Answer:
x = 10
Step-by-step explanation:
Two less than three times a number is 28
Let's break it up.
2 less than: -2
3 times a number: 3x (x is representing a number")
is 28: = 28
So, let's put that together.
Two less than three times a number is 28
3x - 2 = 28
Now, let's solve this.
First, let's isolate the x.
To do this, we must add 2 to each side.
3x - 2 = 28
+2 +2
3x - 2 + 2 = 3x
28 + 2 = 30
We have 3x = 30
Now, we must simplify.
To do this, we must divide each side by 3.
This, in term, will tell us what x equals.
3x = 30
--- ----
3 3
3x/3 = x
30/3 = 10
x = 10
Final answer:
The answer to the algebraic equation 'Two less than three times a number is 28' is 10. This is solved by setting up the equation 3x - 2 = 28 and solving for x.
Explanation:
The student's question involves solving a basic algebraic equation. To find the number in question, we can set up the equation 3x - 2 = 28, where x represents the unknown number. By adding 2 to both sides of the equation, we get 3x = 30, and then by dividing both sides by 3, we arrive at x = 10. Thus, the number that the student is looking for is 10.
Step-by-step-explanation:
Two less than three times a number is 28.
Let's define the unknown number as x.
Translate the given sentence into an equation: 3x - 2 = 28.
Solve for x: 3x = 30, x = 10.
factorise 3×15×1/15
Answer:
3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
[tex]3.15.\frac{1}{15}\\\\3.\frac{15}{15}\\\\3.1\\\\3[/tex]
HELP ASAP ILL GIVE U BRAINLEST
Answer:
the answer is A
Step-by-step explanation:
Answer:
(-1,5)
Step-by-step explanation:
(?,0)
(-1,0)
(5,0)
find an equation of the line that passes through the point (3,-1) and is perpendiculor to line with slope -1/2
Answer:
perp. 2
y + 1 = 2(x - 3)
y + 1 = 2x - 6
y = 2x - 7
What is the value of x that makes the given equation true? 2(x−8)=x+5x
Answer:
x = - 4
Step-by-step explanation:
Given
2(x - 8) = x + 5x ← distribute left side and simplify right side
2x - 16 = 6x ( subtract 6x from both sides )
- 4x - 16 = 0 ( add 16 to both sides )
- 4x = 16 ( divide both sides by - 4 )
x = - 4
is (-2,-1) , (1,-4) and (5,-3) , (-2,-8) perpendicular?
keeping in mind that perpendicular lines have negative reciprocal slopes, let's find the slopes of these two, if they're indeed perpendicular, they'll be negative reciprocal of each other, meaning one slope will be the same as the other, but negative and upside-down, and thus their product will just be -1.
[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-2)}}}\implies \cfrac{-4+1}{1+2}\implies \cfrac{-3}{3}\implies \boxed{-1} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-8}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{5}}}\implies \cfrac{-8+3}{-7}\implies \cfrac{-5}{-7}\implies \boxed{\cfrac{5}{7}}[/tex]
well, 5/7 is not the negative reciprocal of -1.
If G={(-1,7),(8,2),(0,0),(6,6)}, then the range of G is
Answer: [tex]Range:\{0,2,6,7\}[/tex]
Step-by-step explanation:
By definition:
1) The Domain is the the set of all the input values, which are the x-coordinate of each ordered pair (the first number in each pair).
2)the Range is the set of all output values, which are the y-coordinate of each ordered pair (the second number in each pair).
In this case you have the following relation "G":
[tex]G=\{(-1,7),(8,2),(0,0),(6,6)\}[/tex]
Based on the definition shown before, you can conclude that the Domain of G is:
[tex]Domain: \{-1,0,6,8\}[/tex]
And the Range of G is the following:
[tex]Range:\{0,2,6,7\}[/tex]
43-3d = d+9
Solve the equation
Answer:
8.5 (plz give me the brainliest answer for this!!!!!!!!)
Step-by-step explanation:
43-3d=d+9
34=4d
8.5=d
Have a nice day!!!!!!!! :-)
KA
Answer: 8.5=d
Step-by-step explanation:
First u need to subtract nine on both sides of the equal sign canceling the nine on the right side, then it will leave you with 34-3d=d so then u add 3d to both sides again canceling the 3d on the left side, which leaves u with 34=4d then just divide the 4 on both sides leaving u with 8.5=d
Faye has 5 pieces of ribbon, each 1 yard long. She cuts each ribbon into sixths.
a. How many sixths will she have after cutting all the ribbons?
b. How long will each of the sixths be in inches?
