The number of gums available, with the 12 boxes, each containing 12 dozens of gums and one open box containing 32 gums, found using the values of the non verbal units of measure, indicates that the number of gums are 1760 gums.
What is a non verbal unit of measure?Non verbal units of measure are used to describe the quantity of an item using verbal terms such as pairs (2 units), dozens (12 units), scores (20 units), gross (12 dozens or 144 units), bushels (8 gallons or 4 pecks), ream (500 units).
The number of dozens of pieces of gum are in a box = 12 dozens
The number of boxes of gum available = 12 boxes
The remaining number of gums = 1 open box with 32 gums
1 dozen of an items = 12 units of the specified item
12 dozens of an item = 1 gross of the item
The number of pieces of gums in a box, therefore is 1 gross of gums.
Therefore, the number of pieces of gum in all = 12 × 12 × 12 + 32 = 1760
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A circle with a radius 7 cm long is centered at an angle's vertex, and the angle's rays subtend an arc length of 15 cm along the circle. The subtended arc is how many times as long as the circle's radius? 07 _ 15 = 8 O15 _ 7 = 8 7 0.467 15 15 0.341 2T0 15 2.143
The subtended arc is 2.14 times as long as the circle's radius.
What is radius of circle?
A circle or sphere's radius is any line segment that connects the object's center to its perimeter in classical geometry; in more contemporary usage, it also refers to the length of those line segments. The word "radius" is derived from Latin and means "ray" as well as "the spoke of a chariot wheel."
Given:
A circle with a radius 7 cm long is centered at an angle's vertex, and the angle's rays subtend an arc length of 15 cm along the circle.
The radius of the circle is 7 and length of the subtend are is 15 cm. The required value is given by:
Subtended arc / Radius = 15 / 7 = 2.14
Therefore, option (e) is the correct answer.
Hence, the subtended arc is 2.14 times as long as the circle's radius.
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What is the length hypotenuse of a right triangle with legs 8 units and 6 units?; What is the length of the hypotenuse for a right triangle with leg a 8 and leg B 15?; How do you find the length of one leg of a right triangle?; How do you find the length of the legs of a right triangle with the hypotenuse?
The length of the hypotenuse with legs 8 units and 6 units is 10 units and with leg 8 units and 15 units is 17 units. We calculate the length of a leg of the right triangle by using formula [tex]h ^ {2} = p ^ {2} + b ^{2}[/tex]
What is a right-angle triangle?If one of the angles in a triangle is 90 degrees, the triangle is said to have a right angle. The term "right angle" refers to angles in right triangles that are 90 degrees. The side opposite in a 90° angle is the hypotenuse. The hypotenuse is always the longest side. The sum of the other two inner angles is 90 degrees.
What is the Pythagorean theorem for right angle triangle?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.
length of legs = 8 units and 6 units
hypotenuse = [tex]\sqrt {8 ^ {2}+6 ^ {2}}[/tex] = 10 units
length of legs = 8 units and 15 units
hypotenuse = [tex]\sqrt {8 ^ {2}+15 ^ {2}}[/tex] = 17 units
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Determine which integers in the set S: {−2, −3, −4, −5} will make the inequality 2p − 8 < 5p + 4 true.
S:{−2, −3}
S:{−3, −4}
S:{−4, −5}
S:{−2, −5}
Answer:
A
Step-by-step explanation:
2p - 5p < 8 + 4
- 3p < 12
-3/-3 p > 12/-3
p > -4
-2, - 3
A rectangle measures 75 cm by 15 cm.Find the length of the perimeter?
Answer:
P = 180 cm
Step-by-step explanation:
A rectangle measures 75 cm by 15 cm.Find the length of the perimeter?
P = (L + W) × 2P = (75 + 15) x 2
P = 90 x 2
P = 180 cm
Solve by using substitution. Express your answer as an ordered pair.
{4x+y=1
y=x−4
Answer:
The correct answer is (1, -3).
Step-by-step explanation:
To solve this question, we should use substitution. This means we can substitute the value given for y (as indicated by the second equation) into the first equation. This is shown below:
4x + y = 1
4x + (x - 4) = 1
We simplify the left side of the equation and then solve for x.
