Answers:
1) The value of AB is: " 59 units."
2) The value of BC is: "21 units."
_______
3) The value of AB + BC ;
= 59 units + 21 units ;
= [the value of AC ] ;
= {" 80 units ".}.
_______
Step-by-step explanation:
Given the following—and based on the assumption that we are dealing with: "geometric lines"—and/or: "geometric line segments"—we are asked to:
"Find the value of: " AB and BC" .
{Given: " AB = (8x + 3) ; BC = (2x + 7) ; AC = 80 ".}.
----------------------------------------------------------------------------------------------=-
Note: The following "line graphs" are "Not Drawn to Scale."
| (8x + 3) | (2x + 7) |
|<--------------->|<------------------->|
<----·|----------------->|<------------------->| {Note: "Not drawn to scale."}.
A B C
<-----|----------------->|<------------------->|
A C
<-----|<--------------------------------------->|
<-----|----------------------------------------->|
A {"AC = 80 ".} C
<---|------------------------------------------>|
A {"AC = 80 ".}. C
| (8x + 3) ; + (2x + 7) = 80 ;
<-----|----------------->|<--------------------->I
A B C
So: We have to find the value of:
1) AB ; which is: (8x + 3) ; And:
2) BC ; which is: (2x + 7) .
To get these values; we need to find the value for "x".
So: (8x + 3) + (2x + 7) = 80 ;
➝ 8x + 3 + 2x + 7 = 80 ;
➝ Now, Let us combine the "like terms" on the "left-hand side" of the equation:
+8x + 2x + 3 + 7 ;
➝ to get: + 8x + 2x = + 10x ; and:
+3 + 7 = 10 ;
To get: "10x + 10" ;
Now, we can rewrite the equation:
{" 70 ÷ 10 = 7 ."}. " 10x + 10 = 80 ;
_____________________
To solve for "x" ; there are many ways:
_____________________
Method 1) We have: " 10x + 10 = 80 " ;
➝ Now, subtract "10" from each side of the question;
10x + 10 − 10 = 80 − 10 ;
to get: 10x = 70 ;
➝ Now, divide each side of the equation by: "10" ; to isolate "x" on one side of the equation; & to solve for "x" ;
10x /10 = 70 /10 ; to get: " x = 7 "
Method 2)
At the moment above in which we have:
" 10x = 70 " ; we know that "10x ÷ 10 = 1x" ; and then "70 ÷ 10 = 7 ".
{Note that any value; divided by "10" ; is equal to:
{"that value" moved Back by: "One" decimal space.}.
So: " 1x = 7 " ; ↔ " x = 7 ".
_____________
Method 3) :
When we have: " 10x /10 = 70 /10 " ; we have " 1x " on the "left-hand side" of the equation; and: "{ 70 /10 }" = {" 70 ÷ 10 = 7 ."}.
Note that: {" 70 ÷ 10 = 7 "} ; can be determined in many ways;
For instance: {" 70 ÷ 10 = ? "} ;
➝ The zeros for Both the numerator and denominator "cancel out"—
and we have: " [tex]\frac{70}{10}[/tex] " ;
➝ Cancel out each of the two (2) "zeros" ; and we have: " [tex]\frac{7}{1} = 7.[/tex] "
➝ This is assuming that we figure out that: " [tex]\frac{10x}{10}=1x =x[/tex] ."
___________
Now; let's find the correct values for this Brainly Question:
1) AB = 8x + 3 ;
Substitute our calculated value for "x" ; and solve:
➝ AB = 8x + 3 ; ↔ 8(7) + 3 = 56 + 3 = 59 .
➝ BC = 2x + 7 ; ↔ 2(7) + 7 = 14 + 7 = 21 .
Note:
➝ AC = 80 = AB + BC ≟ 59 + 21 ≟ 80 ? Yes!
____________
Answers:
1) The value of AB is: " 59 units."
___
2) The value of BC is: "21 units."
___
3) The value of AB + BC ;
= 59 units + 21 units = {The value of AC } = "80 units".}.
