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]
Ingrid wants to buy a $20000 car in 8 years. How much money must she deposit at the end of each quarter in an account paying 5.9% compounded quarterly so that she will have enough to pay for her car?
Ingrid must deposit $402.74 at the end of each quarter for 8 years in order to have enough money to pay for her car.
4. Solve the quadratic equation 4x² + 7 = 25.
use the formula 「x= [-b±✓(b²-4ac)]/2a」a= 4, b= 0, c= -18x= [-0±✓(0²-4(4)(-18))]/2(4)x= 2.1213... , x= -2.1213...
Andrew decided so joys a tenner clench. Below is a chart that displays how many games of lenis he has played and the meatal cost of playing those panes. In this scenario, C ( y ) represents the total cost for playing games.
The linear function that represents the situation is of:
C(y) = 13y + 145.
The intercept is of:
C(0) = 145, meaning that the flat fee to pay the game is of $145.
What is the linear function?The slope-intercept representation of a linear function is given by the rule presented as follows:
y = mx + b
The coefficients of the function and their meaning are listed as follows:
m is the slope of the function, representing the rate of change of the function.b is the y-intercept of the function, representing the initial value of the function.Two points of the function, from the table, are given as follows:
(8, 249) and (13,314).
The slope is given by the change in y of the two points divided by the change in x, hence:
m = (314 - 249)/(13 - 8) = 13.
Hence:
C(y) = 13y + b
When y = 8, C(y) = 249, hence the intercept b of the function is obtained as follows:
249 = 13(8) + b
b = 249 - 13 x 8
b = 145.
Meaning that the flat fee to pay the game is of $145.
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Write an equation that represents the line. Use exact numbers.
Answer:
[tex]y=-\dfrac{1}{3}x+5[/tex]
Step-by-step explanation:
A line's slope is defined as rise over run.
The rise and run between the coordinates (0, 5) and (3, 4) is:
rise: -1
run: 3
Therefore, the slope of the line is -1/3. This is what x is multiplied by.
Next, to find what is added to x, find where the line crosses the y-axis. IN this case, that point is when y = 5, so in the second blank put 5.
how much would it cost to replace all the windows on all the building in the united states?
The cost to replace all the windows on all the building in the United States is $7,200,000.
What is the expression to find the total cost?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
Given that the cost to replace a window is $3 per window. IT should be noted that when there are 2,400,000 windows, the cost to replace all the windows on all the building in the United States will be:
= Cost of replacement × Total window
= $3 × 2,400,000
= $7,200,000
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The cost to replace a window is $3 per window. If there are 2,400,000 windows, how much would it cost to replace all the windows on all the building in the United States?
help meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeee
Answer:
500 rounded to the nearest tenth equal 500
Find WY.
W
8
X
39°
Y
Write your answer as an integer or as a decimal round
WY =
Find the perimeter of the shape made up of rectangles and squares
Answer: p = 45
Step-by-step explanation:
10 + 7 + 7 + 12 1/2 + 3 + 5 1/2
24 + 18 + 3
27 + 18 = 45
Your friend bought a new pair of shoes. He said the regular price was $75 but he got a 40% discount from the sales clerk. What is the sale price of the shoes
Answer:
40% off of 75 is 45$
Step-by-step explanation:
Divide the number by 100 (move the decimal place two places to the left).Multiply this new number by the percentage you want to take off.Subtract the number from step 2 from the original number. This is your percent off number.20 points and brainliest
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
-2x + 8 = -2x + 8
-2 makes the equation equal.
Option A 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.
Example:
2x + 4 = 6 is an equation.
We have,
-2x + 8 = __x + 8
The equation has infinitely many solutions when both sides of the equation are equal.
Now,
-2x + 8 = -2x + 8 is equal on both sides.
Thus,
-2x + 8 = -2x + 8
-2 makes the equation equal.
Option A is the correct answer.
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"Use the given conditions to write an equation for x-intercept = -3/8 and y-intercept = 4 Write an equation for the line in point-slope form.
(Simplify your answer. Use integers or fractions for any
"
Answer:
y - 4 = 32/3 x
Step-by-step explanation:
A (-3/8; 0)
B (0; 4)
slope = (4-0)/(0-(-3/8)
4/3/8
4 * 8/3
32/3
y-4 = 32/3 (x-0)
y -4 = 32/3 x
Simplify to create an equivalent expression 7n-(4n-3)
The expression 3(n + 1) is equivalent to the given expression 7n-(4n-3).
