Answer:
C. y = 45.6 in
Step-by-step explanation:
Given equation:
[tex]y=\dfrac{2}{5}x-60[/tex]
where:
y is the depth of the water (in inches).x is the distance a guest lands away from the far wall (in inches).If a guest lands 36 inches from the wall, then x = 36.
Substitute x = 36 into the equation:
[tex]\implies y=\dfrac{2}{5}(36)-60[/tex]
[tex]\implies y=\dfrac{2 \cdot 36}{5}-60[/tex]
[tex]\implies y=\dfrac{72}{5}-60[/tex]
[tex]\implies y=14.4-60[/tex]
[tex]\implies y=-45.6[/tex]
Therefore, the depth of the water is 45.6 inches (since -45.6 inches means it is that distance below the surface).
Jackson’s motorcycle gets 28 kilometers per liter. He drives 336 kilometers and gas is $1.43 per liter. Complete parts (a) and (b) below.
(A) how much does the gas used for the trip cost?
-round to the nearest cent as needed-
(B) how many miles per gallon does Jackson’s motorcycle get?
-round to the nearest cent as needed-
The gas for the Trip cost is $8.39
The amount of gas motorcycle needed is 12 Liter of gas.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Jackson’s motorcycle gets 28 kilometers per liter.
He drives 336 kilometers and gas is $1.43 per liter.
The amount of gas motorcycle needed
= 336/28
= 12 Liter of gas
and, The gas for the Trip cost = 12/1.43
= $8.39
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A scientist polls 40 people, asking if they would participate in a study. 55% say yes. How many people said yes
Answer:
22 people
Step-by-step explanation:
First, let's convert the percentage into a decimal so we can multiply the two.
55% = 0.55
Next, we'll multiply 40 times 0.55. This is so we can find the amount of people who said yes. (55% of people said yes.)
0.55*40 = 22
22 people said yes.
I need help please help me
Answer:
GM = 18
Step-by-step explanation:
JK = KL = 2
GJ = LM =7
GM = 7+2+2+7 = 18!
So the answer it is 18.
What are the steps to answer this question 5x60=5xtens
Answer: 12
Step-by-step explanation:
1 2
5 ⟌ 6 0
- 5
1 0
- 1 0
0
The radius of a cone is 2.5 units. The volume of the cone is 19 cubic units
The formula for the volume of a cone is given by the following equation:
V = 1/3 * π * r2 * h
where V is the volume of the cone, r is the radius of the cone, and h is the height of the cone.
In this case, we are given that the radius of the cone is 2.5 units and the volume of the cone is 19 cubic units. We can use this information to complete the expression that represents the height of the cone as follows:
V = 1/3 * π * r2 * h
19 cubic units = 1/3 * π * 2.5 units2 * h
19 cubic units = 1/3 * π * 6.25 units2 * h
19 cubic units = 1/3 * 19.63 units2 * h
19 cubic units = 6.54 units2 * h
h = 19 cubic units / 6.54 units2
h = 2.9 cubic units / 6.54 units
Therefore, the expression that represents the height of the cone is 2.9 cubic units / 6.54 units.
Owen went to Best Buy to purchase a new laptop. He put a down payment of $200 and will pay $75 each month until he pays it off. Use the
formula p= 200 + 75c to identify which statement below is false.
The ‘p’ is represented as the dependent variable
The ‘c’ represents the number of months
The independent variable is 75
The ‘c’ is represented as the independent variable
Owen went to Best Buy to purchase a new laptop. He put a down payment of $200 and will pay $75 each month until he pays it off. Use the
formula p= 200 + 75c to identify which statement below is false.
The ‘p’ is represented as the dependent variable [true]
The ‘c’ represents the number of months [true]
The independent variable is 75 [FALSE]
The ‘c’ is represented as the independent variable [true]
Evaluate
15 ÷ (3+1/3) ²
Answer:
[tex]\dfrac{27}{20}[/tex]
Step-by-step explanation:
First, convert both numbers into fractions:
[tex]\dfrac{15}{1} \div \left(\dfrac{10}{3}\right)^2[/tex]
Then, apply the exponent of the second fraction in parentheses to its numerator and denominator.
[tex]\dfrac{15}{1} \div \left(\dfrac{10^2}{3^2}\right)[/tex]
[tex]\dfrac{15}{1} \div \dfrac{100}{9}[/tex]
Finally, multiply the first fraction by the reciprocal of the second fraction.
(Skip, Flip, Multiply)
[tex]\dfrac{15}{1} \times \dfrac{9}{100}[/tex]
[tex]\dfrac{135}{100}[/tex]
And simplify.
[tex]\dfrac{135 \div 5}{100 \div 5}[/tex]
[tex]\dfrac{27}{20}[/tex]
Is (x + 7) a factor of f(x) = x3 − 3x2 + 2x − 8? Explain your reasoning.
X + 7 is not a factor of [tex]x^{3}[/tex] -3[tex]x^{2}[/tex] +2x -8 because it gives a remainder when x + 7 divides it.
What is a remainder?The remainder is the portion of the dividend that cannot be fairly divided by the divisor. After dividing whole numbers to find the quotient, the part that is left is called the remainder.
to know if x + 7 is a factor, x = -7 when substituted should give 0 as a remainder otherwise it is not a factor.
By substituting x = -7 we have
[tex](-7)^{3}[/tex] [tex]-3(-7)^{2}[/tex] +2(-7) - 8 = -343 -147 -14 - 8 which is -512
Therefore x + 7 is not a factor of the function.
In conclusion x + 7 is not a factor of [tex]x^{3}[/tex] -3[tex]x^{2}[/tex] +2x -8
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Answer:
What he said!
Step-by-step explanation:
help meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeee
Answer:
t = 11.7
Step-by-step explanation:
r
A = P (1 + -------)^(nt)
n
A = 5000 = (2500 × 2)
P = 2500
n = 2
t = ?
0.06
5000 = 2500 (1 + ----------)^(2)(t)
2
0.06
5000 = 2500 (1 + ----------)^(2)(t)
÷2500 ÷2500 2
0.06
2 = (1 + ----------)^(2)(t)
2
0.06
log₁₀ 2 = log₁₀ (1 + ----------)^(2)(t)
2
0.06
log₁₀ 2 = 2t × log₁₀ (1 + ----------)
2
0.06 0.06
÷ log₁₀ (1 + ----------) ÷ log₁₀ (1 + ----------)
2 2
log₁₀ 2
----------------------------- = 2t
0.06
log₁₀ (1 + -------- )
2
log₁₀ 2
(1/2) ----------------------------- = 2t (1/2)
0.06
log₁₀ (1 + -------- )
2
(1/2) 23.44977225 = 2t (1/2)
11.72488613 = t
11.7 ≈ t
I hope this helps!
Solve 4x - 3 = 17
x = ?…
Answer: x=5
Step-by-step explanation:
4x-3=17 Add three to both sides
4x=20 Divide both side by 4 to isolate x
x=5
30+ w =150 what does w equal?
Alang is going to invest in an account paying an interest rate of 5.7% compounded
continuously. How much would Alang need to invest, to the nearest dollar, for the
value of the account to reach $113,000 in 5 years?
The investment amount is $37263.09.
What is continuous compound interest?Interest that compounded continuously to the principal amount. This interest rate provides exponential growth to period of time.
Formula of continuous compound interest rate;
P(t) = P₀ [tex]e^{rt}[/tex] , where P₀ is the principal amount, r is the interest rate and t is the time period.
Given that the Alang is going to invest with the continuous compound interest rate 5.7%.
Using the formula of continuous compound interest rate,
P(t) = P₀ [tex]e^{rt}[/tex]
P(t) = $113000 x [tex]e^{(5.7)(5)}[/tex]
P(t) = $37263.09
Therefore, the investment amount is $37263.09.
