the two solutions are approximately [tex]\( x_1 \approx 2.95 \) and \( x_2 \approx -0.042 \).[/tex]
To find the value of x that satisfies the equation [tex]\( 32x^2 - 93x - 4 = 0 \)[/tex], we can use the quadratic formula:
[tex]\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]
Where:
- a = 32
- b = -93
- c = -4
Now, let's plug these values into the quadratic formula:
[tex]\[ x = \frac{{-(-93) \pm \sqrt{{(-93)^2 - 4 \cdot 32 \cdot (-4)}}}}{{2 \cdot 32}} \]\[ x = \frac{{93 \pm \sqrt{{8649 + 512}}}}{{64}} \]\[ x = \frac{{93 \pm \sqrt{{9161}}}}{{64}} \]\[ x = \frac{{93 \pm 95.7}}{{64}} \][/tex]
Now, we have two possible solutions:
[tex]\[ x_1 = \frac{{93 + 95.7}}{{64}} \]\[ x_2 = \frac{{93 - 95.7}}{{64}} \]\[ x_1 \approx \frac{{188.7}}{{64}} \]\[ x_2 \approx \frac{{-2.7}}{{64}} \]\[ x_1 \approx 2.95 \]\[ x_2 \approx -0.042 \][/tex]
Therefore, the two solutions are approximately [tex]\( x_1 \approx 2.95 \) and \( x_2 \approx -0.042 \).[/tex]
The probable question maybe:
What are the solutions for x in the equation [tex]\( 32x^2 - 93x - 4 = 0 \)[/tex]?
Is (-1,8),(0,15),(1,-4),(2,0) a function
Answer:
?
Step-by-step explanation:
It could be
Answer:
Yes
Step-by-step explanation:
Yes because it is a one-to-one relation. Every x-value maps to a unique value of y.
Daily High Temperatures in New York City
Day High Temperature (Degrees F)
Sunday 63
Monday 55
Tuesday 59
Wednesday 56
Thursday 57
Friday 60
Saturday 88
The table shows the daily high temperatures for a week in April in New York City. What is the RANGE of the temperatures?
A) 32°F
B) 33°F
C) 59°F
D) 62.6°F
Answer:
The answer is B
Step-by-step explanation:
You just have to subtract the lowest temp by the highest temp
Convert 2000 ft./min. to miles per hour round to the nearest 10th
Answer:
The conversion of 2000 ft per min into miles per hour is 2.268 miles per hour .
Step-by-step explanation:
Given as :
The speed = s = 2000 ft per min
Now, ∵ 5280 feet = 1 miles
so, 1 feet = [tex]\dfrac{1}{5280}[/tex] miles
∴ 2000 feet = [tex]\dfrac{1}{5280}[/tex] × 2000 miles
i.e 2000 feet = 0.378 miles
Again
∵ 1 minute = [tex]\dfrac{1}{60}[/tex] hour
So, The speed in miles per hour
s = [tex]\dfrac{distance}{time}[/tex]
∴ s = [tex]\frac{0.378}{\frac{1}{60}}[/tex]
i.e s = 2.268 miles per hour
Hence, The conversion of 2000 ft per min into miles per hour is 2.268 miles per hour . answer
To convert 2000 ft./min. to miles per hour, multiply by appropriate conversion factors, and round the result, yielding 22.7 miles per hour.
To convert 2000 ft./min. to miles per hour, follow these steps:
Convert feet to miles: 2000 ft/min x (1 mile/5280 ft) = 0.3788 miles/min
Convert minutes to hours: 0.3788 miles/min x 60 min/hr = 22.73 miles/hr
Rounded to the nearest tenth, 2000 ft/min is 22.7 miles per hour.
What is 10*10? Please help! :)
Answer:
100
Step-by-step explanation:
It will help in the future to memorize your time tables
10*10 is basically 10 plus 10, 10 times but in a easier form
10+10+10+10+10+10+10+10+10+10=100
10+10=20
20+10=30
30+10=40
40+10=50
50+10=60
60+10=70
70+10=80
80+10=90
90+10=100
Which of the following numbers could be the sides of a right triangle. A)8,15,17. B)6,8,12 C)9,11,21 D)4,13,16
Answer:
A) 8, 15, 17.
Step-by-step explanation:
Right triangle obey the Pythagorean theorem. Thus, we choose the two smaller numbers (being the cathetus) and if after applying the P. Theorem we get the biggest of each option (the hypotenuse) that means that those numbers could be the sides of a right triangle.