What is the expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
The expression is given in the question following:
7n - (4n-3)
We have to determine the equivalent expression
As per the question, we have
⇒ 7n - (4n-3)
Open the parentheses and distribute the negative sign,
⇒ 7n - 4n + 3
⇒ 3n + 3
⇒ 3(n + 1)
Thus, the expression 3(n + 1) is equivalent to the given expression.
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Please help heres a pic
The fourth arrow is used to represent inequality x>3.2
What is Number system?A number system is defined as a system of writing to express numbers.
Number line is a picture of a graduated straight line that serves as visual representation of the real numbers.
All the positive numbers are represented on the right side of the origin and all the negative numbers are represented on the left side of the origin, with a definite scale.
Here x>3.2 which means that values of x are greater than 3.2 so we use Open circle with right arrow.
Hence, the fourth arrow is used to represent inequality x>3.2
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en una expresion algebraica la reduccion de terminos semejantes se da entre los terminos de igual
Answer:990
990
990
990
990
990
Step-by-step explanation:
Answer:
Variable y exponente.
Step-by-step explanation:
En una expresión algebraica la reducción de términos semejantes se da entre los términos de igual variable o incógnita y exponente.
Por ejemplo:
3x² + 5x²
se pueden reducir pues tienen la misma variable x y el mismo exponente 2, su resultado se genera solo sumando, restando, los coeficientes, en este caso 3 y 5
3x² + 5x² = 8x²
En el caso:
3y² + 5x²
No se puede reducir pues la variable o incógnita no son iguales:
x≠y
En el caso:
3x² + 5x³
No se pueden reducir pues su exponente no es igual.
I need help please help me with this
Answer:
67.38°
Step-by-step explanation:
AD = DB = 24/2 = 12
<bcd = 12/5
< bcd = 67.38°
Explain how to find the distance between 1 and -3 on a number line.
Answer:
count backwards
Step-by-step explanation:
1, 0, -1, -2, -3
Answer:two ways
Step-by-step explanation: you can either count the spaces or you could just add until you get one of the answers -3 +4 =1 1- 4=-3
A rectangular piece of metal is 9 centimeters long and 6 centimeters wide. What is its area?
Answer:
54
Step-by-step explanation:
9x6
I need help on my homework ASAP!! PLEASE HURRY I HAVE 20 MINUTES
Answer: 10) 18x+21 11) 20 + 30a 12) 8x + 10y
Step-by-step explanation:
Distributive property means to multiply each number within the parenthesis by the number outside of the parenthesis.
10) 3(6x + 7)
3*6x + 3*7
18x + 21.
With that, you should be able to see how the other questions were answered.
A movie theater sells popcorn in a reusable bucket for $3.50. They offer refills for $2.50 each.
Write an equation in slope-intercept form to model the cost in dollars, y, for x refills.
The linear function that models the problem of movie theater sells popcorn is
y = 2.50x + 3.50 How to model the required equationA linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
definition of variable to suit the problem
y = output variable
m = slope
x = input variable
c = y intercept
The equation as described in the problem is represented using linear function as as follows
c = cost of the bucket = $3.50
m = cost of refills = $2.50
y = 2.50x + 3.50
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Prove that () = + 5 and () = √ − 5 are inverse functions without finding the inverse of either function.
if two functions are inverse of each other, that means that their composite will result in "x" alone.
meaning, that if f(x) and g(x) are inverse of each other, then f( g(x) ) = x and the other way around will be the same, hmmm let's see if that's true
[tex]f(x)=x^3 + 5\hspace{5em}g(x)=\sqrt[3]{x-5} \\\\[-0.35em] ~\dotfill\\\\ f( ~~ g(x) ~~ )=[g(x)]^3 + 5\implies f( ~~ g(x) ~~ )=[\sqrt[3]{x-5}]^3 + 5 \\\\\\ f( ~~ g(x) ~~ )=(x-5) + 5\implies f( ~~ g(x) ~~ )=x ~~ \textit{\LARGE \checkmark} \\\\[-0.35em] ~\dotfill\\\\ g( ~~ f(x) ~~ )=\sqrt[3]{[f(x)]-5}\implies g( ~~ f(x) ~~ )=\sqrt[3]{[x^3 + 5]-5} \\\\\\ g( ~~ f(x) ~~ )=\sqrt[3]{x^3}\implies g( ~~ f(x) ~~ )=x ~~ \textit{\LARGE \checkmark}[/tex]
Given the table below, write a linear equation that defines the
dependent variable, c, in terms of the independent variable, a.
