----------------------------------------------------------------------------------------------------------------
(a)(i)
To evaluate f(4), we take the functional value at x = 4.
Looking at the graph, it is:
At x = 4, y = 2 [counting units]
Thus,
[tex]f(4)=2[/tex](a)(ii)To evaluate f(-3), we take the functional value at x = -3.
Looking at the graph, it is:
At x = -3, y = -5 [counting units]
Thus,
[tex]f(-3)=-5[/tex](b)The zeros are the x-intercepts of a graph. Looking at the graph, the x-axis cutting points are:
Zeros
[tex]x=2,x=-5[/tex](c)The function f(x) is increasing where the slope of the graph is positive.
Looking at the graph, the increasing part is from x = -3 to x = 5.
That is
- 3 < x < 5
The correct choice is (2).
(d)The relative minimum is the lowest point of the graph shown and the relative maximum is the highest point of the graph.
Looking at the graph,
The lowest point occurs at --- (-3, -5)
The highest point occurs at --- (-7, 5)
So,
Relative Maximum: (-7, 5)
Relative Minimum: (-3, -5)
(e)We want the interval in which f(x) < 0.
This means where the function is less than zero, or below the x-axis.
Looking at the graph,
from x = -5 to x = 2, the graph of f(x) is below the x-axis.
That is -5 < x < 2.
The correct choice is (3).
(f)A new function --
[tex]g(x)=2f(x)+5[/tex]Let's evaluate g(0) by using the formula:
[tex]g(0)=2f(0)+5[/tex]From the graph, f(0) = -2, thus,
g(0) = 2(-2) + 5
g(0) = -4 + 5
g(0) = 1
This means that the functional value of 'g' is 1 at x = 0.
(g)
A new function --
[tex]h(x)=x^3-3[/tex]We need to find g(h(2)). Let's boil it down to the function f(x).
[tex]\begin{gathered} h(x)=x^3-3 \\ h(2)=2^3-3 \\ \therefore h(2)=5 \\ \text{Now, we need g(5).} \\ g(x)=2f(x)+5 \\ g(5)=2f(5)+5 \\ g(5)=2(3)+5 \\ g(5)=6+5 \\ g(5)=11 \\ \text{ Final answer:} \\ g(h(2))=11 \end{gathered}[/tex]Thus, the answer is:
[tex]g(h(2))=11[/tex]Spencer went to the county fair and spent his money only on ride tickets and fair admission. He bought 17 tickets for the rides and spent a total of $30.75 at a county fair. The county fair charges $1.25 per ticket for the rides and the price of the fair admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets. (a) Write a linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission. (b) Explain your answer to Part 1a.
The linear equation y = 1.25x + 9.5 can be used to determine the cost for anyone who only pays for ride tickets and fair admission.
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.
It is given that:
Spencer bought 17 tickets for the rides and spent a total of $30.75 at a county fair.
Let x be the number of tickets and y be the total cost:
Total ticket cost = 17×1.25 = $21.25
Admission fari = 30.75 - 21.25 = $9.5
The linear equation is:
y = 1.25x + 9.5
Here 9.5 represents the fixed admission fair.
Thus, the linear equation y = 1.25x + 9.5 can be used to determine the cost for anyone who only pays for ride tickets and fair admission.
