Factor out the common term; 3
(3(x + 1))^2 = 36
Use the Multiplication Distributive Property; (xy)^a = x^ay^a
3^2(x + 1)^2 = 36
Simplify 3^2 to 9
9(x + 1)^2 = 36
Divide both sides by 9
(x + 1)^2 = 36/9
Simplify 36/9 to 4
(x + 1)^2 = 4
Take the square root of both sides
x + 1 = √4
Since 2 * 2 = 4, the square root of 2 is 2
x + 1 = 2
Break down the problem into these 2 equations
x + 1 = 2
x + 1 = -2
Solve the first equation; x + 1 = 2
x = 1
Solve the second equation; x + 1 = -2
x = -3
Collect all solutions;
x = 1, -3
plz help me thank you so much
Hello There!
Answer Is In Image Provided.
2/7x+1/4x=3/14x+1 help me please
8x+7x=6x+28
15x=6x+28
15x-6x=28
9x=28
X=28/9
I hope this helps
What is 24 expressed as a decimal?
Enter your answer in the box.
0.24/100 is the answer
.24 :) i hope this helped
What is the general form of the equation of the line shown?
a.)x + y = 0
b.)x - y = 0
c.)-x - y = 0
Check the picture below. So let's use those two points on the line.
[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{3}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3-0}{3-0}\implies \cfrac{3}{3}\implies 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=1(x-0)\implies y=x \\\\\\ -x+y=0\implies \stackrel{\textit{standard form}}{x-y=0}[/tex]
bearing in mind that the standard form is also a general form.
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
Answer:
B. x - y = 0
Step-by-step explanation:
Find the volume of a square pyramid with a base area of 18 in.² and a height of 6 in
ANSWER
36 cubic inches.
EXPLANATION
The volume of a square pyramid is calculated using the formula:
[tex]V = \frac{1}{3} {l}^{2} \times h[/tex]
where l² is the area of the base and h= 6 inches is the height of the square pyramid.
We substitute the values into the formula to get,
[tex]V = \frac{1}{3} \times 18 \times 6 \: {in}^{3} [/tex]
We simplify to get:
[tex]V = 6 \times 6 =3 6 {in}^{3} [/tex]
Therefore the volume of the square pyramid is 36 cubic inches.
please I don’t understand this I need help #2
Answer:
True for B)y=-4x^2+9
Step-by-step explanation:
The a part of the equation is negative (-4x^2), and this quadratic function has a maximum, which means it opens down not up.
(I hope this helps)
Find the circumference of the following
Pythagorean Theorem
[tex]7^2 + 24^2 = x^2[/tex]
[tex]49 + 576 = x^2[/tex]
[tex]x^2=625[/tex]
[tex]x = 25[/tex]
Circumference
1. Since the diameter is 25 the formula to find the circumference is [tex]c = d\pi[/tex]
2. Plug in 25 into the formula
3. [tex]c = 25\pi[/tex]
Answer
[tex]25\pi[/tex]
The circumference of the circle is approximately 78.54 cm.
To find the circumference of the circle, we first need to find the length of the hypotenuse (which is also the diameter of the circle) using the Pythagorean theorem. Then, we can use the formula for the circumference of a circle, which is C = π * d, where C is the circumference and d is the diameter.
Let's calculate it step by step:
Step 1: Find the length of the hypotenuse using the Pythagorean theorem:
[tex]a^2 + b^2 = c^2[/tex]
where a and b are the lengths of the chords (24 cm and 7 cm, respectively), and c is the length of the hypotenuse (diameter).
[tex]24^2 + 7^2 = c^2\\\\576 + 49 = c^2\\\\625 = c^2[/tex]
c = √625
c = 25 cm
Step 2: Calculate the circumference using the formula C = π * d:
C = π * 25 cm
C ≈ 78.54 cm
The circumference of the circle is approximately 78.54 cm.
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help ASAP!!! .........................
Answer: The answer to your question is B.
Step-by-step explanation:
what is the product of 10√20 and 9√8
[tex]10 \div 20 = 0.5 \: and \: 9 \div 8 = 1.125[/tex]
Answer:
1800
Step-by-step explanation:
10√20 × 9√8
10 × 5√2 × 9 × 2√2
50√2 × 18√2
50 × 18 × 2 = 1800
EMERGENCY!!PLEASE HELP
What features would need to be included on a scatterplot so that the data can be easily analyzed? Make a list of needed features and explain why each is important to the graph.
