Answer:
do the butterfly method if you don't know how to do that comment and I'll show you a screenshot
1)What value of b will complete the square in the expression below and make the expression a perfect square trinomial? X^2+bx+16/49
2) Enter the perfect square trinomial as a squared binomial.
The value of b in x²+ bx + 16/49 is 8/7 and the squared binomial is (x + 4/7)²
How to determine the value of b?From the question, we have the following parameters that can be used in our computation:
X^2+bx+16/49
Rewrite properly
So, we have the following representation
x²+ bx + 16/49
When represented as a square, we have
x²+ bx + 16/49 = (x + a)²
Expand the bracket
So, we have the following representation
x²+ bx + 16/49 = x² + 2ax + a²
By comparison, we have
bx = 2ax
a² = 16/49
Take the square root of both sides
a = 4/7
Substitute a = 4/7 in bx = 2ax
bx = 2 * 4/7x
So, we have
b = 2 * 4/7
Evaluate
b = 8/7
The squared binomialIn (a), we have
x²+ bx + 16/49 = (x + a)²
Where
a = 4/7
So, we have
x²+ bx + 16/49 = (x + 4/7)²
Hence, the binomial is (x + 4/7)²
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Answer:
[tex]\textsf{1)} \quad b = \dfrac{8}{7}[/tex]
[tex]\textsf{2)} \quad \left(x+\dfrac{4}{7}\right)^2[/tex]
Step-by-step explanation:
Perfect Square Trinomial
A trinomial that can be written as the square of a binomial.
For example the perfect trinomial x²+2dx+d² can be written as (x+d)².
Given trinomial:
[tex]x^2+bx+\dfrac{16}{49}[/tex]
To express the given trinomial as a perfect square trinomial, determine the value of b.
As the coefficient of the x² term is one, b equals twice the square root of the constant of the trinomial:
[tex]\implies b = 2 \sqrt{\dfrac{16}{49}}[/tex]
[tex]\implies b = 2 \cdot \dfrac{4}{7}[/tex]
[tex]\implies b = \dfrac{8}{7}[/tex]
Therefore, the perfect square trinomial is:
[tex]x^2+\dfrac{8}{7}x+\dfrac{16}{49}[/tex]
To factor in the form of a squared binomial (x + d)², d is half the value of b:
[tex]\implies d = \dfrac{1}{2}b[/tex]
[tex]\implies d = \dfrac{1}{2} \cdot \dfrac{8}{7}[/tex]
[tex]\implies d=\dfrac{8}{14}[/tex]
[tex]\implies d=\dfrac{4}{7}[/tex]
Therefore, the perfect square trinomial as a squared binomial is:[tex]\implies \left(x+\dfrac{4}{7}\right)^2[/tex]
Which statement about the value of x is true?
x > 38
x < 39
x < 77
x > 103
Answer: x> 38
Step-by-step explanation:
The best way to find the answer is to solve for x. To start you would add 38 and 39, getting 77, then subtract that from 180 to get the last angle in the triangle, 103. Finally, you would subtract 103 from 180, getting 77, to get x. The only thing you need to do now is to look at all of the answers and figure out which one makes sense for the answer you got. You know it can't be x<77 because it doesn't have the or equal to sign. You know it can't be x>103 because 77 is lower than 103. You know it can't be x<39 because 77 is greater than 39, so the answer has to be x > 38. (this was copy'd n pasted from another question that is the exact same.)
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A(t)A0e-0.355t where t is the time in years
Based on the function, the population of the small town in 5 years is 3898
How to determine the population in 5 years?The complete question is added at the end of this solution
From the question, we have the following parameters that can be used in our computation:
Initial population = 23000
Number of years = 5
These parameters can be represented as
Ao = 23000
t = 5
From the question, we have the following formula that can be used in our computation:
A(t) = A0e^(-0.355t)
Substitute Ao = 23000 and t = 5 in the above equation
So, we have the following representation
A(5) = 23000 * e^(-0.355 * 5)
Evaluate the products
A(5) = 3898
Hence, the population in 5 years is 3898
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Complete question
The population of a small town follows A(t) = A0e-0.355t where t is the time in years
What is the population in 5 years if the initial population is 23000
. The electricity cost y, in dollars, to use a
hair dryer for x minutes can be represented
by the equation y = 0.002x. The electricity
cost to use a space heater is shown on the
graph. Which appliance is more expensive
to use? Explain. (Example 4)
Space Heater
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
Electricity Cost ($)
y
123456789
Time (min)
X
Answer:
D)The space heater, because it has the greater unit rate for electricity cost.
