Answer:
2/3
Step-by-step explanation:
25=125^k
5^2=5^3k
2=3k
k=2/3
The value of k is k = 2/3.
What is an exponent?The number of times a number is multiplied by itself is referred to as an exponent.
Given that, [tex]25 = 125^k[/tex].
Follow the steps to find the value of k:
[tex]25 = 125^k\\\\5^2=(5^3)^k\\\\5^2=5^{3k}[/tex]
Since the base of the exponents is the same, it follows:
2 = 3k
k = 2/3
Hence, the value of k is k = 2/3.
Learn more about exponents here:
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Kofi and Kojo were given 380 cedis to share, Kojo had 15 cedis more than Kofi. If Kofi's share is x, find an expression for Kojo's share.Hence find how much each received.
Answer:
kojo = x + 15
kofi = $182.50
kojo = $197.50
Step-by-step explanation:
kofi = x
kojo = x + 15 (since Kojo h as 15 cedis more than Kofi)
380= x + 15 + x
2x + 15 = 380
combine like terms
2x = 380 - 15
2x = 365
x = 182.50
Kojo = 15 + 182.50 = $197.50
What value of x is in the solution set of 9(2x + 1) < 9x - 18?
-4
-3
-2
-1
Answer:
The only possible answer that is correct is the first one, x = -4.
Step-by-step explanation:
Simplify the given inequality as much as possible, and then substitute each of the given x values one by one to determine which is in the solution set.
9(2x + 1) < 9x - 18 becomes 18x + 9 < 9x - 18, which, if reduced by dividing all four terms by 9, becomes 2x + 1 < x - 2.
Simplifying further, we get x < - 3. The only possible answer that is correct is the first one, x = -4. -4 < -3 is true.
Step-by-step explanation:
9(2x + 1)<9x - 1818x + 9 < 9x - 1818x - 9x < - 18 - 99x < 27x = 27/9x = 3.What is the solution to the equation
[tex] \frac{1}{4} x + 2 = - \frac{5}{8}x - 5 [/tex]
Which statements regarding the vertex of a quadratic function are true? Select all that apply.
Answer:
the rules regarding the vertex of a quadratic function are:
the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function. If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value. In either case, the vertex is a turning point on the graph.
Hope This Helps!!!
What is the area of this figure? Round to the tenth if necessary.
Answer:
b) 850.1 centimeters.Step-by-step explanation:
To find the area of this figure, we must first find the areas of the shapes that compose this figure.
This figure is made up of a rectangle and a semicircle.
Remember: To find the area of a semicircle, multiply the radius by itself twice, then multiply the product pi, lastly divide the product by 2.
[tex]a=\pi r^2/2[/tex]
3.14 will be used for pi!
To find the area of a rectangle, multiply the length by the width. The product is the area of the rectangle.
[tex]a=lw[/tex]
Now, let's solve.
The diameter of the semicircle is 32 centimeters.
To find the radius of a semicircle, divide the diameter by 2.
[tex]32/2=16[/tex]
The radius of the semicircle is 16 centimeters.
Now that we have the radius, we can find the area of the semicircle.
[tex]\pi 16^2/2=401.92[/tex]
The area of the semicircle is 401.92 centimeters.
Furthermore, we find the area of the rectangle.
[tex]14*32=448.[/tex]
The area of the circle is 448 centimeters.
Next, we add the areas of both shapes to find the area of this figure.
[tex]401.92+448[/tex]
[tex]=849.92[/tex]
The final step is to round 849.92 to the nearest tenth.
Even though 849.92 to rounded to the nearest tenth is 849.9, there is no answer choice for this. The closest one to this answer is choice 'b.'
I, therefore, believe the area of this figure is 850.1 centimeters.
The equation x^2+ y^2+ 8x - 12y + 43 = 0 is the equation of a circle. Complete the square to change this
equation to standard form. Find the radius and the coordinates of the center of the circle and then graph the
circle.