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what is [tex]\sqrt{49}[/tex]
Answer:7
Step-by-step explanation:
What it is asking you is what multiplied by it self gets you to 49. the answer would be 7 because 7*7=49
The area of the smaller regular pentagon is about 27.5 cm².
What is the best approximation for the area of the larger regular pentagon?
11cm²
172 cm²
70 cm²
275 cm²
Answer:172 cm²
Step-by-step explanation:
when we use the formula, and we can solve out is like 172.05 and round to tenth and will have the answer
Formula is 1/2 × p × a
Rewrite in simplest terms:
−
6
(
6
p
−
9
)
−
10
p
−6(6p−9)−10p
Answer:
Step-by-step explanation:
6(6p-9)-10p-6(6p-9)-10p
36p-54-10p-36p+54-10p
36p-36p-54+54-10p= -10p
11. Ms. Still is ordering pizza and breadsticks for a school pizza party and has a budget of no more than
$91. An order of breadsticks, x, costs $7 and a pepperoni pizza, y, costs $13.
a. Write a linear inequality that describes the situation.
b. Graph the situation. Label the axes.
c. Is (5, 5, 4) a solution to the inequality? Does this oved pair make sense for this situation? Explain.
The inequality that represents the situation given will be
7x + 13y ≤ 91.
What is inequality?
An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
The inequality that represents the situation given will be 7x + 13y ≤ 91.
From the information given, Crawford is ordering pizzas and breadsticks for a school pizza party and has a budget of $91, but no more and an order of breadsticks costs $7 while a pepperoni pizza costs $13.
Therefore, the inequality that represents the situation given will be
7x + 13y ≤ 91.
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If a certain electromagnetic wave has a wavelength of 100m, what type of electromagnetic wave is it?
Answer: Radio
Step-by-step explanation:
An electromagnet wave with a wavelength of 100m is a Radio. These signals are invisible to the human eye, humans are only able to detect visible light.
What must be a factor of the polynomial function f(x) graphed on the coordinate plane below? On a coordinate plane, a parabola opens up. It goes through (0, 3), has a vertex at (3.5, 3), and goes through (6, 0). Group of answer choices x – 3 x + 1 x – 1 x + 3
The answer choice which must be a factor of the polynomial in discuss is; (x - 1).
What must be a factor of the polynomial as described?It follows from the vertex form equation of a parabola; f(x) = a ( x - h )² + k where the vertex of the parabola is; (h, k).
Therefore, the equation of the parabola in discuss is;
f(x) = a (x - 3.5)² + 3.
Recall that the x coordinates of the vertex, h is given by; h = (p + q) / 2
where p and q are the zeroes of the quadratic function.
Therefore, since one of the zeroes is given as; 6 ( from (6, 0) ); it follows that the second zero can be determined as follows;
3.5 = ( 6 + q ) / 2
7 = 6 + q
q = 1
Therefore, since the second zero is; 1. It follows that the associated factor as required is; ( x - 1 ).
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f(x)=1/2x+8 reflect x axis
The function of reflect x-axis is g(x) = -(1/2)*x - 8, according to the question.
What do you mean by function?
A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
According to the given question,
First, let's define a reflection over the x-axis.
If we have a point (x, y) and we reflect it over the x-axis, our new point will be (x, -y).
Now, when we have a function
f(x) = y, the points can be written as:
(x, y = f(x) ) = (x, f(x))
Then, after the reflection over the x-axis, we have:
(x, y = g(x)) = (x, -f(x))
So now we have g(x) = -f(x)
and we know that f(x) = (1/2)*x + 8
then our new function is g(x) = y = -f(x) = -( (1/2)*x + 8) = -(1/2)*x - 8.
g(x) = -(1/2)*x - 8.
Therefore, the required answer is g(x) = -(1/2)*x - 8.
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how much does a basket of apples weigh
Answer:
42-48 pound" number.
Step-by-step explanation:
The variables a, b, c, and d are graphed on the number line shown.