_____
Hope this answer—along with explanations—is helpful to you.
Best wishes in your academic pursuits!
______
pls help asap, find the height of the cylinder and round to the nearest tenth
Answer:
h = 2.4
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h where r is the radius and h is the height
271.4 = pi ( 6)^2 *h
271.4 = 36* pi* h
Letting 3.14 = pi
271.4 = 113.04 h
Divide each side by 113.04
271.4 /113.04 = 113.04h/113.04
2.424805379 = h
Rounding to the nearest tenth
2.4 = h
OR if we use the pi button
271.4 = 36 * pi *h
Divide each side by 36 pi
271.4/36pi = h
h=2.3997
Rounding to the nearest tenth
h =2.4
a school district transported a total of 409 students and teachers to a zoo buses and vans
each bus transported a total of 55 students and teachers
each van transported a total of 12 students and teachers there were 5 more buses
what is the total number of students and teachers who rode to the zoo vans
Answer: There are 385 students and teachers who rode to the zoo in buses and 24 students and teachers who rode to the zoo in trains.
Step-by-step explanation:
Since we have given that
Total number of students and teachers = 409
Let the number of vans be x
Let the number of buses be x+5
Number of students and teachers each bus transported = 55
Number of students and teachers each van transported = 12
According to question,
Total number of students and teachers who rode to the zoo in buses will be
Total number of students and teachers who rode to the zoo in vans will be
Hence, there are 385 students and teachers who rode to the zoo in buses and 24 students and teachers who rode to the zoo in trains.
calculate exact value of 4 1/5-(1 1/9 ×3)
Answer:
Exact form - 13/15
Decimal Form - 0.86
Step-by-step explanation:
Convert the mixed numbers to improper fractions, then find the LCD and combine
Question
The temperature in Scranton was -12°F at 10 am. By 1 pm the temperature was 1 °F. What was the difference between
the 10 am and 1 pm temperatures?
Provide your answer below:
degrees Fahrenheit
Content attribution
FEEDBACK
MORE INSTRUCTION
I
SUBMIT
Answer:
Step-by-step explanation:
difference=1-(-12)=13°F
To be competitive for admission to four-year universities (UCF, UF, FSU, FAU, FIU, UCF, USF, etc.) what courses should you try to have each year of high school no matter the intended college major or current status of high school graduation requirements?
Answer:
Ask your guidance counselor or a college admissions counselor
Step-by-step explanation:
Keith tabulated the following values for time spent napping in minutes of six of his friends: 23, 35, 17, 30, 20, and 19. The standard deviation is 7.043.
Keith reads that the mean nap is 22 minutes.
t equals fraction numerator x with bar on top minus mu over denominator begin display style bevelled fraction numerator s over denominator square root of n end fraction end style end fraction
The t-statistic for a two-sided test would be __________. Answer choices are rounded to the hundredths place.
Using the t-distribution, the t-statistic for the two-sided test would be of t = 0.7.
What is the test statistic for a t-distribution hypotheses test?The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the expected value.s is the standard deviation of the sample.n is the sample size.The values of the parameters are given as follows:
[tex]\mu = 22, s = 7.043, n = 6[/tex].
The sample mean is:
[tex]\overline{x} = \frac{23 + 35 + 17 + 30 + 20 + 19}{6} = 24[/tex]
Hence the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{24 - 22}{\frac{7.043}{\sqrt{6}}}[/tex]
t = 0.7.
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Using the combination formula, the probability that Rosa's mom chooses sausage and onion is given by:
B. [tex]\frac{1}{C_{8,2}}[/tex].
The order in which the toppings are chosen is not important, hence the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
2 toppings are chosen from a set of 8, hence the number of options is given by:
[tex]C_{8,2}[/tex].
