Answer:
x = 4
Step-by-step explanation:
Use order of operations (PEMDAS) to simplify and solve algebraic equations:
P - Parentheses: Simplify all parentheses in the equation first.
E - Exponents: Evaluate all exponential expressions in the equation next.
M/D - Multiplication/Division: After P and E, Multiplication in the equation comes next. These are interchangeable, so if these are the only operations left, calculate in the direction left to right.
A/S - Addition/Subtraction: After everything else has been done, move on to Addition/Subtraction. These two are also interchangeable, so you must also calculate in the direction left to right.
First, implement the order of operations to simplify the equation:
2²(x + 3) + 9 - 5 = 32 --- Evaluate the exponent.
4(x + 3) + 9 - 5 = 32 --- Use the Distributive Property to multiply.
4x + 12 + 9 - 5 = 32 --- Add/Subtract (Combine like terms).
4x + 16 = 32
Next, isolate the variable x to solve for its value:
4x + 16 = 32 --- Subtract 16 from both sides of the equation.
4x = 16 --- Divide both sides of the equation by 4 to get the value of x.
x = 4
To confirm that x = 4, you can substitute x for 4 in the original equation and see if both sides of the equation are equal:
2²[(4) + 3] + 9 - 5 = 32 --- Simplify the parentheses.
2²(7) + 9 - 5 = 32 --- Evaluate the exponent.
4(7) + 9 - 5 = 32 --- Multiply.
28 + 9 - 5 = 32 --- Simplify the equation using Addition/Subtraction.
32 = 32
After using substitution, we can confirm that x = 4.
To solve for the x-variable in a linear equation, we will need to isolate it on one side of the equation. If the x-variable is inside a parenthesis, we will need to open the parenthesis first, then isolate the variable. To solve/simplify the equation, we will need to use PEMDAS. It is a common method used to simplify equations and inequalities through priorities.
Concept: PEMDASThe word "PEMDAS" is a shortened word of "Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction". We follow this order (left-right) to simplify algebraic terms. Since parenthesis is the first priority, we would simplify the expression inside the parentheses. There are two exceptions to this priority in PEMDAS. (1) One of the terms in the expression is a variable, so the expression cannot be simplified, or (2) if there was no parenthesis in the first place. The next priority is "Exponents". This priority is used if there are any exponents used in the equation. The only exception to this priority is when there are no exponents used in the equation. The next priority is "Multiplication". This means that you have to simplify any products "multiplying terms" first. The only exception to this is when there are no terms being multiplied. The next priority is "Division". This priority tells that we need to simplify any division occurring the equation next. There is only one exception to this priority. Only possible if there is no division occurring in the equation. Then, we have "addition" as our 5th priority. This priority states that simplifying any expression that is being added next. The only exception to this priority is when there are no terms being added. The last and final priority is subtraction. This priority states that simplify any expression that is being subtracted. There is no exception to this priority.
Solving for the x variable:Simplifying the equation using PEMDAS:
We have the following equation: 2²(x + 3) + 9 - 5 = 32
Let us simplify using our first priority. Unfortunately, there is a variable inside the parenthesis. Therefore, we can't simplify the expression inside the parenthesis. Let us now simplify using out second priority. We can see a term outside the parenthesis "2²". Since that term has an exponent, let us simplify that term! Eventually, the term will simplify to 4.
⇒ 4(x + 3) + 9 - 5 = 32Before we move onto the next priority, let us open the parenthesis as we need to isolate the x-variable. This basically means that we need to simplify the distributive property. To simplify the distributive property, we need to multiply the term outside the parenthesis to all the terms inside the parenthesis. So, we have the following simplified equation:
⇒ 4(x) + 4(3) + 9 - 5 = 32⇒ 4x + 4(3) + 9 - 5 = 32Our next priority is multiplication. So, let us simplify any products occurring in the equation. We can see 4 being multiplied to 3. Therefore, let us simplify that term! Simplifying that term basically gives us 12. So:
⇒ 4x + 12 + 9 - 5 = 32Now, our next priority is division. However, we do not see any division occurring in the equation. Therefore, this follows the exception of the division priority in PEMDAS. So, let us move on to the next priority.
