Find the surface area of D
Answer:
151 cm² (i don't know what unit you were given so im going to use cm)
Step-by-step explanation:
Part One: finding the missing side (h)
h = a² = b² + c²
13² = 12² + c²
169 = 144 + c²
169 - 145 = c²
= 25
square root of 25 = c
5 = c
area of top triangular area = ½ b × h
= ½ × 12 × 5
= 30 cm²
Part Two
area of rectangle = l × b
= 12 × 8
= 96 cm²
Part Three
area of square = l × l
= 5 × 5
= 25 cm²
total surface area = (30 + 96 + 25) cm²
= 151 cm²
Help please asap anyone
Answer:
x= 0 (B)
Step-by-step explanation:
hope this helps
Find the inverse of each function. Is the inverse a function? f(x)=x⁷
The inverse of the function x^7 is x^-7 and it is also a function.
An inverse function or an anti function is defined as a function, which can reverse into another function.
A standard method to find inverse of a function is to set y=f(x)
let y= f(x)=x^7
thus
[tex]\sqrt[7]{y}[/tex]=x
thus [tex]f^{-1}[/tex](y)=[tex]\sqrt[7]{y}[/tex]
thus [tex]f^{-1} (x)=\sqrt[7]{x}[/tex]
(To verify this if a function is inverse or not we are required to check for the identity)
f([tex]f^{-1}[/tex](x))=[tex]f^{-1}[/tex](f(x))=x
Therefore, The inverse of the function x^7 is x^-7 and it is also a function.
For further reference:
https://brainly.com/question/2541698?referrer=searchResults
#SPJ4
Expand each logarithm.
log√2x/y
Using logarithmic quotient rule, we expand each logarithm function log√2x/y as 1/2 log (2x) - log (y).
According to the question, we need to expand we expand logarithm function log√2x/y .In Logarithms, the power is raised to some numbers (usually, base number) to get some other number. It is an inverse function of exponential function.
Quotient rule for logarithm: log (a/b) = log (a) - log(b).
⇒ log√2x/y
Applying quotient rule to the above logarithm function, we get
log√2x/y = log (√2x) - log (y)
= log (2x)^1/2 - log (y) →(1)
Power rule for logarithm: log (a)ˣ = x log (a)
Applying power rule to the equation (1), we get
log (2x)^1/2 - log (y) = 1/2 log (2x) - log (y)
Hence, using logarithmic quotient rule, we expand each logarithm function log√2x/y as 1/2 log (2x) - log (y).
Learn more about logarithmic function here
brainly.com/question/14412094
#SPJ4
HELP ASAP!!!!
WRITE A finite plane is a plane that has boundaries or does not extend indefinitely. The sides of the cereal box shown are finite planes. Give a
real-life example of a finite plane. Is it possible to have a real-life object that is an infinite plane? Explain your reasoning.
Answer:
trust me a shoe box or a board game box or a small container
Solve each equation. Check your answers.
log (3 x+1)=2
log ( 3x + 1 ) = 2 => x = 33, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Given: log (3x + 1) = 2
Raising both the sides by 10, in order to remove the logarithm:
=> [tex]10^{log_{10}(3x+1)} = 10^{2}[/tex]
=> 3x + 1 = 100 (as [tex]a^{log_a(x)} = x[/tex])
=> 3x = 99
=> x = 33
Hence, log ( 3x + 1 ) = 2 => x = 33, by properties of logarithm.
To learn more about logarithms, refer to the link: brainly.com/question/25710806
#SPJ4
If mWVY = 70, find mYVX.
Answer:
Can I see a diagram?
Step-by-step explanation:
David travelled 4/5 of his trip by bicycle and the rest of the distance by foot. if the whole trip was 160 km, how many kilometers did he travel by foot?
David travelled 32 kilometres of the entire trip by foot
How to calculate the distance David travelled by foot ?David travelled 4/5 of his trip by bicycle and the rese was done by foot
The whole trip was 160 km
The first step is to calculate the distance travelled with the bicycle
4/5 × 160
= 128
Therefore the distance travelled by foot can be calculated as follows
= 160-128
= 32
Hence David travelled 32km by foot
Read more on distance here
https://brainly.com/question/13331563
#SPJ1
Answer:32
Step-by-step explanation:32
There are 3 consecutive integers. Four times the smallest integer is equal to six more than more than three times the largest. What is the smallest of the 3 integers?