5x - 4 = 1
5x = 5
x = 1
We must also solve for y. To do this, we can plug in x = 1 into either of the given equations.
y = x - 4
y = 1 - 4
y = -3
Therefore, x = 1 and y = -3. The question asks us to express the answer as an ordered pair (x,y), so the answer is (1, -3).
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Which of the following statements is TRUE? O a. If f(a) and g(x) are differentiable functions defined on the closed interval [a, b], and f(x) attains its global maximum at x = c and g(x) attains its global maximum at x = d, then the function f(x) · g(x) attains its global maximum on [a, b] at x = cºd. O b. All of the statements are false. a O c. Every local maximum is a global maximum d. The global maximum value of a differentiable function f(x) on a closed interval (a, b) must occur at a critical value or an endpoint e. The critical points of f'(2) are same as the critical points of f(x)
ANSWER
c
It is c because i did the work and i know.
Determine whether AB and XY are parallel, perpendicular, or neither. Graph each line to verify your answer. A(8, 1), B(-2, 7), X(-6, 2), Y(-1, 1)
The slope of the line AB and XY is different. Then the line AB and XY is neither parallel nor perpendicular. The lines are intersecting line.
What is the slope?The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.
The slope of the line is given as,
m = (y₂ - y₁) / (x₂ - x₁)
The points are given as,
A(8, 1), B(-2, 7), X(-6, 2), Y(-1, 1)
The slope of line AB is given as
m₁ = (7 - 1) / (-2 - 8)
m₁ = 6 / (-10)
m₁ = - 0.6
The slope of line XY is given as
m₂ = (1 - 2) / (-1 + 6)
m₂ = - 1 / (5)
m₂ = - 0.2
The slope of the line AB and XY is different. Then the line AB and XY is neither parallel nor perpendicular. The lines are intersecting line.
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Roy is skiing on a circular ski trail that has a radius of 0.7 km. Roy starts at the 3-o'clock position and travels 2.15 km in the counter-clockwise direction. a. How many radians does Roy sweep out? _____ radians Preview b. When Roy stops skiing, how many km is Roy to the right of the center of the ski trail? _____ v km Preview c. When Roy stops skiing, how many km is Roy above of the center of the ski trail? _____ * km
Part a: Roy sweeps out 2.15/0.7 radians.
Part b: When Roy stops skiing, he is cos(3.071)(0.7) km to the center of the ski trial
Part c: When Roy stops skiing he is sin(3.071)(0.7) km above the centre of the ski trail
The radius of the ski trail= 0.7 km
Roy starts 3 o'clock position and travels 2.15 km in the counter-clockwise direction.
Let O be the centre of ski trial, A be the starting point(3-o'clock position) and consider he is now at point B.
Now, using the formula for arc length.
Arc length=(Radius)(angle at center)
2.15=(0.7)θ
θ=2.15/0.7
Roy sweep out 2.15/0.7 radians.
Part b:
When Roy stops skiing how many km is Roy to the right of the ski trial
In part, a figure draws the vertical line from point B on the horizontal line. Get the right-angle triangle
Here to find the length OP. In right angle triangle cos θ=Adjacent side/hypotenuse,
As in part, a central angle is 2.15/0.7=3.071.
Therefore,
cos(3.071)=OP/0.7
OP=cos(3.071)(0.7)
cos(3.071)(0.7) km.
Part c:
When Roy stops skiing how many km is Roy above the centre of the ski trial
From figure part of part b, we have to calculate side BP.
In right angle triangle sin(θ)=Opposite side/hypotenuse
Therefore,
sin(3.071)=BP/0.7
BP=sin(3.071)/(0.7)
sin(3.071)(0.7) km.
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an = r·(an-1)
determine the recrusive function to model the geometric sequence.
24, 6, 1.5
show work
On solving the provided question, we got to know that - recursive function to model the geometric sequence is 0.25
What is recursive function?In order to create a sequence of terms, a recursive function either repeats itself or uses a previous term to compute a new term. An arithmetic-geometric series with terms that differ from each other frequently is used to explain this function.
