Answer:
Step-by-step explanation:
There are 2 very distinct and important things that we need to know before completing the problem. First is that we are given that the cos of an angle is 1/3 (adjacent/hypotenuse) and it is in the first quadrant. We also need to know that the identity for sin2θ = 2sinθcosθ.
We already know cos θ = 1/3, so we need now find the sin θ. The sin ratio is the side opposite the angle over the hypotenuse, and the side we are missing is the side opposite the angle (we do not need to know the angle; it's irrelevant). Set up a right triangle in the first quadrant and label the base with a 1 (because the base is the side adjacent to the angle), and the hypotenuse with a 3. Find the third side using Pythagorean's Theorem:
[tex]3^2=1^2+y^2[/tex] which simplifies to
[tex]9=1+y^2[/tex] and
[tex]y^2=8[/tex] so
[tex]y=\sqrt{8}=2\sqrt{2}[/tex] so that's the missing side. Now we can easily determine that
[tex]sin\theta=\frac{2\sqrt{2} }{3}[/tex]
Now we have everything we need to fill in the identity for sin2θ:
[tex]2sin\theta cos\theta=2(\frac{2\sqrt{2} }{3})(\frac{1}{3})[/tex] and multiply all of that together to get
[tex]2sin\theta cos\theta=\frac{4\sqrt{2} }{9}[/tex]
two triangles are similar what is x
Answer:
x = 10
Step-by-step explanation:
smaller triangle / bigger triangle = 20 / 28
hence,
3x / (4x+2) = 20/28
28(3x) = 20(4x+2)
84x = 80x + 40
4x = 40
x = 10
y= -(x+3)^2 -5
What is the leading coefficient?
How do you find the vertex?
Answer:
To find the leading coefficient, first expand the function:
[tex]y= -(x+3)^{2} -5\\\\y=-(x^{2} +6x+9)-5\\\\y=-x^{2} -6x-9-5\\\\y=-x^{2} -6x-14[/tex]
The leading coefficient is the coefficient of the highest-order term, which, in this case, would be the -1 from -x².
To find the vertex: see image below
Vertex = (-3, -5)
Challenge: For a particular job, the Amax Employment Agency charges a fee that is equal to 15% of the first
month's pay. If the job pays X dollars annually, express the agency fee algebraically.
Answer:
0.0125x or x/80
Step-by-step explanation:
Salary: x dollars per year
To find the pay per month, we divide the annual pay by 12.
The monthly pay is x/12
15% of the first month's salary is
15% of x/12 = 0.15 * x/12 = 0.0125x = x/80
Answer: 0.0125x
Find the value of x in the given
right triangle.
10
х
Answer:
44.4
Step-by-step explanation:
Since we have a right triangle, we can use trig functions
sin theta = opp / hyp
sin x = 7/10
Taking the inverse sin of each side
sin^-1 (sin x) = sin^-1(7/10)
x = 44.427
Rounding to the nearest tenth
x = 44.4
question 3&4 help me please
Answer:
3. (1-7/9)÷2 = 2/9÷2 = 1/9
reciprocal of 1/9 is 9
4. x+2/x=3
if you solve it, you get x = 1 and x = 2, so last option, 1 and 2, is the answer
Answered by GAUTHMATH
Which functions have a maximum value greater than the maximum of the function g(x) = -(x + 3)2 - 4?
Answer:
max: -4
Step-by-step explanation:
(x+3)^2 》0 mọi x
<=> -(x+3)^2 《0
<=> -(x+3)^2 -4 《 -4
What is the answer when you evaluate m + p - p2 ÷ 6; use m = 5 and p = 6 ?
Answer:
5
Step-by-step explanation:
m + p - p^2 ÷ 6
Let m = 5 and p=6
5 + 6 - 6^2 ÷ 6
Exponents first
5 + 6 - 36 ÷ 6
Then divide
5 + 6 - 6
Then add and subtract from left to right
11-6
5
5. Which pair of equations represents parallel lines?
A. y =2x+7
Y=2x-7
B. Y=7
X=7
C. Y=2x-7
Y=-1/2-7
D. Y=2x+7
Y=x+7
Answer:
C
Step-by-step explanation:
(06.01)
Write the following expression in exponential form:
1.6 × 1.6 × 1.6 × 1.6
41.6
1.64
1.6 × 4
1.6 + 4
Answer:
[tex]1.6^{4}[/tex]
Step-by-step explanation:
1.6 is multiplied by itself 4 times. This is represented in exponential form as
[tex]1.6^{4}[/tex]
In Exercises 1-4, determine whether the dilated figure or the original figure is closer to the center of dilation. Use the given location of the center of dilation and scale factor k.
1. Center of dilation inside the figure; k = 3
Center of ditation inside the figure, k = 1/2
3. Center of dilation outside the figure: = 120%
4. Center of dilation outside the figure; k = 0.1
When the Center of dilation is inside the figure
The original figure is closer to the center of dilationThe dilated figure is closer to the the center of dilationWhen the Center of dilation is outside the figure
3. The original figure is closer to the the center of dilation
4. The dilated figure is closer to the center of dilation
The center of dilation is the fixed point from which the distances in a dilation are measured
The scale factor is ratio of the side lengths of an original figure or preimage to the side lengths of the newly formed image
Center of dilation is inside the figure
Where the center of dilation is inside the figure, and the scale factor is larger than 1, k = 3 > 1, we have;The distance of a point on the dilated figure, including the distances from the center of dilation is 3 times the distances of points on the original image from the center of dilation
Therefore, the original figure has a shorter distance to and is therefore closer to the the center of dilation than the dilated figure
2. Where the center of dilation is inside the figure, and the scale factor is a fraction between 0 and 1 k = 1/2, we have;
The distance of a point on the dilated figure, including the distances from the center of dilation is 1/2 times the distances of points on the original image from the center of dilation
Therefore, the dilated figure has a shorter distance to and is therefore closer to the the center of dilation than the original figure
Center of dilation outside the figure
3. Given that the center of dilation is outside the figure and the scale factor is larger than 1, k = 120% = 120/100 = 1.2 > 1, we have;
The distance of the dilated figure from the center of dilation is 120% of the distance of the original figure from the center of dilation, therefore, the original figure is closer to the the center of dilation than the dilated figure
4. Where the center of dilation is outside the figure and the scale factor is a fraction between 0 and 1, k = 0.1 < 1
The distance of the dilated figure from the center of dilation is only 0.1 times the distance of the original figure from the center of dilation, and therefore, the dilated figure is closer to the center of dilation
Learn more about scale factors and center of dilation here;
https://brainly.com/question/12162455
Find the circumference and the area of a circle with diameter equal to 8.6 inches. Use 3.14 for pi
Please answer it will mean a lot thanks
Answer: Circumference of circle = 27.004 inches
Area of circle = 58.0586 inches²
Step-by-step explanation:
Diameter of circle = 8.6 inches
Pi ([tex]\pi[/tex]) = 3.14
Circumference of circle (With diameter) = [tex]\pi \\[/tex]d ([tex]\pi[/tex]×diameter)
= 3.14 × 8.6
= 27.004 inches
Area of circle (With diameter) = [tex]\pi[/tex][tex]d^{2}[/tex]/4
= 3.14 × 8.6 × 8.6 / 4
= 3.14 × 73.96 / 4
= 58.0586 inches²
one class collects 8 1/4 pounds of recyclable materials. Another class collects 1 1/2
Step-by-step explanation:
what to find then??.........
***CAN SOMEONE HELP ME PLEASE!!***
The polygon in each pair are similar. Find the missing side length
Answer:
45 / 27 = 30 / 18 = x / 24
x = 40
Step-by-step explanation:
Hi there!
The question here states that the two polygons are similar
Polygons that are similar have similar side length ratios.
If we want to find a side length we must create a proportional relationship
We are already given a partial proportional relationship.
Which is...
