find the value of x if log3 (x+6) =2
Answers
Answer:
3(x+6) =2
3x+18 =2
3x=2-18
3x=16
x=16/3
x=5.33333333
Related Questions
Solve the system of equations.
−2x+5y =−35
7x+2y =25
Answers
Answer:
The equations have one solution at (5, -5).
Step-by-step explanation:
We are given a system of equations:
[tex]\displaystyle{\left \{ {{-2x+5y=-35} \atop {7x+2y=25}} \right.}[/tex]
This system of equations can be solved in three different ways:
Graphing the equations (method used)Substituting values into the equationsEliminating variables from the equationsGraphing the Equations
We need to solve each equation and place it in slope-intercept form first. Slope-intercept form is [tex]\text{y = mx + b}[/tex].
Equation 1 is [tex]-2x+5y = -35[/tex]. We need to isolate y.
[tex]\displaystyle{-2x + 5y = -35}\\\\5y = 2x - 35\\\\\frac{5y}{5} = \frac{2x - 35}{5}\\\\y = \frac{2}{5}x - 7[/tex]
Equation 1 is now [tex]y=\frac{2}{5}x-7[/tex].
Equation 2 also needs y to be isolated.
[tex]\displaystyle{7x+2y=25}\\\\2y=-7x+25\\\\\frac{2y}{2}=\frac{-7x+25}{2}\\\\y = -\frac{7}{2}x + \frac{25}{2}[/tex]
Equation 2 is now [tex]y=-\frac{7}{2}x+\frac{25}{2}[/tex].
Now, we can graph both of these using a data table and plotting points on the graph. If the two lines intersect at a point, this is a solution for the system of equations.
The table below has unsolved y-values - we need to insert the value of x and solve for y and input these values in the table.
[tex]\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & a \\ \cline{1-2} 1 & b \\ \cline{1-2} 2 & c \\ \cline{1-2} 3 & d \\ \cline{1-2} 4 & e \\ \cline{1-2} 5 & f \\ \cline{1-2} \end{array}[/tex]
[tex]\bullet \ \text{For x = 0,}[/tex]
[tex]\displaystyle{y = \frac{2}{5}(0) - 7}\\\\y = 0 - 7\\\\y = -7[/tex]
[tex]\bullet \ \text{For x = 1,}[/tex]
[tex]\displaystyle{y=\frac{2}{5}(1)-7}\\\\y=\frac{2}{5}-7\\\\y = -\frac{33}{5}[/tex]
[tex]\bullet \ \text{For x = 2,}[/tex]
[tex]\displaystyle{y=\frac{2}{5}(2)-7}\\\\y = \frac{4}{5}-7\\\\y = -\frac{31}{5}[/tex]
[tex]\bullet \ \text{For x = 3,}[/tex]
[tex]\displaystyle{y=\frac{2}{5}(3)-7}\\\\y= \frac{6}{5}-7\\\\y=-\frac{29}{5}[/tex]
[tex]\bullet \ \text{For x = 4,}[/tex]
[tex]\displaystyle{y=\frac{2}{5}(4)-7}\\\\y = \frac{8}{5}-7\\\\y=-\frac{27}{5}[/tex]
[tex]\bullet \ \text{For x = 5,}[/tex]
[tex]\displaystyle{y=\frac{2}{5}(5)-7}\\\\y=2-7\\\\y=-5[/tex]
Now, we can place these values in our table.
[tex]\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & -7 \\ \cline{1-2} 1 & -33/5 \\ \cline{1-2} 2 & -31/5 \\ \cline{1-2} 3 & -29/5 \\ \cline{1-2} 4 & -27/5 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}[/tex]
As we can see in our table, the rate of decrease is [tex]-\frac{2}{5}[/tex]. In case we need to determine more values, we can easily either replace x with a new value in the equation or just subtract [tex]-\frac{2}{5}[/tex] from the previous value.
For Equation 2, we need to use the same process. Equation 2 has been resolved to be [tex]y=-\frac{7}{2}x+\frac{25}{2}[/tex]. Therefore, we just use the same process as before to solve for the values.
