Answers
Answer:
A
Step-by-step explanation:
9x^2-25=0
x= 5/3 and -5/3
By solving quadratic equation [tex]9x^2-25=0[/tex] we got solution set as [tex]\{\frac{-5}{4}, \frac{5}{4} \}[/tex]
What is quadratic equation ?Any equation that can be written in form as [tex]ax^{2}+bx+c=0[/tex] , where x is variable and a, b and c are any real numbers and a ≠ 0 is called quadratic equation .
given quadratic equation :
[tex]9x^2-25=0\\\\[/tex]
Adding 25 both sides
[tex]9x^2-25+25=0+25\\\\\Rightarrow 9x^2=25[/tex]
Dividing by 9 on both sides
[tex]\frac{9x^2}{9}=\frac{25}{9}\\\\x^2= \frac{25}{9}[/tex]
Taking square root both sides
[tex]x= \pm \sqrt(\frac{25}{9})[/tex]
[tex]x= \pm \frac{5}{4}[/tex]
[tex]x= \{\frac{-5}{4}, \frac{5}{4} \}[/tex]
By solving quadratic equation [tex]9x^2-25=0[/tex] we got solution set as [tex]\{\frac{-5}{4}, \frac{5}{4} \}[/tex]
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Related Questions
Graph each linear equation that passes through the given pair of points. Use graph paper.
1. (2,2) and (4,5)
2. (0,1/2) and (2,3/2)
3. (-1,2) and (5,0)
4(-5,-3) and (-3,5)
Answers
Answer:
The easier way to solve this is to find the two points in the coordinate axis, and just draw a line that passes through the two points.
But let's be more complete:
Let's find the equations for each line:
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
1) Here the points are (2,2) and (4,5)
then the slope is:
a = (5 - 2)/(4 - 2) = 3/2
y = (3/2)*x + b
And to find the value of b, we just replace the values of one of the points in the equation, in this case i will use (2, 2)
2 = (3/2)*2 + b
2 = 3 + b
2 - 3 = b
-1 = b
y = (3/2)*x - 1
2) Here the points are (0,1/2) and (2,3/2)
then the slope is:
a = (3/2 - 1/2)/(2 - 0) = 1/2
y = (1/2)*x + b
And to find the value of b, we just replace the values of one of the points in the equation, in this case i will use (0, 1/2)
1/2 = (1/2)*0 + b
1/2 = b
y = (1/2)*x + 1/2
3) Here the points are (-1,2) and (5,0)
then the slope is:
a = (0 - 2)/(5 + 1) = -1/3
y = (-1/3)*x + b
And to find the value of b, we just replace the values of one of the points in the equation, in this case i will use (-1, 2)
2 = (-1/3)*-1 + b
2 = 1/3 + b
2 - 1/3 = b
5/3 = b
y = (-1/3)*x + 5/3
4) Here the points are (-5,-3) and (-3,5)
then the slope is:
a = (5 + 3)/(-3 + 5) = -4
y = -4*x + b
And to find the value of b, we just replace the values of one of the points in the equation, in this case i will use (-3, 5)
5 = -4*-3 + b
5 = 12 + b
5 - 12 = b
-7 = b
y = -4*x - 7
Now that we have all the equations, we can find the graphs.
where the colors are:
(4) green
(3) orange
(2) Blue
(1) Gray.
3. In the figure shown, a circle with center O and radius of length 3 units is
inscribed in a square. What is the area of the shaded region? *
A. 3.86 square units
B. 7.73 square units
C. 28.27 square units
D. 32.86 square units
Answers
Answer:
C
Step-by-step explanation:
To find the area of a circle, take its radius (3) and square it. In this case, 3 times 3 = 9. Then, you multiply the answer by pi, which rounds to 3.14, but is more like 3.14159265......etc, etc. There is a rhyme for that: May I have a large container of coffee beans? Where the length of each word is a number of pi. Anyway, most people would write 9pi, but this is asking for the exact answer, so you can do 3.14 times 9, which equals roughly 28.27. Hope this helped!
Steven is making bags of trail mix for hiking club. He will use 23 ounces of walnuts, 11.2 ounces of almonds, and 14.3 ounces of cashews. This amount makes 25 bags of trail mix. How many ounces are in each bag?
Answers
Answer:
1.94 ounces are in each bag.
Step-by-step explanation:
The total ounces of nuts in the bag is calculated as:
23 ounces of walnuts + 11.2 ounces of almonds + 14.3 ounces of cashews = 48.5 ounces.
