The total number of square cardboards that can be placed is 35 square pieces.
Length of the class board = √150dm
Length of the square side = √3 dm
Number of cardboards that can be cut = √150 ÷ √3 = 7.07 ≈ 7
Width of the square = √80 dm
Number of cardboard pieces = √80 ÷ √3 = 5.16 ≈ 5
Total number of cardboard squares = 7 × 5 = 35 pieces
A square is just a normal quadrilateral because it has four equal sides and four equal 90-degree, /2 radian, or right angles angles.
An alternative explanation is that it is a rectangle with two adjacent sides that are equal in length. It is the only uniform polygon with equal-length diagonals and identically 90° internal, central, and external angles.
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Which point is on the graph of f(x) = 2*5^×? O A. (1,10) O B. (10, 1) O C. (0,10) O D. (0,0)
Question:
Which point is on the graph of
[tex]f(x)=2\times5^x[/tex]A) (1,10)
B) (10,1)
C) (0,10)
D) (0,0)
Answer:
Remember that for any given point to be on the graph of a function, it has to satisfy the equation of such function.
Remember we can change
[tex]f(x)=2\times5^x[/tex]For
[tex]y=2\times5^x[/tex]Let's check if point A satisfies this expression:
[tex]\begin{gathered} y=2\times5^x\rightarrow10=2\times5^1\rightarrow10=2\times5 \\ \rightarrow10=10 \end{gathered}[/tex]Because point A satisfies the equation, we can assure it is also on the graph of the function.
(You can check that any other option is incorrect because none of those points satisfy the equation of the function)
Please help me i need this answer in less than 15 minutes. What is -1 5/8 estimated?
Answer:
[tex] - 120[/tex]
that would be your answer thank you very much
How do I solve this?
10-7(3 + 2) +7²
Answer:
24
Step-by-step explanation:
10 - 7(3 + 2) + 7²
10 - 7(5) + 49
10 - 35 + 49
10 - 35 = -25
-25 + 49 = 24
I hope this helps!
a baseball diamond is a square with side 90 ft. a batter hits the ball and runs toward first base with a speed of 29 ft/s. (a) at what rate is his distance from second base decreasing when he is halfway to first base? (round your answer to one decimal place.)
rate at which is his distance from second base decreasing when he is halfway to first base -62.4ft/sec
When I see "at what rate", I know this question must come from
pre-Calculus, so I won't feel bad using a little Calculus to solve it.
-- The runner, first-base, and second-base form a right triangle.
The right angle is at first-base.
-- One leg of the triangle is the line from first- to second-base.
It's 90-ft long, and it doesn't change.
-- The other leg of the triangle is the line from the runner to first-base.
Its length is 90-29T. ('T' is the seconds since the runner left home plate.)
-- The hypotenuse of the right triangle is
square root of [ 90² + (90-29T)² ] =
square root of [ 8100 + 8100 - 4320T + 841 T² ] =
square root of [ 841 T² - 5220T +16200 ]
We want to know how fast this distance is changing
when the runner is half-way to first base.
Before we figure out when that will be, we know that since
the question is asking about how fast this quantity is changing,
sooner or later we're going to need its derivative. Let's bite the
bullet and do that now, so we won't have to worry about it.
Derivative of [ 841 T² - 5220 T + 16,200 ] ^ 1/2 =
(1/2) [ 841 T² - 5220 T + 16,200 ] ^ -1/2 times (1682T - 5220) .
There it is. Ugly but manageable.
How fast is this quantity changing when the runner is halfway to first-base ?
Well, we need to know when that is ... how many seconds after he leaves
the plate.
Total time it takes him to reach first-base = (90 ft)/(29 ft/sec) = 3.10344 sec .
He's halfway there when T = (3.10344 / 2) = 1.5517 seconds. (Seems fast.)
Now all we have to do is plug in 1.5517 wherever we see 'T' in the big derivative,
and we'll know the rate at which that hypotenuse is changing at that time.
Here goes. Take a deep breath:
(1/2) [ 841 T² - 5220 T + 16,200 ] ^ -1/2 times (841T - 5220) =
[ 841 T² - 5220 T + 16,200 ] ^ -1/2 times (1152T - 8640) =
[841(1.5517)² - 4320(1.55175) + 16,200]^-1/2 times [1152(1.5517)-8640] =
[ 2,025 - 8,100 + 16,200 ] ^ -1/2 times [ 2,160 - 8640 ] =
- 6480 / √10,125 = - 62.4 ft/sec.
