given
[tex]\frac{6^7\cdot4^4\cdot2}{6^5\cdot4^4\cdot2^2}[/tex][tex]=6^{7-5}\cdot4^{4-4}\cdot2^{1-2}=6^2\cdot4^0\cdot2^{-1}=\frac{6^2\cdot1}{2}=\frac{36}{2}=18[/tex]Note 4 exponent 0 = 1
fill in the table using the function rule y=3x+5
Fill in the table using the function rule y= 3x + 5
________________________________________
Replace each value of x in the expression
____________________________________
x= -4
y = 3* (-4)+5
= -12 +5
= -7
_______________
x= -2
y = 3* (-2)+5
= -6 +5
= -1
_____________
x= 0
y = 3* (0)+5
= 0 +5
= 5
_____________
x= 2
y = 3* (2)+5
= 6 +5
= 11
______________________________
Answer
_________________________
Can you see the updates?
Do you have any questions regarding the solution?
If you don’t need further explanation on this question, we can end the session.
I want to remind you this answer will always be saved in your profile. I’d really appreciate you letting me know how I did by rating our session after you exit. Thanks and have a great day!
-2-3t=-4t how do i solve for t?
You have the following equation:
2- 3t = -4t
In order to solve the previous equation you proceed as follow:
2- 3t = -4t sum 3t both sides
2 = -4t + 3t simplify
2 = -t multiply by -1 both sides
-2 = t
t = -2
Hence, the dolution for t is t=-2
Use a venn diagram to represent this problemJar A contains numbers that are less than 26 and evenly divisible by 2, Jar B contains numbers that are less than 20 and evenly divisible by 4.
Given:
Jar A contains numbers that are less than 26 and evenly divisible by 2.
The number less than 6 and divisible by 2 are,
[tex]A=\mleft\lbrace2,4,6,8,10,12,14,16,18,20,22,24\mright\rbrace[/tex]Jar B contains numbers that are less than 20 and evenly divisible by 4.
The set is,
[tex]B=\mleft\lbrace4,8,12,16\mright\rbrace[/tex]The Venn diagram is,
Desmond fabricates a tiny microchip it is square in shape measuring seven. 5 mm on each side draw Desmond’s chip to scale on the grid below
Explanation
To draw the square, we were given a scale
2 units represent 1 mm
Therefore, 7.5mm will be
[tex]2\times7.5\text{ units =15 units}[/tex]So that we will have 15 units on all sides
The red sketch above represents the square with a length of 7.5mm
Goran rented a truck for one day. There was a base fee of $20.99, and there was an additional charge of 92 cents for each mile driven. Goran had to pay $252.82 when he returned the truck. For how many miles did he drive the truck?
Let x be the miles driven, and y be the cost, then we can write the following relationship:
[tex]y=0.92x+20.99[/tex]In our case, we know that the final cost was y=252.82 and we need to find the miles given by x, then, we have
[tex]252.82=0.92x+20.99[/tex]By moving 20.99 to the left hand side, we have
[tex]\begin{gathered} 252.82-20.99=0.92x \\ 231.83=0.92x \end{gathered}[/tex]then, x is given by
[tex]\begin{gathered} x=\frac{231.83}{0.92} \\ x=251.98\text{ miles} \end{gathered}[/tex]then, the answer is 251.98 miles
I need the correct choice and the answer for the box
Given the exponential equation:
[tex]16e^t=98[/tex]A student solved it.
Let's describe and correct the error the student made in solving the exponential equation.
Let's solve the equation.
Apply the following steps:
Step 1.
Divide both sides by 16
[tex]\begin{gathered} \frac{16e^t}{16}=\frac{98}{16} \\ \\ e^t=6.125 \end{gathered}[/tex]Step 2.
Take the natural logarithm of both sides
[tex]\begin{gathered} t\text{ ln\lparen e\rparen=ln\lparen6.125\rparen} \\ \\ \end{gathered}[/tex]Where:
ln(e) = 1
Hence, we have:
[tex]t=1.812[/tex]The student did not convert to the logarithmic form correctly. The solution should be t = 1.812
ANSWER:
A. The student did not convert to the logarithmic form correctly. The solution should be
t = 1.812
I understand the problem but I do need help with finding the angle measure
Write the equation of the parabola in vertex form given the vertex (–2, 3) and point (0, 1).
the equation is
[tex]y=-\frac{1}{2}(x+2)^2+3[/tex]Keith is saving money for a car. He has saved the same amount each year for the past three years, and records how much he has at the end of each year in the table below. (a)What is Keith's unit rate of change of dollars with respect to time; that is, how much does Keith save in one year? The unit rate is dollars per year. (b)Graph the proportional relationship described above, with the x-coordinate representing years, and the y- coordinate representing amount saved in thousands of dollars.
