The equation that can be used to solve for n, the smaller of the two numbers would be n² + n - 210 = 0.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
If we use n to be the smaller number of two integer numbers, then the next consecutive number is n + 1.
The product of those two numbers would become n × (n + 1) = n (n + 1).
Half of that product is n (n + 1) / 2.
And the question states that the equation is equal to 105, so the equation becomes,
n (n + 1) / 2 = 105
Now we have to simplify that equation until we get an expression equal to one of the choices,
Multiply both sides by 2
n (n + 1) = 210
n² + n = 210
Subtract 210 from both sides
n² + n - 210 = 0
Thus, the equation formed is the quadratic equation.
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Answer:
n² + n - 210 = 0 is your answer! hope it helps!
Step-by-step explanation:
Segment bc is parallel to De. Use the proportion from a B to BD to find the missing length of CE
Answer:
CE = 6
Step-by-step explanation:
we use the proportion relationship:
[tex]\frac{AB}{BD} = \frac{AC}{CE\\}\\then[/tex]
[tex]\frac{2}{3} = \frac{4}{CE}\\\\then[/tex]
2×CE = 3 ×4 (cross multiply)
then
2×CE = 12
then
CE = 12/2 = 6
Explain how to graph the point (-4, 6)
Answer:
four spaces to the left, and 6 spaces up.
double d, then subtract 9 from the result
Answer:
2d - 9.
Step-by-step explanation:
That would be
double d = 2d
subtract 9 = -9 to give:
2d - 9.
The graph below shows a linear function and an exponential function.
What is the minimum y-value after which the exponential function will always be greater than the linear function?
y = 1
y = 3
y = 4
y = 5
Answer:
4
Step-by-step explanation:
Look at △ABC and △DEF on this coordinate grid.
Which transformation shows that △ABC and △DEF are similar?
A
a dilation of △ABC with a scale factor of 2
B
a translation of △ABC 1 unit up and 3 units to the right
C
a dilation of △ABC with a scale factor of 12
D
a translation of △ABC 3 units up and 3 units to the right
Answer:
A
Step-by-step explanation
Dilation: A shape is scaled up or down by a scale factor
Translation: A shape is moved on a coordinate plane to a different spot.
A works because lets you one side (the bottom side). The bottom has a length of 3, and the bigger one has a length of 6, showing a scale factor of 2.
Rebecca bought 6 boys' bicycles and 8 girls' bicycles. If it takes her 22 minutes to unpack and assemble each one, how long will it be before they are all assembled?
Answer:
308 minutes or 5 hours and 8 minutes
Step-by-step explanation:
First, let's add the bicycles of both boys and girls together:
6 + 8 = 14
Now, let's multiply that number by 22 since she will have to assemble all of those bicycles and it will take 22 minutes for each:
22 x 14 = 308
It will take a total of 308 minutes or 5 hours and 8 minutes to assemble all of those bicycles.
What is
5d- 1 = -11
Can I get a breakdown on the answer please
Answer: d=-2
Step-by-step explanation:
As we know the order of operations are
1) Parenthesis/Brackets
2) Exponents
3) Multiplication/Division
4) Addition/Subtraction
However, when you solve equations you must do the order of operations backwards
So start by adding 1 to both sides because whatever you do to one side of the equation you must do to the other side
[tex]5d-1=-11\\5d-1+1=-11+1\\5d=-10[/tex]
Now divide both sides by 5 to isolate d
[tex]5d=-10\\\frac{5d}{5} =\frac{-10}{5} \\d=-2[/tex]
Mr. Lee has 61 pencils. He gave some pencils away. Now he has 33 pencils left. Which equation can be used to find how many pencils Mr. Lee gives away.
Answer:
61-33...
Step-by-step explanation:
If he gave away 61 from his 33 then its 61-33
Jane has two savings accounts, Account S and Account C. Both accounts are opened with an initial
deposit of $400 and an annual interest rate of 4.5%. No additional deposits are made, and no withdrawals
are made. Account S earns simple interest, and Account c earns interest compound annually. Which account will earn more interest after 10 years? How much more?
Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. The account which is earning compount interest will earn $41.19 more on interest.
What is simple interest?Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,
[tex]\text{Simple Interest}= \dfrac{P \times R \times T}{100}[/tex]
where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.
The interest on account S which earns simple interest at rate of 4.5% can be written as,
[tex]\text{Interest in Account S}= \dfrac{P \times R \times T}{100} = \dfrac{\$400 \times 4.5 \times 10}{100} = $180[/tex]
The interest on accout C which earns compound interest at a rate of 4.5% can be written as,
[tex]\text{Interest in Account C}=P(1+r\%)^n - P\\[/tex]
[tex]\text{Interest in Account C}=\$400(1+4.5\%)^{10} - $400 = $221.19[/tex]
The difference in the amount earned by the two account will be,
[tex]\rm Difference = (Interest\ in\ Account\ C) -(Interest\ in\ Account\ S)[/tex]
[tex]=\$221.19 - \$180\\\\=\$ 41.19[/tex]
Hence, the account which is earning compount interest will earn $41.19 more on interest.
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The wavelength of a sound wave in this room is 4. 13 m and the frequency is 75 Hz. What is the speed of the wave in the room?
if you double the frequency of the sound wave but keep the wavelength the same, determine the new speed of the wave.
Answer:
[tex]\color{indigo}\rule{1pt}{1000000pt}[/tex]
Which statement best describes the value of 18 ?
A. The value of 18 is between 2 and 2.5.
B. The value of 18 is between 2.5 and 3.
C. The value of 18 is between 3 and 3.5.
D. The value of 8 is between 3.5 and 4.
Answer:
B. The value of [tex]\sqrt{8}[/tex] is between 2.5 and 3.
Step-by-step explanation:
The square root of 8 is 2.83
Which is f(6) for the quadratic function graphed?
-2
-0.5
1.5
ОО
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
The Correct choice is 4
If we take value of x as 6 in the given function, then we will get the value of y as 4, as shown in the graph.
Consider the quadratic function.
f(p) = p2 – 8p – 5
What are the values of the coefficients and the constant in the functio
The values of the coefficients and constant are 1, -8 and -5
Standard quadratic equation
The standard quadratic expression is given as:
y = ax^2 + bx + c
where a, b and c are the constant
Given the quadratic function f(p) = p2 – 8p – 5, on comparing:
a = 1
b = -8
c = -5
Hence the values of the coefficients and constant are 1, -8 and -5
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the perimeter of a room is pm and height hm write the formula to calculate the area of four walls
Answer:
Volume of Cube = length cube
Total surface area=2(lb+lh+bh)
Volume of Cuboid=l×b×h
I think it will help you.
...................................................................
Answer:
b=2 and c=6
Step-by-step explanation:
According to the question,
a+b=c
Let b=2 and c =6 then, we get,
4+2=6
or, 6=6
proved
Propane is stored in a cylindrical tank with a diameter of 15 inches and a height of 48 inches. Which equation could be used to determine the radius of a spherical tank with the same volume?
Step-by-step explanation:
remember. the radius is always half the diameter.
volume of a cylinder
pi × r² × height
pi×7.5²×48 = pi×56.25×48 = 8,482.300165... in³
volume of a sphere
4/3 × pi × r³
and that volume should be the same as the cylinder. so,
4/3 × pi × r³ = pi×56.25×48
4/3 × r³ = 56.25 × 48
1/3 × r³ = 56.25 × 12
r³ = 56.25 × 36 = 7.5² × 6² = (7.5×6)² = 45² = 2025
[tex]r = \sqrt[3]{2025} [/tex]
which would be 12.65148998... in.
What is the volume of a moving crate with a length of 3 feet, a width of 2 feet, and a height of 5 feet?
Answer:
30ft³
Step-by-step explanation:
asuming it has the shape of a rectangular prism
formula would be
V=whl
step 1 swap the numbers
V= (2)(5)(3)
step 2 multiply
V= 30
step 3 add the labels
V=30ft³
To sew a pair of jeans, 630 feet of thread is needed. Unfortunately the fabric store only sells thread in yards. How many yards of fabric would you need to buy from the store to make a pair of jeans?
Answer:
210
Step-by-step explanation
One yard is equal to 3 feet so the simplest way is to divide the number of feet by 3 and that will give you your answer.
