3x - 5
In answering the question, our chosen unknown number will be represented by a variable x
3 times a number
= 3 * x = 3x
decreased by 5 means we are going to subtract 5 from our previous answer
Thus, we have 3x - 5
10. Reasoning Find the value of 12 +9+3+82-3³. Then change twooperation signs so that the value of the expression is-22.
We are given the following operation:
[tex]12+9\div3+8^2-3^3[/tex]First, we will solve the exponents:
[tex]12+9\div3+8^2-3^3=12+9\div3+64-27[/tex]Now, we solve the division:
[tex]12+9\div3+64-27=12+3+64-27[/tex]Now, we solve the addition and subtraction:
[tex]12+3+64-27=52[/tex]Therefore, the result of the operation is 52.
Now, we will change the last plus sing for a minus sign and the last minus sign for a plus sign:
[tex]12+9\div3-8^2+3^3[/tex]Now, we solve the exponents:
[tex]12+9\div3-64+27[/tex]Now, we solve the division:
[tex]12+3-64+27[/tex]Solving the addition and subtraction we get:
[tex]-22[/tex]And thus we have solved the operation with a final result of -22.
Identify the hole(removable discontinuity) of the function F(x) =x^2-2x-24/x+4 give your answer as an ordered pair.
Answer:
[tex]\lparen x,y)=\left(-4,0\right)[/tex]Explanation:
We were given the function:
[tex]f\left(x\right)=\frac{x^2-2x-24}{x+4}[/tex]Discontinuity occurs when the denominator equals zero
[tex]\begin{gathered} x+4=0 \\ x=-4 \end{gathered}[/tex]When x = -4, the value of the denominator is zero
Removable discontinuity occurs when both the numerator and denominator are zero
We will check this by inputting x = -4 in the expression, we have:
[tex]\begin{gathered} f(x)=\frac{x^{2}-2x-24}{x+4} \\ x=-4 \\ f\mleft(x\mright)=\frac{-4^2-2\left(-4\right)-24}{-4+4} \\ f\lparen x)=\frac{16+8-24}{-4+4} \\ f\mleft(x\mright)=\frac{24-24}{-4+4} \\ f\mleft(x\mright)=\frac{0}{0} \end{gathered}[/tex]Thus, when x = -4, we have a removable discontinuity
Hence, our answer is: (x, y) = (-4, 0)
Simplify the expression 4(x+2)+x+3
Explanation
[tex]4\mleft(x+2\mright)+x+3[/tex]
Step 1
use distributive property to break the parenthesis:
remember the distributive property
[tex]a(b+c)=ab+ac[/tex]Hence
[tex]\begin{gathered} 4(x+2)+x+3 \\ (4x+8)+x+3 \\ 4x+8+x+3 \\ \end{gathered}[/tex]Step 2
add like terms
[tex]\begin{gathered} 4x+8+x+3 \\ 5x+11 \end{gathered}[/tex]so, the answer is
[tex]5x+11[/tex]I hope this helps you
convert the ex to a logarithmic form : 10^4 = 10, 000
[tex]\begin{gathered} \text{ 10}^4\text{ = 10000} \\ \log _{\square}4\text{ = 10000} \end{gathered}[/tex]
I think the answer is the last one
it is my answer
I need help with a problem
Two triangles are shown, one is triangle AXM and the other one is triangle TBE
In both triangles the markings show sides that are congruent, hence you have;
XM = BE
MA = ET
Angle M = Angle E
Hence the rule that makes them is the SSA rule.
Two sides and an angle are congruent
I don’t get how I get the numerators to be -8-3 here
First, notice that:
[tex]\begin{gathered} 10=5\cdot2,\text{ } \\ \frac{2}{2}=1. \end{gathered}[/tex]Therefore:
[tex]-\frac{4}{5}=-\frac{4}{5}\cdot1=-\frac{4}{5}(\frac{2}{2})=-\frac{4\cdot2}{5\cdot2}=-\frac{8}{10}\text{.}[/tex]That is how you go from -4/5 to -8/10.
Since -3/10 already has 10 as its denominator then it remains the same.
[tex]-\frac{8}{10}-\frac{3}{10}=-\frac{11}{10}\text{.}[/tex]Examples (negative numbers):
[tex]\begin{gathered} -1-3=-(1+3)=-4, \\ 1-3=-2, \\ -1+3=2, \\ 1+3=4. \end{gathered}[/tex][tex]-1+3=3-1=2.[/tex][tex]\begin{gathered} -5+8=8-5=3, \\ -3+5=5-3=2. \end{gathered}[/tex]Suppose that function h is defined as h(x)=f(x)/g(x).what exactly is the function?