Answer:
The answer is 12.
Step-by-step explanation:
Let the smallest number = x and the largest number = x+2(since the three numbers are consecutive, we would have to use x+2. If we wanted the second largest number, it would be x+1)
We would write the statement "four times the smallest integer is equal to six more than more than three times the largest" as:
4x = 3(x+2) + 6
Now just solve.
4x = 3x+6+6 distributive property
4x = 3x+12 simplify
x = 12 subtraction property
And since x is the smallest number, we have our answer.
Therefore, the answer is 12.
The product of 3 different positive integers is 15.
What is their sum?
A. 8
B. 9
C. 15
D. 45
I think B.9 is correct
1*3*5=15
1+3+5=9
Evaluate the function for the given value
f(x) = 6x − 6 use x = −6
-6
Your answer
1 point
value
Answer:
y=-42 or f(x)=-42
Step-by-step explanation:
1. Substitute x for -6. Equation: f(x)=6(-6) + -6
2. Turn f(x) into y. Equation: y=6(-6) + -6
3. Multiply 6 and -6. Equation: y=-36 + -6
4. Add -36 and -6. Equation: y=-42 or f(x)=-42
The sides of certain right triangles are Pythagorean triples. In some such triangles, the sum of one
of the sides of the triangle plus the hypotenuse equals 49 cm. Find the sum, in cm, of the lengths of
the third sides of all triangles that satisfy this criteria.
Using the Pythagorean Theorem, the length of the third sides in a triangle that satisfy this criteria is given by:
[tex]l_2^2 = 49 - 2l_1^2[/tex]
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
For this problem, considering the description of a Pythagorean triple, we have that:
[tex]h^2 + l_1^2 = 49[/tex].[tex]h^2 = 49 - l_1^2[/tex]Hence the length of the third side can be given as follows:
[tex]49 - l_1^2 = l_1^2 + l_2^2[/tex]
[tex]2l_1^2 + l_2^2 = 49[/tex]
[tex]l_2^2 = 49 - 2l_1^2[/tex]
Hence the length of the third sides in a triangle that satisfy this criteria is given by:
[tex]l_2^2 = 49 - 2l_1^2[/tex]
More can be learned about the Pythagorean Theorem at https://brainly.com/question/26396675
#SPJ1
A car wash washes 68 vehicles in an 8 hour day.At this rate,how many vehicles are washed in 1 hour
Answer: 8 and a half vehicles (if no halves are allowed just 8)
Step-by-step explanation:
We divide 68 vehicles by 8 hours bringing us to 8 and a half vehicles an hour
HELP PLS ILL MARK YOU BRAINLIST
What is the next fraction in this sequence? Simplify your answer.
4/5
13/20
1/2
, 7/20
The next fraction in this sequence 4/5, 13/20, 1/2, 7/20,.... is; 1/5
What is the next term of the sequence?Arithmetic sequence are sequence that are separated by a common difference.
We are given the sequence as;
4/5, 13/20, 1/2, 7/20,....
The fractions expressed as percentage is given as:
80%, 65%, 50%, 35%...
The general formula for the nth term of the sequence is;
Tₙ = a + (n - 1)d
where;
a is first term
d is common difference
n is position of term
Thus, the fifth term is;
T₅ = 80 + (5 - 1)(-15)
T₅ = 80 + (4)(-15)
T₅ = 80 - 60
T₅ = 20
Expressing 20% as a fraction gives us;
20% = 20/100 = 1/5
Thus the next fraction in the given sequence is 1/5
Read more about next term of the sequence at; https://brainly.com/question/7882626
#SPJ1
What is the slope of the line that passes
through the points (8, 2) and (10, 2)?
Write your answer in simplest form.