Given, geometric sequence
24, 6, 1.5
First term of this sequence = 6
a1 = 6
Recursive formula geometric sequence
[tex]a_{n} = a_{(n-1)}r[/tex]
[tex]Here r = common. ratio .of .successive. and previous term\\From .the given .sequence\\[/tex]
r = a2/a1
r = 6/24
r = 0.25
[tex]Recursive formula of the given sequence will be,[/tex]
[tex]a_{n} = a_{(n-1)}(0.25)[/tex]
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which graph represents the function fx x2 5
In the picture we can see the graph represents of the function f(x)=-x²+5 that is curve graph.
Given that,
We have to find the graph represents the function f(x)=-x²+5.
We know that,
The quadratic function is f(x)=-x²+5.
This is a vertical parabola open downward
The vertex is a maximum
We know,
A vertical parabola's equation in vertex form is equal to
y= a(x-h)²+k
where
a is a coefficient
(h,k) is the vertex
Here
a=-1
(h,k)=(0,5) is vertex
The y-intercept is the point (0,5) is value of y when the value of x is equal to zero (is the same point that the vertex)
The x-intercepts are the points is values of x when the value of y is equal to zero
Therefore, In the picture we can see the graph represents of the function f(x)=-x²+5.
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bro just help me pks
Answer:
6
Step-by-step explanation:
3 is 3/5 of 5 therefore 6 would be 3/5 of 10 and the triangles are similar so
Houa works at an electronics store as a salesperson. Houa earns a 9% commission on the total dollar amount of all phone sales she makes, and earns a 6% commission on all computer sales. Houa made a total of $1700 in sales and earned $135 in commission. Write a system of equations that could be used to determine the dollar amount of phone sales Houa made and the dollar amount of computer sales she made. Define the variables that you use to write the system.
The required amount for phone and computer sales is $1100 and $600 respectively.
Given that,
Houa works at an electronics store as a salesperson. Houa earns a 9% commission on the total dollar amount of all phone sales she makes and earns a 6% commission on all computer sales. Houa made a total of $1700 in sales and earned $135 in commission.
What are simultaneous linear equations?
Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
here,
Let the number of phone sales be x and the number of computer sales be y,
According to the question,
0.09x+0.06y=135, - - - - - (1}
x+y=1700 - - - - - - - (2)
Solving equation 1 and 2
Gives, x = $1100 and $600
Thus, the required amount for phone and computer sales is $1100 and $600 respectively.
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McDonald’s Corp (MCD) stock is selling for $90.24 per share. They offer a dividend of $2.80 per share. What is the stock yield? (Round to nearest tenth.)
Multiple Choice
3.1%
.031%
5.8%
.059%
The value of the stock yield will be;
⇒ 3.1%
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
McDonald’s Corp (MCD) stock is selling for $90.24 per share.
And, They offer a dividend of $2.80 per share.
Now,
Since, McDonald’s Corp (MCD) stock is selling for $90.24 per share.
And, They offer a dividend of $2.80 per share.
Hence, The value of the stock yield is;
⇒ 2.80/90.24 × 100
⇒ 0.0310 × 100
⇒ 3.1%
Thus, The value of the stock yield will be;
⇒ 3.1%
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9. Which graph shows the following system of equations and its solution?
[-2x-y=-2
13x-y=-2
I WILL GIVE BRANILIEST
The graph of the system of equations -2x - y = -2 and 13x - y = -2 is attached and the solution is
(0, 2)
How to get solutions using graphical methodGraphs are plotted using the input values in the x coordinates and the output in the y coordinate
assuming an input of -4 0 4 we calculate the output for the graphs as
-2x - y = -2
y = -2x + 2
For x = -4, y = -2 * -4 + 2 = 10
For x = 0, y = -2 * 0 + 2 = 2
For x = 4, y = -2 * 4 + 2 = -6
table of values
x y
-4 10
0 2
4 -6
13x - y = -2 rearranging gives y = 13x + 2
y = 13x + 2
For x = -4, y = 13 * -4 + 2 = -50
For x = 0, y = 13 * 0 + 2 = 2
For x = 4, y = 13 * 4 + 2 = 54
table of values
x y
-4 -50
0 2
4 54
The point of intersection of the two line is the solution and this is (0, 2)
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Blood pressure in a population of very at risk people has expected value of 195 and a standard deviation of 20. Suppose you take a random sample of 100 of these people: There would be a 68% chance that the average blood pressure would be between Select one: 155 to 235 193 to 197 175 to 215 191 to 199 200 to 230
There would be a 68% chance that the average blood pressure would be between 193 to 197.
