Answer:
Let two consecutive multiples of 3 be x and (x+3)
A/q,
x * (x+3) = 648
➡ x² + 3x = 648
➡ x² + 3x -648 = 0
➡ x² + 27x - 24x -648 = 0
➡ x ( x + 27 ) -24 ( x +27)
➡ ( x - 24) ( x + 27)
➡ x = 24 and x = -27
so, we take x = 24.
Required multiples of 3
➡ x = 24
➡ x +3 = 24+3 = 27.
Answer:
The three consecutive multiples are 210, 216, 222
Step-by-step explanation:
3 consecutive multiples of 6 be : 6n , 6n + 6 , 6n + 12
Given sum of these 3 numbers is = 648
That is ,
6n + 6n + 6 + 6n + 12 = 648
18 n + 18 = 648
18n = 648 - 18
18 n = 630
n = 35
Therefore the three consecutive multiples are :
6 x 35 , 6 x 35 + 6, 6 x 35 + 12
210 , 210 + 6 , 210 + 12
210 , 216, 222
20 points and Brainliest !
Find the equation of the line with y-intercept 6 and slope -5/6 . What is the equation of the line in slope-intercept form?
Answer:
y = -5/6x + 6
Step-by-step explanation:
Slope intercept form is: y = mx + b
- where m is the slope
- where b is the y-intercept.
The problem already gives you the slope and y-intercept, so all you have to do is put it in for m and b respectively. Therefore, we have:
y = -5/6x + 6
Answer:
[tex]y = - \frac{5x}{6} + 6[/tex]
Step-by-step explanation:
1: Formulate equations/expressions:
[tex]based \: on \: the \: given \: conditions \: formulate[/tex]
[tex]m = - \frac{5}{6} \\ b = 6[/tex]
2: Write the equation:
[tex]write \: the \: equation \: of \: linear \: function[/tex]
[tex]y = mx + b[/tex]
3: substitute:
[tex]y = mx + b \\ m = - \frac{5}{6} \: b = 6 \\ y = - \frac{5}{6} x + 6[/tex]
4: rewrite the equation:
[tex]y = - \frac{5}{6} x + 6 \\ slope - intercept \: form \\ fin \: the \: required \: form: \\ y = - \frac{5x}{6} + 6[/tex]
The profit earned by a hot dog stand is a linear function of the number of hot dogs sold. It costs the owner $48 dollars each morning for the day’s supply of hot dogs, buns and mustard, but he earns $2 profit for each hot dog sold. Which equation represents y, the profit earned by the hot dog stand for x hot dogs sold?
y=48x−2
y=48x+2
y=2x−48
y=2x+48
Answer:
I think y=,48x+2 is correct
The equation y = 2x - 48 represents y, the profit earned by the hot dog stand for x hot dogs sold. Hence, 3rd option is the right choice.
What are equations?Equations are relations between two equal expressions, usually used to find the values of unknown variables using the constants and the values of other variables (if any).
How do we solve the given question?In the question, we are informed that the profit earned by a hot dog stand is a linear function.
We are also informed that it costs the owner $48 each morning for the day's supply and that he earns $2 profit on each hot dog he sells.
We are asked to find the equation of profit y, for the number of hot dogs sold x.
The basic cost to the owner is $48. This will be his fixed cost, irrespective of the number of hot dogs he sells.
His profit on one hot dog is $2. So, his profit on x number of hot dogs sold will be $2x.
His total profit will be equal to the profits he earned by selling x hot dogs minus the basic cost he needs to pay.
∴ Profit earned = Profit on x hot dogs - Basic cost
or, y = 2x - 48.
∴ The equation y = 2x - 48 represents y, the profit earned by the hot dog stand for x hot dogs sold. Hence, 3rd option is the right choice.
Learn more about equations at
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ACTUALLY ANSWER FULLY OR U WIL BE REPORTED Help pls I do need it
Answer:
125 people
Step-by-step explanation:
P( green) = number of green / total
= 25/120
=5/24
Multiply this probability by 600
5/24 * 600 =125
Answer:
out of 120 people 25 people has chosen green
out of 1 people green will be chosen by 25/120 people
out of 600 people green colour will be chosen by( 25/120)×600 people =25×5=people
hey again, could you help me with this and explain? thank you
Answer:
option 2
in the first equation y is greater than so it would be shaded above the line and in the second equation y is less than so it would be shaded below the line
Step-by-step explanation:
Match the rates with their equivalent unit rates. Match the rates with their equivalent unit rates. arrowRight arrowRight arrowRight arrowRight arrowRight arrowRight arrowRight arrowRight arrowRight arrowRight
Answer:
[tex]\frac{47}{2} \to 6[/tex]
[tex]\frac{60}{12} \to 5[/tex]
[tex]\frac{40}{10} \to 4[/tex]
[tex]\frac{56}{8} \to 7[/tex]
[tex]\frac{64}{8} \to 8[/tex]
Step-by-step explanation:
Given
See attachment
Required
Complete the blanks
To do this, we simply carry out the division operation.
