Answers
Step-by-step explanation:
13x - 12 = 7x - 6( remaining side of the similar triangle is equal).
Related Questions
What is the soution of (Image below)
Answers
Answer:
A
Step-by-step explanation:
Starting with the original equation:
[tex]\sqrt{1-3x} =x+3[/tex]
Squaring both sides to remove the root, and expanding the right side:
[tex]1-3x=(x+3)(x+3)[/tex]
Multiplying the right side:
[tex]1-3x=x^{2} +6x+9[/tex]
Combine like terms:
[tex]x^{2} +9x+8[/tex]
Factor:
(x+8)(x+1)
If x+8=0, then x= -8
If x+1=0, then x=-1
For the given triangle find the exact value for sin(A). Assume angle C is a right angle.
Answers
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
The x- intercepts of a parabola are (0,-6) and (0,4). The parabola crosses the y- axis at -120. Lucas said that an equation for the parabola is y=5x^2+10x-120 and that the coordinates of the vertex are (-1, -125). Do you agree or disagree? List why?
Answers
Given:
The x- intercepts of a parabola are (0,-6) and (0,4).
The parabola crosses the y- axis at -120.
Lucas said that an equation for the parabola is [tex]y=5x^2+10x-120[/tex] and that the coordinates of the vertex are (-1, -125).
To find:
Whether Lucas is correct or not.
Solution:
The x- intercepts of a parabola are (0,-6) and (0,4). It means (x+6) and (x-4) are the factors of the equation of the parabola.
[tex]y=a(x+6)(x-4)[/tex] ...(i)
The parabola crosses the y- axis at -120. It means the equation of the parabola must be true for (0,-120).
[tex]-120=a(0+6)(0-4)[/tex]
[tex]-120=a(6)(-4)[/tex]
[tex]-120=-24a[/tex]
Divide both sides by -24.
[tex]\dfrac{-120}{-24}=a[/tex]
[tex]5=a[/tex]
Substituting [tex]a=5[/tex] in (i), we get
[tex]y=5(x+6)(x-4)[/tex]
[tex]y=5(x^2+6x-4x-24)[/tex]
[tex]y=5(x^2+2x-24)[/tex]
[tex]y=5x^2+10x-120[/tex]
So, the equation of the parabola is [tex]y=5x^2+10x-120[/tex].
The vertex of a parabola [tex]f(x)=ax^2+bx+c[/tex] is:
[tex]Vertex=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)[/tex]
In the equation of the parabola, [tex]a=5,b=10,c=-120[/tex].
[tex]-\dfrac{b}{2a}=-\dfrac{10}{2(5)}[/tex]
[tex]-\dfrac{b}{2a}=-\dfrac{10}{10}[/tex]
[tex]-\dfrac{b}{2a}=-1[/tex]
Putting [tex]x=-1[/tex] in the equation of the parabola, we get
[tex]y=5(-1)^2+10(-1)-120[/tex]
[tex]y=5-10-120[/tex]
[tex]y=-125[/tex]
So, the vertex of the parabola is at point (-1,-125).
Therefore, Lucas is correct.
There are 11900 films on Netflix. 13% of the films are action. How many films are action?
Answers
13% of 11900 films are action films =1547 films.
Answer:
[tex]{ \tt{ = \frac{13}{100} \times 11900 }} \\ = 1547 \: action \: films[/tex]
(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
Answers
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!
Find the measure of the indicated angle
Answers
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
Decrease £19064.67 by 9.5%
Give your answer rounded to 2 DP. (decimal place)
Please Help !!!
Answers
Answer:
17253.52
Step-by-step explanation:
100-9.5=90.5
19064.67*0.905=17253.52
how do you get sin theta
Answers
And 1/csc
And root 1-cos^2
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.
Answers
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! :)
Solve for x. Round to the nearest tenth, if necessary.
Answers
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 property does each equation demonstrate?
x2 + 2x = 2x + x2
Answers
The price of a jacket usually costing £50 is increased to £65.
Work ou the percentage increase.
Answers
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%.
