The value of angle m∠F is 42°.
What are the Exterior angle properties of triangle?
If in a triangle any side is extended, the outside angle or exterior angle formed results is equal to the sum of the two opposite internal angles.
Here we are given a triangle ΔGHF
m∠F = ∠HFG = 4x + 6
∠G = ∠FGH = 70°
and exterior angle ∠GHJ = -5 + 13x
Here side FH of ΔGFH is extended .
so by using exterior property of triangle i.e,
Exterior angle = sum of opposite interior angles.
∠GHJ =∠FGH + ∠GFH
-5 + 13x = 70 + (4x + 6)
13x - 4x = 70 + 6 + 5
9x = 81
x = 81/9
x = 9.
Therefore m∠F = ∠GFH = (4x+6)
m∠F = 4×9+6
m∠F = 42°
So we got the value of angle m∠F is 42°.
To learn more about properties of Triangles from the given link
brainly.com/question/30166682
#SPJ1
A cone has a height of 6 inches and a diameter of 10 inches. What is its volume?
Use ≈ 3.14 and round your answer to the nearest hundredth
Answer:
V = 157 in³
Step-by-step explanation:
the volume (V) of a cone is calculated as
V = [tex]\frac{1}{3}[/tex] πr²h ( r is the radius and h the height )
here diameter = 10 , then r = 10 ÷ 2 = 5 , then
V = [tex]\frac{1}{3}[/tex] × 3.14 × 5² × 6 ( cancel 3 and 6 by 3 )
= 3.14 × 25 × 2
= 3.14 × 50
= 157 in³
Answer the following questions
The answers are given below.
What are trigonometric functions?In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.
Given:
1) 2Sin(9θ).Cos(5θ)=1/2(Sin14θ+Sin4θ)
2) Sin(3θ)Sin(5θ)Cos(3θ)Cos(5θ)=1/2(Sin8θ+Sin2θ)
3)Cos6θ+Cos4θ=2Cos5θCosθ
4)Sin(13θ/2)+Sin9θ=2Sin(11θ/2)Sinθ
5)Cosθ=2√5/5
6)Cos2θ=23/2
7)Tan(π/12)=2-√3
8)Sin(165°)=√6-√2 /4
9)Cos(5π/18)Cos(2π/9)-Sin(5π/18)Sin(2π/9)=Cos(π/2)
=0
Hence, these are the answers .
Learn more about Trigonometric functions here:
https://brainly.com/question/6904750
#SPJ1
Data was collected on the amount of time that a random sample of 8 students spent studying for a test and the grades they earned on the test. A scatter plot and line of fit were created for the data.
scatter plot titled students' data, with points plotted at 1 comma 75, 2 comma 70, 2 comma 80, 2 comma 90, 3 comma 80, 3 comma 100, 4 comma 95, and 4 comma 100, and a line of fit drawn passing through the points 0 comma 60 and 2 comma 80
Determine the equation of the line of fit.
y = 5x + 60
y = 5x + 80
y = 10x + 60
y = 10x + 80
The equation of the line of best fit for this data-set is given as follows:
y = 10x + 60.
How to obtain the equation for the line of best fit?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the coefficients are given as follows:
m is the slope, representing the rate of change of the output of the function relative to the input.b is the y-intercept, representing the value assumed by the function the input assumes a value of zero.The function goes through point (0,60), hence the intercept b of the line of fit is given as follows:
b = 60.
When x increases by 2, from 0 to 2, y increases by 20, from 60 to 80, hence the slope m is obtained as follows:
m = 20/2 = 10.
Hence the line of fit is given as follows:
y = 10x + 60.
Meaning that the third option is correct.
More can be learned about a line of fit at https://brainly.com/question/29613968
#SPJ1
Answer:
y = 10x + 60.
Step-by-step explanation:
Find the slope and y-intercept of the graph of the equation.
y=4 x+8
Select the correct choice and fill in any answer boxes in your choice below.
A. The slope is ____ .
B. The slope is undefined.
The slope of the equation y = 4x + 8 is 4 and the y-intercept is 8.
How to find the slope and y-intercept of an equation?The slope of a line is the change in the dependent variable with respect to the change in the independent variable.
The slope is rise over run.
Therefore, the equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptHence,
y = 4x + 8
Therefore, the slope is 4 and the y-intercept is 8
learn more on slope here; https://brainly.com/question/29112593
#SPJ1
sofia is making a bath of slime using a recipe that includes glue, water, and a salt solution. She uses 7.5 fl oz of glue. The amount of glue is 12.5 times the amount of salt solution. There are 4.2 less fluid ounces of salt solution than water.
