Answer:
C
Step-by-step explanation:
The angle 160° and the interior angle of the triangle form a straight angle
interior angle = 180° - 160° = 20°
Similarly with angle 131° and the interior angle at the top of the triangle
interior angle = 180° - 131° = 49°
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
n is an exterior angle, hence
n = 20° + 49° = 69° → C
Lily has two times as much money invested in 8% stocks as she has in bonds paying 6%. How much she has invested in stocks if her annual income from stocks and bonds is $325.6?
Answer:
Final answer is $4440.
Step-by-step explanation:
Let amount of money invested in 8% stock = x
Let amount of money invested in 6% stock = y
then total money invested $325.6 gives equation
8% of x + 6% of y = 325.6
0.08x + 0.06y = 325.6
8x + 6y = 32560...(i)
other equation will be x=2y...(ii)
plug (ii) into (i)
8x + 6y = 32560
8(2y) + 6y = 32560
16y+ 6y = 32560
22y = 32560
[tex]y=\frac{32560}{22}[/tex]
y=1480
plug y=1480 into (ii)
x=2y=2(1480)=2960
Then total money invested in stocks = x+y= 1480+2960=4440
Hence final answer is $4440.
what is 18.23 rounded to the nearest tenth?
Answer:
The answer is 18.2.
Hope this helps!
Answer: 18.2
Step-by-step explanation:
you would round to 18.2 because with 5 and above, you give it a shove, 4 and below let it go
which expression is equivalent to (2x-3) (x+5
2x^2+10x-3x-15= 2x^2+7x-15
Answer:
2x^2+10x-3x-15= 2x^2+7x-15
Step-by-step explanation:
Zoologists are studying two newly discovered species of insects in a previously unexplored section of rain forest. They estimate the current population of insect A to be 1.3 million and the current population of insect B to be 2.1 million. As development is encroaching on the section of rain forest where these insects live, the zoologists estimate the populations of insect A to be reducing at a rate of 3.8% and insect B to be reducing at a rate of 4.6%.
If P represents the population of each species of insect in millions, and t represents the elapsed time in years, then which of the following systems of equations can be used to determine how long it will be before the populations of the two species are equal?
Answer: Obtion B
[tex]P = 1.3e ^ {-0.038t}\\\\P = 2.1e ^ {-0.046t}[/tex]
Step-by-step explanation:
The equation for exponential decay has the following form:
[tex]y = pe ^{-rt}[/tex]
Where
p is the initial population
r is the rate of decrease
t is time.
In this problem we have to:
The current population of insect A to be 1.3 million and the current population of insect B to be 2.1 million.
So
[tex]p_1 = 1.3[/tex] in millions
[tex]p_2 = 2.1[/tex] in millions
We also need the populations of insect to be reduced at a rate of 3.8% and insect to be reduced at a rate of 4.6%.
so:
[tex]r_1 = 0.038\\\\r_2 = 0.046[/tex]
then the exponential decay equation for insect A is:
[tex]P = 1.3e ^ {-0.038t}[/tex]
the exponential decay equation for insect B is:
[tex]P = 2.1e ^ {-0.046t}[/tex]
Finally, the system of equations is:
[tex]P = 1.3e ^ {-0.038t}\\\\P = 2.1e ^ {-0.046t}[/tex]
The answer is the Option B
What is the reciprocal of tanB in the triangle below?
Answer:
Step-by-step explanation:
Note that the reciprocal of tan B is by definition the cotangent (cot) of B:
1 adjacent side BC
---------- = cot B = ----------------------- = ---------
tan B opposite side AC
Answer:
Hence, The reciprocal of tan B is tan A
B is correct.
Step-by-step explanation:
We are given a right angle triangle. Right angle at ∠C
We need to find the reciprocal of tan B
First we write the formula of tan B using trigonometry identity.
[tex]\tan\theta=\dfrac{\text{Opposite}}{\text{Base}}[/tex]
In ΔABC, ∠C=90°
[tex]\tan B=\dfrac{AC}{BC}[/tex]
Now we reciprocal it.
[tex]\dfrac{1}{\tan B}=\dfrac{BC}{AC}[/tex]
[tex]\tan A=\dfrac{BC}{AC}[/tex]
Comparing both equation ( Right sides equal )
[tex]\dfrac{1}{\tan B}=\dfrac{BC}{AC}=\tan A[/tex]
[tex]\dfrac{1}{\tan B}=\tan A[/tex]
Hence, The reciprocal of tan B is tan A.
Find the circumference of a circle with an area of 254.47 square inches.
Answer:
56.5 inches
Step-by-step explanation:
We are given the area of a circle and we are to find the circumference of the same circle.
We know that the area of a circle is given by [tex]\pi r^2[/tex] so equating the given value to get.
