Answers
The logarithmic property of base change given that
logx (b) = logc (b) / logc (x)
Therefore, the same property applies to this problem and the correct expression for this question is:
y1 = log (x + 3) / log 4
y2 = log (2 + x) / log2
Related Questions
Giovanni justifies whether the expression -4x-8 is equivalent to -2(x+1)-2(x+3)by letting x=3 in both expressions. What is the value of each expression when x=3
3 and -20
4 and 4
-20 and -20
3 and 4
Answers
-4x-8
-2 (x + 1) -2 (x + 3)
Evaluating x = 3 in both expressions we have:
-4 (3) -8 = -12 - 8 = -20
-2 (x + 1) -2 (x + 3) = -2 (3 + 1) -2 (3 + 3) = -2 (4) -2 (6) = -8-12 = -20
Answer:
the value of each expression when x = 3 is:
-20 and -20
Jennifer works in a flower shop on Saturday she started work at 8:45 a.m. she spent 3/4 hours at lunch she finished at 4:15 p.m. how many hours did she work on Saturday?
Answers
3.45pm to 4.15pm = 30 minutes
3/4 hours = 45 minutes
7 hours 30 mins minus 45 minutes = 6 hours 45 minutes
Answer : She worked 6 hours 45 minutes on Saturday.
Hope this helps. - M
HURRYYYYY PLZ
Enter the values for the highlighted variables that show how to subtract the rational expressions correctly:
A
B
C
D
E
F
G
Answers
x ^ 2 + 6x = x (x + a) = x (x + 6)
a = 6
For b we have:
b = 2
For c we have:
x-c = x-6
c = 6
For d and e we have:
bx-x + c = dx-x + e
b = d = 2
c = e = 6
For f we have:
dx-x + e = x (d-1) + e = x (2-1) + e = x + e = x + f
e = f = 6
For g we have:
(x + f) / (x + 6) = (x + 6) / (x + 6) = g = 1
g = 1
What is the domain of the function y=3\sqrt(6x+42)
Answers
Please help thank you.
Lacey's mom makes her a birthday cake in the shape of an "L" . Lacey loves frosting, so her mom covers the entire outside of the cake in frosting, even the bottom of the cake.
How much space does Lacey's mom cover in frosting?
And PLEASE explain.
Answers
You can separate the shape into two rectangular prisms
prism 1 - 9, 2 ,4
prism 2 - 4, 2, 8
Since the frosting is on the outside of the cake you have to find the surface area
To find the surface area you use the equation
2(wl + hl + hw)
Put in the values you know
2(9 * 2 + 4 * 2 + 9 * 4)
multiply
2(18 + 8 + 36)
Add
2(62) = 124
Now you find the surface area of the second prism
2(4 * 2 + 2 * 8 + 4 * 8)
Multiply
2( 8 + 16 + 32)
Add
2(56) = 112
Now add the two surface areas to get the surface area of the whole shape
112 + 124 = 236
The answer is 236in squared
Hope this helps!
Answer:
220
Step-by-step explanation:
Lacey's mom makes her a birthday cake in the shape of an "L" . Lacey loves frosting, so her mom covers the entire outside of the cake in frosting, even the bottom of the cake.
How much space does Lacey's mom cover in frosting?
The surface area of the the cake is made up of rectangles. The formula for find the area of a rectangle is A = lw
We can divide the top of the cake into 2 rectangles.
The rectangle on the left is 12 inches by 4 inches.
A=lw
A=12*4
A=48
There is a rectangle this size on the top and bottom of the cake, so we can multiply to find the area of both. 20*2=40
The rectangle on the right is 5 inches by 4 inches. We can use the formula A = lw to find the area.
A=lw
A=5*4
A=20
There is a rectangle this size on the top and bottom of the cake, so we can multiply to find the area of both.
48*2=96
Now we need to add in the area of the rectangles that make the sides of the cake. Let's look at the sides of the large rectangle first.
The total for these 3 surfaces is 48 .
Now let's look at the 3 remaining rectangles.
The total for these 3 surfaces is 36.
Now let's add all the surfaces together.
96+40+48+36=220
The surface area of Lacey's cake is 220 inches
Are these ratios equivalent?
84,000 paintings for every 16,000 photographs
63,000 paintings for every 12,000 photographs
Answers
Dirk can clean a playground in 5 hours. Geralyn can clean a playground in only 4 hours. Which of the following can be used to determine the amount of time it would take for Dirk and Geralyn to clean a playground together?
Answers
What is 15% of 90? I need help
Answers
The answer is
1. We assume, that the number 90 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 90 is 100%, so we can write it down as 90=100%.
4. We know, that x is 15% of the output value, so we can write it down as x=15%.
5. Now we have two simple equations:
1) 90=100%
2) x=15%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
90/x=100%/15%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for what is 15% of 90
90/x=100/15
(90/x)*x=(100/15)*x - we multiply both sides of the equation by x
90=6.66666666667*x - we divide both sides of the equation by (6.66666666667) to get x
90/6.66666666667=x
13.5=x
x=13.5
now we have:
15% of 90=13.5
Have a nice day
Your answer is 13.5
Explanation:
STEP 1: 1% of 90 = 90/100 = 0.9
STEP 2: 15% of 90 = 15 * 0.9 = 13.5
Here is another way to do it:
Explanation 2:
STEP 1: Write 15% as a decimal number: 15% = 15/100 = 0.15
STEP 2: Multiply 0.15 by 90: 0.15* 90 = 13.5
I hope I helped!
Let me know if you need anything else!
~ Zoe
there are 50 instruments in lincoln middle orchesha if 1/2 of the instruments are strings. how many strings are in lincoln orchestra
Answers
A student has successfully passed 60 percent of the 20 quizzes he has written so far. If the student writes 50 quizzes during the year, and successfully passes 80 percent of the remaining quizzes, what is his percent success rate for all his quizzes for the entire year? help
Answers
Answer:
74.29%
Step-by-step explanation:
A student passed 60%, or a proportion of 0.60 of the 20 quizzes he's written so far. This means he has passed [tex]0.60*20=12[/tex] quizzes so far.
Now he has written 50 quizzes and passed 80% of them, or [tex]50*.8=40[/tex] quizzes.
To find the success rate, take the number of quizzes passed and divide by total number of quizzes.
[tex]\frac{Passed}{Total}[/tex]=[tex]\frac{12+40}{20+50}[/tex]=[tex]\frac{52}{70}[/tex]=.7429
To get a percentage, multiply this proportion by 100 to get 74.29%
what is the value of B in the equation y ^ b ^ 4 equals 1 / y ^ 24
A) -20
B)-6
C)6
D)20
Answers
Step-by-step explanation:
y^b^4=1/y^24
y^b^4xy^24=1
b^4y^25=1
b^4=1/y^25
√b^4=√1/y^25
b=√1/y^25
It's B. -6
apparently i have to write at least 20 characters so,,,, sorry yall.
∠AZB and ∠CZB are supplementary. The m∠AZB = 2x - 4 and m∠CZB = 8x + 4. What is the measure of each angle?
A. m∠AZB = 32° and m∠CZB = 148°
B. m∠AZB = 12° and m∠CZB = 76°
C. m∠AZB = 43° and m∠CZB = 22°
D. m∠AZB = 68° and m∠CZB = 292°
Answers
The drawing isn't to scale
A hamster wheel has a diameter of 8.5 in. How many inches does the hamster run in one revolution? Use 3.14 to approximate for π .
Answers
As hamster wheel is circular so for revolution we will find the circumference.
Diameter of the Hamster wheel = 8.5 in
One revolution of the wheel = circumference of the wheel
Circumference = π × d
π = 3.14 and d = 8.5
So, Circumference = 3.14 × 8.5
Circumference = 26.69 in
So in one revolution the hamster wheel travels a distance of 26.69 in
when factored completely,x³-13x²-30x is
Answers
Answer:
[tex]x(x+2)(x-15)[/tex]
Step-by-step explanation:
we have
[tex]x^{3}-13x^{2}-30x[/tex]
step 1
Factor x
[tex]x^{3}-13x^{2}-30x=x(x^{2}-13x-30)[/tex]
step 2
Find the solutions of [tex](x^{2}-13x-30)[/tex]
Complete the square
[tex](x^{2}-13x)=30[/tex]
[tex](x^{2}-13x+6.5^{2})=30+6.5^{2}[/tex]
[tex](x^{2}-13x+42.25)=72.25[/tex]
[tex](x-6.5)^{2}=72.25[/tex]
square root both sides
[tex](x-6.5)=(+/-)8.5[/tex]
[tex]x=6.5(+/-)8.5[/tex]
[tex]x1=6.5(+)8.5=15[/tex]
[tex]x2=6.5(-)8.5=-2[/tex]
so
[tex](x^{2}-13x-30)=(x+2)(x-15)[/tex]
substitute
[tex]x^{3}-13x^{2}-30x=x(x+2)(x-15)[/tex]
if cos a = 3/5 in the first quadrant, what does cot a equal
Answers
then:
a=arccos 3/5
but
cot θ=1/tan θ
thus to evaluate our vale we shall obtain the value for height since
adjacent=3
hypotenuse=5
thus
using Pythagorean theorem:
c²=a²+b²
hence
5²=3²+b²
b²=25-9=16
b=4
thus
tan θ=opposite/adjacent
tan a=4/3
thus
cot a=1/(4/3)=3/4
Final answer:
To find cot a when cos a = 3/5 in the first quadrant, we first determine the length of the opposite side using the Pythagorean theorem, which gives us 4. Subsequently, cot a is calculated as the ratio of the adjacent to the opposite side, resulting in cot a = 3/4.
Explanation:
If cos a = 3/5 in the first quadrant, we use trigonometric identities to find cot a. First, recognize that in a right triangle, the Pythagorean theorem states a² + b² = c². Given cos a = adjacent/hypotenuse = 3/5, and the fact that we are in the first quadrant (where all trigonometric values are positive), we can solve for the opposite side using the Pythagorean theorem.
Let the opposite side be b, the adjacent side (corresponding to cos a) be 3, and the hypotenuse be 5. The equation becomes b² + 3² = 5² which simplifies to b² = 25 - 9 = 16, giving b = 4.
We know that cot a = adjacent/opposite = cos a / sin a. Thus, sin a = b / hypotenuse = 4/5. Therefore, cot a = 3/4.
according to the graph........
Answers
The solution is:
H(w) gets very small when w gets very large .
What is graph?In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.
Here, we have,
Considering the graph H(w),
As w gets larger, H(w) continues to approach a horizontal asymptote.
we know that,
A horizontal asymptote of a graph is a horizontal line y = b where the graph approaches the line as the inputs approach ∞ or –∞. A slant asymptote of a graph is a slanted line y = mx + b where the graph approaches the line as the inputs approach ∞ or –∞.
Hence, H(w) gets very small.
Therefore, the correct option is option D
Hence, The solution is:
H(w) gets very small when w gets very large .
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What is 3 to the power of 2 over 3 equal to?
cube root of 9
square root of 9
cube root of 27
square root of 27
Answers
What is the approximate volume if this cone 9cm by 15cm
A. 1272cm3
B.2120cm3
C.4239cm3
D.6359cm3
Please Hurry!
Answers
Short answer: A. 1272 cm³
Why?
When finding the volume of a cone, you use the formula V = πr²h/3. R = 9, H = 15. V = π9²15/3 9² = 81 | 15 / 3 = 5 | 3.14 * 81 = 254.34 | 254.34 * 5 = 1271.2 1272 rounded.
Hope this helped you! ♥
Final answer:
The approximate volume of a cone with a radius of 9 cm and a height of 15 cm, calculated using the formula for the volume of a cone, is closest to option A, which is 1272 cm³.
Explanation:
To find the approximate volume of a cone, we use the formula V = 1/3 πr²h, where V is the volume, r is the radius of the base, and h is the height of the cone. Given that the dimensions provided are 9 cm for the radius and 15 cm for the height, the calculation is as follows:
V = 1/3 π (9 cm)² (15 cm) = 1/3 π (81 cm²) (15 cm)
Now multiply these values:
V = 1/3 π (1215 cm³) ≈ 1/3 (3817.005 cm³) ≈ 1272.335 cm³
The approximate volume of the cone is therefore closest to 1272 cm³, which makes the correct answer A. 1272cm³.
For the situation, identify what information is given and what information you need to find, and define a variable for each unknown quantity.
A museum sold adult and child tickets for an upcoming event. There were 10 more child tickets sold than adult tickets. Child tickets cost $5, and adult tickets cost $8. The sales totaled $550. How many adult tickets were sold?
For the situation, identify what information is given and what information you need to find, and define a variable for each unknown quantity.
Answers
A = The number of adult tickets sold
C = The number of child tickets sold
Your equations could be:
8A + 5C = 550
C - 10 = A
The school is 625 meters far from Alex house. It took him 15 minutes to go from home to school, and run back to home in 10 minutes. What was Alex's average speed?
Answers
It is given in the question that
The school is 625 meters far from Alex house. It took him 15 minutes to go from home to school, and run back to home in 10 minutes.
Total distance is 625 meters and total time taken is
[tex] (10+15) minutes=25minutes [/tex]
Average speed is
[tex] \frac{total \ distance \ travelled}{total \ time \ taken} [/tex]
[tex] = \frac{625}{25}meter/minute = 25 meter/minute [/tex]
Answer:
25 minutes
Step-by-step explanation:
Anthony observes that when people are leaving class, about 50% turn left and about 50% turn right. Anthony wants to estimate the probability that fewer than 3 of the first 4 students will turn left when leaving class tomorrow. To do this, he lets H represent turning left when leaving class and T represent turning right. He then flips a coin 4 times, recording the results. He repeats this process for a total of 20 trials. HHTT THHT HTTT HTHH HHTT HTHT THTH TTHH HHHH HTTH HHHT TTHT THHH THTH HHTT HTTT HTTH HHTT HTHH HHTH Drag and drop the correct fraction to the box to estimate the probability, using this simulation. Estimated probability that fewer than 3 of the first 4 students leaving class tomorrow will turn left:
Answers
There are 14 outcomes in this simulation with fewer than 3 left turns, out of 20 times the simulation was run:
14/20 = 7/10
The fact that Anthony repeats the test [tex]n[/tex] times doesn't change anything, because he already know that you have a 50/50 chance of turning left of right.
Given that, Anthony observes that when people are leaving class, about 50% turn left and about 50% turn right.
What is the probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
H represent turning left when leaving class and T represent turning right,
Both of them have a 50% probability of happening and he wants to know the probability of less than 3 turn left so we want to know the probability for only one to turn left and the probability for only two.
Only one:
If you use the fact that we have a binomial distribution, then the possibility that only one turns left is:
So, [tex]P(1)=\frac{4!}{3!} \times0.5^{4[/tex]
= 4×0.0625 = 0.25
Only two with the same reasoning.
[tex]P(2) = \frac{4!}{(2!\times2!)} \times0.0625=6\times0.0625 = 0.375[/tex]
Here you can see that the probability is bigger because here are mass combinations that in the previous case.
So the total probability is 0.25 + 0.375 = 0.625.
The fact that he repeats the test [tex]n[/tex] times doesn't change nothing, because he already know that you have a 50/50 chance of turning left of right.
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Numbers 37 and 39. I’m not sure how to solve them
Answers
You can get this by dividing 3/4 by 2.
The key to doing these types of problems is remembering that if they are going faster by that much, it doesn't matter what the speeds are. You can treat it as if one is standing still and the other is going 2mph.
a car model comes with the following choices: 9 colors,with or without air conditioning,with or without sunroof ,with or without automatic transmission ,with or without a spoiler,and with or without anti lock brakes. in how many ways can it be ordered
Answers
There 288 ways the car can be ordered.
What is Combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.
Given:
There are five Categories as
with or without air conditioning,with or without sunroof ,with or without automatic transmission ,with or without a spoiler,and with or without anti lock brakes.Total colors for car= 9
Now, the possible number of ways can it be ordered
= 9 x 2 x 2 x 2 x 2 x 2
= 9 x 32
= 288 ways
Hence, there 288 ways the car can be ordered.
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Final answer:
To determine the number of ways a car model can be ordered based on given feature choices, multiply the number of options for each feature. In this case, it's 9 colors multiplied by 2 options for each of the 5 binary features (with or without), leading to a total of 288 different combinations.
Explanation:
To determine the number of different ways a car can be ordered based on the given options, we simply need to multiply the number of choices available for each feature.
First, there are 9 colors. Then for each feature such as air conditioning, sunroof, automatic transmission, spoiler, and anti-lock brakes, there are two options available: with or without.
So, for each of these five binary options (yes or no), we multiply the number of choices by 2 (with or without).
Colors: 9 choices
Air conditioning: 2 choices
Sunroof: 2 choices
Automatic transmission: 2 choices
Spoiler: 2 choices
Anti-lock brakes: 2 choices
Now, we can calculate the total number of ways the car can be ordered:
Total ways = 9 (colors) * 2 (air conditioning) * 2 (sunroof) * 2 (automatic transmission) * 2 (spoiler) * 2 (anti-lock brakes)
Total ways = 9 * 25 = 9 * 32 = 288.
Therefore, there are 288 different combinations in which the car can be ordered.
A number j minus 14 is less than −21.
Answers
j - 14 < -21
j represents the number j
minus 14 is taking away or subtracting 14
together, they are less than -21, which is why < is used
j - 14 < -21
if you need to find j then
j - 14 < -21
+14 +14
j < -7
hope it helps
LAST QUESTION!! PLEASE HELP!
Answers
8. yes a diameter is a chord. A chord is any line that connects 2 points on a circle
What is the decimal equivalent of the fraction?
4/30
A) 0.13⎯⎯⎯⎯
B) 0.13
C) 0.1⎯⎯3
D) 0.13⎯⎯
Answers
4 ÷ 30 = 0.13 (3 goes on forever)
I am assuming the answer is A) 0.13 ---------------------
because the line is longer.
Answer:
Option A [tex]\frac{4}{30}=0.13333...=0.1\bar3[/tex]
Step-by-step explanation:
Given : Expression [tex]\frac{4}{30}[/tex]
To find : What is the decimal equivalent of the fraction?
Solution :
Step 1 - Write the fraction
[tex]\frac{4}{30}[/tex]
Step 2 - Divide the numerator by denominator,
[tex]\frac{4}{30}=0.13333...[/tex]
or [tex]\frac{4}{30}=0.13333...=0.1\bar3[/tex]
Therefore, Option A is correct.
Find the area of the trapezoid.
A) 18 cm2
B) 22.5 cm2
C) 27 cm2
D) 45 cm2
Answers
Answer:
27 cm2
Step-by-step explanation:
The answer is 27 cm 2 because if you use length x base x height you would get your answer. So 6 x 3 x 3 = 54 and then if you divide that by 2 you would get 27
Answer:
the answer is C), 27 cm2
Step-by-step explanation:
Perry divides up some candy to give equally to his six friends. If c represents the total amount, write the expression to represent how much candy each friend receives.
Answers
c needs to be divided by 6 to evenly distribute the candy with all 6 friends.
The expression is c÷6.
Hope this helped.
how many milligrams are in 0.5ml of a 1:1000 solution
Answers
1 ml = 1g
1/1000 *.5ml* 1g/1ml * 1000mg/1g = .5 mg
To find the number of milligrams in 0.5 mL of a 1:1000 solution, we can set up a proportion: 1 mg / 1000 mL = x mg / 0.5 mL. Cross-multiplying, we get: x mg = (1 mg / 1000 mL) * 0.5 mL. Therefore, there are 0.0005 milligrams in 0.5 mL of a 1:1000 solution.
Explanation:To determine the number of milligrams in 0.5 mL of a 1:1000 solution, we need to understand the ratio. In a 1:1000 solution, the first number represents the amount of solute (in this case, milligrams) and the second number represents the amount of solvent (in this case, milliliters). So, in a 1:1000 solution, there is 1 milligram of solute in 1000 milliliters of solvent.
To find the number of milligrams in 0.5 mL, we can set up a proportion:
1 mg / 1000 mL = x mg / 0.5 mL
Cross-multiplying, we get:
x mg = (1 mg / 1000 mL) * 0.5 mL
x mg = 0.0005 mg
Therefore, there are 0.0005 milligrams in 0.5 mL of a 1:1000 solution.
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[WILL GIVE BRAINLIEST]
15 machines work at the same rate.
Together, the 15 machines can complete an order in 8 hours.
3 of the machines break down after working 6 hours. The other machines carry on working until the order is complete.
In total how many hours does each of the other machines work