The compound interes formula is given by:
[tex]P_N=P_0(1+\frac{r}{k})^{Nk}[/tex]where P0 is the principal (the initial amount), r is the interes rate (in decimal form), k is the number of times the interest is compounded and N is the time elapsed.
Plugging the values given we have:
[tex]\begin{gathered} P_N=10000(1+\frac{0.04}{12})^{12\cdot25} \\ =27,137.65 \end{gathered}[/tex]Therefore the future amount is $27,137.65 and the interest earned is $17,137.65.
Hi I need the answer to the question quickly if possible please
The log function can be graphed using the vertical asymptote at x = 1 and the points (2,0), (5,1) & (3,0.5).
Given graph is [tex]g(x) = log_{4}(x-1)[/tex]
We have to find the asymptotes.
Set the argument of the logarithm equal to zero.
x - 1 = 0
Now add 1 to both the sides of the equation.
x - 1 + 1 = 0 + 1
= x = 1
The vertical asymptote occurs at x = 1
So, vertical asymptote: x = 1
Now, find the point at x = 2
Replace the variable x with 2 in the expression.
[tex]f(2) = log_{4}((2) - 1)[/tex]
Simplify the result
Subtract 1 from 2
[tex]f(2) = log_{4}(1)[/tex]
Logarithm base 4 of 1 is 0
f(2) = 0
The final answer is 0.
y = 0
Now find the point at x = 5
Replace the variable x with 5 in the expression.
[tex]f(2) = log_{4}((5) - 1)[/tex]
[tex]f(2) = log_{4}(4)[/tex]
Logarithm base 4 of 4 is 1
so, f(5) = 1
y = 1
Now find the point at x = 3
Replace the variable x with 3 in the expression.
[tex]f(2) = log_{4}((3) - 1)[/tex]
[tex]f(2) = log_{4}(2)[/tex]
Logarithm base 4 of 2 is [tex]\frac{1}{2}[/tex].
Rewrite as an equation.
[tex]log_{4}((2) = x[/tex]
Rewrite [tex]log_{4}((2) = x[/tex] in exponential form using definition of a logarithm. If x and b are positive real numbers and b does not equal 1, then [tex]log_{b}((x) = y[/tex] is equivalent to [tex]b^{y} = x.[/tex]
[tex]4^{x} = 2[/tex]
Create expressions in the equation that all have equal bases.
[tex](2^{2})^{x} = 2^{1}[/tex]
Rewrite [tex](2^{2})^{x} as 2^{2x}[/tex]
[tex]2^{2x} = 2^{1}[/tex]
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
2x = 1
solve for x
[tex]x = \frac{1}{2}[/tex]
The variable x is equal to [tex]\frac{1}{2}[/tex]
[tex]f(3) = \frac{1}{2}[/tex]
The final answer is [tex]\frac{1}{2}[/tex]
So, y = 0.5
The log function can be graphed using the vertical asymptote at x = 1 and the points (2,0), (5,1) & (3,0.5).
x y
2 0
3 0.5
5 1
Hence the answer is the log function can be graphed using the vertical asymptote at x = 1 and the points (2,0), (5,1) & (3,0.5).
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I need your help know
Answer : 87.9 square inches
Given the following data
Radius of the cylindrical cup = 2 inches
Height of the cylindrical cup = 5 inches
Surface area is given as
[tex]\begin{gathered} A\text{ = 2}\pi rh\text{ + 2 }\cdot\pi\cdot r^2 \\ \text{Where }\pi\text{ = 3.14} \\ A\text{ = 2}\pi r(h\text{ + r)} \\ A\text{ = 2 x 3.14 x 2(5 + 2)} \\ A\text{ = 12.56(7)} \\ A\text{ = 12.56 x 7} \\ A=87.9inches^2 \end{gathered}[/tex]Jake drives Go-Karts at an average speed of 2.75 laps per minute. If the relationship between the number of laps completed and numberof minutes varies directly, how long would it take him to complete 41.25 laps?O A. 0.07 minutesOB. 15 minutesO C. 38.5 minutesO D. 113 minutes
Since the number of minutes and number of laps completed varies directly, therefore if 2.75 laps correspond to 1 min then:
[tex]\frac{2.75\text{laps}}{1\min}=\frac{41.25\text{laps}}{x\min }\text{.}[/tex]Solving for x we get:
[tex]x\min =\frac{41.25}{2.75}1\min =15\min \text{.}[/tex]Answer: Option B.
You are comparing two savings accounts based on the interest you would earn and the fees they charge. Assuming you have a savings account with an average balance of $500, which combination of interest rates and fees are a better deal? (Hint: Using a one year period, determine the balance that you would have at Bank A and Bank B). O Bank A offers you a savings account with a 10% annual interest rate and $5/month in fees O Bank B offers you a savings account with 2% annual interest rate and no fees O The two banks deals are equivalent O Trick question -- it's a bad idea to open a savings account with just $500
Bank B gives the better deal to open the savings account rather than Bank A.
Given that:-
Average balance of savings account = $ 500
Annual interest rate of Bank A = 10 %
Fees of Bank A = $ 5/month
Annual interest rate of Bank = 2 %
We have to find which bank gives the better deal.
In Bank A, after one year the amount of money in my bank account will be:-
500 + 10 % of 500 - 5*12 = 500 + 50 - 60 = 500 - 10 = $ 490.
In Bank B, after one year the amount of money in my bank account will be:-
500 + 2 % of 500 = 500 + 10 = $ 510.
Hence,
Bank B gives the better deal to open the savings account rather than Bank A.
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Plot three points for the line and graph the line. X-3y=6
x-3y = 6
Pick 3 points
Let x = 0
0 -3y = 6
Divide by -3
-3y/-3 = 6/-3
y = -2
(0,-2)
Let y =0
x - 3(0)=6
x = 6
(6,0)
Let x=3
3 - 3y = 6
Subtract 3 from each side
3-3y-3 = 6-3
-3y = 3
Divide by -3
-3y/-3 = 3/-3
y = -1
(3,-1)
Simplify the following expression by multiplying by theconjugate:6+3/5√5-2
Answer:
Simplifying the given expression gives;
[tex]27+12\sqrt[]{5}[/tex]Explanation:
Given the expression;
[tex]\frac{6+3\sqrt[]{5}}{\sqrt[]{5}-2}[/tex]Multiplying both the denominator and numerator by the conjugate of the denominator;
[tex]\begin{gathered} \frac{6+3\sqrt[]{5}}{\sqrt[]{5}-2}\times\frac{\sqrt[]{5}+2}{\sqrt[]{5}+2}=\frac{(6+3\sqrt[]{5})(\sqrt[]{5}+2)}{(\sqrt[]{5}-2)(\sqrt[]{5}+2)} \\ =\frac{6\sqrt[]{5}+6\sqrt[]{5}+12+3(5)}{5-4} \\ =\frac{12\sqrt[]{5}+12+15}{1} \\ =27+12\sqrt[]{5} \end{gathered}[/tex]Therefore, simplifying the given expression gives;
[tex]27+12\sqrt[]{5}[/tex]a line segment has the endpoint T(2,4) and the midpoint of (3,6.5). find the coordinates of the other point B.
a line segment has the endpoint T(2,4) and the midpoint of (3,6.5). find the coordinates of the other point B.
we know that
The formula to calculate the midpoint between two points is equal to
[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]In this problem we have
M=(3,6.5)
(x1,y1)=T(2,4)
(x2,y2)=B
substitute the given values in the formula above
[tex](3,6.5)=(\frac{2+x2}{2},\frac{4+y2}{2})[/tex]Find the value of x2 coordinate
3=(2+x2)/2
x2+2=6
x2=6-2=4
Find the value of y2 coordinate
6.5=(4+y2)/2
y2+4=13
y2=13-4=9
therefore
the coordinates of point B(4,9)
One side of a triangles two centimeters shorter than the base. The other side is four centimeters longer than the base. What lengths of the base will allow the perimeter to be greater than 29 cm?
Answer:
x > 9 cm
Explanation:
Let the length of the base = x cm
One side of a triangle is 2 cm shorter than the base.
Length = (x-2)cm
The other side is 4 cm than the base, therefore:
Length of the other side = (x+4)cm
Perimeter = x+(x-2)+(x+4)
If the perimeter is greater than 29, then:
x+(x-2)+(x+4)>29
3x-2+4>29
3x+2>29
3x>29-2
3x>27
x>27/3
x>9
The length of the base greater than 9cm will allow the perimeter to be more than 29 cm.
