When the area is 24 cm², the height of the triangle is 4 cm.
What is area?The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The area is the region defined by an object's form. The area of a form is the space covered by a figure or any two-dimensional geometric shape in a plane.
Here,
area=1/2(bh)
h=b-8
24=1/2(b(b-8))
48=b²-8b
b²-8b-48=0
b²-12b+4b-48=0
b(b-12)+4(b-12)=0
b=-4,12
b=12 cm
h=12-8
h=4 cm
The height of triangle is 4 cm when area is 24 cm².
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Complete the proof of the identity by choosing the Rule that justifies each step. Sin^2x + 4cos^2x = 4 -3sin^2x To see a detailed description of a Rule in the Rule menu, select the corresponding question mark. Statement Rule sin^2 x + 4cos^2 x sin^2 x + 4 (1 -sin^2 x) Rule? sin^2 x + 4 -4sin^2 x Rule? 4 -3sin^2 x Rule? Reciprocal identities: sin u = 1/csc u cos u = 1/sec u tan u = 1/cot u csc u = 1/sin u sec u = 1/cos u cot u = 1/tan u Quotient identities: tan u = sin u/cos u cot u = cos u/sin u Pythagorean identities: sin^2u + cos^2u = 1 tan^2u + 1 = sec^2 u cot^2 u + 1 = csc^2 u Odd/Even function identities: sin(-u) = -sin(u) cos(-u) = cos(u) tan(-u) = -tan(u) csc(-u) = -csc(u) sec(-u) = sec(u) cot(-u) = -cot(u)
Previous question
Hence, the proof is completed by choosing the identities of the rules.
Trigonometry identities
Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation. There are various distinct trigonometric identities involving the side length as well as the angle of a triangle. The trigonometric identities hold true only for the right-angle triangle.Given that :
Complete the proof of the identity by choosing the Rule that justifies each step.
Sin^2x + 4cos^2x = 4 -3sin^2x
Statement Rule
[tex]sin^{2} x + 4 cos^{2}x[/tex]
= [tex]sin^{2}x + 4 (1 - sin^{2} x )[/tex] [tex]sin^{2}u + cos^{2}u = 1[/tex]
[by using Pythagorean identities]
= [tex]sin^{2}x + 4 - 4 sin^{2}x[/tex] [tex](1 - sin^{2}x )[/tex]
[ multiplied by 4 ]
= [tex]4 - 3 sin^{2}x[/tex]
Sin^2x + 4cos^2x = 4 -3sin^2x
Hence proved.
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I'm not sure how to solve the probability for the question.
Thank You for your help
The statement that corresponds to P(X = 48), using continuity correction, is given as follows:
c. P(47.5 < x < 48.5).
What is continuity correction?Continuity correction is used as a "correction" when a continuous distribution is used to approximate a discrete distribution. One example of this is the approximation of the binomial distribution to the normal distribution.
Hence, using continuity correction, the range of values that corresponds to a number of exactly x is given as follows:
x - 0.5 < x < x + 0.5.
Thus the range for exactly 48 successes is of:
47.5 < x < 48.5.
Meaning that option c is correct.
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Need Help ASAP!!! Giving away 50 pts
Given the equation 7m − 11 = 5m + 43 and the possible solution set S: {2, 27, 54, 86}:
Determine which integer(s) in the solution set makes the equation false. Show all work.
The required integers from the solution set are 2, 54 and 86.
How to solve a linear equation?A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.
The given equation is 7m − 11 = 5m + 43.
It can be solved as follows,
7m − 11 = 5m + 43
⇒ 7m - 5m = 43 + 11
⇒ 2m = 54
⇒ m = 27
Now, in the given solution set {2, 27, 54, 86}, only one integer 27 satisfies the given equation.
Hence, the integers in the solution set that make the equation false are 2, 54 and 86.
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All fourth grade children on Long Island are given an examination on mathematical achievement. A random sample of 60 fourth graders are selected. Their examination results are summarized in the following stem-and-leaf plot. Find the sample upper quartile.4 6 6 6 88 01 7 7 7 7 7 8 33 445 6667777 8888889 00011111 2233333 4455 66777 8 8 8 8 899 9 001 9 223 45 9
The sample upper quartile of the data set is 91 and the lower quartile is 67 for the students of the given examination.
The median and quartiles of a data set:
The data set's median, or 50th percentile, separates the bottom half from the higher half.
The first quartile is the median of the data set's first half.
