Answer:
6748'
Step-by-step explanation:
The long diagonal is the third leg of a triangle with the given side lengths and an angle between them that is the supplement of the given angle. Its length can be found from the Law of Cosines.
a^2 = b^2 +c^2 -2bc·cos(A)
a^2 = 3473^2 +4822^2 -2·3473·4822·cos(180° -72.23°)
a^2 = 45,535,553.83
a ≈ 6748.004
The longer diagonal is about 6758 feet long.
A certain server works four 6-hour shifts a week at a restaurant and has a base salary of $9.75/ℎ. An average server sells $1400 in a single shift. If the server makes an average of 14% tip of a bill, what is the annual gross income of the server?
Answer:
The annual gross income of the server is $52936
Step-by-step explanation:
The server works four 6-hour shift a week.
the server earns $9.75/h
An average seller sells $1400 in a single shift, and makes 14% tip of a bill.
For the 6-hour shift, the server earns
6 x $9.75 = $58.5 a shift
in a week, the total money made for the four shifts in a week will be
4 x $58.5 = $234
The server makes an average of 14% of a bill, and makes about $1400 in a single shift.
In a single shift he makes a tip of
14% of $1400 = 0.14 x $1400 = $196
in a week he makes 4 x $196 = $784
Total money the server makes in a week is
==> $234 + $784 = $1018
There are 52 weeks in a year.
The server's annual gross income will be
52 x $1018 = $52936
What is the domain of the function shown on the graph? A. -10
Answer:
Option (C)
Step-by-step explanation:
Domain of any graph is defined by the x-values or the input values of a function.
Similarly, y-values on the graph of a function define the Range.
In the graph attached, x-values varies from (-∞) to (+∞).
Therefore, Domain of the graphed function will be (-∞, ∞)
Or -∞ < x < ∞
Similarly, y-values of the graph varies from (-∞) to (1)
Therefore, range of the graphed function will be (-∞, 1).
Or -∞ < y < 1
Option (C) will be the answer.
Angle ABC is a straight angle. MAngleDBC = 130° and Ray B E bisects AngleABD. The center of line A C is point B. Two lines extend from point B. One line extends to the left and contains point E. Another line extends up and to the left and contains point D. What is mEBA? °
Answer:
25°
Step-by-step explanation:
Since ∠DBC = 130°, ∠DBC + ∠ABD = 180° (sum of angles on a straight line is 180°). Solving for ∠ABD:
∠DBC + ∠ABD = 180°
130 + ∠ABD = 180°
∠ABD = 180° - 130°
∠ABD = 50°
∠ABD is bisected by line BE, therefore ∠ABD = ∠EBA + ∠DBE (angle addition postulate).
The angle addition postulate states that if w is the interior of xyz then ∠XYZ = ∠XYW + ∠ZYW
Since E is the interior of ∠ABD, then:
∠ABD = ∠EBA + ∠DBE
But ∠EBA = ∠DBE
∠ABD = 2∠EBA
50 = 2∠EBA
∠EBA = 25°
Answer:
The answer is 25 degrees
Find the slope of the line passing through the points D(10, 8) and E(-4, 4).
Answer:
[tex]\frac{2}{7} x[/tex]
Step-by-step explanation:
To find the slope of a line with 2 points we use the following formula.
[tex]\frac{y^2-y^1}{x^2-x^1}[/tex]
So with the following points,
E(-4,4)
D(10,8)
So 8 is y2 and 4 is y1 8-4 = 4
10 - -4 = 14
Slope: 2/7x
Thus,
the slope of the line is 2/7x.
Hope this helps :)
When x is divided by 4, the remainder is 3. When r^2 is divided by
4, what must the remainder be?
Answer:
If x=7 that means that if 7 substitute r which is 7^2 and 7*7=49 and 49/4
=12 1/4
So the remainder is 1
Step-by-step explanation:
There are 20 cars in my building’s parking lot. All of the cars are red or white. 12 of them are red, 15 of them are 4-door, and 4 of them are 2-door and white. How many of the cars are 4-door and red?
Answer:
11 cars
Step-by-step explanation:
There are 20 cars in my building's parking lot, 15 cars are 4-door, then
20 - 15 = 5 cars are 2-door.
5 cars are 2-door, 4 of them are 2-door and white, then
5 - 4 = 1 car is 2-door and red.
12 cars are red, 1 car is 2-door and red, then
12 - 1 = 11 cars are 4-door and red.
plz give me brianlist
Triangle T U V is shown. Side T U has a length of 5 units, side U V has a length of 8 units, and side T V has a length of 11 units. Which statement is true regarding triangle TUV? Angle T is the smallest angle. Angle V is the smallest angle. Angles U and V must be equal. Angles U and T must be equal.
Answer:
b
Step-by-step explanation:
edg 2020
The smallest measure of angle is angle ∠ V due to opposite angle of smallest side which is correct option(B).
What is a Triangle?A triangle is defined as simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric shapes, it is represented by the symbol of Δ and consists of three connected vertices. Triangles can be categorized into a number of different varieties according on their sides and angles.
A triangle has three sides, three vertices, and three interior angles.
The angle sum property of a triangle states that the sum of the three interior angles of a triangle is always 180°
In ΔTUV,
Length of Side TU = 5 units
Length of Side UV = 8 units
Length of Side TV = 11 units
Side TU is opposite of angle ∠ V
Side UV is opposite of angle ∠ T
Side TV is opposite of angle ∠ U
The sides in order from longest to shortest : Side TV > Side UV = Side TU
The longest side is always opposite of the largest angle, and the smallest side is always opposite of the smallest angle.
Hence, the angle in order from longest to shortest : angle ∠ U > angle ∠ T > angle ∠ V
Thus, the smallest measure of angle is angle ∠ V.
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How many real solutions In this problem
Answer:
D
Step-by-step explanation:
Given
y = x² + 1
y = x
Equating gives
x² + 1 = x ( subtract x from both sides )
x² - x + 1 = 0
Consider the discriminant Δ = b² - 4ac
with a = 1, b = - 1 and c = 1
b² - 4ac = (- 1)² - (4 × 1 × 1) = 1 - 4 = - 3
Since b² - 4ac < 0 then there are no real solutions
Question 1
Solve the equation that models the volume of the shipping box, 8(n + 2)(n + 4) = 1,144. If
you get two solutions, are they both reasonable?
Answer:
n = -15 and n = 9. n = -15 is not reasonable because you can't have negative boxes or negative units of measurement.
Step-by-step explanation:
8(n + 2)(n + 4) = 1,144
(n + 2)(n + 4) = 143
n^2 + 2n + 4n + 8 = 143
n^2 + 6n - 135 = 0
(n + 15)(n - 9) = 0
n + 15 = 0
n = -15
n - 9 = 0
n = 9
I got two solutions: n = -15 and n = 9. Only one is reasonable because you cannot have a negative number of boxes or negative weight.
Hope this helps!
Simplify the equation, and set it equal to zero to prepare for factoring.
Multiply the two factors in parentheses using the distributive property:
8(n2 + 2n + 4n + 8) = 1,144
Combine like terms inside the parentheses:
8(n2 + 6n + 8) = 1,144
Multiply the terms inside the parentheses by 8 using the distributive property:
8n2 + 48n + 64 = 1,144
Set the equation equal to zero by subtracting 1,144 from each side:
8n2 + 48n − 1,080 = 0
Factor out the GCF, which is 8:
8n2 + 48n − 1,080 = 0
8(n2 + 6n − 135) = 0
Divide both sides of the equation by 8:
n2 + 6n − 135 = 0
Compare the equation with the standard form ax2 + bx + c = 0, and get a, b, and c:
a = 1, b = 6, c = -135
The leading coefficient of the equation is 1. So, find two numbers that have a sum of 6 and a product of -135:
6 = -9 + 15
-135 = -9 • 15
The two numbers are -9 and 15. Use the two numbers to write the factors of the quadratic expression:
(n − 9)(n + 15) = 0
Use the zero product property, and solve for n:
n − 9 = 0 or n + 15 = 0
n = 9 or n = -15
There are two solutions for n. But since n represents the width of the helmet box, it can’t be negative. Therefore, the only reasonable solution is n = 9
Two cars are traveling north along a highway. The first drives at 40 mph, and the second, which leaves 3 hours later, travels at 60 mph. How long after the second car leaves will it take for the second car to catch the first?
Answer:
Step-by-step explanation:
We will make a table and fill it in according to the information provided. What this question is asking us to find, in the end, is how long did it take the cars to travel the same distance. In other words, how long, t, til car 1's distance = car 2's distance. The table looks like this:
d = r * t
car1
car2
We can fill in the rates right away:
d = r * t
car1 40
car2 60
Now it tells us that car 2 leaves 3 hours after car 1, so logically that means that car 1 has been driving 3 hours longer than car 2:
d = r * t
car1 40 t + 3
car2 60 t
Because distance = rate * time, the distances fill in like this:
d = r * t
car1 40(t + 3) = 40 t+3
car2 60t = 60 t
Going back to the interpretation of the original question, I am looking to solve for t when the distance of car 1 = the distance of car 2. Therefore,
40(t+3) = 60t and
40t + 120 = 60t and
120 = 20t so
t = 6 hours.
