Answer:
15/p and -3
Step-by-step explanation:
4(px+1)=64
Distribute 4: 4px + 4=64
Subtract 4 from both sides : 4px+4-4=64-4
Divide by 4p: 4px/4p=60/4p
x=15/p
you have a $20 bill. If you buy 24 pensa and 12 pencils, you will get $1.40 change. If you buy 12 pens and 24 pencils, you will get 4.40 change. How much does each pen and each pencil cost
Answer:
The cost of a pen is $0.60 and the cost of a pencil is $0.35
Step-by-step explanation:
Let
x-----> the cost of a pen
y----> the cost of a pencil
we know that
24x+12y=20-1.40
24x+12y=18.60 -----> equation A
12x+24y=20-4.40
12x+24y=15.60 -----> equation B
Solve the system of equations by graphing
Remember that the solution is the intersection point both graphs
The solution is the point (0.60,0.35)
see the attached figure
therefore
The cost of a pen is $0.60
The cost of a pencil is $0.35
A 150 pound woman would receive 24 grams of a certain medicine. How many grams should a 120 pound woman receive?
Answer : 19.23 round if you have to
Step-by-step explanation:
Divide 150 by 24 which is 6.15
Then divide 120 by 6.15
Which is 19.23
And thats your answer :)
Answer:
19.2 grams of medicine should be received by 120 pound woman
Step-by-step explanation:
150 pound woman receive medicine = 24 grams, we need to find how many grams of medicine should 120 pound women receive?
Solution:
150 pound woman receive medicine = 24 grams
1 pound woman receive medicine = 24 /150
120 pound woman receive medicine = (24 /150) * 120 = 19.2 grams.
So, 19.2 grams of medicine should be received by 120 pound woman.
For what value of a does (1/9)^a+1 =81^a+1 x 27^2-a ?
-4
-2
2
6
Answer:
- 4
Step-by-step explanation:
Using the rule of exponents
• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]
• [tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]
[tex](\frac{1}{9}) ^{a+1}[/tex] = [tex]9^{-(a+1)}[/tex] = [tex]3^{-2(a+1)}[/tex]
and right side
= [tex]3^{4(a+1)}[/tex] × [tex]3^{3(2-a)}[/tex]
Hence
[tex]3^{-2a-2}[/tex] = [tex]3^{4a+4}[/tex] × [tex]3^{6-3a}[/tex]
[tex]3^{-2a-2}[/tex] = [tex]3^{a+10}[/tex]
Equating exponents on both sides gives
a + 10 = - 2a - 2 ( add 2a to both sides )
3a + 10 = - 2 (subtract 10 from both sides )
3a = - 12 ( divide both sides by 3 )
a = - 4
Answer:
the answer to the question you is A on edg
Step-by-step explanation:
A decagon has angles that measure 156°, 135°, 147°, 160°, 116°, 150°, 150.2°, 119.2°, 146.6°, and z. What is z?
bearing in mind that the sum of all interior angles in a polygon is
180(n - 2) n = number of sides in the polygon
a DECAgon, DECA=10, has 10 sides, and thus the sum of all its interior angles is 180(10 - 8) = 1440.
[tex]\bf 156+135+147+160+116+150+150.2+119.2+146.6+z=1440 \\\\\\ 1280+z=1440\implies z=1440-1280\implies z=160[/tex]
Final answer:
The angle z in the decagon is calculated by subtracting the sum of the given angles from the total interior angle sum of a decagon, which is 1440°. The measure of angle z is 159.8°.
Explanation:
In geometry, the sum of the interior angles of an n-sided polygon is given by the formula (n - 2) × 180°. For a decagon, which is a 10-sided polygon, this sum is (10 - 2) × 180° = 8 × 180° = 1440°. To find the measure of the unknown angle z in the decagon with the given angle measurements, we can subtract the sum of the known angles from this total.
