Total number of plants is p³ +2 ; when p = 3 the number of plants is 29 , Option D is the right answer.
What is an Equation ?Equation is mathematical statement formed when two algebraic expressions are equated using an equal sign.
It is given that
Let p represent the original number of plants in her garden.
then total number of plants in her garden = p³ +2
the total number of plants if p = 3 is
=3³ +2
= 29
p³ +2 ; when p = 3 the number of plants is 29 , Option D is the right answer.
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The first term of an arithmetic sequence is 1 and the sum of the first four terms is 100. Find the first four terms
Answer:
1, 17, 33, 49
Step-by-step explanation:
given the first term is 1 then the next 3 terms are
1 + d, 1 + 2d, 1 + 3d ( d is the common difference )
the sum of the first 4 terms is 100 , then
1 + 1 + d + 1 + 2d + 1 + 3d = 100 , that is
4 + 6d = 100 ( subtract 4 from both sides )
6d = 96 ( divide both sides by 6 )
d = 16
1 + d = 1 + 16 = 17
1 + 2d = 1 + 2(16) = 1 + 32 = 33
1 + 3d = 1 + 3(16) = 1 + 48 = 49
the first 4 terms are
1, 17, 33, 49
Answer:
see the file attached!!!!
Unit 8:Right triangles & Trigonometry
Answer:
[tex]24\sqrt{5}[/tex]
Step-by-step explanation:
So for this problem you can use the law of sines which states
[tex]\frac{a}{sin A} = \frac{b}{sin B}\\[/tex]
Since the angle is a right triangle we can find the hypotenuse by plugging in the values.
[tex]\frac{4\sqrt{15}}{sin 60} = \frac{hypotenuse}{sin 90}\\\\\frac{4\sqrt{15}}{sin 60} = hypotenuse\\hypotenuse = \frac{4\sqrt{15}}{\frac{\sqrt{3}}{2}} = \frac{8\sqrt{15}}{\sqrt{3}}\\hypotenuse = \frac{8\sqrt{45}}{3} = \frac{24\sqrt{5}}{3}\\[/tex]
we now just multiply that side by 3since all the sides should be equal since all the angles are equal and we get the length of 24sqrt(5)
HELPPP PLEASE!!!!!!!!!!!
Answer:
C
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (4, 0) ← 2 points on the line
m = [tex]\frac{0-2}{4-0}[/tex] = [tex]\frac{-2}{4}[/tex] = - [tex]\frac{1}{2}[/tex]
the y- intercept is the value of y where the line crosses the y- axis , then
y- intercept = 2
what is 1/5 plus 1/10
Step-by-step explanation:
hope it helps you and give me a brainliest
Step-by-step explanation:
[tex] = \frac{1}{5} + \frac{1}{10} \\ [/tex]
Now make the denominator same...
[tex] = \frac{1}{5} \times \frac{2}{2} + \frac{1}{10} \\ [/tex]
[tex] = \frac{2}{10} + \frac{1}{10} \\ [/tex]
[tex] = \frac{3}{10} \\ [/tex]
:)
..
a. Write an expression for the value of the account at the end of three years in terms of the growth factor x
Determine the correct equation of the following graph.
The equation of the given sine graph is gotten as; y = 4 sin [(0.4(x + 2.5)] - 1
How to find the equation of a sine graph?
We know that the general formula for equation of a sine graph is;
y = A sin [(B(x - D)] + C
where;
A is Amplitude
Period = 2π/B.
Phase Shift = -C/B.
Vertical Shift = D.
From the graph;
A = 4
B = 2π/5π = 2/5
C = -1
D = -5/2
Thus;
y = 4 sin [(0.4(x + 2.5)] - 1
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Please Help Me!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
Answer:
(-2, 11) and (2, 3)
Step-by-step explanation:
Given system of equations:
1) f(x) = x² - 2x + 3 ⇒ y = x² - 2x + 3
2) f(x) = -2x + 7 ⇒ y = -2x + 7
Solve Using the Substitution Method:
Step 1: Substitute the the first equation into the second.
⇒ x² - 2x + 3 = -2x + 7
Step 2: Solve for x.
x² - 2x + 3 = -2x + 7 [ Add 2x to both sides. ]
x² - 2x + 2x + 3 = -2x + 2x + 7
⇒ x² + 3 = 7 [ Subtract 3 from both sides. ]
x² + 3 - 3 = 7 - 3
⇒ x² = 4 [ Take the square root of both sides. ]
√x² = √4
x = ± 2
⇒ x = -2, x = 2
Step 3: Solve for y.
Substitute the found x-values into one of the given equations.
y = -2x + 7 ⇒ y = -2(-2) + 7 ⇒ y = 4 + 7 ⇒ y = 11
y = -2x + 7 ⇒ y = -2(2) + 7 ⇒ y = -4 + 7 ⇒ y = 3
The solutions to the system of equations are: (-2, 11) and (2, 3).
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Which features are present in this polar graph?
A. No symmetry
B. Symmetry about the pole (0,0)
C. Symmetry about the line Theta=pi/2
D. Symmetry about the polar axis Theta=0
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\texttt {D. Symmetry about the polar axis Theta = 0} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The given graph is symmetric along Theta = 0
[ polar axis ]
Because it's a horizontal line that divides the features on the graph into two equal halves. and there's no other suitable symmetric relation.
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
2ⁿ+2ⁿ+2ⁿ+2ⁿ=2¹⁶
value of n?
Answer:
[tex]n = 14[/tex]
Step-by-step explanation:
[tex]~~~~~~~2^n+2^n+2^n+2^n = 2^{16}\\\\\implies 4 \cdot 2^n = 2^{16}\\\\\implies 2^2 \cdot 2^n = 2^{16}\\\\\implies 2^{n+2} = 2^{16}~~~~~~~~~~~~~~~~~~~~~~~~~~~~;[a^m \cdot a^n = a^{m+n}]\\\\\implies n+ 2 = 16\\\\\implies n = 16-2 \\\\\implies n = 14[/tex]
please solve this question
Step-by-step explanation:
please give this answer brainlist answer
What are the solutions to the quadratic equation below in factored form?
(2x - 1)(3x + 4) = 0
0x=
0x =
O
X =
2
16
-
x =
x =
29
3|4
x = = 1/1, X =
2
4/3
x = − 1/1
1
حرا من
Answer:
[tex]\cfrac{-4}{3} [/tex] and [tex]\cfrac{1}{2} [/tex].
Step-by-step explanation:
Equation:
[tex] \rm \: \: (2x - 1)(3x + 4) = 0[/tex]
Solution:
Set factors equal to zero,that is:
[tex](2x - 1) = 0 \: \: \: \: \: \: \: \: \: \: \: ...(1)[/tex]
[tex](3x + 4) = 0 \: \: \: \: \: \: \: \: \: \: \: \: ...(2)[/tex]
Solving for equation 1:
[tex]2x - 1 = 0[/tex][tex]2x = 0 + 1[/tex][tex]2x = 1[/tex][tex] \boxed{x = \cfrac{ 1}{2} }[/tex]Solving for equation 2:
[tex]3x + 4 = 0[/tex][tex]3x = 0 - 4[/tex][tex]3x = - 4[/tex][tex]\boxed{x = \cfrac{ - 4}{3} }[/tex]Hence,the solutions to the quadratic equation in factored form is [tex]\cfrac{-4}{3} [/tex] and [tex]\cfrac{1}{2} [/tex].
[tex]\rule{225pt}{2pt}[/tex]
Good luck on your assignment!
x=1/2 and x=-4/3 are the solutions of the equation (2x - 1)(3x + 4) = 0
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
The given equation is (2x - 1)(3x + 4) = 0
We have to find the solutions of the equation
As the equation is in factored form
We take each factor and solve for solution
2x-1=0
2x=1
Divide both sides by 2
x=1/2
Now 3x+4=0
3x=-4
Divide both sides by 3
x=-4/3
Hence, x=1/2 and x=-4/3 are the solutions of the equation (2x - 1)(3x + 4) = 0
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Given the figure below solve for X
Answer:
x = 37
Step-by-step explanation:
Solve the following inequality |x| < 13
Answer:
x < 13 and x > -13
Step-by-step explanation:
Split the absolute value equation into 2 equations to account for the positive and negative answers possible with absolute values.
