The best way to rewrite the sentence is option D: "While he was driving on the highway, Paul saw a billboard advertising a music festival."
The original sentence is a bit awkward in its structure. Let's evaluate the options:
A. "While he was driving on the highway advertising a music festival, Paul saw a billboard."This option is incorrect because it suggests that Paul was the one advertising the music festival while driving, which is not the intended meaning.
B. "Advertising a music festival, Paul saw a billboard driving on the highway."This option is incorrect because it implies that the billboard itself was driving on the highway, which is illogical.
C. "No change"This option maintains the original structure of the sentence, which is awkward and does not convey the intended meaning clearly.
D. "While he was driving on the highway, Paul saw a billboard advertising a music festival."This option correctly places the modifier "advertising a music festival" next to "billboard," clarifying that it was the billboard, not Paul, advertising the music festival.
x + y = 3
3x + 2y = 14
The solution is x = 8 and y = -5
Solution:
Given system of equations are:
x + y = 3 ------ eqn 1
3x + 2y = 14 ------ eqn 2
We have to find the solution to the equations
We can use substitution method to solve
From eqn 1,
x + y = 3
Isolate for "x"
x = 3 - y ------ eqn 3
Substitute eqn 3 in eqn 2
3(3 - y) + 2y = 14
9 - 3y + 2y = 14
-y = 14 - 9
-y = 5
y = -5Substitute y = -5 in eqn 3
x = 3 - (-5)
x = 3 + 5 = 8
x = 8Thus the solution is x = 8 and y = -5
Find the area of the circle. Use 3.14 for pi
Answer:
C
Step-by-step explanation:
if you multiply 2.3 times pi you get the answer
Answer:
3. A
4. D
Step-by-step explanation:
r : radius
area of a circle = 3.14×r²
3,14×11^2 = 379,94
3,14×(2,3÷2)^2 = 4,15265
I don't think anyone will respond to a good attempt
The answer is gonna be 15
Which equations have the same value of x as StartFraction 5 over 6 EndFraction x + two-thirds = negative 9? Select three options.
6 (StartFraction 5 over 6 EndFraction x + two-thirds) = negative 9
6 (StartFraction 5 over 6 EndFraction x + two-thirds) = negative 9(6)
5 x + 4 = negative 54
5 x + 4 = negative 9
5 x = negative 13
5 x = negative 58
Answer:
6 (StartFraction 5 over 6 EndFraction x + two-thirds) = negative 9(6)
5 x + 4 = negative 54
5 x = negative 58
Step-by-step explanation:
we have
[tex]\frac{5}{6}x+\frac{2}{3}=-9[/tex]
solve for x
Multiply by 6 both sides
[tex]6(\frac{5}{6}x+\frac{2}{3})=6(-9)[/tex]
[tex]5x+4=-54[/tex]
subtract 4 both sides
[tex]5x=-54-4\\5x=-58[/tex]
divide by 5 both sides
[tex]x=-\frac{58}{5}[/tex]
Answer:
6 (StartFraction 5 over 6 EndFraction x + two-thirds) = negative 9(6)
5 x + 4 = negative 54
5 x = negative 58
Step-by-step explanation:
Sarah answered 24 questions on her test correctly and earned an 80%. How many questions were on the test?
Answer:
43 questions in total
Step-by-step explanation:
the original equation with the unknown (total number of questions on the test) will look like this
[tex] \frac{total \: number \: of \: questions \: on \: exam}{24 \: answered \: questions} = 80\%[/tex]
we know this because to work out a percentage in the 1st place you need the total ÷ number (in this case it's ÷ how many questions out of the total she did answer)
now you rearrange.
you need to move the 24 to get the total on it's own here's how you do it
[tex] \frac{tot \: num \: of \: qs}{24} \times 24 = 80\% \times 24[/tex]
what you do to one side of equation you have to do to the other. the 24 and 24 on the left will cancel because 24÷24=1 and we don't write
got mum of Q's x 1= 80 x 24
now you convert % to decimal
[tex]80\% \times 100 = 0.80[/tex]
replace
[tex]tot \: num \: qs \: = 24 \times 0.80 = 19[/tex]
now you take the original and + the 19
[tex]24 + 19 = 43[/tex]
therefore there are a total of 43 questions on the exam
To find the total number of questions on the test, we set up a ratio where 24 questions represents 80%. By comparing it to a ratio where X represents 100%, and solving for X, we get the total number of questions.
Explanation:The question pertains to the concept of percentages. In Sarah's case, she answered 24 questions correctly and got an 80%, meaning that these 24 questions represent 80% of the total questions on the test. Hence, to find the total number of questions on the test, we set up a ratio such as this: 24 is to 80 as X (total questions) is to 100. We solve for X by multiplying the cross products and dividing by 80. The result will give us the total number of questions on the test.
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blairs new computer cost 5$ less than twice the cost og her old computer. Her new computer cost 709$. how much did blairs old computer cost?
i need help asap! i will mark brainliest answer and i will give 5 stars for the answer! thank you :)
The cost of old computer is $ 357
Solution:
Let "x" be the cost of old computer
From given,
Cost of new computer = $ 709
Blairs new computer cost 5$ less than twice the cost of her old computer
Therefore,
Cost of new computer = twice the cost of old computer - 5
Cost of new computer = 2x - 5
709 = 2x - 5
2x = 709 + 5
2x = 714
Divide both sides by 2
x = 357
Thus the cost of old computer is $ 357
Answer:
$357
Step-by-step explanation:
709=2x-5
+5 +5
cross the right column out
709+5 = 714
714=2x
divide 714 by 2 and get 357
HOPE THIS HELPS!!!
The quotient of the complex # below (7-2i)/(4 +3i)
Answer:
Step-by-step explanation:
hello :
(7-2i)/(4 +3i)
=(7-2i)×(4-3i)/(4 +3i)×(4-3i)
but : (7-2i)×(4-3i) =28-21i-8i+6i²
(7-2i)×(4-3i) = 22-29i ....i² = -1
(4 +3i)×(4-3i) = 4²-(3i)²...(identity)
= 16+9 =25
so :
(7-2i)×(4-3i)/(4 +3i)×(4-3i)
=(22-29i)/25
(7-2i)/(4 +3i) = 22/25 -29/25i
(form : a+ib)
To divide complex numbers, multiply the numerator and denominator by the conjugate of the denominator.
Explanation:To divide complex numbers, we need to multiply the numerator and denominator by the conjugate of the denominator. The conjugate of 4 + 3i is 4 - 3i. So, we have ((7 - 2i) * (4 - 3i)) / ((4 + 3i) * (4 - 3i)).
Multiplying the numerators and the denominators, we get (28 - 21i - 8i + 6i^2) / (16 - 12i + 12i - 9i^2).
This simplifies to (28 - 29i - 6) / (16 + 9).
Finally, dividing the real parts and the imaginary parts separately, the quotient is:
Quotient = (22 - 29i) / 25
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Sara worked 40 hours per week
A married couple together earn $75,000. The husband earns $15,000 more than five times what his wife earns. What does the wife earn?
Answer:
$12,000
Step-by-step explanation:
Let's say the husband's income was $H, and the Wife's was W.
h + w = 75,000
H = 5w + 15, 000
Substitute that for H.
5w + 15,000 + w = 75,000
6w + 15,000 = 75,000
6w=60,000
w=12,000, So the wife earned $12,000.
Mrs. Pythagoras compares the distance traveled by three of her students. • Jason's distance travelled is given by the equation d =m, where, the total distance d traveled is given in m minutes. • Susan traveled(3 miles in 5 minutes.) The graph below represents the distance Mickey traveled.
please help me answer this math question
The student with the lowest unit rate is Mickey, with a unit rate of 0.3 miles per minute.
What is the relation of speed and distance?
Speed describes how accelerated something or somebody is moving. If you know the distance traveled and the time it took, we can calculate the average speed of an object.
The speed formula is speed = distance / time.
We are given that;
Equation d=m
Susan distance travelled=3 miles in 5 minutes
Now,
To find the unit rate, we need to divide the distance traveled by the time taken. Let's start by calculating the unit rate for each student:
Jason: The equation given for Jason's distance traveled is d = m, where d is the distance traveled in m minutes. Therefore, his unit rate is 1 mile per minute.
Susan: She traveled 3 miles in 5 minutes. To find her unit rate, we divide 3 miles by 5 minutes:
Unit rate = 3 miles / 5 minutes = 0.6 miles per minute
Mickey: The points on Mickey's distance vs time graph are (20,6), (40,12), and (60,18). We can use these points to calculate the unit rate for Mickey.
Between the points (20,6) and (40,12), the distance traveled is 12 - 6 = 6 miles, and the time taken is 40 - 20 = 20 minutes. Therefore, the unit rate is:
Unit rate = 6 miles / 20 minutes = 0.3 miles per minute
Between the points (40,12) and (60,18), the distance traveled is 18 - 12 = 6 miles, and the time taken is 60 - 40 = 20 minutes. Therefore, the unit rate is:
Unit rate = 6 miles / 20 minutes = 0.3 miles per minute.
Therefore, by distance given the answer will be 0.3 miles per minute.
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What inequality describes the situation?
5. Let t = the amount Thomas earned. Thomas earned $49 or more. (1 point)
Ots49
ta 49
Ot> 49
Ot<49
Answer:
[tex]t \geqslant 49[/tex]
Step-by-step explanation:
If Thomas earned $49 OR more, therefore he could have earned either $49 or greater. Please mark brainliest! : )
The inequality that describes the situation is t >= 49. This means that the amount Thomas earned, represented by the variable t, is greater than or equal to $49.
Explanation:The inequality that describes the situation is t >= 49.
This means that the amount Thomas earned, represented by the variable t, is greater than or equal to $49.
For example, if Thomas earned $49, the inequality is true. If Thomas earned more than $49, the inequality is also true.
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I need some help here??
x = 11 (or) x = –13
Solution:
Theorem:
If three or more parallel lines are cut by a transversal then they divide the transversals proportionally.
Given lines l, m, n are parallel lines cut by a two transversal lines.
Therefore, they are in proportion by the above theorem.
[tex]$\Rightarrow\frac{x+5}{10}=\frac{12.8}{x-3}[/tex]
Do cross multiplication.
[tex]$\Rightarrow(x+5)\times(x-3)=12.8\times10[/tex]
[tex]$\Rightarrow x^2+5x-3x-15=128[/tex]
[tex]$\Rightarrow x^2+2x-15=128[/tex]
Arrange all terms in one side.
[tex]$\Rightarrow x^2+2x-15-128=0[/tex]
[tex]$\Rightarrow x^2+2x-143=0[/tex]
[tex]$\Rightarrow x^2-11x+13x-143=0[/tex]
Take common terms outside
[tex]$\Rightarrow x(x-11)+13(x-11)=0[/tex]
[tex]$\Rightarrow (x-11)(x+13)=0[/tex]
[tex]$\Rightarrow (x-11)=0\ \text{(or)}\ (x+13)=0[/tex]
⇒ x = 11 (or) x = –13
Hence x = 11 (or) x = –13.
Answers to questions
Solve the inequality.
3< -5n+2n
Answer:
n < -1
Step-by-step explanation:
3 < -5n+2n ⇔ 3 < -3n ⇔ -1 > n
How many solutions does this equation have?
9x + 2
3
= 3x + 3
Answer:
Only one solution my boiiii
Answer:
Step-by-step explanation:
9x + 23 = 3x + 3
9x - 3x = 3 - 23
6x = -20
x = -20/6
x = - 10/3
x = -3 1/3
calculate the number in the middle of 15 and 24
Final answer:
To find the number in the middle of 15 and 24, you calculate the mean, which is (15 + 24)/2, resulting in 19.5.
Explanation:
How to Calculate the Number in the Middle of 15 and 24
To calculate the number in the middle of two values, we are essentially seeking the mean or average of those two numbers. This can be done by adding the two numbers together and then dividing by the number of values, which is 2 in this case. Thus, the calculation would be (15 + 24)/2.
Let's do the math: (15 + 24)/2 = 39/2 = 19.5.
Therefore, the number in the middle of 15 and 24 is 19.5.
At midnight the temperature is -6°C. At midday the temperature is 9°C. By how much did the temperature rise?
The temperature increased by 15°C.
What is the temperature?Temperature is a physical quantity that expresses the perceptions of hotness and coldness
Given that at midnight the temperature is -6°C. At midday the temperature is 9°C. Therefore, the difference in the temperature can be written as,
The difference in temperature
= Temperature in Midday - Temperature at midnight
= 9°C - (-6° C)
= 15° C
Therefore, The difference in the temperature is 15°C.
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if the function f(x) has a domain of -2≤x≤8 and a range of -4≤y≤6 and the function g(x) is defined by the formula g(x)= 5f(2x) then what are the domain and range of g. explain your thought process
Answer:
Domain: -1 ≤ x ≤ 4
Range: -20 ≤ 5f(2x) ≤ 30
Step-by-step explanation:
Inputs of f are between -2 and 8
Input is now 2x, so
-2 ≤ 2x ≤ 8
-1 ≤ x ≤ 4
(Horizontal stretch, factor 1/2)
Range of f is -4 ≤ y ≤ 6
So,
-20 ≤ 5y ≤ 30
(Vertical stretch, factor 5)
The domain of g(x) is [-1, 4].
The range of g(x) is [-20, 30].
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Domain of f(x) = [-2, 8]
Range of f(x) = [-4, 6]
g(x) = 5 f(2x)
Since -2 ≤ x ≤ 8 and -2 ≤ 2x ≤ 8 = -1 ≤ x ≤ 4.
The domain of g(x) = [-1, 4]
Now,
The range of g(x) = [-20, 30]
Since -4 ≤ y ≤ 6,
5 x (-4) ≤ 5y ≤ 5 x 6
-20 ≤ 5y ≤ 30
Thus,
The domain and range of g(x) are
[-1, 4] and [-20, 30].
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does anyone know the answer.
What is the inverse of the following statement?
If ∆ABC is equilateral, then it is isosceles.
A. If ∆ABC is not equilateral, then it is not isosceles.
B. If ∆ABC is isosceles, then it is equilateral.
C. If ∆ABC is equilateral, then it is isosceles.
D. If ∆ABC is not isosceles, then it is not equilateral.
Answer:
it's A.
Step-by-step explanation:
eqilateral means allsides equal while isosceles means two sides are equal.
Answer:
A
Step-by-step explanation:
Ms. Ruiz is 9 years older than 6 times as many years old as Carlos. Ms. Ruiz is 57 years old.
Answer:
Carlos is 8
Step-by-step explanation:
I solved this by subtracting 9 from her age, which gets rid of that. 57-9=48
Carlos is 48/6 years old, or 8
Answer:
The answer is 8
Step-by-step explanation:
Find the inequality represented by the graph.
Answer:
Step-by-step explanation:
y intercept is 3
y - 4 = 3 ( x - 4)
y - 4 = 3x - 12
y < 3x - 8
not equal to because the line is dashed.
not greater than because the shading is below the line
find the error in lin’s solution.
Look at the figure below.
66) In figure ABCD shown, which of the following statements
are true?
A) AD intersects BC
B) BA is parallel to CD
C) BA is a diagonal of ABCD
D) BA is perpendicular to AD
How many inches are in 43 yards
Answer:
1548
Step-by-step explanation:
Their are 36 inches in a yard multiply by 43 it’s 1548
Evaluate 6(x+2)=6x+12
Answer:
12=12 Many Solutions
Step-by-step explanation:
6(x+2)=6x+12
6x+12=6x+12
-6x -6x
12=12
*MANY SOLUTION
*THERE IS A SOLUTION
negative 5 and 3/4 multiplied by 8/23
Answer:
[tex] - 5 \frac{3}{4} \times \frac{8}{23} = - \frac{23}{4} \times \frac{8}{23} = - 2[/tex]
Bananas cost .89cents, I have $11.75, how many bananas can I buy?
Answer: you will be able to buy 13.20224719101124 bananas.
3 times 2/3 will be less then,greater then or equal to 3
Answer:
Equal to 3
The drawing will help
Answer: Less than
Step-by-step explanation:
The answer will be 2 causing it to be less than 3
multiply 3*2 and get 6
1*3 and get 3
6/3 = 2
3 tuns into 3/1
Remember: Any whole numbers by itself turns into a fraction when multiply fractions and a whole number. So 3 becomes 3/1
if you have 108 inches of wood to make a picture fram what is the greatest area if a = -w2 + 54w
Answer:
The greatest area possible is 729[tex]inch^{2}[/tex]
Step-by-step explanation:
i) If a = [tex]-w^{2} + 54w[/tex] where w is the width of the picture frame
differentiating on both sides we get
[tex]\frac{da}{dw} = -2w + 54[/tex]
Differentiating the above again on both sides we get [tex]\frac{d^2a}{dw^2}[/tex] = -2
Since the second order derivative is negative then we can get the solution for the maximum area by equating the fist order derivative equation to 0.
Therefore -2w + 54 = 0 therefore w = 27.
ii) If we substitute w = 27 into the equation in ii) we get
a = [tex]-(27)^2 +(54\times 27)[/tex] = (54 - 27) [tex]\times[/tex](27) = [tex]27^{2}[/tex] = 729
The population of Birmingham is 1,274,589. What is the value of the 7?
Answer:
70,000
Step-by-step explanation:
In the population number 1,274,589 for Birmingham, the 7 is in the ten thousands place. Therefore, its value is 70,000.
Explanation:This problem revolves around understanding of place values in Mathematics. Specifically, we are asked
what is the value of 7
in the population number 1,274,589 for Birmingham. A critical observation is that each position of a digit in a number has a different value. Counting from right (or the ones position) to left, we find that the number 7 is in the ten thousands place. Therefore, the value of 7 in this number is actually 70,000.
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