The trigonometric equation 7cos(9x) - 1 = 17 has an undefined solution.
How to solve the trigonometric equation?The trigonometric equation for this problem is defined as follows:
7cos(9x) - 1 = 17
Isolating the cosine, we have that:
7cos(9x) = 18
cos(9x) = 18/7
Now we isolate x applying the arc cosine, which is the inverse of the cosine, as follows:
9x = arccos(18/7)
9x = undefined.
The solution is undefined because the arccosine only exists for values between -1 and 1, as the cosine of an angle is always going to assume a value between -1 and 1.
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15% of the contents of a 454 gram can of dog food is protein. How many grams of protein are in the can?
Answer:
68.1 grams
Step-by-step explanation:
454 × .15 = 68.1
What is the measure of the missing angle?
46°
73°
for
The third angle of the triangle must have a measure of 180° minus the sum of the other two angles, which is 180° - (46° + 73°) = 61°. Therefore, the measure of the missing angle is 61°.
What are the angles of a triangle?The internal angles of a triangle are measured in degrees and are known as triangle angles. The sum of a triangle's angles is always 180°.
Triangle angles are classified into three types: acute angles, right angles, and obtuse angles.
An acute angle is one that is smaller than 90 degrees. This is the most common form of angle in a triangle and is regarded the most desirable.
A right angle is one that is exactly 90 degrees. This sort of angle is the most stable and sturdy in a triangle, therefore it is usually employed to make a triangle.
An obtuse angle is one that is larger than 90 degrees but less than 180 degrees. This form of angle is common in triangles, however it is less desirable than an acute angle.
The sum of the three angles of a triangle is always 180°. Acute angles are the most desirable and stable, whereas obtuse angles are present in certain triangles but are not as ideal.
In the given question,
The measure of the missing angle is 180° - (46° + 73°).
180° - (46° + 73°) = 180° - 119° = 61°
Therefore, the measure of the missing angle is 61°.
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How might I rewrite 125% of 440 is B as a simpler equation?
Answer:1.25(400)
Step-by-step explanation:
Please help im on a time limit and i need to turn this in asap!!
Questuon:Susan works for the school newspaper and wants to conduct a survey to ask students whom they will vote for in the upcoming School elections which sample should she choose to best represent the entire population ?
They will vote for in the upcoming School actions maybe they have to choose example should to best represent the entire population is they have to ask to every tenth student in the cafeteria.
Every Nth name from the list of target population members is chosen in systematic sampling. For instance, every tenth member on the list will be included in the sample. Thus, the 10th, 20th, 30th, and so forth will be chosen to make up the sample group.
According to this, they must consult a student in the tenth grade because he is the most knowledgeable about school and has the most experience of anybody.
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The amount a tree grows in one month is directly proportional to the amount of water it is given When the tree is given 23 gallons of water, it grows 4 cm that month. What is the constant of proportionality for this variation? Round your answer to the nearest thousandth
The constant of proportionality for this variation is 0.174cm/gallon .
Every relationship that always maintains the same ratio is referred to be proportionality. For instance, the average amount of apples per tree determines the proportionality between both the quantity of apples in a crop and the number of trees in the orchard.
Let the amount a tree grows in one month be - x
The amount of water given be - y
If the amount a tree grows in one month is directly proportional to the amount of water given, then
x ∝ y
x = ky
k is defined as the constant of proportionality
k = [tex]\frac{x}{y}[/tex]
Given
x = 4cm
y = 23 gallons
k = [tex]\frac{4}{23}[/tex]
k = 0.174cm/gallon
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Dean's savings account started with $100. After one year, it had $110. The
second year, it had $121. The third year it had $133.10.
Is a single linear model a reasonable option for this data? Yes or No?
The statement that answers the linear model possibility is NO
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
Initial = 100
Year 1 = 110
year 2 = 121
year 3 = 133.10
The savings account balance is increasing at an inconsistently increasing rate, which is not linear.
The savings account starts with $100, and increases by $10 in the first year, by $11 in the second year, and by $12.10 in the third year.
This is an example of exponential growth, which cannot be modeled by a single linear equation.
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A cone has a diameter of
36 meters and a slant height of
24 meters. What is the height of the cone to the nearest tenth?
The height of the cone is about 15.9 meters.
The hypotenuse of the right triangle, which also contains the cone height as one of its legs, is formed by the radius (18 m) and slant height. You may find out the height (h) using the Pythagorean theorem.
The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a2 + b2, are equal to the squares on the legs.
So,
18² + h² = 24²
h = √(576 -324) = √252
h ≈ 15.9 . . . . . meters
The height of the cone is about 15.9 meters.
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Noah and Lin are making paper cones to hold popcorn to hand out at a parent math night. They want the cones to hold 9π cubic inches of popcorn. What are two different possible values for height h and radius r for the cones?
The two different possible values for height h and radius r for the cones are height = 3 inches when radius = 3 inches and height = 4.5 inches when radius = 2 inches.
The volume of a cone is given by the formula [tex]V = (1/3)\pi r^2 h[/tex].
We can use this formula to find the values of h and r that will give us a cone with a volume of 9π cubic inches.
We have a volume of the cone -
(1/3)π[tex]r^2[/tex]h = 9π
solving for h, we get,
h = (3/[tex]r^2[/tex]) * 9
Now we have a formula for h in terms of r. We can substitute different values for r and see what values of h we get. Let's consider two possibilities:
case 1: r = 3 inches:h = (3/[tex]3^2[/tex]) * 9 = 3 inches
case 2: r = 2 inches:h = (3/[tex]2^2[/tex]) * 9 = 4.5 inches
So, one possible cone has a height of 3 inches and a radius of 3 inches, and another possible cone has a height of 4.5 inches and a radius of 2 inches.
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If a figure is a quadrilateral, then it has four sides.
A triangle does not have four sides.
A closed quadrilateral is a kind of polygon having 4 sides, 4 vertices, and 4 angles. A triangle doesn't have four sides because if it did, it wouldn't be a triangle. It would be a quadrilateral, the term used to describe geometric objects with four sides.
Three line segments combine to form a triangle, which is a straightforward closed curve or polygon. In Euclidean geometry, any three points, notably non-collinear ones, independently create a singular triangle and a singular plane.
In Euclidean geometry, any three points, notably non-collinear ones, independently create a singular triangle and a singular plane. polygon with 4 sides that is a quadrilateral.
One fascinating feature of a quadrilateral is that its opposite parallel sides are possible. Four non-collinear points are joined to create it. Since a triangle would not have four sides
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Please help me ASAP please please please
The two column proof to show that ABCD is a parallelogram is as shown below
How to complete two column proof?A two-column proof is defined as a geometric proof that consists of a list of statements, and the reasons that we know those statements are true.
Statement 1; BD bisects AC
Reason 1; Given
Statement 2; ∠BAC ≅ ∠DCA
Reason 2; Given
Statement 3; AB║ CD
Reason 3; Properties of parallelogram
Statement 4; ∠BEA ≅ ∠CED
Reason 4; Alternate Interior angles
Statement 5: AE ≅ EC
Reason 5: Diagonals of a parallelogram bisect each other
Statement 6: ΔABE ≅ ΔCDE
Reason 6: SAS Congruency postulate
Statement 7: BA ≅ DC
Reason 7: Properties of parallelogram
Statement 8: ABCD is a parallelogram
Reason 8: Corresponding parts of congruent triangles are congruent
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9. Joseph is teaching a PE class today and he has a bag of balls for the students to play with.
The bag has 5 timers as many basketballs as soccer balls in the bag. If there is a total of 63 balls
in the bag, how many basketballs and soccer balls are there?
The number of basketballs and soccer balls that there are in the bag are;
Soccer balls = 10
Basketballs = 53
How to solve Algebra Word Problems?We are told that Joseph has a bag of balls for the students to play with. The bag has 5 times as many basketballs as soccer balls in the bag.
Let basketballs be b
Let soccer balls be s.
Thus;
b = 5s
Total number of balls is 63 balls. Thus;
5s + s = 63
6s = 63
s = 63/6
s = 10.5
b = 5(10.5)
b = 52.5
We can estimate an approximate value of s = 10 and b = 53
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Explain whether there is enough information given in each figure to prove that the triangles are congruent using SSS or SAS. Fill in the table.
The triangles in this problem are similar using the SSS theorem.
What are similar triangles?Similar triangles are triangles that share these following two features:
Congruent angle measures.Proportional side lengths.For this problem, we have that the two triangles share two common angle measures.
A triangle is composed by three angles, and the sum of their measures is of 180º, hence the third angle measure will be equal for both triangles.
As the angle measures are equal, the side lengths are going to be proportional, thus the triangles are similar by the SSS theorem.
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marco made 124 free throws this season.ryan made132,if each free throw is worth 2 points,how many points did the boys score together?
Answer:
512 points altogether.
Step-by-step explanation:
This is a guess hope it helps :D
Answer:
512
Step-by-step explanation:
&:(::6)6/$/):&;!4):$:$:$:&):=512
Simplify
3√x^5/
5√x^2
Answer:
3√x^5/=15√x
5√x^2=10√x
Step-by-step explanation:
multiply 5 by 3.
multiply 2 by 5.
In ΔSTU, t = 390 cm, s = 900 cm and ∠S=48°. Find all possible values of ∠T, to the nearest degree
The values of ∠T is 18.78 degree.
In ΔSTU ,
We have:
T = 390 cm,
S = 900 cm
and ∠S=48°.
Using the sine rule which works law of sin with the formula:
[tex]\frac{SinT}{T} = \frac{SinS}{S}[/tex]
Plug all the values in above formula:
sinT/ 390 = sin48°/900
sin T = 0.743 × 390 / 900
sin T = 0.3220
T = [tex]sin^-^1[/tex](0.3220)
T = 18.78 degree.
Hence, The values of ∠T is 18.78 degree.
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What is the Value of X
3x=17x
Answer:
14X
Step-by-step explanation:
a ship at position (1, 0) on a nautical chart (with north in the positive y direction) sights a rock at position (4, 5). what is the vector joining the ship to the rock?
The vector joining the ship to the rock is t= 5i+5 j
A vector is a quantity or phenomenon that has two independent properties: magnitude and direction, a quantity that has both magnitude and direction but not position.
The direction is 0.9505 radians east of north.
The position vector of the ship: r= 1i+0j
The position vector of the ship: s= 4i+5j
The vector joining the ship to the rock is: t=r+s
t=(1 i + 0 j) + (4i + 5 j)
t=5i+5j
Θ=π/2-arctan(5/7)
Θ=0.9505 radians
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How do you solve this problem?
Answer:
x = -1
Step-by-step explanation:
Since a triangle's angles all add up to 180 based on this formula: 180(n-2) (n being the # of sides of the shape you're solving for, and the total being the interior), we can set up this equation:
46 + (x+62) + 73 = 180
Now, we can solve for x:
x = 180-73-62-46
x = -1
Brianna has a points card for a movie theater.
She receives 55 rewards points just for signing up.
She earns 14. 5 points for each visit to the movie theater.
She needs at least 235 points for a free movie ticket.
Which inequality can be used to determine v, the minimum number of visits Brianna needs to earn her first free movie ticket?
The inequality 14.5v ≥ 235 can be used to determine the minimum number of visits Brianna needs to earn her first free movie ticket.
The inequality 14.5v ≥ 235 can be used to determine the minimum number of visits Brianna needs to earn her first free movie ticket.14.5v ≥ 235
To figure out how many visits Brianna needs to earn her first free movie ticket, we can set up an inequality. We'll set the left side of the equation equal to the total points needed for a free movie ticket (235 points). We'll set the right side of the equation equal to the points earned per visit (14.5 points) multiplied by the number of visits (v).
14.5v ≥ 235
The inequality 14.5v ≥ 235 can be used to determine the minimum number of visits Brianna needs to earn her first free movie ticket.
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a fair six-sided die is tossed 300 times. find the expected value of the sample mean of the values obtained in these 300 tosses (write it up to first decimal place).
The expected value of the sample mean of the values obtained in these 300 tosses is 3.5
300 fair throws of a six-sided die are made.
The expected value of the sample mean of the results acquired from these 300 tosses must be determined.
Six sides make up a dice:
Every side of a fair dice has an equal chance of happening.
Now, each side's likelihood of being present is 1/6.
Now, the sample mean of the values collected in these 300 tosses is predicted to be equal to:
E(x) = Σx P(x =x)
= 1*1/6 + 2*1/6 + 3*1/6 + 4*1/6 + 5*1/6 + 6*1/6
= 1/6 + 2/6 + 3/6 + 4/6 + 5/6 + 6/6
= 1/6 (1+2+3+4+5+6)
= 1/6 (21)
= 21/6
E(x) = 3.5
Hence, the expected value of the sample mean of the values obtained in these 300 tosses is 3.5
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A large district employs 3,461 teacher. If there are 28 students per teacher, how many students are there?
Answer:
If there are 3,461 teachers and 28 students per teacher, to find the total number of students, you can multiply the number of teachers by the number of students per teacher:
3,461 teachers * 28 students/teacher = 97,268 students
So there are 97,268 students in the district.
Write 5y without exponents.
Answer:
Step-by-step explanation:
5y/5=y+y+y+y+y
4 is 20% of what number
Answer:
20
Step-by-step explanation:
Three lots with parallel side boundaries extend from the avenue to the boulevard find to the nearest tenth of a meter the fronteages of the lots
Three lots with parallel side boundaries extend from the avenue to the boulevard.
x + y + z = 140 meters
According to the proportion theorem,
Solving for x, using cross multiplication:
Similarly,
x/40 = z/35
solving for z by cross multiplication,
z = 35x/40
z = 7x/8
Now, the third proportions,
y/30 = z/35
Solving for y,
y = 30z/35
y = 6z/7
x + y + z = 140
4y/3 + 6z/7 + 7x/8 = 140
(224y + 144z + 147x)/168 = 140
224y + 144z + 147x = 23520
Substituting z = 7x/8,
224y + (144 × 7x/8) + 147x = 23520
224y + 126x + 147x = 23520
224y + 273x = 23520
Now,
Substitute y = 3x/4
(224×3x/4) + 273x = 23520
168x + 273x = 23520
441x = 23520
x = 53.33
Now,
We know that
y = 3x/4
so,
y = 40
And,
z = 7x/8
Z = 46.66
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a personal trainer analyzes the progress of her clients. so she calculates the body mass index (bmi) for each. the bmis for all of her current clients are summarized in the histogram below. histogram with 5 bars of heights 1, 3, 5, 2, 1 and bar edges of 18.1, 20.7, 23.3, 25.9, 28.5, and 31.1. the horizontal axis is labeled bmi and the vertical axis is labeled clients. she would like to offer a discount to her clients that have a current bmi of at least 25.9 in order to encourage them to keep working with her. the discount is for $50 off of their next month's training. if she were to offer these, how much total money would she give in discounts next month?
The total number of clients with a BMI of 25.9 or higher is therefore equal to 1 * 2.6 + 3 * 2
The total amount of money she would need to give in discounts next month can be found by calculating the total number of clients with a BMI of 25.9 or higher. To calculate this, the frequencies of each BMI range need to be multiplied by the width of the corresponding bar. The total amount of money she would need to give in discounts is then equal to the total number of clients with a BMI of 25.9 or higher multiplied by $50.
Using the histogram, the number of clients in each BMI range are: 18.1-20.7 (1), 20.7-23.3 (3), 23.3-25.9 (5), 25.9-28.5 (2), 28.5-31.1 (1).
The width of each bar is: 18.1-20.7 (2.6), 20.7-23.3 (2.6), 23.3-25.9 (2.6), 25.9-28.5 (2.6), 28.5-31.1 (2.6).
The total number of clients with a BMI of 25.9 or higher is therefore equal to 1 * 2.6 + 3 * 2
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Solve these equations for x.
-(3x - 12) = 9x -4
Answer:
x= 4/3
Step-by-step explanation:
Think the negative sign outside the parentheses as -1. Then do distributive property to the numbers inside the parentheses.
-1 x 3x and -1 x -12
That equals to -3x + 12 so now your entire equation is -3x + 12 = 9x - 4. Now lets take away 9x from both sides like this,
9x - 9x and -3x - 9x.
That equation is now -12x + 12 = -4.
Now subtract 12 from both sides like this,
12 - 12 and -4 - 12.
And then you have -12x = -16.
Now you divide both numbers by -12 like this,
-12x/-12 which equals to just x and then do -16/-12 which would equal as 1.3333 and repeating but, it can be put as 4/3 for a clearer answer.
So your answer is
x = 4/3
If point A (-4,5) is reflected over the line y=2 and then translated according to the rule open parentheses (x-1, y-4), what quadrant will point A be in?
The new point A(-5,1) will lie in quadrant 3.
what is the Cartesian coordinate system?A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates,
Given here: The point A(-4,5) is translated over y=2
Thus after the transformation( translation), the new points are
A(-4,5)→A(-4-1,5-4)=A(-5,1)
The point was translated horizontally by 1 to the left and then translated vertically by 4 units downwards.
Hence, The new point will lie in quadrant 3.
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Find the slope of a line parallel to the line whose equation is 2x+4y=56, fully simplify your answer.
Answer:
Step-by-step explanation:
m= -1/2
A blender has blades as shown.
A rotation of the 270º will map the blade formed by triangle CBD onto the blade formed by triangle EDF.
How to obtain the counter clockwise rotation?The rotations are defined as clockwise or counterclockwise as follows:
Clockwise: from right to left.Counterclockwise: from left to right.The entire circumference formed by the image has an angle measure given as follows:
360º.
Triangle EDF is 3/4 of the circumference away from triangle CBD, hence the angle measure of the counterclockwise rotation is given as follows:
3/4 x 360º = 0.75 x 360º = 270º.
Which is the angle measure used to complete the blank in this problem.
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So I’ve answered everything but perimeter can someone please figure that out for me?
The area of rectangle WXYZ is 115. 5 in. ² what is the perimeter of triangle XYZ

The perimeter of triangle XYZ is 38.95 inches
Consider the following figure.
The area of rectangle WXYZ is 115. 5 in.²
From given figure we can observe that PQ = 4 in.
So, XW = YZ = 2 × PQ
XW = YZ = 2 × 4
XW = YZ = 8 inches
This means, the width of rectangle WXYZ is 8 inches
We know that the area of the reactngle is given by the formula,
A = length × width
here, A = 115.5 in.² and width = 8 in.
115.5 = length × 8
length = 115.5 / 8
length = 14.44 in.
So, XY = WZ = 14.44 in.
For right triangle XYZ using Pythagoras theorem,
XZ² = XY² + YZ²
XZ² = 14.44² + 8²
XZ² = XY² + YZ²
XZ² = 272.51
XZ = 16.51 in.
So, the perimeter of triangle XYZ would be,
P = XY + YZ + XZ
P = 14.44 + 8 + 16.51
P = 38.95 inches
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