Answer:
A. 32.08
Step-by-step explanation:
The figure given is a right triangle. We would apply trigonometric ratios formula to find x.
Reference angle = 58°
Hypotenuse = x
Adjacent length = 17
Thus, we would apply the following:
[tex] Cos(\theta) = \frac{Adjacent}{Hypotenuse} [/tex]
Plug in the values
[tex] Cos(58) = \frac{17}{x} [/tex]
Multiply both sides by x
[tex] Cos(58) \times x = \frac{17}{x} \times x [/tex]
[tex] Cos(58) \times x = 17 [/tex]
Divide both sides by Cos(58)
[tex] \frac{Cos(58) \times x}{Cos(58)} = \frac{17}{Cos(58)} [/tex]
[tex] x = \frac{17}{Cos(58)} [/tex]
[tex] x = 32.08 [/tex] (2 d.p)
Your first job after college has a salary of $35,000 and will increase 6.5% each year. If you stay with the same position, what you will make after working for 8 years?
Answer:
Step-by-step explanation:
35000*6.5%= 2275+35000=37275 year one
37275*6.5%=2422.88+37275=39697.88 year two
It comes out to $18200 more or 53,200
Neil and Joey share a 30-ounce bucket of clay. By the end of the week, Neil has used 1/10 of the bucket, and Joey has used 2/5 of the bucket of clay. How many ounces are left in the bucket?
Answer:
15 ounces
Step-by-step explanation:
1/10 of the bucket is 3 ounces and 2/5 is 12 ounces. add those to get 15 and then do 30-15 which is 15
Write the sentence as an equation.
124 is 96 reduced by f
Answer:
f-96=124
Step-by-step explanation:
This is the equation of the sentence that has been mentioned.
Show work
will mark best answer as brainliest
Will report wrong answers
Someone please help me I really forgot how to do this!
y = mx + b
m = slope or rate of change
b = y-intercept
x = input
y = output
Answer:
x= input
y= output
Step-by-step explanation:
when you flip 1/6 it is?
Answer:
1/6 flipped is 6/1, which equals 6
Step-by-step explanation:
you flipped the numbers.
i need help please!
Answer:
C
Step-by-step explanation:
Adding 30and 70 first gives 100.
5) Diseñar un sistema de ecuaciones lineales y resolverlo a través del método de Gaussiana, que permita resolver el siguiente problema: -Un ingeniero realiza las siguientes observaciones sobre las ventas de impresoras en una tienda: Hay impresoras Epson, Hp y Cannon. El número de impresoras Epson y Hp es cinco veces el número de las Cannon. Además, el número de impresoras Epson es el triple que el de la Cannon y el total de impresoras Cannon y Hp asciende a 12.
Answer:
[tex]X=12[/tex]
[tex]Y=8[/tex]
[tex]Z=4[/tex]
Step-by-step explanation:
Comencemos definiendo las variables ⇒
[tex]X:[/tex] '' Número de impresoras Epson ''
[tex]Y:[/tex] '' Número de impresoras Hp ''
[tex]Z:[/tex] '' Número de impresoras Cannon ''
Ahora , dado que tenemos las variables definidas podemos escribir el sistema de ecuaciones lineales
''El número de impresoras Epson y Hp es cinco veces el número de las Cannon''
Para esa oración escribimos la siguiente ecuación :
[tex]X+Y=5Z[/tex] (I) que se puede reescribir como
[tex]X+Y-5Z=0[/tex] (II)
''El número de impresoras Epson es el triple que el de las Cannon''
Para esa oración escribimos la siguiente ecuación :
[tex]X=3Z[/tex] (III) que se puede reescribir como
[tex]X-3Z=0[/tex] (IV)
''El total de impresoras Cannon y Hp asciende a 12''
Para ésta última frase escribimos la última ecuación :
[tex]Y+Z=12[/tex] (V)
Con (II), (IV) y (V) armamos el sistema de ecuaciones lineales :
[tex]X+Y-5Z=0\\X-3Z=0\\Y+Z=12[/tex]
Lo resolvemos a través del método de Gauss insertando el sistema en una matriz y realizando operaciones de fila entre las respectivas filas de la matriz :
[tex]\left[\begin{array}{ccxc}1&1&-5&0\\1&0&-3&0\\0&1&1&12\end{array}\right][/tex]
Realizando operaciones entre filas se lleva a la siguiente matriz equivalente :
[tex]\left[\begin{array}{cccc}1&1&-5&0\\0&-1&2&0\\0&0&3&12\end{array}\right][/tex] En esta matriz el sistema de ecuaciones asociado es
[tex]X+Y-5Z=0\\-Y+2Z=0\\3Z=12[/tex]
De aquí encontramos que [tex]Z=4[/tex] , [tex]Y=8[/tex] y [tex]X=12[/tex] (encontramos primero el valor de [tex]Z[/tex] en la última ecuación, de allí reemplazamos en la segunda ecuación para hallar el valor de [tex]Y[/tex]. Finalmente el valor de [tex]X[/tex] se calcula con la primera ecuación)
La solución a éste sistema de ecuaciones es
[tex]X=12[/tex]
[tex]Y=8[/tex]
[tex]Z=4[/tex]
Es recomendable reemplazar éstos valores en el sistema original para verificarlos.
