Answer:
The ratio of their areas is 4:9
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z ---> the scale factor
x ---> the area of the smaller polygon
y ---> the area of the larger polygon
[tex]z^2=\frac{x}{y}[/tex]
we have
[tex]z=\frac{2}{3}[/tex] ---> the scale factor is given
substitute
[tex](\frac{2}{3})^2=\frac{x}{y}[/tex]
[tex]\frac{4}{9}=\frac{x}{y}[/tex]
Rewrite
[tex]\frac{x}{y}=\frac{4}{9}[/tex]
therefore
The ratio of their areas is 4:9
What is the instataneous rate of change at x=2 of the function f given by f(x)= x^2-2÷x-1
Answer:
4.5
Step-by-step explanation:
To find the instantaneous rate of chance, take the derivative:
[tex]f(x) = {x}^{2} - \frac{2}{x} - 1 \\ \frac{d}{dx} f(x) = 2x + \frac{2}{ {x}^{2} } [/tex]
Remember to use power rule:
[tex] \frac{d}{dx} {x}^{a} = a {x}^{a - 1} [/tex]
To differentiate -2/x, think of it as:
[tex] - 2 {x}^{ - 1} [/tex]
Then, substitute 2 for x:
[tex]2(2) + \frac{2}{ {2}^{2} } \\ 4 + \frac{2}{4} = 4.5[/tex]
Answer:
2
Step-by-step explanation:
Assuming the function is:
f(x) = (x² − 2) / (x − 1)
Use quotient rule to find the derivative.
f'(x) = [ (x − 1) (2x) − (x² − 2) (1) ] / (x − 1)²
f'(x) = (2x² − 2x − x² + 2) / (x − 1)²
f'(x) = (x² − 2x + 2) / (x − 1)²
Evaluate at x=2.
f'(2) = (2² − 2(2) + 2) / (2 − 1)²
f'(2) = (4 − 4 + 2) / 1
f'(2) = 2
Find the cosine of ∠R.
A)
12
13
B)
13
12
C)
5
12
D)
5
13
Solution: [tex]\frac{12}{13}[/tex]. The cosine of an acute angle of a right triangle is the adjacent side divided by the hypotenuse.
[tex] \sqrt[3]{128} [/tex]
what is the steps to brake down this equation?
∛128
Divide 128 by 2 to get 64
Now you have: ∛(64 *2)
Rewrite 64 as 4³
Now you have:
∛(4³ *2)
Pull Terms out of the radical to get the final answer:
4∛2
Which multiplication expression is equivalent to
2x - 5x - 3 / 4x2 + 12x + 5 divided by 3x2 - 11x + 6 / 6x2 + 11x - 10
Answer:
1
Step-by-step explanation:
Correct question: 2x2 - 5x - 3 / 4x2 + 12x + 5 divided by 3x2 - 11x + 6 / 6x2 + 11x - 10.
As given: [tex]\frac{(2x^{2}-5x-3) }{(4x^{2}+12x+5 )} \div \frac{(3x^{2} -11x+6)}{(6x^{2}+11x-10) }[/tex]
Solving it by using quadratic equation.
= [tex]\frac{(2x^{2}-6x+1x-3) }{(4x^{2}+10x+2x+5) } \div \frac{(3x^{2}-9x-2x+6 }{(6x^{2}+15x-4x-10) }[/tex]
= [tex]\frac{(2x+1) (x-3)}{(2x+1) (2x+5)} \div \frac{(3x-2) (x-3)}{(2x+5) (3x-2)}[/tex]
To divide fraction take the reciprocal of divisor and multiply the dividend.
= [tex]\frac{(2x+1) (x-3)}{(2x+1) (2x+5)} \times \frac{(2x+5) (3x-2)}{(3x-2) (x-3)}[/tex]
We solve it to get 1 as it cancel fraction on both side.
Answer is 1.
Answer:
First part: C
Second part: 1
Step-by-step explanation:
How to resolve this ?
Answer:
3: 6,9,12,15,18,21 and 24.
7: 14,21,28,35,42,49 and 56.
5: 10,15,20,25,30,35 and 40.
9: 18,27,36,45,54,63 and 72
4: 8,12,16,20,24,28 and 32.
Step-by-step explanation:
Given are the number at the beginning of each strings.
