Answer:
The correct next step is the answer choice
[tex]x^{2} +\frac{b}{a}x=-\frac{c}{a}[/tex]
Step-by-step explanation:
we have the quadratic equation in standard form
[tex]ax^{2}+bx+c=0[/tex]
The steps in the derivation of the quadratic formula by completing the square are
step 1
[tex]ax^{2}+bx+c=0[/tex] ----> given equation
step 2
Move the constant term over to the right-hand side
[tex]ax^{2}+bx=-c[/tex]
step 3
The leading term is multiplied by a
so
Divide by a both sides
[tex]x^{2} +\frac{b}{a}x=-\frac{c}{a}[/tex]
step 4
Multiply the linear term by 1/2
[tex]\frac{b}{a}(\frac{1}{2})=+\frac{b}{2a}[/tex]
step 5
square this derived value
[tex]+\frac{b^2}{4a^2}[/tex]
step 6
Add this squared value to either side of the equation
[tex]x^{2} +\frac{b}{a}x+\frac{b^2}{4a^2}=-\frac{c}{a}+\frac{b^2}{4a^2}[/tex]
step 7
convert to the common denominator, and combine on the right-hand side
[tex]x^{2} +\frac{b}{a}x+\frac{b^2}{4a^2}=\frac{b^2-4ac}{4a^2}[/tex]
step 8
convert the left-hand side to completed-square form
[tex](x+\frac{b}{2a})^{2}=\frac{b^2-4ac}{4a^2}[/tex]
step 9
take the square roots of either side
[tex](x+\frac{b}{2a})=(+/-)\sqrt{\frac{b^2-4ac}{4a^2}} \\\\(x+\frac{b}{2a})=(+/-)\frac{\sqrt{b^2-4ac}}{2a}[/tex]
step 10
solving for the variable
[tex]x=-\frac{b}{2a}(+/-)\frac{\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-b(+/-)\sqrt{b^2-4ac}}{2a}[/tex]
Answer:
C on edge
Step-by-step explanation:
What is the sum of 12 and 34
12+34 = 46
Please mark Brainliest if this helps!
Sum: the total of 2 or more numbers added together
12 + 34 = 46
After a snow storm, michael measured 6 7/8 inches of snow. What is this amount as a decimal????? URGENTTTTT!!
Answer:
The answer is 6.875 inches.
Step-by-step explanation:
After a snow storm, Michael measured [tex]6\frac{7}{8}[/tex] inches of snow.
We will convert this to improper fraction and then solve.
[tex]6\frac{7}{8}=\frac{55}{8}[/tex]
Now we can divide 55 by 8 to get decimal value.
This becomes 6.875 inches.
The Cooking Club made some pies to sell
at a basketball game to raise money for the
new math books. The cafeteria
contributed three pies to the sale. Each
pie was then cut into five pieces and sold.
There were a total of 40 pieces to sell.
How many pies did the club make?
Division the action of separating something into the parts. It is a basic mathematics operation. The number of pies made by the cooking club to sell at a basketball game to raise money for the new math books is 2.
Given-The cafeteria contributed three pies to the sale.
Each pie was then cut into five pieces and sold.
There were a total of 40 pieces to sell.
What is division?Division the action of separating something into the parts. It is a basic mathematics operation.
Total 40 pieces are there to sell. Each pie was cut into five pieces. Hence the total pie in 40 pieces were,
[tex]=\dfrac{40}{8}[/tex]
[tex]=5[/tex]
Thus total 5 pies was made.
Now as the cafeteria contributed three pies to the sale but we have total 5 pieces was made. For find out the number of pies made by the cooking club we have to subtract the total pies made to the pies contributed by the cafeteria.Thus the number of pies made by the cooking club,
[tex]=5-3[/tex]
[tex]=2[/tex]
Hence the number of pies made by the cooking club to sell at a basketball game to raise money for the new math books is 2.
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Find the volume of the earth if the diameter is 7917.5 miles.
Final answer:
The volume of the earth is approximately 1.0839 x 10¹⁵ cubic miles.
Explanation:
To find the volume of the earth, we can use the formula for the volume of a sphere: V = (4/3)πr³. Since we are given the diameter of the earth, we can calculate the radius by dividing the diameter by 2. In this case, the diameter is 7917.5 miles, so the radius is 3958.75 miles. Now, we can substitute the radius into the formula to find the volume:
V = (4/3)π(3958.75 miles)³
V ≈ 1.0839 x 10¹⁵ cubic miles.
