Step-by-step explanation:
We will need to use logs here...
First divide each side by 3
[tex]3(10)^x=30000[/tex]
[tex]10^x=10000[/tex]
Then take the log of each side
Keep in mind that [tex]log_{10} (10)[/tex] gets canceled out to leave x
[tex]log_{10} (10^x)=log(10000)[/tex]
Finally, log(10000) = 4 because [tex]10^4=10000[/tex]
[tex]x = 4[/tex]
f(x)=x^2. which of these is g(x) ?
a. g(x)=(1/5x)^2
b. g(x)=5x^2
c.g(x)=(1/4x)^2
d.g(x)=1/5x^2
Answer:
a
Step-by-step explanation:
we know that g(x) means y therefore in this case let's suppose we have the coordinate (5;y) so we must find the corresponding y value
*DO THE TRIAL AND ERROR METHOD*
take any equation above and substitute the value of x of which is 5 and the corresponding value should be 1.
[tex]g(x) = (\frac{1}{5} x) {}^{2} [/tex]
Someone help me with this math word questions
2) The three ways of naming an angle are by the letter at the vertex, by placing a number or variable inside the angle, or by two letters with the vertex letter placed in the middle.
3) [tex]\angle WXY, \angle YXZ, \angle WXZ[/tex]
4) [tex]X[/tex]
Find the length of side AB.
Give your answer to 3 significant figures.
Answer:
[tex]\huge\boxed{\sf AB = 8.86 \ cm}[/tex]
Step-by-step explanation:
Given:θ = 41°
Hypotenuse = BC = 13.5 cm
Required:opposite = AB = ?
We will use the trigonometric ratio of sin.
Solution:[tex]\displaystyle sin \ \theta = \frac{opposite }{hypotenuse} \\\\sin \ 41=\frac{AB}{13.5} \\\\0.656 = \frac{AB}{13.5} \\\\0.656 \times 13.5 = AB\\\\8.86 \ cm = AB\\\\\boxed{ AB = 8.86 \ cm}\\\\\rule[225]{225}{2}[/tex]
Which ordered pair makes both inequalities true?
y < –x + 1
y > x
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, 0). Everything below and to the left of the line is shaded. The second dashed line has a positive slope and goes through (negative 1, negative 1) and (1, 1). Everything above and to the left of the line is shaded.
(–3, 5)
(–2, 2)
(–1, –3)
(0, –1)
Inequalities help us to compare two unequal expressions. The correct option is B.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
For the given inequalities, the graph can be plotted as shown below. Now when the coordinates have been plotted the point that will satisfy both the inequalities is (-2,2).
Hence, the correct option is B.
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Help please.. z zzz z Z z z z z z z z z z z z z zz
DF=
Help me please:))
Answer:
[tex]\fbox {DF = 20}[/tex]
Step-by-step explanation:
Given :
ΔSDF ~ ΔRTY = 4 : 9 (Ratio of similitude)SF = RT - 2TY = RY + 9SD = 8Step 1 : Find RT
SD : RT = 4 : 98 : RT = 4 : 9RT = 18Step 2 : Find SF
SF = RT - 2SF = 18 - 2SF = 16Step 3 : Find RY
SF : RY = 4 : 916 : RY = 4 : 9RY = 36Step 4 : Find TY
TY = RY + 9TY = 36 + 9TY = 45Step 5 : Find DF
DF : TY = 4 : 9DF : 45 = 4 : 9DF = 20Answer:
DF = 20
Step-by-step explanation:
Triangle SDF has side lengths SD, DF, SF.
Triangle RTY has side lengths
RT = (9/4)SD
RY = (9/4)SF
TY = (9/4)DF
"SF is 2 less than RT" Given
SF = RT - 2
SF = (9/4)SD - 2
"SD = 8" Given
SF = (9/4)(8) - 2
SF = 16
"TY is 9 more than RY" Given
TY = RY + 9
(9/4)DF = (9/4)SF + 9
(9/4)DF = (9/4)(16) + 9
(9/4)DF = 45
DF = 45 × 4/9
DF = 20
5/8 divided by 15/32
Answer: [tex]\frac{4}{3}[/tex] or about 1.333
Step-by-step explanation:
We will use the "keep, change, flip" method to solve. Keep the first number the same, change the division to multiplication, and flip the second number so we have the reciprocal.
