The required simplified solution of the given expression is 8x + 9.
Given that,
To determine the simplified solution of the expression 3(2x+1)+2(x+3).
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let,
y = 3(2x+1)+2(x+3)
y = 6x + 3 + 2x + 6
y = 8x + 9
Thus, the required a simplified solution of the given expression is 8x + 9.
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An object is thrown upward at a speed of 152 feet per second by a machine from a height of 9 feet off the ground. The height h of the object after t seconds can be found using the equation h=−16t^2+152t+9
When will the height be 231 feet?
When will the object reach the ground?
Answer:
First part:
Set h(t) = 231and solve for t.
-16t²+ 152t + 9= 231
-16t² + 152t - 222= 0
Solve this quadratic equation for t. You should get 2 positive solutions. The lower value is the time to reach 231 on the way up, and the higher value is the time to reach 231 again, on the way down.
Second part:
Set h(t) = 0 and solve the resulting quadratic equation for t. You should get a negative solution (which you can discard), and a positive solution. The latter is your answer.
Select the correct answer
Which expression represents the series 1 + 5 + 25 + 125 + 6252
Answer:
The expression is 5⁵-1 (=3124)
Step-by-step explanation:
A fair number cube is rolled. What is the probability that a number greater than 2 is rolled
Answer:
2/3
Step-by-step explanation:
Ah, I see. A 1-6 die.
Probability of one number = 1/6
2 numbers? = 2/6
6/6-2/6=4/6
4/6=2/3
[tex]\huge{\boxed{\frac{2}{3}}}[/tex]
There are [tex]4[/tex] numbers on a number cube that are greater than [tex]2[/tex]. They are [tex]3, 4, 5, 6[/tex].
Write this as a fraction. [tex]\frac{\text{4 favorable outcomes}}{\text{6 total outcomes}}[/tex]
Divide both the numerator and denominator by [tex]2[/tex] to simplify. [tex]\boxed{\frac{2}{3}}[/tex]
Use the substitution method to solve the system of equations choose the correct ordered pair
Answer:
C. (4,28)
Step-by-step explanation:
The substitution method requires you to input a specified number in place of a variable. In this case, the variable 'x' should be replaced by the number 4. Using the order of operations, we know that multiplication should be applied before subtraction. When we replace 'x' with 4, we get the equation 'y=8(4)-4'. Multiplying 8 and 4 gives us 32. If we subtract 4 from 32, we get 28. The answer ends up being 'y=28'.
That is the first part of our solution. What we are actually looking for is an ordered pair. We know ordered pairs are written in the form (x, y). First, we need to find the 'x'. The 'x' has been given to us from the beginning, it is 4. Next is the 'y'. This is what we needed to find using substitution. We ultimately concluded that the 'y' is equivalent to 28. Therefore our ordered pair is (4, 28), the letter choice C.
I hope this helped you and that I clearly elaborated on the answer choice.
1pt Which of these constructions will NOT result in a point of concurrency?
O A. the three altitudes of a triangle
B. the three angle bisectors of a triangle
C. the three midsegments of a triangle
O D. the three medians of a triangle
O
E. the three perpendicular bisectors of a triangle
The constructions will NOT result in a point of concurrency is C. the three midsegments of a triangle.
What forms the three central segments of a triangle?The central segment is parallel to the sides of the non-intersecting triangles. There are three congruent triangles formed by the central segment and sides of the triangle. Every triangle has three central segments.
The central segment is a line segment connecting the midpoints of the two sides of a triangle. Each triangle has three central segments because each triangle has three sides. The center segment of the triangle is parallel to the third side of the triangle and half the length of the third side.
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What is the slope of the line that contains the points (-1, 2) and (3, 3)?
A -4
B 4
C 1/4
D -1/4
Answer:
[tex]\Huge \boxed{\frac{1}{4}}[/tex]
Step-by-step explanation:
Slope formula:
[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\displaystyle \frac{3-2}{3-(-1)}=\frac{1}{4}[/tex]
Therefore, the slope is 1/4, and the correct answer is 1/4.
