Answer:
x=4 and y=5
Step-by-step explanation:
The given system of equations are
[tex]2x+6y=38[/tex]
[tex]5x-y=15[/tex]
The matrix form is
[tex]\begin{bmatrix}2&6\\ \:5&-1\end{bmatrix}\begin{bmatrix}x\\ \:y\end{bmatrix}=\begin{bmatrix}38\\ \:15\end{bmatrix}[/tex]
Let as assume
[tex]A=\begin{bmatrix}2&6\\ \:5&-1\end{bmatrix}[/tex]
[tex]X=\begin{bmatrix}x\\ \:y\end{bmatrix}[/tex]
[tex]B=\begin{bmatrix}38\\ \:15\end{bmatrix}[/tex]
then,
[tex]AX=B[/tex]
[tex]X=A^{-1}B[/tex]
We know that,
[tex]\begin{bmatrix}a\:&\:b\:\\ c\:&\:d\:\end{bmatrix}^{-1}=\frac{1}{\det \begin{bmatrix}a\:&\:b\:\\ c\:&\:d\:\end{bmatrix}}\begin{bmatrix}d\:&\:-b\:\\ -c\:&\:a\:\end{bmatrix}[/tex]
[tex]A^{-1}=\frac{1}{\det \begin{bmatrix}2&6\\ 5&-1\end{bmatrix}}\begin{bmatrix}-1&-6\\ -5&2\end{bmatrix}[/tex]
[tex]A^{-1}=\frac{1}{-32}\begin{bmatrix}-1&-6\\ -5&2\end{bmatrix}[/tex]
[tex]X=\frac{1}{-32}\begin{bmatrix}-1&-6\\ -5&2\end{bmatrix}\begin{bmatrix}38\\ \:15\end{bmatrix}[/tex]
[tex]X=\frac{1}{-32}\begin{bmatrix}\left(-1\right)\cdot \:38+\left(-6\right)\cdot \:15\\ \left(-5\right)\cdot \:38+2\cdot \:15\end{bmatrix}[/tex]
[tex]X=\frac{1}{-32}\begin{bmatrix}-128\\ -160\end{bmatrix}[/tex]
[tex]\begin{bmatrix}x\\ \:y\end{bmatrix}=\begin{bmatrix}4\\ 5\end{bmatrix}[/tex]
Therefore, the value of x is 4 and value of y is 5.
you have a list of 7 numbers. the average of the numbers is 9. if you take away one of the numbers, the average of the numbers is 8. what number did you take away?
Answer:
There was a 15 among the 7 numbers. That is the number you removed.
Step-by-step explanation:
x/7 = 9 (1)
(x - y)/6 = 8 (2)
Multiply 1 by 7
x/7 * 7 = 9*7
x = 63
Put 63 for x into equation 2
(63 - y)/6 = 8 Multiply by 6
6*(63-y)/6 =8*6
63 - y = 48 Add y to both sides
63-y+y = 48+y
63 = 48 + y Subtract 48 from both sides
63-48=48-48+y
y = 15
Final answer:
The number removed from the list to change the average from 9 to 8 is 15, calculated by finding the difference between the total sum of the original and remaining lists.
Explanation:
To find the number that was taken away from a list when the average changes, you can first calculate the total sum of the original list, then the sum of the list after the number is removed.
Initially, the average of the 7 numbers is 9. To find the total sum of all 7 numbers, you multiply the average by the number of values.
Total sum of original list = 7 (number of values) × 9 (original average) = 63
After removing one of the numbers, the average of the 6 remaining numbers is 8.
Total sum of the remaining list = 6 (remaining values) × 8 (new average) = 48
The number that was removed can be found by subtracting the sum of the remaining list from the sum of the original list.
Number removed = Total sum of original list - Total sum of the remaining list = 63 - 48 = 15
Therefore, the number that was taken away from the list is 15.
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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[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
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
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
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:
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.
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:
In a competitive exam 84% of candidate passed and 780 failed find the number of candidates appeared for the examination
Answer:
4875
Step-by-step explanation:
100%-84%=16%
16%x=780
x=4875
what is the equation, in slope-intercept form, of the line that passes through (9, 2) and is perpendicular to y= -1/2x + 7
Answer:
y-2=2(x-9)
Step-by-step explanation:
Perpendicular means negative reciprocal of the slope.
y-y1=m(x-x1)
y-2=2(x-9)
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.
Renata wins a $20 gift card to an online music site. After Renata purchases 16 songs, the gift card has a remaining
balance of $0. Which equation represents the relationship between y, the remaining balance on Renata's gift card,
and x, the number of songs purchased?
The equation that represents the relationship between the remaining balance on Renata's gift card and the number of songs purchased is y = 20 - 1.25x, where x represents the number of songs purchased.
Explanation:The equation that represents the relationship between the remaining balance on Renata's gift card and the number of songs purchased is y = 20 - 1.25x.