Answer:
a ) total number of sixth in 5 ribbon will be 6\times 5 = 30
b) length of each sixth will be = 5.97 inches
Step-by-step explanation:
given data:
Number of pieces of ribbon is 5
each piece length 1 yard
total number of cut in one piece of ribbon = 6
a) one piece of ribbon consist of 6 sxiths
therefore total number of sixth in 5 ribbon will be 6\times 5 = 30
b) each ribbon length is 1 yard
so, whole ribbon is divided into 1\6 yard length which is length of individual division
we know that one yard is 36 inches
therefore, in 1/6 yard = 5.97 inches
Answer:
a. She will have 30 sixths after cutting all the ribbons.
b. 6 inches.
Step-by-step explanation:
a. You know that the lenght of each piece of ribbon is 1 yard.
She cuts each ribbon into sixths, then the lenght of each one of them is:
[tex]\frac{1}{6}\ yd[/tex]
So:
[tex]\frac{6}{6}=1\ yard[/tex]
Since Faye has 5 pieces of ribbon, after cutting all the ribbons she will have:
[tex](5)(\frac{6}{6})=\frac{30}{6}[/tex]
She will have 30 sixths after cutting all the ribbons.
b. You need make the conversion from yards to inches.
Knowing that [tex]1\ yd=36\ in[/tex], you get:
[tex](\frac{1}{6}\ yd)(\frac{36\ in}{1\ yd})=6\ in[/tex]
What is the equation of the least squares regression line for the data set?
Answer:
y = 1.862x − 0.138
Step-by-step explanation:
The equation of the least squares regression line is ŷ = -173.51 + 4.83x.
Explanation:The equation of the least squares regression line for a data set is represented as ŷ = a + bx, where a is the y-intercept and b is the slope of the line. To calculate the values of a and b, you minimize the sum of squared errors (SSE). Using calculus, you can determine the values that make SSE a minimum. In this case, the equation of the least squares regression line is ŷ = -173.51 + 4.83x.
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What is the true solution to the equation below?
In elnx+ In enx=-2 In 8
To solve the given equation, w need to review some rules:
The given equation is :
⇒⇒⇒⇒ rule (2)
⇒⇒⇒⇒ rule (1) and rule (2)
⇒⇒⇒⇒ rule (3)
removing the nature logarithm from both sides
∴ x = 4
So, the correct answer is option (2) ⇒⇒⇒⇒ x = 4
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The solution of the logarithmic equation is x = 4
What is Logarithm?The power to which a number must be increased in order to obtain another number is known as the logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm
The properties of Logarithm are :
log A + log B = log AB
log A − log B = log A/B
log Aⁿ = n log A
Given data ,
Let the logarithmic equation be represented as A
Now , the value of A is
[tex]ln[e^{ln ( x )} ] + ln[e^{ln (x^{2} )} ] = 2ln(8)[/tex]
On simplifying , we get
The value of ln e = 1
From the laws of logarithm , we get log Aⁿ = n log A
ln ( x ) ln ( e ) + ln ( x )² ln ( e ) = 2 ln ( 8 )
On further simplification , we get
ln ( x ) + ln ( x )² = ln ( 8 )²
From the laws of logarithm , we get log A + log B = log AB
ln ( x )³ = ln ( 64 )
ln ( x )³ = ln ( 4 )³
So , the value of x = 4
Hence , the logarithmic equation is solved
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Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x – 3)?
Which equation has solutions of 6 and -6?
Answer:
x^2-36=0
Step-by-step explanation:
x^2-36=0
(x-6)(x+6)
Answer:
[tex]x^2-36=0[/tex]
Step-by-step explanation:
Solution is 6 and -6. Lets check with each option
[tex]x^2-12x+36=0[/tex]
[tex](x-6)(x-6)=0[/tex]
x-6=0 so x=6
Solutions are 6 and 6. First option does not gives us solution 6 and -6
[tex]x^2+12x-36=0[/tex]. It is not factorable
[tex]x^2+36=0[/tex]. It is not factorable
[tex]x^2-36=0[/tex]
[tex](x+6)(x-6)=0[/tex]
x-6=0 , so x=6
x+6=0, so x=-6
[tex]x^2-36=0[/tex] is the final answer
Subtract 582,295 from670,63
Answer: 100,335
Step-by-step explanation: Whenever you see the terms "subtract _____ from blank," the numbers in the equation will be reverse. For example, subtract 76 from 100 would be translated as 100-76. This applies here. The equation is 670,630-582,295, which is 100,335
Consider the quadratic function:
f(x) = x2 – 8x – 9
Vertex: (StartFraction negative b Over 2 a EndFraction, f (StartFraction negative b Over 2 a))
What is the vertex of the function?