Solve the equation -2/3d - 1/4d = -22 for d.
Answer:
d=24
Step-by-step explanation:
create a common denominator of 12
[tex]\frac{-2}{3}[/tex]d-[tex]\frac{1}{4}[/tex]d=[tex]\frac{-22}{1}[/tex]
[tex]\frac{-2}{3}[/tex]*4 [tex]\frac{1}{4}[/tex]*3 [tex]\frac{-22}{1}[/tex]*12
[tex]\frac{-8}{12}[/tex]d - [tex]\frac{3}{12}[/tex]d = [tex]\frac{-264}{12}[/tex]
[tex]\frac{-11}{12}[/tex]d=[tex]\frac{-264}{12}[/tex]
multiple each side by reciprocal ([tex]\frac{12}{-11}[/tex]) and simplify
d=24
The value of d from the given equation is 24.
The given equation is [tex]-\frac{2}{3}d - \frac{1}{4}d=-22[/tex].
We need to solve the given equation for d.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation can be solved for d as follows:
Take LCM of denominators
LCM of denominators 3 and 4 is 12
Now equate denominators to LCM, that is
[tex]d(-\frac{2}{3} - \frac{1}{4})=-22[/tex]
⇒ [tex]d(-\frac{8}{12} - \frac{3}{12})=-22[/tex]
⇒ [tex]d(\frac{-8-3}{12} )=-22[/tex]
⇒ [tex]d(\frac{-11}{12} )=-22[/tex]
⇒ d=24
Therefore, the value of d from the given equation is 24.
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What does This equation equal ?3.91 x 10-2 =
Answer:
37.1
Step-by-step explanation:
Hope this is the right answer.
Casey's mom is the baseball coach for his team. She spent $150 on baseballs. Each baseball cost $5. How many baseballs did she buy?
Answer:
nicw
Step-by-step explanation:
150-5=145
The Jeffer's company has a debt ratio (total debt to total assets) of 0.365. If their total debt is $500,000, what are their total assets?
Given:
Total debt ratio (total debt to total assets) = 0.365
Total debt = $500,000
To find:
The total assets.
Solution:
We know that,
[tex]\text{Total debt ratio}=\dfrac{\text{Total debt}}{\text{Total assets}}[/tex]
On substituting the given values, we get
[tex]0.365=\dfrac{500,000}{\text{Total assets}}[/tex]
[tex]\text{Total assets}=\dfrac{500,000}{0.365}[/tex]
[tex]\text{Total assets}=1369863.0137[/tex]
Therefore, the value of total assets is $1369863.0137.
Solve x+4/4 = x/x-2
Answer:
After solving the equation [tex]\frac{x+4}{4}=\frac{x}{x-2}[/tex] we get x=-2 and x= 4 i.e {-2,4}.
Option B is correct.
Step-by-step explanation:
We need to solve [tex]\frac{x+4}{4}=\frac{x}{x-2}[/tex]
Solving:
[tex]\frac{x+4}{4}=\frac{x}{x-2}[/tex]
Cross multiply
[tex](x-2)(x+4)=x*4[/tex]
Multiplying:
[tex]x(x+4)-2(x+4)=4x\\x^2+4x-2x-8=4x\\x^2+2x-8-4x=0\\x^2-2x-8=0[/tex]
Now, we have got quadratic equation [tex]x^2-2x-8=0[/tex]
Solving this quadratic equation using quadratic formula
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\[/tex]
We have a=1, b=-2 and c=-8 Putting values
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(-8)}}{2(1)}\\x=\frac{2\pm\sqrt{4+32}}{2}\\x=\frac{2\pm\sqrt{36}}{2}\\x=\frac{2\pm6}{2}\\x=\frac{2+6}{2} \ or \ x=\frac{2-6}{2}\\x=\frac{8}{2} \ or \ x=\frac{-4}{2}\\x=4 \ or \ x=-2[/tex]
So,after solving the equation [tex]\frac{x+4}{4}=\frac{x}{x-2}[/tex] we get x=-2 and x= 4 i.e {-2,4}.