The more plot point the better but you must have at least three points, a labeled X-axis and Y-axis, and a table for the data to be organized into.
Answer:
See the explanation below
Step-by-step explanation:
Scatter plot is a graph that employs Cartesian coordinates to show the values of typically two variables plotted on the horizontal and vertical axes for a given set of data. The name of the relationship between the two variables that is shown by the scatter plot is referred to as correlation.
The following are the features of a scatter plot:
1. An X axis also known as the horizontal axis), and a Y axis which is also known as the vertical axis.The reason for these two axes is to obtain the Cartesian coordinates of the two variables X and Y.
2. Dots: There are must be dots on a scatter graph. The purpose of each of the dots is to indicate one observation of the data set.
3. Unique position of each dot: The purpose of the position of each dot is to indicate the meeting point of X and Y values.
a square has a diagonal length of 5 cm what is the area of a square
Answer:
Area of square = 12.48 cm^2
Step-by-step explanation:
Since the square has all sides equal, and when diagonal is made, square form two right angled triangles. Using Pythagoras theorem we can find the length of side of the square.
[tex]c^2 = a^2 + b^2[/tex]
where c = 5cm and a==b (square has all sides equal)
Putting value of b = a
[tex](5)^2 = a^2 + a^2\\25 = 2 a^2\\25/2 = a^2\\=> a^2 = 12.5\\ => \sqrt{a^2} = \sqrt{12.5}\\=> a = 3.53\, cm[/tex]
So, length of side of square = 3.53
Area of square = (3.53)^2
Area of square = 12.48 cm^2.
The answer is:
The area of the given square is equal to [tex]12.5cm^{2}[/tex]
[tex]Area=12.5cm^{2}[/tex]
Why?To solve the problem, we don't need to calculate the length of the sides of the square. We are given the diagonal length of the square, so using the following formula, we can calculate the are of the square without knowing the sides:
[tex]Area=\frac{diagonal^{2} }{2}[/tex]
So, substituting we have:
[tex]Area=\frac{(5cm)^{2} }{2}=\frac{25cm^{2} }{2}=12.5cm^{2}[/tex]
Hence, we have that the area of the given square is equal to [tex]12.5cm^{2}[/tex]
Have a nice day!
The price, p, for different size orders of custom printed shirts, n, is given in the table.
Can a linear equation be used to model the situation? If it can, what is the slope and the y-intercept of the equation?
Answer:
linear: slope =10,y-intercept=25
Step-by-step explanation:
Yes, a linear equation can be used to model the situation because for any two given pints, there is a constant value of 10 for change in (p) over change in (n).
The slope is given by:
[tex]m=\frac{Change\:in\:p}{Change\:in\:n}[/tex]
Using (1,35) and (5,75) from the table, we have:
[tex]m=\frac{75-35}{5-1}[/tex]
[tex]m=\frac{40}{4}=10[/tex]
Therefore the slope is 10.
Using the formula
[tex]y=mx+b[/tex], and the point (1,35) we have:
[tex]35=10(1)+b[/tex]
[tex]\implies 35-10=b[/tex]
[tex]\implies 25=b[/tex]
Therefore the y-intercept is 25.
(HELP ASAP PLEASE!!)
Two brothers went shopping at a back-to-school sale where all shirts were the same price, and all the shorts too. The younger brother spent $79 on 4 new shirts and 3 pairs of shorts. The older brother purchased 7 new shirts and 8 pairs of shorts and paid a total of $185. How much did each item cost?
Each shirt cost $ ___ and each pair of shorts cost $ ___ .
Answer:
Each shirt cost $7 and each pair of shorts cost $17 .
Step-by-step explanation:
let shirts be represented as x
let shorts be represented as y
Younger brother spent $79 on 4 new shirts and 3 pairs of shorts.
4 x + 3 y = $79 .......equation 1
Older brother purchased 7 new shirts and 8 pairs of shorts and paid a total of $185.
7 x + 8 y = $185 .......equation 2
multiply equation 1 by 7 and equation 2 by -4 and add both equations to get the value of y.