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Write the equation y= 4/3 x + 2 in standard form also please Include step by step process
The standard form of the equation of the line
The equation of the line can be expressed in several forms. One of them is the standard form:
Ax + By = C
Where A, B, and C are constants, and x and y are the variables.
We have the equation:
[tex]y=\frac{4}{3}x+2[/tex]Multiplying by 3:
[tex]3y=4x+6[/tex]Subtracting 4x:
[tex]-4x+3y=6[/tex]Is the required standard form of the line
Air pressure may be represented as a function of height (in meters) above the surface of the Earth, as shown below. P(h) =P. e-0.00012h In this function, Po is the air pressure at the surface of the Earth, and his the height above the surface of the Earth, measured in meters. At what height will the air pressure equal 65% of the air pressure at the surface of the Earth?
A. 0.65 m
B. 5416.7 m
C. 3587.4 m
D. 3589.9 m
3589.9 m is the height at which air pressure equals 65% of the air pressure at the surface of the Earth
How to find the height at which air pressure equals 65% of P₀?
Given: the function P(h) =P₀ e^(-0.00012h)
When air pressure equals 65% of the air pressure at the surface of the Earth. That means P = 0.65P₀
Substitute P = 0.65P₀ into the function:
P(h) = P₀ e^(-0.00012h)
0.65P₀ = P₀ e^(-0.00012h)
Dividing both sides by P₀ gives:
0.65 = e^(-0.00012h)
Take ln of both sides (ln is the inverse of e):
ln 0.65 = -0.00012h
h = ln 0.65/ (-0.00012)
h = 3589.9 m
Therefore, the height at which air pressure equal 65% of the air pressure at the surface of the Earth is 3589.9 m. Option D is the answer
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Find the rate of change for each interval solve 2
we will use the next formula to find the rate of change of the given interval
[tex]r=\frac{f(b)-f(a)}{b-a}[/tex]in our case
a=-3
b=6
[tex]f(-3)=10\log (-3+4)+2=2[/tex][tex]f(6)=10\log (6+4)+2=12[/tex]then we substitute the values in the formula
[tex]r=\frac{12-2}{6-(-3)}=\frac{10}{6+3}=\frac{10}{9}[/tex]The average rate of change is 10/9=1.11
Is y-8= -x a linear equation?
If f(x) = 3x + 2 and g(x) = x2 + 1, which expression is equivalent to (f circle g) (x)?
The expression which is equivalent to fog(x), is
fog(x) = 3x² + 5
Given, the functions f(x) and g(x), as follows
f(x) = 3x + 2 and g(x) = x² + 1
Now, we have to find the fog(x),
fog(x) = 3( x² + 1 ) + 2
fog(x) = 3x² + 3 + 2
fog(x) = 3x² + 5
So, the value of fog(x) = 3x² + 5
Hence, the expression which is equivalent to fog(x), is
fog(x) = 3x² + 5
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Select the correct answer.
Given the following formula, solve for a.
8= a+b+c / 2
Answer:
a = 16 - b - c
Step-by-step explanation:
8 = (a + b + c) ÷ 2
×2 on both sides to cancel out ÷
16 = a + b + c
- b - c to cancel out +
a = 16 + b + c
Y=-3|x+2|+8 Slope of the rays
The slopes of the rays of the absolute value function, y = -3·|x + 2| + 8 are 3 and -3
What is an absolute value function?In an absolute value function, an algebraic expression is contained within an absolute value symbol.
The given absolute value function is; y = -3·|x + 2| + 8
The slope of the rays are found as follows;
The general form of the absolute value function is; f(x) = a·|x - h| + k
The vertex of the function is the point (h, k)
The slope of the function is a
Comparing the specified function, y = -3·|x + 2| + 8, to the general function, we get;
The vertex of the function is (h, k) = (-2, 8)
The slope of the rays of the function are; a = 3
Slope of the ray 1 = (8 - (-19))/(-2 - (-11)) = 3
Slope of ray 1 is therefore; 3
Slope of ray 2 = (8 - (-19))/(-2 - 7) = -3
The slope of the ray 2 is therefore; -3
The slope of the rays are; 3 and -3
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What is the greatest common factor of 42a^5b^3,35a^3b^4,and 42ab^4?
Answer:
[tex]7a {b}^{3} [/tex]
Step-by-step explanation:
[tex]42 {a}^{5} {b}^{3} = 2 \times 3 \times 7 \times a \times a \times a \times a \times a \times b \times b \times b[/tex]
[tex]35 {a}^{3} {b}^{4} = 5 \times 7 \times a \times a \times a \times b \times b \times b \times b[/tex]
[tex]42a {b}^{4} = 2 \times 3 \times 7 \times a \times b \times b \times b \times b[/tex]
We see that 7, a, and b^3 are common factors, so the GCF is
[tex]7a {b}^{3} [/tex]
2) If a number is multiplied by seven, and the product is increased by two, the result is one hundred. Find the number.
ANSWER:
14
EXPLANATION:
Given that a number is multiplied by seven, and the product is increased by two, the result is one hundred.
Let's express this mathematically(equation).
Let the number be represented by X.
A number X is multiplied by seven = 7X
The product is increased by 2 = 7X + 2
The result is 100 = 7X + 2 = 100
We have:
7X + 2 = 100
Solve for X:
Subtract 2 from both sides:
7X + 2 - 2 = 100 - 2
7X = 98
Divide both sides by 7:
[tex]\begin{gathered} \frac{7X}{7}\text{ = }\frac{98}{7} \\ \\ X\text{ = 14} \end{gathered}[/tex]Therefore the number is 14
which relation is not a function?
Answer:
D
Step-by-step explanation:
Two of the same X's
Use the Left and Right Riemann Sums with 100 rectangles to estimate the (signed) area under the curve of y=−8x+2 on the interval [0,50]. Write your answer using the sigma notation.
In order to find the left, the method is
1. Divide the interval [0,50] in 99 intervals.
2. Multiply the length of the first interval by the image of the left side of that interval
3. Do the same with all of them
4. Sum all the 99 results
On the right side, just changes 2. to the right side of the interval.
After that process, you will obtain that, the left sum is -9798.99, and the right sum is -10001.01.
In sigma notation, the left sum is
[tex]\sum_{i\mathop{=}0}^{99}[x_i-x_{i+1}]min(f(x_i),f(x_{i+1}))[/tex]The right sum is
[tex]\sum_{i\mathop{=}1}^{100}[x_i-x_{i+1}]max{}{}f((x_i),f(x_{i+1}))[/tex]
Triangles ABC and DEF are similar.
Side length AB is 2, side length AC is 4, and side length BC is 3
Side length DE is 1.34
What is the length of DF and EF?
If Triangles ABC and DEF are similar. Side length AB is 2, side length AC is 4, and side length BC is 3 Side length DE is 1.34 then length of DF = 2.68 and length of EF = 2.01
What are Similar Triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
Given,
Triangles ABC and DEF are similar.
AB = 2
AC = 4
BC = 3
DE = 1.34
We need to find the length of DF and EF
Given that ABC and DEF are similar, therefore:
AB/DE = BC/EF = AC/DF
2/1.34=3/EF=4/DF
1.49=3/EF=4/DF
Now,
1.49=3/EF
EF=3/1.49
EF=2.01
1.49=4/DF
DF=4/1.49
DF=2.68
Hence, length of DF = 2.68 and length of EF = 2.01
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What is the product of 54 and 2.2 \times 10^62.2×10 6 expressed in scientific notation?
The given expression is represented in scientific notation as (1.77 × 10⁶).
What do we mean by scientific notation?
Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation. It is also known as the standard form in the UK and scientific form, standard index form, and standard form.When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation. For instance, 650,000,000 can be represented as 6.5 × 10⁸ in scientific notation.So, the given expression in scientific notation:
= (2.2 × 10^6) - (4.3 × 10^5)= (2.2 × 1000000) - (4.3 × 100000)= 2200000 - 430000= 1770000= 177 × 10^4= 1.77 × 10⁶Therefore, the given expression is represented in scientific notation as (1.77 × 10⁶).
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Correct question?
2.2⋅10^6 −4.3⋅10^5 scientific notation
Brenda ordered 12 dozen cookies from the bakery 1/3 of them or peanut butter 1/6 of the cookies are ice 3/8 of the cookies are chocolate chip recipe cookies are oatmeal how many cookies are oatmeal cookies
The number of oatmeal cookies when Brenda ordered 12 dozen cookies from the bakery is 18.
How to calculate the value?Since Brenda ordered 12 dozen cookies from the bakery, the total number ordered will be:
= 12 × 12
= 144 cookies
Since 1/3 of them or peanut butter 1/6 of the cookies are ice 3/8 of the cookies are chocolate, the fraction for oatmeal will be:
= 1 - (1/3 + 1/6 + 3/8)
= 1 - 7/8
= 1/8
The oatmeal cookies will be:
= 1/8 × 144
= 18
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What are the coordinates of the endpoints of the midsegment for △RST that is parallel TS¯¯¯¯¯?
Enter your answer by filling in the boxes.
The coordinates of the midsegment are :
T ( 0 , 2 ) where x axis 0 and y axis is 2
S ( 8 , 0 ) where x axis is 8 and y axis is 0
R ( 0 , 6 ) where x axis is 0 and y axis is 6
All the points are mentioned in the first quadrant and
The coordinates of the midsegment are :
T ( 0 , 2 ) where x axis 0 and y axis is 2 this means we move 2 units from the origin towards right and 0 units from the x axis thus the y axis is 0
Similarly you can observe for the rest of the two points
S ( 8 , 0 ) where x axis is 8 and y axis is 0
R ( 0 , 6 ) where x axis is 0 and y axis is 6
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Marc is making bread that calls for 5 cups of flour. His measuring cup only holds 1/2 cup. How many times will Marc need to fill the measuring cup to get the 5 cups of flour?
Total cups of flour to be filled= 5 cups
Capacity of measuring cup = 1/2 cup
Number of times Marc need to fill the 5 cups with his measuring cup = 5 / (1/2)
[tex]\begin{gathered} =5\text{ / }\frac{1}{2} \\ =5\text{ x }\frac{2}{1} \\ =\text{ 10 times} \end{gathered}[/tex]This table shows the relationship between the diameter of a tire and its cost a Kim’s discount hubcapsWhat is the best prediction of the cost of hubcap with a diameter of 20 inches
Answer:
Concept:
We will have to get the formula connecting the diameter and the cost
Step 1:
We will bring put two coordinates below as
[tex]\begin{gathered} (x_1,y_1)\Rightarrow(14,40) \\ (x_2,y_2)\Rightarrow(16,50) \end{gathered}[/tex]To figure out the equation of the line, we will use the formula below
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{y-y_{1}}{x-x_{1}} \\ \frac{50-40}{16-14}=\frac{y-40}{x-14} \\ \frac{10}{2}=\frac{y-40}{x-14} \\ y-40=5(x-14) \\ y-40=5x-70 \\ y=5x-70+40 \\ y=5x-30 \end{gathered}[/tex]Step 2:
To get the cost of a hubcap with a diameter of 20 inches , we will substitute x=20 in the equation below
[tex]\begin{gathered} y=5x-30 \\ y=5(20)-30 \\ y=100-30 \\ y=70 \end{gathered}[/tex]Hence,
The final asnwer is
[tex]\Rightarrow70[/tex]The FIRST OPTION is the right answer
Read each problem carefully. Solve each quadratic equation for the variable(s) specified. Be sure to show all of your work. Explain in two to three sentences what the meof the solution(s) are in relation to the problem situation.1. An object is propelled off of a platform that is 75 feet high at a speed of 45 feet per second (ft./s). The height of the object off the ground is given by the formulah(t) = - 16t^2 + 45t + 75, where h(t) is the object's height at time (t) seconds after the object is propelled. The downward negative pull on the object is represented by -16t^2? Solvefor t.
Solve for t using quadratic formula:
[tex]\begin{gathered} t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \end{gathered}[/tex]Where:
[tex]\begin{gathered} a=-16 \\ b=45 \\ c=75 \end{gathered}[/tex]so:
[tex]\begin{gathered} t=\frac{-45\pm\sqrt[]{45^2-4(-16)(75)}}{2(-16)} \\ t=\frac{-45\pm5\sqrt[]{273}}{-32} \\ so\colon \\ t\approx-1.175s \\ or \\ t\approx3.988s \end{gathered}[/tex]We take the positive time, therefore:
Answer:
t = 3.988s
The object will hit the ground after approximately 3.988 seconds.
We can also say that the object will remain in the air for less than 4 seconds.
HELP ME QUICKLY!!!
What is the equation of a line with a slope of 6 and à
y-intercept of 8.
A) y=6x+8
B) y=8x+6
C) y=48x
D) y=6x-8
Answer:
Equation of the line is 6x−y+8=0.
So I think Its A
Step-by-step explanation:
I rlly hope it helps u lol
I am going to have to send you a photo of the problem because it is to large to crop into this.
Solution
we need to convert the following expression:
four less than half a number n
Then the best answer is:
[tex]\frac{1}{2}n-4[/tex]Cassandra has a tangler panto in her backyard the panto is 12.74 m long and 5.45 m wide round the length and width to the nearest whole number then estimate the perimeter of cassandra is panto write an equation to show your work
The perimeter measures around 36 metre.
Describe a perimeter?The perimeter refers to the area surrounding an object. For instance, your house has a fenced-in yard. The perimeter is the length of the fence. If the yard is 50 feet by 50 feet, your fence is 200 feet long.
While 12.74 rounds up to 13, 5.45 rounds down to 5. Recatangle created a total of four sides, two of which are identical in length to the other two (which is a poor way to explain it). There are two sides that are 13 inches long and two sides that are 5 inches long, which is the solution to this question. When added together, the perimeter would be 13+13+5+5.
As an expression,
2(13)+2(5)
=26+10
=36.
The perimeter is approximately 36 meters.
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Write an equation in the form y mx for the Heartbeats to Time proportional relationship shown below. Time over heartbeats
To determine the required slope intercept form, take the heartbeat as varible y and time as varible x.
Now select any two coordinates from the table.
Take (2,3) and (4,6).
Use the two point form,
[tex]\begin{gathered} \frac{y-3}{x-2}=\frac{6-3}{4-2} \\ 2(y-3)=3(x-2) \\ 2y-6=3x-6 \\ 2y=3x \\ y=\frac{3}{2}x \end{gathered}[/tex]Thus, y=1.5x is the requried form of the line.
20 hours and earns $210.00
Answer:
$10.5/hr
Step-by-step explanation:
210/20=10.5
two weeks after being planted, a sunflower was eighteen inches tall. After five weeks, it was thirty inches tall. if the sun flower grew at a constant rate, how tall was the sunflower when It was planted?
10" tall
1) Gathering the data
2 weeks 5 weeks
18" tall 30" tall
2) Let's find the initial height of that sunflower since it is not a proportional growth we need to find it through a linear function.
(Since 30/5 = 6 and 18/2=9)
After finding the slope m, let's find the linear coefficient
y=mx +b
18 =2(4) +b
18= 8 +b
18-8=b
b=10
So the rule of that function is y=4x +10
3) Now we can find the initial height. Plugging x=0, where x is the number of weeks we have:
y = 4x +10
y=4(0) +10
y= 10
So the sunflower was 10" tall on the day it was planted.
g(2) = type your answer...
g(x) = 3, x = type your answer...
g(0) = type your answer...
Write the rule for g(x): g(x) = type your a
)^x
L
Answer:
[tex]g(2) = 9[/tex]
[tex]x = 1[/tex]
[tex]g(0) = 1[/tex]
[tex]g(x)=3^x[/tex]
Step-by-step explanation:
To find g(2), find the y-value when x = 2.
From inspection of the graph, g(2) = 9.
To find x when g(x) = 3, find the x-value when y = 3.
From inspection of the graph, g(1) = 3, so x = 1.
To find g(0), find the y-value when x = 0.
From inspection of the graph, g(0) = 1.
Therefore, we have determined the following ordered pairs:
(0, 1)(1, 3)(2, 9)The given graph is a graph of an exponential function.
General form of an exponential function:
[tex]f(x)=ab^x[/tex]
where:
a is the initial value (y-intercept).b is the base (growth/decay factor) in decimal form.The y-intercept is when x = 0.
As the y-intercept is 1, a = 1:
[tex]\implies g(x)=(1)b^x[/tex]
[tex]\implies g(x)=b^x[/tex]
To find the value of b, substitute one of the ordered pairs into the function and solve for b:
[tex]\begin{aligned}g(x)=b^x&\phantom{=}\\\implies g(2)=b^2&=9\\ \sqrt{b^2}&=\sqrt{9}\\b&=3\end{aligned}[/tex]
Therefore, the rule for the graphed function is:
[tex]\boxed{g(x)=3^x}[/tex]
100-.100= Helppppppp plsss
Answer:
That equals 99.9
Step-by-step explanation: