x^-4/x^3 times x^-7 in equivalent expression is x⁻¹⁴
What are index forms?The index form of a number can be defined as the number that is written as an exponential expression.
It is also seen as the single number that is raised to another number.
The rules of index forms are;
Multiplying the index forms when they have the same base, add the exponents or powersDividing indices, in dividing, they must have the same base so subtract the powers Brackets with indices. When there is a power outside the parentheses, then multiply the powersFrom the information given, we have that;
x⁻⁴/x³ × x⁷
Since the denominators are of the same base, add the powers
x⁻⁴/x³⁺⁷
Add the values
x⁻⁴/x¹⁰
Now, subtract the powers
x⁻¹⁴
Hence, the value is x⁻¹⁴
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On March 14 at 1:59, people celebrate Pi Day by eating pie. Why do you
think people celebrate on thi day at thi time?
People celebrate Pi Day on March 14th at 1:59 because this date and time is an easy way to remember the mathematical constant pi (π).
Pi, which is represented by the Greek letter π, is an irrational number that starts with 3.14 and continues for an infinite amount of digits. The numerical value of pi is the ratio of a circle's circumference to its diameter, and is approximately equal to 3.1415926535897932384626433832795. The date and time of March 14th, 1:59 is a way to represent the first four digits of pi (3.14). People celebrate Pi Day by eating pie, making pi-related crafts, and sharing facts about pi. People celebrate Pi Day on March 14th at 1:59 because this date and time is an easy way to remember the mathematical constant pi (π).
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The area of a rectangle is 81m'n' square units. If the length of the rectangle is 9mn', how many
units wide is the rectangle?
Answer:
9
Step-by-step explanation:
9x9=81
Answer:
Step-by-step explanation:
So the rectangle is 9 units wide.
becuase given that the area of the rectangle is 81m'n' square units and the length of the rectangle is 9mn', we can set up the equation as:
81 = 9 x width
To solve for width, we can divide both sides of the equation by 9:
width = 81/9
width = 9
Reflected over the x-axis, then translated 6
units left
Write an equation to represent the function
Required equation to represent the translation 6 units left and reflected over x-axis is y = - (x + 6 ).
Let us consider the original equation be y = x.
Translation to the left by k unit is f(x) = f ( x + k )
Now the equation gets translated 6 units to the left represents as
y = ( x + 6 )
Now the reflected over the x-axis is represented by :
Here y -coordinates change the sign.
If ( x, y ) after reflection over x -axis it is ( x , -y ).
y = - ( x + 6 )
Equation to represents the reflected over x-axis and translated 6 units left of the original function y = x is written as y = - ( x + 6 ).
Therefore, the equation to represent the required translation and reflection is given by y = - ( x + 6 ).
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A net of a rectangular pyramid is shown. The rectangular base has length 25 ft and width 22 ft. The net of the pyramid has length 74.8 ft and width 70.4 ft. Find the surface area of the pyramid.
The surface area of the pyramid is 5,685 ft².
Solving for the surface area of the pyramid:To find the surface area of the pyramid, we need to find the area of the base and the area of the four triangular faces. Since the base is a rectangle, we can find its area by multiplying the length and width:
length, l = 25 ft
width,w = 22 ft
Area = l x w
Area = 25 ft x 22 ft
Area = 550 ft².
To find the area of each triangular face, we first need to find the slant height of the pyramid, which can be found by using the Pythagorean theorem on the net dimensions. The slant height is the square root of
Net dimensions of the pyramid:
length, l = 74.8 ft
width, w = 70.4 ft
h = [tex]\sqrt{l ^{2} +w^{2} }[/tex]
h = [tex]\sqrt{(74.8^{2} + 70.4^{2} ) }[/tex]
h = 102.7 ft.
Now, we can use the formula for the area of a triangle:
Area = (1/2) x base x height,
where,
base,b = the length of the rectangular base (25 ft)
height = the slant height (102.7 ft).
So, the area of each triangular face is:
A = (1/2) x 25 ft x 102.7 ft
A = 1283.75 ft².
Since there are four triangular faces, the total area of all the triangular faces is:
A= 4 x 1283.75 ft²
A = 5,135 ft².
To find the surface area of the pyramid, we add the area of the base to the area of the triangular faces:
SA= 550 ft² + 5,135 ft² = 5,685 ft².
Hence, the surface area of the pyramid is 5,685 ft².