Answer:
C 1/4
Step-by-step explanation:
To find the slope of the line given two points, we use the formula
m = (y2-y1)/(x2-x1)
= (3-2)/(3--1)
= (3-2)/(3+1)
= 1/4
Circle A has a radius of 6. Which circles are congruent
to circle A? Check all that apply.
E
circle D
circle E
circle F
circle G
circle H
Answer:
The correct answer options are:
Circle E
Circle F
Step-by-step explanation:
We are given that a circle A has a radius of 6 and we are to determine whether which of the circles from the answer options are congruent to circle A.
We know that radius is the distance from the center of the circle to any point on circle's circumference.
Circle E, F show the radius of 6, therefore they are congruent to circle A.
Plot the point (2,-pi/4)
Answer:
Step-by-step explanation:
Attached below. pi = 180°
Answer:
a
Step-by-step explanation:
Which of the following is the measure of xba if ray ba bisects xby which measures 86 degrees
Answer:
The measure of angle xba is 43°
Step-by-step explanation:
we know that
If ray ba bisects the angle xby, then the measure of angle xby is divided into two equal angles
see the attached figure to better understand the problem
so
∠xba=∠aby
∠xba+∠aby=∠xby
we have
∠xby=86°
therefore
∠xba=∠xby/2=86°/2=43°
The function y=-4(x - 3)2 + 8 shows the daily profit (in hundreds of dollars)
of a taco food truck, where x is the price of a taco (in dollars). Find and
interpret the zeros of this function,
Select two answers: one for the zeros and one for the interpretation.
O
A. Interpretation: The zeros are where the daily profit is $0.00.
O B. Zeros: x = 3 - V3 = 1.58 and x = 3 + v = 4.41
O
c. Interpretation: The zeros are where the price of a taco is $0.00.
O D. Zeros: x = 3 and x = -3
Answer:
Step-by-step explanation:
To find the zeros, set y=-4(x - 3)2 + 8 = 0. Then -4(x - 3)^2 = -8, and:
4(x - 3)^2 = 8. Dividing both sides by 4 yields (x - 3)^2 = 2.
Taking the square root of both sides yields x - 3 = ±2, so that
x = 3 ±2, or x = 5 and x = 1. These are the zeros. The correct interpretatioon is A: where the daily profit is $0.
Answer:
Interpretation: The zeros are where the daily profit is $0.00.
Zeroes are x = 1.58 and x = 4.41.
Step-by-step explanation:
Given function,
[tex]y=-4(x-3)^2+8[/tex]
For finding the zeros,
y = 0,
[tex]-4(x-3)^2+8=0[/tex]
[tex]-4(x-3)^2=-8[/tex]
[tex](x-3)^2=2[/tex]
[tex]x-3=\pm \sqrt{2}[/tex]
[tex]\implies x = 3\pm \sqrt{2}[/tex]
[tex]\implies x\approx 4.41\text{ or }x=1.58[/tex]
Hence, the zeroes of the function are x = 1.58 and x = 4.41,
∵ x represents the price of a taco and y represents daily profit,
Therefore, the zeroes are where the daily profit is $ 0.00.
