Answer:
x=7
EF = 5
DF = 16
Step-by-step explanation:
DF = DE + EF
3x-5 = 11 + 2x-9
Combine like terms
3x-5 = 2x+2
Subtract 2x from each side
3x-5 -2x = 2x+2-2x
x-5 = 2
Add 5 to each side
x-5+5 = 2+5
x=7
EF = 2x-7 =2*7-9 = 14-9 = 5
DF = 11 +5 =16
Answer:
x=7
Step-by-step explanation:
11+(2x-9) = 3x-5
2+2x=3x-5
7=x
Find the area of this circle
Answer:
314ft²
Step-by-step explanation:
A = 3.14(10²)
A = 3.14 x 100
A = 314ft²
Answer:
Area is 314 ft²
Step-by-step explanation:
[tex]A = \pi {r}^{2} [/tex]
r is radius,
[tex]r = \frac{diameter}{2} = \frac{20}{2} = 10 \: ft[/tex]
therefore:
[tex]A = 3.14 \times {10}^{2} \\ A = 3.14 \times 100 \\ A = 314 \: {ft}^{2} [/tex]
15. Ankita bought 20 copy for Rs. 25 each. She got profit of Rs.200 while selling it. Find selling price of the copies. no
Answer:
SP=Rs.700
Step-by-step explanation:
cost price of a copy=R's.25
cost price of 20copy=20×25=Rs.500
profit=Rs.200
selling price of 20 copies=?
Now, we know that,
profit=sp-cp
or, 200=sp-500
or, 200+500=sp
thus, SP=Rs.700
Hence, the selling price of 20copies is 700.
test the validity of the following whenever he participates in a race, he is the winner. either he participates in the race or he is sick he is not the winner. therefore he is sick
To test the validity of a given argument, we need to see if we can find a counter-example that makes one of the statements non-valid. If after analyzing the statements we can't find a counterargument, then we can conclude that the argument is valid.
Here we will find that the argument is valid.
We can write this as:
If he participates in a race then he is the winner.
Either he participates in the race, or he is sick.
He is not the winner, then, he is sick.
Now, from the first statement, we know that always that this person participates in a race, he wins.
From the second statement we know that he only participates if he is not sick, we can rewrite that one as:
"If he is sick, then he does not participate in the race".
Finally, from the third one, if he does not win, then he is sick.
This makes sense, he only does not participate when he is sick, then the only races where he is not the winner, are these races where he does not participate, and he does not participate only if he is sick, then this is a valid argument.
Concluding, the 3 statements are valid, as we can't find any counterargument to any of these 3.
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What is the exact maximum and minimum values of f(x)=[tex]\sqrt{x+x^2} -2\sqrt{x}[/tex] on [0,4]?
Answer:
[tex]\displaystyle \text{min} = \frac{\sqrt{3+2\sqrt{3}}}{2} - \frac{2\sqrt[4]{3}}{\sqrt{2}} \text{ at } x = \frac{\sqrt{3}}{2}\text{ and } \\ \\ \text{max} = 2\sqrt{5} -4 \text{ at } x = 4[/tex]
Step-by-step explanation:
We want to find the maximum and minimum values of the function:
[tex]\displaystyle f(x) = \sqrt{x + x^2} - 2\sqrt{x}[/tex]
On the interval [0, 4].
First, evaluate its endpoints:
[tex]\displaystyle \begin{aligned} f(0) &= \sqrt{(0)+(0)^2} - 2\sqrt{0} \\ &= 0 \\ \\ f(4) &= \sqrt{(4)+(4)^2} - 2\sqrt{(4)} \\ &= 2\sqrt{5} -4 \end{aligned}[/tex]
Recall that the extrema of a function occurs at its critical points; that is, where its derivative equals zero (or is undefined).
Take the derivative of both sides:
[tex]\displaystyle f'(x) = \frac{d}{dx}\left[ \sqrt{x + x^2} - 2\sqrt{x}\right][/tex]
Differentiate:
[tex]\displaystyle \begin{aligned} f'(x) &= \frac{1}{2\sqrt{x + x^2}} \cdot (1 + 2x) - 2\left(\frac{1}{2\sqrt{x}}\right) \\ \\ &= \frac{2x+1}{2\sqrt{x+x^2}} - \frac{1}{\sqrt{x}} \\ \\\end{aligned}[/tex]
Note that the derivative is undefined at x = 0. Hence, x = 0 is a critical point.
