Answer:
6 miles
Step-by-step explanation:
Let the route length be r. The distance the cyclist has already covered is then (5/7)r + 40. This plus 0.75r - 118 must = r, the length of the entire route.
Then:
(5/7)r + 40 + (3/4)r - 118 = r
The LCD of the fractions 5/7 and 3/4 is 28. We thus have:
(20/28)r + 40 + (21/28)r - 118 = r, or
(41/28)r - 78 = (28/28)r
Combining the r terms, we get 13r = 78, and so r = 78/13 = 6.
The cyclist's bike route is 6 miles long.
Answer:
168 miles
Step-by-step explanation:
You reach into a bag of coins and withdrew two coins. What is the probability you withdrew a nickel and then a dime if the bag held ten pennies, six nickels, and five dimes? A. 5/14 B. 30/441 C. 1/14 D. 15/441
Answer:
1/14
Step-by-step explanation:
The total number of coins in the bag is 10+6+5, or 21.
You reach into the bag and take ONE coin. The chances of that being a nickel is 6/21, or 2/7, since nickels compose 6 of the 21 coins in the bag.
You don't replace the nickel.
Now you have 20 coins in the bag, including 5 nickels.
The chances of your next draw being a dime is 5/20, or 1/4, since there are 5 dimes in the bag.
The joint probability of drawing a nickel and then a dime is then the product of these two probabilities:
(2/7)(1/4) = 2/28 = 1/14
Which pair of points is in the solution set for the system of linear inequalities below?
2x + y < 2
6x + 3y > 2
a.) (0, 3/2) and (3/4, 1/4)
b.) (1/2, 1) and (1/2,1/2)
c.) (-1,-1) and (0,-3)
d.) (0,2) and (1/3,0)
Final answer:
The correct pair of points that is in the solution set for the given system of linear inequalities is option a) (0, 3/2) and (3/4, 1/4). Each point in this pair satisfies both of the inequalities when substituted into them.
Explanation:
The question asks which pair of points is in the solution set for the given system of linear inequalities:
2x + y < 2
6x + 3y > 2
To verify if the points provided are solutions, we plug them into the inequalities to see if they satisfy both conditions.
Let's test each pair:
For pair a) (0, 3/2), the first inequality becomes 2(0) + (3/2) = 3/2, which is less than 2, so it satisfies the first inequality. For the second inequality, 6(0) + 3(3/2) = 9/2, which is greater than 2, so it satisfies the second inequality as well. Therefore, (0, 3/2) is a solution. However, for the second point (3/4, 1/4), the first inequality becomes 2(3/4) + (1/4) = 3/2 + 1/4 = 7/4, which is less than 2, satisfying the first inequality. But for the second inequality, we get 6(3/4) + 3(1/4) = 9/2 + 3/4 = 21/4, which is greater than 2, satisfying the second inequality, so (3/4, 1/4) is also a solution.
For pair b), to be brief, one point does not satisfy both inequalities.
For pair c), one point does not satisfy both inequalities.
For pair d), one point does not satisfy both inequalities.
Therefore, the correct pair of points is option a) (0, 3/2) and (3/4, 1/4), as they both are solutions to the system of inequalities.
Translate to algebraic expression
29 increased by n
Answer:
29 + n
Step-by-step explanation:
To increase 29 by n, we add n to 29. Then we get 29 + n.
hope it helps.
PS plzzzz mark me brainliest
Answer:
29 + n
Step-by-step explanation:
When we increase a number by another number, we're performing the operation of addition, so the phrase here would translate to the expression 29 + n.
BRAINLIEST!!!!
Identify the equation of the translated graph in general form
Answer:
Hyperbola:
[tex]x^2-y^2-8x+6y-1=0[/tex]
Step-by-step explanation:
the given hyperbola has equation:
[tex]x^2-y^2=8[/tex]
This is an equation of a hyperbola centered at the origin.
This hyperbola is translated so its center is now at T(4,3)
[tex](x-4)^2-(y-3)^2=8[/tex]
We expand to get:
[tex]x^2-8x+16-(y^2-6y+9)=8[/tex]
[tex]x^2-8x+16-y^2+6y-9=8[/tex]
[tex]x^2-8x-y^2+6y+7=8[/tex]
[tex]x^2-8x-y^2+6y+7-8=0[/tex]
[tex]x^2-y^2-8x+6y-1=0[/tex]
Answer:
Its B
Step-by-step explanation:
it just is lol
Find the surface area of the right square pyramid. Round your answer to the nearest hundredth.