The next priority is addition. We can see 12 being added to 9. Therefore, let us simplify the expression. Simplifying that expression gives us 21. So:
⇒ 4x + 21 - 5 = 32The last and final priority is subtraction. We can see 5 being subtracted from 21. Therefore, let us simplify the expression, which gives us 16. So:
⇒ 4x + 16 = 32Solving for the x-variable by isolating it:
Now, let us isolate the x-variable to determine its value. This can be done by subtracting 16 on both sides of the equation. Then, we can divide 4 both sides to cancel out the coefficient of x.
⇒ 4x + 16 - 16 = 32 - 16⇒ 4x = 16⇒ 4x/4 = 16/4⇒ x = 4Therefore, the value of x in the equation is 4.
Find the measure of angle DCF=
help me please :)) ty
Answer:
∠ DCF = 39°
Step-by-step explanation:
the secant- secant angle DCF is half the difference of the measures of the intercepted arcs, that is
∠ DCF = [tex]\frac{1}{2}[/tex] (EG - DF) = [tex]\frac{1}{2}[/tex] (127 - 49)° = [tex]\frac{1}{2}[/tex] × 78° = 39°
Please help me asap.
Answer:
B
D
A
C
Step-by-step explanation:
Whatever is listed 2nd in the parentheses, do that function first. Then take that result & do the function listed first.
Fred's garage has a leaky roof. There are 24 holes in the roof. If it costs $124 to fix each hole, how much will it cost to fix all of the holes?
A. Subtract 24 from 124
B. Multiply 24 by 124
C. Add 124 to 24
D. Divide 124 by 24
If geometry symbol represented as small triangle with three sides. abc a geometry symbol represented as small triangle with three sides. dec, what is the value of x? a. x = 8 b. x = 5 c. x = 4 d. x = 1 e. x = 2
Answer:
D. X=1
Step-by-step explanation:
It's clear if you work through it just use substitution and you'll get the same answer yourself
What is the range of the function on the graph?
Answer:
the answer is [1, infinity)
Suppose that g(x) = f(x) + 6. Which statement best compares the graph of g(x) with the graph of f(x)?
A) The graph of g(x) is the graph of f(x) shifted 6 units down.
B) The graph of g(x) is the graph of f(x) shifted 6 units to the left.
C) The graph of g(x) is the graph of f(x) shifted 6 units up.
help please D:
From the graph attached below, we can see that the graph of g(x) is the graph of f(x) shifted 6 units up. the correct option is C.
How to know if a point lies in the graph of a function?All the points (and only those points) which lie on the graph of the function satisfy its equation.
Thus, if a point lies on the graph of a function, then it must also satisfy the function.
Given;
Suppose that g(x) = f(x) + 6.
From the graph attached below, we can see that the graph of g(x) is the graph of f(x) shifted 6 units up.
Hence, the correct option is C.
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The complete question is
"Suppose that g(x) = f(x) + 6. Which statement best compares the graph of g(x) with the graph of f(x)?
A) The graph of g(x) is the graph of f(x) shifted 6 units down.
B) The graph of g(x) is the graph of f(x) shifted 6 units to the left.
C) The graph of g(x) is the graph of f(x) shifted 6 units up.
D. The graph of g(x) is the graph of f(x) shifted 6 units to the right."
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What are the zeros of this function?
g(x) = 2(x + 2)(x - 9)
The zeros of function g are located at
and
You can walk over the mountains to
your campsite or take a safer, easier trip around the mountains. You
are on the ground at P(0, 0) and the campsite is at C(-2, 7). You
travel around the mountain by going to A(2, 5). The coordinate
system is measured in meters. Draw a diagram of the situation.
Find PA and AC.
Answer:
PA = [tex]\sqrt{29}[/tex]
AC =[tex]\sqrt[2]{5}[/tex]
Step-by-step explanation:
distance formula : if [tex](x_{1},y_{1}) and (x_{2},y_{2})[/tex] are two points on a line segment then distance between both the points is given by distance formula.
