Answer:
[tex]\large\boxed{A.\ \dfrac{1}{2}x+\dfrac{11}{2}}[/tex]
Step-by-step explanation:
[tex]-3x-(x-1)+\dfrac{3}{2}(3x+3)\qquad\text{use the distributive property}\\\\=-3x-x-(-1)+\left(\dfrac{3}{2}\right)(3x)+\left(\dfrac{3}{2}\right)(3)\\\\=-3x-x+1+\dfrac{9}{2}x+\dfrac{9}{2}\qquad\text{combine like terms}\\\\=\bigg(-3x-x+\dfrac{9}{2}x\bigg)+\bigg(1+\dfrac{9}{2}\bigg)\\\\=\bigg(\dfrac{-6}{2}x-\dfrac{2}{2}x+\dfrac{9}{2}x\bigg)+\bigg(\dfrac{2}{2}+\dfrac{9}{2}\bigg)\\\\=\dfrac{-6-2+9}{2}x+\dfrac{2+9}{2}=\dfrac{1}{2}x+\dfrac{11}{2}[/tex]
an elevator in a hotel moves at 20 feet per second. leaving form the ground floor, its height in feet after t second is given by the formula h(t)=20t. a bolt comes loose in the elevator shaft above, and its height in feet after falling for t second is given by h(t)=-16t^2+200. at what time and at what height does the bolt hit the elevator?
After 3 seconds and at 60 feet, the bolt hit the elevator if the height in feet after t second is given by the formula h(t)=20t.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] Where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
When the bolt hit the elevator, they would be at the same height.
∴ 16t²+200 = 20t
16t² -20t + 200 = 0
It is a quadratic equation:
a = 16, b = -20, and c = 200 plug this values in the formula.
After calculating, we will get:
t = -4.2 or t = 3
Time cannot be negative.
So t = 3 seconds
And height h(3) = 20(3) = 60 feet
Thus, after 3 seconds and at 60 feet, the bolt hit the elevator if the height in feet after t second is given by the formula h(t)=20t.
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what are the next three terms in the sequence -1, 9, 19, 29
39. each term is ten more than the term before it :)
Answer:
39, 49, 59
Step-by-step explanation:
Note the difference between consecutive terms
9 - (- 1) = 9 + 1 = 10
19 - 9 = 10
29 - 9 = 10
The difference is a constant + 10
To obtain the next term in the sequence add 10 to the previous term
29 + 10 = 39
39 + 10 = 49
49 + 10 = 59
The next 3 terms are 39, 49, 59
The price of a bag of bagels rose from $2.80 in January to $3.50 in April. What was the percent increase of the price of a bag of bagels
Answer:
25%
Step-by-step explanation:
% increase = (3.50 - 2.80)/(2.80) x 100
= 25% increase
The required percent increase of the price of a bag of bagels from $2.80 to $3.50 is 25%.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
To find the percent increase of the price of a bag of bagels, we can use the formula,
percent increase = [(new value - old value) / old value] x 100%
In this case, the old value is $2.80 and the new value is $3.50. Substituting these values into the formula, we get:
percent increase = [(3.50 - 2.80) / 2.80] x 100%
percent increase = (0.70 / 2.80) x 100%
percent increase = 0.25 x 100%
percent increase = 25%
Therefore, the percent increase in the price of a bag of bagels from $2.80 to $3.50 is 25%.
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Select ALL the correct answers.
Ms. Simon uses six different colored pens to grade papers. She has one of each of the following colors: red, purple, green, blue, orange, and black. Determine which statements are true.
A.The probability of randomly not choosing a black pen is.
B.The probability of randomly choosing a black pen is.
C.The probability of randomly choosing either a red or blue pen is.
D. The probability of randomly choosing an orange pen is about 0.17.
E. The probability of randomly not choosing a purple or blue pen is about 0.67.
F. The probability of randomly choosing a green or red pen is about 0.5.
I WILL NAME THE BRAINLESS IF CORRECT!!
