Company Price Per Share Devidend
a. The regression equation is: y = 24.659 + 1.8435x
b-2. H0 is the null hypothesis (b1 = 0), t is the test statistic, and tc is the critical value from the t-distribution with n-2 degrees of freedom.
b-3. The t-statistic: t = (b1 - 0)/SEb1 = 7.7083
c. R² = 0.3703
d-1. The correlation coefficient is 0.9873.
e. The predicted price per share for a dividend of [tex]$10[/tex] is [tex]$8.1189[/tex].
f. The 95% prediction interval of price per share for a dividend of [tex]$10[/tex] is [tex]($7.1059, $9.1319)[/tex].
The regression equation that predicts price per share based on the annual dividend, we need to perform a linear regression analysis.
Using a statistical software or calculator, we obtain the following regression equation:
Price per share = -30.0145 + 2.1132 × Dividend
The regression equation that predicts price per share based on the annual dividend is:
Price per share = -30.0145 + 2.1132 × Dividend
The decision rule for testing the significance of the regression slope coefficient at the 0.05 significance level is:
Reject the null hypothesis if the p-value is less than 0.05.
To compute the value of the test statistic, we need to perform a hypothesis test on the slope coefficient using the regression output.
The null hypothesis is that the slope coefficient is zero, and the alternative hypothesis is that the slope coefficient is not zero.
Using the regression output, we obtain the following results:
Slope coefficient (b1) = 2.1132
Standard error (SE) = 0.1988
Degrees of freedom (df) = 28
t-statistic = b1 / SE = 2.1132 / 0.1988 = 10.6178
p-value = P(|t| > 10.6178) < 0.0001
The value of the test statistic is 10.6178.
The coefficient of determination, denoted by R², measures the proportion of variation in the dependent variable (price per share) that is explained by the independent variable (dividend).
Using the regression output, we obtain R² = 0.9748.
The coefficient of determination is 0.9748.
The correlation coefficient, denoted by r, measures the strength and direction of the linear relationship between the two variables.
Using the regression output, we obtain r = 0.9873.
The correlation coefficient is 0.9873.
To predict the price per share for a dividend of [tex]$10[/tex], we plug in the value of 10 for Dividend in the regression equation:
Price per share = -30.0145 + 2.1132 × 10 = [tex]$8.1189[/tex]
The predicted price per share for a dividend of [tex]$10[/tex] is [tex]$8.1189[/tex].
The 95% prediction interval of price per share for a dividend of [tex]$10[/tex], we use the following formula:
y = b0 + b1x ± tα/2, n-2 × SE (y -hat)
where y-hat is the predicted value of price per share for a dividend of $10, SE (y -hat) is the standard error of the estimate, n is the sample size, and tα/2, n-2 is the t-value from the t-distribution with n-2 degrees of freedom and a significance level of α/2 = 0.025. Using the regression output, we obtain:
y-hat = -30.0145 + 2.1132 × 10 = [tex]$8.1189[/tex]
SE(y -hat) = 0.5079
n = 30
tα/2, n-2 = 2.0452 (from the t-distribution table)
Substituting these values, we obtain:
95% prediction interval =[tex]$8.1189 \pm 2.0452 \times 0.5079[/tex] = [tex]($7.1059, $9.1319)[/tex]
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a. The regression equation that predicts price per share based on the annual dividend is: Price per share = -2.8991 + 0.6761 * Dividend.
b-2. The decision rule states that if the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis. b-3. The value of the test statistic is 4.6053. c. The coefficient of determination (R-squared) is 0.5063.
d-1. The correlation coefficient is 0.7113. e. If the dividend is $10, the predicted price per share is $13.8629. f. The 95% prediction interval of price per share, given a dividend of $10, is approximately $9.2236 to $18.5023.
To calculate these values, linear regression is performed on the given data. The regression equation is obtained, indicating the relationship between price per share and the annual dividend.
The decision rule is based on the significance level, determining the critical value for hypothesis testing. The test statistic is calculated to assess the significance of the regression coefficient. The coefficient of determination measures the proportion of the variation in price per share explained by the dividend.
The correlation coefficient quantifies the strength and direction of the linear relationship. Finally, using the regression equation, the predicted price per share for a given dividend value and the prediction interval are determined.
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The constant of 2/3 cupcakes per minute means that in a minute, 2/3 of a cupcake is made.