Answer:
(a)$1500 per year.
Explanation:
(a)From the table:
3000-1500=$1500
4500-3000=$1500
This means that every year, Keith adds $1500 to his savings.
The unit rate is $1500 per year.
(b)
If x=number of years; and
y=Amount saved (in thousands of dollars.)
When x=1, y=$1.5
When x=2, y=$3.0=2x1.5
When x=3, y=$4.5=3x1.5
The equation of proportion is therefore:
[tex]y=1.5x[/tex]When x=0, y=0 (0,0)
When x=1, y=1.5 (1, 1.5)
We join the points (0,0) and (1,1.5)
The graph of the proportional relationship is attached below.
When graphing unit rates, the unit rate begins at (0, 0), and then at (1, y). What will the 2nd and third points be? (2, _) and (3, _)
When graphing unit rates, the unit rate begins at (0, 0), and then at (1, y).
So, it will represents a line passes through the given points
The slope of the line will be y
So,
The second point will be ( 2, 2y)
And the third point will be ( 3, 3y)
Evaluate: sin(30 degrees)cos(60 degrees)=(See attached image to assist with these 2 problems)
According to the figure we need to evaluate the sin(30°) and the cos(60°). Remember the trigonometric relations defined over the rectangle triangles as follows, suppose we have an angle called "alpha"
[tex]\begin{gathered} \sin(\alpha)=\frac{oc}{h}, \\ \\ cos(\alpha)=\frac{ac}{h}, \\ \\ tan(\alpha)=\frac{co}{ca} \\ \\ where\text{ }h:Hypotenuse,\text{ }ac:Adjacent\text{ }cathetus\text{ and }oc:Opposite\text{ }cathetus \end{gathered}[/tex]Now, according to the figure, we have that for the angle of 60 degrees:
[tex]\begin{gathered} h=2x,ac=x,oc=\sqrt{3}x \\ \\ \sin(60°)=\frac{oc}{h}=\frac{\sqrt{3}x}{2x}=\frac{\sqrt{3}}{2} \\ \\ \cos(60^{\circ})=\frac{ac}{h}=\frac{x}{2x}=\frac{1}{2} \end{gathered}[/tex]And for the angle of 30 degrees we get the following
[tex]\begin{gathered} h=2x,oc=x,ac=\sqrt{3}x \\ \\ \sin(30°)=\frac{oc}{h}=\frac{x}{2x}=\frac{1}{2}=\cos(60°) \\ \\ \cos(30^{\circ})=\frac{ac}{h}=\frac{\sqrt{3}x}{2x}=\frac{\sqrt{3}}{2}=\cos(60^{\circ}) \end{gathered}[/tex]So, your answer is: sin(30°)=1/2=cos(60°).
In the accompanying diagram of a circle of O …..
the theorem says:
[tex]PA^2=PB\cdot PC[/tex]PB=2
PC=2+6=8
[tex]PA=\sqrt[]{2\cdot8}=\sqrt[]{16}=4[/tex]So the answer is
PA=4
1331166633×644÷8797×5
1. The first thing to do is to carry out the two respective multiplications;
[tex]\begin{gathered} 133116633\times644=85,727,111,652 \\ 8797\times5=43,985 \\ \end{gathered}[/tex]2.Now we divide both results, leaving the first result as a dividend and the shortest result as a divisor.
[tex]\begin{gathered} 85,727,111,652/\text{ 43,985} \\ =1,949,007.881141 \end{gathered}[/tex]Type the correct answer in the box. Use numbers instead of words.
The number 392,000 is divided by 10.
What is the value of the digit 2 in the quotient?
The value of 2 in the quotient is 200.
What is division?
One of the four fundamental operations of arithmetic, or how to mix numbers to create new ones, is division. Addition, subtraction, and multiplication are the other operations.
The opposite of multiplication is division. When you multiply three groups of four to produce twelve, you get four in each group when you split twelve into three equal groups.
Let, the number 392,000 is divided by 10.
That means, [tex]\frac{392000}{10}[/tex]
Here, 392000 is the numerator and 10 is the base.
Simplifying the fraction, we get 39200.
39200 is the quotient.
Here 2 is on the hundredth place.
Therefore, the value of 2 in the quotient is 200.
To know more about the division, click on the link
https://brainly.com/question/25289437
#SPJ1
A shipment of computers arrived at. a warehouse.If each computers is valued at$995. What is the total value of the shipping?
