Steps Using Factoring By Grouping
[tex]4 {s}^{2} - 12s = - 9[/tex]
[tex]4 {s}^{2} - 12s + 9 = 0[/tex]
[tex](4 {s}^{2} - 6s) + ( - 6s + 9) = 0[/tex]
[tex]2s(2s - 3) - 3(2s - 3) = 0[/tex]
[tex](2s - 3)(2s - 3) = 0[/tex]
[tex](2s - 3) {}^{2} = 0[/tex]
[tex]2 s - 3 = 0[/tex]
[tex] \: \: \: \: \: \: \: 2s = 0 + 3[/tex]
[tex] \: \: \: \: \: \: \: 2s = 3[/tex]
[tex] \: \: \: \: \: \: \: \: \: s = \frac{3}{2} [/tex]
[tex] \: \: \: \: \: \: \: \: \: s = 1 \frac{1}{2} [/tex]
[tex] \: \: \: \: \: \: \: \: \: s = 1,5[/tex]
[tex] \green {\boxed{s = \frac{3}{2} = 1 \frac{1}{2} =1,5}}[/tex]
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Write 9.84 as a mixed number in simplest form
Answer:
[tex]9\frac{21}{25}[/tex]
Step-by-step explanation:
Simplify the 0.84. It is 84/100, or divided by 4, it is 21/25.
Hope this helped! :))
Answer:
Step-by-step explanation:
Mixed numbers are a whole number and a fraction together
sooo 9.84= 9 84/100 but we can reduce 84 /100 to 42/50 and that can be reduced to 21/25
so write 9 21/25
Hannah likes candy. She wants to purchase some candies all varieties of candy are $4.20 each. Hannah buys one mango candy and one apple candy. Write an expression that represents the total cost,t,of the candy if m represents the number of mango candies and a represents the number of apple candies
Answer: 4.20(2)
Step-by-step explanation:
The lengths of salamanders have a normal distribution with mean 15cm, and standard deviation 2cm. What is the probability a salamander has length between 12.2cm and 16.5cm
Answer:
The probability a salamander has a length between 12.2cm and 16.5cm is 0.6930
Step-by-step explanation:
We start by finding the z-score of each
Mathematically;
z-score = (x - mean)/SD
for 12.2 cm
z-score = (12.2 - 15)/2 = -2.8/2 = -1.4
For 16.5 cm
z-score = (16.5 -15)/2 = 1.5/2 = 0.75
So the probability we want to calculate is;
P( -1.4 < z < 0.75)
we can calculate this using the normal distribution table
Mathematically;
P( -1.4 < z < 0.75) = P( z < 0.75) - P( z < -1.4)
= 0.2263 + 0.30738
= 0.69262
Fill in the blank for each part below.
1) The slope is...
A. zero
B. Undefined
2) The equation is...
A. y=-1
B. X=-1
Albert's mom has 2,523 reward points from shopping at an online store. She uses the points to buy gift cards for free cups of coffee. Each gift card costs 75 points. What is the greatest number of gift cards Albert's mom can buy? How many reward points will she have left? Use the drop-down menus to choose the numbers that make the statement true.
Answer:
Maximum number of gift cards she can purchase = 33
Reward points left with her = 48
Step-by-step explanation:
Let Albert's mom buys the number of gift cards = x
Points for each gift card = 75
Total points consumed to buy x gift cards = 75x
If total points with Albert's mom = 2523
So the remaining points with her = (2523 - 75x)
Inequality representing the remaining points will be,
(2523 - 75x) ≥ 0
75x ≤ 2523
x ≤ [tex]\frac{2523}{75}[/tex]
x ≤ 33.64
Maximum number of cards she can buy = 33
Therefore, reward points with her = 2523 - (75 × 33)
= 2523 - 2475
= 48
PLEASE HELP HELP PLEASEEEEEEEEEEEEE
Answer:
D
Step-by-step explanation:
So it needs to go down because its negative. So B and C are out. Now if you look at the y intercept (4), you just have to look at which graph has a y intercept that's positive. So that's D
a number k is less than 3 units from 10
Answer:
-7 < k < 7
Step-by-step explanation:
The absolute value of the variable k will be less than 7.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result. The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
A number k is less than 3 units from 10. Then the equation is given as
k + 3 < 10
Simplify the equation, then the value of the variable k will be
k + 3 < 10
k < 10 - 3
k < 7
The absolute value of the variable k will be less than 7.