Given: r || s, and t is a transversal that cuts both r and s. Prove: <1 = <5, <2 = <6, <3 = <7, and <4 = <8 Write a paragraph proof to prove that the corresponding angles shown are congruent.
Answer:
Lines r and s are parallel as Corresponding Angles given. There are four pairs of corresponding angles: angle 1 and angle 5, angle 2 and angle 6, angle 3 and angle 7, and angle 4 and angle 8. Since r and s are parallel, the slope of r is equal to the slope of s. Since t is a straight line, the slope of t is the same at both intersections, by the definition of a straight line. Thus, the corresponding angles created at both intersections must have the same measure, since the difference of the slopes at each intersection is the same, and the intersections share a common line. So, corresponding angles must have equal measure. Therefore, by definition of congruent angles, corresponding angles are congruent: angle 1 is congruent to angle 5, angle 2 is congruent to angle 6, angle 3 is congruent to angle 7, and angle 4 is congruent to angle 8.
Step-by-step explanation
answer from haven
A box contains 4 white ribbons and 8 pink ribbons. Determine whether the events of picking a white ribbon and then another white ribbon without replacement are independent or dependent. Then identify the indicated probability.
a. independent; 1/11
b. dependent; 1/12
c. dependent; 1/11
d. independent; 1/12
Answer:
dependent, 1/11
Step-by-step explanation:
the probability of picking a white ribbon at first is 1/3
the probability of picking a white ribbon next is 3/11
1/3 * 3/11 = 3/33 = 1/11
it is dependent because picking the first ribbon affects picking the second.
What is the slope of the line through the points (4,2) and (-16,-6)
Answer:
2 / 5.
Step-by-step explanation:
The slope is the rise over the run.
In this case, the rise is 2 - (-6) = 2 + 6 = 8.
The run is 4 - (-16) = 4 + 16 = 20.
So, the slope is 8 / 20 = 4 / 10 = 2 / 5.
Hope this helps!
Answer:
the slope of the line that goes through (4,2) and (-16,-6) is 2/5
m= 2/5
Step-by-step explanation:
in order to find the slope we use the ∆y/∆x which is really the change in y over the change in x.
so all you have to do is find your y's and X's.
your y's are -6 and 2
your X's are -16 and 4
now in order to find the change in y and x you subtract your y's and x'x
the formula for this is:
∆y/∆x = y1-y2/x1-x2= (m aka the slope)
y1 is -6
and y2 is 2
-6 - 2 = -8
now do the X's
X1 is -16
and X2 is 4
-16 - 4 = -20
put that in fraction form and it's -8/-20
simplify that you get 2/5
6
R). Express 2x2 - 8x + 5 in the form a(x + b)² + c where a, b and
c are integers
Answer:
[tex]\large \boxed{\sf \ \ a = 2, \ b = -2, \ c = -3 \ \ }[/tex]
Step-by-step explanation:
Hello,
[tex]2x^2 - 8x + 5=2(x^2-4x)+5\\\\\text{*** We notice that *** }\\\\\text{*** } x^2-4x=(x-2)^2-2^2=(x-2)^2-4\\\\\text{*** So we can write ***}\\\\2x^2 - 8x + 5=2(x^2-4x)+5=2\left( (x-2)^2-4\right)+5\\\\=2\left(x-2\right)^2-8+5=\boxed{2\left(x-2\right)^2-3}[/tex]
So a = 2, b = -2, c = -3
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Nancy needs at least 1000 gigabytes of storage to take pictures and videos on her upcoming vacation. She
checks and finds that she has 105 GB available on her phone. She plans on buying additional memory
cards to get the rest of the storage she needs.
The cheapest memory cards she can find each hold 256 GB and cost $10. She wants spend as little
money as possible and still get the storage she needs.
Let C represent the number of memory cards that Nancy buys. 2)what is the least amount of money Nancy can spend to get the storage she needs?
Answer:
The answer to this question can be defined as follows:
In option 1, She buys 4 memory cards.
In option 2, The cost of memory is $40
Step-by-step explanation:
Given:
Available space is = 105 GB
required space = 1000 GB
256 GB memory cost $10.
Find needed memory:
= 1000 GB - 105 GB
= 895 GB
∴ the available memory is 256 GB.
∵ 256 × 4 = 1024 GB
The total memory she have = 1024 + 105 = 1129 GB
And she needs to buy 4 memory cards.
The cost of the four memory cards is= 4 ×10 = $40.
Using proportions, it is found that the least amount of money Nancy can spend to get the storage she needs is of $40.