Answer:
ans: centre of circle is ( -4 , 6 )
and radius is 3 unit
if 24= 2f+3f+f, find f
Answer:
6f = 24
f = 4
Step-by-step explanation:
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\textsf{24= 2f + 3f + f}\\\text{COMBINE the LIKE TERMS}\\\\\textsf{2f + 3f + f}\\\textsf{2f + 3f = \bf 5f}\\\textsf{5f + f}\\\textsf{= \bf 6f}\\\text{New equation: \textsf{6f = 24}}\\\text{DIVIDE 6 to BOTH SIDES}\\\mathsf{\dfrac{6f}{6}=\dfrac{24}{6}}\\\textsf{CANCEL out: }\mathsf{\dfrac{6}{6}}\textsf{ because that gives you 1}\\\textsf{KEEP: }\mathsf{\dfrac{24}{6}}\textsf{ because that helps solve for the f-value}\\\\\mathsf{\dfrac{24}{6}=\bf f}\\\\\\\mathsf{\dfrac{24}{6}=24\div6=\bf 4}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \huge \bf f = 4}}}\huge\checkmark[/tex]
~[tex]\large\textsf{Good luck on your assignment and your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Change 1/3 to a decimal number (show the working)
Answer:
0.33
Step-by-step explanation:
1/3 can also be written as 1 ÷ 3 which equals 0.33
Answer:
0.333333333
Step-by-step explanation
Question 2 (Essay Worth 10 points)
(03.01 MC)
Look at the rectangle and the square:
A rectangle PQRS and square LMNO are drawn side by side. The length SR of the rectangle is labeled as 12 inches, and the width QR is labeled as 6 inches. The side LM of the square is labeled as 6 inches.
Sam says that the length of diagonal SQ is two times the length of diagonal OM.
Is Sam correct? Justify your answer and show all your work. Your work should state the theorem you used to find the lengths of the diagonals.
Answer:
Sam is incorrect.
Step-by-step explanation:
Using Pythagorean Theorem, we can find the length of diagonal SQ as 13.4 (6^2 + 12^2 = c^2, 36 + 144 = c^2, sqrt(180) = c, c is approx 13.4). We can do the same for diagonal OM (6^2 + 6^2 = c^2, 36 + 36 = c^2, 72 = c^2, sqrt(72) = c, c is approx 8.5). Sam is therefore incorrect because 13.4 is not double of 8.5.
Answer:
Sam is incorrect.
Step-by-step explanation:
Sam is incorrect. By using the Pythagorean theorem, we can find out what each diagonal is equal to.
Starting with diagonal SQ...
6^2 + 12^2
= 36 + 144
= 180
Square root of 180?
= 13.41
Diagonal OM...
6^2 + 6^2
= 36 + 36
= 72
Square root of 72?
= 8.48
Therefore, Sam is incorrect because 8.4 isn't half of 13.4.
When drawn in standard position, in which quadrant does the terminal side of the angle −240° lie?
Answer:
Option (2)
Step-by-step explanation:
All angles are positive when measured counterclockwise from the x-axis.
Terminal side of 240° degrees when measures counterclockwise will lie in the 3rd quadrant.
But the angle is -240°.
That means angle is being measured clockwise from the x-axis.
Therefore, terminal side of the of the angle will be in the 2nd quadrant.
Option (2) will be the correct option.
Help me or Shrek's donkey won't get pancakes!
Answer:
A. y=x and y=x+2
Step-by-step explanation:
A.
y=x and y=x+2
The equations both match the slope and intercept of the graphed equations.
Can I have the pancakes instead of the donkey?
Solve for X:
-2(x+2) < 14
Answer:
answer is 45 + 5 so it's 50
Answer:
-2X-4<14
-2X<18
X>9
Step-by-step explanation:
If you have 36 ft of fencing, what are the bases and side lengths of the different parallelograms you could enclose with the fencing? Consider only whole-number dimensions.
Answer:
[tex](l,w) = (1,17)[/tex]
[tex](l,w) = (2,16)[/tex]
[tex](l,w) = (3,15)[/tex]
---
---
-
[tex](l,w) = (9,9)[/tex]
Step-by-step explanation:
Given
[tex]P = 36ft[/tex] --- perimeter
[tex]l \to length[/tex]
[tex]w \to width[/tex]
Required
Possible dimension of different parallelogram
The perimeter is calculated as:
[tex]P=2(l+w)\\\\\\[/tex]
So,we have:
[tex]2(l+w)=36[/tex]
Divide by 2
[tex]l + w = 18[/tex]
Since l and w must be positive integers, the possible dimensions are:
[tex](l,w) = (1,17)[/tex]
[tex](l,w) = (2,16)[/tex]
[tex](l,w) = (3,15)[/tex]
---
---
-
[tex](l,w) = (9,9)[/tex]
On a piece of paper, graph y = 3x - 2. Then determine which answer choice
matches the graph you drew. Find the slope of the line.
Identify the solution that has the correct graph and the correct slope.
Answer:
NOT A or B
probably C ?
Step-by-step explanation:
A food sample contains 300 bacteria. The doubling time for bacteria left at room temperature is 20 minutes. How many minutes will it take to reach an unsafe level of 100000 bacteria?
Answer:
167.6 minutes
Step-by-step explanation:
The formula is given as:
P(t) = Po × (2)^t/k
Where
P(t) = Population after time t = 100000
Po = Initial population = 300
k = Doubling time = 20 minutes
t = Time = ?