Your question was incomplete, your question was probably be...
A number k is less than 3 units from 10.
What's the absolute value inequality?
More about the solution of the equation link is given below.
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A sample of 100 mg of cobalt is studied over time. After 1 year, the sample was measured at 97.5 mg. If the size of the sample continues to change at the same rate, which equation models the change?
Answer: B
Step-by-step explanation: The answer is B
Answer:
B
Step-by-step explanation:
A popular band is trying to raise at least $20,000 for charity by holding multiple concerts at a park. It plans to sell tickets at $25 each. For each 2-hour concert, the band would need to pay the park $1,250 in fees for security, cleaning, and traffic services
The complete question is;
A popular band is trying to raise at least $20,000 for charity by holding multiple concerts at a park. It plans to sell tickets at $25 each. For each 2-hour concert, the band would need to pay the park $1,250 in fees for security, cleaning, and traffic services.
The band needs to find the combinations of number of tickets sold, t, and number of concerts held, c, that would allow it to reach its fundraising goal.
Write an inequality to represent the constraints in this situation.
Answer:
(25t)c - 1250 ≥ $20,000
Step-by-step explanation:
We are told the band is trying to raise at least $20,000.
It's trying to sell tickets at $25 each.
We are told that they pay the park $1,250 in fees for security, cleaning, and traffic services.
Now, expenses for each concert is $1,250.
Now, we are told that the number of tickets sold is t, and number of concerts held, c.
Thus, total amount that can be realized for "c" number of concerts is;
A = (25t)c
Now, expenses for each concert is $1,250.
Thus, total profit for "c" number of concerts is;
P = (25t)c - 1250
Now, they are trying to raise at least $20,000. Meaning greater than or equal to $20,000.
Thus, the profit must be greater than or equal to $20,000.
Thus, the inequality is;
(25t)c - 1250 ≥ $20,000
Please help me i can’t get this one right. someone help me please if you know how to do this.
Answer:
it’s going up by 3 boys per girl!
Step-by-step explanation:
Correct me if I’m wrong by commenting down below.
An archer is shooting at targets. The height of the arrow is 5 feet above the ground. Due to safety rules, the archer much aim the arrow parallel to the ground.
How long does it take for the arrow to hit a target that is 3 feet above the ground? Round your answer to the nearest hundredth.
Answer:
The time it takes to hit a target that is 3 feet above ground is approximately 0.35 seconds
Step-by-step explanation:
The given parameters are;
The height of the arrow above the ground = 5 ft.
The height of the target above the ground = 3 ft.
The time it takes the arrow to fall to 3 ft. from 5 ft. above the ground is given by the free fall formula, since the arrow has no vertical velocity component
The equation for free fall is h = 1/2·g·t²
Where;
h = The height of fall = 5 - 3 = 2 feet
g = The acceleration due to gravity = 32.17405 ft/s²
t = How long it takes to fall (to its target)
∴ 2 = 1/2 × 32.17405 × t²
t² = 2/(1/2 × 32.17405) ≈ 0.1243
t = √0.1243 ≈ 0.353
t = 0.35 seconds, to the nearest hundredth
Therefore, the time it takes to fall 2 ft to hit a target that is 3 feet above ground = 0.35 seconds.
The time to hit the target is simply the period the arrow gets to the target from the arch.
The time to hit the target is 0.35 seconds
The height of a parabola is calculated as:
[tex]\mathbf{h = \frac{1}{2}gt^2}[/tex]
Where:
[tex]\mathbf{h =5 - 3 = 2}[/tex] --- the difference between the height of the arrow and the height of the target.