Options for the first box: 6,500, 10,500, 11,500, 14,000Options for the second box are: 11,500, 18,500, 14,000, 10,500
Answer:
Explanation:
Given the equation:
y = -2500x + 19,000
For cars between 2 and 3 years,
The minimum is 2 and the maximum is 3 years
For the minimum, we have x = 2
So,
y = -2500(2) + 19000
= 14000
For maximum, we have x = 3
so,
y = -2500(3) + 19000
=
Bentley and Arianys are reading the same book. At the beginning of the month, Bentley was on page 39 and Arianys was on page 19. Bentley will read 16 pages per day and Arianys will read 18 pages per day. Let BB represent the page of the book that Bentley is on at the end of tt days into the month, and let AA represent the page of the book that Arianys is on at the end of tt days into the month. Write an equation for each situation, in terms of t,t, and determine whether Bentley or Arianys is farther along in the book after 15 days.
a) An equation representing the number of pages of the book that Bentley is on at the end of t days is A = 39 + 16t.
b) An equation representing the number of pages of the book that Arianys is on at the end of t days is B = 19 + 18t.
c) Arianys is farther along in the book after 15 days than Bentley because Arianys is on page 289 of the book while Bentley lags on page 279.
What is an equation?An equation is a statement showing the equality of two or more mathematical expressions.
Equations are depicted using the equation symbol (=).
The pages of the book already covered by Bentley at the beginning of the month = 39
The pages of the book already covered by Arianys at the beginning of the month = 19
Bentley's reading speed per day = 16 pages
Arianys' reading speed per day = 18 pages
The page already read by Bentley = A
The page already read by Arianys = B
Equations:For the pages already read by Bentley, A = 39 + 16t
For the pages already read by Arinys, B = 19 + 18t
After 15 days, who has read more?
Bentley, A = 39 + 16t = 39 + 16(15) = 279 pages
Arianys, B = 19 + 18t = 19 + 18(15) = 289 pages
Thus, using equations, we can conclude that Arianys can conclude the book faster than Bentley if it takes up to 15 days in the month to complete the book.
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Which equation represents a circle? (x – 2)222+(y – 3)232=1 (x – 4)232+(y + k)212=1 x222+y222=1 x212+y232=1
Given:
Four different equations are given
Required:
To tell Which equation represents a circle?
Explanation:
The formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. If a circle is tangent to the x-axis this means it touches the x-axis at that point
[tex]\begin{gathered} \frac{x^2}{2^2}+\frac{y^2}{2^2}=1 \\ \\ x^2+y^2=2^2 \\ \\ so\text{ r =2} \end{gathered}[/tex]That is others are in the form of ellipse equation.
How do you find the general form of an ellipse?
The equation of an ellipse written in the form (x−h)2a2+(y−k)2b2=1. The center is (h,k) and the larger of a and b is the major radius and the smaller is the minor radius.
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]else three options resemble with ellipse equation
Required answer:
[tex]\frac{x^{2}}{2^{2}}+\frac{y^{2}}{2^{2}}=1[/tex]A pianist plans to play 6 pieces at a recital from her repertoire of 26 pieces.
Answer:
[tex]230230\text{ Recital programs are possible}[/tex]Explanation:
Here, we want to get the number of possible recital programs
We are not concerned about arrangements here
Thus, we have to use combination
We have this as:
[tex]^nC_r\text{ = }\frac{n!}{(n-r)!r!}[/tex]where in this case, n is 26 and r is 6
Substituting the values in the combination formula, we have it that:
[tex]^{26}C_6=\text{ }\frac{26!}{(26-6)!6!}\text{ = 230230}[/tex]
Another photo is 20 inches long. How much wood is4needed for the frame? SHOW your WORK.
Given :
width of frame = 10.5 inches
length of frame = 20.75 inches
The amount of wood that she'll need for each photograph can be determined using the perimeter of the rectangular frame:
Perimeter(P) of rectangular frame:
[tex]\begin{gathered} P\text{ = 2l + 2w} \\ =\text{ 2 }\times\text{ 20.75 + 2}\times\text{ 10.5} \\ =\text{ 62.5 inches} \end{gathered}[/tex]Amount of wood needed in perimeter = 62.5 inches
what is the area of the triangle formed from (0,-1) (0,4) and (4,-1)
The area of the triangle is 10 square units formed from (0,-1), (0,4), and (4,-1).
What is the Area of a Triangle?A triangle is a closed shape composed of three angles, three sides, and three vertices.
The triangle is formed from (0,-1), (0,4), and (4,-1) which are given in the question.