7 × (4 x + 3 y = $79) ⇒ +28 x + 21 y = $553
-4 × (7 x + 8 y = $185) ⇒ -28 x - 32 y = - $740
0 - 11 y = - $187 ⇒ -11 y = - $187
y = [tex]\frac{- $187}{- 11}[/tex] ⇒ y = $17
shorts = y = $17
put value of y in equation 1
4 x + 3 ( $17 ) = $79 ⇒ 4x + $51 = $79 ⇒ 4x = $79 - $51
4x = $28 ⇒ x = [tex]\frac{$28}{4}[/tex] ⇒ x = $7
Shirts = x = $7
x − 78 = −42
x = 78 − 42
x = −36
Answer:
x= 36
(it is positive since 78 is larger than 42, everything else is correct)
Step-by-step explanation:
Lani's mom wants to put a fence around her garden. garden is 22 feet × 18 feet How many feet of fencing will she need?
Answer:
Lani's mom will need 80 ft of fencing
Step-by-step explanation:
We are looking for the perimeter of the garden. We know that the garden is 22 ft x 18 ft. This means that we can find the perimeter using this equation
[tex]22(2)+18(2)=80[/tex]
Joe is filling the washing machine to wash clothes. After one minute, there are 1.75 gallons of water in the washing machine. After two minutes, there are 3.5 gallons of water in the machine. After three minutes, there are 5.25 gallons in the machine. If this pattern continues, how many gallons of water will be in the washing machine after six minutes?
Answer:
Final answer is 10.5 gallons of water.
Step-by-step explanation:
Given that Joe is filling the washing machine to wash clothes. After one minute, there are 1.75 gallons of water in the washing machine. After two minutes, there are 3.5 gallons of water in the machine. After three minutes, there are 5.25 gallons in the machine. Now we need to determine If this pattern continues then about how many gallons of water will be in the washing machine after six minutes.
Look at the pattern of volume of the water at given minutes.
We see that 1.75 is added each minute.
then required equation of volume is
V=1.75t
So for t=6 minutes, volume is given by
V=1.75*6=10.5
Hence final answer is 10.5 gallons of water.
The amount of water in the washing machine after six minutes can be determined using an arithmetic sequence formula. The machine fills at a constant rate of 1.75 gallons per minute, so after six minutes, there will be 10.5 gallons of water in the machine.
The question provided concerns a pattern of water filling a washing machine, which falls under the subject of arithmetic sequences in mathematics. To determine how many gallons of water will be in the washing machine after six minutes, we need to recognize the sequence and apply the appropriate formula.
To solve this problem, we note that the washing machine fills at a constant rate of 1.75 gallons per minute because the amount of water increases by 1.75 gallons with each passing minute (1.75 gallons at minute one, 3.5 gallons at minute two, which is 1.75 x 2, and 5.25 gallons at minute three, which is 1.75 x 3).
Mathematically, this can be represented as an arithmetic sequence with the first term a1 = 1.75 gallons and the common difference d = 1.75 gallons. The nth term of an arithmetic sequence is given by the formula an = a1 + (n - 1)d. So, to find the amount of water after six minutes, substitute 6 for n, which yields:
a6 = 1.75 + (6 - 1) times 1.75
a6 = 1.75 + 5 times 1.75
a6 = 1.75 + 8.75
a6 = 10.5 gallons
Therefore, after six minutes, there will be 10.5 gallons of water in the washing machine if the pattern continues.
If a baseball player hits a baseball from 4 feet off the ground with an initial velocity of 64 feet per second, how long will it take the baseball to hit the ground? Use the equation h = −16t2 + 4t + 4. Round your answer to the nearest hundredth.
0.36
0.39
0.61
0.65
Answer:
0.64 seconds.
Step-by-step explanation:
When it hits the ground h(t) = 0.
0 = -16t^2 + 4t + 4
-4(4t^2 - t -1) = 0
t = [-(-1) +/- sqrt (1 - 4*4*-1)] / 8)
t = 0.64, -0.39
answer is 0.64 seconds.
it will take the baseball 0.64 seconds to hit the ground.
The equation representing the height is:
h = -16t² + 4t + 4
When the baseball hits the ground, the height will be 0. That is,h =0
Substitute h =0 into the equation above
0 = -16t² + 4t + 4
Rearrange the given equation to be:
16t² - 4t - 4 = 0
Solving the quadratic equation above:
t = -0.39 and 0.64
Since time cannot be negative, it will take the baseball 0.64 seconds to hit the ground.
