Answer:
A:$2478
B:$728
Total:$3206
Step-by-step explanation:
2.95x3000=8850
1.30x2000=2600
8850x0.28=2478
2600x0.28=728
2478+728=3206
Write an equation showing the relationship between the lengths of the three sides of a right triangle.
Answer:
Below
Step-by-step explanation:
First triangle)
This triangle is a right one so we will apply the pythagorian theorem.
● 25 is the hypotenus
● 25^2 = b^2 + 24^2
■■■■■■■■■■■■■■■■■■■■■■■■■■
Seconde triangle)
Again it's a right triangle
x is the hypotenus.
● x^2 = 12^2 +5^2
● 12^2 = x^2-5^2
■■■■■■■■■■■■■■■■■■■■■■■■■■
This is a right triangle
AC is the hypotenus.
● AC^2 = BC^2 + BA^2
Notice that: BC = BE+EC and BA=BD+DA
● AC^2 = (BE+EC)^2 + (BD+DA)^2
Answer: 2) b = 7 3) x = [tex]\sqrt{119}[/tex]
Step-by-step explanation:
Use Pythagorean Theorem: (leg₁)² + (leg₂)² = hypotenuse²
2) b² + 24² = 25²
b² + 576 = 625
b² = 49
[tex]\sqrt{b^2}=\sqrt{49}[/tex]
b = 7
3) 5² + x² = 12²
25 + x² = 144
x² = 119
[tex]\sqrt{x^2}=\sqrt{119}[/tex]
[tex]x=\sqrt{119}[/tex]
Candice spent 5 1/4 hours doing her homework. Her brother, Ronald, spent 1/2 that number of hours doing his homework. How many hours did Ronald spend on his homework?
Answer:
Step-by-step explanation:
½ of 5¼
½×(21/4)
=21/8
=2⅝ hours
Answer:
2 5/8
Step-by-step explanation:
you would divide 5 1/4 by 2 :
5 divided by 2 =2 1/2
1/4 divided by 2=1/8
then make the numbers have the same denomanator
1/2, 2/4, 4/8
1/8,
then you add
2 4/8+1/8=2 5/8
1. What is the difference between an exponential growth and exponential decay? 2. What is an example equation for expoential growth and an example equation for exponential decay?
Answer: see below
Step-by-step explanation:
The standard form of an exponential equation is: y = a(b)ˣ where
a is the initial valueb is the rateGrowth:
Exponential growth is where the final value (y) is greater than the initial value (a).
An example would be the spreading of a rumor:
You tell 1 person (a = 1) who then tells 2 people each minute (b = 2). How many people will they have spread the rumor to after 5 minutes (x = 5)?
y = 1(2)⁵
= 32
Decay:
Exponential decay is where the final value (y) is less than the initial value (a).
An example would be the decrease of bacteria in a person:
A person has 100 bacteria (a = 1) who takes a pill that is supposed to cut in half the number of bacteria each hour (b = 1/2). How many bacteria will the person have after 2 hours (x = 2)?
[tex]y=100\bigg(\dfrac{1}{2}\bigg)^2\\\\\\.\quad =100\bigg(\dfrac{1}{4}\bigg)\\\\\\.\quad = 25[/tex]
The graph of the function f(x) = (x − 3)(x + 1) is shown.
On a coordinate plane, a parabola opens up. It goes through (negative 1, 0), has a vertex at (1, negative 4), and goes through (3, 0).
Which describes all of the values for which the graph is positive and decreasing?
all real values of x where x < −1
all real values of x where x < 1
all real values of x where 1 < x < 3
all real values of x where x > 3
Answer:
x < -1
Step-by-step explanation:
Since the parabola opens upward, it is positive and decreasing where the left branch is above the x-axis: all points to the left of x=-1.
all real values of x where x < -1
find the value of X?
Answer:
x = 58
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
90 = 32+x
Subtract 32 from each side
90-32 = x
58 =x
The algebraic expression for the product of five and the cube of a number decreased by 40
Answer:
5a³ - 40
Step-by-step:
The algebraic expression is:
5a³ - 40
What is the area of the house (including the drawing room, TV room, balcony, hallway, kitchen, and bedroom)?
Answer:
1256 i think
Step-by-step explanation:
Which of the following is the graph of the quadratic parent function
This is the graph of y = x^2. It is a parabola that opens upward and has its vertex at the origin. Applying various transformations to the parent function will allow us to produce any parabolic graph we want. In effect, the parent function is like the most basic building block.
