1. A MAP SCALE READS 1CM:5KM. IF A DISTANCE ON THE MAP MEASURES 7CM, THE ACTUAL DISTANCE WILL BE?. 2. A SCHOOL DINING HALL IS 35M LONG. IF ON A PLAN, THIS LENGTH IS REPRESENTED BY 7CM, WHAT IS THE SCALE?. 3. THE LENGTH OF A BUILDING IS 30 METRES. A SCALE DIAGRAM OF THE BUILDING IS BEING DRAWN TO A SCALE OF 1CM TO 5 METRES. THE LENGTH OF THE BUILDING ON THE SCALE DIAGRAM IS?. 4. IF THE ANGLE OF ELEVATION OF A FROM B IS 42°, WHAT IS THE ANGLE OF DEPRESSION OF B FROM A?. 5. A BOY IS FLYING A KITE, THE STRING IS 25M LONG AND IS AT AN ANGLE OF 42° WITH THE HORIZONTAL, USING A SCALE DIAGRAM, FIND HOW HIGH THE KITE IS ABOVE THE BOY’S HEAD?
Answers
Answer:
1. 35 km
2. 1 cm to 5m
3. 6 cm
4. [tex]42^\circ[/tex]
5. 16.73 m
Step-by-step explanation:
Solution 1.
Reading of map scale = 1cm:5km
i.e. 1 cm is equivalent to 5 km
Measurement of map = 7 cm
Actual distance = Measurement of map [tex]\times 5[/tex]
Actual distance = 7 [tex]\times 5[/tex] = 35 km
-------------------
Solution 2.
Length of dining hall = 35 m
Measurement of map = 7 cm
Scale = Measurement of map : Length of dining hall (i.e. ratio)
Scale = 7 cm :35 m = 1 cm : 5 m
-------------------
Solution 3.
Length of building = 30 m
Scale = 1 cm to 5m
5 m is equivalent to 1 cm on scale
1 m is equivalent to [tex]\frac{1}{5}[/tex] cm on scale
30m is equivalent to [tex]\frac{1}{5} \times 30[/tex] = 6 cm on scale
-------------------
Solution 4.
Angle of elevation of A from B = [tex]42^\circ[/tex]
Angle of depression of B from A = ?
Please refer to the image attached, we can clearly observe that both the angles (i.e. angle of elevation from A to B and angle of depression from B to A )will be equal.
Angle of depression of B from A = [tex]42^\circ[/tex]
-------------------
Solution 5.
Given that:
String length, or hypotenuse of triangle BC= 25 m
Angle of string with horizontal, [tex]\angle B = 42^\circ[/tex]
Please refer to the attached image for the clear understanding of the situation.
To find:
Height, AC = ?
We can use trigonometric identity:
[tex]sin\theta = \dfrac{Perpendicular}{Hypotenuse}[/tex]
OR
[tex]sinB = \dfrac{AC}{BC}\\\Rightarrow sin42^\circ = \dfrac{AC}{25}\\\Rightarrow AC = 25 \times 0.67\\\Rightarrow AC = 16.73 m[/tex]
============
So, the answers are:
1. 35 km
2. 1 cm to 5m
3. 6 cm
4. [tex]42^\circ[/tex]
5. 16.73 m
Related Questions
What is the sum of this arithmetic series?
Answers
Answer:
The sum of the arithmetic series
[tex]S_{n} = \frac{n}{2} (2 a + (n-1) d)[/tex]
Step-by-step explanation:
Explanation
Let a , a+d , a+2 d , ..........a+(n-1)d +....... is an arithmetic sequence
The sum of the sequence is called arithmetic series
The [tex]n^{th}[/tex] term of the sequence
[tex]t_{n} = a + (n-1) d[/tex]
The sum of the arithmetic series
[tex]S_{n} = \frac{n}{2} (2 a + (n-1) d)[/tex]
Here 'a' is the first term of the sequence
and 'd' be the difference between two values
sum of first term
put n=1 ⇒ [tex]S_{1} = a[/tex]
Put n =2 ⇒ [tex]S_{2} = \frac{2}{2} (2 a + (2-1)d)[/tex]
[tex]S_{2} = 2 a + d[/tex]
......and so on
The sum of the arithmetic series
[tex]S_{n} = \frac{n}{2} (2 a + (n-1) d)[/tex]
Solve for x -2x + 5<7
a)x>-1
b)xc-1
c)x>-6
d)x<-6
Answers
Answer:
x>−2
Step-by-step explanation:
Let's solve your inequality step-by-step.
x−2x+5<7
Step 1: Simplify both sides of the inequality.
