1. A rectangle has a length of 5cm and a height of 4cm.
a. Find the area of the rectangle
b. Find the perimeter of the rectangle.
c. A scale factor of .5 is used to reduce the rectangle. What is the new area?
d. A scaled factor of 2 is used to increase the triangle. What is the new area?
Answer:
a
20cm squared
b
18cm
c
5cm
d
80cm
Step-by-step explanation:
a
Area is height multiplied by length in a regular quadrilateral
b
Perimeter is calculated by adding all the sides together
c
0.5 is effectively halving, so instead of 4 multiplied by 5 it is 2 multiplied by 2.5
d
2 is effectively doubling, so instead of 4 multiplied by 5 it is 8 multiplied by 10
Answer:
20 cm²18 cm5 cm²80 cm²Step-by-step explanation:
Q1(a)
Area = length x heightArea = 5 x 4Area = 20 cm²Q1(b)
Perimeter = 2(length + height)Perimeter = 2(5 + 4) = 2(9)Perimeter = 18 cmQ1(c)
New dimensions are : 5/2 = 2.5 and 4/2 = 2New Area = 2.5 x 2New Area = 5 cm²Q1(d)
New dimensions are : 2 x 5 = 10 and 2 x 4 = 8New Area = 10 x 8New Area = 80 cm²what is a greatest common denominator?
Answer:
GCF
Step-by-step explanation:
sorry if you dont understand
Expand:
[tex]f(z) = \frac{1}{z(z - 2)} [/tex]
for ;
[tex] |z| > 2[/tex]
Expand f(z) into partial fractions:
[tex]\dfrac1{z(z-2)} = \dfrac12 \left(\dfrac1{z-2} - \dfrac1z\right)[/tex]
Recall that for |z| < 1, we have the power series
[tex]\displaystyle \frac1{1-z} = \sum_{n=0}^\infty z^n[/tex]
Then for |z| > 2, or |1/(z/2)| = |2/z| < 1, we have
[tex]\displaystyle \frac1{z-2} = \frac1z \frac1{1 - \frac2z} = \frac1z \sum_{n=0}^\infty \left(\frac 2z\right)^n = \sum_{n=0}^\infty \frac{2^n}{z^{n+1}}[/tex]
So the series expansion of f(z) for |z| > 2 is
[tex]\displaystyle f(z) = \frac12 \left(\sum_{n=0}^\infty \frac{2^n}{z^{n+1}} - \frac1z\right)[/tex]
[tex]\displaystyle f(z) = \frac12 \sum_{n=1}^\infty \frac{2^n}{z^{n+1}}[/tex]
[tex]\displaystyle f(z) = \sum_{n=1}^\infty \frac{2^{n-1}}{z^{n+1}}[/tex]
[tex]\displaystyle \boxed{f(z) = \frac14 \sum_{n=2}^\infty \frac{2^n}{z^n} = \frac1{z^2} + \frac2{z^3} + \frac4{z^4} + \cdots}[/tex]
please help! will give brainliest!
The perimeter of a rectangle is 72 cm one side is 3 times the length of the other form an equation and solve for the length and width
Answer:
2(length) +2(width)=perimeter
2(3(width))+2(width)=72
8×width=72
width=9
length=3×9=27
area=27×9
247=area
Step-by-step explanation:
If f{x)=-4(x-6)+15,what is f(3)?
A -3 B3 C27 D51
Answer:
C. f(3)=27
Step-by-step explanation:
f(3)=-4(3-6)+15
f(3)=-4(-3)+15
f(3)=12+15
f(3)=27
During the first four weeks of her life a baby girl increases her mass from 3.2kg to 4.7th what percentage increase does this represent give your answer to 3 so. F
Answer:
46.875%
Step-by-step explanation:
increase mass = 4.7 - 3.2 = 1.5kg
percentage increase = 1.5/3.2 = 46.875%
A quadratic function has zeros −3 and 5 and contains the point (4, 14).
a) Find the equation of the quadratic function in standard form.
b) Complete the square to determine the vertex of the function.
c) Find the equation of a second quadratic function in the same family as the function in part that contains the point (1, −48).
The quadratic function which has zeros −3 and 5 and contains the point (4, 14) is 2x²+4x+30 and the vertex points are (-1,28).
What is a quadratic equation?A quadratic equation is the equation in which the unknown variable is one and the highest power of the unknown variable is two.
The standard form of the quadratic equation is,
ax²+bx+c=0
Here,(a,b, c) is the real numbers and (x) is the variable.
