Answer:
46°
Step-by-step explanation:
Points of note
two angles are complementary in a right trianglesin 44° = cos x°Solving
The first thing to understand is "complementary" means that the two angles add up to 90°Therefore, 44 + x = 90x = 46°Answer:
46°
Step-by-step explanation:
Complementary angles
Two angles whose measures sum to 90°
In a right triangle, the angle opposite the hypotenuse is always 90°.
The interior angles of a triangle sum to 180°, therefore the other two angles are complementary angles since their sum is always 90°.
So we can label one angle as [tex]x[/tex] and the other as [tex](90-x)[/tex].
The side opposite angle [tex]x[/tex] is the side adjacent to angle [tex](90-x)[/tex].
Therefore, using trig ratios, we can say that [tex]\sin(x) = \cos(90-x)[/tex]
So, if [tex]x=44[/tex] then:
[tex]\implies \sin(44) = \cos(90-44)=\cos(46)[/tex]
How many solutions are there to the equation below?
x²=9
A. 9
B. 0
C. 4
D. 2
E. 3
F. 1
Answer: D) 2
Step-by-step explanation:
x² = 9 means what number times itself is equal to 9
We know that 3×3=9 so that is already one solution, but there is another
-3×-3 is also equal to 9
A negative number times a negative number results in a positive number so -3 is another solution.
That gives us two solutions
Answer:
D; only 2
Step-by-step explanation:
Solve for x over the real numbers:
x^2 = 9
Take the square root of both sides:
Answer: x = 3 or x = -3
Researchers would like to assess the overall health of white pine trees in a state park. The park has a paved road that runs through the middle of the park. To select trees to assess for damage, the ranger parks at the side of the road and chooses 100 trees near the road to assess for damage. Which of the following statements best describes the bias that may arise from the results?
Because only 100 trees were selected, the overall damage of trees in the park may be underestimated.
The ranger should take another sample of trees near the road and compare it to the first sample to reduce bias.
Because a random sample of trees was chosen, the sample should provide a suitable estimate of the overall health of the trees.
Trees near the road may have more damage than trees away from it, so the results may overestimate the overall damage of the trees.
Trees near the road may have more damage than trees away from it, so the results may overestimate the overall damage to the trees.
What is a random sample space?The sample space S of a random experiment is defined as the set of all possible outcomes of an experiment. In a random experiment, the outcomes, also known as sample points, are mutually exclusive
Given, The ranger parks at the side of the road and chooses 100 trees near the road to assess for damage hence, trees near the road may have more damage than trees away from it, so the results may overestimate the overall damage of the trees.
So, Consequently, the results can exaggerate the total amount of tree damage.
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The perimeter of a rectangle is 120 meters and the length is 20 meters longer than the width. Find the dimensions of the rectangle. Let x = the length and y = the
2+2y = 12)
width. The corresponding modeling system is 2x + 2y =120 x-y = 20
Solve the system graphically
The dimension of the rectangle is 40meters by 20meters
What is the perimeter of a figure?The perimeter of a figure is the sum of all the external sides of the figure
The formula for calculating the perimeter of rectangle = 2(l+w)
If the length is 20 meters longer than the width, then;
l = 20 + w
Substitute
120 = 2(20+2w)
60 = 20 + 2w
30 = 10 + w
w = 20 meters
Since l = 20 + w
l = 20 + 20
l = 40 meters
Hence the dimension of the rectangle is 40meters by 20meters
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A sector of a circle has a central angle of 45 ∘ . Find the area of the sector if the radius of the circle is 18 cm. cm2
Answer:
1,090
Step-by-step explanation:
write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants.
x-2
________
x^2+11x+28
Answer:
A/(x+7) +B/(x+4)
Step-by-step explanation:
The denominators of the partial fraction expansion are the factors of the denominator of the rational function.
__
Here, the rational function's denominator can be factored as ...
x² +11x +28 = (x +7)(x +4)
Then the form of the decomposition is ...
[tex]\dfrac{x-2}{x^2+11x+28}=\boxed{\dfrac{A}{x+7}+\dfrac{B}{x+4}}[/tex]
_____
Additional comment
Here, A=3. B=-2.
If the factors of the denominator have multiplicity greater than 1, then there is a fraction with each power of that factor up to the multiplicity. For example, if there is a factor (x+4)³, then the decomposition would include fractions A/(x+4) +B/(x+4)² +C/(x+4)³.