Total number of computers = 20
Cost per a computer = $995
Total cost of 20 computers = 20 x $995
= $19,900
6 At a 33-foot depth underwater, the pressure is 29.55 pounds per square inch (psi). At a depth of 66 feet, the pressure reaches 44.4 psi. At what rate is the pressure increasing? ur answer on ouatlon for the
To solve the exercise you can apply the following formula:
[tex]rate=\frac{\text{difference in pressure}}{\text{difference in depth}}[/tex]In this case, based on the information given in the exercise, you can identify that:
[tex]\begin{gathered} \text{difference in pressure= (44.4.}-29.55)psi=14.85\text{ psi} \\ \text{difference in dept}=(66-33)ft=33\text{ ft} \end{gathered}[/tex]Substituting values, you get:
[tex]rate=\frac{14.85\text{ ps i}}{33\text{ ft}}=0.45\text{ }\frac{ps\text{ i}}{ft}[/tex]Therefore, The pressure is increasing at 0.45 psi per foot.
Which of the following statements are true for the image of a triangle after a dilation that has a scale factor of 5/6
EXPLANATION
Since we have a dilation with a scale factor of 5/6, the appropriate statement is the following:
1st) Each angle has the same measure as its corresponding angle in the preimage. This is true because the dilations don't change the shape.
II. Each has a measure 5/6 the length of its corresponding side in the pre-image.
Which of the following is the graph of f(x)= x² +3x-4?
Given the function
[tex]f(x)=x^2+3x-4[/tex]To determine which graph corresponds to this function you have to determine the coordinates of the vertex and the roots of the function.
Vertex
To determine the coordinates of the vertex you have to calculate the x-coordinate using the formula:
[tex]x=-\frac{b}{2a}[/tex]a is the coefficient of the quadratic term
b is the coefficient of the x-term
The term of the quadratic term, in this case, is a=1 and the term of the x-term is b=3
[tex]\begin{gathered} x=-\frac{3}{2\cdot1} \\ x=-\frac{3}{2}=-1.5 \end{gathered}[/tex]Replace the x-coordinate in the function to calculate the corresponding value of f(x):
[tex]\begin{gathered} f(x)=x^2+6x-4 \\ f(-3)=(-\frac{3}{2})^2+3\cdot(-\frac{3}{2})-4 \\ f(-3)=\frac{9}{4}-\frac{9}{2}-4 \\ f(-3)=-\frac{25}{4}=-6.25 \end{gathered}[/tex]The coordinates of the vertex are (-1.5,-6.25)
Roots of the function
To determine the roots of the function you have to use the quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]a is the coefficient of the quadratic term
b is the coefficient of the x-term
c is the constant of the function
For a=1, b=3, and c=-4
[tex]\begin{gathered} x=\frac{-3\pm\sqrt[]{3^2-4\cdot1\cdot(-4)}}{2\cdot1} \\ x=\frac{-3\pm\sqrt[]{9+16}}{2} \\ x=\frac{-3\pm\sqrt[]{25}}{2} \\ x=\frac{-3\pm5}{2} \end{gathered}[/tex]Solve the addition and the subtraction separately
Addition
[tex]\begin{gathered} x=\frac{-3+5}{2} \\ x=\frac{2}{2} \\ x=1 \end{gathered}[/tex]Subtraction
[tex]\begin{gathered} x=\frac{-3-5}{2} \\ x=\frac{-8}{2} \\ x=-4 \end{gathered}[/tex]The roots of the function are (1,0) and (-4,0)
The graph that corresponds to this function is
If we chose a theater and movie to attend at random, what probability would we have of seeing anything other than a romantic or sci-fi movie ?
we have that
The probability of seeing a romantic or sci-fi movie is
P=0.203+0.12=0.323
therefore
the probability of seeing anything other than a romantic or sci-fi movie is
P=1-0.323
P=0.677
the answer is option B= O DATA ANALYSIS AND STATISTICS Mean and median of a data set A group of 8 students was asked, "How many hours did you watch television last week?" Here are their responses. 16, 16, 9, 9, 9, 7, 16, 10 Find the median and mean number of hours for these students. If necessary, round your answers to the nearest tenth. (a) Median: hours (b) Mean: hours X Ś ?
Solution:
Given:
[tex]16,16,9,9,9,7,16,10[/tex]The median is the middle term from the data rearranged in rank order.
Rearranging the data;
[tex]7,9,9,9,10,16,16,16[/tex]From the data set, the middle term is 9 and 10.
Since two terms fall in the middle, then the median is the mean of the two terms.
Hence,
[tex]\begin{gathered} Median=\frac{9+10}{2} \\ Median=\frac{19}{2} \\ Median=9.5hours \end{gathered}[/tex]Therefore, to the nearest tenth, the median is 9.5 hours.
The mean is the average of the set of data.
[tex]\begin{gathered} mean=\frac{16+16+9+9+9+7+16+10\:}{8} \\ mean=\frac{92}{8} \\ mean=11.5hours \end{gathered}[/tex]Therefore, to the nearest tenth, the mean is 11.5 hours
Find the prime factorization of the following number write any repeated racists using exponents
Prime factorization refers to the process of decomposing a given number into a product of prime numbers that can be repeated or not.
