Answers
[tex]\qquad\qquad\huge\underline{\boxed{\sf Answer}}[/tex]
The sign of a will be negative ~
let the value of be be ' -x ' , -x is a negative number (b = -x < 0)
[tex]\qquad \sf \dashrightarrow \: a \times \frac{ - b}{b} [/tex]
[tex]\qquad \sf \dashrightarrow \: a \times \frac{ - ( - x)}{ - x} [/tex]
[tex]\qquad \sf \dashrightarrow \: a \times \frac{ x}{ - x} [/tex]
[tex]\qquad \sf \dashrightarrow \: a \times \frac{ - x}{ x} [/tex]
[tex]\qquad \sf \dashrightarrow \:a \times - 1[/tex]
[tex] \qquad \sf \dashrightarrow \:- a[/tex]
Therefore, the term a, has a negative sign unless it's value is substituted, I.e -a = 0 ( having no sign )
Related Questions
Researchers are recording how much of an experimental medication is in a person's bloodstream every hour. they discover that half-life of the medication is about 6 hours.
Answers
By using the known half-life, we can see that if the initial dose is 500mg, after 4 days the medication will be 0.0076 mg.
What is the half-life?
We define half-life as the time such that the initial amount is reduced to its half.
So, if a given substance has a half-life T, then the amount of substance as a function of time, we have:
S(t) = A*e^{-t*ln(2)/T}
Where t is the variable in time units.
We know that T = 6 hours, and A, the initial dose, is 500 mg, so the formula is:
S(t) = 500mg*e^{-t*ln(2)/6h}
Then after 4 days (or 4*24h = 96h) the amount of medication is:
S(96h) = 500mg*e^{-96h*ln(2)/6h} = 0.0076 mg.
If the initial dose was 750mg, after 4 days the person would have:
S(96h) = 750mg*e^{-96h*ln(2)/6h} = 0.0114 mg
So the person would have:
0.0114 mg - 0.0076 mg = 0.038 mg more of medication.
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The number of radians in a 540540540-degree angle can be written as a\piaπa, pi, where aaa is a constant, what is the value of aaa ?
Answers
Using proportions, it is found that the value of a is of 3.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, a 180º angle has a measure of [tex]\pi[/tex] radians. What is the measure of a 540º angle? The rule of three is given by:
180º - [tex]\pi[/tex] rad.
540º - x [tex]\pi[/tex] rad.
Applying cross multiplication:
180x = 540.
x = 540/180 = 3.
The value of a is of 3.
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Using proportions, the value of a is 3.
What is proportion?Proportion is a mathematical comparison between two numbers.
When going from degrees to radians, 180 degrees is always going to equal π radians.
The conversion of angle from radian to degree;
[tex]\rm 180-\ 1 \\\\540-a[/tex]
The value of a is;
[tex]\rm \dfrac{180}{540}=\dfrac{1}{a}\\\\\dfrac{1}{3}=\dfrac{1}{a}\\\\1 \times a=1\times 3\\\\a=3[/tex]
Hence, the value of a is 3.
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#SPJ4
Use the equation, (1/27)^x = 3^-4x+6, to complete the following problems
(a) Rewrite the equation using the same base.
(b) Solve for x. Write your answer as a fraction in simplest form.
Answers
Answer:
[tex]\sf 3^{-3x}=3^{(-4x+6)}[/tex]
[tex]\sf x=6[/tex]
Step-by-step explanation:
[tex]\sf Given \ equation: \left(\dfrac{1}{27}\right)^x=3^{(-4x+6)}[/tex]
[tex]\sf As \ \dfrac{1}{27}=\dfrac{1}{3^3} \ and \ \dfrac{1}{a^b}=a^{-b} \ then \ \dfrac{1}{27}=3^{-3}[/tex]
Therefore, we can rewrite the given equation with base 3:
[tex]\implies \sf (3^{-3})^x=3^{(-4x+6)}[/tex]
Apply the exponent rule [tex]\sf (a^b)^c=a^{bc}[/tex] :
[tex]\implies \sf 3^{-3x}=3^{(-4x+6)}[/tex]
[tex]\sf If \ a^{f(x)}=a^{g(x)} \ then \ f(x)=g(x)[/tex]
[tex]\implies -3x=-4x+6[/tex]
Add 4x to both sides to solve for x:
[tex]\implies \sf x=6[/tex]
This is getting more difficult!