Step-by-step explanation:
I DID IT AND GOT IT RIGHT!
20 + 0.44x + 4 = 19 + 1.69x. please show how you got it
Answer: x =4
Step-by-step explanation: The solution of the given equation 24 + 0.44x = 19 + 1.69x will be x = 4 thus option (A) will be correct.
What is the equation?
There are many different ways to define an equation.
More than one variable may be present inside a linear equation.
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
As per the given equation,
24 + 0.44x = 19 + 1.69x
24 - 19 = 1.69x - 0.44x
5 = 1.25x
x = 4
Hence "The solution of the given equation 24 + 0.44x = 19 + 1.69x will be x = 4".
4. Ms. Wagner painted the outside of the patio
door to her house, as shown below. She did
not paint the window or the doorknob.
Answer: 18 ft ^2
Step-by-step explanation:
Find the slope of the line that passes through all of the points
on the table.
Someone help I’ll give Brainliest
what is the solution to the equation below 2x+13=x-1
You are a store clerk assigned to stack notebooks in a box for shipment. Each notebook is 29 centimeters long, 21.5 centimeters wide, and 1.5 centimeters thick. The box can hold a maximum of 12 notebooks.
To the nearest whole number of cubic centimeters, what is the minimum volume of the box?
A. 64
B. 624
C. 935
D. 7,500
E. 11,223
The minimum volume of the box = 11220 cubic centimeters
What is volume?
In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.
One notebook:
length, l= 29 cm
width = 21.5 cm
height = 1.5 cm
Volume of 1 notebook = l*w*h
= 29*21.5*1.5
= 935.25
≈ 935 cubic centimeters ( nearest whole number )
Volume of 12 notebooks = 935 * 12 = 11220 cubic centimeters
So, the minimum volume of the box = 11220 cubic centimeters
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Answer:
11,223
Step-by-step explanation:
A man pays a total of 4800 in flat rental for 3 months. Find his monthly rental rate.
Answer:
The man's monthly rental rate is $1600.
Step-by-step explanation:
To figure out the answer to your question, it says to find how much is monthly rental is. So, we can do this by simply dividing the two numbers:
4800 ÷ 3 = $1600
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 6 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Convert the numeral to a numeral in base ten
24^five
Answer:
14 base 10
Step-by-step explanation:
Remember what the digits mean in the base 10 system we use.
For example, the number 539 (base 10) means:
The 5 in the hundreds place means 5 × 100 = 500.
The 3 in the tens place means 3 × 10 = 30.
The 9 in the ones place means 9 × 1 = 9.
The number 539 means
5 × 100 + 3 × 10 + 9 × 1 = 500 + 30 + 9 = 539
Also keep in mind one more thing. The ones digit means the number of ones. 1 = 10^0. The number in the ones digit means the number if 10^0 you have.
The ten digits is the digit of 10^1.
The hundreds digit is the digit of 10^2 since 10^2 = 100.
In other words, the ones digit is the number of 10^0 you have.
The tens digit is the number of 10^1 you have.
The hundreds digit is the number of 10^2 you have.
Now let's look at base 5.
Here, each place to the left is a successively higher power of 5 instead of a power of 10.
Think of the number 432 base 5.
The 2 is in the units place. it represents the number of 5^0 or ones you have. In this case, it is 2 × 5^0 = 2 × 1 = 2
The 3 is in the 5^1 place. It represents the number of fives you have.
3 × 5 = 15
The 4 is in the 5^2 place. It represents the number of 25's you have.
4 × 25 = 100
The number 432 base 5 means:
4 × 5^2 + 3 × 5^1 + 2 × 5^0
= 4 × 25 + 3 × 5 + 2 × 1
= 100 + 15 + 2
= 117 base 10
In other words, 432 base 5 = 117 base 10.
Now we do the same with your number, 24 base 5.