The correct probabilities are that not choosing a black pen is about 0.83, choosing a black pen is about 0.17, choosing a red or blue pen is about 0.33, choosing an orange pen is about 0.17, not choosing a purple or blue pen is about 0.67, and finally, choosing a green or red pen is about 0.33.
Explanation:In this mathematics problem, we discuss the probabilities related to Ms. Simon and her colored pens, specifically black and red.
A. The probability of randomly not choosing a black pen is 5/6 or about 0.83 (there are five other colors).
B. The probability of randomly choosing a black pen is 1/6 or about 0.17 (only one black pen out of six).
C. The probability of randomly choosing a red or blue pen is 2/6 or about 0.33 (two desired colors out of six).
D. This is correct because The probability of randomly choosing an orange pen is 1/6, which rounds to about 0.17.
E. The probability of randomly not choosing a purple or blue pen is 4/6 or about 0.67 (four other colors), so this is correct.
F. The probability of randomly choosing a green or red pen is 2/6 or about 0.33 (not 0.5 as stated).
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which equation can be used to find the measure of an angle that is supplementary to POS I will make BRAINLIEST
Answer:
B
Step-by-step explanation:
This is the Georiga Mile STONE?????????????
HELP ME WITH THIS MATH PROBLEM FOR 17 POINTS!!
Maureen deposited $19,000 at 11 percent interest compounded annually. What was the total interest earned at n = 8 years?
Answer:
%88 i believe
Step-by-step explanation:
hope this helps!
Answer: $43786.22 (Round)
Step-by-step explanation: Use this formula: A= P(1+r/n)^nt
We are trying to find A in this problem.
Plug it in:
A= 19,000(1+0.11/1)^(1)(8)
The lengths of the sides of a right triangle are 10in, 24in, and 26in. What is the area of the triangle?
The area of a right triangle with legs of 10in and 24in is 120 square inches, calculated using the formula Area = 0.5 * base * height.
Explanation:The area of a right triangle can be calculated using the formula:
Area = 0.5 * base * height
In this case, the base and height can be taken as the two legs of the right triangle. Given the lengths of the legs as 10in and 24in, the area can be calculated as:
Area = 0.5 * 10in * 24in = 120 square inches
1 and 1/3 mineus 3/4
Answer:
7/12
Step-by-step explanation:
1 1/3 - 3/4
= 4/3 - 3/4
= 16/12 - 9/12
= 7/12
Answer:
[tex]1\frac{1}{3}-\frac{3}{4}=\frac{7}{12}[/tex]
change [tex]1\frac{1}{3}[/tex] into [tex]\frac{4}{3}[/tex]
[tex]=\frac{4}{3}-\frac{3}{4}[/tex]
get like denominators:
12
[tex]\frac{16}{12}-\frac{9}{12}[/tex]
16 - 9 = 7
Hope this helps and have a great day!!!
a group of musicians wants to sell a total of 1,000 tickets for 20 concerts suppose they sell the same number of tickets for each concert how many tickets with they sell for each concert?
Answer:
50 tickts
Step-by-step explanation:
We want to spread 1,000 tickets equally over 20 concerts. This calls for division
1000/20=50
50 tickets are sold each concert
3.
Franco deposits $3600.00 in a savings account. The account pays an annual interest rate of 4%. He makes no other deposits or withdrawals. After 3 months, the interest is calculated. How much simple interest did his money earn?
36.00
38.00
35.47
37.00
Answer:
His money earned $36 after 3 months
Step-by-step explanation:
* Lets revise the rules of simple interest
- Simple Interest Equation (Principal + Interest)
A = P(1 + rt)
- Where:
• A = Total amount (principal + interest) future amount
• P = Principal Amount
• I = Interest Amount
• r = Rate of Interest per year in decimal; r = R/100
• t = Time Period involved
* To calculate the interest I use the formula
I = P × r × t
* Lets solve the problem
- The rate is annual
- The interest calculated after 3 months
∴ I = P × R/100 × t/12
∵ P = $3600.00
∵ R = 4%
∵ t = 3 month
∴ I = 3600.00 × 4/100 × 3/12 = $36
* His money earned $36 after 3 months
When constructing an inscribed polygon with a compass and straightedge ,how should you start the construction?