We need to write multiples of number on first light of string on rest of lights on the string.
3: [tex]3\times 1= 3 (given)[/tex]
[tex]3\times 2= 6\\3\times 3= 9\\3\times 4= 12\\3\times 5= 15\\3\times 6= 18\\3\times 7= 21\\3\times 8= 24[/tex]
7: [tex]7\times 1= 7 (given)[/tex]
[tex]7\times 2= 14\\7\times 3= 21\\7\times 4= 28\\7\times 5= 35\\7\times 6= 42\\7\times 7= 49\\7\times 8= 56[/tex]
5: [tex]5\times 1= 5 (given)[/tex]
[tex]5\times 2= 10\\5\times 3= 15\\5\times 4= 20\\5\times 5= 25\\5\times 6= 30\\5\times 7= 35\\5\times 8= 40[/tex]
9: [tex]9\times 1= 9 (given)[/tex]
[tex]9\times 2= 18\\9\times 3= 27\\9\times 4= 36\\9\times 5= 45\\9\times 6= 54\\9\times 7= 63\\9\times 8= 72[/tex]
4: [tex]4\times 1= 4 (given)[/tex]
[tex]4\times 2= 8\\4\times 3= 12\\4\times 4= 16\\4\times 5= 20\\4\times 6= 24\\4\times 7= 28\\4\times 8= 32[/tex]
When a faction of 17 is taken away from 17 , what remains exceeds of seventeen by six
Answer:
The fraction taken from 17 is [tex]$ \frac{16}{3}$[/tex].
Step-by-step explanation:
Let the fraction that is taken from 17 be 'a'.
Writing the given statement mathematically, we would have:
[tex]$ 17 - a = \frac{17}{3} + 6$[/tex]
⇒ 51 - 3x = 17 + 18
⇒ 51 - 3x = 35
⇒ 3x = 16
⇒ x = [tex]$ \frac{16}{3} $[/tex] is the answer.
Hello. please help me step by step, thank you.
Marco bakes cookies for his class. He use 3/4 cup butter in each batch cookies and bakes 2 1/2 batches. what number of cups of butter Marco uses to bake cookies ??
Answer:
Step-by-step explanation:
he uses 3/4 cup of butter in each batch...and he made 2 1/2 batches..
so he used :
2 1/2 * 3/4 =
5/2 * 3/4 =
15/8 =
1 7/8 cups of butter <====
A 5/3x3/4=1 7/8 because 15/8 is 5/3 x 3/4 = 1 7/8
What is 3.6 divided by 81
Answer: 2.5 would be the answer
The given line passes through the points and (4, 1).
On a coordinate plane, a line goes through (negative 4, negative 3) and (4, 1).
What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (, 3)?
Answer:
[tex]y-3=-2(x+4)[/tex]
Step-by-step explanation:
The complete question is
The given line passes through the points (−4, −3) and (4, 1).
What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (−4, 3)?
step 1
Find the slope of the given line
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
(−4, −3) and (4, 1)
substitute the values
[tex]m=\frac{1+3}{4+4}[/tex]
[tex]m=\frac{4}{8}[/tex]
[tex]m=\frac{1}{2}[/tex]
step 2
Find the slope of the perpendicular line to the given line
we know that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
so
[tex]m_1*m_2=-1[/tex]
we have
[tex]m_1=\frac{1}{2}[/tex] ---> slope of the given line
so
[tex]m_2=-2[/tex] ---> slope of the perpendicular line to the given line
step 2
Find the equation in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-2[/tex]
[tex]point\ (-4,3)[/tex]
substitute
[tex]y-3=-2(x+4)[/tex] ----> equation in point slope form
Answer:
A
Step-by-step explanation:
did the edge quiz
Can someone help solve this for me
Answer:
um whats the question
Step-by-step explanation:
The length of a rectangle is three times its width. If the perimeter is at most 128cm, what is the greatest possible value for the width?
Answer:
16 cm
Step-by-step explanation:
Let the width be x
The length will be 3 x since the length is three times the width
Perimeter=2(l+w) where l is length and w is width
By substituting 128 cm for perimeter, x for w and 3 x for l then
128=2(3x+x)
128=8x
[tex]x=\frac {128}{8}=16[/tex]
Therefore, the width is 16 cm, the width is 16*3=48 cm
The correct answer is:
The greatest possible width for the rectangle, with length three times, is 16 cm, ensuring the perimeter doesn't exceed 128 cm.
