The sum of the interior angles of any triangle is always 180°.
For the given right triangle:
\(m\angle2+m\angle3+90=180\)Use the given meauste for triangles 2 and 3:
\((x+8)+(2x+7)+90=180\)Solve the equation above for x:
\(\begin{gathered} x+8+2x+7+90=180 \\ 3x+105=180 \\ \\ \text{Subtract 105 in both sides of the equation:} \\ 3x+105-105=180-105 \\ 3x=75 \\ \\ \text{Divide both sides of the equation into 3:} \\ \frac{3}{3}x=\frac{75}{3} \\ \\ x=25 \end{gathered}\)Use the value of x=25 to find the measure of angle 2:
\(\begin{gathered} m\angle2=x+8 \\ m\angle2=25+8 \\ m\angle2=33 \end{gathered}\)Then, the measure of angle 2 is 33°Please solve 13 and 14 I need help
Answer:
13. a
14.c
Step-by-step explanation:
It is shown in figure
Name the solid figure formed by the net.
Answer:
square
Step-by-step explanation:
it is a square because all the shapes/parts are the same size
it also has 6 faces, 12 vertices
The equation of the line L is 2y-x=10.Find the coordinates of the point where L intersects the y-axis
Equation:- 2y-x=10
For L to intersects Y axis then X cordinate must be zero
so put value of X as zero (0)
2y=10
So Y cordinate is equal to 5
Cordinate:- (0,5)
Consider the line 5x+2y=−4. What is the equation of the line parallel to the given line that passes through the point (−2, 6) in slope-intercept form? Enter your answer by filling in the boxes to complete the equation.
Answer:
y = -5/2x +1
Step-by-step explanation:
You want the slope-intercept form equation for the line through the point (-2, 6) that is parallel to 5x +2y = -4.
Parallel lineThe equation of a parallel line can be the same as the given equation, except for the constant. The new constant can be found by substituting the given point coordinates:
5(-2) +2(6) = c
-10 +12 = c
2 = c
Now we know the equation of the parallel line can be written as ...
5x +2y = 2
Slope-intercept formSolving for y puts this in slope-intercept form:
2y = -5x +2 . . . . . . . . subtract 5x
y = -5/2x +1 . . . . . . . . divide by 2
We don't know what your boxes look like, but we can separate the numbers to make it look like this:
\(\boxed{y=\dfrac{-5}{2}x+1}\)
#95141404393
This is pretty simple, but the wording gets me. Is choice B correct as well, I’m not really sure. Please help
6 + 4|2x + 6| = 14
Solve for x
Answer:
x = -1
Step-by-step explanation:
6+4 = 10
14-10 = 4
2x + 6 = 4
2x (-2) = -2
-2 + 6 = 4
A geologist measures the mass of some rocks to the nearest tenth of a gram and makes a dot plot of the data. The masses are: 5.3, 5.5, 5.6, 5.4, 5.4, 5.3, 5.8, 5.7, 5.8, 5.5, 5.5, and 5.3 grams. She lists two numbers on the number line. How many more numbers will she put on the number line?
Answers:
A: 2
B: 3
C: 4
D: 5
Answer:
A:2
Step-by-step explanation:
Expand the function.
f(x) = (3x-4)4
81x4 − 432x³ + [? ]x²
+
-
X +
PLS HELP
The expansion of the function \((3x - 4)^4\) simplifies to \(81x^4 - 432x^3 + 864x^2 - 768x + 256.\)
To expand the function \(f(x) = (3x - 4)^4\), we can use the binomial theorem. According to the binomial theorem, for any real numbers a and b and a positive integer n, the expansion of \((a + b)^n\) can be written as:
\((a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^{(n-1)} b^1 + C(n, 2)a^{(n-2)} b^2 + ... + C(n, n-1)a^1 b^{(n-1)} + C(n, n)a^0 b^n\)
where C(n, k) represents the binomial coefficient, which is given by C(n, k) = n! / (k!(n-k)!).
Applying this formula to our function \(f(x) = (3x - 4)^4\), we have:
\(f(x) = C(4, 0)(3x)^4 (-4)^0 + C(4, 1)(3x)^3 (-4)^1 + C(4, 2)(3x)^2 (-4)^2 + C(4, 3)(3x)^1 (-4)^3 + C(4, 4)(3x)^0 (-4)^4\)
Simplifying each term, we get:
\(f(x) = 81x^4 + (-432x^3) + 864x^2 + (-768x) + 256\)
Therefore, the expanded form of the function \(f(x) = (3x - 4)^4\) is \(81x^4 - 432x^3 + 864x^2 - 768x + 256\).
Note that the coefficient of \(x^3\) is -432, the coefficient of \(x^2\) is 864, the coefficient of x is -768, and the constant term is 256.
For more question on function visit:
https://brainly.com/question/11624077
#SPJ8
Note the complete question is
I NEED HELP ON C,E,F,G PLEASE ASAP!!!!
the sum of three consecutive integers is 78. what are the three Integers
Answer:
25, 26, and 27 are the three consecutive integers.
