explanation:
Compound interest formula:
[tex]Compound \space\ Interest= P(1 + \frac{r}{100})^{n} - P[/tex] ,
where P is the principal amount ($4000), r is the interest rate (2%), and n is the time period (2 years and 3 months = 2.25 years).
Using formula:
CI = [tex]4000(1 + \frac{2}{100} )^{2.25} - 4000[/tex]
CI = $182.25
Given the function f(x) = 8x^2-3x+2 Calculate the following values
[tex]1) \text{ } f(-2)=8(-2)^{2}-3(-2)+2=\boxed{40}\\\\2) \text{ } f(-1)=8(-1)^{2}-3(-1)+2=\boxed{13}\\\\3) \text{ } f(0)=8(0)^{2}-3(0)+2=\boxed{2}\\\\4) \text{ } f(1)=8(1)^{2}-3(1)+2=\boxed{7}\\\\5) \text{ } f(2)=8(2)^{2}-3(2)+2=\boxed{28}[/tex]
12. Use the diagram to determine the value of x
Answer:
127 degrees = x
Step-by-step explanation:
A six sided polygon has interior angles that sum to
(n-2)(180) = (6-2)(180 = 720
so all of the angles in the question add to 720
98 + 133 + x + x + 155 + 80 = 720
solve for x = 127 degrees
Answer:
x = 127
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 6 , then
sum = 180° × 4 = 720°
sum the interior angles and equate to 720
x + x + 155 + 80 + 98 + 133 = 720 , that is
2x + 466 = 720 ( subtract 466 from both sides )
2x = 254 ( divide both sides by 2 )
x = 127
Help me with this question please and thank you!! :)
[tex]A \cup B[/tex] represents the set that contains all the elements that are in at least one of the sets, so [tex]A \cup B=\{1, 2, 5, 6, 7, 8, 9, 10, 12, 16, 18, 19, 20, 21, 22, 23, 25\}[/tex].
We want the complement of this set (in other words, the set with all the elements in the universal set but not in the given set).
This set is {3, 4, 11, 13, 14, 15, 17, 24}
The following table shows how far a bus has gone in t hours. Which of the following equations represents this information?
Step-by-step explanation:
You need to attach the table in order to get an answer.
Please please help me with my math
Answer:
D
Step-by-step explanation:
In functions like this, its best to pay attention to the end points of the rays.
On the lower line:
it ends at x -1
because it is a closed circle, that means x can also equal -1.
x≤-1
On the upper line:
it starts at -1
it is an open circle, meaning x cannot be -1
x>-1
Determine the rank of A
Answer:
The rank of a matrix is the number of nonzero rows in the reduced matrix, so the rank is 3. option (C)
Step-by-step explanation:
Echelon Form : it is used to find the rank of matrix by reducing rows into zeros then the number of non zero rows is the rank of the matrix
[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\2&-2&-2&5&1\\1&0&-12&9&-3\\-1&1&7&-7&1\end{array}\right][/tex]
apply row operations:
R₂= R₂ - 2 R₁
[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\1&0&-12&9&-3\\-1&1&7&-7&1\end{array}\right][/tex]
R₃= R₃ - R₁
[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\0&0&-17&11 &-5\\-1&1&7&-7&1\end{array}\right][/tex]
R₄ = R₄ +R₁
[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\0&0&-17&11 &-5\\0&0&12&-9 &3\end{array}\right][/tex]
R₄ = R₄ +R₃
[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\0&0&-17&11 &-5\\0&0&0&0 &0\end{array}\right][/tex]
we can clearly see that after performing row operations there are 3 non zero rows,
therefore the Rank of the given matrix is 3
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The following excerpt comes from the International Bottled Water Association
"In 2012, total U.S. bottled water consumption increased to 9.67 billion gallons, up from 9.1 billion gallons in 2011. In fact, 2012's consumption growth was the strongest it has been in five years. In addition,
per-capita consumption is up 5.3 percent in 2012, with every person in America drinking an average of 30.8 gallons of bottled water last year. Bottled water increased in absolute volume more than any other
beverage category in the U.S. Bottled water sales increased by 6.7 percent in 2012, and now total $11.8 billion."
(i) Estimate the per capita consumption from 2011 from data in the statement. Express your answer rounded correctly to the nearest tenth of a gallon.
Using proportions, the estimate of the per capita consumption from 2011 is of 29.2 gallons.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
From the data, the 2012 consumption was 5.3% percent higher than in 2011, that is 105.3% of 1.053x. This consumption was of 30.8 gallons, hence:
1.053x = 30.8.
x = 30.8/1.053
x = 29.2.
