Answer:
[tex](a)\ y = 4\ or\ y = -\frac{1}{2}[/tex]
[tex](b)\ x = 2 \ or\ x = -\frac{1}{4}[/tex]
Step-by-step explanation:
Solving (a)
[tex]2y^2 - 7y - 4 = 0[/tex]
Expand
[tex]2y^2 +y - 8y - 4 = 0[/tex]
Expand
[tex]y(2y + 1) -4(2y + 1) = 0[/tex]
Factor out 2y + 1
[tex](y -4)(2y + 1) = 0[/tex]
Split
[tex]y - 4 =0\ or\ 2y + 1 = 0[/tex]
Solve:
[tex]y = 4\ or\ y = -\frac{1}{2}[/tex]
Solving (b):
[tex]2(2x)^2 - 7(2x) - 4 = 0[/tex]
Compare the above with the equation in (a)
[tex]2y^2 - 7y - 4 = 0[/tex]
We have:
[tex]2x = y[/tex]
So:
[tex]2x = 4 \ or\ 2x = -\frac{1}{2}[/tex]
Solve for x in both cases
[tex]x = 2 \ or\ x = -\frac{1}{4}[/tex]
If < A and < B are a linear pair, and < A = 68 °, then < B = _____.
Select one:
a. 68 °
b. 112 °
c. 101 °
d. 90 °
Answer:
Option b, 112°
Step-by-step explanation:
<A+<B=180
or, 68+<B=180
or, <B=112
Answered by GAUTHMATH
Between the numbers 15/20 and 35/40 , the greater number is
a. 15/20 b. 20/15 c. 35/40 d. 45/30
Answer:
35/40
Step-by-step explanation:
To compare, both denominator should be same.
[tex]\frac{15}{20}=\frac{15*2}{20*2}=\frac{30}{40}\\\\\\\frac{30}{40} \ < \ \frac{35}{40}\\\\\\\frac{15}{20} \ < \ \frac{35}{40}[/tex]
[tex]\sf{\bold{\blue{\underline{\underline{Given}}}}}[/tex]
⠀the numbers 15/20 and 35/40⠀⠀⠀[tex]\sf{\bold{\red{\underline{\underline{To\:Find}}}}}[/tex]
⠀⠀⠀⠀
the greater number is[tex]\sf{\bold{\purple{\underline{\underline{Solution}}}}}[/tex]
we have to find the greater number between 15/20 and 35/40
To do this,
we have to compare the denominator same.
[tex]\sf{\dfrac{35}{40}=\dfrac{35×1}{40×1}=\dfrac{35}{40} }[/tex] [tex]\sf{\dfrac{15}{20}=\dfrac{15×2}{20×2}=\dfrac{30}{40} }[/tex]According to the question,
we have to find the greatest one
[tex]\sf{\dfrac{35}{40} > \dfrac{30}{40} }[/tex] [tex]\sf{\dfrac{35}{40}>\dfrac{15}{20} }[/tex][tex]\sf{\bold{\green{\underline{\underline{Answer}}}}}[/tex]
⠀⠀
[tex]\therefore\mathrm{\dfrac{35}{40} > \dfrac{15}{20} }[/tex]
⠀⠀
a right triangle has a leg of length 13 and a hypotnuse of length 41 yards. find the length of the other leg (nearest tenth)
Use slope to determine if lines AB and CD are parallel, perpendicular, or neither. A(0,2), B(5,4), C(1,8), and D(3,3). What is the slope of line CD? Enter as a ratio in its lowest terms.
Answer:
Perpendicular, CD has a slope of -5/2
Step-by-step explanation:
Parallel lines have the same slope, perpendicular have slopes that are negative reciprocals, or in other words if one slope is m then the other's slope is -1/m and if it is neither fo those then it is neither parallel or perpendicular. Also, if two lines have the same slope you have to make sure they are not the same line.
Now, to find the slope when you have two points you use the formula (y2 - y1)/(x2 - x1), where the points are (x1, y1) and (x2, y2). You can make either point point 1 or point 2. Just make sure x1 and y1 are from one point and x2 and y2 are from the other point.