The third quartile is the median of the data set's second half.
Because there are an even number of items 60, the median is the mean of the31st element elements, with the first half consisting of 30 elements ranging from 1 to 29, and the second half consisting of 12 elements ranging from 31 to 60.
The first quartile is the mean of the elements, 67 and 68, respectively, therefore Q1 = 60/4 =15th element = 67
The third quartile is defined as the mean of the sixth and seventh elements of the second half, hence Q3 = 3×60 / 4 = 91.
Hence the quartiles are at 67 and 91 respectively.
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Mona's school tennis team is running a car wash this weekend. They will charge $13 per car, and they are hoping to
aise $200. How much money will the team have left to raise once they have washed 10 cars?
Write and solve an equation to find the answer.
Answer:
$70
Step-by-step explanation:
x = 200 - 10 · 13
x = 200 - 130
x = 70
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse.
If b = 16 units and c = 20 units, what is the perimeter? If necessary, round your answer to the nearest tenth.
Answer: 48
Step-by-step explanation: Use this to help you!
NEED HEEEEELP PLEEEEASE HEEEEELP Solve. 4/5x+9/10=5 1/5 Enter your answer as a mixed number in simplest form in the box. x =
The value of x in the fraction 4/5x+9/10=5 1/5 is 5 3/8.
How to calculate the fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, the fraction is given as:
4/5x + 9/10 = 5 1/5
0.8x + 0.9 = 5.2
Collect like terms
0.8x = 5.2 - 0.9
0.8x = 4.3
Divide
x = 4.3 / 0.8
x = 5.375
x = 5 3/8
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Find dy/dx for the indicated function y
The derivative of the function [tex]y = 5^x + e^7[/tex] with respect to 'x'
is [tex]\frac{dy}{dx} = 5^xln5 + 0[/tex].
What is differentiation?Differentiation, in mathematics, process of finding the derivative, or rate of change, of a function also known as the slope.
We know, [tex]\frac{dy}{dx} a^x = a^xlna[/tex], where 'a' is a constant.
Given, [tex]y = 5^x + e^7[/tex].
Now, The derivative of the function with respect to 'x' is,
[tex]\frac{dy}{dx} = 5^xln5 + 0[/tex], As [tex]e^7[/tex] is a constant, and the derivative of any constant term is zero because the slope of a constant term is zero.
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Helppp! I need an answer asap pls!
Answer: (2*sqrt3)/3
Step-by-step explanation:
csc(x)=1/sin(x)
sin(q)= 15/(10*sqrt3)= 3/(2*sqrt3)
1/(3/(2*sqrt3))= (2*sqrt3)/3
A heavy rope, 40 ft long, weighs 0.5 lb/ft and hangs over the edge of a building 90 ft high. (Let x be the distance in feet below the top of the building. Enter xi* as xi.) (a) How much work W is done in pulling the rope to the top of the building? Show how to approximate the required work by a Riemann sum. lim( lim n-00 ) i = 1 Express the work as an integral. 160_v (10.5x , ) Jo Evaluate the integral. 900 X ft-lb (b) How much work W is done in pulling half the rope to the top of the building? Show how to approximate the required work by a Riemann sum. lim n7009 i = lim E(L Dax 1 Express the work as an integral. dx Evaluate the integral. ft-lb
According to Riemann sum and expressing the work as an integral,400 ft/lb work is done in pulling the rope to the top of the building.
Given,
heavy rope length = 40ft
weighs = 0.5 lb/ft
building height = 90 ft
If we divide rope into small parts with length Δx, rope weighs 0.5 lb/ft force work on each section is x*i is a point in i the such intervals.
The work done on ith part is
x*i0.5Δx
So the total done is
[tex]\lim_{n \to \infty}[/tex]= ∑0.5x*iΔx expressing work as an integral
[tex]\int\limits^40_0 {(0.5x)} \, dx[/tex] = [0.5 × x²/2]
= [0.5 × 40²/2 - 0.5 × 0²/2]
= [0.5 × 1600/2 - 0]
= 0.5 × 800 - 0
= 400 - 0
= 400 ft/lb
The work done in lifting the pieces in upper half of rope is
x*i0.5Δx
The work done in lifting lower half of the rope is
0.5Δx × 20
10Δx
Total workdone,
[tex]\lim_{n \to \infty}[/tex]∑0.5x*iΔx + [tex]\lim_{n \to \infty}[/tex]∑10Δx
= [tex]\lim_{n \to \infty}[/tex]∑(0.5x*i + 10)Δx work as an integral
[tex]\int\limits^25_0 {0.5} \, dx[/tex] + [tex]\int\limits^50_25 {10} \, dx[/tex]
= [ 0.5 * x²/2] + [10x]
= [0.5 * 20²/2] +[10(40-20)]
= [0.5 * 400/2] + [10*20]
= 100 + 200
= 300 ft/lb
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a sequential circuit has two jk flip-flop a and b and one input x. the circuit is described by the following flip-flop input equations:
D flip flop stands for a delay flip flop that produces output that is identical to input after a brief delay. The flip flop's input and next state are equal.
Z is an output, and x and x inputs.
x'y + xA = DA= A*
B* = x'B + xA
z=A (output is independent of input) (output is independent of input)
The next states are A(t+1) and B(t+1). We must provide the next state value to D of the D flip flop in order to obtain the next states A(t+1), and B(t+1) for A, B(present state). So the sequential circuit will be:
To get the next state as A(t+1)= x’A + xA, B(t+1)= x’B + xA, we have to give them to DA, DB of D flip flop because for D flip flop whatever is given to DA, DB will appear at output A, B.
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Write 2 equations and solve for the numbers
Answer:
y + x = 87
y = x + 35
x = 26
y = 61
Step-by-step explanation:
y + x = 87
y = x + 35
substitute y with x + 35 in the first equation:
(x + 35) + x = 87
2x + 35 = 87
2x = 87 - 35
2x = 52
x = 52/2
x = 26
Find y by substituting x with 26:
y = (26) + 35
y = 61
Henry correctly factored 42? + 52 - 6 as (4% - 3)(₴ + 2)
• He then claimed that the zeros of that quadratic function are located at
*=-=
and r = 2 . Did Henry correctly find the zeros of the function?
O Yes, Henry correctly found the zeros of the function.
O No, the zeros of the function are at x = 4 and =-2
• No, the zeros of the function are at z = - 5 andx = 2.
• No, the zeros of the function are at & = 4 and ≥ = -2
I attached the question and answer choices
Please help
Answer:
No, the zeros of the function are at x = 3/4 and x = –2
Step-by-step explanation:
the equation
4x² + 5x – 6 = 0
(note: since there is a coefficient of x² we need to multiply it to the last term(6))
4x² + 5x – 24 = 0
the factors are :- 8x and – 3x
4x² + 8x – 3x – 6 = 0
4x( x + 2) –3( x + 2) = 0
( 4x – 3)( x + 2) = 0
the zeros will be
4x – 3 = 0
4x = 3
[tex]x = \frac{3}{4} [/tex]
x + 2 = 0
x = – 2
the zeros are x= 3/4 or –2
i hope this helps
Use the given information to prove that ΔPQR ≅ ΔPSR.
Given: QR ≅ SR
PQ ≅ PS
Prove: ΔPQR ≅ ΔPSR
Based on the given information , the proof of triangle PQR ≅ triangle PSR is shown below .
In the question ,
two triangles PQR and PSR are given where ;
it is given that side QR ≅ SR
and PQ ≅ PS .
we have to prove that ΔPQR congruent to ΔPSR .
In triangle PQR and triangle PSR .
side QR = side SR .....given that QR ≅ SR ;
side PQ = side PS .....given that PQ ≅ PS ;
side PR = side PR .....because PR is the common side ;
Hence by SSS congruence , triangle PQR ≅ triangle PSR .
Therefore , it is proved that triangle PQR ≅ triangle PSR .
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What are the vertex and range of y = |2x + 6| + 2?
(0, 2); 2 < y < ∞
(0, 2); −∞ ≤ y < ∞
(−3, 2); 2 < y < ∞
(−3, 2); −∞ ≤ y < ∞
The vertex and the range of y = |2x + 6| + 2 are (c) (-3, 2); 2 ≤ y < ∞
How to determine the vertex and the range?The equation is given as
y = |2x + 6| + 2
The above equation is an absolute value function
An absolute value function represented as
y = a|x - h| + k
Where
Vertex = (h, k)
So, we have
y = |2x + 6| + 2
This gives
y = 2|x + 3| + 2
This means that the vertex is
Vertex = (-3, 2)
Remove the x value
y = 2
Because the leading coefficient is positive, then the vertex is a minimum
i.e.
y ≥ 2
So, the range is 2 ≤ y < ∞
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One week gas was $1.75 per gallon. The next week gas was $2.10 per gallon. By what percentage did the price increase or decrease? % (increase or decrease)
5 1/2x + 2/3x =37
Solve for x and show your work
The value of x will be;
⇒ x = 6
What is linear expression?A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
The expression is,
⇒ 5 1/2x + 2/3x = 37
Now,
Since, The expression is,
⇒ 5 1/2x + 2/3x = 37
Solve for x as;
⇒ 11/2x + 2/3x = 37
⇒ (33 + 4)x/6 = 37
⇒ 37x = 37 × 6
⇒ x = 6
Thus, The value of x = 6
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Rachel has \frac{7}{15}
15
7
of her project done. If she can finish \frac{7}{45}
45
7
of her project each day, how many more days will it take her to complete it?
Answer:
4 days
Step-by-step explanation:
If Rachel has 7/15 of her project done, then she has 8/15 of her project left to complete.
Convert 8/15 and let it have a denominator of 45, and you get 24/45. If she can finish the rest of her project 7/45 each day, and she has 24/45 left to go, then divide 24 by 7, and you get 3 R3.
Afterwards round that to 4, because Rachel can't leave 3/45 of her project unfinished, she just doesn't have as much work the last day.
So then Rachel can finish her project in 4 days.
Hope this helps!
Answer:
4 days
Step-by-step explanation:
7/15 done ...then 8/15 to go
8/15 = 24 / 45 if she can do 7/45 per day, she will need 4 more days
(24/7) = 3.4 =~ 4 days
34 In the appeal of the People v. Collins case (see Exercise 4.1.28), the counsel for the defense argued as follows: Suppose, for example, there are 5,000,000 couples in the Los Angeles area and the probability that a randomly chosen couple fits the witnesses’ description is 1/12,000,000. Then the probability that there are two such couples given that there is at least one is not at all small. Find this probability. (The California Supreme Court overturned the initial guilty verdict.)
The probability that there are two such couples given that there is at least one is 1 - (4999999/12000000) = 4/12 = 1/3.
What is probability?Probability is the measure of the likelihood that a given event will occur. It is expressed as a number between 0 and 1 (or 0% to 100%). A probability of 1 indicates that the event is certain to occur, while a probability of 0 indicates that it is impossible for the event to occur. Probability is used in a wide range of disciplines including mathematics, science, engineering, finance, and philosophy. Probability can be used to make predictions and help inform decision-making. By understanding probability, we can better understand the chances of certain outcomes and make more informed decisions.
This is because the probability that the first couple matches the description is 1/12000000, and the probability that the second couple matches the description, given that the first couple does, is 1/(12000000-1). Since there are 4999999 other couples, the probability that the second couple matches the description is (4999999/12000000). Thus, the probability that there are two such couples is 1 minus the probability that the second couple does not match the description, which is 1 - (4999999/12000000) = 4/12 = 1/3.
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HELP IM IN K12 AND THERS MORE OF THESE
X
y
13
45° I need this
Answer:
Step-by-step explanation:
you times 13 times 45 degrees and that equals to 585
Zachariah paid $126 for 6 concert tickets. At this rate, what is the cost of 10 concert tickets?
Write an equation for a parabola with x-intercepts (-1,0) and (3,0) ehich pass the point (1,-16)
The equation for a parabola with x-intercept is y = 4/3x² + 8/3x - 20.
What is equation?
In arithmetic, an equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.
Main body:
The equation has the form y = Ax² + Bx + C
Since (3,0), (-1,0), (1,-16) are points on the graph, we get the following system of equations:
9A + 3B + C = 0
A - B + C = 0
A + B + C = -16
Subtracting the first 2 equations and subtracting the 3rd equation from the first, we obtain:
8A - 4B = 0
8A + 2B = 16
Since 8A - 4B = 0, 8A = 4B. So, A = 1/2B.
Therefore, 8A + 2B = 16
6B = 16 So , B = 8/3 and A = 8/6
Since A + B + C = -16 and A = 8/6 , B = 8/3, we have 4 + C = -16. So, C = -20.
An equation of the parabola is y = 4/3x² + 8/3x - 20
Hence , the equation for a parabola with x-intercept is y = 4/3x² + 8/3x - 20.
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Twelve percent of the manufactured parts were defective and had to be pulled from the assembly line. Forty-eight defective parts
were pulled from the line. How many total parts were manufactured during this run?