Answer:
Submit Answer
undefined
attempt 1 out of a
Answer:
slope = 0
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (8, 2 ) and (x₂, y₂ ) = (10, 2 )
m = [tex]\frac{2-2}{10-8}[/tex] = [tex]\frac{0}{2}[/tex] = 0
Express each of the following values in words.
a. 0.005
b. 11.037
c. 403.608
Answer:
a. zero point zero zero 5
b. eleven point zero three seven
c. four hundred and three point six zero eight.
I really hope this helps you!!! Have a great day :).
Fabian took a taxi from his house to an airport. The taxi company charge to pick up the fee of 4.80 plus 4 per mile . The total fare was 44.80, not including the tip. how many miles was the taxi ride?
The taxi ride was 11.2 miles
The number of miles can be calculated as follows ?Fabian took a ride from his house to the airport
The taxi company charged 4.80 and 4 per miles
The total fare amount was 44.80, the fee was not inclusive
The number of miles can be calculated as follows
= 44.80/4
= 11.2
Hence the taxi ride was 11.2 miles
Read more on miles here
https://brainly.com/question/27826115?referrer=searchResults
#SPJ1
please help with this
Answer: i got no clue
Step-by-step explanation:
Densità di benzina= 0,75
Qual’è il volume occupato da 1kg di benzina?
Answer:
ecdqwef
Step-by-step explanation:
Write the equation of a line perpendicular to 6x-7y=-4 that passes through the point (-6,5).
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]6x-7y=-4\implies 6x=7y-4\implies 6x+4=7y \\\\\\ \cfrac{6x+4}{7}=y\implies \qquad \stackrel{\stackrel{m}{\downarrow }}{\cfrac{6}{7}} x+\cfrac{4}{7}=y\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
now, since we know that slope, let's check for a perpendicular line to it
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{6}{7}} ~\hfill \stackrel{reciprocal}{\cfrac{7}{6}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{7}{6}}}[/tex]
so we're really looking for the equation of aline whose slope is -7/6 and that it passes through (-6 , 5)
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{7}{6} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- \cfrac{7}{6}}(x-\stackrel{x_1}{(-6)}) \implies y -5= -\cfrac{7}{6} (x +6) \\\\\\ y-5=-\cfrac{7}{6}x-7\implies {\LARGE \begin{array}{llll} y=-\cfrac{7}{6}x-2 \end{array}}[/tex]
Answer:
Please read and try to understand it :>
Step-by-step explanation:
[tex]6x-7y=-4[/tex] is not the standard format for a straight line so you have to rearrange it:
[tex]y=\frac{6}{7} x +\frac{4}{7}[/tex]
To find the equation of a perpendicular line to the given equation, you have to first find the negative reciprocal of the gradient:
[tex]-\frac{7}{6}[/tex]
Since you want to find the equation of a perpendicular line that passes a certain point, you have to substitute the coordinates to the equation to find the y-intercept:
[tex]5=-\frac{7}{6} (-6)+c[/tex]
Solving:
[tex]5=-\frac{7}{6} (-6) +c\\ \\ 5=\frac{42}{6} +c\\ \\-\frac{42}{6} +5=c\\ \\-7+5=c\\\\ -2=c[/tex]
Final equation: [tex]y=-\frac{7}{6} x -2[/tex]
help me please just answer the question.
Answer:
the answer is A
Answer:
Step-by-step explanation:
b is the aswswer
Solve the following equation for B.
h=m+1/5rB
Solving for B in the equation gives B = 5( h - m) / r
What is subject of formula?
A subject of formula can be defined as a variable that is expressed in terms of other variables in an equation or expression.
It is also known as the variable that is being worked out in an equation or given expression.