(
,
)
Answer:
vertex = (4, - 25 )
Step-by-step explanation:
Given a quadratic function in standard form : f(x) = ax² + bx + c : a ≠ 0
The the x- coordinate of the vertex is
[tex]x_{V}[/tex] = - [tex]\frac{b}{2a}[/tex]
f(x) = x² - 8x - 9 ← is in standard form
with a = 1, b = - 8, thus
[tex]x_{V}[/tex] = - [tex]\frac{-8}{2}[/tex] = 4
Substitute x = 4 into f(x) for corresponding value of y
f(4) = 4² - 8(4) - 9 = 16 - 32 - 9 = - 25
vertex = (4, - 25 )
Answer:
vertex is (4,-25)
Step-by-step explanation:
[tex]f(x) = x^2 - 8x - 9[/tex]
To find out the vertex we use formula
[tex]x=\frac{-b}{2a}[/tex]
From the given f(x), the value of a=1, b=-8 and c=-9
Plug in the values in the formula
[tex]x=\frac{-(-8)}{2(1)}[/tex]
x=4
Now find the value of y
plug in 4 for x in f(x)
[tex]f(4) = 4^2 - 8(4)- 9=-25[/tex]
The value of y is -25
The vertex is (4,-25)
Jeremiah and Cynthia each run a lemonade stand. They decide that they will share the
money they make evenly Jeremiah makes $237 at his stand and Cynthia makes $218.
After they combine and split up their money evenly, which statement must be true
a. They each get $229 with no money left over
b. They each get $228 with $1 left over
C. They each get $910 with no money left over
d. It is not possible to share their money evenly
Answer:
I believe it's D.
Step-by-step explanation:
if you add 237 + 228 you get 455. 455 divide by 2 is 227.5 which doesn't make it even.
Alex went to the grocery store and bought 5 avocados. He paid $10 and received $4.50 in change. How much did each avocado cost if they are each the same amount?
Answer:
$1.10
Step-by-step explanation:
We have been that Alex went to the grocery store and bought 5 avocados. He paid $10 and received $4.50 in change.
First of all, we will find amount paid for 5 avocados by subtracting $4.50 from $10.
[tex]\text{Amount paid for 5 avocados}=\$10-\$4.50[/tex]
[tex]\text{Amount paid for 5 avocados}=\$5.50[/tex]
Now, we will divide $5.50 by 5 to find cost of each avocado.
[tex]\text{Cost of each avocado}=\frac{\$5.50}{5}[/tex]
[tex]\text{Cost of each avocado}=\$1.10[/tex]
Therefore, the cost of each avocado is $1.10.
A principal evenly distributes 6 reams of copy paper to 8 fifth-grade teachers.
a. How many reams of paper does each fifth-grade teacher receive? Explain how you know using pictures, words, or numbers.
b. If there were twice as many reams of paper and half as many teachers, how would the amount each teacher receives change? Explain how you know using pictures, words, or numbers.
Answer: We start with 6 reams of copy paper and 8 teachers.
a) if we distribute the paper equally between all the teachers, then each teacher receive 6/8 (here we are dividing the total number of reams by the number of people that we are are splitting it). but 6/8 is less than one, so we must open the reams in order to split them.
b) If there were twice as many reams of paper, then we will have 2*6 = 12 reams of paper, and if there where half the number of teachers, then we have 8/2 = 4 teachers.
Doing the same procedure as before, we have 12 teams for 4 teachers, then each teacher has 12/4 = 3 reams
before, each teacher received 6/8 reams, and now, each one receive 3.
if we want to know the change, we need to see the difference between these numbers, so 3 - 6/8 = 3*8/8 - 6/8
notice that i am multiplying the 3 by 8/8, this is one, but this way i can have the same denominator in both numbers.
24/8 - 6/8 = 18/8 = 9/4 = 8/4 + 1/4 = 2 + 1/4
so each teacher receive 2 + 1/4 reams than before.
Venetta buys 2 pounds of pistachios and 3 pounds of almonds. The pistachios cost $4 more per pound than the almonds. She pays a total of $48. Which of the following are true? Select all that apply.