O d) 126
O a) 400
O c) 383
Ob) 48
Answer:
a) 400---------------------------
Let the number of total parts be x.
12% of x were defective and it is 48 in number.
Find x:
0.12x = 48x = 48/0.12x = 400Correct choice is A.
draw in all lines of symmetry of the blue square
Answer:
Step-by-step explanation:
6x^2 + 36x + 3 in standard form
Answer:
its the
Step-by-step explanation:
set up, but do not evaluate, a triple integral that gives the volume of the right circular cylinder enclosed by the surfaces x^2 +y^2 =4,z=−10, and z=0
This triple integral gives the volume of the right circular cylinder which is enclosed by the given surfaces and extends from z = 0 to z = -10.
What in mathematics is an integral?
Mathematicians define an integral as either a number equal to the area under the graph of a function for a certain interval or as a new function whose derivative is the original function (indefinite integral).
In general, the word "integral value" refers to the result of integrating or summing the terms of a function that has an infinite number of terms.
The triple integral that gives the volume of the right circular cylinder enclosed by the surfaces x^2 + y^2 = 4 , z=-10 and z=0 is:
∫∫∫dV = ∫∫∫dx dy dz
where the limits of the integration are:
0 ≤ x ≤ 2*sqrt(2), -2*sqrt(2) ≤ y ≤ 2*sqrt(2), 0 ≤ z ≤ -10.
This triple integral gives the volume of the right circular cylinder which is enclosed by the given surfaces and extends from z = 0 to z = -10.
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A container that weighs 23 2/5pounds
holds sports equipment. Of the
equipment in the container, of the
1
3
weight is baseball equipment. What is the
weight of the baseball equipment?
The weight of the baseball equipment will be 39/5 pounds.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A container that weighs 23 2/5pounds holds sports equipment.
And, Of the equipment in the container, of the 1/3 weight is baseball equipment.
Now,
Since, A container that weighs 23 2/5pounds holds sports equipment.
And, Of the equipment in the container, of the 1/3 weight is baseball equipment.
Hence, The weight of the baseball equipment = 23 2/5 × 1/3
= 117/5 × 1/3
= 39/5 pounds
Thus, The weight of the baseball equipment = 39/5 pounds
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Suppose you have two Single Factor ANOVA experiments with the same degrees of freedom, if the resulting F test statistics are: Experiment 1, F = 2.68 Experiment 2, F = 20.15 Which statement is TRUE in regards to comparing Experiment 1 and Experiment 2? A.Procedure 1 has a smaller test statistic and therefore will result in stronger evidence in favor of the alternative hypothesis. B.Procedure 2 has a larger test statistic and therefore will result in stronger evidence in favor of the alternative hypothesis. C.We should reject the null for both tests. D.Impossible to know without more information.
TRUE - Procedure 2 has a larger test statistic and therefore will result in stronger evidence in favor of the alternative hypothesis.
what is degrees of freedom?Degrees of freedom are the maximum number of logically independent, or potentially different, values in the sample of data. One is subtracted from the number of elements in the data sample to determine the degree of freedom.
There are degrees of flexibility in the third column. Degrees of freedom (df1) between treatments equals k-1. df2 = N - k is the degree of freedom for the error. The total degree of freedom is N-1; additionally, (k-1) plus (N-k) equals N-1.
Fisher's Least Significant Difference (LSD) and the Bonferroni Method stand out among the techniques. These two use the t-test as their foundation. According to Fisher's LSD, run an F-test first, then if you find evidence to reject the null hypothesis, run regular t tests on all possible pairs of means. Similar but only requiring that you choose beforehand is the Bonferroni technique.
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A speech class has eight freshmen and five sophomores. Three people are selected at random to give speeches in sequence. Find the probability that
(a) the first is a sophomore, the second is a freshman, and the third is a sophomore.
(b) all three are freshmen.
(c) the first is a sophomore and the other two are freshmen.
1716 is the probability that a sophomore, the second is a freshman, and the third is a sophomore.
What is probability explained with an example?
A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty. The likelihood that an event will occur increases with its probability.
The flip of a fair (impartial) coin serves as a straightforward illustration. The probability of an event occurring, or P(E), is defined as the ratio of the number of favorable outcomes to the total number of outcomes in the probability formula.
The total number of ways in which 3 students can be arranged for speech out of total 13 students is,
P(13,3) = 13 * 12 * 11
= 1716
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