Here's how we get to this equation:
Let x represent the number of songs purchased.Since Renata starts with a $20 gift card, the initial balance is $20.For each song purchased, $1.25 is deducted from the balance, so the remaining balance can be represented as y = 20 - 1.25x.For example, if Renata purchased 16 songs, the equation becomes y = 20 - 1.25(16) = 20 - 20 = 0, which matches the given information that the gift card has a remaining balance of $0 after 16 songs are purchased.
Find the missing factor. Does anybody know the answer 8b*2+7b-1= (b+1) ( )
Answer:
[tex]8b^2+7b-1=(b+1)(8b-1)[/tex]
The missing factor is: [tex](8b-1)[/tex]
Step-by-step explanation:
Given expression:
[tex]8b^2+7b-1=(b+1)(_-)[/tex]
To find the missing factor of the given expression.
Solution:
In order to factor the given term, we will split the middle term into two terms such that the product of the two terms is equal to the product of the first and last term of the expression.
The product of first and last term for the expression is = [tex](8b^2)(-1)=-8b^2[/tex]
The middle term = [tex]7b[/tex] which can be split into [tex](8b-b)[/tex] as their product = [tex]-8b^2[/tex]
Thus, the expression can be rewritten as:
⇒ [tex]8b^2+8b-b-1[/tex]
We will factor in pairs by taking GCF.
⇒ [tex]8b(b+1)-1(b+1)[/tex]
Factoring the whole expression by taking the common factor.
⇒ [tex](b+1)(8b-1)[/tex]
Thus, the missing factor is: [tex](8b-1)[/tex]
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
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
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
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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Which point could be removed in order to make the relation a function?
{ (-4,3),(-5,6),(1,0),(-4,5),(9,5),(0,-7)}
A. (1,0)
B.(-4,5)
C.(-5,6)
D.(9,5)
Answer:
B. (-4,5)
Step-by-step explanation:
a function cannot have any repeating x values....it can have repeating y values, just not the x values
so..going by ur answer choices, u can remove (-4,5) and it would be a function. The reason is because u have two sets of points with the same x value...so it is not a function unless u take out either (-4,5) or (-4,3)...because they both have the same x value.
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.
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
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]
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.
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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I NEED HELP WITH THESE QUESTIONS!!DOES ANY ONE KNOW HOW TO DO PROOFS?
Problem 1
Answer: v = 8--------------
Work Shown:
For any convex polygon, the sum of the exterior angles is always 360 degrees
Add up all the angles shown, set the sum equal to 360, then solve for v.
9v+(19v-21)+45+(v+48)+7v = 360
36v+72 = 360
36v+72-72 = 360-72
36v = 288
36v/36 = 288/36
v = 8
===============================================
Problem 2
Answer: D. None of these--------------
Explanation:
Segment WU is not an altitude because we have no angle markers to show if WU is perpendicular to VT.
Segment WU is not a median since we dont know if TU = UV or not.
Segment WU is not an angle bisector. If it were an angle bisector, then the two angles marked (33 and 40) should be equal angles. In other words, an angle bisector cuts an angle into two equal halves.
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 value of y varies inversely as the square of x, and y=4, when x=3.
Find the value of x when y=9
The value of x when y = 9 is x = 2 or x = -2
Solution:
Given that value of y varies inversely as the square of x, and y=4, when x=3.
Therefore the initial statement is:
[tex]y \propto \frac{1}{x^{2}}[/tex]
To convert to an equation, multiply by k, the constant of variation
[tex]y = k \times \frac{1}{x^2}[/tex]
[tex]y = \frac{k}{x^2}[/tex] --- eqn 1
Given that,
y = 4 when x = 3
Now find value of k
[tex]4 = \frac{k}{3^2}\\\\4 \times 9 = k\\\\k = 36[/tex]
Find the value of x when y = 9
x = ?
y = 9
From eqn 1,
[tex]9 = \frac{k}{x^2}\\\\9 = \frac{36}{x^2}\\\\x^2 = 4\\\\x = \pm 2[/tex]
Thus value of x is found
Final answer:
To find the value of x when y=9 for a scenario where y varies inversely as the square of x, and given y=4 when x=3, we first determine the constant of variation and then solve for x, resulting in x=2.
Explanation:
The student's question concerns an inverse variation where the value of y varies inversely as the square of x, with an initial condition that when x=3, y=4. To find the value of x when y=9, we recall that an inverse variation can be expressed as y = k/x², where k is a constant. Using the given condition, we can solve for k: 4 = k/3², leading to k = 36. To find x when y=9, we set up the equation 9 = 36/x² and solve for x, yielding x = 2.
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
Can someone help solve this for me
Answer:
um whats the question
Step-by-step explanation:
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.
To learn more about the percentage visit:
brainly.com/question/24159063.
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