The Pythagorean theorem states that: [tex]a^2+b^2=c^2[/tex]
Thus:
[tex]\sqrt{a^2+b^2}=c[/tex]
Option A:
[tex]\sqrt{8^2+15^2}=17[/tex] → 17 = 17 OK!
Option B:
[tex]\sqrt{6^2+8^2} = 10[/tex] → 10 ≠ 12 NO
Option C:
[tex]\sqrt{9^2+11^2} = [tex]\sqrt{202}[/tex][/tex] → [tex]\sqrt{202}[/tex] ≠ 21 NO
Option D:
[tex]\sqrt{4^2+13^2} = \sqrt{185}[/tex] → [tex]\sqrt{185}[/tex] ≠ 16 NO
A stack of 250 cards are placed next to a ruler, and the height of the stack is measured to be 5/8 inches. How thick is one card?
Answer:
The thickness of 1 card = 0.0025 inches
Step-by-step explanation:
Here, the total number of cards in the stack = 250 cards
The total height of the stack = 5/8 inch = 0.625 in.
[tex]\textrm{Thickness of one card} = \frac{\textrm{The total thickness of the stack}}{\textrm{The total cards in the stack}}[/tex]
[tex]\implies \textrm{Thickness of one card} =\frac{0.625}{250} = 0.0025[/tex]
Hence, the thickness of 1 card = 0.0025 inches
what is the average height of a person
Answer:
well it would kinda depend on their age,and size,but the average height of an ADULT male is : 5.6 ft
ADULT female:5.2ft
(remember it would depend on their age,but some people might even have medical reasons to be shorter or taller than their original height too. At a age children don't HAVE to be that exact height,but atleast close enough to that height.)
(changes may occur depending on medical reasons,or age too!)
Gwen Mows 1/4 acre 3/4 hour. How many acres will Gwen mow in one hour
Answer:
0.33...acre
Step-by-step explanation:
1/4=0.25
3/4=0.75
-------------
0.25/0.75=x/1
cross product
0.75*x=0.25*1
0.75x=0.25
x=0.25/0.75
x=0.3
A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 30 books and each large box can hold 40 books. There were twice as many large boxes sent as small boxes, which altogether can hold 330 books. Determine the number of small boxes sent and the number of large boxes sent.
3 small boxes and 6 large boxes were sent to the retailer.
Step-by-step explanation:
Number of books held by small boxes = 30
Number of books held by large boxes = 40
Total books held by boxes = 330
Let,
x represent the number of small boxes
y represent the number of large boxes
According to given statement;
y = 2x Eqn 1
30x+40y=330 Eqn 2
Putting value of y from Eqn 1 in Eqn 2
[tex]30x+40(2x)=330\\30x+80x=330\\110x=330[/tex]
Dividing both sides by 110
[tex]\frac{110x}{110}=\frac{330}{110}\\x=3[/tex]
Putting x=3 in Eqn 1
[tex]y=2(3)\\y=6[/tex]
3 small boxes and 6 large boxes were sent to the retailer.
Keywords: linear equation, substitution method
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Mia's mother gives her $10 per week for allowance Mia gets an additional $3 for every hour she spends watching
Ther. Mia wants to make at least $25 this week to spend shopping with her friends. Use this
information to answer the questions below.
10 Write an inequality, using variables to represent the number of times that Mia has to watch her brother in order to
get at least $25.
Answer:
5 times
Step-by-step explanation:
$25 - $10 (fixed rate) = $15
$15 / $3 = 5 times.
Mia must watch her brother 5 times within the week to make the desired amount. Hope this helps :)
a circle is centered at the point 0,0 and has a radius of the square root of 53. Where does the point -3,-7 lie? I will give the brainiest Help Please
Answer:
The point lie outside the circle
Step-by-step explanation:
step 1
Find the distance between the center of the circle and the given point
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
(0,0) and (-3,-7)
substitute the values
[tex]d=\sqrt{(-7-0)^{2}+(-3-0)^{2}}[/tex]
[tex]d=\sqrt{58}\ units[/tex]
step 2
Compare the distance with the radius
If d=r ----> the point lie on the circle
If d > r -----> the point lie outside the circle
If d < r -----> the point lie inside the circle
we have
[tex]d=\sqrt{58}\ units[/tex]
[tex]r=\sqrt{53}\ units[/tex]
so
[tex]\sqrt{58}\ units > \sqrt{53}\ units[/tex]
[tex]d > r[/tex]
therefore
The point lie outside the circle
Answer:
C outside the circle
Step-by-step explanation:
khan
Identify the interval(s) on which the function y = x + 12x + 27 is positive.
Answer:
So the values of x for which the function is positive are x ≥ -3 and x ≤ -9.
Step-by-step explanation:
We are given a function and we have to find the intervals in which the function has positive value.
y = [tex]x^{2} +12x+27[/tex]
y =(x + 3)(x + 9)
For the function to be positive , y ≥ 0
(x + 3)(x + 9) ≥ 0
Here there are two cases , either both should be positive or both should be negative.
If both are positive,
(x + 3)≥0 and (x + 9)≥0
So, x ≥ -3
If both are negative,
(x + 3)≤0 and (x + 9)≤0
So, x ≤ -9
So the values of x for which the function is positive are x ≥ -3 and x ≤ -9.
The intervals on which the function y = x² + 12x + 27 is positive are
x > -3 and x > -9
For the function given to be positive, it has to be greater than zero.
Since the expression is greater then zero, hence;
x² + 12x + 27 > 0
Factorize the resulting expression
x² + 3x + 9x + 27 > 0
x(x+3) + 9(x+3) > 0
(x+3) (x+9) > 0
x+3 > 0 and x + 9 > 0
x > -3 and x > -9
Hence the intervals on which the function y = x² + 12x + 27 is positive are
x > -3 and x > -9
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Let $x=(0.\overline{6})(0.\overline{60})$. When $x$ is written out as a decimal, what is the sum of the first $15$ digits after the decimal point?
Answer:
[tex]32\text{ for }x=0.\overline{40}[/tex]
Step-by-step explanation:
It looks like you want the sum of digits of the product ...
[tex]x = (0.\overline{6})(0.\overline{60})=\dfrac{2}{3}\cdot\dfrac{20}{33}=\dfrac{40}{99}=0.\overline{40}[/tex]
Since the decimal fraction starts off with 4 and has an even number of repeating digits, there will be 8 4's and 7 0's in the sum of the first 15 decimal digits:
sum = 8×4 +7×0 = 32
The sum of the first 15 digits after the decimal point is 32.
To make 5 batches of cookies, 10 cups of flour are required. Consider the question: How many cups of flour does each batch require? Please also work out the problem.
Answer:
2 cups of flour
Step-by-step explanation:
To make 5 batches of cookies, 10 cups of flour are required.
To make 1 batch of cookies:
10 cups ÷ 5 cups = 2 cups of flour.
To find out how many cups of flour are required for each batch of cookies, divide the total cups of flour (10 cups) by the number of batches (5 batches), which equals 2 cups of flour per batch.
Explanation:To determine how many cups of flour are needed for each batch, we can set up a simple division equation where we divide the total amount of flour by the number of batches. The student is given that 10 cups of flour make 5 batches of cookies. Using this information, we calculate the amount of flour per batch as follows:
Amount of flour per batch = Total cups of flour ÷ Number of batches
Amount of flour per batch = 10 cups ÷ 5 batches
Thus, the amount of flour required for each batch is:
Amount of flour per batch = 2 cups
Write an equation in point-slope form for the line that is perpendicular to the given line and passes through the given point.
Y - 3 = 4 (x + 2) through the point (- 2,6)
Answer: 4y + x - 22 = 0
Step-by-step explanation:
Recall that for two lines to be perpendicular m1m2 = -1 ie, the product of their gradients must = -1
from the equation given, y - 3 = 4(x + 2), we need to rearrange it in the form
y = mx + c in order for us to ascertain the gradient.
y -3 = 4x + 8
y = 4x + 8 + 3
y = 4x + 11
Therefore, m1 = 4 while m2 = -1/4
The coordinate of the line = (-2, 6) . We now use this to find the value of c.
6 = -1/4 x -2 + c
6 = 1/2 + c
multiply by 2
12 = 1 + 2c
12 - 1 = 2c
11 = 2c
c = 11/2
now to find the equation of the second line
y = -x/4 + 11/2
now multiply through by 4
4y = -x + 22
4y + x - 22 = 0 is the required equation
x+1/x=3,x^5+1/x^5=? What is the answer
Answer:
The answer is 123.
Step-by-step explanation:
Given that-
( [tex]x + \frac{1}{x}[/tex] ) = 3.....................(i)
To find -
( [tex]x^{5} + \frac{1 }{x^{5} }[/tex] ) = ?