45 / __ = __ / 18 = x / __
First let's fill in the blanks
The side that is corresponding to the side with a length of 45 has a length of 27. So it would be 45/27
The side that is corresponding to the side with a length of 18 has a length of 30. So it would be 30/18
The side corresponding to side labeled "x" has a length of 24. so it would be x/24
So we would have
45 / 27 = 30 / 18 = x / 24
Now let's find x
We only need 2 ratios ( the one including x of course, and the other one can either be 30/18 or 45/27)
30 / 18 = x / 24
Now let's solve for x
Cross multiply
30*24=720
18*x=18x
We now have 18x = 720
Divide both sides by 18
18x / 18 = x
720 / 18 = 40
x = 40
To check our answers we can see if the ratios are similar
If they are then we are correct
45/27 = 1.66
30/18 =1.66
40/24 = 1.66
They are all equivalent meaning that our answers are correct
[tex]3-\sqrt{x} 1-16x^{2}[/tex]
Answer:
Step-by-step explanation:
This equation turns out to be a quartic. I'm not sure what should be done with. I can't believe you were asked to find its roots which are unbelievably complex. Here is a graph with the only 2 points that are easily found. If I am not solving what you need, please leave a note.
The angle made by the ladder with the ground is degrees, and the length of the ladder is inches.
Answer:
59.04°
58.31 inches
Step-by-step explanation:
The solution triangle is attached below :
Since we have a right angled triangle, we can apply trigonometry to obtain the angle ladder makes with the ground;
Let the angle = θ
Tanθ = opposite / Adjacent
Tanθ = 50/30
θ = tan^-1(50/30)
θ = 59.036°
θ = 59.04°
The length of ladder can be obtained using Pythagoras :
Length of ladder is the hypotenus :
Hence,
Hypotenus = √(adjacent² + opposite²)
Hypotenus = √(50² + 30²)
Hypotenus = √(2500 + 900)
Hypotenus = 58.309
Length of ladder = 58.31 inches
Answer:
59°
58.3 inches
Step-by-step explanation:
Here is the full question :
A ladder is placed 30 inches from a wall. It touches the wall at a height of 50 inches from the ground. The angle made by the ladder with the ground is degrees, and the length of the ladder is inches.
Please check the attached image for a diagram explaining this question
The angle the ladder makes with the ground is labelled x in the diagram
To find the value of x given the opposite and adjacent lengths, use tan
tan⁻¹ (opposite / adjacent)
tan⁻¹ (50 / 30)
tan⁻¹ 1.667
= 59°
the length of the ladder can be determined using Pythagoras theorem
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
√(50² + 30²)
√(2500 + 900)
√3400
= 58.3 inches
Let A represent the average value of the function f(x) on the interval [0,6]. Is there a value of c for which the average value of f(x) on the interval [0,c] is greater than A?
Answer:
The average value of the Function f(x) by squeeze theorem states that no extreme or greater value will exist within the designated area for f(x)
what is the answer? I need help!! please and thank you
Answer:
B
Step-by-step explanation:
27%=0.27 and sqrt(2)<2.75
Find the slope intercept form and the point slope the line perpendicular to 4x-7y=2 going through (-6,1)
Answer:
Slope-intercept form: [tex]y=-\frac{7}{4}x-\frac{19}{2}[/tex]
Point-slope-form: [tex]y-1=-\frac{7}{4}(x+6)[/tex]
Step-by-step explanation:
Hi there!
We want to find the equation of the line perpendicular to the line 4x-7y=2 that goes through (-6, 1) in slope-intercept form, as well as the point-slope form
Slope-intercept form is defined as y=mx+b, where m is the slope and b is the y intercept
Point-slope form is defined as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point
Meanwhile, perpendicular lines have slopes that are negative and reciprocal. When they are multiplied together, the result is -1
So let's find the slope of the line 4x-7y=2
The equation of the line is in standard form, which is ax+by=c, where a, b, and c are integer coefficients a is non-negative, and a and b aren't 0
So let's find the slope of the line 4x-7y=2
One way to do that is to convert the equation of the line from standard form to slope-intercept form
Our goal is to isolate y onto one side
Subtract 4x from both sides
-7y=-4x+2
Divide both sides by -7
y=[tex]\frac{4}{7}x-\frac{2}{7}[/tex]
So the slope of the line 4x-7y=2 is [tex]\frac{4}{7}[/tex]
Now, we need to find the slope of the line perpendicular to it
Use this formula: [tex]m_1*m_2=-1[/tex]
[tex]m_1[/tex] in this case is [tex]\frac{4}{7}[/tex]
[tex]\frac{4}{7}m_2=-1[/tex]
Multiply both sides by [tex]\frac{7}{4}[/tex]
m=[tex]-\frac{7}{4}[/tex]
Let's see the equation of the perpendicular line so far in slope-intercept form:
y=[tex]\frac{-7}{4}x[/tex]+b
We need to find b now
The equation of the line passes through (-6,1), so we can use it to solve for b.
Substitute -6 as x and 1 as y
[tex]1=-\frac{7}{4}*-6+b[/tex]
Now multiply
1=[tex]\frac{42}{4}+b[/tex]
Subtract 42/4 from both sides to isolate b
-19/2=b
Substitute -19/2 as b into the equation
The equation in slope-intercept form y=[tex]\frac{-7}{4}x-\frac{19}{2}[/tex]
Now, here's the equation in point-slope form
Recall that the slope is [tex]\frac{-7}{4}[/tex] , our point is (-6, 1), and point-slope form is [tex]y-y_1=m(x-x_1)[/tex]
Let's label the value of everything to avoid any confusion
[tex]m=-\frac{7}{4} \\x_1=-6\\y_1=1[/tex]
Now substitute those values into the equation
[tex]y-1=-\frac{7}{4}(x--6)[/tex]
We can simplify the x--6 to x+6
[tex]y-1=-\frac{7}{4}(x+6)[/tex]
Hope this helps!
The graph of a line is shown below. What is the equation of the line, in slope-intercept form, that is parallel to this line and has a y-intercept of 1?
Answer:
[tex]y = - \frac{3}{2} x + 1[/tex]
Step-by-step explanation:
Slope -intercept form: y= mx +c, where m is the slope and c is the y-intercept.
Parallel lines have the same slope. Let's find the slope of the given line.
Given points: (-2, 0) and (0, -3)
[tex]\boxed{slope = \frac{y1 - y2}{x1 - x2} }[/tex]
slope of given line
[tex] = \frac{0 - ( - 3)}{ - 2 - 0} [/tex]
[tex] = \frac{0 + 3}{ - 2} [/tex]
[tex] = - \frac{3}{2} [/tex]
[tex]y = - \frac{3}{2} x + c[/tex]
Given that the y- intercept is 1, c= 1.
[tex]y = - \frac{3}{2} x + 1[/tex]
Triangle XYZ is isosceles. The measure of the vertex angle, Y, is twice the measure of a base angle. What is true about triangle XYZ? Select three options.
Answer:
A. Angle Y is a right angle.
B. The measure of angle Z is 45°.
E. The perpendicular bisector of creates two smaller isosceles triangles.
Step-by-step explanation:
Let x represent the measures of base angles X and Z. 2x is the measure of vertex angle Y.
x + x + 2x = 180°
x = 45°
2x = m∠Y = 90°
The triangle is an isosceles right triangle which has base angles of 45°.
The perpendicular bisector of line XZ creates two smaller isosceles triangles with acute angles of 45°
Answer:
The answers are A B E
Step-by-step explanation:
If Tan A=5/12 then find cot A, cos A and Sin A
Cot A=1/tan A=12/5
cos A= 12/13
sin A=5/13
Draw a right angled triangle
the hypotenuse is the longest side which is 13 using Pythagoras theorem
the side opposite the angle A is 5
the side closest to the angle A which is called the adjacent is 12
sinA =opp/hyp
cos A= adj/hyp
cotA =1/tanA=cos A/sinA
Note: Pythagoras theorem is
hyp²=opp²+adj²
Answer:
Step-by-step explanation:
[tex]tan \ A = \frac{5}{12}=\frac{opposite \ site}{adjacent \ side}[/tex]
hypotenuse² = (opposite side)² + (adjacent side)²
= 5² + 12²
= 25 + 144
= 169
hypotenuse = √169 = √13*13 = 13
[tex]Cot \ A = \frac{adjacent \ side}{opposite \ side}=\frac{12}{5}\\\\Cos \ A = \frac{adjacent \ side}{hypotenuse}=\frac{12}{13}\\\\Sin \ A = \frac{opposite \ side}{hypotenuse}=\frac{5}{13}[/tex]
please help me i will give 20 points for this question
Answer:
1. a. 2
b. -½
c. y - 3 = -½(x - 8) => point-slope form
y = -½x + 7 => slope-intercept form
2. a. -1
b. 1
c. y - 5 = 1(x - 3) => point-slope form
y = x + 2 => slope-intercept form
Step-by-step explanation:
1. (8, 3) and (10, 7):
a. The gradient for the line joining the points:
Gradient = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Let,
[tex] (8, 3) = (x_1, y_1) [/tex]
[tex] (10, 7) = (x_2, y_2) [/tex]
Plug in the values
Gradient = [tex] \frac{7 - 3}{10 - 8} [/tex]
Gradient = [tex] \frac{4}{2} [/tex]
Gradient = 2
b. The gradient of the line perpendicular to this line = the negative reciprocal of 2
Negative reciprocal of 2 = -½
c. The equation of perpendicular line if it passes through the first point, (8, 3):
Equation of the perpendicular line in point-slope form can be expressed as y - b = m(x - a).
Where,
(a, b) = (8, 3)
Slope (m) = -½
Substitute (a, b) = (8, 3), and m = -½ into the point-slope equation, y - b = m(x - a).
Thus:
y - 3 = -½(x - 8) => point-slope form
We cam also express the equation of the perpendicular line in slope-intercept form by rewriting y - 3 = -½(x - 8) in the form of y = mx + b:
Thus:
y - 3 = -½(x - 8)
y - 3 = -½x + 4
y - 3 + 3 = -½x + 4 + 3
y = -½x + 7
2. (3, 5) and (4, 4):
a. The gradient for the line joining the points:
Gradient = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Let,
[tex] (3, 5) = (x_1, y_1) [/tex]
[tex] (4, 4) = (x_2, y_2) [/tex]
Plug in the values
Gradient = [tex] \frac{4 - 5}{4 - 3} [/tex]
Gradient = [tex] \frac{-1}{1} [/tex]
Gradient = -1
b. The gradient of the line perpendicular to this line = the negative reciprocal of -1
Negative reciprocal of -1 = 1
c. The equation of perpendicular line if it passes through the first point, (3, 5):
Equation of the perpendicular line in point-slope form can be expressed as y - b = m(x - a).
Where,
(a, b) = (3, 5)
Slope (m) = 1
Substitute (a, b) = (3, 5), and m = 1 into the point-slope equation, y - b = m(x - a).
Thus:
y - 5 = 1(x - 3) => point-slope form
We can also express the equation of the perpendicular line in slope-intercept form by rewriting y - 5 = 1(x - 3) in the form of y = mx + b:
Thus:
y - 5 = 1(x - 3)
y - 5 = x - 3
y - 5 + 5 = x - 3 + 5
y = x + 2
help! please!!!!!! look at photo :))
Hey there!
We know that Danielle earns $10 per hour, so muliply that by 3 and get 30.
Because Danielle works an extra half an hour, divide 10 by 2 and get 5.
Danielle earns $35 in 3 hours and a half.
Hope this helps! Please mark me as brainliest!
Have a wonderful day :)
Charlene is a salesperson. Let y represent her total pay (in dollars). Let x represent the number of
items she sells. Suppose that x and y are related by the equation y=32x + 1900.
What is Charlene's total pay if she doesn't sell any items?
A. $32
B. $1,900
C. $3,200
D. $19
Marking brainliest
If a job interview says “tell me about yourself” what do u say
Answer:
I start to say from my name,age,family,qualifications and etc.
Answer:
In your response, do the following:
1. Mention past experiences and proven successes as they relate to the position.Begin by rereading the job description. Take note of the required skills that you have, and identify recent stories that demonstrate them . Ideally, you should draw primarily from recent professional experience; however, volunteer work can also support your narrative while demonstrating a commitment to your community.
2. Consider how your current job relates to the job you’re applying for.Is it a more senior role? If so, explain how you are taking on more responsibilities in your current position. If you are making a lateral transition to a role with different skills, describe how your current skills translate into the new position.
3. Focus on strengths and abilities that you can support with examples.When you start building the script of each example, focus on details and outcomes that you can quantify if possible. For example, stating that you “improved customer service” is less impactful than “increased customer service response rates each quarter by 10–15%.” If you don’t have the exact information, estimate a realistic value.
4. Highlight your personality to break the ice.Since the “Tell me about yourself” interview question is about getting to know you, it’s a good idea to share your personality with your interviewer—but not personal details. You may want to briefly mention hobbies that demonstrate intellectual development and/or community engagement (e.g., reading, music, sports league, volunteering) or those that showcase personal discipline and achievement (e.g., learning a new skill, training for a half marathon). Discussing personal interests is a good way to wrap up your response while maintaining a professional tone.
5. Format your response.For your response to be clear and concise, you’ll want to make sure you organize your answer following a format or formula. There are two common formulas you may consider:
Present, Past, FuturePast, Present, FutureBoth of these formulas work for your response, but you may choose one over the other based on the roles from your experience that are most relevant to the position you're interviewing for. For example, if your most recent role highlights many of the skills and qualifications that are required for the role you’re interviewing with, you may want to lead with the present. However, if you're making a career transition and your past experience is more closely related to the role than your current position, you may want to lead with your past.
PROBLEM
9a
The breadth of a rectangle is 4 units less than its length. If the perimeter of the rectangle is
20 units, write a pair of linear equations to model the above situation, assuming the length to be l units
and the breadth to be b units.
Equation 1 :
Equation 2 :
Here, we are to find the length and the , breadth of the rectangle
The length of the rectangle = 7 units and Breadth of the rectangle = 3 units
Let
length = l units
Breadth = b units
Perimeter of the rectangle = 20 units
length is the distance measured along the longest dimension of an object
width is the wideness of an object
perimeter refers to the total measurements of an objects
The breadth of a rectangle is 4 units less than its length
If,
Length = l
Then,
b = l - 4
Perimeter of a rectangle = 2(length + breadth)
20 = 2{l + (l - 4)
20 = 2(l + l - 4)
20 = 2(2l - 4)
20 = 4l - 8
20 + 8 = 4l
28 = 4l
l = 28/4
l = 7
b = l - 4
b = 7 - 4
b = 3 units
Read more:
https://brainly.com/question/24371440
PLEASE HELP!! Important test!! Option 1 isn't coming up so if you could try to solve others that would be great!
Answer:
4
Step-by-step explanation:
Func 2 is -2
Func 3 is 1
Func 4 is 8
Func 1 is unknown
Convert 75 mg into gram
Answer:
[tex]{ \tt{1 \: mg = 1 \times {10}^{ - 3} \: g}} \\ { \tt{75 \: mg = (75 \times 1 \times {10}^{ - 3} ) \: g}} \\ { \bf{ = 75 \times 10 {}^{ - 3} \: grams}} \\ { \bf{ = 0.075 \: grams}}[/tex]
3. If triangle ABC has the following measurements, find the measure of angle A.
a = 17
b = 21
C = 25
9514 1404 393
Answer:
(a) 42.3°
Step-by-step explanation:
Side 'a' is the shortest of three unequal sides, so angle A will be the smallest angle in the triangle. Its measure can be found from the Law of Cosines.
a² = b² +c² -2bc·cos(A)
cos(A) = (b² +c² -a²)/(2bc) = (21² +25² -17²)/(2·21·25) = 777/1050
A = arccos(777/1050) ≈ 42.3°
The measure of angle A is about 42.3°.
_____
Additional comment
The smallest angle in a triangle can never be greater than 60°. This lets you eliminate choices that exceed that value.
Answer:
(a) 42.3°
Step-by-step explanation:
Write an equation in standard form of the line that passes through the given point and has the given slope (-8,0); m= -4 PLEASE HELP NEED DONE ASAP WILL GIVE BRAINLIEST
Answer:
4x+y=-32
Step-by-step explanation:
given,
slope (m) = -4
point: (-8,0)
as we know the slope intercept form of the line is, y=mx+b, b=y-mx, now we put x=-8, y=0 to find b [because the point is given (-8,0) so it must satisfy the equation]
so,
b = 0-(-4)×(-8) = -32
y=mx+b
or, y=-4x-32
or, 4x+y=-32
(this is the standard form of the line)
Using the equation y - y1 = m(x - x1)
y - 0 = -4(x - (-8))
y = -4(x + 8)
y = -4x - 32