In the graph you can see that f(x) and g(x) are lines, so the first step to know what function is h(x) is to find the functions f(x) and g(x).
Since a single line passes through two points, then to find the functions f(x) and g(x) you can take two points that pass through the graph of each function and obtain the slope, then use the point-slope formula. Then, you have
For f(x)
You can take for example the points (0,-3) and (3,0). Now calculating the slope:
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1),(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}[/tex][tex]\begin{gathered} (x_1,y_1)=(0,-3) \\ (x_2,y_2)=(3,0) \\ m=\frac{0-(-3)}{3-0} \\ m=\frac{3}{3} \\ m=1 \end{gathered}[/tex]Now using the point-slope formula:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-3)=1(x-0) \\ y+3=x \\ \text{Subtract 3 from both sides of the equation} \\ y+3-3=x-3 \\ y=x-3 \end{gathered}[/tex]Then, the function f(x) would be
[tex]f(x)=x-3[/tex]For g(x)
You can take for example the points (0,4) and (4,0). Now calculating the slope:
[tex]\begin{gathered} (x_1,y_1)=(0,4) \\ (x_2,y_2)=(4,0) \\ m=\frac{0-4}{4-0} \\ m=\frac{-4}{4} \\ m=-1 \end{gathered}[/tex]Now using the point-slope formula:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-4=-1(x-0_{}) \\ y-4=-x \\ \text{ Add 4 to both sides of the equation} \\ y-4+4=-x+4 \\ y=-x+4 \end{gathered}[/tex]Finally, the function h(x) will be
[tex]h(x)=\frac{f(x)}{g(x)}=\frac{x-3}{-x+4}[/tex]Find the first term given two terms from an arithmetic sequence.a_6 = 12 and a_{14} = 28the common difference is Answerand a_1= Answer
Answer:
the common difference is 2
and a₁ = 2
We need to find the first term given two terms of an arithmetic sequence:
a₆ = 12
a₁₄ = 28
First, we will solve for the common difference 'd'. To do this, we will create a system of equations using the given terms and the following formula:
[tex]a_n=a_1+\lparen n-1)d[/tex]From the given, we can have:
[tex]\begin{gathered} a_6=a_1+\operatorname{\lparen}6-1)d \\ 12=a_1+5d-------Eq1 \\ \end{gathered}[/tex][tex]\begin{gathered} a_{14}=a_1+\operatorname{\lparen}14-1)d \\ 28=a_1+13d \\ a_1=28-13d------Eq2 \end{gathered}[/tex]We will then substitute Eq.2 with Eq.1 to solve for the common difference 'd'
[tex]\begin{gathered} 12=a_1+5d----Eq.1 \\ a_1=28-13d----Eq.2 \\ 12=\left(28-13d\right)+5d \\ 12=28-13d+5d \\ 12-28=-13d+5d \\ -16=-8d \\ d=2 \end{gathered}[/tex]We now have a common difference d = 2
We can now solve the first term of the arithmetic sequence using any of the equations that we had. In this case, let us use Eq.2
[tex]\begin{gathered} \begin{equation*} a_1=28-13d \end{equation*} \\ a_1=28-13\left(2\right) \\ a_1=28-26 \\ a_1=2 \end{gathered}[/tex]Therefore, the first term of the sequence is 2.
What is the solution to | X-6 2 5?OA.1 sxs 11OB.-11 Sxs1O C. x 11 or xs1OD.X 1 or xs-11
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
[tex]|x\text{ - 6| }\ge\text{ 5}[/tex]Step 02:
[tex]\begin{gathered} |x-6+6|\ge5+6 \\ |x|\ge11 \end{gathered}[/tex]The answer
4). A Sweet Angelic Child is playing on a basketball team. Their goal is to average 12points a game for the season. They have played 6 of their 7 games already (it is ashort season). They have scored 10 points, 12 points, 10 points, 8 points, 14 points,and 15 points. What is the least amount of points they need to score in their finalgame to have a season average of 12?3158411
The average points per game is computed as follows:
(10 + 12 + 10 + 8 + 14 + 15 + x)/7
where x are the points in the last game. We want the average to be 12, then:
(10 + 12 + 10 + 8 + 14 + 15 + x)/7 = 12
Solving for x:
10 + 12 + 10 + 8 + 14 + 15 + x = 12*7
69 + x = 84
x = 84 - 69
x = 15
Which graph best represents the solution set of the inequality, y>3/5x−6?