Hence:
100000 = 300 × (2)^t/20
Divide both sides by 300
100000/300 = (300 × (2)^t/20)/300
333.3 = 2^t/20
Take the In of both sides
In 333.3 = In (2^t/20)
In 333.3 = t/20 In 2
Divide both sides by In 2
In 333.3/In 2 =( t/20 In 2)/In 2
8.3806775072 = t/20
Cross Multiply
t = 8.3806775072 × 20
t = 167.61355014 minutes
Approximately = 167.6 minutes
Therefore, the time it will take to reach an unsafe level of 100000 bacteria is 167.6 minutes
Figure ABCD is a parallelogram.
Parallelogram A B C D is shown. The length of A B is 4 y minus 2, the length of B C is 2 x + 2, the length of D C is 2 y + 6, and the length of A D is 3 x minus 1.
What is the perimeter of ABCD?
14 units
38 units
44 units
49 units
Answer:
It is 44
Step-by-step explanation:
The perimeter of the paralllelogram given is: 44 units.
What is the Perimeter of a Parallelogram?Perimeter = 2(a + b), where a and b are the legs of the sides adjacent to each other.
Given the following:
AB = 4y - 2BC = 2x + 2DC = 2y + 6AD = 3x - 1Since opposite sides of a parallelogram are equal, therefore:
4y - 2 = 2y + 6
4y - 2y = 2 + 6
2y = 8
y = 4
2x + 2 = 3x - 1
2x - 3x = -2 - 1
-x = -3
x = 3
Perimeter of the paralllelogram = 2(AB + AD) = 2(4y - 2 + 3x - 1)
Plug in the values of x and y
Perimeter of the paralllelogram = 2(4(4) - 2 + 3(3) - 1)
Perimeter of the paralllelogram = 2(16 - 2 + 9 - 1)
Perimeter of the paralllelogram = 44 units.
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Pls answer……………………..
Answer:
Step-by-step explanation:
J and k are parallel if
angle 1 = angle 4 (vertically opposite angles)
angle 2 + angle 5 = 180 degree (being co interior angles)
angle 4 = angle 5 (being alternate interior angles)
angle 1 = angle 5 (being corresponding angles)
Answer:
2 and 5 are co - interior angles
1 and 3 are corresponding angles
1 and 4 are alternate
6 and 8 are corresponding angles
Step-by-step explanation:
Emma wants to give someone 5.2m every day she can donate 10k how long will it take her to donate 5.2m?
Answer:
520 days
Step-by-step explanation:
--------------------------------------
5.2 million = 5,200,000
10 thousand = 10,000
5,200,000 ÷ 10,000 =
= 520 days
---------------
Hope this helps.
Answer:
520 days
Step-by-step explanation:
thanks for the pts
✌️❤️✌️
What is the total number of digits required in numbering the pages of a book, which has 1, 150 pages?
Answer:
3,493 digits
Step-by-step explanation:
Total pages of the book = 1,150
Page 1 - 9 = 9 digits
Page 10 - 99
= 2 * 90 pages
= 180 digits
Page 100 - 999
= 3 × 900 pages
= 2,700 digits
Page 1000 - 1,150
= 4 × 151 pages
= 604 digits
Total digits required in numbering 1,150 pages = 9 + 180 + 2,700 + 604
= 3,493 digits
Total digits required in numbering 1,150 pages = 3,493 digits
What is Euclid's fifth postulate?
How would you rewrite Euclid’s fifth postulate so that it would be easier to understand?
Step-by-step explanation:
espero que te ayude amigo
De las ventas obtenidas en el mes de enero , el dueño de " La chiquita " tiene la obligación de entregar el 16 % de IVA . Si en un mes se vendieron en la tienda $80,000 ¿ Cuánto tendrá que reportar de IVA al gobierno ?
Answer:
The amount paid as VAT is $ 12800.
Step-by-step explanation:
Sales = $ 80,000
VAT = 16 %
The amount of VAT paid to the government is
= 16 % of $ 80,000
= 0.16 x $ 80,000
= $ 12800
The amount paid as VAT is $ 12800.
The money m (in £) Billy has to spend each week is his wage w (in £) subtract the tax t (in £) he pays on his income. Enter a formula for the money he can spend and enter how much he has to spend if he earns £150 a week and pays £42 in tax.
Answer:
m = w - t
£108
Step-by-step explanation:
m = Money Billy has to spend per week :
m = wage, w - tax, t
Hence,
m = w - t
Given;
Wage = £150 ; tax = £42
m = £150 - £42
m = £108
question 1:
[tex]f(x) = {x}^{2}[/tex]
and
[tex]k(x)=2x + 1[/tex]
im supposed to simplify
[tex](k \times f)(x)[/tex]
Answer:
(k × f)(x) = 2x³ + x²
General Formulas and Concepts:
Algebra I
FunctionsFunction NotationExpand by FOILStep-by-step explanation:
Step 1: Define
Identify
f(x) = x²
k(x) = 2x + 1
(k × f)(x) = k(x)f(x)
Step 2: Find
Substitute in functions: (k × f)(x) = x²(2x + 1)Expand [FOIL]: (k × f)(x) = 2x³ + x²Expand.
Your answer should be a polynomial in standard form.
(x - 4)(x - 6) =
Answer:
x^2 - 10x + 24
Step-by-step explanation:
(x - 4)(x - 6)
x(x - 6) -4(x - 6)
x^2 -6x -4x + 24
x^2 - 10x + 24
Answer:
[tex] {x}^{2} - 10x + 24[/tex]
Step-by-step explanation:
[tex](x - 4)(x - 6) \\ = x(x - 6) - 4(x - 6) \\ = {x}^{2} - 6x - 4x + 24 \\ = {x}^{2} - 10x + 24 \\ [/tex]
Mario sells electronics at Big Box Electronics Store. He is paid a salary of $250 a week
plus 7% commission on his sales.
a) Write an equation for the line, in slope/y-intercept form, representing his weekly
earnings, E, where Sis his weekly sales. Put this answer into Blank #1.
b) Identify the slope. Put this answer into Blank #2.
c) What does the slope represent? Put this answer into Blank #3.
c) What does the E-intercept represent? Put this answer into Blank #4.
d) What were Mario's sales in the week he earned $530? Put this answer into Blank
#5.
Blank # 1
Blank # 2
Blank # 3
Blank #4
Blank # 5
Answer:
Step-by-step explanation:
E = 0.07s + 2500.07Salary per weekWhat he makes if he doesn't sell anything that week $4000someone PLSSS HELPPP fast plsss !!!
The problem has been started for you.
What is the quotient?
86
86.6
86.ModifyingAbove 6 with bar
87
Answer:
the third one
Step-by-step explanation: 6 22 22 24
the quotient is 86.6666666 the repeating 6 is sometimes written with a bar above the .6 like
86.6 except the bar is on top of the second 6
3. A student gets a grant of $10 000 a year. Assuming her grant is increased by 7% each year, what will her grant be in four years time?
Answer:
that's all~~~~~~~~~~~~~~~~~~
The pH of a solution is a measure of the quantity of hydrogen atoms (H) in the solution. It is given by the formula f(x) = −log x. In the formula, x = [H+], the molar concentration of hydrogen atoms, or the number of moles of hydrogen atoms per liter of solution
The question is incomplete. The complete question is :
The pH of a solution is a measure of the quantity of hydrogen atoms (H) in the solution. It is given by the formula f(x) = −log x. In the formula, x = [H+], the molar concentration of hydrogen atoms, or the number of moles of hydrogen atoms per liter of solution
The approximate molar concentration of several chemicals are given. Find the pH of each. Use the calculator and round to the nearest tenth, if necessary.
Oven cleaner: [H+] = 10−13 pH =
Water: [H+] = 0.0000007 pH =
Blood: [H+] = 0.00000004 pH =
Vinegar: [H+] = 0.0063 pH =
Solution :
Given formula :
f(x) = −log x
Here, x = [H+] = molar concentration of hydrogen atoms
Therefore, the pH of each of the following solution are :
Oven cleaner
[[tex]$H^+$[/tex]] = [tex]$10^{-13}$[/tex]
pH = - log [[tex]$H^+$[/tex]]
= [tex]$- \log 10^{-13}$[/tex]
= 13
Water
[[tex]$H^+$[/tex]] = 0.0000007
pH = - log [[tex]$H^+$[/tex]]
= - log 0.0000007
= 6.2
Blood
[[tex]$H^+$[/tex]] = 0.00000004
pH = - log [[tex]$H^+$[/tex]]
= - log 0.00000004
= 7.4
Vinegar
[[tex]$H^+$[/tex]] = 0.0063
pH = - log [[tex]$H^+$[/tex]]
= - log 0.0063
= 2.2
(Find m∠RTS) m∠RTS=
Answer:
[tex]m\angle RTS=34^{\circ}[/tex]
Step-by-step explanation:
From the Isosceles Base Theorem, the two base angles of an Isosceles Triangle are equal. Therefore, [tex]m\angle RTS=m\angle TRS[/tex].
Since the sum of the interior angles of a triangle is 180 degrees, we have:
[tex]m\angle RTS +m\angle TRS+112=180,\\2\cdot m\angle RTS+112=180,\\2\cdot m\angle RTS=68,\\m\angle RTS=\boxed{34^{\circ}}[/tex]