Henry buys a large boat for the summer, however he cannot pay the full amount of $32,000 at once. He puts a down payment of $14,000 for the boat and receives a loan for the rest of the payment of the boat. The loan has an interest rate of 5.5% and is to be paid out over 4 years. What is Henry’s monthly payment, and how much does he end up paying for the boat overall? (Please show steps) Thanks:)
Answer:
Henry's monthly payment is $457.5
Henry pays up for the boat at the end overall $35,960
Step-by-step explanation:
* Lets explain how to solve the problem
- Henry buys a large boat with full amount of $32,000
- He cannot pay the full amount at once
- He puts a down payment of $14,000
- He receives a loan for the rest of the payment
∵ The rest of payment = 32,000 - 14,000 = $18,000
- The loan has an interest rate of 5.5%
∴ The rate of interest = 5.5/100 = 0.055
- It is to be paid out over 4 years
∵ The amount of interest = P × r × t , where
# P is the principle amount
# r is the rate
# t is the time
∵ P = 18, 000 , r = 0.055 , t = 4
∴ The amount of interest = 18,000 × 0.055 × 4 = $3960
- The total remaining amount is the sum of the rest of payment and
the amount of interest
∵ The rest of payment is $18,000
∵ The interest amount = $3,960
∴ The total remaining amount = 18,000 + 3,960 = $21960
- The number of monthly payments = 12 × t
∵ t = 4
∴ The number of monthly payment = 12 × 4 = 48 months
- The monthly payment = the total remaining ÷ the number of
monthly payment
∵ The total remaining is 21960
∵ The number of monthly payment = 48
∴ The monthly payment = 21960 ÷ 48 = $457.5
* Henry's monthly payment is $457.5
- The total paying for the boat is the sum of the payment down and
the remaining total payment
∵ The payment down is $14,000
∵ The remaining total payment is 21,960
∴ The total payment for the boat = 14,000 + 21,960 = $35,960
* Henry pays up for the boat at the end overall $35,960
find the quotient. PIC PROVIDED PLATO
Answer:
D is the correct option
Step-by-step explanation:
2x-3/x ÷ 7/x²
Change the division sign into multiplication and the second term will be flipped(denominator will become numerator)
2x-3/x * x²/7
x will be cancelled out by x²
2x-3/1 * x/7
Now multiply 2x-3 by x
2x²-3x/7
Take x as a common:
x(2x-3)/7
Thus the correct option is D....
ind an equation for the nth term of the arithmetic sequence.
a14 = -33, a15 = 9
Answer:
[tex]a_n=42n-621[/tex]
Step-by-step explanation:
This is arithmetic sequence so you should go to linear equations in your head.
Think of the question asking you to find the equation of line going through the points:
(14,-33) and (15,9).
First, let's find the slope.
You need to compute y's change over x's change.
The way I like to do that is line up the points vertically, subtract them, and then put 2nd difference over first.
Like this:
( 15 , 9)
-( 14 , -33)
------------------
1 42
So the slope is 42/1=42.
(The slope is our common difference.)
Now point slope form is:
y-y1=m(x-x1) where m is the slope and (x1,y1) is a point you know on the line.
So we have m=42 and (x1,y1)=(15,9). (You could have chose the other point.)
y-9=42(x-15)
I'm going to put in slope-intercept form. Slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.
y-9=42(x-15)
Solve for y by adding 9 on both sides:
y=42(x-15)+9
Distribute 42 to terms in the ( ) :
y=42x-42(15)+9
y=42x-630+9
y=42x-621
So we can which back to n now:
[tex]a_n=42n-621[/tex]
The amount in dollars an electrician charges in terms of the number of hours worked is represented by the function y=22x+42.
From the function, Identify all the phrases that hold true for the situation.
Answer:
Step-by-step explanation:"
The electrician charges an initial fee of $42", AND "The electrician charges $22 for every hour worked" is true.
The equation is y=22x+42. The formula is y=mx+b.m is the slope, or is this case, the number of dollars for every "x", which is the number of hours worked. So you have to pay $22 for every hour the electrician works.b is the y-intercept, or the amount it starts with, in this case, you have to pay a fee of $42 even when the electrician worked 0 hours. This is because $42 is the amount it starts with.On a graph, the line will start at (0,42) because that is when you start paying. And then it will increase by 22 for each hour, so the next coordinate would be (1,64).
The given function y=22x+42 represents the electrician’s charges. The electrician charges $22 for each hour worked and has a flat service fee of $42.
