Answer:
A set is a well-defined collection of distinct mathematical objects.
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
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}
If f(x) = x², and
g(x) = x1, then
f(g(x)) = ?
will give brainliest answer !!
Answer: 1, -2, 1
Step-by-step explanation:
[tex]f(g(x))=f(x-1)=(x-1)^{2}=x^{2}-2x+1[/tex]
A cake recipe requires 4 and one-half cups of flour to make 1 cake. How many cakes can be made by a baker who has 16 cups of flour?
Answer:
3 cakes
Step-by-step explanation:
just flow by the formula then ignore the remainder and take the whole number which is 3 then that becomes your answer good day.
A tank weighs 5.6kg when it 1/4 filled with water.If it weighs 10.4kg when it is full ,what will be it's weight when it is empty.
Answer:
4 kg
Step-by-step explanation:
so 1.6 * 4 is 6.4 so you just double check if you want
4 + 1.6 which is 1/4 of 6.4 will be 5.6 (matches with the question)
4 + (1.6*4) (indicates it's full) = 10.4( also Matches with the question)
there is another way by setting up an equation. let me know in comments if you want to see it that way
If tank weighs 5.6kg when it 1/4 filled with water. If it weighs 10.4kg when it is full , then weight when it is empty is 0.93kg
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
A tank weighs 5.6kg when it 1/4 filled with water
Tank weighs 10.4kg when it is full
We need to find the weight when it is empty.
Let weight of the tank “x” and the weight of the water in the full tank “y”.
From the problem statements, we deduce the following equations:
x + y/4 = 5.6kg => x = 5.6kg - y/4
x + y = 10.4kg => y = 10.5kg - x
y = 10.5kg - (5.6kg - y/4)
3y/4 = 4.9
Thus y = 6.53kg; x = 0.93kg
Hence, weight of the tank when it is empty is 0.93kg.
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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.
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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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
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
3x - [2 +3 (2-x) = S-(3-X)
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. : )
Which algebraic expression is equivalent to the expression below
5(4x + 5) - 17
A.
20x + 9
B.
5x + 9
C.
20x + 42
D.
20x + 8
Answer:
20x + 8
Step-by-step explanation:
5*4x + 5*5 -17
20x +25 -17
20x + 8
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
urgent algebra 2 help please
Answer:
y = 4x - 5
Step-by-step explanation:
y = mx + b
By putting above values in equation (i)
-1 = 4 (1) + b
-1 = 4 + b
-5 = b
b = -5
y = 4x - 5
f(x) = x² + (k-6) x +9, k * 0. The roots of the equation f(x) = 0 are a and B. (a) Find, in terms of k, the value of (i) a² + ß² (ii) a² ß² Given that 9(a²+ B²) = 2a²p². find the value of k. (b) (c) Using your value of k, and without solving the equation f(x) = 0. form a quadratic equation, with integer coefficients, which has roots and 33² f ( x ) = x² + ( k - 6 ) x +9 , k * 0 . The roots of the equation f ( x ) = 0 are a and B. ( a ) Find , in terms of k , the value of ( i ) a² + ß² ( ii ) a² ß² Given that 9 ( a² + B² ) = 2a²p² . find the value of k . ( b ) ( c ) Using your value of k , and without solving the equation f ( x ) = 0 . form a quadratic equation , with integer coefficients , which has roots and 33²
(a) If [tex]\alpha[/tex] and [tex]\beta[/tex] are roots of [tex]f(x)[/tex], then we can factorize [tex]f[/tex] as
[tex]f(x) = x^2 + (k - 6) x + 9 = (x - \alpha) (x - \beta)[/tex]
Expand the right side and match up coefficients:
[tex]x^2 + (k-6) x + 9 = x^2 - (\alpha + \beta) x + \alpha \beta \implies \begin{cases} \alpha + \beta = -(k-6) \\ \alpha \beta = 9 \end{cases}[/tex]
Now, recall that [tex](x+y)^2 = x^2 + 2xy + y^2[/tex]. It follows that
[tex]\boxed{\alpha^2 + \beta^2} = (\alpha + \beta)^2 - 2\alpha\beta = (-(k-6))^2 - 2\times9 = \boxed{k^2 - 12k + 18}[/tex]
and
[tex]\boxed{\alpha^2\beta^2} = 9^2 = \boxed{81}[/tex]
(b) If [tex]9(\alpha^2+\beta^2) = 2\alpha^2\beta^2[/tex], then
[tex]9 (k^2 - 12k + 18) = 2\times81 \implies 9k^2 - 108k = 0 \implies 9k (k - 12) = 0[/tex]
Since [tex]k\neq0[/tex], it follows that [tex]\boxed{k=12}[/tex].