Sausage and onion correspond to one topping, hence the probability is given by:
B. [tex]\frac{1}{C_{8,2}}[/tex].
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How many cubic meters are in 122047.5 cubic inches (with formula please)
Answer:
2 cubic meters
Step-by-step explanation:
1 Cubic Meter = 61023.7441 Cubic Inch
dexamethasone 4 mg/1 ml is available. the MD orders 6000 mcg. how much will the nurse give? (Round to the tenth)
Answer:
1.5 mL
Step-by-step explanation:
The abbreviation mcg stands for "microgram," or 10^-6 grams. The abbreviation mg stands for "milligram," or 10^-3 grams. The relationship between these is ...
1 mg = 1000 mcg
DoseThe order for 6000 mcg is an order for 6(1000 mcg) = 6(1 mg) = 6 mg. At 4 mg/mL, the quantity of dexamethasone required is ...
(6 mg)/(4 mg/mL) = (6/4) mL = 1.5 mL
The nurse will give 1.5 milliliters of dexamethasone.
Yvonne is solving the quadratic equation 6x2 + 24x + 7 = 0 by completing the square. Her first four steps are shown in the table.
A table listing the first few steps in deriving the quadratic formula
In which step did Yvonne first make an error?
The step in which Yvonne first makes an error while solving the quadratic equation by completing the square in step 1.
What is a quadratic equation?A quadratic equation is an equation in which the highest power of the variable is two.
Yvonne is solving the quadratic equation, which is,
6x² +24x +7 =0
He is solving the above equation by completing the square.
The first step to solving this quadratic equation by completing the square is, Take the constant value 7 at the opposite side of the equation as,
6x² +24x = -7
Here, the number seven was a positive number, which we have changed to negative because this number brings the other side of the equation.
In the image attached below, the first step of the Yvonne while solving the equation by completing the square is,
6x² +24x = 7
Here, Yvonne does not change the sign of the number 7 while taking it to another side of the equation.
Hence, the step in which Yvonne first makes an error while solving the quadratic equation by completing the square is step 1.
The table is attached with the answer below
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Use the data tab of the graphing tool to display the data from Luther’s table in a scatter plot, with x representing the number of pitches thrown and y representing the average speed of the pitches. Select the relationship tab to add the best fit linear function to the graph.
What are the equation of the line of best fit and the absolute value of the correlation coefficient?
The equation of the line of best fit is y = -4.75X + 88.6 and the absolute value of the correlation coefficient is 0.906
The equation of the line of best fitThe data values of the question are as follows:
(1, 88), (2, 75), (3, 71), (4, 69), (5,66), (6, 68), (7, 50)
To determine the equation of the line of best fit, we make use of a graphing calculator.
From the graphing calculator, we have the following summary:
Sum of X = 28Sum of Y = 487Mean X = 4Mean Y = 69.5714Sum of squares (SSX) = 28Sum of products (SP) = -133The value of R is: -0.906.The line of best fit equation is
y = bx + a
Where
b = SP/SSX = -133/28 = -4.75
a = MY - bMX = 69.57 - (-4.75*4) = 88.57143
So, we have:
y = -4.75X + 88.57143
Approximate
y = -4.75X + 88.6
Hence, the equation of the line of best fit is y = -4.75X + 88.6
The absolute value of the correlation coefficientIn (a), we have:
The value of R is: -0.906.
This represents the correlation coefficient.
The absolute value is
|R| = 0.906.
Hence, the absolute value of the correlation coefficient is 0.906
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find the volume pls
Answer:
i think it is 340
Step-by-step explanation:
Find the equations of the following lines.
a) Parallel to 2 + − 3 = 0 and passing through ( −4, 5)
b) Perpendicular to 2 = + 5 and passing through ( −1, 4)
Which of these graphs represents a function?
Answer:
Should be W
Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function.
Hope this helps!!
math
look at the picture
Answer:
Rational
Step-by-step explanation:
cause I don't know how to explain
Solve the system of equations
1/2x+6y=12
y=x+15
Please I need help. Also if you know the answer could you help me learn how to solve it?