Explanation:
The given function y=22x+42 stands for the electrical work charges in terms of hours worked. Here 'y' represents the total amount charged, 'x' represents the number of hours worked, '22' is the hourly rate and '42' is likely a fixed service fee regardless of the hours worked. So the aspects that holds true for this function are: (1) The electrician charges $22 per hour of work, (2) The electrician has a fixed service fee of $42 whether or not they have worked any hours
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2 2/3 + 12 6/8 how do I work this
Answer:
[tex]\large\boxed{2\dfrac{2}{3}+12\dfrac{6}{8}=15\dfrac{5}{12}}[/tex]
Step-by-step explanation:
[tex]2\dfrac{2}{3}+12\dfrac{6}{8}=2\dfrac{2}{3}+12\dfrac{6:2}{8:2}=2\dfrac{2}{3}+12\dfrac{3}{4}\\\\\text{Find}\ LCD:\\\\\text{List of multiples of 3:}\ 0,\ 3,\ 6,\ 9,\ \boxed{12},\ 15,\ ...\\\text{List of multiples of 4:}\ 0,\ 4,\ 8,\ \boxed{12},\ 16,\ ...\\\\12=3\cdot4\\\\\text{therefore}\\\\\dfrac{2}{3}=\dfrac{2\cdot4}{3\cdot4}=\dfrac{8}{12}\\\\\dfrac{3}{4}=\dfrac{3\cdot3}{4\cdot3}=\dfrac{9}{12}\\\\2\dfrac{2}{3}+12\dfrac{3}{4}=2\dfrac{8}{12}+12\dfrac{9}{12}=(2+12)+\dfrac{8+9}{12}=14+\dfrac{17}{12}\\\\=14+1\dfrac{5}{12}=15\dfrac{5}{12}[/tex]
Which sentence uses capitalization correctly?
(A)The book is about a japanese prince.
(B)Have you ever read Murasaki Shikibu’s book?
(C)His book is called The tale of genji.
Answer:
The answer Is B.
Step-by-step explanation:
In "A" I believe japanese should be capatalized and in "C" "genji" should be capitalized but In "B" Murasaki Shikibu’s is a name so it should be capitalized.
PLEASE HURRY
BRAINLIEST TO THE FIRST ONE TO ANSWER
Answer:
[tex]cos^{-1}[\frac{6.3}{9.8}][/tex]
[tex]sin^{-1}[\frac{7.5}{9.8}][/tex]
Step-by-step explanation:
step 1
Find the measure of angle ABC using the function cosine
we know that
The function cosine of angle ABC is equal to divide the adjacent side to angle ABC by the hypotenuse of the right triangle
cos(∠ABC)=BC/AB
substitute
cos(∠ABC)=6.3/9.8
[tex]ABC=cos^{-1}[\frac{6.3}{9.8}][/tex]
step 2
Find the measure of angle ABC using the function sine
we know that
The function sine of angle ABC is equal to divide the opposite side to angle ABC by the hypotenuse of the right triangle
sin(∠ABC)=AC/AB
substitute
sin(∠ABC)=7.5/9.8
[tex]ABC=sin^{-1}[\frac{7.5}{9.8}][/tex]
A triangle has sides of lengths 4, 3, and 5. Is it a right triangle? Explain.
Answer:
yes; 4² + 3² = 5²
Step-by-step explanation:
Pythagorean theorem.
In a right triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides. Hypotenuse is the longest side of the triangle.
4² + 3² = 5²
16 + 9 = 25
25 = 25
What is the scale factor of ALMN TO AOPO?
Answer:
There is a scale factor of 1
Step-by-step explanation:
the ratio 1:1 means that there is no difference between the two triangles, and that they are congruent.