From the question we are told that these amounts make 25 bags.
The number of ounces that are in each bag is calculated as:
25 bags = 48.5 ounces
1 bag = x ounces
Cross Multiply
25 bags × x ounces = 1 bag × 48.5 ounces
x ounces = 1 bag × 48.5 ounces/25 bags
x ounces = 1.94 ounces
Therefore, there are 1.94 ounces in each bag
Im so confused pls help
Answers
Step-by-step explanation:
[tex] f(x) \: = \: \frac{4}{5} - \frac{5}{x + 1} [/tex]
[tex]f(x) \: \: = \: \: \frac{(4)(x + 1) - 5(5)}{5x + 5} [/tex]
[tex]f(x) \: \: = \: \: \frac{4x + 4 - 25}{5x + 5} [/tex]
[tex]f(x) \: \: = \: \: \frac{4x - 21}{5x + 5} [/tex]
f(x) = g(x)
[tex] \frac{4x - 21}{5x + 5} = \frac{2}{5x + 5} [/tex]
4x - 21 = 2
x = (21 + 2)/4
x = 5.75
Student answers 90% of the questions on the math exam correctly if she answers 27 questions correctly how many questions are on exam
Answers
Answer:
30 questions
Step-by-step explanation:
if you cross multiply and divide like this,
[tex]\frac{27}{x}= \frac{90}{100}[/tex]
27 x 100 = 2700
2700 / 90 = 30
you'll get ; 30 !
Answer:
There are 30 total questions on the exam
Explanation:
90% = 0.9
0.9 x TOTAL = 27
27/ 0.9 = TOTAL
30 = TOTAL
Your neighbor leaves his yard, which is 120 ft from the bus stop. He begins to
walk toward you at the bus stop and then passes you. He walks at a speed of
4 ft/s. His distance d from you after t seconds is given by d = 1120 - 4tl. After
how many seconds is your neighbor 30 ft from you?
Answers
Answer:
22.5 seconds and 37.5 seconds
I hope this is helpful!
A company makes 130 bags.
49 of the bags have buttons but no zips.
32 of the bags have zips but no buttons.
39 of the bags have neither zips nor buttons.
A bag is selected at random.
What is the probability that the bag has buttons?
Answers
130-49 = 81
Answer 81/130
The probability that the bag has buttons is 0.38.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favorable outcomes/Total number of outcomes.
Given that, a company makes 130 bags.
Here, the number of favorable outcomes = 49 and the total number of outcomes =130
Now, probability of an event = 49/130
= 0.38
Therefore, the probability that the bag has buttons is 0.38.
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Point P′(–6, –4) is the image of point P(–2, 3) under a translation. What is the image of (5, –1) under the same translation?
A. (9, 6)
B. (–1, –5)
C. (1, –8)
D. (3, 2)
Answers
Answer:c
Step-by-step explanation:
Match the vocabulary word with the correct definition.
Answers
Answer:
1. right triangle - a triangle with one angle that measures 90 degrees
2.radius- a line segment from the center of a circle to any point on the circle
3. ray- a part of a line that has 1 endpoint that goes in one direction forever
4. rotational symmetry- a property that allows a figure to be rotated less than 360 degrees and still look the same
5. regular polygon- a polygon whose sides are all the same lengths and whose angles are the same measure
6. reflection- a transformation in which a figure is flipped across a line to give a mirror image of the original figure
Step-by-step explanation:
Your cell phone plan costs $34.99 per month plus $0.15 for each text message you send or receive. You have at most $40 to spend on your cell phone bill. what is the maximum number of text messages that you can send or receive next month?
Answers
Answer:
33 texts
Step-by-step explanation:
34.99+0.15(t)=40
lets say t is number of texts
subtract 34.99 from both sides
0.15(t)=$5.01
divide 5.01 by .15
33.4
but you cant send .4 of a text
so 33 texts
What is the solution set for
3x 2 + 48 = 0 ?
O {6.9, -6.9}
O {4, -4}
O {21, -21]
O {41 , -4; }
Answers
Answer:
{ 4i, - 4i }
Step-by-step explanation:
Given
3x² + 48 = 0 ( subtract 48 from both sides )
3x² = - 48 ( divide both sides by 3 )
x² = - 16 ( take the square root of both sides )
x = ± [tex]\sqrt{-16}[/tex] = ± 4i
solution set is { - 4i, 4i }
Help me plzzzzz
A cyclist rides her bike at a speed of 9 kilometers per hour. What is this speed in kilometers per minute? How many kilometers will the cyclist travel in 10 minutes? Do not round your answers.
