Line segment AB and CD both are congruent with the length of 16 units.
We have been given two line segment AB and CD of whose coordinates are :
A = -7 , B = 9 and C = -4 , D = 12
The distance formula is given as |x2 – x1|
Therefore the length of AB = |9 – (-7)|
= 9 + 7
= 16
The length of CD = |12-(-4)|
= 12 + 4
= 16
Note that when two line segments are congruent then their distance is equal.
Thus both the line segment AB and CD are congruent with a length 16 unit.
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After a 7.5% pay rise Mr Jones salary was £29455. What was his salary before the pay rise?
Answer:
£27400
Step-by-step explanation:
The original salary of x.
The raise was 7.5% = 7.5/100 = 0.075 of the salary.
The original salary plus the raise is x + 0.075x = 1.075x.
The new salary is £29455.
Therefore,
1.075x = £29455
Divide both sides by 1.075.
x = £27400
Answer: £27400
Help me please I will mark the person as a brainliest.
Answer:
200 km/hr
Step-by-step explanation:
We can find the speed by dividing the distance by the time taken for the trip.
[tex]\sf \boxed{Speed = \dfrac{distance }{time}}[/tex]
[tex]\sf r = \dfrac{300}{t}[/tex]
In the above equation, substitute t = 1.5 hours and find the train's rate.
[tex]\sf r = \dfrac{300}{1.5}\\\\= \dfrac{300*10}{1.5*10}\\\\= \dfrac{3000}{15}\\\\r = 200 \ kilometers \ per \ hour[/tex]
One month, a homeowner used 150 units of gas and 520 units of electric for a total of 54.20. The next month he used 210 units of gas and 405 units of electric for a total of 82.35.
I understand the 2 equations are
150g + 520e = 84.20
210g + 405g = 82.35
I dont understand how to get the value of g and e though, like someone said to use 7 to multiply against the first equation and -5 the second, but like where are we getting 7 and -5 from.
The solution to the system of equations is:
e = 0.109
g = 0.183
How to solve the system of equations?Defining the variables:
g = cost of the unit of gas.
e = cost of the unit of electricity.
Then the system of equations is:
150*g + 520*e = 84.20
210*g + 405*e = 82.35
Now we want to solve this.
To do so, we need to isolate one of the variables in one of the equations. Let's isolate g in the first one:
g = (84.20 - 520*e)/150
Now we replace that in the other equation so we get:
210*(84.20 - 520*e)/150 + 405*e = 82.35
Now we can solve this for e:
210*(84.20 - 520*e)/150 + 405*e = 82.35
(210/150)*(84.20 - 520*e) + 405*e = 82.35
117.6 - 728*e + 405*e = 82.35
117.6 - 323*e = 82.35
e = (117.6 - 82.35)/323 = 0.109
Then:
g = (84.20 - 520*0.109)/150 = 0.183
Then we can conclude that:
e = 0.109
g = 0.183
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I will Award A Brainlist Hello please Help its a Math Problem !!!
Thank you so much ! for your time.
Answer:
12.8 i don't know oof
Step-by-step explanation:
8.2 + 4.6 is 12.8, but I'm not completely sure it's the right answer.
The cost to rent a boat is $25 per hour plus a non-refundable $30 deposit
A. write an expression to rent a boat for h hours
B. Evaluate the expression for h=2
Answer:
A. 25h+30=80
B.25(2)+30=80
angle A and angle B are vertical angles. If m angle A=(2x+20)^ and m angle B=(3x+1)^ then find the value of x.
If angle A and angle B are vertical angles. If m angle A=(2x+20)^ and m angle B=(3x+1)^ then x has a value of 19.
What is the Vertical Angles Theorem?
The Vertical Angles Theorem states that if two lines intersect, then the vertical angles formed by the intersecting lines are congruent.
Vertical Angles Theorem states that vertical angles, angles that are opposite each other and formed by two intersecting straight lines, are congruent. Vertical angles are always congruent angles,
By the Vertical Angles Theorem, we know that angle A is congruent to angle B.