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If the quotient of three times a number and five is increased by
four, the result is no more than 34.
Answer: We can start by using algebra to represent the given information. Let's call the number we're trying to find "x".
We know that:
quotient = (3x)/5
quotient + 4 <= 34
We can simplify the first equation:
(3x)/5 + 4 <= 34
We can then solve this inequality for x:
(3x)/5 + 4 <= 34
3x/5 <= 30
3x <= 150
x <= 50
So the quotient of three times a number and five is no more than 34 if that number is less than or equal to 50.
Step-by-step explanation:
Find the lateral area for the prism.
36 in 2
54 in 2
27 in 2
81 in 2
The lateral area for the prism is equal to 54 square inches. (Correct choice: B)
How to determine the lateral area of the prism
Herein we have the case of a prism with five faces, two triangles and three rectangles. The lateral area for the prism is the sume of the areas of the three rectangular faces, whose formula is described below:
Rectangle
A = w · l
Where:
l - Length of the rectangle, in inches.w - Width, in inches.A - Area, in square inches.Finally, we proceed to determine the lateral area of the prism:
A = 3 · (3 in) · (6 in)
A = 54 in²
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AJSKASJASJJAJSKJSAKSJAJKS What is x
You know your cousin's phone number is
8675309, so you dial that number to call
him. Is person being called a function of phone
number dialed?
Function? Explain.
The person being called is a function of the phone number, as for each phone number, there is only one person associated with the number.
When does a relation represents a function?A relation represents a function when each input value is mapped to a single output value.
The input and output variables for this problem are given as follows:
Input: phone number.Output: person.Each phone number is mapped to a single person, meaning that the relation is in fact a function.
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What is AC?
A. 25‾√
B. 35‾√
C. 6
D. 9
The side length of AC is 6 units for the shown triangle. The correct answer would be an option (C).
What are Similar Triangles?Similar Triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.
The right triangle is given in the question, as shown.
AD = 4 cm and BD = 5
In ΔACD and ΔABC
∠ACD = ∠ABC
∠ACD = ∠BAC = 90°
∠CAD = ∠ACD (remaining)
So ΔACD and ΔABC are similar
Hence
AD / AC = AC/ BC
Apply the cross-multiplication operation, and we get
AC² = AD × BC
AC² = 4 × 9
AC² = 36
AC = 6 cm
So, the side length of AC is 6 units.
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Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
The three (3) true statements about the quadratic function, f(x) = x^2 – 5x + 12 and its graph include the following:
A. The value of f(–10) = 82
B. The graph of the function is a parabola.
D. The graph contains the point (20, –8).
How to determine the true statements about this quadratic function?Generally speaking, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. For this quadratic function, the graph is a upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero.
Next, we would determine the other true statements about the graph of this quadratic function:
At data point (-10, 82), we have the following:
Quadratic function, f(x) = 1/5 x² – 5x + 12
Quadratic function, f(x) = x²/5 – 5x + 12
Quadratic function, f(-10) = -10²/5 – 5(-10) + 12
Quadratic function, f(-10) = 82
At data point (20, -8), we have the following:
Quadratic function, f(x) = 1/5 x² – 5x + 12
Quadratic function, f(x) = x²/5 – 5x + 12
Quadratic function, f(20) = 20²/5 – 5(20) + 12
Quadratic function, f(20) = -8
In conclusion, the graph of this quadratic function, f(x) = x^2 – 5x + 12 does not contain the data point (0, 0) as shown in the image attached below.
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a blind man is alone on a deserted island. he has two blue pills and two red pills. he must take exactly one red pill and one blue pill or he will die. how does he do it?
Some of the other types of the separation process are used in every house and company. The process of segregating undesirable particles from necessary components is the essence of the separation method. We will study in-depth information about several physical separation techniques in this particular article. The discussion's conclusion would allow students to recognize various techniques and their importance.
The blind man could use one hand to separate the pills by color, for example by holding one group of pills in one hand and the other group of pills in the other hand. Then, he could reach into one hand and take one pill, and reach into the other hand and take one pill, ensuring that he has taken one red pill and one blue pill. Another way could be to put each color pill in a different pocket, so he can feel the different pockets and take one pill of each color.
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Another submarine’s descent can be represented as y=-3100xy=−3100x , where y is the elevation and x is time in hours. How long will it take this submarine to make the descent? Explain in detail how you found your answer in Part C
The time taken by the submarine to make the descent when the equation of descent is given is 0.677 hours.