[tex]\pi r^2=254.47[/tex]
[tex]r^2=\frac{254.47}{\pi }[/tex]
[tex]r=\sqrt{81.00}[/tex]
r = 9 inches
Since we now know the radius of the circle so we can find its circumference.
Circumference of circle = [tex]2\pi r[/tex] = [tex]2\pi (9)[/tex] = 56.5 inches
Answer: 56.54 in
Step-by-step explanation:
The area can be calculated with this formula:
[tex]A=\pi r^2[/tex]
Where r is the radius
And the circumference can be calculated with this formula:
[tex]C=2\pi r[/tex]
Where r is the radius
Solve for the radius from [tex]A=\pi r^2[/tex]. Then, tha radius is:
[tex]r=\sqrt{\frac{A}{\pi }}=\sqrt{\frac{254.47in^2}{\pi }} =9in[/tex]
Then, the circumference is:
[tex]C=2\pi (9in)=56.54in[/tex]
each column of the matrix T=[0,0,3,0,3,0] represents a vertex of a triangle. if rosa scales the triangle by fining 3T what are the vertices of the scaled triangle?
Answer:
(0,0), (0,9), (9,0)
Step-by-step explanation:
The matrix corresponding vertices are:
(0,0)
(0,3)
(3,0)
Rosa scales by 3T, so we need to multiply each point by 3.
(3*0, 3*0)
(0*3, 3*3)
(3*3, 0*3)
=
(0,0)
(0,9)
(9,0)
last answer choice is right.
Answer:
[tex]\large\boxed{(0,\ 0),\ (0,\ 9),\ (9,\ 0)}[/tex]
Step-by-step explanation:
[tex]n\cdot\left[\begin{array}{ccc}a&b&c\\d&e&f\end{array}\right] =\left[\begin{array}{ccc}(n)(a)&(n)(b)&(n)(c)\\(n)(d)&(n)(e)&(n)(f)\end{array}\right] \\\\============================[/tex]
[tex]\text{We have:}\\\\T=\left[\begin{array}{ccc}0&0&3\\0&3&0\end{array}\right] \Rightarrow\text{vertex}\ (0,\ 0),\ (0,\ 3),\ (3,\ 0)\\\\-----------------------------\\\\3T=\left[\begin{array}{ccc}(3)(0)&(3)(0)&(3)(3)\\(3)(0)&(3)(3)&(3)(0)\end{array}\right] =\left[\begin{array}{ccc}0&0&9\\0&9&0\end{array}\right] \\\\\text{new vertex:}\ (0,\ 0),\ (0,\ 9),\ (9,\ 0)[/tex]
I need some help with #15
Answer:
B. 1184
Step-by-step explanation:
Answer is B
See photo
math help uwu ,,, will reward tyvm. (─‿‿─)
Answer:
Step-by-step explanation:
Here's how I would do it (not necessarily the only way or best way).
Draw an imaginary line from A to C. This splits the kite into two triangles: ABC and ADC. Since AB ≅ AD, CB ≅ CD, and AC ≅ AC, the two triangles must be congruent by SSS. Therefore, ∠B ≅ ∠D.
How many different ways can the 11 letters in the word PROBABILITY be arranged?
There are 11 letters in "probability"
There are two B's and two I's
11!/(2!2!) = 9,979,200
hope that helps. please name me brainliest
Answer:
8
6
Using all the letters of the word ARRANGEMENT how many different words using all letters at a time can be made such that both A, both E, both R both N occur together .
Hope this helps <3<3<3 Aaliyah
Step-by-step explanation:
What is the area of point O?
Answer:
28.26 cm²
Step-by-step explanation:
It's not the point O, but the circle O.
The area of a circle is given by the formula A = π r²
We already have r (3cm)... so we can plug it directly into the equation:
A = π r² = π 3² = 9π = 28.26 cm²
Answer:
A = 28.27
Step-by-step explanation:
A = π r^2
A = π 3^2
A= π (9)
A = 28.27433
Which expressions are equivalent to 5+(−3)(6x−5)
Choose all answers that apply:
A
18x−20
B
3x-3
C
None of the above
Answer:
C. None of the aboveStep-by-step explanation:
[tex]5+(-3)(6x-5)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=5+(-3)(6x)+(-3)(-5)\\\\=5-18x+15\qquad\text{combine like terms}\\\\=-18x+(5+15)\\\\=-18x+20[/tex]
Answer:
none of the above
Step-by-step explanation:
just for people who dont want one
Use complete sentences to describe the domain of the cosine function
The domain of a function is the complete set of possible values of the independent variable.
The cosine function is represented by the expression: y=cos(x), where "x" is the independent function, and "y" the dependent function. So the domain comes to be all the values that "x" can take.
The domain of the cosine function is all the real numbers. All this can be verified by looking at its graph (attached)
Can someone help me with this math problem
The answer is D. you would do 0.25 x 6.5. you add 2 to the original needed batches of 4.5.
Answer:
1.125 (A)
Step-by-step explanation:
First you multiply 0.25 x 4.5=1.125
line p has an x-intercept of 5 and a y-intercept of 3. Find the slope of line p
Answer:
-3/5
Step-by-step explanation:
you can use the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] to find the slope of a line when given two points.
we are given both the x and y intercepts, and we can use those in the formula.
the x intercept is (5,0) and the y intercept is (0,3)
i will treat (5,0) as my x1 and y1, and (0,3) as my x2 and y2
[tex]\frac{3-0}{0-5}[/tex] = -3/5
the slope is -3/5
The slope of the line is -3/5 if the line p has an x-intercept of 5 and a y-intercept of 3.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have a line p:
The x-intercept of line p is 5 or (5, 0)
The y-intercept of line p is 3 or (0, 3)
The slope m can be evaluated:
[tex]\rm m =\dfrac{3-0}{0-5}[/tex]
m = -3/5
Thus, the slope of the line is -3/5 if the line p has an x-intercept of 5 and a y-intercept of 3.
Learn more about the slope of the straight line here:
brainly.com/question/3493733
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Vertical angles must: check all that apply
Answer:
Have the same vertex , and be congruent.
Step-by-step explanation:
Answer:Have the same vertex , and be congruent.
Step-by-step explanation:
Which of the following is an example of a variable expense?
Rent
Groceries
Wages
Car insurance
PLEASE HELP!!
Answer:
Step-by-step explanation:
Rent, wages and car insurance don't vary much. Grocery expenses depend upon the particular groceries purchased each time one goes to the grocery store, and are least likely to be steady / constant from week to week.
simplify sin x / CSC x + cos x / sec x
The expression sin x / csc x + cos x / sec x simplifies to sin^2 x + cos^2 x by using the reciprocal identities of the trigonometric functions csc x and sec x.
Explanation:The expression sin x / csc x + cos x / sec x can be simplified by substituting the reciprocal identities for the trigonometric functions csc x and sec x. The reciprocal of csc x is sin x and the reciprocal of sec x is cos x. Thus, sin x / csc x becomes sin x / (1/sin x) which simplifies to sin^2 x. Similarly, cos x / sec x becomes cos x / (1/cos x) or cos^2 x. Therefore, the simplified form of the expression is sin^2 x + cos^2 x.
Learn more about Trigonometric Simplification here:https://brainly.com/question/34160320
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If sin 0=3/5, then cos 0=
Answer:
[tex]\frac{4}{5}[/tex]
Step-by-step explanation:
Given
sinΘ = [tex]\frac{3}{5}[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]
Then the hypotenuse = 5 and one leg of the right triangle is 3
Using Pythagoras' identity to find the second leg (x)
x² + 3² = 5²
x² + 9 = 25 ( subtract 9 from both sides )
x² = 16 ⇒ x = 4
cosΘ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{5}[/tex]
Meaning of tan sin and cos
Answer:
Those are trigonometric identities. and tan is just a shortened version of tangent, same for cos is means cosine
The sine/sin of the angle = the length of the opposite side divided by the length of the hypotenuse.
The cosine/cos of the angle = the length of the adjacent side divided by the length of the hypotenuse.
The tangent/tan of the angle = the length of the opposite side divided by the length of the adjacent side.
Suppose you need to choose a new combination for your combination lock. You have to choose 3 numbers, each different and between 0 and 40. How many combinations are there? Explain
Answer:
63,960 possibilities in total.
Step-by-step explanation:
For the first number, you can choose from 41 different numbers, so there are 41 possibilities.
For the second number, you cannot choose the same as the first one, so you are now limited to 40 possibilities.
For the third number, you are down to 39 possibilities since you cannot pick the same as the first two ones.
So, you have 41 * 40 * 39 = 63,960 possibilities in total.
Picking a new combination is easy... remembering it is the hard part :-)
If you want to calculate it from a formula standpoint, the base formula would be:
[tex]P(n,r) = \frac{n!}{(n-r)!} = \frac{41!}{(41-3)!} = 63960[/tex]
Where n is the total numbers possible and r is the quantity of numbers you have to pick.
HELPPPP ASAP!!!!!!!!!!!! Using the distributive property, which of the following expressions is equivalent to 5(3 + 5y)?
A. 8 + 5y
B.15 + 5y
C.15 + 25y
D. 8 + 10y
Answer:
C.15+25y
Step-by-step explanation:
5(3+5y) solved via distribution is 15+25y
Happy to help :D
C. Because 5(3+5y) is the same as 5x3 plus 5x5y which is 15 + 25y
can someone help me out please:(:(
Answer:
[tex]\large\boxed{\sqrt{20}-\sqrt{80}=-2\sqrt5}[/tex]
Step-by-step explanation:
[tex]\text{Use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\\sqrt{20}=\sqrt{4\cdot5}=\sqrt4\cdot\sqrt5=2\sqrt5\\\\\sqrt{80}=\sqrt{16\cdot5}=\sqrt{16}\cdot\sqrt5=4\sqrt5\\\\\sqrt{20}-\sqrt{80}=2\sqrt5-4\sqrt5=(2-4)\sqrt5=-2\sqrt5[/tex]
If h(x)=6-x what is the value of (hxh)(10)?
Answer:
16
Step-by-step explanation:
h(x) × h(x) = (6 - x)²
(h × h)(10) = (6 - 10)² = (- 4)² = 16
For this case we have by definition, that given two functions, then:
[tex](f * g) (x) = f (x) + g (x)[/tex]
Here, we want to find ([tex](h * h) (x):[/tex]
[tex](h * h) (x) = (6-x) (6-x)\\(h * h) (x) = 36-6x-6x + x ^ 2\\(h * h) (x) = 36-12x + x ^ 2[/tex]
We want to find the value of the function when [tex]x = 10[/tex].
[tex](h * h) (10) = 36-12 (10) + (10) ^ 2\\(h * h) (10) = 36-120 + 100\\(h * h) (x) = 16[/tex]
Answer:
[tex](h * h) (x) = 16[/tex]
Solve log 60 - log 30
Answer:
log(2)
Step-by-step explanation:
property of logs says
Log(60) - Log(30) = Log(60/30) = Log (2)
Answer:
1.20
Step-by-step explanation:
properties of log
log x - log y = logx/logy
The Cooking Club made some pies to sell during lunch to raise money for an end-of-year banquet. The Cafeteria contributed pies to the club. Each pie was then cut into four pieces to the club. Each pie then cut into four pieces and sold. There were a total of 36 pieces to sell. How many pies did the club make?
Answer:pies 9 :p
Step-by-step explanation:
36÷4=9
Factor completely 49x^2-25
Answer:
(7x-5)(7x+5)
Step-by-step explanation:
Answer:
(7x + 5)(7x - 5)
Step-by-step explanation:
49x² - 25 ← is a difference of squares and factors in general as
a² - b² = (a + b)(a - b)
49x² = (7x)² ⇒ a = 7x
25 = 5² ⇒ b = 5
49x² - 25
= (7x)² - 5² = (7x + 5)(7x - 5)
Need help very badly
Find the area of the yellow region.
Round to the nearest tenth.
Answer:
5.4 ft²
Step-by-step explanation:
Since the circle is inscribed in the square then radius r = 2.5
Area of yellow = area of square - area of circle
A = (5 × 5) - (π × 2.5²)
= 25 - 6.25π ≈ 5.4 ft²
Answer:
Area of the Yellow Region is 5.4 ft²
Step-by-step explanation:
Given:
Length of the side of the square = 5 ft
Diameter of the Circle = Length of the side = 5 ft
⇒ Radius of the circle, r = 5/2 = 2.5 ft
To find: Area of the Yellow region from the figure.
Area of the Yellow Region = Area of the Square - Area of the Circle
= Side × Side - πr²
= 5 × 5 - 3.14 × (2.5)²
= 25 - 3.14 × 6.25
= 25 - 19.625
= 5.375
≈ 5.4 ft² (nearest tenth)
Therefore, Area of the Yellow Region is 5.4 ft²
equivalent 0f 2(2a-5)-(a-3)
Answer:
3a-7
Step-by-step explanation:
2(2a-5)-(a-3)
Distribute the 2
2*2a -2*5 - (a-3)
4a -10 - (a-3)
Distribute the minus sign
4a-10 -a +3
Combine like terms
4a-a -10+3
3a-7
Tonya bought gifts for her family that cost $25, $14, $33, and $19. She has to buy one more gift and wants her mean cost to be $25. What should she spend on the last gift?
____________________________________________________
Answer:
Your answer would be $34.
____________________________________________________
Step-by-step explanation:
In order to get the mean cost that she wants from the gift, we would need to get the numbers that we already had, and have another set of row with the amount of gifts she needs with the mean she wants.
Here is how it should look like:
$25 $14 $33 $19 x
$25 $25 $25 $25 $25
We are trying to find the number for "x"
Therefore, we would need to use the process of adding, then subtracting after.
Lets add:
[tex]25+14+33+19=91\\\\25+25+25+25+25=125[/tex]
What we would do now is subtract the numbers in order to get the price that Tonya wants from her gift, if she buys another gift.
[tex]125-91=34[/tex]
Tonya should spend $34 on her last gift.
$34 should be your FINAL answer
____________________________________________________