Use the number you answer the questions in the chart
The correct values are;
⇒ a - d = - 2
⇒ c - a = 7
⇒ b - c = - 8
⇒ d - c = - 5
What is Number line?
Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.
Given that;
The number line is shown in figure.
The values are,
a = - 3
b = - 4
c = 4
d = - 1
Now,
All the values are find as;
⇒ a - d = - 3 - (- 1)
= - 3 + 1
= - 2
⇒ c - a = 4 - (-3)
= 4 + 3
= 7
⇒ b - c = - 4 - 4
= - 8
⇒ d - c = - 1 - 4
= - 5
Thus, The correct values are;
⇒ a - d = - 2
⇒ c - a = 7
⇒ b - c = - 8
⇒ d - c = - 5
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A bakery can make 640 bagels in 4 hours how many can it make in 8 hours and 6 hours.PLEASE HURRY UP THIS IS DUE IN 10 MINUTES <3333
Hello!
What does this problem want:
how many bagels in 8 hourshow many bagels in 6 hoursWhat we need to find: rate of bagels made per hour
[tex]\text{Rate}=\frac{\text{Total number of bagels}}{\text{Number of hours}} =\frac{640}{4} =160 \text{ bagels per hour}[/tex]
Thus
how many bagels in 8 hours8 * 160 = 1280 bagels
how many bagels in 6 hours6 * 160 = 960 bagels
Hope that helps!
Realice los siguientes ejercicios de lenguaje algebraico
Considerando que Soraya tiene x naranjas
Considerando que y es la edad de José.
Las expresiones algebraicas que completan la tabla son 200+x, 2(200+x), 650+ 2(200+x), y -5, y+ 10, y+8, 75- y
¿Qué es el lenguage algebraico?El lenguaje algebraico es simbólico es decir se expresa mediante consonantes o vocales, el lenguaje algebraico nos permite expresar de manera sencilla y practica el valor desconocido de una determinada cantidad.
¿Cómo se expresan los enunciados dados?A partir de la información dada es decir "x" naranjas y "Y" que es la edad de José vamos a expresar las respuestas en lenguaje algebraico. Para esto se debe relacionar la x o y con el valor dado y el signo matemático correspondiente:
Luis tiene 200 naranjas mas que Soraya = 200+x
Susana tiene el doble de Luis = 2(200+x)
Juan tiene 650 naranjas mas que susana = 650+ 2(200+x)
Considerando que Y es la edad de José
Los años que tenia hace 5 años = y -5
Los años que tendrá en 10 años = y+ 10
Los años que tendrá dentro de 8 años = y+8
Los años que faltan para que cumpla 75 años = 75- y
Podemos concluir que el lenguaje algebraico nos permite representar de manera practica un valor desconocido y de igual manera obtener respuestas practicas y sencillas a partir de variables.
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I need help in this 8th grade only part B and D
a) The first term of the sequence is; ³¹/₆
b) The term to term rule is; aₙ = ³¹/₆ + (n - 1)²/₆
c) The next three terms are; ³⁷/₆, ³⁹/₆, ⁴¹/₆
d) The 10th term in the sequence is; a₁₀ = ⁴⁹/₆
How to find the nth term of a sequence?The first term of the sequence is given by the expression;
2 ÷ ¹²/₃₁ = ³¹/₆
The second term of the sequence is given by the expression;
3 ÷ ⁶/₁₁ = ³³/₆
The third term of the sequence is given by the expression;
5 ÷ ⁶/₇ = ³⁵/₆
These are the first three terms of a sequence and so the sequence is;
³¹/₆, ³³/₆, ³⁵/₆,....
d = ³³/₆ - ³¹/₆ = ²/₆
Thus, term to term rule is given by the nth term of an arithmetic progression;
aₙ = ³¹/₆ + (n - 1)²/₆
The next three terms are; ³⁷/₆, ³⁹/₆, ⁴¹/₆
The 10th term in the sequence is;
a₁₀ = ³¹/₆ + (10 - 1)²/₆
a₁₀ = ³¹/₆ + ¹⁸/₆
a₁₀ = ⁴⁹/₆
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How many real solutions does the system have ? y = - 3x - 1; y = x ^ 2 - 3x + 4
The only solution the system of the equation has is x = -1/3.
