Answer:
x = 1
Step-by-step explanation:
Let's solve your equation step-by-step.
3x+5=6x+2
Step 1: Subtract 6x from both sides.
3x+5−6x=6x+2−6x
−3x+5=2
Step 2: Subtract 5 from both sides.
−3x+5−5=2−5
−3x=−3
Step 3: Divide both sides by -3.
−3x−3=−3−3
x=1
Answer:
x=1
Hope this helps! <3
Answer:
stuff, look to the explanation for your answers
Step-by-step explanation:
Procedures for the left side: dividing 3 and subtracting 5
Procedures on the left side: subtracting 2 and dividing by 6.
You do these procedures to both sides to get your answer.
Is this relation a function? Justify your answer. 10 9 8 7 5 3 2 1 1 2 3 4 5 6 7 8 9 10 11 A. Yes, because the number of x-values is the same as the number c y-values. B. No, because two points with the same x-value have different y- values. C. Yes, because every x- and y-value is positive. f se two points with the same vevalue have different x-
The correct answer is option B that is No, because two points with the same x-value have different y values.
A relation in mathematics may be defined as the term which describes the relationship between the input and output variables. A function may be defined as the expression in which for one value of input variable x there is only one output variable y. The input variable is called independent variable and output variable is called dependent variable. From the graph given in question it can be seen that at point x = 2 there are two points on the y axis that are y = 2 and y = 11. So, this violates the basic definition of function as for input x there are two outputs y and hence it cannot be regarded as function.
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The next two problems show the attempts of two different students to provide a proof of the same statement. Each proof has something about it that is not quite correct. Explain how you would improve the argument.
We will improve the argument by stating that two intersecting lines have vertically opposite angles equal in magnitude.
We are given a diagram in which we have two lines, namely "m" and "n".The intersection point of the two lines is P.We need to prove that ∠1≅∠3.We know that line "m" is a straight line, so it makes a total angle of 180° on either of its sides.∠1+∠2 = 180°We know that line "n" is a straight line, so it makes a total angle of 180° on either of its sides.∠3+∠2 = 180°From the above two equations, we find that :∠1+∠2 = 180° = ∠3+∠2∠1+∠2 = ∠3+∠2∠1 = ∠3Thus, ∠1≅∠3.To learn more about lines, visit :
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Denasia and Kenya are training to run a half marathon. In the first week of training, Denasia runs 11 miles and Kenya runs 14 miles.
Each week, Denasia increases her weekly total by 2 miles, and Kenya increases her weekly total by 1.5 miles. Write and solve an
equation to find how many weeks after the first week of training Denasia and Kenya will be running the same number of miles.
A. 2w + 14 = 1.5w+11; w=-6 weeks
B. 2w + 11 = 1.5w+14; w=6 weeks
C. 11w+2= 14w +1.5; w=0, 167 weeks
Option B. 2w + 11 = 1.5w + 14, w = 6 weeks is the correct answer
Miles run by Denasia = 11 miles
Miles run by Kenya = 14 miles
Let w represent the number of weeks after which both Kenya and Denasia will be running the same number of miles
Formulating the equation we get:
Miles run by Denasia + Increase in miles each week*Number of weeks = Miles run by Kenya + Increase in miles each week*Number of weeks
11 + 2w = 14 + 1.5w
0.5w = 3
w = 6
Hence, option B is the correct answer according to the given contraints and both Denasia and Kenya will run the same distance in the 6th week
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There are 3 consecutive integers with a sum of 45. What are the integers?
The three consecutive integers are 14, 15, and 16.
Assume the three consecutive integers to be x-1, x, and x+1.
Sum of all three = 45.
x-1 + x + x+1 = 45
3x = 45 (-1 and +1 get cancelled)
x = 45/3
x = 15
the first integer is x-1 = 15 - 1 = 14
the second integer is x = 15
the third integer is x+1 = 15 + 1 = 16
So, the three consecutive integers are 14, 15, and 16.
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PLEASE HELP ASAP!!!!!!!
Rotate R and reflect 90
Step-by-step explanation:
The figure below shows a triangle with vertices A and B on a circle and vertex C outside it. Side AC is tangent to the circle. Side BC is a secant intersecting the circle at point X.What is the measure of angle ACB? (6 points)O 29°O 8°O 16°O 21°
The Solution.
