[tex]\bf 60z+50-97z=-37z+49\implies 50~~\begin{matrix} -37z \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~=~~\begin{matrix} -37z \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~+49\implies \stackrel{\textit{the what?!}}{50=49}[/tex]
well, clearly 50 ≠ 49.
but, whenever we get a result of this kind, is just a way to say no solutions.
you can look at it this way, is a system of equations, the equations are
y = -37z + 50
y = -37z + 49
now, notice, since both equations are in slope-intercept form, both equations have the same slope of -37, however, the y-intercept differs, meaning both equations are parallel and never touch each other.
since a solution for them is where they intercept and they never do, no solutions.
The given equation will have no solution.
What is equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given is an equation, 60z+50-97z=-37z+49
On solving, we get,
0 = -1
Which is not possible.
Hence, There is no solution.
For more references on equation, click;
https://brainly.com/question/29657983
#SPJ2
Help what answer choice is this?
Answer:
Option A
Step-by-step explanation:
The domain must be
[a,∞)
That means that x must have as an argument a square root, because, it cannot take negative arguments for real numbers (a>0)
√(x-a)
x-a≥0
x ≥ a
The only possible option is
Option A.
Please take a look at the attached graph
A pet store sells mice reptiles and birds Let event A = a customer buys a mouse Let event B = A customer buys a reptile What does P(A or B) = 0.25 mean in the term of this problem
A
B
C
or D
Answer:
The correct option is C.
Step-by-step explanation:
According to the question given in the attached picture:
Event A = a customer buys a mouse
Event B = A customer buys a bird
P(A or B) = 0.25
Now have a look at the probability P(A or B). Here or means either..Its means that the customer will purchase either a mouse or a bird. That means that there is 0.25 or 25% probability that the customer will purchase either a mouse or a bird. In this case there are only 3 choices, which are: the customer will either purchase a mouse, a bird or a reptile because the pet store has only these three possible outcomes. We are not told that how much of each animal they have. Thus the probability that the customer will either purchase either a mouse or a bird is 0.25 or 25%. That means that the probability of either purchasing a mouse or a bird is added together which is 0.25 or 25%
Thus the correct option is C....
Answer: C
Step-by-step explanation:
confirmed
booker has a bag of marbles.there are 10 marbles 6 yellow marbles and 4 red marbles .book 4 teacher reaches into the bag without looking and picks a marble.what is the probability that he picks a red marbles
Answer: 40% or 2/5
Step-by-step explanation:
10 total marbles
6 yellow
4 red
Probability of blindly picking a red marble is 4/10 or 2/5 which can be written as 40%
The probability of picking a red marble from a bag containing 10 marbles, where 4 are red, is 4 out of 10 or 0.4.
The question asks about the probability of picking a red marble from a bag containing 6 yellow marbles and 4 red marbles, totaling 10 marbles. To calculate the probability, you divide the number of favorable outcomes (picking a red marble) by the number of possible outcomes (total marbles). In this case, the probability of picking a red marble is 4 out of 10, which can be simplified to 2 out of 5 or 0.4.
How to solve the inequality to -2(k+3) < -2k - 7
[tex]-2(k+3) < -2k - 7\\-2k-6<-2k-7\\-6<-7\\k\in\emptyset[/tex]
Answer:
No solutions
Step-by-step explanation:
-2(k+3) < -2k - 7
Distribute the -2
-2k-6 < -2k - 7
Add 2k to each side
-2k+2k-6 < -2k+2k - 7
-6 < -7
This is always false, so the inequality is never true
There are no solutions
Using the translation that maps (3,-4) to its image (1,0), what is the image of any point (x,y)?
[tex]\huge{\boxed{(x-2, y+4)}}[/tex]
[tex]x_1 \bf{-2} =x_2[/tex]
[tex]y_1 \bf{+4} =y_2[/tex]
This means that the answer is the subtract [tex]2[/tex] from the [tex]x[/tex] and add [tex]4[/tex] to the [tex]y[/tex], which is represented as [tex]\boxed{(x-2, y+4)}[/tex]
Also, thank you for posting your first question, and welcome to the community! If you have any questions, don’t hesitate to reach out to me!
The translation that maps (3,-4) to its image (1,0) is given by:
(x, y) ⇒ (x - 2, y + 4)
Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.
Translation is the movement of a point either up, down, left or right.
If a point A(x, y) is moved a units left and b units up, the new point is at A'(x - a, y + b).
The translation that maps (3,-4) to its image (1,0) is given by:
(x, y) ⇒ (x - 2, y + 4)
Find out more at: https://brainly.com/question/18303818
Use the diagram to find the measure of the given angle.
Given measure of the angle: EAD
Answer:
The measure of the angle EAD is 90°Explanation:
Angles may be named by three letters, each represented a point on each of the angle's ray or by the vertex.
The angle EAD is the angle A (the letter of the center is the vertex).
In this case it is indicated the measure of the angle on the diagram using a small square.
The small square is a conventional symbol to indicate that the angle is 90°, which is named right angle. That determines that the rays, segments or lines meet perpendicularly.
That is one fourth (1/4) of the complete circle (1/4 × 360° = 90°).
By using the dagram, the measure of the given angle include the following:
m∠EAD = 90°
In Mathematics and Euclidean Geometry, a right angle is a type of angle that is formed in a triangle by the intersection of two (2) straight lines at 90 degrees.
Generally speaking, a perpendicular bisector can be used to bisect or divide a line segment exactly into two (2) equal halves, in order to form a right angle that has a magnitude of 90 degrees at the point of intersection;
In this context, we can logically deduce that segment AE is the perpendicular bisector of diameter ED in circle A. Therefore, the measure of angle EAD must be 90 degrees;
m∠EAD = 90°
Line segment AB is reflected across the y–axis to form line segment CD. Then, line segment CD is rotated 90° clockwise about the origin to form line segment EF.
Answer:
The coordinates of EF are E(5,-4) and F(1,-4).
The line segment EF is in QIV
Step-by-step explanation:
The line segment AB has vertices at: A(-4,5) and B(-4,1).
We apply the rule [tex](x,y)\to (-x,y)[/tex] to reflect AB in the y-axis to obtain CD.
[tex]\implies A(-4,5)\to C(4,5)[/tex]
[tex]\implies B(-4,1)\to D(4,1)[/tex]
We apply the rule [tex](x,y)\to (y,-x)[/tex] to rotate CD 90 degrees clockwise about the origin to obtain EF.
[tex]\implies C(4,5)\to E(5,-4)[/tex]
[tex]\implies D(4,1)\to F(1,-4)[/tex]
The coordinates of EF are E(5,-4) and F(1,-4).
See attachment
Answer:
probably
The coordinates of EF are E(5,-4) and F(1,-4).
The line segment EF is in QIV
Step-by-step explanation:
Find four integers whose sum is 400 such that the first integer is equal to twice the second integer, three times the third integer and four time the fourth integer.
Answer:
a=192
b=96
c=64
d=48
Step-by-step explanation:
So we have [tex]a+b+c+d=400[/tex] where [tex]a,b,c,[/tex] and [tex]d[/tex] are integers.
We also have [tex]a=2b[/tex]and [tex]a=3c[/tex]and [tex]a=4d.[/tex]
[tex]a=2b[/tex] means [tex]a/2=b[/tex]
[tex]a=3c[/tex] means [tex]a/3=c[/tex]
[tex]a=4d[/tex] means [tex]a/4=d[/tex]
Let's plug those in:
[tex]a+b+c+d=400[/tex]
[tex]a+\frac{a}{2}+\frac{a}{3}+\frac{a}{4}=400[/tex]
Multiply both sides by 4(3)=12 to clear the fractions:
[tex]12a+6a+4a+3a=4800[/tex]
Combine like terms:
[tex]25a=4800[/tex]
Divide both sides by 25:
[tex]a=\frac{4800}{25}[/tex]
Simplify:
[tex]a=192[/tex].
Let's go back and find [tex]b,c,d[/tex] now.
b is half of a so half of 192 is 96 which means b=96
c is a third of a so a third of 192 is 64 which means c=64
d is a fourth of a so a fourth of 192 is 48 which means d=48
So
a=192
b=96
c=64
d=48
Answer:
a=192
b=96
c=64
d=48
Step-by-step explanation:
hope this helps
Two painters can paint a room in 2 hours if they work together. The inexperienced painter takes 3 hours more than the experienced painter to finish the job. How long does it take for each painter to paint the room individually?
Answer:
The experienced painter takes 3 hours to paint the room
The inexperienced painter takes 6 hours to paint the room
Step-by-step explanation:
* Lets explain how to solve the problem
- Two painters can paint a room in 2 hours if they work together
- Assume that the experienced painter can paint the room in a hours
∴ Its rate is 1/a
- Assume that the inexperienced painter can paint the room in b hours
∴ Its rate is 1/b
∵ When they working together they will finish it in two hours
∴ Their rate together is 1/2
- Equate the sum of the rate of each one and the their rate together
∴ [tex]\frac{1}{a}+\frac{1}{b}=1/2[/tex]
-To add two fraction with different denominators we multiply the 2
denominators and multiply each numerator by the opposite
denominator
∴ [tex]\frac{b+a}{ab}=\frac{1}{2}[/tex]
- By using the cross multiplication
∴ 2(b + a) = ab
∴ 2b + 2a = ab ⇒ (1)
- The inexperienced painter takes 3 hours more than the experienced
painter to finish the job
∵ The experienced painter can finish the room in a hours
∵ The inexperienced painter can finish the room in b hours
∵ The inexperienced painter takes 3 hours more than the experienced
painter to finish the job
∴ b = a + 3 ⇒ (2)
- Substitute equation (2) in equation (1)
∴ 2(a + 3) + 2a = a(a + 3)
∴ 2a + 6 + 2a = a² + 3a ⇒ add like terms
∴ 4a + 6 = a² + 3a ⇒ subtract 4a from both sides
∴ 6 = a² - a ⇒ subtract 6 from both sides
∴ a² - a - 6 = 0 ⇒ factorize it
∵ a² = (a)(a)
∵ -6 = -3 × 2
∵ -3(a) + 2(a) = -3a + 2a = -a ⇒ the middle term in the equation
∴ a² - a - 6 = (a - 3)(a + 2)
∵ a² - a - 6 = 0
∴ (a - 3)(a + 2) = 0
∴ a - 3 = 0 ⇒ add 3 to both sides
∴ a = 3
- OR
∴ a + 2 = 0 ⇒ subtract 2 from both sides
∴ a = -2 ⇒ rejected because there is no negative value for the time
- Substitute the value of a in equation (2) to find b
∵ b = 3 + 3 = 6
∴ The experienced painter takes 3 hours to paint the room
∴ The inexperienced painter takes 6 hours to paint the room
Experienced painter needs 3 hours to paint the room individually.
Inexperienced painter needs 6 hours to paint the room individually.
Further explanationThis problem is related to the speed of completing the work.
To solve this problem, we must state the formula for the speed.
[tex]\large {\boxed {v = \frac{x}{t}} }[/tex]
where:
v = speed of completing the work( m³ / s )
x = work ( m³ )
t = time taken ( s )
Let's tackle the problem!
Painter A can complete work by herself in t_a hours.
[tex]\text{Painter A's Speed} = v_a = x \div t_a[/tex]
[tex]v_a = x \div t_a[/tex]
Painter B can complete work by herself in t_b hours.
[tex]\text{Painter B's Speed} = v_b = x \div t_b[/tex]
[tex]v_b = x \div t_b[/tex]
The inexperienced painter takes 3 hours more than the experienced painter to finish the job
[tex]\text{Painter B's Time} = 3 + \text{Painter A's Time}[/tex]
[tex]t_b = 3 + t_a[/tex]
Two painters can paint a room in 2 hours if they work together
[tex]\text{Total Speed} = v = v_a + v_b[/tex]
[tex]\frac{x}{t} = \frac{x}{t_a} + \frac{x}{t_b}[/tex]
[tex]\frac{1}{t} = \frac{1}{t_a} + \frac{1}{t_b}[/tex]
[tex]\frac{1}{2} = \frac{1}{t_a} + \frac{1}{3 + t_a}[/tex]
[tex]\frac{1}{2} = \frac{3 + t_a + t_a}{t_a(3 + t_a)}[/tex]
[tex]\frac{1}{2} = \frac{3 + 2t_a}{t_a(3 + t_a)}[/tex]
[tex]t_a(3 + t_a) = 2(3 + 2t_a)[/tex]
[tex]t_a^2 + 3t_a = 6 + 4t_a[/tex]
[tex]t_a^2 + 3t_a - 4t_a - 6 = 0[/tex]
[tex]t_a^2 - t_a - 6 = 0[/tex]
[tex](t_a -3)(t_a + 2) = 0[/tex]
[tex](t_a -3) = 0[/tex]
[tex]t_a = \boxed{3 ~ hours}[/tex]
[tex]t_b = 3 + t_a[/tex]
[tex]t_b = 3 + 3[/tex]
[tex]t_b = \boxed {6 ~ hours}[/tex]
Learn moreInfinite Number of Solutions : https://brainly.com/question/5450548System of Equations : https://brainly.com/question/1995493System of Linear equations : https://brainly.com/question/3291576Answer detailsGrade: High School
Subject: Mathematics
Chapter: Linear Equations
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point
In △ABC, m∠A=57°, m∠B=37°, and a=11. Find c to the nearest tenth.
Answer:
c = 13.1
Step-by-step explanation:
* Lets explain how to solve the problem
- In Δ ABC
# ∠A is opposite to side a
# ∠B is opposite to side b
# ∠C is opposite to side c
- The sine rule is:
# [tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex]
* Lets solve the problem
- In Δ ABC
∵ m∠A = 57°
∵ m∠B = 37°
∵ The sum of the measures of the interior angles of a triangle is 180°
∴ m∠A + m∠B + m∠C = 180°
∴ 57° + 37° + m∠C = 180°
∴ 94° + m∠C = 180° ⇒ subtract 94° from both sides
∴ m∠C = 86°
- Lets use the sine rule to find c
∵ a = 11 and m∠A = 57°
∵ m∠C = 86°
∵ [tex]\frac{sin(57)}{11}=\frac{sin(86)}{c}[/tex]
- By using cross multiplication
∴ c sin(57) = 11 sin(86) ⇒ divide both sides by sin(57)
∴ [tex]c=\frac{11(sin86)}{sin57}=13.1[/tex]
* c = 13.1
Solve this equation for x. Round your answer to
the nearest hundredth.
7 = In(x + 5)
Answer:
x ≈ 1091.63
Step-by-step explanation:
Using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
note that ln x is to the base e
Given
ln(x + 5) = 7, then
x + 5 = [tex]e^{7}[/tex] ( subtract 5 from both sides )
x = [tex]e^{7}[/tex] - 5 ≈ 1091.63 ( nearest hundredth )
Given the Arithmetic series A1+A2+A3+A4 13 + 18 + 23 + 28 + . . . + 113 What is the value of sum?
Answer:
The value of sum is 1323
Step-by-step explanation:
First of all we will find the value of n:
The value of n can be determined by the following formula:
an = a1 + (n - 1)d
where an= 113
a1= 13
d=5
Difference between the values = d=5
Now put the values n the formula:
113=13+(n-1)5
113=13+5n-5
Solve the like terms:
113=8+5n
Move constant to the L.H.S
113-8=5n
105=5n
Divide both sides by 5
21=n
Now put these values in the formula to find the sum:
Sn = n/2(a1 + an)
S21=21/2(13+113)
S21=21/2(126)
S21=21(63)
S21=1323
The value of sum is 1323....
PLEASE HELP! Urgent!!!
Which of the following expressions represents the area of the composite figure ( i said 18 pi + 35 and it said it was wrong)
Answer:
[tex]\frac{9}{2}\pi +35[/tex]
Step-by-step explanation:
The area of trapezoid is given by the formula:
[tex]A=\frac{1}{2}(b_1+b_2)h[/tex]
Where
A is the area
b_1 is base 1
b_2 is base 2, and
h is the height
Looking at the figure, base 1 is the left line which goes from y = 3 to y = 3, so 6 units. Also, base 2 is the right line which goes from y = -3 to y =5, so 8 units.
The height is the horizontal distance in the middle, which goes from x = -2 to x = 3, so 5 units. Hence area of trapezoid is:
[tex]A=\frac{1}{2}(b_1+b_2)h\\A=\frac{1}{2}(6+8)*5\\A=35[/tex]
Now, area of semicircle is:
[tex]A=\frac{\pi r^2}{2}[/tex]
Where
A is the area
r is the radius
Looking at the figure, the diameter (twice radius) goes from y = -3 to y = 3, so 6 units. But radius is half of that, so 3 units. Hence area of semicircle is:
[tex]A=\frac{\pi r^2}{2}\\A=\frac{\pi (3)^2}{2}\\A=\frac{9}{2} \pi[/tex]
Total area of the figure is [tex]\frac{9}{2}\pi +35[/tex]
I need help!! Will mark brainlist
Answer:
10
Step-by-step explanation:
Just by eyeballing it EB is half of AB which looks like the same length of CD so you would times EB(5) by 2 to get the full length of CD which is 10 Hope it helps :)
Me ajuda ai por favor tenho que entregar amanhã
a) (2a - b)² = (4a² - 4ab + b²)
b) (10m - n²)² = (100m² - 20mn² + n⁴)
c) (4x - 4²) = (16x² - 8x + 4⁴)
d)[tex] {( \frac{1}{3} x - y) }^{2} = ({ \frac{1}{9}x }^{2} - \frac{2}{3} xy + {y}^{2} )[/tex]
e)
[tex](0.25 - a) ^{2} = (0.25^{2} - (2)(0.25)a + {a}^{2} ) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = ( \frac{1}{16} - \frac{1}{2} a + {a}^{2} )[/tex]
f)
[tex] {( \frac{2x}{3} - \frac{1}{2} )}^{2} = ( \frac{4 {x}^{2} }{9} - \frac{2x}{3} + \frac{1}{4} )[/tex]
What is the area of this triangle ?
Answer:
Area of triangle is 9.88 units^2
Step-by-step explanation:
We need to find the area of triangle
Given E(5,1), F(0,4), D(0,8)
We will use formula:
[tex]Area\,\,of\,\,triangle =\sqrt{s(s-a)(s-b)s-c)} \\where\,\, s = \frac{a+b+c}{2}[/tex]
We need to find the lengths of side DE, EF and FD
Length of side DE = a = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
Length of side DE = a = [tex]=\sqrt{(5-0)^2+(1-8)^2}\\=\sqrt{(5)^2+(-7)^2}\\=\sqrt{25+49}\\=\sqrt{74}\\=8.60[/tex]
Length of side EF = b = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
Length of side EF = b = [tex]=\sqrt{(0-5)^2+(4-1)^2}\\=\sqrt{(-5)^2+(3)^2}\\=\sqrt{25+9}\\=\sqrt{34}\\=5.8[/tex]
Length of side FD = c = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
Length of side FD = c = [tex]=\sqrt{(0-0)^2+(8-4)^2}\\=\sqrt{(0)^2+(4)^2}\\=\sqrt{0+16}\\=\sqrt{16}\\=4[/tex]
so, a= 8.60, b= 5.8 and c = 4
s = a+b+c/2
s= 8.6+5.8+4/2
s= 9.2
Area of triangle=[tex]=\sqrt{s(s-a)(s-b)s-c)}\\=\sqrt{9.2(9.2-8.6)(9.2-5.8)(9.2-4)}\\=\sqrt{9.2(0.6)(3.4)(5.2)}\\=\sqrt{97.5936}\\=9.88[/tex]
So, area of triangle is 9.88 units^2
Which shows the correct substitution of the values a, b, and c from the equation 1 = –2x + 3x^2 + 1 into the quadratic formula? Quadratic formula:
Given [tex]1 = -2x + 3x^2 + 1\), identify \(a = 3\), \(b = -2\), and \(c = 1\).[/tex]Substitute into the quadratic formula to find the roots [tex]\(x = \frac{{1 \pm i\sqrt{2}}}{{3}}\).[/tex]
[tex]\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]
let's substitute the values of a, b, and c into the quadratic formula. The quadratic formula is:
[tex]\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]
Given the equation[tex]\( 1 = -2x + 3x^2 + 1 \)[/tex], we can identify:
a = 3
b = -2
c = 1
Now, let's substitute these values into the quadratic formula:
[tex]\[ x = \frac{{-(-2) \pm \sqrt{{(-2)^2 - 4(3)(1)}}}}{{2(3)}} \][/tex]
[tex]\[ x = \frac{{2 \pm \sqrt{{4 - 12}}}}{{6}} \][/tex]
[tex]\[ x = \frac{{2 \pm \sqrt{{-8}}}}{{6}} \][/tex]
Now, we have a negative value under the square root, which indicates that the equation has complex roots. We can simplify this further using the imaginary unit (i):
[tex]\[ x = \frac{{2 \pm \sqrt{{-1 \times 8}}}}{{6}} \][/tex]
[tex]\[ x = \frac{{2 \pm 2i\sqrt{2}}}{{6}} \][/tex]
[tex]\[ x = \frac{{1 \pm i\sqrt{2}}}{{3}} \][/tex]
So, the roots of the equation [tex]\(1 = -2x + 3x^2 + 1\) are \(x = \frac{{1 + i\sqrt{2}}}{{3}}\) and \(x = \frac{{1 - i\sqrt{2}}}{{3}}\).[/tex]
when you divide an even number by an even number, is the resut always an even number
Answer:
false
Step-by-step explanation:
if you do 4/4 it is 1 which is odd
Answer:
No, the result is not always even.
Step-by-step explanation:
No, this is not necessary.
There is no general rule that states that an even number divided by another even number will always be an even number.
Few example are:
[tex]\frac{6}{2}=3[/tex]
[tex]\frac{10}{2}=5[/tex]
[tex]\frac{60}{4}=15[/tex]
Two arcs of a circle are congruent if and only if their associated chords are congruent. True or False.
Answer:
True
Step-by-step explanation:
It would be true.
"Two arcs of a circle are congruent if and only if their associated chords are congruent." is False statement.
What is Congruency?If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent, or to be in the relation of congruence. When two sides and their included angle in one triangle are equal to two sides and their included angle in another, two triangles are said to be congruent.
If and only if the related chords of two arcs are congruent, they are said to be congruent.
The radii of the circles that the arcs are in are the related radii of the arcs. Yet, it is possible to have two arcs that are incongruent in a single circle.
The arcs wouldn't necessarily be congruent, but the circle wouldn't have two distinct radii either.
Thus, the given statement is False.
Learn more about Congruency here:
https://brainly.com/question/10677854
#SPJ7
Which of the following is formed by the intersection of a right circular cone and a plane?
A. Conic section
B. Nappe
C. Linear equation
D. Vertex
Answer:
B. Nappe
Step-by-step explanation:
A Nappe is formed by the intersection of a right circular cone and a plane.
Answer:
A. Conic section.Step-by-step explanation:
If you intersect a right circular cone with a plane you can form a conic section: circumference, hyperbole, ellipse and parable; like is show in the image attached.
A point on the ground is 50 feet from my house. The angle of elevation to the top of the house is 48∘. Find the height of the house to the nearest tenth.
Answer:
55.5 feet
Step-by-step explanation:
the scenario is attached in the form of a picture
We have to find h.
We will use the trigonometric ratio of tan to find the height of the house.
[tex]tan\ 48 = \frac{h}{50}\\ 1.1106*50=h\\55.53=h[/tex]
Hence the height of the house is 55.53 feet
Rounding off to nearest 10th
height = 55.5 feet ..
The height of the house is approximately 55.5 feet.
To find the height of the house, let's use trigonometry based on the given information:
Given:
Distance from the point on the ground to the house (adjacent side of the triangle): ( AB = 50 ) feet
Angle of elevation from the ground to the top of the house [tex](\( \theta \))[/tex]: [tex]\( \theta[/tex] = [tex]48^\circ \)[/tex]
We need to find:
Height of the house (opposite side of the triangle): h
We use the tangent function because it relates the opposite side to the adjacent side in a right triangle:
[tex]\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]Substituting the given values:\[ \tan(48^\circ) = \frac{h}{50} \]To find \( h \), multiply both sides by 50:\[ h = 50 \times \tan(48^\circ) \]Now, calculate \( \tan(48^\circ) \):\[ \tan(48^\circ) \approx 1.1106 \][/tex]
Therefore,
[tex]\[ h \approx 50 \times 1.1106 \]\[ h \approx 55.53 \]Rounding to the nearest tenth:\[ h \approx 55.5 \text{ feet} \][/tex]
So, the height of the house is approximately 55.5 feet.
What is the measure of arc AC
Answer:
D. 88 degrees
Answer:
D. 88 degrees
Step-by-step explanation:
it is an inscribed angle
What is m
(3x - 35) (x - 35)
115°
Got it right on the test.
I could use some help! During the day, Lisa’s dog is tied by rope to a tree in the center of her yard. The scale drawing below shows the area that the dog has to run. If the actual length of the rope is 4 5/6 feet, what is the scale used in the drawing?
Step-by-step explanation:
Considering Lisa's yard is allowing the dog to run around a circumscribed circle with a ray of 4 5/6 feet then the maximum of the area that he could cover is the area of that circle A= 3.14×(4 5/6)^2/2
Not being able to see the drawing, I assume that if the area of the yard has a value below the value described above then the dog would run around the yard untill the rope's fully swirled around the tree or untill Lisa comes home
In △ABC,a=13, b=21, and c=27. Find m∠A.
A. 18.4
B. 31.5
C. 28.0
D. 103.0
Answer:
Option C (28.0°)
Step-by-step explanation:
The questions which involve calculating the angles and the sides of a triangle either require the sine rule or the cosine rule. In this question, the three sides are given and one unknown angle has to be calculated. Therefore, cosine rule will be used. The cosine rule is:
a^2 = b^2 + c^2 - 2*b*c*cos(A°).
The question specifies that a=13, b=21, and c=27. Plugging in the values:
13^2 = 21^2 + 27^2 - 2(21)(27)*cos(A°).
Simplifying gives:
-1001 = -1134*cos(A°)
Isolating cos(A°) gives:
cos(A°) = 0.88271604938
Taking cosine inverse on the both sides gives:
A° = arccos(0.88271604938). Therefore, using a calculator, A° = 28.0 (correct to one decimal place).
This means that the Option C is the correct choice!!!
For this case we have that by definition, the cosine theorem states that:
[tex]a ^ 2 = b ^ 2 + c ^ 2-2bc * Cos (A)[/tex]
According to the data we have:
[tex]a = 13\\b = 21\\c = 27[/tex]
Substituting we have:
[tex]13 ^ 2 = 21 ^ 2 + 27 ^ 2-2 (21) (27) * Cos (A)\\169 = 441 + 729-1134 * Cos (A)\\169 = 1170-1134 * Cos (A)\\169-1170 = -1134 * Cos (A)\\-1001 = -1134 * Cos (A)\\Cos (A) = \frac {1001} {1134}\\Cos (A) = 0.8827\\A = arc cos (0.8827)\\A = 28.03[/tex]
Answer:
Option C
The accounting department at Nagata Glass reimbursed Abba Jay for traveling to two sales presentations in New Orleans this month. He drove a total of 610 miles to and from the city. The company will pay him $0.32 per mile. His other travel expenses included $6.50 in tolls, and $260.40 per night for two nights in a hotel. The costs of his meals are listed in the table. What were his total expenses for the two trips?
It's a fill in the blank question.
Which of the following best describes the relationship between (x-3) and the polynomial x^3 + 4x^2 + 2?
A. (x-3) is not a factor
B. (x-3) is a factor
C. It is impossible to tell whether (x-3) is a factor
Answer:
A) (x-3) is not a factor of x^3+4x^2+2
Step-by-step explanation:
(x-3) is a factor of f(x)=x^3+4x^2+2 if f(3)=0. This is by factor theorem.
So let's check it.
f(x)=x^3+4x^2+2
f(3)=3^3+4(3)^2+2
f(3)=27+4(9)+2
f(3)=27+36+2
f(3)=63+2
f(3)=65
Since f(3) doesn't equal 0, then x-3 is not a factor.
Answer:
A. (x-3) is not a factor
Step-by-step explanation:
You can find if (x-3) is a factor of the polynomial by dividing the polynomial by (x-3) by using long division or synthetic division.
Long division:
x^2+x+3
(x-3)/x^3+4x^2+0x+2
-(x^3-3x^2)
x^2+0x
-(x^2-3x)
3x+2
-(3x-9)
-7
Here you can see that (x-3) is not a factor of the polynomial because when you divide x^3 + 4x^2 + 2 by (x-3), there is a remainder of -7
Synthetic Division (A shortcut version of long division just to see if there is a remainder and if the supposed factor is really a factor) :
3 1 4 0 2
- 3 21 63
1 7 21 65
As seen before (x-3) is not a factor of the polynomial because there is a remainder. If 65 were 0, the (x-3) would be a factor of the polynomial.
which of the following statements are true? Please help
Answer:
B and C
Step-by-step explanation:
- The answer in the attached file
plz turn 1452 into word form, will give thanks and brainliest
Answer:
one thousand four hundred fifty two
Step-by-step explanation:
Answer:
One thousand four hundred and fifty-two.
One thousand = 1000
Four hundred = 400
Fifty-two = 52
Which of the diagrams below represents the statement “if it is a tree, then it has leaves”
Answer:
Fig A
Step-by-step explanation:
in fig A, we can see that the subset that represents "trees", lies inside the subset that "has leaves". Hence in figure A, we can say that "All trees have leaves" or "if it is a tree, it has leaves"
in fig B however, we see that "has leaves" is inside of "trees", this means that the area in-between "has leaves" and "tree" represents the subset that there are trees without leaves. This is in contradiction to the statement "if it is a tree, it has leaves", hence this is not the answer.
Answer
A
Step-by-step explanation:
hope this helps :)