[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$8000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, then fifty two} \end{array}\dotfill &52\\ t=years\dotfill &6 \end{cases}[/tex]
[tex]\bf A=8000\left(1+\frac{0.055}{52}\right)^{52\cdot 6}\implies A\approx 8000(1.00106)^{312}\implies A\approx 11133.81[/tex]
Mark's account balance after six years is $ 11126.
What is compound interest?The term compound interest refers to the interest that accrues both on the principal and on the interest.
P = $8,000
r = 5.5% or 0.055
t = 6 years
n = 52 times
Hence;
A = 8,000(1 + 0.055/52)^(6 × 52)
A =$ 11126
Learn more about compound interest: https://brainly.com/question/731147?
Which of the following lists of ordered pairs is a function
Answer:
A
Step-by-step explanation:
A function can't have the same number more than once, so the answer is A since there are no repeating numbers.
Audrey has .x pounds of red grapes and y pounds of
green grapes. She has less than 5 pounds of grapes in
Which are reasonable solutions for this situation?
Check all that apply.
(-1,2)
(1.3.5)
(2, 2)
(4.5, 0.5)
(5,0)
Answer: (1,3,5) & (2,2)
Step-by-step explanation:
Tina's favorite shade of teal is made with 7 ounces of blue paint for every 5 ounces of green paint. Tyler's favorite shade of teal is made with 5 ounces of blue paint for every 7 ounces of green paint.
How does Tina's favorite shade of teal compare to Tyler's shade of teal?
A. Tina's favorite shade is more blue than Tyler's
B. Tina's favorite shade is greener than Tyler's
C. The two colors are the same
Answer:
A. Tina's favorite shade is more blue than Tyler's
Answer: The correct option is
(A) Tina's favorite shade is more blue than Tyler's.
Step-by-step explanation: Given that Tina's favorite shade of teal is made with 7 ounces of blue paint for every 5 ounces of green paint.
Tyler's favorite shade of teal is made with 5 ounces of blue paint for every 7 ounces of green paint.
We are to find how Tina's favorite shade of teal compare to Tyler's shade of teal.
The fraction of blue paint in Tina's favorite shade of teal is given by
[tex]F_{ti}=\dfrac{7}{7+5}=\dfrac{7}{12}[/tex]
and the fraction of blue paint in Tyler's favorite shade of teal is given by
[tex]F_{ty}=\dfrac{5}{7+5}=\dfrac{5}{12}[/tex]
We get
[tex]F_{ti}-F_{ty}=\dfrac{7}{12}-\dfrac{5}{12}=\dfrac{2}{12}=\dfrac{1}{6}>0\\\\\\\Rightarrow F_{ti}>F_{ty}.[/tex]
That is, the fraction of blue paint in Tina's favorite shade is more than the fraction of blue paint in Tyler's favorite shade.
Thus, Tina's favorite shade is more blue than Tyler's.
(A) is the correct option.
10 points for this! btw it’s really easy to some people so yea
Answer:
C
step-by-step explanation:
you just have to subtract them 9/16-1/4=8/12
Let y = safe load in pounds and x = length in feet of a horizontal beam. A constant of proportionality k exists such that Y=k/x If a beam can hold 2,000 pounds at 15 feet, what is the safe load if the length of the beam is 10 feet?
Answers: 300 pounds, 3,000 pounds, 20,000 pounds
Answer:
3000 pounds
Step-by-step explanation:
first sub in info to find k
2000=k/15 ; multiply both sides by 15 ; k=30000. if k is the constant, then to find the safe load (y) with the new beam (x), we input our new info into the equation.
y=30000/10 ; y=3000
Answer:
Safe load of the beam is 3000 pounds.
Step-by-step explanation:
If a horizontal beam of x feet length can hold y pounds safe load, the expression that represents the relation between load and length of the beam is
y = [tex]\frac{k}{x}[/tex]
If y = 2000 pounds and x = 15 feet
then 2000 = [tex]\frac{k}{15}[/tex]
k = 15×2000 = 30000
Now we will calculate the safe load when beam is 10 feet long.
From the formula,
y = [tex]\frac{30000}{10}=3000[/tex] pounds
Therefore, safe load of the beam is 3000 pounds.
what is the area of a rectangle that is 3/5 of a meter long and 7/12 of a meter long
Answer:
7/20 m^2
Step-by-step explanation:
A = l*w
=3/5 * 7/12
Multiplying the numerators
3*7 =21
Multiplying the denominators
5*12= 60
Putting the numerator over the denominator
21/60
Divide the top and bottom by 3
7/20
Answer:
7/20
Step-by-step explanation:
Which functions has the graph shown?
Answer:
C.
Step-by-step explanation:
Let's identify some points here that are on the graph:
(0,0), (pi/2,-1), (pi,0).
Let's see if this is enough.
We want to see which equation holds for these points.
Let's try A.
(0,0)?
y=cos(x-pi/2)
0=cos(0-pi/2)
0=cos(-pi/2)
0=0 is true so (0,0) is on A.
(pi/2,-1)?
y=cos(x-pi/2)
-1=cos(pi/2-pi/2)
-1=cos(0)
-1=1 is false so (pi/2,-1) is not on A.
The answer is not A.
Let's try B.
(0,0)?
y=cos(x)
0=cos(0)
0=1 is false so (0,0) is not on B.
The answer is not B.
Let's try C.
(0,0)?
y=sin(-x)
0=sin(-0)
0=sin(0)
0=0 is true so (0,0) is on C.
(pi/2,-1)?
y=sin(-x)
-1=sin(-pi/2)
-1=-1 is true so (pi/2,-1) is on C.
(pi,0)?
y=sin(-x)
0=sin(-pi)
0=0 is true so (pi,0) is on C.
So far C is winning!
Let's try D.
(0,0)?
y=-cos(x)
0=-cos(0)
0=-(1)
0=-1 is not true so (0,0) is not on D.
So D is wrong.
Okay if you do look at the curve it does appear to be a reflection of the sine function.
identify the transformation taking place in this function. y = x^2 +8. a. translation down 8 units. b. translation left 8 units. c. translation right four units. d. translation up 8 units.
Answer:
D. if we are describing how to get from y=x^2 to y=x^2+8.
Step-by-step explanation:
If we are describing how to get from y=x^2 to y=x^2+8, then the transformation is just a translation of 8 units up.
If the equation was y=x^2-8, it would have been down 8 units.
If the equation was y=(x-8)^2, it would have been right 8 units.
If the equation was y=(x+8)^2, it would have been left 8 units.
Which statements about the graph of the function Fx=-x2-4x+2 are true check all that apply
Step-by-step explanation:
Just graph it and see if the descriptions fit the graph
(see attached)
A. We can see from the graph that the possible x-values are -∞ ≤ x ≤ +∞ . Hence limiting to domain to x≤ -2 this is obviously not true.
B. We can see from the graph that the vertex is y = 6 and that the entirety of the graph is under this point, hence range y<6 is true
C. We can see that the vertex is located at x=-2. Every part of the graph to the left of this point has a positive slope, hence the function is increasing for negative infinity to this point x=-2 is true
D) We can see that for the interval -4<x<∞, the graph actually increases between -4<x<-2, and then decreases after that. Hence this statement is not true.
E. it is obvious that the y intercept is y=2 which is positive. Hence this is true.
The graph of F(x)=-x^2-4x+2 is a downward-opening parabola with its vertex serving as the local and global maximum. There are no asymptotes for this quadratic function. The shape of the graph is best understood by examining its behavior over a range of x-values and by sketching it with the vertex and axis of symmetry.
The graph of the function F(x) = -x^2 - 4x + 2 represents a parabola opening downward because the coefficient of x^2 is negative. To understand the nature of the graph, we evaluate its characteristics by identifying the vertex, the axis of symmetry, and whether it has local or global extrema. The vertex of this parabola can be found using the formula -b/2a, which gives us the x-coordinate, and by substituting that back into the function for the y-coordinate. The axis of symmetry will be a vertical line passing through the vertex's x-coordinate.
Since this is a quadratic function, it does not have asymptotes because it extends indefinitely in both the positive and negative directions of the y-axis. Instead, the parabola will have a maximum point at the vertex, which is a local and global maximum because the parabola opens downward. Moreover, we should evaluate the function for a range of x-values to understand its behavior for large negative x, small negative x, small positive x, and large positive x.
Sketching the graph of this function would involve plotting the vertex, drawing the axis of symmetry, and selecting a few points around the vertex to determine the shape of the parabola.
2 + (-2 + 23) – Ӏ 8 - 9 Ӏ =
Answer:
Step-by-step explanation:
2+(-2+23)-/8-9/=
2+ 21- /-1/=
2+21-1=
2+20=
22
Please mark as brianliest! Hope this helps!
Answer:
Solution of the expression is 22.
Step-by-step explanation:
The given expression is 2 + (-2 + 23) – Ӏ 8 - 9 Ӏ
We have to solve this expression
2 + (-2 + 23) - | 8-9 |
= 2 + (21) - |-1 |
= 2 + 21 - 1 [Since absolute value of (-x) is x or |-x | = x ]
= 23 - 1
= 22
Solution of the expression is 22.
If sin A = 3/5 and the cosA =4/5 then what is tan A
Answer:
Tan A = 3/4
Step-by-step explanation:
sin A = y/r
Cos A = x/r
Tan A = y/x
Answer:
3/4
Step-by-step explanation:
sin A = 3/5
cosA =4/5
We know that tan A = sin A / cos A
= 3/5 / 4/5
= 3/5 * 5/4
= 3/4
The graph below shows a system of equations: Draw a line labeled y equals minus x plus 5 by joining the ordered pairs 0, 5 and 5, 0. Draw a line labeled y equals x minus 1 The x-coordinate of the solution to the system of equations is ___ . (5 points)
Answer:
The x-coordinate of the solution is x=3
Step-by-step explanation:
we have
[tex]y=-x+5[/tex] ------> equation A
[tex]y=x-1[/tex] ------> equation B
Solve the system of equations by substitution
Substitute equation B in equation A and solve for x
[tex]x-1=-x+5[/tex]
[tex]x+x=5+1[/tex]
[tex]2x=6[/tex]
[tex]x=3[/tex]
Find the value of y
[tex]y=x-1[/tex] ------> [tex]y=3-1=2[/tex]
The solution of the system of equations is the point (3,2)
therefore
The x-coordinate of the solution is x=3
Answer:
x = 3
Step-by-step explanation:
i did the same test and got it right
(07.03 MC)
Choose the correct simplification of the expression (3xy4)2(y2)3.
6x2y14
9x2y14
9x3y11
6x3y11
Answer:
9x²y¹⁴
Step-by-step explanation:
[tex]\tt (3xy^4)^2(y^2)^3\\\\=3^2x^2y^{4\cdot2}\cdot y^{2\cdot3}\\\\=9x^2y^{8}\cdot y^{6}\\\\= 9x^2y^{8+6}\\\\= 9x^2y^{14}[/tex]
How do you solve 0.3r = 2.1
I know the answer I just need to show my work
Answer:
7
Step-by-step explanation:
0.3r = 2.1
r = 2.1 ÷ 0.3
r = 7
A bank features a savings account that has an annual percentage rate of r=5.2% with interest compounded quarterly. Marcus deposits $8,500 into the account.
The account balance can be modeled by the exponential formula S(t)=P(1+rn)^nt, where S is the future value, P is the present value, r is the annual percentage rate written as a decimal, n is the number of times each year that the interest is compounded, and t is the time in years.
(A) What values should be used for P, r, and n?
P= _____ , r=______ , n=________
(B) How much money will Marcus have in the account in 7 years?
Answer = $______ .
Round answer to the nearest penny.
Answer:
Part A)
[tex]P=\$8,500\\ r=0.052\\n=4[/tex]
Part B) [tex]S(7)=\$12,203.47[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]S(t)=P(1+\frac{r}{n})^{nt}[/tex]
where
S is the Future Value
P is the Present Value
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
Part A)
in this problem we have
[tex]P=\$8,500\\ r=5.2\%=5.2/100=0.052\\n=4[/tex]
Part B) How much money will Marcus have in the account in 7 years?
we have
[tex]t=7\ years\\ P=\$8,500\\ r=0.052\\n=4[/tex]
substitute in the formula above
[tex]S(7)=8,500(1+\frac{0.052}{4})^{4*7}[/tex]
[tex]S(7)=8,500(1.013)^{28}[/tex]
[tex]S(7)=\$12,203.47[/tex]
In this problem, we find that Marcus should use the values P = $8,500, r = 0.052 and n = 4 for the given savings account. After calculating, we conclude that Marcus would have approximately $11,713.69 in the account after 7 years.
Explanation:This problem involves the concept of compound interest in mathematics. Let's break it down:
For part (A), we are given that the initial deposit or the present value P is $8,500, the annual percentage rate, r, is 5.2% (but for the formula we need to use this as a decimal, so divide by 100: r = 0.052), and the interest is compounded quarterly, or 4 times a year so n = 4.For part (B), we need to find out the future value S of the deposit after 7 years.We use the formula S(t)=P(1+rn)^(nt):
S(7) = 8500(1 + 0.052/4)^(4*7)
By calculating the above, we find the balance after seven years to be approximately $11,713.69 when rounded to the nearest penny.
Learn more about Compound Interest here:https://brainly.com/question/14295570
#SPJ3
if the translation T maps point A(-3,1) onto point A'(5,5), what is he translation T?
Answer:
< 8, 4 >
Step-by-step explanation:
Consider the coordinates
x- coordinate A - 3 → A' 5 → that is + 8
y- coordinate A 1 → A' 5 → that is + 4
Hence T = < 8, 4 >
or (x, y) → (x + 8, y + 4)
The translation T is given by:
T(x,y)=(x+8,y+4)
i.e. it shifts the point 8 units to the right and 4 units up.
Step-by-step explanation:The translation is the transformation that changes the location of points of the figure but there is no change in the shape as well as size of the original figure.
It is given that:
The translation T maps point A(-3,1) onto point A'(5,5).
so, if the translation rule that is used is:
(x,y) → (x+h,y+k)
Here
(-3,1) → (5,5)
i.e.
-3+h=5 and 1+k=5
i.e.
h=5+3 and k=5-1
i.e.
h=8 and k=4
Hence, the translation is 8 units to the right and 4 units up.
A garden has an area of 240 ft. Its length is 8 ft more than its width. What are the dimensions of the
garden?
Answer:
w=12
l=20
Step-by-step explanation:
The area can be found using the following equation:
[tex]A=lw[/tex]
Given the information provided, we are also told the following:
[tex]l=w+8[/tex]
Therefore, we can plug in our length and our area:
[tex]240=w(w+8)\\240=w^2+8w\\\\w^2+8w-240=0[/tex]
We can solve by using the quadratic formula.
[tex]w=\frac{-8+\sqrt{8^2-4(1)(-240)} }{2(1)}=12 \\\\[/tex]
w=12, so w+8=20.
Make y the subject of:
X=5y+4/2y-3
Step-by-step explanation:
I have answered ur question
To make y the subject, distribute and simplify the equation, then isolate y on one side by performing the necessary operations.
Explanation:To make y the subject of the equation X = 5y + 4/2y - 3, we need to isolate y on one side of the equation.
Distribute the 5 to both terms within the parentheses: X = 5y + 2 - 3.Combine the constants: X = 5y - 1.Move the constant term to the other side of the equation by subtracting 1 from both sides: X + 1 = 5y.Divide both sides of the equation by 5: (X + 1)/5 = y.Therefore, y = (X + 1)/5 is the solution.
Learn more about Solving for a Variable here:https://brainly.com/question/35263223
#SPJ2
can someone plz help me plz
Answer:
[tex]\large\boxed{C.\ y=2+x^4}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of linear function:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
============================
[tex]A.\\\\9y+3=0\qquad\text{subtract 3 from both sides}\\\\9y=-3\qquad\text{divide both sides by 9}\\\\y=-\dfrac{3}{9}\\\\y=-\dfrac{1}{3}\to m=0,\ b=-\dfrac{1}{3}[/tex]
[tex]B.\\\\y-4x=1\qquad\text{add}\ 4x\ \text{to both sides}\\\\y=4x+1\to m=4,\ b=1[/tex]
[tex]C.\\\\y=2+x^4\qquad\text{nonlinear, because}\ x\ \text{is in fourth power}[/tex]
[tex]D.\\\\x-2y=7\qquad\text{subtract}\ x\ \text{from both sides}\\\\-2y=-x+7\qquad\text{divide both sides by (-2)}\\\\y=\dfrac{1}{2}x-\dfrac{7}{2}\to m=\dfrac{1}{2},\ b=-\dfrac{7}{2}[/tex]
[tex]E.\\\\\dfrac{x}{y}+1=2\qquad\text{subtract 1 from both sides}\\\\\dfrac{x}{y}=1\to y=x\to m=1,\ b=0[/tex]
Today, Jana picked 15 flowers from her garden. This is 5 more than what she picked yesterday. How many flowers did Jana pick yesterday? F. 10. G. 20. H. 25. I. 30.
Answer:
F. 10
Step-by-step explanation:
She had 15 flowers today
So if she had 5 more than yesterday
You subtract the 5 to get how much she had yesterday
15-5=10
Answer:
F. 10
Step-by-step explanation:
Today: 15 flowers
: 5 more than yesterday
more than means add
15 = 5+ yesterday
Subtract 5 from each side
15-5 = 5+ yesterday -5
10 = yesterday
how many solutions does the following equation have?
13 - |3x-9| = 2
It has _____ solutions
[tex]13 - |3x-9| = 2\\|3x-9|=11\\3x-9=11\vee 3x-9=-11\\3x=20 \vee 3x=-2\\x=\dfrac{20}{3} \vee x=-\dfrac{2}{3}[/tex]
TWO
Answer:
2
Step-by-step explanation:
[tex]13-|3x-9|=2[/tex]
Subtract 13 on both sides.
[tex]-|3x-9|=2-13[/tex]
Simplify right hand side.
[tex]-|3x-9|=-11[/tex]
Take the opposite of both sides (also known as multiply both sides by -1).
[tex]|3x-9|=11[/tex].
Let u=3x-9.
Since we have |u|=positive, we will have two solutions for x.
If we had |u|=negative, we will have no solutions for x.
If we had |u|=0, we would have one solution for x.
Find the vertices and foci of the hyperbola with equation x^2/4 - y^2/60 = 1
Answer:
Vertices of hyperbola: (2,0) and (-2,0)
Foci of hyperbola: (8,0) and (-8,0)
Step-by-step explanation:
The given equation is:
[tex]\frac{x^2}{4}-\frac{y^2}{60}=1[/tex]
The standard form of equation of hyperbola is:
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]
Center of hyperbola is (h,k)
Comparing given equation with standard equation
h=0, k=0
so, Center of hyperbola is (0,0)
Vertices of Hyperbola
Vertices of hyperbola can be found as:
The first vertex can be found by adding h to a
a^2 - 4 => a=2, h=0 and k=0
So, first vertex is (h+a,k) = (2,0)
The second vertex can be found by subtracting a from h
so, second vertex is ( h-a,k) = (-2,0)
Foci of Hyperbola
Foci of hyperbola can be found as
The first focus of hyperbola can be found by adding c to h
Finding c (distance from center to focus):
[tex]c=\sqrt{a^2+b^2} \\c=\sqrt{(2)^2+(2\sqrt{15})^2}\\c=8[/tex]
So, c=8 , h=0 and k=0
The first focus is (h+c,k) = (8,0)
The second focus is (h-c,k) = (-8,0)
How do I solve this problem? Thanks!
Answer:
92
Step-by-step explanation:
87 + 91 + 92 = 270
270 / 3 = 90
alpha and beta are the zeros of the polynomial x^2 -(k +6)x +2(2k -1). Find the value of k if alpha + beta = 1/2 alpha beta(ITS URGENT)
Answer:
[tex]k=\frac{-11}{2}[/tex].
Step-by-step explanation:
We are given [tex]\alpha[/tex] and [tex]\beta[/tex] are zeros of the polynomial [tex]x^2-(k+6)x+2(2k-1)[/tex].
We want to find the value of [tex]k[/tex] if [tex]\alpha+\beta=\frac{1}{2}[/tex].
Lets use veita's formula.
By that formula we have the following equations:
[tex]\alpha+\beta=\frac{-(-(k+6))}{1}[/tex] (-b/a where the quadratic is ax^2+bx+c)
[tex]\alpha \cdot \beta=\frac{2(2k-1)}{1}[/tex] (c/a)
Let's simplify those equations:
[tex]\alpha+\beta=k+6[/tex]
[tex]\alpha \cdot \beta=4k-2[/tex]
If [tex]\alpha+\beta=k+6[/tex] and [tex]\alpha+\beta=\frac{1}{2}[/tex], then [tex]k+6=\frac{1}{2}[/tex].
Let's solve this for k:
Subtract 6 on both sides:
[tex]k=\frac{1}{2}-6[/tex]
Find a common denominator:
[tex]k=\frac{1}{2}-\frac{12}{2}[/tex]
Simplify:
[tex]k=\frac{-11}{2}[/tex].
Someone help that is good in math
For this case we have:
[tex]x <2[/tex]Represents the solution of all strict minor numbers to 2.
[tex]x \geq2[/tex] Represents the solution of all numbers greater than or equal to 2.
The solution set, according to the figure, is given by the union of [tex]x <2[/tex] and [tex]x\geq2[/tex]. Thus, the complete solution is given by all the real numbers.
Answer:
Option D
Mark is playing soccer. He is 150 yards from the center goal. When he kicks the ball it goes 145 yards at an angle of 2 degrees off to the right. How far is the ball from the goal?
Answer:
8 yards
Step-by-step explanation:
This can be illustrated from drawing it. (Attachment)
Scale- Real : Map
10 yard : 1 cm
150 yard : 15 cm
145 yard : 14.5 cm
Step 1: Draw a 7.5 cm line from origin to Point A
Step 2: Form a 2 degree angle from the origin
Step 3: Draw a 7.25 cm line 2 degree angle from the origin to Point B
Step 4: Measure the distance in cm from Point A to Point B
Step 5: Convert the distance from Point A to Point B in yards.
Therefore, the ball is 8 yards far from the goal.
!!
Answer:
The ball is 7.176 yards away from the center of the goal.
Step-by-step explanation:
Given distance between the center goal and Mark is AB = 150 yards
Distance traveled by ball at angle 2 degree off to the right from Mark is
AC = 145 yards
We have to find the distance BC in triangle ABC
Using cosine rule
[tex]BC^{2}=AB^{2}+AC^{2}-2AB\times AC\times \cos \Theta[/tex]
=>[tex]BC^{2}=[150^{2}+145^{2}-2\times 150\times 145\times \cos (2^{\circ})] yards^{2}[/tex]
=>BC^{2}=51.5 yards^{2}
=>[tex]BC=\sqrt{(51.5 yards^{2})}=7.176yards[/tex]
Thus the ball is 7.176 yards away from the center of the goal.
Trey is a car salesman who earned a base pay of $47,300 and was paid
commission of 15% for each car he sold. If x represents total sales in dollars,
then which of the following equations best represents Trey's total pay in
dollars?
Answer:
Trey earns a base pay of $47,300 plus 15% for each car sold.
The equation that represets Trey's total pay in dollars is:
y = $47,300 + 0.15x
Where $47,300 represents the base pay, and 0.15x represents the money he earn for the total cars sold.
Answer:
[tex]y=47,300+0.15x[/tex]
Step-by-step explanation:
Let x represent total sales in dollars.
We have been given that Trey earns base pay of $47,300 and was paid commission of 15% for each car he sold.
Since Trey is paid 15% for each car he sold and total sales were x dollars, this means his commission would be 15% of x that is [tex]\frac{15}{100}x=0.15x[/tex].
The total salary of Trey would be base salary plus commission: [tex]y=47,300+0.15x[/tex]
Therefore, the equation [tex]y=47,300+0.15x[/tex] represents Trey's total pay in dollars.
can someone help me pls?
Answer:
graph c
Step-by-step explanation:
there is no slope since it doesn't go up/down by anything or over by anything. meaning there is no increase or decrease.
if you can buy 1/4 pizza for 5 dollars, how much can you purchase for 8 dollars? write your answer as a fraction
Step-by-step explanation:
¼ pizza is to 5 dollars as x pizza is to 8 dollars.
¼ / 5 = x / 8
Cross multiply:
5x = 2
Divide:
x = ⅖
You can buy ⅖ of a pizza.
Which of the following reveals the minimum value for the equation 2x2 − 4x − 2 = 0?
2(x − 1)2 = 4
2(x − 1)2 = −4
2(x − 2)2 = 4
2(x − 2)2 = −4
Answer:
[tex]2(x-1)^{2}=4[/tex]
Step-by-step explanation:
we have
[tex]2x^{2} -4x-2=0[/tex]
This is the equation of a vertical parabola open upward
The vertex is a minimum
Convert the equation into vertex form
Group terms that contain the same variable and move the constant to the other side
[tex]2x^{2} -4x=2[/tex]
Factor the leading coefficient
[tex]2(x^{2} -2x)=2[/tex]
[tex]2(x^{2} -2x+1)=2+2[/tex]
[tex]2(x^{2} -2x+1)=4[/tex]
Rewrite as perfect squares
[tex]2(x-1)^{2}=4[/tex] -----> this is the answer
The vertex is the point (1,-4)