Considering triangle ABC, we have
[tex]\begin{gathered} angle\text{ACB}=180-(90+40+42) \\ =180-172=8^o \end{gathered}[/tex]Hence, the correct answer is 8 degrees (option B)
4x + 10 =-26 solve for x
Answer:
x=-9Step-by-step explanation:
To solve for x, isolate this equation from left to right.
4x+10=-26
First, subtract by 10 from both sides.
4x+10-10=-26-10
Solve.
-26-10=-36
4x=-36
Then, you divide by 4 from both sides.
4x/4=-36/4
Solve.
-36/4=-9
[tex]\Rightarrow \boxed{\sf{x=-9}}[/tex]
As a result, the solution is x=-9, which is the correct answer.
I hope this helps, let me know if you have any questions.
Answer:
-9
Step-by-step explanation:
First you subtract 10 from each side
4x + 10 = -26
-10 -10
then you divide by your x
4x = -36
4 4
the 4s cancel out leaving you with x only
x = -36/4
x = -9
i’ll mark brainliest!
1. (a)The vertex of the function [tex]y=x^{2} +5x-7[/tex] is [tex](-\frac{5}{2} ,-\frac{53}{4} )[/tex]
How is the vertex calculated?
In function [tex]y=x^{2} +5x-7[/tex],
a= 1 ,b= 5, c= -7
For a function [tex]y=ax^{2} +bx+c[/tex] , where (a≠0),
The vertex is [tex](-\frac{b}{2a} ,\frac{4ac-b^{2} }{4a} )[/tex]
[tex]x_v=-\frac{b}{2a}\\\\ =-\frac{5}{2*1} \\\\=-\frac{5}{2} \\\\\\y_v=\frac{4ac-b^{2} }{4a} \\\\=\frac{4*1*(-7)-(5^{2} )}{4*1}\\\\ =-\frac{53}{4}[/tex]
So, vertex [tex](-\frac{5}{2} ,-\frac{53}{4} )[/tex] is minimum because a>0
(b)The solutions are [tex](\frac{\sqrt{53} -5}{2},0) (\frac{-5-\sqrt{53} }{2},0)[/tex]
How is the solution calculated?
When a function [tex]y=ax^{2} +bx+c =0[/tex] where (a≠0),
[tex]x=\frac{-b\pm\sqrt{b^{2} -4ac} }{2a} \\\\x=\frac{-5\pm\sqrt{5^{2} -4(1)(-7)} }{2(1)} \\\\x=\frac{-5\pm\sqrt{53} }{2} \\\\x=\frac{\sqrt{53} -5}{2} , x=\frac{-5-\sqrt{53} }{2} \\\\\text{The solutions are } (\frac{\sqrt{53} -5}{2},0) (\frac{-5-\sqrt{53} }{2},0)[/tex]
2. (a)The vertex of the function [tex]y=-x^{2} +3x+8[/tex] is [tex](\frac{3}{2} ,\frac{41}{4} )[/tex]
How is the vertex calculated?
In function [tex]y=-x^{2} +3x +8[/tex]
a= -1 ,b= 3, c= 8
For a function [tex]y=ax^{2} +bx+c[/tex] , where (a≠0),
The vertex is [tex](-\frac{b}{2a} ,\frac{4ac-b^{2} }{4a} )[/tex]
[tex]x_v=-\frac{b}{2a}\\\\ =-\frac{3}{2*(-1)} \\\\=\frac{3}{2} \\\\\\y_v=\frac{4ac-b^{2} }{4a} \\\\=\frac{4*(-1)*(8)-(3^{2} )}{4*(-1)}\\\\ =\frac{41}{4}[/tex]
So, vertex [tex](\frac{3}{2} ,\frac{41}{4} )[/tex] is maximum because a<0
(b)The solutions are [tex](\frac{3+\sqrt{41} }{2},0) (\frac{3-\sqrt{41} }{2},0)[/tex]
How is the solution calculated?
When a function [tex]y=ax^{2} +bx+c =0[/tex] where (a≠0),
[tex]x=\frac{-b\pm\sqrt{b^{2} -4ac} }{2a} \\\\x=\frac{-3\pm\sqrt{3^{2} -4(-1)(8)} }{2(-1)} \\\\x=\frac{-3\pm\sqrt{41} }{-2} \\\\x=\frac{3\pm\sqrt{41} }{2}\\\\x=\frac{3-\sqrt{41}}{2} , x=\frac{3+\sqrt{41} }{2} \\\\\text{The solutions are } (\frac{3+\sqrt{41} }{2},0) (\frac{3-\sqrt{41} }{2},0)[/tex]
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Find the slope of the line that passes through (1, 6) and (3, 7)
[tex]m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{7 - 6}{3 - 1} \\ m = \frac{1}{2} [/tex]
I ALSO PROVIDED YOU WITH THE FORMULA OF FINDING THE GRADIENT/SLOPE FOR FUTURE USE
HOPE THIS HELPS.
Answer: Y= 1/2x + 5.5
Which number is the smallest?
pls answer fast
Responses
A 4.68 x 10−44.68 x , 10 -4
B 5.48 x 10−85.48 x , 10 -8
C 2.85 x 10−62.85 x , 10 -6,
D 3.24 x 10−53.24 x , 10 -5,
E 1.28 x 10−4
The smallest number from the given options is
[tex]5.48 × {10}^{ - 8} [/tex]
The correct answer option is option d
How to find the smallest number?A.
[tex]1.28 × {10}^{ - 4} [/tex]
= 1.28 × 0.0001
= 0.000128
B.
[tex]2.85 × {10}^{ - 6} [/tex]
= 2.85 × 0.000001
= 0.00000285
C.
[tex]3.24 × {10}^{ - 5} [/tex]
= 3.24 × 0.00001
= 0.0000324
D.
[tex]5.48 × {10}^{ - 8} [/tex]
= 5 48 × 0.00000001
= 0.0000000548
Therefore, the smallest number is
[tex]5.48 × {10}^{ - 8} [/tex]
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PLS HELP!!
Answers: 8,20,35,12
Answer:
the answer is 8.
Step-by-step explanation:
Use the Pythagoras Theorem since it is a triangle.
[tex]a^{2}+b^{2}= c^{2}\\\\a^{2}+15^{2}= 17^{2}\\ a^{2}+225=289\\ a^{2}=289-225\\ a^{2}= 64\\ \sqrt{a}= \sqrt{64}\\ a=8[/tex]
Since you have the hypotenuse and base, just put those into the equation and find the missing side.
The remainder when the expression x^3+6x^2+x+c is divided by x-2 is twice the remainder when the expression is divided by x-1.
show that c=24
Answer:
c = 18
Step-by-step explanation:
According to the remainder theorem, the remainder when f(x) is divided by (x - n) is f(n).
As per question we are given:
f(2) = 2f(1)Substitute and solve for c:
2³ + 6*2² + 2 + c = 2(1³ + 6*1² + 1 + c)8 + 24 + 2 + c = 2(1 + 6 + 1 + c)34 + c = 2(8 + c)34 + c = 16 + 2c2c - c = 34 - 16c = 18Note: I got a different value of c. This may be a result of a typo in the given expression. I provided a guide to solve such problems. Let me know is anything is unclear.
Function: g(x) = 2x2 – 8
For x ≥ 0, the inverse function is f(x)= √
1
2
x + 4
For x ≤ 0, the inverse function is d(x)= – √
1
2
x + 4
A 3-column table has 3 rows. The first column is labeled x with entries negative 8, 0, 10. The second column is labeled f (x) with entries 0, r, s. The third column is labeled d (x) with entries q, negative 2, t.q =
r =
s =
t =
The inverse function of g(x) = 2x² - 8 for each case is given as follows:
x ≥ 0: y = √(0.5x + 4).x < 0: y = -√(0.5x + 4).Inverse functionTo find the inverse function, we exchange the variables x and y in the original function, and then isolate the variable y.
The original function in this problem is given as follows:
g(x) = 2x² - 8.
The function is not one-to-one, hence the inverse is different for x ≥ 0 and for x < 0.
Exchanging the variables, we have that:
x = 2y² - 8.
Isolating the variable y, we have that:
2y² = x + 8
y² = 0.5x + 4 (the entire equation was divided by 2 to isolate y)
y = ± sqrt(0.5x + 4).
For non-negative values, the inverse function is:
y = sqrt(0.5x + 4) = √(0.5x + 4).
For negative values, the inverse function is:
y = -sqrt(0.5x + 4) = -√(0.5x + 4).
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Answer: 0,2,3,-3
Step-by-step explanation:
Tanya sells cars. Her yearly salary is $35,000 plus 8% of her sales. Type and solve an inequality to determine her necessary sales to earn over $50,000.
Tanya yearly salary is
$35000 + 8% of her sales
Let her sales be x
Since, her sales is x
35000 + 0.08x > salary
To determine her necessary sales to earn over $50, 000
Let $50, 000 be her benchmark salary
35,000 + 0.08 * x > 50000
35000 + 0.08x > 50000
0.08x > 50000 - 350000
0.08x > 15000
Divide both sides by 0.08
0.08x/0.08 > 15000/0.08
x > 15000 / 0.08
x > 187,500
Therefore, she will need a sales of 188,000 and above to earn above $50,000
i'm still confused. helpppppppppppppppppppppppppppppppppppppppppppppppppppppp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
I believe you forgot to add the attachment
Step-by-step explanation:
There is no math problem I can see to help you
8.
S
-80
ZX D
lo
Please help
HELP PLEASE
Answer:
[tex]\begin{aligned}&\phantom{=.} \dfrac{1}{8}x \cdot \dfrac{-4}{5}x\\\\&=\dfrac{1}{2} \cdot \dfrac{\boxed{-1}}{5} \cdot x \cdot \boxed{x}\\\\& = \dfrac{\boxed{-1}}{\boxed{10}} \;x\;^\boxed{2}\end{aligned}[/tex]
Step-by-step explanation:
According to the Commutative Property Law of Multiplication, changing the order or position of the numbers does not change the end result.
Therefore, collect like terms by moving the fractions to the left and the variables to the right.
As the denominator of the first fraction has been divided by 4, the numerator of the second fraction should also be divided by 4.
Therefore:
[tex]=\dfrac{1}{2} \cdot \dfrac{\boxed{-1}}{5} \cdot x \cdot \boxed{x}\\[/tex]
[tex]\textsf{Apply\;the\;fraction\;rule} \quad \dfrac{a}{c}\cdot \dfrac{b}{d}=\dfrac{ab}{cd}.[/tex]
[tex]\textsf{Apply\;the\;exponent\;rule}\quad \:aa=a^2.[/tex]
Therefore:
[tex]=\dfrac{\boxed{-1}}{\boxed{10}} \;x\;\boxed{^2}[/tex]
Which exponential equation is equivalent to this logarithmic equation? \log _(5)x - \log _(5)25=7
The exponential equation [tex]14=5^x[/tex] is equivalent to the given logarithmic equation.
Which is the Exponential function?The exponential function that is represented as y=[tex]m^x[/tex], where:
m=base, m>0
x= exponent
Logarithm PropertiesKnowing some of the main logarithm rules.
Product Rule with the same base: you should repeat the base add the logarithms of the factors.example: [tex]log(a*b)= log a + log b[/tex]
Quotient Rule: you should subtract the logarithm of the numerator with the logarithm of the denominator.example: [tex]log\frac{a}{b} = log a - log b[/tex]
Power Rule: you should multiply the exponent by the logarithm of the base
example: [tex]log\frac{a^b} = b*log a[/tex]
For solving this question, you should apply the logarithm rules and rewrite the function as an exponential equation.
[tex]log_5(x)}-{log_5(25)=7[/tex]
[tex]\frac{log_5(x)}{log_5(25)} =7[/tex]
[tex]{log_5(x)}=7{log_5(25)}[/tex]
[tex]{log_5(x)}=7{log_5(5^2)}[/tex]
[tex]{log_5(x)}=7*2[/tex]
[tex]{log_5(x)}=14[/tex]
[tex]x=5^{14^}[/tex]
Therefore, the exponential function is [tex]14=5^x[/tex]
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Can someone please help me! I have no idea what I am doing and have no book to look from!
Answer:
Step-by-step explanation:
1) Find DGE
Bisecting an angle makes it half. A straight line is 180
180/2 = DGE
90 = DGE
2) Find FGE
Bisecting an angle makes it half. A straight line is 180
180/2 = FGE
90 = FGE
3(5y-7)-2(9y-11)=4(8y-13)-17
Answer:[tex]3(5y - 7) - 2(9y - 11) = 4(8y - 13) - 17 \\➪ 15y - 21 - 18y + 22 = 32y - 52 - 17 \\ ➪15y - 18y - 32y = - 52 - 17 + 21 - 22\\➪-35y = - 70 \\➪35y = 70 \\ \: (cancel \: \: out \: "-" \: from \: both \: sides) \\ ➪y = \frac{ 70}{35} = 2 \\ \\ [/tex]
Tʜᴀɴᴋs| (• ◡•)|Hᴏᴘᴇ ɪᴛ ʜᴇʟᴘsHELP MEEE HELP ME HLSP ME
The inequality for the temperature in the house measured by thermostat is; 24° ≤ t ≤ 26°. The highest temperature is 26° C.
What is defined as the term inequality?In mathematics, an inequality is a relationship representations or values that aren't equal to each other. When two numbers are equal, we use the symbol '=', and if they are not equal, we use the symbol ≠.For the given question.
The thermostat at the house is set at 25° C.
Now, there is a deviation of the temperature of 1° C.
Thus,
The lowest temperature measured = 25° C - 1° C = 24° C.
The highest temperature measured = 25° C + 1° C = 26° C.
Let 't' be the temperature of the house.
The inequality will be;
24° ≤ t ≤ 26°
Thus, the maximum value of the temperature will be 26° C.
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-7 -6 -5 -4 -3 -2 ONO MN ++ HA -6-5-4-3-2-1 + 11 2 3 4 5 6 7 8 9 -2 -3 F-4 -5 -6 -7 -A + jo voo Alcon ixth If this is the graph of f(-x) = a +k, then : A. 0 < a < 1 B. a < 0 O c. a> 1 O D. K> 1
The function is
[tex]f(x)=a^{(x+h)}+k[/tex]The limit when x->+/- infinite are (analitically)
[tex]\begin{gathered} \lim _{x\to\infty}f(x)=a^{(\infty+h)}+k=a^{\infty}+k \\ \text{and} \\ \lim _{x\to-\infty}f(x)=a^{(-\infty+h)}+k=\frac{1}{a^{\infty}}+k \\ \end{gathered}[/tex]And, from the figure,
[tex]\begin{gathered} \lim _{x\to\infty}f(x)=\infty \\ \text{and} \\ \lim _{x\to-\infty}f(x)=-4 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \Rightarrow a^{\infty}+k=\infty \\ \Rightarrow a>1 \\ \text{and} \\ \Rightarrow-4=\frac{1}{a^{\infty}}+k,a>1 \\ \Rightarrow-4=k \end{gathered}[/tex]Therefore, the answer is option C, a>1.
n/−3 +5>4 Solve for this
Answer:
N<3
Step-by-step explanation:
0.194805194805...
Convert the decimal into a fraction.
Answer:
The fraction is 15/77Step-by-step explanation:
The repeated part is 194805, six digits. Let the fraction be x.
Convert as follows:
1000000x - x = 194805.194805 ... - 0.194805 ... 999999x = 194805x = 194805/999999Find prime factors of both numerator and denominator and simplify by cancelling common factors:
194805 = 3⁴*5*13*37,999999 = 3³*7*11*13*37.The common factors are:
3³*13*37When they cancel we are left with:
x = (3*5)/(7*11) x = 15/77identify the paragraph proof for the two-column proof. Given: m∠d=125° and m∠r=125° Prove: ∠d≅∠r Two-Column Proof 1. m∠d=125° (Given) 2. m∠r=125° (Given) 3. m∠d=m∠r (Trans. Prop. of = ) 4. ∠d≅∠r (Def. of ≅∠s)
The two column proof is written as follows
Statement Reason
1. m ∠ d = 125° Given
2. m ∠ r = 125° Given
3. m ∠ d = m ∠ r Definition of equality
4. ∠ d ≅ ∠ r Definition of congruent angles
What is two column proof?This is a method of proof used in geometry. It helps to show how the required proof came to be possible. The major items in two column proof is:
StatementReasonwhat is equality?The term equality as used in mathematics is defined to mean that the terms in comparison can be replace by the other
Using the given question as an instance:
m ∠ d = 125° and m ∠ r = 125°
This means that the two angles have same value and they can replace each other.
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Which functions are equivalent to f (x) = RootIndex 4 StartRoot 162 EndRoot Superscript x? Check all that apply.
The functions that are equivalent are
f (x) = 162 Superscript StartFraction x Over 4f (x) = (3 RootIndex 4 StartRoot 2 EndRoot) Superscript xf (x) = left-bracket 3 (2 Superscript one-fourth Baseline) right-bracket Superscript xWhat are roots of a number?
The root of a number is the inverse of the exponents. for instance
a squared has an inverse of square root of a.
mathematically:
a^2 = (a)^1/2 has an inverse of √a
How to find the equivalents of the given dataThe data given:
[tex]\sqrt[4]{162^{x} }[/tex]
Solving the given data for the equivalence
[tex]\sqrt[4]{162^{x} }=162^{x/4}[/tex]
The above proves option A correct
[tex]\sqrt[4]{(3*3*3*3*2)^{x} }[/tex]
[tex]\sqrt[4]{(3^{4} *2)^{x} }[/tex]
[tex](3\sqrt[4]{(2) })^{x}[/tex]
The above solution makes option B correct
[tex](3\sqrt[4]{(2) })^{x}=(3{(2)^{1/4} })^{x}[/tex]
The above proves Option D correct
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complete question
Which functions are equivalent to f (x) = RootIndex 4 StartRoot 162 EndRoot Superscript x? Check all that apply.
f (x) = 162 Superscript StartFraction x Over 4
f (x) = (3 RootIndex 4 StartRoot 2 EndRoot) Superscript x
f (x) = 9 RootIndex 4 StartRoot 2 EndRoot Superscript x
f (x) = 126 Superscript StartFraction 4 Over x
f (x) = left-bracket 3 (2 Superscript one-fourth Baseline) right-bracket Superscript x
Compare these two fractions: 3/10 and 4/5*03/10 > 4154/5>3/10О4/5 = 3/10
3. a person is watching the space shuttle launch. the person is 3000 ft from the launch pad. how fast is the distance between the person and the shuttle changing when the shuttle is 4,000 ft high and rising at a rate of 800 ft/sec?
The distance between the person and the shuttle is changing at a rate of 640 feet/sec when the shuttle is 4000 ft high and is rising at a rate of 800 ft/sec.
Considering x to be the height of the triangle and y to be the hypotenuse of the triangle, a right-angled triangle will be formed according to the given information having a base of 3000 feet which is the distance of the person from the launch pad.
In this right-angle triangle x will be the height of the shuttle and y will be the distance between the person and the shuttle.
Now we apply the Pythagorean theorem to the triangle;
y² = x²+(3000)²
Now differentiating this equation with respect to time,t :
2y (dy/dt) = 2x(dx/dt) + 0
dy/dt = x(dx/dt)/y
As the shuttle is rising at a speed of 800 ft/sec, (dx/dt)=800
Substitute 4000 for x into the equation, y²=x²+(3000)², to find y;
y² = (4000)²+(3000)²
y = 5000
Now we substitute 4000 for x, 5000 for y, and 800 for dx/dt in the equation, dy/dt = x(dx/dt)/y
dy/dt = 4000(800) / 5000
dy/dt = 640
Therefore, the distance between the person and the shuttle is increasing at a rate of 640 feet/sec.
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Simplify 5(−4−8w)−3w.
Answer:
-20-43w
Step-by-step explanation:
5(-4-8w)-3w
-20-40w-3w
-20-43w
how many of these figures have atleast one vertex
work out the value of 6 2 plus 3 3
Answer:95
Step-by-step explanation:
This can simply be answered by adding the first digit of both numbers which would be 9 then add the secound number of both numbers and that would be 5
The answer is 95
Answer:
if its 6^2 + 3^3 then its 63
Step-by-step explanation:
6^2 simplified is 36 and 3^3
6 x 6 = 36 + 27 = 63
3 x 3 x 3 =27
3 x 3= 9
9 x 3= 27