Let's denote:
- Width of the rectangle as [tex]\( w \)[/tex] cm
- Length of the rectangle as [tex]\( 3w \)[/tex] cm (since it is three times the width)
The perimeter of a rectangle is given by:
[tex]\[ \text{Perimeter} = 2 \times (\text{Length} + \text{Width}) \][/tex]
Given the perimeter is at most 128 cm, we can write:
[tex]\[ 2 \times (3w + w) \leq 128 \][/tex]
Now, let's solve for [tex]\( w \)[/tex]:
[tex]\[ 2 \times (3w + w) \leq 128 \]\[ 2 \times 4w \leq 128 \]\[ 8w \leq 128 \]\[ w \leq \frac{128}{8} \]\[ w \leq 16 \][/tex]
So, the width of the rectangle must be less than or equal to 16 cm. Therefore, the greatest possible value for the width is 16 cm.
Order from least to greatest.
0.044
0.445
0.004
0.040
A) 0.004
0.040
0.044
0.445
B)
0.040
0.004
0.044
0.445
C)
0.040
0.004
0.044
0.445
D)
0.445
0.044
0.040
0.004
Answer:
your answer is option A
Answer:
A is the correct answer... ten hundreths thousandths
βrainliest pleaseeeeeeeeeeeee
Two spies have to communicate using a secret code. They need to create exactly 30 possible precoded messages, using a single number and letter. Which structure should the code have?
A.
Select a number from {1, 2, 3, 4} and a vowel.
B.
Select a number from {1, 2, 3, 4, 5} and a vowel.
C.
Select a number from {1, 2, 3, 4, 5, 6} and a vowel.
D.
Select a number from {1, 2, 3, 4, 5} and a consonant.
Answer:
C. Select a number from {1, 2, 3, 4, 5, 6} and a vowel.
Step-by-step explanation:
Let's start this with a simple example: how many messages are possible using one number from {7, 9} and one letter from {a, b}. It will be 4 as 7a, 7b, 9a and 9b. This result can also come by multiplying the number of digits used and number of alphabets used - here number of digits are 2 (they are 7 and 9) and number of alphabets used are 2 (they are 'a' and 'b'). So 2 × 2 = 4.
[NOTE : In this question 7a and a7 are same]
Maximum number of options consists of vowels as letters so we will first find the number of digits needed if vowels are used as letters.
The number of vowels are 5 (they are 'a', 'e', 'i', 'o', 'u').
The number of possible precodes needed = 30
Let the number of digits needed be 'n'.
Then n × 5 = 30
∴ n = 6
Therefore the number of digits needed is 6 which is there in option C. The digits are {1, 2, 3, 4, 5, 6}
Therefore option C is the answer.
Answer:
See image
Step-by-step explanation:
Plato
Shanika is thinking of a rational number, but tells you its opposite. What is true about the number she is thinking of?
Answer: It is the same distance from zero as the number she tells you.
Step-by-step explanation:
For this exercise it is important to remember the definition of opposite numbers.
Opposite numbers are defined as those numbers that are in opposite positions on a number line, but their distance from zero is the same. Then, one of them is positive and the other one is negative.
The sum of opposite numbers is zero.
For example, the following numbers are opposite:
[tex]8[/tex] and [tex]-8[/tex]
[tex]31[/tex] and [tex]-31[/tex]
[tex]105[/tex] and [tex]-105[/tex]
Therefore, if Shanika says the opposite of a rational number, you can conclude that the number she is thinking is the same distance from zero as the number she tells you.
It is the same distance from zero as the number she tells you.
Step-by-step explanation:
Alaina has $28 in her account.She wants to purchase a pair of shoes that costs $45.If Alaina makes the purchase,which integer will represent the amount of money in Alaina’s account?
Answer:
-17
Step-by-step explanation:
28 - 45 = -17$ in her account
The integer will represent the amount of money in Alaina’s account is -17 dollars.
Given that, Alaina has $28 in her account. She wants to purchase a pair of shoes that costs $45.
