Answer:99904.
Step-by-step explanation:
Find the LCM of
5
10 = 2x5
15 = 3x5
20 = 2x2x5
25 = 5x5
LCM = 2x2x3x5x5 = 300
Take the smallest 5-digit number: 10000 and divide it by 300 to get 33.33. Round it off to 34 and multiply it by 300 to get 10200. Finally add 4 to 10200 to get 10204 which is the smallest final 5-digit number.
Check: 10204/5 = 2040 as quotient and a remainder of 4. Correct.
10204/10 = 1020 as quotient and a remainder of 4. Correct.
10204/15 = 680 as quotient and a remainder of 4. Correct.
10204/20 = 510 as quotient and a remainder of 4. Correct.
10204/25 = 408 as quotient and a remainder of 4. Correct.
Answer: 10204.
To get the greatest 5-digit number take 99999 and divide it by 300 to get 333.33. Round it off to 333 and multiply it by 300 to get 99900. Finally add 4 to 99900 to get 99904 which is the final greatest 5-digit number.
Check: 99904/5 = 19980 as quotient and a remainder of 4. Correct.
99904/10 = 9990 as quotient and a remainder of 4. Correct.
99904/15 = 6660 as quotient and a remainder of 4. Correct.
99904/20 = 4995 as quotient and a remainder of 4. Correct.
99904/25 = 3996 as quotient and a remainder of 4. Correct.
Answer: 99904.
Triangle ABC is an equilateral triangle with vertices at A(-2,2), B(1,5), and C(-3,6) (Round your answers to the nearest hundredth, 2 decimal places) . a) (2 pts) Determine the length of a side of the triangle. b) (2 pts) Calculate the perimeter of the triangle. c) (2 pts) Now increase the triangle by a scale factor of 4. How long is each side now? d) (2 pts) What is the perimeter of the new triangle? e) (2 pts) What is the area of the original triangle?
Answer:
The answer is below
Step-by-step explanation:
The distance between two points A(x₁, y₁) and B(x₂, y₂) on the coordinate is:
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\[/tex]
An equilateral triangle is a triangle with three equal sides (all sides are equal).
a) Given vertices at A(-2,2), B(1,5), and C(-3,6):
[tex]AC=\sqrt{(-3-(-2))^2+(6-2)^2}=\sqrt{1+16}=\sqrt{17}=4.12\ unit\\\\AB=BC=AC=4.12\ unit[/tex]
b) Perimeter = AB + BC + AC = 3 * AC = 3 * 4.12 = 12.36 unit
c) If the scale factor is increased by 4, all the sides would also increase by 4. Hence the new length would be:
A'B' = B'C' = A'C' = 4 * AC = 4 * 4.12 = 16.48 unit
d) Perimeter = A'B' + B'C' + A'C' = 3 * A'C' = 3 * 16.48 = 49.44 unit
e) Area = [tex]\frac{\sqrt{3} }{4}*AC^2=\frac{\sqrt{3} }{4} *4.12^2=7.35\ unit^2[/tex]
can someone please help me in this question
Answer:
a. 26 cm²
b. 55 cm²
c. 78 cm²
d. 89.27 cm²
Step-by-step explanation:
a. The shape can be decomposed into two rectangles
Area of the larger rectangle = L*W
L = 7 cm
W = 2 cm
Area of the larger rectangle = 7*2 = 14 cm²
Area of the smaller rectangle = L*W
L = 4 cm
W = 5 - 2 = 3 cm
Area of the larger rectangle = 4*3 = 12 cm²
Area of the compound shape = 14 + 12 = 26 cm²
b. The shape can be decomposed into a rectangle and a triangle.
Area of the compound shape = area of rectangle + area of triangle
= L*W + ½*b*h
L = 8 cm
W = 5 cm
b = 5 cm
h = 14 - 8 = 6 cm
Plug in the values
Area = 8*5 + ½*5*6
Area = 40 + 15
= 55 cm²
c. The shape can be decomposed into a rectangle and a trapezoid
Area of the compound shape = area of the rectangle + area of the trapezoid
= L*W + ½(a + b)h
L = 12 cm
W = 3 cm
a = 12 cm
b = 9 cm
h = 4 cm
Plug in the values
Area = 12*3 + ½(12 + 9)4
Area = 36 + 42
Area = 78 cm²
d. The shape can be decomposed into a rectangle and a semicircle
Area of the compound shape = area of the rectangle + area of the semicircle
= L*W + ½(πr²)
L = 10 cm
W = 5 cm
r = ½(10) = 5 cm
Plug in the values
Area = 10*5 + ½(π*5²)
Area = 50 + 39.27
Area = 89.27 cm²
Summation properties and rules hurry please
Answer:
It is c
Step-by-step explanation:
HELP!!! I'm struggling in this class could you please help a person out?
Answer:
Options (2) and (3)
Step-by-step explanation:
Rigid transformation like translation, rotation or reflection form the image with no change in the area or shape.
By applying dilation, area of the image shape gets dilated by the scale factor 'k'.
If k > 1, area of the image will be greater than the original shape.
If 0 < k < 1, are of the image will be smaller than the original.
Option (1),
There is a dilation by a scale factor of [tex]\frac{2}{3}[/tex] and [tex]0<\frac{2}{3}<1[/tex],
Therefore, image will be smaller than the original.
Option (2)
There are two dilations.
First dilation is by a scale factor of 2 and the second is by a scale factor of [tex]\frac{2}{3}[/tex].
By first dilation area of the image will get doubled.
Followed by the dilation by a scale factor of [tex]\frac{2}{3}[/tex], area of the image will be dilated by the scale factor = [tex]2\times \frac{2}{3}[/tex]
= [tex]\frac{4}{3}[/tex]
Since, [tex]\frac{4}{3}>1[/tex], image will be greater than the original.
Option (3)
In this option polygon is dilated by a scale factor [tex]\frac{3}{2}[/tex].
Since, [tex]\frac{3}{2}>1[/tex]
Image will have the greater area than the original.
Option (4)
In this option polygon is dilated by a scale factor [tex]\frac{1}{2}[/tex].
Therefore, area of the image will be less than the area of the original.
Options (2) and (3) will be the correct options.
Can somebody help plz help me with this?
Answer:
N-8
Step-by-step explanation:
PLEASE HELP MEE!! 50 POINTS
URGENT
The function y= x^2-10x+31 has a _____ (minimum, maximum) value of __ (5, 10, 31, 6)
Answer:
minimum value of 6
Step-by-step explanation:
Given
y = x² - 10x + 31
with a = 1, b = - 10
Since a > 0 then the function has a minimum value
The minimum value is the y- coordinate of the vertex.
The x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex] = - [tex]\frac{-10}{2}[/tex] = 5
Substitute x = 5 into the function for y- coordinate of vertex
y = 5² - 10(5) + 31 = 25 - 50 + 31 = 6
The function has a minimum value of 6
look at the image for the question
Answer:
Answer is y = 6
Step-by-step explanation:
Solve for y.
Answer:
Y=6 I think but I’m not positive.
sorry if I’m wrong.
haha
get it? POSITIVE?
PLEASE I NEED HELP!!!!
Q. Determine if the rates are equilvalent. Explain your reasoning. 25 hours in 5 days; 8 hours in 2 days. . .
[tex] \dashrightarrow [/tex] No!, as, we have 25 hours in 5 dyas is the equals to 5. While, 8 hours in 2 days is equals to 4.
Here, is a difference of 1 in 5 and 4.
What is the probability of living another year for a woman who is 73 years old ?
a) 0.951716
b) 0.968048
c) 0.980413
d) 0.991871
Answer:
0.980413
Step-by-step explanation:
The table for the deaths and death rate per 100,000 population is attached below ;
73 years fall in the 65 - 74 years category ; with 1958.7 deaths (Female)
Hence, the probability of living another year is :
Number of deaths per 100,000 population ;
P(death) = 1958.7 / 100,000 = 0.019587
Probability of living another year = 1 - P(death)
1 - 0.019587 = 0.980413
Answer:
C. 0.980413
FHKEDIbEDSAJFWBHES
explain everything you know about y=x^2-5x-6
y = x^2 -5x-6 is a quadratic equation.
On a graph, rather than a straight line, this type of equation forms what is known as a parabola, which means it goes one direction and then makes almost like a U-turn.
The point in which the parabola (as mentioned before) changes direction is called the vertex.
Specifically, y = x^2 -5x-6 has exactly 2 solutions. This means that there are 2 different possible answers to this equation.
The solutions, or roots, to this equation are x= 6 and x= -1.
If you look at the graph for this equation, the parabola opens upwards like a U, and the vertex is ( 5/2, -49/4).
Question 27(Multiple Choice Worth 1 points)
(07.03 LC)
How many solutions does the equation 4y - 4y - 12 = 14-2 have?
One
None
Two
Infinite
Answer:
none
Step-by-step explanation:
any value on y cancel 4y and then we will have -12=12 which is not true.
Carlos keeps his cards in an album. So far he has lots of full pages plus another 48 cards ready to go in. Altogether, he has more than 500 cards. If each page holds 20 cards, write an inequality that represents how many pages of cards Carlos might have. Solve the inequality. Guys how do i do this, this is hard, pls pls help.
Answer:
x ≥ 22.6 pages
Step-by-step explanation:
Each page = 20 cards
Cards ready to go in = 48
Let x = number of pages of cards Carlos might have
The inequality:
20x + 48 ≥ 500
20x ≥ 500 - 48
20x ≥ 452
x ≥ 452 / 20
x ≥ 22.6 pages
I really, REALLY need help. I will give brainliest to whoever figures it out.
Answer:
79.5 + 5.5x = Y
Step-by-step explanation:
Sumo wrestler gained 5.5 kg per month
After 11 month, he weighed 140 kg.
Let x be his current weight.
Then x + 11(5.5) = 140
x = 140 - 60.5
x = 79.5
If Y is the weight of the wrestler after t months, then the linear equation would be:
79.5 + 5.5t = Y
what is the measure of each exterior angle of a regular dodecagon?
Answer:
30°
Hope this answer is right!
Step-by-step explanation:
to go around the shape, you make a complete circle: 360°. So, divide 360° by the dodecagon's twelve exterior angles. Each exterior angle is 30°.
In 2014, a town's population was 795 people. By 2020, the population had grown to 1262 people. a. Create an exponential equation for the town's population "n" years from 2014. Round your multiplier to the nearest hundredth (2 decimal places).
Answer: [tex]P=795(1.84)^n[/tex]
Step-by-step explanation:
Given
Initial population was [tex]795[/tex] people
By 2020, it becomes [tex]1262[/tex] people
Suppose the population follows the trend [tex]P=P_oa^{n}[/tex]
where, [tex]n[/tex] is the number of years after 2014
For year 2020 it is 6. Insert the values
[tex]\Rightarrow 1262=795a^{6}\\\\\Rightarrow 1.587=a^{6}\\\\\text{Taking log both sides}\\\\\Rightarrow \log (1.587)=6\log (a)\\\Rightarrow \log (a)=0.2645\\\\\Rightarrow a=10^{0.2645}\\\Rightarrow a=1.84[/tex]
Thus, the exponential population trend is [tex]P=795(1.84)^n[/tex]
Simplify (3x2 + 2x - 3) (x + 5)
Answer:
3(x)^3 + 2(x)^2 + 22x - 15
Step-by-step explanation:
(3(x)^2 + 2x - 3) (x + 5)
=>(3(x)^2 + 2x - 3) (x) + (3(x)^2 + 2x - 3) (5)
=>3(x)^3 + 2(x)^2 - 3x + 15x + 10x - 15
=>3(x)^3 + 2(x)^2 + 22x - 15
A. write the ratio of girls to boys in the class with 12 girls and 15 boys. reduce to the lowest terms.
B. use the information from part A to estimate the number of girls in the school if there are a total of 1350 students in the whole school and in part A is representative of all classes in the school
WILL GIVE BRAINLIEST
Answer:
A. 4:5
B. 600 girls
Step-by-step explanation:
A. g : b = 12 : 15 = 4 : 5
B. the numbers of girls = 4/(4+5) × 1350
= 4/9 × 1350 = 600
Help me now now now now now
Answer:
-2 = -6
Step-by-step explanation:
first, you type -2 in the left box and -6 in the middle box
use counters to add 2+ -1.
Answer:
the answer is 1
Step-by-step explanation:
2+(-1)
2-1
1
+ and - always result in - so +(-1) is -1 and 2-1 is 1.
Answer:
1
Step-by-step explanation:
Negative 1 is used as a minus sign. I canceled the plus and now the equation is 2-1
Write an equation that represent the value of an 8700 investment that has 9.1% interest rate compounded yearly y=a(b)^x
Answer:
future value = $8700(1.091)^x
Step-by-step explanation:
The formula for calculating future value:
FV = P (1 + r) n
FV = Future value
P = Present value = 8700
R = interest rate = 9.1%
N = number of years = x
future value = $8700(1.091)^x
1. Given that (27 ^ (n + 3))/(81 ^ (p - 1)) = 3 , express p in terms of h.
9514 1404 393
Answer:
p = 3/4n +3
Step-by-step explanation:
Expressing the given equation in terms of powers of 3, we have ...
(27^(n+3))/(81^(p-1)) = 3
(3^3)^(n+3)/(3^4)^(p-1) = 3^1 . . . . as powers of 3
3(n +3) -4(p -1) = 1 . . . . . . . . . . . . log base 3 (or, equate exponents)
3n +9 -4p +4 = 1 . . . . . . . . . . . . . eliminate parentheses
3n +12 = 4p . . . . . . . . . . . . . . . . add 4p -1
p = 3/4n +3 . . . . . . . . . . divide by 4
how do i do this, please explain....
Answer:
this is from a angle I think you want to write perimeter and area of this ×+1= and you want see that
What is the height of the tower? Round to the nearest tenth.
How tall is the tower?
Step-by-step explanation:
call the height of the tower x
we have tan30°=x:200 so we can find x
The function a(b) relates the area of a trapezoid with a given height of 14 and one base length of 5 with the length of its other base. It takes as input the other base value, and returns as output the area of the trapezoid a(b) = 14 * (b + 5)/2 Which equation below represents the inverse function b(a) , which takes the trapezoid's area as input and returns as output the length of the other base? N(c) = (c + 15)/20; n(c) = (c + 20)/15; n(c) = (c - 20)/15; n(G) = (Q - 15)/20
Answer:
[tex]b(a) = \frac{a}{7} -5[/tex]
Step-by-step explanation:
Given
[tex]a(b) = 14 * \frac{b + 5}{2}[/tex]
Required
The inverse function
We have:
[tex]a(b) = 14 * \frac{b + 5}{2}[/tex]
[tex]a(b) = 7(b + 5)[/tex]
Rewrite as:
[tex]a = 7(b + 5)[/tex]
Divide by 7
[tex]\frac{a}{7} =b + 5[/tex]
Subtract 5
[tex]b = \frac{a}{7} -5[/tex]
Express as:
[tex]b(a) = \frac{a}{7} -5[/tex] --- the inverse function
Age of car = 8 years. Original cost = $18,000. The cost of maintenance and repairs is $
From the graph it seems to be around the area of 10%.
So,
18,000 * 0.10 = $1,800
if a number is divided by three and then two is added,the answer is twenty-nine.what is the number
Answer:
81
Step-by-step explanation:
the answer is 81, just out this in the solution
Answer:
81
Step-by-step explanation:
29-2=27
27*3=81
if we divide 81 by 3 we get 27 and 27 plus 2 is 29 so it is 81
A larger number is double the sum of 3 and a smaller number. The larger number is 2 less than 3 times the smaller number. If y represents the larger number and x represents the smaller number, which equations model the situation? Check all that apply.
y=3x-2
3x-y=2
3x-y=-2
y=2-3x
y=2(x+3)
Answer:
1,2, and 5
Step-by-step explanation:
y=2*(3+x)
y=3x-2
3x-y=2
Given the formula below, solve for x.
Answer:
find X in X with x if you find X with x in with x you got a formula
The diameter of a circle is 19 inches. If the diameter is extended 5 inches beyond the circle to point C, how long is the tangent segment from point C to the circle? Use the figure below to help guide your response. Explain your answer and show all work.
Answer:
Exact Length = 2*sqrt(30)
Approximate Length = 10.95445
======================================================
Work Shown:
(tangent)^2 = (external secant)*(whole secant)
(CD)^2 = (CB)*(CA)
(CD)^2 = (CB)*(CB+BA)
x^2 = 5*(5+19)
x^2 = 120
x = sqrt(120)
x = sqrt(4*30)
x = sqrt(4)*sqrt(30)
x = 2*sqrt(30) .......... exact length
x = 10.95445 ............. approximate length
The length of the tangent segment is; x = 10.95
Length of TangentFrom secant theorem, we know that;
Tangent ² = length of external secant × total length of secant.
From the image, we see that;
Length of tangent is x.
External secant = 5
Total length of secant = 19 + 5 = 24
Thus;
x² = 5 × 24
x² = 120
x = √120
x ≈ 10.95
Read more about length of tangent at;https://brainly.com/question/9132922
There are 20 chocolates in a box.
Some of the chocolates contain nuts and the rest do not.
The probability that a chocolate containing nuts is picked at random from the
box is 0.6
How many of the chocolates in the box contain nuts?
Answer:
12 nutted chocolates
Step-by-step explanation:
0.6 is equal to 60% and 60% 0f 20 is 12.