Therefore, the graph will be definitely C. Note the line should be a broken line /
Answer:
Answer is 3rd
Step-by-step explanation:
Answer is 3rd graph. y is higher than the function, so the area that is above the function is bolded. Also, as it is a strict inequation, the line will be dashed.
a group of scientists studied the amount of erosion at a beach. the scientists determined that the equation y=-0.5x+26 models the amount of shoreline, y, in feet, x decades after 1950. which statement is true based on the model?
Take into account that x represents the number of decades after 1950. Moreover, consider that -0.5x is a decrease in the values of y, each decade.
Then, you can conclude that each decade, that is, every 10 years, the shoreline reduces 0.5 feet.
Hnece, you have:
The shoreline is reduced by 0.5 foot every 10 years
Do you add, subtract, multiply, or divide FIRST to solve the expression: 14-(6+4)•6÷2
Multiply
1) In the expression 14-(6+4)•6÷2, following the acronym PEMDAS to solve that
We will prioritize the Parentheses, Multiplication, and Division.
2) So the answer is Multiply at first the 6/2 by the (6+4)
how many 1/4 are in 3
Answer and explanation
In 3 we have 12 lots of 3/4. We can get this dividing 3 by 1/4.
3/1/4 = 12
In the problem 2 * 4, the 2 and the 4 are called
In this multiplication, the 2 and the 4 are called factors.
They are also called multiplicand (2) and multiplier (4). And the result is called the product.
In the following exercises, determine whether each equation is a function. y-3x^3=2
Given the function:
[tex]y-3x^3=2[/tex]Clearing y:
[tex]y=3x^3+2[/tex]And now, we are going to analyze the domain of the function:
As you can see, the function is a polynomial. In this case the function will exist at all values of x.
that is, there will always be an image in y for each value of x.
Therefore, the equation is a function.
I need help with my precalculus homework, the image of the problem is attached.Directions: Complete the operations to write as a single rational expression
Given:
[tex]\frac{8v+40}{8}\text{.}\frac{9v}{v+5}[/tex]To write it as a single rational expression:
On simplification we get,
[tex]\begin{gathered} \frac{8v+40}{8}\text{.}\frac{9v}{v+5}=\frac{8(v+5)}{8}\text{.}\frac{9v}{v+5} \\ =9v \end{gathered}[/tex]Hence, the answer is, 9v.
You can measure the diameter of a spherical object by putting the object on a flat surface and placing blocks or books on either side of the objectThe ruler is used to measure the distance between the blocks or books. The length on the ruler is 7.3 inches. Give the diameter and volume of the sphericalobject. Round the volume to the nearest tenth.Enter the correct answer in the box.
Solution:
Given that;
You can measure the diameter of a spherical object by putting the object on a flat surface and placing blocks or books on either side of the object.
The ruler is used to measure the distance between the blocks or books.
The length on the ruler is 7.3 inches, i.e. the diameter of the sphere is the length on the ruler
Hence, the diameter of the sphere is 7.3 inches
To find the radius, r, the formula is
[tex]\begin{gathered} r=\frac{d}{2}=\frac{7.3}{2}=3.65\text{ in} \\ r=3.65\text{ in} \end{gathered}[/tex]To find the volume, V, of a sphere, the formula is
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ Where\text{ r is the radius} \end{gathered}[/tex]Substitute the value of r into the formula above
[tex]\begin{gathered} V=\frac{4}{3}\times\pi\times3.65^3 \\ V=203.7\text{ in}^3\text{ \lparen nearest tenth\rparen} \end{gathered}[/tex]Hence, the volume is 203.7 in³
Point H is between points R and G. RG = 8y -8, RH= 2y-3, and HG= 4y + 3. Find RH and HG
From the figure,
RG=RH+HG
So,
[tex]\begin{gathered} 8y-8=2y-3+4y+3 \\ 8y-2y-4y=-3+3+8 \\ 2y=8 \\ y=4 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} RH=2\times4-3=5 \\ \\ HG=4\times4+3=19 \end{gathered}[/tex]Reflect the figure over the line y = 1. Which is point A' after the reflection? O A(-3, 1) O A(-3, 3) O A'(-3,2) O A(1, 1)
from point A to the line y = 1 measure 2 units, then
extends the line segment in the same direction and to the same extent.