[tex]\bullet \ \text{For x = 0,}[/tex]
[tex]\displaystyle{y=-\frac{7}{2}(0)+\frac{25}{2}}\\\\y = 0 + \frac{25}{2}\\\\y = \frac{25}{2}[/tex]
[tex]\bullet \ \text{For x = 1,}[/tex]
[tex]\displaystyle{y=-\frac{7}{2}(1)+\frac{25}{2}}\\\\y = -\frac{7}{2} + \frac{25}{2}\\\\y = 9[/tex]
[tex]\bullet \ \text{For x = 2,}[/tex]
[tex]\displaystyle{y=-\frac{7}{2}(2)+\frac{25}{2}}\\\\y = -7+\frac{25}{2}\\\\y = \frac{11}{2}[/tex]
[tex]\bullet \ \text{For x = 3,}[/tex]
[tex]\displaystyle{y=-\frac{7}{2}(3)+\frac{25}{2}}\\\\y = -\frac{21}{2}+\frac{25}{2}\\\\y = 2[/tex]
[tex]\bullet \ \text{For x = 4,}[/tex]
[tex]\displaystyle{y=-\frac{7}{2}(4)+\frac{25}{2}}\\\\y=-14+\frac{25}{2}\\\\y = -\frac{3}{2}[/tex]
[tex]\bullet \ \text{For x = 5,}[/tex]
[tex]\displaystyle{y=-\frac{7}{2}(5)+\frac{25}{2}}\\\\y = -\frac{35}{2}+\frac{25}{2}\\\\y = -5[/tex]
And now, we place these values into the table.
[tex]\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & 25/2 \\ \cline{1-2} 1 & 9 \\ \cline{1-2} 2 & 11/2 \\ \cline{1-2} 3 & 2 \\ \cline{1-2} 4 & -3/2 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}[/tex]
When we compare our two tables, we can see that we have one similarity - the points are the same at x = 5.
Equation 1 Equation 2
[tex]\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & -7 \\ \cline{1-2} 1 & -33/5 \\ \cline{1-2} 2 & -31/5 \\ \cline{1-2} 3 & -29/5 \\ \cline{1-2} 4 & -27/5 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}[/tex] [tex]\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & 25/2 \\ \cline{1-2} 1 & 9 \\ \cline{1-2} 2 & 11/2 \\ \cline{1-2} 3 & 2 \\ \cline{1-2} 4 & -3/2 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}[/tex]
Therefore, using this data, we have one solution at (5, -5).
Multiply. Express your answer in simplest form.
5/9 x 3/10
Answers
Answer:
5/9 x 3/10 = 15/90 as simplified as 1/6 in fraction form.
5/9 multiplied by 3/10 is equal to 1/6 in its simplest form.
We have,
To multiply fractions, we multiply the numerators together and the denominators together.
The resulting fraction is then simplified to its simplest form.
Let's multiply 5/9 by 3/10:
(5/9) x (3/10) = (5 x 3) / (9 x 10) = 15/90
To simplify the fraction 15/90, we can divide both the numerator and denominator by their greatest common divisor, which is 15:
15/90 = (15 ÷ 15) / (90 ÷ 15) = 1/6
Therefore,
5/9 multiplied by 3/10 is equal to 1/6 in its simplest form.
Learn more about fractions here:
https://brainly.com/question/24370499
#SPJ6
Answer the question, considering an event to be "unusual" if its probability is less than or equal to 0.05. If you drew one card from a standard deck, would it be "unusual" to draw a 6?
Answers
Answer:
No it's not unusual
Step-by-step explanation:
That's an unusual definition for unusual if you don't mind me saying so.
There are 4 sixes in a standard deck of cards without the jokers. There are 52 cards in that deck
4/52 = 0.077
This is greater than 0.05 so it is not unusual.
Let's add the 2 jokers and see what happens.
4/54 = 0.074
That's still not going to get the situation defined as unusual.