First, let's add up the given angles: 156° + 135° + 147° + 160° + 116° + 150° + 150.2° + 119.2° + 146.6° = 1280.2°. Now, subtract that sum from the total sum of the angles for a decagon: 1440° - 1280.2° = 159.8°. Therefore, the measure of angle z is 159.8°.
Find the infinite geometric sum of 80 + 10 +1.25 + ... to 5 decimal places past the decimal point.
To find the infinite geometric sum of the series 80 + 10 + 1.25 + ..., use the formula S = a / (1 - r), with 'a' as the first term and 'r' as the common ratio. Apply the significant figures principle for accurate rounding when approximating to a certain number of decimal places.
Explanation:The student's question involves finding the infinite geometric sum of the series 80 + 10 + 1.25 + .... To determine this sum, we use the formula for the sum of an infinite geometric series, S = a / (1 - r), where 'S' is the sum of the series, 'a' is the first term, and 'r' is the common ratio between terms. In this series, 'a' is 80, and the common ratio 'r' can be found by dividing the second term by the first term, which is 10/80 or 1/8.
Plugging the values into the formula gives us S = 80 / (1 - (1/8)) which simplifies to S = 80 / (7/8) = 80 * (8/7) = 640/7. Calculating this yields an infinite sum which can be approximated to decimal places as needed.
For precise calculations, especially when rounding to a certain number of decimal places or significant figures, the rules of significant figures must be followed. As the sample information shows, if a number in the tenths place is to be dropped and it's greater than 5, we round up to ensure the final value adheres to the significant figures principle, consistently providing a more accurate and professional result.
5. Kalen is trying to find the average of three measurements. The measurements are 13.8, 15.64, and 22.51. He adds the
numbers and divides by three. The result on the calculator shows 17.3167. Where should Kalen round? Explain.
he should round to the hundredths place so 17.32
Answer:
Karen should round to hundredth place.
Step-by-step explanation:
We are given that Kalen is trying to find the average of three measurements.
The measurements are 13.8, 15.64, and 22.51.
Now we are given that He adds the numbers and divides by three. The result on the calculator shows 17.3167
Now we are asked Where should Kalen round the final answer.
Since the values in the given data is upto hundredth place
So, we are supposed to round the final answer to hundredth place.
So, final answer after round off = 17.32
Hence Karen should round to hundredth place.
15 ft
7 ft
144
20 ft
III. Solve.
(10) A bedroom is 15 ft long and 12 ft wide.
How much will it cost to carpet the room
if carpeting costs $22 per square yard?
(1 yd = 3 ft)
......... ANSW
...........
It will cost $440 to carpet the room.
To find the cost of carpeting the room, we need to calculate the area of the room in square yards.
First, let's convert the dimensions of the room from feet to yards:
15 ft = 5 yd (since 1 yd = 3 ft, 15 ft = 5 yd)
12 ft = 4 yd
Next, calculate the area of the room in square yards:
Area = Length x Width = 5 yd x 4 yd = 20 square yards
Finally, multiply the area by the cost per square yard:
Cost = Area x Price
= 20 x $22/square yard
= $440
Complete question
A bedroom is 15 ft long and 12 ft wide. How much will it cost to carpet the room if carpeting costs $22 per square yard?
how to factor 25v^2+5v^2+30v+6 (please show work)
So you have:
25v² + 5v² + 30v + 6
First you combine the like terms (all of the v²)
25v² + 5v² + 30v + 6
= 30v² + 30v + 6 (25v² + 5v² = 30v²)
Now notice that the largest common factor of all those numbers is 6. So you can take out a factor of 6:
30v² + 30v + 6
= 6 (5v² + 5v + 1)
----------------------------------------------------------
Answer:
25v² + 5v² + 30v + 6
= 30v² + 30v + 6
= 6 (5v² + 5v + 1)
Can u pls help I’ll help back I don’t want to fail!!!:(((((((:[
It looks like the practice ones are all that matter so I'm only going to answer those. If you need the others answered let me know.
