Solve the equation and check.
7x-5= 3 + 3x
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
OA. The solution is
(Simplify your answer.)
OB. The solution is all real numbers
OC. There is no solution
Answer: x = 2
OA. The solution is
(Simplify your answer.)
Step-by-step explanation:
find DF if D is between E and F, ED = 6x-4 , DF =3x+5 and EF= 46
Answer:
DF= 20
Step-by-step explanation:
6x-4+3x-5=46
then you solve for x (x=5).
then plug it it : 3(5)+5=20
Value of DF is 20 unit
Given that;ED = 6x - 4
DF = 3x + 5
EF = 46
Find:Value of DF
Computation:We know that;
EF = ED + DF
46 = 6x - 4 + 3x + 5
46 = 9x + 1
9x = 45
x = 5
Value of DF = 3x + 5
Value of DF = 3(5) + 5
Value of DF = 15 + 5
Value of DF = 20 unit
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A volcano in the ocean rises approximately 14,000 feet above sea level. Its base is approximately 20,000 feet below sea level. What is the total height of the volcano?
Answer:
6,000 feet
Step-by-step explanation:
You have three consecutive odd integers. Four times the smallest decreased by 5 is the same as the largest increased by 12. What is the smallest of the integers?
Answer:
The smallest of the integers is 7
Step-by-step explanation:
Let the integers be x, y and z
From the question, the integers are consecutive odd integers.
Hence,
If the smallest of the integers is x and the largest is z, then we can write that,
x + 2 = y and
y + 2 = z
Then, x + 2 + 2 = z
∴ x + 4 = z ....... (1)
From the question, four times the smallest decreased by 5 is the same as the largest increased by 12, that is
4x -5 = z + 12 ....... (2)
Put the value of z = x + 4 in equation (1) into equation (2),
We then get
4x - 5 = x + 4 + 12
4x - x = 4 + 12 + 5
3x = 21
x = 7
Hence, the smallest of the integers is 7
The other integers are 9 and 11 ( y= 9 and z = 11)
Solve the following equation for b be sure to take into account whether a letter is capitalized or not f = ad
Answer:
Step-by-step explanation:
J
need help with this
please
Answer:
[tex]x^{\frac{2}{3} }[/tex]
Step-by-step explanation:
Exponent Rules: [tex](b^m)^n = b^{mn}[/tex]
Exponent Rules: [tex]\frac{x^m}{x^n} = x^{m-n}[/tex]
Step 1: Write expression
[tex]\frac{\sqrt[4]{x^3} }{x^{\frac{1}{12} }}[/tex]
Step 2: Rewrite radical
[tex]\frac{{(x^3)^{\frac{1}{4} }} }{x^{\frac{1}{12} }}[/tex]
Step 3: Multiply powers (numerator)
[tex]\frac{{x^{\frac{3}{4} }} }{x^{\frac{1}{12} }}[/tex]
Step 4: Subtract powers
[tex]x^{\frac{2}{3} }[/tex]
Please help me to prove this!
Answer: see proof below
Step-by-step explanation:
Given: A + B = C → A = C - B
→ B = C - A
Use the Double Angle Identity: cos 2A = 2 cos² A - 1
→ (cos 2A + 1)/2 = cos² A
Use Sum to Product Identity: cos A + cos B = 2 cos [(A + B)/2] · 2 cos [(A - B)/2]
Use Even/Odd Identity: cos (-A) = cos (A)
Proof LHS → RHS:
LHS: cos² A + cos² B + cos² C
[tex]\text{Double Angle:}\qquad \dfrac{\cos 2A+1}{2}+\dfrac{\cos 2B+1}{2}+\cos^2 C\\\\\\.\qquad \qquad \qquad =\dfrac{1}{2}\bigg(2+\cos 2A+\cos 2B\bigg)+\cos^2 C\\\\\\.\qquad \qquad \qquad =1+\dfrac{1}{2}\bigg(\cos 2A+\cos 2B\bigg)+\cos^2 C[/tex]
[tex]\text{Sum to Product:}\quad 1+\dfrac{1}{2}\bigg[2\cos \bigg(\dfrac{2A+2B}{2}\bigg)\cdot \cos \bigg(\dfrac{2A-2B}{2}\bigg)\bigg]+\cos^2 C\\\\\\.\qquad \qquad \qquad =1+\cos (A+B)\cdot \cos (A-B)+\cos^2 C[/tex]
[tex]\text{Given:}\qquad \qquad 1+\cos C\cdot \cos (A-B)+\cos^2C[/tex]
[tex]\text{Factor:}\qquad \qquad 1+\cos C[\cos (A-B)+\cos C][/tex]
[tex]\text{Sum to Product:}\quad 1+\cos C\bigg[2\cos \bigg(\dfrac{A-B+C}{2}\bigg)\cdot \cos \bigg(\dfrac{A-B-C}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =1+2\cos C\cdot \cos \bigg(\dfrac{A+(C-B)}{2}\bigg)\cdot \cos \bigg(\dfrac{-B-(C-A)}{2}\bigg)[/tex]
[tex]\text{Given:}\qquad \qquad =1+2\cos C\cdot \cos \bigg(\dfrac{A+A}{2}\bigg)\cdot \cos \bigg(\dfrac{-B-B}{2}\bigg)\\\\\\.\qquad \qquad \qquad =1+2\cos C \cdot \cos A\cdot \cos (-B)[/tex]
[tex]\text{Even/Odd:}\qquad \qquad 1+2\cos C \cdot \cos A\cdot \cos B\\\\\\.\qquad \qquad \qquad \quad =1+2\cos A \cdot \cos B\cdot \cos C[/tex]
LHS = RHS: 1 + 2 cos A · cos B · cos C = 1 + 2 cos A · cos B · cos C [tex]\checkmark[/tex]
Can you help me please?
Answer:
the answer is 2.620
Step-by-step explanation:
the way u will get this is at the top there pattern is adding the bottom they are subtracting 2
The function g(x) = x2 – 10x + 24 is graphed on a coordinate plane. Where will the function cross the x-axis
Answer:4.0 and 6.0
Step-by-step explanation:
Mandy has a piece of ribbon measuring 3.2 m and Cheryl has a piece of ribbon measuring 4.7 m select the point on this number line that represents the ribbon lengths
Answer:
3.2
Step-by-step explanation:
3.2/1
I don’t know how to do this
Answer:
60yd
Step-by-step explanation:
First you multiply 3yd, and 6yd to get the area of 18 yards.
Second, you multiply the length of the triangle, so 6*7 is 42.
Finally you add both of the areas together to get the area of the full shape.
Find the parabola through
(
−
7
,
−
39
)
(
-
7
,
-
39
)
with vertex
(
−
4
,
−
12
)
Answer:
y = - 3x² - 24x - 60
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (- 4, - 12 ), thus
y = a(x + 4)² - 12
To calculate a substitute (- 7, - 39) into the equation
- 39 = a(- 7 + 4)² - 12 ( add 12 to both sides )
- 27 = 9a ( divide both sides by 9 )
- 3 = a
y = - 3(x + 4)² - 12 ← in vertex form
Expand (x + 4)²
y = - 3(x² + 8x + 16) - 12
= - 3x² - 24x - 48 - 12
y = - 3x² - 24x - 60 ← in standard form
= - 3(x²
A queen ant lays 1.83 x 10^6 eggs over a period of 30 days. Assuming she lays the same number of eggs each day, about how many eggs does she lay in one day? Express your answer in scientific notation.
x-7/4 =-2 I need helpp
Answer:
x = -1
Step-by-step explanation:
x-7/4=-2
x-7=-8
x=-1
Please help me!! What is the value of???
-4×3
12÷(-6)???
Answer:
-4x3=12
12÷-6=-2
hope this helps
does a function have to be linear
Answer:
Hi there
Step-by-step explanation:
A linear function is a type of function and so must follow certain rules to be classified as a “function”. For example, functions can only have one output for each input. On the other hand, equations are just statements that make two things equal, like x = y or 52x = 100.
~Your Welcome! :)
a group of 4 students needs to share 20 paper clips equally. how many paper clip does each students get
Answer:
5 paper clips each
Step-by-step explanation:
20/4 = 5
Answer:
They each get 5
Step-by-step explanation:
Xian and his cousin Kai both collect stamps. Xian has 52 stamps, and Kai has 72 stamps. The boys recently
joined different stamp-collecting clubs. Xian's club will send him 12 new stamps per month. Kai's club will
send him 8 new stamps per month. After how many months will Xian and Kai have the same number of
stamps? How many stamps will each have?
After
months Xian and his cousin will have
stamps each.
Answer:
Step-by-step explanation:
Let the x be the number of months.
In x months, xian will have:
(52+16x) stamps
and kai will have:
(76+12x)stamps
To find out how many months they will have the same number of stamps, we evaluate the two expressions:
52+16x=76+12x
52+4x=76
4x=24
x=6
So xian and kai will have the same number of stamps after 6 months.
Using either of two expressions, each will have:
52+16(6)=76+12(6)= 148 stamps.
Would appreciate if you could give brainiest have a great day
Answer:
6 months
Step-by-step explanation:
56+ 12x = 80 + 8x
Factorize completely
- 3a² + 4a + 4
The price to mail a letter at the post office is $0.49 for the first ounce
and $0.21 for each additional ounce. Amrit paid $1.96 to mail his letter.
How much did the letter weigh?
helphelphelphelphelp
Answer:
Point A
Step-by-step explanation:
if a =1 + r + 7r and b = 1 -r ,find an expression that equals A+ 3B in standard form. Answer:
Answer:
A+3B=4+5r
Step-by-step explanation:
Given that,
A = 1+r+7r
B = 1-r
We need to find an expression that is equal to A+3B.
Putting the values of A and B in A+3B, we get :
A+3B = 1+r+7r + 3(1-r)
=1+8r+3-3r
=(1+3) +(8r-3r)
=4+5r
Hence, the values of A+3B equals 4+5r.
Pls help me out and follow the steps
Answer:
4w + 3 = 2w + 7
-[2w] -2w
-----------------------
2w + 3 = 7
-3 -[3]
----------------------
2w = [4]
2w = 4
---- ----
2 [2]
w = [2]
Find the midpoint between (-1, -1) and (-9,6).?
Answer:
(-5,-3.5) is the midpoint
Step-by-step explanation:
See photo for the step-by-step explanation
Answer:
(4, -3.5)
Step-by-step explanation:
what is another way to represent this solution set?
Answer:
What solution set? I think you forgot to add a picture..
What solution do you need help with? :)
When dividing two numbers with the same base
Answer:
you subtract the exponents
A truck enters a highway at 60 mph. A car enters the highway at the same place 11 minutes later and drives 74 mph in the same direction. From the time the car enters the highway, how long will it take the car to pass the truck?
Answer:
3/20
Step-by-step explanation:
Solve for x.
5/3=x-4/2
Simplify your answer as much as possible.
Answer:
22
Step-by-step explanation:
5/3=x-4/2
10=x-12
x=22
Answer:
[tex]3 \frac{2}{3}[/tex]
Step-by-step explanation:
5/3 = x - 4/2
5/3 + 4/2 = x
11/3 = x
x = 3 2/3
The proceeds from a car wash are directly proportional to the number of cars washed. The total after 9 cars was $180. How much can be raised if 60 cars
are washed?
60 cars washed?
Answer:
$1200
Step-by-step explanation:
180 divided by 9 is 20, so they earned $20 per car washed. They want to wash 60 cars, and if they wash 60 cars they would earn $1200. (60 x 20)
Answer:
$1200
Step-by-step explanation:
Our revenue is directly proportional to the number of cars. That means our revenue is increasing at a constant rate, and thus, we are getting the same amount of money per car. That means we can find out how much we get from washing 1 car.
[tex]\frac{180}{9} = 20[/tex]
$20 per car.
If we washed 60 cars, we'd earn 60 * $20:
[tex]60*20 = 1200[/tex]
Answer: $1200
-12=x-1 Please help need help
Answer:
x = -11
Step-by-step explanation:
-12 = x - 1
-12 + 1 = x
x = -11
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = - 11}}}}}[/tex]
Step-by-step explanation:
[tex] \bigstar{ \sf{ \: - 12 = x - 1}}[/tex]
[tex] \tt{Step \: 1 \: }[/tex] : Swap the sides of the equation
[tex] \hookrightarrow{ \sf{x - 1 = - 12}}[/tex]
[tex] \tt{Step \: 2 \: }[/tex] : Move 1 to right hand side and change it's sign
[tex] \hookrightarrow{ \sf{x = - 12 + 1}}[/tex]
[tex] \tt{Step \: 3}[/tex] : Calculate
Remember : The negative and positive integers are always subtracted but posses the sign of the bigger integer.
[tex] \hookrightarrow{ \sf{x = - 11}}[/tex]
The value of x = 11
Hope I helped!
Best regards! :D
~TheAnimeGirl