The expression equivalent to the given expression is 10p²z⁴.
What is expression?An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation, this maths operation can be addition, subtraction, multiplication, or division.
An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.
you can recognize that an equation is simply two expressions joined together by an equal sign.
Given that, an expression, [tex]\sqrt{100p^{4} z^{8} }[/tex]
Solving, [tex]\sqrt{100p^{4} z^{8} }[/tex]
The square root of 10 = 100, p² = p⁴ and z⁴ = z⁸
Therefore, finding the square root,
= √100x√p⁴x√z⁸
= 10×p²×z⁴
= 10p²z⁴
Hence, [tex]\sqrt{100p^{4} z^{8} }[/tex] = 10p²z⁴
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Point B has coordinates (5,2). The x-coordinate of point A is -3. The distance between point A and point B is 10 units. What are the possible coordinates of point A?
Answer:
The possible coordinates of point A are (-3, 8) and (-3, -4).
Step-by-step explanation:
We can find the possible coordinates of point A by using the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is equal to the square root of (x2-x1)^2 + (y2-y1)^2. We know that the x-coordinate of point A is -3 and the distance between point A and point B is 10 units. We can use this information to solve for the y-coordinate of point A:
Copy code
d = sqrt((x2-x1)^2 + (y2-y1)^2)
d = sqrt((5-(-3))^2 + (2-y1)^2)
d = sqrt(8^2 + (2-y1)^2)
d = sqrt(64 + (2-y1)^2)
d = sqrt(64 + (y1-2)^2)
d = 10
sqrt(64 + (y1-2)^2) = 10
64 + (y1-2)^2 = 100
(y1-2)^2 = 36
y1-2 = +/- 6
y1 = 8 or -4
Therefore, the possible coordinates of point A are (-3, 8) and (-3, -4).
Anton mows two lawns. The first lawn is 8 feet long and 5 feet wide. The second lawn has the same length, and width that is 4 times the first one. What is the total area of the two lawns?
The total area of the two lawns is 200 ft²
What is Area?Area is the region occupied by an object.
What is the total area of the two lawns?Since Anton mows two lawns. The first lawn is 8 feet long and 5 feet wide. The second lawn has the same length, and width that is 4 times the first one, since the lawns are rectangles, their area is the area of a rectangle.
What is the area of a rectangle?The area of a rectangle is given by
A = LW where
L = length of rectangle and W = width of rectangle.Given that for the first lawn it is 8 feet long and 5 feet wide, we have that
L = 8 ft and W = 5 ftSo, its area A = LW
= 8 ft × 5 ft
= 40 ft²
Also, for the second lawn, the same length, and width that is 4 times the first one. So, we have that
L' = 8 ft and W' = 4W = 4 × 5 ft = 20 ftSo, its area A' = L'W'
= 8 ft × 20 ft
= 160 ft²
So, the total area of the two lawns is A" = A + A'
= 40 ft² + 160 ft²
= 200 ft²
So, the total area is 200 ft²
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Select the correct answer. Which values of x make this equation true? -x^2+8x=-15
The price of a pair of shoes after 8% sales tax was added was $77.76. Find the original price before sales tax
Answer: $71.53
Step-by-step explanation:
77.76 = 100%
HELP ME PLEASE!!!!!!!!!!!!!!!!!
The figure shows three quadrilaterals on a coordinate grid: A coordinate grid is shown from positive 8 to negative 8 on the x-axis and from positive 8 to negative 8 on the y-axis. An image of a rectangle labeled A is shown on ordered pair 1, 1 and 3, 1 and 3, 2 and 1, 2. Another image of a rectangle labeled B is shown on ordered pair 2, 2 and 6, 2 and 6, 4 and 2, 4. Another image of a rectangle labeled C is shown on ordered pair negative 1, 1 and negative 1, 2, and negative 3 , 2 and negative 3, 1. Which of the following statements is true about the three quadrilaterals? (5 points) A and B are similar but not congruent. A and C are similar but not congruent. A and B are similar and also congruent. B and C are similar and also congruent.