Given the graph of w(x), w(2) = ?
(the graph is below)
Based on the graph of the cupcakes done, we find that w(2) = 5.
How many cupcakes are made by the cooker?
Herein we have an application of linear equations to the production of cupcakes. In accordance with the graph, the horizontal axis is for the preparation time (x) and the vertical axis is for the quantity of cupcakes done (w). Based on the graph, we find that w(2) = 5.
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Scott counted 23 beats in 10 seconds. What is his approximate heart rate?
123 bpm
130 bpm
138 bpm
230 bpm
Anyone is here
Answer:
138
Step-by-step explanation:
There is 60 seconds in a minute, so if the heart beats 23 times in 10 seconds, it is 138 bpm.
23 * 6 = 138
How many distinct triangles can be formed for which m∠E = 64°, g = 9, and e = 10?
triangle(s)
Using the law of sines, it is found that 1 triangle can be formed with the given conditions.
What is the law of sines?Suppose we have a triangle in which:
The length of the side opposite to angle A is a.The length of the side opposite to angle B is b.The length of the side opposite to angle C is c.The lengths and the sine of the angles are related as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
Hence, for this problem, we have that the relation is:
[tex]\frac{\sin{64^\circ}}{10} = \frac{\sin{G}}{9}[/tex]
[tex]\sin{G} = 0.9\sin{64^\circ}[/tex]
[tex]\sin{G} = 0.8089[/tex]
[tex]G = \arcsin{0.8089}[/tex]
G = 54º
A triangle can have one angle of 64º and another of 54º, hence 1 triangle can be formed with the given conditions.
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determine the slope of the line
Answer: -1/2
Step-by-step explanation:
The slope of a line tells you how steep the line is, and what direction it is going in. We can calculate the slope by seeing how much the line moves horizontally and vertically.
We can calculate the slope using [tex]\frac{rise}{run}[/tex], which is how much a point rises (goes up or down) and runs (goes left or right) to go to the next point.
Let's take two points on the graph: (-2, 0) and (0, -4). The rise will be the difference of the y-values, and the run will be the difference of the x-values.
[tex]\frac{-2-0}{0-(-4)}=\frac{-2}{4}=\frac{-1}{2}[/tex]
Hence, the slope of this line is [tex]\frac{-1}{2}[/tex]
If three different orders are selected, find the probability that they are all from Restaurant B
If three different orders are selected, find the probability that they are all from Restaurant B is; 0.026
How to find the probability?Total orders both accurate and not accurate = 1131
Total orders from restaurant B (both accurate and not accurate) = 337
Probability of first order from B = 337/1131
Probability of second order from B = 336/1130
Probability of third order from B = 335/1129
Probability of the first three orders from B = 337/1131 × 336/1130 × 335/1129
Probability of the first three orders from B = 0.026
Complete question is;
Use the data in the following table , which lists drive - thru order accuracy at popular fast food chains Assume that orders are randomly selected from those included in the table Drive thru Restaurant A B C D Order Accurate 312 277 250 144 Order Not Accurate 32 60 37 19 If three different orders are selected , find the probability that they are all from restaurant A
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The triangles are similar. Find the value of the variable.
Please help me! Giving brainliest!
Identify the surface area
A. S=2332 m²
B. S=2283 m²
C. S=2234 m²
D. S=1919 m²
Using it's formula, the surface area of the figure is:
A. S=2332 m²
What is the surface area of a rectangular prism?The surface area of a rectangular prism of dimensions l, w and h is given by:
S = 2(lw + lh + wh)
In this problem, the dimensions are:
35m, 9m, 16m
Hence the surface area of the rectangular prism is:
S = 2(35 x 9 + 35 x 16 + 16 x 9) = 2038 m².
What is the surface area of a cube?The surface area of a cube of side length l is given by:
S = 6l².
In this problem, we have that l = 7 m, hence the surface area is:
S = 6 x 7² = 294 m².
What is the total surface area?
The total surface area is the sum of the surface areas, hence:
T = 2038 m² + 294 m² = 2332 m².
Which means that option A is correct.
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What is the polar form of -2√3-6i ?
Any complex number [tex]z[/tex] can be written in polar/exponential form as
[tex]z = |z| e^{i\arg(z)} = |z| (\cos(\arg(z)) + i \sin(\arg(z)))[/tex]
In the complex plane, the given complex number belongs to the third quadrant since both its real and imaginary parts are negative. This means the argument must be between π and 3π/2, so the first two options are eliminated.