Evaluate function from their graph
Answers
Answer:
f(-5) = 7
Step-by-step explanation:
f(-5) means find the y value when x = -5
y = 7 when x = -5
Tìm x €N: a) 24:(2x-4)+14=26
Answers
B a 135899933
Last year, sales at a book store increased from $5,000 to $10,000. This year, sales decreased to $5,000 from $10,000. What percentage did sales
increase last year? What percentage did sales decrease this year?
Sales increased
last year, from $5,000 to $10,000. When sales dropped from $10.000 to $5,000 this year, sales decreased
Answers
Answer:
Last year sales increased by 200%. This year sales decreased by 50%.
Step-by-step explanation:
Can someone help me with this math homework please!
Answers
Answer:
1 = Input G
2 = Input F
3 = Input H
Step-by-step explanation:
The area of a wall in a house is 10.37 square metres. If a can of paint covers 3.1 square metres, how many cans of paint are needed to paint the wall?
Answers
Answer:
4 cans of paint
Step-by-step explanation:
Take the area of the wall and divide by the area that the can of pain will cover
10.37 / 3.1
3.34516129 cans
We need to round up to make sure we buy enough cans of paint
4 cans of paint
We can take area as,
Area = A
The required formula is,
→ A of wall ÷ A that paint's can will cover
Then find the no. of cans of paint that are needed to paint the wall.
Now use the formula,
→ A of wall ÷ A that paint's can will cover
→ 10.37 ÷ 3.1
→ 3.34516129032
→ 4 cans (by nearest value)
Hence, we need 4 cans to paint the wall.
Which of the following is an extranous solution
Answers
Answer:
x=2 is the answer
Step-by-step explanation:
if x-y=9 and xy=2,find the value of (x square + y square)
Answers
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
A oil company has a large tank that holds the oil before it is distributed. If it costs $3.20 per cubic meter for oil, how much money would it cost to fill the entire tank?
A. $65,280
B. $68,000
C. $5,440
D. $67,200
Answers
Answer:
Option A, $65,280
Step-by-step explanation:
The volume of the tank is,
12×20×15+40×(50-15)×12
= 3600+16800
=20400 cubic meters
For each cubic meter, it costs $3.20, so for 20400 cubic meters it'll cost,
20400×$3.20
= $65,280
Answered by GAUTHMATH
the area of the rectangle is 48cm^2
show that x satisfies the equation x^2 + 7x -78 = 0
Answers
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]
In which figure is DE BC
Answers
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
Evaluate each of the following. help plz
Answers
Answer:
5!= 120
13!= 6227020800
12!/6!= 665280
10!/7! 3!= 120
5(4!)= 120
Step-by-step explanation:
received good return from m center of rs 5000 (journal entry)
Answers
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 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
Answers
Step-by-step explanation:
The correct answer is f(x)=3^(x+3)
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.
Answers
Step 1: Write equation
To solve for the radius, we must first find the equation. We will use the formula for a circumference. The circumference is equal to 2 times pi (π) times the radius. Let’s write the equation now.
C=2πr
Step 2: Substitute information
Before we find the radius, we must first substitute the information provided to us. In this case, we can substitute c for 20, as that is the circumference.
C=2πr
20= 2πr
Step 3: Solve for the radius
Now that we have steps one and two done, we can solve for the radius. Let’s start by rewriting the equation.
20= 2πr
Great! Now let’s get rid of the constant on the right side. Let’s divide each term by 2.
20= 2πr
10= πr
Now let’s move the pi side to the left. Divide each term by pi to do so.
10= πr
10π= r
This is your answer! If desired, you could divide the term by pi to get the proper answer of 3.18. Since this is not an option provided, I will leave the answer as 10π, assuming that the teacher would like you to leave the pi symbol.
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?
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
Answers
3:8
The ratio of small circle
12:32
If we divide both of them by 4 we get 3:8
Please help with this!!! 8 points!!!
Answers
Answer:
d
Step-by-step explanation:
Factor completely x2 + 16
Answers
Answer:
not a factorable number i think
Step-by-step explanation:
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?
Answers
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)