therefore:
A' is ( - 3, 3 )
Multiply 4x(8x^4-9x^2-4x)
The given expression is,
[tex]4x(8x^4-9x^2-4x)[/tex]Multiply using distributive property(A(B+C)=AB+AC),
[tex]\begin{gathered} 4x\times8x^4-4x\times9x^2-4x\times4x \\ =32x^{1+4}-36x^{1+2}-16x^{1+1} \\ =32x^5-36x^3-16x^2 \end{gathered}[/tex]Therefore, the final expression is,
[tex]32x^5-36x^3-16x^2[/tex]Find the equation of the line that passes through the given point and has the given slope. Express your answer in slope-intercept form.1(3,0), m= -8
Given the word problem, we can deduce the following information:
1. Point (3,0)
2. m=-1/8
To find the slope-intercept form of the equation, we use the formula:
[tex]y=mx+b[/tex]where:
m=slope
b=y-intercept
First, we plug in x=3, y =0, and m=-1/8 into y=mx+b to find the value of b:
[tex]\begin{gathered} y=mx+b \\ 0=-\frac{1}{8}(3)+b \\ \text{Simplify and rearrange} \\ b=\frac{3}{8} \end{gathered}[/tex]Then, we plug in b=3/8 and m=-1/8 into the slope-intercept form formula:
[tex]\begin{gathered} y=mx+b \\ y=-\frac{1}{8}x+\frac{3}{8} \end{gathered}[/tex]Therefore, the answer is:
[tex]y=-\frac{1}{8}x+\frac{3}{8}[/tex]Determine the value that would complete the perfect squaretrinomial.x2 + 20
The answer is
STEP 1
Let the value be k and compare the resulting equation with the general quadratic equation
[tex]\begin{gathered} \text{General equation =ax}^2+bx+c \\ \text{Given equation = x}^2+2x+k \\ \text{Therefore;} \\ a=1,\text{ b=2, c=k} \end{gathered}[/tex]A bottled water distributor wants to estimate the amount of water contained in1 -gallon bottles purchased from a nationally known water bottling company. The water bottling company's specifications state that the standard deviation of the amount of water is equal to 0.03 gallon. A random sample of 50 bottles is selected, and the sample mean amount of water per 1-gallon bottle is 0.968 gallon.
The interval estimate shows that the amount of water contained in 1-gallon bottles purchasing the nationally-known water bottling company lies between 0.995 gallons and 1.005 gallons.
What is an interval estimate?An interval estimate shows the range of values within which the sample mean falls.
Interval estimates show the lower and upper limits, using the margin of error around the sample mean.
Standard deviation, σ = 0.03 gallons
Random sample size, n = 50 bottles
The sample mean per 1-gallon bottle, μ = 0.968
Observed value, x = 1-gallon bottle
Z-score = (x-μ)/σ
= (1 - 0.968)/0.03
= 1.067
The Margin of Error = z-score x standard deviation/√sample size
= 1.067 x 0.03/√50
= 1.067 x 0.03/7.07
= 1.067 x 0.0042
= 0.005
Lower Limit = Observed value - Margin of Error
= 1 - 0.005
= 0.995
Upper Limit = Observed Value + Margin of Error
= 1 + 0.005
= 1.005
Thus, the interval estimate shows that the water contained in 1-gallon bottles is 1 ± 0.005.
Learn more about interval estimates at https://brainly.com/question/28545662
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I need help figuring out if these are functions or not.
Answer: NO
we have two variables x and y
Variable y is dependent on variable x
Hence, variable while can either increase or decrease with respect to variable y but it cannot be equal to variable x
Hence, graph 1 is not a function
Answer : NO
how do you solve 5e=3e+36
Given the expression:
[tex]\text{ 5e = 3e + 36}[/tex]Let's simplify.
Step 1: Apply the Inverse Property of Addition.
[tex]\text{ 5e = 3e + 36}[/tex][tex]\text{ 5e - 3e = 3e + 36 - 3e ; Subtract 3e to both sides.}[/tex][tex]\text{ 2e = 36}[/tex]Step 2: Apply the Inverse Property of Multiplication.
[tex]\text{ 2e = 36}[/tex][tex]\text{ }\frac{\text{2e}}{2}\text{ = }\frac{\text{36}}{2}\text{ ; Divide both sides by 2}[/tex][tex]\text{ e = 18}[/tex]Therefore, the answer is e = 18.
