Answer:
[tex]\bold{x = 34^\circ}[/tex]
Step-by-step explanation:
Given:
[tex]cos x = sin (x + 22^\circ)[/tex]
To solve:
The given equation.
Solution:
First of all, let us consider an important property of sine and cosine.
[tex]sin(90^\circ-\theta )=cos\theta[/tex]
OR
[tex]cos(90^\circ-\theta )=sin\theta[/tex]
We can apply above property to solve for [tex]x[/tex] as per given equation.
[tex]cos x = sin (x + 22^\circ)[/tex]
Changing [tex]cosx[/tex] to sine form:
[tex]cosx=sin(90^\circ-x)[/tex]
[tex]cosx=sin(90^\circ-x) = sin(x+22^\circ)[/tex]
[tex]\therefore 90^\circ-x=x+22^\circ\\\Rightarrow 90^\circ-22^\circ=x+x\\\Rightarrow 2x=68^\circ\\\Rightarrow \bold{x = 34^\circ}[/tex]
So, solution to the equation [tex]cos x = sin (x + 22^\circ)[/tex] is:
[tex]\bold{x = 34^\circ}[/tex]
pls help asp [(4+3)⋅5−6]⋅2
23
24
29
58
Solve the equation
(If possible please show work)
Answer:
x=2
Step-by-step explanation:
1+4x=7+x
↦4x-x=7-1
↦3x=6
↦x=6/3
↦x=2
.°. x=2
Hope you understand it
Answer:
x = 2
Step-by-step explanation:
For this equation, we simply need to solve for x.
1 + 4x = 7 + x
1 + -1 + 4x = 7 + -1 + x
4x = 6 + x
4x + -x = 6 + x + -x
3x = 6
3x * (1/3) = 6 * (1/3)
x = 2
So the solution to this equation is x = 2.
Cheers.
measures of two supplementary are consecutive odd integers find the angles
Answer:
89 , 91
Step-by-step explanation:
let one be x and the other be x+2
Supplementary angles are those angles that sum up to [tex]180^{o}[/tex]
equating both sides
x+x+2 = 180
2x+2 = 180
2x = 180-2
2x = 178
x = 89
x+2 = 89+2 = 91
Answer:
its a.
Step-by-step explanation:
Fatimah is 5 years older than Dollah. If the product of their ages is 234, how old is Dollah?
Data:
age of Dollah = x (unknown element)
age of Fatimeh = x + 5 (age of Dollah + 5)
the product is 234
Equation:
x * (x + 5) = 234
x² + 5x = 234
x² + 5x - 234 = 0
Δ = b² - 4 a c = 5² - 4 (1 * -234) = 25 - 4 (-234) = 25 - (-936)
= 25 + 936 = 961
x₁,₂=[tex]\frac{b^{2} ± \sqrt{delta} }{2a}[/tex] = [tex]\frac{5^2 +/- \sqrt{961} }{2}[/tex] = [tex]\frac{25 +/- 31}{2}[/tex]
x1 = (25+31)/2 = 56 / 2 = 28
x2 = (25 -31)/2 = -6 / 2 = -3 [age can't be negative, so the first one is accettable]
So:
Dollah's age (x) = 28 years old
Fatima's age (x + 5) = 28 + 5 = 32 years old
need help with this linear equation
Answer:ok
Step-by-step explanation:wow
Answer:
y = ½x + ¾
slope (m) = ½
y-intercept(b) = ¾
Step-by-step explanation:
4y - 2x = 3
4y = 2x + 3
y = (2x + 3) ÷ 4
y = 2/4x + 3/4
y = ½x + ¾
slope (m) = ½
y-intercept(b) = ¾
For equation r4=16, select the appropriate property of equality to move the coefficient to the right side of the equation. . A. Subtraction Property of Equality . B. Addition Property of Equality . C. Division Property of Equality . D. Multiplication Property of Equality
Answer:
DIVISION PROPERTY OF EQUALITY
Step-by-step explanation:
Given the equation r4 = 16,wm we can rewrite the equation as 4r = 16
The coefficient at the left hand side of the equation that we are to move to rge right is 4 (the number attached to the r variable). To do this we are going to apply the Division property of equality. This property is a property where both sides of an equation is divided through by the same constant without affecting the equality sign or by still keeping the equation.
To move the coefficient of r to the other side, we will divide both sides of the equation by 4 as shown;
4r/4 = 16/4
r = 4×4/4
r = 4
Hence the property that is used to move the coefficient (4) to the other side of the equation is the DIVISION PROPERTY OF EQUALITY.
What is 5x - 2y = -5 and 5x + 6y =35
Answer:
x = 1
y = 5
Step-by-step explanation:
5x - 2y = -5
5x + 6y = 35
=> 5x + 6y = 35
=> 5x - 5x + 6y = 35 - 5x
=> 6y = 35 - 5x
=> 6y/6 = 35/6 - 5/6x
=> y = 35/6 - 5/6x
=> 5x - 2 (35/6 - 5/6x) = -5
=> 5x - 35/3 + 5/3x = -5
=> 15/3x -35/3 + 5/3 = -15/3
=> 20/3x -35/3 = -15/3
=> 20/3x -35/3 + 35/3 = -15/3 + 35/3
=> 20/3x = 20/3
=> 20/3x * 3 = 20/3 * 3
=> 20x = 20
=> 20x/20 = 20/20
=> x = 1
=> 5x + 6y = 35
=> 5(1) + 6y = 35
=> 5 + 6y = 35
=> 5 -5 + 6y = 35 -5
=> 6y = 30
=> 6y/6 = 30/6
=> y = 5
So, x = 1
y = 5
HELP!!!!!!!!!!!!!!!!!!!!
20=2(y-6)+10
Answer:
2+2y
Step-by-step explanation:
20=2(y-6)+10
20= (2×y-2×6)+10
20= (2y-12)+10
Open the bracket
20=2y-12+10
Collect liked terms
20=12+10+2y
20=22+2y
=22-20+2y
2+2y
Hope this helps
Comment for more explanation
Use the graph to determine the domain and range of the exponential function.
Answer:
Domain= possible x values
Range= possible y values.
Domain= all real numbers
Range= all numbers greater than -2.
Let me know if this helps :)
Domain = all real numbers and Range = ( -2 , ∞) of the given exponential graph
What is domain and range of exponential function?
" Domain of exponential function y = aˣ is all the values of x and range is the all calculated values of 'y' after substituting value of x."
General exponential function
y = aˣ
According to the graph,
Given exponential function,
y = 3ˣ - 2
x represents the domain of the function.
y represents the range of the function
compare with exponential equation
a= 3 >1
As the value of 'x' increases value of 'y' moves to infinity.
Therefore, value of y defined for all the values of 'x'.
Therefore,
Domain is set of all real numbers.
Function y is transformed by -2.
Substitute x=0 in y = 3ˣ-2 we get,
y = -2
Therefore,
Range = (-2 , ∞)
Hence, Domain = all real numbers and Range = ( -2 , ∞) of the given exponential graph.
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Please help me lorddddd
Answer:
Option two and three for the domain and range question
Problem 1: Joseph is going to buy a cell phone plan on his own. The most important thing for him is being able to text. So, he has narrowed down her choices to only 2 companies, Cell Text and Data City. Cell Text is charging $40 to start the service and $0.01 for each text message. Data City, on the other hand, is charging $25 for service and $0.05 for each text message. Question: How many text messages does Joseph need to send in order for Cell Text to be the cheaper service?
Step-by-step explanation: lol like a dozen
On Monday, Brian counted 28 ducks and Cathy counted 15 ducks. On Tuesday,
they counted 37 ducks altogether. How many more ducks did they count on
Monday than Tuesday?
Answer:
6 ducks
Step-by-step explanation:
Monday, Brian counted 28 ducks and Cathy counted 15 ducks
= 28+15 =43
Tuesday, they counted 37
Monday count - Tuesday count
43 - 37 =6
Solve: -5 - (-1) I know it sounds really easy but i can figure this out
Answer:
Step-by-step explanation:
-5+1
-4
Find the perimeter of the rectangle with the following vertices.
(-6, -2), (0, - 10), (5,2), (-1, 10)
A. 52
B. 46
C. 23
D. 40
The answer to the question is 46
please someone help me....
Answer: see proof below
Step-by-step explanation:
Use the following Product to Sum Identities:
2 sin A sin B = cos (A - B) - cos (A + B)
2 sin A cos B = sin (A + B) + sin (A - B)
Use the Unit Circle to evaluate: cos 120 = -1/2 & sin 60 = √3/2
Proof LHS → RHS
LHS: sin 20 · sin 40 · sin 80
Regroup: (1/2) sin 20 · 2 sin 40 · sin 80
Product to Sum Identity: (1/2) sin 20 [cos(80-40) - cos (80+40)]
Simplify: (1/2) sin 20 [cos 40 - cos 120]
Unit Circle: (1/2) sin 20 [cos 40 + (1/2)]
Distribute: (1/2) sin 20 cos 40 + (1/4) sin 20
Product to Sum Identity: (1/4)[sin(20 + 40) + sin (20 - 40)] + (1/4) sin 20
Simplify: (1/4)[sin 60 + sin (-20)] + (1/4) sin 20
= (1/4)[sin 60 - sin 20] + (1/4) sin 20
Unit Circle: (1/4)[(√3/2) - sin 20] + (1/4) sin 20
Distribute: (√3/8) - (1/4) sin 20 + (1/4) sin 20
Simplify: √3/8
LHS = RHS: √3/8 = √3/8 [tex]\checkmark[/tex]
We are given the equation cos(20°)(cos(40°)(cos(60°)(cos(80°) = √3 / 8. Let's once again start by applying the identity 'sin(s)sin(t) = - cos(s + t) + cos(s - t) / 2. In this case if we focus on the expression 'cos(20°)(cos(40°),' s would be = 20°, and t = 40°.