A. One pound of pistachios plus 1 pound of almonds cost $20.
B. The pistachios cost twice as much per pound as the almonds.
C. Reducing the number of pounds of almonds by 1 results in a total cost of $40.
D. The cost a, in dollars, of 1 pound of almonds is modeled by 2(a – 4) + 3a = 48.
E. The cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48.
Answer:
A. One pound of pistachios plus 1 pound of almonds cost $20
C. Reducing the number of pounds of almonds by 1 results in a total cost of $40.
E. The cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48.
Step-by-step explanation:
Let
x ----> the cost of one pound pistachios
y ----> the cost of one pound of almonds
we know that
x=y+4 -----> equation A
2x+3y=48 -----> equation B
substitute equation A in equation B and solve for y
2(y+4)+3y=48
2y+8+3y=48
5y=48-8
y=8
Find the value of x
x=8+4 =12
therefore
The cost of one pound pistachios is $12 and the cost of one pound of almonds is $8
Verify all statements
case A) One pound of pistachios plus 1 pound of almonds cost $20.
Is True
x+y=$12+$8=$20
case B) The pistachios cost twice as much per pound as the almonds
Is false
Because
2y=2(8)=$16
$16≠$12
case C) Reducing the number of pounds of almonds by 1 results in a total cost of $40
Is True
Because
2x+2y=2(12)+2(8)=$40
case D) The cost a, in dollars, of 1 pound of almonds is modeled by 2(a – 4) + 3a = 48.
Is false
The equation will be
2(a + 4) + 3a = 48.
case E) The cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48
Is true
Because
p=a+4
Solve for a
a=p-4
write three numbers that have GCF of 7
Answer:
21, 35 , 49
Step-by-step explanation:
21 = 3 * 7
35 = 5 * 7
49 = 7 * 7
GCF = 7
∡rst is a right angle. if rs has a slope of 3, what must be the slope of st?
Answer:
The slope of st is -1/3
Step-by-step explanation:
we know that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
[tex]m1*m2=-1[/tex]
we have
[tex]m1=3[/tex]
substitute and solve for m2
[tex](3)*m2=-1[/tex]
[tex]m2=-\frac{1}{3}[/tex]
therefore
The slope of st is -1/3
Help me with answer 9
Answer:
64
Step-by-step explanation:
2 to the power of 3 is 8 and 2 to the power of 4 is 16 and 2 to the power of 1 is 2 and 16 divided by 2 is 8 and 8 times 8 equals 64
rearrange the formula to make a) f the subject and b) v the subject. 1/v+1/u=1/f
Answer:
see explanation
Step-by-step explanation:
Multiply through by the lowest common multiple of u, v and f, that is uvf
uvf × [tex]\frac{1}{v}[/tex] + uvf × [tex]\frac{1}{u}[/tex] = uvf × [tex]\frac{1}{f}[/tex], that is
uf + vf = uv ← factor out f on the left side → (1)
f(u + v) = uv ← divide both sides by (u + v)
f = [tex]\frac{uv}{u+v}[/tex]
(b)
Using line (1)
uf + vf = uv ( subtract uv from both sides )
uf + vf - uv = 0 ( subtract uf from both sides )
vf - uv = - uf ← factor out v on the left side
v(f - u) = - uf ← divide both sides by (f - u)
v = - [tex]\frac{uf}{f-u}[/tex]
can someone help me solve this?
1.8
to find the circumference of a circle you have to multiple the diameter by pi (3.14). so if you have the circumference already just switch around the equation (since you don’t know the diameter) to 10.99 divided by 3.14 to find the diameter and you get 3.5. but thats the diameter and you have to find the radius so divide 3.5 by two and you get 1.75 and 1.75 rounded to the nearest tenths is 1.8
Answer is provided in the image attached.
What is the value of x?
12 units
15 units
20 units
24 units
Answer:
Answer: The value of x is 15 units. Step-by-step explanation: In the given triangle RSQ and ΔRST it is given that. ∠RTS ≅ ∠SRQ ≅ 90°.
Step-by-step explanation:
Answer:
20 units
Step-by-step explanation:
I got it wrong with 15 for the cumulative exam on EDGE 2020/2021
Find y if the line through (3,5) and (6,y) has a slope of 2
Answer:
The answer is y = 11.
