Answer:
the answer is B. They are perpendicular because their slopes are negative reciprocals.
Step-by-step explanation:
what is the fifth term in the geometric sequence described by this explicit formula y=40×(-2)^(n-1)
Answer:
The fifth term is 620
Step-by-step explanation:
y=40×(-2)^(n-1)
The 5th terms means n=5
y = 40 * (-2) ^ (5-1)
= 40 * (-2) ^4
= 40 * (16)
= 640
Find the coordinates of the point which divides the join of (-1,7) and (4,-3) in the ratio 2:3
Answer:
The coordinates of the point in question is (1, 3).
Step-by-step explanation:
Point (-1, 7) is above and to the left of the point (4, -3). The point in question is to the right and below the point (-1, 7).
What will be the horizontal distance between the point (-1, 7) and the point in question?
The horizontal distance between the point (-1, 7) and (4, -3) is 5. Let the horizontal distance between the point (-1, 7) and the point in question be [tex]a[/tex]. Let the horizontal distance between the point in question and point (4, -3) be [tex]b[/tex].
[tex]\displaystyle \frac{a}{b} = \frac{2}{3}[/tex].
[tex]\displaystyle a = \frac{2}{3} \; b[/tex].
[tex]\displaystyle b = \frac{3}{2}\; a[/tex].
However,
[tex]a + b = 5[/tex].
[tex]\displaystyle a + \frac{3}{2}\; a = 5[/tex].
[tex]\displaystyle \frac{5}{2}\; x= 5[/tex].
[tex]a = 2[/tex].
In other words, the point in question is 2 units to the right of the point (-1, 7). The x-coordinate of this point shall be [tex]-1 + 2 = 1[/tex].
The vertical distance between the point (-1, 7) and the point (4, -3) is 10. Similarly, the point in question is [tex](2/5) \times 10 = 4[/tex] units below the point (-1, 7). The y-coordinate of this point will be [tex]7 - 4 = 3[/tex].
Thus, the point in question is (1, 3).
Answer:
To solve our given problem we will use section formula :]
Section Formula states that, when a point divides a line segment internally in the ratio m:n, So the coordinates are :]
[tex]\tiny: \implies (x,y) = \bigg \lgroup x = \frac{m. {x}_{2} +n. {x}_{1} }{m + n} ,y= \frac{m. {y}_{2} +n. {y}_{1} }{m + n} \bigg \rgroup \\ \\ \\ [/tex]
Let
(-1 , 7) = (x₁ , y₁)
(4 , -3) = (x₂ , y₂)
m = 2
n = 3
Upon Substituting coordinates of our given points in section Formula we get :][tex]\tiny: \implies (x,y) = \bigg \lgroup x = \frac{2 \times 4 +3 \times - 1 }{2 + 3} ,y= \frac{2 \times - 3 +3 \times 7}{2 + 3} \bigg \rgroup \\ \\ \\ [/tex]
[tex]\tiny: \implies (x,y) = \bigg \lgroup x = \frac{8 - 3 }{2 + 3} ,y= \frac{ - 6 +21}{2 + 3} \bigg \rgroup \\ \\ \\ [/tex]
[tex]\tiny: \implies (x,y) = \bigg \lgroup x = \frac{5 }{5} ,y= \frac{15}{5} \bigg \rgroup \\ \\ \\ [/tex]
[tex]\tiny: \implies (x,y) = \bigg \lgroup x = 1,y= 3 \bigg \rgroup \\ \\ [/tex]
Last year amusement park received 236,758 visitors it was open every day of the year but 7 Holliday’s what was the average number of visitors to the park per day
Answer:
An average of 661 people per day.
Step-by-step explanation:
1. 365-7= 358
2. 236,758/ 358= 661.3351
3. Round to 661
find the sum of 7 E 3i - 15
i =2
answers :
9
0
-9
6
Answer:
-9
Step-by-step explanation:
find the value of i2, which is -9, find the value of i7, which is 6
Then, add them together and multiply by the number of terms in the sequence divided by 2 (6/2=3)
What is the center point
Answer:
Center of the circle= (-9,6)
Radius = 5 units
Step-by-step explanation:
Once the equation of the circle has been written in the format
(x-h)²+(y-k)²=r² , (h,k) is the center while r is the radius of the circle.
From the given equation, -h=9 therefore h= -9.
-k = -6 therefore k = 6. r² = 25 therefore r= √25=5
Center of the circle= (-9,6) radius = 5 units
Which expression is equivalent to sqrt10/4sqrt8
Answer:
Step-by-step explanation:
Since it's a division we need to look for a common factor to cancel
so first we try to break the numbers to there prime factors
[tex]\frac{\sqrt{10} }{4\sqrt{8} } = \frac{\sqrt{2.5} }{4\sqrt{2.2.2} }[/tex]
So , now we try to factors that are common in top and bottom
[tex]= \frac{\sqrt{2} \sqrt{5}}{4\sqrt{2}\sqrt{4} }[/tex]
common factor is sqrt 2 so lets cancel it
we get
[tex]\frac{\sqrt{5} }{4\sqrt{4} }[/tex]
[tex]\frac{\sqrt{5} }{8}[/tex]
x(x-3)=x then the possible value of X are...
[tex]x(x-3)=x\\x^2-3x-x=0\\x^2-4x=0\\x(x-4)=0\\x=0\vee x=4[/tex]
[tex]\text{Hey there!}[/tex]
[tex]\text{In order for you can do the distributive property then work from there}[/tex]
[tex]\text{x(x - 4) = x}\\\\\text{x(x)=x}^2\\\\\text{x(-3)= -3x}[/tex]
[tex]\text{Subtract by the value of x on your sides!}[/tex]
[tex]\text{Your new equation becomes: x}^2\text{- 3x = x}[/tex]
[tex]\text{Like}\downarrow[/tex]
[tex]\text{x}^2\text{- 3x - x = x - x}[/tex]
[tex]\text{x - x = 0 }[/tex]
[tex]\text{-3x + (-1x) = -4x}[/tex]
[tex]\text{Our equation becomes: x}^2\text{- 4x = 0}[/tex]
[tex]\text{Next, we have to FACTOR on the LEFT side of your equation}[/tex]
[tex]\text{x(x - 4) = 0}[/tex]
[tex]\text{Set the numbers to FACTOR out to 0}[/tex]
[tex]\text{Like: x = 0 or x - 4 = 0}\text{ (solve that and you SHOULD have the x-values)}[/tex]
[tex]\boxed{\boxed{\bf{Answer: x = 0\ or \ x =4}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirt:)}[/tex]
what is the answer to this 3x8y4
The answer is [tex]\( 24xy^2 \)[/tex].
To solve the expression [tex]\( 3x \cdot 8y^4 \)[/tex], we first multiply the coefficients and the variables separately. The coefficients are 3 and 8, and when multiplied, they give us 24. For the variables, we multiply x by [tex]\( y^4 \)[/tex], keeping in mind that when multiplying exponents with the same base, we add the exponents. Therefore, [tex]\( x \cdot y^4 \)[/tex] remains [tex]\( xy^4 \)[/tex].
Combining the coefficient and the variables, we get \( 24xy^4 \). However, we can simplify this further by recognizing that any variable raised to the power of 1 is simply the variable itself. Thus, [tex]\( xy^4 \)[/tex] is equivalent to [tex]\( xy^2 \)[/tex] because [tex]\( y^1 \)[/tex] is just [tex]\( y \)[/tex].
So the final simplified expression is [tex]\( 24xy^2 \)[/tex].
What is the fourth term of the sequence?
ar = 2.41-2
Enter your answer in the box.
HELPPPP!!!!
Answer:
32
Step-by-step explanation:
Substitute n = 4 into the formula
[tex]a_{4}[/tex] = 2 × [tex]4^{4-2}[/tex] = 2 × 4² = 2 × 16 = 32
Kevin is responsible for delivering sacks of grains to a grocery shop on the tenth floor of a departmental store. Each sack weighs 364 pounds and Kevin weighs 150 pounds. The capacity of the elevator is 2,000 pounds.
If six sacks are to be taken at a time, what should be the weight of each sack?
Final answer:
Kevin can safely take sacks weighing up to 308.33 pounds each in the elevator, provided he takes six sacks at a time and the elevator's capacity is 2,000 pounds with Kevin weighing 150 pounds.
Explanation:
The student's question is asking for the maximum weight of each sack of grain that Kevin can deliver on the elevator, given the elevator's weight capacity and the additional weight of Kevin himself. To answer this question, we need to consider the weight that the elevator can hold minus Kevin's weight, and then determine how much weight is left for the sacks of grain.
The elevator has a capacity of 2,000 pounds, and Kevin weighs 150 pounds. This means the total weight that the elevator can carry in addition to Kevin is:
2000 pounds (elevator capacity) - 150 pounds (Kevin's weight) = 1850 pounds (available for sacks)
If Kevin needs to deliver six sacks at a time, we can divide the total available weight by six to find the maximum weight for each sack:
1850 pounds / 6 sacks = approximately 308.33 pounds per sack
Therefore, the weight of each sack must be 308.33 pounds or less for Kevin to safely use the elevator without exceeding its capacity.
Which method would you use to prove that the two triangles are congruent?
Answer:
AAS
Step-by-step explanation:
Given one pair of congruent angles and one pair of congruent sides.
When two lines intersect they form a pair of congruent angles (vertical angles are equal)
So the two triangles are congruent by AAS.
Answer: AAS
Step-by-step explanation:
By the figure we can say that the have one side equal. Now for the angles we have that in the part of the triangles are touching we have an oposite angles then these two angles have to be equals. Finally the two triangles have two equal angles and ones equal side. we can conclude that the correct method is AAS.
Which equation is the inverse of 2(x - 2)^3=8(7+y)
Answer:
[tex]\large\boxed{y=2\pm\sqrt{28+4x}}[/tex]
Step-by-step explanation:
[tex]2(x-2)^2=8(7+y)\\\\\text{exchange x to y, and vice versa:}\\\\2(y-2)^2=8(7+x)\\\\\text{solve for y:}\\\\2(y-2)^2=(8)(7)+(8)(x)\\\\2(y-2)^2=56+8x\qquad\text{divide both sides by 2}\\\\(y-2)^2=28+4x\iff y-2=\pm\sqrt{28+4x}\qquad\text{add 2 to both sides}\\\\y=2\pm\sqrt{28+4x}[/tex]
Answer:
y is inverse: 2 ±[tex]\sqrt{28+ 4x}[/tex] .
Step-by-step explanation:
Given: 2(x - 2)²=8(7+y).
To find: Find inverse.
Solution : We have given
2(x - 2)²=8(7+y).
Step 1: inter change the x and y.
2(y - 2)²=8(7+x).
Step 2:
Solve for y
On dividing both sides by 2
(y - 2)² = 4 (7+x).
Distributes 4 over ( 7 + x)
(y - 2)² = 28 + 4x
Taking square root both sides.
[tex]\sqrt{(y-2)^{2} } = ±\sqrt{28+ 4x}[/tex].
y - 2 = ±[tex]\sqrt{28+ 4x}[/tex].
On adding both sides by 2
y = + 2 ±[tex]\sqrt{28+ 4x}[/tex] .
Therefore, y is inverse : 2 ± [tex]\sqrt{28+ 4x}[/tex].
What is the slope of the equation y - 3 = -4(X - 5)?