[tex]\mathrm{Use\:the\:following\:identity}:\quad \sin \left(s\right)\sin \left(t\right)=\frac{-\cos \left(s+t\right)+\cos \left(s-t\right)}{2}[/tex]
[tex]\sin \left(20^{\circ \:}\right)\sin \left(40^{\circ \:}\right)=\frac{-\cos \left(20^{\circ \:}+40^{\circ \:}\right)+\cos \left(20^{\circ \:}-40^{\circ \:}\right)}{2}[/tex]
[tex]\mathrm{Substitute}:\frac{-\cos \left(20^{\circ \:}+40^{\circ \:}\right)+\cos \left(20^{\circ \:}-40^{\circ \:}\right)}{2}\sin \left(80^{\circ \:}\right)[/tex]
[tex]\mathrm{Multiply\:fractions}:\frac{\sin \left(80^{\circ \:}\right)\left(-\cos \left(60^{\circ \:}\right)+\cos \left(-20^{\circ \:}\right)\right)}{2}[/tex]
Remember that cos(- x) = cos(x). Respectively cos(- 20°) = cos(20°). Let's substitute and afterwards apply the identity 'cos(60°) = 1 / 2.'
[tex]\frac{\sin \left(80^{\circ \:}\right)\left(-\cos \left(60^{\circ \:}\right)+\cos \left(20^{\circ \:}\right)\right)}{2} = \frac{\sin \left(80^{\circ \:}\right)\left(-\frac{1}{2}+\cos \left(20^{\circ \:}\right)\right)}{2}[/tex]
And if we further simplify the expression, we should receive the following...
[tex]\frac{\sin \left(80^{\circ \:}\right)\left(-1+2\cos \left(20^{\circ \:}\right)\right)}{4}[/tex]
Now we want to prove that this expression = √3 / 8. The denominator here is 4 so we can multiply the whole thing by 2 to have a denominator of 8. 2((sin(80°)(- 1 + 2cos(20°)) when simplified = √3. Therefore the expression is true.
Eric is studying people's typing habits. He surveyed 525 people and asked whether they leave one space or two spaces after a period when typing. 440 people responded that they leave one space. Create a 90% confidence interval for the proportion of people who leave one space after a period. Round your results to four decimal places.
Answer: (0.8115, 0.8645)
Step-by-step explanation:
Let p be the proportion of people who leave one space after a period.
Given: Sample size : n= 525
Number of people responded that they leave one space. =440
i.e. sample proportion: [tex]\hat{p}=\dfrac{440}{525}\approx0.838[/tex]
z-score for 90% confidence level : 1.645
Formula to find the confidence interval :
[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
[tex]0.838\pm (1.645)\sqrt{\dfrac{0.838(1-0.838)}{525}}\\\\=0.838\pm (1.645)\sqrt{0.00025858285}\\\\=0.838\pm (1.645)(0.01608)\\\\= 0.838\pm0.0265\\\\=(0.838-0.0265,\ 0.838+0.0265)\\\\=(0.8115,\ 0.8645)[/tex]
Hence, a 90% confidence interval for the proportion of people who leave one space after a period: (0.8115, 0.8645)
How many solutions does the system have?
8x+ 2y = 14
8x+ 2y =4
Choose 1 answer:
A. Exactly one solution
B. No solutions
C. Infinitely many solutions
Answer:
B. No solutions
Step-by-step explanation:
8x+2y=14
8x+2y=4
These linear equations are in standard form, and the Ax values are the same (8x) and the By values are the same (2y). The only value that is the different is the C values (14 and 4), which will be the cause of a no solution for this system of equations.
Answer:
b
..........
Step-by-step explanation:
0≠14-4
...
Find the indicated side of the triangle
Answer:
7√2
Step-by-step explanation:
Knowing that the angle is 45° (or π/4 radians) and the opposite leg has a length of 7, you can find the length of b with:
7 / b = sin(π / 4)
7 / (sin(π / 4)) = b
b = 7 / (1 / √2)
b =7√2
A simpler way to get the answer is to note that a right triangle with one 45° angle must be an isoceles right triangle, so both legs are the same length. Using the Pythagorean Theorem:
a² + 7² = b²
Since we know a = 7,
7² + 7² = b²
b = √(2 * 49)
b = 7√2
negative number definition
it is a number less then zero
Answer:
a negative number is when a number exceeds below zero
for example 7 --8 would be -1
If the “a” term of a quadratic is positive (+), the U-shape will
f(x) = 1x² + 2x + 1
The U shape is called a parabola
If the "a" is positive, then the parabola opens upward as shown in the graph on the left.
If "a" is negative, then the parabola opens downward. This is the parabola on the right.
The way I remember is that "a" being positive means it puts a smile on, which is what the parabola on the left resembles. The parabola on the right is a frowny face so "a" is negative.
A parabola is vertically cut in half by the axis of symmetry. One half mirrors over this vertical line to get the other half. The axis of symmetry passes through the vertex. The vertex is either the highest point or the lowest point depending on whether 'a' is negative or positive.
g(x)
2x + 3, find g(-3)
cuanto es 8x3 cuarto
Answer:
24
Step-by-step explanation:
What is the sum of the first five prime numbers?
18
26
OOOO
28
39
Answer:
28
Step-by-step explanation:
The first five prime numbers are = 2,3,5,7,11
Addition of the prime nos. = 2+3+5+7+11=28
The first prime numbers are: 2, 3, 5, 7, 11.
The sum is 2 + 3 + 5 + 7 + 11 = 28, so option 4
Solve for x 2/3x-5=21
Answer:
2x/3 - 5 = 21
2x/3 = 26
2x = 78
x = 39
Step-by-step explanation:
Answer:
x = 39
Step-by-step explanation:
what is x? please answer asap thanks!
==================================================
Work Shown:
Straight lines DF and EC intersect at point A. Because of this, angle DAF is a 180 degree angle.
Angles DAB, BAC, and CAF all combine to form a straight 180 degree angle.
Add up the angles mentioned, set the sum equal to 180, and solve for x
-----------
(angle DAB) + (angle BAC) + (angle CAF) = 180
x + 80 + 60 = 180
x + 140 = 180
x + 140-140 = 180-140 ... subtract 140 from both sides
x = 40
Answer:
[tex]\Huge \boxed{x=40\°}[/tex]
Step-by-step explanation:
Angles on a straight line add up to 180 degrees.
We can create an equation and solve for x.
x + 80 + 60 = 180
Add the numbers on the left side.
x + 140 = 180
Subtract 140 from both sides.
x + 140 - 140 = 180 - 140
x = 40
In order to mix mortar, water, sand, and cement mix must be mixed in the ratio of a: b: c respectively.
If Herschel uses 3b pounds of sand to make the mortar for a brick wall that he is building, how many
pounds of mortar will he end up with in all?
Answer:
Step-by-step explanation:
That will be 3a + 3b + 3c pounds of mortar.
as there will be 3a pounds of water and 3c pounds of cement.
|-12-(-8)|= simplify the expression
Answer:
4
Step-by-step explanation:
- and - become +
so, -12 + 8 = -4
but we remove the minus and make it a positive 4
which of the following are solutions to the quadratic equation 2x^2+5x-10=x^2+4
Answer:
E. - 7
Step-by-step explanation:
2x2-X2+5X-10-4=0
X2+5X-14=0
X2-2X+7X-14.=0
X(X-2). 7(X-2)=0
(X+7). (X-2)
X=-7, X=2
Answer:
the answer is -7 and 2
Step-by-step explanation:
Solve this linear equation: 3x-5=2.5x+3-(x-4)
Answer:
x=8
Step-by-step explanation:
3x -5 =2.5x + 3 - (x-4)
3x - 5 = 2.5x + 3 -x+4
3x - 5 = 1.5x +7
1.5x = 12
x =8
The solution to the linear equation 3x - 5 = 2.5x + 3 - (x-4) is x = 8.
The given expression is,
x-5=2.5x+3-(x-4)
Simplify the equation by combining like terms.
Start with the terms on the right-hand side of the equation:
2.5x+3-(x-4)
= 2.5x + 3 - x + 4 (distributing the negative sign)
= 1.5x + 7
Now let's combine the terms on the left-hand side of the equation:
3x - 5
Now the reduced equation be,
3x - 5 = 1.5x + 7
Isolate the variable (x) on one side of the equation.
Subtracting 1.5x from both sides:
3x - 1.5x - 5 = 1.5x - 1.5x + 7
1.5x - 5 = 7
Add 5 to both sides:
1.5x - 5 + 5 = 7 + 5
1.5x = 12
Solve for x by dividing both sides by 1.5:
1.5x/1.5 = 12/1.5
x = 8
So the solution to the linear equation 3x - 5 = 2.5x + 3 - (x-4) is x = 8.
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which fractions are equivalent to 2/3
Answer:
4/6 and 8/12 and 16/24
Step-by-step explanation:
well because it is math and math works like this basically all of theese are equal to 2/3