ANSWER
C. 145.75 yd²
EXPLANATION
First we need to calculate the area of the four triangular faces.
The lateral surface area
[tex] = 4 \times \frac{1}{2} \times 5.3 \times 11.1[/tex]
[tex] = 117.66 {yd}^{2} [/tex]
The area of the base is
[tex] = 5.3 \times 5.3[/tex]
[tex] = 28.09[/tex]
To find the total surface area, we add the area of the square base to the area of the 4 triangular faces.
Therefore the total surface area is
[tex] = 117.66 + 8.09 = 145.75 {yd}^{2} [/tex]
Answer: Option C.
Step-by-step explanation:
To calculate the surface area of the right square pyramid, you need to use the following formula:
[tex]SA=\frac{1}{2}(4s)(l)+(s^2)[/tex]
Where "s" is the length of any side of the base and "l" is the slant height.
You can identify in the figure that:
[tex]s=5.3yd\\l=11.1yd[/tex]
Therefore, substituting these values into the formula, you get this result:
[tex]SA=\frac{1}{2}(4(5.3yd))(11.1yd)+((5.3yd)^2)\\\\SA=145.75yd^2[/tex]
The last time Esteban checked his credit score, it was 740, and his only credit event since has been applying for a store credit card. Which of these is most likely to be his credit score now?
According to the information, it can be inferred that the current credit score for Esteban is 730 because he has not used more transactions than eleven of his credit score.
What is the credit score?A credit score is a term that refers to an index that is intended to predict the chances that you will repay a loan on time.
This takes into account different factors related to your economy, so it is likely that the more movement of money you have, your score will be higher.
Based on the foregoing, it can be inferred that Esteban's score dropped because he has not made important transactions in recent months. Additionally, it has no recent transaction history.
Note: This question is incomplete due to missing information. Here is the complete information:
Options.
A. 730
B. 740
C. 750
D. 760
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A store marks up merchandise 40% to make a profit. If the item costs the store $12, what is the selling price?
Answer:
$16.80
Step-by-step explanation:
The item costs the store $12.00
12 x 40% or 12 x 0.4 = 4.8
Add 4.8 to 12
And you get the price the store sells the product for profit, $16.80
Which angles are congruent to each other?
Answer:
Angle 1 and 3
Step-by-step explanation:
Those angles are vertical angles,and vertical angles are always congruent.
Which expression is equivalent to (x2 − 8) − (−2x2 + 4)?
A) x2 + 12
B) 3x2 + 12
C) −x2 + 12
D) 3x2 − 12
Answer:
the answer is D. mark me brainliest if im correct.
Step-by-step explanation:
The equivalent expression for (x² - 8) - (-2x² + 4) is 3x² - 12
Option D is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
(x² - 8) - (-2x² + 4)
Remove the parenthesis.
x² - 8 + 2x² - 4
Add like terms.
3x² - 12
Thus,
The equivalent expression is 3x² - 12
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Which set of measures would give a clear conclusion about the data. Help please.
Suppose a population of 250 fleas doubles in size every month. The function f(x)=250(2^x) gives the population after x months. How many fleas will there be after 1 year?
A. 500
B. 1,024,000
C. 6,000
D. 2,280
I'm not the best at math, but I tried.
x= the amount of months passed
The question asks for the population of fleas in 1 year, and 1 year = 12 months, then x would equal 12 months
Therefore, you substitute that x with 12
f(x)=250(2^x)-------f(x)=250(2^12)
Now you can solve that part of the problem:
2 to the power of 12= 4096
f(x)=250(4096)
now multiply that:
250×4096= 1024000
The answer is C. 1024000
The answer is 1,024,000 fleas.
The function f(x)=250(2^x) gives the population of fleas after x months. To find out how many fleas there will be after 1 year, substitute x=12 into the function:
f(12) = 250(2^12) = 250 * 4096 = 1,024,000 fleas.
One side of a rectangle is 6 yd longer than three times another side. The area of the rectangle is 72 yd2. Find the length of the longer side.
Answer:
18 yds
Step-by-step explanation:
Let the length and width be L and W respectively.
Then L· W = area = 72 yd², so that L = (72 yd²) / W.
But also L = 3W + 6 yd. Subbing this into L· W = area = 72 yd², we get:
(3W + 6) · W = 72, or
3W² + 6W - 72 = 0. Since all four terms are evenly divisible by 3, we get:
W² + 2W - 24 = 0, which factors as follows:
(W + 6)(W - 4) = 0. Then W + 6 = 0, or W = -6 (makes no sense for a length), and W - 4 = 0 yields W = 4 yds.
If the shorter side is of length 4 yds, then the longer side is of length
L = 3(4 yds) + 6 yds = 18 yds
Answer:
18 yd
Step-by-step explanation:
(3x + 6) * x = 72
Use the distributive property
3x^2 + 6x = 72
3x^2 + 6x - 72 = 0
3(x^2 + 2x - 24) = 0
X^2 + 2x - 24 = 0
X can equal -6 and 4.
4 only works for this problem
4 * 3 = 12
12 + 6 = 18
So, the answer is 18 yd.
Let’s check our work.
3 * 4 = 12
12 + 6 = 18
18 * 4 = 72
So, we know for a fact that the longer side is 18 yd long.
I hope I helped!
Let me know if you need anything else!
~ Zoe
what is 43.2÷16= in partial quotients
43.2\16= 2.7 hope this helps
Answer:
2.7
Step-by-step explanation:
well 43.2/16 is 2.7 hopefully this is helpful :3
Use set builder notation to represent the following set. {... -3, -2, -1, 0}
Answer:
[tex]\left\{x\in \mathbb {Z}\ : \ x \le 0 \right\}[/tex]
Step-by-step explanation:
Set-Builder Notation: A shorthand used to describe sets, often sets with an infinite number of elements.
The set {...,-3, -2, -1, 0} is the set of all negative integers and 0, so you can use such set-builder notation:
[tex]\left\{x\in \mathbb {Z}\ : \ x \le 0 \right\}[/tex]
Note: Here [tex]\mathbb{Z}[/tex] represents the set of all integers.
Final answer:
The set {... -3, -2, -1, 0} can be represented in set builder notation as {x ∈ ℤ | -3 ≤ x < 1 }, which describes all integers x that are greater than or equal to -3 and less than 1.
Explanation:
To express the set that includes the numbers -3, -2, -1, and 0 using set builder notation, we start by recognizing that these numbers can be described by a pattern or rule, which is that they are all the integer numbers greater than or equal to -3 and less than 1. We can then write this using set builder notation as:
{x ∈ ℤ | -3 ≤ x < 1 }
In this notation, the variable 'x' represents the elements of the set and ∈ stands for 'element of.' ℤ is the symbol for integers. The vertical bar or colon (|) stands for 'such that.' Our notation reads as 'the set of all integers x such that -3 is less than or equal to x and x is less than 1.'
Suppose you are simplifying 4 + 3(8 - 3·2)2.
Choose all the steps which will be part of your work.
7(8 - 6)2
4 + 3(2)2
4 + 3(8 - 3·4)
4 + 3(5·)2
4 + 3·4
4 + 3(8 - 6)2
4 + 12
4 + 62
Answer:
4 + 3(2)2
4 + 3·4
4 + 3(8 - 6)2
4 + 12
Step-by-step explanation:
I am assuming the *2 after the parentheses is a power? if so, these would be your correct choices
Answer:
The steps used are 2,5,6,7.
Step-by-step explanation:
Given : Expression [tex]4+3(8-3\cdot 2)^2[/tex]
To find : Simplify and choose all the steps which will be part of your work ?
Solution :
Step 1 - Write the expression,
[tex]4+3(8-3\cdot 2)^2[/tex]
Step 2 - Solve the multiplication in bracket,
[tex]=4+3(8-6)^2[/tex]
Step 3 - Solve the bracket,
[tex]=4+3(2)^2[/tex]
Step 4 - Solve the square term,
[tex]=4+3\cdot 4[/tex]
Step 5 - Solve the product,
[tex]=4+12[/tex]
Step 6 - Add the terms,
[tex]=16[/tex]
Therefore, The steps used are 2,5,6,7.
factor this polynomial completely x2-6x+9
Answer:
Step-by-step explanation:
(x-3)^2
Answer:
(x-3)
Step-by-step explanation:
asap asap asap now now now plz 12 20 and 21
Answer:
12. AM= 2x+4
MB= 5x-8
AB= ?
So to get AB, you would need to find the total measurements of AM and MB.
AM=MB
2x+4=5x-8
2x=5x-12
-3x=-12
x=4
20. AE= 37
21. AC= 16
Step-by-step explanation:
24,042 in expanded form
Answer:
20,000
+ 4,000
+ 0
+ 40
+ 2
Step-by-step explanation:
Brainiest please!
I think it's 4,000 I could be wrong
Evaluating expressions for the value of x 4.5x-12 x=2
X = 2
4.5(2) -12
9 -12
= -3
Answer is -3
help fast ok thx!!!!
Answer:
C
Step-by-step explanation:
Given
[tex]\sqrt{3x+8}[/tex] = [tex]\sqrt{4x+1}[/tex]
[ note that ([tex]\sqrt{x}[/tex])² = x ]
Square both sides
3x + 8 = 4x + 1 ( subtract 4x from both sides )
- x + 8 = 1 ( subtract 8 from both sides )
- x = - 7 ( multiply both sides by - 1 )
x = 7 → C
Answer:
x = 7.
Step-by-step explanation:
Squaring both sides:
3x + 8 = 4x + 1
3x - 4x = 1 - 8
-x = -7
7 = x.
3.4(x+1.58)=-11.288 value of x.
3.4(x+1.58)= - 11.288
Step 1: Distribute 3.4 to the numbers inside the parentheses (x+1.58)
3.4x + (3.4×1.58)= - 11.288
3.4x + 5.372 = -11.288
Step 2: Bring 5.372 to the right side by subtracting it to both sides
3.4x + (5.372 - 5.372 ) = (-11.288 - 5.372)
3.4x + (0) = (-16.66)
3.4x = -16.66
Step 3: Isolate x by dividing 3.4 to both sides
[tex]\frac{3.4x}{3.4} = \frac{-16.66}{3.4}[/tex]
x = -4.9
Hope this helped!
jack has x pence, jill has 6 pence less then jack, write down in terms of x, the number of pence that jill has
Answer:
x-6
Step-by-step explanation:
6 pencils less than x in terms of x it would be x-6
hope it helps
In the given problem, the amount of pence that Jill has can be expressed in terms of x (the amount of pence that Jack has) as x - 6. This means Jill has 6 pence less than Jack. If Jack has a certain number of pence represented as x, then Jill would have that number minus 6.
Explanation:The question asks for the amount of pence that Jill has in terms of x, where x is the amount of pence that Jack has. Given that Jill has 6 pence less than Jack, we can represent the amount of pence Jill has as x - 6. Therefore, if Jack has x pence, Jill would have x - 6 pence. For example, if Jack (x) has 10 pence, Jill would have 4 pence (x - 6 = 10 - 6).
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What is the discriminante of 9x^2 + 2 = 10?
Answer:
C
Step-by-step explanation:
Use the formula for the discriminant.
[tex]b^2-4ac[/tex]
[tex](-10)^2-4(9)(2)[/tex]
[tex]100-72[/tex]
[tex]28[/tex]
Evaluate the expression when m= 6 and n = 7.
4n+m
Answer:
34
Step-by-step explanation:
4(7)+6
Answer:
34
Step-by-step explanation:
Substitute the m and n : 4(7) + 6
Solve: 28 + 6 = 34
Find the later area of the figure
Answer:
[tex]\large\boxed{60\pi\ sq.in.}[/tex]
Step-by-step explanation:
The formula of a lateral area of a cone:
[tex]L.A.=\pi rl[/tex]
r - radius
l - lateral height
We have the radius r = 6in and the height H = 8in.
Use the Pythagorean theorem to calculate the lateral height:
[tex]l^2=6^2+8^2\\\\l^2=36+64\\\\l^2=100\to l=\sqrt{100}\\\\l=10\ in[/tex]
Substitute:
[tex]L.A.=\pi(6)(10)=80\pi\ in^2[/tex]
Which of the following is the solution to the compound inequality 7x+3/2>13 or 5/2x-1/3>-11/2
Answer:
[tex]\large\boxed{\text{If is "or", then}\ x>-2\dfrac{1}{15}}\\\boxed{\text{If is "and", then}\ x>1\dfrac{9}{14}}[/tex]
Step-by-step explanation:
[tex]7x+\dfrac{3}{2}>13\qquad\text{multiply both sides by 2}\\\\14x+3>26\qquad\text{subtract 3 from both sides}\\\\14x>23\qquad\text{divide both sides by 14}\\\\x>\dfrac{23}{14}=1\dfrac{9}{14}\\=====================\\\\\dfrac{5}{2}x-\dfrac{1}{3}>-\dfrac{11}{2}\qquad\text{multiply both sides by 2}\\\\5x-\dfrac{2}{3}>-11\qquad\text{multiply both sides by 3}\\\\15x-2>-33\qquad\text{add 2 to both sides}\\\\15x>-31\qquad\text{divide both sides by 15}\\\\x>-\dfrac{31}{15}=-2\dfrac{1}{15}\\=====================[/tex]
Final answer:
To solve the compound inequality, each inequality is solved individually. The first inequality yields x > 1.64285714, and the second yields x > -2.06666667. As this is an 'or' compound inequality, the solution is the union of both, leading to x > 1.64285714.
Explanation:
To solve the compound inequality 7x + 3/2 > 13 or 5/2x - 1/3 > -11/2, we need to treat each inequality separately and then find the union of their solutions.
For the first inequality:
Subtract 3/2 from both sides to get 7x > 11.5.
Divide both sides by 7 to find x > 11.5/7, which simplifies to x > 1.64285714.
For the second inequality:
Multiply both sides by 6 to clear the fraction, leading to 15x - 2 > -33.
Add 2 to both sides to get 15x > -31.
Divide both sides by 15 to find x > -31/15, which simplifies to x > -2.06666667.
The solution is the set that satisfies at least one of these inequalities. Since x > 1.64285714 or x > -2.06666667, the overall solution is x > 1.64285714.
In an experiment, a number cube is rolled 4 times. The number of times a 5 shows is recorded. Sixty trials of the experiment are run.
The table shows the frequency of any number of 5s occurring in the trials.
Number of 5s 0 1 2 3 4
Frequency 6 9 33 9 3
Create a probability distribution for the discrete variable.
Drag the sliders on the horizontal axis to represent the probability distribution.
Answer:
Step-by-step explanation:
Given that in an experiment, a number cube is rolled 4 times. The number of times a 5 shows is recorded. Sixty trials of the experiment are run.
No of 5's Freq Prob
0 6 0.1
1 9 0.15
0 33 0.55
3 3 0.05
4 9 0.15
60 1
The above is the probability distribution of the discrete variable.
Which expression is equal to (f · g)(x)?
Answer:
A
Step-by-step explanation:
Note that
x² + 12x + 36 is a perfect square → (x + 6)², hence
[tex]\sqrt{x^2+12x+36}[/tex] = [tex]\sqrt{(x+6)^2}[/tex] = (x + 6)
Hence
f(x) × g(x)
= (x + 6)(x³ - 11)
= [tex]x^{4}[/tex] - 11x + 6x³ - 66
= [tex]x^{4}[/tex] + 6x³ - 11x - 66 → A
(f·g)(x) in mathematics denotes the product of two functions, f(x) and g(x). Its interpretation and output may vary depending on the functions f(x) and g(x), but essentially, it is a multiplication of these two functions.
Explanation:In mathematics, expressing (f·g)(x) indicates the product of two functions at a given x-coordinate. This is equivalent to f(x) multiplied by g(x). For instance, if f(x) = 2x and g(x) = 3x, then (f · g)(x) would yield (2x)(3x), resulting in 6x².
It's important to note that mathematical functions can vary, and this expression can take on various forms based on the nature of f(x) and g(x).
The provided reference information appears to be a mix of rules from differential calculus and mathematical definitions, which lack a direct relation to the original question about (f·g)(x). The primary concept here is understanding function multiplication.
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Arithmetic placement test
Your question doesn't look like one, but I'll give you a set of 10 questions of arithmetic. Do not forget to use PEMDAS.
6 × 7 + 87 + 19 ÷ 276 - 14 + 1291 × 2 - 4625 ÷ 5 × 74 + 6 ÷ 287 × 4 + 747 × 5 + 736 × 5 + 810 × 7 + 24
Another answer will be available in the comments just in case if this is not what you wanted.
(7x+5)(2x^3-4x^2+9x-3)
Answer:
[tex]\large\boxed{(7x+5)(2x^3-4x^2+9x-3)=14x^4-18x^3+43x^2+24x-15}[/tex]
Step-by-step explanation:
Use FOIL: (a + b)(c + d) = ac + ad + bc + bd
[tex](7x+5)(2x^3-4x^2+9x-3)\\\\=(7x)(2x^3)+(7x)(-4x^2)+(7x)(9x)+(7x)(-3)\\+(5)(2x^3)+(5)(-4x^2)+(5)(9x)+(5)(-3)\\\\=14x^4-28x^3+63x^2-21x+10x^3-20x^2+45x-15\\\\\text{combine like terms}\\\\=14x^4+(-28x^3+10x^3)+(63x^2-20x^2)+(-21x+45x)-15\\\\=14x^4-18x^3+43x^2+24x-15[/tex]