[tex]\displaystyle \frac{\frac{5}{8} }{\frac{15}{32} } \,\,\,\,\text{ becomes } \,\,\,\,\frac{5}{8} *\frac{32}{15} =\frac{5*32}{8*15} =\frac{160}{120} =\frac{4}{3}[/tex]
Answer: 4/3
Step-by-step explanation:
find the reciprocal of the divisor
15/32
32/15
Now multiply it with the dividend
5/8
15/32
=5/8
32/15
=5/32
8/15
=160/120
after reducing the fraction the answer is 4/3
in mix form 1 1/3
If price of 12 eggs is Rs. 192, how many eggs can be bought for Rs. 160?
Answer:
10
Step-by-step explanation:
First, divide 192 by 12, you get a unit rate of Rs. 16 per egg, then divide Rs. 160 by 16 and you get 10
The number of eggs that can be purchased at Rs. 160 is 10.
What is a division operator?The division operator ( / ) has the quotient of its operands where the left operand exists the dividend and the right operand exists the divisor.
The cost of 12 eggs = Rs. 192
The cost of 1 egg = 192/12 = Rs. 16.
The number of eggs that can be purchased is Rs. 160 = 160/16 = 10.
Therefore, the number of eggs that can be purchased at Rs. 160 is 10.
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describe the effect of the transformation (x,y) to (x,y+4)
A. vertical stretch without reflection
B. horizontal translation of 4 units
C. vertical stretch with reflection
D. Vertical translation of 4 units
given, what are the domain and range?
Factor the rational function,
.
.
.
.
Notice that the denominator and numerator both have x-1. This means that we have a removable discontinuity there so set x-1=0.
.
.
So our domain can be all reals except 1.
Range: First factor out the x-1. We will be left with
.
Since 1 isn't in the domain, plug in 1 to find the what won't be in the range
.
So 7 isn't in the range,
End Behavior:
Since the rational function numerator is a quadratic and the denominator is a linear function, the rational function will approach will not have a horizontal asymptotes.
The pipe has a length 29cm, internal diameter 6.5cm and thickness 0.5cm. What is the Volume
Answer:
Length of pipe = 21 cm
Internal diameter = 4 cm
Internal radius = \frac{4}{2} = 2 cm24=2cm
Thickness = 0.5 cm
Outer radius = 2+0.5=2.5 cm
Volume of pipe =\pi R^2 h - \pi r^2 hπR2h−πr2h
Volume of pipe =\frac{22}{7} (2.5)^2 (21)-\frac{22}{7}(2)^2(21)=148.5 cm^3
=\frac{22}{7} (2.5)^2 (21)-\frac{22}{7}(2)^2(21)=148.5 cm^3722(2.5)2(21)−722(2)2(21)=148.5cm3
Hence The volume is 148.5 cubic cm.
#more
The thickness of a metal pipe is 1.5cm. The inner diameter is 21cm. What is the volume of metal required for a pipe of length 7cm
if 9^x=25, what does 3^x equal?
Answer:
[tex]3^x=5[/tex]
Step-by-step explanation:
Given:
[tex]9^x=25[/tex]
Rewrite 9 as 3²:
[tex]\implies (3^2)^x=25[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 3^{2x}=25[/tex]
Apply the same exponent rule:
[tex]\implies (3^x)^2=25[/tex]
Square root both sides:
[tex]\implies \sqrt{(3^x)^2}=\sqrt{25}[/tex]
[tex]\implies 3^x=5[/tex]
What is m∠M? I don't exactly remember how to do this type on problem...