Place a point on your paper and then use a compass to construct a circle.
Answer with explanation:
To construct an inscribed polygon with a compass and straightedge:
The first step is:
1.⇒Draw the polygon either it is Regular or Irregular
→A polygon is said to be regular, if it's all sides and all Interior Angles are equal.
→Draw the perpendicular bisector of all the sides of Polygon.
→The point where these two perpendicular bisector meet is center of the circle.
→Draw the circle which will pass through all the vertices of the Polygon you have drawn.
What are the excluded values of x for 2-3x-28/х2-2x-35
х= -7, x= 4
x=-7, х = 5
x=-5, х = 7
х= 4 х=7
Answer:
C
Step-by-step explanation:
The excluded values are the values of x that make the denominator of the rational function equal to zero as this would make the function undefined.
Equate the denominator to zero and solve for x to obtain the values that x cannot be.
x² - 2x - 35 = 0
(x - 7)(x + 5) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 7 = 0 ⇒ x = 7
x + 5 = 0 ⇒ x = - 5
Excluded values of x are x = - 5, x = 7 → C
HELPPPP ME PLSSSS!!!!!
Answer:
I believe the answer would be C.
Step-by-step explanation:
First, simply look at the roots of each answer choice. A rational number is any number that can be written as a fraction.
In the first option choice [A.], the square root of 8 is 2.8284.... a long decimal that continues for a whi;e. So, it can't be written as a fraction.
In the second option choice [B.], the square root of 24 is 4.8989.... another long decimal that continues for a while. So, it can't be written as a fraction.
In the third option choice [C.], the square root of 81 is 9. 9 can be written as a fraction [for example 27/3] So it's the correct answer.
In the last option choice [D.], the square root of 2 is 1.4142.... another long decimal that continues for a while. So, it can't be written as a fraction.
This is why C. is the right answer! I hope this helps!!!
What is the value of x? Round to the nearest tenth. Please Help
Answer:
x = 6.5 cmStep-by-step explanation:
The segment 20.2 cm is the tangent. Therefore x and 20.2cm are perpendicular.
Use the Pythagorean theorem:
[tex]leg^2+leg^2=hypotenuse^2[/tex]
We have
[tex]leg=x,\ leg=20.2cm,\ hypotenuse=(14.7+x)cm[/tex]
Substitute:
[tex]x^2+20.2^2=(14.7+x)^2[/tex] use (a + b)² = a² + 2ab + b²
[tex]x^2+408.04=14.7^2+(2)(14.7)(x)+x^2[/tex] subtract x² from both sides
[tex]408.04=216.09+29.4x[/tex] subtract 216.09 from both sides
[tex]191.95=29.4x[/tex] divide both sides by 29.4
[tex]x\approx6.5\ cm[/tex]
what is the volume of the sphere? round to the nearest cubic unit.
diameter: 16cm
a)268cm
b)2145cm
c)17, 157cm
d)536cm
Volume of a sphere:
(4/3)(pi)r^3
.
radius (r) is half the diameter or 8 inches.
(4/3)(3.14)8^3
2144 cubic inches
The volume of the sphere would be 2144 cubic inches
What is the Volume of a sphere?A sphere is a three-dimensional shape analouge of a circle.
The Volume of a sphere = 4/3πr^3
We are given that the diameter of the sphere as 16 cm.
Since radius (r) is half the diameter or 8 inches.
Volume of a sphere:
= 4/3πr^3
= (4/3)(3.14)8^3
2144 cubic inches
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What is the perimeter of the trapezoid 10 POINTS
Answer:
19 units
Step-by-step explanation:
There are two sides that are equal; they are 4 units long.
The unequal sides are 7 and 4 in length.
Add up these four sides to obtain the perimeter:
P = 4 + 4 + 4 + 7 = 19 units
The perimeter of a figure is the distance around the figure.
To find the perimeter of the trapezoid shown, we can simply add the sides. Each square represents 1 unit.
Once we count each square that has a line through it, we will get
7 + 4 + 4 + 4 = 19
Therefore, the perimeter of the trapezoid is 19 units.