1. 5k-9=-3k+7
Add 9 to both sides: 5k-9+9=-3k+7+9
5k=-3k+16
Add 3k to both sides: 5k+3k=-3k+16+3k
(You are adding 3 and 9 instead of subtracting them because in the equation, they are negative numbers and you have to do the opposite operation to get rid of them.)
8k=16
Divide both sides by 8: 8k/8=16/8
k=2
2. 2(w-3)+5=3w-2
Use the distributive property: 2*w-2*3+5=3w-2
2w-6+5=3w-2
Combine like terms: 2w-1=3w-2
Add 1 to both sides: 2w-1+1=3w-2+1
2w=3w-1
Subtract 3w from both sides: 2w-3w=3w-1-3w
-w=-1
Divide both sides by -1: -w/-1=-1/-1
w=1
3. 8t+9=7t+6
Subtract 9 from both sides: 8t+9-9=7t+6-9
8t=7t-3
Subtract 7t from both sides: 8t-7t=7t-3-7t
t=-3
Plz help math matitions
For this case we have that by definition, the circumference of a circle is given by:
[tex]C = \pi * d[/tex]
Where:
d: It is the diameter of the circle
We have as data that:
[tex]C = 6 \pi[/tex]
So:
[tex]6 \pi = \pi * d[/tex]
Thus, the diameter of the circle is 6, therefore the radius is 3.
The area of a circle is given by:
[tex]A = \pi * r ^ 2[/tex]
Where:
r: It is the radius of the circle
[tex]A = \pi * 3 ^ 2\\A = 9 \pi[/tex]
Answer:
Option B
Answer:
9π in. ²
Step-by-step explanation:
The circumference of a circle is diameter times pi.
To find the area of a circle, you multiply the radius by itself, and the product by pi.
Diameter (6 in.) divided by two equals the radius (3 in.).
3 x 3 = 9 in.²
Then multiply by pi to get, 9π in.²
Hope this helps! :)
If 9999 = 4, 8888 = 8, 1816 = 6, 1212 = 0, then 1919=??
Answer:
2
Step-by-step explanation:
9999 = 4, so each 9 has a value of 1.
8888 = 8, so each 8 has a value of 2.
1212 = 0, so each 1 and 2 has a value of 0.
1816 = 6, so 6 has a value of 4.
Therefore, 1919 = 0 + 1 + 0 + 1 = 2.
PLEASE ANSWER RIGHT AWAY
Answer:
The 3rd sequence could not be described by the following recursive definition tn+1 = tn + 6
Step-by-step explanation:
* Lets revise the recursive formula
1. Determine if the sequence is arithmetic (Do you add, or subtract, the
same amount from one term to the next?)
2. Find the common difference. (The number you add or subtract.)
3. Create a recursive formula by stating the first term, and then stating
the formula to be the previous term plus the common difference.
a1 = first term;
an+1= an + d
- Where:
# a1 = the first term in the sequence
# an = the nth term in the sequence
# an+1 = the term after the nth term
# n = the term number
# d = the common difference.
* Now lets solve the problem
∵ tn+1 = tn + 6
∴ d = 6 ⇒ common difference
- The 1st sequence 5 , 11 , 17 , 23 , 29 , .... has common difference 6
- The 2nd sequence 0 , 6 , 12 , 18 , 24 , .... has common difference 6
- The 3rd sequence 6 , 9 , 12 , 15 , 18 , .... has common difference 3
∴ This sequence could not be described by the following recursive
definition tn+1 = tn + 6
* The 3rd sequence could not be described by the following recursive
definition tn+1 = tn + 6
Use the function f(x) = 2x3 - 3x2 + 7 to complete the exercises.
f(−1) =
f(1) =
f(2) =
Answer:
Step-by-step explanation:
The value of the function f(x) at x=a can be determined by substituting a instead of x into the function expression.
1. When x=-1, then
f(-1)=2\cdot (-1)^3-3\cdot (-1)^2+7=-2-3+7=2.
2. When x=1, then
f(1)=2\cdot 1^3-3\cdot 1^2+7=2-3+7=6.
3. When x=2, then
f(-1)=2\cdot 2^3-3\cdot 2^2+7=16-12+7=11.
Answer:
f(-1)=2
f(1)=6
f(2)=11
Step-by-step explanation:
The given function is [tex]f(x)=2x^3-3x^2+7[/tex]
Substitute x = -1 to find the value of f(-1)
[tex]f(-1)=2(-1)^3-3(-1)^2+7\\\\=-2-3+7\\\\=2[/tex]
Thus, f(-1)=2
Substitute x = 1 to find the value of f(1)
[tex]f(1)=2(1)^3-3(1)^2+7\\\\=2-3+7\\\\=6[/tex]
Thus, f(1)=6
Substitute x = 2 to find the value of f(2)
[tex]f(2)=2(2)^3-3(2)^2+7\\\\=16-12+7\\\\=11[/tex]
Thus, f(2)=11
Help me with this question
Answer:
Step-by-step explanation:
The sum of the angles in a triangle is 180. So for the triangle on the right:
36 + 84 + x = 180
x = 60
The two angles in the corner add up to 90. So:
60 + y = 90
y = 30
Finally, for the triangle on the left:
30 + 86 + z = 180
z = 64
Isabella has $6,000. She gave her mother $1,800. She donated 1/4 of the remaining amount to a charity. What percent of her money did Isabella donate? *
6,000 - 1,800 = 4,200
4,200 / 1/4 (or 25)
she donated 168.0% of her money.
Answer:
Step-by-step explanation:
6000-1800 = 4200 divided by 1/4 = 1050
the equation tx^2+3x-7=0 has two real solutions.what can dedused about the value of t?
Answer:
if it has two real repeated solutions then t=-9/8
if it has two real distinct solutions then t>-9/28
Step-by-step explanation:
Given:
tx^2+3x-7=0
Also above equation has two real solutions
Now what can deduced about the value of t?
For any quadratic equation "ax^2 +bx +c=0" the solution is given by the quadratic formula
x= [tex]\frac{-b+/-\sqrt{b^{2}-4ac } }{2a}[/tex]
The part under the square root i.e b^2 - 4ac is called the discriminant and it decides whether the equation will have 1 solution, 2 solution or no solution.
if discriminant is negative, i.e. <0 then equation will have no real solution
if discriminant is zero, i.e. =0 then equation will have two repeated real solution
if discriminant is positive, i.e >0 then equation will have two real distinct solution
As given equation has two real solutions:
if they are distinct then
b^2-4ac>0
Putting values of a=t, b=3, c=-7 in above we get,
9+28t>0
28t>-9
t>-9/28
if they are repeated then
b^2-4ac=0
Putting values of a=t, b=3, c=-7 in above we get,
9+28t=0
28t=-9
t=-9/28!
figure 1 is dilated yo get figure 2 what is the scale factor figure 1 24 figure 2 8
Answer:
1/3
Step-by-step explanation:
Find two corresponding sides that have lengths.
24 in Figure 1 corresponds to 8 in Figure 2.
Divide the length in Figure 2 by the corresponding length in Figure 1.
scale factor = (length in Figure 2)/(corresponding length in Figure 1)
scale factor = 8/24
scale factor = 1/3
What is the mean of the data set? 108, 305, 252, 113, 191. Enter your answer in the box.
please show the work
step by step
Answer:
193.8
Step-by-step explanation:
Add each value together, we get 969.
Divide by the number of values in the set, we get (969)/5, or 193.8
I'm only a few Brainliests away from ranking up, so one would be much appreciated. Thank you!
Answer:
193.8
Step-by-step explanation:
A bent coin has probability 0.55 of landing heads up. What is the probability that two tosses of the coin will both result in heads?
Use four decimal places in your answer.
Answer:
Required probability is 0.3025.
Step-by-step explanation:
Given that probability of landing heads up in a toss of bent coin = 0.55
Then probability of getting head in 1st toss = 0.55
2nd toss is independent of the first toss.