Write the positive value first by removing the absolute value symbol.
x < 13
Flip the inequality and make the 13 negative for the other side.
x > -13
If R = {(x, y): y = x = 2, 4, 6}, find the range of R. , 4 , 6 } , find the range of R.
what is the factored form of x^3 - 729
Answer:
(x - 9)(x^2 + 18x + 81).
Step-by-step explanation:
Use the difference of cubes factorization, which claims that a^3 - b^3 = (a - b)(a^2 + ab + b^2)
x^3 - 729 = (x - 9)(x^2 + 18x + 81)
Answer:[tex](x-9) (x^{2} +9x + 81)[/tex]
Step-by-step explanation:
The price of a coat is $65. In sale, the price is reduced by 15%. What is the price of the coat in sale?
In the equation below, variables X and Y represent two matrices. Which property of matrix addition is illustrated below?
X+Y=Y+X
O inverse property
O commutative property
O associative property
O identity property
Answer: the answer is b
Step-by-step explanation:
y = 3x - 5.1, (-1.2, -3.1)
Answer:
This point is not on the line, NOT TRUE
Step-by-step explanation:
The equation of the line is written in the slope-intercept form,
y = mx + b
where m represents the slope
b represents the y-intercept
where the format of a point is (x, y)
Given: y = 3x - 5.1, (-1.2, -3.1)
we can plug in the point (-1.2, -3.1)
-3.1 = 3(-1.2) - 5.1
-3.1 = -3.6 - 5.1
-3.1 = -8.7
-3.1 does not equal -8.7 so this point is not on the line
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The function f(x)= 4x + 3 represents the length of a rectangle. The function g(x)=2x-5 represents the width of the rectangle. Use ( g(4) to determine the area of the rectangle.
57
19
16
3
Answer:
57 square units
Step-by-step explanation:
Area is = Length x Width
Given:
f(x)= 4x + 3 Length
g(x)=2x-5 Width
x = 4
============
Width
g(x)=2x-5
g(4)=2(4)-5
g(4)= 3
Length
f(x)= 4x + 3
f(4) = (4)(4) + 3
f(4) = 19
Area = (length)*(width)
Area = f(x)*g(x) for x = 4
Area = (f(4))*(g(4))
Area = (19)*(3)
Area = 57 square units
when using the rational root theorem, which of the following is a possible root of the polynomial function below? f(x)=2x^2-4x+9
a)4
b)3
c)2
d)5
The only option that meets the root theorem is option b.
which of the following is a possible root of the polynomial function below?
The polynomial function is:
[tex]f(x) = 2x^2 - 4x + 9[/tex]
The rational root theorem says that if a root is a rational number, then the leading coefficient must be divisible by the denominator of the rational number and the constant term must be divisible by the numerator.
In this case, the constant is 9, and the only option such that the constant is divisible by the numerator is option b: 3
Where 3 is a rational number:
3 = 3/1
The numerator is 3 (which divides 9) and the denominator is 1 (which divides the leading coefficient 9. (notice that it meets the theorem, but it is not an actual root).
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What’s the value of x?
Answer:
the two angles equal 180 degree
so 2x+2+5x+3=180
2x+5x+3+2=180
7x=180-5
7x/7=175/7
x=25
Step-by-step explanation:
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Edgar runs 8/9 of a mile each day. what is the total distance that edgar runs in a 5-day week?
The distance that edgar runs in a 5-day week will be 4.45 miles.
What is the distance?Distance is defined as the length between the two points it can be represented in mm,cm, meters,km, and miles.
Given that:-
Edgar runs 8/9 of a mile each day. what is the total distance that Edgar runs in a 5-day week?
The total distance will be calculated as:-
D = [tex]\dfrac{8}{9}[/tex] x 5
D = 4.45 miles
Therefore the distance that edgar runs in a 5-day week will be 4.45 miles.
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Solve: |2x − 1| < 11.
STEP 1 : Rearrange this Absolute Value Inequality
Absolute value inequalitiy entered
|2x-1| < 11
STEP 2 : Clear the Absolute Value Bars
Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.
The Absolute Value term is |2x-1|
For the Negative case we'll use -(2x-1)
For the Positive case we'll use (2x-1)
STEP 3 : Solve the Negative Case
-(2x-1) < 11
Multiply
-2x+1 < 11
Rearrange and Add up
-2x < 10
Divide both sides by 2
-x < 5
Multiply both sides by (-1)
Remember to flip the inequality sign
x > -5
Which is the solution for the Negative Case
STEP 4 : Solve the Positive Case
(2x-1) < 11
Rearrange and Add up
2x < 12
Divide both sides by 2
x < 6
Which is the solution for the Positive Case
STEP 5 : Wrap up the solution
-5 < x < 6
Solution in Interval Notation
(-5,6) .
help me to find b please
Answer:
its right there.
Step-by-step explanation:
Rayonnia is buying cans of frozen lemonade concentrate to make punch for a holiday party with each can she can make 6  cups of lemonade write an equation which gives the number of cups of lemonade that can be made with any number of cans of frozen lemonade concentrate
The number of cups of lemonade, y that can be made with any number of cans of frozen lemonade concentrate, x is y=6x.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that with a single can of frozen lemonade concentrate 6 cups of lemonade can be made. Therefore, the number of cups that can be made with x number of cans is,
Number of cups that can be made, y = 6x
Hence, the number of cups of lemonade, y that can be made with any number of cans of frozen lemonade concentrate, x is y=6x.
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A cube has a side length x and an each dimension is being increased by y, guys. :)
A). Write an expression for the surface area of the new cube, and then expand, and simplify, guys. :)
B). Please find the difference of the surface areas of the new cube and the original cube, guys. :)
Surface area of old cube
6(side)²6x²Side of new cube
x+ySurface area
6(x+y)²6(x²+y²+2xy)6x²+6y²+12xyDifference
6y²+12xyAnswer:
A) 6(x + y)² = 6x² + 12xy +6y²
B) 12xy +6y²
Step-by-step explanation:
Surface area of a cube = 6s² (where s is the side length)
Part A
Given:
x = side length of original cube⇒ Surface area of the original cube = 6x²
If the side length of the cube is increased by y, then:
(x + y) = side length of new cube⇒ Surface area of the new cube = 6(x + y)²
Expand and simplify:
⇒ 6(x + y)²
⇒ 6(x + y)(x + y)
⇒ 6(x² + xy + xy + y²)
⇒ 6x² + 12xy +6y²
Part B
To find the difference between the surface areas of the new and original cubes, subtract the surface area of the original cube from the surface area of the new cube:
⇒ SA of new cube - SA of original cube
⇒ 6x² + 12xy +6y² - 6x²
⇒ 12xy +6y²
Which expression represents the product of negative three-fourths x and –8x?
Answer:
6x²
Step-by-step explanation:
[tex]-\frac{3}{4} x\times \left( -8x\right) =\frac{3}{4} x\times 8x[/tex]
[tex]=\frac{3}{4} \times 8\times x\times x[/tex]
[tex]=\frac{24}{4} \times x^{2}[/tex]
[tex]=6x^2[/tex]
A hiker is climbing down a valley. He stops for a water break 4 times. Between each break, he descends 15 meters. How many meters did he descend?
Ju Chan answered the question by writing the following:
4(−15) meters = −60 meters.
Which word in the problem indicates that a negative number should be used?
The word in the problem that indicates that a negative sign should be used is "descend"
How many meters did he descend?We know that he stops for water breaks four times, and between each water break, he descends 15 meters.
The written equation is:
4*(-15)m = -60m
Why the negative sign is used?
The negative sign is used because the hiker is descending, so its height is decreasing. The word in the problem that indicates that a negative sign should be used is "descend"
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Find the distance between the pair of points given on the graph. Distance = √ (blank)
Answer:
√2.236
Step-by-step explanation:
(2,0) (5,-2). 2 - 5 = -3. 0 - -2 = 2. -3 squared = -9. 2 squared = 4. -9 + 4 = -5. Square root of -5 = 2.236, so the distance would be √2.236
For what values of x does f(x) = 0?
O-4, 0, 2
O-2, 0, 4
O-5, 0, 17
O-17, 0,5
The values of x does f(x) = 0 will be -4,0,2.Option A is corect.
What is a graph?A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.
The graph shows the cubic polynomial equation found as;
⇒(x+4)(x)(x-2)
The points f(x) = 0 is;
⇒(x+4)(x)(x-2)
⇒(-4+4)(0)(2-2)
⇒0
The values of x does f(x) = 0 will be -4,0,2.
Hence, option A is corect.
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