Answer:
12
Step-by-step explanation:
28 / 4 = 7
1) -2
2) -2+7=5
3) 5+7=12
4) 12+7=19
5)19+7=26
When moving in equal steps from -2 to 26 over four steps, each step increases the value by 7. Therefore, after two steps from -2, the third number you reach is 12.
Explanation:The question is about stepping evenly or moving in equal intervals from an initial number. Given that the first number is -2 and the fifth number is 26, we need to determine what the third number would be. Taking -2 being the first and the fifth being 26 means there are 4 steps between them. To find the equal steps between, you need to subtract -2 from 26 and divide by 4 (the steps in between), which gives you 7. This means each step increases the value by 7. Therefore, the first number is -2, the second number is -2+7 = 5, and third number is 5+7=12.
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What is the value of (f o g)(7)
F(x)=x^2; g(x)= x-4
Answer:
Step-by-step explanation:
(f o g)(7) = f(g(7))
but g(7) = 7-4 =3
(f o g)(7) = f(g(7)) = f(3) = 3² =9
Derive the equation of the parabola with a focus at (−2, 4) and a directrix of y = 6. Put the equation in standard form.
f(x) = one fourthx2 − x + 4
f(x) = −one fourthx2 − x + 4
f(x) = one fourthx2 − x + 5
f(x) = −one fourthx2 − x + 5
Answer:
B
Step-by-step explanation:
From any point (x, y) on the parabola the focus and directrix are equidistant.
Using the distance formula
[tex]\sqrt{(x+2)^2+(y-4)^2}[/tex] = | y - 6 |
Squaring both sides
(x + 2)² + (y - 4)² = (y - 6)² ← distributing
x² + 4x + 4 + y² - 8y + 16 = y² - 12y + 36 ( subtract y² - 12y + 36 from both sides )
x² + 4x + 4 + 4y - 20 = 0 ( subtract x² + 4x + 4 from both sides )
4y - 20 = - x² - 4x - 4 ( add 20 to both sides )
4y = - x² - 4x + 16 ( divide through by 4 )
y = - [tex]\frac{1}{4}[/tex] x² - x + 4, that is
f(x) = - [tex]\frac{1}{4}[/tex] x² - x + 4 → B
Answer:
Option B
Step-by-step explanation:
Given that a parabola has a focus at (−2, 4) and a directrix of y = 6.
We have to find the equation of the parabola in std form
We know that a parabola is a conic section in which all points are equidistant from the focus and vertex.
Let (x,y) be any point on the parabola
Distance of (x,y) from the focus =[tex]\sqrt{(x+2)^2+(y-4)^2}[/tex] ...i
Distance of (x,y) from directrix = difference in y coordinate = [tex]|y[-6|[/tex]...ii
Since i = ii, square and equate both
[tex](x+2)^2+(y-4)^2=(y-6)^2\\x^2+4x+4 -8y+16 = -12y+36\\4y=-x^2-4x+16\\y = \frac{-1}{4} d^2-x+4[/tex]
Hence option B is right.
Simplify:(-3x)(-2x5)
Answer: 30x
Multiply
−
2
by
5
.
−
3
x
⋅
−
10
Multiply
−
10
by
−
3
.
30
x
Answer:
6[tex]x^{6}[/tex]
Step-by-step explanation:
Using the rule of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]
Given
(-3x)(-2[tex]x^{5}[/tex])
= - 3 × [tex]x^{1}[/tex] × - 2 ×[tex]x^{5}[/tex]
= (- 3 × - 2) × [tex]x^{(1+5)}[/tex]
= 6[tex]x^{6}[/tex]
Which equation could be solved using the graph above?
X^2+x-2=0
X^2+2x+1=0
X^2-1=0
X^2-2x+1=0
The equation that could be used to solve the graph above is x² - 1 = 0.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
The graph of a quadratic equation y = x² is a parabola that opens upwards.
By observing the graph we conclude that when x = 0, y = - 1 and when
x = ± 1, y = 0.
Now going through the options we conclude that x² - 1 = 0 is the equation that satisfies this criterion.
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The equation that can be solved using the graph is x^2 - 2x + 1 = 0.
Explanation:The equation that could be solved using the graph above is x2 - 2x + 1 = 0. This is because the graph intersects the x-axis at the point where y=0, and this represents the solutions to the equation.
If we solve the equation x2 - 2x + 1 = 0 using factoring or the quadratic formula, we would find that the solutions are x=1 and x=1. These are the same x-values where the graph intersects the x-axis on the graph provided.