Answer:
x=-12,y=3
Step-by-step explanation:
1/2x+6y=12
y=x+15
since y=x+15
substitute y in first equation, we have
1/2x+6(x+15)=12
open the bracket
1/2x+6x+90=12
1/2x+6x=12-90
x/2+6x= -78
13x/2=-78
13x=2×-78
x=-12
Now x=-12, put x=-12 in the second equation, we have
y=x+15
y=-12+15
y=3
hope it helps
Answer:
x=-8, y=2
Step-by-step explanation:
if 1/2x+6y=12 then 1/2x+y=2 and x+y=1 and y=1-x..if y=1-x then 1-x=x=15 and 2x=16 so x=8 if x=8 then 1/2(8) +6y=12 or 4=6y=12.. then 2y=4 and y=2
a family has 8 girls and 4 boys. a total of 3 children must be chosen to speak on behalf of their family at a local benefit. what is the probability that no girls and 3 boys will be chosen help quickly someone
Answer:
1/55
Step-by-step explanation:the probability of choosing 3 boys.
The probability of choosing the first boy =4/12
The probability of choosing the second boy =3/11
The probability of choosing the third boy =2/10
The probability of choosing the 3 boys will be,
=4/12×3/11×2/10
=24/1320
Find the value of z. You must show work to receive full credit.
The value of z from the cyclic quadrilateral as described is; 173/22.
What is the value of z?Since the quadrilateral TUVW is a cyclic quadrilateral, it follows that the opposite angles of the quadrilateral are supplementary and hence, amount to 180.
On this note, 14z -7 +8z = 360
22z -7 = 180
22z = 180 -7
z = 173/22
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Sketch the graph by hand using asymptotes and intercepts, but not derivatives. Then use your sketch as a guide to producing graphs (with a graphing device) that display the major features of the curve. Use these graphs to estimate the maximum and minimum values. (Round your answers to three decimal places.)
f(x) = (2x+3)²(x-2)^5/x³(x-5)²
The local minima of [tex]f\left(x\right)=\ \frac{\left(2x+3\right)^2\left(x\ -2\right)^5}{x^3\left(x-5\right)^2}[/tex] are (x, f(x)) = (-1.5, 0) and (7.980, 609.174)
How to determine the local minima?The function is given as:
[tex]f\left(x\right)=\ \frac{\left(2x+3\right)^2\left(x\ -2\right)^5}{x^3\left(x-5\right)^2}[/tex]
See attachment for the graph of the function f(x)
From the attached graph, we have the following minima:
Minimum = (-1.5, 0)
Minimum = (7.980, 609.174)
The above means that, the local minima are
(x, f(x)) = (-1.5, 0) and (7.980, 609.174)
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Ali rented a truck for one day. There was a base fee of , and there was an additional charge of cents for each mile driven. Ali had to pay when he returned the truck. For how many miles did he drive the truck?
Using a linear function, it is found that he drove the truck for 240 miles.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Researching the problem on the internet, there was a base fee of $18.99, which is the y-intercept, and there was an additional charge of 75 cents for each mile driven, which is the slope, hence the cost function for m miles driven is given by:
C(m) = 18.99 + 0.75m.
He paid $199, hence the number of miles he drove is found as follows:
C(m) = 18.99 + 0.75m.
199 = 18.99 + 0.75m
m = (199 - 18.99)/0.75
m = 240 miles.
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Rebecca earned $115 in simple interest for 8 months at an annual interest rate of 3%. How much money did she start with in her account?
The amount of money she started with is $5750
How to determine the amount she start with?The given parameters are:
Interest = $115
Rate = 3%
Time = 8 months
The amount she start with (P) is calculated using:
P = I/(RT/12)
This gives
P = 115/(3% * 8/12)
Evaluate the product
P = 115/(0.02)
Divide
P = 5750
Hence, the amount of money she started with is $5750
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Geometry
Pls list steps so I can learn :)
(a) The arc length of each of the two smaller semicircles is [tex]4\pi[/tex], and the arc length of each of the two larger semicircles is [tex]15\pi[/tex]. Therefore, the perimeter is [tex]2(4\pi)+2(15\pi)=38\pi[/tex].