So the two lines are AB and CD. Since the question asks I will start with CD. The points are (1,8) and (3,3) So I will call C point 1 and D point 2.
(y2 - y1)/(x2 - x1)
(3 - 8)/(3 - 1)
-5/2
Thankfully this is lowest terms.
Now for AB. A will be point 1 and B will be point 2
(y2 - y1)/(x2 - x1)
(4-2)/(5-0)
2/5
So they are not the same, so what if you take negative 1 over one of the slopes.
well. -1/(2/5) = -5/2
So these are perpendicular.
If you would like an explanation for how to find the full equation of a line I can explain that.
A) { -3 , -1 , 1, 3 , 6 }
B) { 3, -1 , 2, 0, -2}
C) all real numbers
D) {3,-2,-1,0,1,2,3,4,5,6,7,8}
The quadratic function f has a vertex at (3,4) and opens upward. The quadratic function g is shown below. Which statement is true? A. The minimum value of g is greater than the minimum value of f. B. The maximum value of g is greater than the maximum value of f. C. The minimum value of f is greater than the minimum value of g. D. The maximum value of f is greater than the maximum value of g.
Answer:
The minimum value of f(x) is greater than the minimum value of g(x).
Step-by-step explanation:
Given
[tex](h_1,k_1) = (3,4)[/tex] --- vertex of f(x)
[tex]g(x) = 4(x - 4)^2 + 3[/tex] --- g(x) equation
Required
Which of the options is true
First, we identify the vertex of g(x)
A quadratic function is represented as:
[tex]g(x) =a(x - h)^2 + k[/tex]
Where:
[tex](h,k) \to[/tex] vertex
So, we have:
[tex](h_2,k_2) = (4,3)[/tex]
[tex]a = 4[/tex]
If [tex]a>0[/tex], then the curve opens upward
From the question, we understand that f(x) also open upward. This means that both functions have a minimum
The minimum is the y (or k) coordinate
So, we have:
[tex](h_1,k_1) = (3,4)[/tex] --- vertex of f(x)
[tex](h_2,k_2) = (4,3)[/tex] --- vertex of g(x)
The minimum of both are:
[tex]Minimum = 4[/tex] ---- f(x)
[tex]Minimum = 3[/tex] ---- g(x)
By comparison:
[tex]4 > 3[/tex]
Hence, f(x) has a greater minimum
Answer:
The minimum value of f(x) is greater than the minimum value of g(x).
Step-by-step explanation:
On the last math test in Kenzie’s class, 17 out of 25 students scored an 80 or higher. Which percent is closest to the experimental probability that a student selected at random will score an 80 or higher on the next test?
Answer
There is a 68 percent that a student selected a random will score an 80 or higher on the next test.
Explanation
You just need to find the percentage of 17 out of 25, or 17/25.
You can do this by dividing 17 by 25.
17/25 equals 0.68, or 68 percent.
If f(a) is an exponential function where f(-3) = 18 and f(1) = 59, then find the
value of f(0), to the nearest hundredth.
Given:
For en exponential function f(a):
[tex]f(-3)=18[/tex]
[tex]f(1)=59[/tex]
To find:
The value of f(0).
Solution:
The general form of an exponential function is:
[tex]f(x)=ab^x[/tex] ...(i)
Where, a is the initial value and b is the growth/ decay factor.
We have, [tex]f(-3)=18[/tex]. Substitute [tex]x=-3,f(x)=18[/tex] in (i).
[tex]18=ab^{-3}[/tex] ...(ii)
We have, [tex]f(1)=59[/tex]. Substitute [tex]x=1,f(x)=59[/tex] in (i).
[tex]59=ab^{1}[/tex] ...(iii)
On dividing (iii) by (ii), we get
[tex]\dfrac{59}{18}=\dfrac{ab^{1}}{ab^{-3}}[/tex]
[tex]3.278=b^{1-(-3)}[/tex]
[tex]3.278=b^{4}[/tex]
[tex](3.278)^{\frac{1}{4}}=b[/tex]
[tex]1.346=b[/tex]
Substituting the value of b in (iii).
[tex]59=a(1.346)^1[/tex]
[tex]\dfrac{59}{1.346}=a[/tex]
[tex]43.83358=a[/tex]
[tex]a\approx 43.83[/tex]
The initial value of the function is 43.83. It means, [tex]f(0)=43.83[/tex].
Therefore, the value of f(0) is 43.83.
1 + 3 + 4 = 4 + 3 + 1. What property is being described here?
Associative Property of Addition
Commutative Property of Addition
Associative Property of Multiplication
Answer: Commutative property of addition
Step-by-step explanation:
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\text{1 + 3 + 4 = 4 + 3 + 1}[/tex]
[tex]\large\text{1 + 3 + 4}[/tex]
[tex]\large\text{4 + 4}[/tex]
[tex]\large\text{= \bf 8}[/tex]
[tex]\large\text{4 + 3 + 1}[/tex]
[tex]\large\text{7 + 1}[/tex]
[tex]\large\text{= \bf 8}[/tex]
[tex]\large\text{\bf 8 = 8}[/tex]
[tex]\large\textsf{We could remove Option C. because there’s no sign of multiplication.}[/tex]
[tex]\large\textsf{This leaves us to Option A and Option B because the equation(s) has}\\\large\textsf{sum/addition}[/tex]
[tex]\large\textsf{Associative Property of Addition formula is:}[/tex]
[tex]\bullet\large\text{ \bf (a + b) + c = a + (b + c)}[/tex]
[tex]\large\textsf{Commutative Property of Addition formula is:}[/tex]
[tex]\bullet\large\text{ \ \bf a + b = b + a}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \huge \bf Commutative Property of Addition}}}\\\boxed{\huge\textsf{(Option B.)}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
the width of a newspaper is 13 3/4 inches. The left margin is 7/16 inch and the right margin is 1/2 inch. what is the width of the written page inside the margin?
Answer:
biggafigure a
mnn
Step-by-step explanation:
Match each percent with the fraction or decimal equivalent. 5% 0.25 15% 0.07 6.5% 1 20 25% 0.065 7% 3/20
Answer:
5% = 1/20
15% = 3/20
6.5% = 0.065
25% = 0.25
7% = 0.07
Step-by-step explanation:
I hope this helps! Just ask me if you have any questions.
Have a nice dayy! :)
Answer:
.05 25% .15 7% .065 100% 2000% .25
Step-by-step explanation:
Percentages to decimals :
example
5% = .05
First remove the % sign: 5
Where is the decimal? Here : 5.00
Now move the decimal to the left two places. Fill the gaps with zeros : .05
Another way to do it is by divide the number by 100. Use a calculator if necessary.
Example 2: 6.5%
Move decimal two places to left: .065
Example 3: .56%
Move decimal to places to the left: .0056
Decimals to percentages. Do the exact opposite. Move decimal to places to the right then add the % sign.
Example: .25 becomes 25%
.07 becomes 07% or just 7%
Use the initial term and the recursive formula to find an explicit formula for the sequence an. Write your answer in simplest form.
Answer:
[tex]a_n = -11-14n[/tex]
Step-by-step explanation:
Given
[tex]a_1 = -25[/tex]
[tex]a_n = a_{n-1}-14[/tex]
Required
The explicit formula
First, calculate [tex]a_2[/tex]
Set n=2; So:
[tex]a_2 = a_{2-1}-14[/tex]
[tex]a_2 = a_{1}-14[/tex]
Substitute -25 for [tex]a_1[/tex]
[tex]a_2 = -25-14[/tex]
[tex]a_2 = -39[/tex]
Calculate the common difference (d)
[tex]d = a_2 - a_1[/tex]
[tex]d = -39 --25[/tex]
[tex]d = -14[/tex]
So, the nth term is:
[tex]a_n = a_1 + (n - 1)d[/tex]
[tex]a_n = -25+ (n - 1)*-14[/tex]
Open bracket
[tex]a_n = -25-14n + 14[/tex]
Collect like terms
[tex]a_n = 14-25-14n[/tex]
[tex]a_n = -11-14n[/tex]
What is the next term in the sequence below?
-324,108,-36,12
Answer:
-4
Step-by-step explanation:
bc it is
.......................
given g(x) = square root of x - 4 and h(x) = 2x - 8 What is g(h10))?
Step-by-step explanation:
First find h(10)
h(10)=2(10)-8
h(10)=12
Now plug in 12 as the value of x in g(x) ie.g(12)
So g(12)=√12-4=√8=2√2
When 7 times a number is decreased by 8, the answer is the same as when 3 times the number is increased by 4. Find the number.
Answer:
x=3
Step-by-step explanation:
Equation: 7x-8=3x+4
4x=12
x=3
BRAINlIEST FOR CORRECT ANSWER
Answer:
ok
Step-by-step explanation:
mark me the brainlieast since your question is incomplete
Find the measure of the angle indicated.
1
2
4
3
151°
6
8
7
The measure of angle 7 is
............................
...............................................................................................................................................................................................................................................................................................................
What do you know about the hypotenuse of triangle abc
Step-by-step explanation:
it is the longest side of the triangle and to find it we must appy a formula c square =a square + b square..thats all i know hehe
Can someone help me with this math homework please!
Answer:
First dropbox: 7h + 43 = 64
Second dropbox: $3
Step-by-step explanation:
Here's what we know about the question so far:
$43 is the initial fee
The rototiller worked for 7 hours
$64 is the total cost (including initial fee)
h = hourly fee
The answer should be 7h + 43 = 64 because:
- It includes the initial fee of $43
- It sets the equation equal to $64, which is the total cost
- The hourly fee is being multiplied with 7 hours, which is correct since the h variable is hourly (not sure how to explain this part ;w; )
For the 2nd drop box, we will use basic algebra to solve for h:
7h + 43 = 64
(subtract both sides by 43)
7h = 21
(divide both sides by 7)
h = 3
There's your 2 answers!
Hope it helps (●'◡'●)
Write using exponents. Rewrite the expression below in the same sequence.
Answer:
[tex]10^2a^2b[/tex]
Step-by-step explanation:
Exponents are a way of shortening multiplication statements. The exponent represents how many times a term is being multiplied by itself. So, when two terms have the same base it can be written with exponents. For example. 10*10 can be written as [tex]10^2[/tex] because 10 is being multiplied 2 times. Therefore, if we do this with every term you get [tex]10^2a^2b[/tex].
How do relational databases work mathematically?
Answer:
A relational database stores data in a series of tables so that the data models a mathematical theory of relations. The model allows for queries based on projection, selection, and join, among other operations, and connects the data in the tables by way of keys.
Answer:
Well, I guess in a formal sense you could call relational algebra a type of logic, which puts it into the realm of ‘math’, though I don’t think most mathematicians would look at it as being a very significant area, more ‘applied logic’ than anything else.
That being said, relational algebra DOES present some formalisms in the shape of relations, tuples, normalizations, and denormalization, etc. There is also a model of sequential operations and thus the underpinnings of the ACID database concept.
Since the overwhelming primary use of RA has been as a way to structure our ideas about SQL RDBMSes there isn’t really a lot of deep theory there. I don’t think anyone has really built any other models of RA beyond an RDBMS. There have been limited non-SQL RDBMS implementations, but AFAIK none of them are really actively maintained today.
measured the volume of an object and recorded it as 46 cubic cm
which was 15% high from the actual volume. Find the actual volume.
Answer:
[tex]40\ cm^3[/tex]
Step-by-step explanation:
Let the actual volume is V.
The measured volume of an object is 46 cubic cm which was 15% high from the actual volume.