Point E lies within rectangle ABCD. If AE = 6, BE = 7, and CE = 8, what is the length of DE?
Answer:
[tex]\sqrt{51}[/tex] units.
Step-by-step explanation:
Point E is inside a rectangle ABCD.
Please refer to the attached image for the given statement and dimensions.
Given that:
Sides AE = 6 units
BE = 7 units and
CE = 8 units
To find:
DE = ?
Solution:
For a point E inside the rectangle the following property hold true:
[tex]AE^2+CE^2=BE^2+DE^2[/tex]
Putting the given values to find the value of DE:
[tex]6^2+8^2=7^2+DE^2\\\Rightarrow 26+64=49+DE^2\\\Rightarrow DE^2=100-49\\\Rightarrow DE^2=51\\\Rightarrow \bold{DE = \sqrt{51}\ units}[/tex]
Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 4x2 − 3x + 2, [0, 2]
Answer:
Yes , it satisfies the hypothesis and we can conclude that c = 1 is an element of [0,2]
c = 1 ∈ [0,2]
Step-by-step explanation:
Given that:
[tex]f(x) = 4x^2 -3x + 2, [0, 2][/tex]
which is read as the function of x = 4x² - 3x + 2 along the interval [0,2]
Differentiating the function with respect to x is;
f(x) = 8x - 3
Using the Mean value theorem to see if the function satisfies it, we have:
[tex]f'c = \dfrac{f(b)-f(a)}{b-a}[/tex]
[tex]8c -3 = \dfrac{f(2)-f(0)}{2-0}[/tex]
since the polynomial function is differentiated in [0,2]
[tex]8c -3 = \dfrac{(4(2)^2-3(2)+2)-(4(0)^2-3(0)+2)}{2-0}[/tex]
[tex]8c -3 = \dfrac{(4(4)-3(2)+2)-(4(0)-3(0)+2)}{2-0}[/tex]
[tex]8c -3 = \dfrac{(16-6+2)-(0-0+2)}{2-0}[/tex]
[tex]8c -3 = \dfrac{(12)-(2)}{2}[/tex]
[tex]8c -3 = \dfrac{10}{2}[/tex]
8c -3 = 5
8c = 5+3
8c = 8
c = 8/8
c = 1
Therefore, we can conclude that c = 1 is an element of [0,2]
c = 1 ∈ [0,2]
Lisa built a rectangular flower garden that is 4 meters wide and has a perimeter of 26 meters.
What is the length of Lisa's flower garden?
Answer:
9 m
Step-by-step explanation:
Given that
Width of rectangular flower garden, w = 4 m
Perimeter of rectangular flower garden, p = 26 m
To find:
Length of Lisa's flower garden = ?
Solution:
First of all, let us understand perimeter, length and width of a rectangle.
Let ABCD be a rectangle. Please refer to the attached image.
Opposite sides of a rectangle are equal to each other.
AB = CD = Length
Let the length be [tex]l[/tex] m.
BC = DA = Width = 4 m
Perimeter of a closed image is equal to the sum of all the sides of the image.
So, perimeter of ABCD:
[tex]p = AB + BC + CD + DA \\\Rightarrow \bold{ p = 2 \times (Length +Width)}[/tex]
[tex]26 = 2 \times (l +4)\\\Rightarrow 2l =26-8\\\Rightarrow \bold{l = 9 m}[/tex]
I NEED HELP WITH THESE 4 ASAP
Answer:
I'm confused by this. What do they mean by prove?
Step-by-step explanation:
PLEASE ANSWER ASAP!!!
Answer options given in picture
Michael can skateboard 100 feet in 5.4 seconds. Which choice below shows how fast Micheal is going miles per 1 hour? Remember that since you are using multiplication to make conversions, you need to set up the units diagonal from each other in order to cancel.
any unrelated answer will be reported
Answer:
A
Step-by-step explanation:
Residents of four cities are able to vote in an upcoming regional election. A newspaper recently conducted a survey to gauge support for each of the two candidates. The results of the poll are shown in the two-way frequency table below.
Answer:
3 only
Step-by-step explanation:
Consider the statement, "The two cities with the highest number of respondents, both show more support for candidate A." In the total column, the two highest number of respondents are 471 and 463 which represent Carsonville and Appleton. For Carsonville, the number of respondents who prefer candidate A is 205, which is less than the number of respondents who prefer candidate B, 266. Therefore, this statement is not true.
