Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
tan x = [tex]\frac{sinx}{cosx}[/tex] , sin²x + cos²x = 1
Consider the left side
[tex]\frac{1-tan^2x}{1+tan^2x}[/tex]
= [tex]\frac{1-\frac{sin^2x}{cos^2x} }{1+\frac{sin^2x}{cos^2x} }[/tex] ← multiply numerator/ denominator of the whole fraction by cos²x
= [tex]\frac{cos^2x-sin^2x}{cos^2x+sin^2x}[/tex]
= [tex]\frac{cos^2x-sin^2x}{1}[/tex]
= cos²x - sin²x
= cos²x - (1 - cos²x)
= cos²x - 1 + cos²x
= 2cos²x - 1
= right side , thus proven
[tex]\frac{1 - \tan^2(x)}{1 + \tan^2(x)}\\= \frac{\frac{\cos^2(x)}{\cos^2(x)} - \frac{\sin^2(x)}{\cos^2(x)}}{\frac{\cos^2(x)}{\cos^2(x)} + \frac{\sin^2(x)}{\cos^2(x)}}\\= \frac{\frac{\cos^2(x) - \sin^2(x)}{\cos^2(x)}}{\frac{\cos^2(x) + \sin^2(x)}{\cos^2(x)}}\\= \frac{\cos^2(x) - \sin^2(x)}{\cos^2(x)} \cdot \frac{\cos^2(x)}{\cos^2(x) + \sin^2(x)}\\= \frac{(\cos^2(x) - \sin^2(x)) \cdot \cos^2(x)}{\cos^2(x) \cdot (\cos^2(x) + \sin^2(x))}\\= \frac{\cos^2(x) - \sin^2(x)}{\cos^2(x) + \sin^2(x)}[/tex]
[tex]= \cos^2(x) - \sin^2(x)\\= \cos^2(x) - (1 - \cos^2(x))\\= \cos^2(x) - 1 + \cos^2(x)\\= 2\cos^2(x) - 1[/tex]
What statements about dilations are true? Check all that apply.
A dilation preserves side lengths.
A dilation preserves angle measures.
A dilation preserves the direction that the shape faces.
A dilation is a type of isometric transformation.
The side lengths of a dilated image are proportional to the side lengths of the pre-image.
Answer:
B, C, E
Step-by-step explanation:
Edg 2021
A dilation preserves angle measures. A dilation preserves the direction that the shape faces. The side lengths of a dilated image are proportional to the side lengths of the pre-image.
Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.
Dilation is the increase or decrease in the size of a figure by a factor k, hence the side lengths of a dilated image are proportional to the side lengths of the pre-image.
Dilation does not preserve the side lengths but it preserves the angle measures. Dilation also preserves the orientation (i.e. the direction that the shape faces).
Dilation is not an isometric transformation.
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r = sec(θ) − 2cos(θ), where -π/2 < θ < π/2
Convert this equation to rectangular coordinates.
Answer:
y = (x/(1-x))√(1-x²)
Step-by-step explanation:
The equation can be translated to rectangular coordinates by using the relationships between polar and rectangular coordinates:
x = r·cos(θ)
y = r·sin(θ)
x² +y² = r²
__
r = sec(θ) -2cos(θ)
r·cos(θ) = 1 -2cos(θ)² . . . . . . . . multiply by cos(θ)
r²·r·cos(θ) = r² -2r²·cos(θ)² . . . multiply by r²
(x² +y²)x = x² +y² -2x² . . . . . . . substitute rectangular relations
x²(x +1) = y²(1 -x) . . . . . . . . . . . subtract xy²-x², factor
y² = x²(1 +x)/(1 -x) = x²(1 -x²)/(1 -x)² . . . . multiply by (1-x)/(1-x)
[tex]\boxed{y=\dfrac{x\sqrt{1-x^2}}{1-x}}[/tex]
__
The attached graph shows the equivalence of the polar and rectangular forms.
The Square Root Property is used in solving incomplete quadratic equations where b is equal to _______.
A. Zero B. One C. Two D. Three
Answer: A. Zero
Step-by-step explanation: If the quadratic equation is incomplete, b will always equal 0.
The Square Root Property is used in solving incomplete quadratic equations where b is equal to zero. Then the correct option is A.
What is a quadratic equation?The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.
If the value of the a is zero, then the equation will be linear, So the value of the variable a can not be zero.
But the value of the b and c can be zero for a quadratic equation, but the number of the terms will be missing, so the quadratic equation is incomplete.
The Square Root Property is used in solving incomplete quadratic equations where b is equal to zero. Then the correct option is A.
More about the quadratic equation link is given below.
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A carpet cleaner charges $59 for a service call and $30 for each room cleaned. A customer does not want to spend more than $125 for having the carpets in his house cleaned. Choose the correct inequality for the situation and the total number of rooms the customer can afford to have cleaned.
Answer:
[tex]59 + 30c \leq 125[/tex]
2 rooms
Step-by-step explanation:
Given
[tex]Base\ Amount = \$59[/tex]
[tex]Additional = \$30[/tex] per carpet
[tex]Customer\ Budget = \$125[/tex]
Required
Write an inequality to determine the situation
Represent the number of carpets with c
First, we need to determine an expression for the cleaner's charges:
This is:
[tex]59 + 30 * c[/tex]
[tex]59 + 30c[/tex]
Since the customer's budget do not exceed $125.
This implies that the cleaner's charges must be less than or equal to the budget.
So, we have:
[tex]59 + 30c \leq 125[/tex]
Solving further: [Collect Like Terms]
[tex]30c \leq 125 - 59\\[/tex]
[tex]30c \leq 66[/tex]
Divide through by 30
[tex]c \leq 66/30[/tex]
[tex]c \leq 2.2[/tex]
Since number of rooms can't be fraction;
The maximum number of rooms the customer can afford is 2
Answer:
No sé exactamente de qué se trata el ejercicio, hay muchas respuestas posibles
Step-by-step explanation:
I have tried this question for several times but i cant
help me please
Answer:
a) Rs. 2425.55, Rs. 2626.36 (2 d.p.)
b) Rs. 1320
Step-by-step explanation:
Please see the attached pictures for the full solution.
Answer:
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Line M passes through points (2,-5) and (4, -3). Line N passes through points (-4, -8) and (-6,-6). Are lines M and N perpendicular? Explain.
A. No, the lines are not perpendicular because the product of their slopes equals -1.
B. Yes, the lines are perpendicular because the product of their slopes equals-1.
C. No, their lines are not perpendicular because the product of their slopes does not equal-1.
D. Yes, the lines are perpendicular because the product of their slopes does not equal -1.
Answer:
Yes, the lines are perpendicular because the product of their slopes equals -1 ⇒ B
Step-by-step explanation:
The product of the slopes of the perpendicular lines is -1
So to prove that the lines are perpendicular let us find their slopes
The rule of the slope is:
[tex]m=\frac{y2-y1}{x2-x1}[/tex] , where (x1, y1) and (x2, y2) are two points on the line
∵ Line M passes through points (2, -5) and (4, -3)
∴ x1 = 2 and x2 = 4
∴ y1 = -5 and y2 = -3
→ By using the rule of the slope above
∴ [tex]m=\frac{-3-(-5)}{4-2}=\frac{-3+5}{2}=\frac{2}{2}[/tex]
∴ The slope of line M is 1
∵ Line N passes through points (-4, -8) and (-6, -6)
∴ x1 = -4 and x2 = -6
∴ y1 = -8 and y2 = -6
→ By using the rule of the slope above
∴ [tex]m=\frac{-6-(-8)}{-6-(-4)}=\frac{-6+8}{-6+4}=\frac{2}{-2}[/tex]
∴ The slope of line N is -1
∵ 1 × -1 = -1
∴ The product of the slopes of lines M and N is -1
∴ Lines M and N are perpendicular
∴ Yes, the lines are perpendicular because the product of their
slopes equals -1.
ANSWER ASAP What is true for naming a ray? (6 points)
A ray must be named by first its endpoint and then another point the ray goes through.
More than two points can be used to name a ray.
A ray is named by two random points.
No matter the direction of the ray, the ray is named by the left point first.
Answer:
a ray must be named by its endpoint first then an another point it that the ray goes through
Step-by-step explanation:
a ray has 1 endpoint and it goes through an infinite number of points but you name a ray by naming it's endpoint than a other point which the ray goes through hopes this helps have a nice day and good luck
The width of a rectangle is (4x + 3) in. The length of the rectangle is twice the width. Find the area of the rectangle in terms of the variable x.
Step-by-step explanation:
Width = 4x + 3
Length = 2(4x + 3) = 8x + 6
Area = Width x Length
Area = (4x + 3)(8x + 6)
Area = 32x² + 24x + 24x + 18
Area = 32x² + 48x + 18
Find the measure of each angle indicated 40 ° 85° ?
Answer: 55 degrees
Step-by-step explanation:
Angle sum of a triangle = 180 degrees
40+85= 125
180-125= 55
i need help ASAP will give brainliest if correct please show your work:
.Ava’s gym membership costs $50 each month plus a one-time $100 fee. Mark’s gym
membership costs $60 each month plus a one-time $50 fee. At how many months will
Ava and Mark pay the same amount for a gym membership?
Answer:
5 Months
Step-by-step explanation:
For Avas its 50 dollars times 5 months which equals 250 plus the 100 dollar fee makes 350
For Mark its 60 times 5 equals 300 plus the 50 dollar fee makes also 350
Answer:the correct answer would be 5 months
Step-by-step explanation:
10. The longest fish Dave caught was 2 ft. 7in. long. His brother caught a fish which was 33 inches long. Who caught the longest fish?
Answer:
his brother
Step-by-step explanation:
because 2 foot 7 inches in inches is 31 inches so therefore his brother has the longer fish.
1 foot = 12 inches.
2 feet x 12 = 24 inches + 7 = 31 inches.
Daves fish was 31 inches.
his brothers fish was bigger.
0/1 Roy is going to increase the size of his patio to make room for a new BBQ grill. The ratio of the area of the old patio to the area of the new patio is 2 2 \frac{1}{4} 4 1 : 6 6 \frac{3}{4} 4 3 . Convert this ratio to a unit rate
Given:
Ratio is [tex]2\dfrac{1}{4}:6\dfrac{3}{4}[/tex]
To find:
Convert this ratio to a unit rate.
Solution:
We have,
[tex]2\dfrac{1}{4}:6\dfrac{3}{4}=\dfrac{2\times 4+1}{4}:\dfrac{6\times 4+3}{4}[/tex]
[tex]2\dfrac{1}{4}:6\dfrac{3}{4}=\dfrac{8+1}{4}:\dfrac{24+3}{4}[/tex]
[tex]2\dfrac{1}{4}:6\dfrac{3}{4}=\dfrac{9}{4}:\dfrac{27}{4}[/tex]
[tex]2\dfrac{1}{4}:6\dfrac{3}{4}=\dfrac{\dfrac{9}{4}}{\dfrac{27}{4}}[/tex]
[tex]2\dfrac{1}{4}:6\dfrac{3}{4}=\dfrac{9}{27}[/tex]
[tex]2\dfrac{1}{4}:6\dfrac{3}{4}=\dfrac{1}{3}[/tex]
[tex]2\dfrac{1}{4}:6\dfrac{3}{4}=0.333...[/tex]
[tex]2\dfrac{1}{4}:6\dfrac{3}{4}\approx 0.33[/tex]
Therefore, the unit rate is about 0.33.
At an archery competition, Jamie and Marshall's team tied Shawna and Wyatt's team for the top team score. Team scores are determined by adding the two teams members individual scores. Marshall scores 12 less than Jamie. Shawna scored twice as much as Marshall. Wyatt scored 4 less than Shawna. What was each person's individual score?
Given:
Jamie and Marshall's team tied Shawna and Wyatt's team for the top team score.
Marshall scores 12 less than Jamie. Shawna scored twice as much as Marshall. Wyatt scored 4 less than Shawna.
To find:
The individual score of each person.
Solution:
Let x be the score of Jamie.
Marshall scores 12 less than Jamie.
Marshall score = x-12
Shawna scored twice as much as Marshall.
Shawna score = 2(x-12)
Wyatt scored 4 less than Shawna.
Wyatt score = 2(x-12)-4
Now,
Score of Jamie and Marshall's team [tex]=x+(x-12)[/tex]
Score of Shawna and Wyatt's team [tex]=2(x-12)+2(x-12)-4[/tex]
Jamie and Marshall's team tied Shawna and Wyatt's team
[tex]x+(x-12)=2(x-12)+2(x-12)-4[/tex]
[tex]x+x-12=2x-24+2x-24-4[/tex]
[tex]2x-12=4x-52[/tex]
Isolate x.
[tex]2x-4x=-52+12[/tex]
[tex]-2x=-40[/tex]
Divide both sides by -2.
[tex]x=\dfrac{-40}{-2}[/tex]
[tex]x=20[/tex]
So, Jamie score = 20
Marshall score = 20-12
= 8
Shawna score = 2(20-12)
= 2(8)
= 16
Wyatt score = 2(20-12)-4
= 2(8)-4
= 16-4
= 12
Therefore, the scores of Jamie, Marshall, Shawna and Wyatt are 20, 8, 16 and 12 respectively.
What is the value of x?
Answer:
its 68mm
Step-by-step explanation:
Problem is in the image
Answer:
0 < c < 1
Step-by-step explanation:
Descarte's rule of signs tells you the quadratic will have two or zero positive real roots when the sign of c is positive. (c > 0)
The discriminant tells you the quadratic will have real roots when ...
b² -4ac > 0 . . . . . . where a, b, c are the coefficients of ax² +bx +c = 0
(-2)² -4(1)c > 0
1 -c > 0
c < 1
The equation will have two positive real roots when 0 < c < 1.
20% of a university's 4,000 students have a scholarship
a. What percentage of the students do not have a scholarship?
b. How many students have a scholarship?
c. How many students don't have a scholarship?
a. What percentage of the students do not have a scholarship?
80% don't have a scholarship
b. How many students have a scholarship?
800 students
c. How many students don't have a scholarship?
3200 students dont have a schscholarship
Which of the following logarithmic expressions have been evaluated correctly?
A. ln 1=0
B. log2 9=3
C. log 1/100=12
D. log3 (−1)=1/3
E. log5 1/125=−3
The correctly evaluated logarithmic expressions are expressions that are true on both sides of the equation, and the expression is ln 1=0
How to determine the correctly evaluated expressionsA. ln 1=0As a general rule, ln 1 = 0
B. log2 9=3Express 9 as 3^2
[tex]\log_2(3^2) =3[/tex]
Apply the law of logarithm
[tex]2\log_2(3) = 3[/tex]
Evaluate
[tex]3.17 = 3[/tex]
The above is not true
C. log 1/100=12Express 1/100 as 10^-1
[tex]\log(10^{-2}) = 12[/tex]
Apply law of logarithm
[tex]-2\log(10) = 12[/tex]
Evaluate
[tex]-2 = 10[/tex]
The above is not true
Options (d) and (e) are also false
Hence, the correctly evaluated logarithmic expressions is ln 1=0
Read more about logarithmic expressions at:
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ANSWER FAST PLS!
Question 5
What is the equation of the line?
У.
y= 2x4
y = 2x + 2
-1
y=-x - 4
y = x + 2
☆▪︎y=-x-4▪︎☆
☆▪︎mark me brainlist ▪︎☆
if answered please explain because this is really hard
This is really simple, all you have to do is establish a new relation which describes this particular case;
For example if i wanted to find the area of the full circle (360°), i would use the equation which states that;
[tex]a = \pi \: r {}^{2} [/tex]
[tex]a = \pi \: 8 {}^{2} [/tex]
[tex]a = 3.14 \times 64[/tex]
[tex]a = 201.06 \: inches {}^{2} [/tex]
But do i really wan the full 360 degrees?
In reality i only need a 70 degree circle (in a sense).
If 360 makes a full circle
How many circles is 70?
Use the triple rule to find that;
[tex]x = \frac{70}{360} = 0.1945 \: cirles[/tex]
So that area would be;
[tex] \alpha = 0.1945 \times 201.06 = 39.0617 \: [/tex]
That is your area. a=39 inches² rounded to the nearest tenth.
We need right now pleaseee
Answer:
x=49/3
Step-by-step explanation:
move all terms that don't contain x to the right side and solve the problem.
Answer:
Step-by-step explanation:
7. 3x + 6 = 55
- 6 - 6
3x = 49
/3 /3
x = 49/3 OR x = 16.33
8. 50 = 6x + 2
- 2 - 2
48 = 6x
/6 /6
8 = x
Check/verify your answer:
50 = 6x + 2
50 = 6(8) + 2
50 = 48 + 2
50 = 50
This statement is correct.
Hope this helps!
Determine the slope from the following order pairs:
(1,3) (0,1)
Answer:2/1
Step-by-step explanation:
Y1-y2/ x1-x2= 2/1
What is the equation of the line in slope intercept form from the graph.
Answer:
y=4/3x-2
Step-by-step explanation:
We know the base equation is mx+b and the y-intercept is at -2 so we can determine that as the b value. The m value is 4/3 because if you look at where the line meets the next point is over 3 and up 4 indicating that the m value is 4/3. Hope this helps!
The equation of the line is y = 4/3x -2.
The y-intercept is -2 because the line crosses the y-axis at (0,-2).
The slope is 4/3x because the rise over run of the line is 4/3.
17.Tickets for this prom cost $20 for a single ticket and $35 for a couple of tickets.
Ticket sales are totaled $2845 and 128 tickets were purchased. With a system of
equations that can model the situation and then solve it by any method. *A. Write
a system of equations to model this situation. . *B. Solve the system of equations.
How many single tickets [blank] couple tickets sold [blank]
20s + 35c = 2845
20s + 35c + 128
Step-by-step explanation:
Let S be the number of single tickets sold.
Let C be the number of couple tickets sold.
[tex]20s + 35c = 2845[/tex]
[tex]s + c = 128[/tex]
Multiplying the lower system by -20 we get;
[tex]20s + 35c = 2845[/tex]
[tex] - 20s - 20c = - 2560[/tex]
Adding the two systems i get;
[tex]35c - 20c = 2845 - 2560[/tex]
[tex]15c = 285[/tex]
[tex]c = \frac{285}{15} = 19[/tex]
Substituting C=19 in s+c=128,
we get that;
[tex]s + 19 = 128[/tex]
[tex]s = 128 - 19[/tex]
[tex]s = 117[/tex]
Erik used 16 centimeters of tape to wrap 2 presents. Then, he used an additional 24 centimeters of tape to wrap another 3 presents. How many centimeters of tape does Erik use to wrap each present?
Answer:
Erik uses 8 centimeters of tape to wrap each present.
Step-by-step explanation:
16 centimeters can wrap 2 presents.
24 centimeters can wrap 3 presents.
Add both amounts of tape together to find the total amount of tape used. Then add the number of presents wrapped together.
16 + 24 = 40 centimeters
2 + 3 = 5 presents
40/5
In order to find how much tape wraps one present, divide both the top and bottom by the denominator (5)
40/5 = 8 centimeters
5/5 = 1 present
Erik uses 8 centimeters of tape to wrap each present.
The measures of the angles of a triangle are shown in the figure below . Solve for x
Answer: x = 23
Step-by-step explanation:
The sum of interior angles in a triangles is equal to 180°, therefore:
(2x - 1) + 110 + 25 = 180
1. Get rid of parentheses.
2x - 1 + 110 + 25 = 180
2. Add the number up in the left side.
2x + 134 = 180
3. Subtract 134 from both sides.
2x = 46
4. Divide by 2 from both sides.
x = 23
Quadrilateral DEFG is dilated by a factor of 0.5 with the center (0,0) what are the new coordinates of point D?
Answer:
-3,-2
Step-by--step explanation:
7.) Given f(x) = 6(x - 1). what is the value of f(-8)? * A) 42 B) -42 C) 54 D) -54
Answer:
D) -54
Step-by-step explanation:
To solve this question, simply plug in -8 for x:
f(-8)=6(-8-1)
f(-8)=6(-9)
f(-8)=-54
Hope this helps!!
