Answer:
First angle: 60°
Second angle: 30°
Step-by-step explanation:
Let the two angles be signified by the variables x & y.
Let the first angle = x, and the second angle = y.
It is given that:
"The measure[ments] of the complementary angles...": x + y = 90°
"The measure of the first angle is 30 greater than the measure of the second angle": x = y + 30°
Use the system of equations. Plug in y + 30 for x in the first equation:
(y + 30) + y = 90
Combine like terms:
(y + y) + 30 = 90
2y + 30 = 90
Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. First, subtract 30 from both sides of the equation:
2y + 30 (-30) = 90 (-30)
2y = 90 - 30
2y = 60
Next, divide 2 from both sides of the equation:
(2y)/2 = (60)/2
y = 60/2
y = 30°
Plug in 30 for y in one of the equations:
x = y + 30
x = (30) + 30
x = 60°
Your answers:
First angle: 60°
Second angle: 30°
The price of a jacket usually costing £50 is increased to £65.
Work ou the percentage increase.
Answer:
So the answer is 30%
Step-by-step explanation:
1. For 50 = 15 increase euros
2. For 100 = 15/50 x 100 = 30 increase in euros
3. 30/100 = 30%
OR....
1. Ten percent of 50 is 5.
2. 5x3= 15(increase in euros)
3. 10 percent three times which is equal to 30%.
Solve for x. Round to the nearest tenth, if necessary.
Hi there!
1. Trigonometric Ratio
For this question, we will be knowing legs or sides of the right triangle and its ratio. Trigonometric Ratio or Trigonometry is very useful when it comes to solve for legs or sides. Because it has something to do with angles.Currently, there are 6 Trigonometric Ratios. 2 ratios are the main topic which are sine and cosine. Both can be shortened as sin, cos. While the other 4 ratios are defined by these two ratios.
2. Adjacent, Hypotenuse, Opposite
There are 3 sides in a right triangle. Opposite is a side or length of a triangle that is opposite of a specific angle. For example in the picture. CD is opposite of 65 degrees. ED is opposite of angle C.Adjacent is a leg or we can call it a base of right triangle.Hypotenuse is the longest side of right triangle according to Pythagorean Theorem. It is also the opposite of right angle.3. Using Cosine Ratio
Cosine Ratio is defined as adjacent to hypotenuse or adjacent/hypotenuse. Since we focus on the 65 degree. We can conclude that the adjacent side is x and the hypotenuse side is 7.Cosine Ratio is:
[tex] \large \boxed{ \tt{ cos 65 \degree= \frac{x}{7} }}[/tex]
For this part, use the calculator to find the value of cos65 degrees. When you put cos65 degree in a calculator, you should get 0.42261826... round to the nearest tenth as we get 0.4
Hence, the new equation is:
[tex] \large{0.4 = \frac{x}{7} }[/tex]
4. Solve The Equation
The best way to deal with decimal number when solving the equation is to multiply the whole equation by 10. Because we want to turn 0.4 to 4 which will be easier in solving the equation.[tex] \large{0.4 \times 10 = \frac{x}{7} \times 10} \\ \large{4 = \frac{10x}{7} }[/tex]
Multiply 7 both sides to get rid of the denominator.
[tex] \large{4 \times 7 = \frac{10x}{7} \times 7} \\ \large{28 = 10x}[/tex]
Divide both sides by 10 so we can finally isolate x.
[tex] \large{ \frac{28}{10} = \frac{10x}{10} } \\ \large{ \frac{28}{10} = x}[/tex]
Since the denominator is 10. We can convert to the decimal as 2.8
[tex] \large \boxed{ \tt{2.8 = x}}[/tex]
Because you want the nearest tenth then 2.8 is your answer!
5. Final Answer
x = 2.8Which of the following is an extranous solution
Answer:
x=2 is the answer
Step-by-step explanation:
Sean is a bookworm. On average, he reads pages in minutes.
