The cake is divided into 12 equal slices. Jake had eaten 5 slices after 3 days. The weekly cake consumption rate is 11.6
What is algebraic expression?An algebraic expression is one that is composed of integer constants, variables, and algebraic operations. 3x2 2xy + c, for example, is an algebraic expression. Algebraic expressions have at least one variable and one operation (addition, subtraction, multiplication, division). 2(x + 8y) is an algebraic expression, for example. An algebraic expression is one that contains constants, variables, and algebraic operations. 3x2 2xy + d, for example, is an algebraic expression. Thus, an algebraic expression is composed of three types of fundamental elements: Coefficient (i.e. numbers) (i.e. numbers)Therefore,
The weekly cake consumption rate is 11.6
we have 7 days.
7days-3days =4
in 3 days he has eaten 5 slices
again 4-3 days=1
so in 6 days, he has eaten 10 slices
we have 1 day left.so if he eats 5 slices in 3 days, how many does he eat slices in 1 day?
5/3=1.6
10+1.6= 11.6
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A website recorded the number y of referrals it received from social media websites over a 10-year period. The results can be modeled by y = 2500(1.50), where t is the year and 0 ≤ t ≤9.Interpret the values of a and b in this situation.O a represents the number of referrals after 9 years; b represents the growth factor of the number of referrals each year.a represents the number of referrals it received at the start of the model; b represents the decay factor of the number of referralseach year.O a represents the number of referrals after 9 years; b represents the decay factor of the number of referrals each year.a represents the number of referrals it received at the start of the model; b represents the growth factor of the number ofreferrals each year.What is the annual percent increase?The annual percent increase is%.
In this problem
we have an exponential growth function
[tex]y=2500(1.50)^t[/tex]where
a=2500 ----> initial value of the number of referrals at the start of the model
b=1.50 ---> the base of the exponential function (growth factor of the number of referrals each year
therefore
The answer Part 1 is the last option
Part 2
Find out the annual percent increase
we know that
b=1+r
b=1.50
1.50=1+r
r=1.50-1
r=0.50
therefore
r=50%
The annual percent increase is 50%2x^3+ 15^2+ 27x + 5= x^2+ 5x + 12x + 5
To determine if the equation is true we multiply the expression on the right side by the denominator on the left; if the result is the numerator on the left then the equation is true:
[tex]\begin{gathered} (2x+5)(x^2+5x+1)=2x^3+10x^2+2x+5x^2+25x+5 \\ =2x^3+15x^2+27x+5 \end{gathered}[/tex]Since the result is the numerator on the left side we conclude that the equation is true.
2. The product of two consecutive odd numbers is 143. Find the numbers. (Hint: If the first odd number is x, what is the next odd number?)
Step-by-step explanation:
we have the 2 numbers x and (x+2).
x × (x + 2) = 143
x² + 2x = 143
x² + 2x - 143 = 0
the general solution to such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case this is
x = (-2 ± sqrt(2² - 4×1×-143))/(2×1) =
= (-2 ± sqrt(4 + 572))/2 = (-2 ± sqrt(576))/2 =
= (-2 ± 24)/2 = (-1 ± 12)
x1 = -1 + 12 = 11
x2 = -1 - 12 = -13
so, we have 2 solutions : 11 and 13, -13 and -11
11× 13 = 143
-11×-13 = 143
How many arrangements of the word NEWFOUNDLAND are there?Page 5 of 12Previous PageNext Page
Step 1:
Concept
Number of way of arranging n different objects = n!
Step 2:
Word = NEWFOUNDLAND
N = 3
E = 1
W = 1
F = 1
O = 1
U = 1
D = 2
L = 1
A = 1
Step
Number of ways of arranging the word NEWFOUNDLAND
[tex]\begin{gathered} \text{ = }\frac{12!}{3!\text{ 2!}} \\ =\text{ }\frac{12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{3\times2\times1\times2\times1} \end{gathered}[/tex][tex]\begin{gathered} \\ =\text{ }\frac{479001600}{12} \\ =\text{ 39916800 ways} \end{gathered}[/tex]5 Which equations have the same value of x as 6 2 3 -9? Select three options. -9(6) 5x+4=-54 5x+4=-9 5x=-13 5X=-58
The given equation is-
[tex]\frac{5}{6}x+\frac{2}{3}=-9[/tex]If we multiply the equation by 6, we would have the same value for the variable x since we are multiplying the same number on each side. So, the second choice is an equivalent equation to the given one.