[tex]d = \sqrt{[(x_{2} - x_{1} )^2 +(y_{2} - y_{1})^2]}[/tex]
therefore ,
given points are , A(2, 5), P(0, 0), C(-2, 7).
so PA = [tex]\sqrt{[({2} - {0} )^2 +({5} - {0})^2]} = \sqrt{({2} )^2 +({5} )^2}[/tex]
PA = [tex]\sqrt{\229}[/tex]
similarly,
AC = [tex]\sqrt{[({-2} - {2} )^2 +({7} - {5})^2]} = \sqrt{({4} )^2 +({2} )^2}[/tex]
AC = [tex]\sqrt{20} = \sqrt[2]{5}[/tex]
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a woman bought some oranges and 30% of them were bad if there were 60 bad oranges how many oranges did she buy
Answer:
if 60 is 30%, then add up to 100%
60+60+60= 180
but we still have 10% left so divide 30% by 3 to get 10% then add
30% (or 60) /3 is 20
add 20 to 180
boom you get 200 she bought 200 oranges i wonder how shes gonna fit them in her car that's a lot of oranges
Answer:
200
Step-by-step explanation:
To calculate 30 percent of a number, we multiply the number by 30 and then divide by 100. Therefore, we can make the following function:
30 ∗ x÷100
= 60
To solve for x, we first multiply both sides by 100 and then divide both sides by 30 to get the x = 200. Therefore, the answer to 60 is 30 percent of what number? is:
200
The area of a rectangle, A = l • w is represented by the expression 24x^6y^15. Which could be the dimensions of the rectangle?
After calculating the value, l & w could be [tex]2x^{5} y^{8}[/tex] & [tex]12x^{} y^{7}[/tex].
Calculation:The inquiry relates to the laws of indices
where, [tex]x^{a} * x^{b}=x^{a+b}[/tex]
Provided the query, A= [tex]24x^{6}y^{15}[/tex]
[tex]2* 12[/tex] might be used to calculate the length and width of 24.
Hence,
[tex]x^{6}=x^{5} * x^{1} =x^{5+1}[/tex]
& [tex]y^{15}= y^{8} * y^{7} =y^{8+7}[/tex]
So, it can be written as,
A=l * w
⇒ [tex]24x^{6}y^{15}[/tex] = [tex]2x^{5}y^{8}[/tex] * [tex]12xy^{7}[/tex]
Therefore, it is concluded that the dimensions of the rectangle could be [tex]2x^{5} y^{8}[/tex] & [tex]12x^{} y^{7}[/tex].
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Question 9 of 10
If f(x)= (3 + x) over (x-3)
what is f(a + 2)?
A. 3+ f(a+2) over f(a)-1
B. (5+ a) over (a-1)
c. (3+a) +2
(a-3)
Answer:
[tex]\huge\boxed{\sf f(a+2)=\frac{5+a}{a-1}}[/tex]
Step-by-step explanation:
Given function:[tex]\displaystyle f(x)=\frac{3+x}{x-3}[/tex]
Put x = a + 2
[tex]\displaystyle f(a+2)=\frac{3+a+2}{a+2-3} \\\\f(a+2)=\frac{5+a}{a-1} \\\\\rule[225]{225}{2}[/tex]
[tex]2^{x^2-5x}=\frac{1}{64}[/tex]
Answer:
2, 3
Step-by-step explanation:
See attached images for work.
18% Commission on a $500 couch
Step-by-step explanation:
please mark me as brainlest
Answer:
$90
Step-by-step explanation:
Rate of commission = 18%Amount = $500Commission = 18% 0f 500 = 0.18*500 =$90Given that 2x − 1∶ − 4 = 16x + 1 ∶ 2x − 1 find the possible values of
The possible values of x are 5 and -1/12
Complete questionGiven that 2x − 1∶ x − 4 = 16x + 1 ∶ 2x − 1 find the possible values of x
How to determine the possible values of x?The ratio is given as:
2x − 1∶ x − 4 = 16x + 1 ∶ 2x − 1
Express as fraction
[tex]\frac{2x - 1}{x-4} = \frac{16x + 1}{2x -1}[/tex]
Cross multiply
4x^2 -4x + 1 = 16x^2 + x -64x - 4
Collect like terms
-16x^2 + 4x^2 + 64x - x - 4x + 1 + 4 = 0
Evaluate the like terms
-12x^2 + 59x + 5 = 0
Divide through by -1
12x^2 - 59x - 5 = 0
Expand
12x^2 + x - 60x - 5 = 0
Factorize
x(12x + 1) - 5(12x + 1) = 0
Factor out 12x + 1
(x - 5)(12x + 1) = 0
Expand
x - 5 = 0 or 12x + 1 = 0
Solve for x
x = 5 or x = -1/12
Hence, the possible values of x are 5 and -1/12
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If 45 is added to half a number, the result is triple the number. find the number
Answer:
18
Step-by-step explanation:
x = number
45 + 1/2 x = 3x
45 = 2.5 x
x = 45/2.5 = 18
Answer:
18
Step-by-step explanation:
Hello!
"Half a number" can be represented by 0.5x and "triple the number" can be represented by 3x.
This just becomes a one variable equation: 45 + 0.5x = 3x
Solve:
45 + 0.5x = 3x45 = 2.5x18 = xThe missing number is 18.
Samuel and 4 of his friends entered a chili cook-off. The rules allowed them
to spend a certain amount on supplies. If each person spent $15 for
supplies, how much did they spend in all?
Answer:
$75
[It is easy to say $60, but don't forget to add Samuel to the total]
Step-by-step explanation:
There are 5 people in total:
1 Samuel
4 friends
5 people who can spend up to $15 each.
(5 people)*($15/person) = $75 total spent on supplies
what is 349,001 + 209, 499?
Answer:
558, 500
Step-by-step explanation:
round 349,001 to 349,000 subtracted 1
round 209, 499 to 209, 500 added 1
349,000 + 209, 500 = 558, 500
Now, the added and subtract 1 cancel out so that is the final answer
Sweet corns purchased for $9 are markup by 10%. When no one bought the sweet corns, they decided to markdown the corn by 10% from the markup price. What is the selling price of the corn?
The slope-intercept form of the equation of a line that passes through point (-2,-13) is y=5x-3. What is the point-slope form of the equation for this line?
Answer:
y + 13 = 5(x + 2)
Step-by-step explanation:
Point - slope form of equation:[tex]\sf \boxed{\bf y - y_1=m(x-x_1)}[/tex]
Slope intercept of the line : y =5x - 3
Comparing with y = mx +b , m =slope = 5
m = 5 and Point (-2 ,-13)
y - [-13] = 5(x - [-2])
y + 13 = 5(x + 2)
which statement is true of the function f(x) = -3 squared root x
Using translation concepts, it is found that the function [tex]f(x) = -3\sqrt{x}[/tex] is the function [tex]g(x) = \sqrt{x}[/tex] reflected over the x-axis and vertically stretched by a factor of 3.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, from [tex]g(x) = \sqrt{3}[/tex] to [tex]f(x) = -3\sqrt{x}[/tex], g(x) was multiplied by -3, that is, it was reflected over the x-axis(due to the multiplication by the negative number) and vertically stretched by a factor of 3.
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A company makes 130 bags.
28 of the bags have buttons but no zips.
33 of the bags have zips but no buttons.
49 of the bags have neither zips nor buttons.
How many bags have zips on them?
Please answer in fraction form
Answer:
33 bags or 33/110 (which can be expressed as about 30%)
Step-by-step explanation:
BUTTONS ZIPS
28 Y N
33 N Y
49 N N
The only bags with zips is the second group of 33 bags. There are 110 bags in total, so the fraction would be (33/110)
In a cake recipe, 400 grams of butter is mixed with 800 grams of flour. What is the ratio of the butter to the flour? Write it in its simplest form.
