Answer:
its 3/4
Step-by-step explanation: i got it right trust me
The solution to the system of equations will be x= 9 / 2 and y= 3 / 4.
What is a system of equations?A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.
An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
The given equations are y=(3/ 2 )x-6 and y=(-9/2)x+21 to calculate the values of x and y using the substitution method.
Since both equations are equated to y, you just need to use substitution to create the equation below:
(3/ 2 )x-6 =(-9/2)x+21
Solve the equation for x:
(3/ 2 )x + (9/2)x = 27
x = 27 / 6 = 9 / 2
Plug x into any one of the given equations to find the value of y:
y=(3/ 2 )x-6
Solve for the value of y.
y=(3/2) x (9 / 2)-6
y = ( 27 / 4 ) - 6
y = ( 27 - 24 ) / 4
y = 3 / 4
Hence, the solution for the equation will be x = 9 / 2 and y = 3 / 4.
To know more about the system of linear equations follow
brainly.com/question/14323743
#SPJ5
Solve log x = 3. (2 points)
Answer:
x=1000
Step-by-step explanation:
log x = 3
log10 ( x) = 3
Raise each side to the power of 10
10^( log10 ( x)) =10 ^3
x = 10 ^3
x = 1000
Answer:
[tex]\boxed{x=1000}[/tex]
Step-by-step explanation:
[tex]log (x)= 3[/tex]
[tex]log_{10} (x)= 3[/tex]
Use logarithmetic definition:
[tex]log_a(b)=c[/tex]
[tex]b=a^c[/tex]
[tex]a=10\\b=x\\c=3[/tex]
Plug in the values.
[tex]x=10^3[/tex]
[tex]x=1000[/tex]
a lottery game has balls numbered 1 through 19. what is the probability selected ball is an even numbered ball or a 4 g
Answer:
Probability ball is an even numbered ball or a 4 [P(A or B)] = 9 / 19
Step-by-step explanation:
Given:
Number of balls = 1 to 19
Find:
Probability ball is an even numbered ball or a 4
Computation:
Total even number = 2, 4, 6, 8, 10, 12, 14, 16, 18
Probability to get even number P(A) = 9 / 19
Probability to get 4 number P(B) = 1 / 19
P(A and B) = 1 / 19 (4 common)
Probability ball is an even numbered ball or a 4 [P(A or B)]
P(A or B) = P(A) + P(B) -P(A and B)
P(A or B) = [9 / 19] + [1 / 19] - [1 / 19]
Probability ball is an even numbered ball or a 4 [P(A or B)] = 9 / 19
The height of an object dropped from the top of a 144-foot building is given by . How long will it take the object to hit the ground?
They left off the equation but we can know it's
y(t) = h₀ - g t² / 2
That's
y(t) = 144 - 16 t²
It hits the ground when
0 = 144 - 16 t²
16 t² = 144
t² = 144 / 16 = 9
t = 3 seconds
Answer: 3 seconds
In the periodic compound interest formula Upper A equals Upper P (1 plus StartFraction r Over n EndFraction )Superscript nt , what does the variable n represent?
Answer:
The variable n represents the number of times in a year in which we compound the interest rate
Step-by-step explanation:
The periodic compound interest formula is given as;
A = P( 1 + r/n)^nt
The variable n represents the number of times in a year in which the interest rate is compounded
is any answers loading for you guys or is it just me
Answer:
not just you
Step-by-step explanation:
Please explain this to me If f(x)=4x-2 than f(x-1)= A. 4x^2-6x+2 B. 4x^2+2x+2 C. 4x+2 D. 4x-6 E. 4x-1
Answer:
D. 4x − 6
Step-by-step explanation:
f(x) = 4x − 2
f(x−1) = 4(x−1) − 2
f(x−1) = 4x − 4 − 2
f(x−1) = 4x − 6
Find the vertical and horizontal asymptotes, domain, range, and roots of f (x) = -1 / x-3 +2.