Answer:
(a) A and B are similar but not congruent
Step-by-step explanation:
All of the rectangles have sides in the ratio of 2:1, so are all similar. Only the rectangles that are the same size are congruent: A and C.
What is the solution to this
inequality?
8.6 ≤ x - 5 4/5
Answer:
x ≥ 72/5
8.6 ≤ x -5 4/5= 8.6 ≤ x -29/5
8.6 ≤ x -29/5= x ≥ 72/5
Rob and Jeni each recruit three people to be election campaign volunteers. The next week they ask each of those volunteers to recruit three more campaign volunteers. They want all new volunteers each week to recruit three more volunteers.
The number of volunteers recruited for the first 5 weeks is; 486 people
How to calculate the geometric sequence?
A geometric sequence is defined as a sequence in which the result of the division of consecutive terms is always the same, called common ratio r.
The nth term of a geometric sequence is given by:
aₙ = a₁rⁿ⁻¹
where;
a₁ is the first term
r is the common ratio
In this question, on the first week there are 6 people, and since each new people involve three more, the common ratio is 3, hence the parameters for the geometric sequence are:
a₁ = 6
r = 3
Hence the number of people after n weeks is:
aₙ = 6(3)ⁿ⁻¹
Thus, the number of volunteers recruited for the first 5 weeks is;
a₅ = 6(3)⁵⁻¹
a₅ = 6 * 3⁴
a₅ = 486
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What is the area of this triangle?
Answer:
D
Step-by-step explanation:
base= y2-y1
height = x3-x1
so (1/2)×(y2-y1)×(x3-x1)
2(2x-20)= -12
6x-20= -12
6x=8
X=8
_
6
Find the mistake
Answer:
The mistake was made when we rewrote the equation wrong after dividing 2 to both sides
Step-by-step explanation:
After we divide two on both sides the equation should have been rewriting as [tex]2x-20=-6[/tex] not [tex]6x-20=-12[/tex]
Which formula correctly shows how to find the 21st term in the geometric sequence?
2000, 1000, 500, 250, 125, ...
Answer: Therefore, the correct formula is {a}_{21} = 2000 * 0.5^{20}.
Step-by-step explanation:
A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous term by a constant factor called the common ratio. In this case, the common ratio is 0.5, since each term is found by dividing the previous term by 2.
To find the nth term in a geometric sequence, we can use the formula:
a_n = a_1 * r^(n-1)
where a_1 is the first term in the sequence, a_n is the nth term, and r is the common ratio. In our case, the first term is 2000, the nth term is the 21st term, and the common ratio is 0.5. Therefore, the formula we need to use is:
a_21 = 2000 * 0.5^(21-1)
= 2000 * 0.5^20
Therefore, the correct formula is {a}_{21} = 2000 * 0.5^{20}.
A customer paid a total of $6.00 for 68 copies at a print shop. Some copies were black and white copies, the rest were color copies.
• each black and white copy cost $0.08
• each color copy cost $0.15
Which system of equations can be used to find b, the number of black and white copies and c, the number of color copies that the customer paid for at the print shop?
Answer:
D. b + c = 68
0.08b + 0.15c = 6.00
Step-by-step explanation:
The total cost is $6.00
The total amount of copies is 68
To find the total cost, we multiply the amount of copies by the individual price. So we get
0.08b + 0.15c = 6.00
We add the amount of copies bought to get a total of 68, so we get this equation:
b + 6 = 68
The real root of the equation x3 10x2 29x 30 = 0 is –6. what are the nonreal solutions? 2 i, 2 – i –2 i, –2 – i –4 2i, –4 – 2i 4 2i, 4 – 2i
The non-real roots of the polynomial x³ - 10x² + 29x - 30 are; x = 2 + i or 2 - i
What is the root of the polynomial?We are given the polynomial as;
x³ - 10x² + 29x - 30
We are told that the real root of the polynomial is -6. Thus, (x + 6) is a factor of the polynomial.
Now, we can use polynomial long division to get;
x³ - 10x² + 29x - 30
- divisor * x² x³ - 6x²
remainder - 4x² + 29x - 30
- divisor * -4x¹ - 4x² + 24x
remainder 5x - 30
- divisor * 5x⁰ 5x - 30
remainder 0
Quotient : x² - 4x + 5 Remainder: 0
x² - 4x + 5_______
(x + 6) | x³ - 10x² + 29x - 30
- x³ - 6x²
-4x² + 29x - 30
- - 4x² + 24x
5x - 30
- 5x - 30
0
Now, using quadratic calculator to find the roots of the quotient, we get;
x = 2 + i or 2 - i
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equivalent expression for 1.2 cubed over 1.3 raised to the fourth power all raised to the power of negative seven
Answer:
management accountant prepared a decision model which solve sell at split off or process
further decision problem. Which function did he provided?
A. Scorekeeping function C) Problem solving function
B. Attention directing function. D) Record keeping function E) None
Help me !!??!!!????please
1.You have one full pizza, out of which your friend eat one-hundredths six
times from it. There is some part of the pizza left for you. How much you will
get to eat?
Answer:
there will be only 1 more slice to eat
Write an equation and use it to solve for x.
The value of the x would be 9.
Option (A) is correct.
What is a complementary angle?
A complementary angle is an angle that, when added to another angle, forms a right angle (90 degrees). Complementary angles are pairs of angles that add up to 90 degrees.
Angle JKM and angle MKN are complementary angles
so
(3x + 2) + (6x + 7) = 90
9x + 9 = 90
9(x + 1) = 90
x + 1 = 10
x = 9
Hence, the value of the x would be 9.
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After solving the equation the value of the x would be 9. Therefore, the correct option is A.
What is a complementary angle?
A complementary angle is a pair of angles that add up to 90 degrees. Complementary angles can be adjacent angles, or angles that share a common vertex and side, or they can be nonadjacent angles that have no common points or sides. Complementary angles are usually referred to by their sum, such as "90-degree angles" or "angles that add up to 90 degrees." Complementary angles can also be called supplementary angles when they add up to 180 degrees.
Angle JKM and angle MKN are complementary angles
so (3x + 2) + (6x + 7) = 90
9x + 9 = 90
9(x + 1) = 90
x + 1 = 10
x = 9
Hence, the value of the x would be 9.
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Which expression is equivalent to the perimeter of your the rectangle shown below?
The expression that is equivalent to the perimeter of the rectangle in the image shown is, 6x + 8.
How to Find the Perimeter of a Rectangle?To find the perimeter of a rectangle, add all the four sides of the rectangle. The following formula can be used:
Perimeter (P) = 2(length + width).
In the rectangle shown below, the dimensions are:
Length of rectangle = 2x + 3
Width of rectangle = x + 1
Substitute into the perimeter each expression of the dimensions:
Perimeter = 2[(2x + 3) + (x + 1)]
Open the parentheses by applying the distributive property of equality:
Perimeter = 2(2x + 3 + x + 1)
= 2(3x + 4)
= 2(3x) +2(4)
= 6x + 8
Therefore, the expression is, 6x + 8.
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Four integers have a mean of 8, a median of 6, a mode of 6 and a range of 14
Find the four integers
Answer:
Step-by-step explanation:
Let's call the four integers x, y, z, and w. We know that the mean of these four integers is 8, so:
x + y + z + w = 8 * 4 = 32
We also know that the median of these four integers is 6, which means that two of the integers are less than 6 and two are greater than 6. The mode of 6 means that one of the integers is 6.