Juan writes the expression below to determine the total cost of 1 sandwich and n side dishes. 10 . 50 + 1 . 50 ( n − 1 ) Juan orders a sandwich and the same number of side dishes each of the five days this week. All together, Juan pays $75 for these 5 lunches. Write an equation that can be used to find the number of side dishes Juan orders for lunch this week.
Answer:
She has n= 4 side dishes.
Total side dishes ordered = 5n = 20
Step-by-step explanation:
The total cost is given by
TC= 10 . 50 + 1 . 50 ( n − 1 )
She orders same 5 lunches for $ 75
$ 75= 5{ 10 . 50 + 1 . 50 ( n − 1 ) }
Or
Cost of 1 lunch would be $ 15
$ 75/5 = { 10 . 50 + 1 . 50 ( n − 1 ) }
or
$ 15 = 10 . 50 + 1 . 50 ( n − 1 )
$ 15-$ 10 . 50 = 1 . 50 ( n − 1 )
$ 4.5/ 1.5= n-1
$ 3= n-1
3+1= n
n= 4
She has n= 4 side dishes.
Total side dishes ordered = 5n = 20
She spent
$ 1.50 ( 4-1) = $ 4.5 each day or $22.5 on side dishes for 5 days.
What is 25% of 60% on a fraction ?%
?% x ? =15
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{25\% of 60}}{\left( \cfrac{25}{100} \right)60}\implies 15[/tex]
about Mark and his Pizzas
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{35\% of 12}}{\left( \cfrac{35}{100} \right)12}\implies 4.2~\hfill \underset{cheaper~price}{\stackrel{12~~ - ~~4.2}{7.80}}[/tex]
8 4/5 - 5 1/10?
PLEASE ANSWER QUICK!! D:
Answer:
3 7/10
Step-by-step explanation:
Hope this helps and good luck!
Answer: [tex]3\frac{7}{10}[/tex] or [tex]\frac{37}{10}[/tex]
Step-by-step explanation:
Hey there! I will give the following steps, if you have any questions feel free to ask me in the comments below. Follow these steps I made for you.
Step 1: Convert [tex]8\frac{4}{5}[/tex] to an improper fraction. Use this rule: [tex]a\frac{b}{c} = \frac{ac + b}{c}[/tex].
[tex]\frac{8 * 5 + 4}{5} - 5\frac{1}{10}[/tex]
Step 2: Simplify 8 × 5 to 40.
[tex]\frac{40 + 4}{5} - 5\frac{1}{10}[/tex]
Step 3: Simplify 40 + 4 to 44.
[tex]\frac{44}{5} - 5\frac{1}{10}[/tex]
Step 4: Convert [tex]5\frac{1}{10}[/tex] to an improper fraction. Use this rule [tex]a\frac{b}{c} = \frac{ac + b}{c}[/tex].
[tex]\frac{44}{5} - \frac{50 * 10 + 1}{10}[/tex]
Step 5: Simplify 5 × 10 to 50.
[tex]\frac{44}{5} - \frac{50 + 1}{10}[/tex]
Step 6: Simplify 50 + 1 to 51.
[tex]\frac{44}{5} - \frac{51}{10}[/tex]
Step 7: Find the Least Common Denominator (LCD) of [tex]\frac{44}{5}, \frac{51}{10}[/tex]. In other words, find the Least Common Multiple (LCM) of 5, 10.
LCD = 10
Step 8: Make the denominators the same as the LCD.
[tex]\frac{44 * 2}{5 * 2} - \frac{51}{10}[/tex]
Step 9: Simplify. Denominators are now the same.
[tex]\frac{88}{10} - \frac{51}{10}[/tex]
Step 10: Join the denominators.
[tex]\frac{88- 51}{10}[/tex]
Step 11: Simplify.
[tex]\frac{37}{10}[/tex]
Step 12: Convert to a mixed fraction.
[tex]3\frac{7}{10}[/tex]
~I hope I helped you! :)~