Answer:
a) 4-5 = -1
b) -6+6 = 0
c) 6+(-4) = 2
As shown in Figure 2, it is known that PQRS, VWXY and RTU are all straight lines.
a）Find the value of a + b + c + d + e;
b）Find the sum of the interior angles of the polygon QRTXW.
Answer:
a. 360°
b. 540°
Step-by-step explanation:
a The sum of the exterior angles of any n-sided polygon is always 360°. Therefore:
a + b + c + d + e = 360°
b. Sum of interior angles of an n-sided polygon is given as (n - 2) × 180
The polygon, QRTXW is a 5 sided polygon, therefore n = 5.
Plug in the value of 5 into the equation:
Sum of interior angles of QRTXW = (5 - 2) × 180
= 3 × 180
= 540°
Just need 1 answered
family of solutions of the second-order DE y y 0. Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions. 12. y(1) 0, y(1) e
Answer:
[tex]y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}[/tex]
Step-by-step explanation:
Given
[tex]y=c_1e^x +c_2e^{-x[/tex]
[tex]y(1) = 0[/tex]
[tex]y'(1) =e[/tex]
Required
The solution
Differentiate [tex]y=c_1e^x +c_2e^{-x[/tex]
[tex]y' = c_1e^x - c_2e^{-x}[/tex]
Next, we solve for c1 and c2
[tex]y(1) = 0[/tex] implies that; x = 1 and y = 0
So, we have:
[tex]y=c_1e^x +c_2e^{-x[/tex]
[tex]0 = c_1 * e^1 + c_2 * e^{-1}[/tex]
[tex]0 = c_1 e + \frac{1}{e}c_2[/tex] --- (1)
[tex]y'(1) =e[/tex] implies that: x = 1 and y' = e
So, we have:
[tex]y' = c_1e^x - c_2e^{-x}[/tex]
[tex]e = c_1 * e^1 - c_2 * e^{-1}[/tex]
[tex]e = c_1 e - \frac{1}{e}c_2[/tex] --- (2)
Add (1) and (2)
[tex]0 + e = c_1e + c_1e + \frac{1}{e}c_2 - \frac{1}{e}c_2[/tex]
[tex]e = 2c_1e[/tex]
Divide both sided by e
[tex]1 = 2c_1[/tex]
Divide both sides by 2
[tex]c_1 = \frac{1}{2}[/tex]
Substitute [tex]c_1 = \frac{1}{2}[/tex] in [tex]0 = c_1 e + \frac{1}{e}c_2[/tex]
[tex]0 = \frac{1}{2} e+ \frac{1}{e}c_2[/tex]
Rewrite as:
[tex]\frac{1}{e}c_2 = -\frac{1}{2} e[/tex]
Multiply both sides by e
[tex]c_2 = -\frac{1}{2} e^2[/tex]
So, we have:
[tex]y=c_1e^x +c_2e^{-x[/tex]
[tex]y = \frac{1}{2}e^x -\frac{1}{2} e^2 * e^{-x}[/tex]
[tex]y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}[/tex]
what is 9.7 as a fraction ?
Answer:
Step-by-step explanation:
9.7 = [tex]\frac{97}{10}[/tex]
Count the number of places in the decimal number after the decimal point.
Here , there is only one place.
So, multiply and divide by 10. 9.7 *10/1*10 = 97/10
Which set of variables below is most likely to have a positive correlation?
A. Amount of miles driven in a car and country in which the car doing the driving was made
B. Amount of miles driven in a car and amount of gasoline left in the gas tank
C. Amount of miles driven in a car and model year of the car used to do the driving
D. Amount of miles driven in a car and amount of gasoline used
Answer:
D
Step-by-step explanation:
The amount of miles increase and the amount of gasoline used increases
Xavier leans a 28-foot ladder against a wall so that it forms an angle of 69 degrees with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary.
Answer:
[tex]\approx 26.14[/tex]
Step-by-step explanation:
In this problem, one is given a right triangle, with the length of the hypotenuse given and one of the angles in the triangle. One is asked to find the length of one of the legs. In this situation, one can use right-angle trigonometry. Right angle trigonometry has the following ratios,
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]
Please note that the sides named (opposite) and (adjacent) are subjective depending on the angle of reference. The side named (hypotenuse) is the side opposite the right angle, its name does not change. In this case, one is given an angle measure and the measurement of the hypotenuse. One is asked to find the length of the side opoosite this angle. One should use the ratio of sine (sin) to achieve this.
[tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]
Substitute,
[tex]sin(69)=\frac{opposite}{28}[/tex]
Inverse operations,
[tex]28(sin(69))=opposite[/tex]
[tex]26.14\approx opposite[/tex]
Answer:
26.14
Step-by-step explanation:
One number is 96 more than another. Their ratio is 5:17. Find the numbers
Answer:
40 and 136
Step-by-step explanation:
The ratio of the 2 numbers = 5 : 17 = 5x : 17x ( x is a multiplier )
One number is 96 more than the other then
17x = 5x + 96 ( subtract 5x from both sides )
12x = 96 ( divide both sides by 12 )
x = 8 , then
5x = 5 × 8 = 40
17x = 17 × 8 = 136
The 2 numbers are 40 and 136
A department store holds a year-end clearance sale that includes a 5.5% discount on cosmetics. Find the sale price of a bottle of perfume if its original price was $48.41.
Answer:
Sale price = $45.75
Step-by-step explanation:
Original price = $48.41
Percentage Discount = 5.5%
Amount of discount = Percentage Discount × Original price
= 5.5% × $48.41
= 5.5/100 × $48.41
= 0.055 × $48.41
= $2.66255
Sale price = Original price - Amount of discount
= $48.41 - $2.66255
= $45.74745
Approximately,
Sale price = $45.75
Find the distance between (1, 2) and (5,2)
The points lie in______
The distance is________
Use the zero product property to find the solutions to the equation x2 + 12 = 7x.
x = –4 or x = 3
x = –4 or x = –3
x = –3 or x = 4
x = 3 or x = 4
Answer:
In a product like:
a*b = 0
says that one of the two terms (or both) must be zero.
Here we have our equation:
x^2 + 12 = 7x
x^2 + 12 - 7x = 0
Let's try to find an equation like:
(x - a)*(x - b) such that:
(x - a)*(x - b) = x^2 + 12 - 7x
we get:
x^2 - a*x - b*x -a*-b = x^2 - 7x + 12
subtracting x^2 in both sides we get:
-(a + b)*x + a*b = -7x + 12
from this, we must have:
-(a + b) = -7
a*b = 12
from the first one, we can see that both a and b must be positive.
Then we only care for the option with positive values, which is x =3 or x = 4
replacing these in both equations, we get:
-(3 + 4) = -7
3*4 = 12
Both of these equations are true, then we can write our quadratic equation as:
(x - 3)*(x - 4) = x^2 + 12 - 7x
The correct option is the last one.
Answer:
d
Step-by-step explanation:
When solving algebraic expressions involving fractions with different denominators, you just have to determine the LCM and multiply it across each term
Answer:
b
Step-by-step explanation:
if 8 out of every 10 high school students take a math class, how many students in a high school with 700 students are in the math class?
Answer:
560
Step-by-step explanation:
8 out of 10 is 80%, so then the answer would be 80% of 700, which would be 560
solve the simultaneous equation: x-y=2
xy=36
Answer:
Y= –7.08, 5.08
Step-by-step explanation:
hope ya ready bro.
X=36/Y
replace 36/y instead of X
36/Y–Y=2===> 36–Y²=2Y===> Y²+2Y–36=0
Y1= –1+√37≈ –7.08
Y2= –1–√37≈ 5.08
y =2/3x + 20
when x = 21
Answer:
34
Step-by-step explanation:
First we need to do 2/3*21, which equals 14 as 3 and 21 can be simplified to 1 and 7. 7 * 2/1= 14. Then we add the 20 to 14, 20+14= 34
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{y = \dfrac{2}{3}x + 20}[/tex]
[tex]\mathsf{y =\dfrac{2}{3}(21) + 20}[/tex]
[tex]\mathsf{\dfrac{2}{3}(21) + 20 = y }[/tex]
[tex]\mathsf{\dfrac{2}{3}(21)=\bf14}[/tex]
[tex]\mathsf{14 + 20 = y}[/tex]
[tex]\mathsf{14 + 20 = \bf 34}[/tex]
[tex]\huge\checkmark\boxed{\huge\textsf{y = 34}}\huge\checkmark[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: \bf y = 34}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\huge\text{Amphitrite1040:)}[/tex]
What is the classification for this polynomial? X2y+3x3
Answer:
quadratic
Step-by-step explanation:
hope you got it
What is the explicit formula for this sequence?
7, 2, -3, -8...
Answer:
The explicit formula of that sequence is T - 5
Step-by-step explanation:
Let T represent each term in the sequence. So now try replacing T with each term in the sequence. Like this ;
7 - 5 = 2
2 - 5 = -3
-3 - 5 = -8
hope this helps
For f(x) = 6x + 20, what is the value of x for which f(x)= -4 ?
Answer:
x = -4
Step-by-step explanation:
Plug in -4 into the function and solve for x:
f(x) = 6x + 20
-4 = 6x + 20
-24 = 6x
-4 = x
So, the answer is x = -4
help me to solve this question please faster thankyouu
Answer:
Step-by-step explanation:
u799
What is the vertex of the function?
Consider the quadratic function:
f(x) = x2 - 8x - 9
Vertex: (zo
(2)
Answer:
(4 , -25)
Step-by-step explanation:
that is the procedure above
the vertex of the parabola is calculated by the formula
[tex]\displaystyle\ ax^2+bx+c\quad ;\quad \boxed{x_0=\frac{-b}{2a} \ \ ;\quad y_0 =ax_0^2+bx_0+c} \\\\x_0=-\frac{-8}{2} =4 \quad ; \ \ y_0 =16-32-9=-25 \\\\\ \ Answer: Coordinates \ \ of \ the \ vertex \ of \ the \ \ parabola \ \ (4;-25)[/tex]
help me pls pls !!!!! help
Dan invests £13000 into his bank account. He receives 4.7% per year simple interest. How much will Dan have after 6 years? Give your answer to the nearest penny where appropriate.
Step-by-step explanation:
SI = PxTxR/100
SI= (13000)(6)(4.7)/100
SI = 366600/100
SI= 3666
Find the length of side xx in simplest radical form with a rational denominator.
Answer:
Solution given:
it is a right angled isosceles triangle
so
perpendicular [p]=base[b]=3
hypotenuse [h]=x
we have
by using Pythagoras law
p²+b²=h²
3²+3²=h²
18=h²
h=[tex]\sqrt{18}[/tex]
x=[tex]\bold{3\sqrt{2}}[/tex]
What is the sum of x2 − 3x + 7 and 3x2 + 5x − 9
Answer:
4x²+2x-2
Step-by-step explanation:
x²-3x+7
+
3x²+5x-9
Answer:
4x² + 2x - 2
General Formulas and Concepts:
Algebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
x² - 3x + 7 + 3x² + 5x - 9
Step 2: Simplify
Combine like terms (x²): 4x² - 3x + 7 + 5x - 9Combine like terms (x): 4x² + 2x + 7 - 9Combine like terms: 4x² + 2x - 2Which segment is opposite to∠E?
Answer:
UJ
Step-by-step explanation:
The side that is opposite angle E is UJ
Since this is a triangle, we use the corners that do not touch the angle, U and J and the segment is the one that connects them
What is the slope of the line? What is the y-intercept of the line? y = -x - 6
Answer:
m = -1
y intercept = -6
Step-by-step explanation:
The given equation of the line is ,
[tex]\implies y = -x -6[/tex]
We know that the Standard equation of Slope Intercept Form of the line is,
[tex]\implies y = mx + c[/tex]
Where ,
m is slope c is y intercept .On comparing to the Standard form of the line we get ,
[tex]\implies Slope = -1 [/tex]
[tex]\implies y - intercept= -6 [/tex]
Slope: -1
Solution:This equation is written in slope-intercept form (y=mx+b).In this formula, "m" stands for the line's slope and "b" stands for the y-intercept of the line.Also, please notice that the slope of the line is the coefficient of x (the number next to x)If we don't have a number next to x, then the coefficient is equal to 1.If we have a minus sign next to x, then the coefficient is equal to -1.Therefore, the slope of the line is -1.Now, the y-intercept is a constant that's subtracted from/added to the slope.Therefore, the y-intercept of the line is -6.Hope it helps.
Do comment if you have any query.
Solve. Algebra 1
1-4p-2p=1-5p
Answer:
p = 0
Step-by-step explanation:
1 - 4p - 2p = 1 - 5p
-6p + 1 = -5p + 1
-p + 1 = 1
-p = 0
p = 0
Which ordered pair is the best estimate for the solution of the
system of equations?
y= -1/2x +4 and y=1/2x - 3
Answer:
Where are the ordered pairs?
Step-by-step explanation:
Solve for x. Round to the nearest tenth, if necessary.
Answer:
5.3938654741
Step-by-step explanation:
x=5.1/cos(19) = 5.39386547405
The value of the variable 'x' using the cosine formula will be 5.4 units.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
The value of 'x' is given by the cosine of the angle ∠LKM. And the cosine of an angle is the ratio of the base and hypotenuse of the right-angle triangle. Then we have
cos 19° = 5.1 / x
x = 5.4
The value of the variable 'x' using the cosine formula will be 5.4 units.
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
#SPJ7
Have a good day everybody.......
thank you, you too! :D
** I need help for this one***
Answer:
60
Step-by-step explanation:
the two angles are equal angle x and the one opposite
=180-40
=120 ÷2
=60
Answer is
z = 70
x = 70
Step-by-step explanation:
z is also equal to x because two sidess are equal
40 + x + x =180
40 + 2x = 180
2x = 140
x =70
so x and z are 70 each