24 base 5 =
= 2 × 5^1 + 4 × 5^0
= 2 × 5 + 4 × 1
= 10 + 4
= 14
2y-5+123=180
help me
Answer:
y = 31
Step-by-step explanation:
2y-5+123=180
123 - 5 = 118
2y+118=180
subtract 118 from both sides
2y+118 - 118 = 180 - 118
180 - 118 = 62
2y = 62
divide 2 by both sides
2y/2 = 62/2
y = 31
Answer:
Step-by-step explanation:
2y+−5+123=180
Step 1: (Combine Like Terms)
(2y)+(−5+123)=180
Step 2: (Subtract 118 from both sides)
2y+118−118=180−118
2y=62
Step 3: Divide both sides by 2
2y/2= 62/2
y=31
Suppose that you roll a fair, six-sided die 10 times. What’s the probability that you get at least one 6?
Answer:
0.8385, turned into a percentage is 83.9%
Step-by-step explanation:
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Answer:210
Step-by-step explanation:
20 POINTS will give brainliest
Find the missing number so that the equation has no solutions
–2x + 11 = x + 21 + __x
a 5
b 2
c -2
d -3
Answer: d -3
Step-by-step explanation:
The answer I got was 11 = 21, which does not make sense
–2x + 11 = x + 21 + (-3)x
+3x +3x
x + 11 = x + 21
-x -x
11 = 21
Answer:
-3
Step-by-step explanation:
You are saving to buy a brand new car in 6 years? You predict the car will cost $32000 but you have already saved $6500.
How much work do you have if you put the $6,500 in an account paying 5% APR compounded continuously?
How much should you invest into an account paying 5% APR compounded continuously to have the entire $32000 in the 6 years?
The amount you will have $6,500 with 5% in six years using continuous compounding is of:
$8,774.
The amount you will need to have the entire $32000 in the 6 years is of:
$18,890.46.
What is continuous compounding?The balance of an account after t years, using continuous compounding, is given as follows:
[tex]B(t) = Pe^{kt}[/tex]
In which the parameters are given as follows:
P is the principal, which is the initial investment.k is the APR, as a decimal.Putting the $6,500 into the account, the values of the parameters are given as follows:
P = 6500, k = 0.05, t = 6.
Hence the balance will be of:
B(6) = 6500 x e^(0.05 x 6) = $8,774.
The balance to have the entire $32,000, considering what you already have, will be of:
32000 - 6500 = 25500
Hence the principal is obtained as follows:
Pe^(0.05 x 6) = 25500
P = 25500/e^(0.3)
P = $18,890.46.
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Michael averages 12 points in each basketball game. His team plays 2 games each week. About how many points will he score in 12 weeks? Explain your reasoning.
Michael will score about 288 points in 12 weeks. This is because he scores 12 points in each game and there are 2 games each week, so he will score 24 points in each week. Multiplying 24 points by 12 weeks, Michael will score 288 points.
of the car was marked as $14,000.
The price
The end of the month sale has
lowered the price to $12,500. What is the percent decrease to the nearest
percent?
Answer: the percent decrease is 9%
Step-by-step explanation:
Formula :12500/14000x100% and this formula can use in any of question likes this
Help i think it’s b i don’t know!!
Answer: It is B
Step-by-step explanation:
If you put leg a (3) and leg b (4) into a Pythagorean equation it will turn out like this
3^2+4^2=x^2
9+16=x^2
25=x^2
√25=√x
5=x
5 is the missing side length, which corresponds to option b
What is the x-coordinate of the midpoint of the segment between (4 , -5) and (8 , 2)?
Answer:
(6, -1.5) or (6, -1 1/2)
Last week, a dairy farm produced p kg of cheese. The dairy farm also produced 24 kg more yoghurt than cheese and 3 times as much ice cream as cheese. The dairy farm produced more kilograms of ice cream than yoghurt last week. Write and solve an inequality to work out the possible values of p.
Answer:
4w>39+w
3w>39
w>13
Step-by-step explanation:
Serena estimates that she can paint 60 square feet of wall space every half-hour.write an equation for the relationship with time in hours as the independent variable.can Serena paint 400 square feet of wall space in 3.5 hours?why or why not?
Answer:x=3.5 x 60
the answer is yes because when she's doing 3.5 hour, and she can do 420 square feet
What is x+y=-15 converted to slope intercept form
Answer: y = -x - 15
Step-by-step explanation:
Slope intercept form is written as y = mx + b where m is the slope and b is the y-intercept. In other words, we need to isolate the y-variable.