1. A printer prints 12 pages per minute. Which will deter
pages per minute. Which will determine the total
number of pages that can be printed by 3 printers in an hour
12 per Minute
A (12 x 3) x 60
B. 12 + 3 + 60
C. (12 + 3) x 60
D. 12 x 3 + 60
Answer:
A
Step-by-step explanation:
if you need one comment below
Answer: A. (12x3) x 60= 2160 pages per 60 minutes or 1 hour.
(12x3) solve first = 36 pages printed per minute by 3 printers.
36 pages per minute x times 60 minutes =
= 2160 pages, is how many pages 3 printer printing 12 pages a minute can print in 60 minutes or 1 hour.
Step-by-step explanation:
Please explain your answer. THX!!!!
Answer:
1)[tex]cos(x)sin^{2}x[/tex]
2)0
Step-by-step explanation:
for part 1:
Given cos(x) - cos^3(x)
= cos(x) (1- cos^2(x))
Using the identity [tex]cos^{2}x +sin^{2}x=1\\ sin^{2}x=1-cos^{2}x[/tex]
= cos(x)sin^2(x)
for part 2:
given
=[tex]cos\frac{5\pi }{8}cos\frac{\pi }{8} + sin\frac{5\pi }{8}sin\frac{\pi }{8}[/tex]
Using the identity cos(a)cos(b) + sin(a)sin(b)= cos(a-b)
=[tex]cos(\frac{5\pi }{8} -\frac{\pi }{8})[/tex]
=[tex]cos\frac{4\pi }{8}[/tex]
=[tex]cos\frac{\pi }{2}[/tex]
=0!
Helllllppppppp!! Can i have an explanation of this?
Okay so if the regular price of the shirt is 100% as $25 and you have a 30% discount you are still paying 70% (100-30=70) so 70% as a decimal is .70 and $25 x .70 is $17.50. Therefore the shirt is $17.50 after the discount.
Alright so, what it’s basically asking for is 70% of 25. This is the price of the shirt after you’ve accounted for the 30% discount
Then you would multiply 25 by .70, giving you $17.50
Hope this helps!
Please help anyone and explain please
So if you distribute 4 in the first parentheses, you get 12x+20y+8z.
Then you distribute 3 in the second parentheses. You'll get 3x-3z. That all equals 12x+20y+8z+3x-3z.
Now you have to start combining numbers with the same variable. Start with x. 12x+3x is 15x.
y has no other common variable, it's left alone.
8z-3z is 5z
All together now with the numbers in simpler form, the equation is 15x+20y+5z
Jenna's would be the right answer because when you distribute 5 in her answer you get 15x+20y+5z
Answer:is jennas right i think i got it ty
Solve for x. (X+10)(x+10)=0
Answer:
use foil method-first inside outside last
Step-by-step explanation:
Answer:
X = -10
Step-by-step explanation:
Adding negative ten and ten results in zero, and zero multiplied by anything is, of course, still zero.
(-10 + 10) * (-10 + 10) = 0
0 * 0 = 0
X=-10
Because (x+10)(x+10)=0
So it becomes (x+10)^2=0
And therefore x=-10
which of the following is an equivalent expression?
just open the bracket and do algebra. the answer should be C
what is the value of Tan A
8/10
6/10
8/6
6/8
Answer:
6/8
Step-by-step explanation:
Formula
Tan(A) = side opposite / side adjacent
Givens
side opposite = 6
side adjacent = 8
Tan(A) = 6/8
Answer:
6/8
Step-by-step explanation:
tan A = opp / adj = 6 / 8 = 3/4. This corresponds to the last answer choice.
Simplify the following radicals (in exponential notation) (x^9y^6z^15)^1/3
[tex]\bf (x^9y^6z^{15})^{\frac{1}{3}}\implies \stackrel{\textit{distributing the exponent}}{\left(x^{9\cdot \frac{1}{3}}y^{6\cdot \frac{1}{3}} z^{15\cdot \frac{1}{3}} \right)}\implies x^3y^2z^5[/tex]
What quadratic has roots x=8 and x= -5
Answer:
The quadratic function x^2 -3x + 40 has roots x=8 and x= -5.
Step-by-step explanation:
If a polynomial has roots x=8 and x=-5, then we know that the factorized form is:
(x-8)(x+5)
So, to find the polynomial we need to expand the polynomials:
(x-8)(x+5) = (x^2 +5x - 8x + 40) = x^2 -3x + 40
Answer:
x² - 3x - 40 = 0
Step-by-step explanation:
The roots are x=8 and x= -5
The quadratic equation will be;
(x-8)(x+5) = 0
Therefore;
x² - 8x + 5x -40 = 0
x² - 3x - 40 = 0
On a scale drawing, the height of a tree is 3.75 inches.if the scale of the drawing is 1 in: 50ft,how tall is the tree?
Answer:
187.5
Step-by-step explanation:
50 × 3 =150
50 ÷ 4 = 12.5
12.5 ×3= 37.5
150 + 37.5 =187.5
Answer:
187.5
Step-by-step explanation
50 × 3 =150
50 ÷ 4 = 12.5
12.5 ×3= 37.5
150 + 37.5 =187.5
What is the first step when rewriting y=3x^2 +9x-18 in the form y=a(x-h)^2 +k?
ANSWER
3 must be factored from 3x² +9x
EXPLANATION
The given function is
[tex]y = 3 {x}^{2} + 9x - 18[/tex]
To write the given function in vertex form, we need to complete the square.
But before we come complete the square, we must ensure that the coefficient of the quadratic term is unity.
Hence we factor 3 from 3x² +9x to obtain:
[tex]y = 3( {x}^{2} + 3x) - 18[/tex]
The first choice is correct.
The first step to rewrite the equation y=3x^2 + 9x - 18 in the form y=a(x-h)^2 + k is to complete the square.
Explanation:The first step to rewrite the equation y=3x^2 + 9x - 18 in the form y=a(x-h)^2 + k is to complete the square. To do this, we need to factor out a from the quadratic term:
y=3(x^2 + 3x) - 18
Next, we take half of the coefficient of x (which is 3) and square it to find h:
h = (3/2)^2 = 9/4
Now, we add this value inside the parentheses and subtract it outside:
y=3(x^2 + 3x + 9/4) - 18 - 9/4
Simplifying further, we get:
y=3(x + 3/2)^2 - 81/4
So, the equation y=3x^2 + 9x - 18 can be rewritten in the form y=a(x-h)^2 + k as y=3(x + 3/2)^2 - 81/4.
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a ladder that is 26 feet in length touches a house at a height of 24 feet from the ground. how far from the house is the base of the ladder?
The house is 10 units far from the base of the ladder?
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that
length of ladder = 26 feet
And height of house = 24 feet
According to given scenario it will form a right angled triangle.
In which the length of ladder is hypotenuse
Height of house be perpendicular
And base we have to calculate.
We know that the Pythagoras theorem for a right angled triangle:
(Hypotenuse)²= (Perpendicular)² + (Base)²
Now plug the values
(26)²= (24)² + (Base)²
(26)²= (24)² + (Base)²
676 = 576 + (Base)²
(Base)² = 100
Base = 10 units
Thus, the base is of 10 units.
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VARIABLE ON BOTH SIDES. PLEASE HELP! 40 PTS
2x + 4 = 3 (x-2) + 2 show your work
2x+4= 3x-6+2
2x+4=3x-4
2x-3x+4=3x-3x-4
-x+4=-4
-x+4-4= -4-4
-x=-8
Need to multiply by -1 for x to be positive and also for -8
-1(-x)= -1(-8)
x=8
Answer:
Step-by-step explanation:
2x+4=3(x-2)
2x+4=3x-6
+6 -2x
10 = 1x
1 = 1x
10= x
Martin has a business washing cars. Last year he washed 20 cars a week. This year, he wants to increase his business to 1,200 cars a year. How many cars will he have wash each month on average?
Great Question!
The last year part is extra information. 1200÷12 (months in a year)= 100
He will have to wash 100 cars each month.