Please help. Answer with method please, thanks a lot
Answer:
62.83 m²
Step-by-step explanation:
The area of the path is calculated as
area of outside circle - area of reservoir
= πr₁² - πr₂²
where r₁ is the radius of the outer circle and r₂ the radius of the reservoir
diameter of reservoir = 8 m, hence radius = 4 m
radius of outer circle = radius of reservoir + width of path = 4 + 2 = 6 m, thus
area of path = π × 6² - π × 4² = 36π - 16π = 20π ≈ 62.83 m²
Two planes , which are 2445 miles apart fly toward each other. Their speed differ by 65mph. If they pass each other in 3 hours , what is the speed of each?
The speed of each planes are 375 mph and 415 mph.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now,
Let x be the speed of the slower plane, in mph.
Then, the speed of the other plane is x +40 mph.
Hence, The distance between two planes decreases at the rate;
⇒ x + (x+40)
⇒ 2x + 40 mph.
So, we can write equation as;
⇒ 3950 / (2x+40) = 5
⇒ 3950 = 10x + 200
⇒ 10x = 3750
⇒ x = 375
Thus, The speed of the slower plane = x
= 375 mph.
And, The speed of the other plane = x +40
= 375 + 40
= 415 mph.
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Final answer:
To solve the problem, we use the concept of relative speed and set up an equation with the combined distance traveled by both planes. Solving the equation reveals that the speed of the slower plane is 375 mph and the faster plane is 440 mph.
Explanation:
The problem of two planes flying toward each other with a speed difference and meeting after a certain amount of time is a typical algebra question in relative speed and motion. We can let the slower plane's speed be x mph and the faster plane's speed be x + 65 mph. Since they meet after 3 hours and are 2445 miles apart, the sum of their distances traveled will equal 2445 miles.
Using the equation d = rt, where d denotes distance, r the rate, and t the time, we set up two expressions for the distances each plane travels:
Distance by slower plane: 3xDistance by faster plane: 3(x + 65)We then add these expressions and set the sum equal to the total distance:
3x + 3(x + 65) = 2445
Solving for x, we get:
6x + 195 = 2445
6x = 2445 - 195
6x = 2250
x = 375
Therefore, the speed of the slower plane is 375 mph and the speed of the faster plane is 375 + 65 = 440 mph.
8.
f(x) = -0.75x
find the inverse function f-1(x) for the given functions f(x)
The inverse function of f(x) = -0.75x is [tex]\(f^{-1}(x) = -\frac{4}{3}x\)[/tex].
What is the inverse of the function?To find the inverse function [tex]\( f^{-1}(x) \)[/tex]for the given function f(x) = -0.75x , you can follow these steps:
1. Start with the original function:
f(x) = -0.75x
2. Replace f(x) with y:
y = -0.75x
3. Swap x and y to solve for x:
x = -0.75y
4. Solve for y:
Divide both sides by -0.75:
[tex]\( y = \frac{x}{-0.75} )\\ \( y = -\frac{4}{3}x \)[/tex]
5. Replace y with [tex]\( f^{-1}(x) \)[/tex]:
[tex]\( f^{-1}(x) = -\frac{4}{3}x \)[/tex]
So, the inverse function for f(x) = -0.75x is [tex]\( f^{-1}(x) = -\frac{4}{3}x \)[/tex].
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Final answer:
The response provides the inverse function of f(x) = -0.75x step-by-step.
Explanation:
Given: f(x) = -0.75x
To find the inverse function f-1(x):
Replace f(x) with y: y = -0.75x
Swap x and y: x = -0.75y
Solve for y: y = x/-0.75 = -4/3x
Therefore, f-1(x) = -4/3x
Find the area of the figure. (Sides meet at right angles.)
Answer:
The area of the figure is 48 cm^2
Step-by-step explanation:
Break it into 3 different quadrilaterals and find the area of each one.
Fill in the blanks to make the statement true
2t - t +4= 0
Solving this equation will result in a [quadratic/linear]
equation that
[Can/cannot]
be solved by factoring.
Answer:
[tex]2t-t+4=0[/tex] gives me [tex]t=-4[/tex]
This is a linear equation.
Did you really mean [tex]2t-t+4=0[/tex]? I just want to make sure since you said something about a quadratic in your question.
Step-by-step explanation:
[tex]2t-t+4=0[/tex] can be simplified to [tex]t+4=0[/tex].
This is a linear equation since the exponent on all the variables we have is 1.