Show all work to multiply
Answer:
-42+10i
Step-by-step explanation:
*start with the square roots
\sqrt{-25} \\ =5i
\sqrt{-100} \\ = 10i
*then insert values
(2+5i)(4-10i)
*Use FOIL to multiply
2x4 + 2x-10i + 5ix4 + 5ix10i
*Simplify
8-10i+20i+50i(squared)
*Add like terms
-42+10i
*( i squared = -1 )
Find the first and second derivative of the function defined by the parametric equation.
x = 3e and y= 3^3t - 1
Answer:
Step-by-step explanation:
Given two parametric equations [tex]x(t)[/tex] and [tex]y(t)[/tex], the first derivative can be found using the following equation:
[tex]\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}[/tex]
In this problem, [tex]x(t) = 3e[/tex] and [tex]y(t) = 3^{3t} - 1[/tex]. Finding the derivative of each of these functions with respect to [tex]t[/tex] gives us the following:
[tex]\frac{dx}{dt} = 0[/tex]
[tex]\frac{dy}{dt} = 3^{3t + 1}\log{3}[/tex]
Because [tex]\frac{dx}{dt} = 0[/tex], that means the function is a vertical line and has an infinite first derivative.
Final answer:
The first derivative of the x-component is zero, and the first derivative of the y-component is 27. The second derivatives of both components are zero.
Explanation:
To find the first and second derivatives of the function defined by the parametric equation, we need to differentiate each component with respect to the parameter (in this case, t). Let's start with x = 3e, which is a constant, so its derivative is zero. Next, let's differentiate y = 3^3t - 1. The derivative of 3^3t with respect to t is (3^3)(1) = 27, and since the derivative of -1 with respect to t is 0, the y-component's derivative is 27.
Now, to find the second derivative, we differentiate the derivatives we found. The second derivative of x is still zero since the first derivative is zero. The second derivative of y (27) is also zero since it is a constant. Therefore, the first and second derivatives of the parametric equation are dx/dt = 0 and dy/dt = 27, respectively.
When rounding to the nearest hundred, what is the least whole number that rounds to 900?
Answer:
850 rounds up to 900
Step-by-step explanation:
if it's 5 or more it will go up, if it were 840 it'll drop to 800
You are given the expressions 76+ n and 2n + 26 what is the smallest value of n that will make each number rational ?
Answer:
A proof that square root of 2 is irrational. ... An equation x² = a, and the principal square root ... The number under the radical sign is called the radicand. ... the given square numbers, each product of square numbers is equal to what square ... are relatively prime -- and it will be impossible to divide n· n into m· m and get 2.
Step-by-step explanation:
Rational numbers are numbers that can be represented as a fraction of two integers. For [tex]\sqrt{76 + n}[/tex] and [tex]\sqrt{2n + 26}[/tex] to be rational, the smallest value of n is 5
Given that:
[tex]\sqrt{76 + n}[/tex] and [tex]\sqrt{2n + 26}[/tex] --- correct expressions
For both numbers to be rational, we should be able to represent the numbers as a fraction of two integers.
There are no straight ways to solve this, except trial by error.
When [tex]n = 1[/tex]
[tex]\sqrt{76 + n} = \sqrt{76 + 1} = \sqrt{77} = 8.77496.......[/tex]
The above is not rational
When [tex]n = 2[/tex]
[tex]\sqrt{76 + n} = \sqrt{76 + 2} = \sqrt{78} = 8.83176......[/tex]
The above is not rational
When [tex]n = 3[/tex]
[tex]\sqrt{76 + n} = \sqrt{76 + 3} = \sqrt{79} = 8.88819......[/tex]
The above is not rational
When [tex]n = 4[/tex]
[tex]\sqrt{76 + n} = \sqrt{76 + 4} = \sqrt{80} = 8.944271......[/tex]
The above is not rational
When [tex]n = 5[/tex]
[tex]\sqrt{76 + n} = \sqrt{76 + 5} = \sqrt{81} = 9[/tex]
The above is rational
So, we try [tex]n = 5[/tex] for the second expression
[tex]\sqrt{2n + 26} = \sqrt{2\times 5 + 26} = \sqrt{10 + 26}=\sqrt{36}= 6[/tex]
The above is also rational
Hence, the smallest value of n that makes each of the expression rational is [tex]n = 5[/tex]
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Sam bought one dozen eggs from the grocery store to bake some cakes.how many eggs did Sam buy?
Answer:
He buy 12 eggs from grocery.
Because,
1 dozen of a thing(x) = 12 things(x)
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