How do subtract integers?To subtract two integers, rewrite the subtraction expression as the first number plus the opposite of the second number.
Now, 28-45=-17
Therefore, the integer will represent the amount of money in Alaina’s account is -17 dollars.
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A crayon company recently changed its labels it currently has a total of 2,776 crayons in stock 1,174of which have new label How many crayons with the old labels does the company have in stock
Answer: 1,602 Crayons with old labels that the company has in stock
Step-by-step explanation:
The total is 2,776 and 1,174 of the total have new labels so you would have to subtract 1,174 from 2,776. Your welcome
Loren and Julie have different part time jobs after school. They are both paid at a constant rate of dollars per hour. The table below show Loren and Julie's total income (amount earned) for working a given amount of time.
Loren
Hours
2
4
6
8
10
12
14
16
18
Dollars
18
36
54
72
90
108
?
?
162
Julie
Hours
3
6
9
12
15
18
21
24
27
Dollars
36
?
108
144
180
216
?
288
324
Who makes more per hour?
Answer:
Julie made $3 /hour more than Loren
Step-by-step explanation:
Loren makes 18 /2 = 9 ($9 / hour constant ratio)
Julie: 36 /3 = 12 ($12 / hour)
Julie - Loren = 12 -9 = 3
? in Loren's : 126, 144
? in Julie's : 72, 252
The diagram below represents a 155-newton box
on a ramp. Applied force F causes the box to
slide from point A to point B.
What is the total amount of gravitational potential
energy gained by the box?
A. 28.4)
B. 279)
C. 868J
D. 2740 J
Answer:
279J is the total amount of gravitational potential energy gained by the box.
Step-by-step explanation:
Note: As you missed to add the diagram. So, I found and have attached the diagram as shown in figure a which is attached below, based on which I am answering your question. Hopefully, it would help understand the concept.
The energy stored in an object near the surface of the Earth due of its state in a gravitational field is termed as Gravitational potential energy.
The formula to get gravitational potential energy: [tex]Ep_}=mgh[/tex]
Here,
m = mass of the object normally measured in kg
g = gravitational acceleration having constant value as 9.8 m/s²
h = height in m
As from the diagram a, we observe that object carries 155-newton force and at point B, the height is 1.80 m, as shown in figure a.
So,
F = 155 N
h = 1.80 m
From F = mg, we can get the mass of object
F = mg ∵ g = gravitational acceleration
m = F/g
m = 155/9.8 ⇒ m = 15.81
The gravitational potential energy is measured in joule which is abbreviated as 'J'.
The formula to get gravitational potential energy:
[tex]Ep_}=mgh[/tex]
[tex]Ep_}=(15.81)(9.8)(1.80)[/tex]
[tex]Ep_}=278.88J[/tex] ≈ [tex]279J[/tex]
Therefore, 279J is the total amount of gravitational potential energy gained by the box.
Keywords: potential energy, force
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If F(x) = 5x-7 and G(x) = -2x+9 , what is F(G(x))?
Answer:
Step-by-step explanation:
To find the composition of two functions F(G(x)), substitute the value of G(x) into F(x). The result for F(G(x)) in this case is -10x + 38.
Explanation:This question pertains to the mathematical concept of functions. Specifically, you are being asked to find the composition of two functions, F(x) and G(x).
To find F(G(x)), you substitute the value of G(x) into the function F(x). Recall that G(x) = -2x + 9. So, you need to replace 'x' in F(x) = 5x -7 by the value of G(x). Thus, F(G(x)) = 5(-2x+9) - 7 = -10x + 45 - 7 = -10x + 38.
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Ethan ate 1/5 of a chocolate bar and gave 1/3 to his friend. If their were 15 pieces in the chocolate bar; how many were eaten in total?
Answer:22/18 or 1 4/15
First, you have to find out how many pieces were eaten in all. This could be done with addition. 1/5+1/3= (3/15+5/15)= 8/15
Lastly, you have to find out how much they ate from 15 pieces. This could be done with subtraction. Since 15 is a whole number, the fraction for it would be 15/1. 15/1-8/15=(30/15-8/15)=22/18 or 1 4/15
Can anyone pls help me I really need help pls help me I will mark them as brainiest pls!!! Can u do it in a paper and then send it to me
(ﾉ◕ヮ◕)ﾉ*:･ﾟ✧ ✧ﾟ･: *ヽ(◕ヮ◕ヽ)
Answer:
see them bellow
Step-by-step explanation:
How many rectangle 5cm multiply 2cm
Can fits in a square that has one side 10cm long
Answer:
10 rectangles can fit in the square that has one side 10 cm long.