From the information given, we have the equation;
h = m + 1/5rB
To make 'B' the subject of formula, we have to take the following crucial steps;
Take 'm' over the equality sign
h - m = rB/ 5
Now, cross multiply
5( h - m) = rB
To make 'B' stand alone, divide both sides by r
B = 5( h - m) / r
Thus, solving for B in the equation gives B = 5( h - m) / r
Learn more about subject of formula here:
https://brainly.com/question/10643782
#SPJ1
A certain star is 4.6 x 10^2 light years from the Earth. One light year is about 5.9 x 10^12 miles. How far from the earth (in miles) is the star? Has to be answered in scientific notation
The distance of the earth from the star is mathematically given as
2.537 x 10¹⁵ miles
How far from the earth (in miles) is the star?Generally, the Coefficients for the problem are mathematically given a
Coefficients =4.6 x 5.9
Coefficients =27.14
For Exponents
Exponents 10² x 10¹² = 10⁽²⁺¹²⁾
Exponents =10¹⁴
In conclusion, After that, we put them together once again to produce a scientific notation:
25.37 x 10¹⁴
2.537 x 10¹⁵ miles
Read more about distance
https://brainly.com/question/13034462
#SPJ1
Write each expression as a single logarithm. Identify any properties used. log x-log y
log x-log y = log ( x/y) we use this properties Quotient in the equation.
A logarithm is defined simply?
The power to which a number must be increased in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents). For instance, since ten raised to the power of two equals 100, the base ten logarithm of 100 is 2: log 100 = 2.How does exponential growth utilise e?
e is the constant growth rate that all processes that are growing continuously share. With e, you may compare a simple growth rate—where all change occurs at the end of the year—with a compound, continuous growth rate, where growth occurs once per nanosecond or quicker.You use this properties Quotient in the equation -
log x-log y = log ( x/y)
Learn more about logarithm
brainly.com/question/11487261
#SPJ4
a town's january high temperatures average f with a standard deviation of , while in july the mean high temperature is and the standard deviation is . in which month is it more unusual to have a day with a high temperature of ? explain.
It is more unusual to have a day with a high temperature of 55 F. A high temerature of 55 F in July is 2.2 std deviation below the mean and a high temperature of 55 F in January is only 1.889 std deviation above the mean.
What is a temperature that's too high?103 degrees or above is considered a high fever. When your temperature reaches at least 104 degrees, a potentially hazardous fever starts to develop. You require emergency medical care if your fever is 105 degrees or greater.COVID-19 symptoms can include a fever (high temperature of 38 degrees Celsius or higher). The temperature of your body is usually between 36 and 36.8 degrees Celsius. For most people, a body temperature of 38 degrees Celsius or greater is considered to be a high temperature or fever. This may indicate that you are ill.No medication is required. If you get a strong headache, stiff neck, shortness of breath, or any other unusual signs or symptoms in addition to the temperature, call your doctor right once. Take acetaminophen (Tylenol, other), ibuprofen (Advil, Motrin IB, other), or aspirin if you're feeling uncomfortable.Which month is more unusual to have a day with a high temperature?
Here z score =(X-mean)/std deviation
Therefore for temperature 55 F ; zscore for January =(55-38)/9=1.889
And for temperature 55 F ; zscore for July =(55-77)/10=-2.2
As z score reflect that 55 F is farthest from the mean of July in terms of std deviation
It is more unusual to have a day with a high temperature of 55 F. A high temperature of 55 F in July is a 2.2 std deviation below the mean, and a high temperature of 55 F in January is only a 1.889 std deviation above the mean.
To learn more about high temperature, refer to:
https://brainly.com/question/25677592
#SPJ4
Write each expression as a single natural logarithm. ln 3-5 ln 3
Expression as a single natural logarithm is 0.01234567901.
What is natural logarithm?Given in the question an expression
ln 3 + 5 ln 3
ln 3 + ln [tex]3^{5}[/tex]
Apply multiplication rule
ln (3/[tex]3^{5}[/tex])
[tex]3^{5}[/tex] = 243
so
expression as a single natural logarithm is 0.01234567901.
The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.
The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).
To learn more about natural logarithm from the given link:
brainly.com/question/20785664
#SPJ4
What does this simplify to? -
-4(3-x) - 7x
Answer:
Step-by-step explanation:-12+4x-7x=12-3x.
UR MOM IS GONNA BE SO PROUD OF YOU!!!!!!!!!!!!!
a box in a certain supply room contains four 40-w light bulbs, five 60-w light bulbs, and six 75-w light bulbs. suppose that three bulbs are randomly selected. (a) what is the probability that exactly two of the selected bulbs are rated 75-w? (b) what is the probability that one bulb of each type is selected? (c) what is the probability that all three of the selected bulbs have the same rating?
