Answer:
a. 7cm
b. 30m
Step-by-step explanation:
b. Formula of perimeter is 2(l + b)
= 2(10 + 5) = 2(15) = 30 m
a. Capacity of the cylinder is 1078 cm^3 but we have equal radius and height
Let’s call the height h which of course is the depth.
The radius is also h too
Using the formula for the volume of a cylinder;
Mathematically we have;
V = pi * r^2 * h
but in this case;
V = pi * h^2 * h
V = pi * h^3
1078 = 22/7 * h^3
h^3 = (1078 * 7)/22
h^3 = 343
h = cube root of 343
h = 7cm
So the depth of the cylindrical tank when full is 7cm
What is the measure of XYZ?
Answer:
C
Step-by-step explanation:
The measure of the chord- chord angle XYZ is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is
∠ XYZ = [tex]\frac{1}{2}[/tex] ( arc XZ + arc VW )
= [tex]\frac{1}{2}[/tex] ( 17 + 55)° = 0.5 × 72° = 36° → C
I'm on my last question and now I'm stuck. help
Answer:
11
Step-by-step explanation:
The fraction of students expected to get an A is 5/15 or 1/3
Multiply 1/3 by the number of students
1/3 * 32 = 10.666666
Rounding to the nearest number
11 students
Un taxi de la empresa “El rápido” se desplaza hacia el sur a una velocidad comprendida entre 60 km/h y 80 km/h. ¿Entre que valores oscila la distancia del auto al punto de partida al cabo de 5 horas
Answer:
Los valores entre los cuales oscila la distancia del automóvil después de 5 horas es entre 300 metros y 400 metros.
Step-by-step explanation:
Dado que la velocidad mínima del taxi = 60 km / h, la velocidad máxima del taxi = 80 km / h
Por lo tanto, tenemos la distancia mínima cubierta después de una hora = 60 km / h × 5 h = 300 m
La distancia máxima recorrida después de una hora = 80 km / h × 5 h = 400 m, lo que da el rango de variación de la distancia recorrida entre 300 my 400 metros.
Donde, la distancia cubierta = x, tenemos
300 metros ≤ x ≤ 400 metros.
City planners want to design a park between parallel streets, Main Street and Willow Lane, in the shape of a trapezoid. There are two paths of equal length on the east and west sides of the park. The border of the park makes a 60° angle between Willow Lane and the east path. A trapezoid is shown. The west path is the left side and the east path is the right side and they are congruent. Main street is the top side and willow lane is the bottom side and they are parallel. The angle formed by willow lane with the east path is 60 degrees.
Question Completion
What is the angle between Main Street and the west path? What is the angle between the west path and Willow Lane?Answer:
[tex](a)120^\circ\\(b)60^\circ[/tex]
Step-by-step explanation:
In the diagram BC(Main Street) is parallel to AD(Willow Lane)
Therefore, ABCD is a Trapezoid.
Since in a trapezoid, adjacent angles are supplementary
Therefore:
[tex]\angle C+ \angle D=180^\circ\\\angle C+ 60^\circ=180^\circ\\\angle C=180^\circ- 60^\circ\\\angle C=120^\circ[/tex]
Since [tex]AB \cong CD[/tex], ABCD is an Isosceles Trapezoid.
In an Isosceles trapezoid, the base angles are congruent:
Therefore:[tex]\angle A \cong \angle D$ and \angle B \cong \angle C[/tex]
Therefore:
[tex]\angle A \cong \angle D=60^\circ\\\angle B \cong \angle C=120^\circ[/tex]
(a)
The angle between Main Street and the west path is [tex]\angle CBA = 120^\circ[/tex]
(b)
The angle between the west path and Willow Lane is [tex]\angle BAD =60^\circ[/tex]
Urgent pls. The diagram shows a parallelogram. Work out the area of the parallelogram. Give your answer to 2 significant figures.
Answer:
54.88 square cm
Step-by-step explanation:
If d1 and d2 are the diagonal of parallelogram and [tex]\alpha[/tex] is the angle between then
then its area is given by
area = d1*d2 sin [tex]\alpha[/tex]
given
in the problem
for one diagonal one part is 7cm
we know that diagonal intersects each other to divide each part of same diagonal equally.
hence if one part is of length 7 then other part is also of 7cm length
hence full length of this diagonal is 7+7 = 14cm
similarly full length of other diagonal is 4+4 = 8cm
now area of this parallelogram
area = d1*d2 sin [tex]\alpha[/tex] = 14*4 sin100
we know sin100 = 0.98
area = 56*0.98
area = 54.88
Thus, area of given parallelogram is 54.88 square cm.