Step-by-step explanation:
Given:
Rectangle 5 cm multiply 2 cm .
Square that has one side 10cm long.
Now, to find the number of rectangle that can fits in the square.
So, for getting the number of rectangle we need to get the area first:
Area of rectangle as given 5 cm multiply 2 cm :
[tex]5\ cm\times 2\ cm=10\ cm^2[/tex]
Then the area of square as given side is 10 cm:
Area of square = (side)²
[tex]Area\ of\ square=10^2[/tex]
[tex]Area\ of\ square=100\ cm^2[/tex]
Now, for getting the number of rectangle we divide the area of square by area of rectangle:
Number of rectangle = Area of square ÷ Area of rectangle
[tex]Number\ of\ rectangle=100\ cm^2\div 10\ cm^2[/tex]
[tex]Number\ of\ rectangle=10.[/tex]
Therefore, 10 rectangles can fit in the square that has one side 10 cm long.
X^2 + 1/4 or 7 or 7/2 x + 49
Answer:
14
Step-by-step explanation:
Squaring a number (a+b) for example is a^2+2ab+b^2. So you square root x^2 and 49, you get x and seven respectively. you multiply them together and on top of that multiply the product by 2. so 7x*2 is 14x and ye
The path of a model rocket can be represented by the equation h(t) = - t ^ 2 + 20t + 12 where h(t) is the height , in feet of the rocket at any given time, t. What is the height of the model rocket after 3 seconds from launch?
Answer:
The height of the rocket after 3 seconds is 63 feet.
Step-by-step explanation:
The path of a model rocket is represented by:
[tex]h(t)=-t^2+20t+12[/tex]
where [tex]h(t)[/tex] represents the height in feet of rocket and [tex]t[/tex] represents time in seconds.
To find the height of the model rocket after 3 seconds from launch.
Solution:
In order to find the height of the model rocket after 3 seconds from launch, we will plugin [tex]t=3[/tex] in the given function of path of rocket.
Thus, we have
[tex]h(3)=-(3)^2+20(3)+12[/tex]
[tex]h(3)=-9+60+12[/tex]
[tex]h(3)=63[/tex]
Thus, height of the rocket after 3 seconds is 63 feet.
PLEASE HURRY I NEED HELP ON MY EXAM! 15PTS!
In which quadrants do solutions for the inequality y is greater than one fifth times x plus 3 exist?
I and II
I, II, and III
I, III, and IV
All four quadrants
The solutions for the inequality y > (1/5)x + 3 exist in Quadrants I and II.
Explanation:The inequality y > (1/5)x + 3 represents a line with a positive slope of 1/5.
The solutions for this inequality exist in the quadrants where y is greater than the value of (1/5)x + 3.
When x is positive and y is positive, the solutions exist in Quadrant I. When x is negative and y is positive, the solutions exist in Quadrant II.
Since the inequality is y > (1/5)x + 3 and not y >= (1/5)x + 3, the solutions do not exist in Quadrant III or IV where y would be negative.
Therefore, the solutions for the inequality y > (1/5)x + 3 exist in Quadrants I and II.
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Find percentage:
3/4% of 9.6
Answer:
0.072
Step-by-step explanation:
3/4 percent of the number 9.6 is 0.072.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, 3/4% of 9.6.
Now, 0.75% of 9.6
= 0.0075×9.6
= 0.072
Therefore, 3/4 percent of the number 9.6 is 0.072.
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Which of the following tables represents a function?
Answer:
The second one
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
A function is where one x value only matches up to one y value.
Widget Wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x.
The company also discovered that it costs $29 to produce 2 widgets, $115 to produce 4 widgets, and $757 to produce 10 widgets.
How much does it cost to make 3 widgets?
Answer:
The total cost to make 3 widgets is $64.