A 0.8-liter bottle of Mexican wine costs 100 pesos. At that price, how much would a halfgallon jug of the same wine cost in dollars? Mexican peso Dollars per foreign: 0.07855 Foreign per dollar: 12.73
Answers
Answer:
$11.83
Step-by-step explanation:
1 gallon = 3.785 litres
0.5(1/2gallon) = x liters
x = 0.5 × 3.785 liters
x = 1.89271 liters
0.8 liter = 100 pesos
1.89271 liters = x pesos
x = 1.89271 × 100/0.8
x = 236.58875 pesos
Converting to dollars
1 mexican peso = $0.050
236.58875 pesos = x
x = 236.58875 × $0.050
x = $11.8294375
Approximately = $11.83
A half gallon jug of the same wine cost in dollars $11.83
What is the approximate area of the triangle below?
Answers
Answer:
3
Step-by-step explanation:
1+1=2
At Green Island Farms the annual Turkey Trot is being held. This year’s contestants are Tom Turkey, Gary Gobbler and Donny Drumstick. The turkeys chase little RC cars loaded with feed. The buzzer sounds and the turkeys are off. Gary Gobbler chases his RC car trying to eat that sweet turkey feed for 15 feet before he manages to side swipe the RC car and knock it on its side. All the feed spills out and Gary Gobbler gobbles it down. That silly turkey happily eats his food for 1.75 seconds. A mouse comes out of the hay bale and tries to join Gary Gobbler in his feasting. But Gary Gobbler is scared of mice so when he sees the mouse he freaks out and tears down the racetrack.
Write a similar story for Tom Turkey making sure to include the different segments of the graph.
Answers
Answer:
The company is expected the company will receive
si me dan 200 pesos a la semana y quiero comprar algo de 15000 pesos cuantas semanas tengo que ahorrar
Answers
Answer:
75 semanas
Step-by-step explanation:
15,000 = 200s
15,000/200 = s
75 = s
A 3-column table with 4 rows. Column 1 is labeled Inequality with entries 6 greater-than 4, negative 11 less-than negative 3, 7 greater-than negative 6, negative 5 less-than 1. Column 2 is labeled Multiply each side by: with entries 4, 2, 3, 5. Column 3 is labeled New Inequality with entries A, B, C, D. The table gives an inequality and a number to multiply both sides of the inequality by. Identify the new, true inequality. A: B: C: D: Multiplying both sides of an inequality by a positive number the inequality symbol
Answers
Answer:
1. A
2. B
3. A
4. B
5. A
Step-by-step explanation:
Edge 2022
Answer:
A: 24 > 16B: -22 < -6C: 21 > -18D: -25 < 5E: does not changeExplanation: Correct on Edg 2020.
Cara has saved $4,000 to buy a car. Rick wants to buy a new television set. He has saved 1/10 as much as Cara. How much has Rick saved?
Answers
Answer:
Step-by-step explanation:
4000*1/10= $400
5. *
17 points
Which answer shows 9x 10-written in standard form?
-.000009
.000009
-900,000
.00009
Answers
q(x)=2 −2+? please solve this huhu
Answers
Answer:
I mean it would just be q(x) = 0
Step-by-step explanation:
Answer: q=0
Step-by-step explanation: Let's solve for q.
qx=2−2
Step 1: Divide both sides by x.
qx
x
=
0
x
q=0
Answer:
q=0
What is the result of 4 divided by one-half? A number line going from 0 to 4. 2 8 12 16
Answers
Answer:
2
4/.5 = 2
Therefore, your answer is 2, or A. Hope this helped!
Answer:
the answer is B) 8
Step-by-step explanation:
hope this helped sorry if it didn't and if it's wrong sorry for that also.
Find the value of x
Answers
x = 10.4 (1dp)
Step-by-step explanation:
Using Pythagoras' theorem, a^2 = b^2 + c^2 where a is the hypotinues; b and c is the two sides
a^2 = b^2 + c^2
12^2 = 6^2 + x^2
144 = 36 + x^2
x^2 = 144 - 36
x^2 = 108
x = _/108
x = 10.4 (1dp)
If x = 3 + 2√2, then the value of (x - 1/x) is
a) 4√2
b) 2√4
c) 8
Answers
Hope this helps and happy holidays!!
Complete the blank with either ∈ or ∉ so that the resulting statement is true. −2__{−6,−3,−5,−1}
Answers
Answer:
−2 ∉ {−6,−3,−5,−1}
Step-by-step explanation:
Given
Set = {−6,−3,−5,−1}
Element = -2
Required
The interpretation of the question is to state if -2 is an element of the given set or not
The first thing to do is to check through the set to count the number of occurrence of -2
Looking through Set = {−6,−3,−5,−1}, we have that the occurrence of -2 is 0
This implies that -2 is not an element of the given set and this is represented by the symbol ∉
Hence:
−2 ∉ {−6,−3,−5,−1}
at is the equation of the line passing through the points (2/5, 19/20) and (1/3, 11/12) slope-intercept form? y = 1/2 * x - 3/4 y = 1/2 * x + 3/4 y = 3/4 * x - 1/2 y = 3/4 * x + 1/2
Answers
Answer:
Step-by-step explanation:
2/5, 19/20) and (1/3, 11/12) in slope-intercept form? ... B. y = 1/2x + 3/4 ... D. y = 3/4x + 1/2 ... [tex]3}^{2}x = \frac{1}{?27} [/tex]find x.
sisktzkyzktRkzkKKRpyxdypzoyzitzotkg
Answers
Pick two points: (2,6), (4,8)
(8-6)/(4-2) = 2/2 = 1
The gradient is 1
A store has a sale with 10% off every item. When you enter the store, you receive a coupon that states that you receive an additional 40% off. Is this equal to a discount? Explain your answer.
The total percent of reduction is _____% , so this __ * is or is not * __equal to a discount.
Answers
Step-by-step explanation:
Step one:
We are told that the store offers off 10% of sales, this means that the store is offsetting the price down by 10% hence a price reduction.
Moreso, a coupon is a voucher entitling the holder to a discount off a particular product. the coupon is 40%, hence this is equal to a discount, that is price reduction by 40%.
Step two:
Say the price of an item is $100, a coupon if 40% will entitle the holder to only pay $60, that is
=40/100*100
=0.4*100
=$40 off
= 100-40
=$60
The total percent of reduction 10+40= 50%
This is equal to a discount on the sales price
Miguel has $25. He spends $6.75 on a movie ticket, $3.70 for snacks, and $2.00 for bus fare each way.
How much money does Miguel have left?
Miguel has $_____
left.
Answers
Answer:
$12.55
Step-by-step explanation:
25-6.75=18.25
18.25-3.70=14.55
14.55-2=12.55
Miguel has $12.55 left
Are 12:14 and 60:70 equivalent ratios?
yes
no
Answers
Answer:
Yes, they are equalent
Step-by-step explanation:
12:14 = 6:7
60:70 =6:7
both can be simplified to 6:7
What's the largest odd number you can make using all four digits 4, 5, 3, 6
Answers
Answer:
6543
Step-by-step explanation:
Not much to explain lol
Here,
Odd numbers are 3 and 5.
5>3The largest odd number =6543
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Input the equation of the given line.
The line including (4, 7) and (0, 7).
Answers
Answer:
[tex]y=7[/tex]
Step-by-step explanation:
First, let's use the two given points to find the slope. Remember the slope equation:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
[tex]m=\frac{7-7}{0-4}[/tex]
[tex]m=\frac{0}{-4}[/tex]
[tex]m=0[/tex]
If we're following slope-intercept form, what we have so far is
[tex]y=0x+b[/tex]
Substitute one of the given points for the [tex]x[/tex] and [tex]y[/tex] values in order to find [tex]b[/tex]:
[tex]7=0(4)+b[/tex]
[tex]7=b[/tex]
Now, if we put that back into our slope-intercept equation we get
[tex]y=0x+7[/tex]
or,
[tex]y=7[/tex]
Right off the bat, we can see how we ended up with this equation because both points have the same y-values. This indicates a horizontal line.
I hope this helps!
