Answer:
x = -14
Step-by-step explanation:
Look at the image attatched. I have labeled the angles for better explanation.
We know that angle 1 is 54 degrees as is rests on a straight line with its adjacent angle at 126 degrees. This means that angle 1 would be 180 - 126 degrees, or 54 degrees. We also know that angle 1 and 3 must be congruent as the sides of the triangle opposite those angles are congruent as well. This means that both those angles are 54 degrees. Since the sum of all angles in a triangle must equal 180 degrees, we can get that angle 4 is 180 - (2*54) degrees, or 72. Since angle two and angle 4 both lie on a straight line, they must add up to 180 degrees. This means that the value of angle 2 would be 180 - 72, or 108 degrees. Since angle 2 is also equal to x+122, we get the equation:
108 = x + 122.
We then solve this by getting:
x = 108 - 122
which gives us the answer of
x = -14
Answer: x = -14
Step-by-step explanation:
a) Top triangle, top angle: Using the Linear Pair Postulate, 180° - 126° = 54°
b) Top triangle, bottom left angle: Congruent sides implies congruent angles = 54°
c) Bottom triangle, top left angle: Using the Complimentary Angles Postulate, 90° - 54° = 36°
d) Bottom triangle, bottom angle: Congruent sides implies congruent angles = 36°
Triangle Sum Theorem states that the sum of the three angles must equal 180°.
36° + ∠2 + 36° = 180°
36° + (x + 22) + 36° = 180°
x + 194 = 180
x = -14
If a and b must be positive integers, what is the largest integer n such that 13a + 18b = n has no solutions?
Answer:
Any integer that is not integer multiple of 234 is not a solution.
Step-by-step explanation:
We are required to find the largest integer n such that 13a + 18b = n has no solution, where a and b are integers.
13a + 18b = n
For a = 1, b = 0
n = 13
For a = 0, b = 1
n = 18
So, for the solution sets (1, 0), (0, 1), n will always have a solutions.
Consider n = 13 × 18 = 234
This means that any integer that is not integer multiple of 234 is not a solution.
surface area of a triangular prism
Answer:
54ft squared
Step-by-step explanation:
All faces:
Front: 2*3/2=4.5f squared * 2 (other side)= 9ft squared
Sides: 10*3/2= 15ft squared * 2 (other side)= 30ft squared
Bottom: 3*10/2= 30/2= 15ft squared
=54 ft squared
Surface area of the triangular prism is 96 feet.
What is Surface Area?The area of a three dimensional object on it's outer surface is called the surface area of the object.
A triangular prism has 2 triangular bases and 3 rectangular lateral faces.
Area of a triangle = [tex]\frac{1}{2}[/tex] × base × height
There are 2 triangles at the top and bottom.
Here base = 3 feet and height = 2 feet
Total surface area on the top and bottom = 2 × [tex]\frac{1}{2}[/tex] × base × height
= base × height
= 3 × 2
= 6 feet
There are 3 rectangular faces.
Area of the rectangle = Length × width
Here, length = 10 feet and width = 3 feet
Area of the rectangular face = 10 × 3 = 30 feet
Since there are 3 rectangular faces,
Total lateral surface area = 3 × 30 = 90 feet
Total surface area of the triangular prism = 90 + 6 = 96 feet
Hence the total surface area of the given triangular prism is 96 feet.
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please can you guy help for this questiong
Answer:
Reason 1. Given
Statement 2. <CAD is congruent to <BAD
Reason 2. Definition of angle bisector
Statement 3. Segment AD is congruent to segment AD
Reason 4. All right angles are congruent
Reason 5. ASA
A single card is drawn at random from a standard 52 card deck.
Work out in its simplest form:
P(10)
=
P(not 10)
=
There are four 10 cards in the deck, so P(10) = 4/52 = 1/13
P(not 10) = 1 - P(10). This is because the maximum probability is 1, and the card you draw will either be 10, or not a 10.
P(not 10) = 1 - 1/13 = 13/13 - 1/13 = 12/13
which of the following descriptions represents the transformation shown in the image? part 2b
Answer: b) rotation of 180°, reflection across y-axis
Step-by-step explanation:
The black triangle is in Quadrant IV.
A rotation of 180° will move it to Quadrant II.
The red triangle is in Quadrant I so you must reflect it across the y-axis.
Divide x4 + 7 by x-3.
Answer:
x^3 + 3x^2 + 9x + 27 + 88 / [x - 3]
Step-by-step explanation:
x ^4 + 7 by x - 3 x^3 + 3x^2 + 9x + 27 x - 3 [ x^4 + 0x^3 + 0x^2 + 0x + 7 ]. x^3 -
3x^3 ________________________________ 3x^3 + 0x^2 3x^2
- 9x^2 ______________ 9x^2 + 0x 9x^2
- 27x ____________ 27x + 7 27x
- 81 _________ 88 S
Answer: So the result is : x^3 + 3x^2 + 9x + 27 + 88 / [x - 3]
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- 2.5f + 0.4f - 15 - 4
Answer:
Simplify the f's variables -2.1
Simplify the numbers -19
-2.1f -19 is the answer
-2.1f -19Answer-2.1f-24:
Step-by-step explanation:
PLEASE HELP!! Rick uses this exponential expression to determine what the value of his bank account will be in three years. Select the value in the expression that represents the number of times per year that interest is compounded on the account.
5,000(1+0.04/12)^12t
Answer:
12
Step-by-step explanation:
A compound interest equation is represented as A = P(1 + r/n)^nt, where n=the number of times per year the interest is compounded. In the given equation, n=12.
Answer:
12
Step-by-step explanation:
HELP ASAP PLEASE!!! Explain how you will benefit most from improving your math skills.
Answer:
Some of the most lucrative jobs are all about math. Most engineering fields are all about sharp math skills, whether it’s civil and mechanical or software engineering. Working in finance also obviously involves a lot of math, and what better way to make money than working in the field that’s all about money? You can also become a statistician or actuary; it’s not easy to find good statisticians, despite the need for them. If you want to earn good money, then you do need good math skills.Then again, you could use math in life anyway.
Step-by-step explanation:
Evaluate the expression for
m = -3.
-4 |5+m |
Answer: the correct answer is -8
Step-by-step explanation:
Substitute the given value of m into the expression:
-4|5 + (-3)|.
Then evaluate using the order of operations:
-4|5 + (-3)|
= -4|2|
= -4(2)
= -8
Substitute the given value of m into the expression:
-4|5 + (-3)|.
Then evaluate using the order of operations:
-4|5 + (-3)|
= -4|2|
= -4(2)
= -8
What is the first step in evaluating an expression?The first step in evaluating an expression is to substitute the given value of a variable into the expression. Then you can finish evaluating the expression using arithmetic.
What is an example of evaluating expressions?A variable is a letter, for example, x, y, or z, that represents an unspecified number. To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12.
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Reflect triangle A in the line y=x
please can you just state all the coordinates to make up the triangle
Answer:
(5,6), (3, 6) and (3, 5).
Step-by-step explanation:
If we imagine the line y = x to be a mirror , the image of each point is the same perpendicular distance to the mirror has the original point.
So the image of (6,5) = (5,6)
(6, 3) ---> ( 3, 6)
(5,3) ---> (3, 5).
Note that the coordinates are reversed in each case.
In this case the general rule for the reflection is (x, y) ---> (y, x).
A teenager's heart pumps an average of 7200 L of blood every 24 hours. What is the rate of change of volume of blood?
How to solve this:
1: 7200/24 = x/1
2: 7200/24 = 300/1
3: 300 L of blood per hour
We know that an average is 7200 for heart pumps so we divide 7200 by 24 hours = x/1
Second step is the same 7200 divided by 24 = 300/1
So the correct answer is 300. 300 L of blood per hour.