Step-by-step explanation:
As cost is give by quadratic function such as [tex]c(x) = ax^2 + bx + d[/tex]
As it costs $29 to produce 2 widgets. So,
[tex]c(2) = a(2)^2 + b(2) + d[/tex]
[tex]29= 4a+2b+d ....[A][/tex]
As it costs $115 to produce 4 widgets. So,
[tex]c(4) = a(4)^2 + b(4) + d[/tex]
[tex]115= 16a+4b+d ....[B][/tex]
As it costs $757 to produce 10 widgets. So,
[tex]c(10) = a(10)^2 + b(10) + d[/tex]
[tex]757= 100a+10b+d ....[C][/tex]
In order to find the values of a, b, c and d, we have to equations [A], [B] and [C]
Subtracting Equation [A] from [B] and [B] from [C]
12a + 2b = 86 ........[D]
84a + 6b = 642 ........[E]
Multiplying Equation [D] by 3 and subtracting from [E]
84a + 6b + 3(12a + 2b) = 642 - 86
48a = 384
a = 8
Putting value of a = 8 in equation [D]
12(8) + 2b = 86
96 + 2b = 86
2b = -10
b = -5
Substituting the value of a = 8 and b = -5 in Equation [A].
29= 4a+2b+d
29 = 4(8) + 2(-5) + d
29 = 32 - 10 + d
d = 29 + 10 - 32
d = 7
The required form of equation can be obtained by substituting a = 8, b = -5 and d = 7 in the cost equation. So,
[tex]c(x) = 8x^2 - 5x + 7[/tex] is the required form of equation.
Therefore, the total cost to make 3 widgets will be:
Putting x = 3 in [tex]c(x) = 8x^2 - 5x + 7[/tex]
[tex]c(3) = 8(3)^2 - 5(3) + 7[/tex]
[tex]c(3) = 72 - 15 + 7[/tex]
[tex]c(3) = 64[/tex]
Hence, the total cost to make 3 widgets is $64.
Keywords: quadratic equation, cost
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In slope-intercept form, what is the equation of the line passing through the points (-4.26) and (6-4)?
y=-3x - 14
y = 3x - 14
y = -3x - 14
y=-x
-2
Answer:
y=-3x+14
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-4-26)/(6-(-4))
m=-30/(6+4)
m=-30/10
m=-3
y-y1=m(x-x1)
y-26=-3(x-(-4))
y-26=-3(x+4)
y=-3x-12+26
y=-3x+14
EMERGENCY!!! OK SO I need help on 4 questions! Lots of points for this :) Also please make sure it's correct cause this is for a grade! Please and thank you so much! :D
1. Erika estimates that she is 200 to 300 miles away from her destination. If her car travels 25 miles per gallon of gas and each gallon costs $4.00, what is the best estimate for the amount of money, x, that Erika has to pay to get to her destination? A. 24≤x≤38
B. 64≤x≤82
C. 12≤x≤18
D. 32≤x≤48
2. Consultant A chargers $160 for the first hour and $75 per hour after the first. Consultant B charger a flat rate of $90 per hour. Consultant C charges $140 for the first hour and $80 per hour after the first. For a five hour session, which consultant offers the cheapest price? A. Consultant A
B. Consultant B
C. Consultant C
D. All three offer the same price.
3. A hotel chargers $225 per night to rent a suite. The hotel also charges $75 per day for full room service. If Jessica and Ashely purchased full room service for every night they stayed at the hotel and spent a total of $1,200, how many nights did they stay at the hotel? A. 3
B. 4
C. 5
D. 6
4. A certain ride at an amusement park requires that children be at least 50 inches tall but no more that 65 inches tall. Which of the following absolute values best represents this restriction, where ( h ) represents height?
A. |h−57.5|≤7.5
B. |h+7.5|≤65
C. |h+50|≤65
D. |h+65|≤50
Question # 1 Solution
Answer:
32≤x≤48 is the best estimate for the amount of money, x, that Erika has to pay to get to her destination. Hence, option D is correct.
Step-by-step Explanation:
Information Fetching and Solution Steps
Erika estimates that she is 200 to 300 miles away from her destinationCar travels 25 miles per gallon of gasCost of each gallon being $4.00As Erika estimates that she is 200 to 300 miles away from her destination, and car travels 25 miles per gallon of gas. So,
First dividing 200 by 25 to get the number of gallons a car needed to make 200 milesi.e 200/25 = 8 gallons.
