Answer:
Area of the garden in standard form:
Area = (2t^2) + 7t - 4
The dimension of the garden is 8ft × 7ft
Step-by-step explanation:
Length of the rectangular garden, L = t+4
Width of the garden, B = 2t - 1
Area = length * width
Area = (t+4) * ( 2t-1)
Area = (2t^2) + 7t - 4..….......(1)
If the Area = 56 ft^2
Substitute Area into (1)
56 = (2t^2) + 7t - 4
(2t^2) + 7t - 60 = 0
(2t^2) - 8t + 15t - 60 = 0
2t(t - 4) + 15(t - 4) = 0
(2t+15) (t-4) = 0
Let 2t + 15 =0
t = -7.5
Let t - 4 = 0
t = 4
* When t = -7.5
Length, L = -7.5 + 4 = -3.5 ft
Width, B = 2(-7.5) -1 = -16 ft
Since length and breadth cannot be negative, t = -7.5 is not possible
** When t = 4
Length, L = 4+4 = 8 ft
Width, B = 2(4) - 1 = 7 ft
Therefore, the dimension of the garden is 8ft × 7ft
Answer:
The dimension is 8ft by 7ft
Step-by-step explanation:
Given data
Length l = [tex](t+4)[/tex]
Width w= [tex](2t-1)[/tex]
the area is expressed as [tex]A= length * width[/tex]
[tex]A= (t+4)*(2t-1)\\A= t(2t-1) +4(2t-1)\\A= 2t^{2}-t+8t-4\\[/tex]
collecting like terms we have
[tex]A= 2t^{2} +7t-4[/tex]
hence our expression for area is [tex]A= 2t^{2} +7t-4[/tex]
given that the area is [tex]56ft^{2}[/tex] to solve for the sides we need to first solve fot t
equating the expression for area to 56 we can solve for t
[tex]A= 2t^{2} +7t-4= 56[/tex]
taking the constant term to the other side and solve we have
[tex]A= 2t^{2} +7t-4-56\\A= 2t^{2} +7t-60\\[/tex]
we can substitute two factors for 7t that when multiplied we give -60 and when added we give 7 these factors are 15 and -8
[tex]A= 2t^{2} +7t-60\\\\A= 2t^{2} -8t+15t-60\\2t^{2} -8t+15t-60=0\\\\2t(t-4) +15(t-4)= 0\\2t+15=0, (t-4)= 0\\2t=-15, t= -7.5\\t= 4[/tex]
t=4 hence the length is
[tex](t+4)\\(4+4)= 8ft\\[/tex]
hence the width is
[tex](2t-1)\\(2*4-1)= (8-1)= 7ft[/tex]
A bag contains yellow marbles and blue marbles, 23 in total. The number of yellow marbles is 7 less than 2 times the number of blue marbles. How many yellow marbles are there? Please help its due really soon!
Answer:
b=10, a=13
Step-by-step explanation:
let s number of yellow = a
number of blue = b
we have
a+b =23
2b - a = 7
->a+b +2b -a = 23+7
-> 3b = 30
->b = 10
->a = 13
Write this number in scientific notation.
0.0000071=
Answer:
7,1 × 10-⁶
Step-by-step explanation:
Once you move the comma 1 time by right (,) you have -1, so by moving it six times, you have 7,1 × 10-⁶
The quadratic equation x^2−8x+16=0 can be rewritten as (x−4)(x−4)=0.
What is the multiplicity of the root x=4?
The multiplicity of the root is 4.
The multiplicity of the root is 2.
The multiplicity of the root is 1.
The multiplicity of the root is 3.
Answer:
The multiplicity of the root is 2Step-by-step explanation:
Multiplicity of a number is the number of times the factor of a given function appears in the factor form of such given equation. For us to know the multiplicity of the root of the function, first we must know its root.
Factorizing the given quadratic function x²−8x+16=0
[tex]x^{2} -4x-4x+16 = 0\\x(x-4)-4(x-4)=0\\(x-4)(x-4) = 0\\x-4 = 0 and x-4 = 0\\x = 4\ twice[/tex]
Since the root of the function which is 4 appears twice then the multiplicity of the root is 2
Rewrite the following equation in logarithmic form.