------------------------------
This question is solved by proportions, using a rule of three.Nancy needs at least 1000 GB, but she only has 105 GB available. Thus, she needs to buy 1000 - 105 = 895 GB.The cheapest cards she can buy have 256 GB. How many of these cards she has to buy?The rule of three is of:
1 card - 256 GB
x cards - 895 GB
Applying cross multiplication:
[tex]256x = 895[/tex]
[tex]x = \frac{895}{256}[/tex]
[tex]x = 3.5[/tex]
Rounding, she has to buy 4 cards.
Each card costs $10, thus, she has to spend $10 x 4 = $40.A similar problem is given at https://brainly.com/question/17594062
what are three different whole numbers whose sum and product are equal
Three different whole numbers whose sum and product are equal are 1, 2, and 3.
1 + 2 + 3 = 6
1 x 2 x 3 = 6
As demonstrated above, the sum and product of 1, 2, and 3 is the same.
Hope this helps!! :)
Answer:
1 2 and 3
Step-by-step explanation:
The denominator of a rational number is greater than its numerator by 3. If 3 is subtracted from the numerator and 2 is added to its denominator, the new number becomes 1/5 . find the original number
Answer:
5/8
Step-by-step explanation:
Let the numerator = n.
Let the denominator = d.
The fraction is
n/d
"The denominator of a rational number is greater than its numerator by 3."
d = n + 3
The fraction is
n/(n + 3)
"If 3 is subtracted from the numerator and 2 is added to its denominator, the new number becomes 1/5."
(n - 3)/(n + 3 + 2) = 1/5
(n - 3)/(n + 5) = 1/5
Cross multiply.
5(n - 3) = 1(n + 5)
5n - 15 = n + 5
4n = 20
n = 5
d = n + 3 = 5 + 3 = 8
n/d = 5/8
The original number is 5/8.
Which ordered pair is a solution of this equation?
Please and thank you
Answer:
Hey there!
-9x-y=-15
9x+y=15
A solution with integer values would be 9(1)+6=15
Thus, x=1 and y=6
(1, 6)
Hope this helps :)
Answer:
(6,1)
Step-by-step explanation:
NEED HELP ASAP!! FIRST ONE TO GET THE ANSWER RIGHT GETS THE MOST BRAINLIEST
Answer:
125
Step-by-step explanation:
Add all the angles then subtract by 360.
Answer:
Vp-by-step explanation:
please help!!!!! idk how to do this
Answer:
30 seconds.
Step-by-step explanation:
So, we have the equation:
[tex]h(t)=-16t^2+h[/tex]
Where t is the time in seconds and h is the initial height.
A barometer falls from a weather balloon at a height of 14,400 feet. In other words, the initial height is 14,400. Substitute for h:
[tex]h(t)=-16t^2+14400[/tex]
We need to find when the barometer hits the ground. Ground level is 0 feet. Therefore, we can substitute h(t) for 0 and solve for the equation (solve for t) in order to find how long (in seconds) it took for the barometer to fall:
[tex]0=-16t^2+14400\\-14400=-16t^2\\900=t^2\\t=\pm\sqrt{900} \\\text{Time cannot be negative.}\\t=\sqrt{900}\\ t=30 \text{ seconds}[/tex]
Therefore, it took 30 seconds for the barometer to hit the ground when it fell at a height of 14,400 feet.
Edit: Spelling.
PLEASE help me with this question! No nonsense answers and answer with full solutions please!
Answer: b) {-3, 0.5}
Step-by-step explanation:
The new equation is the original equation plus 6. Move the original graph UP 6 units. The solutions are where it crosses the x-axis.
[tex]\text{Original equation:}\quad f(x)=\dfrac{15}{x}-\dfrac{9}{x^2}\\\\\\\text{New equation:}\quad\dfrac{15}{x}+6=\dfrac{9}{x^2}\\\\\\.\qquad \qquad f(x)= \dfrac{15}{x}-\dfrac{9}{x^2}+6[/tex]
+6 means it is a transformation UP 6 units.
Solutions are where it crosses the x-axis.
The curve now crosses the x-axis at x = -3 and x = 0.5.
Please answer this question now
Answer:
7.8
Step-by-step explanation:
To do this problem you need to know Pythagorean Theorem which is also known as [tex]a^{2} +b^{2} =c^{2}[/tex].
In this problem 6 would be a, 5 would be b, and d would be c. So to do this we would do 5 squared (which is 25)+ 6 squared which is 36) and you would get 61 and when you do that you will just take the square root of that which is 7.81 and round it to the nearest tenth which is 7.8 and that would be the final answer
evaluate the following using suitable identities : (102)^2
You answer is 10404 to get this answer multiply the 102 double time
help me answer this question.
