The distance between the points (-7, -3) and (-3, -5) in simplest radical form is 2√5.
What is the distance between the given points?The distance formula used in finding the distance between two points is expressed as;
[tex]d = \sqrt{( x_2 - x_1 )^2 + ( y_2 - y_1)^2 }[/tex]
Given the points in the question:
Point 1 (-7,-3)
x₁ = -7y₁ = -3Point 2 (-3,-5)
x₂ = -3y₂ = -5Plug the given values into the distance formula and simplify.
[tex]d = \sqrt{( x_2 - x_1 )^2 + ( y_2 - y_1)^2 }\\\\d = \sqrt{( -3 - (-7) )^2 + ( -5 - (-3))^2 }\\\\d = \sqrt{( -3 + 7 )^2 + ( -5 + 3)^2 }\\\\d = \sqrt{( 4 )^2 + ( -2)^2 }\\\\d = \sqrt{16 + 4 }\\\\d = \sqrt{20 }\\\\d = 2\sqrt{5}[/tex]
Therefore, the distance between the points is 2√5 .
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Write a linear function containing the following parts: (0,-8) and (2,0)
y = 4x - 8 is linear equation .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Linear equations with two variables, and so forth, are what the equation is known as if it has two variables. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and x + y = 2. Another example is 3x - y + z = 3.
(0,-8) and (2,0)
m = 0 - (-8)/2 - 0
= 8/2 = 4
y - (-8) = 4 ( x - 0)
y + 8 = 4x
y = 4x - 8
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A regular hexagon is shown. Select all of the transformations that carry the hexagon onto itself.
In shown regular hexagon, all of the transformations that carry the hexagon onto itself are, 180° rotation counterclockwise and reflection in 'l'. So Options D,E,F are correct.
What is Hexagon?It is a type of polygon, which has 6 equal sides and all the interior angles are 120°.
Given that,
We have one hexagon and axis of rotation l,
lets check the given options
A. at 60° rotation clockwise it makes certain angle from the initial position, it will not onto itself
B. at 60° rotation counter-clockwise it makes certain angle from the initial position, it will not onto itself
C. at 90° rotation counter-clockwise and 180° rotation clockwise it makes 90° angle from initial position, it will not onto itself
D. 180° rotation counter-clockwise it will be in same plane of original position. So it will onto itself
E. Reflection in L again it will be in same plane, So it will onto itself
F. Reflection in L and 180° rotation counter-clockwise gain it will be in same plane, So it will onto itself
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Insert parentheses to make the equation true 5-3-1+6^2=50
The equation is true when putting parentheses. The equation becomes:
(5 - 3)(-1 + 6)² = 50.
What is an equation?
In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
The given equation is 5 - 3 - 1 + 6² = 50.
Here we need two parentheses.
Since 50 can be written as 50 = 25 × 2 = 5² × 2
Now 2 can be written as (5-3) and 5 can be written as (-1+6).
Now put the parentheses:
(5 - 3)(- 1 + 6)²
= 50
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How is 8 to the power of 0?
Answer:
One
Step-by-step explanation: Anything that has the exponent of 0 will always be 1
The school's track is 1/4 mile long. If Janice can compete each lap in 1/10 of on hour, what is Janice's running speed? Include units of measure.
Answer: To find Janice's running speed, we need to determine how many miles she runs per hour.
We know that the track is 1/4 mile long and Janice can complete each lap in 1/10 of an hour. To find the total number of miles Janice runs in an hour, we can multiply the length of the track by the number of laps she completes in an hour.
Length of the track * number of laps = total miles
1/4 mile * (1/10 hour)^-1 = total miles
On the second equation, we are using the inverse of the time, to get the number of laps completed in an hour
The speed is distance over time, so we need to express the distance in miles and the time in hours.
So Janice's running speed is 4 miles/hour.
Step-by-step explanation:
Solve the compound inequality
M - 3<6 and m + 2>4
The solution to the inequality is m ∈ (2, 9)
What is the Compound inequality?
A compound inequality is an inequality that contains two or more conditions that must be met simultaneously. It is formed by connecting two or more simple inequalities using the words "and" or "or". The word "and" indicates that all the conditions must be true at the same time, while the word "or" indicates that at least one of the conditions must be true.