As per the attached graph,
The length of the base of the triangle = 4 units
The length of the height of the triangle = 5 units
The area of the triangle = 1/2 × 4 × 5
The area of the triangle = 10 square units
Therefore, the area of the triangle is 10 square units formed from (0,-1), (0,4), and (4,-1).
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Ryhanna has a container with a volume of 1.5 liters. She estimates the volume to be 2.1 liters. What is the percent error?
We know that Ryhanna has a container with a volume of 1.5 liters and that she estimates the value to be 2.1 liters. We want to find the percent error.
For doing so, we remember that the percent error is given by the expression:
[tex]=\frac{\mleft|v_{true}-v_{estimated}\mright|}{v_{true}}\cdot100[/tex]In this exercise, we have that:
[tex]\begin{gathered} v_{\text{true}}=1.5 \\ v_{\text{estimated}}=2.1 \end{gathered}[/tex]So, replacing we obtain:
[tex]\text{error}=\frac{\mleft|1.5-2.1\mright|}{1.5}\cdot100=\frac{0.6}{1.5}\cdot100=0.4\cdot100=40[/tex]This means that Ryhanna estimated the value of the volume with an error of 40%.
solve the equation 3b-13+4b=7b+1
Answer:
The given equation has no solution.
Explanation:
Given the equation:
[tex]3b-13+4b=7b+1[/tex]To solve, Firstly let's collect the like terms;
[tex]\begin{gathered} 3b-13+4b=7b+1 \\ 3b+4b-13=7b+1 \\ 7b-13=7b+1 \end{gathered}[/tex]From the resulting equation, we can see that the left side of the equation is not equal to the right side.
Adding 13 to both sides;
[tex]\begin{gathered} 7b-13+13=7b+1+13 \\ 7b=7b+14 \end{gathered}[/tex]Therefore, the given equation has no solution.
The scale factor of a model of a warehouse to the actual warehouse is 1 to 2. The volume of theactual warehouse is 8,455 ft^3. Find the volume of the model. Round to a whole number.
Question
The scale factor of a model of a warehouse to the actual warehouse is 1 to 2. The volume of the actual warehouse is 8,455 ft^3. Find the volume of the model. Round to a whole number.
Solution
The scale factor (or ratio) of the model to the actual is
[tex]1\colon2[/tex]The scalar factor (or ratio) for the volume will be
[tex]\begin{gathered} 1^3\colon2^3 \\ 1\colon8 \end{gathered}[/tex]To find the volume of the model
Let the volume of the model by denoted with x
We use the ratio
[tex]\begin{gathered} \frac{1}{8}=\frac{x}{8455} \\ \text{cross multiply} \\ 8\times x=1\times8455 \\ 8x=8455 \\ x=\frac{8455}{8} \\ x=1056.875 \\ x=1057ft^3\text{ (to the nearest whole number)} \end{gathered}[/tex]Thus, the volume of the model is 1057ft^3
Which of the following is an example of independent events? A. Drawing a king from a standard deck of cards and then drawing an 8 without replacing the kingB. Four people are drawn successively without replacement from a group of 30 to represent the groupC. Spinning a 3 on a spinner and getting a head from a coin tossD. Selecting a head from a bag of 9 different colored breads and then selecting a second bead without putting the first back
Two events are independent if the fact that one takes palce does not affect the probability of the other. This means that spinning a spinner and tossing a coin are indepent events since the probabilities do not affect each other.
Evaluate (10²-8²)÷(5+7)-6
BODMAS RULE is used in simplification problems. The opertation are done in the following order in simplification.
B-->Bracket
D-->Division
M-->Multiplication
A-->Addition
S-->Subtraction
[tex]\begin{gathered} (10^2-8^2)\div(5+7)-6 \\ =(100-64)\div(12)-6\text{ (Did operations inside brackets)} \\ =36\div12-6\text{ } \\ =3-6\text{ (Did division 36 }\div\text{ 12)} \\ =-3 \end{gathered}[/tex]Therefore, the answer is -3.
find the x-intercept and the y-intercept of the graph of the equation 6X + 4y equals 72
the given equation is
6x + 4y = 72
divide the equation by 2
3x + 2y = 36
3x + 2y - 36 = 0
compare with ax+by +c = 0
a = 3
b = 2
c = -36
x-intercept will be, -c/a = -(-36)/3 = 12
y intercept will be c/b = -36/2 = -18
you start on the unit circle at 0 negative one and move 300 degrees counterclockwise which angle in degrees will you end up on the unit circle Answer Choices:30330210120
By definition, it is important to remember that a circle has 360 degrees.