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Find the numeral preceding and succeeding each of the following numerals. Use T as the digit for 10.
a. TTO eleven
b. 100000 nine
c. 222 three
The numeral preceding and succeeding each of the following numerals.
Now, what happens when you add 1 or subtract 1 from 100 in the familiar base 10.
Adding adds 1 to the unit digit.
Subtracting 1 gives 99 because 9 is the largest digit in base 10.
So A. 100 base 8
The largest digit in base 8 is 7, so
..., 77, 100, 101,...
B. 10000 base 7
What is the largest digit in base 7?
The largest digit in base 7 is 6, so
..., 6666, 10000, 10001, ...
Next what happens when you add 1 to 509 in base 10. 9 is the largest digit in base 9, so adding 1 makes the units digit 0, and you carry a 1 to the next digit to the left:
509 + 1 = 510.
C. 305 base 6
5 is the largest digit in base 6, so
..., 304, 305, 310, ...
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Select the correct answer.
What is the solution to this equation?
log(2x - 100) = 3
A = 1,000
B = 450
C = 550
D = 100
Find the unit rate (constant of proportionality) of the distance traveled.
Number of hours
0.25 1.5 2.5 3
Distance traveled (km) 3 18 30 36
Answer:
12.
Step-by-step explanation:
if to re-write the given condition, then
[tex]\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;[/tex]
it is clear, the required constant is 12 (12 per hour).
Help please I need asap
Answer: -120
Step-by-step explanation:
[tex]2\sum^{4}_{p=1} (p^{2}-9p)=2[(1^{2}-9(1))+(2^{2}-9(2))+(3^{2}-9(3))+(4^{2}-9(4))]=\boxed{-120}[/tex]
On a coordinate plane, an absolute value graph has a vertex at (10, 6).
The graph of h (x) = StartAbsoluteValue x minus 10 EndAbsoluteValue + 6 is shown. On which interval is this graph increasing?
(–∞, 6)
(–∞, 10)
(6, ∞)
(10, ∞)
Answer: (10, ∞)
Step-by-step explanation:
See the graph in the attached image.
curved surface area of a cone = Trl, where r is the
radius and is the slant height.
The cone below has a radius of 3 cm and a slant height
of 7 cm.
Work out the total surface area of the cone.
Give your answer in terms of π.
7 cm
3 cm
The total surface area of the cone is 3π + 10 cm².
What is the curved surface area?A cone is a three-dimensional object that consists of a circular base and a vertex.
Total surface area = πr (r + l)
Where:
r = radius l = slant heightπ = piπ x 3 + (3 + 7)
3π + 10 cm²
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Y=-1/3x+2
A.
B.
C.
D.
Answer:
C
Step-by-step explanation:
The slope is -1/3, so it will go down and to the right. Down 1, to the right 3 (rise over run!)
The y intercept is 2.
What is the solution to the following equation?
-3+x= -8
A. x = -5
B. x=5
C. x = 11
D. x=-11
Answer:
[tex]\mathsf {A. x = -5}[/tex]
Step-by-step explanation:
[tex]\implies \mathsf {-3 + x = -8}[/tex]
[tex]\implies \mathsf {x = -8 + 3}[/tex]
[tex]\implies \mathsf {x = -5}[/tex]
In our QR class, 43% live in Massachusetts. Of the Massachusetts residents, 67% live in
Boston. What percentage of the class lives in Boston?
Answer:
The answer will be 63%.
Step-by-step explanation:
they have all ready mentioned that.
Use the moving and additivity principles to explain and she weighs why the next triangle has an area of 1/2 (b*h) Square units for the given choices of B and H. One! If it naturally with the expression b*(1/2h) and the other should fit naturally with the expression 1/2(b*h)
Answer: The given triangles have an area [tex]1/2[/tex] × [tex]base[/tex] × [tex]height[/tex]
Step-by-step explanation:
The moving principle states that if you move a shape rigidly without stretching it the area does not change whereas the additivity principle states that if you combine different shapes without overlapping them then the area is the cumulative sum of each of the figures.
Since both, the principle will give out the same answers. the arrangement for the expression can be manipulated also.
For the first triangle applying the moving principle gives,
Area [tex]=[/tex] [tex]b[/tex] × [tex](\frac{1}{2}[/tex] · [tex]h)[/tex]
For the second triangle applying the additivity principle,
Area [tex]=\frac{1}{2}[/tex] ([tex]b[/tex] · [tex]h[/tex])
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which law would you use to simplify the expression....
Answer:
power of a power
Step-by-step explanation:
the power of a power law says that, "if a base raised to a power is being raised to another power, the exponents are multiplied and the base remains the same."
for example, for this problem, you would do:
[tex](x^4)^9\\= x^4^*^9\\= x^3^6[/tex]