Submarine's descent can be represented by the equation, y = -3100 x
where,
y is elevation
x is time in hours
We need to determine how long it will take this submarine to travel 2,100 feet below the surface of the ocean.
Since the submarine to make the descent to the seafloor 2,100 feet below the surface
So, y = - 2100
y = - 3100x gives
- 2100 = - -3100 x
Divide both sides by -3100,
x = 2100/3100 = 0.677 hours
As a result, the submarine will need 0.677 hours to complete the descent.
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An acute angle, θ, is in a right triangle such that sin of theta is equal to 2/5. What is the value of cot θ?
Answer:
cotθ=√21/2
Step-by-step explanation:
we have,
sinθ= 2/5= perpendicular/hypotenuse
here,
perpendicular=2
hypotenuse = 5
Now using Pythagorean theorem,
h^2 = p^2+ b^2
(5)^2 = 2^2 +b^2
b= √21
so,
cotθ= base/perpendicular = √21 /2
Hope you like the explanation.
Part 2 out of 2 Isabella spends $5.86 on paint brushes and paint. How many of each item does she buy? Complete the explanation how you found your answer. By using compatible numbers, you find a total of used guess and check to find that she buys items that had a total cost of $5.86. Then you paint brushes and jars of paint. Check Next
Based on the information, it can be concluded Isabella bought 2 paintbrushes and 3 jars of paint.
How many items can Isabella buy?The average of buying a product is 0.97, which means Isabella can buy a total of 5 items (0.97 x 5 = 4.85)
Based on this different combinations of products are possible, for example, 1 paintbrush and 4 jars or 3 jars and 2 paintbrushes. However, the one that fits the final price is:
2 paintbrushes x 0.95 = $1.9
3 jars of paint x 0.99 = $2.97
$2.97 + 1.9 = $4.87
Note: This question is incomplete, here is the missing information
The paintbrushes cost $0.95 and the jar of paint cost $.099
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39:11
Heights of four-year-olds are Normally distributed, with a mean of 40 inches and a standard deviation of 3 inches. At
his four-year checkup, Marlon's height is measured as taller than 70% of boys his age. How tall is Marlon?
Find the z-table here.
SECCO
38. 4 inches
41. 6 inches
42. 5 inches
43. 8 inches
Marlon's height is 42.52 inches.
Since the heights of four-year-old's are normally distributed with a mean of 40 inches and a standard deviation of 3 inches, we can use the z-score formula to find Marlon's height.
z = (x - mean) / standard deviation
where x is Marlon's height, mean is the population mean of 40 inches, and standard deviation is the population standard deviation of 3 inches.
We know that Marlon's height is taller than 70% of boys his age, so we can find his z-score using the cumulative standard normal distribution table, which tells us the proportion of the population that is less than a given value.
A z-score of 0.84 corresponds to a cumulative probability of 0.70.
So we can substitute this value into the z-score formula:
0.84 = (x - 40) / 3
Solving for x, we get:
x = 40 + (3 * 0.84) = 40 + 2.52 = 42.52 inches
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Which of the following triangle types is impossible to draw?
a scalene, right-angled triangle
an isosceles, acute-angled triangle
an isosceles, obtuse-angled triangle
an equilateral, right-angled triangle
The triangle types is impossible to draw is
an isosceles, obtuse-angled trianglean equilateral, right-angled triangleWhat is Right Angled Triangle?A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees. The other two angles sum up to 90 degrees. The sides that include the right angle are perpendicular and the base of the triangle.
Given:
First, a scalene with right-angled triangle is possible to make.
Now, an isosceles with acute-angled triangle is possible to make such triangle in which all three angles are less than 90°, and at least two of its angles are equal in measurement.
Now, an isosceles with obtuse-angled triangle is not possible to make because if two angles are greater than 90 then sum of angles exceed 180.
and, an equilateral with right-angled triangle is not possible to make because in Equilateral triangle are angles are of equal measurement 60.
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A 3-kg bowling ball rolls at a speed of 5 m/s on the roof of the building that is 75 m tall.
Circle one: KE / GPE / both
Show your work for finding the values of each type of energy the object has:
KE GPE=mgh
Mass = Mass =
Velocity = Gravity (g) = 9.8 m/s2
Velocity2=Height =
KE = ½ (M) (V)2GPE=mgh
The ball has both kinetic energy and potential energy.