Which could be the graph of f(x) = |x - h| + k if h and k are both positive? On a coordinate plane, an absolute value graph has a vertex at (2, 1). On a coordinate plane, an absolute value graph has a vertex at (1, negative 4). On a coordinate plane, an absolute value graph has a vertex at (negative 3, 2). On a coordinate plane, an absolute value graph has a vertex at (negative 4, negative 5).
Answer:
Step-by-step explanation:
f(x) = |x - h| + k has a vertex at (h, k), where both h and k are positive. Only
"On a coordinate plane, an absolute value graph has a vertex at (2, 1)" satisfies those requirements.
The vertex of an absolute function is the minimum or the maximum point of the graph
The graph that could be [tex]f(x) = |x - h| + k[/tex] is (a) an absolute value graph has a vertex at (2, 1)
The function is given as:
[tex]f(x) = |x - h| + k[/tex]
And the coordinates of the vertex (h,k) are said to be positive.
From the list of given options, only the first option has both coordinates of the vertex to be positive i.e. (2,1)
Hence, the graph that could be [tex]f(x) = |x - h| + k[/tex] is (a)
Read more about absolute value functions at:
brainly.com/question/2166748
Evaluate function from a graph i need help URGENT!
Answer:
-2
Step-by-step explanation:
Simply find the y-value when x = -5. Looking at the graph, we should get y = -2
Answer:
f(-5) = -2
Step-by-step explanation:
f(-5)
x=-5
Go x=-5 on the graph and see what the y value of the function is
The y value is -2
f(-5) = -2
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each system of equations to its graph.
Answer:
1) y = 2x + 1
y = x + 2 Corresponding with the third graph
2) y = 3x
y = x + 3 Corresponds with the first graph
3) y = 2x - 2
y = x - 2
4) y = 2x + 3
y = x + 5
Likely correspond with the fourth graph
5) y = 4x + 2
y = 2x + 2 Corresponding with the second equation
Step-by-step explanation:
The groups of equation are;
1) y = 2x + 1
y = x + 2
The y-intercept of equation (1) = 1
The x-intercept of equation (1) = -1/2
The slope of equation (1) = 2
So at x = 0 y = 1 and at y = 0 x = -1/2 and at x = 2 y = 3
Corresponding with the third graph
The same can be shown with the second equation
2) y = 3x
y = x + 3
The y-intercept of equation (1) = 0
The x-intercept of equation (1) = 0
The slope of equation (1) = 3
So at x = 0 y = 0 and at x = 2 y = 6
Corresponds with the first graph
The same can be shown with the second equation
3) y = 2x - 2
y = x - 2
4) y = 2x + 3
y = x + 5
Likely correspond with the fourth graph
5) y = 4x + 2
y = 3x + 2
The y-intercept of equation (1) = 2
The x-intercept of equation (1) = -1/2
The slope of equation (1) = 4
So at x = 0 y = 2 and at y = 0 x = -1/2 and at x = 0.5 y = 4
Corresponding with the second equation
The same can be shown with the second equation
We have to determine, The tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each system of equations to its graph.
The groups of equation are as follows;
The given system of equation is,
[tex]y = 2x + 1\\y = x + 2[/tex]
The y-intercept of equation = 1
The x-intercept of equation = -1/2
And The slope of equation = 2
Then,
At x = 0, y = 1
And at y = 0, x = -1/2
And at x = 2, y = 3
The first and second equation Corresponding with the third graph.
The given system of equation is,
[tex]y = 3x\\y = x + 3[/tex]
The y-intercept of equation = 0
The x-intercept of equation = 0
The slope of equation = 3
So at x = 0, y = 0 and at x = 2, y = 6
The equation Corresponds with the first graph
The given system of equation is,
[tex]y = 2x - 2\\y = x - 2[/tex]
The y-intercept of equation = -2
The x-intercept of equation = 2
The slope of equation = 2
So at x = 0, y = -2 and at x = 2, y = 0
The equation Corresponds with the first graph.