So, we have:
[tex]\frac{47}{2} \to 6[/tex]
[tex]\frac{60}{12} \to 5[/tex]
[tex]\frac{40}{10} \to 4[/tex]
[tex]\frac{56}{8} \to 7[/tex]
[tex]\frac{64}{8} \to 8[/tex]
The rates of the given equivalent unit rates are properly matched as follows:
42/7 = 6
60/12 = 5
40/10 = 4
56/8 = 7
64/8 = 8
How to find Unit RateTo find the unit rate, the numerator is divided by the denominator such that the denominator is reduced to 1.
Thus, let's find the unit rates that matches with the equivalent rates given (see attachment below).
Divide the numerators by the denominators such that the value of the denominators are reduced to 1.
42/7 = 660/12 = 540/10 = 456/8 = 764/8 = 8Learn more about unit rate on:
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Which two of the following mapping statements describe the same translation?
O 6.-9) - (0,1)
0 (-3,7) (-9,10)
(1, -5) (-5, -2)
(2, 4) + (-4,1)
Answer:
The mapping statements (-3,7) -> (-9,10) and (1, -5)-> (-5, -2) describe the same translation.
Step-by-step explanation:
In a translation, we have that:
(x,y) -> (x+a,y+b)
In which a and b are how much the values change.
(6.-9) -> (0,1)
x subtracted by 6, y added by 10. So, the translation rule is:
(x,y) -> (x - 6, y + 10).
(-3,7) -> (-9,10)
x subtracted by 6, y added by 3. So
(x,y) -> (x - 6, y + 3).
(1, -5)-> (-5, -2)
x subtracted by 6, y added by 3. So
(x,y) -> (x - 6, y + 3)
Same rule as the above, so the mapping statements (-3,7) -> (-9,10) and (1, -5)-> (-5, -2) describe the same translation.
(2, 4) -> (-4,1)
x subtracted by 6, y subtracted by 3. So
(x,y) -> (x - 6, y - 3)
It is given the quadratic equation (q + 1 )x² - 8x + p = 0,where p and q are constants,has two equal real roots.Express p in terms of q.
Do help meeee!!!
Step-by-step explanation:
answer is in the photo above
Answer:
[tex]\displaystyle p = \frac{16}{q + 1}[/tex].
Step-by-step explanation:
Factor out the coefficient of [tex]x^{2}[/tex]:
[tex]\displaystyle \frac{1}{q + 1}\, [(q + 1)\, x^2 - 8\, x + p] = 0[/tex].
[tex]\displaystyle x^2 - \frac{8}{q + 1} \, x + \frac{p}{q + 1} = 0[/tex].
Let [tex]m[/tex] denote the real root of this equation. By the Factor Theorem, this equation would have the factor [tex](x - m)[/tex] repeated for two times in total:
[tex](x - m)^{2} = 0[/tex].
Expand to obtain: [tex]x^2 - 2\, m\cdot x + m^{2} =0[/tex].
Compare this expression with [tex]\displaystyle x^2 - \frac{8}{q + 1} \, x + \frac{p}{q + 1} = 0[/tex]:
[tex]\displaystyle -\frac{8}{q + 1} = -2\, m[/tex] (for the coefficient of [tex]x[/tex].)
[tex]\displaystyle \frac{p}{q + 1} = m^2[/tex] (for the constant.)
Rewrite the first equation to find an expression for [tex]m[/tex] in terms of [tex]q[/tex]:
[tex]\displaystyle m = \frac{4}{q + 1}[/tex].
Substitute this expression for [tex]m[/tex] into the second equation to find an expression for [tex]p[/tex] in terms of [tex]q[/tex]:
[tex]\displaystyle \frac{p}{q + 1} = m^2[/tex].
[tex]\displaystyle \frac{p}{q + 1} = \frac{4^2}{(q+1)^{2}}[/tex].
[tex]\displaystyle p = \frac{16}{q + 1}[/tex].
Verify that this expression for [tex]p[/tex] satisfies the requirements:
[tex]\displaystyle (q + 1) \, x^{2} - 8\, x + \frac{16}{q + 1} = 0[/tex].
[tex]\displaystyle x^2 - \frac{8}{q + 1} + \frac{16}{(q+1)^2} = 0[/tex].