0.25 = 2^-2
Rewrite the following equation in exponential form.
log8 (512) = 3
Answer:
log2(0.25) = -2
512 = 8^3
Step-by-step explanation:
Use of formula: loga (b) = c ⇔ b = a^cRewrite the following equation in logarithmic form. 0.25 = 2^-2
log2(0.25) = -2Rewrite the following equation in exponential form. log8 (512) = 3
512 = 8^3An irregular figure was broken into a triangle and rectangle. The area of the triangle is in2. The area of the rectangle is in2. The area of the irregular figure is in2.
Answer:
the anser is 24,32,56
Step-by-step explanation:
i did it got it wrong and then it gave me the right anser witch is that
Answer:
24,32,and 56 is right. trust me
Step-by-step explanation:
How do you simplify [tex]\frac{\sqrt{2} +\sqrt{6} }{\sqrt{8} + \sqrt{6} }[/tex]?
The trick is to exploit the difference of squares formula,
[tex]a^2-b^2=(a-b)(a+b)[/tex]
Set a = √8 and b = √6, so that a + b is the expression in the denominator. Multiply by its conjugate a - b:
[tex](\sqrt8+\sqrt6)(\sqrt8-\sqrt6)=(\sqrt8)^2-(\sqrt6)^2=8-6=2[/tex]
Whatever you do to the denominator, you have to do to the numerator too. So
[tex]\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=\dfrac{(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)}{(\sqrt8+\sqrt6)(\sqrt8-\sqrt6)}=\dfrac{(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)}2[/tex]
Expand the numerator:
[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=\sqrt{2\cdot8}+\sqrt{6\cdot8}-\sqrt{2\cdot6}-(\sqrt6)^2[/tex]
[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=\sqrt{16}+\sqrt{48}-\sqrt{12}-6[/tex]
[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=4+\sqrt{48}-\sqrt{12}-6[/tex]
[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=-2+\sqrt{12}(\sqrt4-1)[/tex]
[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=-2+\sqrt{12}(2-1)[/tex]
[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6}=-2-\sqrt{12}[/tex]
So we have
[tex]\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=-\dfrac{2+\sqrt{12}}2[/tex]
But √12 = √(3•4) = 2√3, so
[tex]\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=-\dfrac{2+2\sqrt3}2=\boxed{-1-\sqrt3}[/tex]
The exterior angle of a regular polygon is 30°. What is the measure of an interior angle of the polygon.
B. How many sides does this polygon have.
C. What is the sum of all the interior angels.
This is all the same polygon.
Answer:
A) Measure of an interior angle of polygon = 150°
B) No of sides = 12
C) Sum of all interior angles = 1800°
Step-by-step explanation:
Measure of interior angle of polygon = 180°- measure of exterior angle of polygon
= 180°-30°
= 150°
B.
[tex]No.\: of \: sides = \frac{360\degree}{30\degree} = 12\\\\C.\\Sum\:of\: all \:interior\: angles \\= (n-2)\times 180\degree\\= (12-2) \times 180\degree\\= 10\times 180\degree\\= 1800\degree[/tex]
What is the Volume and surface area of a cone with a diameter of 18ft and a slant height of 30ft
Answer:
A cone with a diameter of 18ft and a slant height of 30ft
Using Pythagorean theorem, the height is calculated by:
H = sqrt(18^2 - (30/2)^2) = 9.95
The surface area:
A = lateral surface area + base
A = pi x radius x slant height + pi x radius^2
A = pi x (30/2) x 18 + pi x (30/2)^2 = ~1555.1 (ft2)
The volume:
V = base x height x (1/3)
V = pi x radius^2 x height
V = pi x (30/2)^2 x 9.95 = 7033.2 (ft3)
Hope this helps!
:)
I need help with this question please.
Answer:
work is shown and pictured
5x + 7 + 2x anwer plz
Answer:
The final answer is [tex]7x +7[/tex] .
Step-by-step explanation:
-Solve equation:
[tex]5x + 7 + 2x[/tex]
-Combine like terms:
[tex]5x + 7 + 2x[/tex]
[tex]7x +7[/tex]
-Result:
[tex]7x +7[/tex]
What is the solution set to the equation x^2=-1
Answer:
Step-by-step explanation:
For example, if your money earns an 8 percent interest rate, it will triple in 14 years and 5 months (115 divided by 8 equals 14.4). If your money earns a 5 percent interest rate, it will triple in 23 years (115 divided by 5 equals 23).
Evaluate sin^2Θ, for Θ=45°
Answer:
sin^2(45) = (√2/2)^2 = 1/2
Step-by-step explanation:
sin2x = sin2 * x = 0.909x
sin(2(45)) = sin90 = 1
Hope this helps.
Answer:
The answer to this is [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
I did the assignment, hope it helps! :)
please help 50 points and brainliest!!!!!!!!
Answer:
To do this you need to fill in the equation: 1/2 height*sidelength *width. So, height = 8 ft, side length = 4 ft, and width = 24 ft. So, plugging in the numbers you get:
1/2(8) * 4 * 24 =
4*4*24 = 384 ft
Step-by-step explanation:
Answer:
345 ft^3
Step-by-step explanation:
B=1/2(5)(6)=15
V=15(23)=345
One of the solutions to x^2 – 2x – 15 = 0 is x = -3. What is the other solution?
x = -5
x = -1
x = 1
x = 5
Answer:
work is shown and pictured
2 mil 20 yd = ____ yd
Answer:
3540
Step-by-step explanation:
There are 3520 yards in two miles and 1760 in one mile you multiply 1760 by 2 then add 20
how are u supposed to find the area only with the circumference?
Answer:
We can find the radius from circumference and then area
Circumference(C) = 2πr
r = C/2π
r = 20/2π
r = 10/π
Area = πr²
Area = π × 10/π × 10/π
Area = 100/π
Area = 100/3.14
Area = 10000/314 = 31.84 cm² (approx)
Area = 32 cm² (Rounding to nearest whole number)
Answer:
32 m²
Step-by-step explanation:
We need to work out the area of the flower garden when we are given the circumference. First we need to know the formula's for area of circle and circumference of circle which are
→ Area of a circle = π × r² where 'r' is the radius
→ Circumference of a circle = 2 × π × r where 'r' is the radius
So we need to form an equation with the circumference of a circle formula and work out the radius in order to find the area so,
In an equation our aim is to find the value of what we are looking for as well as keeping the equation balanced. For example if we divided by 2 only from one side then the equation would change so it's an important rule to keep in mind when solving equations, that you need to keep both sides of the equation the same.
2 × π × r = 20
→ Substitute 3.14 for π
2 × 3.14 × r = 20
→ Simplify
6.28 × r = 20
→ Divide both sides by 6.28 to isolate 'r'
r = 3.18471338
So now we now the radius of the circle we can substitute the radius into the area of circle formula
Area = π × r²
→ Substitute 3.14 for π and r for 3.18471338
Area = 3.14 × 3.18471338²
Area = 31.847133842
To the nearest whole number your answer is 32 m²
The table shows the estimated number of bees, y, in a hive x days after a pesticide is released near the hive. Which function best models the data?
A) y = 9,958(0.972)^x
B) y = 0.972(9,958)^x
C) y = 9,219x– 150
D) y = –150x + 9,219
Answer:a
Step-by-step explanation:
Answer:
It is A, y = 9,958(0.972)x
Step-by-step explanation:
I’m just confused on how to find the equation with the quadratic function given.
option b is the correct answer
What is the probability that I will choose a cat owner and a bird owner. Please help. Thanks
Answer:
The probability is 1/36.
Step-by-step explanation:
2/3 are dog owners
1/6 are cat owners
1/6 are bird owners
If you choose two owners, there is a 1/6 chance that you will choose a cat owner and a 1/6 chance you will choose a bird owner. Each of these are independent, so you simply multiply 1/6 by 1/6.
1/6 * 1/6= 1/36
What numbers would make 4a ≤ 16 true?
Answer: a ≤ 4 or (-∞, 4]
Step-by-step explanation:
Here we have the inequality:
4a ≤ 16
this means that the left sides is less or equal than the right side.
First, find the equal part:
4*a = 16
a = 16/4 = 4
So the maximum possible value of a is 4.
Now, all the values of a smaller than 4 also make the inequality true (even the negative values) so the possible values of a are:
a ≤ 4 or (-∞, 4]
Answer:
Any number that is less or equal to 4 makes this inequality true.
Step-by-step explanation:
In order to calculate the numbers that make this inequality valid, we need to solve it for "a". This can be done in the same manner as we would solve an equation, although we must pay attention to the inequality. This is done below:
[tex]4*a \leq 16\\a \leq 16/4\\a \leq 4[/tex]
Any number that is less or equal to 4 makes this inequality true.
Write the composite number for each prime factorization. You may wish to use a calculator.
5) 22 x 3 x 52
6) 2x32x7
7) 33 x 5
8) 2 x 53
Only one of those is actually a prime factorization. Demand better from your teacher. Anyway, I think they're just asking us to take out the calculator and enter the multiplication into it.
5) 22 isn't prime, neither is 52. Answer: 3432
6) 32 isn't prime. Answer: 448
7) 33 isn't prime. Answer: 165
8) Finally a real prime factorization. Answer: 106
Five 12s is equal to how many 48s?
Answer:
1 1/4 48's.
Step-by-step explanation:
5 * 12 = 60
60 / 48 = 1 12/48
= 1 1/4.
Answer:
1 48
Step-by-step explanation:
if 2 twelve is equal to 24 and 24+24= 48 then 4 12s would equal one 48 with 12 still remaining
Given that events A and B are independent with P(A)=0.24P(A)=0.24 and P(B|A)=0.85P(B∣A)=0.85, determine the value of P(B)P(B), rounding to the nearest thousandth, if necessary.
Answer:
P(B) = 0.85
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
[tex]P(A) = 0.24, P(B|A) = 0.85[/tex]
These events are independent.
This means that [tex]P(A \cap B) = P(A)*P(B)[/tex]. So
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(B|A) = \frac{P(A)*P(B)}{P(A)}[/tex]
[tex]P(B|A) = P(B)[/tex]
So
[tex]P(B) = 0.85[/tex]
which of the binomials below is a factor of this trinomial? x^2+6x-40
Answer:
C
Step-by-step explanation:
(x-4)(x+10)=x^2+6x-40
Answer:
C. X-4
Step-by-step explanation:
A P E X
correct expression equivalent to 9-(3-6x)
Answer:
6 + 6x
Step-by-step explanation:
9 - (3-6x) = 9 - 3 - (-6x)
= (9-3) +6x
= 6 + 6x
1) expand the bracket
2) group like terms together
3) simplify to form expression
Solve for b.
-3b = 9 - 4b
B=
Answer:
b=9
Step-by-step explanation:
move the 4b over to the other side by adding it to both sides
[tex]-3b(+4b)=9-4b(+4b)[/tex]
[tex]1b=9[/tex]
Please help me ASAP and I have more so PLEASE
The answer is B part
As the requirement for the student is either a senior or one who studies maths or both.
So, just add the values within the two venn circles divide it by total no of values.
=> 240+40+110/240+40+110+840
=> 360/1200
Answer:
B
Step-by-step explanation:
840 people aren't senior or don't takes math.
210 + 40 = 250 are seniors
110 + 40 = 150 people take math
In this class has 840 + 210 + 40 + 110 = 1200 people => All
210 + 40 + 110 = 360 people are seniors or take math. => P( S U M)
Probabilty that a randomly selected student is a senior or takes math =>[tex]\frac{P(S U M)}{All}[/tex]
[tex]\frac{P(S U M)}{All} = \frac{360}{1200}[/tex]
Hope this helps ^-^
What value of z makes the following equation true?
−3z+3=35
Answer:
-10 2/3Step-by-step explanation:
Given
−3z+3=35Solving for z:
-3z = 35 - 3-3z = 32z = 32/-3z = -10 2/3How do I do Radicals?
Answer:
For online calculators you can type sqrt() or just sqrt and it will do it for you
Answer:
See belowStep-by-step explanation:
To simplify radicals that are not perfect squares, we need a new method.
Example: [tex]\sqrt{27}[/tex]
27 is not a perfect square square the square root cannot be used.
[tex]\sqrt{27} = 5.19615242271[/tex]
To solve this, we need to break down the radical into simpler parts.
[tex]\sqrt{27} = \sqrt{3} * \sqrt{9}[/tex]
[tex]\sqrt{9} = 3[/tex]
[tex]\sqrt{3}[/tex] cannot be simplified
[tex]\sqrt{27}[/tex] = 3[tex]\sqrt{3}[/tex]
Good luck on your test!
I'm always happy to help :)
Tina loves to read. Before breakfast, she read 21/2 pages, at lunch she read 31⁄5 pages, and after dinner she read 11⁄3 pages. How much did Tina read in total?
Answer: 7 1/30
Step-by-step explanation:
Tina loves to read. Before breakfast, she read 2 1/2 pages, at lunch she read 3 1/5 pages, and after dinner she read 1 1/3 pages. To find the total, we add all the pages together. This will be:
2 1/2 + 3 1/5 + 1 1/3
The LCM of 2, 5 and 3 is 30.
= 2 15/30 + 3 6/30 + 1 10/30
= 6 31/30
= 7 1/30.