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What is the 8th term of the geometric sequence with this explicit formula?
an= 7• (-2) (n - 1)
Answer:
- 896
Step-by-step explanation:
To find the 8 th term substitute n = 8 into the explicit formula
[tex]a_{8}[/tex] = 7 × [tex](-2)^{7}[/tex] = 7 × - 128 = - 896
The 8th term of the given geometric sequence is -896.
The explicit formula
an = 7 × (-2)(n - 1).
To find the 8th term, simply substitute 8 for n in the formula, giving us:
a(8) = 7 × (-2[tex])^{(8 - 1)}[/tex] a(8) = 7 × (-2[tex])^{7}[/tex] a(8) = 7 × (-128)a(8) = -896The steps to derive the quadratic formula are shown below: Step 1 ax2 + bx + c = 0 Step 2 ax2 + bx = − c Step 3 Step 4 x2 + Step 5 x2 + Step 6 Step 7 Step 8 x = − Step 9 x = Which of the following is the first incorrect step? Step 2 Step 3 Step 4 Step 7
Its a bit late, but i wish someone would had answered so
Step 3:
✔ B
Step 5:
✔ D
Step 6:
✔ A
Step 8:
✔ C
:)
The first incorrect step in the given sequence is Step 3, where the equation is divided by 'a' on both sides instead of factoring it out and grouping the terms.
Explanation:The quadratic formula is derived by completing the square on the general quadratic equation ax^2 + bx + c = 0. The first incorrect step in the given sequence is Step 3. In Step 3, the equation ax^2 + bx + c = 0 is divided by a on both sides, which results in the equation x^2 + (b/a)x + (c/a) = 0. However, the correct next step should be factoring out the leading coefficient a and grouping the terms.
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Theo started to solve the quadratic equation (x + 2)2 - 9 = -5. He added 9 to both sides and the resulting equation was
(x + 2)2 = 4. Next, he took the square root of each side.
Which was the resulting equation of that step?
Answer:
[tex] x + 2 = \pm \sqrt{4} [/tex]
Step-by-step explanation:
(x + 2)^2 - 9 = -5
Add 9 to both sides.
(x + 2)^2 = 4
Take the square root of both sides.
[tex] x + 2 = \pm \sqrt{4} [/tex]
Answer:
A
Step-by-step explanation:
ed 2020
lots of points and not really hard and wont take too long to solve!!! plz help
Here all you need to know to solve this exercise:
1) When you write the equation of a line in the form
[tex]y=mx+q[/tex]
the slope is the coefficient m.
2) When you know that the line passes through a point [tex](x_0,y_0)[/tex] and has slope m, the equation of the line is given by
[tex]y-y_0=m(x-x_0)[/tex]
3) Let [tex]m_1,m_2[/tex] be the slopes of two lines. If the lines are parallel, then [tex]m_1=m_2[/tex]. If the lines are perpendicular, then [tex]m_1m_2=-1[/tex].
In the first exercise, using point 1, you can see that the slope of the given line is 2. We want a parallel line passing through the given point. So, our line has the same slope, and its equation is (see point 2)
[tex]y-2=2(x+1) \iff y = 2x+4[/tex]
Similarly, in the second exercise, the original slope is 1/3, so the perpendicular slope is -3. The equation will be, imposing the passage through the given point,
[tex]y-6 = -3(x-0) \iff y = -3x+6[/tex]
Answer:
see explanation
Step-by-step explanation:
19
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c yje y- intercept )
y = 2x - 3 is in this form with slope m = 2
• Parallel lines have equal slopes, hence
y = 2x + c ← partial equation of parallel line
To find c substitute (- 1, 2) into the partial equation
2 = - 2 + c ⇒ c = 2 + 2 = 4
y = 2x + 4 ← equation of parallel line
20
Rearrange x - 3y = 5 into slope- intercept form
Subtract x from both sides
- 3y = - x + 5 ( divide all terms by - 3 )
y = [tex]\frac{1}{3}[/tex] x - [tex]\frac{5}{3}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{1}{3}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{3} }[/tex] = - 3, so
y = - 3x + c
The line passes through (0, 6) ⇒ c = 6
y = - 3x + 6 ← equation of perpendicular line
If PA = 6, PD = 4 and BE = 5. Find PE
A) 4
B) 5
C) 6
Answer:
Option A) 4
Step-by-step explanation:
we know that
Applying the Intersecting Secant-Tangent Theorem
[tex]PA^{2}=(BE+PE)( PE)[/tex]
substitute the given values
[tex]6^{2}=(5+PE)( PE)\\ \\36=PE^{2}+5PE\\ \\PE^{2}+5PE-36=0[/tex]
Solve the quadratic equation by graphing
The solution is PE=4 units
see the attached figure
Answer:
The answer is 4
Step-by-step explanation:
Consider the combined function
Given:
f(x)=4x-3
f(x) +g(x) =9x +4
To find:g(x)
Solution:
f(x) + g(x) =9x +4
Replacing f(x) with its value.