The given system of equation is,
[tex]y = 2x + 3\\y = x + 5[/tex]
The y-intercept of equation = 3
The x-intercept of equation = -2
The slope of equation = 2
So at x = 0, y = 3 and at x = -5, y = 0
The equation Corresponds with the fourth graph.
The given system of equation is,[tex]y = 4x + 2\\y = 3x + 2[/tex]
The y-intercept of equation = 2
The x-intercept of equation = -1/2
The slope of equation = 4
So at x = 0 y = 2 and at y = 0 x = -1/2 and at x = 0.5 y = 4
The equation Corresponding with the second graph.
For more information about Equation click the link given below.
https://brainly.com/question/17267403
Rodrigo compro 1/5 de los pasteles que venden la señora carmen , carlos 1/10 y francisca 1/3 del total . El resto de los pasteles no se vencio . Que parte del total aun esta disponible?
Se asume que en la pregunta: "El resto de los pasteles no se venció", se quiso decir en realidad: "El resto de los pasteles no se vendió".
Answer:
La parte del total que aún está disponible es [tex] \\ \frac{11}{30}[/tex].
Step-by-step explanation:
El total de los pasteles que se compraron es la suma de las fracciones del total que compró Rodrigo, [tex] \\ \frac{1}{5}[/tex], de la fracción del total que compró Carlos, [tex] \\ \frac{1}{10}[/tex], y de la fracción del total que compró Francisca, [tex] \\ \frac{1}{3}[/tex].
Numericamente hablando, Rodrigo, Carlos y Francisca compraron:
[tex] \\ \frac{1}{5}+\frac{1}{10}+\frac{1}{3}[/tex] [1]
Del total de los pasteles que vende la Señora Carmen.
La suma de las fracciones en [1] se puede realizar de distintas maneras, una posible es la siguiente:
Podemos aplicar la propiedad asociativa para la suma, es decir, primero sumamos dos fracciones y el resultado lo sumamos a la fracción restante.Debemos recordar que, en general, en la suma de fracciones tenemos los siguientes casos:
Fracciones con denominadores diferentes
Si los denominadores de las fracciones son diferentes, los denominadores se multiplican. Este será el nuevo denominador para la suma de dos fracciones.Luego, cada denominador se multiplica con el numerador de la otra fracción. El resultado de cada multiplicación se suma y el total forma el nuevo numerador.Simplificar la fracción de ser posible, es decir, si el numerador y el denominador pueden dividirse por un mismo número, la división resultante para el numerador y el denominador formarán la nueva fracción. El número que simplifica la fracción a su "mínima expresión" es el máximo común divisor de ambos números.Fracciones con iguales denominadores
Se deja el mismo denominador y se suman los numeradores.Seguir el paso 3 del caso anterior para simplificar la fracción.De esta forma:
[tex] \\ (\frac{1}{5}+\frac{1}{10})+\frac{1}{3}[/tex]
Se desarrolla primero la operación entre las fracciones dentro del paréntesis conforme a lo explicado anteriormente:
[tex] \\ (\frac{1*10+5*1}{5*10})+\frac{1}{3}[/tex]
[tex] \\ (\frac{10+5}{50})+\frac{1}{3}[/tex]
[tex] \\ \frac{15}{50} + \frac{1}{3}[/tex]
Se divide el numerador y el denominador de la fracción [tex] \\ \frac{15}{50}[/tex] entre cinco (5):
[tex] \\ (\frac{\frac{15}{5}}{\frac{50}{5}})+\frac{1}{3}[/tex]
Resultando:
[tex] \\ (\frac{3}{10})+\frac{1}{3}[/tex]
Esta fracción se suma a la siguiente y se procede de igual manera:
[tex] \\ \frac{3}{10}+\frac{1}{3}[/tex]
[tex] \\ \frac{3*3+10*1}{10*3}[/tex]
[tex] \\ \frac{9+10}{30}[/tex]
[tex] \\ \frac{19}{30}[/tex]
El número 19 es primo, es decir, sólo lo puede dividir el 1 y el mismo número (19). El 30 no es divisible por 19, por lo tanto, la fracción queda expresada de esa manera.Tenemos entonces que:
El total de los pasteles vendidos fue la fracción [tex] \\ \frac{19}{30}[/tex].La parte que aún está disponible hay que restarla del total. El total es 1.De esta manera, la parte que aún está disponible es:
[tex] \\ 1 - \frac{19}{30}[/tex]
Podemos hacer [tex] \\ 1 = \frac{30}{30} = 1[/tex] (o un número dividido por si mismo es igual a la unidad) para que la operación se haga más fácilmente (caso de suma de fracciones con iguales denominadores):
[tex] \\ \frac{30}{30} - \frac{19}{30}[/tex]
[tex] \\ \frac{30 - 19}{30}[/tex]
[tex] \\ \frac{11}{30}[/tex]
El número once es también un número primo y la fracción no se puede simplificar más porque el 30 no es divisible por 11.
