Step-by-step explanation:
13x_6=9x+14
13x_9x=14+6
5x=20
x=20÷5
x=4
a cottage is on a bearing of 200° and 110° from Dogbe's and Manu's farm respectively. If Dogbe walked 5km and Manu 3km from the cottage to their farm, find and correct to 2 s.f the distance between the two farms and correct to the nearest degree, the bearing of Manu's farm from Dogbe's
PLEASE NOTE: DOGBE AND MANU ARE NAMES
Based on the drawing obtained from the description, the location of
Manu's farm is located relatively south to Dogbe's farm.
The distance between the two farms is approximately 3.8 kmThe bearing of Manu's farm from Dogbe is approximately 238°Reasons:
The bearing of the cottage to Dogbe's farm = 200°
The distance Dogbe walks from the cottage to his farm = 5 km
The bearing of the cottage from Manu's farm = 110°
The distance Manu walks from the cottage to his farm = 3 km
Required:
The distance and between the two farms.
Solution:
Please find attached a drawing showing the position of the cottage
By cosine rule, we have;
a² = b² + c² - 2·b·c·cos(A)Where;
b = The distance Dogbe walks from the cottage to his farm = 5 km
c = The distance Manu walks to his farm from the cottage = 3 km
a = The distance between the two farms = d
A = The angle between the paths to the cottage from the farms = 50°
By plugging in the values, we have;
d² = 5² + 3² - 2 × 5 × 3 × cos(50°)
d = √(5² + 3² - 2 × 5 × 3 × cos(50°)) ≈ 3.8
The distance between the two farms, d ≈ 3.8 kmRequired:
The bearing of Manu's farm from Dogbe's
Solution:
By sine rule, we have;
[tex]\displaystyle \frac{3}{sin(C)} = \mathbf{ \frac{d}{sin(50^{\circ})}}[/tex]Which gives;
[tex]\displaystyle sin(C) = \mathbf{\frac{3 \times sin(50^{\circ})}{\sqrt{5^2 + 3^2 - 2 \times 5 \times 3 \times cos(50^{\circ})} }}[/tex]
[tex]\displaystyle \angle C = arcsine \left(\frac{3 \times sin(50^{\circ})}{\sqrt{5^2 + 3^2 - 2 \times 5 \times 3 \times cos(50^{\circ})} } \right) \approx 38 ^{\circ}[/tex]
The bearing of Manu's farm from Dogbe's = 200° + ∠C
Therefore;
The bearing of Manu's farm from Dogbe's ≈ 200° + 38 = 238°Learn more about bearings in mathematics here:
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Here is a linear equation: y = 1/4x + 2 What is the x-intercept of the graph of the equation?
Answer:
(−8,0)
Step-by-step explanation:
The x- intercept is (-8, 0)
What is Intercept?A line's slope and intercept give information on its steepness and the point at which it crosses an axis, respectively. The linear relationship between two variables is defined by the slope and intercept, which can be used to calculate the average rate of change.
Given:
Equation: y= -1/4 x + 2
Now, for x- intercept take y= 0
So, 0 = 1/4x + 2
1/4x = -2
x= -8
Hence, the x- intecrcept is (-8, 0)
Learn more about intercept here:
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A sum of money is shared in the ratio 3:7.
If the smaller share is $450, what is the
8
larger share?
(A) $315
(B) $1050
$1500
(D)
$3150
| (C)
Answer:
B) $1050
Step-by-step explanation:
[tex]450(7/3)=(450)(7)/3=3150/3=1050[/tex]
Hope this helps
Mali has half of the cost of a day trip to a theme park for two people, and Sarah has one-third of the cost. What fraction of the cost do they have?
Answer:
5/6
Step-by-step explanation:
1/2=3/6
1/3=2/6
2/6+3/6=5/6
solve pls brainliest
Answer:
Yes, This is a repeating decimal
No, This is a decimal that neither terminates or repeats
No, This is a decimal that neither terminates or repeats
Yes, This is a terminating decimal
Solve the math problem
Answer:
1 -66
2. 162
3.11/-2
4. 8/-11
5.12/0
6. 0
7. 15/14
8. 2/-5
Step-by-step explanation:
10x + 44
8x - 23
It’s solving for X in triangles
Answer:
x=33.5
Step-by-step explanation:
8x+y= -16
-3x+y= -5
Elimination Hard. Write the System of Equations in Section #5 on your lined paper.
Multiply one of the equations by a (-1), so that the coefficients in both equations will be opposites.
- Solve the System of Equations using Elimination.