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Solve the inequality and express your answer in intervalvenation use decimal form for numeric values
Given:
[tex]\frac{20}{4}<\frac{z+7}{2}<\frac{25}{4}[/tex]Required :
To solve this
Explanation:
[tex]\begin{gathered} first\text{ of all separate compound inequalities into system of inequalities} \\ \\ \frac{z+7}{2}>\frac{20}{4}\text{ }\frac{z+7}{2}<\frac{25}{4} \\ \\ reduce\text{ the fraction} \\ \\ \frac{z+7}{2}>5\text{ or z+7>2}\times5 \\ \\ z+7>10 \\ \\ z>10-7 \\ \\ z>3 \end{gathered}[/tex][tex]\begin{gathered} \frac{z+7}{2}<\frac{25}{4} \\ \\ multiply\text{ both sides of the inequality by the least common denominator} \\ \\ 4\times\frac{z+7}{2}<4\times\frac{25}{4} \\ \\ reduce\text{ the expression to the lowest term} \\ \\ 2(z+7)<25 \\ \\ 2z+14<25 \\ \\ 2z<25-14 \\ \\ z<\frac{11}{2} \end{gathered}[/tex][tex]\begin{gathered} z>3\text{ and z <}\frac{11}{2} \\ \\ 3Required answer:3
Part A: At a fair, Derrick used a total of 16 tickets to ride the roller coaster 4 times and the bumper cars 2 times. Javier used a total of 12 tickets to ride the roller coaster 2 times and the bumper cars 3 times. Let x represent the number of tickets it takes to ride a roller coaster. Let y represent the number of tickets it takes to ride the bumper cars. Model Derrick and Javier's trip to the fair by creating linear equations to represent how Derrick and Javier each used their ride tickets. 4 X + y = Derrick: Javier: X + Blank 1: 4 Blank 2: Blank 3: Blank 4:
x: number of tickets it takes to ride a roller coaster
y: number of tickets it takes to ride the bumper cars
Derrick used a total of 16 tickets to ride the roller coaster 4 times and the bumper cars 2 times, that is,
4x + 2y = 16
Javier used a total of 12 tickets to ride the roller coaster 2 times and the bumper cars 3 times, that is,
2x + 3y = 12
I would like to this math sentence question that I will send a picture of
Let
x -----> number of hours
we have that
the inequality that represents this situation is
[tex]45-12t\ge9[/tex]solve for t
[tex]\begin{gathered} -12t\ge9-45 \\ -12t\ge-36 \\ t\leq3 \end{gathered}[/tex]that means
the bakery can sell bread for a timeless than or equal to 3 hours
Graph the image of the figure on the right under the given translation.T(3,2)(x,y)
To translate the triangle we will translate each vertex using the rule of translation given
The vertice of the triangle are
(-1, 4), (-5, -2), (-8, 2)
The translation rule is T (3, 2)
That means we will add the x-coordinate of each point by 3,
and the y-coordinates by 2
The image of point (-1, 4) = (-1 + 3, 4 + 2) = (2, 6)
The image of point (-5, -2) = (-5 + 3, -2 + 2) = (-2, 0)
The image of point (-8, 2) = (-8 + 3, 2 + 2) = (-5, 4)
That means the triangle will move 3 units right and 2 units up
The images of the vertices are (2, 6), (-2, 0), (-5, 4)
identify which value is not in the domain of the piecewise function
From the graph we notice that the only value of x for which the fuction generating the graph it not defined is x=-3.
Answer: A).
Opens down with compression coefficient of 0.2. Shifted right 1 unit and down 6 unitshow do I right this as a parabola equation?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
opens down
compression coefficient = 0.2
translated:
right 1
down 6
parabola equation = ?
Step 02:
opens down
(x - h)² = -4p (y - k)
compression coefficient = 0.2
0.2 (x - h)² = -4p (y - k)
translated:
right 1
down 6
0.2 (x - 1)² = -4p (y + 6)
The answer is:
0.2 (x - 1)² = -4p (y + 6)
a1.Find the equation for a polynomial f(x) that satisfies the following:Degree 5Root of multiplicity 1 at x = 3• Root of multiplicity 2 at x = 2• Root of multiplicity 2 at x = -3y-intercept of (0, -216)f(x) =
we have that
the polynomial is of the form
f(x)=a(x-3)(x-2)^2(x+3)^2
where
a is the leading coefficient
y-intercept -----> (0,-216)
For x=0
substitute and solve for a
-216=a(0-3)(0-2)^2)(0+3)^2
-216=a(-3)(-2)^2(3)^2
-216=a(-3)(4)(9)
-216=-108a
a=2
therefore
[tex]f(x)=2(x-3)(x-2)^2(x+3)^2[/tex]Which of the following inequalities is false?
A: 10 < 9 incorrect answer
B: 9 < 10 incorrect answer
C: 10 > 9 incorrect answer
D: 9 (is less than or equal to)
The inequalities 9 < 10 incorrect answer and 10 > 9 incorrect answer are false. Option (B) and Option (C) are false.
Before we determine the false statement, we must understand that all negative values are less than positive values and all positive values are greater than negative values,
For the inequality 10 < 9 incorrect answer
Since, it is given that 10 is less than 9 is incorrect answer and we know that 10 is greater than 9 . Therefore, this inequality is true.
For the inequality 9 < 10 incorrect answer
Since, it is given that 9 is less than 10 is incorrect answer but we know that 9 is less than 10. Therefore, this inequality is false.
For the inequality 10 > 9 incorrect answer
Since, it is given that 10 is greater than 9 is incorrect answer but we know that 10 is greater than 9 . Therefore, this inequality is false.
For the inequality 9 (is less than or equal to) 10 incorrect answer
Since, it is given that 9 (is less than or equal to) 10 is incorrect answer and we know that 9 is less than 10. Therefore, this inequality is true.
Therefore, Option (B) and Option (C) are false.
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which statements are true about points A,B, and C check all that applyA. the coordinates of point a are (3, -3)B. the coordinates of point B (1, -3)C. the coordinates of Point C are (-2,2)D. Point C is the closest to the Y axisE. points A and B are the same distance from the y-axisIk the pic is blurry sorry
By the graph, we can see that the only statement that apply is B. the coordinates of point B is (1, -3).
Your company fireworks show is getting bigger, The boss has requested that the viewing area (which is 4 ft x 6 ft) be doubled; the parking area (which is 540 ft x 75 ft) be doubled; and the city ordinance requires the fireworks to be in the air less than 4 seconds and not go any higher than 600 feet.
Answer the following questions:
1. Determine the dimensions of the new viewing area. The existing area is 6 ft long by 4 ft wide.
2. Determine the dimensions of the new parking area. The existing area is 540 ft long by 75 feet wide.
3. Determine the height of the fireworks and how long they are in the air using the following equation:
ℎ= −500/9 t^2 + 1000/3 t + 10
The solution to the questions are
New viewing area dimension: 8 ft by 12 ftNew parking area dimension: 1080 ft by 150 ftHeight of fireworks: 510 unitsThe dimension of the new viewing areaFrom the question, we have the following parameters:
Initial dimension of the viewing area:
4 ft by 6 ft
The scale of dilation is given as
Scale = 2 (i.e. doubled)
Using the above as a guide, the new dimensions are calculated using
New = Old * Scale
So, we have
New = (4 ft by 6 ft) x 2
Evaluate
New = 8 ft by 12 ft
The dimension of the new parking areaThe given parameters are
Initial dimension of the parking area:
540 ft by 75 ft
We use the same scale factor as (a) i.e.
Scale = 2 (i.e. doubled)
Using the above as a guide, the new dimensions are calculated using
New = Old * Scale
So, we have
New = (540 ft by 75 ft) x 2
Evaluate
New = 1080 ft by 150 ft
The height of fireworksThe function is given as
ℎ= −500/9 t^2 + 1000/3 t + 10
Differentiate the function
So, we have
ℎ'= −1000/9 t + 1000/3
Set the differentiated function to 0
So, we have
−1000/9 t + 1000/3 = 0
This gives
1000/9 t = 1000/3
Multiply both sides by 9/1000
t = 3
Substitute 3 for t in ℎ= −500/9 t^2 + 1000/3 t + 10
ℎ = −500/9 x 3^2 + 1000/3 x 3 + 10
Evaluate
ℎ = 510
Hence, the height is 510 units
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Question 2 of 5
Which of the following is not an expression?
A. + 1 = 4
B. 3 - 2x
C. 4x+7
D. x/3 - 1
Answer:
A.
Step-by-step explanation:
The answer is A, because an expression does not have an equal sign.
I need to show you a pic of the question
The y-intercept and the x-intercept are the various points on the y and x axes where the graph cuts through.
In this our graph, there are interceptions at y = 0.4 and x = 0.3.