Therefore, we can set their angle measures equal to each other and solve for x:
2x + 20 = 3x + 1
Subtract 2x from both sides:
20 = x + 1
Subtract 1 from both sides:
19 = x
Hence, x has a value of 19.
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Please help asap
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Solve five sixths times c minus 1 equals 1 plus five sixths times c.
Infinite solutions
No solution
c equals five sixths
c equals twelve tenths
Answer:
No solution!
Step-by-step explanation:
I just took the quiz and got 100%
-11 to the power of 0
It’s probs easy but help pls
Answer:
frequency =12 and mass x (kg)=20<=x<30Triangle UML has coordinates U (-3, -4), M(-1, -1) , and L(-2, -5). If the triangle is translated 5 units up and 1 unit left to form triangle U’M’L’, what will be the coordinates of L’?
After the translation the coordinates of L' are (-3, 0) for the new triangle of U’M’L’.
What is defined as the translation?In geometry, translation refers to a function which moves an object a specified distance. The object is not elsewhere altered. It is not rotated, mirrored, or resized.Every location of the object should be moved within the same direction for the same distance during a translation.When performing a translation, this same initial object is referred to as the pre-image, and also the object just after translation is referred to as the image.The coordinates of triangle are-
U (-3, -4), M(-1, -1) , and L(-2, -5).
The triangle is translated 5 units up and 1 unit left to its original place.
Thus, for the 5 units up translation 5 units will get added to the y-coordinates.
New y-coordinate of L' is -5 + 5 = 0.
For 1 unit left , 1 units will get reduced from the original x-coordinate.
New x-coordinate = -2 - 1 = -3
Thus, the new coordinates L' becomes (-3, 0).
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Four times a number, subtracted from 8, is twice the number. Find the number.
Answer:
3/4 or 0.75
Step-by-step explanation:
8-4x=2x
-4x-2x=-8
-6x=-8
x=-6/-8
=3/4 or 0.75
A 5-foot board is cut into 4 equal pieces. Which equation shows how to find the length of each piece?
What sets of elements does the square root of square root of -10 apply to?
Integer
Real number
Rational
Irrational
Natural
Whole
The square root of - 10 is not a real number but a complex number, an irrational number.
What number set does an element belong to?
Numbers can be classified in real numbers and complex numbers. Real numbers are classified in natural numbers (i.e. 1, 4, 5), whole numbers (i.e. 0, 1, 4, 5), integers (i.e. - 4, -1, 0, 5, 6) and rational numbers (i.e. 5 / 7, 0, - 13 / 3) and part of the irrational numbers (i.e. √3, π) and the rest of irrational numbers are complex numbers (i.e. i 4, - 4 + i 5).
In consequence, the square root of - 10 is not a real number but a complex number, an irrational number.
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Total number of possible equal parts in a fraction (a) denominator (b) numerator (c) mixed number (d) divisor?
Denominator: The value in a fraction that appears below the fractional bar and indicates the total number of equal parts.
In a fraction, the value that appears above the horizontal line is referred to as the numerator. It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the vinculum.
A mixed number is a representation of both a whole number and a legal fraction. In most cases, it denotes a number that falls between any two whole numbers.
An integer that totally or partially divides another integer is known as a divisor.
In a division equation, a divisor is represented by the formula
Dividend ÷ Divisor = Quotient.
The correct option is (a).
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EASY POINTS WILL GIVE BRAINLIST TO BEST ANSWER
What is the result of solving this equation for t ?
Mt – 5ab = nRT
explain!!
The required equation would be t = (nRT + 5ab)/M which is the result of the equation for t.
What is an equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The equation is given as
Mt - 5ab = nRT
We have to determine the result of solving this equation for t
⇒ Mt - 5ab = nRT
⇒ Mt = nRT + 5ab
⇒ t = (nRT + 5ab)/M
Therefore, the required equation would be t = (nRT + 5ab)/M which is the result of the equation for t.
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Solve the equation x+ 4x-7 = 0 by completing the square. give your answers correct to 2 decimal places.
[tex] {x}^{2} + 4x - 7 = 0 \\ → {x}^{2} + 4x = 7[/tex]
Add the square of the half of the coefficient of the unknown(x) to both sides of the equation.
[tex] {x}^{2} + 4x + ( \frac{4}{2} {)}^{2} = 7 + ( \frac{4}{2} {)}^{2}[/tex]
[tex] {x}^{2} + 4x + (2 {)}^{2} = 7 + (2 {)}^{2} [/tex]
[tex] {x}^{2} + 4x + (2 {)}^{2} = 7 + 4[/tex]
Bring out x and 2 and square them as shown below:
[tex](x + 2 {)}^{2} = 11[/tex]
Now, square root both sides of the equation to find the value of x as shown below:
[tex] \sqrt{(x + 2 {)}^{2} } = \sqrt{11} [/tex]
Add a + or - sign since it is a quadratic equation
[tex]x + 2 = \binom{ + }{ - } \sqrt{11} [/tex]
[tex]x + 2 = \binom{ + }{ - } 3.3166[/tex]
[tex]x = - 2 + 3.166 [/tex] or
[tex]x = - 2 - 3.166[/tex]
Therefore:
[tex]x = 1.17[/tex] or
[tex]x = - 5.17[/tex]
to two decimal places.
Five more than the quotient of eight and two
Answer:
9
Step-by-step explanation:
a quotient is the result of dividing one number by the other, so we know 8 is being divided by 2
8÷2 is 4
five more just means adding 5
so we are left with 4+5 which =9
ridden a bike course that is 40 miles long. so far he has ridden 28 miles of the course. what percentage of the course has he ridden so far
So far, he has ridden 70% of the bike course.
Percentage, which was adapted from the Latin word "per centum", which means "by the hundred", is a fraction or a ratio in which the value of whole is always 100. It is represented by the symbol "%".
The formula to get the percentage is:
Percentage = (Value / Total Value) × 100
If the total value of the bike course is 40 miles and the value which the percentage we are looking for is 28 miles, evaluating the equation:
Percentage = (Value / Total Value) × 100
Percentage = (28 / 40) × 100
Percentage = (0.7) × 100
Percentage = 70
Therefore, he has ridden 70% of the bike course so far.
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in the dominican republic in august, the distribution of daily high temperature is approximately normal with mean 86 degrees fahrenheit (°f). approximately 95% of all daily high temperatures are between 83°f and 89°f. what is the standard deviation of the distribution? 1°f 1 degree fahrenheit 1.5°f 1.5 degrees fahrenheit 2°f 2 degrees fahrenheit 3°f 3 degrees fahrenheit 6°f
The standard deviation of the distribution = 1.5°F
Given that the distribution of daily high temperature is approximately normal.
Population mean, [tex]\mu[/tex] = 86°F
Also approximately 95% of all daily high temperatures are between 83°F and 89°F.
So here [tex]X_1[/tex] = 83°F and [tex]X_2[/tex] = 89°F
We have the z - statistic ,
[tex]z=\frac{x-\mu}{\sigma}[/tex]
where [tex]\sigma[/tex] is the Standard deviation.
For 95% probability, the z-value for normal distribution is 1.96.
As we consider the positive z-value, take X = [tex]X_2[/tex] = 89°F
So, [tex]z=\frac{x-\mu}{\sigma}[/tex]
⇒ [tex]\sigma = \frac{x-\mu}{z} = \frac{89-86}{1.96} =1.53[/tex] ≈ 1.5°F
So the standard deviation of the distribution = 1.5°F
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What is the value of the expression below when x=7
The value of the expression when x = 7 is 70
What are algebraic expressions?Algebraic expressions are expressions made up of variables, terms, coefficients, factors and constants.
They are also made up of mathematical operations such as addition, multiplication, division, subtraction, etc.
Given the expression;
2x^2- 5x - 3
To determine the the value, we substitute the value of x a 7 into the expression, we have;
2(7)² - 5(7) - 3
expand the bracket
2(49) - 25 - 3
98 - 25 - 3
Find the difference
70
Thus, the value of the expression when x = 7 is 70
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Determine which integer in the solution set will make the equation true.
2s − 10 = −12
S: {−1, 0, 1, 2}
−1
0
1
2
Answer:
- 1 makes the equation true
Step-by-step explanation:
2s - 10 = - 12 ( isolate the term in s by adding 10 to both sides )
2s = - 2 ( divide both sides by 2 )
s = - 1
The integer ion in the solution set will make the equation true is -1. The correct option is a.
What are integers?Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.
An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."
Given equation is
2s - 10 = - 12 ( isolate the term in s by adding 10 to both sides )
2s = - 2 ( divide both sides by 2 )
s = - 1
Therefore, the correct option is a, −1.
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Please Help due tonight.
Answer:
D. -3b + 5 divided by -3
Step-by-step explanation:
I'm not too sure but i think its this because when you divide by a negative number you have to flip the sign and since you are solving for x you will minus the b term on both sides. But im not too sure keep thinking about it
3) Which TWO expressions will have a POSITIVE product?
a) -9x7x4
b) -4 x (-3) x 2
c) -5 x (-12) × (-1)
d) -1 x 1 x (-1)
e) 5x0x (-5)
Answer: B and D
Step-by-step explanation:
B.) -4 x (-3) x 2
-4 x (-3) = 12 x 2 = 24
D. -1 x 1 x (-1)
-1 x 1 = -1 x (-1) = 1
Mo is sorting number cards with ratios. All of these ratios are equivalent to 3:5. Circle the ratios that are not equivalent.
13:15
30:50
7:9
3x:5x
5:3
Ratios which are not equivalent to 3: 5 are 13: 15, 7:9, 5:3.
As given in the question,
Mo is sorting number cards with ratios
Ratio = 3 : 5
Equivalent ratio to 3 : 5
13 : 15 cannot be reduced.
13 : 15 not equivalent to 3:5
30:50 = (3 ×10) : (5×10)
= 3:5
7:9 cannot be reduced . It is not equivalent to 3:5
3x:5x = 3:5
5:3 reciprocal of 3:5 .It is not equivalent to 3:5.
Therefore, ratios which are not equivalent to 3: 5 are 13: 15, 7:9, 5:3.
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Five more than twice a number is equal to 3 more than triple a number. Write the equation and solve.
Answer:
Equation: 5 + 2x = 3x + 3 ; Answer: x = 2
Step-by-step explanation:
Try and re-reading the question until you truly grasp the concept of it or write an equation by reading each word and making sure the operations are suitable according to the text. Then, finally, simply just solve.
Hope this helps! :D
help pleaseeeeeee :(((
Answer: are there any options?
Step-by-step explanation:
5x-5=9x+3 Solve for x
Answer:
x = -2
Step-by-step explanation:
5x - 5 = 9x + 3
- 5 = 4x + 3
- 8 = 4x
- 8/4 = 4x/4
x = -2
In the diagram below of triangle OPQ, R is the midpoint of OQ and S is the
midpoint of PQ. If RS = -3x + 38, and OP = 4x - 14, what is the measure of
RS?
Step-by-step explanation:
dyfyfyffufururrufuufguugvjiy
Step-by-step explanation:
i dont understand the answer noksf okay
If AD=5x+8 and BD=3x-10, what is the length of AB?
A)28
B)148
C)74
D)222
Determine if 0.18750.1875 is rational or irrational and give a reason for your answer. is it or not??
The number 0.1875 is a Rational number.
What is Rational number?
If a number can be expressed as a fraction of two integers then its called Rational number.
Given that;
The number = 0.1875
Now, Determine if it is rational or not we can convert it into fraction as;
0.1875 = 1875/10000
Divide numerator and denominator by 25,
= 75/400
Again, Divide numerator and denominator by 25,
= 3/16
Clearly, The above is a rational number because it can be expressed as a fraction of two integers.
So, The number 0.1875 is a Rational number.
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