Let's multiply by 6.
[tex]\begin{gathered} 6\cdot\frac{5}{6}x+6\cdot\frac{2}{3}=-9\cdot6 \\ 5x+4=-54 \end{gathered}[/tex]So, the third expression is also an equivalent expression.
Then, let's subtract 4 on each side.
[tex]\begin{gathered} 5x+4-4=-54-4 \\ 5x=-58 \end{gathered}[/tex]The last choice is also an equivalent expression.
Therefore, the right choices are 2, 3, and 6.A gift box is 12 inches long 8 inches wide and 2 inches high how much wrapping paper is needed to wrap the gift box
Given that a box is 12 inches long 8 inches wide and 2 inches high, the area of wrapping paper needed to wrap the gift box is equal to the total surface area of the box.
[tex]\begin{gathered} \text{length l =12 inches} \\ \text{width w = 8 inches} \\ \text{ height h = 2 inches} \end{gathered}[/tex]The total surface area of the box can be calculated using the formula;
[tex]undefined[/tex]What is the slope of the line that passes through the points (6,-10) and (3,-13)? Write in simplist form
Use the slope formula to find the slope of a line that goes through two points:
[tex]\begin{gathered} \text{Coordinates of two points}\rightarrow\text{ }(x_1,y_1),(x_2,y_2) \\ \text{Slope of a line through those points}\rightarrow m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Substitute the coordinates (6,-10) and (3,-13) into the slope formula:
[tex]\begin{gathered} m=\frac{(-13)-(-10)}{(3)-(6)} \\ =\frac{-13+10}{3-6} \\ =\frac{-3}{-3} \\ =1 \end{gathered}[/tex]Therefore, the slope of a line that passes through those points, is 1.
Brady needs to fill his daughter's sandbox that is 5 feet by 7 feet. He wants to buy sand bags to fill the sand 2 feet deep. He compares the prices found for sand at two different stores.PART AWhat is the unit rate that store X is selling for? ____ lbs/dollarPART BWhich store is offering the better price?____PART CBrady finds online that it takes 100 pounds of sand to fill 1 cubic foot. Using the better priced store, compute how much it will cost him to purchase enough sand to fill the sandbox. Use the volume formula, V = I × w × h, to determine your answer.$____from____
The sand box is rectangular with
Wide= 5feet
Length= 7feet
He wants to fill the box with a depth of 2 feet
Graph the line with the given slope m and y-intercept b.
m = 4, b = -5
Answer:
Step-by-step explanation:
What we know:
m = 4, b = -5
y = mx + b where m is the gradient/slope and b is the y-intercept
Substitute m and b values:
y = 4x + -5 which is the same as y = 4x - 5
Substitute all x values to find y coordinate:
When x = -7, y = (4 x -7) - 5 = -33
When x = -6, y = (4 x -6) - 5 = -29
When x = -5, y = …
Continue for all x values
The displacement (in meters) of a particle moving in a straight line is given by s = t^2 - 9t + 15,where t is measured in seconds.(A)(i) Find the average velocity over the time interval [3,4].Average Velocity = ___ meters per second(ii) Find the average velocity over the time interval [3.5,4].Average Velocity=____meters per second(iii) Find the average velocity over the time interval [4,5].Average Velocity= ____meters per second(iv) Find the average velocity over the time interval (4,4.5] Average Velocity = ____meters per.(B) Find the instantaneous velocity when t=4.Instantaneous velocity= ____ meters per second.
Given
The displacement (in meters) of a particle moving in a straight line is given by s = t^2 - 9t + 15,
An 80% confidence interval for a proportion is found to be (0.27, 0.33). Whatis the sample proportion?
Step 1
Given;
Step 2
When repeated random samples of a certain size n are taken from a population of values for a categorical variable, the mean of all sample proportions equals the population percentage (p).