(c) The simplest quadratic expression with roots [tex]\frac1{\alpha^2}[/tex] and [tex]\frac1{\beta^2}[/tex] is
[tex]\left(x - \dfrac1{\alpha^2}\right) \left(x - \dfrac1{\beta^2}\right)[/tex]
which expands to
[tex]x^2 - \left(\dfrac1{\alpha^2} + \dfrac1{\beta^2}\right) x + \dfrac1{\alpha^2\beta^2}[/tex]
Reusing the identity from (a-i) and the result from part (b), we have
[tex]\left(\dfrac1\alpha + \dfrac1\beta\right)^2 = \dfrac1{\alpha^2} + \dfrac2{\alpha\beta} + \dfrac1{\beta^2} \\\\ \implies \dfrac1{\alpha^2} + \dfrac1{\beta^2} = \left(\dfrac{\alpha + \beta}{\alpha\beta}\right)^2 - \dfrac2{\alpha\beta} = \left(\dfrac{-(k-6)}9\right)^2 - \dfrac29 = \dfrac29[/tex]
We also know from part (a-ii) that [tex]\alpha^2\beta^2=81[/tex].
So, the simplest quadratic that fits the description is
[tex]x^2 - \dfrac29 x + \dfrac1{81}[/tex]
To get one with integer coefficients, we multiply the whole expression by 81 to get [tex]\boxed{81x^2 - 18x + 1}[/tex].
Select the correct answer.
What is the solution to this equation?
log(2x - 100) = 3
A = 1,000
B = 450
C = 550
D = 100
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.
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]
15
16
Matt had 1 pound of dog food in a bag.
He fed his puppy pound of the food.
How much dog food is left in the bag?
Give your answer in simplest form.
pound
WOOF!
Step-by-step explanation:
1/2 represents every fraction, where the denominator (bottom part) is twice the numerator (top part).
like 4/8 or 6/12 or 128/256 or ...
what do we need in the denominator to calculate with 15/16 ?
the same : 16.
and what is half of 16 ? 8.
so, we need the 1/2 based on 16th = 8/16.
so, the dog ate 8/16 (1/2) of the original 15/16.
what was left was
15/16 - 8/16 = 7/16 pound
an airplane that is flying at an altitude of 30 000 ft is beginning to descend at a rate of 1000 feet per minute. a helicopter is beginning its trip, starting at an altitude of zero feet. the helicopter ascends more slowly than the airplane, going up at a rate of 500 feet per minute. after how many minutes will the airplane and the helicopter be at the same altitude
Based on the altitudes of both the airplane and the helicopter, the number of minutes until they are at the same altitude is 20 minutes.
When will the airplane and helicopter be at the same altitude?Assuming the minute both will be on the same altitude is x, the altitude that the airplane would be at that point is:
= 30,000 - 1,000x
The helicopter's altitude would be:
= 0 + 500x
Putting them together gives:
30,000 - 1,000x = 500x
30,000 = 1,500x
x = 30,000 / 1,500
= 20 minutes
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Write 31/8 as a mixed number.
Reward: Mark as brainlist.
Answer:
[tex]3 \frac{7}{8}[/tex]
Step-by-step explanation:
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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Need help please answer!!!
It can be modeled by an exponential function because each time x increases by 1, f(x) is multiplied by 4.
This means the base of the exponential function is 4, and since f(x)=3 when x=0, [tex]f(x)=3(4)^{x}[/tex]
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).
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]
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
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.
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).
IMPORTANT, PLEASE HELP QUICKLY! 40 POINTSS
Answer the following questions given that Angles A and B are the acute
angles found in a right triangle.
1. If tan (A) = 3/4, then tan (B) equals?
2. If tan (B) = 2/7, then tan (A) equals?
3. Based on the information in #2, which angle would be bigger, A or B?
Use a diagram to help justify your answers.
Answer:
[tex]\sf 1. \quad \tan(B)=\dfrac{4}{3}[/tex]
[tex]\sf 2. \quad \tan(A)=\dfrac{7}{2}[/tex]
[tex]\sf 3. \quad \angle A[/tex]
Step-by-step explanation:
Acute angle: an angle less than 90°
Tan trigonometric ratio
[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleQuestion 1
Refer to the first attached diagram.
If tan(A) = 3/4 then the side opposite ∠A is 3 units, and the side adjacent ∠A is 4 units.
Therefore:
[tex]\implies \sf \tan(B)=\dfrac{4}{3}[/tex]
Question 2
Refer to the second attached diagram.
If tan(B) = 2/7 then the side opposite ∠B is ,and the side adjacent ∠B is 7.
Therefore:
[tex]\implies \sf \tan(A)=\dfrac{7}{2}[/tex]
Question 3Angle A would be bigger (see second attachment).
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