Answer:
210
Step-by-step explanation:
100 POINTS BRSAINLIEST ASAP 2 MINUTES LEFT
Answer: 12
Step-by-step explanation:
[tex]\mathrm{The\:mode\:is\:the\:term\:in\:the\:data\:set\:that\:appears\:the\:most.}[/tex]
[tex]\mathrm{If\:there\:is\:more\:than\:one\:term\:that\:appears\:the\:most,\:then\:there\:is\:no\:mode.}[/tex]
[tex]\mathrm{Count\:the\:number\:of\:times\:each\:element\:appears\:in\:the\:list}[/tex]
[tex]\begin{pmatrix}11&13&14&12\\ 1&2&2&3\end{pmatrix}[/tex]
[tex]\mathrm{The\:most\:common\:element\:in\:the\:list\:is\:12}[/tex]
Answer:
I'm sure It's 12
Step-by-step explanation:
To find the mode, order the numbers lowest to highest and see which number appears the most often.
11, 12, 12, 12, 13, 13, 14, 14
11=1
12=3 is the most common element
13=2
14=2
The quotient of (x5 – 3x3 – 3x2 – 10x 15) and (x2 – 5) is a polynomial. what is the quotient? x5 – 3x3 – 2x2 – 10x 10 x7 – 8x5 – 3x4 5x3 30x2 50x – 75 x3 2x – 3 x5 – 3x3 – 4x2 – 10x 20
The quotient of (x^5 – 3x^3 – 3x^2 – 10x + 15) and (x^2 – 5) is a (x^5-3x -3 - 24x/(x²-5)) polynomial.
What are the Quotients?Quotients are the number that is obtained by dividing one number by another number.
The quotient of (x^5 – 3x^3 – 3x^2 – 10x + 15) and (x^2 – 5) is a polynomial.
(x^5 - 3x³ - 3x² - 10x + 15) / p = x² - 5
p = (x^5 -3x³ - 3x² - 10x + 15)/(x² - 5)
= x^5 -3x - 3 - 24x/(x² - 5)
x^5 3x³ + 15x
x^5 - 3x² - 24x + 15
x^5 - 3x² + 15
0 - 24x + 0
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Answer: C
Step-by-step explanation:
The sum of two numbers is 53 The larger number is 11 more than the smaller number. What are the numbers?
Answer:
21 and 32 are the numbers
Step-by-step explanation:
Let assume that the the two numbers are X and Y and that X is the large number.
According to the question,
X + Y = 53 .................. Equation 1
then, X = 11 + Y........... Equation 2
Substitute equation 2 into equation 1.
[11 + Y] + Y = 53
11 + 2Y = 53
2Y = 53 - 11 = 42
2Y = 42
Y = 42 / 2 = 21,
Therefore, Y = 21 [Small number].
According to equation 1,
X +Y = 53
X + 21 = 53
X = 53 - 21 = 32.
Therefore, X = 32 [Big number]
The table below represents the data collected at a sandwich shop for the last six months with respect to the type of bread people ordered (sourdough or wheat) and whether or not they got cheese on their sandwich.
What is the P(cheese | wheat) ? Show all work to receive full credit.
Answer:
The number of times people got cheese and wheat is 1200
Step-by-step explanation:
Hope this helps! Have a good day! :)
Answer:
[tex]\sf \dfrac{12}{19}[/tex]
Step-by-step explanation:
To begin, add the column and row totals to the table (see attachment).
Let W = Wheat
Let C = With cheese
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
[tex]\implies \sf P(W)=\dfrac{1900}{3125}=\dfrac{76}{125}[/tex]
[tex]\implies \sf P(C)=\dfrac{2000}{3125}=\dfrac{16}{25}[/tex]
[tex]\implies \sf P(W \cap C)=\dfrac{1200}{3125}=\dfrac{48}{125}[/tex]
As the events W and C are not independent, we can use the formula:
[tex]\sf P(C\: | \:W)=\dfrac{P(W \cap C)}{P(W)}[/tex]
Substituting the values into the formula:
[tex]\sf P(C\: | \:W)=\dfrac{\frac{48}{125}}{\frac{76}{125}}=\dfrac{48}{76}=\dfrac{12}{19}[/tex]
The solid below is dilated by a scale factor of 5. Find the surface area of the solid
created upon
dilation.
W = 3
L = 6
H= 3
Considering the dilation, the surface area of the rectangular prism is of 0.432 units².
What is the surface area of a rectangular prism?The surface area of a rectangular prism of dimensions l, w and h is given by:
Sa = lwh.