Answer:
First of all this is 5th grade math but 400/800 = 1/2
Step-by-step explanation:
Answer:
1:2
Step-by-step explanation:
400/800=1/2 as 400*2=800
can someone please help mee
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:Domain = [-9, -1][/tex]
[tex]\qquad \tt \rightarrow \:Range = [-1 , 3][/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Domain = All possible values of x for which f(x) is defined
[ generally the extension of function in x - direction ]
Range = All possible values of f(x)
[ generally the extension of function in y - direction ]
[tex] \large\textsf{For the given graph : } [/tex]
[tex]\qquad \tt \rightarrow \: domain = [ - 9, -1][/tex]
[tex]\qquad \tt \rightarrow \: range= [ -1,3][/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
PLS HELP ME I WIL MARK BRAINLEST
Find the area for a triangle that has a base of 24 inches and a height of 4 inches. 96 in 2 48 in 2 cannot be determined 28 in 2
Answer:
48 in²
Step-by-step explanation:
triangle = bh/2
triangle = 24 x 4 / 2
triangle = 48 in²
Jillian is trying to determine what helium tank pressure she needs to fill balloons for the student council dance. Find the unknown numbers in the table until you find the best answer to the question.
Which cylinder pressure will Jillian need if she plans to fill 90 balloons?
According to the typical Helium Cylinder/Balloon Chart, she will need 300 pounds of pressure to fill 90 balloons. Option D is correct.
What is pressure?The force applied perpendicular to the surface of an item per unit area across which that force is spread is known as pressure. The force involved vertically to the surface of an object per unit area is pressure.
It is denoted by P. The pressure relative to the ambient pressure is known as the gauge pressure.
The complete question is:
Jillian is trying to determine what helium tank pressure she needs to fill balloons for the student council dance. Find the unknown numbers in the table until you find the best answer to the question. Which cylinder pressure will Jillian need if she plans to fill 90 balloons? Tank Pressure and Balloon Quantity Pressure in the helium cylinder (psi) Number of 9-inch balloons 100 30 150 ? 200? 250? 300?
According to the typical Helium Cylinder/Balloon Chart, she will need 300 pounds of pressure to fill 90 balloons (PSI.)
Simply divide the number of balloons by the total PSI to arrive at this figure.
⇒990/300
⇒3.333333 psi each.
The no of the 90-inch balloon is found as;
⇒3.33333 × 90
⇒300
According to the typical Helium Cylinder/Balloon Chart, she will need 300 pounds of pressure to fill 90 balloons.
Hence option D is correct.
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Which table represents a linear function?
Answer:
1st one.
Step-by-step explanation:
Shapes A and B are similar.
a) Calculate the scale factor from shape A to
shape B.
b) Find the value of r.
Give each answer as an integer or as a fraction in
its simplest form.
5 cm
11 cm
A
20 cm
3 cm
rcm
B
12 cm
Not drawn accurately
The scale factor from A to B is 5/3 and the value of r is 33/5
The scale factor from A to BFrom the figure, we have the following corresponding sides
A : B = 5 : 3
Express as fraction
B/A = 3/5
This means that, the scale factor from A to B is 5/3
The value of rFrom the figure, we have the following corresponding sides
A : B = 11 : r
Express as fraction
B/A = r/11
Recall that:
B/A = 3/5
So, we have:
3/5 = r/11
Multiply by 11
r = 33/5
Hence, the value of r is 33/5
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how do i Solve this equation
√x+5-2=0
Answer:
9
Step-by-step explanation:
√x+5-2=0
√x+3=0
√x= -3
x=9 [(-3)*(-3) = 9]
A candle on Pauline’s dresser is 4 inches tall and burns at a rate of 0.6 inches per hour. How many hours will it take for the candle to burn down to a height of 1.3 inches?
Answer:
4 1/2 hours
Step-by-step explanation:
first i subtracted 1.3 from 4 and got 2.7
Next i just multiplied 0.6 by random numbers ubtil i got something close to 2.7
i ended up with 2.4 when I multiplied 0.6 by 4
it still is .3 short
since it takes an hour for the candle to burn, then if you cut it in half, that means 30 minutes
therfore, 4.5 hours