4x -3 +g(x) = 9x +4
=> g(x) = 9x+ 4 -(4x-3)
=> g(x) = 9x+4 -4x +3
=> g(x) = 5x +7
Hence;
Option A g(x)=5x+7 is the answer.
Hope it helps...
Regards;
Leukonov/Olegion.
Solve for y.
28+19y=-8+15y
symplify your answer as much as possible
Use Vocabulary in Writing
11. Explain why the order of operations is important. Use at least three
terms from the Word List in your explanation.
Topic 13
Vocabulary Review
766
Answer: The Order of Operations is very important when simplifying expressions and equations. The Order of Operations is a standard that defines the order in which you should simplify different operations such as addition, subtraction, multiplication and division.
Step-by-step explanation:
Help please I don’t know please
Answer:
[tex]-\frac{3}{10}[/tex]
Step-by-step explanation:
Slope is the change in y coordinates by change in x coordinates.
Or [tex]m=\frac{\delta y}{\delta x}[/tex]
Looking at the table, the change in each value of x is 10 (10 to 20 to 30 to 40).
Also, the change in each valueof y is -3 (20 to 17 to 14 to 11).
Note: change in y is negative since it is DECREASING.
Hence the slope would be -3/10
Vincent borrowed $500 from Mitchell for six months. How much interest will Mitchell earn if he charges Vincent a simple interest rate of 3 percent? simple interest = P × r × t
Principal P = $500, Rate = 3 % = 3/100 = 0.03 would assume per year,
Time t = 6 months = (6/12) year = 0.5 year.
Simple Interest, I = P*r*t
= 500*0.03*0.5 = 7.5
Simple interest = $7.50
Simplify the difference. (–7x – 5x^4 + 5) – (–7x^4 – 5 – 9x)
Answer: [tex]2x^4+2x+10[/tex]
Step-by-step explanation:
You need to remember the mulplication of signs:
[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-[/tex]
Knowing this, you can distributive the negative sign. Then you get:
[tex](-7x- 5x^4 + 5) - (-7x^4 - 5 - 9x)=-7x- 5x^4 + 5 +7x^4 + 5 + 9x[/tex]
Now you need to add the like terms. Then:
[tex]=2x+2x^4+10[/tex]
Finally, you can order the polynomial obtained in descending order. Therefore, the answer is:
[tex]=2x^4+2x+10[/tex]
Simplify:
Simplity: – V2.25
It is best to consider the radicand as a fraction,
Start by entering 2.25 as an improper fraction in simplest form in the
box
Convert the decimal number to a fraction by placing the decimal number over a power of ten. So convert the mixed number which is 2 1 /4 into an improper fraction first by multiplying the denominator which is (4)(4) by the whole number part which is (2)(2) and add the numerator (1)(1) to get the new numerator.
Place the new numerator (9)(9) over the old denominator (4)(4).94
Ben and jack took part in a cycle race Ben took 47 minutes 39 seconds and jack took 54 minutes 12 seconds to complete the race
What is the difference between the two times
Answer:
Jack took 6 minutes and 33 seconds longer to complete the race.
Step-by-step explanation:
54 minutes minus 47 minutes would equal 7 minutes longer, but Jack was not as far into the minute when he completed it as Ben was when he completed it, so the difference in time is actually going to be a bit less than 7 minutes. So the difference is going to be 6 minutes and the number of seconds between 39 and 12, with 39 going past the minute, that is. That equals out to 33 seconds, so the total difference in time is 6 minutes and 33 seconds.