Step-by-step explanation:
Let the numbers be represented as x, x + 1 and x + 2.
We can write the equation:
\(x+(x+1)+ (x+2)=78\)
Opening the brackets and simplifying:
\(x+x+1+x+2=78\)
\(3x+3=78\)
Subtract 3 from both sides.
\(3x=75\)
Divide both sides by 3.
\(x=25\)
Since the three consecutive integers are x, x + 1 and x + 2, replace x with 25.
∴ 25, 26 and 27 are the three consecutive integers.
Answer:
25 , 26 and 27
Step-by-step explanation:
48=5(10+z)+18 easy points:)
Answer: z = -4
Step-by-step explanation: I thinks
Answer:
z=-4
Step-by-step explanation:
48=50+5z+18
48=68+5z
-20/5=5z/5
-4=z
Graph the parabola y=-3x^2+24x-42
There are 18 boys in a class. There are a fewer boys than girls. How many students are there?
pls help with exterior angles. le annoying
Answer:
8π/45 rad or 0.558505
Step-by-step explanation:
to convert into radian measure, multiply by π/180° rad
32°x π/180° rad
reduce the expression with 4° = 8 x π/45 rad
calculate the product = 8π/45 rad
you get
8π/45 rad
alternate form:
0.558505
SLOPE DIGITAL ESCAPE ROOM
I need help finding the code
By finding all the four slopes, we can see that the word is ECHA.
How to find the word?We know that the general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
We know that if the line passes through (x₁, y₁) and (x₂, y₂) then the slope is:
s = (y₂ - y₁)/(x₂ - x₁)
With that formula we can get the slopes.
1) Using the points (0, 3) and (2, 4).
m = (4 - 3)/(2 - 0) = 1/2, so the letter is E.
2)Using (-1, -12) and (1, -8)
m = (-8 + 12)/(1 + 1) = 4/2 = 2, so the letter is C.
3) We have (2, -6) and (-4, -3) so:
m = (-3 + 6)/(-4 - 2) = 3/-6 = -1/2, so the letter is H
4)we can use the points (0, 3) and (1, 1), so:
m = (1 - 3)/(1 - 0) = -2, so the letter is A
Then the word is ECHA
Learn more about slopes at:
https://brainly.com/question/3493733
#SPJ1
How do find the median and range..?
give examples!
Answer:
Count how many numbers you have. If you have an odd number, divide by 2 and round up to get the position of the median number. If you have an even number, divide by 2. Go to the number in that position and average it with the number in the next higher position to get the median.
The range is calculated by subtracting the lowest value from the highest value.
Step-by-step explanation:
hope this helped!
Answer:
It is the number in the middle of a set of numbers arranged in ascending order, it will be easier to find median if the set of given numbers are even if its an odd number, then divide the number by 2.
To find the range subtract the lowest value from the highest value
Step-by-step explanation:
What is the theoretical probability of rolling a sum of 6 on one roll of two standard number cubes?
Answer:
Hi there, the answer is 5 / 36
Draw the net and calculate the surface area .
Hello!
surface area
= 2(4 x 2) + 2(12 x 4) + 2(12 x 2)
= 160cm²
You draw a rectangle with vertices at (-3.5,3), (3.5,3), (3.5,-3), and (-3.5,-3).
What is the perimeter and area of the rectangle?
The perimeter and the area of the rectangle are 26 units and 42 square units, respectively.
What is a rectangle?A rectangle is a quadrilateral with all four interior angles 90°.
Given that, the vertices of the rectangle are (-3.5,3), (3.5,3), (3.5,-3), and (-3.5,-3).
The length of the rectangle is:
l = 3.5 - (-3.5)
l = 3.5 + 3.5
l = 7
The width of the rectangle is:
w = 3-(-3)
w = 3 + 3
w = 6
The perimeter of the rectangle is given by:
P = 2 (l +w)
P = 2(7 + 6)
P = 26
The area of the rectangle is:
A = l × w
A = 7 × 6
A = 42
Hence, the perimeter and the area of the rectangle are 26 units and 42 square units, respectively.
Learn more on rectangles here:
https://brainly.com/question/15019502
#SPJ1
Please Help
Find (f+g)(x)if f(x)=4x2-5x+8 and g(x)=2x2+x-2
Answer: (f+g)(x) = 6x²- 4x + 6
Step-by-step explanation:
We add f(x) and g(x) together, (4x²-5x+8) + (2x²+x-2)
Add like terms together, (4x²+2x²) + (-5x+x) +(8-2)
We are left with (f+g)(x) = 6x²- 4x + 6
13 out of 25 people agreed to help at a charity event. What percentage is
this?
21 out of 40 children arrived on time. What percentage were late? *
Find the percentage
A French test is out of 48 marks.
Simone scores 30 marks.
What is Simone's score as a percentage?
Answer:
Hi! The correct answer is 3.25, 7.6 and 0.3!
