Answer:
4,5,6 are the three consecutive numbers. 16, 25 and 36 are their squares.
Step-by-step explanation:
Let the three consecutive numbers be x, (x+1), (x+2)
Now, the squares of these three numbers are [tex]x^{2} ,(x+1)^{2} ,(x+2)^{2}[/tex]
Sum = 77
∴by the problem ,
[tex]x^{2} +(x+1)^{2}+(x+2)^{2} = 77\\x^{2} +(x^{2} +2x+1)+(x^{2}+4x +4) = 77\\x^{2} +x^{2} +2x+1+x^{2} +4x +4 = 77\\3x^{2} +6x+5 = 77\\3x^{2} +6x = 77-5\\3x^{2} + 6x = 72\\3x^{2} +6x-72= 0\\[/tex]
{Taking 3 common }
[tex]x^{2} +2x- 24 = 0\\[/tex]
{By factorization}
[tex]x^{2} +2x- 24 =0\\ x^{2} +6x-4x-24=0\\x(x+6)-4(x+6)=0\\(x+6)(x-4)=0\\[/tex]
Therfore,
[tex]x= -6,4\\[/tex]
X can't be negetive
∴ [tex]x =4\\x+1=5\\x+2=6[/tex]
The squares of the three consecutive numbers are 16, 25, 36
The three consecutive numbers whose sum is 77 are 4, 5, 6
please help on how to get last few marks
Answer:
K = 12
Step-by-step explanation:
10 Cos 30° – 3 Tan 60°
The above expression can be simplified as follow:
10 Cos 30° – 3 Tan 60°
Recall:
Cos 30° = √3/2
Tan 60° = √3
Therefore,
10 Cos 30° – 3 Tan 60°
10 (√3/2) – 3(√3)
5√3 – 3√3
(5 – 3) √3
2√3
To write the above expression 2√3 in the form √K, we simply do the following:
2√3
Find a number, such that the square root of the number will result to 2. The number is 4 as shown below
√4 = 2
Next, replace 2 with √4 in the expression above
2√3
= √4 × √3
= √(4 × 3)
= √12
Therefore,
2√3 = √12
Comparing √12 with √K,
√12 = √K
K = 12
factoring trinomials: 8)-2x2 + 8x + 10 *
Answer:
-2(x - 5)(x + 1)
Step-by-step explanation:
-2x² + 8x + 10
-2(x² - 4x - 5)
-2(x - 5)(x + 1)
Step-by-step explanation:
Hey, there!!
Let's do it simply, ok.
Given that,
[tex] = - 2 {x}^{2} + 8x + 10[/tex]
Take (-2) common to make it easy.
[tex] = -2( 2 {x}^{2} - 8x - 10)[/tex]
= -2{ x^2-(5-1)x -5}
Multily with x,
= -2 {x^2-5x+x-5}
Taking common,
= -2{x(x-5) +1(x-5)
= -2{(x+1)(x-5)}...is your required answer.
Hope it helps...
The original price of a toy was $400. It was increased by 20%. after some time the sale of toys decreased. So, the shop owner decided to decrease the price by 20%
What is the final price of the toy.
Answer:
$384
Step-by-step explanation:
Original price = $ 400
Increased price = 20% of 400
= [tex]\frac{20}{100}[/tex] * 400
= $ 80
Price after increase = 400 + 80 = $ 480
Decreased price = 20% of 480
= [tex]\frac{20}{100}\\[/tex] * 480
= $ 96
Price after decreasing 20% = 480 - 96 = $ 384
Final price of the toy = $ 384
Simply this expression: -2+3-(5-6x)
Answer:
6x-4
Step-by-step explanation:
Answer:
-4-6x
Step-by-step explanation:
you would just combine -2 and 3 so you get 1 and then you would get 1-(5-6x) and you can just take away the parenthesis since in this case it doesn't matter and when you simplify that you get -4-6x
what is blank plus 1/2 to equal 4
Answer:
either 3 1/2 or 7/2
Step-by-step explanation:
4 is equal to 8/2
8/2 minus 1/2 is 7/2
7/2 can be simplified to be 3 1/2
Determine the intercepts of the line. 2x+5y=-62x+5y=−62, x, plus, 5, y, equals, minus, 6 yyy-intercept: \Big((left parenthesis ,,comma \Big))right parenthesis xxx-intercept: \Big((left parenthesis ,,comma \Big))right plz just give the Y and X intercepts
Answer:
y- intercept (0, -1.2)
x- intercept (-3, 0)
Step-by-step explanation:
Line is given:
2x + 5y = -6Y- intercept:
When x= 0
2*0 + 5y = -65y = -6y = -6/5y = -1.2Point is (0, -1.2)
X- intercept:
When y = 0
2x + 5*0 = -62x = -6x = -6/2x = -3Point is (-3, 0)
On a zip-line course, you are harnessed to a cable that travels through the treetops. You start at platform A and zip to each of the other platforms. How far do you travel from Platform B to Platform C? (Please add the EXPLANATION)
Answer:
We have to travel 26.93 units from platform B to C.
