Solve the triangle. A = 52°, b = 10, c = 7 (5 points)
The solutions to this triangle are:
7.944.1 degrees83.7 degreesHow to solve for the triangleUsing the law of cosine we would have
a²=b²+c²-2bc cos A
a² =100+49-2(10)(7)cos 52
This would give us
=149 -140 x (0.6157)
=62.82
We take the square root of 62.82 =
7.93 or 7.9
We have to use the sine law to find the other side
7.9/sin 52=10.057
10.06=7/sin C
such that
sin C = sin(0.6958)
=44.1°
10.06=10/sin B
cross multiply
sin B=10/10.06
= sin⁻¹0.9940
Then B = 83.7°
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What proportion could you use to find the value of x
The proportion that could be used to find the value of x is 3/x= x/11
How to determine the proportion?The complete question is added as an attachment
From the attachment, the common side length between both right triangles is x
While the other sides are adjacent sides.
This means that the proportion is:
3/x= x/11
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Pleaseeeeeee helppppl asap
Answer:
37
Step-by-step explanation:
Let's use the rule GEMDAS (Grouping, Exponents, Multiply, Divide, Add, Subtract) from left to right. Therefore, we will simplify the equation in the parentheses. [tex]2^{3} = 8. (1-8= -7)[/tex]. -(-7) creates a double negative, deeming the 7 positive, because when there is two negatives the number will turn into a positive. [tex]7^{2}[/tex] = 49, -3 x 4= -12. Therefore the final form of the equation will be 49 - 12 = 37.
Let me know if there are mistakes.
find the equation of the line shown
i will put brainliest
Find the measure of each
angle in the isosceles
trapezoid.
D
A
136⁰
B
с
Answer:
b=136, c=44, d=44
Step-by-step explanation:
B is the same measure as A. C = D and A+B+C+D=360; C+D=88; C=44; D=44
Under a certain transformation △ABC→△A′B′C′ such that AB≠A′B′. The triangles are:
Triangle ABC was dilated by a scale factor to form triangle A'B'C', such that AB≠A′B′
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
Dilation is the increase or decrease in the size of a figure by a scale factor.
Dilation does not preserve the size of a figure, it only preserves the shape and angle.
Triangle ABC was dilated by a scale factor to form triangle A'B'C', such that AB≠A′B′
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Round these numbers as shown.
(i) 0.0975 to 1 d.p
(¡) 58.361 to nearest whole number
(in) 145676 to nearest 1000 (iv) 22567 to nearest 100
Answer:
0.1?
58
146,000?
22600
Step-by-step explanation:
So I assume first is 1st decimal place, so that would be the first after the decimal and then the number after has to be 5 or above, which it is. So then its just 0.1
This is easy, look at the decimal, its below .5, so 58.
Same thing for the rest, just look at the digit before.
factorizacion de x^4+12x^3-64x^2=0
Hello,
x⁴ + 12x³ - 64x² = 0
x²(x² + 12x - 64) = 0
x² = 0 or x² + 12x - 64 = 0
x = 0
∆ = b² - 4ac = 12² - 4 × 1 × (-64) = 400
x1 = (-b -√∆)/2a = (-12 - 20)/2 = -32/2 = -16
x2 = (-b + √∆)/2a = (-12 + 20)/2 = 8/2 = 4
S = {-16 ; 0 ; 4 }
→ factorizacion de x⁴ + 12x³ - 64x² : x(x - 4)(x + 16)
On a statistic exam, a class of 25 students had a mean score 75.2 and a standard deviation of 5.7. using the empirical rule, what would be the range of scores for 95% of the class?
The range of scores for 95% of the class is 63.8 to 86.6 using the empirical rule.
What is the empirical rule?A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, almost all observed data will lie within three standard deviations.
The empirical rule specifically states that 68 percent of data will fall inside the first standard deviation, 95 percent will fall within the first two standard deviations, and 99.7 percent will fall within the first three standard deviations.
According to the question,
μ=75.2 and σ=5.7
So, according to the empirical rule, the range of scores for 95% of the class:
μ – 2σ =75.2-2*5.7=63.8
and μ + 2σ=75.2+2*5.7=86.6
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What kind of compound inequality is
x≥-3
and
x<3
?
a. disjunction
b. hole
c. union
d. intersection
[tex]x \geqslant - 3 \: \: \: \: \: \: x < 3[/tex]
Interval 1: x ε [ - 3 , ∞ )Interval 2: x ε ] - ∞ , 3 [Solution: x ε [ - 3 , 3 [d. IntersectionAnswer:
The answer is D intersection
Remember that AND indicates an intersection and OR indicates a union.
