Answer:
The new dimensions are 6.18 cm by 16.18 cm.
Step-by-step explanation:
Original dimensions were 30 cm by 20 cm.
We decrease length and width by x and calculate the area:
Area = (length)(width)
= (30 - x)(20 - x) = 100
Performing the indicated multiplication, we get:
600 - 30x - 20x + x^2 = 100, or, after simplification,
x^2 - 50x + 500 = 0
Let's solve this by completing the square:
x^2 - 50x + 500 = x^2 - 50x + 625 - 625 + 500 = 0
This simplifies to (x - 25)^2 - 125 = 0, or (x - 25)^2 = 125
Taking the square root of both sides, we get:
x - 25 = ±√125, or
x = 25 ± 5√5
The two results are x = 36.18 (not possible, because we DECREASED the original dimensions) and x = 13.82 (possible)
The dimensions of the new rectangle are
(30 - 13.82) cm by (20 - 13.82) cm, or
16.2 cm by 6.18 cm
Check: With these dimensions is the area 100 cm^2, as expected?
(6.18)(16.18) = 99.9979 YES
Evaluate the Following
Answer:
see explanation
Step-by-step explanation:
cscΘ = [tex]\frac{hypotenuse}{opposite}[/tex] = [tex]\frac{25}{7}[/tex]
secΘ = [tex]\frac{hypotenuse}{adjacent}[/tex] = [tex]\frac{25}{24}[/tex]
cotΘ = [tex]\frac{adjacent}{opposite}[/tex] = [tex]\frac{24}{7}[/tex]
PLEASE HELP - Find the area of a regular octagon with a side length of 5 cm. Round to the nearest tenth. (Please explain in full detail the process, im trying to learn how to do these) thank you!!
Answer:
120.7
Step-by-step explanation:
The formula for finding the area of a regular octagon is: A = 2(1+[tex]\sqrt{2}[/tex])[tex]a^{2}[/tex].
Using the formula I got 120.7(rounded).
The area of the regular octagon with a side length of 5 cm is approximately 120.7cm².
We have,
To find the area of a regular octagon with a side length of 5 cm, you can use the following formula:
Area = 2 * (1 + √2) * (Side Length)²
Plugging in the values:
Area = 2 * (1 + √2) * (5 cm)² ≈ 120.7 cm²
Therefore,
The area of the regular octagon with a side length of 5 cm is approximately 120.7cm².
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At the beginning of year 1, Josie invests $400 at an annual compound interest rate of 5%. She makes no deposits to or withdrawals from the account. Which explicit formula can be used to find the account's balance at the beginning of year 3?
A. A(3) = 400 • (1 + 0.05)3 – 1
B. A(3) = 400 + (3 – 1)(0.05 • 400)
C. A(3) = 400 + (0.05 • 400)3 – 1
D. A(3) = 400 • (1 + 0.05)3
Answer: A
Step-by-step explanation:
Since she invested $400 in the beginning if the 1st year and we are asked to find the balance at the beginning of the third year, she earns interest only for the first two years. So, the formula will be
Amount = 400 (1 + 0.05) ^3-1
To find the balance in Josie's account at the beginning of the the third year we have to use A(3)=[tex]400*(1+0.05)^{3-1}[/tex]
What is Compound interest?It is the interest calculated on the initial principal amount and the accumulated interest. The formula to calculate the sum after compound interest is
Sum= [tex]P(1+r/m)^{tm}[/tex] where P=principal, r= rate of interest, m= number of times compounded in a year, t=time
How to calculate sum when interest is compounding?At the beginning of year 1, Josie invests $400 at an annual compound interest at the rate of 5%,then the amount at the beginning of year 3 is calculated as:
The amount in beginning of 1 year=$400
The amount at the end of the year 1=400+400*0.05=400(1+0.05)
The amount at the end of year 2=400(1+0.05)+400(1+0.05)*0.05
=[tex]400(1+0.05)^{2}[/tex]
=[tex]400(1+0.05)^{3-1}[/tex]
Hence the option A is correct which is to be used to calculate the amount in Josie's account at the beginning of year 3.
