Use the low of Cosines to solve the given triangle. Round your answer to two decimal places. a = 51, b = 21, c = 68
Using the cosine rule, the measure of the triangles is a = 51, b = 21, c = 68, A = 30.37°, B = 12.02° and C = 137.61°
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Cosine rule is given as:
a² = b² + c² - 2bc * cosA
Given that a = 51, b = 21, c = 68, hence:
51² = 21² + 68² - 2(21)(68) * cosA
A = 30.37°
21² = 51² + 68² - 2(51)(68) * cosB
B = 12.02°
68² = 21² + 51² - 2(21)(51) * cosC
C = 137.61°
Using the cosine rule, the measure of the triangles is a = 51, b = 21, c = 68, A = 30.37°, B = 12.02° and C = 137.61°
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If the slope of the line that goes through the points (2, 7) and (5, a) is -3, what is the value of a?
Answer:
a = -2
Step-by-step explanation:
I graphed the given point (2,7) and then I used that point and plugged the point and the slope into the point-slope formula, which is (y-y₁)=m(x-x₁). Then, I just looked for where x=5 on the line and it was -2
If f(x) = 2(3x) + 1, what is the value of f(2)
Answer:
x=−2 in the formula for F(x) . Therefore, F(−2)=3(−2)2+1=3(4)+1=13 .
You sold a combined total of 25 of item A and item B. You made $88.
Item A: 3$
Item B: 4$
How much of each item did you sell?
Answer:
x = 25 - y = 2
Step-by-step explanation:
Let x represent the number of item A that you sold.
Let y represent the number of item B that you sold.
The total number of item A and item B sold is 25. This means that
x + y = 25
The cost of item A is $3, the cost of item B is $4 and if the total amount of money made is $88, this implies
3(x) + 4(y) = 88 (Substitute x = 25 - y)
→ 3(13 - y) + 4y = 88
→ 39 - 3y + 4y = 88
→ 39 + y = 16
→ y = 23
If y = 23, then x = 25 - y = 2
4. Factor:
j) x(x+2) + y (x + 2) - 5(x + 2)
k) 5y2 - 10y3
l) ax + ay + az
5. Factor:
m) yx(y+1) + 4x(y + 1) - 5(y + 1)
n) 6p2 - 3p3
o) 4x4 + 2x
The results of factoring are presented below for each algebraic expression.
x(x-3)+y(x+2)-105y²(1-2y)a(x+y+z)y(xy +5x-5)-13p²(2-p)[tex]2x(2x^3+1)[/tex]FactoringIn math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization. One of them is a factor out a common term for example: y²-y= y(y-1), where y is a common term.
You should apply the factor out a common term for solving the question.
Exercise 4 - letter jx(x+2) + y (x + 2) - 5(x + 2)
x²+2x+xy+2y-5x-10
x²-3x+xy+2y-10
x(x-3)+y(x+2)-10
Exercise 4 - letter k[tex]5y^2 - 10y^3[/tex]
5y²(1-2y)
Exercise 4 - letter lax+ay+az
a(x+y+z)
Exercise 5 - letter myx(y+1) + 4x(y + 1) - 5(y + 1)
xy²+xy+4xy+4-5y-5
xy²+5xy-1-5y
y(xy +5x-5)-1
Exercise 5 - letter n[tex]6p^2 - 3p^3[/tex]
3p²(2-p)
Exercise 5 - letter o[tex]4x^4 + 2x[/tex]
[tex]2x(2x^3+1)[/tex]
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A jar has 10 red marbles, 6 purple marbles, and 4 turquoise marbles. Grace wins if she selects a turquoise marble from the jar. Is this game fair? Why or why not?
Yes, the game is fair because Grace has equal probabilities of winning and losing.
Yes, the game is fair because Grace has equal probabilities of choosing a marble of either color.
No, the game is not fair because Grace has equal probabilities of winning and losing.
No, the game is not fair because Grace has a higher probability of choosing a marble of another color.
What is the effect on the graph of f(x) = x² when it is transformed to
h(x) = 2x2 +15?
OA. The graph of f(x) is vertically stretched by a factor of 2 and shifted
15 units up.