Answers
The equation [tex]y = x^2 - 8x + 3[/tex] is an illustration of a quadratic equation
The vertex of the quadratic equation [tex]y = x^2 - 8x + 3[/tex] is (4,-13)
How to determine the vertex?The equation is given as:-
[tex]y = x^2 - 8x + 3[/tex]
A quadratic equation is represented as:
[tex]y = ax^2 + bx + c[/tex]
By comparison, we have:
a = 1; b = -8; c = 3
The x-coordinate of the vertex is:
[tex]x = -\frac b{2a}[/tex]
So, we have:
[tex]x = \frac 8{2*1}[/tex]
[tex]x = 4[/tex]
Substitute 4 for y in [tex]y = x^2 - 8x + 3[/tex]
[tex]y = 4^2 - 8 * 4 + 3[/tex]
[tex]y = -13[/tex]
When x = 2 and 3, we have:
[tex]y = 2^2 - 8 * 2 + 3 = -9[/tex]
[tex]y = 3^2 - 8 * 3 + 3 = -12[/tex]
When x = 5 and 6, we have:
[tex]y = 5^2 - 8 * 5 + 3 = -12[/tex]
[tex]y = 6^2 - 8 * 6 + 3 = -9[/tex]
So, the table of values is:
x y
2 -9
3 -12
4 -13
5 -12
6 -9
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What is the standard form of the equation of a circle given by x2 y2 – 18x 8y 5 = 0? ( )² ( )² =
Answers
The standard form of the given equation [tex]x^2+y^2-18x+8y+5=0[/tex] will be given as [tex](x-9^2)+(y+4)^2=(2\sqrt{23} )^2[/tex]
What is the equation of a circle?The general form of the equation of the circle is given as
[tex](x-h)^2+(y-k)^2=r^2[/tex]
We have the equation
[tex]x^2+y^2-18x+8y+5=0[/tex]
By adding 81 and 16 on both sides
[tex]x^2-18x+81+y^2+8y+16=-5+81+16[/tex]
[tex](x-9)^2+(y+4)^2=92[/tex]
[tex](x-9)^2+(y+4)^2=(2\sqrt{23})^2[/tex]
Thus the standard form of the given equation [tex]x^2+y^2-18x+8y+5=0[/tex] will be given as [tex](x-9^2)+(y+4)^2=(2\sqrt{23} )^2[/tex]
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Answer:
x-9, y+4, & 92
Step-by-step explanation:
i did it
4x : 3 = 6 : 5
Calculate the value of x.
Answers
Answer:
x = 9/10
Step-by-step explanation:
This problem features a ratio: 4x/3 = 6/5
By cross multiplying you get that 4x*5 = 3*6 or 20x = 18. By dividing both sides by 20, you get that x = 18/20, and when simplified, 9/10.
Julia’s gross pay was $4,500 last year. the federal income tax withholding from her pay was 13% of her gross pay. julia determined the federal income tax she owes is $495. how much of a refund can julia expect? $64.35 $90.00 $430.65 $585.00
Answers
The amount of the refund Julia gets as a federal income tax will be $90.
What will be Julia's refund?It is given in the question:
Julia's gross pay = $500
federal income tax withholding from her pay was 13% of her gross pay
federal income tax she owes is = $495
To find out the refund we will first find the amount of Federal income which is 13% of the gross pay.
