You have the following expression:
10x⁴(10x)⁻²
in order to simplify the previous expression proceed as follow:
10x⁴(10x)⁻² = 10x⁴/(10x)² = 10x⁴/10²x²
by simplifying the previous fraction, you obtain:
10x⁴/10²x² = 10⁻¹x²
where you have taken into account that the quotient between factors with different exponents, is equal to the same factor powered to the difference of the exponents:
Hence, the answer is:
10⁻¹x²
1. Here is an inequality below: Select ALL of the values that are a solutionto the inequality.*72 +62<3r+2X=-3X-2X = -1X=0x= 1x = 2X = 3
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given inequality
[tex]\frac{7x+6}{2}\le3x+2[/tex]STEP 2: Solve for x
[tex]\begin{gathered} \frac{7x+6}{2}\le3x+2 \\ \mathrm{Multiply\: both\: sides\: by\: }2 \\ 7x+6\le2(3x+2) \\ 7x+6\le\: 6x+4 \\ \mathrm{Subtract\: }6\mathrm{\: from\: both\: sides} \\ 7x+6-6\le\: 6x+4-6 \\ \text{By simplification,} \\ 7x\le\: 6x-2 \\ \mathrm{Subtract\: }6x\mathrm{\: from\: both\: sides} \\ 7x-6x\le\: 6x-2-6x \\ x\le\: -2 \end{gathered}[/tex]STEP 3: Select the values that are a solution to the inequality
[tex]\begin{gathered} \text{ Since }x\le-2,\text{ this means that x is less than or equal to -2} \\ \text{This implies that all values less than or equal to 2 are a solution to the inequality} \\ \text{Looking at the options, the values that are less than or equal to 2 are:} \\ x=-3,x=-2 \end{gathered}[/tex]Hence, the values that are a solution to the inequality are:
The y-value of which function’s y-intercept is larger, f or h?
Answer:
h
Explanation:
The y-value of the y-intercept is the value of y when x is equal to 0, so for the first function, we need to calculate f(x) for x = 0 as:
[tex]\begin{gathered} f(x)=\log _2(x+8) \\ f(0)=\log _2(0+8) \\ f(0)=\log _2(8) \\ f(0)=3 \end{gathered}[/tex]So, the y-value of the first function's y-intercept is 3.
On the other hand, for the second function, when x = 0, h(x) is 4. It means that the y-value of the second function's y-intercept is 4.
Since 4 is larger than 3, the function with the largest y-value in its y-intercept is h(x). So, the answer is h(x)
11. Reflect quadrilateral CONE with C(5,1), 0(1,6),N(-7,0) and E(-2,-4) in the line y = -2.
Step 1
y = -2 is the mirror line.
Step 2
The graph below shows the result after reflection about y = -2.
For each row of the table, choose the equivalent expression
Ok, so:
Let's make all operations and then choose the equivalent expression for each one.
Let's start in order:
a. 4/12 + 4/12 = 8/12
b. 1/12 + (3/12 + 3/12) = 7/12
c. 4/12 + 5/12 = 9/12
d. 2/12 + 2/12 + 2/12 = 6/12.
Notice that the last operations are the columns of the table.
So, let's do it the same with the upper rows:
e. 5/12 + 4/12 = 9/12
f. (1/12 + 3/12) + 3/12 = 7/12
g. 1/12 + 2/12 + 3/12 = 6/12
h. 15/12 - 7/12 = 8/12.
Now, let me draw the table to make this problem more understandable.
This is the order you have to put the answer:
Bea crió algunas vacas y algunos pavos. Crió un total de 28 vacas y pavo. habia 96 patas en total cuantas vacas y cuantos pavos crió bea?
1) Coletando los datos:
Vacas: v
Pavos: p
p+v =28
2p+4v=96 Como las vacas tienen 4 patas e los pavos tienen 2 patas
2) Multiplicando por - 2, la primera ecuación
-2p -2v =-56
2p +4v =96
-------------------
2v = 40
v= 20
3) Substituindo en la primera ecuación
p +20 =28
p =28 -20
p=8
Entonces, había 20 vacas y 8 perus
given the definitions of f(x) and g(x) below find the value of g(f(1)).f (x)= -3x + 4 g(x)= x squared + 7x + 5
f(x) = -3x + 4
g(x) = x^2 + 7x + 5
g(f(x)) = put x = f(x) in equation g(x)
g(f(x)) = (-3x + 4)^2 + 7(-3x + 4) + 5
put x = 1
g(f(1)) = (-3(1) + 4)^2 + 7(-3(1) + 4) + 5
= (-3+4)^2 + 7(-3 + 4) + 5
= 1^2 + 7(1) + 5
= 1 + 7 + 5
= 13
so the answer is 13
Joni took out a loan for $21,912. To pay it back, she will make 42 monthly paymentsof $931. How much will he pay in interest? Round answer to a whole number.