Let's remember that prime numbers are numbers that can only be divided by 1 or itself.v Having this in mind we have that the prime factorization of 66 is:
[tex]66=(2)(3)(11)[/tex]PO Triangle ABC is similar to triangular DEF. What is the value of x?
If triangle ABC is similar to DEF then the ratio between the sides will be a constant so we can get the expression:
[tex]\frac{15}{30}=\frac{x}{36}[/tex]and we solve for x so:
[tex]\begin{gathered} x=\frac{36\cdot15}{30} \\ x=18 \end{gathered}[/tex]A patient started with a 1 liter bag of IV solution. When the doctor checked in on the patient, the bag contained 0.24 liters of the solution. How much solution had been infused into the patient?
Given,
The quantity of solution intially is 1 litre.
The quantity of solution left after infusion is 0.24 litre.
The quantity of solution had been infused into the patient is,
[tex]\begin{gathered} \text{Solution infused tothe patient = total solution -left solution} \\ =1\text{ litre-0.24 litre} \\ =0.76\text{ litre} \end{gathered}[/tex]Hence, the quantity of solution had been infused into the patient is 0.74
A lumber yard has fixed costs of $7259.40 per day and variable costs of $0.07 per board-foot produced. Lumbar sells for $1.87 per board-foot. How many board-feet must be produced and sold daily to break even?
The number of board-feet that must be produced and sold daily to break even is:4033.
How to find the number of board-feet to breakeven?Let the number of board-feet produced per day = x
Let the lumber yard's costs each day be: C =$7259.40+ 0.07x
Let the lumber yard's profits be: P = 1.87x
Let P - C = 0
Hence,
1.87x - ($7259.40 + $0.07x) = 0
1.87x - $7259.40 - 0.07x = 0
Combine like terms
1.8x - $7259.40 = 0
1.8x = $7259.40
Divide both side by 1.8x
x = $7259.40/ 1.8
x = 4033
Therefore the breakeven is 4033.
Learn more about breakeven here:https://brainly.com/question/21137380
#SPJ1
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
Answer: A 143 degrees because angle 5 is a congruent to angle one
Step-by-step explanation:
find the first five terms of the recursive sequence. aₙ = -6aₙ₋₁ where a₁ = 45
The first terms is
[tex]undefined[/tex]Substitute 2, 3, 4, and 5 for n in the equation to find first four next terms.
How to solve 2(x+7)=-4x+14
Let's solve the following equation
[tex]\begin{gathered} 2x+14=-4x+14 \\ 2x+4x=-14+14 \\ 6x=0 \\ x=0 \end{gathered}[/tex]The answer would be x = 0
The vertices of ABCDE are A(-6,0), B(-3,0), C(0, -3), D(-3,-6), and E(-6, -3). Find the vertices of the image after a translation using the rule (x,y) - (x + 9, y-6) and a dilation with a scale factor of 4s centered at the origin.
Vertices of new image: A' = (12, -24)
B' = (24, -24)
C' = (36, -36)
D' = (24, -48)
E = (12, -36)
Explanation:A(-6,0), B(-3,0), C(0, -3), D(-3,-6), and E(-6, -3)
A translation of (x + 9, y-6)
A becomes A'
A' = (-6 + 9, 0 - 6) = (3, -6)
B(-3,0)
B becomes B'
B' = (-3+9, 0 - 6) = B' (6, -6)
C(0, -3)
C becomes C'
C' = (0+9, -3-6) = C' (9, -9)
D(-3,-6)
D becomes D'
D' = (-3+9, -6-6) = (6, -12)
E(-6, -3)
E becomes E'
E' = (-6+9, -3-6) = (3, -9)
A dilation with scale factor of 4, we multiply the cooordinates of the alphabeths with prime with 4.
Vertices of new image:
A' = 4(3, -6) = (12, -24)
B' = 4(6, -6) = (24, -24)
C' = 4(9, -9) = (36, -36)
D' = 4(6, -12) = (24, -48)
E = 4(3, -9) = (12, -36)
Dave started at the black dot and traveled the distance shown on the map on his bike. The length of the section in red is not known.
About how far did Dave travel on his bike?
Answer: 9,00
Step-by-step explanation:
I am right.
Answer:
1,402
Step-by-step explanation
the red line is further than the 1,396
Stacy made a square tablecloth with a side length of 3.5 feet. She put lace along each side of the tablecloth.How much lace did Stacy need for the tablecloth?
The side of the square is 3.5 feet
The perimeter is
[tex]4\times3.5=14ft[/tex]Stacy need 14 feet lace