Solve the following inequality algebracially -2 < x/3 + 1 <5
Answer:
-9 < x < 12Step-by-step explanation:
[tex]-2<\dfrac{x}{3}+1<5\qquad\text{subtract 1 from both sides}\\\\-2-1<\dfrac{x}{3}+1-1<5-1\\\\-3<\dfrac{x}{3}<4\qquad\text{multiply both sides by 3}\\\\(3)(-3)<3\!\!\!\!\diagup^1\cdot\dfrac{x}{3\!\!\!\!\diagup_1}<(3)(4)\\\\-9<x<12[/tex]
Draw a graph of this linear inequality y<2
Answer:
Observe the attached image
Step-by-step explanation:
The inequality we have is:
[tex]y <2[/tex]
This means that the region represented by this inequality includes all the values below the horizontal line [tex]y = 2[/tex].
To graph this region, draw a dotted horizontal line that intersects the y axis at [tex]y = 2[/tex]. Then shade all the region that is below the horizontal line, as shown in the attached image.
in a 45-45-90 triange, what is the ratio of the length of on leg to the length of the other leg? A,1:1 B. square root of 2:1 C. 2:1 D. 1: square root of 2
Answer:
A) 1:1
Step-by-step explanation:
Each leg is the same value and the hypotenuse is [tex]\sqrt{2}[/tex] of the value.
Answer:
Answer A: 1:1
Step-by-step explanation:
In a 45-45-90 triangle, the two legs are of equal length.
Thus, Answer A: 1:1, is the correct one.
Point G is rotated 90ﾟ the coordinate of the pre image point G was (7 ,-5), and its image G is at coordinate (5, 7) what is the direction of the rotation
Answer: The direction of the rotation is counterclockwise about the origin.
Step-by-step explanation:
A Rotation is a transformations in which a figure is rotated about a specific point, which is the know as "Center of rotation". Rotation is described in terms of degrees. The initial figure is called "Pre-image" and the rotated figure is called "Image". According to Rule for 90° counterclockwise rotation about the origin:[tex](x,y)[/tex] → [tex](-y, x)[/tex]
In this case, we can observe that the coordinates of the Pre-image of the Point G are:
[tex](7 ,-5)[/tex]
And the coordinates of its Image are:
[tex](5, 7)[/tex]
Then:
[tex](x,y)[/tex] → [tex](-y, x)[/tex]
[tex](7 ,-5)[/tex] → [tex](5, 7)[/tex]
Therefore, the direction of the rotation is counterclockwise about the origin.
Hi I have another question like this that I can’t figure out :)
Answer:
f(g(-1)) = -8 and g(f(1/2) = 4/19.
Step-by-step explanation:
The question specifies f(x) = x^2 + 9x and g(x) = 1/x. The question requires that there should be composite functions. This means a function in a function. Therefore, f(g(x)) means that the function g(x) is taken is an input in the function f(x). Simply replace g(x) instead of x in f(x). This gives:
f(g(x)) = (1/x)^2 + 9(1/x) = x^(-2) + 9/x.
Similar process for g(f(x)) gives:
g(f(x)) = 1/(x^2 + 9x).
Now there are two separate composite functions. Now taking inputs in the composite functions:
f(g(-1)) = (-1)^(-2) + 9/(-1) = 1 - 9 = -8.
g(f(0.5) = 1/(0.5^2 + 9(0.5)) = 1/(0.25+4.5) = 1/4.75 = 100/475 = 4/19.
Therefore f(g(-1)) = -8 and g(f(1/2) = 4/19!!!
Solve for x in the equation X2 - 12x+36-90
X = 6+3/10
X=6+2V7
X= 12+3 22
x= 12+3/10
Answer:
x = 6 + 3√10
Step-by-step explanation:
Since this is an unfactorable expression, we need to apply the Quadratic Formula, -b ± √b² - 4ac\2a [radical wrapped around b² - 4ac]. Evaluate, then you will end up with the answer above.
I am joyous to assist you anytime.
70% of all us households have vcrs. In a random sample of 15 households, what is the probability that the number of households with vcrs is between 10 and 12, inclusive?