Consider the statement, "The number of people who support candidate B in Carsonville is twice the number of people who support candidate B in New Thomas." In the table, the number of people who support candidate B in Carsonville is observed to be 266 and the number of people who support candidate B in New Thomas is 138. Since 266 is not equal to twice 138, this statement is not true.
Consider the statement, "More residents of Center City responded to the poll than the number who responded from New Thomas." In the total column, it can be observed that 350 people responded to the poll in Center City and 318 people responded to the poll in New Thomas. Since, 350 is greater than 318, this statement is true.
Consider the statement, "Overall, more residents support candidate A than candidate B." The bottom row of the table represents the total number of responses for each candidate. The number of people supporting candidate A is 797, which is less than the number of people supporting candidate B, 805. So, this statement is not true.
Therefore, the true statement is III only.
More residents of the center city responded to the pole than the number who responded from New Thomas, which is the only correct option. Option B. is correct.
Data given in the table shows the data of elections between two candidates among the different cities.
What is Statistic?
Statistics is the study of mathematics that deals with relations between comprehensive data.
I.The two cities with the highest number of respondents both show more support for candidate A. This statement is false because carsonville is the second highest support for A but it does not show more support for candidate A.
II.The number of people who support candidate B in Carsonville is twice the number of people who support candidate B in New Thomas. It is false
III. More residents of Center City responded to the pole than the number who responded from New Thomas. It is true.
IV. Overall, more residents support candidate A than candidate B. it is also false.
Thus, more residents of the center city responded to the pole than the number who responded from New Thomas, which is the only correct option. Option B. is correct.
Learn more about Statistics here:
https://brainly.com/question/23091366
#SPJ5
Please help me with this question
Answer:
0 ≤ x ≤ 10
Step-by-step explanation:
The domain of f(x) is the set of values of x for which the function is defined. Here, the square root function is only defined for non-negative arguments, so we require ...
-x^2 +10x ≥ 0
x(10 -x) ≥ 0
The two factors in this product will both be positive only for values ...
0 ≤ x ≤ 10 . . . . the domain of f(x)
Find the equation of a parabola that has a vertex (3,5) and passes through the point (1,13).
Oy= -27 - 3)' +5
Oy=2(x + 3) - 5
Oy=2(0 - 3)' + 5
Oy= -3(2 – 3) + 5
PLEASE HELP ME!!
Answer:
y = 2(x - 3)² + 5
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (3, 5), thus
y = a(x - 3)² + 5
To find a substitute (1, 13) into the equation
13 = a(1 - 3)² + 5 ( subtract 5 from both sides )
8 = 4a ( divide both sides by 4 )
a = 2, then
y = 2(x - 3)² + 5 ← equation of parabola in vertex form
A triangle has vertices at (-4,-6),(3,3),(7,2). Rounded to two decimal places, which of the following is closest aporoximation of the perimeter of the triangle
Answer:
Perimeter= 29.12 unit
Step-by-step explanation:
Perimeter of the triangle is the length of the three sides if the triangle summef up together
Let's calculate the length of each side.
For (-4,-6),(3,3)
Length= √((3+4)²+(3+6)²)
Length= √((7)²+(9)²)
Length= √(49+81)
Length= √130
Length= 11.40
For (-4,-6),(7,2)
Length= √((7+4)²+(2+6)²)
Length= √((11)²+(8)²)
Length= √(121+64)
Length= √185
Length= 13.60
For (3,3),(7,2)
Length=√( (7-3)²+(2-3)²)
Length= √((4)²+(-1)²)
Length= √(16+1)
Length= √17
Length= 4.12
Perimeter= 4.12+13.60+11.40
Perimeter= 29.12 unit
how many meters are in 250 centimeters
Answer:
2.5 meters
Step-by-step explanation:
Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?
(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5
Answer:
(A) 37.5 miles
Step-by-step explanation:
The trains x and y are travelling on tracks starting simultaneously from a from opposite ends of 100 miles roads.
Translate these information into a simple represention to visualize the problem. (Picture below)
■■■■■■■■■■■■■■■■■■■■■■■■■■
First let's calculate the velocity of both trains.
The velocity formula is:
● V = d/t
d is the distance travelled and t is the tile needed to do it.
● V(x) = 100/5 = 20 miles per hour
● V(y) = 100/3 = 33.33.. wich is approximatively 33 after rounding to the nearest unit.
■■■■■■■■■■■■■■■■■■■■■■■■■■
After calculateingboth velocities, Let's find when the trains meet.
First understand what does it mean matematically when both trains meet.
Go back to the representation and notice what happens when the trains meet.
Let t be that moment.
When x and y reches the meeting point at t, the sum of the distances they have travelled is equal to the total distance wich is 100 miles .
We khow that V = d/t so d = V×t
Let's find the expression of the distances both trains travelled when they have met each other.
● d = V(x) × t
● d' = V(y) × t
■■■■■■■■■■■■■■■■■■■■■■■■■■
So the equation will be:
● V(x) × t + V(y) × t = 100
Factor using t
● t (V(x) + V(y) ) = 100
Replace V(x) and V(y) by their values
● t (20+33) = 100
● 53 t = 100
Divide both sides by 53
● 53t /53 = 100/53
● t = 1.88
■■■■■■■■■■■■■■■■■■■■■■■■■
Replace t in the expression of the distance that train x has travelled when meeting y.
● d = V(x) × t
● d = 20 × 1.88
● d = 37.6 wich is approximatively 37.5 miles
Given the graph, find an equation for the parabola.
Answer:
[tex]\Large \boxed{\sf \bf \ \ y=\dfrac{1}{16}(a-3)^2-2 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
When the parabola equation is like
[tex]y=a(x-h)^2+k[/tex]
The vertex is the point (h,k) and the focus is the point (h, k+1/(4a))
As the vertex is (3,-2) we can say that h = 3 and k = -2.
We need to find a.
The focus is (3,2) so we can say.
[tex]2=-2+\dfrac{1}{4a}\\\\\text{*** We add 2. ***}\\\\\dfrac{1}{4a}=2+2=4\\\\\text{*** We multiply by 4a. ***}\\\\16a=1\\\\\text{*** We divide by 16. ***}\\\\a=\dfrac{1}{16}[/tex]
So an equation for the parabola is.
[tex]\large \boxed{\sf y=\dfrac{1}{16}(a-3)^2-2 }[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Best Buy is currently selling the latest model of the iPad
Pro for $549.99. Since you are an employee there, you
receive a 5% discount. How much will the iPad Pro cost
you if you use your employee discount (before taxes).
Answer:
$522.49
Step-by-step explanation: 549.99*.05=27.50 (discount)
549.99-27.50=$522.49
Answer:
$522.49
Step-by-step explanation:
First, find the discount amount. You can do this by multiplying the original cost by the discount amount. A little trick for remembering to multiply instead of divide is to think "five percent of the original amount"
5% = 0.05
549.99 ⋅ 0.05 = 27.4995
That means the discount amount is $27.50
Subtract the discount amount from the original price
$549.99 - $27.50 = $522.49
A charity organization is holding a food drive with a goal to collect at least 1,000 cans of
food by the end of the month. It currently has 565 cans from donations and is having an
event where 87 guests will attend and bring cans. Which solution set represents the
number of cans each guest must bring to meet the goal?
+
OA
++
0
1
2
3
4
5
6
7
8
9
10
---
+
OB. 4
+
0
1
2
3
4
5
6
7
8
9
10
OC.
+
1
2
3
5
6
7
8
9
10
OD. +
+
++
-
6
+
7.
+
0
1
2
3
4
5
8
9
10
Answer:
Each guest must bring 5 cans.
Step-by-step explanation:
1000-565=435
435/87=5
Evaluate the expresión 6c-d when c=2 and d=10 I need help?
Answer:
the answer is 18
Step-by-step explanation:
8 is the answer
Quadrilateral RSTV is dilated with respect to the origin by a scale factor of 1.5 to produce quadrilateral R'S'T'V' . Vertex R is located at (6, -9). Which ordered pair represents R' after the dilation?
Answer:
(9, -13.5)
Step-by-step explanation:
It's given in the question that a quadrilateral RSTV is dilated with a scale factor of 1.5 with respect to the origin to form R'S'T'V'.
Rule for dilation is,
(x, y) → (kx, ky)
where 'k' is the scale factor.
If vertex R of the quadrilateral is (6, -9),
By the given rule of dilation,
R(6, 9) → R'[(1.5 × 6), -(1.5 × 9)]
→ R'(9, -13.5)
Therefore, Option given in bottom right (9, -13.5) will be the answer.
A project has an initial cost of $40,000, expected net cash inflows of $10,000 per year for 8 years, and a cost of capital of 14%. What is the project's NPV? (Hint: Begin by constructing a time line.) Do not round intermediate calculations. Round your answer to the nearest cent.
Answer:
50k
Step-by-step explanation:
Cases Prudence has a special (cubic) die. The values on its face are the integers from 1 to 6, but they are not arranged ae in a normal die. When Prudence first tosses the die, the sum of the values on the four side faces is 15. In her second toss, the sum of these values is 12. Find what value appears in the face opposite 6 on Prudence’s special die. (Hint: what are possible values for the top and bottom face when the sum of the side faces is 12).
Answer: 3
Step-by-step explanation:
first, we know that:
1 + 2 + 3 + 4 +5 +6 = 21
Now, which two numbers we should take out in order to have 15?
we can remove the 2 and the 4, or the 1 and the 5.
so here we have two possibilities, 2 and 4 are opposite, or 1 and 5 are opposite (they are located in opposite faces of the die)
in the other arrange, we have that removing two numbers we should get 12.
in order to reach 12, we should remove two numbers that add 9 together.
those can be 4 and 5, or 6 and 3.
Now, notice that in the first restriction we have that:
Or 2 and 4 are opposite,
or 1 and 5 are opposite.
So 4 and 5 can never be opposite, so we should have that 6 and 3 are opposite.
Then we can affirm that the value that appears in the face opposite to the 6, is the 3.
A line runs tangent to a circle at the point (4, 2). The line runs through the origin. Find the slope of the tangent line.
Answer:
Slope of the tangent line (m) = 1 / 2
Step-by-step explanation:
Given:
Point A = (4,2)
Origin point = (0,0)
Find:
Slope of the tangent line (m)
Computation:
Slope of the tangent line (m) = (y2-y1) / (x2-x1)
Slope of the tangent line (m) = (2-0) / (4-0)
Slope of the tangent line (m) = 2 / 4
Slope of the tangent line (m) = 1 / 2
Billy has x marbles. Write an expression for the number of marbles the following have… a) Charlie has 5 more than Billy b) Danny has 8 fewer than Billy c) Eric has three times as many as Billy
Answer:
Charlie: 5 + xDanny: x - 8Eric: x × 3Calculate, correct to one decimal plice
the acute angle between the lines
3x - 4y + 5 = 0 and 2x + 3y -1 = 0
A. 70.69
B. 50.2
C. 39.8
D. 19.4
Answer:
A. 70.69 is the correct answer.
Step-by-step explanation:
Given:
Two lines:
[tex]3x - 4y + 5 = 0 \\2x + 3y -1 = 0[/tex]
To find:
Angle between the two lines = ?
Solution:
Acute Angle between two lines can be found by using the below formula:
[tex]tan \theta = |\dfrac{(m_1 - m_2)}{ (1 + m_1m_2)}|[/tex]
Where [tex]\theta[/tex] is the acute angle between two lines.
[tex]m_1, m_2[/tex] are the slopes of two lines.
Slope of a line represented by [tex]ax+by+c=0[/tex] is given as:
[tex]m = -\dfrac{a}{b }[/tex]
So,
[tex]m_1 = -\dfrac{3}{- 4} = \dfrac{3}{4}[/tex]
[tex]m_2 = -\dfrac{2}{ 3}[/tex]
Putting the values in the formula:
[tex]tan \theta = |\dfrac{(\dfrac{3}{4}- (-\dfrac{2}{3}))}{ (1 + \dfrac{3}{4}\times (-\dfrac{2}{3 }))}|\\\Rightarrow tan \theta = |\dfrac{\dfrac{3}{4}+\dfrac{2}{3}}{ (1 -\dfrac{1}{2})}|\\\Rightarrow tan \theta = |\dfrac{\dfrac{17}{12}}{ \dfrac{1}{2}}|\\\Rightarrow tan \theta = \dfrac{17}{6}\\\Rightarrow \theta = tan^{-1}(\frac{17}{6})\\\Rightarrow \theta = \bold{70.69^\circ}[/tex]
So, correct answer is A. 70.69
Kent Co. manufactures a product that sells for $60.00. Fixed costs are $285,000 and variable costs are $35.00 per unit. Kent can buy a new production machine that will increase fixed costs by $15,900 per year, but will decrease variable costs by $4.50 per unit. What effect would the purchase of the new machine have on Kent's break-even point in units?
0riginal break even point:
285000/ 60/35 = $166,250
New break even point = new fixed costs / ( selling price - variable cost/ selling price)
New break even point = 285,000 + 15,900. / ( 60-( 35-4.50)/60
300,900 / 60-30.50/60 = $612,000
The new break even point increases.