−x+5<7
Step 2: Subtract 5 from both sides.
−x+5−5<7−5
−x<2
Step 3: Divide both sides by -1.
−x
−1
<
2
−1
x>−2
Answer:
x>−2
For the last 4.5 hours, the temperature has decreased at a rate of 2.8 Degrees Fahrenheit per hour. Which best represents the overall change in temperature over this time period?
Answers
Answer:
The overall change in temperature over the time period ∆T = -12.6°F
Step-by-step explanation:
Rate of change of temperature r = -2.8°F per hour
Time t = 4.5 hours
The overall change in temperature ∆T = Rate of change of temperature × time period
∆T = r × t
∆T = -2.8°F per hour × 4.5 hours
∆T = -12.6°F
The overall change in temperature over the time period is -12.6°F
Answer: -12.6
Step-by-step explanation:
Solve for j.
-2j + 39 = 111
j=
Answers
Answer:
reeeeeerre
Step-by-step explanation:
Answer:
-2j+39=111=
-2j+39=111-39
-2j=72
-2j÷2=72÷2=
j=36
the answer is j=36
I need help ASAP please help me I’ll give brainliest
Answers
Answer:
Volume = 1,017.4m^3 .
Step-by-step explanation:
[tex]V = \frac{1}{3} pir^{2}h \\h (height) = 12m\\r (radius ) = 9m\\PI = 3.14\\V =\frac{1}{3} * 3.14 *9^{2} *12\\\\V = 1,017.36\\V = 1,017.4m^{3} .[/tex]
find the area of the shape
Answers
37.68 is the area of the Pac-Man
OA ⊥ OC start overline, O, A, end overline, \perp, start overline, O, C, end overline \qquad m \angle BOC = 6x - 6^\circm∠BOC=6x−6 ∘ m, angle, B, O, C, equals, 6, x, minus, 6, degrees \qquad m \angle AOB = 5x + 8^\circm∠AOB=5x+8 ∘ m, angle, A, O, B, equals, 5, x, plus, 8, degrees Find m\angle BOCm∠BOCm, angle, B, O, C:
Answers
Answer:
42 degrees.
Step-by-step explanation:
[tex]\angle BOC+\angle AOB=90^\circ $(Complementary Angles)\\6x - 6^\circ+5x + 8^\circ=90^\circ\\6x+5x-6^\circ+ 8^\circ=90^\circ\\11x+ 2^\circ=90^\circ\\11x=90^\circ-2^\circ\\11x=88^\circ\\$Divide both sides by 11\\x=8^\circ\\$Therefore:\\m\angle BOC=6x - 6^\circ\\=6(8) - 6^\circ\\=48-6\\=42^\circ[/tex]
The measure of angle BOC is 42 degrees.
Answer:
BOC = 42º
Step-by-step explanation:
Angle BOC is equal to 42 degrees, due to these steps -
1. Create the equation which will result to be -
6x - 6 + 5x + 8 = 90
2. Simplify by adding variables and numbers together -
11x + 2 = 90
3. Subtract 2 from both sides to get -
11x = 88
4. Divide by 11 on both sides to get-
x = 8
5. Substitute x in angle BOC as 8 to get this equation -
6(8) - 6
6. Solve
48 - 6 =
42º
Your final answer for angle BOC is 42º!
In a true-false test containing 50 questions, a student is to be awarded 2 marks for every correct answer and -2 for every incorrect answer and 0 for not supplying any answer. If Yash scored 94 marks in a test, what are the possibilities of his marking correct or wrong answer
Answers
Answer:
1. 47 correct, 0 wrong and 3 unanswered
2. 48 correct, 1 wrong and 1 unanswered
Step-by-step explanation:
Given;
Total number of questions = 50
For correct answers = 2
For wrong answers = -2
Unanswered questions = 0
Yash scored 94 marks
Let c, w and u represent the number of correct, wrong and unanswered questions
2×c - 2 × w + 0×u = 94
2c -2w = 94 .....1
And;
c + w + u = 50 .....2
We have 2 equations and 3 unknowns
By observing the problem, we can see two possible solutions;
Case 1: Assuming he did not miss (get wrong) any answer;
He needs to score 47 answers right;
47 × 2 = 94
Then;
c = 47 w = 0 and u = 50 - (47+0) = 3
47 correct, 0 wrong and 3 unanswered
Case 2: Assuming he got one answer wrong;
He would need to score one more answer right compared to the first case;
(47+1) × 2 - 1 × 2 = 96 - 2 = 94
c = 47+1 = 48
w = 1
u = 50 - (48+1) = 1
So he need to score 48 correct answers, 1 wrong answer and 1 unanswered.