[tex]\displaystyle x = \frac{4}{q + 1}[/tex] is the (repeated) real root of this quadratic equation.
increase 80 in the ratio 3:2 how
Answer:
Step-by-step explanation:
the second number be 2x. Therefore, the number 80 is divided in the ratio of 3:2 is, 48 and 32.
-1/2(-3/2x + 6x + 1) - 3x what is the equivalent expression
Answer:
Step-by-step explanation:
Apply the Distributive Property of Multiplication. Multiply each of the three terms inside parentheses by -(1/2):
(3/4)x - 3x - (1/2) - 3x, or
(3/4)x - 6x - 1/2
The first two terms can be combined, to obtain:
(-5 1/4)x - 1/2, or (-21/4)x - 1/2
Angela plays soccer and golf for a total of 125 minutes every day. She plays soccer 45 minutes more than she plays golf.
Part A: Write a pair of linear equations to show the relationship between the number of minutes Angela plays soccer (x) and the number of minutes she plays golf (y) every day. (5 points)
Part B: How much time does Angela spend playing golf every day? (3 points)
Part C: Is it possible for Angela to have spent 80 minutes playing soccer every day? Explain your reasoning. (2 points)
Answer:
Part A: x = y+45
Part B: 40 125-45 = 80, 80÷2 = 40
Part C: Yes, because 80+45 adds up to 125.
Hope this helps! :)
The graph shown here is the graph of which of the following rational
functions?
FN
O A. F(x)
O B. F(x)
O C. F(x) =
Help
Answer:
I think it's option B ...
Answer:
A.) F(x)=1/x-5
Step-by-step explanation:
Find the common ratio of the geometric sequence -13, 117, -1053,...
Answer:
-9
Step-by-step explanation:
Find the common ratio by dividing one of the numbers in the sequence by the previous number:
117/-13
= -9
So, the common ratio is -9.
Does it have a solution?
Answer:
It does since lets say X and Y equal 10 it works
Step-by-step explanation:
The amount of radium 226 remaining in a sample that originally contained A grams is approximately C(t) = A(0.999 567)t. Where t is time in years find the half-life to the nearest 100 years
Answer:
The half-life of the substance is of 1600 years.
Step-by-step explanation:
Amount of the substance:
The amount of the substance after t years is given by the following equation:
[tex]C(t) = A(0.999567)^t[/tex]
In which A is the initial amount.
Find the half-life:
This is t for which [tex]C(t) = 0.5A[/tex], that is, the amount is half the initial amount. So
[tex]C(t) = A(0.999567)^t[/tex]
[tex]0.5A = A(0.999567)^t[/tex]
[tex](0.999567)^t = 0.5[/tex]
[tex]\log{(0.999567)^t} = \log{0.5}[/tex]
[tex]t\log{0.999567} = \log{0.5}[/tex]
[tex]t = \frac{\log{0.5}}{\log{0.999567}}[/tex]
[tex]t = 1600[/tex]
The half-life of the substance is of 1600 years.
What are the challenges of similar triangles?
Answer:
There are two types of similar triangle problems; these are problems that require you to prove whether a given set of triangles are similar and those that require you to calculate the missing angles and side lengths of similar triangles. Subtract both sides by 130°. Hence; By Angle-Angle (AA) rule, ΔPQR~ΔXYZ.
Step-by-step explanation:
Help pls pls pls pls
Answer:
(C).
[tex]height = \sqrt{ {29}^{2} - {21}^{2} } \\ = \sqrt{400} \\ = 20 \: units[/tex]
if 1,a,5 and 15 are in proportion ,find the value of a
Answer:
a=3
Step-by-step explanation:
Given :
1:a :: 5: 15
To find a
a=15×1/5
a=3
Therefore, value of a =3
Given that ABCD is a rhombus, what is the value of X?
Answer:
3
Step-by-step explanation:
x=(5x-13)
so you work that equation out
take the 5x to the side of x and equate it to what you get
x=5x-13
5x+x=13+5
6x = 18 = x=3
6 6
x=3
Help!!!!!!!!!!! :((((
Answer:
just subtract
Step-by-step explanation:
first go number by number and then subtract them and see the average rate of change and input that number
1hr left on this test so confused
Which statement is true regarding the functions on the
graph?
Of(-3) = g(-4)
Of(-4)= (-3)
f(-3) = g(-3)
f(-4) = g(-4)
f(-3)=g(-4) 123456789012345
A sphere fits tightly in cylinder. The surface area of the sphere is 100π square inches. Find Volume of the cylinder.