Option B is correct.
I cant wait till Thanksgiving break bc computer work is so lammmmmmmmme.
Which value of x is in the solution set of -2(3x + 2) > -8x + 6?
Step-by-step explanation:
-2(3x+2)>-8x+6
when eq. is divided by 2,
-3x-2>-4x+3
x >5
The solution set of -2(3x+3)>-8x+6 is {x/x>5}.
whats 5x4 x7x2x8= blank? commet your down below
Answer:
The answer would be 2,240
Step-by-step explanation:
Answer:
2240
Step-by-step explanation:
1. 5x4=20x7 and keep on going
how to solve -7(8s+9f) s=-5 f=-3
Answer:
469
Step-by-step explanation:
plug in values and solve
Given:5y-1/2=7 prove y=3
I am confused on the steps to get 3!
Answer:
y=3/2
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
5y+ −1/2=7
Step 2: Add 1/2 to both sides.
5y+/−1/2+1/2=7+1/2
5y=15/2
Step 3: Divide both sides by 5.
5y/5
=
15/25
y=3/2
The solution of the given equation is y = 3/2.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
The operator that performs the arithmetic operations is called the arithmetic operator.
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
/ Division operation: Divides left-hand operand by right-hand operand
For example 4/2 = 2
We have given the equation as
⇒ 5y - 1/2 = 7
Add 1/2 to both sides in the above equation.
⇒ 5y - 1/2 + 1/2 = 7 + 1/2
⇒ 5y = 15/2
Divide both sides by 5
⇒ y = 15/10
⇒ y = 3/2
Hence, the solution of the given equation is y = 3/2.
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How can you tell if a linear system of equations has an infinite number of solutions?
what is the value of x
1. 124
2. 62
3. 112
4. 68
explain why the answer is correct
Answer:
3.112 because 56+56=112Answer:
The answer is 4. 68
Step-by-step explanation:
since equal sides of triangle,it has equal angle at the base of triangle.So, the two angles of triangle at base is 56. The sum of angles in a triangle is 180.Therefore,56+56+x=180
x=180-112
x=68
Write a compound inequality that the graph could represent.
x ≥ –4 or x < 2
–4 < x ≤ 2
–2 ≤ x < 4
–4 ≤ x < 2
The compound inequality is represented by –4 ≤ x < 2 , Option C is the answer.
What is an Inequality ?An inequality is a statement that consist of expressions equated by constants or other expressions by an inequality operator.
From the line shown below , the compound inequality has to be determined
There is an open dot on + 2 and closed dot on -4
so x ≥ –4 , x < 2
and this is represented by –4 ≤ x < 2
Therefore Option C is the answer.
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Identify the matrix transformation of ΔMNO, which has coordinates M(1, 3),N(5, 2), and O(3, −3), for a translation 2 units left and 4 units up. Then identify the correct vertices of the image
Answer:
M(-1,7), N(3,6), O(1,1)
Step-by-step explanation:
The coordinates of ΔMNO are M(1, 3),N(5, 2), and O(3, −3).For a translation, 2 units left and 4 units up the correct vertices of the image will be M'(-1,7), N'(3,6), and O'(1,1).
It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
It is given that the coordinates are M(1, 3),N(5, 2), and O(3, −3).
We have to translate 2 units left and 4 units up.
The coordinates obtained after applying the given geometric transformation are M'(-1,7), N'(3,6), O'(1,1)
Thus, the coordinates of ΔMNO are M(1, 3),N(5, 2), and O(3, −3).For a translation, 2 units left and 4 units up the correct vertices of the image will be M'(-1,7), N'(3,6), and O'(1,1).
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At JR Market, soda costs $2.55 for 3 liters. How much will it cost for 5 liters?
Answer:
It will cost $4.25 for 5 liters.
Step-by-step explanation:
$2.55 ÷ 3 = $0.85
$0.85 x 5 = $4.25
Can someone help me with 3.7.2 walking your dog business the whole assignment
The whole assignment?
PLEASE HELPP !!
4 friends shot free throws for a charity event. Adam scored 8 more points than Cheryl. Laura scored twice as many points as Adam. Tom scored 10 points less than Laura. Together the four friends scored a total of 66 points.
Answer:
c = 6
a = 14
l = 28
t = 18
Step-by-step explanation:
Free throws are usually worth one point each. We can assign variables and use equations to link information between Adam, Cheryl, Laura, and Tom. Then, we can just substitute in our information and solve.
"Adam scored 8 more points than Cheryl"
a = c + 8
"Laura scored twice as many points as Adam"
l = 2a
"Tom scored 10 points less than Laura"
t = l - 10
"Together the four friends scored a total of 66 points"
a + c + l + t = 66
Now we substitute in our variables and solve from there (see attached image)
c = 6
a = 14
l = 28
t = 18
HELP PLS‼️Given j || k, give two angles that are corresponding
Answer:
angle 6 and angle 2 are corresponding
Hi. I need help with these questions.
See image for question.
Answer 14 and 13
Answer:
13) 36x² + 9x - 4 = 014) 21x² + 20x + 100 = 0Step-by-step explanation:
13.
GivenQuadratic equation
4x² - 3x - 4 = 0With the roots of α and βTo Find The quadratic equation with roots of 1/(3α) and 1/(3β)SolutionThe sum and the product of the roots of the given equation:
α + β = -b/a ⇒ α + β = -(-3)/4 = 3/4αβ = c/a ⇒ αβ = -4/4 = - 1New equation is:
(x - 1/(3α))(x - 1/(3β)) = 0x² - (1/(3α) + 1/(3αβ))x + 1/(3α3β) = 0x² - ((3α + 3 β)/(3α3β))x + 1/(3α3β) = 0x² - ((α + β)/(3αβ))x + 1/(9αβ) = 0x² - (3/4)/(3(-1))x + 1/(9(-1)) = 0x² + 1/4x - 1/9 = 036x² + 9x - 4 = 0===================
14.
GivenQuadratic equation
3x² +2x + 7 = 0With the roots of α and βTo Find The quadratic equation with roots of α + 1/β and β + 1/αSolutionThe sum and the product of the roots of the given equation:
α + β = -b/a ⇒ α + β = -2/3αβ = c/a ⇒ αβ = 7/3New equation is:
(x - (α + 1/β))(x - (β + 1/α)) = 0x² - (α + 1/β + β + 1/α)x + (α + 1/β) (β + 1/α) = 0x² - (α + β + (α + β)/αβ )x + αβ + 1/αβ + 2 = 0x² - (-2/3 - (2/3)/(7/3))x + 7/3 + 1/(7/3) + 2 = 0x² - (-2/3 - 2/7)x + 7/3 + 3/7 + 2 = 0x² + (14 + 6)/21x + (49 + 9 + 42/21) = 0x² + 20/21x + 100/21 = 021x² + 20x + 100 = 0Please help and give an explanation!:)
Answer: D) All real numbers greater than or equal to -4.
Explanation:
The lowest point occurs when y = -4, which is where the vertex is located.
The range consists of y values such that y = -4 or y > -4. We can shorten that last sentence to say [tex]y \ge -4[/tex]. So y is greater than or equal to -4.
As you can probably tell, the range is the set of all possible outputs of a function.
En una fábrica, dos trabajadores llenan envases de gel
antibacterial. El primer trabajador los empaca en grupos de 8
botellas y el segundo en grupos de 12. Si ambos empiezan a
trabajar simultáneamente y lo hacen a la misma velocidad,
¿cuántos envases tendrán que llenar para completar sus
respectivos paquetes al mismo tiempo?
Responder:
Contenedor 24
Explicación paso a paso:
Para obtener la cantidad de contenedores que deberán llenar para completar sus respectivos paquetes al mismo tiempo; obtener el mínimo común múltiplo de la agrupación adoptada por el primer y segundo trabajador;
Múltiplos de:
8: 8, 16, 24, 32, 40, 48, 56, ...
12:12, 24, 26, 48, 60, ....
Por lo tanto, el mínimo común múltiplo de 8 y 12 es 24.
Llenarán 24 contenedores
Is (0,1) included in the solution of the system
−x + y < 1 and
x + y ≥ −3
True
False