Given:
Loan of $21,912
42 monthly payments of $931.
Find amount of interest.
First, find the total amount that Joni will pay.
[tex]42\times\$931=\$39,102[/tex]Next, subtract the result by the amount of loan
[tex]\$39,102-$\$21,912=$\$17,190[/tex]Therefore, Joni will pay $17,190 in interest.
i start at (3,2). You move down 1 unit and left 3 units. Where do u end
Given the initial coordinate: (3,2)
Moving down 1 unit means a negative displacement of 1 unit to the y-axis.
Moving left 3 units means a negative displacement of 3 units to the x-axis.
We get,
[tex](x^{\prime},y^{\prime})\text{ = (x + A,y + B) = (3 - 3, 2 - 1) = (0, 1)}[/tex]Therefore, after moving down 1 unit and left 3 units, you end at coordinate 0,1.
In the diagram, GH bisects ∠FGI.Solve for x and find m∠FGH.a. X=b. Find m∠HGI.C. Find m∠FGI.(Simplify your answer.)
Answer:
(a)19 degrees
(b)29 degrees
(c)58 degrees
Explanation:
If GH bisects ∠FGI, it means it divides it into two equal parts ∠FGH and ∠HGI.
[tex]\begin{gathered} m\angle FGH=m\angle\text{HGI} \\ (2x-9)^0=(3x-28)^0 \end{gathered}[/tex](a)We solve the equation above for x.
[tex]\begin{gathered} 3x-2x=-9+28 \\ x=19 \end{gathered}[/tex](b)
[tex]\begin{gathered} m\angle HGI=3x-28 \\ =3(19)-28 \\ =57-28 \\ =29^0 \end{gathered}[/tex](c)
[tex]\begin{gathered} m\angle FGI=2\times m\angle HGI \\ =2\times29^0 \\ =58^0 \end{gathered}[/tex]The citizens of a city were asked to choose their favorite pet. The circle graph shows how the citizens answered the questions, how many chose hamsters, birds, or fish.
To find how many chose hamsters, birds, or fish we first verified that the sum of all the percentages is 100% to check that the citizens answered just one time each one.
We have that 17+22+21+27+7+6 = 100.
Now hamsters, birds, or fish is an union of the people that answered this is a sum 6+21+17 = 44 in this case because the events are independients this means the intersection is empty. So the answer is 44.
Which of these four figures are congruent to the top figure? OD ОС ОА B
Congruency is the the quality of two things to be similar to each other.
The shape we use as reference is a parallelogram that has the three blue dots distributed along its longer diagonal with minimal space between them.
Therefore, any other shape congruent to it must agree to this condition.
Option C agrees to this condition.
Jeff receive six dollars for each hour he babysits how much money will just make after six hours eight hours 10 hours in 12 hours right the function and then find each answer to the correct function table that matches this situation
Jeff receive six dollars for each hour he babysits
Function:
f(x) = 6x
Where x is the number of hours
for 6 hours:
F(6) = 6(6) = 36
For 8 hours:
F(8)= 6(8) = 48
For 10 hours:
F(10)= 6(10)= 60
For 12 hours:
F(12)=6(12)=72
Find q4(q - 15) = 20
Answer
q = 20
Explanation
Given equation:
[tex]4(q-15)=20[/tex]The first step in finding q is open the parenthesis:
[tex]\begin{gathered} 4\times q-4\times15=20 \\ 4q-60=20 \end{gathered}[/tex]Add 60 to both sides of the equation:
[tex]\begin{gathered} 4q-60+60=20+60 \\ 4q=80 \end{gathered}[/tex]Finally, divide both sides by 4 to get q:
[tex]\begin{gathered} \frac{4q}{4}=\frac{80}{4} \\ q=20 \end{gathered}[/tex]consider the following data. Find the standard variance .round your answer to one decimal place .
The variance of a data set is given by the formula:
[tex]s^2=\sum ^{}_i(x_i-\mu)^2P(x_i)[/tex]Where μ is the mean given by the formula:
[tex]\mu=\sum ^{}_ix_iP(x_i)[/tex]Therefore, in our problem:
[tex]\begin{gathered} \mu=3\cdot0.3+4\cdot0.1+5\cdot0.2+6\cdot0.2+7\cdot0.2=4.9 \\ \Rightarrow\mu=4.9 \end{gathered}[/tex]Then, the variance is:
[tex]\begin{gathered} s^2=0.3(3-4.9)^2+0.1(4-4.9)^2+0.2((5-4.9)^2+(6-4.9)^2+(7-4.9)^2) \\ \Rightarrow s^2=2.29 \end{gathered}[/tex]Thus, the variance is 2.29
A polynomial has one root that equals 2 + i. Name one other root of thispolynomial.
In a polynomial, if it has an imaginary root, then it also has the conjugate of that root. In this case, since 2 + i, is a root then 2 - i, is also a root.
Perform the indicated operation numbers be sure to express your answer in reduced form
We need to calculate the following sum:
[tex]\frac{8}{15}+\frac{7}{25}[/tex]The first step is to calculate the least common multiplier between the two denominators. This is done below:
[tex]\begin{gathered} 15=3\cdot5 \\ 25=5\cdot5 \end{gathered}[/tex]We broke down the two denominators into their factors, now we need to multiply the factors that are unique. This is done below:
[tex]\text{LCM}=3\cdot5\cdot5=75[/tex]Now we have to replace the denominators by 75 and calculate new numerators. The new numerators must be calculated as follows:
1 - Divide the LCM by the old denominator
2 - Multiply the result of 1 by the old numerator.
This is done below:
[tex]\begin{gathered} \frac{5\cdot8}{75}+\frac{3\cdot7}{75} \\ \frac{40}{75}+\frac{21}{75} \end{gathered}[/tex]Since both fractions have their denominators with the same value, we can just directly add them.
[tex]\frac{40+21}{75}=\frac{61}{75}[/tex]The fraction is already in its most reductable form, therefore the answer is 61/75.
what is the area of triangle Givenchy height 137 and base 203
the area is calculated according to:
[tex]area=\frac{1}{2}\times203\times137=13,905.5[/tex]
Use a property to write a equivalent expression for 12 *(100-5). Which property did you use
Equivalent expression to the given expression 12 × ( 100 - 5 ) using distributive property multiplication over subtraction is given by
12 × 100 - 12 × 5.
As given in the question,
Given expression is equal to :
12 × ( 100 - 5 )
Simplify it using distributive property multiplication over subtraction to get its equivalent expression we have,
A × ( B - C ) = A × B - A × C
Here , Value of A = 12 , value of B = 100 , and value of C = 5
12 × ( 100 - 5 )
= 12 × 100 - 12 × 5
= 1200 - 60
= 1140
Therefore, equivalent expression to the given expression 12 × ( 100 - 5 ) using distributive property multiplication over subtraction is given by
12 × 100 - 12 × 5.
Learn more about equivalent expression here
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factoring out; 50y + 100
Factor the expression 50y + 100.
[tex]\begin{gathered} 50y+100=50y+50\cdot2 \\ =50(y+2) \end{gathered}[/tex]So answer is 50(y + 2).
There are 23 students in a class, and 6 of them will be chosen to go on a field trip. How many ways can these students be chosen?
To find how many ways a group of 23 students can be chosen from a group of 6, we use combinations, where the order doesn't matter.
Combinations are found with the next formula:
[tex]\text{nCr}=\frac{n!}{r!(n-r)!}[/tex]Where n is the total of persons and r is the sample asked.
Therefore:
n=23 and r=6
Replacing the values:
[tex]23C6=\frac{23!}{6!(23-6)!}[/tex]Then:
[tex]23C6=100947[/tex]Hence, there are 100947 ways that 23 students can be chosen from a group of 6.
Which information is not enough to prove quadrilateral ABCD is a parallelogram?
To prove :
ABCD is a parallelogram
For parallelogram, if one pair of opposite sides of a quadrilateral are congruent and parallel then the quadrilateral is a parallelogram.
Thus, in option (2) their is not enought information to prove that ABCD is a parallelogram because AB and CD are given congruent but not given parallel.
Similarly, BC and DA are given congruent but not given parallel.
So, the correct option is (2)
17. Darla Waters has a gross weekly pay of $475.00. Her earnings to date for this year is $ 5700.00. What is thetotal deduction this week for Social Security taxes (1 point) and Medicare taxes (1 point)?
Solution:
Icomplete information.
determine whether the line is a tangent, secant, a secant that contains the diameter, or none of these. Graph the circle using your calculator or online calculator or graph paper. Then graph this line.
As suggested, we will use a diagram that includes the circle and the line to decide what type of chord is the line to the circle.
The graph of the circle and the line is:
From the above graph, we get that the line is exterior to the circle and never touches it. Therefore, the line is not a tangent, a secant, or a secant that contains the diameter.
Answer:
None
What is f(2) for the function f(x) = 2x^2 + 6x – 5?
f(x) = 2x² + 6x – 5
To find f(2) you have to replace x = 2 into the function, as follows:
f(2) = 2(2)² + 6(2) – 5
f(2) = 2(4) + 12 – 5 Solving the square and the multiplication
f(2) = 8 + 12 – 5 Solving the multiplication
f(2) = 15
this is just a normal not really a long question which we would like to check how it looks in session history.
check how sort question looks
Cindy has a jacket with the first letter of her school's name on it. determine the area of the letter on Cindy's jacket.
To find the area of the letter, use the area of a rectangle formula below:
Area = Length x Width
Find the
Total area = ( 10 x 2) + (6 x 2) + (6 x 2)
= 20 + 12 + 12
= 44 in²
Therefore, the area of the letter on Cindy's jacket is 44 in²
ANSWER:
44 in²
(F.LE.5) The function f(x) = 7.75x models the amount of money that Jimearns for each hour of work. What is the meaning of the coefficient of x?A. There is no initial amount of money he gets paid prior to startingB. His hourly wageC. His total amount he gets paid for the dayD. The number of hours Jim has worked
Solution
Given the function f(x) = 7.75x
The coefficient of x is 7.75
7.75 represents his hourly wag
Need help with this graph.Given the inequality: y < 3x+1. Identify the graph that describes the inequality.
The Solution:
Given the inequality below:
[tex]y<3x+1[/tex]We are required to the graph that describes the graph above.
[tex]\begin{gathered} \text{ when x=0} \\ y=3(0)+1=1 \\ (0,1) \\ \text{ When y=0} \\ 0=3x+1 \\ -1=3x \\ x=-\frac{1}{3} \\ (-\frac{1}{3},0) \end{gathered}[/tex]The required graph is attached below:
Decide whether the relation defines y as a function of x. Give the domain. x+2y=——— 5A) Does the equation describe y as a function of x?1. Yes2. NoB) Give the domainThe domain is _____
Answer:
A) 1.yes
B) The domain is All real numbers.
Explanation:
The problem gives us a relationship:
[tex]y=\frac{x+2}{5}[/tex]For this relationship to be a function, for each value of x, we should get a single value of y. We can see that this is true, given a value of x, we get a unique value of y. Thus, A is true.
Now, we need to find the domain. The domain is the set of all values of x for which the function is defined. In this case, the function is a line:
[tex]\begin{gathered} y=\frac{x+2}{5} \\ . \\ y=\frac{x}{5}+\frac{2}{5} \\ . \\ y=\frac{1}{5}x+\frac{2}{5} \end{gathered}[/tex]The equation is a line with slope 1/5 and y-intercept 2/5. We know that any line is defined for all real numbers.
Thus, the domain is all real numbers.
Rewrite to give an equation without logarithm. Do not solve for X. Solve the equation select the correct choice below and if necessary fill in the answer back to complete your choice
Given:
[tex]log_2(2x+9)=2[/tex]Required:
We need to solve the given equation.
Explanation:
Consider the formula.
[tex]log_a(b)=x\Rightarrow a^x=b.[/tex]The given equation can be written as follows.
[tex]2^2=2x+9[/tex][tex]4=2x+9[/tex]Solve for x.
[tex]4=2x+9[/tex]Subtract 9 from both sides of the equation.
[tex]4-9=2x+9-9[/tex][tex]-5=2x[/tex]Divide both sides by 2.
[tex]-\frac{5}{2}=\frac{2x}{2}[/tex][tex]-\frac{5}{2}=x[/tex]Final answer:
Rewrite the given equation without logrithmic.
[tex]4=2x+9[/tex]The solution for x.
[tex]x=-\frac{5}{2}[/tex]