Answer:
Step-by-step explanation:
y - 3 = -4(x - 5)
Add 3 to both sides to isolate y
y = -4 ( x - 5 ) + 3
Distribute
y = -4x +20 + 3
Combine like terms
y = -4x + 23
y = mx + b is standard form for which m is slope
m = -4
Please mark for brainliest!! :D Thanks!!
If you have any questions or need more information, please comment below and I'll respond asap!!
Answer:
-4
Step-by-step explanation:
Distribute -4 into the parenthesis and get -4x + 20. The number paired with x is the slope, usually represented by m in y = mx + b. So, the slope is -4. For the full slope intercept format, move the -3 on left side to the right by adding 3. The new equation is y = -4x + 23.
What is the equation of the line that passes through (-3, -1) and has a slope of 2/5? Put your answer in slope-intercept.
[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-1})~\hspace{10em} slope = m\implies \cfrac{2}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-1)=\cfrac{2}{5}[x-(-3)]\implies y+1=\cfrac{2}{5}(x+3) \\\\\\ y+1=\cfrac{2}{5}x+\cfrac{6}{5}\implies y=\cfrac{2}{5}x+\cfrac{6}{5}-1\implies y=\cfrac{2}{5}x+\cfrac{1}{5}[/tex]
Graph y = -|x| + 2. Click on the graph until the correct one appears.
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]y=-\left|x\right|+2[/tex]
we know that
The graph is inverted V-shaped.
The x-intercepts are the points (-2,0) and (2,0)
The vertex is the point (0,2)
The domain is all real numbers
The range is all real numbers less than or equal to 2
using a graphing tool
The graph in the attached figure
What is the value of x?
[tex]x+40=3x\\2x=40\\x=20[/tex]
For this case we have by definition of angles between secant lines that:
[tex]x + 40 = 3x[/tex]
Also, the angle between T and V is equal to the angle between S and W.
Returning to the question, we have to:
[tex]x + 40 = 3x[/tex]
We must know the value of "x":
Subtracting 3x on both sides of the equation we have:
[tex]x-3x + 40 = 0[/tex]
Subtracting 40 from both sides of the equation:
[tex]-2x = -40[/tex]
Dividing between -2 on both sides of the equation:
[tex]x = \frac {-40} {- 2}\\x = 20[/tex]
So, the value of x is 20
Answer:
[tex]x = 20[/tex]
The area of a circle with radius r is given by A = π r2. Find the area of a circle with radius 7 centimeters. Use 3.14 for π.
Answer:
The area is 0.015m²
Step-by-step explanation:
Step one
Given that the expression for area of the circle is A = π r²
Step two
Now our raduis r= 7cm - - - meter =7/100= 0.07
And Pi = 3.142
Step three
Substituting r in the formula for area we have
A= 3.142*(0.07)²
A=3.142*0.0049
A= 0.015m²
write 3 times the square root of 2 plus the 2 times the square root of 3 in simplest form
Answer: Option 'D' is correct.
Step-by-step explanation:
Since we have given that
3 times the square root of 2 +2 times the square root of 3 =3sqrt2+2sqrt3
We need to simplify the above expression.
In addition and subtraction, there is a rule of adding or subtracting of like terms is possible only.
But, here, √2 ad √3 are unlike term.
so, we cannot simplified it.
Hence, Option 'D' is correct.
Step-by-step explanation:
Please mark brainliest and have a great day!
Answer:
Step-by-step explanation:
3√2 + 2√3 is as simple an expression as you'll get for this quantity.
X = y +3, 0.8 x + 1.2 y = 6.4
Answer:
y=2
x=5
Step-by-step explanation:
What is the following quotient? 2/sqrt13+sqrt11
Answer:
Answer is [tex]\sqrt{13}-\sqrt{11}[/tex]
Step-by-step explanation:
We need to divide
[tex]\frac{2}{\sqrt{13}+\sqrt{11}}[/tex]
For solving this, we need to multiply and divide the given term with the conjugate of [tex]{\sqrt{13}+\sqrt{11}[/tex]
The conjugate is: [tex]{\sqrt{13}-\sqrt{11}[/tex]
Solving
[tex]=\frac{2}{\sqrt{13}+\sqrt{11}} *\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}} \\=\frac{2(\sqrt{13}-\sqrt{11})}{(\sqrt{13}+\sqrt{11})(\sqrt{13}-\sqrt{11})}\\We\,\, know\,\, that\,\, (a+b)(a-b) = a^2-b^2\\=\frac{2(\sqrt{13}-\sqrt{11})}{(\sqrt{13})^2-(\sqrt{11})^2}\\=\frac{2(\sqrt{13}-\sqrt{11})}{13-11}\\=\frac{2(\sqrt{13}-\sqrt{11})}{2}\\=\sqrt{13}-\sqrt{11}[/tex]
So answer is [tex]\sqrt{13}-\sqrt{11}[/tex]
Answer:
The correct Answer is D[tex]\sqrt{13} - \sqrt{11}[/tex]
Step-by-step explanation:
Solve for
5(x + 1) = 4x + 8)
Answer:
x =3
Step-by-step explanation:
5(x + 1) = 4x + 8
Distribute the 5
5x+5 = 4x+8
Subtract 4x from each side
5x-4x+5 = 4x-4x+8
x+5 =8
Subtract 5 from each side
x+5-5 = 8-5
x =3
The graph below plots the values of y for different values of X:
Which correlation coefficient best matches the data plotted on the graph? (1 point)
Answer:
0.50
Step-by-step explanation:
we know that
Observing the graph
we have the following points
(1,3),(2,4),(3,9),(4,7),(5,2),(6,18)
Using a Excel tool (Correl function)
The correlation coefficient is equal to r=0.605639
see the attached table
therefore
The correlation coefficient that best matches the data plotted on the graph is 0.50
two square regions have an area of 125 and 5 how many yards of fencing is needed to enclose? ( assume regions fenced separately)
Answer:
[tex]24\sqrt{5}\ yards[/tex]
Step-by-step explanation:
Let A1 be the area of one square and A2 be the area of second square
So,
A1 = s^2
where s is side of square
[tex]s^2=125\\\sqrt{s^2}=\sqrt{125}\\s=\sqrt{25*5}\\ s= \sqrt{5^2 * 5}\\ s= 5\sqrt{5}[/tex]
So side of one square is [tex]5\sqrt{5}[/tex]
To calculate the length of fence we need to find the perimeter of the square
So,
P1 = 4 * s
[tex]=4*5\sqrt{5} \\=20\sqrt{5}[/tex]
For second square:
[tex]A_2=s^2\\5=s^2\\\sqrt{s^2}=5\\{s}=\sqrt{5}[/tex]
The perimeter will be:
[tex]P_2 = 4*s\\=4 * \sqrt{5} \\=4\sqrt{5}[/tex]
So the total fence will be: P1+P2
[tex]= 20\sqrt{5}+4\sqrt{5} \\= 24\sqrt{5}\ yards[/tex]
find (fof)(0) f(x)=x^2
a.1
b.0
c.-8
d.-1
Answer:B
f(0)=0
Step-by-step explanation:
when 0 is squared it’s just 0
Answer: option b.
Step-by-step explanation:
Given the function f(x):
[tex]f(x)=x^2[/tex]
In order to find [tex](fof)(x)[/tex], the first thing you must do is to substitute the function f(x) into the same function f(x). Observe the procedure:
[tex](fof)(x)=(x^2)^2[/tex]
Now, you need to simplify:
[tex](fof)(x)=x^4[/tex]
Finally, to find [tex](fof)(0)[/tex] you need to substitute [tex]x=0[/tex] into [tex](fof)(x)=x^4[/tex], then you get:
[tex](fof)(0)=(0)^4[/tex]
[tex](fof)(0)=0[/tex]
Which is a correct classification for the triangle?
Step-by-step explanation:
All three sides are equal, so this is an equilateral triangle.
Answer:
This is an equilateral triangle
Step-by-step explanation:
All three sides are equal, making it equilateral
Susan is paying $0.30 per $100 on her $483,000 home in homeowners insurance annually. If her annual homeowners insurance premium is divided into twelve equal monthly installments to be included on each of her monthly mortgage payments of $2128.00, what is her total monthly payment? a. $2,248.75 b. $2,409.75 c. $3,381.00 d. $3,577.00 Please select the best answer from the choices provided
Answer:
a) $2248.75
Step-by-step explanation:
Susan pays $0.3 per $100
For $483000, she pays $1449 insurance annually : Calculation shown below
483000/100 x 0.3 = $1449
Monthly instalments of the insurance premium for 12 months :
annual insurance premium/ 12 months
1449/12 = $120.75
Monthly mortgage payments = $2128
Monthly total payments = monthly mortgage payments + monthly insurance premium instalment.
= 1449 + 120.75
= $2248.75
!!
27. A watch cost $75.99. If the sales tax
rate is 6.25%, what is the amount of
sales tax?
A $0.48
B $2.19
C $4.75
D $474.94
Step-by-step explanation:
75.99 ×.0625=4.749
75.99+4.75(because I rounded)=
$80.74 total cost incase you have another step
75.99 ×.0625 = 4.749
I rounded to get 4.75.
75.99 + 4.75 = $80.74
$80.74 - $75.99 = $4.75
Answer: $4.75
What is the explicit formula for this sequence -7, -4, -1, 2, 5
[tex]a_n=3n-10[/tex]
Answer:
an = -7 + (n - 1) 3
Step-by-step explanation:
Let v=−3i
v
=
−
3
i
and w=2−4i
w
=
2
−
4
i
. Find v−w
v
−
w
.
Answer:
-2 + i
Step-by-step explanation:
v = -3i
w = 2 - 4i
v - w =
= -3i - (2 - 4i)
= -3i - 2 + 4i
= -2 + i
The given value of v = -3i and w = 2-4i, so v-w = -2 + i.
Given: v = -3i, w = 2-4i
To find: v - w
Solution:
Substitute the values of v and w into the expression v - w.
v - w = -3i - (2-4i)
v - w = -3i - 2 + 4i
v - w = -2 + i
A company makes globes with a radius of 11 inches. The material to make the globes costs the company $0.04 per square inch. To the nearest cent, how much does the company pay for the material to create one globe? Use 3.14 for pi.
Recall the formula SA=4 pi r^2.
$11.05
$60.79
$243.16
$607.90
Answer:
One globe costs $60.79
Step-by-step explanation:
The area of the globe is
A = 4.π.r^2
Since the radius is 11 inches
A = 4*(3.14)*(11 in)^2 = 1519.76 in^2
We apply a rule of three
1 in^2 --------------------------------- $0.04
1519.76 in^2 ------------------------- x
x = (1519.76 in^2/ 1 in^2)*$0.04
x = (1519.76)*$0.04
x = $60.79
x ≈ $60.8
Answer: Second Option
$60.79
Step-by-step explanation:
To solve this problem let's suppose that the balloons are spherical
Then the surface area of a sphere is given by the formula:
[tex]SA=4\pi r^2[/tex]
Where r is the radius of the sphere
In this case we know that the radius of each globes is 11 inches, then:
[tex]SA=4(3.14) (11)^2[/tex]
[tex]SA=4(3.14)(121)[/tex]
[tex]SA=1519.76\ in^2[/tex]
If the material to make globes costs $ 0.04 per square inch then the cost of a globes is:
[tex]C=1519.76*0.04[/tex]
[tex]C=\$60.79[/tex]