Step-by-step explanation:
Solve each inequality and then find the intersection.
Inequality Form: −3≤ x<3
Interval Notation:[−3,3)
PLEASE HURRY!!!!!!!
Ms. Green, a physical education teacher in a middle school, conducted a survey to find out what the favorite athletic activity of the students in the middle school was. she chose every 10th student's name on and alphabetical list of all studentsin the school to make up a sample. Was this a random sample and if so, which sampling method did she use?
A. Yes, she used simple random sampling.
B. Yes, she used systematic random sampling.
C. No, she used stratified random sampling.
D. No, she did not choose a random sample.
Answer:
B. Yes, she used systematic random sampling
Explanation :
Systematic random sampling is method of sampling use in term of finding the the percent of a given population to find the final sample.
Please solve correctly
Answer:
f(-3) =8
Step-by-step explanation:
Answer:
Step-by-step explanation:
Answer
f(x) has the same meaning as y. So you could rewrite the question as "What value of x gives y a value of 8"
The graph tells you that x = - 3 when y = 8.
f(-3) = 8
The circumference of a circular garden is 141.3 feet. What is the radius of the garden? Use 3.14 for π and do not round your answer.
Answer:
22.5 feetStep-by-step explanation:
The formula for circumference is 2(3.14)r
So, we divide 141.3 by 6.28 and get 22.5
The radius is 22.5 feet.
Simplify the expression (startfraction 1 over 4 a b endfraction) superscript negative 2. assume a not-equals 0, b not-equals 0. negative startfraction 1 over 16 a squared b squared endfraction startfraction a squared b squared over 4 endfraction negative 16 a squared b squared 16 a squared b squared
Answer:
16a^2b^2
Step-by-step explanation:
An exponent that is over a whole entire fraction can be split up and put separately onto the numerator (top number) and denominator (bottom number) See image.
Then you can get rid of a negative exponent (make it positive) by moving the whole term across the fraction bar. The top moves to the bottom and the bottom moves to the top. See image.
In the term (4ab)^2, the exponent 2 can be passed out to the 4 and the a and the b. See image.
Answer: D
Step-by-step explanation:
Before changes to its management staff, an automobile assembly line operation had a scheduled mean completion time of minutes. The standard deviation of completion times was minutes. An analyst at the company suspects that, under new management, the mean completion time, , is now less than minutes. To test this claim, a random sample of completion times under new management was taken by the analyst. The sample had a mean of minutes. Assume that the population is normally distributed. Can we support, at the level of significance, the claim that the population mean completion time under new management is less than minutes
No, we don't have evidence to support that the mean completion time under new management has decreased but we can conclude that it remains at 15.5 minutes.
Given mean of 15.5 minutes , standard deviation of 1.7 minutes, sample size of 90 and sample mean of 15.4 minutes.
We can do the following study for conclusion:
Firstly the null hypothesis is
[tex]H_{0}: x=15.5[/tex]
The alternate hypothesis is
[tex]H_{1}: x < 15.5[/tex]
since the value is less than this is a one tailed test.
Z=x bar-x/d/[tex]\sqrt{n}[/tex]
where x is sample mean and d is standard deviation.
Z=15.4-15.5/1.7/[tex]\sqrt{90}[/tex]
=-0.1/1.7/9.4868
=-0.560
Critical value of Z at 0.1 level of significance
Z=-1.28
We fails to reject the null hypothesis since -0.560>-1,28
Hence we don't have evidence to support that the mean completion time under new management has decreased but we can conclude that it remains at 15.5 minutes.
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Question is incomplete. It should include:
mean of 15.5 minutes ,
standard deviation of 1.7 minutes,
sample size of 90
and sample mean of 15.4 minutes.
| -4 + 5\2 | - (-x) =-3
Answer:
x = -4.5
Step-by-step explanation:
Solving the equation :
[tex]\left\vert -4+\frac{5}{2} \right\vert -\left( -x\right) =-3[/tex]
[tex]\Longleftrightarrow \left\vert \frac{-8}{2} +\frac{5}{2} \right\vert +x =-3[/tex]
[tex]\Longleftrightarrow \left\vert \frac{-8+5}{2} \right\vert +x =-3[/tex]
[tex]\Longleftrightarrow \left\vert \frac{-3}{2} \right\vert +x =-3[/tex]
[tex]\Longleftrightarrow \frac{3}{2} +x =-3[/tex]
[tex]\Longleftrightarrow x =-3-\frac{3}{2}[/tex]
[tex]\Longleftrightarrow x =-\frac{6}{2} -\frac{3}{2}[/tex]
[tex]\Longleftrightarrow x = -(\frac{6}{2} +\frac{3}{2} )[/tex]
[tex]\Longleftrightarrow x =-\frac{9}{2}[/tex]
[tex]\Longleftrightarrow x =-4.5[/tex]
Which of the following is correct equation for the trend line in the scatter plot? A. Y= 2/5 x -2 B. Y= 5x-1 C. Y= 5x +5 D. Y= -x+5
The equation for the trend line in the scatter plot will be Y= 5x-1. Option B is correct.
What is a scatter plot?In an effort to demonstrate how much one variable is influenced by another, scatter plots are used to depict data points on a horizontal and vertical axis.
When there is no connection between two variables, it is called a zero correlation. For instance, there is no correlation between IQ level and the quantity of tea consumed.
The graphs are attached in the attachment.
The equation for the trend line in the scatter plot will be Y= 5x-1.
Hence, option B is correct.
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Question 3 of 10 True or False? A circle could be circumscribed about the quadrilateral below.
95, 80, 85, 100
True, a circle can be circumscribed about the quadrilateral described in the task content.
What is the condition to circumscribe a circle about a quadrilateral?It follows from the task content that quadrilateral in discuss has angles; 95, 80, 85 and 100.
By convention, it follows that circles can be circumscribed about only cyclic quadrilaterals in which case their opposite angles are supplementary. Hence, since opposite angles of the quadrilateral are supplementary (i.e amount to 180). Then, True, the circle can be circumscribed about the quadrilateral.
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Please help
Which box is in the wrong spot?
The only wrong spot would be box 1 because the graph is not decreasing over the longest interval.
How to interpret the y-intercept of graphs?In the first graph, we see that the y-intercept which is the point where the curve crosses the y-axis is at y = -1. However, the interval for which it is decreasing is from x = -1 to x = 0.5.
For the second table, we see that the y-intercept is -1 and that as values of x keeps increasing, g(x) becomes more negative. Thus, it is decreasing on the longest interval.
For the third function which is;
h(x) = 3 + 4x³
The y-intercept is 3.
However, the higher the value of x, the greater the function.
Thus, the only wrong spot would be box 1 because the graph is not decreasing over the longest interval.
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If sinA= find the value of sin2A
Step-by-step explanation:
sinA=sinA
sin2A
(sinA)2
(1 + cos(x))(l — cos(x))
The expression given in the task content can be evaluated and simplified to be equal to; sin²(x).
What is the result of the product?It follows from the task content that the result of the product given is to be determined.
Hence, the multiplication is as follows;
1 -cos(x) +cos(x) -cos²(x).
1 -cos²(x).
However, since sin²(x) + cos2(x) = 1; it therefore follows that;
1 -cos²(x) = sin²(x)
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Could you help me with this geometry question?
The value of <RQZ has been calculated as 21 from the solution we have below.
How to solve for RQZWe have
< PZQ= <PQZ
PQR - PRQ = 42
Let < PZQ = y⁰
PQZ = y⁰
Let PRQ = x⁰
< PQR = x + 42⁰
< QpZ + y + y = 180⁰
such that
QPZ + 2y = 180⁰
<QPZ = 180⁰ - 2y
<(QPZ + PQR + PRQ) = 180
Adding these equations, we would have
180 - 2y + x + 42 + x = 180⁰
180 would cancel out
We have
2x - 2y + 42 = 0
x- y +21 = 0
We have to add 21 to both sides of the equation
x- y + 42 = 21
(x + 42) - y = 21
(x + 42) = <PQR and y = < PQZ
Hence 21 = <RQZ
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Copy the figure below onto a separate sheet of paper. Find the image of the figure under reflections in line m and then line t. In the box below, descibe the new location of point F in relation to lines m and t.
The image of the figure under reflections in line m and then line t is shown below.
What is a transformation of geometry?A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.
Reflection does not change the size and shape of the geometry.