4.8 fl oz is the amount of water that is used by Sofia to make the slime
How many fluid ounces of water does Sofia use to make a batch of slime?
A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation
Given that:
Sofia is making a bath of slime using a recipe that includes glue, water, and a salt solution. She uses 7.5 fl oz of glue.
The amount of glue is 12.5 times the amount of salt solution.
There are 4.2 less fluid ounces of salt solution than water.
We can set up equations using the three statements:
Let G, S and W represent glue, salt solution and water respectively
G = 7.5
G = 12.5S
S = W - 4.2
Since G = 7.5, we can write:
7.5 = 12.5S
S = 7.5/12.5 = 0.6
S = W - 4.2
0.6 = W - 4.2
W = 0.6 + 4.2
W = 4.8
Thus, the amount of water that is used by Sofia to make the slime is 4.8 fl oz.
Learn more about word problems on:
brainly.com/question/1781657
#SPJ1
Complete Question
Sofia is making a batch of slime using a recipe that includes glue, water, and salt solution. She uses 7.5 fl. oz of glue. The amount of glue is 12.5 times the amount of salt solution. There are 4.2 less fluid oz of salt solution in the water. How many fluid ounces of water does Sofia use to make a batch of slime?
5) Jackson bought an ultra-slim Television. The screen measures 13 cm in length and 12 cm in width. Television screen sizes are decided by the length of the diagonal. What is size of this screen? Round your answer to the nearest whole number.
6) A handicap camp ramp is located at the back of the building. The ramp has a 550 incline. The height of the ramp is 15m. How long is the ramp?
HELP PLEASE :?
5. If Jackson bought an ultra-slim Television. The size of this screen is 17.69.
6. If the ramp has a 550 incline and the height of the ramp is 15m. The height of the ramp is -68.24.
How to find the height?5. Size of the screen
Pythagorean theorem
c²= a² + b²
c² = 12² + 13²
c²= 144+169
c = √313
c = 17.69
6. Height
Using SOH CAH TOA
sin550= 15/x
x= 15/sin550
x= 15/-0.2195
x= -68.24
Therefore the size is 17.69 and the height is -68.24.
Learn more about height here:https://brainly.com/question/1739912
#SPJ1
The distance around a circle is 37.7 meters long. What is the area of the circle?
Answer:
≈ 113.16
Step-by-step explanation:
The circumference of a circle (the distance around) is equal to [tex]\pi[/tex] * diameter
[tex]\pi * diameter = 37.7[/tex]
[tex]\frac{\pi }{\pi } *diameter = \frac{37.7}{\pi }[/tex]
diameter = 12.006
radius = diameter / 2
radius = 6.003
The area of a circle is [tex]\pi r^{2}[/tex]
[tex]\pi 6.003^{2}[/tex]
= 113.16
steps and how to do it
The ratio of the shapes' perimeters and areas are 2/3 and 4/9 respectively
How to find the ratio perimeters and areas of two similar shapes?In order for two shapes to be similar, the corresponding angles of the shapes must be congruent and the ratios of corresponding sides must be equal.
If the two shapes are similar, then the ratio of their perimeters will be equal to the ratio of the corresponding side lengths, and the ratio of their areas will be equal to the square of the ratio of the corresponding side lengths.
Thus, in this case, we have:
Ratio of perimeter = 12/18 = 2/3
Ratio of area = 12²/18² = 4/9
Learn more about similar shapes on:
brainly.com/question/14285697
#SPJ1
Why should I use a decimal
Answer:
We use decimals every day while dealing with money, weight, length, etc. Decimal numbers are used in situations where more precision is required than whole numbers can provide. For example, when we calculate our weight on the weighing machine, we do not always find the weight equal to a whole number on the scale.
Step-by-step explanation:
Hope this helps!
Somebody please help me
Answer:
70
Step-by-step explanation:
On Tuesday, the balance in your bank account is $40.
Since from Wednesday to Friday you withdraw $10 a day, keep adding $10 to each day.
On Wednesday the balance is $40 + $10 = $50
On Thursday the balance is $50 + $10 = $60
On Friday the balance is $60 + $10 = $70
The balance in your bank account at the end of the day on Friday is $70
4. Chrissy had 4 gallons of gas in her tank when she arrived at the gas
station. She pumped gas into her car at a rate of 3/10 gallon per
second. How many gallons of gas were in the tank after s seconds?
