The blank is -8
Step-by-step explanation:
Let us revise some rules of indices:
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{m+n}[/tex] [tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{m-n}[/tex] [tex]a^{m}[/tex] = [tex]a^{n}[/tex] , them m = n∵ [tex]4^{3}[/tex] × [tex]4^{-6}[/tex] = [tex]4^{5}[/tex] × [tex]4^{x}[/tex]
∵ All bases are equal
∴ Use the first and third rule above to find x
∵ [tex]4^{3}[/tex] × [tex]4^{-6}[/tex] = [tex]4^{3+-6}[/tex]
∴ [tex]4^{3}[/tex] × [tex]4^{-6}[/tex] = [tex]4^{-3}[/tex] ⇒ L.H.S
∵ [tex]4^{5}[/tex] × [tex]4^{x}[/tex] = [tex]4^{5+x}[/tex] ⇒ R.H.S
Equate L.H.S and R.H.S
∴ [tex]4^{-3}[/tex] = [tex]4^{5+x}[/tex]
Equate the indices of the two sides
∴ -3 = 5 + x
- Subtract 5 from both sides
∴ -8 = x
∵ x represents the blank
∴ The blank = -8
The blank is -8
Learn more:
You can learn more about the indices in brainly.com/question/4419221
#LearnwithBrainly
Four to the power of three times four to the power of negative six is equal to four to the power of five times four to the power of negative eight.
To solve for the missing exponent, we can use the following properties of exponents:
Multiplying exponents with the same base: When multiplying powers with the same base, we add their exponents.
Negative exponents: A number raised to a negative exponent is equal to its reciprocal raised to the positive exponent.
Applying these properties:
4^3 * 4^-6 = 4^(3 - 6) = 4^-3 (since 4^-6 = 1/4^6)
4^5 * 4^x = 4^(5 + x)
Setting these equal to find x:
4^-3 = 4^(5 + x)
Therefore, x = -3 - 5 = -8.
In the basketball game, you made 12 baskets and scored 19 points. How many 2-point shots did you make? How many free throws did you make?
Answer:
0.5
Step-by-step explanation:
Answer:12 baskets - 19pts
2×7= 14pts
1×5= 5pts
Therefore: (7+5) baskets= (14+5)pts
> 12 baskets = 19pts
Step-by-step explanation:
For a 2-point shots to make 14pts, there will be 7 baskets/throws.
A free throw shot is 1pts, so there has to be about five (5) free throws which will make 5pts.
Therefore, there will be (7+5 baskets) 12 shots in total.
2-point shots = 7
1-free throws = 5
Please help, I’m really stuck on this question!
How can you make different triangles with the same angle measures?
Form different triangles with angle measures 90°, 60°, and 30°
How can you make different triangles with the same angle measures?
OA. Make triangles with the same side lengths but different angle measures
OB. It is not possible to make different triangles with the same angle measures.
OC. Make triangles with the same angle measures and the same side lengths
OD. Make triangles with the same angle measures but different side lengths
Click to select your answer and then click Check Answer.
Answer:
D. Make triangles with the same angle measures and different side length.
Step-by-step explanation:
Since the values of the angles of the triangle are constant, varying the length of the sides would give series of triangles. Note that the length of the three sides must not be equal at any stage of the varying process.
Which equation results from adding the equations in this system? 11 x minus 3 y = -17. Negative 4 x + 3 y = - 18.
- 7 x = negative 35
- 7 x = 35
7 x = negative 35
7 x = 35
Answer:
Therefore the results from adding the equation in this system is
[tex]7x=-35[/tex]
Step-by-step explanation:
Given:
Equations as
[tex]11x-3y=-17[/tex] .......................1
[tex]-4x+3y=-18[/tex] .......................2
To Find :
Result when adding equation 1 and 2 = ?
Solution
On adding equation 1 and 2 the "3y" term will get cancel and the like terms will combine that is add (11x and -4x ) and ( -17 and - 18) as shown below
11x - 3y = -17
-4x + 3y = - 18
-------------------------------------------
7x + 0 = - 35
---------------------------------------------
Therefore the results from adding the equation in this system is
[tex]7x=-35[/tex]
Answer:
C
Step-by-step explanation:
did test
How do you solve s=5/6t
Answer:
if you want to solve for t: t = 6s / 5
if you want to solve for s: s = 5t / 6
Step-by-step explanation:
HELP I AM DYEING STUCK ON THIS QUESTION
Q: v-14≤-18
I'm gonna assume you want us to simplify it.
v-14≤-18. Add 14 to both sides:
v ≤ -4
Answer:
v ≤ -4
Step-by-step explanation:
v - 14 ≤ -18
v -14 + 14 ≤ -18 + 14
v ≤ -4
the cruise ship is traveling at a uniform speed. after 11 hours, the cruise ship will be____nautical miles from light house.
Hence, After 11 hours, the cruise ship will be 244.25 nautical miles from the lighthouse. Hence, At the start of the journey, the cruise ship was 10.5 nautical miles from the lighthouse.
Answer:
the answer is the ship is traveling at 21.25 MPH, started 10.5 miles from lighthouse and after 11 hours will be 244.25 miles from the lighthouse.
Step-by-step explanation:
Solve the following equation: 3x^3+5x^2-4x-4=0
Answer:
1
Step-by-step explanation:
Simplifying
3x + 2(4x + -4) = 3
Reorder the terms:
3x + 2(-4 + 4x) = 3
3x + (-4 * 2 + 4x * 2) = 3
3x + (-8 + 8x) = 3
Reorder the terms:
-8 + 3x + 8x = 3
Combine like terms: 3x + 8x = 11x
-8 + 11x = 3
Solving
-8 + 11x = 3
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '8' to each side of the equation.
-8 + 8 + 11x = 3 + 8
Combine like terms: -8 + 8 = 0
0 + 11x = 3 + 8
11x = 3 + 8
Combine like terms: 3 + 8 = 11
11x = 11
Divide each side by '11'.
x = 1
Simplifying
x = 1
What is the answer to the question ?
Answer:
si amuigos hasta luego to es bien cien nueve
Step-by-step explanation:
Terrance buys a new car for $20,000. The value of the car depreciates by 15% each year. If f(x) represents the value of the car after x years, which function represents the car’s value?
Leila‘s coffee shop makes a blend that is a mixture of two types of coffee type a coffee cost Layla $4.85 per pound and type B coffee cost $5.90 per pound this month leather made it 142 pounds of the blend for the total cost of $781.10 how many pounds of type B coffee did she use
Answer:
Therefore she used (142-54)=88 pounds of type B coffee.
Step-by-step explanation:
Given, Leila's coffee shop makes a blend that is a mixture of two types of coffee.Type A coffee $4.85 per pound and type B coffee cost $5.90 per pound. She made 142 pounds of the blend for the total cost of $781.10.
The cost price of the blend per pound is = $(781.10÷142)
=$5.5
Let , the amount type A in the blend be x
Then the amount of type B in the blend is (142-x)
The cost price of x pound of type A coffee is = $(4.85×x) =$4.85x
The cost price of(142- x) pound of type B coffee is =$(142-x)×5.90
According to the problem,
4.85x+(142-x)×5.90 = 781.10
⇔4.85x +837.8-5.90x=781.10
⇔1.05x=56.7
⇔x=(56.7÷1.05)
⇔x=54
Therefore she used (142-54)=88 pounds of type B coffee.
adam sells medical magazine and books. the table shows price for both Magazine £8
books £15
each week Adam earns £ 200 basic pay 10% of the magazine price for each sold
15% of the books price for each sold
last week Adam sold 42 magazines and 14 books
work out the total amount Adam earned last week
Adam earned a total of £265.10 last week.
Step-by-step explanation:
Step 1; Adam earns a basic pay of £200 each week. He earns 10% of the magazine price for each sold and 15% of the book price for each sold. Each magazine costs £8 and each book costs £15. He sells 42 magazines and 14 books.
Money earned for selling a magazine = 10% × £8 = 0.10 × £8 = £0.80,
Money earned for selling a book = 15% × £15 = 0.15 × £15 = £2.25,
Money earned for selling 42 magazines = 42 × £0.80 = £33.60,
Money earned for selling 14 books = 14 × £2.25 = £31.50,
Money earned for selling 42 magazines and 14 books = £33.60 + £31.50 = £65.10.
Step 2; Now we have to calculate his last week's salary which is his weekly pay and his earnings from selling magazines and books. We found that he earned £31.50 from selling books and magazines. His weekly salary is £200.
Last week's salary = £200 + £65.10 = £265.10.
Answer: £265.10
Step-by-step explanation:
Adam gets £200 each week.
10% of 42 magazines
Magazines opcost £8
10% × £8 = 0.10 × £8 = £0.80
42 × £0.80 = £33.60
15% of 14 books
Each book cost £15
15% × £15 = 0.15 × £15 = £2.25,
14 × £2.25 = £31.50
Last Week's Salary:
£31.50 + £33.60 = £65.10
£200 + £65.10 = £265.10 (last weeks salary)
Write a number of your choice, using the following clues:
a two digit number
greater than 40
divisible by both 2 and 3
Answer:
42
Step-by-step explanation:
42/2 = 21
42/3 = 14
Answer:
54 is what I thought of.
Select all equations that have no solution.
A. 12x – 3 – 6x = 6x – 3
B. 3 + 16x = 3 + 24x – 8x
C. 2 + 12x - 4x = 2 + 8x
D. 12x – (6x + 8) = 6x + 4
Answer:
D
Step-by-step explanation:
A.
12x – 3 – 6x = 6x – 3
12x - 3 = 12x -3
-3 = -3 infinite solution
B.
3 + 16x = 3 + 24x – 8x
3 + 16x = 3 + 16x
3 = 3 infinite solution
C.
2 + 12x - 4x = 2 + 8x
2 + 8x = 2 + 8x
2 = 2 infinite solution
D.
12x – (6x + 8) = 6x + 4
6x - 8 = 6x + 4
-8 = 4 no solution
HELP ME!!! I've been stuck!
Answer:
You have to fill the blank squares to complete the table.See the figure attached and the explantion below.Explanation:
The figure attached shows the three squares that you have to fill to complete the table to summarize the different theorems to prove triangles are congruent.
1. SAS
SAS stands for Side Angle Side. That means that whenever two sides and the included angle on one triangle are congruent to two sides and the included angle of another triangle, then those two triangles are congruent.
Thick marks are used to mark the corrsponding parts, sides or angles that are congruent. That is why the two triangles to the first triangles on the image (on the upper square to the right) are marked:
One thick straight mark for two sides that are congruentTwo thick straight marks for the other two sides that are congruentOn thick curved mark for the two angles that are congruentIn that way, the figures show two triangles, with two congruent sides and the included angle congruent, to prove that the two triangles are congruent by the SAS theorem.
2. ASA
ASA stands for Angle Side Angle.
The ASA congruency theorem states that if two angles of a triangle and the included side are congruent, then the two triangles are congruent.
Thus you have to add the legend "Two congruent angles with and included side", which means that if the two angles and the included side on one triangle are congruent to two angles and the included side of other triangles, then both triangles are congruent.
The rule to mark the sides and angles that are congruent is with the use of thick marks. This is how it was done in the drawing of the two triangles in the lower right square:
One thick straight mark for two sides that are congruentOne thick curved mark for two angles that are congruentTwo thick curved marks for the other two angles that are congruentEvaluate the expression below when x=9.5 and y=3. 12x - 3y exponent 2
How do you find the percent increase from 120 to 144
Answer:
20%
Step-by-step explanation:
If 120 = 100%
144 = x
By cross multiplication,
120x = 144 * 100
120x = 14400
x = 14400/120
x = 120%
The percentage increase is 20%
How much larger is the volume of a cylinder with a height of 8.5 inches and a radius of 4 inches compared to a cylinder with a volume of 390 cm^3?
______cm^3 larger
The first cylinder is larger by 6607.9 cm³.
Step-by-step explanation:
Step 1: Calculate volume of cylinder 1 using formula V(1) = πr²h, where r = 4 in = 10.16 cm and h = 8.5 in = 21.59 cm⇒ V(1) = 3.14 × 10.16² × 21.59 = 6997.9 cm³
Step 2: Find the difference between the volumes of the 2 cylinders.V(2) = 390 cm³
⇒ Difference = 6997.9 - 390 = 6607.9 cm³
Answer:
37.04
Step-by-step explanation:
(0, 3) and (-2,5);
(5,-2) and (0, 3)
Answer:
Step-by-step explanation:
Solve.
4x2 + 6 = 40
Round to the nearest hundredth.
Enter your answers in the boxes.
Do 4x^2 = 16x
16x+6 = 40
-6 -6
16x = 34
/16 /16
x=2.125
Rounded to the nearest hundredth is, 2.13
IF THIS IS HELPFUL PLS GIVE ME BRAINLIEST AND ANSWER MY MATH PROBLEM.
Answer:
-2.92 and 2.92
i took the test
Wh
at is 15,000:00 in ratio of 5:3
Answer:
9375 : 5625
Step-by-step explanation:
The total of the ratio units is 5+3=8, so each ratio unit stands for ...
15000/8 = 1875
Multiply each number of ratio units by this value to get your division:
5(1875) : 3(1875) = 9375 : 5625
The value of w is:
show work for brainlist
Step-by-step explanation:
By angle bisector property:
[tex] \frac{w}{30} = \frac{15}{18} \\ \\ \therefore \: w = \frac{15 \times 30}{18} \\ \\ \therefore \: w = \frac{15 \times 30}{6 \times 5} \\ \\ \therefore \: w = 3 \times 5\\ \\ \huge \orange{ \boxed{ \therefore \: w = 15}}[/tex]
The formula below is used to convert a temperature in degrees Celsius,C, to a
temperature in degrees Fahrenheit, F.
F= 1.8C + 32
on temperature in a mountain city was 15°C. What was the high temperature in
degrees Fahrenheit?
Answer:
is
47 degree fahrenheit
The high temperature in degrees Fahrenheit was [tex]\( 59^\circ \)[/tex] Fahrenheit.
To convert a temperature from Celsius to Fahrenheit using the formula F = 1.8C + 32, where F is the temperature in Fahrenheit and C is the temperature in Celsius, you simply plug in the value of C and solve for F.
Given that the high temperature in the mountain city was [tex]\( 15^\circ \)[/tex] Celsius, we can plug this value into the formula:
F = 1.8 * 15 + 32
F = 27 + 32
F = 59
So, the high temperature in degrees Fahrenheit was [tex]\( 59^\circ \)[/tex]Fahrenheit.
What is X +2/5 equals 3 1/3
Answer:
Exact Form: X = 44/15
Decimal Form: X = 2.93¯
Mixed Number Form: X = 2 14/15
Step-by-step explanation:
{(-2, 6), (-5, -1), (3, 7), (-5, 0)}
Domain:
Range:
Function?
{(-2, 6), (-5, -1), (3, 7), (-5, 0)}
Domain: The domain is all the x-values (-2, -5, 3, -5)
Range: The range is all the y-values (6, -1, 7, 0)
Function: It's not a function because of the x-value -5 is repeating.
Answer:
Step-by-step explanation:
domain (ur x values) = [ -5,-2,3 ]...only write repeating values once
range (ur y values) = [ -1,0,6,7]
a function will not have any repeating x values....it can have repeating y values, just not the x ones...all x's have to be different
therefore, this is not a function because u have repeating x values of -5
HELP ME PLEASE :( <3 Which expression is equivalent to 4147−−−√ a - 37√ . b - 283√ . c - 127√
The simplified expression equivalent to 4147−−−√ a - 37√ . b - 283√ . c - 127√ is 64 - 6√ * b - 283√ * c - 127√.
To simplify the expression 4147−−−√ a - 37√ . b - 283√ . c - 127√, we can first try to identify any common factors among the terms.
However, since each term involves a different square root, it's not possible to simplify the expression further using common factors.
To proceed, we can try to simplify each term individually. For instance, we can simplify 4147−−−√ by identifying that 4147 is a perfect square. Since 4147 = 64 * 64, we can rewrite the expression as:
4147−−−√ = √(64 * 64) = 64
Similarly, we can simplify 37√ . b by identifying that 37 is a perfect square. Since 37 = 6 * 6, we can rewrite the expression as:
37√ . b = √(6 * 6) * b = 6√ * b
Applying the same logic to the remaining terms, we get the simplified expression:
64 - 6√ * b - 283√ * c - 127√
Therefore, the simplified expression equivalent to 4147−−−√ a - 37√ . b - 283√ . c - 127√ is:
64 - 6√ * b - 283√ * c - 127√
UREGENT HELP please quick
Answer:
A
Step-by-step explanation:
In the figure, AE, BF, DG, and HC intersect at point H, and FHG is a right angle.
Somebody help, I don't get this!
Answer:
1. False
2. True
3. True
Step-by-step explanation:
1. ∠AHB and ∠AHG are vertical angle False
2.∠EHF and ∠DHE are adjacent angle True
3. The measure of ∠FHG is equal to the measure ∠DHF True
Jackson is building a double desk.The tops need to be 120 in long.Each board is 66 inches.How much will he need to cut if he buys 2 ?
He will need to cut altogether 12 inches to fit on the top if h buys 2 to adjust on the double desk.
Step-by-step explanation:
Jackson building a double desk requires 120 in long.When each board is 66 inches Therefore, if he buys 2 Boards, 2 x 66 = 132He needs to cut . subtracting 132 - 120 to adjust on the desk.132-120 = 12 if he cuts the board to adjust on each desk.max spends three times as long on his math homework than he does on his science homework
3m=s
Where m= math homework and s= science homework.
nannie
9/11 times 7/10 simplified