Enter your answer as (___,___)
Answer:
dude i have the same question
Step-by-step explanation:
WHAT IS THE ANSWER
a number of students are standing in a circle. they are evenly spaced and the fith student is directly opposite the eleventh student. how many students are there all together
Answer:
There would be 12
Step-by-step explanation:
how to solve | k-10 | = 3
Answer:
k=7 or k=13
Step-by-step explanation:
I I is absolute value
Ik-10I=3 I13-10I=3 k=13
Ik-10I=33 I7-10I=3 I7-10I=-3 I-3I=3 k=7
if my perimeter is 17 then how much is n in this question/photo?
Answer:
hope it helps you........
The domain for f(x) is all real numbers ___ than or equal to 2
Step-by-step explanation:
f(x) = 2x² + 5√(x - 2)
Domain
√(x - 2) ≥ 0
x - 2 ≥ 0
x ≥ 2
x is greater than or equal to 2
Answer: Greater than
Step-by-step explanation:
Please help the screenshot is below. Find the domain. THE ANSWER IS NOT x≠2.
Answer:
x>2 or (2,∞)
Step-by-step explanation:
if x≤2, 3*|2-x| = 3*(2-x) = 6-3x
3*|2-x| +3x-6 = (6-3x) + 3x-6 = 0 ... f(x) -> ∞ denominator = 0
if x>2, 3*|2-x| = 3*-(2-x) = -6+3x
3*|2-x| +3x-6 = (-6+3x) + 3x-6 = 6x - 12 >0
The other question is in the picture
Activity 2: of Directions: Write T before each item if the statement is TRUE, otherwise write F.
For items 1-2: Use the problem below to answer the following questions.
Your mother invested PhP 10,000.00 in an investment institution at 5% compounded semi-annually for x years.
___1. y = 10 000(1.025)2x is the function that represents mother's total investment
Using compound interest, it is found that the correct options are:
1. True.
2. True.
Compound interest:
[tex]A(x) = P\left(1 + \frac{r}{n}\right)^{nx}[/tex]
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year. x is the time in years for which the money is invested or borrowed.Item 1:
Invested 10000, hence [tex]P = 10000[/tex].Semi-annually, hence [tex]n = 2[/tex].Interest rate of 5%, hence [tex]r = 0.05[/tex]Then:
[tex]A(x) = P\left(1 + \frac{r}{n}\right)^{nx}[/tex]
[tex]A(x) = 10000\left(1 + \frac{0.05}{2}\right)^{2x}[/tex]
[tex]A(x) = 10000(1.025)^{2x}[/tex]
Hence option 1 is True.
Item 2:
Quarterly, hence [tex]n = 4[/tex].Then:
[tex]A(x) = P\left(1 + \frac{r}{n}\right)^{nx}[/tex]
[tex]A(x) = 10000\left(1 + \frac{0.05}{4}\right)^{4x}[/tex]
[tex]A(x) = 10000(1.0125)^{4x}[/tex]
Hence option 2 is also True.
A similar problem is given at https://brainly.com/question/24507395
At midnight, the temperature was - 5°C.
At midday, the temperature was 7°C.
Work out the temperature which is halfway between -5°C and 7°C
Answer: 12 °C
Step-by-step explanation:
The difference between -5 and +7 is (7 - (-5)) = 12 °C.
Question
The dimensions of a sports pennant are given in the diagram. Find the values of x and y.
Answer:
x= 79° y= 22°
Step-by-step explanation:
x is the same as 79
79+79= 158
180° in a triangle
180-158= 22°
Identify the restrictions on the domain of f(x) =
X +5
X-2
Ox#5
OX-5
Ox=2
Ox= -2
2. The delivery trucks are all different sizes. That means the workers have to change the number of boxes that go on a truck. Three small delivery trucks can hold 330 boxes. If the same number of boxes is in each truck, how many boxes can one small delivery truck hold?
Answer:
Each small truck can hold a total of 110 boxes.
Step-by-step explanation:
It says three small delivery trucks can hold 330. That meant all three together. So you just have to do 330 divided by 3 and you get 110. So that's the number of boxes ONE small truck can hold. Also, If u do it backward, 3 x 110 =330.
What is the x-intercept of the line with this equation 1/3x + y =-15?
Enter your answer in the box.
( ,0)
Answer:
(-45,0)
Step-by-step explanation:
??????????????????????????????????????????????
Answer:
C. No, because one x-value corresponds to two different y-values.
Step-by-step explanation:
name the congruent triangles
will give brainliest
Answer:
ΔOGD ≅ΔPRC
Step-by-step explanation:
SAS
Please help me asap
The line passing through which two points is perpendicular to the line 10x + 2y = 2?
A.) (-2, -7) and (1, 8)
B.) (-5, 5) and (0, 4)
C.) (0,-9) and (5, -8)
D.) (-4, 12) and (-2,2)
E.) (-2, 11) and (1, -4)
Considering the definition of perpendicular line, the correct option is option C): the line passing through (0,-9) and (5, -8) is perpendicular to the line 10x + 2y = 2.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.
m is the slope.
b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.
Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:
m= (y₂ - y₁)÷(x₂ - x₁)
Perpendicular linePerpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Perpendicular line in this caseIn this case, the line is 10x + 2y=2. Expressed in the form y = mx + b, you get:
2y=2 - 10x
y= (-10x +2)÷ 2
y= -10/2x +2/2
y= -5x +1
The line has a slope of -5. If you multiply the slopes of two perpendicular lines, you get –1, you get:
-5× slope perpendicular line= -1
slope perpendicular line= (-1)÷ (-5)
slope perpendicular line= 1/5
The line through two points must have a slope equal to 1/5. So you calculate the slope of each line that passes through two points as follows:
(x₁, y₁)= (-2, -7) and (x₂, y₂)= (1, 8): m= (8 - (-7))÷(1 - (-2)) → m= (8+7)÷ (1+3) → m= 15÷4= 15/4(x₁, y₁)= (-5, 5) and (x₂, y₂)= (0, 4): m= (4- 5)÷(0 - (-5)) → m= (-1)÷ (0 + 5) → m= -1÷5= -1/5(x₁, y₁)= (0, -9) and (x₂, y₂)= (5, -8): m= (-8 - (-9))÷(5 - 0) → m= (-8+9)÷ (5) → m= 1÷5= 1/5(x₁, y₁)= (-4, 12) and (x₂, y₂)= (-2, 2): m= (2 - 12)÷(-2 - (-4)) → m= (-10)÷ (-2+4) → m= -10÷2= -5(x₁, y₁)= (-2, 11) and (x₂, y₂)= (1, -4): m= (-4 -11)÷(1 - (-2)) → m= (-15)÷ (1+2) → m= -15÷3= -5Since the perpendicular line must have a slope equal to 1/5, the line passing through (0,-9) and (5, -8) is the correct line.
Learn more about perpendicular line:
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PLS HELP ASAP ILL GIVE BRAINLKEST THANKS
Answer:
B is the answer
Triangle EFG is dilated by a scale factor of \frac{2}{3}
3
2
to form triangle E'F'G'. What is the measure of side FG?
Answer:
B. 36°
Step-by-step explanation:
Dilation does not change the angle measures or the direction of the lines. Angle F is the same as corresponding angle F'.
Alberto has $2.25 in dimes and nickels in his pocket. He has nine more nickels than dimes. How many of each type of coin does he have?
I really need help!
Alberto has 12 Dimes and 21 Nickels in his pocket.
How many of each type of coin does he have?Dimes value = 0.10$
Nickels value = 0.05$
Let d = number of dimes = 0.10d
Let d+9 = number of nickels = 0.05(d + 9)
Value of the Dimes + Value of the Nickels = total value of the coins
Write the equation:
0.10d + 0.05(d + 9) = 2.25
Distribute:
0.10d + 0.05d + 0.45 = 2.25
0.15d + 0.45 = 2.25
Subtract 0.45 from each side:
0.15d = 1.80
Divide to find the number of dimes.
d = 12
The number of nickels is d +9 = 12 + 9 = 21
Alberto has $2.25 in dimes and nickels in his pocket. He has 12 Dimes and 21 Nickels in his pocket.
Learn more about problem-solving here: brainly.com/question/23945932
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Jessica and her family bought 5 tickets to a
music concert. Tickets for adults cost $5.10 and
tickets for children cost $3.60. Jessica and her
family spent a total of $21. How many tickets
for adults (a) and how many tickets for children
(c) did they buy?
a + c = 5
5.1a + 3.6C = 21
[?] adults [ ] children
Step-by-step explanation:
work is shown and pictured
make a conjecture (prediction) about the table. what will happen if we continue the table, going down?
purchased two candles from Target. The first candle has a height of 10 inches and burns at a rate of 3 inches per hour. The second candle has a height of 8 inches and burns at a rate of 2 inches per hour. After how many hours will both candles be at the same height?
Answer:
In 2 hours
Step-by-step explanation:
10/3 8/2
10-6 = 4
6 from 3*2(aka the hours)
8-4 = 4 from 2*2(aka the hours)
you can also set this up like
10-3x=8-2x and solve for it
Answer: At the 2 hour mark.
Step-by-step explanation:
10-3=7. 7-3=4
8-2=6. 6-2=4
What is the solution to the equation?
a+5 2/3=9
Answer:
A= 3 1/3
Step-by-step explanation:
Which statement is true?
A. 4.273 > 4.289
B. 5.306 > 5.360
C. 6.724 > 6.719
D. 7.428 < 7.423
Answer:
C
Step-by-step explanation:
6.724 is larger than 6.719