Answer:
4 + 0.3s------------------------------------------
Initial volume of gas was 4 gallons.
The volume of gas pumped into tank after s seconds was:
(3/10)s = 0.3sThe total volume of gas become:
4 + 0.3sPLEASE HELP please..
Answer:
2nd choice
Step-by-step explanation:
m/54.2 = 82.5/271
Cross multiply:
m(271) = (82.5)(54.2)
m = 4471.5/271 = 16.5
Write the number that represents the give secasrio. (DOK 1)
6. One-fourth of the students brought their hunch to school.
7. After the penalty, there was a loss of 15 yards on the play.
8. He gained 6 pounds of muscle.
9. He made a 535 deposit into a bank account.
10. The temperature was 9 degrees below zero.
11. Two-thirds of the crewed left the stadium.
12. She received $20 on her birthday.
13. The student lost 10 points on the final exam.
14. He made a 570 withdrawal from a bank account.
15. One-half of the gallon of milk is gone.
Write the number that represents the given scenario. (DOK 1)
11. A submarine is 350 feet below sea level.
12. The family traveled 500 miles south on a road trip.
13. A rabbit hops 10 feet forward.
14. The temperature dropped 13 degrees.
15. A hot air balloon traveled 20 miles north.
The expression of the numbers as negative or positive is as follows;
6. ¹/₄
7. -15 yards
8. +6 pounds
9. +535 pounds
10. -9 degrees.
11. -²/₃ of the crowd
12. +$20
13. -10 points
14. -570
15. - ½
11. -350 feet
12. -500 miles
13. +10 feet
14. -13 degrees
15. + 20 miles
How to express numbers?We can express numbers in this regards as either positive or negative with a positive number indicating a gain while a negative number indicates a loss.
Thus;
6. One-fourth of the students brought their hunch to school is expressed as; ¹/₄
7. After the penalty, there was a loss of 15 yards on the play is expressed as; -15 yards
8. He gained 6 pounds of muscle is expressed as; +6 pounds
9. He made a 535 deposit into a bank account is expressed as; +535 pounds
10. The temperature was 9 degrees below zero is expressed as; -9 degrees.
11. Two-thirds of the crewed left the stadium is expressed as; -²/₃ of the crowd
12. She received $20 on her birthday is a gain and expressed as; +$20
13. The student lost 10 points on the final exam is a loss and expressed as; -10 points
14. He made a 570 withdrawal from a bank account is a loss and is expressed as; -570
15. One-half of the gallon of milk is gone is a loss and is expressed as; - ½
Write the number that represents the given scenario. (DOK 1)
11. A submarine is 350 feet below sea level is negative and is expressed as; -350 feet
12. The family traveled 500 miles south on a road trip is in the negative y-axis and is; -500 miles
13. A rabbit hops 10 feet forward is positive movement and is; +10 feet
14. The temperature dropped 13 degrees is a loss and is expressed as -13 degrees
15. A hot air balloon traveled 20 miles north is in the positive direction and is expressed as; + 20 miles
Read more about Number expression at; https://brainly.com/question/24368848
#SPJ1
Tisha brought chocolate and vanilla cupcakes to school for her birthday. 50 students decided to take a cupcake, and 27 of them picked vanilla. What percentage of the students picked a vanilla cupcake?
Write your answer using a percent sign (%).
Answer:
48% of students picked a vanilla cupcake
Step-by-step explanation:
We can get 48% from this question by turning this data into a fraction
27 students picked vanilla out of a total amount of 50
= 27/50
= 48%
This equals a percentage of 48% of students picking a vanilla cupcake
Answer:
48%
Step-by-step explanation:
A right circular cylinder with its diameter equal to its height is inscribed in a right circular cone.The cone has diameter 10 and altitude 15, and the axes of the cylinder and the cone coincide. find the volume of the cylinder.
O 30/23
O 30/11
O 15/11
O 17/11
O 3/2
The volume of the cylinder is 169.7. (Option C)
Based on the provided information, let the radius of the cylinder be r and diameter of the cylinder be 2r. The diameter and height of the circular cylinder is the same. When examining the cross section of the cone and cylinder, there are two similar triangles. Hence,
(15 – 2r)/15 = r/5
5(15 – 2r)= 15r
75 – 10r = 15r
r = 3
Volume of the cylinder = πr^2h where r is the radius of the cylinder and h is the height of cylinder. As h = 2r, Hence,
V = πr^2(2r) = (22/7)(3^2)(6) = 169.7
Note: The question is incomplete as the options are incorrect. The correct options are A) 127.5 B) 151.6 C) 169.7 D) 168.5
Learn more about Volume of the cylinder:
https://brainly.com/question/23935577
#SPJ4
Solve for k.
-6k-10 = 10 - 10k
Answer: The solution for k is -3/4.
To solve the equation, you can follow these steps:
Add 10k to both sides of the equation: -6k - 10 = 10 - 10k becomes -6k = 20
Divide both sides by -6: -6k/-6 = 20/-6 becomes k = -3/4
Step-by-step explanation:
Find the vertex of a parabola with an equation of 3x^2+9x-y-3=0.
Answer:
Step-by-step explanation:
We will have to convert this to vertex form.
First we add y to both sides.
y = 3x^2 + 9x - 3
The vertex form is y = a(x – h)^2 + k
y = 3(x^2 + 3x) - 3
We need to complete the square now, and half if 3 is 1.5, and 1.5^2 is 2.25, so we add 2.25 inside the parentheses but we have to be careful, because if we subtract 2.25 from outside the parentheses it wouldn't work because the 2.25 inside the parentheses is being multiplied by 3, so we have to subtract 2.25*3=6.75 from the outside.
y=3(x^2 + 3x + 2.25) - 9.75
we can simplify this now to
y=3(x + 1.5)^2 - 9.75
and now this is vertex form. From here it is incredibly easy to get the vertex. Just take the x value required to make the total in the parentheses zero, so in this problem it would be -1.5 (Because (-1.5+1.5)^2 is zero) and then you have your x coordinate. From there we just take k, which in this problem is -9.75, and it is the y value of our vertex.
In conclusion, the vertex is (-1.5. -9.75)
There are3 numbers for the combination to the skating rink’s safe. The first number is 19. The other2 numbers can be multiplied together to give a product of 42. What are the possibilities?
Answer: 7 and 6
Step-by-step explanation: 7 x 6 = 42
3. On Monday, the price of a share of stock was $45. It fell $2 each day for 12 consecutive days. Which of the following expressions could you use to find the
price of the stock on any one of those days?
A. 2d +45
B. 2d-45
C. -45d + 12
D. 45-2d
The expressions that use to find the price of the stock on any one of those days could be D. 45-2d
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.
We are given that On Monday, the price of a share of stock was $45. It fell $2 each day for 12 consecutive days.
The price of a share of stock = $45
Common difference = -2.
The expression that represent the situation is
45-2d
To know more about an expression follow;
brainly.com/question/19876186
#SPJ1
The function y = f(x) is graphed below. What is the average rate of change of the function f(x) on the interval 1 < x<1?
The average rate of change of the function is: 0
What is average rate of change?You should know that average rate of change is also referred to as the slope of the function
At point where x = -8, the value of f(-8) = -10 and
At x = -1, the value of f(-1) = -10
We have to determine the average rate of change of the function f(x) on the interval -8 ≤ x ≤ -1.
When x₁ = -8, f(x₁) = f(-8) = -10 also
when x₂ = -1, f(x₂) = f(-1) = -10
This implies that
Average rate = [f(x₂) - f(x₁)] / [ x₂ - x₁]
= [f(-1) - f(-8) ] / [-1-(-8)]
= [-10 - (-10)] / [-1+8]
= [-10 + 10] / 7
= 0 / 7
= 0
In conclusion, 0 is the average rate of change which is also the slope of the function
Study about average rate of change on https://brainly.com/question/28744270
#SPJ1
What is the answer to this question and how to solve?
Answer:
Line ZL and line LZ.
Step-by-step explanation:
Since it is a line (because a line needs to have two or more points to be able to graph), it can be represented in two ways. The first being ZL, and the second being LZ.
Brainliest please.
Answer:
Step-by-step explanation
Oh
what is the result when -7/8 is multiplied by -3.5?
Answer:
Step-by-step explanation:
First, I will convert the decimal as a fraction or decimal, whichever one you prefer. I did fraction. So, -3.5 is the same as -7/2.
Second, for fraction multiplication, you will multiply the numerator and then the denominator.
[tex]\frac{-7 times -7}{8 times 2} = \frac{49}{10}[/tex]
Third, we will convert the improper fraction to a mixed fraction by using long division 49 divided by 16 = 3R1.