To solve [tex]t+4=0[/tex] for t we are going to subtract 4 on both sides:
[tex]t+4-4=0-4[/tex]
[tex]t=-4[/tex]
The sum of 8 times a number and 6 is equal to 7 times the number
Answer:
8x + 6 = 7x
x = -6
Step-by-step explanation:
this is the solution
Which ordered pair is part of the solution set of the inequality 12 + y ≤ –3x? Question 11 options: a) (3, –16) b) (4, –1) c) (–16, 3) d) (1, 4)
Answer:
C (-16, 3)
Step-by-step explanation:
[tex] 12 + 3 \leqslant - 3 \times - 16 \\ 15 \leqslant 48[/tex]
replace x and y
Answer:
c) (-16,3)
Step-by-step explanation:
Given: inequality [tex]12+\text{y}\leq -3\text{x}[/tex]
To Find: Which ordered pair is part of the solution set of the inequality
Solution:
Simplifying inequality,
[tex]12+\text{y}\leq -3\text{x}[/tex]
[tex]12}\leq -3\text{x}-\text{y[/tex]
now,
putting ordered pairs from options
a) [tex](3,-16)[/tex]
[tex]-3\times3-(-16)[/tex][tex]16-9=7[/tex]
as [tex]7<12[/tex], it does not satisfy inequality
b) [tex](4,-1)[/tex]
[tex]-3\times4-(-1)[/tex][tex]1-12=-11[/tex]
as [tex]-11<12[/tex], it does not satisfy inequality
c) [tex](-16,3)[/tex]
[tex]-3\times(-16)-(3)[/tex][tex]48-3=45[/tex]
as [tex]45>12[/tex], it satisfy inequality
d) [tex](1,4)[/tex]
[tex]-3\times1-(4)[/tex][tex]-3-4=-7[/tex]
as [tex]-7<12[/tex], it does not satisfy inequality
So, from above only option c is part of the solution set of inequality.
math help owo pls will reword #_# pleath
Question 13: The answer is D
Question 7: The answer is C
Question 14: The answer is B
And the question for the last Pic, the correct graph is B.
Answer:
d
c
b
b
Step-by-step explanation:
at 2 P.M the level of the water in the pool was 10 feet. At 6 P.M the level of water was 2 feet. Find the constant rate of change of the water.
#43. find (e). also please explain it.
Evaluate 4(3 - 1)2
ОА. 32
Ов. 64
Ос. 16
Op. 128
In order to get this answer you will have to use PEMDAS and solve the expression step by step.
[tex]4(3-1)2[/tex]
Using PEMDAS:
[tex]3-1=2[/tex]
[tex]4\times2\times2[/tex]
[tex]2\times4=8[/tex]
[tex]8\times2[/tex]
[tex]8\times2=16[/tex]
[tex]=16[/tex]
Therefore your answer is option C "16."
Hope this helps.
Answer:
C. 16
Step-by-step explanation:
basically the order of operations states you deal with parentheses first then indices then either division/multiplication and then addition/subtraction
So when you deal with 3- 1=2
the only operation left is multiplication(something in parenthesis stuck on another mathematical term without any other operation attached to it signals multiplication and it is commutative so it can be done in any pair. so u have 4×2×2=16
What is the product? -4 x [8 -1 -5 9]
To obtain the product, each element in the expression [tex]\([8, -1, -5, 9]\)[/tex] is multiplied by -4, resulting in [tex]\([-32, 4, 20, -36]\).[/tex]
To find the product of -4 and the expression [tex]\([8, -1, -5, 9]\),[/tex] we multiply each element in the expression by -4.
This involves multiplying -4 by 8, -1, -5, and 9 individually.
The result of these multiplications is [tex]\([-32, 4, 20, -36]\).[/tex]
In other words, each element in the original expression is multiplied by -4 to obtain the corresponding element in the product.
This operation is a scalar multiplication, where a single number (in this case, -4) is multiplied by each element of a vector or array.
Scalar multiplication is a fundamental operation in linear algebra and is used to scale vectors or matrices by a constant factor.
In this context, multiplying the expression by -4 changes the magnitude of each element by a factor of 4 while preserving their relative positions within the array.
Seventeen less than eight times a number is equal to 11 more than six times the number.
What is the number?
Answer:
the answer is 14
Step-by-step-explanation
the first equation is 8x-17
the second one is 6x+11
do some simple calculations to find x on both and compare.
Answer:
its 14
Step-by-step explanation:
the first equation is 8x-17
the second one is 6x+11
do some simple calculations to find x on both and compare.
just did it on a Quiz i hop this helped :D
7(5t - 4) – (2 +15t) < 60
Answer:
Step-by-step explanation:
Pls help :) it would mean a lot
Answer:
17=3x+2 x=5
Step-by-step explanation:
3x+2=17
3x=17-2
x=15/3
x=5
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what is the answer to this product 7 6/7 plus 14/21
Answer:
Exact Form: 179/21
Decimal Form: 8.523809
Mixed Number Form: 8 11/21
Step-by-step explanation:
Convert the mixed numbers to improper fractions, then find the LCD and combine.
What is the distance between the points (2,7) and (-2,7)
0 is the correct answer i dont know anything
Identify the x-intercept.
1) y= 1/5x + 3
2) y= 6x - 7
3) y= -8/3x + 9
What is the y-intercept of y=5?
The y-intercept of the line y = 5 is given as: 5
How to find the y-intercept?The general form of the equation of the line in slope intercept form is expressed as:
y = mx + c
where:
m is slope
c is y-intercept
Now, we are told that the equation is y = 5
This tells us that the y-intercept is 5
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21. (4pts) Please answer in a complete sentence in Spanish.
¿Te gusta jugar videojuegos?
22. (4pts) Please write your answer in a complete sentence in Spanish using the vocabulary from your course. List at least 2 activities from our course to answer the question.
¿Qué te gusta hacer?
23. (4pts) Answer the following question in a complete sentence in Spanish. List at least 2 activities from our course to answer the question.
¿Qué no te gusta hacer?
24. (4pts) Using your course vocabulary what are two ways to agree with someone in Spanish? Hint: These are the ways to say “Me too” and “Me either” in Spanish.
25. (4pts) Answer the following question in a complete sentence in Spanish.
¿Qué te gusta más, esquiar o nadar?
This answer provides complete sentences in Spanish to answer the questions, along with examples of activities and ways to agree in Spanish.
Explanation:21. Sí, me gusta jugar videojuegos. (Yes, I like playing video games.)
22. Me gusta leer y practicar deportes. (I like reading and practicing sports.)
23. No me gusta hacer ejercicio y estudiar matemáticas. (I don't like exercising and studying math.)
24. Dos formas de estar de acuerdo en español son: 1) A mí también, 2) Yo tampoco. (Two ways to agree in Spanish are: 1) Me too, 2) Me either.)
25. Me gusta más nadar que esquiar. (I like swimming more than skiing.)
Learn more about Spanishhttps://brainly.com/question/32661884#SPJ1248 less than 4 times a number is equal to the number
Answer:
Step-by-step explanation:
4x - 48 = x there is the equation
Answer:
x = 48/5
Step-by-step explanation:
Let x = number, then:
[tex]48 - 4x = x[/tex]
By adding 4x on each side:
[tex] 48 - 4x + 4x = x + 4x[/tex], which is [tex] 48 = 5x [/tex]
Then, divide by 5 on both sides:
[tex]\frac{48}{5} = \frac{5x}{5}[/tex]
Simplifying x = 48 / 5
Intr-o clasa sunt 27 de elevi. Daca din clasa ar pleca 3 fete si 4 baieti atunci numarul fetelor ar fii egal cu triplul nr. baietiilor. Cati baieti sunt in casa
The number of boys in class is 9.
How to determine the number of boys in classLet the number of boy = b and girls = g
We can create the following equations from the parameters
b + g = 27 ____(1)
g - 3 = 3(b - 4) ___ (2)
From (1)
g = 27 - b ___(3)
Substitute (3) into (2)
27 - b - 3 = 3(b - 4)
24 - b = 3b - 12
collect like terms
-b - 3b = -12 - 24
-4b = -36
b = 9
Hence, the number of boys is 9
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one positive number is 2 more than another. The sum of their squares is 34. Find the smaller number.
Answer:
the numbers are 3 and 5
Step-by-step explanation:
x = first number
y = second number
a. x+2 = y
b. x^2 + y^2 = 34
Replace y from equation a into equation b:
x^2 + (x+2)^2 = 34
Expand it
x^2 + x^2 + 4x + 4 = 34
2*x^2 + 4x = 30
2x^2 + 4x - 30=0
solving x:
x = -5 and x =3 , it says it is a positive number, then it is x is 3
and the second number, y = x + 2
y = 5
Lets test it!
3^2 + 5^ 2 = 9 + 25 = 34
solve for c: E=mc^2
Answer: E=mc^2
E/m=c^2
Square root of e/m = c
C = square root symbol e/m
Yw :)
What’s 8/15 divided by 4/5
Answer: 2/3
Step-by-step explanation: In this problem, we have 8/15 ÷ 4/5. Dividing by a fraction is the same as multiplying by its reciprocal. In other words, we can change the division sign to multiplication and flip the second fraction.
8/15 ÷ 4/5 can be rewritten as 8/15 × 5/4
Now, we are simply multiplying fractions so we multiply across the numerators and multiply across the denominators.
8/15 × 5/4 = 40/60 = 2/3
1. Laura gave the clerk $20 for purchases of a
$4.25 notebook and a $3.59 set of markers.
How much change did she receive?
A $12.16
B $12.26
© $13.16
D $13.26
Answer:
A
Step-by-step explanation:
1. 3.59 + 4.25 =7.84
2. 20.00 - 7.84 =12.16