The image of the figure under reflections in line m and then line t.
The reflection of the square DEFG will be given in the figure.
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If A+B =45 then prove that
i) CotA.CotB-CotA-CotB=1
Answer:
Step-by-step explanation:
[tex]if A+B=45\\tan(A+B)=tan(45)\\\dfrac{tanA+tanB}{1-tanA.tanB}=1\\ \implies tanA+tanB=1-tanA.tanB\\\frac{1}{cotA}+\frac{1}{cotB}=1-\frac{1}{cotA}\frac{1}{cotB}, \{tanX=\dfrac{1}{cotX} \}\\ cotA+cotB=cotA.cotB-1\\cotA.cotB-cotA-cotB=1.[/tex]
A wire that is 22 feet long connects the top of a pole to the ground. The wire is attached to the ground at a point that is 10 feet from the base of the pole. What is the length of the pole, round o the nearest tenth.
a. 12.00 ft
b. 19.60 ft
c. 24.17 ft
d. 38.40 ft
NEED HELP ASAP
Answer:
19.6ft (nearest tenth)
Step-by-step explanation:
Please refer to the attached photo for better understanding.
Given Length of Wire = BC = 22ft
Given Distance from Grounded Wire to Base of Pole = AC = 10ft
Length of Pole = AB
We can use Pythagoras' Theorem to find Length of Pole, AB.
By Pythagoras' Theorem,
[tex]c^{2} =a^{2} +b^{2} \\BC^{2} =AB^{2} + AC^{2} \\22^{2} =AB^{2} +10^{2} \\484=AB^{2} +100\\AB^{2} =484-100\\AB=\sqrt{384} ft\\=19.6ft (nearest tenth)[/tex]
I am not able to solve this question
Answer:
Choice A
Step-by-step explanation:
[tex] \rm \: a {}^{2} \cdot \{ a \ { {}^{ (\frac{2}{3}) } \}}^{ - 1} [/tex]x^-1 = 1/x[tex] \rm \: a {}^{2} \{ \cdot \: \cfrac{1}{a {}^{ \frac{2}{3} } \ } \}[/tex]
Applying Distributive property;
[tex] \rm \: a {}^{2 \times \cfrac{2}{3} } [/tex][tex] \rm \: a {}^{ \cfrac{4}{3} } [/tex]Choice A is accurate.
If two noncollinear segments in the coordinate plane have slope 3, what can you conclude?
The linear are said to be parallel.
What is Collinear line?Collinear points are the points that lie on the same straight line or in a single line.
Given:
slope= 3
If two non co-linear segments with a slope of 3 in a coordinate plane, which means that the two line segments are parallel to each.
So, the same slope symbolise the concept of parallel line in same plane.
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help me pleaseeeeeeeeeeeeeeeeee
A
this question did by quadratic formula means x = -b ± √b^ - 4ac / 2a by this formula first arrange the equation -5 x^ + 7 -2 and
a = -5
b = 7
C = -2
after that substitute in the formula
In the air, it had an average speed of 16 \text{m/s}m/start text, m, slash, s, end text. In the water, it had an average speed of 33 \text{m/s}m/start text, m, slash, s, end text before hitting the seabed. The total distance from the top of the cliff to the seabed is 127 meters, and the stone's entire fall took 12 seconds.
How long did the stone fall in the air and how long did it fall in the water?
The time taken by the stone to fall in air is 7 seconds and the time taken in water is 5 seconds.
What is Speed?Speed is the distance covered by an object in a fixed period of time. It is measured in m/sec.
The average speed in air is 16m/sec.
The average speed in water is 33m/sec.
The total time taken is 12 seconds.
Total distance covered = Total time taken * speed at which it covered the distance
Let the time taken to fall in air is t
So, the time taken in water will be 12-t
The total distance is equal to
127 = 16*t + 3(12-t)
127 = 16t + 36 - 3t
127 - 36 = 16t - 3t
91 = 13t
t = 91/13 = 7 seconds
12-t = 12-7 =5 seconds
Therefore, the time taken by the stone to fall in air is 7 seconds and the time taken in water is 5 seconds.
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HELP PLS!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
4
Step-by-step explanation:
[tex] \frac{15}{20} = \frac{x + 2}{12 - x} \\ \\ 180 - 15x = 20x + 40 \\ \\ 35x = 140 \\ \\ x = 4[/tex]