The subset chosen from the larger set to make assumptions is known as a random sample. A range of values is a confidence interval.
We know that,
E = z ( α / 2 ) × σ / √n → 1
As per the given question,
Blood pressure in a population of very at risk people has an expected value ( x ) = 195Standard deviation ( σ ) = 20Number of random samples ( n ) = 100For 68% confidence,
z ( α / 2 ) = 0.9944
Substitute the values in 1,
E = z ( α / 2 ) × σ / √n
= 0.9944 × 20 / √100
= 0.9944 × 20 / 10
= 0.9944 × 2
E = 1.9888 ≅ 1.99
Let us consider,
⇒ x - E < μ < x + E
⇒ 195 - 1.99 < μ < 195 + 1.99
⇒ 193.01 < μ < 196.99
⇒ 193 < μ < 197 ( ∵ 193.01 ≅ 193 and 196.99 ≅ 197 )
⇒ μ = ( 193 , 197 )
Therefore, A 68% chance that the average blood pressure lies between 193 to 197. Hence Option b is correct.
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The complete question is
Blood pressure in a population of very at risk people has an expected value of 195 and a standard deviation of 20. Suppose you take a random sample of 100 of these people. There would be a 68% chance that the average blood pressure would be between Select one:
a.) 155 to 235
b.) 193 to 197
c.) 175 to 215
d.) 191 to 199
e.) 200 to 230
st.asp?test=3&course_week=
27.6 yd
Find the circumference of the circle. Round the answer to the nearest tenth
The circumference of the given circle with the diameter 27.6 yards is 86.7 yards.
What is the circumference?The circumference is the length of any great circle, the intersection of the sphere with any plane passing through its center. A meridian is any great circle passing through a point designated a pole.
Given that, the diameter of circle is 27.6 yards
Radius of a circle is the distance from the center of the circle to any point on it's circumference and radius of a circle is half of Diameter.
That is, radius =Diameter/2
So, radius of circle =27.6/2 =13.8 yards
We know that, the circumference of the circle is 2πr
Now, circumference = 2×3.14×13.8
= 86.664
≈ 86.7 yards
Therefore, 86.7 yards is the circumference of the circle.
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The heights of people in a certain population are normally distributed with a mean of 67 inches and a standard deviation of 3.8 inches. Determine the sampling distribution (shape, center, spread) of the mean for samples of size 45 .
The shape of the sampling distribution of the mean for samples of size 45 will be normal.
This is because the sampling distribution of the mean approaches normality as the sample size increases. The center of the sampling distribution will be 67 inches, which is the mean height of the population. The spread of the sampling distribution will be determined by the standard deviation of the population and the sample size. Specifically, the standard deviation of the sampling distribution will be equal to the standard deviation of the population divided by the square root of the sample size. In this case, the standard deviation of the sampling distribution will be 3.8 inches / sqrt(45) = 0.55 inches.
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Find all solution for the angle “theta” and use “K” to be any integer cos(theta+pi/4)-cos(theta-pi/4)
The value of the given trigonometric function equation cos(θ + π/4) - cos(θ - π/4) will be -√2 sinθ.
What is a trigonometric function?The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.
The trigonometric function is very good and useful in real-life problems related to the right-angle triangle.
It is known that,
Cos(A + B) = cosAcosB - sinAsinB
Cost(A - B) = cosAcosB + sinAsinB
As per the given,
cos(θ + π/4) - cos(θ - π/4)
(cosθ cos π/4 - sinθ sin π/4) - (cosθ cos π/4 + sinθ sin π/4)
-2 sinθ sin π/4
-2 sinθ (1/√2)
-√2 sinθ
Hence "The value of the given trigonometric function equation cos(θ + π/4) - cos(θ - π/4) will be -√2 sinθ".
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A bullet train travels in 3 and half hours for 320 km. And ordinary train travels 212 km in 8 and half hours. Work out their average speed. I need it now pls be quick
The average speed of the trains are Bullet train = 91.4 km/hr and Ordinary train = 24.9 km/hr
How to determine the average speed of the trains?From the question, we have the following parameters that can be used in our computation:
Bullet train
Distance = 320 km
Time = 3 and half hours = 3.5
Ordinary train
Distance = 212 km
Time = 8 and half hours = 8.5
By definition, the speed of an object is the ratio of the distance moved by the object and the time travelled by the object
Mathematically, this can be represented as
Speed = Distance : Time
Express as fraction
Speed = Distance/Time
So, we have
Bullet train = 320/3.5 = 91.4
Ordinary train = 212/8.5 = 24.9
Hence, the speed of the ordinary train is 24.9 km per hour
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A line includes the points (4, 4) and (0, 3). What is its equation in slope-intercept form?
The required slope-intercept form of the equation of the line is y = x/4 + 3.
To determine the equation of the line in slope-intercept form passing through the points (4, 4) and (0, 3).
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
here,
m = (y₂ - y₁) / (x₂ - x₁)
Substitute the points,
m = [3 - 4] / [0 - 4]
m = 1 / 4
Standard equation of the line
y - y₁ = m (x - x₁)
Substitute one point and m in the above equaiton
y - 3 = 1/4 [x - 0]
y = x/4 + 3
Thus, the required slope-intercept form of the equation of the line is y = x/4 + 3.
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what is the solution to the system of equations x-y=-1 and x-3=- -13?
Answer:
Write in Standard Form
1. The standard form of a linear equation is
Ax + By = Cx-y=-1
2. x = 16
Ig?
I'm not sure.
What is the slope of a line parallel to the line whose equation is 2x y =- 7?; What is the slope of a line parallel to the line whose equation is Y =- 1 2x 3?; How do you find the slope of a parallel line?; Which is the equation of a line parallel to the line with the equation y 3x 5?
The slope of the line parallel to the given lines are as follow:
a. Slope of the line parallel to 2x + y = -7 is -2.
b. Slope of the line parallel to y = (- 1 + 2x) 3 is 6.
c. Slope of the parallel lines are always equal.
d. Equation parallel to the given line y = 3x -5 are y = 3x + c , c may have any real value.
As given in the question,
Slope of two or more parallel lines are always same.
Equation in the form y = mx + c ,
here 'm' is the slope.
a. Slope of the line parallel to 2x + y = -7
y = -2x -7
Slope of the line is -2.
Slope of the line parallel to the given line is -2.
b. y = (- 1 + 2x) 3
⇒ y = 6x -3
Slope of the line is 6 .
Slope of the line parallel to the given line is also 6.
c. Slope of the parallel lines are always equal.
d. Equation of the line parallel to the given line y = 3x -5 is given by:
y = 3x + c , here slope remain same only c value get change.
Therefore, slope of the given lines are:
a. Slope of the line parallel to 2x + y = -7 is -2.
b. Slope of the line parallel to y = (- 1 + 2x) 3 is 6.
c. Slope of the parallel lines are always equal.
d. Equation parallel to the given line y = 3x -5 are y = 3x + c , c may have any real value
The complete question is:
a. What is the slope of a line parallel to the line whose equation is
2x + y =- 7?
b. What is the slope of a line parallel to the line whose equation is
Y = (- 1 + 2x) 3 ?
c. How do you find the slope of a parallel line?
d. Which is the equation of a line parallel to the line with equation y=3x- 5?
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How much money should be deposited today in an account that earns 4% compounded monthly so that it will accumulate to 12000 dollars in three years?
$9483.774 money should be deposited in the account.
Let the amount to be invested be P=$x so that the amount accumulated is A = $12000. We have t=3 years. The rate of interest is r=0.04 per year. n = 2 as interest will be compounded twice a year.
What is interest?
Interest, in its most simple form, is calculated as a percent of the principal.
Interest is the amount of money a lender or financial institution receives for lending out money. Interest can also refer to the amount of ownership a stockholder has in a company, usually expressed as a percentage.
Now,
[tex]x (1 + \frac{0.04}{2} )^{2 * 3}[/tex] [tex]= 12000[/tex]
[tex]x(1.04)^{6}[/tex] [tex]= 12000[/tex]
[tex]x = \frac{12000}{(1.04)^{6} }[/tex]
≈ 9483.774
∴ Amount invested ≈ $9483.774.
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HELP ME QUICICICKCKC
Answer:
A.
Step-by-step explanation:
Multiply the x like terms than multiply the other like terms
What are all the real zeros of y=(x-12)3-7?
The real zeros in the given equation y = (x-12)³ - 7 will be x = 13.912.
For the real solutions, we know that a real zero is a real number which makes the value of the function zero. By the question, let
y = 0 ..........(1)
Put values of 'y' in equation (1), and we get.
(x-12)³ - 7 = 0 .........(2)
Adding '7' on both sides of equation (2), we get
(x-12)³ = 7
Taking the cube root on sides, the resulting equation will be:
[tex]\sqrt[3]{(x-12)^{3} }[/tex] = [tex]\sqrt[3]{7}[/tex]
x - 12 = 1.912
By adding '12' on both sides.
x = 13.912
So the only real zeros for the given equation will be 13.912. Other solutions are imaginary zeros.
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sorry for asking to much its cause i dont understand please help. whats the answer
The difference between the numbers 4.7 and 2.3 is 2.4
what is number line ?
The visual representation of numbers on a straight line is called a number line. On an endless line that extends on both sides, either horizontally or vertically, this line is used to compare numbers that are spaced at equal intervals. The numbers on a horizontal number line grow as we approach towards the right side and drop as we move towards the left.
Between 4 and 5 , there are 10 divisions. Each division shows the value 0.1.
So, 4.7 is marked as shown in the figure.
To find the difference 4.7 - 2.3 , reverse the direction by 2.3 units from 4.7, will give us 2.4..
So, the difference between 4.7 and 2.3 is 2.4
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you are using the plus sign more than once in the example of 2+3=4+5
Answer:
2-3=4-5
Step-by-step explanation:
:) anything helps. I dont understand
The values of x in the triangles are (a) 15 and (b) 4
How to determine the values of x in the figures?From the question, we have the following parameters that can be used in our computation:
Triangle 1 and Triangle 2
Solving triangle 1
In this triangle, we can see that the side lengths of the triangles are congruent
This means that the triangles is an equilateral triangle
The individual angles in an equilateral triangle are 60 degrees
So, we have the following representation
4x = 60
Divide both sides of the equation by 4
x = 15
So, the value of x is 15
Solving triangle 2
In this triangle, we can see that the length KM of the triangle divides the length JL into congruent parts
This means that the JM and LM are congruent
So, we have the following representation
x + 1 = 5
Subtract from both sides of the equation by 1
x = 4
So, the value of x is 4
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what's 2| -9| - | -2|
Answer:
9
Step-by-step explanation:
2|-9| - |-2|
=2+9-2 the negative number becomes positve when it come out of absolute value
=11-2
=9
SOMEONE HELP ME
Solve. 35.1 = 12.9 + 10.2x Enter your answer as a mixed number in simplest form in the box.
Solving the expression 35.1 = 12.9 + 10.2x gives x to be 2 3/17
What is algebraic expression?A group of numbers or variables coupled with the operations +, -,, or form an expression.
Algebraic expressions with variables, numbers, and mathematical operators, as opposed to arithmetic expressions that simply contain numbers and mathematical operators.
How to find the value of xThe given algebraic expression is 35.1 = 12.9 + 10.2x
solving for x
35.1 - 12.9 = 10.2x
10.2x = 22.2
x = 22.2/ 10.2
x = 2 3/17 as a mixed number in simplest form
the value of x is 2 3/17
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