8.5 hours in a day what total hours they work in a week
Answer:
8.5 hrs * 5 day work week = 42.5 hrs. But usually 0.5 hr per day is considered lunch and is usually not payed so theoretically the workweek is only 40 hrs per week (full time)
Step-by-step explanation:
Evaluate Grace's new budget.
ОА. Her new budget should have money in every budget category, including debts and medical expenses
OB. Her new budget should have money in medical expenses because she does not know what medical problems she will
encounter in the future.
OC. Her new budget is fine because debts and medical expenses were not needed last month.
OD. Her new budget should have money in debts so that she can afford to go into debt if she has medical expenses.
Can I please get help I don’t know how to use the numbers on the front
NEED AN ANSWER RIGHT NOW I HAVE ALMOST NO TIME PLEASE
The zeros of a quadratic relationship are 3 and 7. The optimal value is -3. Is the optimal value a maximum or minimum? Explain.
TYSM IF SOMEONE HELPS
Answer:
Minimum
Step-by-step explanation:
The zeros of a quadratic equation are the points at which the parabola intersects the x-axis.
[tex]\sf x=3 \implies x-3=0[/tex]
[tex]\sf x=7 \implies x-7=0[/tex]
[tex]\sf \implies y=a(x-3)(x-7)[/tex] (for some constant a)
[tex]\sf \implies y=ax^2-10ax+21a[/tex]
The optimal value is the y-coordinate of the vertex.
[tex]\sf \implies vertex=(x,-3)[/tex]
The x-coordinate of the vertex is the midpoint of the zeros:
[tex]\sf x=\dfrac{7-3}{2}+3=5[/tex]
[tex]\sf \implies vertex=(5,-3)[/tex]
Therefore, the vertex will be in Quadrant IV and so the parabola opens upwards into Quadrant I.
So the optimal value is a MINIMUM since the vertex is the minimum point of the curve.
Additional Information to create the equation of the quadratic
Vertex form of quadratic equation: [tex]\sf y=a(x-h)^2+k[/tex]
where (h, k) is the vertex
[tex]\sf \implies y=a(x-5)^2-3[/tex]
[tex]\sf \implies y=ax^2-10ax+25a-3[/tex]
To find the value of a, compare the constants of both equations:
[tex]\sf 21a=25a-3[/tex]
[tex]\sf \implies -4a=-3[/tex]
[tex]\sf \implies a=\dfrac34[/tex]
So the final equation is:
[tex]\sf factor \ form \implies y=\dfrac34(x-3)(x-7)[/tex]
[tex]\sf standard \ form\implies y=\dfrac34x^2-\dfrac{15}{2}x+\dfrac{63}{4}[/tex]
[tex]\sf vertex \ form \implies y=\dfrac34(x-5)^2-3[/tex]
Determine the degree of the polynomial −57.
Answer:
zero (0)
Step-by-step explanation:
The degree of the polynomial -57 is zero (0).
Hope it helps you in your learning process.
Function g is represented by the table. x -1 0 1 2 3 4 g(x) 24 6 0 -2 Which statement correctly compares the two functions? A. They have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞. B. They have different end behavior as x approaches -∞ and different end behavior as x approaches ∞. C. They have different end behavior as x approaches -∞ but the same end behavior as x approaches ∞. D. They have the same end behavior as x approaches -∞ and the same end behavior as x approaches ∞.
The statement which correctly compares the two functions is that they have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Function g is represented by the table.
x -1 0 1 2 3 4 g(x) 24 6 0 -2The line plotted with these data is shown below where y represent the g(x).
In this line,
X-intercept approaches negative infinity (-∞) to positive infinity (∞).Y-intercept approaches -2.426 to 24.86.Thus, the statement which correctly compares the two functions is that they have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞.
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He decided to bike from his home to the library to return some books. Ell biked 110 miles when he remembered that he had left a book at home, so he biked back home to get it. After getting the book from home, he biked to the library. What was the total distance, in miles, en had biked when he finally reached the library Show your work. miles Answer
Answer:
2 2/10 miles
but on the part where he realized he forgot his books was he at the library already when he realized cuz if not them it's more than 2 2/10
Martin is saving money to buy a new phone that costs $1,000 by selling trees. He is using an app to manage his
sales, but it keeps a fraction of each sale. His net pay is modeled by the function P(x) = x2 + 20x– 196, where x
represents the number of sales. How many sales does Martin need to make to earn $1,000?