3 WILL BE YOUR WHOLE NUMBER. 1 IS YOUR NUMERATOR AND 16 IS YOUR DENOMINATOR.
The Answer is 3 [tex]\frac{1}{16}[/tex]. Letter D
how to calculate (1/2)^(4/3)
Answer:0.39685026299
Step-by-step explanation:
...... calculator
Simplify the expression (h+ k)²-(h - k)².
Hence, by substituting a suitable value of h and
of k, find the value of 165²- 35².
If two angles form a linear pair, what else do we know about the angles? List two things that are true about two angles that form a linear pair.
Answer:
When two lines intersect each other at a single point, linear pairs of angles are formed. If the angles so formed are adjacent to each other after the intersection of the two lines, the angles are said to be linear. If two angles form a linear pair, the angles are supplementary, whose measures add up to 180°.
What would the Lateral area and Surface area of this shape would be?
As per the given dimensions of cone in the figure, the Lateral area for the given cone is 123.15 [tex]in^2[/tex] and the surface area is 173.41[tex]in^2[/tex].
What is a cone?A cone is a characteristic three-dimensional geometric shape with a smooth and curving surface that is directed upward ,in mathematics.
What is the lateral surface area of a cone?
The area that the cone's curved surface covers is known as the lateral area of the cone. It is also known as the cone's curved surface area (CSA) or lateral surface area (LSA).
To solve the given question, we first need to use the pythagorus theorem in triangle made by the lateral slant height, actual height and the radius of the given cone,
Hence the pythagorus theorem gives,
[tex]9.8=\sqrt{h^2+4^2}[/tex]where h is the height of the cone.
Now Using the formula for Lateral surface area of the cone,
LSA = [tex]\pi *r=\sqrt{h^2+4^2}[/tex] where , h is height and r =4 in
Hence LSA = 123.15 [tex]in^2[/tex]
Again, Using the formula for Surface area of a cone,
SA = [tex]\pi *r(r+\sqrt{r^2+h^2}[/tex] , where h is height of cone and r = 4in
Hence , SA = 173.41 [tex]in^2[/tex].
To learn more about cones visit:
brainly.com/question/16394302
#SPJ1
Janelle bought a beach chair on sale at 60% of. The original price was 46.95
Answer:
18.78
Step-by-step explanation:
100_60÷100×46.95=18.78
In how many different ways can the ribbons be awarded?
The total number of different ways in which the ribbons can be awarded is 24,024 ways, so the third option is the correct one.
In how many ways can the ribbons be awarded?There is a competition with 14 dogs, and there are 4 prizes for the dogs.
To find the number of ways in which the ribbons (prizes) can be awarded, we need to take the product between the numbers of options for each.
For example for the blue ribbon (first prize) there are 14 dogs to select, so there are 14 options.
For the red one there are 13 options (because one dog is already selected for the blue ribbon).
For the yellow one there are 12 options.
For the white there are 11 options.
Then the total number of different combinations is:
C = 14*13*12*11 = 24,024
Thus, the third option is the correct one.
Learn more about combinations:
https://brainly.com/question/11732255
#SPJ1
PLEASE HELP please..
Answer:
49 ft tall
Step-by-step explanation:
Using a ratio
7 is to 3 as height is to 21 ft
7/3 = height / 21
height = 21 * 7/3 = 49 ft tall
PLEASE HELP
Identify and label the hypotenuse, adjacent and
opposite sides on the given right triangle using
the reference angle.
Solve for the missing side in the given triangle.
Find the sine, cosine, and tangent of the referenced angle.
The missing side in the triangle is 13 units which is the hypotenuse. The values of sine, cosine, and tangent of the referenced angle are 5/13, 12/13, and 5/12 respectively.
What are trigonometric functions?Trigonometry is the branch of mathematics that deals with particular functions of angles and how to apply them in calculations. There are six widely used angles-related trigonometric functions. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant(csc) are their respective names and acronyms.
In the given triangle the reference angle is θ.
So, the adjacent side (P) has a length of 12 units. The opposite (B) is the side having a length of 5 units. So, the hypotenuse will be
Then, acc to Pythagoras theorem, the hypotenuse (H) will be
H² = P² + B²
H² = 5² + 12²
H² = 25 + 144
H² = 169
H = √169
H = 13 units
This is the missing side of the given triangle.
The sine is
sinθ = opposite/ hypotenuse
= 5/13
cosθ = adjacent/ hypotenuse
= 12/13
tanθ = opposite/ adjacent
= 5/12
To know more about trigonometric functions, visit:
https://brainly.com/question/25618616
#SPJ1