Solve for the zeros of the derivative:
[tex]\displaystyle\begin{aligned} \frac{2x+1}{2\sqrt{x + x^2}} - \frac{1}{\sqrt{x}} &= 0\\ \\ \frac{2x+1}{2\sqrt{x}\sqrt{1 + x }} - \frac{1}{\sqrt{x}} &= 0 \\ \\ \frac{2x+1}{2\sqrt{1+x}} - 1 &= 0\\ \\ 2x + 1 &= 2\sqrt{1+x} \\ \\ 4x^2 + 4x + 1 &= 4 + 4x \\ \\ x^2 &= \frac{3}{4} \\ \\ x= \frac{\sqrt{3}}{2} \end{aligned}[/tex]
Therefore, our only two critical points are at x = 0 and x = √3/2:
Evaluate the function at x = √3/2:
[tex]\displaystyle \begin{aligned} f\left(\frac{\sqrt{3}}{2}\right) &= \sqrt{\left(\frac{\sqrt{3}}{2} \right)+ \left(\frac{\sqrt{3}}{2}\right)^2} - 2 \sqrt{\left(\frac{\sqrt{3}}{2}\right)} \\ \\ &= \frac{\sqrt{3+2\sqrt{3}}}{2}- \frac{2\sqrt[4]{3}}{\sqrt{2}} \\ \\ &\approx -0.5900\end{aligned}[/tex]
In conclusion: the exact maximum and minimum values of f on the interval [0, 4] is:
[tex]\displaystyle \text{min} = \frac{\sqrt{3+2\sqrt{3}}}{2} - \frac{2\sqrt[4]{3}}{\sqrt{2}} \text{ at } x = \frac{\sqrt{3}}{2}\text{ and } \\ \\ \text{max} = 2\sqrt{5} -4 \text{ at } x = 4[/tex]
When subtracting a negative number from a positive number, move to the left on the number
line.
A.True
B.False
The product of two whole numbers is 891 and their sum is 60 , what is the two numbers
Answer:
33 & 27
I am positive !!!!!!!!!!!!
if k=(a,b,c) and B=(10,5) find b×k
Answer:
nose eee e e e e e e e e
Step-by-step explanation:
qhhabbejeheh0
Answer:
IS BIGGNER
Step-by-step explanation:
ABC WINNER ZILONG
ANSWERRR BY✏
SUGIONO REALL☠
Use the Distributive Property to multiply. 2(b – 7)
Answer:
2b - 14
Step-by-step explanation:
2(b – 7)
2b - 14
Answer:
[tex]2b-14[/tex]
Step-by-step explanation:
Using the distributive property, [tex]2(b-7)[/tex] can be written as [tex](2\cdot b)-(2\cdot7)[/tex] which solved/simplified is [tex]2b-14[/tex]
Man, it's late! Well, hope this helped you out and answered your question!
2/3|3x-6|=4(x-2)
solve for x; show your work
Will award brainliest
HELP PLEASE I DONT HAVE MUCH TIME!!!
Answer:
B
Step-by-step explanation:
The other answers don't divide into rational numbers
What is 432,553,602 in word form.
Answer:
four hundred and thirty two million, five hundred and fifty three thousand, six hundred and two
Step-by-step explanation:
Answer:
Four hundred thirty-two million, five hundred fifty-three thousand, six hundred and two.
Step-by-step explanation:
Pls Say
hard question
Answer:
Range is 19.54
Step-by-step explanation:
I. If R = H - L
when R is Range, H is highest value and L is lowest value
R = 25.6 - 6.06
R = 19.54
Pls pls pls helpp , im begging you , will mark the brainliest
Answer:
angle f=147 degrees (alternate angles)
angle e= 33 degrees
Step-by-step explanation:
angle d =147 degrees
angle f=147 degrees (alternate angles)
angle e +angle d=180 (allied angles)
e+ 147 =180
e =180-147
e = 33 degrees
help me out with this!
Answer:
k = 70
Step-by-step explanation:
Since we have been given the value of x to be -ve5 (-5),
we multiply 6 and -5( value of x). Which gives;
-30.
Then add the answer (-30) to 100.
-
K = -30 + 100
= 100 - 30
=70
Note;
(+ * + = +)
( + * - = -)
(- * - = +)
I hope this helps you.