[tex]\begin{gathered} Sample\text{ proportion=}\hat{p} \\ \hat{p}\pm margin\text{ error=cofidence interval} \end{gathered}[/tex]Thus;
[tex]\begin{gathered} Let\text{ }\hat{p}=x \\ Margin\text{ of error=y} \\ x-y=0.27 \\ x+y=0.33 \end{gathered}[/tex]checking properly, the sample proportion =0.30, because
[tex]\begin{gathered} 0.30-0.03=0.27 \\ 0.30+0.03=0.33 \end{gathered}[/tex]Answer; Option D
[tex]0.30[/tex]3. An equation that crosses the y-axis at -5 and crosses the x-axis at 24. An equation that crosses the y-axis at -5 and crosses the x-axis at -65. An equation that crosses the y-axis at -5 and crosses the point (2,3)
We need to find the equation of the line which:
• crosses the y-axis at -5
,• crosses the x-axis at 2
The y-axis cutting point is (0,-5)
The x-axis cutting point is (2,0)
The equation of line is:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-axis cutting point
m is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where
y_2 = 0
y_1 = -5
x_2 = 2
x_1 = 0
So, slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{0--5}{2-0}=\frac{0+5}{2}=\frac{5}{2}[/tex]We got m, we also know b.
The y cutting point is -5, so b = -5
The equation is:
[tex]y=\frac{5}{2}x-5[/tex]The graph would look like:
More clear version:
m(25+2)(x-7)(4%-8)"y =
From the figure we can obtain 2 equations:
[tex](2y+2)+(4x-8)=180[/tex]and
[tex](9x-7)+(4x-8)=180[/tex]first lets simplify both equations:
for the first;
[tex]2y+4x=186[/tex]and for the second one:
[tex]9x+4x=195\Rightarrow13x=195\Rightarrow x=\frac{195}{13}=15[/tex]Now we have that x=15 and we can substitute x for 15 in the first equation to find y:
[tex]2y+4(15)=186\Rightarrow2y=126\Rightarrow y=63[/tex]so the final answe is: x=15 and y=63
Use Polya's four-step problem-solving strategy and the problem-solving procedures presented in this section to solve the following exercise.The number of ducks and pigs in a field totals 37. The total number of legs among them is 98. Assuming each duck has exactly two legs and each plg has exactly fourlegs, determine how many ducks and how many pigs are in the field.ducks?pigs?
Lets call x to the number of ducks
and y the number of pigs.
Then:
[tex]2x+4y=98[/tex]Because there are 2 legs per duck and 4 legs per pig.
If the total of animals is 37, then:
[tex]x+y=37[/tex]Then:
[tex]x=37-y[/tex]And replacing on the first equation we get:
[tex]2(37-y)+4y=98[/tex][tex]74-2y+4y=98[/tex][tex]2y=98-74[/tex][tex]2y=24[/tex][tex]y=\frac{24}{2}[/tex][tex]y=12[/tex]There are 12 pigs and therefore 25 ducks.
The graph models the heights, in feet, of two objectsdropped from different heights after x seconds.Which equation represents g(x) as a transformation off(x)?y45+O g(x) = f(x) -5O g(x) = f(x-5)O g(x) = f(x) + 5O g(x) = f(x + 5)40+35y = f(x)30-25+20-15+10+5+ly = g(x)0.5 1.0 1.5 20
For this problem we know that y=f(x) at x=0 is 5 units above y=g(x). So then the best solution for this case it seems to be:
[tex]f(x)=g(x)+5[/tex]And solving for g(x) we got:
[tex]g(x)=f(x)-5[/tex]solver for r: C=2(pie)r
We have the following equation:
[tex]C=2\pi r[/tex]We want to rewrite it in a way 'C' is a function of 'r'. We can accomplish that, if we divide both sides by 2pi.
[tex]2\pi r=C\Rightarrow r=\frac{C}{2\pi}[/tex]From this, we have our result.
[tex]r=\frac{C}{2\pi}[/tex]suppose that you have two square garden plots: One is 10’ x 10’ and the other is 15 x 15’. You want to cover both gardens with a 1 inch layer of mulch. If the 10 x 10 garden took 3 1/2 bags of mulch, could you calculate how many bags of mulch you need for the 15 x 15 garden by setting up the following proportion 3.5/10 = X/15. explain clearly why or why not. If the answer is no is there another proportion that you could set up? it may help you to make drawings of the Gardens
Answer:
Step-by-step explanation:
This question can be solved using a rule of three.
For each configuration, we need the perimeter and the amount of bags of mulch.
For a square of side s, the perimeter is P = 4s
If the 10 x 10 garden took 3 1/2 bags of mulch:
10x10 means that s = 10.
So the perimeter is:
P = 4*10 = 40
The number of bags of mulch is:
3 1/2 = 3 + (1/2) = 3 + 0.5 = 3.5
15 x 15 garden
15x15 means that s = 15.
The perimeter is: P = 4*s = 4*15 = 60.
The number of bags is X.
Now applying the rule of three:
With the number of bags and the perimeter.