Then probability of getting head in 2nd toss = 0.55
Hence probability of getting head in two tosses of the coin = (0.55)(0.55) =0.3025
Hence required probability is 0.3025.
Answer:
0.3025
Step-by-step explanation:
Given:
The probability of landing heads P(h) = 0.55
The probability of landing heads when the coin is tossed again is 0.55 as both the events are independent and we are given the probability of heads P(h) = 0.55
So,
The probability of getting 2 heads in a row=0.55*0.55
=0.3025
find the surface area of a cone with 9 in radius and 13 in height
[tex]\bf \textit{surface area of a cone}\\\\ SA=\pi r\sqrt{r^2+h^2}+\pi r^2~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=9\\ h=13 \end{cases}\implies SA=\pi (9)\sqrt{9^2+13^2}+\pi (9)^2 \\\\\\ SA=9\pi \sqrt{250}+81\pi \implies SA=9\pi (\sqrt{250}+9)\implies SA\approx 701.53[/tex]
Triangle angle theorems?
What is the value of H?
the measure of those two angles equals 180 since it forms a line
so you add up both angles and set that equal to 180.
(I'll use x as the variable but it's still the same answer)
5x-3+9+x=180
combine like terms
6x+6=180
subtract 6
6x=174
then divide by 6
x=29
To find the value of angle H in a triangle, you subtract the sum of the other two angles from 180. This is based on the triangle angle theorems which state that the sum of the angles in a triangle always equals 180 degrees.
Explanation:In triangle angle theorems, the sum of the angles of a triangle always add up to 180 degrees. If you need to find the value of angle H in your triangle, you'll need to know the measures of the other two angles. For example, if one angle measures 60 degrees and the other measures 50 degrees, you would subtract the sum of these two angles from 180 to find the value of angle H.
Sum of angles in triangle = 180 degrees
So, Angle H = 180 - (60 + 50) = 70 degrees
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Jeanine bought a new pair of hiking boots on sale door 15% off the regular price. If the regular price was $115.00, how much did jeanine pay for the hiking boots
Answer:
$97.75
Step-by-step explanation:
since its 15% off, the price would be 85% of its original price.
85/100 x $115 = $97.75
Jeanine paid $97.75 for the hiking boots after receiving a 15% discount on the regular price of $115.00. The discount was calculated by converting the percentage to a decimal and multiplying it by the regular price, then subtracting it from the regular price.
Jeanine bought hiking boots with a 15% discount off the regular price of $115.00. To calculate how much Jeanine paid for the hiking boots, we first need to find the amount of the discount. The discount amount is calculated as 15% of the regular price.
The calculation for the discount is as follows:
Convert the percentage to a decimal by dividing by 100: 15% / 100 = 0.15.
Multiply the regular price by the decimal: $115.00 imes 0.15 = $17.25.
Subtract the discount from the regular price: $115.00 - $17.25 = $97.75.
Thus, Jeanine paid $97.75 for the hiking boots.
Find the 25th term of the sequence -1, 2, 5, 8
Answer:
71
Step-by-step explanation:
This is an arithmetic sequence with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here d = 2 - (- 1) = 5 - 2 = 8 - 5 = 3 and a₁ = - 1, so
[tex]a_{25}[/tex] = - 1 + (24 × 3) = - 1 + 72 = 71
A $79 television is on sale for $65. What percent discount was given?
The percentage of the discount given on television is 17.72%.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that a $79 television is on sale for $65. The percentage of the discount will be calculated as:-
Discount% = ( Original price - Discounted price ) / Original price
Discount% = ( 79 - 65 ) / 79
Discount% = 17.72%
Therefore, the discount per cent on television is 17.72%.
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What is the period for the cotangent function?
The cotangent function has a period of π, and we don't bother with the amplitude.
The period for the cotangent function is equal to π.