Let's assume that x and y are the two integers that are less than 6. This means that z and w are the two integers that are greater than 6. We can then set up the following system of equations to represent this information:
x + y + z + w = 32
x + y < 12
z + w > 12
We also know that the range of these four integers is 14, which is the difference between the largest and smallest integers. Since z and w are the two largest integers, the range is equal to w - x. We can set up another equation to represent this information:
w - x = 14
We can solve this system of equations using substitution. First, we can solve the second equation for x:
x = 12 - y
We can then substitute this expression for x in the third equation to get:
w - (12 - y) = 14
w = 14 + y
Finally, we can substitute this expression for w in the first equation to get:
x + y + z + (14 + y) = 32
x + 2y + z = 18
We can then substitute the expression for x in the third equation to get:
(12 - y) + 2y + z = 18
-y + 2y + z = 18
z = 18 - y
We can then substitute this expression for z in the third equation to get:
w = 14 + y = 14 + (18 - z) = 14 + 18 - y = 32 - y
Substituting this expression for w in the first equation gives us:
x + y + z + (32 - y) = 32
x + 2y + z = 32
We can then substitute the expressions for x and z in the third equation to get:
(12 - y) + 2y + (18 - y) = 32
-y + 2y + 18 - y = 32
18 = 32
This equation is clearly not true, so the original assumptions we made about which integers were less than 6 and which were greater than 6 must be incorrect.
However, we can use a similar process to solve for the other possibility: that x and z are the two integers that are less than 6, and y and w are the two integers that are greater than 6.
In this case, we can set up the following system of equations:
x + y + z + w = 32
x + z < 12
y + w > 12
w - x = 14
Solving this system of equations using substitution gives us the solution x = 4, y = 10, z = 6, and w = 8.
Therefore, the four integers are 4, 6, 8, and 10.
What is (x + 3)(x - 5) in generic rectangle
the area of the generic rectangle will be x²-2x-15.
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A quadrilateral with equal angles and parallel opposite sides is referred to as a rectangle. Around us, there are a lot of rectangle items. The length and width of any rectangle form serve as its two distinguishing attributes. The width and length of a rectangle, respectively, are its longer and shorter sides.
Area of rectangle is A = a*b
(x + 3)(x - 5) in a generic rectangle
The product will give the area
x²-2x-15
hence the area of the generic rectangle will be x²-2x-15.
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Type the correct answer in the box. Use numbers instead of words.Isha is a pet sitter.She earns $5 for each cat.She earns $12 for each dog.Last week, Isha pet sat for 11 cats and 7 dogs.How much money did Isha earn pet sitting last week?
By evaluating a revenue equation, we will see that she earned $139 last week.
How much money did Isha earn pet sitting last week?We know that Isha is a pet sitter, and she earns $5 for each cat and $12 for each dog.
So, if she pet sats for x cats and y dogs, the revenue will be:
R(x, y) = $5*x + $12*y
In this case we know that she pet sat for 11 cats and 7 dogs, then we have:
x = 11
y = 7
So we need to evaluate the above revenue function, we will get:
R(11, 7) = $5*11 + $12*7
R(11, 7) = $55 + $84
R(11, 7) = $139
Isha earned $139 last week.
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ABCD with vertices B (2,1), C (2,5), and D (6,1) has its orthocenter at which point?
A. (0,0)
B. (2,1)
C. (2,5)
D. (6,1)
Step-by-step explanation:
d is the answer as far as I can tell from a little experience
Find the sum of (–4 i) and (10 – 5i). –3 5i –3 – 5i 6 – 4i 6 – 6i
The sum of the two complex numbers will give:
(-4 + i) + (10 - 5i) = 6 - 4i
So the correct option is the third one.
How to add two complex numbers?Let's assume we have two complex numbers which are:
A = a + bi
B = c + di
The sum between these two complex numbers is:
A + B = (a + bi) + (c + di)
Taking i as a common factor we can rewrite:
(a + bi) + (c + di) = a + c + (b + d)i
And that is the general sum.
Here we want to solve:
(-4 + i) + (10 - 5i)
Again, if we take i as a common factor we can rewrite:
-4 + 10 + (1 - 5)*i
6 - 4i
So the correct option is the third one.
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PLS HELP ME I NEED IT I PUT A PICTURE
Answer: <D, < E, <C
Step-by-step explanation:
a rectangle is 3 feet longer than it is wide. find the dimensions of the rectangle if its area is 208 sq-feet
Dimensions of the Rectangle are : 16 feet by 13 feet .
A rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal . A rectangle has two dimensions. we can measure its length and, perpendicular to that, its width.
Rectangle is 3 feet longer than it is wide and its area is 208 sq-feet .
Area of Rectangle = l×b ( Where l = length , b = breadth )
Therefore , Let X be the the width of rectangle . then from given it's length is (X+3).
∴ X × (X+3) = 208
∴ [tex]x^{2}[/tex]+3X-208 = 0
(X+16)(X-13) = 0
X = -16 & X = 13
Distance can't be negative so Width = X = 13 feet.
∴ Length = X+3 = 16 feet.
Thus the Dimensions are 16 feet by 13 feet .
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solve for x.
enter your answer as a mixed number in simplest form in the box.
x =
Answer:
x + x - x = x
explanation:
give us the actual formula lol
the sum of the measures of the interior angles of a convex polygon is eight times the sum of the measures of its exterior angles. find the number of sides of the polygon
Interior angle-
All interior angles of a regular polygon are equal. The formula for calculating the magnitude of the interior angle is:
Interior angle of polygon = sum of interior angles ÷ number of sides. The sum of the exterior angles of a polygon is 360°.
Exterior angle-
An exterior angle is an angle that is parallel to, but outside, the interior angle of a polygon. The exterior angle measurement is equal to the sum of the two opposite interior angles.
according to the question,
given data
interior angle=8 exterior angle
we know that,
interior angle+ exterior angle=180
let us consider ,
exterior angle=x
so we can say that,
8 exterior angle + exterior angle =180
8x+x=180
9x=180
x=20
we know that ,
the number of sides=360/x
=360/20
=36/2
=18
the number of sides of the polygon is 18
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George is given two circles, circle and circle X, as shown. If he wants
prove that the two circles are similar, what would be the correct first step in
his proof?
To prove that the two circles are similar, the answer which would be the correct second step in his proof is:
A - C = 2-pi-r/C = 2-pi-r and C/C = r/r by the division property of equality
What is a Circle?
This refers to a round plane who has a centre as a fixed point that has equal distance from each ot
With this in mind, we can see that Circle O and Circle X are shown and they are said to be similar, hence, the second step to prove that they are similar is A - C = 2-pi-r/C = 2-pi-r and C/C
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find the value of 3x-2 when x=4
find the value of 5x+6 when x=-2
Answer:
3(4) - 2 is 10 the value is 10
5(2) + 6 is 16 the value is 16
I hope this helps have a good day or night!
Hi sorry for the mistake this is the photo I was meant to post and I need help with number 6(iii)
Answer:
-2
Step-by-step explanation:
Given,
g(x) = f(4)
or, 2 - 4x = 3*4 - 2
or, 2 - 4x = 10
or, 2 - 10 = 4x
or, -8 = 4x
or, x = -2
NEED HELP ASAP!
Refer to the triangle.
What is the length of side AB?
(Blank) units
After solving the equation the length of AB is [tex]2\sqrt{3}[/tex]
What do you mean by trigonometry?
Trigonometry “triangle” and “measure”) is a branch of mathematics that studies the relationship between the side lengths and angles of triangles.
A trigonometric ratio is the ratio between the edges of a right triangle.
The sine function (sin) defined as the ratio of the opposite side of the angle to the hypotenuse.
In the given triangle ABC , use sin ratio to find AB.
tan θ = P/B
tan 30 = AB/6
[tex]\frac{1}{\sqrt{3} } =AB/6[/tex]
AB = [tex]\frac{6}{\sqrt{3} }[/tex] = [tex]\frac{6}{\sqrt{3} }\times \frac{\sqrt{3}}{\sqrt{3}}= \frac{6\sqrt{3}}{3}=2\sqrt{3}[/tex]
Therefore, length of AB is [tex]2\sqrt{3}[/tex]
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