Por lo tanto, la parte que aún está disponible es la fracción [tex] \\ \frac{11}{30}[/tex], la cual podría interpretarse como once (11) partes de las treinta (30), [tex] \\ \frac{11}{30}[/tex], que estaban disponibles antes de que Rodrigo, Carlos y Francisca compraran los pasteles.
If f(x) = 8x + 5, what is f(x)-1?
Answer:(x-5)/8
Step-by-step explanation:
f(x)=8x+5
let f(x)-1=y
y=8x+5
interchanging x and y
x=8y+5
y=(x-5)/8
Therfore f(x)-1=(x-5)/8
Answer:
x-5/8
Step-by-step explanation:
what is the slope and y-intercept (−6,5),(-3,-3)
Answer:
Step-by-step explanation:
The values of the slope and y-intercept are
m =- 8/3
and b = − 11
What is the sum of the series represented by:
Answer:
70
Step-by-step explanation:
n =2 ; 3n + 2 = 3*2 + 2 = 6 + 2 = 8
n = 3 ; 3n + 2 = 3*3 + 2 = 9 + 2 = 11
n =4 ; 3n+ 2 = 3*4 + 2 = 12 + 2 = 14
n= 5; 3n +2 = 3*5 + 2 = 15 + 2 = 17
n = 6; 3n + 2 = 3*6 + 2 = 18 + 2 = 20
∑ (3n + 2) = 8 + 11 + 14 + 17 + 20 = 70
Answer:
70
Step-by-step explanation:
TTT
Diane's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Diane $4.05 per pound, and type B coffee costs $5.55 per pound. This month's blend used four times as many pounds of type B coffee as type A, for a total cost of $735.00. How many pounds of type A coffee were used
Step-by-step explanation:
Type A cost 4.05 dollars per pound
Type B cost 5.55 dollars per pound
now...since type A is four times larger than Type B for that month,.the ratio will be 4:1 respectively
total cost was 735 dollars out of which Type A has
4/5 × 735 = 588 dollars while Type B has 1/5 × 735 = 147 dollars
so therefore ....number of pounds of A = 588/4.05=145.18pounds
and number of Pounds of B = 147/5.55= 26.48pounds
Given the function P(x)=(x-1)^2, Write the new function wi†h a dilation of 2 ON THE X
Answer:
P(x2) = (x2/2 -1 )^2
Step-by-step explanation:
From the question, we have a dilation of 2 units on the x-axis
The individual points on the curve can be written as:
(x, P(x))
For the sake of ambiguity, let’s say P(x) is y
Now if the first point is (x1,y1) then the second is (x2,y2)
But since dilation is only on the x-axis y1 is same as y2
What this means is that;
our second point is still same as (x2,y1)
But x2 = 2x1
or x1 = x2/2
Thus; y2 or P(x2) = (x2/2 -1 )^2
Thus the horizontal dilation causes the new curve to be as written above
Use the vertical line test to determine if the relation whose graph is provided is a function
Answer:
the graph represents a function.
Step-by-step explanation:
The vertical line test is a test to check if a graph represents a function.
To proceed, draw (imaginary) vertical lines through the entire domain of the graph. If any of the line intersects the graph at any value of x, then the graph does not represent a function.
Here it is not possible to draw a vertical line to intersect the red curve at any point, therefore the graph represents a function.
Answer:
Yes, the graph represents a function.
Step-by-step explanation:
The vertical line test is a test you can do to determine if a graph is a function. Basically, you draw straight vertical lines, and if it intersects with the line more than once, the graph is not a function.
This is because in a function, each input can only have one output.
So, we can draw vertical lines through the graph, and you'll find that each line will only intersect with the line once.