Someone help I’ll give brainliest only need the answer no need for steps
Answer:
c = -1.75a + 15
solve & check the linear equation
3(x-4) + 14=2(x+3)
Answer:
x = 4
Step-by-step explanation:
3(x - 4) + 14 = 2(x + 3)
3x - 12 + 14 = 2x + 6
3x + 2 = 2x + 6
-2x -2x
-----------------------
x + 2 = 6
-2 -2
---------------
x = 4
I hope this helps!
Helpgggggggggyyuuh
Gggggggggygggggggfffff
Answer:
I believe the answer is 15.
Step-by-step explanation:
let me know if I am correct.
Given f(x) = -3x + 3, solve for x when f(x) = 9.
Answer:
Step-by-step explanation: x=-2. -3•-2=6+3=9
Solve the radical equation. Please explain each step in detail.
Answer:
[tex]x=\frac{1}{2}[/tex]
Step-by-step explanation:
Even roots can NEVER have a negative result, therefore the value of x can ONLY be positive values.
pla help.me with this question
Answer:
7. A
8. B
Step-by-step explanation:
7.
1 3
4 ------- - 2 -------
2 4
9 11
------- - -------
2 4
9(2) 11
------- - -------
2(2) 4
18 11 7 3
------- - ------- = ------- = 1 -------
4 4 4 4
----------------------------------------------------------------------------------------------------------
8.
3 3
13 ------- + 16 -------
8 4
107 67
------- + -------
8 4
107 67(2)
------- + -------
8 4(2)
107 134 241 1
------- + ------- = -------- = 30 -------
8 8 8 8
I hope this helps!
. Lin's family has completed 60% of a trip. They have traveled 30 miles
How many miles is the trip?
A 50 miles
B. 48 miles
C. 30 miles
D. 18 miles
Answer: A 50 miles
Step-by-step explanation:
Its A becuase 60%=0.6 and 0.6 times 50 is 30 which means 60 percent of 50 is 30.
“Benjamin Franklin was born in Milk Street, Boston, on January 6, 1706. His father, Josiah Franklin, was a tallow chandler [candle maker] who married twice, and of his seventeen children Benjamin was the youngest son. His schooling ended at ten, and at twelve he was bound apprentice to his brother James, a printer, who published the ‘New England Courant.’ To this journal he became a contributor, and later was for a time its nominal editor. But the brothers quarreled, and Benjamin ran away, going first to New York, and thence to Philadelphia, where he arrived in October, 1723.”
Which is the best summary of this excerpt?
Benjamin Franklin was born in 1706. He went to Philadelphia in 1723 after a fight with his brother.
Benjamin Franklin, born in Boston in 1706, was the youngest of his father’s seventeen children. He stopped going to school at age ten, and soon after started apprenticing for his brother James, a printer, who published the “New England Courant.” Franklin became a writer and editor for the paper, but left Boston for Philadelphia in 1723 after an argument with James.
Benjamin Franklin, born in 1706, lived in Boston, New York, and Philadelphia in his early life.
Benjamin Franklin was born in Boston in 1706. He was the youngest of his father’s seventeen children. His father, Josiah, was a candle maker. Franklin’s schooling ended at age ten, and at age twelve, he started apprenticing for his brother James, who published the “New England Courant.” After apprenticing, Franklin started contributing to the paper. Later, he became an editor.
Correct answer: Benjamin Franklin held different jobs at "New England Courant".
A roofer creates a price quote to repair a
roof using shingles. Which is least likely to
affect the value of the price quote?
the estimated cost of the shingles
chosen for the roof
the estimated time to lay the
shingles and underlayment
the square footage of the front yard
and backyard
the square footage of the house and
garage
Answer:
Step-by-step explanation:
the estimated time to lay the shingles and underlayment
The Estimation cost of the shingles chosen for the roof.
What is Estimation cost?Estimation cost is the process of predicting how much a project or task will cost. It is used to help make decisions about the feasibility of the project and to plan for its budget. Estimation cost is based on past experiences, the current market and expected future conditions. The accuracy of an estimate can be improved by gathering detailed information about the project and its components. This information can include the cost of materials, labor and time needed to complete the project. Estimation cost is an important part of project management and is used in combination with other project management tools and methods such as scheduling, budgeting and risk management.
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You are planning a picnic for Memorial Day. You need to buy enough hot dogs and hamburgers so that each of your 10 guests can have two servings. You determined that hot dogs cost $0.40 each and hamburgers cost $0.80 each. You have $12 to spend on the hamburgers and hot dogs. How many hot dogs and how many hamburgers should you buy?
Answer:
hamburgers cost $0.80 each
Step-by-step explanation: