Answer:
A
Step-by-step explanation:
The equation of a parabola is y = ax² + bx + c : a ≠ 0
Given
y = 2 (x + 4)² - 7 ← expand the squared factor
y = 2(x² + 8x + 16) - 7 ← distribute the parenthesis by 2
y = 2x² + 16x + 32 - 7 ← collect constant terms
y = 2x² + 16x + 25 → A
For the bar graph, what is the total population surveyed?
A) 303
B) 3,030
C) 3,030,000
D) 303,000
Answer:A
Step-by-step explanation:
80+141+74+4+3+1=303
Answer:A) 303
Step-by-step explanation:
Cathy is organizing the bottles of nail polish at a store. There are a total of 296 bottles. If Cathy puts the same number of bottles on each of 4 shelves, how many bottles will be on each shelf?
Answer:74
Step-by-step explanation:
The expression on the left side of an equation is shown below. 3x+9= If the equation has no solution, which expression can be written in the box on the other side of the equation?
Answer:
12x
Step-by-step explanation:
add the numbers and then put the variable in front of it
Answer:
3*x
Step-by-step explanation:
Note that 3*x + 9 = 3*x if you choose to put the expression 3*x on the right side of the expression.
To solve this equation, you subtract 3 * x on both sides of the equation, obtaining:
3*x+9-3*x=3*x-3*x
9=0
You get 9 = 0. This expression cannot be true regardless of the value taken by x. You can tell then that in this case the equation has no solution.
What are the exact solutions of x2 − 3x − 7 = 0?
x = the quantity of 3 plus or minus the square root of 37 all over 2
x = the quantity of negative 3 plus or minus the square root of 37 all over 2
x = the quantity of 3 plus or minus the square root of 19 all over 2
x = the quantity of negative 3 plus or minus the square root of 19 all over 2
[tex]\bf ~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-3}x\stackrel{\stackrel{c}{\downarrow }}{-7}=0 \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x=\cfrac{-(-3)\pm\sqrt{(-3)^2-4(1)(-7)}}{2(1)}\implies x=\cfrac{3\pm\sqrt{9+28}}{2}\implies x=\cfrac{3\pm\sqrt{37}}{2}[/tex]
Answer:
A. x = the quantity of 3 plus or minus the square root of 37 all over 2
Step-by-step explanation:
Kathy designed a square patio. She made the sides of the patio 15 feet. What is the area of the patio?
Answer:
225 feet.
Step-by-step explanation:
15 X 15
WORTH 98 POINTS
The number of horses occupying stalls at the county fairgrounds can be modeled by the following function, where x represents the number of days since the first of June.
h(x)=-3x^2+30+225
Rewrite this function in the form that reveals when there are no horses occupying stalls at the fairgrounds
Answer:
The equation is -3x^2 + 30x + 225 = 0, and the number of days is 15.
Step-by-step explanation:
I assume an x is missing, and the function is h(x) = -3x^2 + 30x + 225
You want to know the number of days in which the function value is zero.
-3x^2 + 30x + 225 = 0
Divide both sides by -3.
x^2 - 10x - 75 = 0
(x - 15)(x + 5) = 0
x - 15 = 0 or x + 5 = 0
x = 15 or x = -5
We discard the negative solution.
Answer: The equation is -3x^2 + 30x + 225 = 0, and the number of days is 15.
Answer:
h(x) = -3 (x + 5) (x - 15)
Step-by-step explanation:
h(x) = -3x^2 + 30 + 225
= -3(x^2 - 10x - 75)
= -3(x + 5)(x - 15)
x = -5 x = 15
Please help will give brainliest
If we have two functions [tex]f \ and \ g[/tex] such that [tex]f(g(x))=x[/tex] for every [tex]x[/tex] in the domain of [tex]g[/tex], and [tex]g(f(x))=x[/tex] for every for every [tex]x[/tex]in the domain of [tex]f[/tex]. If we prove this, then [tex]g[/tex] is the invers function of [tex]f[/tex] and denoted by [tex]f^{-1}[/tex]
1. We need to prove whether [tex]f(g(x))=x[/tex]. So:
[tex]f(x)=\frac{4}{5}x+1 \\ \\ g(x)=\frac{5x-5}{4} \\ \\ So: \\ \\ f(g(x))=\frac{4}{5}\left(\frac{5x-5}{4})+1 \therefore f(g(x))=\frac{4}{5}\left(\frac{5x-5}{4})+1[/tex]
[tex]\therefore f(g(x))=x-1+1 \\ \\ \boxed{f(g(x))=x}[/tex]
2. We need to prove whether [tex]g(f(x))=x[/tex]. So:
[tex]g(f(x))=\frac{5(\frac{4x}{5}+1)-5}{4} \\ \\ \\ g(f(x))=\frac{4x+5-5}{4} \\ \\ \\ g(f(x))=\frac{4x}{4} \\ \\ \\ g(f(x))=x[/tex]
Since [tex]f(g(x))=g(f(x))=x[/tex], then:
[tex]f(x) \ and \ g(x)[/tex] are inverses to each other.
please help drag and drop
FCH - NPM
PNM - CFH
HF - MN
NP - FC
Find the measure of angle 2
I would say 45 degrees
The whole square is 360 degrees because each corner is a 90 degree angle
Which means each triangle section would be 90 degrees but angle 2 is cut in half, so half of 90 is 45
Hope this helps :)
A school determined that there is about a 33% chance that a student will choose a salad over a grilled chicken sandwich for lunch. Which simulation could you use to answer questions about the type of lunch students will choose?
A Monte Carlo simulation can be used to answer questions about the type of lunch students will choose.
Explanation:A simulation that could be used to answer questions about the type of lunch students will choose is a Monte Carlo simulation.
In this simulation, the probability of a student choosing a salad over a grilled chicken sandwich is represented by a random number generator.
Each time the simulation is run, a random number between 0 and 1 is generated, and if the number is less than or equal to 0.33, it is considered a salad choice. This process is repeated multiple times to generate a distribution of lunch choices.
By analyzing the distribution, you can estimate the likelihood of students choosing a salad over a grilled chicken sandwich.
Final answer:
A simulation to model the 33% chance of students choosing a salad over a grilled chicken sandwich could involve a random generator where the number 1 (out of 1 to 3) represents the choice of a salad, simulating the probability accurately.
Explanation:
To simulate the situation where there is a 33% chance that a student will choose a salad over a grilled chicken sandwich for lunch, you could use a simple random process to model this probability. You might simulate the choice by using a random number generator set to generate numbers from 1 to 3, where one of the numbers (say 1) represents choosing a salad, and the other two numbers (2 and 3) represent choosing a grilled chicken sandwich. Every time the number 1 comes up, it would count as a 'success', representing a student choosing a salad. You could run this simulation a large number of times to answer questions about the likelihood of various outcomes related to the students' lunch choices.
3w - 4z = 8 what is w
Final answer:
To solve the equation 3w - 4z = 8 for w, add 4z to both sides and then divide by 3, resulting in the expression w = (4z + 8) / 3.
Explanation:
The student's equation, 3w - 4z = 8, involves algebraic manipulation to solve for the variable w. To isolate w, we rearrange the equation to get w by itself on one side of the equation:
Add 4z to both sides to get: 3w = 4z + 8
Divide both sides by 3 to solve for w: w = (4z + 8) / 3
Now we have w expressed in terms of z. This is the solution for w assuming you have a specific value for z you can substitute into this expression.
Final answer:
To find w, isolate it by adding 4z to both sides and then dividing by 3, resulting in w = (8 + 4z) / 3.
Explanation:
To solve for w in the equation 3w - 4z = 8, you would isolate w on one side of the equation. First, add 4z to both sides of the equation so that you have 3w = 8 + 4z. Then, divide both sides by 3 to get w by itself. The final equation representing w would be w = (8 + 4z) / 3. This doesn't directly correspond to the provided physics equations; however, we can apply a similar method of isolating the unknown in those as well.
Find the first four iterates of the function f(x) = 2x with an initial value of x0 = 2.
a.
4, 6, 8 ,10
c.
2, 4, 8, 16
b.
2, 4, 6, 8
d.
4, 8, 16, 32
Please select the best answer from the choices provided
Answer:
d. 4, 8, 16, 32
Step-by-step explanation:
We'll use the formula f(x) = 2x for each iteration. The output of the first iteration will be come the input of the second iteration, and so on.
So, we start with x0 = 2 and we plug that into the base equation:
x0 = 2 ==> f(x) = 2(2) = 4
x1 = 4 ==> f(x) = 2(4) = 8
x2 = 8 ==> f(x) = 2(2) = 16
x3 = 16 ==> f(x) = 2(2) = 32
x4 = 32 ==> f(x) = 2(2) = 64
Madison currently has a balance of 5503.51 ina an account earning simple interest. 19 years ago she opend up an account with an intial deposit of 3196. What is the interest rate on the account o
Answer:
The simple interest is 3.80% per year.
Step-by-step explanation:
We are presented with a simple interest problem and the following information has been availed;
Accumulated amount = 5503.51
Time = 19 years
Principal = 3196
The first step is to determine the total interest earned over the entire time period;
Interest = Amount - Principal
= 5503.51 - 3196
= 2307.51
The simple interest formula states the total interest earned is equal to the product of the principal, the interest rate and the time;
[tex]I=\frac{P*R*T}{100}[/tex]
Making R the subject of the formula yields;
[tex]R=\frac{100*I}{P*T}[/tex]
Substituting the values we have and simplifying;
[tex]R=\frac{100*2307.51}{3196*19}=3.80[/tex]
The simple interest is thus 3.80% per year.
e
| 2.
Solve this system of two linear equations using the
linear combination method.
2x - 5y = 18
y-x=-10
Answer:
[tex]x=\frac{32}{3}, y=\frac{2}{3}[/tex]
Step-by-step explanation:
We can multiply the second equation by 2 to eliminate.
[tex]2(y-x)=2(-10) \\ \\ 2y-2x=-20[/tex]
Let's eliminate.
[tex]2x-5y=18 \\ -2x+2y=-20 \\ -3y=-2 \\ y=\frac{2}{3}[/tex]
Now we can substitute back into the equation to find the value of [tex]x[/tex].
[tex]\frac{2}{3}-x=-10 \\ \\ \frac{2}{3}-x=-\frac{30}{3} \\ \\ -x=-\frac{32}{3} \\ \\ x=\frac{32}{3}[/tex]
A linear function includes the ordered pairs (2,5), (6,7) and (k,11). What is the value of k?
A)8
B)10
C)12
D)14
ANSWER
D)14
EXPLANATION
The linear function includes the ordered pairs (2,5), (6,7) and (k,11).
The slope of this line is the same for any two given points:
[tex] \frac{7 - 5}{6 - 2} = \frac{11 - 7}{k - 6} [/tex]
[tex]\frac{2}{4} = \frac{4}{k - 6} [/tex]
Cross multiply,.
2(k-6)=4×4
2(k-6)=16
Divide both sides by 2
k-6=8
k=8+6
k=14
Answer:
Option D will be the answer.
Step-by-step explanation:
y intercept form of a line is represented by y = mx + c
Where m = slope of the line and c = y- intercept of the line.
A line passing through two points (2, 5) and ( 6, 7) has the slope
m = [tex]\frac{y-y'}{x-x'}[/tex]
= [tex]\frac{7-5}{6-2}[/tex]
= [tex]\frac{2}{4}[/tex]
= [tex]\frac{1}{2}[/tex]
Equation will be y = [tex]\frac{x}{2}+c[/tex]
This line passes through (2, 5)
5 = [tex]\frac{1}{2}\times 2+c[/tex]
c = 5 - 1
c = 4
And the equation will be y = [tex]\frac{1}{2}x+4[/tex]
Since a point (k 11) passes through the line then we will plug in these values in the equation to find the value of k.
11 = [tex]\frac{1}{2}\times k+4[/tex]
11 - 4 = [tex]\frac{k}{2}[/tex]
7 = [tex]\frac{k}{2}[/tex]
k = 2×7
= 14
Option D will be the answer.
a pool in the sape of a rectangle has a perimeter of 80 feet. the pool is 8 feet less wide than it is long. find the length and width of the pool
Answer:
Length: 28 ft Width: 12 ft
Step-by-step explanation:
So to solve this, we know that perimeter means the sum of all the lengths added together. And we can start by dividing 80 by 4.
80 ÷ 4 = 20
And now, the width must be eight feet less than the length, meaning we just subtract eight from the width, and add eight to the length.
20 - 8 = 12
20 + 8 = 28
L = 28
W = 12
And now we can double check:
12+ 28 + 12 + 28 = 80
Have a great day:)
The moon has a radius of about 939 leagues long. What is the total surface area of the moon? Rounded to the nearest whole number. (Ex. 3244.55 rounds up to 3245.) *
Radius, r = 939 ft
Then:
Diameter, d = 1878 ft
Circumference, C = 5899.9110034416 ft
Area, A = 2770008.2161158 ft^2
AREA = 2770 if you're shortening.
For this case we assume that the moon is spherical. For definition, the surface area of a sphere is given by:
[tex]S = 4 \pi*r ^ 2[/tex]
Where:
A: It is the radius of the sphere
We have that the radius is 939 leagues.
by definition, 1 league is equivalent to 4.82803 kilometers.
ENtonces 939 leagues represent 4533.52 km.
Substituting:[tex]S = 4 \pi * (4533.52) ^ 2\\S = 20552803.5904 * 4 * \pi\\S = 258,274,147.081[/tex]
It has a surface area of 258,274,147 km
ANswer:
258,274.147 km
Find the area of a circle with a diameter of \color{green}{6}6start color green, 6, end color green.
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal.
units^2
2
start superscript, 2, end superscript
Answer:
9pi
Step-by-step explanation:
Find p(A|A^c)
A.1
B.0
C.1/2
D. Unknown
If [tex]A^C[/tex] has occurred, then [tex]A[/tex] cannot occur, so the probability is 0.
This follow directly from the definition of conditional probability:
[tex]P(A\mid A^C)=\dfrac{P(A\cap A^C)}{P(A^C)}[/tex]
but [tex]A[/tex] and [tex]A^C[/tex] are disjoint, so the probability of their intersection is 0.
Answer:
B.
Step-by-step explanation:
Tell whether the System has one solution infinite solution many solutions or no solutions 5x-3y=10 10x+6y=20
ANSWER
The system has one solution.
EXPLANATION
The given system is
1st: 5x-3y=10
2nd: 10x+6y=20
Make y the subject in the first equation to get:
[tex]y = \frac{5}{3} x + \frac{10}{3} [/tex]
Solve for y in the second equationquation to get;
[tex]y = - \frac{5}{3} x + \frac{10}{3} [/tex]
The slope of the two equations are not the same.
The two lines will intersect at exactly one point.
.The system has one solution.
Answer:
One solution
Step-by-step explanation:
We are given the following system of equations and we are to tell if the system has one solution, infinite solution, many solutions or no solutions:
[tex]5x-3y=10[/tex] --- (1)
[tex]10x+6y=20[/tex] --- (2)
If we take the common out from (2), we get:
[tex]2(5x+3y) = 20 [/tex]
[tex]5x+3y = 10 [/tex] --- (3)
So adding the two equations (1) and (3) gives 10x=20 ⇒ x=2.
Therefore, this system of equations has one solution.
solve for x
x=
the graph shown below
Answer:
x=27
Step-by-step explanation:
Without the arrow crossing through that right angle, it would equal 90 degrees. Since it's cut in half, each part equals 45 degrees. A straight line equals 180 degrees. 3×27=81 and 81+9=90. 90+90=180 :)
Which of the functions have period pi?
A.) y = tan x
B.) y = csc x
C.) y = cot x
D.) y = sec x
ANSWER
A.) y = tan x
C.) y = cot x
EXPLANATION
The period refers to the interval over which the graph completes one cycle
The trigonometric functions
[tex]y = \tan(x) [/tex]
and
[tex]y = \cot(x) [/tex]
are reciprocals of each other.
They have the same period, which is π
Also y=cscx and y=secx are reciprocals of the sine and the cosine functions respectively.
They have periods of 2π
The circumference of a circle is 9 pi.What is the area,in square inches,of a circle?Express your answer in terms of pi.
Answer:
20.25π
Step-by-step explanation:
The circumference (C) of a circle is calculated using the formula
C = 2πr ← r is the radius
given C = 9π, then
2πr = 9π ( divide both sides by 2π )
r = [tex]\frac{9\pi }{2\pi }[/tex] ( cancel the π on numerator/denominator )
= 4.5
The area (A) of a circle is calculated using the formula
A = πr² = π × 4.5² = 20.25π
Pls help me with my math brainliest and 20 points!!
Answer:
23 miles
Step-by-step explanation:
Substitute into the formula d = 3 s + 5
We know s = 6 so
d = 3 s + 5
d = ( 3 × 6 ) + 5
d = ( 18 ) + 5
d = 23
Hope this helps :)
Have a great day !
5INGH
Answer:
23 miles
Step-by-step explanation:
Substitute the numbers into d=3s+5.
d=(3×6)+ 5 (d=18+5)
18+5=23
If p varies directly as r and p=4,r=2,what the value of r when p=12
Answer:
r = 6
Step-by-step explanation:
Given that p varies directly as r, then the equation relating them is
p = kr ← k is the constant of variation
To find k use the condition p = 4, r = 2
k = [tex]\frac{p}{r}[/tex] = [tex]\frac{4}{2}[/tex] = 2
p = 2r ← equation of variation
When p = 12
12 = 2r ( divide both sides by 2 )
hence r = 6
Which step is part of a proof showing the opposite sides of parallelogram ABCD are congruent?
A) show that AC is congruent to BD
B) show that AD is congruent to AB
C) show that angles A and D are supplementary
D) show that triangle ADB is congruent to triangle CBD
I think it’s D. Because A) and B) are not true and im pretty sure that C) is also false
Answer:
its d
Step-by-step explanation:
If a car can go 200 miles in 6hours how far can it go in 7 hours
Answer:
If a car can go 200 miles in 6 hours at a constant rate, in 7 hours it will have gone 233.33 (0.33 repeating) miles.
Step-by-step explanation:
If a car can go 200 miles in 6 hours, then we know it can go about 33.33 miles per hour (found by dividing 200 by 6).
If the car is going at this constant rate we can then multiply 33.33 by 7, which would give us 233.33.
The car can go 233.33 miles in 7 hours
What is Ratio and proportion ?A comparison of two entities by dividing them is called Proportion and when two ratios are equated to one another , they are said to be in proportion.
It is given in the question that
a car can go 200 miles in 6 hours
Distance covered in 7 hours
In the given question the ratio of Distance covered and time is
200/6 = 100/3 = 100:3
Let the distance covered in 7 hours is x
therefore the ratio will be x : 7
These two ratios will be in proportion
100:3 = x: 7
100/3 = x / 7
x = 100 * 7 / 3
x = 700 / 3
x = 233.33 miles
Therefore The car can go 233.33 miles in 7 hours .
To know more about Ratio and Proportion
https://brainly.com/question/26974513
#SPJ2
7x+6(x+10)>5 (-3-3x)+3x
Answer:
[tex]\large\boxed{x>-3\to x\in(-3,\ \infty)}[/tex]
Step-by-step explanation:
[tex]7x+6(x+10)>5(-3-3x)+3x\qquad\text{use the distributive property}\\\\7x+(6)(x)+(6)(10)>(5)(-3)+(5)(-3x)+3x\\\\7x+6x+60>-15-15x+3x\qquad\text{combine like terms}\\\\(7x+6x)+60>(-15x+3x)-15\\\\13x+60>-12x-15\qquad\text{subtract 60 from both sides}\\\\13x>-12x-75\qquad\text{add 12x to both sides}\\\\25x>-75\qquad\text{divide both sides by 25}\\\\x>-3[/tex]
What is the next term in -2, -5, -9, -14, -20.
And why
The next term would be -27
Lets pretend that all the negative signs went away, that way you have the data:
2, 5, 9, 14, 20
^^^In my opinion it just makes it easier because I don't like negative numbers. Keep in mind that the negatives are still there but I just made them "Invisible"
The pic below is how I found the pattern. If you can't tell by the picture from 2 to 5 it increases by 3. From 5 to 9 it increases by 4. From 9 to 14 it increases by 5. From 14 to 20 it increases by 6.
This means the pattern is to increase the number 1 more then the amount the previous number was increased (keep in mind this is the pattern for the positive version and therefore the original pattern would be decreasing (since the bigger a number that is negative is, the farther away it gets from zero, therefor getting smaller.) For the original version the rule would be: it would decrease the number 1 more then the amount the previous number was decreased) <<<Hope that makes sense
That means that 20 will be increased by 7 ( 6+ 1 = 7). Which equals 27. Make the negative sign visible again and your answer is -27.
Let me know if this made sense and if it was helpful!
By visual inspection, determine the best fitting regression model for the data below
Answer:
A) Quadratic
Step-by-step explanation: It has the U shape of a parabola which a quadratic equation has.
Answer:
The correct option is A.
Step-by-step explanation:
In a scatter plot the best fit curve in known as regression curve. Types of regression curves are
1. Linear regression line : If the best fit of a data is a straight line, then it is known as linear regression line.
2. Quadratic regression : If the best fit of a data is a U-shape curve, then it is known as quadratic regression.
3. Exponential regression : If the best fit of a data is an exponential curve, then it is known as exponential regression.
From the given graph it is clear that scatter data forms a U-shaped curve. Since the best fit of a data is a U-shape curve, therefore the quadratic regression model is best for the data.
Thus, option A is correct.