Based on this, the given graph would represent a function.
which point of intersection is the solution to the system of equations
y=2/5x-1/2 and 1/3x+2/3
A
B
C
D
Answer:
B
Step-by-step explanation:
(Looking at the lines in the graph, the second equation is missing a minus sign, and should be [tex]y=-\frac{1}{3}x + \frac{2}{3}[/tex])
To find the intersection point of the pair of linear equations, we just need to equate both values of y.
The equations are:
[tex]y=\frac{2}{5}x - \frac{1}{2}[/tex]
[tex]y=-\frac{1}{3}x + \frac{2}{3}[/tex]
Making the y from one equation equal the y of the other equation, we have:
[tex]\frac{2}{5}x - \frac{1}{2} = -\frac{1}{3}x + \frac{2}{3}[/tex]
[tex]\frac{2}{5}x +\frac{1}{3}x = \frac{2}{3} + \frac{1}{2}[/tex]
[tex]\frac{6}{15}x +\frac{5}{15}x = \frac{4}{6} + \frac{3}{6}[/tex]
[tex]\frac{11}{15}x = \frac{7}{6}[/tex]
[tex]x = \frac{7}{6} * \frac{15}{11} =\frac{35}{22} = 1.591[/tex]
Then the y-coordinate of the point is found using this x-value in any of the two equations:
[tex]y=\frac{2}{5}\frac{35}{22} - \frac{1}{2}[/tex]
[tex]y=\frac{7}{11} - \frac{1}{2}[/tex]
[tex]y=\frac{14}{22} - \frac{11}{22}[/tex]
[tex]y=\frac{3}{22} = 0.136[/tex]
So the coordinate of the crossing point is (1.591, 0.136)
The point that is in this coordinate in the graph is point B.
Answer:
View the picture for the answer!
Step-by-step explanation:
Evaluate the expression. 56 Divided by (-8)
Answer:
-7
Step-by-step explanation:
Help!!!!! please!!!!!
Answer:
250[tex]\pi[/tex] which is around 785 cm (C)
Step-by-step explanation:
Surface area of a cylinder can be found by finding the area of the two circles.
So the diameter of the circle is 10, meaning the radius is 5. (10/2)
[tex]2 * 5^2\pi[/tex] = 50[tex]\pi[/tex]
Multiply by 2 because there are two of these circles.
Now to find the "long part", we find the circumfrence of the circle ([tex]\pi[/tex]d or 2[tex]\pi[/tex]r) and multiply it by the height (15)
10[tex]\pi[/tex] * 15 = 150[tex]\pi[/tex]
add these two up and you get...
250[tex]\pi[/tex] which is around 785 cm. (C)
Find m∠C. please help
Answer: 16.991°
Step-by-step explanation:
Used a triangle calculator hope this helped!
A(7-1), B(6, 4) and C(5, 5) are three
points in a plane.
1). Find the equations of the
perpendicular bisectors of AB and AC
(ü) Determine the point of
intersection of the perpendicular
bisectors in (i).
(WAEC)
Answer:
The answer is below
Step-by-step explanation:
The equation of the line passing through two points is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\[/tex]
The equation of line AB is:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-(-1)=\frac{4-(-1)}{6-7}(x-7)\\\\y+1=-5(x-7)\\y+1=-5x+35\\y=-5x+34[/tex]
The midpoint of two lines is given as:
[tex]x=\frac{x_1+x_2}{2}, y=\frac{y_1+y_2}{2}\\midpoint\ of\ AB \ is:\\x=\frac{7+6}{2}=6.5, y=\frac{-1+4}{2}=1.5\\ = (6.5,1.5)[/tex]
The equation of line AC is:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-(-1)=\frac{5-(-1)}{5-7}(x-7)\\\\y+1=-3(x-7)\\y+1=-3x+21\\y=-3x+20[/tex]
The midpoint of two lines is given as:
[tex]x=\frac{x_1+x_2}{2}, y=\frac{y_1+y_2}{2}\\midpoint\ of\ AB \ is:\\x=\frac{7+5}{2}=6, y=\frac{-1+5}{2}=2\\ = (6,2)[/tex]
The product of the slope of a perpendicular bisector of a line and the slope of the line is -1. That is m1m2 = -1
The slope of the perpendicular bisector of AB is:
m(-5)=-1
m=1/5
The equation of the perpendicular bisector of AB passing through (6.5,1.5) is:
[tex]y-y_1=m(x-x_1)\\y-1.5=\frac{1}{5}(x-6.5)\\y=\frac{1}{5} x-8.25[/tex]
The slope of the perpendicular bisector of AB is:
m(-3)=-1
m=1/3
The equation of the perpendicular bisector of AB passing through (6,2) is:
[tex]y-y_1=m(x-x_1)\\y-2=\frac{1}{3}(x-7)\\y=\frac{1}{3} x-4.33[/tex]
2) The point of intersection is gotten by solving y = 1/5 x -8.25 and y = 1/3 x-4.33 simultaneously.