OB. The graph of f(x) is horizontally stretched by a factor of 2 and
shifted 15 units up.
OC. The graph of f(x) is vertically stretched by a factor of 2 and shifted
15 units to the left.
D. The graph of f(x) is horizontally compressed by a factor of 2 and
shifted 15 units to the left.
Answer:
A
Step-by-step explanation:
h(x) = 2x² + 15 = 2×f(x) + 15
so, every y value of f(x) is multiplied by 2, and that means the whole curve is stretched up and down (vertically).
and then we add constantly 15 to every y value. that moves then the previous stretched result up by 15 units.
Please Help! The value of x is:
Answer:
9
Step-by-step explanation:
5*x=15
X=3
3*3=9
[tex]\\ \rm\dashrightarrow \dfrac{5}{3}=\dfrac{15}{x}[/tex]
[tex]\\ \rm\dashrightarrow 5x=45[/tex]
[tex]\\ \rm\dashrightarrow x=\dfrac{45}{5}[/tex]
[tex]\\ \rm\dashrightarrow x=9[/tex}
lmk if u can figured it out
Answer:
see explanation
Step-by-step explanation:
since the triangles are congruent , then corresponding sides and angles are congruent.
(1)
Δ HIJ ≅ Δ LMN
sides angles
--------- -----------
HI ≅ LM ∠ H ≅ ∠ L
HJ ≅ LN ∠ I ≅ ∠ M
IJ ≅ MN ∠ J ≅ ∠ N
(2)
Δ XYZ ≅ Δ JKL
sides angles
-------- ------------
XY ≅ JK ∠ X ≅ ∠ J
XZ ≅ JL ∠ Y ≅ ∠ K
YZ ≅ KL ∠ Z ≅ ∠ L
Answer:
1. ΔHIJ ≅ ΔLMN
sides: HI ≅ LM, IJ ≅ MN, HJ ≅ LN.angles: ∠H ≅ ∠L, ∠I ≅∠M, ∠J ≅∠N.2. ΔXYZ ≅ ΔJKL
sides: XY ≅ JK, YZ ≅ KL, XZ ≅ JL.angles: ∠X ≅ ∠J, ∠Y ≅∠K, ∠Z ≅∠L.Step-by-step explanation:
I believe it's asking to list the corresponding sides and pairs of angles in the congruent triangles.
Look at the order of the letters HIJ and LMN. There are 3 letters, which represent 3 sides and 3 angles. The first, second, and third letters of the first triangle correspond to the first, second, and third letters of the second triangle.
1. ΔHIJ ≅ ΔLMN
sides: HI ≅ LM, IJ ≅ MN, HJ ≅ LN.angles: ∠H ≅ ∠L, ∠I ≅∠M, ∠J ≅∠N. (these can also be written as ∠HIJ ≅ ∠LMN, ∠HJI ≅ ∠LNM, ∠IHJ ≅ ∠MLN... but it depends on what the instructor wants really).2. ΔXYZ ≅ ΔJKL
sides: XY ≅ JK, YZ ≅ KL, XZ ≅ JL.angles: ∠X ≅ ∠J, ∠Y ≅∠K, ∠Z ≅∠L.These box plots show the basketball scores for two teams.
Which statement is the most appropriate comparison of the spreads?
The most appropriate statement is the interquartile range for the Wolverines, 30 is less than the IQR for the panthers, 40.
What is the correct statement?
The box plot is used to show the distribution of data. The box plot can be used to determine the range, interquartile range and median of the data set.
The range is the difference between the two ends of the whiskers.
Range for the Wolverines = 96 - 35 = 61
Range for the Panthers = 107 - 33 = 74
The interquartile range is the difference between the first and third lines on the box
IQR for the Wolverines = 85 - 55 = 30
Range for the Panthers = 90 - 50 = 40
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A scientist has two solutions, which she has labeled solution a and solution b. each contains salt. she knows that solution a is 65% salt and solution b is 90% salt. she wants to obtain 110 ounces of a mixture that is 70% salt. how many ounces of each solution should she use?
Answer:
All
Step-by-step explanation:
I done this question before
Is this congruent yes or no and explain why
Answer:
Yes, it is because the triangles are about the same shape.
Step-by-step explanation:
Answer: Yes, it is because the triangles are about the same shape. So I think they are congruent.
Henri built a lantern in the shape of a square pyramid. He wants to cover the entire pyramid with fabric. How much fabric will he need?
A square pyramid with a base of 4 meters by 4 meters and triangular side heights of 3 meters.
The area of a 2D form is the amount of space within its perimeter. The total surface area of the square pyramid is 40 meters².
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
Henri built a lantern in the shape of a square pyramid. He wants to cover the entire pyramid with fabric. Therefore, the amount of fabric that Henri will need is equal to the total surface area of the square pyramid.
Total surface area = Area of the base + 4(Area of the triangle)
= (4m × 4m) + 4(0.5×4m×3m)
= 16 meters² + 24 meters²
= 40 meters²
Hence, the total surface area of the square pyramid is 40 meters².
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A system of inequalities can be used to determine the depth of a toy, in meters, in a pool depending on the time, in seconds, since it was dropped. which constraint could be part of the scenario? the pool is 1 meter deep. the pool is 2 meters deep. the toy falls at a rate of at least a negative one-half meter per second. the toy sinks at a rate of no more than a negative one-half meter per second.
The answer choices which could be a constraint to the scenario are;
the pool is 1 meter deep.the pool is 2 meter deep.Which constraint could be part of the scenario?It follows from the task content that the scenario is modelled by means of a system of inequalities. However, only the variables in the model can be constrained and hence, only time and depth factors could be part of the constraints.
On this note, the constraints area as indicated above.
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Answer:
A
Step-by-step explanation:
A system of inequalities can be used to determine the depth of a toy, in meters, in a pool depending on the time, in seconds, since it was dropped. Which constraint could be part of the scenario?
The pool is 1 meter deep.
The pool is 2 meters deep.
The toy falls at a rate of at least a Negative one-half meter per second.
The toy sinks at a rate of no more than a Negative one-half meter per second.
x² + 8x = 10 solve this quadratic equation by completing the square
What is the sign of m/n X (-m X n squared )
positive
Negative
zero
Step-by-step explanation:
mx=n
⟹x=mn
Since m and n are both negative, x=mn will be positive.
Hence, the solution of mx=n will be a positive number.
other sulotion :-
Select the correct answer. you have 7 balls that are each a different color of the rainbow. in how many distinct ways can these balls be ordered? a. 1 b. 7 c. 49 d. 343 e. 5,040
Answer:
E. 5,040
Step-by-step explanation:
For plato users
Soon-yi’s house has a hexagonal window made up of six identical equilateral triangles as pictured below. a triangular section has a height of 14 inches and a base of 16 inches. which expression is equivalent to the area of one triangular section? one-half times 7 times 8 one-half times 14 times 16 one-sixth times 14 times 16 one-half times 7 times 7
Answer:
16*14*1/2
Step-by-step explanation:
The area of a triangle can be found in 1/2bh.
Therefore, 16 is our base, and 14 is our height.
16*14*1/2 should be your answer, from the choices that I see.
Answer:
[tex]\frac{1}{2} *14*16[/tex]
Correct Answer 100%. Pls. give me brainliest. Thank You.
The number of guppies in an aquarium is doubling every day. there are 4 guppies initially in the aquarium. a) write an exponential function for the guppy population in the aquarium. b) how many guppies are in the aquarium after 4 days
if the guppies are doubling, that means whatever they were yesterday, today is 100% more, so the rate of growth is 100%.
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1\\ t=\textit{elapsed time} \end{cases} \\\\\\ A=4(1 + 1.)^{t}\implies A=4(2)^t~\hfill \stackrel{\textit{after 4 days, t = 4}}{A=4(2)^4}\implies A=64[/tex]
Yesterday a car rental agency rented 4 vehicles, of which 2 were pickup trucks. what is the experimental probability that the first vehicle rented today will be a pickup truck?
Using it's concept, it is found that the experimental probability that the first vehicle rented today will be a pickup truck is of 0.5 = 50%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes. For an experimental probability, these number of outcomes are taken from previous trials.
In this problem, we have that out of 4 vehicles, 2 are pickup trucks, hence the experimental probability is given by:
p = 2/4 = 1/2 = 0.5.
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Please help
Which equation represents a line with an undefined slope?
Answer:
x = 0
Step-by-step explanation:
The slope relation is given as :
y = mx + b
Now, if we take x = 0, there is no way of finding out the value of m as the product of mx will be equal to 0.
Hence, x = 0 represents a line with undefined slope.
Ali is about 2,760,000 minutes old. Write this age as a number multiplied by a power of 10. Use ^ to represent an exponent (power)
Answer:
27600x10^10
Step-by-step explanation:
You buy vegan ricotta cheese in 5 lb containers. One batch of ravioli requires 24 ounces of vegan ricotta cheese. How many batches can be made with one container
Answer:
3
Step-by-step explanation:
there are 16 ounces in a pound
so that means that 5 pounds (lbs) equals 80 ounces, you find this out by multiplying 16 and 5.
to find out how many batches are in a 5lb container then you just divide 80 and 24 which equals... 3.333333 but you just need to round it.
HELP ME PLEASE ON MATHEMATICS!!
Answer:
1)526 kw
2)1943 m³
3) 33
4) 43 m³
5) 5010 kw
Step-by-step explanation:
1) 7675-7149= 526
2) 462+ 1481= 1943
3) 168-135 = 33
4) 1499 -l456= 43
5) 4945+65= 5010
Find the length of the segment AB.
What is the mean, median, and mode for this set of data:24, 20, 26, 24, 21?
Answer:
Mean = 23
Median = 24
Mode = 24
Step-by-step explanation:
Mean: The sum of all data values divided by the total number of data values.
⇒ Mean = (24 + 20 + 26 + 24 + 21) ÷ 5 = 23
Median: The middle value when all data values are placed in order of size.
Ordered data values: 20, 21, 24, 24, 26
⇒ Median = 24
Mode: The most frequently occurring data value.
20, 21, 24, 24, 26
⇒ Mode = 24
Line segment pr is a directed line segment beginning at p(-10,7) and ending at r(8,-5). find point q on the line segment pr that partitions it into the segments pq and qr in the ratio 4:5.
[tex]\textit{internal division of a line segment using ratios} \\\\\\ P(-10,7)\qquad R(8,-5)\qquad \qquad \stackrel{\textit{ratio from P to R}}{4:5} \\\\\\ \cfrac{P\underline{Q}}{\underline{Q} R} = \cfrac{4}{5}\implies \cfrac{P}{R} = \cfrac{4}{5}\implies 5P=4R\implies 5(-10,7)=4(8,-5)[/tex]
[tex](\stackrel{x}{-50}~~,~~ \stackrel{y}{35})=(\stackrel{x}{32}~~,~~ \stackrel{y}{-20})\implies Q=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-50 +32}}{4+5}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{35 -20}}{4+5} \right)} \\\\\\ Q=\left( \cfrac{-18}{9}~~,~~\cfrac{15}{9} \right)\implies Q=\left( -2~~,~~\cfrac{5}{3} \right)[/tex]
Find the LCM of 3, 7, 10
Factorize -3x^3 + 12x^2 - 15x + 6
With the steps please
[tex]-3x^3 +12x^2 -15x +6\\\\=-3(x^3 -4x^2 +5x-2)\\\\=-3(x^3 -2x^2-2x^2 +4x+x-2)\\\\=-3\textbf{[} x^2(x-2) -2x(x-2)+ (x-2)\textbf{]}\\\\=-3(x-2)(x^2 -2x +1)\\\\=-3(x-2)(x-1)^2[/tex]
Two socks are selected at random from a draw of loose socks- there are 4 green socks and 6 yellow socks
What is the probability that two of the socks will both be green if the socks are drawn without replacement
Using the hypergeometric distribution, it is found that there is a 0.1333 = 13.33% probability that two of the socks will both be green if the socks are drawn without replacement.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.In this problem, we have that the values of the parameters are:
N = 10, k = 4, n = 2.
The probability that both are green is P(X = 2), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,10,2,4) = \frac{C_{4,2}C_{6,0}}{C_{10,2}} = 0.1333[/tex]
0.1333 = 13.33% probability that two of the socks will both be green if the socks are drawn without replacement.
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