[tex]\mathbf{g = 32.2 fts^{-2}}[/tex] --- acceleration due to gravity
So, we have:
[tex]\mathbf{2 = \frac{1}{2} \times 32.2 \times t^2}[/tex]
Multiply both sides by 2
[tex]\mathbf{4 = 32.2 \times t^2}[/tex]
Divide both sides by 32.2
[tex]\mathbf{0.124 = t^2}[/tex]
Take square roots
[tex]\mathbf{0.35 = t}[/tex]
Rewrite as:
[tex]\mathbf{t = 0.35s}[/tex]
Hence, the time to hit the target is 0.35 seconds
Read more about rates and time at:
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what is the slope of a line that passes through 5,15 and 6,11?
Answer:
slope is -4, equation is y= -4x + 35
Step-by-step explanation:
11-15
______
6-5
-4
____
1
11 = -4(6) + b
b = 35
Solve the following equation for x: 3x - 4 = 8
x=-2
x=-4
x=2
X=4
Answer:
1. Add 4 to both sides. 3x-4+4=8+4
2. Divide 3 from both sides. 3x/3=12/3
3. Solution. x=4.
Step-by-step explanation:
4
The temperature at 6:00 P.M. is 70°F. The
temperature will drop 6°F each hour. Write an
equation in slope-intercept form that models the
temperature in y degrees Fahrenheit after
x hours.
O A y= 70x – 6
B y = 6x - 70
Oc y=-6x – 70
OD y=-6x + 70
Answer:
Step-by-step explanation:
D
Help me please :) have a good day.
Answer:
problem 1: h=a/b problem 2: 5
Step-by-step explanation:
First problem: a=bh
First you have to flip the equation so bh=a
Next you have to divide both sides by b.
bh/b=a/b
so h=a/b
Second problem: 45ft is the area and 9ft is the base so to find the height you have to divide the area by the base
If you only have the base and height you would multiply them to find the area. If you only have area and height you divide area by height to get base.
You have to divide 45 by 9, the answer would be 5.
Hope this helped!
Natalie wants to grow it 4 in. Longer than it is now. She knows that hair grows at an average rate of 15 cm/year. How many more months will she wait to have her hair cut? (1 cm ≈ 0.39 in.) Question 1 First, you will need to convert the rate of 15 cm/year to inches per month. Which two conversion factors should you use? Select all correct answers.
Answer:
8.21 months.
Step-by-step explanation:
The growth rate of hair, R = 15 cm/year
As 1 year = 12 months,
[tex]\Rightarrow R=\frac{15}{12}[/tex] cm/month
As 1 cm ≈ 0.39 in.,
[tex]\Rightarrow R= \frac{15}{12}\times 0.39=0.4875[/tex] inch/month.
As she wants to grow it 4 inches longer than it now, So, the time required for 4 inches growth = 4/0.4875=8.21 months.
Hence, she needs to wait for 8.21 months.
Can anyone help with this one ?
Answer:
1. 35 2. 145 3. 35 4. 90 5. 145
Step-by-step explanation:
A cannery processed 785 pounds of strawberries in 5.5 hours. The cannery processed 1550 pounds in 10 hours. Write a linear equation to model the relationship between the weight of strawberries S and time T. How many pounds of strawberries can be processed in 8 hours?
The Equation is s = 170 t - 150 and 1210 pounds of strawberries can be processed in 8 hours.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
A cannery processed 785 pounds of strawberries in 5.5 hours.
and, The cannery processed 1550 pounds in 10 hours.
let S be weight of strawberries and T be the Time.
So,
slope = (1550 - 785) / (10 - 5.5)
= 170
Using slope- intercept form
y = mx + b
1550 = 170 (10) + b
b= -150
Then, y = 170 x - 150
and the equation is s = 170 t - 150
At t= 8 hour
s= 170x 8 - 150
s = 1210 pound.
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Solve for x and y, will mark brainliest please help!