Any one can help me please please I need help please each one 3 step explanation
Answers
Answer:
a) Area of wall to be painted = 114 sq ft
b) Number of cans required = 2×5 = 10
c) Total cost of paint = $338.43
Step-by-step explanation:
Part a)We are asked to find the area of wall that needs to be painted.
we need to subtract the area of window from the area of wall.
We know that area of a rectangular shape is given by
Area = Width×Length
Area of whole wall = 8×15 = 120 sq ft
Area of window = 2×3 = 6 sq ft
Area of wall to be painted = 120 - 6 = 114 sq ft
Part b)1 can of paint will cover 25 sq ft of area.
So to cover the area of wall to be painted,
114/25 = 4.56
since number of cans cannot be in fraction so we would need 5 cans
Since two coats of paints are needed so
Number of cans required = 2×5 = 10
Part c)1 can of paint costs $29.95
We have total 10 cans
$29.95×10 = $299.5
There is also a 13% tax so the total cost is
$299.5×0.13 = $38.93
Total cost of paint = $299.5 + $38.93
Total cost of paint = $338.43
Ratio of three angles of a triangle is 1 : 2 : 3. Find the angles.
Answers
Answer:
30⁰ , 60⁰ , 90⁰
Step-by-step explanation:
Let the angles x , 2x , 3x
By angle sum property:
x + 2x + 3x = 180⁰
6x = 180⁰
x = 30⁰
Angles are : 30⁰ , 60⁰ , 90⁰
Answer:
30°, 60°, 90°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the parts of the ratio, 1 + 2 + 3 = 6 parts
Divide to find the value of one part of the ratio
180° ÷ 6 = 30° ← value of 1 part of the ratio, thus
2 parts = 2 × 30° = 60°
3 parts = 3 × 30° = 90°
Thus angles are 30°, 60° and 90°
Please help with this question!!!
Answers
What angle corresponds to ∠M?
Answers
Answer:
iuhi on edge its c
Step-by-step explanation:
find the second term of this sequence? 3n^2-1
Answers
Answer:
11.
Step-by-step explanation:
Because you wanted to find the second term, just substutite n=2 into the formula.
Thus, 3(2)^2 - 1 = 3(4) - 1 = 11
Answer:
11Step-by-step explanation:
We get the second term by just plug in 2 (instead of n) in the sequence formula:
second term = 3×(2)² - 1 = 11
can some one help me this please
Answers
5X4=20
£20 for 5 hours
£20+£12=£32
Hope this helped!
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. If Shawn knows that the slope of the line is 4 and the line passes through the point (1,-8), which equation should he use to find the y-intercept and what is the y-intercept of the line?
Answers
Answer:
Equation to be used: Point- Slope form [tex] y-y_1= m(x-x_1)[/tex]
y-intercept = - 12
Step-by-step explanation:
He should use point - slope form equation.
It is given that, line is passing through the points[tex] (1,\: -8) = (x_1\:y_1)[/tex] and has a slope m = 4.
The equation of line in point-slope form is given as:
[tex]y-y_1= m(x-x_1)\\y-(-8) = 4(x-1)\\y+8 = 4x - 4\\y = 4x - 4 -8\\\huge\red{\boxed{y= 4x - 12}}...(1)\\Equating\: equation\: (1) \: with;\\y = mx + b \\y-intercept\: (b) = -12[/tex]
Answer:
The answers are B and D.
Step-by-step explanation:
Which linear equation represents a line with a slope of 9/4 and a y-intercept of 0? plz help giving out brainliest
Answers
Answer:
y = 9/4x.
Step-by-step explanation:
According to slope-intercept form, y = mx + b where m is the slope and b is the y-intercept.
So, y = 9/4x + 0
y = 9/4x.
Hope this helps!
The required equation of the line is given as 9/4x with a slope of 9/4 and a y-intercept of 0.
Given that,
The linear equation represents a line with a slope of 9/4 and a y-intercept of 0 is to be determined.
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,
Standard equation of the line,
y = mx + c
Put , = 9/4 and c = 0
y = 9/4x + 0
y = 9/4x
Thus, the required equation of the line is given as 9/4x.
Learn more about slopes here:
https://brainly.com/question/3605446
#SPJ2
Simplify, using the distributive property and then combining like terms.
5(3a+b)−2(3a+b)
Answers
Answer:
9a + 3b
Step-by-step explanation:
Given
5(3a + b) - 2(3a + b) ← distribute both parenthesis
= 15a + 5b - 6a - 2b ← collect like terms
= 9a + 3b
Answer:
The final answer would be [tex]9a + 3b[/tex] .
Step-by-step explanation:
Solve the following equation:
[tex]5(3a+b)-2(3a+b)[/tex]
Use Distributive Property:
[tex]5(3a+b)-2(3a+b)[/tex]
[tex]15a + 5b - 6a - 2b[/tex]
-Combine [tex]15a[/tex] and [tex]6a[/tex]:
[tex]15a + 5b - 6a - 2b[/tex]
[tex]9a + 5b - 2b[/tex]
-Combine [tex]5b[/tex] and [tex]-2b[/tex]:
[tex]9a + 5b - 2b[/tex]
[tex]9a + 3b[/tex]
So, the answer is [tex]9a + 3b[/tex] .
the weights, in pounds, of the upper class men offensive line players for a college are shown below:
322, 290, 321, 326, 330, 315, 311, 292, 290
What is the average, or mean, weight of the upper-class men offensive players? provide your answer with 3 sig figs.
1) 311 pounds
2) 315 pounds
3) 290 pounds
4) 318 pounds
Answers
Answer:
311 pounds
Step-by-step explanation:
Here, we are to calculate the average weight of the upper-class men offensive players
To calculate this, we need to sum up all the weights and divide by their count
Mathematically, that would be;
Average weight = (322+290+321+326+330+315+311+292+290)/9 = 2,797/9 = 310.77778
Now this written in 3 significant figures would be 311 pounds
Answer:
311
Step-by-step explanation:
You add all of the numbers first (2797)
Then you divide by how many numbers there were (9)
You get 310.7778
Then you round with 3 sig figs.
That is 311
Hope this helps:D
Write this equation in slope-intercept form. 5x - 6y = -6 *
Answers
Answer:
y = 5/6x +1
Step-by-step explanation:
5x - 6y = -6
We want the equation in the form
y = mx+b where m is the slope and b is the y intercept
Subtract 5x from each side
5x -5x - 6y =-5x -6
-6y = -5x -6
Divide each side -6
-6y/-6 = -5x/-6 -6/-6
y = 5/6x +1
Mapiya writes a series of novels. She earned \$75{,}000$75,000dollar sign, 75, comma, 000 for the first book, and her cumulative earnings double with each sequel that she writes.
Answers
Answer:
[tex]E(n)=75000 \times 2^n[/tex]
Complete question:
write a function that gives mapiyas cumulative earnings E(n), in dollars when she has written n sequel's
Step-by-step explanation:
According to the question, she earned $75000 for the first book.
Also,We are given that her cumulative earnings double with each sequel that she writes.
Assuming she has written n sequel's
Now since we are given that her cumulative earnings double with each sequel
So, her initial earning will be [tex]2^n[/tex] times
So, her earning will be : [tex]75000 \times 2^n[/tex]
Now we are given that cumulative earnings is denoted by E(n)
So, the function becomes :[tex]E(n)=75000 \times 2^n[/tex]
Hence a function that gives Mapiya's cumulative earnings E(n), in dollars when she has written n sequel's is [tex]E(n)=75000 \times 2^n[/tex]
What is the highest common factor of 50 and 90?
Answers
Answer: The gcf is 10
Step-by-step explanation:
BEG is a triangle.
ABC and DEF are parallel lines.
Work out the size of angle x.
Answers
A function g(x) is defined as shown.
g(x) =
2 + 3x,
0.5x + 10, 4 < x < 8.
16
What is the value of g(4)?