Answer:
m∠M=98º
Step-by-step explanation
Sum of interior angles;
3x-16+x+6+x = 180
5x = 180-6+16
5x = 190
x = 38º
Angle M;
m<M= 3x - 16 = 3(38)-16= 98º
m∠M=98º
Answer:
<M = 98
Step-by-step explanation:
The sum of the angles of a triangle is 180 degrees
< M + < N + < O = 180
3x-16 + x + x+6 = 180
Combine like terms
5x - 10 = 180
Add 10 to each side
5x-10 + 10 = 180+10
5x = 190
Divide by 5
5x/5 = 190/5
x=38
We want to find <M
<M = 3x-16 = 3*38 -16 = 114-16 =98
Which is an example of a statistical question? Questions Question 1 How many pets does Alisha have at home? Question 2 How old were you when you got your first pet? Do you like having a pet? Question 3 Question 4 What is Alisha's pet's name? question 1 O question 2 O question 3 O question 4
Answer:
Do you like having a pet? - statistcal question
Step-by-step explanation:
^^^^
A student begins a proof of the law of cosines. His work is shown.
(image below)
The student made an error in ___. To correct this error, he should ___.
After correcting this error, the student can use the ___ to relate sides x, y, z, and angle ___.
1st blank answers:
a, step 1
b, step 2
c, step 3
2nd blank answers
a, define side AY in terms of angle X
b, define side XY in terms of angle X
c, define side AX in terms of angle Y
3rd blank answers
a, tangent function
b, law of sines
c, Pythagorean theorem
4th blank answers
a, Z
b, X
c, Y
The student made an error in step 3. To correct this error, he should define side AY in terms of angle X. Pythagorean theorem relates sides x, y, z, and angle X
The law of cosine.In Trigonometry, law of cosine (cos) is given by this mathematical expression:
cosθ = Opp/Hyp
Where:
Opp is the opposite side of a right-angled triangle.Hyp is the hypotenuse of a right-angled triangle.θ is the angle.In this scenario, we can logically deduce that the student made an error in step 3. To correct this error, he should define side AY in terms of angle X.
After correcting this error, the student can use the Pythagorean theorem to relate sides x, y, z, and angle X.
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Which graph represents the solution of x² + y² < 25 and y² <6x?
The graph is shown below
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
As, the equation x² + y² < 25 represents equation of circle.
So, the graph will be of the form circle.
and, y² <6x is the equation to represent parabola
So, the graph will represent a parabola.
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If the proportion of the total disposable income spent on consumer goods and services is 93 percent and if
consumers spend 85 percent of each additional dollar, what is
a. the apc?
b. the aps?
c. the mpc?
d. the mps?
Answer:
what?????????????????
can disjunction introduction (either ∨il or ∨ir ) be used to derive any type of formula other than a disjunction?
It is impossible to use a disjunction introduction to derive any other type of formula besides disjunctive formulas.
What is Disjunction Introduction?A rule of inference in propositional logic and virtually every other deduction system is referred to as disjunction introduction.
It is right to state that it is not possible to use a disjunction introduction to derive any other type of formula besides disjunctive formulas.
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The additive inverse of an element of x of a set is the number, which when added to x gives the answer 0. In the set {-3, -2, -1, 0, 1, 2, 3}, what is the additive inverse of -2?
Answer:
2
Step-by-step explanation:
the additive inverse of - 2 is 2 , since
- 2 + 2 = 0
Which algebraic expression is a trinomial?
Answer:
?
Step-by-step explanation:
because there is no picture or option
It costs $20 a day to rent a car and $30 for a full tank of gas. If Stacy fills up the tank 3 times and has the car rented for 14 days, how much does she owe?
Answer:
$20 × 14 days = $280
&30 × 3 = $90
&280 + $90 = $370
Answer:
For car she owes=
$20 x 14 = $280
For tank she owes=
$30 x 3 = $90
Therfore in total she owes,
$280 + $90 = $370
help me solve this give steps as well please
The total cost of 6 wave pool tickets with the discount included would be $73.5.