Answer:
e = 18
Step-by-step explanation:
5e=3e+36
Subtract 3e from both sides to keep the letters on one side :
2e = 36
Divide both sides by 2 to isolate the e :
e = 18
Hope this helped and have a good day
I’m not quite sure how to answer this question. Excuse the pencil marks this is from an assignment I didn’t do so well on so I’m trying to understand what I did wrong
Given the expressions:
[tex]\begin{gathered} (8x-1)(4x^2+9) \\ \\ 32x^3-4x^2+72x-9 \end{gathered}[/tex]You can multiply the binomials of the first expression in order to expand it. You can use the FOIL Method to multiply them, which states that:
[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]You also need to remember the Sign Rules for Multiplication:
[tex]\begin{gathered} +\cdot+=+ \\ -\cdot-=+ \\ -\cdot+=- \\ +\cdot-=- \end{gathered}[/tex]Then:
[tex]=(8x)(4x^2)+(8x)(9)-(1)(4x^2)-(1)(9)[/tex][tex]=32x^3+72x-4x^2-9[/tex][tex]=32x^3-4x^2+72x-9[/tex]By definition, Equivalent Expressions work the same, but they have different forms.
Since:
[tex](8x-1)(4x^2+9)=32x^3-4x^2+72x-9[/tex]You can conclude that they are Equivalent Expressions.
Hence, the answer is: They are Equivalent Expression, because:
[tex](8x-1)(4x^2+9)=32x^3-4x^2+72x-9[/tex][tex]f(x) = {x}^{3} - 3x { }^{2} [/tex]find the zeros. and show all work please
Given the function:
[tex]f(x)=x^3-3x^2[/tex]The zeros of the function can be said to be the x-intercept of the given function.
To find the zeros, substitute 0 for f(x) and evaluate.
We have:
[tex]\begin{gathered} 0=x^3-3x^2 \\ \\ \text{ Factor out x}^2 \\ \\ x^2(x-3)=0 \end{gathered}[/tex]We have the individual factors:
[tex]\begin{gathered} x^2 \\ (x-3) \end{gathered}[/tex]Equate the individual factors to zero:
[tex]\begin{gathered} x^2=0 \\ x-3=0 \end{gathered}[/tex]Solve each factor for x:
[tex]\begin{gathered} x^2=0 \\ \text{Take the square root of both sides:} \\ \sqrt[]{x^2}=\sqrt[]{0} \\ x=0 \\ \\ \\ x-3=0 \\ \text{Add 3 to both sides:} \\ x-3+3=0+3 \\ x=3 \end{gathered}[/tex]Therefore, the zeros of the function are:
x = 0, 3
In point form, the zeros are:
(0, 0) and (3, 0)
ANSWER:
x = 0, 3
What is the area of the shaded square? A 7 cm² C 49 cm² B 25 cm² D 60 cm² 3 cm 4 cm
The area of a square is given by the square of one of its sides. To find the area of the shaded square first we need to find the length of its side.
The side of the shaded square along the sides of the other squares form a right triangle, where the side of the shaded square is the hypotenuse.
By the Pythagorean Theorem, the square of the hypotenuse is equal to the sum of the squares of the legs. If we call the side of the shaded square as x, using the Pythagorean Theorem we have the following equation
[tex]3^2+4^2=x^2[/tex]Solving for x, we have
[tex]\begin{gathered} 3^2+4^2=x^2 \\ 9+16=x^2 \\ x=\sqrt[]{25} \\ x=5 \end{gathered}[/tex]Then, the area of the shaded square is
[tex]5^2=25[/tex]The area of the square is 25cm².
Which line is parallel to the line that passes through the points (1,7) and (-3, 4)? A.y=-3/4x-5 B.y=3/4x+1 C.y=4/3x-8 D. y=11/4x+3
Answer:
Option B is the correct option
[tex]\begin{gathered} y=\frac{3}{4}x+1 \\ \\ is\text{ the line parallel to the line that passes through the given points} \end{gathered}[/tex]Explanation:
Given the points (1, 7) and (-3, 4), we want to find the line that is parallel to the line that passes through them.
Let us find the slope of the given line, using the formula:
[tex]S=\frac{y_2-y_1}{x_2-x_1}[/tex]Here:
[tex]\begin{gathered} x_1=1 \\ y_1=7 \\ x_2=-3 \\ y_2=4 \end{gathered}[/tex]Using these, the slope is:
[tex]\begin{gathered} S=\frac{4-7}{-3-1} \\ \\ =\frac{-3}{-4} \\ \\ =\frac{3}{4} \end{gathered}[/tex]The slope is 3/4.
Any other line that has a slope 3/4 would be parallel to the line that passes through the given points.