The other equations, x2 + x - 2 = 0, x2 + 2x + 1 = 0, and x2 - 1 = 0, do not have solutions that match the x-values where the graph intersects the x-axis.
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1. Two angles are supplements. The larger is 10 more than 4 times the smaller. Find both angles,
2. Two angles are supplements. They're equal in measure. Find both angles.
3. The supplement of an angle is three times the complement of the angle. Find the angle.
4. The supplement of an angle is 12 less than twice the angle. Find both angles.
Step-by-step explanation:
Supplementary angles equal 180°
1. Let the two angles be x and y
then y = 4x + 10
x + y = 180
x + (4x + 10) = 180
5x + 10 = 180
5x = 180 - 10
5x = 170
x = 170 / 5
x = 34
x = 34y = 146
2. if the two angles are equal then divide 180 by 2 to get 90
3. 180 - x = 3(90 - x)
180 - x = 270 - 3x
2x = 90
x = 45
4. 180 - x = 2x - 12
180 - 12 = 2x + x
168 = 3x
x = 56
Solve for "X".
x2 = 121
X = ? or x = ?
Which of the following properties can be used to show that the expression 4^5/3 is equivalent to ^3√4^5
Answer: First option.
Step-by-step explanation:
For this exercise it is importnatn to to remember the properties that are shown below:
1) [tex]a^\frac{1}{n}=\sqrt[n]{a}[/tex]
2) [tex](a^m)^n=a^{(mn)}[/tex]
Therefore, given the following expression provided in the exercise:
[tex]\sqrt[3]{4^5}[/tex]
You can apply the properties mentioned before, in order to find an equivalent expression.
Therefore, you get:
[tex]\sqrt[3]{4^5}=(4^5)^{\frac{1}{3}}=4^{\frac{5*1}{3}}=4^{\frac{5}{3}}[/tex]
Then the answer is the first option.
Answer:
[tex]\sqrt[3]{4^5}=(4^5)^{\frac{1}{3}}=4^{\frac{5}{3}}[/tex]
Option 1 and Option 3 is correct
Step-by-step explanation:
Given: [tex] 4^{\frac{5}{3}}=\sqrt[3]{4^5}[/tex]
This is exponent to radical change property.
The fraction exponent write as radical.
[tex]a^{\frac{m}{n}}=\sqrt[n]{a^m}[/tex]
Option 1: Radical to exponent[tex]\sqrt[3]{4^5}=(4^5)^{\frac{1}{3}}=4^{\frac{5}{3}}[/tex]
True
Option 2: Addition of exponent if base is same.[tex]4^{\frac{8}{3}}\cdot 4^{\frac{7}{3}}=4^{{\frac{8}{3}+\frac{7}{3}}=4^5[/tex]
False
Option 3: Multiply exponent to exponent, TrueOption 4: Division property of exponent, False9. Solve for x,
9x - 25
5x + 7
N
Answer:
x = 8
Step-by-step explanation:
Simplifying
9x + -25 = 5x + 7
Reorder the terms:
-25 + 9x = 5x + 7
Reorder the terms:
-25 + 9x = 7 + 5x
Solving
-25 + 9x = 7 + 5x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-5x' to each side of the equation.
-25 + 9x + -5x = 7 + 5x + -5x
Combine like terms: 9x + -5x = 4x
-25 + 4x = 7 + 5x + -5x
Combine like terms: 5x + -5x = 0
-25 + 4x = 7 + 0
-25 + 4x = 7
Add '25' to each side of the equation.
-25 + 25 + 4x = 7 + 25
Combine like terms: -25 + 25 = 0
0 + 4x = 7 + 25
4x = 7 + 25
Combine like terms: 7 + 25 = 32
4x = 32
Divide each side by '4'.
x = 8
Simplifying
x = 8
PLEASE HELP! ILL MARK BRAINLIEST!
Describe how to transform the graph of f into the graph of g. f(x) = x^4 and g(x) = -(-x)4
Reflect the graph of f across the x-axis and then reflect across the y-axis.
Shift the graph of f down 1 unit.
Reflect the graph of f across the x-axis.
Reflect the graph of f across the y-axis.
Answer:
Reflect the graph f(x) across the x axis to obtain the graph g(x).
its c
Step-by-step explanation:
following the accepted steps you would first reflect the graph across the y axis due to the negative sign within the function, then you would reflect the result across the x axis due to the negative sign outside of the function.