(b) The area of each of the smaller semicircles is [tex]\frac{1}{2}(\pi)(4^2)=8\pi[/tex], and the areaof each of the larger semicircles is [tex]\frac{1}{2}(\pi)(15^2)}=\frac{225\pi}{2}[/tex].
So, the combined areas of the four semicircles is [tex]241\pi[/tex].
The area of the rectangle is 60, so the total area is [tex]241\pi+60[/tex].
11a.) From the early 1980's through 2012, the number of adults enrolled in Bachelor Degree programs
has steadily increased. In 1983, 10.8 million adults were in enrolled in a Bachelor Degree program while
in 2012, 20.6 million adults were enrolled. Write an approximate linear equation that would model
these data where t = time in years after 1983 and B is the number of adults in millions in the US in a
Bachelor Degree program. (Source: http://nces.ed.gov/)
(a) B = 0.338t+20.6
(b) B = -0.338t+20.6
(c) B = 0.338t - 10.8 (d) B = 0.338t+10.
it's is a if you didn't know
An approximate linear equation that would model these data is:
(a) B = 0.338t+20.6
How to write the linear equation?The general form of a linear equation in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
We are told that In 1983, 10.8 million adults were in enrolled in a Bachelor Degree program while in 2012, 20.6 million adults were enrolled.
Thus:
Rate of increase = (20.6 - 10.8)/(2012 - 1983)
Rate of increase = 9.8/29 = 0.338
Thus, the equation is:
B = 0.338t+20.6
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S
Warm-Up
Determining if a Relationship Is a Function
Determine if each set of ordered pairs represents a function.
(2, 3), (6,-5), (-1, 3)
Function
(1,9), (-3,-2) (1,-4)
(7.-4), (0, 9), (2,-2)
(0, 3), (0, 7), (4,0)
(-6, 5), (-5, 6), (8, 2)
Not a Function
Using it's concept, the set of ordered pairs that represent a function are:
(2, 3), (6,-5), (-1, 3)(7.-4), (0, 9), (2,-2)(-6, 5), (-5, 6), (8, 2)The set of ordered pairs that do not represent a function are:
(1,9), (-3,-2) (1,-4)(0, 3), (0, 7), (4,0)When does a relation represents a function?A relation represents a function if each input X is mapped to only one output Y.
At (1,9), (-3,-2) (1,-4), input 1 is mapped to outputs 9 and -4, hence it is not a function.
At (0, 3), (0, 7), (4,0), input 0 is mapped to outputs 3 and 7, hence it is not a function.
For the other relations, each input is mapped to only one output, hence they are functions.
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The bookstore sells packages of 15 pens
each and 12 pencils each. They want the
same number of pens and pencils in their
next order. Find the smallest number of
packages of each they can buy.
Considering the definition of least common multiple, this means that smallest number of packages of each they can buy is 60.
Least common multipleA number is a multiple of another when it contains it exactly n times. In other words, the multiples of a number are the ones you get when you multiply one number by another.
The least common multiple allows us to know what is the smallest number that is a multiple of a certain set of numbers.
One procedure for calculating the least common multiple is to break each number into prime factors. Then the common and uncommon factors are raised to the highest exponent, which must be multiplied.
Smallest number of packagesTo calculate the smallest number of packages of each they can buy, you calculate the least common multiple.
First, the decomposition of the numbers into prime factors is carried out:
15= 3×5
12= 2×2×3= 2²×3
Then, the least common multiple is calculated as 2²×3×5
Solving, the least common multiple between 12 and 15 is 60.
Finally, this means that smallest number of packages of each they can buy is 60.
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Find the no. of digits in 9 to the power 33
There are 32 no.of digits in
[tex]9[/tex] to the power of [tex]33 = 9^33 = 30 9031543826 3261236192[/tex]0641803529.