Answer:
Therefore the probability of 10 - 12 inclusive = 0.20613 + 0.21862 + 0.17004
= 0.59479
+ 59.5% to one place of decimals
Step-by-step explanation:
P(exactly 10) = 15C10 * (0.70)^10 * (0.30)^5
=15! / (10! * 5!) * (0.70)^10 * (0.30)^5
= (15*14*13*12*11) /(5*4*3*2*1) * (0.70)^10 * (0.30)^5
= 0.20613
P(exactly 11) = 15C11 * (0.70)^11 * (0.30)^4
= (15*14*13*12)/(4*3*2*1) *(0.70)^11 *(0.30)^4
= 0.21862
P(exactly 12) = 15C12 * (0.70)^12 * (0.30)^3
= (15*14*13)/(3*2*1) * (0.70)^12 * (0.30)^3
= 0.17004
Which unit would you most likely use to represent the time it takes to fly from
New York, New York to Portland, Oregon which is 2,442 miles away?
A. Minutes
B. Seconds
C. Hours
D. Days
Answer:
C. Hours
Step-by-step explanation:
It wouldn't take minutes or seconds to travel 2,442 miles so A and B don't make sense.
Also, it wouldn't take days to travel in the same country, it might a day but not days.
So the only answer that would make sense would be C. Hours
Hope This Helps!!
What is the equation of the parabola?
Answer:
D
Step-by-step explanation:
From any point (x, y ) on the parabola the focus and directrix are equidistant
Here the focus = (- 6, 0) and the directrix is x = 6
Using the distance formula
[tex]\sqrt{(x+6)^2+(y-0)^2}[/tex] = | x - 6 |, that is
[tex]\sqrt{(x+6)^2+y^2}[/tex] = | x - 6 |
Squaring both sides
(x + 6)² + y² = (x - 6)² ← distribute factors on both sides
x² + 12x + 36 + y² = x² - 12x + 36
Subtract x² - 12x + 36 from both sides
24x + y² = 0 ( subtract y² from both sides )
24x = - y² ( divide both sides by 24 )
x = - [tex]\frac{1}{24}[/tex] y² → D
What is the volume of a right circular cylinder with a radius of 5 cm and a height of 12 cm?
A. 607 cm
B. 1207 cm
C. 3007 cm
D. 12007 cm
Answer:
V = 942.48cm³
Step-by-step explanation:
The volume of a right circular cylinder with a radius of 5 cm and a height of 12 cm is 942.48.
Formula: V=πr2h
V=πr2h=π·52·12≈942.4778cm³
AB id a diameter of a circle centered at o. C is a point on the circle such that angle BOC is 60 degrees.if the diameter of the circle is 5 inches the length of the chord ac expressed in inches is
A.3
b. 5 square root 2 over 2
c.5 square root 3 over 2
d. 3 square root 3
e. none of the above
Answer:
Option c). 5 square root 3 over 2
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find the measure of angle AOC
we know that
m∠AOC+m∠BOC=180° ----> by supplementary angles
m∠BOC=60° ---> given value
m∠AOC+60°=180°
m∠AOC=180°-60°=120°
step 2
we know that
The triangle AOC is an isosceles triangle
OA=OC=2.5 in -----> the radius of the circle
m∠CAO=m∠OCA ----> base angle
we have that
2m∠CAO=180°-m∠AOC
2m∠CAO=180°-120°
m∠CAO=30°
step 3
Find the measure of the chord AC
we know that
Applying the law of sines in triangle AOC
sin(30°)/2.5=sin(120°)/AC
AC=(2.5)sin(120°)/sin(30°)
sin(30°)=1/2
AC=(2.5)sin(120°)/(1/2)
AC=(5)sin(120°)
Remember that
sin(120°)=sin(60°)
sin(60°)=√3/2
substitute
AC=(5√3)/2
5 square root 3 over 2