Answer: 300 L of blood per hour.
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The rate of change in the volume of blood is 300 liters per hour.
What is the rate?A rate is a type of ratio that compares two values with distinct units. A rate is expressed as a fraction.
The volume of blood pumped by the teenager's heart is expressed as a rate of change in volume per hour.
Rate of change of volume of blood = volume of blood/time
= 7200 L /24
Apply the division operation, and we get
= 300 L/hour
The teenager's heart changes blood volume at a pace of 300 liters per hour. This means that his or her heart is pumping 300 liters of blood every hour.
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what is a listed method in mathematics
Answer:
Listing method is a method to list all the elements separating each element by the comma and enclosing
Step-by-step explanation:
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Answer:
6 seconds
Step-by-step explanation:
- ( 6 - 2)^2 + 16
- (4)^2 + 16
- 16 + 16
= 0
The ball is hits the ground or is at 0 height when x = 6.
this question is my thing
Answer:
Below
Step-by-step explanation:
8 is classified as a rational number because it can be made into a fraction. 8.8 = 8 8/10 = 88/1
Find the measure of each angle of a regular polygon with 8 sides.
Answer:
135 degree
Step-by-step explanation:
total sum of angle = (8-2) * 180 = 1080
each angle = 1080/8 = 135 degree
How would knowing the slope of a linear function help determine whether a function is increasing or decreasing?
Answer:
3
Step-by-step explanation:
Answer:
If the slope is positive, it signifies the function is increasing, and if it's negative, it's decreasing. If the slope is exactly 0, the function is stagnant, a horizontal line
Ur so worth it...ok now enough about u...help plz
Just 20 and 21...also there’s a little hint it says to draw a triangle.
Answer:
20. 13 cm
21. 12 cm
Step-by-step explanation:
20. isosceles means two sides are the same length, so you take the ten off the perimeter to get 26 remaining cm (36 -10) and you then divide that by two to get both sides of 13 cm (26 / 2)
21. because you know that if you split the triangle down the middle you get a right triangle and you can use a^2+b^2=c^2 to find the height, so we take the one side of 13 cm and half of the third side, which is 5, and you can find your answer (a^2 + 5^2 = 13^2 ---> a^2 + 25 = 169 ---> a^2 = 144 ---> a = 12)
The first equation from the previous system of
equations is graphed. Graph the second equation to
find the solution of the system of equations.
y = -2x + 4,
y=-x-1
What is the solution to the system?
Answer: x = 5 and y=-6
Step-by-step explanation:
If we graph both equations, the interception is the point (5,-6). Therefore the solution for x is 5 and for y is -6.
What is the equation of a line with a slope of six and passes through the coordinates 0,1
Answer:
y = 6x + 1
Step-by-step explanation:
Use the point slope equation:
y - y1 = m( x - x1 )
y - 1 = 6 ( x - 0)
y - 1 = 6x
y = 6x + 1
If trapezoid JKLM is translated according to the rule (x,y)—> (x+2, y - 6), what are the coordinates of point L
Answer:
( x, y) is translation '2' units right and '6' units down
(x ,y))—> (x +2 ,y-6)
Step-by-step explanation:
Explanation:-
Type of transformation change to co-ordinate point
vertical translation up 'd' units (x,y) changes to (x , y+d)
vertical translation down 'd' units (x,y) changes to (x , y-d)
Horizontal translation left 'c' units (x,y) changes to (x-c , y)
Horizontal translation right 'c' units (x,y) changes to (x+c , y)
Now by use above table
given data ( x, y) is translation '2' units right and '6' units down
(x ,y))—> (x +2 ,y-6)
Final answer:-
( x, y) is translation '2' units right and '6' units down
(x ,y))—> (x +2 ,y-6)
What is the perpendicular and parallel line of 8x + 5y=4
Answer:
Perpendicular: [tex]y = \frac{5}{8}x+4[/tex]
Parallel: [tex]y=-\frac{8}{5} x+RandomNumberNot4[/tex]
Step-by-step explanation:
I'm going to rewrite the equation:
[tex]y=-\frac{8}{5} x+\frac{4}{5}[/tex]
Perpendicular means that the slope is the opposite reciprocal.
Slope = [tex]\frac{5}{8}[/tex]
[tex]y = \frac{5}{8}x+4[/tex]
Parallel means that the slope is the same but the y - intercept is different:
[tex]y=-\frac{8}{5} x+RandomNumberNot4[/tex]
Solve the following equation for x.
15x^2 – 46x + 16 = 0
Answer:
X=2/5,8/3
Step-by-step explanation:
Look on Tiger Algebra for step by step. JUst put the problem into g-oogle.
Answer:
X=8/3,2/5
Step-by-step explanation:
7th grade math I need some help
Answer:
Step-by-step explanation:
[tex](-14+\frac{3}{2}b)-(1+\frac{8}{2}b)=-14-1+\frac{3}{2}b-4b[/tex]
= ([tex]-15-\frac{5}{2}b[/tex])
[tex](5+2b)+(2b+\frac{3}{2})=(5+\frac{3}{2})+(2b+2b)[/tex]
= [tex](4b+\frac{13}{2})[/tex]
[tex](\frac{7}{2}b-3)-(8+6b)[/tex] = [tex](\frac{7}{2}b-6b)-(3+8)[/tex]
= ([tex]-\frac{5}{2}b-11[/tex])
[tex](-10+b)+(7b-5)=(-10-5)+(b+7b)[/tex]
= [tex](8b-15)[/tex]
How many moles of sulfate will be formed if you start with 2.80 moles of sodium hydroxide and you have an excess of sulfuric acid
Answer:
1.4 mol
Step-by-step explanation:
2NaOH + H2SO4 -----> Na2SO4 + 2H2O
from reaction 2 mol 1 mol
given 2.8 mol x
x = (2.8*1)/2 = 1.4 mol
Hello i really need help
Step-by-step explanation:
The equation is
X + 10205 = 21894
X = 21894 - 10205
X = 11689
Cancel mom please help me with this I’m stuck and I don’t know how to do this
Answer:
20
Step-by-step explanation:
The triangles are similar so we can use ratios
8 32
--- = -----
8+5 32+x
Using cross products
8(32+x) = 32(13)
Divide each side by 8
(32+x) = 32(13)/8
32+x = 4*13
32+x =52
Subtract 32
x = 20
I really need help with this I don't understand it.
Answer:
(10x + 37) and (15x+7) are vertical angles which are always equal
10x + 37 = 15x +7
5x = 30
x = 6
The angle (15x +7) equals 97 and the other angle (10x + 37) also equals 97 degrees. All 4 of the angles add up to 360 degrees.
Therefore, 360 = 2z + 97 + 97
2z = 166
z = 83
Step-by-step explanation:
Ms Adams shares out 21 pencils between Niamah and Jack in the ratio 2:5 how many pencils does each child get
Answer:
niamah : jack
2 : 5
2×3 : 5×3
6 : 15
niamah gets 6 pencils
jack gets 15 pencils
*6+15 = 21
Answer:
Step-by-step explanation:
If the ratio of Niamah to Jack is 2:5, that means that for every 2 pencils that N gets, J gets 5. If there are a total of 21 pencils, then
2x + 5x = 21 and
7x = 21 so
x = 3.
That means that N gets 2(3) which is 6, and J gets 5(3) which is 15. Notice that 6:15 is the same ratio as 2:5 when it is reduced.
Which monomial has a degree of 3?
a. 3
b. 3x2
c. 3x
d. -2x3
Answer:
So a degree means the power. So which ever has a power of three. I think you forgot to show to power, its D i think
D is answer