Answer:
a) The formula for the sequence is
[tex]a_n = 67,000 -3,000(n-1)[/tex]
b) [tex]a_7 = 49,000[/tex]
Step-by-step explanation:
Note that the difference between any two consecutive terms in the sequence is always equal to $3,000
[tex]67,000-70,000= -3,000\\\\64,000-67,000=-3,000[/tex]
Then we have an arithmetic sequence where each term increases by a magnitude of 3,000 with respect to the previous term.
The explicit formula for an arithmetic sequence is:
[tex]a_n = a_1 +d(n-1)[/tex]
Where d is the common difference between the consecutive terms of the sequence
[tex]d = -3,000[/tex]
[tex]a_1[/tex] is the first term, or the value of the house after year 1 [tex]a_1= 67,000[/tex]
n represents the number of years since the house was purchased
With
n={0, 1, 2, 3, 4, 5, 6, 7,.., n}
a) Then the formula for the sequence is
[tex]a_n = 67,000 -3,000(n-1)[/tex]
With
n={0, 1, 2, 3, 4, 5, 6, 7,.., n}
---------------------------------------------------------------------------------------------
b) Now we can use the formula to find the price of the house after 7 years
[tex]a_7 = 67,000 -3,000(7-1)[/tex]
[tex]a_7 = 67,000 -3,000(6)[/tex]
[tex]a_7 = 49,000[/tex]
(3a) 3 = This expression without exponents is 3aaa 3·3·3a 3a3a3a 3·3·3a 3
Answer:
[tex]3a\times 3a\times 3a[/tex]
Step-by-step explanation:
The given expression is;
[tex](3a)^3[/tex]
Recall that;
[tex]a^m=a\times a\times \times a....[/tex] m-times.
In [tex](3a)^3[/tex] means
[tex]3a\times 3a\times 3a[/tex]
The correct choice is the third option
Answer:
3a x 3a x 3a
Step-by-step explanation:
20 points!!!
A wooden board in the shape of a rectangular prism measures 1.5 meters by 0.75 meter by 0.2 meter and has a mass of 146.25 kilograms.
What is the density of the board?
Thank you so much!!!
Answer:
Density of the board = M/V [tex]= 650 kg m^{-3} [/tex]
Step-by-step explanation:
A rectangular prism has six faces which are all rectangular. It has a cross-sectional area with an additional length which makes it a six-sided solid object.
Mass of the board = 146.25 kg
height = 0.75 m
width = 0.2 m
length = 1.5 m
Volume of the rectangular prism = height * width * length
= 0.75*0.2*1.5
=0.225 meters
Density of the board = mass/volume
= 146.25/0.225
[tex]= 650 kg m^{-3} \\[/tex]
Find the indicated limit, if it exists.(7 points)
limit of f of x as x approaches 0 where f of x equals 7 minus x squared when x is less than 0, 7 when x equals 0, and 10 x plus 7 when x is greater than 0
Choices below
3
10
7
The limit does not exist.
Answer:
7
Step-by-step explanation:
The left hand limit is when we approach zero from left. We use the function on this domain in finding the limit.
[tex]\lim_{x \to 0^-} f(x)=7-x^2[/tex]
[tex]\lim_{x \to 0^-} f(x)=7-(0)^2=7[/tex]
The right hand limit is
[tex]\lim_{x \to 0^+} f(x)=10x+7[/tex]
[tex]\lim_{x \to 0^+} f(x)=10(0)+7=7[/tex]
Since the left hand limit equals the right hand limit;
[tex]\lim_{x \to 0} f(x)=7[/tex]
in which of the following equations does f= -12
A.108f-6=3
B.72f+9=15
C.118-4f=166
D.127+5f=187
Answer:
C
118 - 4 (-12)= 166
118 + 48 = 166
166 = 166
Look at picture. Question 1
Answer:
x = 18Step-by-step explanation:
Look at the picture.
ΔABC and ΔDBE are similar.Therefore the corresponding sides are in proportion:
[tex]\dfrac{DE}{AC}=\dfrac{DB}{AB}[/tex]
We have
[tex]DE=x,\ AC=36,\ DB=y,\ AB=y+y=2y[/tex]
Substitute:
[tex]\dfrac{x}{36}=\dfrac{y}{2y}[/tex] cancel y
[tex]\dfrac{x}{36}=\dfrac{1}{2}[/tex] cross multiply
[tex]2x=36[/tex] divide both sides by 2
[tex]x=18[/tex]
when buying a candy bar, there is a 20% chance that it will also include a coupon for a second candy bar. a student wants to determine the probability that, if she buys 7 candy bars, more than 2 will include a coupon.
Answer:
these are the answers -
i took the test theses were the answers -
A1 = more than two 1s
A2 = 0.4286
hope this helped !