Given:
x + y = - 15
Subtract x from both sides of the equation:
y = -x - 15
There is a proportional relationship between the weight and total cost of a bag of cherries. One bag weighs 2.1 pounds and costs $7.98. Another bag weighs 2.8 pounds and costs $10.64.
Describe how you would graph the proportional relationship.
PLEASE HELPPP, I got like three different answers
Answer:
y = 3.8x
Step-by-step explanation:
Let y = the cost of the cherries
Let x = pounds of cherries
We can find the unit rate by either:
[tex]\frac{7.98}{2.1}[/tex] = $3.80 per pound
or
[tex]\frac{10.64}{2.8}[/tex] = $3.80 per pound
Now we can write the equation
hy = 3.8x
Please help asap! thank you
Find the quotient. Round to the hundredths' place when necessary.
Answer:
17: 0.65
18: 0.05
19: 0.27
20: 1840
Step-by-step explanation:
6/9 times 3/8 and what is equals to
Answer:
1/4
Step-by-step explanation:
Answer:
1/4
Step-by-step explanation:
(6/9) × (3/8)
Cross simplify:
(3/3) × (1/4)
3/12
1/4
PLEASE MARK AS BRAINLIESTThe next model of a sports car will cost 5.1% less than the current model. The current model costs $37,000 how much will the price decrease in dollars? What will be the price of the next model?
Decrease in the price is $1887, the price of the next model car is $35,113.
What is percentage?Percentage is a measurement to find value of the given number out of hundred.
Given that,
Price of current model = $37,000
The price of next model car is 5.1% less than the current model.
The price of the next model car = 94.9% of price of current model car
= 94.9 x 37,000/100
= 35,113
The decrease in the price = 37,000 - 35,113 = 1887
The price of the next model car is $35,113 and decrease in the price is $1887.
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What is 3 3/4 ft to yards as a mixed number?
The value of 3¾ft in yards would be = 1 6/25 yard
What is a mixed number?A mixed number is the type of number that is made up of three parts such as the whole number, a numerator and a denominator.
To convert to yards;
1 ft = 0.33 yard
3¾ = X yards
make x yards the subject of formula;
X yards = 3¾ × 0.33
X yards = 3.75×0.33
X yards = 1.24 yards
X yards in mixed number= 124/100 = 31/25 = 1 6/25 yard.
Note that the final value which is 124/100 is reduce to the lower figure by dividing through with 4 to arrive at the mixed number 1⁶/25
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If you estimate that a piece of wood measures 5.5cm if it actually measures 5.62cm what is the percent error of the estimate
The percent error of the estimate is -2.14%
How to determine the percent error of the estimate?In this question, the figures are given as
Estimate = 5.5 cm
Actual = 5.62 cm
The percentage of the error is then calculated using the following equation
Error percentage = (Estimate - Actual)/Actual * 100%
Substitute the known values in the above equation, so, we have the following representation
Error percentage = (5.5 - 5.62)/5.62 * 100%
Evaluate
Error percentage = -2.14%
Hence, the error percentage is -2.14%
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find the cartesian equation of r=3i+paremeter (i+2j)
The Cartesian equation will be;
⇒ (x - 3) / 1 = (y - 0)/2
What is Equation of line?
The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The equation is,
⇒ r = 3i + λ (i + 2j)
Where, 'λ' is a parameter.
Now,
Since, The equation is,
⇒ r = 3i + λ (i + 2j)
Where, 'λ' is a parameter.
Hence, The Cartesian equation is find as;
⇒ xi + yj = 3i + λi + 2λj
By compare, we get;
⇒ x = 3 + λ
⇒ y = 2λ
Thus, The Cartesian equation is;
⇒ (x - 3) / 1 = (y - 0)/2 = λ
Therefore, The Cartesian equation will be;
⇒ (x - 3) / 1 = (y - 0)/2
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the diamter of a circle is 14 yards what is the area of this cirlce
The area of a circle with diameter of 14 yards is 153.86 yards².
How to find area of a circle?The diameter of the circle is 14 yards . The area of the circle can be found as follows;
area of a circle = πr²
where
r = radius of a circleThe radius of a circle is half of its diameter.
Therefore,
r = 14 / 2 = 7 yards
Hence,
area of a circle = πr²
area of a circle = 3.14 × 7²
area of a circle = 3.14 × 49
area of a circle = 153.86 yards²
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