The difference between the remaining two options is the coefficient [tex]|z|[/tex]. We have
[tex]z = -2\sqrt3 - 6i \implies |z| = \sqrt{(-2\sqrt3)^2 + (-6)^2} = 4\sqrt3[/tex]
so (D) (the last option) is the correct choice.
Question 6 (1 point)
Find m/RST.
(4x-24)
U
S/(3x)*
O a m/RST = 72°
Ob
mZRST 108⁰
Oc
mZRST = 156°
Od mZRST = 24°
Answer:
72°
Step-by-step explanation:
3x = 4x - 24 (alternate exterior angles theorem)
x = 24
So, angle RST measures 72°.
Find the probability of randomly selecting 3 red pencils from a box containing 5 red, 3 blue, and 4 green pencils.
The probability of selecting 3 pencils from a box of 5 red , 3 blue, 4 green pencils is 60/1320.
Given that box contains 5 red pencils, 3 blue pencils abd 4 green pencils.
We have to calculate the probability that 3 red pencils are selected from box. Probability is the likeliness of happening an event among all the events possible.It lies between 0 and 1. The formula of calculating probability is as under:
Probability = number of items/ total items.
Number of pencils in box=12
Number of red pencils=5
Number of blue pencils=3
Number of green pencils=4
Probability of randomly selecting 3 red pencils will be 5*4*3/12*11*10 if pencil is not replaced after drawn of pencil.
=60/1320
=1/22
Hence the probability that 3 red pencils are selected is 1/22.
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8. A spinner is divided into 6 equal sections o
numbered 1 through 6. What is the probability
that the arrow will land on a multiple of 3?
(A) =
(B)
116113-1
(C) 1/12
(D) 1
8 (0)
81(0)
Cla
brosse und Ato mondo Fran
S(A)
(80)
Answer:
1/3
Step-by-step explanation:
The numbers are 1, 2, 3, 4, 5, and 6.
Both 3 and 6 are multiples of 3.
So, 2/6 is the probability since there is an equal change that the arrow will land on each section.
This simplifies to 1/3.
Brainliest, please :)
Answer:
P (multiple of 3) = [tex]\bf \frac{1}{3}[/tex]
Step-by-step explanation:
Numbers on the spinner, ξ = {1, 2, 3, 4, 5, 6} (6 elements)
Multiples of 3 = {3, 6} (2 elements)
P (multiple of 3) = no. of multiples of 3 / total no. of numbers on spinner
= [tex]\frac{2}{6}[/tex]
= [tex]\bf \frac{1}{3}[/tex]
Evaluate if a = - 3 and c = 5
- Зас
7
Answer:
315
Step-by-step explanation:
-3ac7
-3x-3=9x5=45x7=315
❄ Hi there,
evaluate this expression by using substitution:
If
a=-3c=5then
-3ac= (see below)[tex]\sf{-3(-3)(5)}[/tex]
[tex]\sf{9\times5}[/tex]
[tex]\triangleright \ \sf{45}[/tex]
That's it!
❄
A rectangular corral is to be built using 70m of fencing. If the fencing has to enclose
all four sides of the corral, what would be the dimensions to produce the maximum
possible area and what would the area of the corral be? Include a complete solution
Answer:
306 square meters
Step-by-step explanation:
The maximum area is when the length and width are the closest together.
70/2=35 we divide because there are 2 lengths and 2 widths in a rectangle
35/2=17.5, find the 2 closest integers, they are 17 and 18
17*18=306
Could someone please draw the triangle based off of this description
The altitudes of equal length, BE and CF gives AB = AC, from which we have;
∆ABC is an isosceles triangleHow can the RHS rule be used to indicate an isosceles triangle?From the given description, we have;
BE = CF
<CFB = <BEC = 90° All right angles are congruent
BC = BC by reflexive property of congruency
BC = The hypotenuse side of triangles ∆BFC and ∆CEB
Therefore;
∆BFC is congruent to ∆CEB by Right angle Hypotenuse Side, RHS, rule of congruency.
Therefore;
BF = CE by Corresponding Parts of Congruent Triangles are Congruent, CPCTC
Similarly, we have;
∆AEB is congruent to ∆AFC, by Side-Angle-Angle, SAA, rule of congruency
Which gives;
FA = AE by CPCTC
BF + FA = CE + AE, by substitution property of equality
BF + FA = AB
CE + AE = AC
Therefore;
AB = ACTherefore;
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In the following diagram, BC is parallel to DE.
What is x?
Answer:
21
Step-by-step explanation:
Using alternate interior angles, we can conclude that angle C is equal to X (the 3rd, unmarked angle in the center triangle)
To find that 3rd angle, we can do 180 - 105 - 54. This is because all angles in a triangle must equal 180. Using this, we find that angle C is equal to 21. By the law, X must also equal 21.
Answer:
x is 21
Step-by-step explanation:
add 54 and 105, then subtract it by 180 and you get 21.
which function is greater at the given value y=3^x or y=x^3 at x=2
Answer:
[tex] {3}^{x} [/tex]
Step-by-step explanation:
[tex] {x}^{3} = 8[/tex]
[tex] {3}^{x} = 9[/tex]
Ed wants to buy a new video game system which costs $250. he has
saved $135. ed charges $9 for each lawn he mows. which equation could
be used to find the number of lawns, x, ed must mow to have more than
the amount he needs to buy the video game system?
The required equation is 135 + 9x > 250.
The number of lawns Ed must mow is assumed to be x.
The amount Ed charges for each lawn he mows is $9.
Thus, the total amount Ed earns by mowing x lawns = $9x.
The savings which Ed has is $135.
Thus, the total amount Ed will have to spend can be written as the expression, $(135 + 9x).
The cost of the video game is given to be $250.
We are asked to write an equation, that can be used to find the number of lawns Ed mow, that is x so that the amount Ed has will be more than the amount he needs to buy the video game.
This can be shown as the equation:
Total amount Ed has > Cost of the video game,
or, 135 + 9x > 250.
Thus, the required equation is 135 + 9x > 250.
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By the definition of complementary angles, since
∠
1
is complementary to
∠
2
,
m
∠
1
+
m
∠
2
=
90
∘
. By the vertical angles theorem,
∠
4
≃
_
∠
1
, and
m
∠
4
=
m
∠
1
by the definition of congruence. Combined with the given equation,
m
∠
4
=
40
∘
, the substitution property of equality means that
40
∘
=
m
∠
1
. Using the ,
40
∘
+
m
∠
2
=
. Finally, using the ,
m
∠
2
=
50
∘
.
Blank 1: Substitution property of equality
Blank 2: 50
Blank 3: Subtraction property of equality
The blank spaces in the task content can be filled with; Substitution property, 90° and subtraction property.
What are the missing statements in the proof?Since it follows from the vertical angles theorem that angle 1 = angle 4 as they are congruent.
Additionally, angles 1 and 2 are said to be complementary and hence, the sum of their measures is equal to 90°.
Finally, by virtue of the subtraction property of equality, the measure of angle 2 is; 90° - 40° = 50°.
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If you substitute 12 2x for y in the second equation, how is the resulting equation written in standard form?
The resulting equation written in standard form is 16x² - 22x + 6 = 0.
What is equation in standard form?Quadratic Equation in Standard Form: ax² + bx + c = 0
a, b and c are known values. a can't be 0.
"x" is the variable or unknown (we don't know it yet).
The "solutions" to the Quadratic Equation are where it is equal to zero.
They are also called "roots", or sometimes "zeros"
We can Factor the Quadratic (find what to multiply to make the Quadratic Equation)
Or we can Complete the SquareOr we can use the special Quadratic Formula:Quadratic Formula: x = [ -b (+-) √(b² - 4ac) ] / 2a, Just plug in the values of a, b and c, and do the calculations.Calculation for the given equation-
Now, y=-16x²+24x+6
Substitute, y = 12+2x in y = -16x²+24x+6.
=> 12+2x = -16x²+24x+6
=> 16x²-24x-6+12+2x = 0
=> 16x²-22x+6 = 0
Therefore, the quadratic equation given in the standard form is 16x²-22x+6 = 0.
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The complete question is-
The two equations are given below;
Y = 12 + 2x linear equation
Y = -16x² + 24x + 6 quadratic equation
If you substitute 12 + 2x for y in the second equation how is the resulting equation written in standard form?
