To convert log4 14 to a logarithm of base 3, you can use the change of base formula. The required conversion would be log3 14 divided by log3 4.
Explanation:To write log4 14 as a logarithm of base 3, we would use the change of base formula. The change of base formula is logba = logca / logcb, where logba is the logarithm we want to convert, c is the new base, a is the number, and b is the original base. So, in this case, we want to write log4 14 as a logarithm of base 3, so using the formula, it would be (log3 14) / (log3 4).
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2) two florist purchased flower bouquets and vases at the same store. The first florist bought 2 flower bouquets and two vases for a total of $12.50. The second florist bought 8 flower bouquets and 2 vases for a total of 29.00
Let b represent the cost of one flower bouquet and v represent the cost of one vase. Write and solve a system of equations to find the price of each type of arrangement. SHOW ALL WORK!
Can this be simplified?
If the lengths of two sides of an isosceles triangle are 10 and 4, respectively, what must be the length of the third side of the triangle?
How do you know if it's 10 or if it's 4?
Javier has a savings account with an interest rate of 3.3%. he deposited $1200.00 into the account. write an equation, then graph it. how much money would he have after 6 years?
I need help with how to solve this geometry question! PLEASE! DESPERATELY NEEDED!!
This table shows the weekly rainfall, in inches, for two cities for ten weeks.
City A 0.2 0 1.5 1.3 2.5 3 0.4 0.3 0.2 1
City B 0 0 0.4 0.2 0.3 1 1 1 0.1 0.1
Which conclusion can be drawn from the data?
During the 10 wk period, the rainfall amount recorded most often for City B was 1 in.
The range between the maximum and minimum values for City B is greater than the range between the maximum and minimum values for City A.
For the ten weeks, City A received less rainfall, on average, than City B
The median for City A is less than the median for City B. pls help me
Answer: A. During the 10 wk period, the rainfall amount recorded most often for City B was 1 in
Step-by-step explanation: k12 test unit 5.10
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MATH HELP. ^^
Answer the two pages below.
The steps used by Taylor to solve the equation 3(x - 2) = 6(2x + 1) + 6 are shown below:
3(x - 2) = 6(2x + 1) + 6
x - 2 = 2(2x + 1) + 2
x - 2 = 4x + 2 + 2
x - 2 = 4x + 4
-3x - 2 = 4
-3x = 6
x = -2
Which properties did Taylor use to solve
the equation? Choose all that apply.
A. Distributive property
B. Commutative property
C. Inverse Operation Property
D. Associative property of multiplication
E. The sum of a number and its additive inverse is 0.
F. The product of a number and its multiplicative inverse is 1.
Pleas help !!!!!
The table below shows some values of f(x) and g(x) for different values of x: x f(x) = 2x + 24 g(x) = 5(0.5)x −2 20 −1 0 5 1 2.5 2 28 Complete the chart and determine the solution of the equation f(x) = g(x). x = −2 x = −1 x = 1 x = 20
what is the solution to the equation(3/m+3)-(m/3-m)=(m^2+9/m^2-9)
it has no solution , yw
y = mx + b Which variable represents the slope?
The variable 'm' represent the slope.
What is slope?The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.
Given:
y= mx + b
The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line.
The net change in y coordinate is Δy, while the net change in the x coordinate is Δx.
So the change in y coordinate with respect to the change in x coordinate can be written as,
m = Δy/Δx
where, m is the slope
The slope of a line can be calculated from the equation of the line. The general slope of a line formula is given as,
y = mx + b
where,
m is the slope, such that m = tan θ = Δy/Δx
θ is the angle made by the line with the positive x-axis
Δy is the net change in y-axis
Δx is the net change in x-axis
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A box measures 6inches by 2inches by 3 inches find the volume of the box in cubic feet enter as a fraction ?
Quick calculus question work doesn't have to be shown
Suppose the radius of a spherical balloon is growing at a rate of 50 cm/s . How quickly is the volume when the radius is 6cm?
A nontoxic furniture polish can be made by combining vinegar and olive oil. the amount of oil should be five times the amount of vinegar. how much of each ingredient is needed in order to make 39 oz of furniture polish?
Final answer:
To make 39 oz of non-toxic furniture polish with the ratio of olive oil being five times the amount of vinegar, 6.5 oz of vinegar and 32.5 oz of olive oil are needed.
Explanation:
We know the oil to vinegar ratio is 5:1.
Let x be the amount of vinegar: We can use any variable to represent the unknown amount.
Set up the equation: Since the total volume is 39 oz and the ratio is 5:1, we have the equation: x (vinegar) + 5x (olive oil) = 39 oz.