The compound inequality "m - 3 < 6 and m + 2 > 4" can be read as "m is less than 6 and 3 less than m and m is greater than 4 and m is 2 more than 4".
To solve the inequality, we can start by isolating the variable on one side of the inequality sign.
m - 3 < 6 => m < 9
m + 2 > 4 => m > 2
The solution is the set of all m that satisfies both inequalities, which is the intersection of the solution sets of each inequality. In this case, it is the set of all real numbers m such that 2 < m < 9.
Hence, the solution to the inequality is m ∈ (2, 9)
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What should be subtracted from x2 y2 2xy to get x2 y2 algebraic expressions?
To get the simplified form of the algebraic expression x²+ y², we need to subtract -2xy from the expression x² +y²-2xy.
To subtract 2xy from the expression x² + y² - 2xy and get x² + y², you can simply remove the -2xy term. This is because subtracting 2xy is the same as adding -2xy, which is the same as negating 2xy and keeping it in the same position.
The reason for this is that subtracting a number is the same as adding its opposite. In this case, -2xy is the opposite of 2xy, so when you subtract 2xy, you are effectively adding -2xy.
Therefore, x² + y² - 2xy and x² + y² are equivalent expressions, since they both represent the same mathematical value.
In mathematical terms:
x² +y²-2xy = x²+ y² +2xy
In other words, the subtraction of 2xy is a commutative operation and the order of the terms does not matter. If you add or subtract the same value, it does not change the final result.
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What should be subtracted from x² +y²-2xy to get x²+ y² algebraic expressions?
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Which of the following graphs represents a linear relationship between x and y?
The third one will represent a linear relationship between x and y.
What is a linear relationship?
A linear relationship is any relationship between two variables that creates a line when graphed in the xy-plane.
Linear equations can be used to represent the relationship between two variables, most commonly x and y. To form the simplest linear relationship, we can make our two variables equal:
y=x
By plugging numbers into the equation, we can find some relative values of
x and y.
0 0
1 1
2 2
3 3
If we plot those points in the xy-plane, we create a line.
Now,
For the given graphs only the third one shows a straight line made from equations.
Hence, It represents the linear relationship between x and y.
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Question content area topPart 1 Two hikers are 22 miles apart and walking toward each other. They meet in 5 hours. Find the rate of each hiker if one hiker walks 2.2 mph faster than the other.
Answer: if one hiker walks faster than the other, their rate would be 9.68mph or 9.7mph if u round up and the rate of the other hiker that is walking slower is 4.4mph.
Step-by-step explanation:
For the hiker walking 2.2mph
I did: 22 x 2.2 = 48.4/5 = 9.68
Rate = 9.68mph
For the other hiker
I did: 22/5= 4.4
rate = 4.4mph
What is the first number of ordered pairs?
The first number in an ordered pair (x,y) is the x-coordinate, also called the "abscissa". It represents the horizontal position of the point on a coordinate plane. The second number in an ordered pair is the y-coordinate, also called the "ordinate". It represents the vertical position of the point on a coordinate plane.
An angle measures 86.6° less than the measure of its supplementary angle. What is the measure of each angle?
This is because the sum of the measures of a pair of supplementary angles is always 180°. Therefore, the measure of the original angle is 93.4° and the measure of its supplementary angle is 180°.
What is the measure ?Plagiarism is the practice of taking someone else's work or ideas and passing them off as one's own. Plagiarism can take many forms, including: copying word-for-word, copying ideas or facts without providing a citation or reference, or paraphrasing someone else's words or ideas without providing a citation or reference. It can be intentional or unintentional, and it is considered a form of academic dishonesty.
The measure of the original angle is 86.6° less than the measure of its supplementary angle. This means that the measure of the original angle is 180° - 86.6° = 93.4°. The measure of the supplementary angle is 180°.
This is because the sum of the measures of a pair of supplementary angles is always 180°. Therefore, the measure of the original angle is 93.4° and the measure of its supplementary angle is 180°.
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mathematicians find an easier way to solve quadratic equations, how do they do it?
Answer:
His secret is in generalizing two roots together instead of keeping them as separate values.
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Solve the inequality and write the solution in set-builder notation. r - 8 <= 7
So on solving the provided question, we can say that inequality equation will be as follows r - 8 <= 7 r<=15 or r >= -15
What is inequality?An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.
here the question, is
r - 8 <= 7
r<=15
or r >= -15
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design a waterskiing ramp. show how you can use direct variation to plan the heights of the vertical supports.
In designing the waterskiing ramp using direct variation the vertical supports, y will be related to the horizontal distance, x by a constant k, as in the relation
k = y/x
What is a constant of proportionality?The ratio between two quantities that are directly proportional is the constant of proportionality.
When two quantities grow and shrink at the same rate, they are directly proportional.
When y and x are two values that are directly proportional to one another, the proportionality constant k is defined as k=y/x.
In the problem, the distances between the vertical supports is x while the height of the support is y. To have a direct proportionality this relationship between x and y must be a constant say k.
Hence we say k = y / x
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What is the area of the trapezoid shown? Express your answer in simplest exact form. [asy] unitsize(1.5cm); pair a=(0,0); pair b=(1,sqrt(3)); pair c=(3,sqrt(3)); pair d=(4,0); draw(a--b--c--d--a); label("2",(a+b)/2,NW); label("2",(b+c)/2,N); label("2",(c+d)/2,NE); label("~$60^\circ$",a,NE); label("$60^\circ$~",d,NW); [/asy]
The area of the trapezium shown is 284.31 in²
What is an equation?An equation is an expression that shows the relationship between variables and numbers.
The area is calculated for a two dimensional shape. It shows the amount of space occupied for that shape.
The area of a trapezium is given by:
Area = (1/2)(sum of parallel sides) * height
For the trapezium shown, the parallel sides have a measure of 17 inches and 31 inches respectively. The height is 11.7 inches, hence:
Area = (1/2)(17 + 31.6)(11.7) = 284.31 in²
The area is 284.31 in²
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What is the absolute value of a complex number called?
The absolute value (Modulus) of a number is the distance of the number from zero.
Absolute value is always acting for in the modulus(|z|) and its value is always positive.
So, the absolute value of the complex number is Z = a + ib is |z| = √ (a2 + b2).
Now, the absolute value of the complex number is the positive square root of the sum of the square of the real part and the square of the unreal part, i.e.,
The complex number is defined as the number in the form a+ib, where a is the real part while ib is the unreal part of the complex number in which i is known as iota and b is a real number.
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Create math problems with the words : increased, sum, found, collected, earned, and spent (for addition)
Assuming the denominator does not equal zero. Simplify the expression
Consider that the denominator is not zero. The formula that results from simplifying will equal -n-5/2n(1+3n).
The denominator does not equal zero?A fraction is divided by multiplying its reciprocal:
6n²-23n+7/8n3-28n2.
2n²-10n/1-9n²
Factoring the phrase: 6n²-23n+7/4n²(2n-7). 2n(n-5)/1-9n²)
A2-b2=(a+b)(a-b) (3n-1) (2n-7)/4n² can be used to factor the expression (2n-7).
2n(n-5)/(1+3n)(1-3n)
By eliminating the most prevalent element, reduce the proportion to its lowest term. 3n-1/4n²
2n(n-5)/(1+3n)(1-3n)
Purge the expression of all except the lowest word Write 1/2n as a single fraction: -n-5/2n(1+3n)\s-n-5/2n(1+3n).
In general, a fraction with a zero denominator cannot have a single value given to it; therefore, the value is left undefined.
Any definitional attempt results in a contradiction, which is why the outcome of a division by zero is not defined. a=r*b. r*0=a. (1) However, r*0=0 for any r, hence unless a=0, there is no solution to the problem (1).
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·
Assume the random variable x is normally distributed with mean u = 50 and standard deviation o = 7.
Find the indicated probability. P(x >43) P(x>43)=
Assume the random variable x is normally distributed with mean u = 81 and standard deviation = 4.
The probability of a random variable x being greater than 43 if it is normally distributed with a mean of 50 and a standard deviation of 7 is 0.22662735237686885.
The formula for the normal distribution is:
P(x) = 1/(sqrt(2*pi*o^2)) * e^(-(x-u)^2/(2*o^2))
where u is the mean and o is the standard deviation.
For the first part, we have u = 50 and o = 7.
So, P(x>43) = 1/(sqrt(2*pi*7^2)) * e^(-(43-50)^2/(2*7^2)) = 0.22662735237686885
For the second part, we have u = 81 and o = 4.
So, P(x<76) = 1/(sqrt(2*pi*4^2)) * e^(-(76-81)^2/(2*4^2)) = 0.8413447460685429
The probability of a random variable x being greater than 43 if it is normally distributed with a mean of 50 and a standard deviation of 7 is 0.22662735237686885. Similarly, the probability of a random variable x being less than 76 if it is normally distributed with a mean of 81 and a standard deviation of 4 is 0.8413447460685429. This can be calculated using the formula for the normal distribution, which is P(x) = 1/(sqrt(2*pi*o^2)) * e^(-(x-u)^2/(2*o^2)), where u is the mean and o is the standard deviation.
the complete question is : Assume the random variable x is normally distributed with mean u = 50 and standard deviation o = 7.
Find the indicated probability. P(x >43) P(x>43)=
Assume the random variable x is normally distributed with mean u = 81 and standard deviation = 4.
Find the indicated probability. P(x <76) P(x<76)= 0.8413447460685429
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Miriam is calculating the budget for her upcoming vacation. She plans to distribute the budget into three categories: lodging, food/dining, and sightseeing. Miriam wants to follow the guidelines below when calculating the budget:
● 2/7 (in fraction) of the budget will be spent on lodging
● The amount spent on sightseeing will be twice as much as the amount spent on lodging.
What fraction of Miriam’s budget would be left for food/dining if Miriam follows these guidelines?
The fraction of Miriam’s budget would be left for food/dining if Miriam follows these guidelines is 1/7.
How to compute the fraction?The fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.
From the information, 2/7 of the budget will be spent on lodging.
The amount spent on sightseeing will be twice as much as the amount spent on lodging. This will be:
= 2 × 2/7
= 4/7
The fraction of Miriam’s budget would be left for food/dining if Miriam follows these guidelines will be:
= 1 - (2/7 + 4/7)
= 1/7
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If you solve this first I’ll make you brainliest and of course take your time good luck.
Answer: 28x^4y^7
Step-by-step explanation: Add exponents of common base
Answer:
28x⁴y⁷
Step-by-step explanation:
First multiply the numbers;
Then combine the exponents;
Then combine the exponents again;
Then you have the answer :)
Identify the value of y.
Therefore , the solution of the given problem of quadratic equation comes out to be the value of y = 12.
Define quadratic equation.x2+ cx + z = 0 is a quadratic problem with one variable in quadratic algebra. a 0. According to the Underpinning Theorem of Algebra, this quadratic's second order ensures that it has at least one solution. The solutions could be simple or complex. Four variables make up a quadratic equation. This implies that at least one word should be squared. "ax2 + bx + c = 0" is one of the basic formulae for solving quadratic equations, where the numbers or integers a, b, and c stand in for the undefined variable "X".
Here,
Given : A right angled triangle with dimension of y, y+3 and 9
To find the value of y :
We use pythagoras theorem :
So,
=> (y+3)² = y²+9²
=> y² + 9 + 6y = y²+ 81
=> y² - y² + 6y = 81-9
=> 6y =72
=>y =72/6
=>y=12
Therefore , the solution of the given problem of quadratic equation comes out to be the value of y = 12.
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What is the rule for Exponent 1?
The rule for any number raised to the power of 1 is that the number remains unchanged.
Mathematically, this can be written as: a^1 = a where "a" is the base number. The rule for a number raised to the power of 1, is also known as the exponent.
For example, if we take the number 2, and raise it to the power of 1, we would get:
2^1 = 23^1 = 3Key points:
This can be thought of as a shorthand way of writing the number without any changes. It is also the identity property of exponents. It is important to note that this rule applies to any base number, whether it is a whole number, fraction, or even a negative number.In addition to this, we know that any number raised to the power of 0 is 1, this is also known as the identity property for exponents.Learn more about exponents here:
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Find the dimensions of a rectangle whose width is 6 miles less than its length, and whose area is 72 square miles.
Answer:
Dimensions are 12 , 6
Step-by-step explanation:
Forming algebraic equations and solving:Let the length be 'x' miles.
width = (x - 6) miles
Area of a rectangle = length * width
x *(x -6) = 72 square miles
x*x - x *6 = 72
x² - 6x -72 = 0
Sum = -6
Product = -72
Factors = -12 , 6 { -12 * 6 = -72 & -12 + 6 = -6}
x² - 12x + 6x - 72 = 0 {Rewrite the middle term using the factors}
x(x - 12) +6(x - 12)=0
(x -12)(x + 6) =0
x - 12 = 0 ;
x = 12
{x + 6= 0 is ignored, as dimensions will not have negative value}
length = 12 miles
widht = 12 - 6 = 6 miles
There is an equal chance of the pointer stopping at each
area of the game spinner below.
What is the theoretical probability of spinning the pointer and having it stop on a green area
A. 0.125
B. 0.25
C. 1.00
D. 0.50
Answer:
B. 0.25
Step-by-step explanation:
There are 8 total pieces.
2 of them are green.
that makes it a 2/8 chance it will land on green.
2/8 = 1/4
1/4 = 0.25
Answer:
B. 0.25
Step-by-step explanation:
There are 8 possible landing areas, all with equal size.
There are 2 green area.
p(event) = (number of desired outcomes)/(number of total outcomes)
The desired outcome is landing on green. There are 2 desired outcomes.
The total number of possible outcomes is 8.
p(green) = 2/8 = 1/4 = 0.25
Answer: B. 0.25
please help me out with this answerr
The angles m∠GFH and m∠HFJ are complementary angles and the correct option for the measure of angle m∠GFH is equal to 61.9°.
What are complementary anglesIn geometry, if two angles are said to be complementary, then the total of their sum is equal to 90°
From the question, we have that the complementary angle m∠HFJ = 28.1° so;
m∠GFH + m∠HFJ = 90°
m∠GFH + 28.1° = 90°
m∠GFH = 90° - 28.1°
m∠GFH = 61.9°
Therefore, the measure for the complementary angle m∠GFH is equal to 61.9°
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Maya wants to be able to take a series of four triangles and place them in a mobile design where all four triangles are attached at one point and are balanced so that they stay horizontal. Which statement best describes where she should attach each triangle?
A) Where the medians intersect
B) where the altitudes intersect
C) where perpendicular bisectors intersect
D) at any vortex
PLS I WILL GIVE BRAINLIEST
The statement best describes where she should attach each triangle is perpendicular bisectors intersect.
What is triangle?When perpendicular bisectors overlap, the sentence best indicates where she should join each triangle. A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same. Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees.
Here,
When perpendicular bisectors overlap, the sentence best indicates where she should join each triangle.
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Etimate how that there are 1. 4 \cdot 10^81. 4⋅10
8
1, point, 4, dot, 10, tart upercript, 8, end upercript pet fih and 9. 4 \cdot 10^69. 4⋅10
6
9, point, 4, dot, 10, tart upercript, 6, end upercript pet reptile in the United State. How many fih and reptile pet are in the United State all together?
Expre your anwer in cientific notation
There are 1.449 × 10⁸ pet fish and pet reptiles all together in the United States.
Total number of pet fish in the United states = 1.4 × 10⁸
Total number of pet reptiles in the United States = 4.9 × 10⁶
So the total number of pet fish and pet reptiles = (1.4 × 10⁸) + (4.9 × 10⁶)
= 1.449 × 10⁸
The final answer is in scientific notation. Scientific notation is the way of writing number that are too big or too small and inconvenient to write in decimal form. They are expressed in the multiple of 10 with a suitable power on 10.
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BRAINLIEST.... PLEASE HELP ASAP *VERY IMPORTANT*
Answer:
[tex]m\angle 1=67^{\circ}[/tex]
Step-by-step explanation:
By the inscribed angle theorem, [tex]m\angle 1=21^{\circ}+46^{\circ}=67^{\circ}[/tex].
For a recipe to make lemonade , every 6 cups of water requires one and a half cups of sugar. if you are using 24 cups of water, how many cups of sugar would you need
The number of cups of sugar that you will need to make lemonade would be = 2 cups of sugar.
What is a recipe?A recipe is defined as the list of condiments that are used for the preparation of a food and it's guidelines.
In the recipe to make lemonade,
6 cups of water = 1/2 cup of sugar
24 cups of water = X cup of sugar.
Make X the subject of formula;
X cup of sugar = 24 × 1/2 ÷ 6
= 12/6 = 2 cups of sugar.
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