Answers
Answer:
per minute: 0.15 km
in 10 minutes: 1.5
Step-by-step explanation:
there are 60 minutes in an hour. we need to find the constant rate of change (is that the name sorry). so 9/60 is 0.15. now we know she goes 0.15 km per minute. then do 10 times 0.15 since 10 minutes. you get 1.5. now we know.
Why would a deferred annuity or annuities due be preferred as a retirement investment?
Answers
I believe the answer is: The tax deferred nature.
Investment is considered to has tax deferred nature if the tax payment for the investment can be made years later after its due. This favoured as a retirement plan because it make the investors have more money to spend during the productive years prior to retirement.
HELP ASAP!! WILL GIVE BRAINLIEST ❤️
Find the slope of the line passing through the given points using the slope formula. Enter the slope in
simplest form. Describe the slope as positive, negative, zero, or undefined.
(-5. 19) and (-1,7)
Answers
Answer:
[tex]m=-3[/tex]
The slope is negative.
General Formulas and Concepts:
Order of Operations: BPEMDASSlope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (-5, 19)
Point (-1, 7)
Step 2: Find slope m
Substitute: [tex]m=\frac{7-19}{-1-(-5)}[/tex]Simplify: [tex]m=\frac{7-19}{-1+5}[/tex]Subtract/Add: [tex]m=\frac{-12}{4}[/tex]Divide: [tex]m=-3[/tex]Evaluate the following expression. Type your answer as a number.
8 + 23 - (4 × 3) =
the 23 is a exponet jus to let you know
Answers
its 2
Hope this helps! <3
Please answer correctly !!!!!!!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!
Answers
Answer:
∠3, it is quite clear
Step-by-step explanation:
Find three consecutive integers such that if the third is subtracted from six times the sum of the first and second, the result is 452 more than twice the second.
Answers
Answer:
The numbers are 50, 51, and 52.
Step-by-step explanation:
The consecutive integers are (x-1), x, and (x+1).
6*(x-1+x)-(x+1)=452+2x
6x-6+6x-x-1=452+2x
9x = 459
x=51
The numbers are 50, 51, and 52.
HELP ME PLEASE!
Complete the work to find the equation of a line that passes through point (–5, –3) and is parallel to line y – 3x = –7. Step 1: Write the equation of the given line in slope intercept form: y = 3x – 7. Step 2: Determine the slope of the parallel line: m = 3. Step 3: Substitute the slope and given point into y = mx + b to find the y-intercept of the new line. –3 = 3 (–5 ) + b 3 = –15 + b b = 12 Step 4: Write the equation of the line parallel to 3x – y = 7 that passes through point (–5, –3).
Answers
Answer:
Y=3x+12 (its the first option)
Step-by-step explanation:
I did the assignment.
The equation of the line parallel to (3x - y = 7) passes through the point (-5, -3) is y = 3x + 2 and this can be determined by using the one-point slope form.
Given :
The line passes through the point (-5, -3) and is parallel to the line (y - 3x = -7).
The following steps can be used in order to determine the equation of a line that passes through the point (-5, -3) and is parallel to the line (y - 3x = -7):
Step 1 - The one-point form of a line is used in order to determine the equation of a line that passes through the point (-5, -3) and is parallel to the line (y - 3x = -7).
Step 2 - The one-point form is given below:
[tex](y-y_1) = m (x-x_1)[/tex]
Step 3 - According to the given data, the line is parallel to the line (y = 3x - 7). So, the slope of the line is 3.
Step 4 - Now, substitute the values of slope and the point in the above expression.
[tex](y+3) = 3 (x+5)[/tex]
y = 3x + 2
For more information, refer to the link given below:
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Apply the distributive property to create an equivalent expression. (4b + 2e + 3) 3 =
Answers
Answer:
12b+6e+9
Step-by-step explanation:
You multiply 3 with every number inside the parentheses.