3.5 bags - 40'
X bags - 60'
Now we apply cross multiplication:
[tex]undefined[/tex]What is the amplitude of the graph g(x)=f(x)+2 Where f(x)=cos x
In the cosine equation
[tex]y=AcosB(x-C)+D[/tex]A is the amplitude
B is using it to find the period
C is the phase shift
D is the vertical shift
Since the given function is
[tex]g(x)=cos(x)+2[/tex]A = 1
B = 1
C = 0
D = 2
The amplitude is 1
The answer is 1
Santa worked 3.5 hours, 6.9 hours, & 4.3 hours in the last three days. If he earns $7.1 an hour, how much did he earn in the last three days?
ANSWER:
$104.37
STEP-BY-STEP EXPLANATION:
To calculate the total profit, we must add the amount he earned each day, multiplying the salary by the number of hours, like this:
[tex]\begin{gathered} e=3.5\cdot7.1+6.9\cdot7.1+4.3\cdot7.1 \\ e=24.85+48.99+30.53 \\ e=104.37 \end{gathered}[/tex]Therefore, he earned in the last three days a total of $104.37
Find the interval in which the following quadratic is decreasing.
The quadratic is decreasing in the interval in which the y values decrease with the increase in x values.
In the interval, (-∞, 0), the y values decrease with increase in x values.
Hence, the quadratic is decreasing in the interval (-∞, 0),
1 pur Una foto de 4 pulgadas por 6 pulgadas se coloca en un marco de imagen con un borde de ancho constante. Si el área del marco, incluida la imagen, es de 80 pulgadas cuadradas, ¿qué ecuación podría usarse para determinar el ancho del borde, x? *
Tenemos una foto de 4 x 6 pulgadas.
Tenemos un marco con borde de ancho constante, lo que significa que alrededor de la foto siempre tenemos un "espesor" constante, que llamaremos "e".
También sabemos que el area total del marco es 80 pulgadas cuadradas.
Podemos dibujar esto así:
El marco tiene un ancho total de 4+2e y un largo de 6+2e.
Entonces, podemos calcular el espesor "e" a partir de calcular el area del marco e igualarlo a 80 pulgadas cuadradas. El area del marco sera igual al ancho por el largo:
[tex]\begin{gathered} A=(4+2e)(6+2e)=80 \\ 4\cdot6+4\cdot2e+2e\cdot6+2e\cdot2e=80 \\ 24+8e+12e+4e^2=80 \\ 4e^2+20e-56=0 \\ 4(e^2+5e-14)=0 \\ e^2+5e-14=0 \end{gathered}[/tex]Debemos aplicar la ecuación cuadrática para calcular e:
[tex]\begin{gathered} e=-\frac{b}{2a}\pm\frac{\sqrt[]{b^2-4ac}}{2a} \\ e=-\frac{5}{2}\pm\frac{\sqrt[]{5^2-4\cdot1\cdot(-14)}}{2} \\ e=-\frac{5}{2}\pm\frac{\sqrt[]{25+56}}{2} \\ e=-\frac{5}{2}\pm\frac{\sqrt[]{81}}{2} \\ e=-\frac{5}{2}\pm\frac{9}{2} \\ e_1=-\frac{5}{2}-\frac{9}{2}=-\frac{14}{2}=-7 \\ e_2=-\frac{5}{2}+\frac{9}{2}=\frac{4}{2}=2 \end{gathered}[/tex]e=-7 no es una solución válida, ya que el espesor debe ser positivo.
Entonces, la solución es e=2.
Respuesta: el ancho del borde es 2 pulgadas.
Exercise 2 Find a formula for Y in terms of X
Given:
y is inversely proportional to square of x.
The equation is written as,
[tex]\begin{gathered} y\propto\frac{1}{x^2} \\ y=\frac{c}{x^2}\ldots\ldots\ldots c\text{ is constant} \end{gathered}[/tex]Also y = 0.25 when x = 5.
[tex]\begin{gathered} y=\frac{c}{x^2} \\ 0.25=\frac{c}{5^2} \\ 25\times0.25=c \\ c=\frac{25}{4} \end{gathered}[/tex]So, the equation of y interms of x is,
[tex]y=\frac{25}{4x^2}[/tex]When x increases,
[tex]\begin{gathered} \lim _{x\to\infty}y=\lim _{x\to\infty}(\frac{25}{4x^2}) \\ =\frac{25}{4}\lim _{x\to\infty}(\frac{1}{x^2}) \\ =0 \end{gathered}[/tex]Hence, the value of x increases then y decreases.
