Factor. 2xy+5x−12y−30
For △ABC, which side is opposite angle B?
side AC
side AB
side BC
Angle D in △EDF is a right angle.
What is the value of tan F ?
4/3
3/4
3/5
4/5
What is the trigonometric ratio for sin Z ?
Enter your answer, as a simplified fraction, in the boxes.
What is the trigonometric ratio for cosD ?
Enter your answer, as a simplified fraction, in the boxes.
Tessa has leaned a ladder against the side of her house. The ladder forms a 63˚ angle with the ground and rests against the house at a spot that is 8 meters high.
Which length is the best approximation for the distance along the ground from the bottom of the ladder to the wall?
2 m
3 m
4 m
5 m
The relationships between the sides and angles of the right triangles in
the question are given by trigonometric ratios.
Correct responses;1. Side AC[tex]\displaystyle 2. \hspace{0.3 cm}\frac{4}{3}[/tex][tex]\displaystyle 3. \hspace{0.3 cm}\frac{3}{5}[/tex][tex]\displaystyle 4. \hspace{0.3 cm}\frac{7}{25}[/tex]5. 4 m.Methods used to arrive at the above responses;1. The given triangle is ΔABC
The side opposite angle B is the side not bearing the letter B which is the side AC
2. The tangent of the angle, F, is given by the following formula;
[tex]\displaystyle tan(F) = \mathbf{\frac{Opposite \ side \ to \ angle \ F}{Adjacent \ side \ to \ angle \ F}}[/tex]
Therefore;
[tex]\displaystyle \underline{ tan(F) = \frac{4}{3}}[/tex]3. The sine of the angle Z is given by the following formula;
[tex]\displaystyle sin (Z) = \mathbf{ \frac{Opposite \ side \ to \ angle \ Z}{Hypotenuse \ side \ of \ right \ triangle}}[/tex]
Therefore;
[tex]\displaystyle sin(Z) = \mathbf{\frac{XY}{40}}[/tex]
XY = √(40² - 32²) = 24
Which gives;
[tex]\displaystyle \underline{sin(Z) = \frac{24}{40} = \frac{3}{5}}[/tex]4. The trigonometric ratio for cos(D) is given as follows;
[tex]\displaystyle cos(D) = \mathbf{ \frac{Adjacent \ side \ to \ angle \ \angle D}{Hypotenuse \ side \ of \ right \ triangle}}[/tex]
Therefore;
[tex]\displaystyle cos(D) = \frac{21}{75} = \frac{7}{25}[/tex]
[tex]\displaystyle \underline{ cos(D) = \frac{7}{25} }[/tex]5. The tangent of the angle 63° is expressed as follows;
[tex]\displaystyle tan(63^{\circ}) = \mathbf{\frac{8 \, m}{Distance \ AB \ (ground \ distance \ from \ wall)}}[/tex]
Therefore;
[tex]\displaystyle Distance \ AB = \frac{8 \, m}{tan(63^{\circ})} \approx \mathbf{4.076 \, m}[/tex]
The approximate distance from the bottom of the ladder o the wall is 4 mLearn more about trigonometric ratios here:
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Calculate 6.75% tax on $2,305
a. Name one line segment that is parallel to AB
b. Name one line segment that is skew to AB
c. Name a pair of parallel planes.
Answer:
A) CD
B) AB
C) Plane ABCD is parallel to EFGH.
Plane BDFH is parallel to ACGE.
Plane ABFE is parallel to CDHG.
Step-by-step explanation:
We are given the following in the question:
A cuboid ABCDEFGH is given.
A) line segment that is parallel to AB
A line segment that is parallel to AB is CD.
B) line segment that is skew to AB
Skew lines are the line that never lie in the same plane and never intersect each other.
Thus line segment FH is skew to line segment AB.
C) pair of parallel planes.
Plane ABCD is parallel to EFGH.
Plane BDFH is parallel to ACGE.
Plane ABFE is parallel to CDHG.
There are 48 chicken farms near an ohio town.if each farm has 9 barns, how many total barns are there? answers
There are 432 total barns when multiplying 48 chicken farms by 9 barns per farm. For question number 27, without knowing the number of mice per barn, we cannot determine the exact number of cats needed to control the grain destruction.
To determine the number of total barns if there are 48 chicken farms near an Ohio town and each farm has 9 barns, we simply need to multiply the number of farms by the number of barns per farm. This can be represented by the equation: 48 farms times 9 barns/farm = 432 barns. Therefore, there are 432 total barns.Now, addressing the second question (Number 27): To calculate the number of cats required to control the destruction of stored grain by mice, we need to find out how many mice are in each barn, and then see how many cats are needed to kill that number of mice. A mouse eats 521 ikats of grain each year, and if we are to prevent the destruction of grain in each of the 24 barns, we need to find out how many mice a single cat can kill in a year, and then divide the number of mice by this figure.If one cat kills 96 mice a year, and assuming each barn has the same number of mice, then for one barn: Total mice killed in one barn/year = Number of cats times 96 mice/cat/year. Therefore, to find the number of cats needed: Number of cats = Total mice in one barn/year extdiv 96 mice/cat/year. Without the number of mice, we cannot complete the calculation. More information on the number of mice per barn is required to give a definitive answer.
p: x – 5 =10 q: 4x + 1 = 61 Which is the inverse of p → q?
a- If x – 5 ≠ 10, then 4x + 1 ≠ 61.
b- If 4x + 1 ≠ 61, then x – 5 ≠ 10.
c-If x – 5 = 10, then 4x + 1 = 61.
d- If 4x + 1 = 61, then x – 5 = 10.
Answer: the correct option is
(a) If x – 5 ≠ 10, then 4x + 1 ≠ 61.
Step-by-step explanation: We are given to select the correct inverse of the conditional statement p → q if
p : x – 5 =10 and q : 4x + 1 = 61.
We know that
the inverse of a conditional statement p → q is given by "not p → not q".
Therefore, the inverse of the given statement is
not p → not q
that is, if x – 5 ≠ 10, then 4x + 1 ≠ 61.
Thus, the required inverse is " x – 5 ≠ 10, then 4x + 1 ≠ 61."
Option (a) is CORRECT.
What is 3.56 x 10^-5 in standard form?
What is the solution to (4 x 10^4) x (3 10^4) write in scientific notation.
A player has 31 hits in 117 times at bat. What is the players average as a decimal? Round to the nearest thousandth.
a sprinter starts from rest, and accelerates at 1.87 m/s2 over a distance of 14.0 m. what is her final velocity
The final velocity of the sprinter is 7.23 meters per second.
What is acceleration?Acceleration of any object is defined as the variation in the speed of the object with the variation of time. Acceleration is a vector term and to define it we require both the magnitude and the direction. The unit of acceleration can be m / sec², miles / sec², etc.
Given that a sprinter starts from rest, and accelerates at 1.87 m/s² over a distance of 14.0 m.
The final velocity will be calculated by the equation of the motion formula as below,
V² = u² + 2as
V² = 2 x 1.87 x 14
V² = 52.36
V = √52.36
V = 7.23 meter per second
Hence, the final velocity is 7.23 meters per second.
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For her tutoring services, Thuy charged Demi $10 per hour and $8 for books and supplies. Demi paid a total of $48.00. Which equation represents this situation?
The equation representing this situation is expressed as [tex]\[ 10h + 8 = 48 \][/tex] and
Demi received 4 hours of tutoring services.
Let's denote the number of hours Demi received tutoring services as [tex]\( h \).[/tex]
The equation representing this situation can be expressed as:
[tex]\[ 10h + 8 = 48 \][/tex]
Now, let's solve for [tex]\( h \):[/tex]
[tex]\[ 10h = 48 - 8 \][/tex]
[tex]\[ 10h = 40 \][/tex]
[tex]\[ h = \frac{40}{10} \][/tex]
[tex]\[ h = 4 \][/tex]
So, Demi received 4 hours of tutoring services.
To find the equation representing the situation, we need to consider the total cost Demi paid. She paid $10 per hour for tutoring services, so the cost for the tutoring service itself is [tex]\( 10h \),[/tex] where [tex]\( h \)[/tex] represents the number of hours of tutoring. Additionally, she paid $8 for books and supplies, which is a fixed cost regardless of the number of hours. Therefore, we add $8 to the cost equation. This gives us [tex]\( 10h + 8 = 48 \).[/tex]
Next, we solve this equation to find the value of [tex]\( h \),[/tex] which represents the number of hours of tutoring. We subtract 8 from both sides to isolate the term [tex]\( 10h \),[/tex] giving us[tex]\( 10h = 40 \)[/tex]. Then, we divide both sides by 10 to solve for [tex]\( h \),[/tex] which gives us[tex]\( h = \frac{40}{10} = 4 \).[/tex]
So, Demi received 4 hours of tutoring services.
Complete question:
For her tutoring services, Thuy charged Demi $10 per hour and $8 for books and supplies. Demi paid a total of $48.00. Which equation represents this situation?
Complete the following multiplication problems. a. 0.34 × 6 b. 0.11 × 4 c. 17 × 0.07 d. 28 × 0.003 e. 3.8 × 5 f. 5.931 × 7 g. 14.07 × 13 h. 3.005 × 32 i. 0.8 × 0.3 j. 0.45 × 0.05 k. 0.09 × 0.02 l. 0.074 × 0.08 m. 2.3 × 0.9 n. 7.25 × 0.3 o. 4.53 × .003 p. 53.67 × 0.056 q. 1.1 × 3.7 r. 3.76 × 18.9 s. 4.57 × 6.1 t. 24.13 × 1.48
Answer with Step-by-step explanation:
a. 0.34 × 6=2.04
b. 0.11 × 4=0.44
c. 17 × 0.07=1.19
d. 28 × 0.003= 0.084
e. 3.8 × 5=19
f. 5.931 × 7=41.517
g. 14.07 × 13=182.91
h. 3.005 × 32=96.16
i. 0.8 × 0.3=0.24
j. 0.45 × 0.05=0.0225
k. 0.09 × 0.02=0.0018
l. 0.074 × 0.08=0.00592
m. 2.3 × 0.9=2.07
n. 7.25 × 0.3=2.175
o. 4.53 × .003=0.01359
p. 53.67 × 0.056=3.00552
q. 1.1 × 3.7 =4.07
r. 3.76 × 18.9 =71.064
s. 4.57 × 6.1 =27.877
t. 24.13 × 1.48=35.7124
Which function is a horizontal compression of its parent function f(x)=x^7 by a factor of 4?
q(x)=(1/4x)^7
r(x)=(4x)^7
s(x)=4x^7
t(x)=1/4x^7
thank you!
The answer is r(x) = (4x)^7
What is the value of g(−3) when g(x)=2x−2 ?
Enter your answer in the box.
g(−3)= ____
Answer:
The answer is -8
Hope this helps :)
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The graph of the function f(x) = x3 + 5x2 + 3x – 9 intersects the x-axis at the points (–3, 0) and (1, 0) as shown. Which expression is equivalent to x3 + 5x2 + 3x – 9?
A) (x – 3)(x – 3)(x + 1)
B) (x – 3)(x + 1)(x + 1)
C) (x – 1)(x – 1)(x + 3)
D) (x – 1)(x + 3)(x + 3)
There are 5 red socks, 2 white socks and 3 blue socks in a basket. What is the probability of picking a pair of red socks?
The probability of picking a pair of red socks is 1/5.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
Given, There are 5 red socks, 2 white socks and 3 blue socks in a basket.
So, The no. of sample space N(S) = 5 + 2 + 3 = 10.
Now pair of red socks means 2 red socks let it be N(A).
∴ The probability of picking a pair of red socks P(A) = N(A)/N(S).
P(A) = 2/10.
P(A) = 1/5.
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At Billy‘s preschool they have bicycles and tricycles with a total of 57 wheels. The number of bicycles is three less than three times the number of tricycles. How many of each are there?
Figure ABCD is a square. Prove BD ≅ AC. Statements Reasons 1. ABCD is a square 1. given 2. ∠DAB, ∠ABC, ∠BCD, and ∠CDA are right angles 2. definition of a square 3. ∠DAB ≅ ∠ABC ≅ ∠BCD ≅ ∠CDA 3. right angles are congruent 4. AB ≅ BC ≅ CD ≅ DA 4. ? 5. △BAD ≅ △ABC 5. SAS 6. BD ≅ AC 6. CPCTC What is the missing reason in the proof? all sides of a square are congruent all right angles measure 90° definition of diagonal definition of perpendicular
The missing reason in the geometric proof for step 4 is that all sides of a square are congruent. This property is part of the definition of a square and justifies the statement AB ≅ BC ≅ CD ≅ DA.
The missing reason in the proof is: "all sides of a square are congruent" Option a.
This reason is necessary to establish statement 4: "AB ≅ BC ≅ CD ≅ DA". It's a critical property of a square that all its sides are congruent to each other. Once you establish this, you can proceed with statement 5 using SAS (Side-Angle-Side) congruence to prove △BAD ≅ △ABC, and then finally, using Corresponding Parts of Congruent Triangles are Congruent to conclude BD ≅ AC.
Here is the corrected step:
ABCD is a square∠DAB, ∠ABC, ∠BCD, and ∠CDA are right angles∠DAB ≅ ∠ABC ≅ ∠BCD ≅ ∠CDAAB ≅ BC ≅ CD ≅ DA△BAD ≅ △ABCBD ≅ ACNitrogen gas accounts for what percentage of the atmosphere? select one:
a. approximately 50%
b. 1%
c. 99%
d. 78%
e. 0.03%
Nitrogen gas makes up approximately 78% of the atmosphere, not 50%, 1%, 99%, or 0.03%.
The correct answer is: d. 78%
Nitrogen gas (N2) makes up a significant portion of the Earth's atmosphere.
To determine the correct percentage, we need to consider the composition of the atmosphere:
The Earth's atmosphere is primarily composed of several gases, with the most abundant being nitrogen (N2) and oxygen (O2).
Other gases such as argon, carbon dioxide, neon, helium, and trace amounts of other gases are also present.
The correct answer is: d. 78%
Nitrogen gas (N2) constitutes approximately 78% of the Earth's atmosphere, making it the most abundant gas.
Oxygen (O2) is the second most abundant gas, accounting for about 21% of the atmosphere.
The remaining 1% consists of trace gases like argon, carbon dioxide, and others.
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Factor completely: x4 + 8x2 + 16
Final answer:
The expression x⁴ + 8x² + 16 is a perfect square trinomial and it can be factored completely as (x² + 4)².
Explanation:
To factor completely the expression x⁴ + 8x² + 16, we should first recognize that this is a perfect square trinomial. A perfect square trinomial takes the form a² + 2ab + b², and can be factored into (a + b)².
Comparing our given expression to the perfect square trinomial, we see that x⁴ is the square of x² and 16 is the square of 4. Moreover, 8x² is twice the product of x² and 4, suggesting that the expression is indeed, a perfect square. Thus, we can factor it as:
(x² + 4)²
In conclusion, the expression x⁴ + 8x² + 16 can be factored completely as (x² + 4)².
Final answer:
To factor the expression [tex]x^4 + 8x^2 + 16[/tex] t is a perfect square trinomial.
Explanation:
To factor the expression [tex]x^4 + 8x^2 + 16[/tex] t is a perfect square trinomial of the form [tex]a^2 + 2ab + b^2[/tex]. The square root of the first term is [tex]x^2[/tex] the square root of the last term is 4, and twice the product of these square roots is [tex]8x^2[/tex], which matches the middle term of the given expression. Therefore, we can rewrite the expression as [tex](x^2 + 4)^2[/tex]. This is the completely factored form of the expression.[tex]a^2 + 2ab + b^2[/tex]
Which expression is equivalent to 3x+10−x+12?
A: 4x + 22
B: 2x + 22
C: 24x
D: 26x
Which of the following is a solution to the equation y=3x - 1?
A. (4, 1)
B. (2, 5)
C. (4, 3)
D. (0, -3)
--------------------------------
2. Which equation matches the statement "The sum of -4x and 2 is 9"?
A. -4x + 2 = 9
B. -4x + 9 = 2
C. -4x(2) = 9
D. -4x - 2 =9
--------------------------------
3. Solve x - 6 = -18
A. X = -24
B. X = -12
C. X = 12
D. X = 6
--------------------------------
4. Solve 4x + 3 = 47
A. X= 11
B. X= 40
C. X= 44
D. X= 50
--------------------------------
Solution to y = 3x - 1: B. (2, 5)
Matching equation for "The sum of -4x and 2 is 9": A. -4x + 2 = 9
Solve x - 6 = -18: A. x = -12
Solve 4x + 3 = 47: A. x = 11
Let's solve each of the given equations one by one:
Solution to y = 3x - 1:
The equation y = 3x - 1 represents a linear relationship between x and y with a slope of 3 and a y-intercept of -1. To find the solution, we can substitute the given options for x and see which one satisfies the equation:
A. (4, 1): 1 = 3(4) - 1 => 1 = 12 - 1 => 1 = 11 (Not a solution)
B. (2, 5): 5 = 3(2) - 1 => 5 = 6 - 1 => 5 = 5 (This is a solution)
C. (4, 3): 3 = 3(4) - 1 => 3 = 12 - 1 => 3 = 11 (Not a solution)
D. (0, -3): -3 = 3(0) - 1 => -3 = 0 - 1 => -3 = -1 (Not a solution)
So, the solution is B. (2, 5).
Matching equation for "The sum of -4x and 2 is 9":
The statement can be translated into the equation: -4x + 2 = 9. So, the correct equation is A. -4x + 2 = 9.
Solving x - 6 = -18:
To solve for x, add 6 to both sides of the equation:
x - 6 + 6 = -18 + 6
x = -12
So, the solution is A. x = -12.
Solving 4x + 3 = 47:
To solve for x, subtract 3 from both sides of the equation:
4x + 3 - 3 = 47 - 3
4x = 44
Now, divide both sides by 4 to isolate x:
(4x)/4 = 44/4
x = 11
So, the solution is A. x = 11.
In summary, the solutions to the given equations are:
B. (2, 5)
A. -4x + 2 = 9
A. x = -12
A. x = 11
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Suppose y varies directly as x and y=21 when x=7. which is an equation relating x and y
A segment of a circle has a 120 arc and a chord of 8 square root 3 in. Find the area of the segment.
To find the area of a segment of a circle, we can use the formula A = (r^2/2)(θ - sinθ), where r is the radius and θ is the central angle in radians. In this case, the arc measure is 120 degrees and the chord length is 8√3 inches. By plugging in the values and following the steps, we can find that the area of the segment is 3840 - 16√3 square inches.
Explanation:To find the area of a segment of a circle, we need to know the measure of the arc and the length of the chord. In this case, the arc measure is 120 degrees and the chord length is 8√3 inches. To find the area, we can use the formula A = (r^2/2)(θ - sinθ), where r is the radius and θ is the central angle in radians.
First, we need to find the radius by using the length of the chord. The formula for the radius is r = 2c/sinθ, where c is the length of the chord and θ is the central angle in degrees. Plugging in the values, we get r = 8√3/(2sin60) = 4√3/sin60 = 4√3/(√3/2) = 8 inches. Now we can find the area using the formula A = (r^2/2)(θ - sinθ). Plugging in the values, we get A = (8^2/2)(120 - sin120) = 32(120 - √3/2) = 3840 - 16√3 square inches.
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What is the value of x?
A. 110 degrees
B. 35 degrees
C. 145 degrees
D. 60 degrees
Item 19 Question 1 A furniture store is having a sale where everything is 40% off. a. Write a function that represents the amount of discount dd on an item with a regular price pp.
To calculate the discount amount on an item with a regular price during a sale of 40% off, use the function d(p) = 0.40 x p.
The question involves creating a mathematical function to calculate the amount of discount during a sale. The store is offering a 40% discount on items, so to find the discount amount d on an item with a regular price p, we can write the function as d(p) = 0.40 * p. Here, p represents the regular price of the item, and d represents the discount amount in dollars that will be subtracted from the regular price.
The figure in the picture is made up of 5 congruent squares. If the perimeter of the entire figure is 21.6 cm, find its area.
HELPPPP!!!!! GEOMETRY IS HARD CX
What is the m∠ABC?
A) m∠ABC = 45°
B)m∠ABC = 15°
C)m∠ABC = 75°
D)m∠ABC = 60°
Answer: it would be (D)
Step-by-step explanation:
There are a total of 84 green cars, 35 blue cars, and 42 red cars parked in the parking lot. How many cars are parked in the parking lot?
Mikw earned %ll.76 per hour for working 23.5 hours last week. how much money did mike earn last week?\
The volume of a sphere is 1372π/3 cubic inches. What is the diameter of the great circle? (Recall that the formula for the volume for a sphere is v=4/3πr^3.)
Answer:
It's 14 inches on Ed
Step-by-step explanation:
Final answer:
The volume of the sphere is given as 1372π/3 cubic inches. Using the volume formula for a sphere, V = (4/3)πr³, we calculate the radius and then double it to find the diameter, which is 14 inches.
Explanation:
The student asks for the diameter of the great circle of a sphere, given its volume is 1372π/3 cubic inches. To find this, we'll make use of the formula for the volume of a sphere, V = (4/3)πr³, where V represents the volume and r is the radius of the sphere.
Let's start by equating the given volume to the volume formula:
1372π/3 = (4/3)πr³
Cancelling out π and the fraction (4/3) on both sides, we get:
1372/4 = r³
This simplifies to:
343 = r³
Taking the cube root of both sides gives us the radius:
r = ∛343
r = 7 inches
The diameter of the sphere is twice the radius, so:
diameter = 2r = 2 × 7 = 14 inches
Therefore, the diameter of the great circle of the sphere is 14 inches.
What is 840 divde by 10 to the third power