Subtracting the two equations from each other gives:
0= -0.133x - 3.92
-0.133x = 3.92
x = -29.5
Put x = -29.5 in y = 1/5 x -8.25 i.e:
y = 1/5 (29.5) -8.25
y = -14.16
The point of intersection is (-29.5, -14.16)
Can someone help me with this question please..
Answer:
7200 cm^2
Step-by-step explanation:
The kitchen dimension on the drawing of 14 cm corresponds to an actual kitchen dimension of 40·14 = 560 cm.
The kitchen dimension on the drawing of 22 cm corresponds to an actual kitchen dimension of 40·22 = 880 cm.
The actual kitchen area is ...
Area = length · width = (880 cm)(560 cm) = 492,800 cm^2.
__
The difference between this area and the bedroom area is ...
500,000 cm^2 -492,800 cm^2 = 7200 cm^2
The kitchen is 7200 cm^2 smaller than the bedroom.
Solve for F:
-3/4f =5/4
If your answer is wrong you're getting blocked
Answer:
f = -5/3
Step-by-step explanation:
-3/4f = 5/4
Multiply both sides by -4/3.
-3/4f × -4/3 = 5/4 × -4/3
f = -20/12
f = -5/3
Plz solve if you can. Show ur work. I will name Brainliest! (: I need help plzzzzzzzzzz, especially on the check your work part. plzzzzzz. ( You get 24 points plus Brainliest (: ) -X + 4 = -2X - 6 solve and check your work: 4R - 4 = 3R + 10 solve and check your work: 2Y - 3 = Y - 4 solve and check your work.
1) -x + 4 = -2x - 6
Add(2x)
x+4=-6
Subtract(4)
x = -10
Check your work
-(-10)+4=-2(-10) - 6
10+4=-2(-10) - 6
14=-2(-10)
14=20 - 6
14=14
Correct :)
2) 4R - 4 = 3R + 10
Add 4
4R=3R+14
Subtract 3R
R = 14
Check your work
4(14)-4=3(14)+10
56-4=3(14)+10
52=3(14)+10
52=42+10
52=52
Correct :)
3) 2Y - 3 = Y - 4
Add 3
2Y = Y - 1
Subtract Y
Y = -1
Check your work
2(-1)-3=-1-4
-2-3=-1-4
-5=-5
Correct :)
Hope it helps <3
Solve for x 8/11 = x/3
Two competing gyms each offer childcare while parents work out. Gym A charges $9.00 per hour of childcare. Gym B charges $0.75 per 5 minutes of childcare.
Answer:
Gym A and B offers the same price
Step-by-step explanation:
[tex]\huge\bold\color{steelblue}{\colorbox{white}{Answer:}}[/tex]
Both of them has the same price
━═━═━═━═━═━═━═━━═━═━━═━═━━═━═━═━═━═━═━═━
If you have any questions, feel free to ask me <33
#CarryOnLearning
#HelpBrainlyCommunityGreat
An integer is three more than another integer. Twice the larger integer is two less
than the square of the smaller integer. Find the two integers.
Answer:
The integers are 4 and 7 or -2 and 1.
Step-by-step explanation:
You can make a system of equations with the description of the two integers.
1. x = y + 3
2. 2x + 2 = y^2
The simplest and the fastest way to solve this system in this case is substitution. You can substitute x for y + 3 in the second equation.
1. x = y + 3
2. 2(y + 3) + 2 = y^2
Now simplify and solve the second one. For convenience, I will just disregard the first equation for now.
2y + 6 + 2 = y^2
y^2 - 2y - 8 = 0
You can factor this equation to solve for y.
(y - 4) (y + 2) = 0
y = 4, y = -2
Now we can substitute the value of y for x in the first equation.
x = 7, x = 1
The two expressions to find the value of the two integers.