Now squaring both sides of equation (i)-
( [tex]x^{2} + \frac{1}{x^{2} } + 2[/tex] ) = 9
( [tex]x^{2} + \frac{1}{x^{2} }[/tex] ) = 7....................(ii)
On cubing equation (i) both sides-
( [tex]x^{3} + \frac{1}{x^{3} } + 3 ( x + \frac{1}{x} )[/tex] ) = 27
( [tex]x^{3} + \frac{1}{x^{3} } + 3 * 3[/tex] ) = 27
( [tex]x^{3} + \frac{1}{x^{3} }[/tex] ) = 27 - 9
( [tex]x^{3} + \frac{1}{x^{3} }[/tex] ) = 18.....................(iii)
Multiply equation (i) and equation (ii)-
( [tex]x^{2} + \frac{1}{x^{2} }[/tex] ) ( [tex]x^{3} + \frac{1}{x^{3} }[/tex] ) = 7 × 18
( [tex]x^{5} + \frac{1}{x^{5} } )+ ( x + \frac{1}{x} )[/tex] = 126
( [tex]x^{5} + \frac{1}{x^{5} } ) = 126 - 3
( [tex]x^{5} + \frac{1}{x^{5} } ) = 123
HELP ASAP 30 POINTS! GIVING BRAINLIEST TO THE CORRECT ANSWER
Which equation has the same solution as this equation?
x^2-16x+12=0
A) (x-8)^2 = 144
B) (x-4)^2 =4
C) (x-8)^2 = 52
D) (x-4)^2 = 16
Answer:
Option C. [tex](x-8)^{2}=52[/tex]
Step-by-step explanation:
we have
[tex]x^{2}-16x+12=0[/tex]
Complete the square
[tex](x^{2}-16x+8^2)+12-8^2=0[/tex]
[tex](x^{2}-16x+64)+12-64=0[/tex]
[tex](x^{2}-16x+64)-52=0[/tex]
rewrite as perfect squares
[tex](x-8)^{2}-52=0[/tex]
Move the constant to the right side
[tex](x-8)^{2}=52[/tex]
Ronnie surveyed the senior class for a math project. Below are the results of his survey.
What type of graph is best for Ronnie to display his data?
A. Double Bar Graph
B. Histogram
C. Double Line Graph
D. Circle Graph
Answer:
i think C
Step-by-step explanation:
a pair of shoes originally cost $250. the price was decreased by 20%. a week later it was marked down again, this time 25%. what is the final price of the shoes?
Answer:
$150.
Step-by-step explanation:
$250 - 0.20 *250 = $200.
Final price = 200 - 0.25*200
= $150.
Ten subtracted from the qoutient of a number 5 is 18
Question:
Ten subtracted from the quotient of a number and 5 is 18. What is the number?
Answer:
140 is the number.
Step-by-step explanation:
Let consider the number as ‘X’
Quotient of a number and 5 can be written as
[tex]X \div 5[/tex]
Ten subtracted from the quotient of a number and 5 can be written as
[tex](X \div 5) - 10[/tex]
Ten subtracted from the quotient of a number and 5 is 18 can be written as
[tex](X \div 5) - 10 = 18[/tex]
By solving the above equation, find ‘X’
[tex](X \div 5) = 18 + 10[/tex]
[tex]\frac{X}{5} = 28[/tex]
[tex]X = 28 \times 5 = 140[/tex]
A pizza delivery person earns AED 30 per house plus AED 10.50 for each delivery made, the expression 30h+10.50d can be used to find the earnings for him how much money will he earn after working for 15 hours and making 8 deliveries
Money earned after working for 15 hours and making 8 deliveries is $ 534
Solution:
Given that pizza delivery person earns 30 per hour plus 10.50 for each delivery made
The expression used to find the earnings for him is given as:
30h + 10.50d
Where "h" is the number of hours and "d" is the number of deliveries
We have to find the money earned by him after working for 15 hours and making 8 deliveries
Therefore we get, h = 15 and d = 8
Substitute h = 15 and d = 8 in given expression
Money earned = 30(15) + 10.50(8)
Money earned = 450 + 84 = 534
Thus money earned after working for 15 hours and making 8 deliveries is $ 534
solve for r 4/r = 5/7
Work is provided in the image attached.
What is the sum of the two expressions -2.9a+6.8 and 4.4a-7.3
Answer:
1.5a - 0.5
Step-by-step explanation:
Add like terms
4.4 - 2.9 = 1.5
7.3 - 6.8 = 0.5
Final answer:
To find the sum of the two expressions -2.9a+6.8 and 4.4a-7.3, you need to combine the like terms. Simply add or subtract the coefficients of like terms while keeping the variable the same, the sum of the two expressions -2.9a+6.8 and 4.4a-7.3 is (4.4a - 2.9a) + (6.8 + (-7.3)). .