Answer: x=37, y=9
Step-by-step explanation:
3x+11+x+21=180
4x+32=180
4x=148
x=37
3(37)+11=14y-4
111+11=14y-4
122=14y-4
14y=126
y=9
[tex]\frac{x^{2} }{3x^{2}+8x-3 } divided \frac{x-3}{x+2}[/tex]
Answer:
ddsdvffgdf gddccd fddf
Answer ASAP!!! First correct answer gets brainliest
Step-by-step explanation:
Given problem;
Write the equation of the line with the given slope and y-intercept
The equation of a line is expressed as;
y = mx + b;
m is the slope and b is the y-intercept
7. m = -5, b = -6
y = mx + b
Input the parameters:
y = -5x -6
8. m = 1, b = -4
y = mx + b
Input the parameters:
y = x - 4
9. m = 0.4, b = -9
y = mx + b
Input the parameters:
y = 0.4x - 9
10. m = 0, b = 3
y = mx + b
Input the parameters:
y = 3
Can a decimal that has repeating digits after the decimal point be converted into a fraction? It depends on what the digits are that repeat. It depends on the number of digits that repeat. No, because the decimal is irrational, and no irrational numbers can be converted to fractions. Yes, because the decimal is rational, and all rational numbers can be converted to fractions.
Answer:
It depends on what digits repeat
Step-by-step explanation:
A decimal with repeating digits after the decimal point can be converted to a fraction depending on the digits after the decimal point.
For example, let’s have 4/3
When we evaluate this using a calculator, we can see that we have recurring 3 after the decimal point
So 4/3 is actually 1.3333333333333
We can see that based on the number after the decimal point we can convert this to 4/3
Answer
It depends on what digits repeat
Step-by-step explanation:
I hope this helps!
through: (-4,5), slope=-7/4
Answer:
[tex]y=-\frac{7}{4}x-2[/tex]
Step-by-step explanation:
There is enough information to create an equation in point - slope form.
[tex]y-y_1=m(x-x_1)[/tex]
We have a slope of -7/4 and the point of (-4,5).
[tex]y-y_1=m(x-x_1)\rightarrow \boxed{y-5=-\frac{7}{4}(x+4)}[/tex]
Convert to slope intercept:
[tex]y-5=-\frac{7}{4}(x+4)\\\\ y-5=-\frac{7}{4}x-7\\\\y-5+5=-\frac{7}{4}x-7+5\\\\\boxed{y=-\frac{7}{4}x-2}[/tex]
Hope this helps.
Last one!
Solve for h.
h- (-3)=9
Hello.
To solve this, isolate h, by adding the two numbers.
9 + (-3) = 6
h = 6
Check: 6 - (-3) = 9
This is true because when subtracting a negative number, it cancels out because of double negative, so it becomes 6 + 3 = 9, which is also true.
Helpppo I’ll name you the brainliest
PLS HELP ME ASAP!!!!!!!!
Answer:
All of the above
Step-by-step explanation:
because all are correct
if 12x+8 is less than 6,what is the value of 8x
Please help. I'm desperate!!!!!!!!!!!
can you please help me solve this
Answer:
The answer is A because the answer to the equation is x^{2}= -6 and the 7 is negative
Step-by-step explanation:
Hope this helps :)
Which could be the first step of an indirect proof of the conditional below?
If x2 = 25, then 5’2= 25 and x = 5,
A. Assume x=5 is true.
B. Assume 52 = 25 is true,
C. Assume x2 + 25 is true.
D. Assume 52.25 and x + 5 are true,
Answer
Option D
Step-by-step explanation
For further help (727) 335-8234
The first step of indirect proof of the conditional below
If x2 = 25, then 5’2= 25 and x = 5 is assume 5² = 25.
Option B is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Conditions:
x² = 25 then 5² = 25 and x = 5
If we have to prove the above conditions indirectly, we have to prove that x² = 25 using the conditions 5² = 25 and x = 5.
So,
We have to assume,
Step 1:
5² = 25
Step 2:
x = 5
Step 3:
x² = 25
Thus,
The first step of indirect proof of the conditional below
If x2 = 25, then 5’2= 25 and x = 5 is assume 5² = 25.
Option B is the correct answer.
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