What is the period for the cotangent function?The period for y=cot(x) is equal to π.Cotangent is the reciprocal of the tangent function.A cotangent graph is a discontinuous graph that is not defined for theta values such that the value of sin theta is equal to 0.The cotangent function has a period equal to π which means that one cycle of a cotangent graph occurs between 0 to π.Hence, The period for the cotangent function is equal to π.
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Simplify the expression below -3(10x + 4y) + 6(6x − 2y)
Answer:
6x - 24y
Explanation:
Expand -3(10x + 4y): -30x - 12y
= [tex]\bold{-30x-12y+6\left(6x-2y\right)}[/tex]
Simplify [tex]\bold{-30x-12y+6\left(6x-2y\right): \ 6x-24y}[/tex]
= 6x - 24y
Mordancy.
For this case we must simplify the following expression:
[tex]-3 (10x + 4y) +6 (6x-2y)[/tex]
We apply distributive property to the terms of the parenthesis, taking into account that:
[tex]- * - = \\- * + = -[/tex]
So, we have:
[tex]-30x-12y + 36x-12y =[/tex]
We add similar terms:
[tex]-30x-12y + 36x-12y =[/tex]
Equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the major is placed:
[tex]6x-24y[/tex]
ANswer:
[tex]6x-24y[/tex]
whats an exponent and how is it used an mathematics
Answer: a quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression
Step-by-step explanation:
for example
10 x 10 = 100
to simplify this you put a small 2 on the top right corner of the number 10
Final answer:
An exponent, or a power, is mathematical shorthand for repeated multiplications. It is used to multiply a number by itself a certain number of times.
Explanation:
An exponent, or a power, is mathematical shorthand for repeated multiplications. For example, the exponent "2" means to multiply the base for that exponent by itself (in the example here, the base is "5").
5² = 5 x 5 = 25
The exponent is "2" and the base is the number "5." This expression (multiplying a number by itself) is also called a square. Any number raised to the power of 2 is being squared. Any number raised to the power of 3 is being cubed.
Simplest form of (36^)1/3
3,301927249 = ³√36
As discussed in one of my videos on my channel [USERNAME: MATHEMATICS WIZARD] on the Six Rational Exponential Rules, this one states that with a numerator of 1 in the exponent, you take the multiplicative inverse [reciprocal] of the fraction, and set the whole number equal to the root, bringing your a inside the radical, which is 36.
ⁿ√aᵐ = aᵐ\ⁿ → works for both: numerator ≥ 1
I am joyous to assist you anytime.
Gianna and her children went into a movie theater and she bought $77.50 worth of bags of popcorn and pretzels. Each bag of popcorn costs $6.50 and each pretzel costs $4.75. She bought a total of 13 bags of popcorn and pretzels altogether. Determine the number of bags of popcorn and the number of pretzels that Gianna bought.
Answer:
4 pretzels and 9 popcorn
Step-by-step explanation:
x=popcorn and y=pretzels
x+y=13 solve for x
x=13-y
6.5x+4.75y=77.5 plug 13-y in for x
6.5(13-y)+4.75y=77.5 distribute
84.5-6.5y+4.75=77.5 combine like terms
84.5-1.75y=77.5
-84.5 -84.5
-1.75y=-7 divide both sides by -1.75
*y=4* plug into x+y=13
x+4=13 subtract 4 from each side
*x=9*
A runner burned 120 calories on a 1.6
km run. How many calories would
they burn on a 5 km run?
Answer: 375 calories
Form a proportion. Let x be the number of calories burned on a 5 km run.
[tex]\frac{120}{1.6} = \frac{x}{5}[/tex]
Solve for x by cross-multiplying.
[tex]1.6x = (120)(5)\\1.6x = 600\\x = 375[/tex]
Answer:
375 calories
Step-by-step explanation:
[tex] \frac{120}{1.6} = \frac{x}{5} [/tex]
next you would cross multiply
[tex]1.6x = 600[/tex]
then you would divide by 1.6 on both sides
[tex]x = 375[/tex]
and 375 calories should be ur answe