The probability that exactly two of selected are 75W is 0.2967 , probability that exactly two of the selected bulbs are rated 75W is 0.2637 , probability that one bulb of each type is selected is 0.0747 .
Probability of an event E denoted by P(E) is defined as number of favorable outcomes divided by total number of outcomes.
In the given question
40W bulbs = 4
60W bulbs = 5
75W bulbs = 6
Total number of bulbs = 4+5+6=15.
Part(a)
probability that exactly two of the selected bulbs are rated 75-w
Selection of 3 bulbs from 15 bulbs can be done in C(15,3) ways.
[tex]=\frac{15!}{3!*12!}[/tex]
[tex]=\frac{15*14*13*12!}{12!*3!} \\ \\ =\frac{15*14*13}{3*2*1}[/tex]
=455 ways
Total number of ways = 455 ...(i)
Now,
Number of ways of selecting 2 ,75W bulbs and 1 bulb from the remaining is C(6,2)*C(9,1).
= C(6,2)*C(9,1)
[tex]=\frac{6!}{2!*4!} *\frac{9!}{1!*8!} \\ \\ =\frac{6*5*4!}{2*4!} *\frac{9*8!}{8!}[/tex]
[tex]=\frac{6*5}{2} *9\\ \\ =15*9\\ \\ =135[/tex]
the probability that exactly two selected bulbs are rated 75W = 135/455 =0.2967
Part(b)
probability that one bulb of each type is selected .
Number of ways of selecting one bulb from each type = selecting 1 bulb from four 40W bulbs + 1 bulb from 60W bulbs + 1 bulb from 75W bulbs.
Number of ways of selecting one bulb from each type=C(4,1)*C(5,1)*C(6,1)
[tex]=C(4,1)*C(5,1)*C(6,1)\\ \\ =\frac{4!}{3!*1!} *\frac{5!}{4!*1!} *\frac{6!}{5!*1!}[/tex]
[tex]=\frac{4*3!}{3!} *\frac{5*4!}{4!} *\frac{6*5!}{5!}[/tex] ...( as 1!=1)
[tex]=4*5*6\\ \\ =120[/tex]
Number of ways of selecting one bulb from each type = 120
Total number of ways = 455 ...from equation (i)
Probability that exactly two bulbs selected are rated 75W =120/455
=0.2637
Part(c)
probability that all three of the selected bulbs have the same rating
Number of ways three bulbs of same rating are selected = (all 3 from 40W bulbs )+(all 3 are from 60W bulbs )+( all 3 are from 75 W bulbs)
[tex]=C(4,3)+C(5,3)+C(6,3)[/tex]
[tex]=\frac{4!}{1!*3!} +\frac{5!}{2!*3!} +\frac{6!}{3!*3!} \\ \\ =\frac{4*3!}{3!} +\frac{5*4*3!}{2!*3!} +\frac{6*5*4*3!}{3*2*3!}[/tex]...( as1!=1)
[tex]=4+10+20[/tex]
[tex]=34[/tex]
Number of ways three bulbs of same rating are selected = 34
Total number of ways = 455 ...from equation (i)
Probability that all three of the selected bulbs have the same rating=34/455 = 0.0747
Therefore ,(a) the probability that exactly two of selected are 75W is 0.2967 , (b) probability that exactly two of the selected bulbs are rated 75W is 0.2637 (c) probability that one bulb of each type is selected is 0.0747 .
Learn more about Probability here https://brainly.com/question/10829092
#SPJ4
1. What is 2/7 + 1/4
2. 5/9 +3/8
3. 3 5/6- 2 7/15
[Mathematical Solutions]
1.) [tex]\frac{2}{7} + \frac{1}{4} = \frac{15}{28}[/tex]
2.) [tex]\frac{5}{9} +\frac{3}{8} = \frac{67}{72}[/tex]
3.) [tex]3\frac{5}{6} - 2\frac{7}{15} =\frac{41}{30}[/tex] as the Exact Form, or [tex]1\frac{11}{30}[/tex] as the Mixed Number Form.
Hope this helps!