Answer: 26 sales
Step-by-step explanation:
If you plug in 26 you will get exactly $1,000
Martin needs to sale 8 pieces to make it $1000.
How to elaborate the problem ?
Martin has to save $1000.
He is using an app to manage all the sales, but if keeps fraction of every sales.
The equation which represents his net pay is P(x)=[tex]x^{2}+20x-196[/tex]
How many sales does martin need ?We have to solve the given quadratic equation.
Here, x= (-b±[tex]\sqrt{ b^{2}-4ac }[/tex])/2a
⇒ x= (-20±[tex]\sqrt{400+4*196}[/tex])/2
⇒ x= (-20±[tex]\sqrt{1184}[/tex])/2
⇒ x= -10±[tex]\sqrt{296}[/tex]
⇒ x= -10±17.2
We habe to take the maximum value of x. So we neglect the negative sign.
Hence, x= -10+17.2 = 7.2 = 8 (approx) ,here we can not take 7 because if he sales 7 pieces then the money should less than $1000.
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[tex]$a+a r+a r^{2}+\ldots \infty=15$$a^{2}+(a r)^{2}+\left(a r^{2}\right)^{2}+\ldots \infty=150$. Find $a r^{3}+a r^{4}+a r^{6}+\ldots \infty$[/tex]
Options:
[tex](a) $\frac{1}{2}$\\(b) $\frac{2}{5}$[/tex]
Let
[tex]S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n[/tex]
where we assume |r| < 1. Multiplying on both sides by r gives
[tex]r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}[/tex]
and subtracting this from [tex]S_n[/tex] gives
[tex](1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}[/tex]
As n → ∞, the exponential term will converge to 0, and the partial sums [tex]S_n[/tex] will converge to
[tex]\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}[/tex]
Now, we're given
[tex]a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a[/tex]
[tex]a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}[/tex]
We must have |r| < 1 since both sums converge, so
[tex]\dfrac{15}a = \dfrac1{1-r}[/tex]
[tex]\dfrac{150}{a^2} = \dfrac1{1-r^2}[/tex]
Solving for r by substitution, we have
[tex]\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)[/tex]
[tex]\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}[/tex]
Recalling the difference of squares identity, we have
[tex]\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}[/tex]
We've already confirmed r ≠ 1, so we can simplify this to
[tex]\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15[/tex]
It follows that
[tex]\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12[/tex]
and so the sum we want is
[tex]ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}[/tex]
which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?
The spinner at the right is spun. what is the probability to spin a blue or red? Write your
answer in simplest form
Answer: The chances of landing on blue are 1 in 4, or one fourth. The chances of landing on red are 1 in 4, or one fourth.
Step-by-step explanation:
Reduce 1/4 to lowest terms14 is already in the simplest form. It can be written as 0.25 in decimal form (rounded to 6 decimal places). Steps to simplifying fractions find the GCD (or HCF) of numerator and denominator GCD of 1 and 4 is 1 divide both the numerator and denominator by the GCD1 ÷ 14 ÷ 1 reduced fraction: 14Therefore, 1/4 simplified to lowest terms is 1/4.
HELP ASAP
What are the solutions to the following system of equations? 2x − y = 6 y = x2 − 9 (3, 0) and (−1, −8) (3, 0) and (4, 2) (−3, 0) and (−1, −8) (−3, 0) and (4, 2)
Answer:
I think so none
answer to the following steps below:-
I hope my answer helps.
Evaluate lim x²-1 x/x^2+3x-4
Nandyan na po
Step-by-step explanation:
I hope I helprena divides a square into 8 equal part. what unit fraction should she write as a label for each parts?
If rena divides a square into 8 equal part then 1/8 is a unit fraction which she has to write as a label for each parts.
What is Fraction?A fraction represents a part of a whole.
Given that rena divides a square into 8 equal part.
A division is a process of splitting a specific amount into equal parts.
Let the whole square is divided into eight equal parts.
Which can be represented by 1/8.
Where the numerator 1 represents the whole and eight represents the parts.
The unit fraction for each part is 1/8 because the square is divided into 8 equal parts.
This means each part is one eighth of the whole.
Hence, if rena divides a square into 8 equal part then 1/8 is a unit fraction which she has to write as a label for each parts.
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solve for x ~
[tex]x {}^{2} - 5x + 6 = 0[/tex]
thankyou ~
[tex]x^2 -5x +6 =0\\\\\implies x^2 -3x -2x +6 = 0\\\\\implies x(x-3) -2(x-3) =0\\\\\implies (x-3)(x-2)=0\\\\\implies x =3, ~ x = 2[/tex]
Answer:
The value of x = 2 or 3
Step-by-step explanation:
By factorisation ,
=> x² - 5x + 6 =0
=> x² - 3x - 2x + 6 = 0
=> x ( x-3 ) -2 ( x-3 ) = 0
=> (x-2) (x-3) = 0
so, the value of x = 3 or 2
Please help EDGINUITY 2022
Please help I’m terrible at math!
Answer:
5) A - slope is positive, b = 0
6) D - slope is negative, b = 1, function is linear
7) D - b = 0
8) C - slope is negative, b = negative
Step-by-step explanation:
Hope this helps!
18. Cancellation refers to the procedure for
A. reducing fractions to make multiplying easier.
B. inverting the divisor in a division problem.
C. changing a mixed number to an improper fraction.
D. finding the lowest common denominator for a group of fractions.
The correct option regarding the operation of cancellation in a fraction is given by:
A. reducing fractions to make multiplying easier.
What is an example of cancellation in a fraction?It happens when two fractions are multiplying each other, and terms are simplified to make the multiplication easier. For example:
[tex]\frac{2}{3} \times \frac{6}{4} = \frac{6}{3} \times \frac{2}{4} = 2 \times \frac{1}{2} = 1[/tex]
The terms 2 and 4, and 3 and 6, were canceled. Hence option A is correct.
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Evaluate e^-1.6 round your answer to five decimal places
At a concession stand, five hot dog(s) and four hamburger(s) cost $15.25, four hot dog(s) and five hamburger(s) cost $16.25. Find the cost of one hot dog and the cost of one hamburger
Answer:
0.45
3.25
Step-by-step explanation:
16.25 ÷ 5 = 3.25
15.25 - 3.25 × 4 = 2.25
2.25 ÷ 5 = 0.45
Check Answer:
3.25 × 5 = 16.25
0.45 × 4 = 2.25
3.25 - 2.25 = 1
16.25 - 1 = 15.25
~lenvy~
Find the area
(Explain)
Answer:
960 cm²
Step-by-step explanation:
Area of trapezoid: (a + b)(h)/2
A = (20 + 40)(32)/2
A = 60(32)/2
A = 1920/2
960 cm²
BRAINLIEST please if this helped!A study of 110 students who had been awarded University scholarship showed that 40 worked part time jobs, 29 made the dean's list the previous semester and 16 both worked a part time job and made the dean's list the previous semester. What is the probability that a student worked a part time job or made the dean's list.
Answer:
i dont understand i need pic
A new board game comes with a deck of 20 cards: 5 red, 3 blue, 2 orange, and 10 green.
After the deck is shuffled, the player is to choose the top card and note its color, replace
the card, shuffle the deck again, and then choose the top card again and note its color.
What is the probability that both cards selected are blue?
A.3%
B.2.25%
C.9%
D.6.25%
Answer:
B
Step-by-step explanation:
3/20x3/20=
15/100x15/100
Please help! I will give Brainliest!!!
Here are 3 receipts for meals at the same restaurant. Fill in the missing values for each recipe.
(receipt one)
burger = 9
18% tip = 2.16
total with tip = 14.16
(receipt two)
salad = 8
total = 11
total with tip = 12.98
(receipt three)
salad = 8
water = 1.5
total = 9.50
18% tip = 1.71
Step-by-step explanation:
calculator
What is the volume of Prism B if the volume of Prism A is 1120 in??
Answer:
140 in³
Step-by-step explanation:
The ratio of volumes of similar objects is proportional to the cube of the ratio of the linear dimensions.
__
Here, prism B is half the height of prism A, so will have (1/2)³ = 1/8 of the volume of prism A:
Vb = (1/8)×Va
Vb = (1/8)×(1120 in³) = 140 in³
The volume of Prism B is 140 cubic inches.
Affordable Auto offered to enter people into a drawing for a free car if they shared the company's advertisement on social media. This table gives the total number of times the advertisement was shared since the promotion began. The data can be modeled by a quadratic function.
Length of promotion (days) 2 4 6 8 10 12
Number of shares 1200 3219 6240 10264 15290 21318
What function best models the data?
y=1.2x^2+20.6x+280
y=125.3x^2+183.3
y=1.2x^2+280
y=125.3x^2+257.8x+183.3
Answer:
D; y=125.3x2+257.8x+183.3
Step-by-step explanation:
I just took the test
have a good day! :)