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Find the value of y.
(03.02 MC) Some researchers claim there is an association between getting a tattoo and contracting hepatitis C. They took a random sample of people living in Los Angeles, California, and recorded whether they had a tattoo and whether they were infected with hepatitis C. The results are shown in the following two-way table: Has Hepatitis C Does Not Have Hepatitis C Does not have a tattoo 5 50 Has one tattoo 10 210 Has more than one tattoo 15 150 If a person is chosen at random, what is the probability that he or she has hepatitis C, given that he or she has one tattoo? (2 points) Select one: a. 0.045 b. 0.333 c. 0.05 d. 0.50
Answer:
The correct option is (b) 0.333.
Step-by-step explanation:
The data provided is as follows:
Hepatitis C No hepatitis C Total
No Tattoos 5 50 55
1 Tattoo 10 210 220
> 1 Tattoo 15 150 165
Total 30 410 440
The probability of an event E is the ratio of the favorable number of outcomes to the total number of outcomes.
[tex]P(E)=\frac{n(E)}{N}[/tex]
The condition probability of an event A provided that another event X has already occurred is:
[tex]P(A|X)=\frac{P(A\cap X)}{P(X)}[/tex]
The number of people who has hepatitis C is:
n (Hepatitis C) = 30
The number of people who has hepatitis C and one tattoo is:
n (Hepatitis C and 1 Tattoo) = 10
Compute the probability that he or she has hepatitis C, given that he or she has one tattoo as follows:
[tex]P(\text{Hepatitis C} |\text{1 Tattoo})=\frac{n(\text{Hepatitis C and 1 Tattoo})}{n(\text{1 Tattoo})}[/tex]
[tex]=\frac{10}{30}\\\\=\frac{1}{3}\\\\=0.333[/tex]
Thus, the correct option is (b).
The probability that he or she has hepatitis C, given that he or she has one tattoo will be 0.333. Then the correct option is B.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
The table is given below.
Hepatitis C No hepatitis C Total
No Tattoos 5 50 55
1 Tattoo 10 210 220
> 1 Tattoo 15 150 165
Total 30 410 440
The number of people who has hepatitis C is 30. And the number of people who has hepatitis C and one tattoo is 10.
The probability that he or she has hepatitis C, given that he or she has one tattoo will be
P = 10/30
P = 1/3
P = 0.333
The probability that he or she has hepatitis C, given that he or she has one tattoo will be 0.333. Then the correct option is B.
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how to do this question plz
Answer:
adult = £7 and child = £2
Step-by-step explanation:
let a represent adult ticket and c child ticket, then
2a + 3c = 20 → (1)
a + 4c = 15 → (2)
Multiply (2) by - 2 and add to (1) to eliminate a
- 2a - 8c = - 30 → (3)
Add (1) and (3) term by term
- 5c = - 10 ( divide both sides by - 5 )
c = 2
Substitute c = 2 into either of the 2 equations and solve for a
Substituting into (1)
2a + 3(2) = 20
2a + 6 = 20 ( subtract 6 from both sides )
2a = 14 ( divide both sides by 2 )
a = 7
Cost of adult ticket is £7 and child ticket is £2
Solve for x 4x−8=3x−8
Answer:
x = 0
Step-by-step explanation:
Step 1: Subtract 3x from both sides
x - 8 = 8
Step 2: Add 8 to both sides
x = 0
Answer:
x = 0
Step-by-step explanation:
1. Get rid of the equal terms
4x = 3x
2. Move the variables to the left side
4x - 3x = 0
3. Collect the like times
4x - 3x = 0
x = 0
Hope this helps!
What is the solution for x in the given equation? sgrt9x+7+sgrt2x=7
Select the interval where h(x)>0 {where h of x is greater than 0}
Option1. -3.5 Option2. -2 Option3. 2.5
Answer:
The correct option is;
Option 3. 2.5
Step-by-step explanation:
From the graph of the function y = h(x), where h of x h(x) > 0 and x > 0 we have;
The first interval where y =h(x) > 0 occurs between x= 0 and x = 0.8
The second interval where y =h(x) > 0 occurs between 2.2 and 4 which is a range of 4 - 2.3 = 1.7
The total interval where y =h(x) > 0 occurs is therefore = 0.8 + 1.7 = 2.5
Thus the function y = h(x), is positive over an interval on the x-axis = 2.5.
Answer:
Option 3. 2.5Step-by-step explanation:
Again. I need help with this
Answer:
Option B.
Step-by-step explanation:
Scale factor of the image = [tex]\frac{\text{One side of the triangle FED}}{\text{Corresponding side of the triangleABC}}[/tex]
= [tex]\frac{\text{DF}}{\text{AC}}[/tex]
= [tex]\frac{3}{6}[/tex]
= [tex]\frac{1}{2}[/tex]
Coordinates of point C → (-2, 2)
Coordinates of the corresponding point C' after dilation with a scale factor [tex]\frac{1}{2}[/tex],
C(-2, 2) → C'(-1, 1)
Coordinates of point C' after reflection across y-axis,
C'(-1, 1) → C"(1, 1)
Followed by the translation of 2 units downwards,
C"(1, 1) → D[1, (1 - 2)]
→ D(1, -1)
From the graph we get the same coordinates of point D as (1, -1).
Therefore, ΔABC was dilated by a scale factor of [tex]\frac{1}{2}[/tex], reflected across the y-axis and moved through the translation of 2 units downwards.
I need help! Thx :) 6th grade
Answer:
0.92
Step-by-step explanation:
To write a percent as a decimal, we divide the value by 100.
Divide 92 by 100.
[tex]\frac{92}{100}[/tex]
[tex]=0.92[/tex]
Answer:
0.92
Step-by-step explanation:
92/100=0.92
Fraction- 92/100 — 46/50 — 23/25
If f(x)=3x+2, what is f(5)
Answer:
f(5) = 17Step-by-step explanation:
f(x)=3x+2
To find f (5) replace every x in f(x) by 5
That's
f(5) = 3(5) + 2
= 15 + 2
= 17Hope this helps you
need help asap!!! WILL GIVE THE MOST BRAINIEST TO WHOEVER ANSWERS IT RIGHT PUT THE ANSWER IN A BOX
Answer:
36PI
113.04
Step-by-step explanation:
4/3*PI*R^3=V
4/3*PI*27=V
36*PI=V
113.04
BRAINLIEST PLS
-ZYLYNN JADE
Answer:
113.10 (to the nearest hundredth)
Step-by-step explanation:
just google volume of a sphere
En una casa de empanadas hornean 1.200 por día. Si las cocinan en fuentes de 75 unidades, colocando siempre la mayor cantidad posible, ¿Cuántas fuentes preparan?
Answer:
16 unidades preparan simultáneamente 1200 empanadas por día.
Step-by-step explanation:
Si cada fuente tiene una capacidad de 75 empanadas por horneada y que la mayor cantidad posible ocurre cuando el volumen de producción se cocina simultáneamente, entonces el total de fuentes es la cantidad total de producción dividida por la capacidad de empanadas por fuente. Es decir:
[tex]x = \frac{1200\,emp}{75\,\frac{emp}{und} }[/tex]
[tex]x = 16\,unidades[/tex]
16 unidades preparan simultáneamente 1200 empanadas por día.
Describe how the graph of y= x2 can be transformed to the graph of the given equation. y = x2 + 3 (5 points)
Answer:
x=-1 1/2,x=-1.5
Step-by-step explanation: x=-3/2
Pqrs is a rhombus. Find x, y and z. Justify your finding.
Answer:
x = 4, y = 2√21, z = 10
Step-by-step explanation:
Since all sides of a rhombus are congruent, z = SR = 10. Since the diagonals of a rhombus bisect each other, x = PO = 4. Using Pythagorean Theorem (look at ΔPSO, we know that PS = 10 and PO = 4), y = 2√21.
find the y-intercept of the function: f(×)=(×+10)/(×-5)
Answer:
(-10,0)
Step-by-step explanation:
Hello
this is (-10,0) point
because f(-10)=0
hope this helps
The price (p), in cents, of a sweet is directly proportional to the mass (m) of the
sweet.
When the sweet cost 55 cents, the mass is 220 g. Find
(a) the equation connecting p and m.
(b) the mass, in grams, of a sweet which cost 540 cents,
(c) the cost of a sweet in cents, with a mass of 115 g
The figure is not drawn to scale. PQ and MN are straight lines. Find
Answer:
a = 138
Step-by-step explanation:
Notice that from the figure, we can see that ∠MOQ and ∠PON are vertical angles, which means that by definition, they're congruent in measure.
∠MOQ = ∠MOR + ∠ROQ = 90 + 48 = 138°
So, this means that ∠PON is also equal to 138, which means a = 138.
Thus, the answer is a = 138.
~ an aesthetics lover
(06.01, 06.02 HC) I WILL MARK YOU BRAINIEST Part A: Create a fourth-degree polynomial in standard form. How do you know it is in standard form? (5 points) Part B: Explain the closure property as it relates to polynomials. Give an example. (5 points)
A fourth-degree polynomial in standard form is :
To write a polynomial in a standard form you have to set its terms according to the variable powers in a descending order.In this example it would give:
−6[tex]x^{4}[/tex]+3[tex]x^{2}[/tex]+4x +2
The degree of a polynomial is the maximum power of an unknown variable in the polynomial.Part B:
The closure property as it relates to polynomials are :
Polynomials are closed for addition and subtraction. This is because the power does not change. Only the coefficients are changed. This is illustrated by the examples below:(2x2 + 3x + 4) + (x2 - 5x - 3)
3x2 - 2x + 1.
The above operation does not change the degree. Only the number next to each variable changes.Therefore, the addition and subtraction of polynomials is closed.
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How many times greater is 700,000 than 70,000??
Answer:
10 times greater hun
Step-by-step explanation:
70000 times 10 equals 700000
Answer:
10 times greater.
Step-by-step explanation:
700,000 / 70,000 = 700 / 70 = 70 / 7 = 10 / 1 = 10
So, 700,000 is 10 times greater than 70,000.
Hope this helps!
If both nappes of a right circular cone are intersected by a plane that does not
pass through the vertex of the cone, the resulting curve will be an)
Answer:
Hyperbola
Step-by-step explanation:
When the two napes of a cone are intersected by a plane, the resulting curve is that of the two branches of a hyperbola. See attached image.
please help i will give out brainliest
Answer:
6, 0, 10
b
Step-by-step explanation:
A chord cuts off a 120 degree arc. If the radius of the circle is 26 inches, find the
chord length
Answer:
26sqrt(3)
Step-by-step explanation:
You end up with two 30-60-90 triangles.
26/2 = 13
2 * 13 * sqrt(3) = 26sqrt(3)
14 + 18 divided by 2 * 18
Is the answer 86 or no?
Answer:
No.
Step-by-step explanation:
Order of Operations using BPEMDAS:
14 + 18/2(18)
14 + 9(18)
14 + 162
176
El área de un decágono regular cuya apotema mide 5,08 cm y la longitud de su lado es 3,3 cm.
Answer:
83.82 cm^2
Step-by-step explanation:
Aquí, queremos calcular el área de un decágono dada su apotema y la longitud de su lado.
Matemáticamente;
Área de decágono = 1/2 * perímetro * apotema
Donde perímetro = 10 * s
donde s es la longitud de los lados
Entonces el área aquí sería; 1/2 * 10 (3.3) * 5.08 = 83.82 cm ^ 2
el perimetro de un terreno rectangular es de 170m y su area es de 170^2hallar la medida de sus lados con ecuacion cuadratica
Answer:
Acá tenemos un sistema de ecuaciones.
El perímetro de un rectángulo es:
2*A + 2*L = 170m
donde A es el ancho y L es el largo.
Y el área del rectángulo es:
A*L = 170m^2.
Entonces, el primer paso es aislar una de las variables en una de las ecuaciones, yo voy a aislar A en la segunda:
A = 170m^2/L.
Ahora reemplazo eso en la primera ecuación y la resuelvo para L.
2*( 170m^2/L.) + 2*L = 170m.
340m^2 + 2*L^2 = 170m*L
ahora tenemos una ecuación cuadrática:
2*L^2 - 170m*L + 340m^2 = 0.
Las soluciones se pueden obtener usando la formula de Bhaskara:
[tex]L = \frac{+170 +- \sqrt{170^2 -4*340*2} }{2*2} = \frac{170 +-161.8}{4}[/tex]
Entonces las soluciones son:
L = (170 + 161.8)/4 = 82.95m
L = (170 - 161.8)/4 = 4.1m
Entonces, si tomamos L = 82.95m, tenemos A = 4.1 m
y el área es:
A*L = 4.1m*82.95m = 170m^2
g(x) = 4x + 1
What is g(3)?
————————————-
A. 13
B. 16
C. 12
D. 8
Answer:
A. 13.
Step-by-step explanation:
g(x) = 4x + 1
g(3) = 4 * 3 + 1 = 12 + 1 = 13
A. 13 is your answer.
Hope this helps!
Answer:
13
Step-by-step explanation:
g(x) = 4x + 1
Let x=3
g(3) = 4*3+1
= 12+1
= 13
PLZ HELP ME!!!! I WILL GIVE BRAINLIEST!!!!!! 5 stars and a thanks!!!! 50 POINTS!!! Type out how you would explain the color blue to a blind person. The blind person has been blind ever since he was born. This is a real challenge question.
Answer:
As color is simply the kind of light reflected by surfaces(if the sun was green, many plants would die), color can be explained fairly simply to a blind person. Each color represents a separate wavelength, and objects that reflect these wavelengths show up in various colors. Thus simply state the following: The color blue is displayed by all objects that reflect wavelengths from 380 and 500 nanometers.
Hope it helps <3
p.s. I know this is supposed to be kind of philosophical, but I'm a nerd, so...
Natalie has 8 socks in a drawer.
5 of the socks are black.
3 of the socks are white.
Natalie takes out a sock at random, writes down its colour and puts it back into
the drawer.
Then Natalie takes out a second sock, at random, and writes down its colour.
Answer:
Probability that the two socks picked by Natalie are of the same colours = (17/32) = 0.53125
Step-by-step explanation:
Complete Question
Natalie has 8 socks in a drawer.
5 of the socks are black.
3 of the socks are white.
Natalie takes out a sock at random, writes down its colour and puts it back into
the drawer. Then Natalie takes out a second sock, at random, and writes down its colour.
Work out the probability that the two socks are of the same colour.
Solution
This is a probability that involves replacement.
Probability of an event is given as the number of elements in the event divided by the total number of elements in the sample space.
If the event that a black socks is picked = P(B)
Then, the event that a white socks is picked = P(W)
P(B) = n(B) ÷ n(S)
n(B) = 5
n(S) = 8
P(B) = (5/8)
P(W) = n(W) ÷ n(S) = (3/8)
Probability that the two socks picked by Natalie are of the same colours = (Probability that the two socks picked are black) + (Probability that the two socks picked by Natalie are white)
Probability that the two socks picked are black = (5/8) × (5/8) (since the socks are picked and replaced, the probability stays the same)
= (25/64)
Probability that the two socks picked by Natalie are white = (3/8) × (3/8) = (9/64)
Probability that the two socks picked by Natalie are of the same colours
= (25/64) + (9/64)
= (34/64)
= (17/32) = 0.53125
Hope this Helps!!!