Answer:
wow thats very interesting
Step-by-step explanation:
whats ur question
There are 11900 films on Netflix. 13% of the films are action. How many films are action?
13% of 11900 films are action films =1547 films.
Answer:
[tex]{ \tt{ = \frac{13}{100} \times 11900 }} \\ = 1547 \: action \: films[/tex]
Among 1,200 Chinese tourists who are visiting Nepal,45 of them already visited India,40 have visited Pakistan and 15 have visited both the countries. Illustrate this information in a venn_diagram and How many tourists have not visited any of these two countries.
30 visited nepal only 25 visited Pakistan only. 15 tourists at the intersection of the two circles and 1130 have not visited either
Answer:
We're provided - Total number of Chinese tourist = 1200 i.e n ( U ) = 1200 , number of Chinese who visited India = 45 i.e n ( I ) = 45 , number of Chinese tourists who visited Pakistan = 40 i.e n ( P ) = 40 & number of tourist who have visited both Pakistan and India = 15 i.e n ( I ⋂ F ) = 15. We're asked to find out the number of tourist who have not visited any of these two counties i.e [tex] \tt{n( \overline{i \:⋃ \: f}) = 15}[/tex].[tex] \large{ \tt{✽ \: SOLUTION}} : [/tex]
[tex] \large{ ✺ \: \tt{n(U) = n(I) + n(P) - n(I ⋂\: P) + n \: ( \overline{I \:⋃ P }\: )}}[/tex]
[tex] \large{ \tt{⟹ \: 1200 = 45 + 40 - 15 + n \: ( \overline{ I \: ⋃ P})}}[/tex]
[tex] \large{ \tt{⟹1200 = 70 + n \: ( \overline{ I \:⋃ P)}}}[/tex]
[tex] \large{ \tt{⟹ \: 1200 - 70 = n \: ( \overline{I\: ⋃ \: P})}}[/tex]
[tex] \large{ \tt{⟹1130 = n \: ( \overline{I \: ⋃ \: P})}}[/tex]
Hence , 1130 Chinese tourists have not visited any of these two countries. [ See the attached picture for Venn diagram ]- Hope I helped! Let me know if you have any questions regarding my answer and also notify me , if you need any other help! :)
received good return from m center of rs 5000 (journal entry)
Answer:
Date Account Title Debit Credit
XX-XX-XXX Sales returns and Allowances Rs. 5,000
Accounts receivable - M Center Rs. 5,000
Inventory Rs. 5,000
Cost of Goods sold Rs. 5,000
Which property does each equation demonstrate?
x2 + 2x = 2x + x2
What is the answer to this question
Answer:
65
Step-by-step explanation:
the angle on top is the same because the lengths of the lines that meet to "H" are the same.
One circle has a circumference of 12π cm. Another circle has a circumference of 32π cm. What is the ratio of the radius of the smaller circle to the radius of the larger circle?
Options:
A: 3:8
B: 8:3
C: 1:3
D: 3:1
3:8
The ratio of small circle
12:32
If we divide both of them by 4 we get 3:8
Use the given conditions to write an equation for the line in point-slope form and slope-intercept form.
Passing through (-3, -6) and (2,9)
What is the equation of the line in point-slope form?
(Simplify your answer. Use integers or fractions for any numbers in the equation.)
What is the equation of the line in slope-intercept form?
Answer:
slope-inercept form: y = 3x + 3 point-slope form: y - 9 = 3(x - 2)
Step-by-step explanation:
slope-intercept form:
y2 - y1 / x2 - x1
9 - (-6)/ 2 - (-3)
= 3
y = 3x + b
9 = 3(2) + b
9 = 6 + b
3 = b
y = 3x + 3
point-slope form:
y - 9 = 3(x - 2)
Evaluate function from their graph
Answer:
f(-5) = 7
Step-by-step explanation:
f(-5) means find the y value when x = -5
y = 7 when x = -5
Please help with this!!! 8 points!!!
Answer:
d
Step-by-step explanation:
For the given triangle find the exact value for sin(A). Assume angle C is a right angle.
Answer:
53.13 degrees
Step-by-step explanation:
In order to use sin we have to use the opposite side over the hypotenuse.
[tex]\frac{4}{5}[/tex] in this case
sin(A) = [tex]\frac{4}{5}[/tex]
[tex]A = sin^{-1} \frac{4}{5}[/tex]
Plugging this into the calculator you get about 53.13 degrees
What is the next term in the pattern 1, -1, 2, -2,3
Answer: -3
Step-by-step explanation:
(05.06 LC)The net of an isosceles triangular prism is shown. What is the surface area, in square units, of the triangular prism?
Three rectangles are shown, one below the other. The middle rectangle has a width of 6 units, and, along each width, is a triangle with a height of 4 units. The length of the lowermost rectangle is 8 units and its width is 5 units.
104 units²
132 units²
152 units²
168 units²
Answer:
C. 152 units²Step-by-step explanation:
Total surface area is the area of the net.
The rectangles have area:
8*(5 + 6 + 5) = 128 units²The triangles have area:
2*(1/2*6*4) = 24 units²Total area is:
128 + 24 = 152 units²Correct choice is C
Answer:
C. 152 square units
Step-by-step explanation:
I'll do the rectangles first because they are the easiest.
8(5)=40. There are 2 of those rectangles, so multiply by 2: 80.
6(8)=48. Add that to 80, you get 128.
The two triangles actually make a rectangle, so to save work, just multiply the base by the height: 6(4). You get 24.
Add them all up, and you get 152.
Hope this helps!
On a horizontal number line, positive numbers are_____
On a vertical number line, negative numbers are_______
The number is_______
Answer:
the horizontal are called x-axis, while the vertical are called y-axis
Can someone help me with this math homework please!
Answer:
1 = Input G
2 = Input F
3 = Input H
Step-by-step explanation:
The circumference of a steering wheel of a car is 20 inches. What is the radius of
the steering wheel?
40 in.
20 in
100 in.
10 in.
The radius of the steering wheel is 10 inches.
What is a circle?A circle is the defined as a closed, two-dimensional curved shape in the geometry. Every point on the circle is equal distance from a certain point known as the centre of circle. A circle is a two-dimensional form that is measured in terms of radius.
What is the circumference of a circle?Circumference of a circle is defined as perimeter of circle is defined as the enclosing boundary of a curved geometrical figure called a circle. It is the product of π and its diameter.
Circumference (C) = π × d , where d is the diameter of a circle.
Given data as :
Circumference of a steering wheel of a car = 20π inches
Circumference(C) = 20π inches
Substitute the value of c in formula of Circumference :
20π = π × d [ diameter(d) = 2 radius(r) ]
20π = π × 2 r
Divided by 2π both the sides
10 = r
r = 10
r = 10 inches
Hence, the radius of the steering wheel is 10 inches.
Learn more about Circumference of a circle here :
https://brainly.com/question/17357009
#SPJ5
Question seems to be incomplete the correct question would be
The circumference of a steering wheel of a car is 20π inches. What is the radius of
the steering wheel?
In which figure is DE BC
Answer:
Given: DB = 7.2 cm, AE = 1.8 cm and EC = 5.4 cm and DE || BC.
DB
AD
=
AC
AE
[by basic proportionality theorem which states that if a line is drawn parallel to one side of a triangle the other two sides in distinct points, then the other two sides are divided in the same.
7.2
AD
=
5.4
1.8
AD=
5.4
7.2×1.8
AD=
10
24
⟹AD=2.4cm
someone help me please with this algebra problem
Answer:
4
Step-by-step explanation:
3r = 10 + 5s
r = 10
3(10) = 10 + 5s
30 = 10 + 5r
20 = 5r
r = 4
Rick has $8x and Helen has twice that amount. They save $3 each per week. What amount will be the sum of their money 4 weeks from now
Answer:
Savings total for both = 24x + 24
Step-by-step explanation:
Rick has 8x to start with
Let w = the number of weeks he will save.