How to calculate the total value of 6 tickets with the discount?To calculate the total cost we must multiply the value of each ticket by the number of tickets to be purchased, in this case there are 6:
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Solve the following
[tex]5x-2= -9x+8[/tex]
Answer:
5x - 2 = (-9x) + 8
5x + 9x = 8 + 2
14 x = 10
x = 10 / 14
x = 5/7
Answer:
5 / 7
Step-by-step explanation:
Step 1: Move the variables to one side and the numbers to the other. We get 14x = 10.
Step 2: Then we solve for x. x is equal to 10 / 14, which simplifies to 5 / 7.
Lily sold 18 items at the street fair. she sold bracelets for $6 each and necklaces for $5 each for a total of $101. which system of equations can be used to find b, the number of bracelets she sold, and n, the number of necklaces she sold? b n = 101 6b 5n = 18 b n = 101 5b 6n = 18 b n = 18 6b 5n = 101 b n = 18 5b 6n = 101
Answer:
[tex]b + n = 18[/tex]
[tex]6b + 5n = 101[/tex]
change 5/8 to percentage
Answer: 62.5%
Step-by-step explanation:
First, you must simplify 5/8 into a decimal and then multiply that by 100 to get the percentage of the fraction.
[tex]\frac{5}{8}=0.625[/tex] [tex]0.625*100=62.5[/tex]%
I hope this helps!! Pls give brainliest :)
What are the solutions to the following system of equations?
y = x² + 7x - 5
2x - y = -9
Answer:
x= -7, y= -5 and
x= 2, y= 13
This may also be written as (-7, -5) and (2, 13).
Step-by-step explanation:
Start by labelling the two given equations:
y= x² +7x -5 -----(1)
2x -y= -9 -----(2)
Let's solve by substitution!
Making y the subject of formula in equation (2):
From (2): y= 2x +9 -----(3)
Substitute (3) into (1):
2x +9= x² +7x -5
x² +7x -5 -2x -9= 0
x² +5x -14= 0
Factorise:
(x +7)(x -2)= 0
x +7= 0 or x -2= 0
x= -7 or x= 2
Find the respective values of y.
Substitute into (1):
y= (-7)² +7(-7) -5 or y= (2)² +7(2) -5
y= 49 -49 -5 or y= 4 +14 -5
y= -5 or y= 13
Thus, the solutions are (-7, -5) and (2, 13).
Find the midpoint of the line segment with end coordinates of:
(-1,7) and (3,-2)
Give coordinates as decimals where appropriate.
Answer:
(1,2.5)
Step-by-step explanation:
On the graph, the (-1,7) lies in the top right grid. The (3,-2) lies in the bottom left grid. If you use a graphing calculator, the middle is hard to find but you will find (1, 2.5) or (1, 5/2).
HELPP
Simplify the expression 6^3+ 5(4 − 2).
28
36
226
234
Answer:
BODMAS
[tex] {6}^{3 } + 5(4 - 2) = 216 + 5(2) \\ = 216 + 10 \\ = 226[/tex]
Answer: Answer is 226
Step-by-step explanation: Do math
What quadrant is the point (2, -5) in?
Answer:
quadrant 4
Step-by-step explanation:
(2,-5) would be in the 4th quadrant
Factorise x³ + 2x I can't understand this please give me the answer
Answer:
[tex]x(x^2+2)[/tex]
Step-by-step explanation:
Since x is the only common term, you factor that part out using the distributive property.
Solution:
Detailed explanation:
Hii! Let's factorise this expression!
Did you see that both terms, x^3 and 2x, have an x in common? That's what we are going to factor out, by dividing x^3 and 2x by x.
x^2+2 is what we obtain.
Now, this can't be the end of the process. We also need to put parentheses around x^2+2.
(x^2+2)
Next we put that x we factored out a short while ago outside the parentheses.
x(x^2+2). Did you get it?
________
Hope I helped, best wishes & happy studies!
Please reach out if any queries arise. Thankyou!!
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