Combine like terms: 6x = 39 oz.
Solve for x (vinegar): x = 39 oz / 6 = 6.50 oz.
Calculate the olive oil amount: Olive oil = 5 × vinegar = 5 × 6.50 oz = 32.50 oz.
Therefore, you'll need 6.50 oz of vinegar and 32.50 oz of olive oil to make 39 oz of furniture polish.
Remember to always test the polish on a small inconspicuous area of the furniture before applying it to the entire surface. And, for best results, use a clean, soft cloth to apply the polish and buff it to a shine.
One card is drawn from a well shuffled deck of 52 cards find the probability of getting a red 10
Which of the following functions has a maximum at x=3? SELECT ALL THAT APLLY.
A. f(x)= (x-3)^2
B. f(x)= (x-2)(4-x)
C. f(x)= -x^2+6x-5
D. f(x)= 1-(x-3)^2
E. f(x)= (x+3)^2-9
F. f(x)= x^2-4x+3
Polynomials Multiply. −3y(5y3+11y2−y+8) Express the answer in standard form. Enter your answer in the box.
The given expression is 3y (-5y³-11y²+y-8)
We use distributive rule to distribute 3y to the terms -5y³-11y²+y-8.
The distributive rule states :To multiply a sum by a number, multiply each term of the sum.
This can be applied to multiply a monomial and polynomial.
The Distributive Property is an algebra property which is used to multiply a single term and two or more terms.In multiplication exponents are added.
3y (-5y³-11y²+y-8) =[tex] -15y^{4} -33y^{3} +3y^{2} -24y [/tex]
What is the explicit rule for the sequence?
34,26,18,10, …
an = 26 − 8n
an = 42 − 8n
an = 34n − 26
an = 34n + 42
Answer:
OPTION B
Step-by-step explanation:
Which statements justify that the dilation of triangle STU is an enlargement increasing its size by the magnitude of the scale factor? Check all that apply.
A. The triangle pre-image is closer to the point of dilation than the image.
B. The triangle image is closer to the point of dilation than the pre-image.
C. The value of the scale factor, , is between 0 and 1.
D. The value of the scale factor, 6, is greater than 1.
E. The vertices of the pre-image are collinear with the vertices of the image.
I need consumer math help!!!!!
1. A house is used as for a loan (1point)
a)an asset
b)security
c)insurance
d)collateral
2.Most credit cards are debt. (1point)
a)unsecured
b)secured
c)collateral
d)relaized
3.You have a balance of $1,678.00 on a credit card with a 15.75% APR. How much intrest is accured if you pay nothing on the principal after 3 months?
a)$22.02
b)$66.07
c)$264.29
d)$88.10
4.you carry a balance of $2,065.00 on a credit card at a 17.25% APR for 5 months. How much is your total payment by the fifth month? (1point)
a)$2,094.68
b)$2,213.42
c)$2,421.21,
1.D) collateral
2.A.) Most credit cards are unsecured debt
3.B.)$66.07
4.B.) 2,213.42
4/4 100%
HOPE I HELP I HAVE A NICE DAY
Which graph represents the solution set for the system 6x + y > -3 and 2x + y ≤ 4?
GRAPH A:
https://cdn.ple.platoweb.com/EdAssets/569ffaae985e4d30af1d47501f6a3071?ts=635295994038270000
GRAPH B:
https://cdn.ple.platoweb.com/EdAssets/a0685f1258de4321b8ad526cba13ea68?ts=635295994033270000
GRAPH C:
https://cdn.ple.platoweb.com/EdAssets/7a8269a9613f472e9fd34597d3a0185c?ts=635295994031070000
GRAPH D:
https://cdn.ple.platoweb.com/EdAssets/9886daa9d6944ccd91d245f0d522c20a?ts=635295994027500000
Answer:
Graph B is the answer.
Step-by-step explanation:
We know that both functions are inequalities, however,
The second one (red on the graph) has 'less or equal sign, ≤' meaning that, the line of the function is included as shown on graph B with a continuous line.
The first one has a 'greater than, >' meaning that the line of the function is not included, therefore the line is a dotted line, as shown on graph B.
The shaded area must be between the two inequalities because that where the X's can be met.
Therefore, the answer is graph B.
Matias and Hannah are responsible for the centerpieces on the buffet tables at the school dance.they have 6 dozen carnations,80 lilies,and 64 rosebuds. all the centerpieces must be identical.determine the greatest number of centerpieces Matias and Hannah can make if they use all the flowers.then describe the centerpiece
Matias and Hannah can make 8 identical centerpieces using all the flowers, with each centerpiece composed of 9 carnations, 10 lilies, and 8 rosebuds, arranged harmoniously.
Explanation:Matias and Hannah can make the greatest number of identical centerpieces by finding the largest number that can divide into the quantities of all three types of flowers without remainder. They have 6 dozen carnations (72 carnations), 80 lilies, and 64 rosebuds. The highest common factor that divides into 72, 80, and 64 is 8. This means they can make 8 centerpieces, with each centerpiece containing 9 carnations, 10 lilies, and 8 rosebuds.
Describing the centerpiece based on the description in the hypothetical art reference: The centerpiece would feature a balanced and harmonious arrangement of flowers with the carnations drawing the viewer's attention at the center. Similar to the composition in Chittenden's paintings, the various flower types, such as lilies and the delicate rosebuds, would be distributed to complement each other in the arrangement, creating an aesthetically pleasing and symmetrical display for the school dance buffet tables.
A serving of a certain cereal has 8 grams of sugar in 1 portion. Which equation shows how the amount of sugar and the number of portions are related? The s stands for the grams of sugar and the p stands for the portions of cereal.
Answer:
The answer was actually s = 8p! Just tried it out on the ttm website. Hope that this helps!
Portion = 8 grams of sugar
The amount of sugar you have is dependent on how many portions of cereal you have (each one is 8), so this would be Sugar = 8 grams multiplied by how many portions you have. :)
For f(x) = 3x +1 and g(x) = x2 – 6, find (f – g)(x).
A. x2 – 3x – 7
B. –x2 + 3x + 7
C. –x2 + 3x – 5
D. 3x2 – 17
Answer:
Option (b) is correct.
[tex](f-g)(x)=-x^2+3x+7[/tex]
Step-by-step explanation:
Given : Functions [tex]f(x) = 3x +1[/tex] and[tex]g(x) = x^2-6[/tex]
We have to choose the correct option from the given options that represents (f-g)(x)
Consider the given functions
[tex]f(x) = 3x +1[/tex] and[tex]g(x) = x^2-6[/tex]
then , (f - g)(x) = f(x) - g(x)
Substitute, we have,
[tex]f(x) - g(x)=3x+1-(x^2-6)[/tex]
Applying plus - minus rule[tex]-(-a)=a[/tex], we have,
[tex]f(x)-g(x)=3x+1-x^2+6[/tex]
Simplify and write in standard form, we have,
[tex]f(x)-g(x)=-x^2+3x+7[/tex]
Thus, The[tex](f-g)(x)=-x^2+3x+7[/tex]
Let f(x)=4x^2+x+1 and g(x)=x^2-2. Find g(f(x)). Show each step of your work.
The height h, in feet, of a projectile t seconds after launch is modeled by the equation h = 32t – 16t2. how long after launch does the projectile return to the ground? 2 seconds4 seconds14 seconds16 seconds
Answer:
The correct option is A. 2 seconds
Step-by-step explanation:
The height h, in feet, of a projectile t seconds after launch is modeled by the equation h = 32·t – 16·t²
Now, we need too find the time after which the fired projectile touches the ground.
So, The fired projectile when touches the ground, The height of the projectile will become 0
⇒ Find the required time t when h = 0
⇒ 0 = 32·t - 16·t²
⇒ 0 = t × (32 - 16·t)
⇒ t = 0 or 32 - 16t = 0
⇒ 16t = 32
⇒ t = 2
So, t = 0 or t = 2
t cannot be 0 because initially the projectile is in the air as it has been already fired
⇒ t = 2 seconds
Therefore, The correct option is A. 2 seconds
I rly need help pls help me
3/10=9/? Equivalent fraction
. Ms. Franco earned $709.54 in net pay for working 25 hours. She paid $87.45 in federal and state taxes, and $38.45 in FICA taxes.
What was her hourly wage?
(Points : 1)
$23.35
$28.38
$32.42
$33.42,
Ms. Franco hourly wage is approximately $33.42
Data
Net pay = $709.54Total hours = 25Federal and state tax = $87.45FICA taxes = $38.45To solve this problem, we have to trace back to know her gross pay and then divide it by the total number of hours worked.
Gross PaySum of all her net pay and all taxes.
[tex]709.54+87.45+38.45=835.44[/tex]
Her total gross pay is $835.44
Hourly WageThis is the amount she earned working for each hour.
Since she worked for a total of 25 hours, let's divide her gross pay by 25
[tex]\frac{835.44}{25}=33.4176[/tex]
Ms. Franco hourly wage is approximately $33.42
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