In practice however you only need to reflect across the x axis as -(-x)^2 simplifies to -x^2
15 divided by a number r
Answer:
6
Step-by-step explanation:
How to solve this question
7(x + 3 ) = 6 - (-7x - 15)
Apply the distributive rule to remove parentheses.
7x + 21 = 6 + 7x + 15
Right away, you should be able to see that 7x will be cancelled rendering this equation to have no solution.
Answer: NO SOLUTION
3 lines are shown. A line with points T, R, W intersects with a line with points S, R, V at point R. Another line extends from point R to point U in between angle V R W. Which pair of angles are vertical angles? AngleWRU and AngleSRT AngleWRS and AngleVRT AngleVRU and AngleTRS AngleVRT and AngleSRT
Answer:
The vertical angles are ∠ WRS and ∠ VRT ⇒ 2nd answer
Step-by-step explanation:
* Lets explain the meaning of the vertical angles
- Vertical angles are the angles opposite to each other when two lines
are intersected
- The vertical angle are equal in measures
- Look to attached figure which represents the lines
∵ Line TW intersects line SV at R
∴ ∠ WRV and ∠ SRT are vertical angle
∴ ∠ WRS and ∠ VRT are vertical angle
∵ RU is between the rays of angle VRW
∴ RU intersects the lines TW and SV at R
∴ No vertical angles between RU and the other two lines because
it intersects them its endpoint R
* Now lets look to the answer to chose the right one
- ∠ WRU and ∠ SRT are not vertical angles
- ∠ WRS and ∠ VRT are vertical angles
- ∠ VRU and ∠ TRS are not vertical angles
- ∠ VRT and ∠ SRT are not vertical angles
The pair of angles that are vertical angles is: ∠WRS and ∠VRT.
What are Vertical Angles?When two straight lines intersect each other at a point, the opposite angles that are vertical to each other are called vertical angles.
∠WRS and ∠VRT are vertically opposite each other.
Therefore, the pair of angles that are vertical angles is: ∠WRS and ∠VRT.
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Apply the power rule to compute the derivative
Answer:
[tex]\displaystyle \frac{d}{dt}[t^{\sqrt{11}}] = \sqrt{11}t^{\sqrt{11} - 1}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationBasic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = t^{\sqrt{11}}[/tex]
Step 2: Differentiate
Basic Power Rule: [tex]\displaystyle y' = \sqrt{11}t^{\sqrt{11} - 1}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Which of the following is most likely the next step in the series?
оооо
Answer:
Answer would be B.
Step-by-step explanation:
1) What is the value for the digit 8 in the given number?
38.165.0479
Answer:
The value of the 8 in the number 38.165.0479 is 8 ones
I am joyus to assist anytime i can :)
|-2| simplified
im a 7th grader in need of help!!!!!!
-9 less than or equal to -8y
Answer:
y≤9/8
Step-by-step explanation:
-9≤-8y
1) Divide both sides by -8 (You must flip the sign when dividing by a negative)
y≤9/8
Solve for m.
m - 5= √49
A.m=2
B.m=7
C.m=12
D.m=35
Answer:
C
Step-by-step explanation:
The square root of 49 equals 7
This equation can be rewritten as m-5=7
m-5=7
1) add 5 to both sides:
m=12
Nothing else can be done so m=12 is your final answer (c)
Emme bought cashews that cost $3.42 per pound which of the following does this situation represent
1. A relation only
2. Both a relation and function
3. Neither a relation or function
4. A function only
Answer:
Step-by-step explanation:
2. Both a relation and function
Answer:
2.
Step-by-step explanation:
Per every pound the price is $3.42
So it does have a relation and function.
The front of an A-frame house is in the shape of a triangle. The height of the house is 20 feet. The area of the front of the A-frame is 600 squared feet. Write and solve an equation to find the base of the A-frame house.
Area of a triangle is 1/2 x base x height.
You are given the area and the height, solve for the base:
600 = 1/2 x base x 20
Multiply both sides by 2:
1200 = base x 20
Divide both sides by 20:
Base = 1200/20
Base = 60 feet.
Answer: 60
A= 1/2BH
600=1/2b*20
20 / 2= 10
600/10=60
the two lines y+7x=14 and y+5=-7x are
Answer:
Parallel
Step-by-step explanation:
The two lines y+7x=14 and y+5=-7x are parallel to each other
The two lines y + 7x=14 and y+5=-7x are parallel to each other.
How are parallel straight lines related?Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness,
thus, are on the same slope.
Since the given parallel line has equation y = 2x + 2, thus its slope is 2 and thus, the slope of the needed line is 2 too.