Step-by-step explanation:
30A cartographer used a scale of 1 inch:300 meters for the heights of differentmountains. If the actual height of one of those mountains is 3,600 meters, what is itsheight on the map?1,080,000 inches108 inches100 inches12 inchesI don't knowOne attempt
1 inch : 300 meters
3600 m
\(3600m\cdot\frac{1in}{300m}=12in\)With the given scale factor 3600m is equivalent to 12 inches
Graph the image of the polygon after the given rotation. 90 degrees
Answer:
qqqqqqqqqqqqqqqqqqqqqqqq
Given the definitions of f(x) and g(x) below, find the value of (fog)(-3).
f(x) = 3x² - 7x-3
g(x) = -4x - 10
The value of the composite function (f o g)(3) is 1603
How to evaluate the composite function?The functions are given as
f(x) = 3x² - 7x - 3
g(x) = -4x - 10
Next, calculate (f o g)(x) using
(f o g)(x) = f(g(x))
So, we have
(f o g)(x) = 3(-4x - 10)² - 7(-4x - 10) - 3
Substitute 3 for x.
So, we have
(f o g)(3) = 3(-4 x 3 - 10)² - 7(-4 x 3 - 10) - 3
Evaluate
(f o g)(3) = 1603
Hence, the value of the composite function (f o g)(3) is 1603
Read more about composite function at
https://brainly.com/question/10687170
#SPJ1
A half circle is joined to an equilateral triangle with side lengths of 12 units.Select all the expressions that correctly calculate the perimeter of the shape.
The perimeter of the figure described in the question is 42.84cm
How to get the perimeter of the figure?The figure is defined by a half circle is joined to an equilateral triangle with side lengths of 12 units.
So the perimeter of the figure will be equal to half of the circumference of the triangle plus the length of the two exposed sides of the triangle.
The diameter of the circle will also be 12 units, remember that the circumference of a circle of diameter D is:
C = 3.14*D
In this case, the circumference of half circle is:
C = 3.14*D/2
Replacing the value of the diameter:
C = 3.14*12cm/2 = 18.84cm
Adding the two sides of the triangle we get the perimeter.
P = 18.84cm + 2*12cm = 42.84cm
Learn more about perimeter:
https://brainly.com/question/24571594
#SPJ1
PLS HELP ASAP
Write a word problem that can be represented by the expression 5/6 divided by 1/3.
Answer:
I have 5/6 of a candy bad and I want to give each of my 3 friends some. How much would each friend get?
Step-by-step explanation:
The word problem that can be represented by the expression 5/6 divided by 1/3 is "There are a total of 5/6 chocolates. Divide these chocolates such that each person will get 1/3 part of that".
Given :
The expression 5/6 is divided by 1/3.
The following steps can be used in order to determine the word problem that can be represented by the expression 5/6 divided by 1/3:
Step 1 - The knowledge of arithmetic operations can be used in order to determine the word problem that can be represented by the expression 5/6 divided by 1/3.
Step 2 - There are a total of 5/6 chocolates. Divide these chocolates such that each person will get 1/3 part of that.
Step 3 - Solve the above problem by dividing 5/6 by 1/3.
\(= \dfrac{5\times 3}{6\times 1}\)
= 2.5
For more information, refer to the link given below:
https://brainly.com/question/25834626
3. Determine if the graph below is a function.
Explain your reasoning.
Answer:
A function defines one variable in terms of another. The statement "y is a function of x" (denoted y = y(x)) means that y varies according to whatever value x takes on. A causal relationship is often implied (i.e. "x causes y"), but does not *necessarily* exist.
Step-by-step explanation:
Area is measured in square units. This means that if we divide the shape into squares that are equal in size and count them up, the area is the total number of squares. Square units are always one unit of length long and one unit of length wide. In the song, the unit of length we use is feet. So each square unit is one foot long and one foot wide, or one square foot. Since there are 72 of these units in total, we say the area is 72 square feet. Square units can use other units of length, like inches or miles. Make sure you know what unit of length you’re using.
Jason is finding the area of a rectangle that is 7 inches long and 4 inches wide. Jason says the area of the rectangle is 28 inches. Is Jason correct or incorrect?
A: Jason is correct because 7 x 4 = 28.
B: Jason is incorrect because the area is 28 square inches.
C: Jason is incorrect because 7 + 4 = 11.
D: Jason is incorrect because the area is 28 square feet.
Answer:
B
Step-by-step explanation:
Area is always squared; area of a rectangle is length x width so 7*4= 24in^2
If this answer helped you I would greatly appreciate brainliest :D.
The ratio of hotdogs sold to hamburgers sold was 10:7.
If 120 hotdogs were sold, how many hamburgers were sold?
Answer:84
Step-by-step explanation:
Answer:
84 hamburgers were sold
The sum of 8 times a number 6 and 4 equals .
Use the variable x for the unknown number.
Answer:
ளுக்கு ஜபல் men's rfugtzxhxxb+_*+_*5#-, '! \(4874 < < ( {55.1 + \times 222y).248 {11243 = 16463xy > < | \leqslant | }^{?} }^{?} \)