Explanation:
To find the sum of the two expressions -2.9a+6.8 and 4.4a-7.3, you need to combine the like terms. Like terms are terms that have the same variable raised to the same power. In this case, -2.9a and 4.4a are like terms because they both have the variable 'a' raised to the first power. Similarly, 6.8 and -7.3 are also like terms because they don't have any variables. To combine like terms, simply add or subtract their coefficients while keeping the variable the same.
So, -2.9a + 4.4a can be combined as (4.4a - 2.9a) and 6.8 - 7.3 can be combined as (6.8 + (-7.3)).
Therefore, the sum of the two expressions -2.9a+6.8 and 4.4a-7.3 is (4.4a - 2.9a) + (6.8 + (-7.3)).
Q1. Ned washes dishes at a constant rate. Ned can hand-wash 18 dirty dishes in 3 minutes. Choose the graph that best represents the number of dishes, d, Ned can wash in any number of minutes, t.
(CHECK Media (picture) for answer choices)
Answer:
Graph A
Step-by-step explanation:
As we know, in 3 minutes he washes 18 dishes. Without even doing any math, you can see that this is the only graph that represents that. The others show that he washes two dishes in 12 minutes, which doesn’t make sense.
Ned's rate of washing dishes is 6 dishes per minute. The graph representing the number of dishes Ned can wash in any number of minutes would be an upward sloping line originating from the origin. The slope of this line, or the rate of change, signifies Ned's dish-washing rate.
Explanation:This is a typical problem in Mathematics subject related to speed or rate, specifically, it involves a rate of washing dishes. Ned can hand-wash 18 dishes in 3 minutes. Thus, Ned's rate of washing is 18 dishes per 3 minutes, or 6 dishes per minute.
The relationship between the dishes and the minutes is a direct proportional relationship since the amount of dishes Ned can hand-wash increases directly as the time increases.
To reflect this in a graph, we would have a straight, upward sloping line originating from the graph's origin (0,0). The slope of this line, or the rate of change, signifies the rate at which Ned can wash dishes.
Given that Ned can wash 6 dishes per minute, each point on the line should increase by 6 dishes for each increment of 1 minute on the time axis. Hence the correct graph would be a straight line with a slope of 6.
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-3x = 2x + 19 solve
Answer:
x=-19/5
Step-by-step explanation:
-3x=2x+19
-3x-2x=19
-5x=19
x=19/-5
Answer:
get x to one side by subtracting 2x from 2x+19
new equation:
-3x-2x=19
-5x=19
divide both sides by -5
x=-19/5
or x=-3 4/5
(-7,5) reflected over y axis
Answer:
add
Step-by-step explanation:
23456
Answer:
( 7, 5 )
Step-by-step explanation:
when reflected over the y axis they numbers are in quadrant 1 which means both numbers are positive.
22,432.49 divided by 61.4
Answer:
365.35
Step-by-step explanation:
USE A CALCULATOR!!!!
The scale on a map is 4cm = 25 mi what is the actual distance in miles represented by a line that is 20 cm on map
Answer:
Step-by-step explanation:
4 cm to 25 miles = 20 cm to x miles
4 / 25 = 20 / x
cross multiply
4x = (25)(20)
4x = 500
x = 500/4
x = 125 miles <=====
Answer:
The correct answer is that the actual distance in miles represented by a line that is 20 cm on map is 125 miles.
Step-by-step explanation:
1. Let's review the information provided to us to answer the question correctly:
Scale on a map: 4 cm = 25 miles
2. What is the actual distance in miles represented by a line that is 20 cm on map ?
For calculating the distance in miles represented, we will use the following equation:
Actual distance in miles represented = Miles in the scale/Centimeters in the scale * 20
Replacing with the real values:
Actual distance in miles represented = 25/4 * 20 = 25 * 5 = 125
The correct answer is that the actual distance in miles represented by a line that is 20 cm on map is 125 miles.
How would the inverse operation of addition be
used to solve this equation?
36 + m = 54
A.
54 - 36 = m
B.
36 + 54 = m
C. 54 - 36 = m
D. 36 x 54 = m
Answer:
(A.C.) 54 - 36 = mStep-by-step explanation:
36 + m = 54 subtract 36 from both sides
36 - 36 + m = 54 - 36
m = 54 - 36
m = 18
Answer:
m=18
Step-by-step explanation:
36+m=54
m=54-36
m=18
What are the possible values of 6
Answer:
The possible values of v are 6 and -6
Step-by-step explanation:
The opposite operation of an absolute value is to add a ± to the other side, so when we solve for v we get
|v|=6
v=±6
Which is the same as
v=-6 and 6
Answer:
C
Step-by-step explanation:
|6| and |-6| have the same meaning. Both are equal to 6
The answer is C