[tex]\rm federal \ amount =\dfrac{4500\times 13}{100} =585[/tex]
The refund Julia will get will be
[tex]=585-495=90[/tex]
Hence the amount of the refund Julia gets as a federal income tax will be $90.
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The owner of a music store ordered new compact disks. Of the new compact disks ordered,1/4 are Jazz, 2/7 are Classical, and the rest of the compact disks are Soft Rock. What fraction of the compact disks ordered are Soft Rock?
Answers
The fraction of the compact disks ordered by the owner of the music store that are Soft Rock is 13/28.
What are fractions?A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator. The numerator is the number above while the denominator is the number below.
What fraction is Soft Rock?1 - (1/4 + 2/7)
1 -[ (7 + 8) /28]
1 - 15/28 = 13/28
The amount of money Camilla earns varies directly with the number of hours she works. If she earns $150 when she works 20 hours, how much will she earn for working 60 hours?
What is k ? (k = y/x)
What is the equation for the direct variation situation? (y = kx)
How much will she earn for working 60 hours?
Answers
What is k ? (k = y/x)
If y is dollars earned and x is hours worked,
k = y/x
k = 150 dollars /20 hours
k = 7.50 dollars per hour
What is the equation for the direct variation situation? (y = kx)
y = kx
y = (7.50)(60)
y = 450
How much will she earn for working 60 hours?
y = $450
She will earn $450 after working for 60 hours.
4 2/4 + 1/9 =
what is the answer i need to know now
Answers
Answer:
4.61
Step-by-step explanation:
Step-by-step explanation:
[tex] = 4 \frac{2}{4} + \frac{1}{9} \\ = \frac{4 \times 4 + 2}{4} + \frac{1}{9} \\ = \frac{18}{4} + \frac{1}{9} [/tex]
Find the LCM
[tex] = \frac{18}{4} \times \frac{9}{9} + \frac{1}{9} \times \frac{4}{4} \\ = \frac{162}{36} + \frac{4}{36} \\ = \frac{166}{36} [/tex]
Convert into lowest term
[tex] \frac{83}{16} \\ [/tex]
Write the polar equation 0= pi/3
Answers
Answer:
1
(
π
3
)
)
Step-by-step explanation:
Explanation:
Substitute
tan
(
y
x
)
for
θ
tan
(
y
x
)
=
π
3
Obtain
y
x
on the left by using the inverse tangent on both sides:
tan
−
1
(
tan
(
y
x
)
)
=
tan
−
1
(
π
3
)
y
x
=
tan
−
1
(
π
3
)
Multiply both sides by x:
y
=
(
tan
−
1
(
π
3
)
)
x
PLS HELP ME I WILL MARK THE BRAINIEST 50 POINTS!!!!!!
Answers
Answer:
Done. Check comments
Step-by-step explanation:
Inscribed angles are half the measure of the intercepted arcs. This example shows major arc BEA being intercepted by the supplement of 74, which is 106. If you double that, you get the arc, 212.
The next example shows 80 and 154 are intersected by two chords. The angle created by that intersection is the average of the two intercepted arcs. 117.
When two secant lines intersect, they form an angle that is half the measure of the DIFFERENCE of the intercepted arcs. 145 - 53 = 92/2 = 46.
This is similar to the previous one. Except the difference is between 263 and 97. ACTUALLY, I MADE AN ERROR on the comment about this one.
263-97 = 166/2 = 83***
Annie wants to use the problem-cause-solution order to organize a persuasive speech to reduce violence on campus. she begins by offering statistics of incidents to show that there is a need for action. what is a possible next step
Answers
The possible next step that Annie should use in the persuasive speech is to discuss the lack of street lamps and campus security as causes of the problem.
What is a persuasive speech?It should be noted that a persuasive speech simply means a speech that is used to convince an individual to agree to a particular perspective.
In this case, the possible next step that Annie should use in the persuasive speech is to discuss the lack of street lamps and campus security as causes of the problem.