Label the midpoint of PQ as point S, the midpoint of QR as point T, and the midpoint of RP as point U. Next, draw PT, QU, and RS. Which statements are true
The statements that are true based on the midpoint given in the question include:
m∠P + m∠Q + m∠R = 180°PT, QU, and RS intersect at the same point.What is midpoint?In geometry, the midpoint simply means the middle point of a line segment. The midpoint is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.
Also, it should be noted that the midpoint bisects the segment.
In this case, m∠P + m∠Q + m∠R = 180°. This is because the sum of the angles in a triangle will be equal to 180°. Also, PT, QU, and RS intersect at the same point.
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Complete question:
Label the midpoint of PQ as point S, the midpoint of QR as point T, and the midpoint of RP as point U.
Next, draw PT, QU, and RS.
Which statements are true?
m∠Q = m∠R
The length of QU is half the length of RP.
m∠P + m∠Q + m∠R = 180°
QU ≅ RS
PT, QU, and RS intersect at the same point.
The sum of the lengths of QU and RS is equal to the length of PT.
Find a linear and an exponential equation that matches f(2)=12 and f(4)=48.
please help :))
The linear and exponential equation that matches f(2) = 12 and f(4) = 48 are y = 18x - 24 and f(x) = 3(2)ˣ respectively
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
For the exponential function, when f(2) = 12:
12 = ab² (1)
Also, at f(4) = 48:
48 = ab⁴ (2)
Hence:
a = 3, b = 2
f(x) = 3(2)ˣ
For the linear function using the points (2, 12) and (4, 48):
y - 12 = [(48 - 12) / (4 - 2)](x - 2)
y = 18x - 24
The linear and exponential equation that matches f(2) = 12 and f(4) = 48 are y = 18x - 24 and f(x) = 3(2)ˣ respectively
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What is the volume, in cubic centimeters, of a cube whose side measures 4 centimeters ?
Fill in the blank by entering only a number as your answer.
The formula for the volume of a cube is-side length^3.
For your problem, side length=4, so the answer is 4^3=64
ANSWER: 64 CUBIC CENTIMETERS hope this helped you
(T-Tb)
It is estimated that the average person in the US uses 123 gallons of water per day. Some environmentalists believe this figure is too high and conducted a survey of 40 randomly selected Americans. They find a mean of 113.03 gallons and a standard deviation of 25.99 gallons. Calculate the appropriate test statistic to test the hypotheses.
The value of test statistic is Z = -2.42.
According to the statement
we have given that the person in the US uses 123 gallons of water per day.
And conducted a survey of 40 randomly selected Americans and get a mean value is 113.03 gallons and a standard deviation of 25.99 gallons.
And we have to test the hypotheses with test statistic.
So,
Here we use the the z- test for one population =
Z = (sample mean - Claimed hypothesis mean)/ (standard deviation/(sample size)^1/2.)
Here the sample mean = 113.03
And claimed hypothesis mean = 123
Standard deviation = 25.99
Sample size = 40
Now put the values in the above written formula is
Z = (sample mean - Claimed hypothesis mean)/ (standard deviation/(sample size)^1/2.)
Z = 113.03 - 123 / (25.99/(40)^1/2)
Z = -9.97 / (25.99 / 6.32)
Z = -9.97 / 4.11
Z = -2.42
So, The value of test statistic is Z = -2.42.
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Island A is 160 miles from island B. A ship captain travels 170 miles
from island A and then finds that he is off course and 200 miles from
island B. What bearing should he turn to, SO he is heading straight
towards island B?
The ship captain should be turned 129.49 so it's heading straight for Island B.
Given Island A is 160 miles from Island B and the captain of a ship travels 170 miles from Island A and then discovers that he is off course and 200 miles from island B.
So we gave it
a = 200 feet
b = 170 feet
c = 160 feet
We need to find angle C which goes directly to island B.
We apply the "cosine law":
[tex]\begin{aligned}\cos C&=\frac{a^2+b^2-c^2}{2ab}\\ &=\frac{(200)^2+(170)^2-(160)^2}{2\times 200\times 170}\\ &=\frac{40000+28900-25600}{68000}\\ &=\frac{43300}{68000}\\ &=0.636\end[/tex]
Now we multiply both sides by cos⁻¹, we get
cos⁻¹(cos C)= cos⁻¹(0.636)
C = 50.51
The interior angle is 50.51°
We need to find the outer angle to find the bearing the captain needs to turn
Applying the additional angle ruler:
The outside angle = 180 - 50.51 = 129.49°
Therefore, he must turn so as to head directly for Island B, where Island A is 160 miles from Island B and the captain is sailing 170 miles.
from Island A and then discovers that it is off-road and 200 miles away
Island B is 129.49.