Answer:
0.148
Step-by-step explanation:
Given that
probability that a candy will include a coupon for second candy bar = 0.20
Each candy having a coupon is independent of the other also there ae ony two outcomes.
Hence X no of candies which attract a coupon for second candy is binomial
with n = 7 and p = 0.20
Probability that if she buys 7 candy bars, more than 2 will include a coupon.
=P(X>2)
=P(x=2)+P(X=3)+P(x=4)+P(x=4)+P(X=5)+P(x=6)+P(x=7)
=0.148
What is the volume of the cone shown below?
17 cm
16 cm
Answer:
V = 1138.77333333 cm^3
Step-by-step explanation:
The volume of a cone is given by
V = 1/3 pi r^2 h
We know the diameter so we can find the radius
d = 16
r = d/2
= 16/2 =8
The radius is 8
V = 1/3 pi (8)^2 * 17
V = 1088/3 *pi
Using 3.14 for pi
V = 1138.77333333 cm^3
Solving for Matrices
Answer:
option A
[tex]\left[\begin{array}{ccc}9&-4&-5|9\\7&4&-4|-1\\6&-6&1|-5\end{array}\right][/tex]
Step-by-step explanation:
Steps to write equations in augmented form
Step 1
Write the coefficients of the x-terms as the numbers down the first column
Step 2
Write the coefficients of the y-terms as the numbers down the second column
Step 3
Write the coefficients of the z-terms as the numbers down the third column
Step 4
Write the constants which are in the end of equation in fourth column
Answer:
a. [tex]\left[\begin{array}{cccc}9&-4&-5&|9\\7&4&-4&|-1\\6&-6&1&|-5\end{array}\right][/tex]
Step-by-step explanation:
The given matrix is
9x-4y-5z=9
7x+4y-4z=-1
6x-6y+z=-5
The augmented matrix is the coefficient matrix combined with the constant matrix.
The coefficient matrix is obtained by writing the coefficient of the variables as a matrix.
The constant matrix is obtained by writing the constants as a column matrix.
Combining the two gives the augmented matrix;
[tex]\left[\begin{array}{cccc}9&-4&-5&|9\\7&4&-4&|-1\\6&-6&1&|-5\end{array}\right][/tex]
A triangle prism has a height of 9 m in triangle base with the following dimensions.
Answer:
36 meters, A
Step-by-step explanation:
I assume that P is the perimeter
So, all you have to do is count the sides and add them up
10+16+10=36 meters
Is this right an of it’s not can you help me ??
Answer:
15. 6 ft
Step-by-step explanation:
Your calculation is correct
note h = 15.6 ft ( to the nearest tenth of a foot )
Yes,your calculation is correct
write an eqaution using for an expotional
I’m assuming you’re saying with an exponent. 7x^2+5
Answer:
7x^2+5
Step-by-step explanation:
How much larger is the value of x than the value of y
A. 20
B. 70
C. 90
D. 110
Answer:
D 110
Step-by-step explanation:
Vertical angles are equal
50 = x+2y
Adjacent angles equal 180 degrees when they make a straight line
50+x-2y = 180
subtract 50 from each side
50-50+x-2y = 180-50
x-2y = 130
Flipping sides on the first equation
x+2y = 50
Adding the two equations together
x-2y = 130
x+2y = 50
-------------------
2x = 180
Divide by 2
2x/2 = 180/2
x = 90
Now we need to find y
x+2y = 50
90 +2y = 50
Subtract 90 from each side
90-90+2y = 50-90
2y = -40
Divide by 2
2y/2 = -40/2
y = -20
We want the difference between x and y
x-y
90-(-20)
90+20
110
which is the graph of f(x)=2(3)^x?
Answer:
Step-by-step explanation:
y = 2*3^x
x = 1
y = ?
y = 2*3^1
y =2 * 3
y = 6
The answer is the first graph.
One bucket of gravel has a mass of 7.05 kg. What is the mass of gravel in kilograms
The weight of 20 buckets is 141 Kg.
The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
weight of 1 bucket of gravel = 7.05
weight of 20 buckets = 7.05 x 20
= 141 Kg
Hence, the weight of 20 buckets is 141 Kg.
Question
One bucket of gravel has a mass of 7.05 kg. what is the mass of 20 buckets of gravel in kilograms?
If the parent function f(x)=3 square root of x is transformed to g(x)=3 square root of x+2-4
Answer:
Graph A is the correct graph for the transformations shown in the function g(x)
Step-by-step explanation:
Within the function [tex]g(x)=\sqrt[3]{x+2} -4[/tex]
We can see two transformations occur from the parent function. The first is a slide along the x-axis and the second is a slide along the y-axis
Under the radicand we see that it is x+2. This means that the function has been shifted 2 units left from the parent function
As there is a -4 outside of the radicand, it would mean that the function has been shifted 4 units down as well.
This means that we are looking for a function centered around the point (-2,-4)
The graph of ∛(x) is shifted backwards by 2 units along the x - axis and then is shifted 4 units in the downward direction along the y - axis.
What is a polynomial?Polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s). For example -
y = 4x⁴ + 3x³ + 2x² + 6x + 7
We have the function -
{∛(x)} and {∛(x + 2) - 4}
We can write the functions as -
[tex]$x^{\frac{1}{3} }[/tex]
and
[tex](x + 2)^{\frac{1}{3} } - 4[/tex]
The graph of ∛(x) is shifted backwards by 2 units along the x - axis. Then it is shifted 4 units in the downward direction.
Therefore, the graph of ∛(x) is shifted backwards by 2 units along the x - axis and then is shifted 4 units in the downward direction along the y - axis.
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This relation is an inverse variation {(-1,8),(4,-2),(-2,4)} what equation represents this relation?
ANSWER
[tex]y = - \frac{8}{x} [/tex]
EXPLANATION
An inverse variation equation is of the form:
[tex]y = \frac{k}{x} [/tex]
We plug in the point (-1,8).
[tex] 8= \frac{k}{ - 1} [/tex]
This implies that k=-8
Therefore the inverse variation equation is :
[tex]y = - \frac{8}{x} [/tex]
Final answer:
The set of points {(-1,8),(4,-2),(-2,4)} represents an inverse variation with the equation xy = -8, as the product of x and y is consistently -8 for all given points.
Explanation:
An inverse variation can be defined by an equation of the form xy = k, where k is a nonzero constant. Given the set of points {(-1,8),(4,-2),(-2,4)}, we can find the constant k by multiplying the x-coordinate with the y-coordinate for each point, as follows:
(-1)(8) = -8
(4)(-2) = -8
(-2)(4) = -8
Since the product of x and y is consistent and equal to -8 across all points, we can confirm that k = -8 and thus the equation representing this relation is xy = -8.
solve the system by substitution.x+5y=-8 -6x+8y=10
Answer:
y=-1, x=-3
Step-by-step explanation:
First isolate x:
x+5y-5y=-8-5y
x=-8-5y
Then substitute (-8-5y) for x:
-6(-8-5y)+8y=10
Distribute and solve for y:
48+30y+8y=10
38y-48=10-48
38y=-38
y=-1
Use y to solve for x:
x+5(-1)=-8
x-5=-8
x-5+5=-8+5
x=-3
Please solve thank you
Answer:
The correct answer would be H
Step-by-step explanation:
H
MSN’s MSN’s
Dnnsnsjsjs
Sjsjkssj
what is the measure of G?
The measure of G is 28 because it is an isosceles triangle
The measure of G depends on the given information or the type of angle it represents.
Explanation:The measure of G refers to the numerical value or the angle of G. To determine the measure of angle G, we need more information, such as the type of angle or any given angles in the problem. However, if we assume that G is a generic angle, we can measure it using a protractor or rely on the properties of different types of angles.
For example, if G is a right angle, it measures 90 degrees. If G is a straight angle, it measures 180 degrees. But without specific details, it is challenging to determine the exact measure of G.
Remember to always provide more information in order to find the measure of an angle accurately.
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PLS HELP ILL GIVE BRAINLIEST
Answer:
1: This is a 8-sided polygon, so it is a octagon.
2: No, this is not a regular polygon.
Step-by-step explanation:
1: Since the polygon has 8 sides, it is an octagon.
2:
This is not a regular polygon.
Regular polygons MUST be equilateral and equiangular.
This polygon is neither, so it is not a regular polygon.
Randy is playing a number game. Beginning with the number 8, he adds 4, multiples by 5, and then divides by -10. He then subtracts 2. What number does he find at the end of the game?
A .-8 B. -6 C. 6 D. 8
Step-by-step explanation:
8+4=12
12×5=60
60÷-10=-6
-6-2=-8
the correct answer is A. -8
A sapling that started out 14 inches tall grew 4 inches per year. How old was the sapling when it was 46 inches tall?
Answer:
8 years old
Step-by-step explanation:
46 - 14 = 32 inches of growth
32 inches / 4 inches = 8 years
The cylinder shown has a volume of 90 cubic units. The cone and the cylinder have the same height and the same base.
What is the volume of the cone?
I NEED THIS FAST ILL MARK YOU AS BRAINILIST
The volume is 45 I think
The cylinder shown has a volume of 90 cubic units. The cone and the cylinder have the same height and the same base. The volume of the cone will be 30 cubic units.
What is a cone?It is defined as the three-dimensional shape in which the base is a circular shape and if we go from circular base to top the diameter of the circle reduces and at the vertex, it becomes almost zero.
Given:
The volume of the cylinder= 90 cubic units
The volume of the cylinder=πr²h
90 cubic units=πr²h
The volume of a cone is;
[tex]\rm V= \frac{1}{3} \pi r^2h \\\\ V=\frac{1}{3} \times 90 \ cubic units \\\\ V=30 \ cubic \ units[/tex]
Hence, the volume of the cone will be 30 cubic units.
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4(3d-2x)-(2d-5x)
Maths help plz.....
Answer:
10d - 3x
Step-by-step explanation:
Distribute the 4: 12d - 8x
Distribute the -1: -2d + 5x
Add like terms: 10d - 3x
Point M lies between points L and N on LN.
If LN=12x+16, what is the length of LN in units?
A. 16 units
B. 40 units
C. 48 units
D. 64 units
Answer:
Option D. LN=64 units
Step-by-step explanation:
step 1
Find the value of x
we know that
LN=LM+MN -----> equation A
we have
LN=12x+16
LM=10x+8
MN=5x-4
substitute the values in the equation A
12x+16=(10x+8)+(5x-4)
Solve for x
12x+16=15x+4
15x-12x=16-4
3x=12
x=4
step 2
Find the value of LN
LN=12x+16
LN=12(4)+16=64 units
The length of LN in units is 64 units
Calculating length of a lineFrom the question, we are to determine the length of LN
In the given diagram
/LM/ = 10x + 8
/MN/ = 5x - 4
We can observe that
/LM/ + /MN/ = /LN/
From the given information,
/LN/ = 12x + 16
Therefore,
10x + 8 + 5x -4 = 12x + 16
Solving for x
15x +4 = 12x + 16
Then,
15x - 12x = 16 - 4
3x = 12
Thus,
x = 4
Then, substitute the value of x into LN = 12x + 16
LN = 12(4) + 16
LN = 48 + 16
LN = 64 units
Hence, the length of LN in units is 64 units
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I little help pls with dis it permutations
1680 is the PERMUTATION answer.
Classify 65 by naming all of the sets to which it belongs (whole number,integer,rational number,real number).
A.Real
B.Rational,Real
C.Integer,Rational,Real
D.Whole,Integer,Rational,Real
Answer:
whole number, integer, real numberrational
Step-by-step explanation:
Which function represents the given sequence?
n 1 2 3 4 5
an 3 18 108 648 3888
( answer choices are above) Thanks!!!
the answer is d bc the common ratio is 6 and the previous term is 3 for a geometric recursive. the formula is a_n=a_n-1(3) btw
How write an equation for a circle using 8x +x^2 - 2y = 64 - y^2
Answer:
see explanation
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
8x + x² - 2y = 64 - y²
Collect the x/y terms, leaving 64 on the right side, that is
x² + 8x + y² - 2y = 64
To obtain standard form use the method of completing the square.
add ( half the coefficient of the x/y terms )² to both sides
x² + 2(4)x + 16 + y² + 2(- 1)y + 1 = 64 + 16 + 1
(x + 4)² + (y - 1)² = 81 ← in standard form
with centre (- 4, 1) and radius = 9
Please help will give brainliest
This relation is a function because a function [tex]f[/tex] from a set [tex]A[/tex] to a set [tex]B[/tex] is a relation that assigns to each element [tex]x[/tex] in the set [tex]A[/tex] exactly one element [tex]y[/tex] in the set [tex]B[/tex]. The set [tex]A[/tex] is the domain (also called the set of inputs) of the function and the set [tex]B[/tex] contains the range (also called the set of outputs). So we have that:
[tex]\left[\begin{array}{cc}x & y\\4 & 5\\8 & 7\\12 & 9\\16 & 11\end{array}\right][/tex]
All these points have been plotted below, so you can realize this is a linear function. Therefore, with two points we can get the equation, so:
[tex]The \ equation \ of \ the \ line \ with \ slope \ m \\ passing \ through \ the \ point \ (x_{1},y_{1}) \ is:\\ \\ y-y_{1}=m(x-x_{1}) \\ \\ \\ y-5=\frac{7-5}{8-4}(x-4) \\ \\ y-5=\frac{2}{4}(x-4) \\ \\ y=\frac{1}{2}x+5-2 \\ \\ y=\frac{1}{2}x+3 \\ \\ \\ Where: \\ \\ (x_{1},y_{1})=(4,5) \\ \\ (x_{2},y_{2})=(8,7)[/tex]
Finally, the equation is:
[tex]\boxed{y=\frac{1}{2}x+3}[/tex]