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[tex]y+2=(x^2/2)-2sin(y)[/tex]
Answers
the assumption being that "y" is encapsulating a function in "x" terms.
[tex]y+2=\cfrac{x^2}{2}-2sin(y)\implies \stackrel{\textit{taking the derivative to both sides}}{\cfrac{dy}{dx}+0=\cfrac{1}{2}(2x)\underset{chain~rule}{-2cos(y)\cdot \cfrac{dy}{dx}}} \\\\\\ \cfrac{dy}{dx}=x-2cos(y)\cfrac{dy}{dx}\implies \cfrac{dy}{dx}+2cos(y)\cfrac{dy}{dx}=x \\\\\\ \cfrac{dy}{dx}\left[ 1+2cos(y) \right]=x\implies \cfrac{dy}{dx}=\cfrac{x}{1+2cos(y)}[/tex]
A total of 275 people took a driving theory test on Monday. Of these people, 68% passed the test.
a) (i) What percentage of people who took the test on Monday did not pass the test?
(ii) How many of the 275 people who took the test on Monday passed the test?
Answers
Answer:
a. 32%
B.8B.88
Step-by-step explanation:
100 -68=32%
32/100=x/275
100x=8800
x=88
The length of a square is 3x - 4 units. Find the area in terms of x.
Answers
Answer:
9x^2 - 24x + 16 is area in terms of x alternativly (3x-4)^2 is also true
Step-by-step explanation:
L * W = area length = width on a sqare so L * L = area too
(3x - 4) * (3x - 4)
use foil method
9x^2 - 24x + 16
Answer:
9x^2 − 24x + 16
Step-by-step explanation:
To find the area of a square, you use the formula
A = x^2
So we plug in 3x-4 for x
A = (3x-4)^2
A = 9x^2 − 24x + 16
A frame contains 4 pounds of gold. suppose gold is worth $1,277 per ounce. how much would the gold in the frame be worth?
Answers
Answer:
$81,728
Step-by-step explanation:
For reference: 1 pound = 16 ounces.
Therefore, 4 pounds of gold must be 16 * 4 = 64 ounces.
Since each ounce is $1,277, we must have the total cost of the gold to be $1,277 * 64 = $81,728.
The key word here is "per", which means to multiply.
Answer:Answer:5,108
Step-by-step explanation:
Which one is it? Im stumped.
Answers
Answer:
rational
Step-by-step explanation:
Hope this helps!
If not I am sorry
let's keep in mind that that same/same = 1 always, so then we can say
[tex]\cfrac{spaghetti}{spaghetti}~~ = ~~\cfrac{hippopotamus}{hippopotamus}~~ = ~~\cfrac{meatballs}{meatballs}~~ = ~~\cfrac{dog}{dog}~~ = ~~\cfrac{0.\overline{55}}{0.\overline{55}}~~ = ~~\textit{\huge 1}[/tex]
well, "1" is a whole number
"1" is also an integer oddly enough
"1" can be written as a ration like 1/1, so is also rational.
Regina created a playlist on her cell
phone. The playlist includes 3 pop songs, hip-hop songs, and 1 blues song. Regina will randomly choose 2 songs, without repeating a song, to play through her new earbuds. What is the probability that Regina will choose a pop song first and a hip-hop song second?
Answers
Answer: a 5/24
Step-by-step explanation:
3 + 5 + 1 = 9
First = Pop Song P = 3/9 = 1/3
Seconed = Hip Hop Song P2 = 5/9-1 = 5/8
So P = 1/3 x 5/8 = 5/24
So that makes A the correct answer
A math class consists of 10 girls and 8 boys. The teacher wants to choose 2 girls and 2 boys to go on a trip. How many different groups could the teacher choose?