Given lines is y + 7x=14 and y+5=-7x.
The slope of the given line;
y + 7x=14
y = -7x + 14
Thus, the slope m = -7.
The slope of the given line;
y+5=-7x
y = -7x - 5
Thus, the slope m = -7.
We can see that the slope are the same.
Thus, The two lines y + 7x=14 and y+5=-7x are parallel to each other.
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URGENT These are just 3 easy fill in the blank math problems. Integers
1. When adding *blank* signs in addition you should add and keep the sign
2. When subtracting integers you can change the minus to a plus and take the *blank* of the next number. Then follow addition integer rules.
3. When adding *blank* signs in addition you should subtract and keep the sign of the larger number
Answer:
Bedhshshhssjbsbwbsbw
Step-by-step explanation:
Fhdhshhehehehehehehshehs
6. [(69 - 9) + 23]4
how do u solve this
Answer:
332
Step-by-step explanation:
69-9=60
+23=83
x4=332
Expanded form of 680,705
[tex]\huge\boxed{600,000 + 80,000 + 700 + 5}[/tex]
To find expanded form, we need to split up the digits. When you do that, you take one digit and cut off everything to the left of it, then make everything to the right zeros.
[tex]600,000 + 80,000 + 0 + 700 + 0 + 5[/tex]
We don't need to keep the zeros.
[tex]\boxed{600,000 + 80,000 + 700 + 5}[/tex]
We can check this by adding the numbers back up to get [tex]680,705[/tex].
[tex]680,000 + 700 + 5[/tex]
[tex]680,700 + 5[/tex]
[tex]680,705[/tex]
What does distributive property look like
Answer:
The distributive property lets you multiply a sum by multiplying each addend separately and then add the products. ... Consider the first example, the distributive property lets you "distribute" the 5 to both the 'x' and the '2'.
Step-by-step explanation:
Answer: 4(x-3)=20
4x-4(3)=20
4x-12=20
4x-12+12=20+12
4x=32
4x/4 = 32/4
x=8
Step-by-step explanation:
To “distribute” means to divide something or give a share or part of something.
How is this wrong? Algebra 1
The total cost of renting a car is determined by the number of days a car is rented, at $75 per day, and the number of miles it is driven, at $0.50 per mile. The company uses the expression 75x +0.50y to evaluate the total cost of renting a car. What does the variable x represent? *
Answer:
Given: The total cost of renting a car is determined by the number of days a car is rented, at $75 per day, and the number of miles it is driven, at $0.50 per mile. The company uses the expression [tex]75x +0.50y[/tex] to evaluate the total cost of renting a car.
To check: We need to check what does the variable x represent.
Here, the company uses the expression [tex]75x +0.50y[/tex] to evaluate the total cost of renting a car.
Here 75 represents the rent per day, and 0.50 represents the cost per mile.
As, x is multiplied by 75. So, the variable x represents the number of day one has taken the car.
write 0.00052 in scientific notation.
The number 0.00052 in standard form can be written as 5.2 × 10⁻⁴ in scientific notation.
Given that:
The number 0.00052 is given in the standard form.
This has to be converted into the scientific notation.
Scientific notation is the notation of writing smaller numbers or larger numbers as the product of an integer from 1 to 10 and the power of 10 is raised to positive or negative power.
Here, the number is very small.
So, the power of 10 is negative.
Here, the integer is 5.2.
The decimal point has to be shifted 4 places to the left.
So, the power of 10 is -4.
Hence, the number can be written as 5.2 × 10⁻⁴.
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For every cup of flour 5 batches of cookies can be made. Create a table showing the cups of flour needed for up to 5 batches of cookies then plot the values on the coordinate plant
Answer:
0,0
1,5
2,10
3,15
4,20
5,25
Step-by-step explanation:
x=cups of flour
y=batches of cookies
Reduce the fractions 32/68,22/28, and
21/49
32/68- divide by 4 . 32/4=8, 68/4=17
22/28- divide by 2. 22/2=11, 28/2=14
21/49- divide by 7. 21/7=3, 49/7=7
Answers:
32/68=8/17
22/28-11/14
21/49=3/7
Step-by-step explanation:
[tex]\dfrac{32}{68}=\dfrac{32:2}{68:2}=\dfrac{16:2}{34:2}=\dfrac{8}{17}\\\\\\\dfrac{22}{28}=\dfrac{22:2}{28:2}=\dfrac{11}{14}\\\\\\\dfrac{21}{49}=\dfrac{21:7}{49:7}=\dfrac{3}{7}[/tex]