Step-by-step explanation: As the exponent is a positive integer, exponentiation means a repeated multiplication:
9 to the 33rd power =[tex]{9*....*9}[/tex] 33times
The exponent of the number 9, 33, also called index or power, denotes how many times to multiply the base (9).
Thus, we can answer what is 9 to the 33rd power as
[tex]9[/tex] to the power of [tex]33 = 9^33 = 30 9031543826 3261236192[/tex]0641803529.
Reference link-
Find the no. of digits in 9 to the power 33 - Brainly.comhttps://brainly.com ›
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There exist 32 digits in 9 to the power [tex]33 = 9^{33}[/tex] of
30903154382632612361920641803529.
How to estimate the power of digits?The power of a numeral stands for how many multiples of the number there exist. The base of the number stands for the number itself and lives in front of the exponent. The exponent stands for the smaller number written above and to the right of the base. Positive exponents result in the base value existing multiplied by itself numerous times.
As the exponent exists as a positive integer, exponentiation signifies repeated multiplication.
9 to the 33rd power [tex]$=9* ........*9*[/tex] 33 times
The exponent of the number 9, 33, even named index or power, indicates how many times to multiply the base (9).
Therefore, we can answer what exists 9 to the 33rd power as 9 to the power of 33 = [tex]9^{33}[/tex] to the power of 30903154382632612361920641803529.
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Common denominator for 16/25 and 13/20
Answer: LCD = 100
Step-by-step explanation:
16/25 = 64/100
13/20 = 65/100
John currently pays $500 monthly towards his minimum payments on his credit cards. , John now pays $350 towards the same credit cards through his debt relief program. How much does John save off his minimums after 3 months
The amount John saves off his minimums after 3 months is $450
Calculating amount savedFrom the question, we are to determine the amount John saves off his minimums after 3 months
The amount John saves off his minimums after 3 months =
($500 - $350) × 3
$150 × 3
= $450
Hence, the amount John saves off his minimums after 3 months is $450
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84 2/3% to a fraction in lowest terms
The evaluation of 84 2/3% to a fraction in its lowest term is [tex]\mathbf{ \dfrac{127}{150} }[/tex]
What is a fraction?Fractions are sections or parts of a whole. They are divided into two parts, the numerator, and the denominator.
From the given information, we are to convert a mixed fraction into its lowest terms. By doing that, we are to convert it to an improper fraction.
[tex]\mathbf{= 84 \dfrac{2}{3}\%}[/tex]
[tex]\mathbf{= \dfrac{(84 \times 3)+2}{3} \%}[/tex]
[tex]\mathbf{= \dfrac{254}{3} \%}[/tex]
[tex]\mathbf{= \dfrac{254}{3} \times \dfrac{1}{100}}[/tex]
[tex]\mathbf{= \dfrac{254}{300} }[/tex]
Divide both the numerator and denominator by (2)
[tex]\mathbf{= \dfrac{127}{150} }[/tex]
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What’s the derivative of the function: A) f(x)= 1/x , in point 2. B) f(x)= 5x^2 , in point 3
Using the power rule, the derivatives are given as follows:
a) [tex]f^{\prime}(2) = -\frac{1}{4}[/tex].
b) [tex]f^{\prime}(3) = 30[/tex].
What is the power rule for a derivative?Suppose we have a power function given by:
[tex]f(x) = x^n[/tex]
The derivative of the function is given by:
[tex]f^{\prime}(x) = n \times x^{n-1}[/tex]
Item a:
The function is:
[tex]f(x) = \frac{1}{x} = x^{-1}[/tex]
Then the derivative is:
[tex]f^{\prime}(x) = -x^{-2} = -\frac{1}{x^2}[/tex]
When x = 2, the derivative is:
[tex]f^{\prime}(2) = -\frac{1}{4}[/tex]
Item b:
The function is:
[tex]f(x) = 5x^2[/tex]
Then the derivative is:
[tex]f^{\prime}(x) = 10x[/tex]
When x = 3, the derivative is:
[tex]f^{\prime}(3) = 30[/tex]
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