The values of each type of energy the object has are KE = 37.5 J and GPE = 2205 J
How to find the energy of the object?Energy is the ability to do work. It can take many forms, such as kinetic energy (energy of motion), potential energy (stored energy) etc.
If a 3-kg bowling ball rolls at a speed of 5 m/s on the roof of the building that is 75 m tall.
Then ball has kinetic energy due to his motion and also has potential energy due to his height.
Thus, M = 3-kg, h = 75 m and V = 5 m/s
KE = 1/2(M)(V)² = 1/2 × 3 × 5² = 37.5 J
GPE = mgh = 3 × 9.8 × 75 = 2205 J
KE + PE = 37.5 + 2205 = 2242.5 J
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Write a ratio in words to compare a whole to a part. Then write the ratio using words. An example is needed
Answer:
A ratio in words compares a whole to a part. For example, the ratio of apples to oranges in a basket is "three to one." This can also be written as "3:1" or "3/1."
Another example: is the ratio of students to teachers in a class is "twenty to one." This can also be written as "20:1" or "20/1."
Step-by-step explanation:
I need help this is due tomorrow!
Used the distributive property a(b+c)=ab+ac, the value of x is x>1/2
Solving inequality using distribution property includes change of inequality signs when multiplied or divided by negative number but, not in the equation.
What is inequality?
An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
Curran:
-4(x-6)< 22
Used the distributive property a(b+c)=ab+ac
-4x+24<22
Then subtracted 24 from bot the sides
-4x<22-24
-4x< -2
Divide both sides by -4 ( inequality changes because of dividing by negative number)
x>1/2
Anjani:
-4(x-6)< 22
Divide both sides by -4
x-6> -22/4
add 6 on both sides
x> -22/4 + 6
x> -11/2 + 6
x> 1/2
Solving inequality using distribution property includes change of inequality signs when multiplied or divided by negative number but, not in the equation.
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an alloy consists of steel gold and brass in the ratio 5:3:7 determine the amount of each metal in 150g of the alloy
Answer: 50g steel, 30g gold and 70g brass
Step-by-step explanation:
This means for every 5g of steel there is 3g of gold and 7g of brass. We will find how many g there are total for every 5g of steel.
5 + 3 + 7 = 15
Next, we will divide 150g by 15g to see how many times the ratio will "repeat" to create the 150g of alloy.
150g / 15g = 10g
Next, we will multiply each amount of metal in one ratio by 10.
5g * 10 = 50g steel
3g * 10 = 30g gold
7g * 10 = 70g brass
Answer:
Step-by-step explanation
150g of the alloy contains a certain amount of steel,gold and brass. We thus find the total ratio of steel,gold and brass which will be equal to 15 {5 + 3 + 7}If 15 which is the total ratio is equal to 150, what about 5 which is the ratio of steel?15=150g 5 * 150g/15[we cross multiply 5=? get 5 times 150 multiply by 15to get 50g of steel.
15=150g 3*150g/15 to get 30g of gold.3=?15=150g 7*150g/15 to get 70g of bras.7=?To confirm the answer, we take 50g of steel + 30g of gold + 70g of brass to get 150g of alloy.\
An artist connects stained glass pieces with lead strips. In this rectangular window, the strips are cut so that FH = 28 in. Find JG. Complete the explanation
An artist connects stained glass pieces with lead strips and cut the strips so that FH = 28 in and JG = 14 in.
Now, According to the question:
A plane shape, as opposed to a square, with four straight sides and four right angles, particularly one with uneven neighboring sides.
Here, we have
FH ≅ GH
FH = EG = 28in
If diagonals bisect each other then, an artist connects stained glass pieces with lead strips
1/2(EG) = JG
1/2 (28) = JG
14 = JG
Hence, an artist connects stained glass pieces with lead strips and cut the strips so that FH = 28 in and JG = 14 in.
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An isosceles triangle has two sides of equal
length. The third side is 5 less than twice the
length of one of the other sides. If the
perimeter of
the triangle is 23 cm, what is the length of the third
side?
Explain how you would define a variable for this
problem.
The required length of of the third side of isosceles triangle is 9 units.
Explain about isosceles triangle.An Isosceles triangle is a triangle that has two equal sides. Also, the two angles opposite the two equal sides are equal. In other words, we can say that “An isosceles triangle is a triangle which has two congruent sides“.
According to question:Let the length of Equal two sides is x.
Third side = 2x - 5
Then, perimeter is 23 cm
x + x + 2x - 5 = 23
4x - 5 = 23
4x = 28
x = 7
Then, third side is 2x - 5
= 2(7) - 5
= 14 - 5
= 9 units
Thus, required length of third side is 9 units.
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8th grade is hard and I do online school it’s hard for me to learn
A. We can see that the intersection made by lines C and D classifies ∠7 and ∠8 as vertically opposite angles.
B. The special angles created by intersection of lines C and D can be used to solve for y by equating the expressions, 5y-29 and 3y+19 as they are vertically opposite angles.
C. Solving for y, we have: y = -5
What is intersection?Intersection, in mathematics, refers to the common elements or overlap between two sets. For example, if set A contains the elements 1, 2, and 3, and set B contains the elements 2, 3, and 4, then the intersection of set A and set B would be the set containing the element 2 and 3. In general, intersection is represented by the symbol ∩. Lines can also intersect to form angles.
Vertically opposite angles are actually known to be equal. It then means that:
∠7 = ∠8 (Vertically opposite angles)
Also, 5y-29 = 3y+19 (Vertically opposite angles)
Thus, solving for y, we have:
5y-29 = 3y+19
5y - 29 -29 = 3y + 19 - 29
5y -3y = - 10
2y = -10
y = -10/2 = -5
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Use the distributive property to fill in the blanks below.
(3 x 5) + (3 x 2) = 3 × (_ + _)
Answer:
3 x (5 + 2)
Step-by-step explanation:
Just use the distributive property, it's very simple.
(2x 2 −6x−5)+(−9x 2 +5x−4)
Answer: -15x - 9
Step-by-step explanation:
(2x ×2 −6x−5)+(−9x ×2 +5x−4)
(4x-6x-5)+(-18x+5x-4)
(-2x-5)+(-13x-4)
-2x-5-13x-4
-15x -
The value of the given equation is −7x2−x−9.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that;
The equation (2x 2 −6x−5)+(−9x 2 +5x−4)
Now,
We need to add the two polynomials by combining like terms. Like terms are terms that have the same variable and exponent. For example, 2x2 and −9x2 are like terms because they both have x2
To add like terms, we just add their coefficients. For example, 2x2+(−9x2)=(−7x2)
We can apply this rule to each pair of like terms in the problem and get:
(2x2−6x−5)+(−9x2+5x−4)
=(2x2+(−9x2))+(−6x+5x)+(−5+(−4))
=(−7x2)+(−x)+(−9)
=−7x2−x−9
Therefore, by algebra the answer will be −7x2−x−9.
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i need help please and thanks
I need help in this problem
The measurement of indicated angle is 20 degree.
What is congruent angle?Congruent angles are those with equal measure. As a result, all angles with equal measure will be referred to as congruent angles.All congruent angles are not supplementary angles in general. Angles that add up to 180 must be supplementary angles. So only right angles and supplementary angles are congruent because they have the same measure and add up to 180.If the corresponding sides and angles of two angles are of equal size, they are said to be congruent. Two angles that are superimposed are also congruent. That is, if they turn and/or move to coincide with each other. The diagonals of a parallelogram also produce congruent vertex angles.Here opposite angles are congruent .
Therefore the indicated angle is 20 degree.
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Can someone please find x for me? Thank you!
The value of the missing angle x of the triangle is; x = 18.67°
How to find the missing angles?The sum of angles on a straight line is 180 degrees. Thus, the supplementary angle to 130 degrees is;
180 - 130 = 50°
Now, the alternate angle to 80 degrees which will be located inside the triangle is 80°.
The sum of angles in a triangle is 180 degrees. Thus;
3x - 6 + 80 + 50 = 180
3x + 124 = 180
3x = 180 - 124
3x = 56
x = 56/3
x = 18.67°
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100 points Factor completely and then place the factors in the proper location on the grid. 5 y2 - 2 y - 3
Answer:
is try ur hardest
Step-by-step explanation:
Seorang mengendarai mobil dengan kecepatan 72 km/jam, tiba-tiba melihat seorang anak kecil di tengah jalan pada jarak 50 m dimukanya. Jika mobil direm dengan perlambatan maksimum sebesar 4 m/s2 , maka terjadi peristiwa ....