Step-by-step explanation:
Length of a segment having coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is determined by the formula,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
From the graph attached,
Coordinates of the points B and C are (-25, -20) and (-15, 5) respectively.
Distance between these points B and C Or length of BC will be,
BC = [tex]\sqrt{(-25+15)^2+(-20-5)^2}[/tex]
= [tex]\sqrt{100+625}[/tex]
= [tex]\sqrt{725}[/tex]
= [tex]5\sqrt{29}[/tex]
= 26.93 units
Therefore, we have to travel 26.93 units from platform B to C.
Answer:
22.4 meters
Step-by-step explanation:
Because the distance and stuff I don't really know sorry
If you transform a line segment with a sequence of reflections, rotations, or translations, is it still a line segment?
Answer:
Yes
Step-by-step explanation:
Transformation of a two-dimensional shape or pre-image or polygon in mathematics is the manipulation of the two-dimensional object or pre-image or polygon within a system of coordinates or plane.
Transformations are a guide to the nature of the pre-image and image of two dimensional shape as it is translated within a system of coordinates
Rigid transformations are those that does not involve a change in the size of the pre-image, and includes reflections, rotations, and translations
Therefore, the line undergoes rigid transformation and the dimensions of the line is preserved making it still a line segment.
Bruhhh, I think we got to the same online school XD
how to put this in a simple form 5*5*5*(-4)*(-4)*(-4)*(-4)*(-4) like i know how to put the 5 exponent of 3 but i don't know ow to do the (-4)
Answer:
5^3 and (-4)^2
Step-by-step explanation:
A^b means a is the base and b is the exponent
*PLEASE HELP , I DONT GET IT* What would be the volume of Prism F after a scale factor of 2 is applied to the dimensions?
Answer:
Increases by a factor 8.
Volume = 685.12.
Step-by-step explanation:
The volume will increase by a factor of 2^3 , because the volume is 3 dimensional.
That is the new volume = 85.64 * 8
= 685.12.
pineapples are on sale for $1.50 per pound. Let y be the total cost in dollars of x pounds of pineapple which equation represents the situation
Answer:
y=1.5x
Step-by-step explanation:
Step 1: State what you know
Pineapples are 1.50 per pound
X represents how many pounds of pineapples you want to buy
Y represents how much do 'x' amount of pineapples cost in dollars
Step 2: Write the equation
y (the price of 'x' pounds of pineapple)=1.5(the cost of a pineapple)x(how many pounds of pineapples you bought)
Therefore the equation that represents the problem is y=1.5x
Answer:
y=1.5x
Step-by-step explanation:
hello, please help asap! Thank you <33
Answer:
1
Step-by-step explanation:
|x| means the absolute value, which is 4 and -4
Answer:
A
Step-by-step explanation:
So we have the equation:
[tex]|x|=4[/tex]
Solve for x. Use the definition of absolute value:
[tex]|x|=4[/tex]
This means that:
[tex]x=4\text{ or } x=-4[/tex]
And... we're done :)
The answer is A.
write 23/25 as a decimal
This diagram is a straightedge and compass construction. A is the center of one circle, and B
is the center of the other. Select all the true statements.
a. AC = BC
b. AC = BD
C. CD = AB
d. ABCD is a square
e. ABD is an equilateral triangle
f. CD = AB + AB
Answer:
Correct choices are a, b, e
Step-by-step explanation:
As per diagram, the circles are equal.
Since the distance AB is the radius of both circles:
AB = AC = BC = BD = AD = rSo the answer choices:
a. AC = BC
Correct, both equal to rb. AC = BD
Correct, both equal to rC. CD = AB
Incorrect. Half of CD is the leg of 30-60-90 triangle and is equal to r√3/2, so CD = AB√3d. ABCD is a square
Incorrect. ACBD is rhombuse. ABD is an equilateral triangle
Correct, all three sides are equal to rf. CD = AB + AB
Incorrect as CD = AB√318 divide by 2/3 ??????????
Answer:
30
Step-by-step explanation:
2/3 = .6
18/.6 = 30
Answer:
27
Step-by-step explanation:
If you want to divide a fraction, you have to divide it from it's reciprocal.
The reciprocal of 2/3 is 3/2.
Now, you have to multiply 3 and 18
18 x 3/2 = 54/2
54 divided by 2 is 27.
Hope it helped :>
Find the solution for the following equation: 3x = 45
Answer: x = 15
Step-by-step explanation: Since x is multiplied by 3, divide both sides
of the equation by 3 to get x by itself, and show all your work!
Put both sides of the equation over 3
and cancel out the 3's on the left side.
It's tempting to want to show off your
math skills by doing the work in your head.
Don't fall into this trap!
It's extremely important to develop the habit
of writing every step down on paper or digitally.
It will serve you very well for many years.
find the perimeter of a semi circle whose diameter is 21cm
Answer:
[tex] \boxed{ \boxed{ \bold{ \purple{16.485 \: cm}}}}[/tex]Step-by-step explanation:
Diameter ( d ) = 21 cm
Radius is just half of the diameter
Radius ( r ) = [tex] \sf{ \frac{21}{2} }[/tex] = 10.5 cm
Now, let's find the perimeter of a semi - circle :
[tex] \sf \frac{1}{2} \pi \: r \: [/tex]
Plug the values
⇒[tex] \sf{ \frac{1}{2} \times 3.14 \times 10.5}[/tex]
Calculate
⇒[tex] \sf{16.485 \: cm}[/tex]
Hope I helped!
Best regards!
Enter the numerator and denominator of a fraction in simplest form that is equivalent to 0.941941 Repeating.
Answer:
[tex]\frac{941}{999}[/tex]
Step-by-step explanation:
Let x = 0.941941........
Three digits are repeating. So, multiply both side by 1000
1000x = 941.941941...... (I)
x = 0.941941....... (II) {subtract equation (II) from (I) }
999x = 941
x = 941/999
Pls help me and thank ya!!
Answer:
Option 1
Step-by-step explanation:
Rational numbers do not have infinite decimals.
Option 1:
-5, 3/4 and √49 are all rational. Correct
√49 = 7
3/4 = 0.75
-5 = -5
Option 2:
1/4 = 0.25
5 = 5
√12 = 3.4641...
Incorrect
Option 3:
-1/2 = -0.5
-3 = -3
√8 = 2.82841...
Incorrect
Option 4:
1/7 = 0.142857...
9 = 9
√11 = 3.31662...
Incorrect
Fill in the blank
answers parallel , congruent, opposite, quadrilateral, four ,four ,rhombus, connected right
pls help
Answer:
Quadrilateral
Four
Parallel
Four
Right
Congruent
Rhombus
Opposite
Connected
Step-by-step explanation:
The volume of a cylindrical soup can is represented by the expression πr3 + 7πr2, where r is the radius of the cylinder. Which statement best interprets the factor (r + 7) in this context
Answer:
Step-by-step explanation:
Given the volume of the cylindrical soup expressed as V = πr³+ 7πr²
From V = πr³ + 7πr²;
factor out the common variable
V = πr³ + 7πr²
V = πr²(r+7) ... 1
The original volume of a cylinder V = πr²h .... 2 where;
r is the radius of the cylinder
h is the height of the cylinder
Equating equation 1 and 2, we will have;
πr²(r+7) = πr²h
Divide both sides by πr²
πr²(r+7)/ πr² = πr²h/ πr²
r+7 = h
h = r+7
Hence the factor in the context given is equivalent to the height of the cylinder written as a function of its radius r. The statement means that the height of the cylindrical soup is 7 more than its radius.
Answer:
Step-by-step explanation:
the height of the cylendar is 7 units greater than the radaius
Solve for x. Evaluate and round your answer to 1 decimal place (tenths place). 10x=3588
Answer:
x =3.6Step-by-step explanation:
[tex]10^x=3588\\\mathrm{If\:}f\left(x\right)=g\left(x\right)\mathrm{,\:then\:}\ln \left(f\left(x\right)\right)=\ln \left(g\left(x\right)\right)\\\ln \left(10^x\right)=\ln \left(3588\right)\\x\ln \left(10\right)=\ln \left(3588\right)\\\mathrm{Solve\:}\:x\ln \left(10\right)=\ln \left(3588\right):\quad x=\frac{\ln \left(3588\right)}{\ln \left(10\right)}\\\\= 3.55485\\=3.6[/tex]
3.3x10^5+44,000 in scientific notation? please please
Answer
4.4×10^4
For converting a number into scientific form just bring the decimal after the first non zero digit and write it with multiplier 10 raising to the number of places you moved the point
Step-by-step explanation:
N=1500(2^018t), t≥0 Find the initial number of cells (N) in the culture, given the exponential function.
Answer:
1500
Step-by-step explanation:
Step 1: Understand what the question is asking you
It wants to know how much cells do you start off with or in other words how much cells are in the culture when time is 0
Step 2: Set t = 0
[tex]N = 1500(2^{0.18(0)} )[/tex]
Step 3: Solve for N
[tex]N = 1500(2^{0.18(0)} )[/tex]
[tex]N = 1500(2^{0} )[/tex]
[tex]N = 1500(1 )[/tex]
[tex]N = 1500[/tex]
Therefore when the initial amount of cells there in the culture is 1500
Consider the function below. g(x) = 4x − 1 Find the difference quotient below (where h ≠ 0) and simplify your answer. g(x + h) − g(x) -------------------- h
Answer:
The difference quotient is 4.
Step-by-step explanation:
Given that:
[tex]g(x) = 4x - 1[/tex]
To find:
Difference quotient = ?
where [tex]h \neq 0[/tex]
Solution:
Formula for Difference quotient is given as:
[tex]\dfrac{g(x+h)-g(x)}{h}[/tex]
First of all, let us find out [tex]g(x+h)[/tex]
Replacing [tex]x[/tex] with [tex]x+h[/tex]
[tex]g(x+h) = 4(x+h)-1 \\\Rightarrow g(x+h) = 4x+4h-1[/tex]
Now,
[tex]g(x+h)-g(x) = (4x+4h-1 )-(4x-1)\\\Rightarrow g(x+h)-g(x) = 4x+4h-1 -4x+1\\\Rightarrow g(x+h)-g(x) = 4h[/tex]
Putting the above value in:
[tex]\dfrac{g(x+h)-g(x)}{h} = \dfrac{4h}{h}[/tex]
We are given that, [tex]h \neq 0[/tex]
[tex]\therefore \dfrac{4h}{h} = 4[/tex]
So, the difference quotient is 4.
order of operations
Simplify z+9(8−x)+8(z+8)=
Simplify (3−10)^2−(5−12)^2
Evaluate 2^2⋅4^3=
Answer:
z+9(8−x)+8(z+8)=
z+72-9x+8z+64=
9z-9x+136
(3−10)^2−(5−12)^2 parenthesis first
(-7)²-(-7)²=
49-(49)=49-49=0
2^2⋅4^3 exponent first
2*2*4*4*4
4*64=256
A jar contains 12 caramels, 7 mints and 16 dark chocolates. The probability of selecting a dark chocolate, eating it, and then a selecting a caramel is the setup. What is the probability fraction of "selecting a caramel" after selecting a dark chocolate and eating it.
Answer:
6/17
Step-by-step explanation:
Given the following :
Number of caramel = 12
Number of dark chocolate = 16
Number of mint = 7
probability fraction of "selecting a caramel" after selecting a dark chocolate and eating it.
After eating means : picking without replacement.
Probability = (Number of required outcomes / total possible outcomes)
Total number of items = ( 7 + 12 + 16) = 35
After first picking a dark chocolate and eating it, total number of items left in the jar becomes:
(35 - 1) = 34
Then,
P(picking a caramel) = (number of caramels / total number of items)
P(picking a caramel) = 12 / 34 = 6/17
Identify the roots of the equation x^2 = 9x − 14 by factoring. x = 2 or x = 7 x = −2 or x = 7 x = 2 or x = −7 x = −2 or x = −7
Answer:
x = 7, x = 2
Step-by-step explanation:
Given
x² = 9x - 14 ( subtract 9x - 14 from both sides )
x² - 9x + 14 = 0 ← in standard form
(x - 7)(x - 2) = 0 ← in factored form
Equate each factor to zero and splve for x
x - 7 = 0 ⇒ x = 7
x - 2 = 0 ⇒ x = 2
PLEASE HELP ME ILL MARK BRIANLIEST I NEED IT ASAP!
Answer:
14(1/2-t)≤28
14(1-2t)/2≤28
14-28t≤28
-28t≤56-14
-28t≤42
t≤42/-28
t≤ -1.5
15k+11≤18k-5
15k-18k≤-5-11
-3k≤-16
k≤-16/-3
k≤-5.333
44y>11+88y-22y
44y>11+66y
44y-66y>11
-22y>11
y>11/-22
y>-0.5
7/9(b-27)>49/81
(7b-180)/9>48/81
81(7b-189)>9(49)
567b>441+15309
567b>15750
b>15750/567
b>27.78
Is it possible to draw a quadrilateral with one pair
of congruent consecutive sides?
- yes or no
It is possible to draw a quadrilateral with one pair of congruent consecutive sides
How to determine the true statement?A quadrilateral has four sides
The four sides can be congruent or not congruent
However, when a pair of consecutive sides are congruent, then the quadrilateral is a square
Hence, the statement is yes
Read more about quadrilaterals at:
https://brainly.com/question/22254043
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