In this problem, the dilation means that all dimensions are divided by 5, hence they will be considered as:
w = h = 0.6, l = 1.2.
Hence the surface area of the prism will be of:
Sa = lwh = 1.2 x 0.6 x 0.6 = 0.432 units².
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The surface area of the solid created upon dilation by a factor of 5 is 2250 unit²
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The solid below is dilated by a scale factor of 5. Hence:
New length = 6 * 5 = 30, new width = 3 * 5 = 15, new height = 3 * 5 = 15
Surface area = 2(30 * 15 + 30 * 15 + 15 * 15) = 2250 unit²
The surface area of the solid created upon dilation by a factor of 5 is 2250 unit²
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PLEASE HELP!!!!!!!!!!!!!!!! what is the perimeter of the trapezoid?
I NEED HELP FAST PLEASE HELP ME
Select the correct answer.
Which stem and leaf plot represents the given data set?
57,28,15,20,21,13,36
42,14,52,15,29,29,13,57
Which agency is responsible for promoting the welfare and opportunities of wage earners? a. fda b. hud c. dol d. cpsc please select the best answer from the choices provided a b c d
Answer:
the answer is (C) DOL
Step-by-step explanation:
PLease help me i will give brainliest
What are the solutions of x2 = 8 – 5x? startfraction 5 minus startroot 57 endroot over 2 endfraction comma startfraction 5 startroot 57 endroot over 2 endfraction startfraction negative 5 minus startroot 57 endroot over 2 endfraction comma startfraction negative 5 startroot 57 endroot over 2 endfraction startfraction negative 47 over 4 endfraction comma startfraction 67 over 4 endfraction startfraction negative 67 over 4 endfraction comma startfraction 47 over 4 endfraction
The solution of the given quadratic equation are,
[tex]x=\frac{-5-\sqrt{57} }{2}[/tex],[tex]x=\frac{-5+\sqrt{57} }{2}[/tex]
The equation to solve is given as
[tex]x^2=-5x+8[/tex]
Rearrange the given equation in standard form, [tex]ax^2+bx+c=0[/tex]
where, a,b and c are constants.
Therefore, we add 5x-8 on both sides to get,
[tex]x^2+5x-8=0[/tex]
Here, a=1,b=5 and c=-8
The solution to the above equation is
What is the quadratic formula?
[tex]x=\frac{-b\±\sqrt{b^2-4ac} }{2a}[/tex]
Use the value of a,b,c in the quadratic formula and solve for x
[tex]x=\frac{-5\±\sqrt{5^2-4(1)(-5)} }{2(1)}[/tex]
[tex]x=\frac{-5\±\sqrt{25+35} }{2(1)}[/tex]
[tex]x=\frac{-5\±\sqrt{57} }{2(1)}[/tex]
Therefore, the solutions are
[tex]x=\frac{-5-\sqrt{57} }{2},x=\frac{-5+\sqrt{57} }{2}[/tex]
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Answer:
answer is b
Step-by-step explanation:
an electrician completes 1/6 of a job in 2/3 hour. at this rate, how long does it take the electrician to complete the job?
PLEASE HELP!!!! IM GONNA GET IN TROUBLE
Answer:
4 hours.
Step-by-step explanation:
2/3 * 6
= 12/3
= 4 hours.
Answer:
4
Step-by-step explanation:
1/6 x 2/3(flip 1/6 to 6/1 so its easier to calculate; they mean the same thing)6/1 x 2/3 = 12/33 x 12 = 4Hope this helps <3
try to stay out of trouble lol
The temperature during a winter day was less than –3 degrees Fahrenheit. Yuri wants to write an inequality for the temperature during the winter day. Yuri uses the
variable t to represent the temperature. Which expression should Yuri write?A: t > -3 B: t > 3 C: t < -3 D: t < 3
Answer:
answer a
Step-by-step explanation:
thats rlly the only one that makes sense to me, i really hope this will help <3
The expression that Yuri should write will be t < -3. Then the correct option is C.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The temperature on a winter day was less than –3 degrees Fahrenheit.
Yuri wants to write an inequality for the temperature on the winter day.
Yuri uses the variable t to represent the temperature.
The sign used for less than is " < ".
t < -3
The expression that Yuri should write will be t < -3.
Then the correct option is C.
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