Answer:
[tex]k=70[/tex]
Step-by-step explanation:
[tex]k=6x+100[/tex]
[tex]x=-5[/tex]
[tex]k=6(-5)+100[/tex]
Remove parentheses:- [tex]\left(-a\right)=-a[/tex]
[tex]k=-6\times 5+100[/tex]
Multiply [tex]6\times5= 30[/tex]
[tex]k=-30+100[/tex]
Add [tex]-30+100=70[/tex]
[tex]k=70[/tex]
OAmalOHopeO
7-15
Dividing decimals
Answer:
7-15= -8
Step-by-step explanation:
Identify A, B and C when the following function is written in Standard Form:
3y - 5 = 0
A=
B =
C=
How many of hours of work is normal for a shift?
Answer: 7-9
Step-by-step explanation: normal job hours
Like an 8, a 9-5 is what most people have so over 40 hours is overtime
The product of 2 and a number k, subtracted from 17
A. 2+k+17
B. 2k+17
c. 17-2k
D. 2k-17
hi <3
product means multiplication, therefore we know there has to be a '2k' and we can eliminate option A
also, there is a mention of subtraction, so we can also eliminate option B
now we are left with C and D
it is stated that it is being subtracted FROM 17, therefore the 17 would have to come first
in short, your answer is option C
hope this helps :)
The product of 2 and a number k, subtracted from 17 is the expression: c. 17-2k.
What is an expression?An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
here, we have,
given that,
The product of 2 and a number k, subtracted from 17
we have to find the expression for given statement.
let the number be x
now, we have,
The product of 2 and a number k,
i.e. 2*k = 2k
then, subtracted from 17
i.e. 17 - 2k
so, we get,
x = 17 - 2k
Hence, The product of 2 and a number k, subtracted from 17 is the expression: c. 17-2k.
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Is (7,-2) a solution to the equation x - 4y = 15?
Please show work to help me understand.
Answer:
yes
Step-by-step explanation:
x - 4y = 15
Substitute the point into the equation and see if the equation is true
7 -4(-2) = 15
7+8 = 15
15 =15
This is true so the point is a solution to the equation
Urgently needed the answer
Answer:
option b is the correct answer.
Explanation is beloe
Step-by-step explanation:
x²+y²=9
xy=8
x+y=?
Now,
(x+y)²=x²+2×x×y+y²
(x+y)²=x²+2xy+y²
(x+y)²=x²+y²+2xy
(x+y)²=9+2×8
(x+y)²=9+16
(x+y)²=25
(x+y)²=5²
x+y=±5
I hope it helped U
stay safe stay happy
Step-by-step explanation:
[tex]we \: have \: {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy \\ here \: {x}^{2} + {y}^{2} = 9 \\ xy = 8 \\ then {(x + y)}^{2} = 9 + 2 \times 8 \\ {(x + y)}^{2} = 9 + 16 = 25 \\ {(x + y)}^{2} = 25 \\ x + y = \sqrt{25} = +/-5 \\ thank \: you[/tex]
Christine made $20,000 in taxable income last year. Suppose the income tax rate is 15% for the first $8000 plus 19% for the amount over $8000. How much must Christine pay in income tax for last year?
Answer:
$3480
Step-by-step explanation:
We know that the tax rate for the first $8000 is 15% and after $8000 the tax is 19%.
This means the total amount of money that Christine have to pay is equal to $8000 × 15% + ($20000 (the total) - $8000 (the amount that she already paid for the first $8000)) × 19%
This is equal to $1200 + $12000 × 19%
= $1200 + $2280
= $3480
Therefore, Christine must pay $3480 in income tax.
A bag contains 8 red marbles, 3 blue marbles, and 1 green marble. What is the probability that a randomly selected marble is not blue?
Answer:
.75
Step-by-step explanation:
8 red marbles, 3 blue marbles, and 1 green marble = 12 marbles
P( not blue) = marbles that are not blue / total
=(8red+1 green) / 12
=9/12
= 3/4
.75
Please Help!!