Give answer in terms of π
Answer:
Volume of the cylinder = 250π inch²
Step-by-step explanation:
Surface area of the cylinder is given by,
Surface area = 4πr²
Here, r = radius of the sphere
Since, surface area = 100π square inches
100π = 4πr²
r² = 25
r = 5
From the picture attached,
Height of the cylinder = diameter of the sphere
= 2(r)
= 2(5)
= 10 inches
Volume of the cylinder is given by,
Volume = πr²h
Here, r = radius of the cylinder
h = height of the cylinder
Therefore, Volume of the cylinder = π(5)²(10)
= 250π square inches
My brain stopped. Please help
Answer:
∠1 = 90°
∠2 = 66°
∠3 = 24°
∠4 = 24°
Step-by-step explanation:
Usually the diagonals of a rhombus bisect each other at right angles.
Thus; ∠1 = 90°
Since they bisect at right angles, then;
∠R1S = 90°
Now, sum of angles in a triangle is 180°
Thus;
66° + 90° + ∠4 = 180°
156 + ∠4 = 180
∠4 = 180 - 156
∠4 = 24°
Now, also in rhombus, diagonals bisect opposite angles.
Thus; ∠4 = ∠3
Thus, ∠3 = 24°
Similarly, the diagonal from R to T bisects both angles into 2 equal parts.
Thus; ∠2 = 66°
Question 7 of 10
In the diagram below, AB is parallel to CD. What is the value of x?
120"
8
A. 80
B. 100
C. 60
D. 120
if sin a=4 by 5,determine cos a
Answer:
3/5
Step-by-step explanation:
[tex]Sin A = \frac{4}{5}=\frac{oppsite side}{hypotenuse}[/tex]
Adjacent side² = hypotenuse² - opposite side²
= 5² - 4²
= 25 - 16
= 9
Adjacent side = √9 = 3
Cos A = [tex]\frac{Adjacent side}{hypotenuse} = \frac{3}{5}[/tex]
Sin = 4/5 = Perpendicular/hypotenuse
CosA = Base/hypotenuse
Base = √hyp. ^- prep.^
Base= 3/5
May it helps yousolve the equation 4x-2 = 8
Answer:
x = 5/2
Step-by-step explanation:
4x-2 = 8
Add 2 to each side
4x-2+2 = 8+2
4x = 10
Divide by 4
4x/4 =10/4
x = 5/2
Answer:
x = 2.5
Step-by-step explanation:
4x - 2 = 8
4x = 8+2
4x = 10
x = 10/4
x = 2.5
. In Standard form 4 283.2 is written as A. 4.2832 x 10-3 B. 4.2832 X 10-1 C. 2832 x 10-2 D. 2832 x 103
What is the solution to the system of equations
Answer:
(8,-9)
Step-by-step explanation:
solve the equation for x
x=13/5-3/5y
7x+8y=-16
substitute the given value of x into the equation 7x+8y= -16
7(13/5-3/5y)+8y= -16
solve the equation for y
7(13/5-3/5)+8y= -16
y= -9
substitute the given value of y into the equation x=13/5-3/5y
x=13/5-3/5x(-9)
solve for x
x=8
the ordered pair is (8,-9)
Answer:
The solution to this system of equations is x = 8, and y = -9
Step-by-step explanation:
Firstly we need to use the first equation to represent "x" in terms of "y", so we do the following...
[tex]5x + 3y = 13\\5x = 13 - 3y\\x = \frac{13}{5} - \frac{3}{5}y[/tex]
Now we take the second equation and replace "x" with an equal value in terms of "y" which we know from the previous equation, and just solve for "y".
[tex]7x + 8y = -16\\7(\frac{13}{5} -\frac{3}{5} y) + 8y = -16\\\\18\frac{1}{5} - 4\frac{1}{5} y + 8y = -16\\\\3\frac{4}{5}y = -34\frac{1}{5} \\\\y = -34\frac{1}{5} / 3\frac{4}{5} \\y = -9[/tex]
After we found the value of "y" we can find the value of "x" by using any of the two equations, we just have put "-9" instead of "y". For example...
[tex]5x + 3y = 13\\5x + 3(-9) = 13\\5x - 27 = 13\\5x = 13 + 27\\5x = 40\\x = 40 / 5\\x = 8[/tex]
Now we know that the solution to this system of equations is x = 8, and y = -9
f(x) = x +1 and g(x) = {1/2x - 4. Which of the following is equal to g(f (2))?
A. -2
B. -5/2
C. 1/2x - 7/2
D. X - 7/2
-
ha Dilruba Hai song Kisne gaya hai
is this an expression or an equation? 4a + 3b-6cx9
Answer:
Expression
Step-by-step explanation:
Given expression :
4a+3b-6cx9
So this is expression not equation because equation consist zero on the righ side
Example: ax+b=0 (This is equation )
And
ax+b (This is expression)