Convert the function p(x) = 2(x – 4)(x + 3)
Expanding the expression,
[tex]\begin{gathered} p(x)=2(x-4)(x+3) \\ \rightarrow p(x)=2(x^2+3x-4x-12) \\ \rightarrow p(x)=2(x^2-x-12) \\ \rightarrow p(x)=2x^2-2x-24 \end{gathered}[/tex]We get that:
[tex]p(x)=2x^2-2x-24[/tex]Which points are included in the solution Set of the systems of equations graphed below?
Given:
Required:
We need to find the points are included in the solution
Explanation:
Recall that the solution of the system of inequalities is the intersection region of all the solutions in the system.
The points G and F lie inside the intersection.
The points in the solution are G and F.
Final answer:
Points F and G.
$(20) = 4x^2+ 5x – 3 g(x) = 4x^3 – 3x^2 + 5 Find (f + g)(x)
The value of (f+g)(x) from the given functions is 4x³+x²+5x+2.
The given functions are f(x)=4x²+ 5x - 3 and g(x)=4x³ - 3x² + 5.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Now, (f+g)(x)=f(x)+g(x)
= 4x²+ 5x - 3+4x³ - 3x² + 5
= 4x³+4x²- 3x²+5x+5-3
= 4x³+x²+5x+2
Therefore, the value of (f+g)(x) from the given functions is 4x³+x²+5x+2.
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Suppose you are completely locked out outside of your house. You remember that you left your bedroom window, which is 12 feet above the ground, unlocked from the inside (meaning you can climb up the window if you have a ladder, which you do!). You go to your garage, grab the 20 ft ladder and place it so that it reaches exactly to your bedroom window. What is the angle of elevation needed to reach your window? How far away will the bottom of the ladder be from your house?
A diagram of the situation is shown below:
In order to determine the angle of elevation x, use the sine function, as follow:
sin x = opposite side/hypotenuse
the opposite side is the distance from the ground to the wi
the diagonal of a rectangular swimming pool measures 19 yd if the length of the pool is 15 yd which measurement is closest to the width of the pool?
Answer:
11.67 yards
Explanation:
From the above figure, we can use the Pythagorean theorem to find the width of the pool as shown below;
[tex]\begin{gathered} 19^2=15^2+w^2 \\ 361=225+w^2 \\ 361-225=w^2 \\ 136=w^2 \\ \sqrt[]{136}=w \\ \therefore w=11.67\text{ yards} \end{gathered}[/tex]what is the area if one of the triangular side of the figure?
Compound Shape
The shape of the figure attached consists on four triangles and one square.
The base of each triangle is B=12 cm and the height is H=10 cm, thus the area is:
[tex]A_t=\frac{BH}{2}[/tex]Calculating:
[tex]A_t=\frac{12\cdot10}{2}=60[/tex]The area of each triangle is 60 square cm.
Now for the square of a side length of L=12.
The area of a square of side length a, is:
[tex]A_s=a^2[/tex]Calculate the area of the square:
[tex]A_s=12^2=144[/tex]The total surface area is:
A = 60*4 + 144
A= 240 + 144
A = 384 square cm
Use the number line to video to find two other solutions to the inequality 7 + m < 20.
Answer:
m = 2 and m = 3
Explanation:
To find the solutions to the inequality, we need to isolate m. So, we can subtract 7 from both sides as:
7 + m < 20
7 + m - 7 < 20 - 7
m < 13
Therefore, any number that is less than 13, is a solution of the inequality.
For example: 2 and 3 are solutions of the inequality.
Hey everybody! Can somebody help me solve this problem? I don't need a big explanation just the answer and a brief explanation on how you get it! Look at photo for problem.
Given the ordered pairs:
(-12, -16), (-3, -4), (0, 0), (9, 12)
Let's say that the first coordinate corresponds to x, and the second one corresponds to y. Then, the constant of variation k relates x and y as:
[tex]y=k\cdot x[/tex]Using the ordered pairs:
[tex]\begin{gathered} -16=-12k\Rightarrow k=\frac{4}{3} \\ -4=-3k\Rightarrow k=\frac{4}{3} \\ 0=0\cdot k\text{ (this means that it is correct)} \\ 12=9k\Rightarrow k=\frac{4}{3} \end{gathered}[/tex]We conclude that the constant of variation is:
[tex]k=\frac{4}{3}[/tex]