Answer:
Vertical asymptote: [tex]x=3[/tex]
Horizontal asymptote: [tex]f(x) =2[/tex]
Domain of f(x) is all real numbers except 3.
Range of f(x) is all real numbers except 2.
Step-by-step explanation:
Given:
Function:
[tex]f (x) = -\dfrac{1 }{ x-3} +2[/tex]
One root, [tex]x = 3.5[/tex]
To find:
Vertical and horizontal asymptote, domain, range and roots of f(x).
Solution:
First of all, let us find the roots of f(x).
Roots of f(x) means the value of x where f(x) = 0
[tex]0= -\dfrac{1 }{ x-3} +2\\\Rightarrow 2= \dfrac{1 }{ x-3}\\\Rightarrow 2x-2 \times 3=1\\\Rightarrow 2x=7\\\Rightarrow x = 3.5[/tex]
One root, [tex]x = 3.5[/tex]
Domain of f(x) i.e. the values that we give as input to the function and there is a value of f(x) defined for it.
For x = 3, the value of f(x) [tex]\rightarrow \infty[/tex]
For all, other values of [tex]x[/tex] , [tex]f(x)[/tex] is defined.
Hence, Domain of f(x) is all real numbers except 3.
Range of f(x) i.e. the values that are possible output of the function.
f(x) = 2 is not possible in this case because something is subtracted from 2. That something is [tex]\frac{1}{x-3}[/tex].
Hence, Range of f(x) is all real numbers except 2.
Vertical Asymptote is the value of x, where value of f(x) [tex]\rightarrow \infty[/tex].
[tex]-\dfrac{1 }{ x-3} +2 \rightarrow \infty[/tex]
It is possible only when
[tex]x-3=0\\\Rightarrow x=3[/tex]
[tex]\therefore[/tex] vertical asymptote: [tex]x=3[/tex]
Horizontal Asymptote is the value of f(x) , where value of x [tex]\rightarrow \infty[/tex].
[tex]x\rightarrow \infty \Rightarrow \dfrac{1 }{ x-3} \rightarrow 0\\\therefore f(x) =-0+2 \\\Rightarrow f(x) =2[/tex]
[tex]\therefore[/tex] Horizontal asymptote: [tex]f(x) =2[/tex]
Please refer to the graph of given function as shown in the attached image.
Construct the cumulative frequency distribution for the given data.
Age (years) of Best Actress when award was won Frequency
20-29 28
30-39 37
40-49 14
50-59 3
60-69 4
70-79 1
80-89 1
Age (years) of Best Actress when award was won Cumulative Frequency
Less than 30
Less than 40
Less than 50
Less than 60
Less than 70
Less than 80
Less than 90
Answer:
Age Frequency Cumulative Frequency
Less than 30 28 28
Less than 40 37 28 + 37 = 65
Less than 50 1 4 65 + 14 = 79
Less than 60 3 79 + 3 = 82
Less than 70 4 82 + 4 = 86
Less than 80 1 86 + 1 = 87
Less than 90 1 87 + 1 = 88
Step-by-step explanation:
Given:
The Frequency Distribution table of ages of best actresses when award was won
To find:
Construct the cumulative frequency distribution
Solution:
In order to construct cumulative frequency distribution for the given data, each frequency from above table is added to the sum of the previous frequencies. For example, frequency for Less than 40 is 37 and the previous frequency (less than 30) is 28 so in order to calculate cumulative frequency 28 i.e. previous frequency is added to 37 (frequency of less than 30) and the cumulative frequency is 65. The complete table is given above.
Please helppp!!!!! Geometry
Answer:
[tex]\boxed{Option \ 4}[/tex]
Step-by-step explanation:
∠YVZ = 180 - 52 - 43 - 38 (Angles on a straight line add up to 180 degrees so if we try to find an unknown angle on the straight line, we need too subtract all the other angles from 180 degrees)
=> ∠YUZ = 47 degrees
Step-by-step explanation: In the figure shown, <UVW is a straight angle.
This means it measures 180 degrees.
So to find <YVZ, we add up all the angles and subtract the sum
from 180 to get the answer to this problem.
43 + 52 + 38 gives us a sum of 133.
Now we take 180 - 133 yo get 47.
So m<YVZ is 47 degrees.
A line with a slope of 5 passes through the point (2,10). What is its equation in slope intercept form
Answer:
The answer is
y = 5xStep-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
From the question
Slope / m = 5
Equation of the line passing through point (2 , 10) is
y - 10 = 5(x - 2)
y - 10 = 5x - 10
y = 5x - 10 + 10
y = 5xHope this helps you
Eight women and six men apply for a job at Google. Four of the applicants are selected for interviews. Let X denote the number of women in the interview pool. a) Give (explicitly) the probability mass function for X. Also describe a plot of F(x). b) Give (explicitly) the cdf, F(x), for X. Also show a plot of it. c) Determine the probability that more women are interviewed than men.
Answer:
See below
Step-by-step explanation:
images attached showing all working
a) The possible values of X are as follows
X = {0,1,2,3,4}
P(x) = P(X=x)
b) The cdf in this case, as in the F(x), comes out to be a step function graph on the basis of values obtained from the probability mass function.
c) To find out the probability when more women are interviewed than me, add together the matrices from when value of X is equal to 2, 3 and 4 (from part a).
Which correlation coefficient could represent the relationship in the scatterpot. Beach visitors
Answer:
A. 0.89.
Step-by-step explanation:
The value of correlation coefficient ranges from -1 to 1. Any value outside this range cannot possibly be correlation coefficient of a scatter plot representing relationship between two variables.
The scatter plot given shows a positive correlation between average daily temperatures and number of visitors, as the trend shows the two variables are moving in the same direction. As daily temperature increases, visitors also increases.
From the options given, the only plausible correlation that can represent this positive relationship is A. 0.89.
Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts.
Diet Regular
μ μ1 μ2
n 20 20
x 0.78062lb 0.81645 lb
s 0.00444 lb 0.00745 lb
A. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda.
What are the null and alternative and hypotheses?
B. What is the test statistic? (Round to two decimal places as needed.)
C. What is the P-value? (Round to three decimal places as needed.)
State the conclusion for the test.
A. Reject the null hypothesis. There is sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.
B. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.
C. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.
D. Reject the null hypothesis. There is not sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.
b. Construct a confidence interval appropriate for the hypothesis test in part (a).
___lb < u1 - u2 < ___lb (Round to three decimal places as needed.)
Does the confidence interval support the conclusion found with the hypothesis test?
(No/Yes) because the confidence interval contains (zero/only positives values/ only negative values)
Answer:
(A) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1 \geq \mu_2[/tex]
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1<\mu_2[/tex]
(B) The value of t-test statistics is -18.48.
(C) The P-value is Less than 0.005%.
(D) Reject the null hypothesis. There is sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.
Step-by-step explanation:
We are given that the Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right;
Diet Regular
μ μ1 μ2
n 20 20
x 0.78062lb 0.81645 lb
s 0.00444 lb 0.00745 lb
Let [tex]\mu_1[/tex] = mean weight of contents of cans of diet soda.
[tex]\mu_2[/tex] = mean weight of contents of cans of regular soda.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1 \geq \mu_2[/tex] {means that the contents of cans of diet soda have weights with a mean that is more than or equal to the mean for the regular soda}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1<\mu_2[/tex] {means that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda}
The test statistics that will be used here is Two-sample t-test statistics because we don't know about population standard deviations;
T.S. = [tex]\frac{(\bar X_1 -\bar X_2)-(\mu_1- \mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ~ [tex]t__n_1_+_n_2_-_2[/tex]
where, [tex]\bar X_1[/tex] = sample mean weight of cans of diet soda = 0.78062 lb
[tex]\bar X_2[/tex] = sample mean weight of cans of regular soda = 0.81645 lb
[tex]s_1[/tex] = sample standard deviation of cans of diet soda = 0.00444 lb
[tex]s_2[/tex] = sample standard deviation of cans of regular soda = 0.00745 lb
[tex]n_1[/tex] = sample of cans of diet soda = 20
[tex]n_2[/tex] = sample of cans of diet soda = 20
Also, [tex]s_p =\sqrt{\frac{(n_1-1)s_1^{2}+ (n_2-1)s_2^{2}}{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(20-1)\times 0.00444^{2}+ (20-1)\times 0.00745^{2}}{20+20-2} }[/tex] = 0.00613
So, the test statistics = [tex]\frac{(0.78062-0.81645)-(0)}{0.00613 \times \sqrt{\frac{1}{20}+\frac{1}{20} } }[/tex] ~ [tex]t_3_8[/tex]
= -18.48
The value of t-test statistics is -18.48.
Also, the P-value of the test statistics is given by;
P-value = P( [tex]t_3_8[/tex] < -18.48) = Less than 0.005%
Now, at a 0.01 level of significance, the t table gives a critical value of -2.429 at 38 degrees of freedom for the left-tailed test.
Since the value of our test statistics is less than the critical value of t as -18.48 < -2.429, so we have sufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda.
A group of patients select from among 38 numbers, with 18 odd numbers (black) and 18 even
numbers (red), as well as 0 and 00 (which are green). If a doctor pays $7 that the outcome is an odd
number, the probability of losing the $7 is 20/38 and the probability of winning $14 (for a net gain of
only $7, given you already paid $7) is 18/38
If a doctor pays $7 that the outcome is an odd number, how would you figure out what is the doctors
expected value is?
Answer: $2.95
Step-by-step explanation:
Given: Probability of losing the $7 = [tex]\dfrac{20}{38}[/tex]
Probability of winning $14 = [tex]\dfrac{18}{38}[/tex]
Then, the expected value = (- $7) x ( Probability of losing the $7) + $14 x(Probability of winning $14)
= [tex](-\$ 7)\times\dfrac{20}{38}+(\$14)\times\dfrac{18}{38}[/tex]
= [tex]-\dfrac{70}{19}+\dfrac{126}{19}[/tex]
= [tex]\dfrac{56}{19}\times\approx\$2.95[/tex]
∴ If a doctor pays $7 that the outcome is an odd number, the doctor's
expected value is $2.95.
The ratio of boys to girls in Jamal's class is 3:2. If four more girls join the class, there will be the same number of boys and girls. What is the number of boys in the class?
Answer:
4 boys
Step-by-step explanation:
Let x represent boys and y represent girls
Hence, x : y = 3 : 2
x/y = 3/2
2x = 3y ------ (1)
x/y + 4 = 3/3
3x = 3(y + 4)
3x = 3y + 12 --------- (2)
From (1): x = 3y/2
Substitute x into (2) we have:
9y/2 = 3y + 12
9y = 6y + 24
9y - 6y = 24
3y = 24
∴ y = 8
From (2) : 3x = 24 - 12 = 12
∴ x = 4
Hence there Four boys
Click on the solution set below until the correct one is displayed.
Answer:
{ } or empty set.
Step-by-step explanation:
The solutions should be where the two lines intersect, but in this case, the parallel lines never intersect. That means that they have no solutions.
Hope this helps!
Answer:
{ } or empty set
Step-by-step explanation:
It's because these lines are parallel so they don't intersect to give you a coordinate.
Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a
mean of 100 and a standard deviation of 15.
n
f0 and
102
130
are
The area of the shaded region is (Round to four decimal places as needed.)
sions
Kented in
V3 and
andomly
d by in-
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Enter your answer in the answer box and then click Check Answer.
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Clear All
Check Answer
All parts showing
Answer: 0.4255
Step-by-step explanation:
Given: IQ scores of adults, and those scores are normally distributed
Mean: [tex]\mu=100[/tex]
Standard deviation: [tex]\sigma= 15[/tex]
Let X denotes the IQ of a random adults.
The area between 102 and 130 = [tex]P(102<X<130)=P(\dfrac{102-100}{15}<\dfrac{X-\mu}{\sigma}<\dfrac{130-100}{15})[/tex]
[tex]=P(0.13<Z<2)\ \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=P(Z<2)-P(Z<0.13)\\\\=0.9772- 0.5517\ [\text{By z-table}]\\\\=0.4255[/tex]
Hence, area between 102 and 130 = 0.4255
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HWS
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The manufacturer's suggested retail price (MSRP) for a particular car is $25,495, and it is expected to be worth $20,081 in 2 years.
(a) Find a linear depreciation function for this car.
(b) Estimate the value of the car 4 years from now.
(c) At what rate is the car depreciating?
(a) What is the linear depreciation function for this car?
f(x) =
(Simplify your answer. Do not include the $ symbol in your answer.)
Answer:
a) y = 25495 - 2707x
b) y = 25495 - 2707(4) = 14,667
c) $2,707 per year
Step-by-step explanation:
Value now: $25,495
Value in 2 years: $20,081
Loss of value in 2 years: $25,495 - $20,081 = $5,414
Loss of value per year: $5,414/2 = $2,707
a) y = 25495 - 2707x
b) y = 25495 - 2707(4) = 14,667
c) $2,707 per year
3x²-9x+1+0 Find the discriminant
Answer:
[tex]\boxed{D = 69}[/tex]
Step-by-step explanation:
The given quadratic equation is:
[tex]3x^2-9x+1 = 0[/tex]
Comparing it with the standard form of Quadratic Equation [tex]ax^2+bx+c = 0[/tex] , we get:
a = 3, b = -9 and c = 1
Discriminant = b² - 4ac
D = (-9)²-4(3)(1)
D = 81 - 12
D = 69
Owen has enough materials to build up to 10 birdhouses in shop class. Each birdhouse needs 12 square feet of wood. The function W(b) = 12b represents the total amount of wood that Owen would need to build b birdhouses. What domain and range are reasonable for the function? A. D: 0 ≤ b ≤ 10 R: 0 ≤ W(b) ≤ 120 B. D: 0 ≤ b ≤ 120 R: 0 ≤ W(b) ≤ 10 C. D: 0 ≤ b ≤ 10 R: 12 ≤ W(b) ≤ 120 D. D: 10 ≤ b ≤ 12 R: 0 ≤ W(b) ≤ 120
Answer:
A. D: 0 ≤ b ≤ 10 R: 0 ≤ W(b) ≤ 120
Step-by-step explanation:
Since b represents the number of birdhouses, it is reasonable for that to have non-negative values. The maximum material availability means that b > 10 is not of practical use. This eliminates choices B and D.
Since W represents the amount of wood required for b birdhouses, it is reasonable for the range of it to match 12 times the domain: 12·0 = 0 to 12·10 = 120. This eliminates choice C.
The appropriate choice is ...
A. D: 0 ≤ b ≤ 10 R: 0 ≤ W(b) ≤ 120
PLEASE HELP Two prisms are composed to form a V shape. The thickness of each prism is 1 unit, and width of each prism is 2 units. If the length of one prism is greater than the length of the other prism by 1 unit and the total volume of the figure is 30 cubic units, what are the lengths of the prisms?
Answer:
7 units, 8 units
Step-by-step explanation:
Apparently, the cross section of each prism is a rectangle 1 unit by 2 units. Hence the total length will be ...
(30 units³)/((1 unit)(2 units)) = 15 units
Two numbers that differ by 1 and have a sum of 15 are 7 and 8.
The lengths of the prisms are 7 units and 8 units.