A. 5040
B. 3060
C. 1260
D. 73
Answers
Answer:1260
Step-by-step explanation: photo of the graded question attached
A math class consists of 10 girls and 8 boys. The teacher wants to choose 2 girls and 2 boys to go on a trip. How many different groups could the teacher
choose?
x3060
073
5040
1260
F(X)= -x^2 + 10x - 12
Answers
Answer:
(0, -22)
Step-by-step explanation:
The y-intercept is the value of y when x is 0,
f(x) = -x² + 10x - 22
f(0) = -(0)² + 10(0) - 22
f(0) = - 22
The y-intercept is -22 at point (0, -22).
-> We can also see this when graphing, please see attached.
Note: If you want me to solve for f(x) = -x² + 10x - 12 as you wrote in text and not f(x) = -x² + 10x - 22 as the picture shows, let me know.
MARKING BRAINLEIST IF CORRECT
Answers
Answer:
A) (-5,0) and (-4,0)...
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♪[/tex]
X - intercepts are the points where the curve cuts x - axis ~
for the given curve (parabola), the intercepts are :
[tex]\qquad \sf \dashrightarrow \:(-5,0) \: \: and \: \: (-4, 0)[/tex]
The Correct choice is A
[tex]➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖[/tex]
5-2x > 3x-10
Solve the inequality
Answers
Answer:x<3 that shout be right. I calculated it.
Step-by-step explanation:
Answer pls in fractions
Answers
Answer:
4/5 yd^3
Step-by-step explanation:
(2/3)(3/1)(2/5) = 12/15 = 4/5
Answer:
4/5 I believe?
Step-by-step explanation:
Multiply all the numbers together :)
by finding tan θ in 2 different triangles find the value of m
Answers
Answer:
m = 3.75
Step-by-step explanation:
tanθ = 3/4θ = 37°⇒ Angle opposing 3 in the left triangle is 53°
sin53° ⇒ 4/5 = 3/m4m = 15m = 15/4m = 3.75The two figures are congruent. Find the values of the unknown variables.
Answers
Answer:
y = 71
z = 18
x = 14
Step-by-step explanation:
Figure on the right is simply figure on the left but flipped on its side. we know this because the question tells us the shapes are congruent (which means equal, the same)
the first day of shooting a movie, a director uses 30% of a film reel. The strip of
film used was 90 meters long.
What is the standard length on a film reel?
Answers
Answer:
27
Step-by-step explanation:
30% of 90 can be written as 30% × 90
= 30/100 × 90
= 27
Select the correct answer.
Which number is an irrational number?
A.
B.
C.
D.
Answers
Answer:
you do not have any numbers, only letters so I cannot answer your question. sorry...
Step-by-step explanation:
Select the correct answer.
Which number is an irrational number?
A.
B.
C.
D.
What percent represents the shaded part of the hundredths grid shown? Please help asap!
Answers
Answer:
C. 5%
Step-by-step explanation:
if u count the shaded part it is 5 shaded out of 100 so that fraction is 5/100 which is .05 as a decimal and 5% as a percent
-2x + 22 < 18
It is an inequality
Answers
Answer:
Solving for x;
-2x + 22 < 18
Get rid of constants:
-22 -22
-2x < -4
Isolate x, by dividing by -2 from both sides since the inverse operation of multiplication is division, and remember when dividing or multiplying by negative integers, you flip the inequality symbol around:
÷-2 ÷-2
x > 2
Answer:
[tex]x > 2[/tex]
Step-by-step explanation:
[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:x > 2\:\\ \:\mathrm{Interval\:Notation:}&\:\left(2,\:\infty \:\right)\end{bmatrix}[/tex]
Given:
-2x + 22 < 18
Solve:
[tex]\mathrm{Subtract\:}22\mathrm{\:from\:both\:sides}[/tex]
[tex]-2x+22-22 < 18-22[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]-2x < -4[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}[/tex]
[tex]\left(-2x\right)\left(-1\right) > \left(-4\right)\left(-1\right)[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]2x > 4[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}2[/tex]
[tex]\frac{2x}{2} > \frac{4}{2}[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]x > 2[/tex]
~Lenvy~