The midpoint of the diagonal of a square is 2 units from the vertex of the square. Calculate the area of the square
I will mark u as the brainliest.
Answer:
8 units²Step-by-step explanation:
Let side of the square = a
The , Area of square = a²
Now, Midpoint of Diagonal DB is E
And DE = 2 units
So, DB = 2 DE = 2 × 2 = 4 units
Now, using Pythagoras theorem in ∆ BCD
DB² = DC² + BC²
plug the values
[tex] {4}^{2} = {a}^{2} + {a}^{2} [/tex]
Collect like terms
[tex] {4}^{2} = 2 {a}^{2} [/tex]
Evaluate the power
[tex]16 = 2 {a}^{2} [/tex]
Swipe the side of the equation
[tex]2 {a}^{2} = 16[/tex]
Divide both sides of the equation by 2
[tex] \frac{2 {a}^{2} }{ 2 } = \frac{16}{2} [/tex]
Calculate
[tex] {a}^{2} = 8[/tex]
Therefore, The area of the square is 8 sq.units.
Hope this helps..
Best regards!!
The area of the square is 8 square units.
Let's assume that the side length of the square is "s". Since the midpoint of the diagonal is 2 units from the vertex of the square, the diagonal of the square is 4 units (twice the distance from the vertex to the midpoint).
We can use the Pythagorean theorem to find the side length "s" of the square:
[tex]s^2 + s^2 = 4^2\\2s^2 = 16[/tex]
Divide both sides by 2:
[tex]s^2 = 8[/tex]
Now, to find the area of the square, we use the formula:
[tex]Area = side length^2\\Area = s^2 = 8[/tex]
So, the area of the square is 8 square units.
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Given the infirmation in the diagram, which theorem best justifies why lines j and k must be parallel
Answer:
Alternate Exterior Angles theorem
Answer:
alternate exterior angles
Step-by-step explanation:
alternate exterior angles are when two angles are on the far side of two lines and are not on the same side of the line cutting through the two parallel lines
Hope this is not redundunt or anything because I thought maybe I should just explain it so you would understand it next time :)
In the figure, m∠CED = m∠A. Complete the following proportions: ED/ A F= CE/? = CD/?
Answer:
The completed proportions are;
ED/A_F = CE/CA = CF/CD
Step-by-step explanation:
The given m∠CED = m∠A
∴ Angle ∠CDE = Angle ∠A_FC, (corresponding angles)
Angle ∠ECD = Angle ∠ACF (reflexive property)
Triangle ΔDCE is similar to triangle ΔACF (Angle Angle Angle (AAA) similarity)
In triangle ΔDCE and triangle ΔACF
m∠A is bounded by CA and A_F
m∠CED is bounded by CE and ED
∠DCE is bounded by CE and DE
∠C is bounded by CA and CF
Based on the orientation of the two triangles, we have
ED is the corresponding side to A_F, CD is the corresponding side to CF, CE is the corresponding side to CA
Therefore, we have;
ED/A_F = CE/CA = CF/CD.
If the triangle on the grid below is translated by using the rule (x, y) right-arrow (x + 5, y minus 2), what will be the coordinates of B prime? On a coordinate plane, triangle A B C has points (negative 1, 0), (negative 5, 0), (negative 1, 2). (–2, 0) (0, –2) (5, –7) (5, –2)
Answer:
(0, –2)
Step-by-step explanation:
I am assuming that point 'B' is (-5 , 0).
The translation rule is: [tex](x,y)\rightarrow(x+5,y-2)[/tex].
Apply the rule to point 'B':
[tex]\frac{(-5,0)\rightarrow(-5+5,0-2)}{(x,y)\rightarrow(x+5,y-2)}\rightarrow\boxed{(0,-2)}[/tex]
B' should be (0, -2).
Answer:
Guy above me might be right but Im not sure. Im on the cumulative exam on edge.
Step-by-step explanation:
find the point of intersection between 2x - 6y = 12 and the line x = -2.
slope intercept: y = 1/3x - 2
Answer:
(-2, -8/3)
Step-by-step explanation:
2(-2) - 6y = 12
-4 -6y = 12
-6y = 16
y = -16/6 = -8/3
What degree of rotation about the origin will cause the triangle below to map onto itself?
Answer:
=360
explanation:
When you’re talking about rotation you go counterclockwise and each quadrant is another 90 degrees.
Answer:
360
Step-by-step explanation:
Help is appreicated! (10 points!)
Answer:
5
Step-by-step explanation:
5