According to the information given in the exercise, you start at this point on the unit circle:
[tex](0,-1)[/tex]Observe the following picture:
By definition, from the point (0,-1) to the point (1,0) there are 90 degrees.
Therefore, if you move 300 degrees counterclockwise from the point (0,-1), you can subtract 90 degrees from the 300 degrees in order to calculate which angle in degrees will you end up on the unit circle:
[tex]300\degree-90\degree=210\degree[/tex]Therefore, you will end up with 210 degrees.
The answer is: Third option.
Arectangular field has an area of 646 square feet. The width of the field is 19 feetWite a number in the box to show the missing measurement What is the length of the field?
The area of a rectangle is
[tex]A=19\cdot x=76[/tex]x is the number missing in the box
[tex]x=\frac{76}{19}=4[/tex]the length of the field is 30+4 =34 feet
A surveying crew has two points A and B marked along a roadside at a distance of 400 yd. A third point C ismarked at the back corner of a property along a perpendicular to the road at B. A straight path joining C to A forms a 28° angle with the road. Find the distance from the road to point C at the back of the property andthe distance from A to C using sine, cosine, and/or tangent. Round your answer to three decimal places.
In order to calculate the distance from B to C, we can use the tangent relation of the angle 28°.
The tangent is equal to the length of the opposite leg to the angle over the length of the adjacent leg to the angle.
So we have:
[tex]\begin{gathered} \tan(28°)=\frac{BC}{AB}\\ \\ 0.5317094=\frac{BC}{400}\\ \\ BC=0.5317094\cdot400\\ \\ BC=212.684 \end{gathered}[/tex]Now, to calculate the distance from A to C, we can use the cosine relation.
The cosine is equal to the length of the adjacent leg to the angle over the length of the hypotenuse.
So we have:
[tex]\begin{gathered} \cos(28°)=\frac{AB}{AC}\\ \\ 0.8829476=\frac{400}{AC}\\ \\ AC=\frac{400}{0.8829476}\\ \\ AC=453.028 \end{gathered}[/tex]1. Determine the difference inclock 12 arithmetic bystarting at the first numberand countingcounterclockwise on theclock the number. Of unitsgiven by the second number 1-11=?
Given:
The identity element is P.
Required:
Determine the inverse if exist of
(a) P (b) Q (c) R
Explanation:
We know that the inverse is the element when combined on the right or the left through the operation, always gives the identity element as the result.
We can see in the first row the identity element P is getting by the operation of P and P. Thus the Inverse of P is itself.
In the second and third rows, the identity element is P is getting by the operation of Q and R.
Thus the inverse of Q is R and the inverse of R is Q.
Both are inverse of each other.
Final Answer:
The Inverse of the following are as:
(a) P = P
(b) Q = R
(c) R =Q
8. Ms. Crockett is trying to teach her nephew to play baseball. Below is a rough sketch of Brandon pitching a baseball. You can model his throw with the quadratic h(t) = -16t^2 +29t + 6 where t is the seconds since the ball left Brandon's hand and h(t) is the height of the ball in feet.
a) b) We have to start by labeling the graph.
This graph relates the height in the vertical axis with the distance in the horizontal axis. The equation that relates y and x is different from h(t), as we are not representing time in the horizontal axis.
Then, both the height and the distance will have units of feet:
The highest point will be at the point where the height stop increasing and start decreasing.
c) We can use the equation fo h(t) to find the value of t when h(t) = 0, that is , when the ball touches the ground.
As h(t) is a quadratic equation, finding t for h(t) = 0 is finding the roots of the quadratic equation:
[tex]\begin{gathered} h(t)=-16t^2+29t+6 \\ t=\frac{-29\pm\sqrt[]{29^2-4\cdot(-16)\cdot6}}{2\cdot(-16)} \\ t=\frac{-29\pm\sqrt[]{841+384}}{-32} \\ t=\frac{-29\pm\sqrt[]{1225}}{-32} \\ t=\frac{29\pm35}{32} \\ t_1=\frac{29-35}{32}=-\frac{6}{32}=-0.1875 \\ t_2=\frac{29+35}{32}=\frac{64}{32}=2 \end{gathered}[/tex]As the first root is a negative number, it does not make sense in this case. The solution then is the other root, that has a value of t=2. As t is in seconds, we know that the ball reaches the ground 2 seconds after the launch.
Answer:
a) The labels and units are Height (in feet) for the vertical axis and Distance (in feet) for the horizontal axis.
b) The highest point corresponds to the point where the height stops increasing and starts decreasing.
c) The ball touches the ground 2 seconds after the launch.
a shipping tube is shaped like a triangular prism the bases are equilateral triangles with edges of 5 in and a height of 4.3 in the tube is 14in long find the total surface area of the shipping tube
The figure is a triangular prism and the formular for total surface area of a triangular prism is represented below
[tex]\begin{gathered} \text{surface area = }bh+2ls+lb \\ \text{surface area=}(5\times4.3)+2(14\times5)+(14\times5) \\ \text{surface area=}21.5+140+70 \\ \text{surface area=}231.5in^2 \end{gathered}[/tex]PLEASEEEE HELPPP!!!!!PLEASEEEEEEEEEEEEE!!!!!!!!Assessment practice!!!!it's URGENT HELP is much appreciated find the vertex of each equation. Then use a table to graph each quadratic equation
Remember that the x-coordinate of the vertex of a quadratic function is -b/2a. In this case is:
[tex]x=-\frac{4}{2\cdot1}=-2[/tex]the y coordinate is
[tex]y=4+4\cdot-2-6=4-8-6=-10[/tex]Cuál es el MCD de 42 y 30 ?. Opción única. (3 puntos) 5 6 7 15
Greatest Common Factor:
The greatest common factor, or GCF, is the greatest factor that divides two numbers.
Given Numbers : 42 & 30
Factors of 42 : 7x3x2x1, 7x6x1,
Factors of 30=5x3x2x1, 5x6,1
Here the common factors of 42 & 30 are : 6,3, 2, 1
The greatest number in 6, 3, 2, 1 is 6
So, the greatest common factor is 6
The greatest common factor of 42 & 30 is 6
Answer: B) 6
Which equation best represents the volume,V, of this cylinder in terms of π
Answer:
[tex]V=18.75\pi[/tex]Step-by-step explanation:
The volume of a cylinder is represented by the following expression:
[tex]V=h\cdot\pi\cdot r^2[/tex]Then, in this case for a radius of 2.5 and height of 3:
[tex]\begin{gathered} V=3\cdot\pi\cdot2.5^2 \\ V=6.25\cdot3\cdot\pi \\ V=18.75\pi \end{gathered}[/tex]Quadrilateral GHJK is a rectangle. Find each measure if m<1=37
Answer:
[tex]\begin{gathered} m\angle2\text{ = 53} \\ m\angle3\text{ = 37} \\ m\angle4\text{ = 37} \\ m\angle5\text{ =53} \\ m\angle6\text{ =106} \\ m\angle7\text{ = 74} \end{gathered}[/tex]Explanation:
Here, we want to find the measure of the given angles
From what we have, the angle marked 1 is of a value 37 degrees
For a rectangle, each angle at the edges equal 90 degrees
That makes a total of 360 degrees
Also, we have four isosceles triangle. These are triangles with equal base angle in each
With these in mind, we can proceed to get the value of the missing indicated angles
a)
[tex]\begin{gathered} m\angle1\text{ + m}\angle2\text{ = 90} \\ m\angle2\text{ = 90-37} \\ m\angle2\text{ = 53} \end{gathered}[/tex]b)
[tex]\begin{gathered} m\angle5\text{ + m}\angle1\text{ = 90} \\ By\text{ transition:} \\ m\angle5\text{ = m}\angle2\text{ = 53} \end{gathered}[/tex]c)
[tex]\begin{gathered} m\angle4\text{ + m}\angle5\text{ = 90} \\ m\angle1\text{ = m}\angle4\text{ = 37} \end{gathered}[/tex][tex]\begin{gathered} d)\text{ m}\angle3\text{ = m}\angle4\text{ = 37} \\ \text{Base angles of isosceles triangle are equal} \end{gathered}[/tex]d)
[tex]\begin{gathered} m\angle6\text{ + m}\angle3\text{ + m}\angle4\text{ = 180} \\ \text{sum of interior angles of a triangle} \\ m\angle6\text{ = 180-37-37} \\ m\angle6\text{ = 106} \end{gathered}[/tex]e)
[tex]\begin{gathered} m\angle6\text{ + m}\angle7\text{ = 180} \\ \text{Sum of angles on a straight line} \\ m\angle7\text{ = 180-106} \\ m\angle7\text{ = 74} \end{gathered}[/tex]f)