According to the given condition,
[tex]V+\dfrac{15V}{100}=46\\\\\dfrac{115V}{100}=46\\\\V=\dfrac{4600}{115}\\\\V=40\ cm^3[/tex]
So, the actual volume was [tex]40\ cm^3[/tex].
Does anyone know the answer to this question?
Answer:
Step-by-step explanation:
Third graph because when x is greater than two the lines slants up
yeaaaaaaaaaa help plzzzzzzzzzz
Answer:
See Explanation
Step-by-step explanation:
Given
The attached graph
Required
Point on the line
The options are not given. So, I will provide general answers.
To do this, we simply write out the coordinates that lie on the line.
Some of them are:
[tex](0.5,3)[/tex]
[tex](1.25,8)[/tex]
[tex](1.5,10)[/tex]
hello can you help me with this?
Answer:
x = 25.5
Step-by-step explanation:
suppose RS and MQ are parallel the sum of angle MRS and RMN would be 180 degrees
2x + x + x 78 = 180 add like terms then subtract 78 from both sides
4x = 102 divide both sides by 4
x = 25.5
convert 0.25151 to a fraction
Answer:
25151/100000
Step-by-step explanation:
The Red Line Below is Parallel To which of the following?
A. The x-axis
B. The origin
C. the y-axis
D. None of those
Answer:
C. y axis
Step-by-step explanation:
y axis is the answer
Зу = х - 9
y = -x + 1
Using the graphing method, which of the following choices is the solution of the system?
A=(-3 ,-2)
B=(3 ,-2)
C= Infinite solutions
D= No solutions
Answer:
did i got it correct if yes follow plz
used a graphing tool to, well, graph it
see the solution in the screenshot, it's the point where the two lines intersect
CUALES SON LOS GRADOS PARA HACER UNA GRAFICA DE PASTEL, CON LOS SIGUIENTES PORCENTAJES( 20%,50%,10%)
Answer:
Lo primero que debemos saber, es que la gráfica de pastel nos permite dividir a una población, la cual sería el 100%, en porcentajes menores que representan algo.
En este caso tenemos los porcentajes 20%, 50%, 10% (notar que no suman 100%, entonces nos falta algún porcentaje)
Bueno, como sabemos el gráfico (el cual es un círculo) representa el 100%.
Y en un círculo, tenemos un ángulo de 360°
Entonces comenzamos con la equivalencia:
360° = 100%
Entonces, ¿a que grado corresponde el 50%? Planteamos la ecuación:
x = 50%
Si tomamos el cociente entre las ecuaciones:
x = 50% y 360° = 100%
obtenemos:
x/360° = 50%/100%
resolviendo para x, obtenemos:
x = (50%/100%)*360° = 0.5*360° = 180°
Para los otros porcentajes hacemos lo mismo.
Para el de 20% tenemos:
y = 20%
planteamos la ecuación:
y/360° = 20%/100%
y = 0.2*360° = 72°
Finalmente, para el de 10% tendremos:
z = 10%
planteando la ecuación como antes:
z/360° = 10%/100%
z = 0.1*360 = 36°
Asi, hemos encontrado los grados correspondientes para cada porcentaje.
Select the correct product. (x^2+4)(x^2-4)
1. X^4-16
2. X^4+16
3. X^2+8x+16
4. X^2-8x-16
Answer:
[tex] ({x}^{2} + 4 )( {x}^{2} - 4) \\ 1)( {x}^{2} - 16) \\ = (x - 4)(x + 4) \\ 2)( {x}^{2} + 16) \\ = (x - 4)(x + 4) \\ 3) {x}^{2} + 8x + 16 \\ {x}^{2} + (4 + 4)x + 16 \\ {x}^{2} + 4x + 4x + 16 \\ x(x + 4) + 4(x + 4) \\ (x + 4)(x + 4) \\ 4) {x}^{2} - 8x - 16 \\ {x}^{2} - (4 + 4)x - 16 \\ {x}^{2} - 4x + 4x - 16 \\ x(x - 4) + 4(x - 4) \\ (x - 4)(x + 4)[/tex]