Answers
Answer:
4
Step-by-step explanation:
I love your name. my friend is also named like that. and she has a twin that is named jessicamarie.......oof!
Find the distance between points (5,1) and (3,4) to the nearest tenth
Answers
Answer:
3.6 units (nearest tenth)
Step-by-step explanation:
distance formula
= [tex] \sqrt{(x1 - x2)^{2} + (y1 - y2)^{2} } [/tex]
Thus, distance between the 2 points
= √[(5 - 3)² + (1 - 4)²]
= √[ 2²+ ( - 3)²]
= √13
= 3.6 units (nearest tenth)
product 48 and sum 14 what are the factors
Answers
6*8 = 48
6+8 = 14
Answer:
Step-by-step explanation:
Let's write a system.
Let's say that the variables are x and y.
xy=48
x+y=14
Solve for one of the variables, let's say, x.
x=14-y.
Now substitute x into the 1st equation.
(14-y)y=48
Simplify.
-y²+14y=48
Make it into a quadratic equation.
-y²+14y-48=0
Make sure y²'s coefficient is one. Divide everything by -1
y²-14y+48=0
Now factor!
What factors add up to 14 and multiply to 48.
6 and 8!
Since the 2nd term is negative, and the 3rd term is positive, the factors have to be negative.
y²-6y-8y+48=0
Group.
(y²-6y)+(-8y+48)=0
y(y-6)-8(y-6)=0
(y-8)(y-6)=0
y-8=0
y-6=0
y=8 y=6
now let's substitute each y value into y²-14y+48=0
8²-14(8)+48=0
64-112+48=0
0=0. so y=8 checks out!
6²-14(6)+48=0
36-84+48=0
0=0 so y=6 also checks out!
Choose one y value and solve for x, in each equation :
xy=48
x+y=14
8x=48
x+8=14
x=6
x=6
It checks out!
so the factors are
x=6 y=8.
I am thinking of a number. It is less than 500. It’s cube root is an integer. What is the largest possible value of this number
Answers
Answer:
[tex]343[/tex]
Step-by-step explanation:
[tex]1^{3} =1\\2^{3} =8\\3^{3} =27\\4^{3} =64\\5^{3} =125\\6^{3} =216\\7^{3} =343\\8^{3} =512[/tex]
[tex]\sqrt[3]{x } >500[/tex]
[tex]\sqrt[3]{343} >500[/tex]
Need Math help ASAP
Answers
Answer:
35 seconds
Step-by-step explanation:
At negative values he is inside the volcano, when he reaches 0 he will be at the top of the volcano
At 35 seconds, the elevation is 0, so he is at the top of the volcano
I need help ASAP please help me I’ll give brainliest :)
“Jackson buys a cherry snow cone on a hot day. What is the volume of “snow” he gets to eat? Use 3.14 for pi. Round you answer to the nearest tenth.”
Answers
Answer:
Correct option: Second one -> 141.3 cm3
Step-by-step explanation:
The volume of "snow" is the sum of the half sphere volume and the cone volume.
The volume of the half-sphere is given by the formula:
V = (2/3) * pi * radius^3
If the half sphere has a radius of 3 cm, we have that:
V1 = (2/3) * pi * 3^3 = 56.5 cm3
The volume of the cone is given by:
V = (1/3) * pi * radius^2 * height
If the radius is 3 cm and the height is 9 cm, we have:
V2 = (1/3) * pi * 3^2 * 9 = 84.8 cm3
So the final volume is:
V = V1 + V2 = 56.5 + 84.8 = 141.3 cm3
Correct option: Second one
Solve the inequality 8(x + 1) > 7(x + 2)
Answers
Answer:
7(2 - x)
Step-by-step explanation:
Answer:
x>6
Step-by-step explanation:
8(×+1)>7(x+2)
(8×x)+(8×1)>(7×x)+(7×2)
8x+8>7x+14
Now subtract 8 and 7x from each side of the inequality to solve for x while keeping the inequality balanced:
-7x+8x+8-8 > -7x+7x+14-8
(-7+8)x+0>0+6
1x>6
x>6
in this figure what is m 5?
Answers
Answer:
m<5 = 95 degrees
Step-by-step explanation:
Let's first find m<1
=> m<1 = 180-85
=> m<1 = 95 degrees
Since,
m<1 = m<5 (Corresponding angles)
So,
m<5 = 95 degrees