Find the equation (in terms of x) of the line through the points (-5,-4) and (4,1)
Step-by-step explanation:
we first find the gradient
when y1=-4, x1=-5 and y2=1, x2=4
gradient={(y2-y1)÷(x2-x1)}
gradient={1-(-4)}÷{4-(-5)}
gradient=(1+4)÷(4+5)
gradient=5÷9 OR 0.5555
To find the equation interm of x
we substitute for the gradient in the formula
y-y1=gradient (x-x1)
y-(-4)=(5÷9)(x-×-5)
y+4=(5÷9)(x+5)
y+4=(5x+25)÷9 Cross multiply ✖️
9(y+4)=(5x+25)(1)
9y+36=5x+25 collect like terms
9y=5x+25-36
9y=5x-11 divide both sides by 9
y=(5x-11)÷9.......ans
14. The cost of 10 dozen of caps is Rs.800. How many caps can bebought for Rs.200.
Answer:
123 456lcm divison method
Bob and Nan have 2 dozen chocolate chip cookies and
18 peanut butter cookies. They are preparing gift baskets for
their friends. They plan to put 4 chocolate chip cookies and
3 peanut butter cookies in each basket. What is the largest
number of baskets they can make and still have enough
cookies?
A 2 baskets
B 4 baskets
C 9 baskets
D 6 baskets
Answer:
it's D
Step-by-step explanation:
2 dozen is 24 so we have 18 pnt butter and 24 choc chip.
they're putting 4 choc chp in each so do 24/4
they're putting 3 pnt butter in each so do 18/3
both are 6 so D is the answer
ANSWER FAST 50 POINTS PLEASE !!!
Identify the property that justifies each step asked about in the answer area below.
Line 1: (9+x)x
Line 2: x(9+x)
Line 3: x(x+9)
Line 1-Line 2-Associative property .
Line 2-Line 3- Distributive property
Solution:-
[tex]\\ \rm\longmapsto (9+x)x[/tex]
[tex]\\ \rm\longmapsto x(x+9)[/tex]
[tex]\\ \rm\longmapsto x(9+x)[/tex]
[tex]\\ \rm\longmapsto x^2+9[/tex]
Complete the following problem "by hand", using pencil and paper. Start with a general equation, and simplify one step at a time. Or, use the shortcut method shown in class (circling the appropriate values). You must show more than just the answer. Use correct math notation and complete math sentences. The goal is not merely to get the right answer, but to show me that you understand the correct process to arrive at the right answer.
The probability that a randomly selected student is female or left-handed is 107/137.
Probability = required outcome / Total possible outcomes
Probability that student is female or left-handed = [(probability that student is female + probability that female is left-handed)]
Therefore,
Probability that student is female :
P(Female student) = number of female / total number of student
Number of female student = 81
Total number of student = 137
P(Female student) = 81 / 137
P(Left handed student) = number of lefthanded student / total number of student
Number of left handed student = 26
Total number of student = 137= 26 / 137
P(student is female or left-handed) :
P(student is female or left-handed) :[(81/137) + (26/137)] = 107/137
Probability that student is female or left-handed is 107/137
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How is 1.2 x 10 written is standard decimal notation?
Answer:
12
Step-by-step explanation:
1.2*10 = 1.2
Answer:
12
Step-by-step explanation:
the "normal form" to write numbers : just the digits and a decimal point when needed.
so, 1.2 × 10 = 12
12 is the normal, standard decimal notation.
in some cases it can be also 12.0 or 12.00 (especially with money).
the other form is the scientific notation, where a number is written with its leading digits and the power of 10 as the total value "weight". like in this example 1.2 × 10¹
Pls help
The formula for the volume of a pipe with outer radius R, inner radius r and length L is
V=π(R2 − r2)L
What is the value of V when π = 22/7, R =11, r = 9 and L = 7?
Answer:
V=880
Step-by-step explanation:
V=π(R^2 − r^2)L
V=(22/7)*7*(11^2-9^2)
V=880
Identify the property of real numbers that justify the work done to simplify the expression below.
The property of real numbers that justifies the work done to simplify the expressions below is the distributive property of multiplication.
What is the distributive property of multiplication?The distributive property of multiplication states that the same result is obtained by multiplying the sum of two or more addends by a number or multiplying each addend individually and adding the products.
The steps for the distributive property of multiplication are:
Expand the equation.Multiply (distribute) the first numbers of each set, outer numbers, inner numbers, and the last numbers. Combine like terms. Solve the equation and simplify.Thus, the property of real numbers that justifies the work done to simplify the expressions below is the distributive property of multiplication.
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