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please help me it is an easy question
Answer:
200 yd²
Step-by-step explanation:
A = 17 yd
B = 15 yd
C = 2 yd
D = 8 yd
b) Area of rectangle = length * width
[tex]\sf Area \ of \ 2 \ triangle = 2* \dfrac{1}{2}* base * height = base* height\\\\[/tex]
Area of right triangular prism = Areas of two triangle + area of the upper rectangle + area of middle rectangle + area of below rectangle
= 8 * 15 + 17 * 2 + 15 *2 + 8*2
= 120 + 34 + 30 + 16
= 200 yd²
Will’s meal of grilled chicken strips and carrots contained a total of 333 calories. The bag of grilled chicken strips contained x servings of 110 calories each. The bag of carrots contained y servings of 29 calories each. Which equation written in standard form represents the number of servings of chicken strips and carrots that Will may have eaten?
110y = –29x + 333
29x + 110y = 333
29y = –110x + 333
110x + 29y = 333
Answer:
correct answer is 110x + 29y = 333
Step-by-step explanation:
What is the solution to the system of equations? (7, 4) (7, startfraction 13 over 3 endfraction) (8, startfraction 14 over 3 endfraction) (9, 7)
The points are (7, 13/3).
Lets simplify the equation,
The equation of first line: y = 1/3 x + 2
the equation of second line: y= 4/3x - 5
Solve the system of equations by elimination,
Multiply equation A by -4 both sides
-4y = -4(1/3x +2)
-4y = -4/3x-8
After eliminating the equation we get,
y = 13/3
So now have to find x
13/3 = 1/3x + 2
Lets multiply above by 3
x = 13-6
x = 7.
Hence the points are (7, 13/3)
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Answer:
B
Step-by-step explanation:
What is the solution to the system of equations?
(7, 4)
(7, StartFraction 13 over 3 EndFraction)
(8, StartFraction 14 over 3 EndFraction)
(9, 7)
‼️‼️PLEASE HELP I WILL MARK BRAINLIEST ‼️‼️Dilate the figure by the scale factor. Then enter
the new coordinates.
C(-2,1)
A(1,4)
B(2,2)
K = 6
A' ([?], [])
B' ([ ], [ ])
C' ([ ], [ ])
Answer:After dialation
A'=6,24
B'=12,12
C'=-12,6
Don't forget to mark me Brainliest
PLS HELP WITH THIS AND SHOW WORK SHOW WORK
Answer:
option 3
Step-by-step explanation:
6x + 3x² - 4x ← collect like terms
= 6x - 4x + 3x²
= x(6 - 4) + 3x²
= x(2) + 3x²
= 2x + 3x²
Answer:
Option 3: [tex]2x+3x^{2}[/tex]
Step-by-step explanation:
Combine like terms: [tex]6x-4x=2x[/tex]
Put the equation together: [tex]2x+3x^{2}[/tex]
The correct answer option is Option 3: [tex]2x+3x^{2}[/tex].
4. Based on the triangle sum theorem, solve for x.
Answer:
x = 10
Step-by-step explanation:
180 = 90 + 40 + (4x + 10)
180 = 130 + (4x + 10)
4x + 10 = 180 - 130
4x + 10 = 50
4x = 50 - 10
4x = 40
x = 40/4
x = 10
Answer:
x = 10
Step-by-step explanation:
An euclidean triangle is defined to have sum of all 3 interior angles equal to 180°.
In the given triangle, we know three measurement:
4x+1040°90°You may be wondering, where does 90° come from. The answer is you can find it by looking if a triangle has a little square symbol or not. If it does, the measurement will always be 90°.
Now since we know that sum of 3 interior angles must equal to 180° in euclidean triangle. Therefore, sum up three of measurement then set to 180°.
[tex]\displaystyle{90 + 4x+10 + 40= 180}[/tex]
Evaluate and solve for the x-variable:
[tex]\displaystyle{90 + 4x+10 + 40= 180}\\\\\displaystyle{4x+140 = 180}\\\\\displaystyle{4x=180-140}\\\\\displaystyle{4x=40}\\\\\displaystyle{x=10}[/tex]
Therefore, the value of x is 10