(3x4b)=12b
(3x2e)=6e
(3x3)=9
Solve for p.
i = prt
p = i-rt
p = (rt)/i
p = i/(rt)
Answers
Answer:
[tex] \sf p = \dfrac{i}{rt} [/tex]
Step-by-step explanation:
Solve for p:
[tex] \longrightarrow [/tex] i = prt
i = prt is equivalent to prt = i:
[tex] \longrightarrow [/tex] prt = i
Divide both sides by rt:
[tex] \longrightarrow [/tex] [tex] \sf \dfrac{prt}{rt} = \dfrac{i}{rt} [/tex]
[tex] \sf \dfrac{prt}{rt} = p: [/tex]
[tex] \longrightarrow [/tex] [tex] \sf p = \dfrac{i}{rt} [/tex]
Giving brainiest explain answer
Answers
Answer:
B.) Carrier B
Step-by-step explanation:
The unit rate would be [tex]c = 12t[/tex]. Since the cost for 2 minutes is $0.24 it is easy to figure out that for 1 minute it would be $0.12.
Might be a bit confusing, but hope it helps.
Susan runs 22 km in 2 hours and 45 minutes. What is her average speed in km an hour? Explain your answer please!
Answers
Answer:
22km= 2 hours and 45 mins
To find speed: Distance/Time
22/2.75 = 8
Your answer 8km/h
Step-by-step explanation: When finding speed, the formula is always distance divided by time. 45 minutes of 60 minutes is 3/4 of an hour, and 3/4 is 0.75 is decimal. So you add the 2 + .75, and you'll get 2.75. After you convert the time, you begin dividing and you'll get your answer!
I need help on this one
Answers
Answer:
A
Step-by-step explanation:
A rectangle has a perimeter of 104 feet. If the
width of the rectangle is one more than twice its
length, determine the dimensions of the
rectangle.
Answers
Answer:
w=35, L = 17
Step-by-step explanation:
the perimeter is all sides added together to total 104. so,
2L + 2W= 104
the width is one more than twice it's length, so W = 2L + 1
plug that into first equation.
2L + 2(2L+1)=104
distribute:. 2L + 4L + 2= 104 and continue to solve for L
6L + 2= 104 subtract 2 from both sides.
6L = 102, divide both sides by 6
L = 17. so the length is 17 ft. now use that number to put it in our equation for width, W= 2L + 1
W= 2(17)+1
W = 35
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Answers
Answer:
whats ur question?
Step-by-step explanation:
Answer:
I don't understand
Step-by-step explanation:
Sorry, I cannot help
What is the percent of change from 4 to 1?
Answers
Answer:
1 is 25% of 4, so 75% decrease
Step-by-step explanation:
Rob buys 50 feet of border to place around the ceiling of a room. The ceiling is shaped like a square with sides that are 10.8 feet long. How many feet of border will Rob have left?
Answers
Answer:
Step-by-step explanation:
Rob needs 43.2 feet of border to place around the ceiling and Rob will have 6.8 feet of border left after placing it around the ceiling.
What is distance?
Distance is the measure of how far apart two objects or locations are from each other. It is usually measured in units such as meters, kilometers, miles, or feet. Distance is a scalar quantity, meaning it has only magnitude and no direction.
The perimeter of the ceiling is equal to the total length of border that Rob will need. The perimeter of a square is given by the formula P = 4s, where s is the length of one side of the square.
In this case, the length of one side of the square ceiling is 10.8 feet, so the perimeter is:
P = 4s = 4(10.8) = 43.2 feet
Therefore, Rob needs 43.2 feet of border to place around the ceiling.
Since he has purchased 50 feet of border, he will have:
50 - 43.2 = 6.8 feet
Rob will have 6.8 feet of border left after placing it around the ceiling.
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Using the divisibility rules, explain why 678 is divisible by 2, 3, and 6.
Answers
Answer:
678
678 is even, so it's divisible by 2
6+7+8 = 21, which is divisible by 3, so 678 is divisible by 3
Since 678 is divisible by both 2 and 3, it has to be divisible by 6
Step-by-step explanation:
9. a - 2a +5
pls help i’m kinda dumb
Answers
First you combine like terms
a-2a equals -a
After that you can’t combine anything else
So the equation simplified is -a+5
Word problem: A High School had a musical in which students ($5 tickets) and adults ($7 tickets) attended. If a total of 47 tickets were sold and they made a total of $269. How many student tickets were sold and how many adult tickets were sold?
Answers
Answer:
30 of them were students
17 were adults
Step-by-step explanation:
bunny and rabbit problems
if they were all adults
7 x 47 = 329
329 - 269 = 60
60/ (7-5) = 30
30 of them were students
17 were adults