The number of solutions is one.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
The system of equations:
y = -3x - 1
y = x² - 3x + 4
The solutions of the equation.
y = 0
So,
-3x - 1 = 0
-3x = 1
x = -1/3
x² - 3x + 4 = 0
It is in the form of ax² + bx + c = 0
a = 1, b = -3, and c = 4
Now,
x = -b ± √(b² - 4ac) / 4a
x = 3 ± √(9 - 16) / 4
x = 3 ±√-7 / 4
x = 3 ±i√7 / 4
This is a complex root.
So,
These are not real solutions.
Thus,
The only solution the system of the equation has is x = -1/3.
The number of solutions is one.
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The equation of line u is y–3=7(x–5). Parallel to line u is line v, which passes through the point (1,9). What is the equation of line v?
Answer:
y - 9 = 7(x - 1)
Step-by-step explanation:
The given equation is in Point Slope Form: y - y₁ = m(x - x₁)
m is the slope, and parallel lines have the same slope (7)
x₁ and y₁ are the coordinates of a point on the line
solve 3x+1=-5 by graphing. then find the x- and y-intercepts
The graph of the equation is shown below
The x-intercept is -2
The y-intercept is undefined
Graph of linear equations and determining the interceptsFrom the question, we are to solve the equation by graphing and determine the x- and y-intercepts
The given equation is
3x + 1 = -5
To determine the x-intercepts, we will solve the equation
3x + 1 =-5
3x = -5 - 1
3x = -6
Divide both sides by 3
x = -2
Since, y is not defined in the equation, the y-intercept is undefined
The graph of the equation is shown below.
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Math Please help!!!!! Linear vs Exponential
Answer:
linearadditivelycommon differenceabout 240.12Step-by-step explanation:
Given the values in the table, you want to know if they represent a linear or exponential relation, along with the common difference or ratio, as applicable.
ChangesThe first attachment shows the differences and ratios between successive table values. Neither the differences nor the ratios are constant. The wide variation in ratios and the relatively smaller variation in differences suggests the table is best modeled by a linear function.
Changes when the function is linear are additive. That is, the function values have a common difference.
Common differenceThe average difference between table values is (949.92 -229.44)/3 = 240.16. A linear regression analysis gives a slope of 240.12 as the "best fit" to the table values.
You can see from the first attachment that the differences are not constant, so there isn't really a common difference. The difference is approximately 240.12.
__
Additional comment
The second attachment shows linear and an exponential regression applied to this data. The residuals are much smaller for the linear approximation.
The slope of the line (common difference) is estimated at 240.12 using the regression formula. This makes the mean square residuals a minimum. As we show above, this slope is different (slightly lower) than the slope of the line through the first and last data points.
What number represents 3,675,100,608 rounded to the nearest million?
The number 3,675,000,000 represents 3,675,100,608 rounded off to the nearest million.
Rounding off large numbers.When we round off large numbers, we consider the digit to the right of the number occupying the place value for which we are rounding off to. If the digit to the right is 4 or less, we round down (we leave the number we are rounding to), but if the digit is 5 or higher, we round up (we increase the digit we are rounding by 1). and thus round to the indicated place value.
From the question, we have the large number;
3,675,100,608
the digit 5 indicates the place value (million)
and the digit 1 is to the right and will be rounded down.
Therefore, the number 3,675,000,000 represents 3,675,100,608, rounded to the nearest million.
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The selling price for a classic speedboat is $12,000, which is $2500 less than two times its original price. What was the original price of the speedboat?
Answer: 29000
Step-by-step explanation:
12000 + 2500 = 14500
14500 * 2 = 29000