Efficiency is the ratio of output work to input work, expressed as a percentage. Light bulbs put out less light energy than the amount of electrical energy that is put into the bulb. An illustration of a wide arrow with a light bulb at the tail of it labeled electrical energy 100 J, breaks into a small arrow going forward labeled light 10 J and a larger curling away labeled heat 90 J. The goal of the bulb is to produce light. What is the efficiency of this bulb as it works to put out light? 10% 80% 90% 100%
Answer:
10%
Step-by-step explanation:
Using the given formula with the given data, we have ...
efficiency = output work / input work
= (10 J)/(100 J) = 0.10 = 10%
Answer:
A) 10%
Step-by-step explanation:
10/100=10
The length of a rectangle is 4yd longer than its width. If the perimeter of the rectangle is 36yd, find its area
Answer:
[tex] \boxed{\sf Area \ of \ the \ rectangle = 91 \ yd^{2}} [/tex]
Given:
Length of the rectangle = 4 yd longer than its width
Perimeter of the rectangle = 36 yd
To Find:
Area of the rectangle
Step-by-step explanation:
Let the width of the rectangle be 'w' yd
So,
Length of the rectangle = (w + 4) yd
[tex] \therefore \\ \sf \implies Perimeter \: of \: the \: rectangle = 2(Length + Width) \\ \\ \sf \implies 36 = 2((4 + w) + w) \\ \\ \sf \implies 36 = 2(4 + w + w) \\ \\ \sf \implies 36 = 2(4 + 2w) \\ \\ \sf 36 =2(2w+4) \: is \: equivalent \: to \: 2(2w + 4) = 36: \\ \sf \implies 2(2w + 4) = 36 \\ \\ \sf Divide \: both \: sides \: of \: 2 (2w + 4) = 36 \: by \: 2: \\ \sf \implies 2w + 4 = 18 \\ \\ \sf Subtract \: 4 \: from \: both \: sides: \\ \sf \implies 2w = 14 \\ \\ \sf Divide \: both \: sides \: of \: 2w = 14 \: by \: 2: \\ \sf \implies w = 7[/tex]
So,
Width of the rectangle = 7 yd
Length of the rectangle = (7 + 4) yd
= 13 yd
[tex] \therefore \\ \sf Area \ of \ the \ rectangle = Length \times Width \\ \\ \sf = 7 \times 13 \\ \\ \sf = 91 \: {yd}^{2} [/tex]
Please help! I got 14 but it says it's incorrect! Find the maximum number of real zeros of the polynomial. f(x)=2x^(6)-3x^(3)+1-2x^(5)
Answer:
There are two or zero positive solutions and zero negative roots (zeros).
Step-by-step explanation:
Use Descartes' Rule of Signs to determine the number of real zeros of [tex]f(x)=2x^6-3x^3+1-2x^5[/tex]
[tex]f(x)=2x^6-2x^5-3x^3+1\\[/tex]
A snake tank measures 1.8 m x 0.5 m x 0.5 m. What is the surface area of the tank including the top? Use the formula: SA = 2hl+2hw+2lw
Answer:
4.1
Step-by-step explanation:
1.8 x 0.5 = 0.9
0.5 x 0.5 = 0.25
2(0.9 + 0.9 + 0.25) = 2(1.8 + 0.25) = 2(2.05)
2 x 2.05 = 4.1
Therefore the answer is 4.1
I hope that was helpful!
DIRECTIONS: Road the question and select the best respons
A right prism of height 15 cm has bases that are right triangles with legs 5 cm and 12 cm. Find the total
surface area of the prism,
OA 315 cm square
OB, 480 cm square
Oc. 510 cm square
OD. 570 cm square
Please explain how to get the answer
Answer:
C. 510 cm^2
Step-by-step explanation:
Well to find TSA or Total Surface Area,
We need to find the area of al the triangles and rectangles.
Let's start with the 2 rectangles facing forwards.
They both have dimensions of 5*15 and 12*15,
75 + 180
= 255 cm ^2
Now let's do the back rectangle which has dimensions of 15 and 13.
15*13 = 195 cm^2
Now we can do the top and bottom triangles,
Since we don't have height we can use the following formula,
[tex]A = \sqrt{S(S-a)(S-b)(S-c)}[/tex]
S is [tex]S = \frac{1}{2} (A+B+C)[/tex]
S= 15
Now with s we can plug that in,
[tex]A = \sqrt{15(15-5)(15-13)(15-12)}[/tex]
The a b and c are the sides of the triangle.
So let's solve,
15 - 5 = 10
15 - 13 = 2
15 - 12 = 3
10*2*3 = 60
60*15 = 900
[tex]\sqrt{900}[/tex] = 30 cm^2
Since there is 2 triangles with the same dimensions their areas combined is 60 cm^2
60 + 255 + 195 = 510 cm^2
Thus,
the TSA of the right triangular prism is C. 510 cm^2.
Hope this helps :)
Answer:
C) 510 square centimetres
Step-by-step explanation:
The surface area of a prism is given as:
A = bh * pL
where b = base length of the prism = 12 cm
h = base width = 5 cm
p = b + h + c
where c = slant height = 13 cm
L = height of the prism = 15 cm
Therefore, the surface area of the prism is:
A = (12 * 5) + (12 + 5 + 13) * 15
A = 60 + (30 * 15)
A = 60 + 450
A = 510 square centimetres
That is the surface area of the prism.
What is the range of the function F(x) graphed below?F(x)= -(x+2)^2+3
Answer:
range of the function F(x) is (-infinity, 3)
Step-by-step explanation:
I do not see the graph function F(x), so will assume that it is a graph of the function F(x) over the complete domain (-inf,inf).
As you can see from the attached graph, the function reaches a maximum at y=+3, and extends all the way to -infinity.
So the range of the function F(x) is (-infinity, 3)
Can you figure out the missing number in this sequence? Type your answer below!
88511,16351,?,10251
Answer:
731`55
Step-by-step explanation:
*Step-by-step explanation:*
The given sequence:
88511, 16351, ?, 10251
To find, the missing number (?) = ?
The pattern follow:
1. To Add the first 2 digits in the number .
2. Subtract digit 3 from Digit 2 .
3. The multiply digit 3 and 4 .
4. To divide digit 4 by 3.
16351 ⇒ 8 + 8 = 16, 8 - 5 = 3, 5 × 1 = 5 and \dfrac{1}{1} =111=1
= 16351
? ⇒ 1 + 6 = 7, 6 - 3 = 3, 3 × 5 = 15 and \dfrac{5}{1}15 = 5
= 73155
10251 ⇒ 7 + 3 = 10, 3 - 1 = 2, 1 × 5 = 5 and \dfrac{5}{5}55 = 1
= 10251
∴ The missing number of the given sequence = 73155
Thus, the missing number of the given sequence is 73155.
The third number in the sequence is : 73155
The given sequence is:
88511, 16351, ?, 10251
Now the pattern to find the missing value is:
Add, subtract, multiply and then divide.
These patterns are applied on the previous number's double digits to get the next number of the sequence.
Example:
Take 88511.
First pair (8,8): Add them: 16
Second pair (8,5): Subtract them: 8-5 = 3
Third pair: (5,1): Multiply them: 5
Fourth pair(1,1): Divide them: 1/1 = 1
Thus the next number of the sequence we get is 16351.
Similarly, doing it on 2nd term (16351) to find the missing third term:
Add (1,6): 7
Subtract (6,3): 3
Multiply (3,5): 15
Divide (5,1): 5
Thus the third number in the sequence is : 73155
Learn more here:
https://brainly.com/question/3000144
what other numbers can you square that result in 9 ?
Step-by-step explanation:
I'm not sure what your answers are, but you can only square 3 and -3 to get 9.
Answer:
3, -3
Step-by-step explanation:
3*3 = 9
-3 * -3 = 9
These are the only two numbers that square to 9
Applications of exponential functions need help ASAP PlZ
Answer:
Second choice is correct.
Step-by-step explanation:
Simple interest = $12600
Compounded interest = $14656
Best Regards!