A quadratic function has zeros −3 and 5 and contains the point (4, 14). The factored form of quadratic equation is,
f(x)=a(x-z₁)(x-z₂)
Here, z₁ and z₂ are the zeros. Thus,
f(x)=a(x-z₁)(x-z₂)
f(x)=a(x-(-3))(x-5)
f(x)=a(x+3)(x-5)
This equation contains the point (4,14). Thus,
14=a(4+3)(4-5)
14=a(7)(-1)
a=14/-7
a=-2
Put the value in above equation and solve it further:
f(x)=-2(x+3)(x-5)
f(x)=-2(x²-5x+3x-15)
f(x)=-2x²-4x-30
Change the sign,
f(x)=2x²+4x+30
The equation of the quadratic function in standard form is,
f(x)=2(x+1)²+28
Thus, the vertex point are -1 and 28. Similarly, the section equation which contains the point (1, −48) can be solved.
Hence, the quadratic function which has zeros −3 and 5 and contains the point (4, 14) is 2x²+4x+30 and the vertex points are (-1,28).
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whats the perimeter of the figure square with 3 semi circles? rounded to the nearest 100th
Answer:
3.1415
×=18
×=(2)
2 If you need something else?
Un círculo con circunferencia igual a 20 tiene un arco con ángulo central igual a 72°.
¿Cuánto mide la longitud del arco?
Answer:
4
Step-by-step explanation:
[tex]\frac{20}{360}=\frac{x}{72}\\x = 4[/tex]
a new tile floor in school cafeteria has been installed within a checkerboard alternating of black and white only. there is a total of 25 tiles including 22 White tiles what is the ratio of black tiles to White tiles
The ratio of the black tiles to White tiles in a school Cafeteria in which new tile floor is installed within a checkerboard is 3/22.
What is a ratio of two numbers?The ratio of two number is the fraction part, which represent that how a number is more or less compare to the other.
A new tile floor in the school cafeteria has been installed within a checkerboard alternating of black and white only.
There is a total of 25 tiles including 22 White tiles. Here,
Total number of white tiles is 22.The total number of tiles is 25.Thus, the total number of white tiles is,
[tex]25-22=3[/tex]
Thus, there is total 3 white tiles. The ratio of black tiles to White tiles is,
[tex]r=\dfrac{3}{22}\\[/tex]
Thus, the ratio of the black tiles to White tiles in a school Cafeteria in which new tile floor is installed within a checkerboard is 3/22.
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A board is 6 1/2 feet long. You cut off a 1 3/4-foot piece and a 2 2/3 foot piece. How much of the original board is left?
Step-by-step explanation:
The feet long that the board is
[tex] = 6 \frac{1}{2} \\ [/tex]
The piece of board cut off
[tex] = 1 \frac{3}{4} + 2 \frac{2}{3} \\ [/tex]
[tex] = \frac{1 \times 4 + 3}{4} + \frac{2 \times 3 + 2}{3} \\ [/tex]
[tex] = \frac{7}{4} + \frac{8}{3} \\ [/tex]
[tex] = \frac{7}{4} \times \frac{3}{3} + \frac{8}{3} \times \frac{4}{4} \\ [/tex]
[tex] = \frac{21}{12} + \frac{32}{12} \\ [/tex]
[tex] = \frac{53}{12} \\ [/tex]
The original board left
[tex] = 6 \frac{1}{2} - \frac{53}{12} \\ [/tex]
[tex] = \frac{13}{2} - \frac{53}{12} \\ [/tex]
[tex]= \frac{13}{2} \times \frac{6}{6} - \frac{53}{12} \times \frac{1}{1} \\ [/tex]
[tex] = \frac{78 - 53}{12} \\ [/tex]
[tex] = \frac{25}{12} \\ [/tex]
[tex] = 2 \frac{1}{12} \\ [/tex]
hope it helped !!!
Joshua wants to buy a pair
of jeans for $45.00. The tax
rate is 3.4%. If Joshua has
$50, does he have enough
money to pay for the jeans?
Justify your answer.
Answer:
yes
Step-by-step explanation:
3.4% = .034
.034 x 45 = 1.53
1.53$ + 45$ = 46.53$
46.53$ > 50
yes, he dose have enough money
2 Richard and Jason each begin filling pools at the same time.
• Richard fills his pool at a rate of 6 gallons per minute.
• Jason's pool already contains 200 gallons, and he fills it at a rate of 2 gallons per
minute.
The quantity of the liquid in Richard's tank after 20 minutes will be 120 gallons and in Jason's tank will be 240 gallons.
What are gallons?
A gallon is a British unit which is used for the measurement of liquids that is equal to eight pints. In Britain, it is equal to about 4.546 litres. In America, it is equal to about 3.785 litres.
It is given in the question that:-
Richard fills his pool at a rate of 6 gallons per minute.
Jason's pool already contains 200 gallons, and he fills it at a rate of 2 gallons per minute.
After 20 minutes the amount of liquid in the tank will be:-
For Richard = 6 gallons per minute. x 20 minutes= 120 gallons
For Jason= 2 gallons per minute x 20 =40 gallons
Jason has 200 gallons already in the tank
So it will become = 200+24=240 gallons.
Hence quantity of the liquid in Richard's tank after 20 minutes will be 120 gallons and in Jason's tank will be 240 gallons.
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write a growth/decay function to model the situation A car was purchased in 2000 for $22,500. It has depreciated at a rate of 5% per year. What was the value of the car in 2011
If the price of the car is $22,500 in 2000. Then the value of the car in 2011 with a decay of 5% every year is $12,798.
What is an exponent?Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.
A car was purchased in 2000 for $22,500.
It has depreciated at a rate of 5% per year.
Then the price of the car in 2011 will be
The decay function is modeled as
[tex]\rm A = P(1-r)^t[/tex]
The number of years has been passed is 11.
Then we have
[tex]\rm A = 22,500(1-0.05)^{11}\\\\A = \$ \ 12798[/tex]
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can you please help me I give you extra points
Answer:
( -2 , 0 ) , (1 , 0 ) , (-2 , 3 )
I'm pretty sure on this!
help again, im in class lol
Answer:
56.55
Step-by-step explanation:
a=3.14*r^2/2
r=6
3.14*6^2/2
3.14*36/2
113.04/2
56.55
Find the slope of a line with equation 4y + x = 8.
Answer:
m = -1/4
Step-by-step explanation:
4y + x = 8
Arrange the equation in a slope intercept form y = mx+b, where m is the slope
4y + x = 8, subtract x from both sides
4y = -x +8, divide both sides by 4
y = -x/4 + 8/4 , simplify
y = -x/4 + 2, compare this to the general form y=mx+b and we see that the slope m = -1/4
Answer:
m = -1/4
Step-by-step explanation:
4y + x = 8
Arrange the equation in a slope intercept form y = mx+b, where m is the slope
4y + x = 8, subtract x from both sides
4y = -x +8, divide both sides by 4
y = -x/4 + 8/4 , simplify
y = -x/4 + 2, compare this to the general form y=mx+b and we see that the slope m = -1/4
Given the equation y= 1/2x + 9, what is the y-intercept?
Answer:
9
Step-by-step explanation:
Y intercept when x = 0
Y = 9
where m is slope and b is y-intercept
Hence,
Here given equation: y = ½ x + 9
Identify,
slope: ½ and y-intercept: 9
An advertisement for a lawn service claims their fertilizer treatment kills weeds in half the
time. When you read the small print at the bottom of the ad, you see that they asked 20 of their
long-term customers to estimate how long it took until their weeds died out before employing
the lawn service. On average, the customers said it took 4 weeks for all the weeds to die before
the service. The company knows that their fertilizer treatment can kill weeds in 2 weeks. Why
is this advertisement misleading?
The reason why the advertisement misleading is: Number of size which is 20 is a very sample size to make this conclusion valid.
What is advertisement?Advertisement can be defined as the process of creating awareness about a product so as to increase sales.
Based on the given scenario the advertisement is misleading based on the following reasons:
The sample size which is 20 is a very small sample size to make this conclusion valid. The customers said it will take 4 weeks for all the weeds to die before while the company on the other hand knew that the fertilizer treatment can kill weeds in 2 weeks.Therefore The reason why the advertisement misleading is: Number of size which is 20 is a very sample size to make this conclusion valid.
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1, 8, 5, 4, 1, 8, 5, 4 mean media mode
Answer:
see below
Step-by-step explanation:
mean: 4.5
median: 1,1,4,4,5,5,8,8
mode: 4.5
pls help me with this math problem
Answer:
Step-by-step explanation:
3,2
the lines meet at 2 y, and 3 x
X goes first, and y goes second
So I’m stuck on these 3 problems can anyone help me? If you can pls simplify the problems are: 20/26 ÷ 5 =? 28/56 ÷ 2 =? 75/90 ÷ 3 =?
Answer:
2/13 or 0.15 , 1/4 and 5 /18 or 0.28
Step-by-step explanation:
20/26 ÷ 5 =?
10/13 ÷ 5 = 2/13 or 0.15
28/56 ÷ 2 =?
1/2 ÷ 2 = 1/4
75/90 ÷ 3 =?
5/6 ÷ 3 =5 /18 or 0.28
Rewrite the following expression using the properties of loy
log2 z + 2 log2 x+ 4 log9 y + 12 log9 x - 2 log2 y
[tex]\\ \rm\Rrightarrow log_2z+2log_2x+4log_9y+12log_9x-2log_2y[/tex]
log_a^b=blogalog_a(bc)=log_a b+log_a cSo
[tex]\\ \rm\Rrightarrow log_2z+log_2x^2-log_2y^2+log_9y^4+log_9x^{12}[/tex]
[tex]\\ \rm\Rrightarrow log_2(zx^2)-log_2y^2+log_9(y^4x^{12})[/tex]
[tex]\\ \rm\Rrightarrow log_2\left(\dfrac{zx^2}{y^2}\right)+log_9(y^4x^{12})[/tex]
Answer:
[tex]\log_2\dfrac{x^2z}{y^2}+\log_9x^{12}y^4[/tex]
Step-by-step explanation:
Log laws
[tex]\textsf{Product law}: \quad \log_axy=\log_ax + \log_ay[/tex]
[tex]\textsf{Quotient law}: \quad \log_a\frac{x}{y}=\log_ax - \log_ay[/tex]
[tex]\textsf{Power law}: \quad \log_ax^n=n\log_ax[/tex]
Given expression:
[tex]\log_2z+2\log_2x+4\log_9y+12\log_9x-2\log_2y[/tex]
Group terms with same log base:
[tex]\implies \log_2z+2\log_2x-2\log_2y+4\log_9y+12\log_9x[/tex]
Apply the power law:
[tex]\implies \log_2z+\log_2x^2-\log_2y^2+\log_9y^4+\log_9x^{12}[/tex]
Apply the product law:
[tex]\implies \log_2x^2z-\log_2y^2+\log_9x^{12}y^4[/tex]
Apply the quotient law:
[tex]\implies \log_2\dfrac{x^2z}{y^2}+\log_9x^{12}y^4[/tex]
The number of people who attended a school's last six basketball games increased as the team neared the state sectional games. The table shows the data.
Game 13, 14 15, 16, 17, 18
Attendance 348, 435, 552, 609, 696, 783
State the type of function that best fits the given data. Justify your choice of a function type.
The function will be a (linear function) linear equation in two variable and the equation of the function is y = 87x - 783
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have given data:
Game(x): 13 14 15 16 17 18
Attendance(y): 348 435 552 609 696 783
If plot these points on a coordinate plane, we will see these points will align in a straight line.
We know we can find a line equation with two points:
(13, 348) and (14, 435)
[tex]\rm (y - 435) = \dfrac{435-348}{14-13}(x-14)[/tex]
y - 435 =87(x-14)
y = 87x - 783
Thus, the function will be a (linear function) linear equation in two variable and the equation of the function is y = 87x - 783
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Drag the operations into the order in which they should be performed to evaluate the expression below. 7 × 6 ÷ ( 13 − 10 ) + 4 addition division multiplication subtraction
First would be subtraction ( do inside parentheses first)
2ndwould be multiplication
3rd would be division
4th would be addition
7 x 6 / (13-10) + 4
7 x 6 / 3 + 4
42 / 3 + 4
14 + 4 = 18
a pet store has 2 gray rabbits. one eight of the rabbits at the pet store are gray. how many rabbits does the pet store have?
2 = 1/8
2 x 8 = 16
16 = 8/8
2 gray rabbits is 1/8 of 16. The store has 16 rabbits.
because if 2 rabbits are gray. and is those two = 1 eighth. then two rabbits would equal 1 out of eight. so whats two x eight? 16. it just seems like the logical answer.
A wiring job requires 5,127 feet of cable. If the cable comes in 250-foot coils, how many coils of cable are required?
Answer:
20.58 (21)
Step-by-step explanation:
5127/250 = 20.58
if the coils are only be imported in full form your gonna need 21
Answer:
21 cables
Step-by-step explanation:
Because the cables come in 250-foot coils, you cannot have a piece of one cable. So, if you take the total amount of cable you need (5,127 feet) and divide it by how long a single cable is (250 feet).
5,127 divided by 250 is 20.508, but you cannot have a piece of one cable. So, you round up to the nearest whole number, 21.
Yesenia eats 3 cookies. Maria eats 4 cookies. Jocelynn eats twice as many cookies as Yesenia. What is the ratio of the number of cookies Jocelynn eats to the number of cookies Yesenia eats?
A:4 to 3
B:2 to 3
C:2 to 1
D:3 to 4
Answer:
C: 2 to 1.
Step-by-step explanation:
Jocelyn eats 3*2 = 6 cookies.
So required ratio = 6:3
= 2:1.
What type of answers to open questions require?
A. A written response
B. A long speech in response
C. Encourage more detail answers
D. Short answers
Answer:
a. written response
Step-by-step explanation:
an open question uses what the reader gathers :)