As cost of each gallon being $4.00.
So, 8 × 4 = 32$ is the amount she needed to make 200 miles.
Then dividing 300 by 25 to get the number of gallons a car needed to make 300 milesi.e 300/25 = 12 gallons.
As cost of each gallon being $4.00.
So, 12 × 4 = 48$ is the amount she needed to make 300 miles.
From the above calculation, we observe that 32$ and 48$ is the best estimate between 200 miles and 300 miles.
Therefore, 32≤x≤48 is the best estimate for the amount of money, x, that Erika has to pay to get to her destination. Hence, option D is correct.
Question # 2 Solution
Answer:
Consultant B offers the cheapest price for a five hour session.
Hence, B. Consultant B is the correct option.
Step-by-step Explanation:
Analyzing the offer price of Consultant A, B and C for a Five hour session:
Consultant A chargers $160 for the first hour $75 per hour after the first.
So, for five hour session, Consultant A is offering the price:
$160 + $75 + $75 + $75 + $75 = $460
Consultant B chargers a flat rate of $90 per hour
So, for five hour session, Consultant B is offering the price:
$90 + $90 + $90 + $90 + $90 = 450 US$
Consultant C chargers $140 for the first hour $80 per hour after the first.
So, for five hour session, Consultant C is offering the price:
$140 + $80 + $80 + $80 + $80 = $460
Comparing the price offers of Consultant A, B and C
So, by comparing the price offers of Consultant A, B and C, we determine that:
Consultant A is offering the price $460 for five hour session.Consultant B is offering the price $450 for five hour session.Consultant C is offering the price $460 for five hour session.So, from this comparison, we conclude that Consultant B offers the cheapest price for a five hour session.
Hence, B. Consultant B is the correct option.
Question # 3 Solution
Answer:
They spent 4 nights at the hotel. Hence, option B is correct.
Step-by-step Explanation:
To determine:
how many nights did they stay at the hotel?
Information Fetching and Solution Steps
A hotel chargers $225 per night to rent a suite.The hotel also charges $75 per day for full room service.Jessica and Ashely purchased full room service for every night.They stayed at the hotel and spent a total of $1,200As the total amount they spent = $1,200
As $75 is the service charges as Jessica and Ashely purchased full room service for every night.
Per night charges = hotel chargers + service charges
Per night charges = $225 + $75 ⇒ $300
So, total nights will be calculated as:
Total nights = total amount they spent ÷ Per night charges
Total nights = $1,200 ÷ $300 ⇒ 4 nights
Therefore, they spent 4 nights at the hotel. Hence, option B is correct.
Question # 4 Solution
Answer:
Hence, |h − 57.5| ≤ 7.5 is the absolute values which best represents this restriction, where ( h ) represents height. Hence, option A is correct.
Information Fetching and Solution Steps
A certain ride at an amusement park requires that children be at least 50 inches tall but no more that 65 inches tall.Let us take the equation of following absolute value:
|h − 57.5| ≤ 7.5
We know h − 57.5 ≤ and h − 57.5 ≥ −50
h − 57.5 ≤ 7.5 (Condition 1)
h − 57.5 + 57.5 ≤ 7.5 + 57.5 (Add 57.5 to both sides)
h ≤ 65
h − 57.5 ≥ −7.5 (Condition 2)
h − 57.5 + 57.5 ≥ −7.5 + 57.5 (Add 57.5 to both sides)
h ≥ 50
So, h ≤ 65 and h ≥ 50
Solution Graph is also attached as shown in attached figure a.
Hence, |h − 57.5| ≤ 7.5 is the absolute values which best represents this restriction, where ( h ) represents height. Hence, option A is correct.
Using same methodology we observe that all other options B, C, and D brings wrong values which is as follows:
|h+7.5|≤65 brings h≤57.5 and h≥−72.5|h+50|≤65 brings h≤15 and h≥−115|h+65|≤50 brings h≤−15 and h≥−115Hence, from all discussion, we conclude that |h − 57.5| ≤ 7.5 is the absolute values which best represents this restriction, where ( h ) represents height, as it brings h ≤ 65 and h ≥ 50. Hence, option A is correct.
Keywords: inequality, graph solution, absolute value
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