Savings = 8x + 3*w
Let w = 4
Savings = 8x + 3*4
Savings = 8x + 12
Helen
Let w = the number of weeks she will save.
Savings = 16x + 3*w
Let w = 4
Savings = 16x + 12
Now we come to the question. It seems to want the total combining both of them.
Rick + Helen = 8x + 12 + 16x + 12 = 24x + 24
The only other possible answer is
Rick = 8x + 12
Helen = 16x + 12
A car and a bus were travelling towards each other at uniform speeds. They were 250 km apart at noon and passed each other at 2 p.m. If the speed of the car was 75 km/h, find the speed of the bus.
Answer:
50 km/hr
Step-by-step explanation:
speed = x + 75
distance = 250km
time = 2
250 = (x + 75) * 2
125 = x + 75
x = 50
x = 4y + 3, 2x + y = -3
System of Equations
Answer:
(- 1, - 1 )
Step-by-step explanation:
Given the 2 equations
x = 4y + 3 → (1)
2x + y = - 3 → (2)
Substitute x = 4y + 3 into (2)
2(4y + 3) + y = - 3 ← distribute parenthesis and simplify left side
8y + 6 + y = - 3
9y + 6 = - 3 ( subtract 6 from both sides )
9y = - 9 ( divide both sides by 9 )
y = - 1
Substitute y = - 1 into (1) for corresponding value of x
x = 4(- 1) + 3 = - 4 + 3 = - 1
solution is (- 1, - 1 )
Find the measure of the indicated angle
Answer:
x=44°..
Step-by-step explanation:
base angle of isosceles triangle are equal68+68+x=180°{sum of angle of triangle}136°+x=180°x=180-136°x=44°hope it helpsstay safe healthy and happy. ..Answer:
the value of x is 44 i hope it will help you
Which function is represented by the graph?
5
4
3
2
Of(x) = -x - 3] + 4
f(x) = -x + 3 + 4
f(x) = -x + 4 + 3
f(x) = -x + 4 + 3
-5 A-3 -2 -1 2 3 4 5
2+
-3
45
Step-by-step explanation:
The correct answer is f(x)=3^(x+3)
the area of the rectangle is 48cm^2
show that x satisfies the equation x^2 + 7x -78 = 0
Answer:
No its doesn't satisfy the equation.
[tex]{ \bf{area = 2(l + w)}} \\ { \tt{48 = 2((x + 10) + (x - 3))}} \\ { \tt{24 = 2x + 7}} \\ 2x = 17 \\ x = 8.5 \\ \\ { \bf{in : \: {x}^{2} + 7x - 78 = 0 }} \\ x = 6 \: \: and \: \: - 13[/tex]
Decrease £19064.67 by 9.5%
Give your answer rounded to 2 DP. (decimal place)
Please Help !!!
Answer:
17253.52
Step-by-step explanation:
100-9.5=90.5
19064.67*0.905=17253.52
The ages of Raju and Ravi are in the ratio 3:4 Four years from now the ratio of their ages will be 4:5 Find their present ages
Answer: Their present age is 12 and 16.
Step-by-step explanation:
Let the required age be 3x and 4x
so
(3x+4)/(4x+4) = 4/5
5(3x+4) = 4(4x+4)
or, 15x + 20 = 16x + 16
or, 15x - 16x = 16-20
or, -x = -4
so, x = 4
now,
3x = 3*4 = 12
4x = 4*4 = 16
if x-y=9 and xy=2,find the value of (x square + y square)
Answer:
x² + y² = 85
Step-by-step explanation:
Using the expansion
(x - y)² = x² + y² - 2xy , then
x² + y² - 2xy = (x - y)² ( add 2xy to both sides )
x² + y² = (x - y)² + 2xy ← substitute given values
= 9² + 2(2)
= 81 + 4
= 85