M = 3N
2M = N² - 2
N = 6.3 and M = 18.9
The two integers are 6.3 and 18.9
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Smaller integer = M
Larger integer = N
Now,
An integer is three more than another integer.
This can be written as,
M = 3N ____(1)
Twice the larger integer is two less than the square of the smaller integer.
This can be written as,
2M = N² - 2 ______(2)
From (1) and (2) we get,
2(3N) = N² - 2
6N = N² - 2
N² - 2 - 6N = 0
N² - 6N - 2 = 0
This is a quadratic equation.
The roots of this quadratic equation are 6.32 and -0.31 (neglected)
N = 6.32
N = 6.3
Now,
M = 3N
M = 3 x 6.3
M = 18.9
Thus,
The two integers are 6.3 and 18.9
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
what number must you add to complete the square x^2+4x=5
Answer:
You should add 4 to both sides because that would make the left side a perfect square which is what you are intending to do when you complete the square.
Answer:
4
Step-by-step explanation:
x² + 4x = 5
b = 4
We need to add (b/2)² to both sides to complete the square.
(4/2)² = 4
x² + 4x + 4 = 5 + 4
x² + 4x + 4 = 9
(x + 2)² = 9
Kini and Duke are each workings during the summer to earn money in addition to their weekly allowance, and they are saving all of their money. Kini earns $9 an hour at her job, and her allowance is $8 per week. Duke earns $7.50 an hour, and his allowance is $17 per week. How many hours do Kini and Duke need to work in order to save the same amount of money in one week?
Answer:
6 hours
Step-by-step explanation:
Kini: 9h+8
Duke: 7.5h+17
9h+8=7.5h+17
8-17=7.5h-9h
-9=-1.5h
6=h
Hope this helps, BRAINLIEST would help me alot!
Answer:
7.3 hours
Step-by-step explanation:
9h+8=7.5+17
-9h -9h
8=1.5h+17
-17 -17
8=1.5h
1.5 1.5
7.3=h
❗️5 points❗️
state the slope of the line.
A. -2
B. 0
C. 1
D. undefined
Answer:
B. 0
Step-by-step explanation:
The slope of a straight horizontal line is always equal to 0.
To support the above statement, we can show working out:
m = slope of the line
m = ( y1 - y2 ) / ( x1 - x2 )
Two points on line = ( 0 , - 2 ) , ( 1 , - 2 )
y1 = - 2
y2 = - 2
x1 = 0
x2 = 1
m = [ ( - 2 ) - ( - 2 ) ] / [ ( 0 ) - ( 1 ) ]
m = ( - 2 + 2 ) / ( 0 - 1 )
m = 0 / - 1
m = 0
The y values on a horizontal line will always be the same. When calculating the subtraction of y values in the numerator of the formula for the slope of a line, a number subtracted by itself will always equal to 0. 0 divided by any number will always equal to 0. Hence, the slope of a straight horizontal line will always equal to 0.
Translate the word problem below into an equation; then solve.
(e) 24. The royal physician failed to produce a cure for the prince's laziness (see practice
problem e), but the queen said she would still let the physician live if he could find a
cure for her husband's snoring instead. Now the physician is nervously combining a 10
ounce substance containing 6% cottonseed with another substance containing 12%
cottonseed to (hopefully) create a snore-suppressing substance with 8% cottonseed.
How many ounces of the 12% substance must he use?
Answer:
The amount of ounces, Y, of the 12% substance is 3.33 ounces
Step-by-step explanation:
The word problem has the task of discovering the required amount of the substance containing the 12% cottonseed required to create a snore suppressing substance with 8% cottonseed
Let the amount of the substance with 6% cottonseed in the 10 ounce substance be X and the amount of the substance with 12% cottonseed be Y
We have;
X×6% + Y×12% = 10 ounce × 8%
Which gives;
0.06×X + 0.12×Y = 0.08×10..........(1)
X + Y = 10.....................................(2)
Putting X = 10 - Y, we have;
0.06×(10 - Y) + 0.12×Y = 0.08×10
0.6 - 0.06·Y + 0.12·Y = 0.8
0.06·Y = 0.8 - 0.6 = 0.2
Y = 0.2/0.06 = 10/3 = 3.33 ounces
X = 10 - Y = 10 - 3.33 = 6.67 ounces
Therefore, the amount of ounces, Y, of the 12% substance = 3.33 ounces.
Answer:
The Answer is actaully 5
Step-by-step explanation: