A triangle is a shape whose all three angles have a sum of 180 degrees. So from the above definition, we know that:
P + Q + R = 180
Q=3P
T=P + 20
Therefore:
P + 3P + P + 20 = 180
5P + 20 = 180
5P = 160
P = 32
Q = 3(32) = 96
R = 32 + 20 = 52
To Additional Control P + Q + R = 32 + 96 + 52 = 180 °Degree
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Find the slope of the line through each pair of points. 3/2 , - (1/2) and -(2/3) , 1/3
The slope of the line of each pair of points 3/2 , - (1/2) and -(2/3) , 1/3 is zero
What is a slope of line?A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.
The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.
Therefore,
m = y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.
Be aware that tan ∅ = y/x.
We also refer to this tan as the line's slope.
We know that slope, slope = m = [tex]\frac{y_2 -y_1}{x_2 -x_1}[/tex]
For the pair of points 3/2 , - (1/2)
m = [tex]\frac{2-2}{-1-3}[/tex]
= 0/(-4)
Hence the slope is zero for these points.
For the pair of points -(2/3) , 1/3
m = [tex]\frac{3-3}{1-(-2)}[/tex]
= 0/3
Hence the slope is zero for these points.
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State whether sentence is true or false. If false, replace the underlined word or phrase to make a true sentence.
The ₋component form of a vector describes the vector in terms of change in x and change in y .
Given statement 'The component form of a vector describes the vector in terms of change in x and change in y.' is True.
For a vector V whose initial point is (x1, y1) and the terminal point is (x2, y2), the component form of a vector V is given as: < x₂ – x₁, y₂ – y₁ >
The coordinates of the component form of vector are nothing but the ordered pair that describes the changes in the x-values and y-values.
Consider a vector v whose initial point is (1, 3) and the terminal point is (3, 6).
The component form of vector v is:
<3 - 1, 6 - 3>
= <2, 3>
Here, 2 is the change in the x-values from initial point to terminal point and 3 is the change in the y-values from the initial point to the terminal point.
Therefore, given statement 'The component form of a vector describes the vector in terms of change in x and change in y.' is True.
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Helpppp need now!! Please thanks you
Answer:
The last one is incorrect
Step-by-step explanation:
Asher's sister is eight years older than Asher. Their combined ages add up fo 20.
How old is Asher?
Answer:14
Step-by-step explanation:X+8=asher's age X=Asher's sisters age
x+x+8 =20
2x+8=20
2x+8-8=20-8
2x=12
2x/2=12/2
x=6
x+8=asher's age
6+8=14
Solve the equation x - 23 = 72
Answer:
Step-by-step explanation:
x=72+23
x=95
Answer: x = 95
Step-by-step explanation:
Add 23 to both sides to isolate x
x - 23 + 23 = 72 + 23
x = 95
1/3a = -5
please help ! ):
The value of a in the expression is 15.
How to illustrate the expression?It should be noted that an expression shows that relationship that exists between variables.
In this case, we are given the expression that 1/3a = -5
To find the value of a will be:
a/3 = 5
Cross multiply
a = 3 × 5.
a = 15
Therefore, the value of a in the expression is 15.
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1/3a = -5. Find the value of a.
ASTRONOMY The Big Dipper is a part of the larger constellation Ursa Major. Three of the brighter stars in the constellation form Δ R S A . If m ∠ R=41 and m ∠S=109 , find m∠ A . (Lesson 4-2),
According to the given data the value of the triangle's angle is m ∠ A =30
What is the triangle's angles?A triangle's inner angles always add up to 180°, whereas its outside angles are equivalent to the sum of its two inside angles. equal toward the combination of the two nearest interior angles Another method for calculating a triangle's exterior angle is to subtract overall angle of something like the vertex of concern from 180°.
According to the given data:m ∠ R=41
m ∠S=109
find m∠ A
We know that the total of the triangle's angles must equal 180°.
So ,
(substitute given values)
m ∠R+ m ∠S +m ∠A =180
(add)
41 + 109 + m ∠A =180
(subtract 150 from both side)
150+m∠A =180
m ∠ A =30
According to the given data the value of the triangle's angle is m ∠ A =30
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Can someone help me with my geometry hw?
Given that line AT bisects angle CAR, the measure of angle TAR is 35 degree.
What is the measure of angle TAR?Given the data in the question;
Line AT bisects ∠CARm∠CAT = 5xm∠CAR = 9x + 7m∠TAR = ?Since Line AT bisects ∠CAR
m∠CAR = 2 × m∠CAT
9x + 7 = 2( 5x )
We solve for x
9x + 7 = 10x
10x - 9x = 7
x = 7
We know that a bisector divides a line or angle into two equal halves.
Hence, m∠CAT = m∠TAR
m∠TAR = m∠CAT = 5x
m∠TAR = m∠CAT = 5(7)
m∠TAR = m∠CAT = 35°
Given that line AT bisects angle CAR, the measure of angle TAR is 35 degree.
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If 5 is lessened by 1/2 of a number the result is the same as subtracting 5/6 from 11.
Write an equation to represent the situation, use X as the variable.
The equation to represent the given situation is 1/2X-5=11-5/6 using X as the variable.
What is an equation and how it can be formed?
Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.
When we are given a mathematical problem that is or may be described using algebraic expressions, we form and solve equations. The information from the situation and the algebraic expressions can be used to create an equation. The equation can then be solved to obtain the answer.
Given the situation: If 5 is lessened by 1/2 of a number the result is the same as subtracting 5/6 from 11.
To write an equation for the given situation.
Let the number be X.
If 5 is lessened by 1/2 of the number, we get the expression 1/2X-5
Subtracting 5/6 from 11 gives the expression 11-5/6
Now, it is given that both the situations are same so equating both the expressions we get,
1/2X-5=11-5/6
⇒1/2X-5=61/6
Hence, the equation to represent the situation is 1/2X-5=11-5/6.
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Simplify by combining like terms.
2 a+3 b+4 a
By combining the like terms, the simplified form of the the expression 2a+3b+4a is 6a+3b
Given,
The algebraic expression = 2a+3b+4a
Rearrange the terms
2a+3b+4a=2a+4a+3b
Combine the like terms
2a+4a+3b=6a+3b
Hence, by combining the like terms, the simplified form of the the expression 2a+3b+4a is 6a+3b
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Note: Please make sure to properly format your answers. All dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma
($2,354.67). All percentage values in the answers need to include a percentage sign (%). For all items without specific rounding instructions, round your answers to two decimal places,
show both decimal places (5.06).
Jerome deposits $3700, in a certificate of deposit that pays 1.8% interest, compounded annually. How much interest does Jerome earn in one year?
He get the approximately $67 as the amount of interest rate.
According to the statement
We have to find that the interest does Jerome earn in one year.
So, For this purpose, we know that the
A Interest is the amount paid by someone who borrows a certain amount of money.
From the given information:
Jerome deposits $3700, in a certificate of deposit that pays 1.8% interest, compounded annually. How much interest does Jerome earn in one year.
Then
The amount deposited = $3700
The interest pays by the bank = 1.8%
Amount he get by the interest rate = 1.8% of 3700
Amount he get by the interest rate = 1.8 / 100 * 3700
Amount he get by the interest rate = 0.018 * 3700
Amount he get by the interest rate = 66.6.
So, He get the approximately $67 as the amount of interest rate.
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pls help solve for x
Answer:
Step-by-step explanation:
x + 80° = 5x ( being corresponding angle )
80° = 5x - x
4x = 80°
x = 80° / 4
x = 20°
☘☘☘...
The midpoint of AB is (6, 3). If the coordinates of A are (4, -2),
what are the coordinates of B?
Answer:
Step-by-step explanation:
M(6,3)
A(4,-2)⇒A(x1,y1) just incase you understand
B(x2,y2),Now I will use the midpoint formula
[tex]M(\frac{x1+x2}{2} ,\frac{y1+y2}{2} )\\=(\frac{4+x2}{2} ,\frac{-2+y2}{2} )\\=separate(x)\\\frac{4+x2}{2} =6\\4+x2=12\\x2=12-4\\x2=8\\\\\frac{-2+y2}{2} =3\\-2+y2=6\\y2=3+2\\y2=5[/tex]
B(8,5)
If f(x)=-3 x+7 and g(x)=-7 x+3 , what is the value of f(-3)-g(3) ?
a. 40 b. 34 c. 8 d. -8
After solving the equation we have concluded that if f(x)=-3 x+7 and g(x)=-7 x+3 , then the value of f(-3)-g(3) is -8
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
f(x) = -3x + 7
f(-3) = -3(-3) + 7 = 9 + 7 = 16
g(x) = -7x + 3
g(-3) = -7(-3) + 3 = 21 + 3 = 24
f(-3) - g(-3) = 16 - 24 = -8
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An aquarium can be modeled as a right rectangular prism. Its dimensions are 17 in by 13 in by 12 in. How many cubic inches of water are in it when it is full? Round your answer to the nearest tenth if necessary.
The total price of a shirt and a cap is $10. If the price of the shirt was doubled and the price of the cap was four times its original price, the total price of a shirt and a
cap would be $26. The following system of equations models this scenario:
x+y=10
2x + 4y = 26
What is the price of each shirt and cap?
A)The price of a shirt is $9, and the price of a cap is $1.
B)The price of a shirt is $8, and the price of a cap is $2.
C)The price of a shirt is $7, and the price of a cap is $3.
D)The price of a shirt is $6, and the price of a cap is $4
Answer:
Step-by-step explanation:
c
C)The price of a shirt is $7, and the price of a cap is $3.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
x+y=10
2x + 4y = 26
solving, we get,
x=7 & y=3
Hence, C)The price of a shirt is $7, and the price of a cap is $3.
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NEEEDDDD HELP ASSAP. This is about math help
So 1st off you divide 25.2 by 36 since it miles is the x and the cost is y
the unit rate is 0.7 since i divided those 2 numbers
now i just have to do 0.7 times 47
The answer is $ 32.9
sorry if its wrong?
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Find the volume of a cone that has a radius of 1cm and a height of 3.4cm.
The volume of a cone that has a radius of 1 cm and a height of 3.4 cm is 3.56 cm³.
Volume of a cone is the space occupied by it in a three - dimensional space.
Volume of a cone is calculated using the formula:
[tex]V = \frac{1}{3} \pi r^{2} h[/tex]
where r is the radius of the base of the cone
[tex]\pi[/tex] is a constant having value 3.14
h is the height of the cone. It is the perpendicular height from the base.
According to the given condition,
r = 1 cm and h = 3.4 cm
Substituting these values in the equation above,
[tex]V = \frac{1}{3} \pi (1^{2}) (3.4)[/tex]
∴ V = 3.56 cm³.
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What is the slope of a line that is parallel to the line y = ?
0
5
undefined
Answer:
I think the answer is ∞ which is the third option, undefined.
the volume of a cube-shaped box for earrings is 125 cubic centimeters. what is the length of one edge of the box?
Answer:
s = 5
Step-by-step explanation:
V=s^3
125 = s^3
s = 125^(1/3) (cube root)
s = 5
Never mind got it wrong
please help me with this question! Thirty dollars is to be divided among three girls and two boys so that each of the girls receives twice as much as each of the boys. How much does each person receive?
Answer:
3.75 dollars for the boys and 7.5 for girls
Step-by-step explanation:
Boys get x amount.
Girls get 2x
6x+2x=8x
30/8=3.75
Each boy receive the amount of $3.75 and Each girl receive the amount of $7.5
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let consider that each boy gets $x
It is given that each of the girls receives twice as much each of the boys
So, each girl receive the amount of 2x
Since there are 3 girls .
So, Three girls received the amount = 3(2x)=6x
2 boys get amount of 2x
Therefore,
6x+2x=8x
30/8
=3.75
Hence Each boy receive the amount of $3.75 and Each girl receive the amount of $7.5
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The graph below shows how the number of donations to a charity affects the expected total value of those donations.
In October, the charity received 80 donations.
If the graph continues in the same way, what is the expected total value of the donations in October?
Based on the graph, the expected total value of the donations in October would be $460.
What is the expected value?When donations were 5 in number, the expected value was £30.
When donations were 8, the expected value was £50.
When donations were 15, the expected value was £90.
The slope of the line is:
= (90 - 50) / (15 - 8)
= 5.71
The y-intercept as seen on the graph is 0.
The equation of the line is therefore:
y = 5.71x
The expected value of £80 in donations is therefore:
y = 5.71 x 80
= $460
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Please help with this question asap (true or false question)
Answer:
Step-by-step explanation:
true if 10=x and y equals 33
A bag contains 3 red chips, 5 green chips, 2 yellow chips, 4 brown chips, and 6 purple chips. One chip is chosen at random, the color noted, and the chip returned to the bag.
b. What is the probability that both chips are purple?
The probability of selecting that both chips are purple is 3/40
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
It is Given that A bag contains 3 red chips, 5 green chips, 2 yellow chips, 4 brown chips, and 6 purple chips. One chip is chosen at random, the color noted, and the chip returned to the bag.
The probability of selecting that both chips are purple
= 6/20 x 5/20
= 30/400
= 3/40
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What is summation notation for the series?
b. 500+490+480+ . . . . . . . +20+10
The summation notation for the series 500+490+480+ . . . . . . . +20+10 is
[tex]25500-10\sum\limits^{50}_{n=1} {n}[/tex]
A summation notation is used to express a long summation into a single notation.
The given series is:
500+490+480+ . . . . . . . +20+10
This is an arithmetic series with:
a(1) = 500, and
d = 490 - 500 = -10
The last term is a(n) = 10. Find n first by using the nth term formula of an arithmetic sequence:
a(n) = a(1) + (n-1) . d
10 = 500 + (n-1) . (-10)
10 = 500 -10n + 10
10 n = 500
n = 50
Write the explicit formula for the nth term:
a(n) = a(1) + (n-1) . d
a(n) = 500 + (n-1) . (-10)
a(n) = 500 -10n + 10
a(n) = 510 - 10n
The series is the summation notation from n=1 to n = 50
[tex]=\sum\limits^{50}_{n=1} {a(n)}[/tex]
[tex]=\sum\limits^{50}_{n=1} {(510-10n)}[/tex]
[tex]=\sum\limits^{50}_{n=1} {510} -\sum\limits^{50}_{n=1} {10n}[/tex]
[tex]=510\times50-10\sum\limits^{50}_{n=1} {n}[/tex]
[tex]=25500-10\sum\limits^{50}_{n=1} {n}[/tex]
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I need to find the perimeter, can you help me?
HELPPPPPPPP CORRECT ANSWER GET BRAINLIEST
Answer:
A. Jake made a mistake in step 2
Step-by-step explanation:
If you subtract a number from one side, you should do the same for the other. In step 2 Jake subtracted 7 from one side but not from another.
Solve. Check for extraneous solutions.
√5x - 3 = √2 x+3
A solution to an equation that appears in the process of solving other equations is known as a extraneous solution.
The value of x = 2 then L.H.S = R.H.S, this equation has no extraneous solutions.
What is extraneous solutions?A solution to an equation that appears in the process of solving other equations is known as a extraneous solution.
To determine if a solution exists extraneous, we simply plug the solution into the original equation.
If it makes a true statement, then it exists not an extraneous solution, but if it makes a false statement, then it is an extraneous solution
Let the equation be,
√5x - 3 = √2x+3
squaring on both sides of the equation, we get
⇒ 5x - 3 = 2x + 3
⇒ 5x - 2x = 3 + 3
simplifying the above equation, we get
⇒ 3x = 6
Divide both sides of the equation by 3,
⇒ x/3 = 6/3
⇒ x = 2
The value of x = 2.
Substituting x = 2 in L.H.S
[tex]$\sqrt{5x-3} =\sqrt{10-3} =\sqrt{7}[/tex]
Substituting x = 2 in R.H.S
[tex]$\sqrt{2x+3} =\sqrt{4+3} =\sqrt{7}[/tex]
Since, L.H.S = R.H.S, this equation has no extraneous solutions.
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Write the equation in slope-intercept form. What are the slope and y -intercept?
b. -7 x-5 y=35
The equation in slope-intercept form is y = - (7/5x - 7 ).
What is slope - intercept form?The equation of a line is found using the slope-intercept form of a straight line. We need to know the slope of the line and the intercept where the line crosses the y-axis in order to use the slope-intercept formula. Consider a straight line with y-intercept b and slope m. For a straight line with slope "m" and y-intercept "b," the slope intercept form equation is: y = mx + b.
Given the equation is -
-7 x-5 y=35
Divide the equation by 5
-7/5x - y = 7
Rearrange the equation -
y = - (7/5x - 7 ) which is the equation in slope-intercept form.
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The distance from Chicago to Cleveland to Cincinnati and back to Chicago is 900 miles. The distance from Chicago to Cleveland is 50 miles more than the distance from Cincinnati to Chicago, and the distance from Cleveland to Cincinnati is 50 miles less than the distance from Cincinnati to Chicago. Find each distance and classify the triangle formed by the three cities.
Answer:
Step-by-step explanation:
Hello, I have a Wonderfull website that can help you with this question. (Mathgenius.com) it should pull it up. its all and every subject you can imagine.
Answer:
Chicago to Cleveland- 350 miles
Cleveland to Cincinnati-250 miles
Cincinnati to Chicago-300 miles
Type of triangle formed? - Scalene
Step-by-step explanation:
so I first give each of them a letter, so I chose a for Chicago to Cleveland, b for Cleveland to Cincinnati, and c for Cincinnati to Chicago. Then I write some equations.
a+b+c =900
b=c-50
a=50+c
i then plug the a and b equation into the first one to get
50+c+c-50+c=900
The fifties cancel out, so we are left with 3c =900 so c=300
From this we can figure out the rest by substituting in 300 for c in the an and b equations.
300-50=250
300+50=350
