Answer:
Exactly 12 years it will take for these trees to be the same height
Step-by-step explanation:
Slope intercept form: An equation of line is in the form of [tex]y = mx+b[/tex] where m is the slope or unit rate and b is the y-intercepts.
Let x represents the time in years and y represents the height of the tree.
Use conversion:
1 ft = 12 inches
As per the given statement:
Type A is 8 feet tall and grows at a rate of 3 inches per year.
⇒unit rate per year = 3 inches = [tex]\frac{1}{4}[/tex] ft
Then, we have;
[tex]y =\frac{1}{4}x + 8[/tex] ......[1]
Similarly for;
Type B is 7 feet tall and grows at a rate of 4 inches per year.
⇒unit rate per year = 4 inches = [tex]\frac{1}{3}[/tex] ft
then;
[tex]y =\frac{1}{3}x + 7[/tex] .....[2]
To find after how many years it will take for these trees to be the same height.
Since, trees to be the same height;
⇒equate [1] and [2], to solve for x;
[tex]\frac{1}{4}x + 8 = \frac{1}{3}x +7[/tex]
Subtract 7 from both sides we get;
[tex]\frac{1}{4}x + 8-7= \frac{1}{3}x +7-7[/tex]
Simplify:
[tex]\frac{1}{4}x + 1= \frac{1}{3}x[/tex]
Subtract [tex]\frac{1}{4}x[/tex] from both sides we get;
[tex]1= \frac{1}{3}x-\frac{1}{4}x[/tex]
Simplify:
[tex]1 = \frac{x}{12}[/tex]
Multiply both sides by 12 we get;
x = 12
Therefore, exactly it will take for these trees to be the same height is, 12 years
Jess has dinner at a restaurant. The dinner bill is B dollars. She pays a 21% tip. Match the expressions to their correct meanings for Jess. Here are the possible answers Jess's bill amount without tip:Jess's tip amount:Jess's total amount: ????B+0.21; B; 2.1B; B/0.21B; 0.21BNot all the answers will be used Please I need help Right away.?
Answer:
Jess's bill amount without tip: B
Jess's tip amount: 0.21B.
Jess's total bill amount: [tex]B+0.21B[/tex]
Step-by-step explanation:
We have been given that Jess has dinner at a restaurant. The dinner bill is B dollars. So the Jess's bill amount without tip will be B dollars.
We are told that she pays a 21% tip. Let us find 21% tip of dinner bill (B).
[tex]\text{Jess's tip amount}=\frac{21}{100}*B[/tex]
[tex]\text{Jess's tip amoun}=0.21B[/tex]
Therefore, Jess's tip amount will be [tex]0.21B[/tex].
Let us find total amount of Jess's bill by adding bill amount (0.21B) to the Jess's bill amount without tip (B).
[tex]\text{Total amount of Jess's bill}=B+0.21B[/tex]
Therefore, the total amount of Jess's bill will be [tex]B+0.21B[/tex].
Jess's bill without tip is B, her tip amount is 0.21B, and her total bill including a 21% tip is 1.21B.
When Jess has dinner at a restaurant with a dinner bill of B dollars and decides to pay a 21% tip, you can calculate her expenditures in the following manner:
Jess's bill amount without tip: This is simply the original amount of the bill, which is B dollars.Jess's tip amount: To calculate the tip, you convert the percentage to a decimal by dividing by 100 (21% = 0.21) and then multiply by the bill amount. The expression for the tip amount is 0.21B.Jess's total amount: To find the total amount Jess pays, you add the original bill amount to the tip amount, resulting in the expression B + 0.21B. This simplifies to 1.21B because you combine like terms.Therefore, the expressions that match their correct meanings for Jess are as follows: Jess's bill amount without tip: B, Jess's tip amount: 0.21B, Jess's total amount: 1.21B.
Let x = 2. Evaluate the expression. x + 4/3x
When x = 2, the expression evaluates to -442/3.
To evaluate the expression when x = 2, we substitute 2 for x in the expression:
x + 4/(3x) - 150
Now, we plug in the value of x:
2 + 4/(3 * 2) - 150
First, we simplify the denominator:
2 + 4/6 - 150
Now, simplify the fraction:
2 + 2/3 - 150
Next, we need to find a common denominator, which in this case is 3:
(3 * 2)/3 + 2/3 - 150
Now, add the fractions with the common denominator:
(6/3) + (2/3) - 150
Combine the fractions:
(6 + 2)/3 - 150
Now, perform the addition in the numerator:
8/3 - 150
To subtract a fraction from a whole number, we need a common denominator. In this case, it's 3:
(8/3) - (150 * 3/3)
Now, subtract:
8/3 - 450/3
Subtract the numerators:
(8 - 450)/3
Now, perform the subtraction in the numerator:
-442/3
So, when x = 2, the value of the expression x + 4/(3x) - 150 is -442/3.
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Which value is equivalent to x+4/4+x?
A. -4
B. -1
C. 1
D. 4
Answer:
Hello :
(x+4)/(4+x) = (x+4)/(x+4) = 1 ( answer : C ) but x+4 no : 0
Answer:
C. 1
Step-by-step explanation:
Commutative property says that changing the order of the operands does not change the result. This can be expressed as:
[tex]a+b=b+a[/tex]
Using the previous information, we can say:
[tex]x+4=4+x[/tex]
And rewrite the equation as:
[tex]\frac{x+4}{x+4}[/tex]
Since the numerator and denominator are the same:
[tex]\frac{x+4}{x+4}=1\\\forall x\neq-4[/tex]
Determine whether 81 − 49n4 is a difference of two squares. If so, factor it. If not, explain why.
A (9 − 7n^4)(9 + 7n^4)
B Not a difference of squares because −49n^4 is not a perfect square.
C (9 − 7n^2)(9 − 7n^2)
D (9 + 7n^2 )(9 − 7n^2 )
We have
[tex]81-49n^4=9^2-(7n^2)^2[/tex]
so this is indeed a difference of squares. Factorizing would give
[tex]81-49n^4=(9-7n^2)(9+7n^2)[/tex]
making the answer D.
We can further factor the first term here and write
[tex]9-7n^2=3^2-(\sqrt 7\,n)^2=(3-\sqrt7\,n)(3+\sqrt7\,n)[/tex]
but that's clearly out of the scope of this question.
Answer:
D is the answer
Would you expect the probability for the simple event "rolling a 6" to be greater than or less thanthe probabilty of the event "rolling a 6 and getting heads on a coin"? Explain
Answer:
just rolling the dice on a 6 would be just fine bby.
Step-by-step explanation:
Rolling a 6 on a dice = 1/6 or 0.16 chance
rolling a 6 and getting heads on the coin = 1/6x1/2= 1/12 or 0.083 chance
Can someone please help me with this question? Thanks if you!
Answer:
the answer is C
Paul's MP3 player has a total of 852 songs. He has 4 different groups of songs. If he puts and equal number of songs in each group, how many songs will be in each group?
Answer:
213
Step-by-step explanation:
You have to divide the 852 songs into the 4 categories.
852/4=
213
A watering can dispenses water at the rate of 0.25 gallon per minute. The original volume of water in the can was 6 gallons. Which set of ordered pairs shows the volume of water in the can in gallons (y), as a function of time in minutes (x), from the first minute after the can starts dispensing water?
{(1, 6.0), (2, 5.75), (3, 5.50)}
{(6.0, 1), (5.75, 2), (5.50, 3)}
{(1, 5.75), (2, 5.50), (3, 5.25)}
{(5.75, 1), (5.50, 2), (5.25, 3)}
Answer:
{(1, 6.0), (2, 5.75), (3, 5.50)}
Step-by-step explanation:
That is most likely the answer. Hope this helps
-Kent
Answer:
a is the answer soooo brainlyist
Step-by-step explanation:
Two trains begin in Milford and end in Pinkerton, which is 300 miles away. Train A leaves Milford at 10:00 a.M. And travels at a rate of 90 miles per hour. Train B leaves Milford at 8:00 a.M. And travels at 70 miles per hour. Which train(s) will arrive in Pinkerton before 1:00 p.M.?
Answer:
Step-by-step explanation:
Alright, lets get started.
For train A:
Distance from Milford and Pinkerton is 300miles.
Speed of train A is 90 miles per hour.
So, time taken to complete this distance = [tex]\frac{distance}{speed}[/tex]
So, time taken to complete this distance =[tex]\frac{300}{90}=3.333[/tex]
Means train A will take 3.33 hours or say 3 hrs and 19.8 minutes to reach Pinkerton.
So,if it starts at 10:00 AM, then it will reach at 01 hrs 19.8 minutes PM (01:19.8 PM).
For train B:
Speed of train B is 70 miles per hour.
Train B will take time =[tex]\frac{300}{70}=4.29[/tex]
Means 4 hrs and 17.4 minutes.
So, if it starts at 8:00 Am, then it will reach at 12 hrs 17.4 minutes PM(12:17.4 PM).
So, train B will be reaching Pinkerton before 1:00 PM : Answer
Hope it will help :)
Answer:
train B will be reaching Pinkerton before 1:00 PM
Step-by-step explanation:
need help asap will give brain and all non helpful answers will be reported
Answer:
Local max is .5
Step-by-step explanation:
The local maximum is for x values between 2 and 4
It looks like the x value is 2.5 and the y value is .5
PLEASE I NEED HELP WITH THIS ONE...I THINK IT IS EITHER A. OR D.
Which of the following is a step in constructing a circle inscribed in a triangle?
A. Construct the perpendicular bisectors of each side.
B. Use a compass to locate the midpoint of each side.
C. Construct the angle bisectors of each side.
D. Use a compass to locate the altitude of each side.
Answer:
Step-by-step explanation:
i'm saying A is the correct answer
Adam bought A new pair of baseball cleats for $65 the sales tax is 5.5% what is the total cost in dollars that Adam will pay
Adam's cleats cost $65 and the sales tax is 5.5%. The sales tax amount is calculated by multiplying the price by the tax rate. The total cost is the sum of the initial price and the sales tax which is approximately $68.58.
Explanation:Adam is buying a new pair of baseball cleats for $65 and the sales tax is 5.5%. To find the total cost, we must find out the cost of the sales tax first. The sales tax can be calculated by multiplying the cost of the cleats by the sales tax percentage (in decimal form).
So, $65 * 0.055 = $3.575 is the tax amount. This means the sales tax on the cleats is $3.575.
The total cost Adam needs to pay is the sum of the cost of the cleats and the sales tax. Hence, $65 + $3.575 = $68.575. Therefore, the total cost that Adam will pay is approximately $68.58, because we usually round the money amount to the nearest cent.
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!!!!!!help plz!!! help
Answer:
it is the two real one
Step-by-step explanation:
Lola rode her bike for 7/10 of an hour on Saturday and 3/5 of an hour on Sunday.How much longer did she ride her bike on Saturday than Sunday?
Answer:
1/10 of an hour
Step-by-step explanation:
3/5 in a decimal is 6/10 and 7/10 - 6/10 is 1/10 of an hour
Which expression is equivalent to (25−−√3)14 ?
A.2 2/20
B.2 5/12
C.2 12/5
D.2 3/4
[tex]Use\\\\\sqrt[n]{a}=a^{\frac{1}{n}}\\\\\left(a^m\right)^n=a^{m\cdot n}\\---------------------\\\\\left(\sqrt[3]{2^5}\right)^{\frac{1}{4}}=\left[\left(2^5\right)^\frac{1}{3}\right]^\frac{1}{4}=2^{5\cdot\frac{1}{3}\cdot\frac{1}{4}}=\boxed{2^\frac{5}{12}}\\\\Answer:\ \boxed{\boxed{\big2^{\frac{5}{12}}}}[/tex]
Answer:
I got it wrong, but here's the answer
Step-by-step explanation:
whats the answer to this question????????????HELP ANYONE!!
Answer:
C.) 768
Step-by-step explanation:
You first solve for the slope, or rate of change, which is 1128. Then you just add 256 to 512 because you are going from gallons equals 4 to gallons equals 6. That gives you 768 for the fluid ounces.
Which of the following statements represents one of the differences between an experiment and an observational study?
Inclusion of random sample.
Introducing a change to the subgroup.
Ability to calculate the mean.
Ability to draw conclusions.
Answer:
Introducing a change to the subgroup
Step-by-step explanation:
Given there are four statements. We have to find the one which represents one of the differences between an experiment and an observational study.
The answer is option 2. Introducing a change to the subgroup
Experimental and observational studies are both types of studies between which a number of differences can be identified. When conducting research studies, various types of research in order to arrive are adopted according to the need.
An experimental study is a study where the researcher has control over most of the variables.
On the other hand, an observation study is a study where the researcher cannot control any variable but merely observes the subject without controlling any variables.
Answer:
B
Step-by-step explanation:
What is the solution to the system of equations represented by the two lines?
Answer:
(3,1)
Step-by-step explanation:
The answer is (3,1) because that's where both lines intersect.
Answer: the answer is (3,1) :)
Step-by-step explanation:
Rob is saving to buy a new mp3 player.For every $15 he earns babysitting,he saved $6.On Sunday,Rob earned $75 babysitting.How much money did he save?
Ok so first of all, Why does rob need a mp3 player? we are in the new age, right?
Secondly, I will answer your question :P
Ok so we have some info here .... we know that Rob earns $15 and saves $6
We can assume that Rob earning's equation would be y = 15x-6x
We are also given that he earned $75 (My gosh Rob nice work man!)
we would plug in 75 for y >>>for now forget the fact that Rob saves<<<
Divide 75 by 15 which = 5
Now multiply 6 by 5 which = 30 (AnSWERR!)
We now also know that out of what Rob earned he used or donated to charity $75-30 = $ 45
We can double check our work here real quick
[tex]45=15x-6x\\45=(15*5)-(6*5)\\45= 75 - 30 \\45 = 45 true[/tex]
(-2 1/3 to the third power) divided by (1 7/8)
Answer:
-2744/405
Step-by-step explanation:
Answer:
-6 314/405
Step-by-step explanation:
( -2 1/3)^3 / (1 7/8)
I am going to change the mixed numbers to improper fractions
2 1/3 = (3*2 +1)/3 = 7/3
1 7/8 = (8*1+7)/8 = 15/8
( -7/3)^3 / (15/8)
I will use copy dot flip
( -7/3)^3 * (8/15)
Now I can split the first term into parts (a/b)^x = a^x/ b^x
(-7)^3/ 3^3 *8/15
-343/27 * 8/15
-2744/405
Now we need to change it back to a mixed number
405 goes into 2744 6 times
6*405 =2430 2744-2430 = 314
-6 314/405
Joan has a prescription for 100 Theophylline capsules. Joan informs the pharmacist that she only has enough money to purchase ¼ of the prescription today. How many capsules will Joan pay for today?
Answer:
25 capsules.
Step-by-step explanation:
We are told that Joan has a prescription for 100 Theophylline capsules. Joan informs the pharmacist that she only has enough money to purchase ¼ of the prescription today.
To find the number of capsules that Joan will pay for today, we will find 1/4 of 100.
[tex]\text{The number of capsules that Joan will pay for today}=\frac{1}{4}\times 100[/tex]
[tex]\text{The number of capsules that Joan will pay for today}=25[/tex]
Therefore, Joan will pay for 25 capsules today.
For the function f(x) = -(x + 1)2 + 4, identify the vertex, domain, and range. (2 points)
The vertex is (-1, 4), the domain is all real numbers, and the range is y ≥ 4.
The vertex is (-1, 4), the domain is all real numbers, and the range is y ≤ 4.
The vertex is (1, 4), the domain is all real numbers, and the range is y ≥ 4.
The vertex is (1, 4), the domain is all real numbers, and the range is y ≤ 4.
Answer:
The second choice.
Step-by-step explanation:
f(x) = -(x + 1)^2 + 4
This is a parabola which opens downwards ( because the coefficient of x is negative).
This is the vertex form of a parabola: f(x) = a(x - b)^2 + c where the vertex is at (b, c). So in this case:-
The vertex is at (-1, 4).
The domain is All Real Numbers and the Range is (-∞, 4] (or y ≤ 4)
Answer:
The vertex is (-1, 4), the domain is all real numbers, and the range is y ≤ 4.
The drawing plan for an art studio shows a rectangle that is 15.2 inches by 8 inches. The scale in the plan is 4 in.: 5 ft. Find the length and width of the actual studio. Then find the area of the actual studio. The length is feet, the width is feet, and the area is square feet.
Answer:
Length: 19 feet
Width: 10 feet
Area: 190 feet[tex]x^{2}[/tex]
Step-by-step explanation:
This is a question about ratio.
Length: let [tex]x[/tex] be the actual length.
[tex]15.2 : x = 4 : 60[/tex]
[tex]x = 19 [/tex]
Width: let [tex]y[/tex] be the actual width.
[tex]8 : y = 4 : 60[/tex]
[tex]y = 10[/tex]
Area: A = xy
[tex] 19 * 10 = 190[/tex]
Final answer:
The actual art studio, based on the scale given, measures 19 feet in length and 10 feet in width, resulting in an area of 190 square feet.
Explanation:
To find the length and width of the actual art studio from the drawing plan, we need to apply the scale given which is 4 inches on the plan representing 5 feet in reality. For calculation, we first write the scale as a ratio: 4 inches ÷ 5 feet. Now, let's calculate the real-life dimensions of the studio.
Length: 15.2 inches on the drawing corresponds to (15.2 ÷ 4) × 5 = 19 feet in reality.
Width: 8 inches on the drawing corresponds to (8 ÷ 4) × 5 = 10 feet in reality.
Next, we calculate the area of the actual studio using the formula for the area of a rectangle, which is length multiplied by width.
Area = Length × Width = 19 feet × 10 feet = 190 square feet.
Find the conjugate of -2 + 3i.
Answer:
- 2 - 3i
Step-by-step explanation:
given a complex number a + bi
then the conjugate is a - bi
The real part a remains unchanged while the sign of the imaginary part is reversed.
the conjugate of - 2 + 3i is - 2 - 3i
Simplify ((–3)^2)^3.
A. (–3)^6
B. (–3)^5
C. (3)^5
D. (3)^6
A recipe for a loaf of bread calls for of a cup of flour. If Milo used 12 cups of flour, how many loafs of bread did he prepare?
A.
18
B.
16
C.
15
D.
12
E.
8
Answer: The answer is D 12 i am pretty sure.
If an ambulance is able to respond to car accident located 5 minutes away in 7 minutes, what is the speed of the ambulance in miles per hour?
Answer:
Speed = 42. 86 miles per hour
Step-by-step explanation:
car accident located 5 miles away in 7 minutes
Given distance d= 5 miles
time = 7 minutes. convert minutes into hours
60 minutes = 1 hour
so 7 minutes = 7 / 60 hours
To find the speed we use formula [tex]s= \frac{d}{t}[/tex]
d= 5 and t = 7/60
Plug in the values in the formula
[tex]s= \frac{d}{t}[/tex]
[tex]s= \frac{5}{\frac{7}{60}}[/tex]
[tex]s= 5* \frac{60}{7}[/tex]
s = 42.85714286
Speed = 42. 86 miles per hour
Identify the equation that does not belong with the other three. Explain your reasoning. 5x = 20, 4b = 7, 8w = 32, 12y = 48
Answer:
4b = 7
Step-by-step explanation:
5x = 20 has solution x = 4
8w = 32 has solution w = 4
12y = 48 has solution y = 4
whereas 4b = 7 has solution b = [tex]\frac{7}{4}[/tex]
The other 3 equations have a solution of 4 making 4b = 7 the odd one out
Evaluate the summation
Answer:
114
Step-by-step explanation:
The first term (a1) = 1 + 3 = 4 (substituting 1 for i)
The last term (L) = 12 + 3 = 15
So the sum of the 12 terms = (n/2)(a1 + L)
= (12/2) (4 + 15)
= 6 * 19
= 114 (answer)
The value of the summation of arithmetic progression is 114
What is Arithmetic Progression?
An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Given data ,
Let the number of terms n = 12
Let the first term a = i + 3
when i = 1
a = 4
So , the first term of the arithmetic progression is a = 4
The second term a₁ = i + 3
when i = 2
a = 5
Now , the common difference d = second term - first term
Common difference d of the arithmetic progression = 5 - 4 =1
So , d = 1
Now , the sum of n terms of an AP is given by
Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Substituting the values in the formula , we get
Sₙ = ( 12/2 ) [ ( 2 x 4 ) + ( 12 - 1 ) x 1 )
Sₙ = 6 [ 8 + 11 ]
Sₙ = 6 x 19
Sₙ = 114
Therefore , the value of Sₙ is 114
Hence , The value of the summation of arithmetic progression is 114
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Please help.
Compare and contrast the processes of solving rational and radical equations
I only need like 2-3 sentences.
Step-by-step explanation:
A rational number can be written as a ratio a/b, where a & b are integers & b \neq 0. Rational numbers are terminating or repeating. The radical sign means "the positive square root of."
Example:
√144 = "the square root of 144" but indicates the positive square root of 144, which is 12
Hope this helps!!! :)
Answer:
Rational equations or expressions (think rational numbers) are any expression which is in fraction form and where the denominator is not equal to zero. Like: [tex]\frac{2}{x} ,\frac{3}{5}[/tex] etc.
Radical expressions are those expressions that contain radicals (square, cube, fourth roots). Like 4 and -4 are the square roots of 16. A square root is written with a radical symbol √ and the number inside the radical symbol is called the radicand.