50 points please help please see image below
Answers
Answer:
395.841Step-by-step explanation:
surface area = 2πrh + 2πr²
where r = 7 m radius
h = 2 m
plugin values into the formula
surface area = 2πrh + 2πr²
= 2π (7) 2 + 2π (7)²
= 87.965 + 307.867
= 395.841 m²
Answer:
395.841 m²
Step-by-step explanation:
surface area = 2πrh + 2πr² and r = 7 m radius
h = 2 m
Plugin
2π (7) 2 + 2π (7)²
multiply into itself than add
87.965 + 307.867
add
395.841 m²
Therefore your answer would be 395.841 m²
16.9 and 1.7 and 0.17 and 2.0 added up
Answers
Answer:
20.77
Step-by-step explanation:
Answer:
20.77
Step-by-step explanation:
Simplify 16.9+ 1.7 to 18.6
18.6 +0.17+2.0
Simplify 18.6+0.17 to 18.77
18.77+2.0
Simplify.
ANddddd the answer is
20.77
Given 2y =a^x +2a ^-x and a^x>0.
Show that a^x= y + sqrt (y^2-)
Answers
Answer:
Answer by Yi Jing
Step-by-step explanation:
The phone company Splint has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 330 minutes, the monthly cost will be $141.5. If the customer uses 890 minutes, the monthly cost will be $337.5.
Required:
a. Find an equation in the form y= mx +b, where x is the number of monthly minutes used and y is the total monthly of the Splint plan.
b. Use your equation to find the total monthly cost if 624 minutes are used
Answers
Answer:
a) $141.5 = 330m + b...... Equation 1
$337.5 = 890m + b..... Equation 2
b) $244.4
Step-by-step explanation:
The phone company Splint has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 330 minutes, the monthly cost will be $141.5. If the customer uses 890 minutes, the monthly cost will be $337.5.
Required:
a. Find an equation in the form y= mx +b, where x is the number of monthly minutes used and y is the total monthly of the Splint plan.
If a customer uses 330 minutes, the monthly cost will be $141.5.
y = mx + b
$141.5 = 330m + b
If the customer uses 890 minutes, the monthly cost will be $337.5.
$337.5 = 890m + b
Combining the equations
$141.5 = 330m + b...... Equation 1
$337.5 = 890m + b..... Equation 2
b. Use your equation to find the total monthly cost if 624 minutes are used
Combining the equations
$141.5 = 330m + b...... Equation 1
$337.5 = 890m + b..... Equation 2
We Subtract Equation 2 from 1
-196 = -560m
m = -196/-560
m = 0.35
$337.5 = 890m + b..... Equation 2
$337.5 = 890 × 0.35 + b
$337.5 - 311.5 = b
b = 26
When x = 624
y = 624× m + b
m = 0.35 , b = 26
y = 624 × 0.35 + 26
y = 218.4 + 26
y = $ 244.4
Is the relation {(2,5), (0, -5), (-2, 6), (2, 3)} a function?
Answers
Answer:
Not a function
Step-by-step explanation:
9) Use the spinner below to answer the following questions
What is the Expected Value of a single spln?
Answers
Answer:
is that paper or did you write on the screen?
Consider parallel lines cut by a transversal.
Parallel lines q and s are cut by transversal r. On line q where it intersects line r, 4 angles are created. Labeled clockwise, from uppercase left: angle 1, angle 2, angle 4, angle 3. On line s where it intersects line r, 4 angles are created. Labeled clockwise, from uppercase left: angle 5, angle 6, angle 8, angle 7.
Explain which theorems, definitions, or combinations of both can be used to prove that alternate exterior angles are congruent.
Answers
Answer:
The alternate exterior angles 2 and 7 are congruent. One way to prove this is through the corresponding angles, vertical angles, and the transitive property.
First, we know <2 and <6 are congruent because of corresponding angles. Then we know they are equal because of the definition of congruent.
Next, we know <6 is congruent to <7 because of vertical angles. Then, we know they are equal because of the definition of congruent.
Finally, we know <2 is equal to <7 because of the transitive property.
Answer:
Here's the sample response!!
Step-by-step explanation:
Because vertical angles are congruent, angles 1 and 4 are congruent. Because corresponding angles are congruent, angles 4 and 8 are congruent. Because angle 4 is congruent to both 1 and 8, angle 1 is congruent to angle 8.
HELP ME PLEASEE ASAPAPAP PLEASE PLEASE PLEASE PLEASE!!!!!!!!!!!
Answers
Answer: AEC = 80
X=30
YW ;)