Thus, y-intercept exists at (0, 0.4) and x intercept at (0.3, 0)
I need help with Slopes!
we know that
To find out the slope of the line, we use the formula
[tex]m=\frac{y2-y1}{x2-x1}[/tex]we need two points
Looking at the graph
we take the points
(1,3 ) and (2,5)
substitute in the formula above
[tex]\begin{gathered} m=\frac{5-3}{2-1} \\ m=\frac{2}{1} \\ m=2 \end{gathered}[/tex]therefore
the slope of the line is 2While visiting Yosemite National Forrest, Joe approximated the angle of elevation to the top of a hill to be 25 degrees. After walking 350 ft closer, he guessed that the angle of elevation had increased by 14 degrees. Approximately how tall is the hill?A. 475 feetB. 385 feetC. 608 feetD. 202 feet
The line sketch of the movement and positioning of Joe and the hill are shown below.
Brief description of the sketch made.
From the sketch, point A is where Joe started from heading towards the hill.
The hill is represented by BC and the height is h
25 degrees was the initial angle of elevation.
After moving 350 ft closer to the hill, the angle of elevation increased by 14 degrees to 25 + 14 = 39 degrees.
From triangle BCD,
Using the trigonometric function of tan,
[tex]\begin{gathered} \tan =\frac{opposite}{\text{adjacent}} \\ \tan 39=\frac{h}{x} \\ 0.8098=\frac{h}{x} \\ \text{Making h subject of the formula,} \\ h=0.8098x \end{gathered}[/tex]From triangle ABC,
Using the trigonometric function of tan,
[tex]\begin{gathered} \tan =\frac{opposite}{\text{adjacent}} \\ \tan 25=\frac{h}{350+x} \\ \text{Substituting the value of h gotten from the previous triangle,} \\ \tan 25=\frac{0.8098x}{350+x} \\ 0.4663=\frac{0.8098x}{350+x} \\ C\text{ ross multiplying,} \\ 0.4663(350+x)=0.8098x \\ 163.205+0.4663x=0.8098x \\ C\text{ ollecting the like terms,} \\ 163.205=0.8098x-0.4663x \\ 163.205=0.3435x \\ \text{Dividing both sides by 0.3435 to get x,} \\ x=\frac{163.205}{0.3435} \\ x=475.124ft \\ \\ \text{The height, h of the hill is;} \\ h=0.8098x \\ h=0.8098\times475.124 \\ h=384.755ft \\ h\approx385ft \end{gathered}[/tex]Therefore, the height of the hill is 385 feet
The correct answer is option B.
Calculate each value requested for the following set of scores.a. ΣΧ=b. ΣΧ2=c. (ΣΧ)2=d. SS=Scores: 2, 3, 0,5Round to the hundredths place.
a.
[tex]\Sigma x=2+3+0+5=5+5=10[/tex]b.
[tex]\Sigma x^2=2^2+3^2+0^2+5^2=4+9+25=38[/tex]c.
[tex](\Sigma x)^2=(2+3+0+5)^2=10^2=100[/tex]d.
[tex]\begin{gathered} SS=\Sigma(x-\bar{x})^2 \\ where: \\ \bar{x}=\frac{2+3+0+5}{4}=\frac{10}{4}=2.5 \\ so: \\ SS=(2-2.5)^2+(3-2.5)^2+(0-2.5)^2+(5-2.5)^2 \\ SS=(-0.5)^2+(0.5)^2+(-2.5)^2+(2.5)^2 \\ SS=13 \end{gathered}[/tex]clasificar el siguiente polinomio2xy +9b -4z + 9
Los polinomios se clasifican según el número de términos que lo componen.
Los términos de una expresión están separados entre sí por los signos "+" y "-"
Se conoce como "monomio" a un polinomio con un solo término.
Son ejemplos de monomios:
6x²
2x
z
Un "binomio" es un polinomio de dos terminos.
Por ejemplo:
2x-3y
4x²+1
5y⁴z-2x²
Un "trinomio" es un polinomio con tres términos.
Por ejemplo:
2x+3y+z
y²-z+7
Un "cuadrimonio" es un polinomio de cuatro términos
Por ejemplo
xy+5y-9z+4
Los polinomios también pueden clasificarse según su grado. El grado del polinomio está dado por el valor del mayor exponente.
Un polinomio de grado cero es aquel que tiene coefficientes igual a cero.
Por ejemplo
0x²+0x
Un polinomio de primmer grado es aquel en el que la variable está elevada a la uno. En general este exponente no se escribe por lo que en un polinomio grado uno las variables no van a tener exponente.
Por ejemplo
x+2
x+y+4
Un polinomio de segundo grado es aquel cuyo mayor exponente es dos, es decir, tiene un termino elevado al cuadrado.
Por ejemplo:
x²
x+y²+3
x-9y+5z²-7
Un polinomio de tercer grado es aquel cuyo mayor exponente es tres, es decir, al menos una variable está elevada al cubo.
Por ejemplo:
x
x³+y²
2x-y³+25
Teniendo estas definiciones en cuenta, puedes clasificar el polinomio:
[tex]2xy+9b-4x+9[/tex]Este polinomio tiene 4 términos, "2xy", "9b", "4x" y "9" por lo que se lo puede clasificar como un cuadrimonio.
Como puedes ver, ninguna de las variables tiene exponente, es decir que, el exponente de mayor valor es 1, por lo que se puede clasificar como un polinomio de primer grado.
Entonces esta expresión es un cuadrimonio de primer grado
Find the minimum and maximum values of the function on the interval [11,27].
Lisa received a 70 gift card for a coffee store. She used it in buying some coffee that cost 8.49 per pound. After buying the coffee, she had 36.04 left on her card. How many pounds of coffee did she buy?
Initially she had 70 pounds in her gift card.
After buying her coffee she was left with 36.04 pounds.
Amount she spent on coffee is 70-36.04=34.96
One pound of coffee costs 8.49
To calculate how many pounds of coffee Lisa bought ->
34.96/8.49= 4
So in total she bought 4 pounds of coffee.
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Rick and Chumlee buy and sell sports collectibles. Rick bought 14 rookie cards and 13 autographed baseballs
for a total of 263 dollars. Chumlee bought 17 cards and 4 baseballs for a total of 284 dollars. Let c be the cost
of each card and let b be the cost of an autographed baseball.
a) Write an equation relating the items bought by Rick:
b) Write an equation relating the items bought by Chumlee:
c) Solve the system above using substitution and interpret in context:
The cost of a card is
dollars.
dollars and the cost of a baseball is
a) equation relating the items bought by Rick is
14c + 13 b = 263
b)equation relating the items bought by Chumlee
17c + 4b = 284
C) The cost of a card is 16
The cost of a baseball is 3
What is basic algebra ?Algebra is a branch of mathematics that helps translate real-world problems or situations into mathematical truths. It takes variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division to generate a meaningful mathematical statement. All branches of mathematics, including coordinate geometry, calculus, and trigonometry, employ algebra. A fundamental algebraic formula is 2x + 4 = 8. Algebraic expressions serve as the mathematical statement when operations like addition, subtraction, multiplication, division, etc. are done on variables and constants.
Rick and Chumlee buy and sell sports collectibles.
Let c be the cost of each card and let b be the cost of an autographed baseball.
Rick bought 14 rookie cards and 13 autographed baseballs
for a total of 263 dollars.
a) equation relating the items bought by Rick is
14c + 13 b = 263
Chumlee bought 17 cards and 4 baseballs for a total of 284 dollars.
b)equation relating the items bought by Chumlee
17c + 4b = 284
C)
14c + 13 b = 263 .....(i)
17c + 4b = 284......(ii)
[tex]b = \frac{284-17c}{4}[/tex]
put the value of b in equation 1 you will get
14c +13([tex]\frac{284 - 17c}{4}[/tex])=263
56c + 3692 - 221c = 1052
175c = 2640
c = 16
[tex]b = \frac{284-17c}{4}[/tex].....(iii)
put the value of c in equation 3
b = [tex]\frac{284 - 17(16)}{4}\\ = \frac{12}{4}[/tex]
= 3
The cost of a card is 16
The cost of a baseball is 3
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use the ratio to solve , how can the table help me to solve ? how do I find part? please assist me
We have to determine te 30 percent of 50.
[tex]\frac{30}{100}\times50=15[/tex]Hence the answer is 15.
3x=8y-34y+2x=5Based on the system of equations above, what is the value of x/y?
To solve the given system of equations, we can solve the first equation for x, then we combine the equations
[tex]\begin{gathered} 3x=8y-3 \\ x=\frac{8y-3}{3} \end{gathered}[/tex]Then,
[tex]\begin{gathered} 4y+2x=5 \\ 4y+2(\frac{8y-3}{3})=5 \\ 4y+\frac{16y-6}{3}=5 \\ 4y+\frac{16}{3}y-2=5 \\ \frac{12y+16y}{3}=5+2 \\ \frac{28y}{3}=7 \\ 28y=7\cdot3 \\ y=\frac{21}{28} \\ y=\frac{3}{4} \end{gathered}[/tex]So, y = 21/28.
Now, we use the y-value to find x.
[tex]\begin{gathered} x=\frac{8\cdot\frac{21}{28}-3}{3}=\frac{\frac{168}{28}-3}{3}=\frac{\frac{84}{14}-3}{3}=\frac{\frac{42}{7}-3}{3} \\ x=\frac{\frac{42-21}{7}}{3}=\frac{\frac{21}{7}}{3}=\frac{3}{3}=1 \end{gathered}[/tex]Hence, the value of each variable is x = 1 and y = 3/4.please help
A bird flying over water drops a crab from a height of 10 feet. The distance
the crab is from the water as it falls can be represented by d in the equation
d equals negative t to the power of 2 end exponent plus 10, where t is time in seconds. To catch the crab as it falls, a different
bird flies along a path represented by the equation d equals 5 t plus 5. In how many
seconds will the second bird catch the crab before it hits the water?
Solving a quadratic equation we can see that the second bird catches the crab after 0.85 seconds.
In how many seconds the second bird catches the crab?
The equation that describes the height of the crab is:
d = -t^2 + 10
The equation that represents the path of the second bird is:
d' = 5t + 5
The bird will be able to catch the crab when both are at the same height, this happens when:
-t^2 + 10 = 5t + 5
We need to solve this for t.
-t^2 + 10 - 5t - 5 = 0
-t^2 - 5t + 5 = 0
Using the quadratic formula we will get:
t = (5 ± √( (-5)^2 - 4*(-1)*5))/(2*-1)
t = (5 ± 6.7)/(-2)
We only care for the positive solution, which is:
t = (5 - 6.7)/(-2) = 0.85
So the bird catches the crab after 0.85 seconds.
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Use the properties of logarithms to write the following expression as a single term that doesn't contain a logarithm.e6-8ln(x)+In(y)
Given:
The expression is,
[tex]e^{6-8\ln (x)+\ln (y)}[/tex]Explanation:
Simplify the expression by using logathimic properties.
[tex]\begin{gathered} e^{6-8\ln (x)+\ln (y)_{}}=e^{6-\ln (x^8)+\ln (y)} \\ =e^6\cdot e^{-\ln (x^8)}\cdot e^{\ln (y)} \end{gathered}[/tex]Simplify further.
[tex]\begin{gathered} e^6\cdot e^{-\ln (x^8)}\cdot e^{\ln (y)}=e^6\cdot\frac{1}{e^{\ln(x^8)}}\cdot e^{\ln (y)} \\ =e^6\cdot\frac{1}{x^8}\cdot y \\ =\frac{e^6y}{x^8} \end{gathered}[/tex]So answer is,
[tex]\frac{e^6y}{x^8}[/tex]Jackie had 2 part time jobs at Shoney's Restaurant. One week she earned a total $306, working 12 hours as a cashier and 10 hours as a cook. The next week, sheworked 14 hours as a cashier and 22 hours as a cook, earning $512. How much doesshe earn per hour as a cashier?
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Represent the terms with a variable
Let x be the amount she earns per hour as a cashier
Let y be the amount she earns per hour as a cook
STEP 2: Interpret the statements in the question as seen below:
[tex]\begin{gathered} 12x+10y=306 \\ 14x+22y=512 \end{gathered}[/tex]STEP 3: Solve the simultaneous equation using elimination to get x and y
[tex]\begin{gathered} 12x+10y=306---(1) \\ 14x+22y=512----(2) \\ \\ \text{ Multiply equation 1 by 14 and equation 2 by 12} \\ 14\lbrack12x+10y=306\rbrack\Rightarrow168x+140y=4284----(3) \\ 12\lbrack14x+22y=512\Rightarrow168x+264y=6144----(4) \\ \\ \text{Subtract equation 4 from equation 3} \\ 168x\text{ cancels 168x, we have;} \\ 140y-264y=4284-6144 \\ -124y=-1860 \\ \text{Divide both sides by -124} \\ \frac{-124y}{-124}=\frac{-18600}{-124} \\ y=15 \end{gathered}[/tex]STEP 4: Solve any of equation to get the value of x
[tex]\begin{gathered} \text{From equation 1} \\ 12x+10y=306 \\ y=15\text{, By substitution;} \\ 12x+10(15)=306 \\ 12x+150=306 \\ \text{Subtract 150 from both sides} \\ 12x+150-150=306-150 \\ 12x=156 \\ \text{Divide both sides by 12} \\ \frac{12x}{12}=\frac{156}{12} \\ x=13 \end{gathered}[/tex]Since x represents the amount she earns as a cashier, hence She earns $13 per hour as a cashier
If the links in a 30-inch necklace each measure three-eights of an inch long, how many links would be in then necklace?
ANSWER
80 links
EXPLANATION
To find how many links would be in the necklace, we have to divide the total length of the necklace, 30 inches, by the length of each link, 3/8 inch,
[tex]30\div\frac{3}{8}[/tex]Use the KCF method:
• K,eep the first fraction
,• C,hange the division sign into a multiplication sign
,• F,lip the second fraction,
[tex]30\div\frac{3}{8}=30\times\frac{8}{3}[/tex]30 and 3 can be simplified - 30 is 3 times 10,
[tex]30\times\frac{8}{3}=10\times8=80[/tex]Hence, the necklace would have 80 links.
-4x + 0.4y = -0.8 6x + 0.4y = 4.2 The solution to the system is ( , ).
An equation is a mathematical statement created by joining two numerical or variable expressions with an equal sign, as in 3x+5=11. A number that may be entered for the variable to produce a true number statement is the answer to an equation.
Explain about the solution?An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.
Take into account the formula 7x - 35 = 0. If we solve, we get either x = 5 or 7x = 35. The following linear equation only has one solution, x = 5, because the above linear equation is only true if x = 5.
The solution to this system (x=0.5 y=3)
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A line passes through (5,-4) and (-1,-4). Write the equation of the line in slope-intercept form.
Explanation:
The formula of the slope of a line that passes through points (x1, y1) and (x2, y2) is:
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]For this problem the slope is:
[tex]m=\frac{-4-(-4)}{5-(-1)}=\frac{-4+4}{5+1}=\frac{0}{6}=0[/tex]A slope of zero indicates that the line is horizontal. Therefore it is a constant.
The slope-intercept form of the equation of a line is:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept. In this case, the slope is zero so we just have:
[tex]y=b[/tex]b is the y-coordinate of the given points: b = -4
Answer:
y = -4
A student must have an average (the mean) on five tests that is greater than or equal to 80% but less than 90% to receive a final grade of B. Devon’s grades on the first four tests were 76%, 65%, 89%, and 80%. What range of grades on the fifth test would him a B in the course? ( Assume that 100% is the highest grade possible.)
Enter the range of grades necessary for Devon to earn a b average.
__% < x < 100%
- -
Answer:
90% ≤ x ≤ 100%Step-by-step explanation:
Test results are:
76, 65, 89, 80 and x.The average of 5 tests should be:
80 ≤ average < 90, to get a B.The average is:
(76 + 65 + 89 + 80 + x)/5 = (310 + x)/5Plug it into inequality:
80 ≤ (310 + x)/5 < 90 Multiply by 5400 ≤ 310 + x < 450 Subtract 31090 ≤ x < 140But the maximum possible result from one test is 100%, considering this top score Devon must get:
90% ≤ x ≤ 100%Can someone give examples of negative exponents in the world
Eg : seize of bacteria 1*10^-4
The example of negative exponent in the real world is the world's smallest bat, the bumblebee bat weighs of 7 × 10^-2 ounces
How to illustrate the information?An exponent's sign indicates how many times to multiply or divide a base number. A negative exponent indicates the opposite.
The multiplicative inverse of the base raised to a power with the opposite sign of the provided power is referred to as a negative exponent. In plain English, we write the number's reciprocal and solve it just like positive exponents. The bat has a negative exponent.
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