Therefore,
[tex]\begin{gathered} \log _ax^3+\log _ay-\log _az^4=\log _a(\frac{x^3y}{z^4}) \\ 3\log _ax^{}+\log _ay-4\log _az=3(3)+7-4(-2)=9+7-8=8 \end{gathered}[/tex]Exit Ticket Which method do you believe is the most efficient when solving for the following equations? n2 – 2n – 3=0 Factor/Zero Product Property Completing the Square Quadratic Formula
The factoYou ar/zero product property is the most efficient method for solving the equation
Explanation:The given quadratic equation can be factored as:
[tex]\begin{gathered} n^2-2n-3=0 \\ (n+1)(n-3)=0 \end{gathered}[/tex]The factor/zero product property is the most efficient method for solving the equation
PLEASE HELPFind the value of x.B68ХDx = [?]
Since the triangles are similar, that means the the prop
Leila purchased 21.5 centimeters of wire for $17.20.Find the unit price in dollars per centimeter.If necessary, round your answer to the nearest cent.
Explanation
Given: Leila purchased 21,5cm of wire for $17.20.
Required: To determine the unit price in dollars per centimeter.
This is achieved thus:
To determine the unit price per centimeter, we divide the cost by the length of wire as follows:
[tex]\begin{gathered} 21.5cm=\text{ \$}17.20 \\ \therefore1cm=\frac{\text{ \$}17.20}{21.5}=\text{ \$}0.80 \end{gathered}[/tex]Hence, the answer is:
[tex]\text{ \$}0.80\text{ }per\text{ }centimeter[/tex] 54. Foucault Pendulum
Foucault used a pendulum to demonstrate the Earth’s rotation. There are now over 30 Foucault pendulum displays in the United States. The Foucault pendulum at the Smithsonian Institution in Washington, DC, consists of a large brass ball suspended by a thin 52-ft cable. If the ball swings through an angle of 1°, how far does it travel?
The distance travelled by the ball is 0.9076 feet.
Foucault used a pendulum to demonstrate the earth’s rotation. There are now over 30 Foucault pendulum displays in the United States. The Foucault pendulum at the Smithsonian Institution in Washington, DC, consists of a large brass ball suspended by a thin 52-foot cable. The ball swings at an angle of 1°. We have to find the distance travelled by the ball.
The ball travels in a circular motion. The radius of the circle is equal to the length of the cable. The distance travelled by the ball is equal to the arc length traversed in circular motion. Let the radius, angle, and distance be denoted by the variables "r", "θ", and "d", respectively.
r = 52 feet
We need to convert the angle from degrees into radians.
θ = 1°
θ = 1°*(π/180°)
θ = π/180
The formula for arc length is used below to calculate the distance.
d = r*θ
d = 52*(π/180)
d = 0.9076
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3. Given the picture below, find the value of x:
The value of x for the given triangle is 65°.
According to the question,
We have the following information:
A figure of triangle is given where two of its angles are 68° and 47°.
We know that the sum of all three angles of a triangle is 180°.
(More to know: all angles in an equilateral triangle are equal and in an isosceles triangle two angles are equal however the sum of three angles is 180°.)
So, we have the following expression:
x+68+47 = 180
x+115 = 180
x = 180-115
x = 65°
Hence, the value of x for the given triangle is 65°.
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There is a rectangular garden with an area of 24 square leel. The garden is 2 feet longer than it is wide. Create an equation that can be used to determine the length and wath of the garden
The equation that can be used to determine the length and width of the garden is x² + 2x - 24 =0, the length is 6 feet and the width is 4 feet.
There is a rectangular garden with an area of 24 square feet
The garden is 2 feet longer than it is wide
Let the width of the garden be x
Then, the length of the garden is x + 2
The area of a rectangular garden = length of the garden x width of the garden
24 = x (x + 2)
x² + 2x - 24 =0
x² + 6x - 4x - 24 = 0
x(x + 6) -4(x + 6) = 0
(x - 4)(x + 6) = 0
x - 4 = 0
x = 4
Width of the rectangular garden is 4 feet
Length of the rectangular garden is (4 + 2) feet = 6feet
Therefore, the equation that can be used to determine the length and width of the garden is x² + 2x - 24 =0, the length is 6 feet and the width is 4 feet.
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what is the measure of m<1 will ensure that the rail is parallel to the bottom of the staircase?
You can observe that angle 1 and angle with 47° are inside a parallelogram.
Consider that the sum of the internal angles of a parallelogram is 360°.
Moreover, consider that the angle at the top right of the parallogram is congruent with the angle of 47°, then, such an angle is if 47°.
Consider that angle down right side is congruent with angle 1, then, they have the same measure.
You can write the previous situation in the following equation:
47 + 47 + ∠1 + ∠1 = 360 simplify like terms
94 + 2∠1 = 360 subtract both sides by 94
2∠1 = 360 - 94
2∠1 = 266 divide by 2 both sides
∠1 = 266/2
∠1 = 133
Hence, the measure of angle 1 is m∠1 = 133°
Question 12 of 19 What is the solution to the system of equations graphed below? -5 y= x + 2 N 5 5 y = -2x - 4 -5 y = -2x - 4 y = x+2
For finding the solutions, you need to match the equations
[tex]\begin{gathered} x+2=-2x-4 \\ x+2x=-4-2 \\ 3x=-6 \\ x=-2 \end{gathered}[/tex]For the next step, you should replace the value for x in any of the equations given
y=x+2
y=-2+2
y=0
(-2,0) Letter a
Exterminator the average rate of change of f(x)3x+2/x+1 as x changes from x=0 to x=2
We can see from the question that we have the following function:
[tex]f(x)=\frac{3x+2}{x+1}[/tex]And we need to find the rate of change from x = 0 to x = 2.
1. To find the average rate of change, we need to remember the formula to find it:
[tex]\text{ Average rate of change}=\frac{\text{ change in y}}{\text{ change in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]And we also have the average rate of change for a function, f(x) between x = a and x = b is given by:
[tex]\text{ Average rate of change}=\frac{\text{ change in y}}{\text{ change in x}}=\frac{f(b)-f(a)}{b-a}[/tex]2. Then we have that the average rate of change between x = 0 and x = 2 is as follows:
[tex]\begin{gathered} x=0,x=2 \\ \\ \text{ Average rate of change}=\frac{f(2)-f(0)}{2-0} \\ \end{gathered}[/tex]3. However, we need to find the values for the function when f(2) and f(0). Then we have:
[tex]\begin{gathered} f(x)=\frac{3x+2}{x+1} \\ \\ x=2\Rightarrow f(2)=\frac{3(2)+2}{2+1}=\frac{6+2}{3}=\frac{8}{3} \\ \\ \therefore f(2)=\frac{8}{3} \end{gathered}[/tex]And we also have:
[tex]\begin{gathered} x=0 \\ \\ f(0)=\frac{3x+2}{x+1}=\frac{3(0)+2}{0+1}=\frac{0+2}{1}=\frac{2}{1}=2 \\ \\ \therefore f(0)=2 \end{gathered}[/tex]4. Finally, the average rate of change is given by:
[tex]\begin{gathered} A_{rateofchange}=\frac{f(2)-f(0)}{2-0}=\frac{\frac{8}{3}-2}{2}=\frac{\frac{8}{3}-2}{2}=\frac{\frac{8}{3}-\frac{6}{3}}{2}=\frac{\frac{2}{3}}{2}=\frac{2}{3}*\frac{1}{2}=\frac{1}{3} \\ \\ \therefore A_{rateofchange}=\frac{1}{3} \end{gathered}[/tex]Therefore, in summary, we have that the average rate of change of the function:
[tex]f(x)=\frac{3x+2}{x+1},\text{ between x = 0 to x =2 is: }\frac{1}{3}[/tex]A mechanic has a length of hose 3 ft long. What is the length after 9in is cut off?The length is _ ft _ in?
ANSWER
[tex]2ft\text{ 3 in}[/tex]EXPLANATION
We want to find the length of the hose after 9 inches have been cut off.
First, convert the original length of the hose from feet to inches by multiplying by 12:
[tex]\begin{gathered} 1ft=12in \\ \Rightarrow3ft=3\cdot12in=36in \end{gathered}[/tex]Next, subtract 9 inches from that value:
[tex]\begin{gathered} 36-9 \\ \Rightarrow27in \end{gathered}[/tex]Finally, convert the length to feet by dividing by 12:
[tex]\begin{gathered} \frac{27}{12}ft \\ \Rightarrow2\frac{3}{12}ft \\ \Rightarrow2ft3in \end{gathered}[/tex]That is the answer.
9. the product of c and 10
SOLUTION
9. We want to find the product of c and 10.
Product means multiplication. So the product of c and 10 means
[tex]c\times10[/tex]So we bring 10 and c together, to get 10c.
Hence the answer is 10c
this is confusing isnt there supposed to be 2 numbers
Let's begin by listing out the information given to us:
Angle U = 27°
TU is tangent to S implies this is a right triangle
Angle T = 90°
The sum of interior angles in a triangle is 180 degrees
U + T + S = 180°
⇒27 + 90 + S = 180
⇒S = 180 - (90 + 27) = 53
S = 53°
Please Help. I will mark you BRAINLIST
Answer:
(D). f(x) = [tex]-\frac{3}{2}[/tex] x² + [tex]\frac{17}{2}[/tex] x - 7
Step-by-step explanation:
( x , y )
ax² + bx + c = y ............ ( 1 )
~~~~~~~~~~~~~~
( 2 , 4 ) --------> ( 1 )
a(2)² + b(2) + c = 4
4a + 2b + c = 4 .............. (2)
( 3 , 5 ) ---------> ( 1 )
a(3)² + b(3) + c = 5
9a + 3b + c = 5 ............... (3)
( 4 , 3 ) ----------> ( 1 )
a(4)² + b(4) + c = 3
16a + 4b + c = 3 .............. (4)
[tex]delta[/tex] = Δ = [tex]\left[\begin{array}{ccc}4&2&1\\9&3&1\\16&4&1\end{array}\right][/tex] = - 2
[tex]delta_{a}[/tex] = [tex]\left[\begin{array}{ccc}4&2&1\\5&3&1\\3&4&1\end{array}\right][/tex] = 3
[tex]delta_{b}[/tex] = [tex]\left[\begin{array}{ccc}4&4&1\\9&5&1\\16&3&1\end{array}\right][/tex] = - 17
[tex]delta_{c}[/tex] = [tex]\left[\begin{array}{ccc}4&2&4\\9&3&5\\16&4&3\end{array}\right][/tex] = 14
a = [tex]delta_{a}[/tex] / [tex]delta[/tex] = [tex]-\frac{3}{2}[/tex]
b = [tex]delta_{b}[/tex] / [tex]delta[/tex] = [tex]\frac{-17}{-2}[/tex] = [tex]\frac{17}{2}[/tex]
c = [tex]delta_{c}[/tex] / [tex]delta[/tex] = [tex]\frac{14}{-2}[/tex] = - 7
f(x) = [tex]-\frac{3}{2}[/tex] x² + [tex]\frac{17}{2}[/tex] x - 7 (D)
Solve the equation3x + 15 = 3(x + 5)
Given the following equation:
[tex]3x+15=3\mleft(x+5\mright)[/tex]You must solve for "x" as following:
1. Apply the Distributive property:
[tex]\begin{gathered} 3x+15=(3)(x)+(3)(5) \\ 3x+15=3x+15 \end{gathered}[/tex]2. Observe the equation. You can notice that left side is equal to right side. If you try to solve for "x", you get:
[tex]\begin{gathered} 3x-3x=15-15 \\ 0=0 \end{gathered}[/tex]Which of the terms cannot be combined with the others?ОЗху2x-5xОх
0x cannot be combined with other terms
Because when it is combined it always results in 0.
Please help with this
Answer:
[tex]y = 100 - \frac{17}{3} x[/tex]
Here you go the visual explanation should be there for you, if your still confused i suggest asking your teacher for help on how to find the slope.
Find the area:*1 point8 in- .Your answerI
Tavon and Raven are feeling backpacks for Arlington woods elementary Schoolthey have 24 boxes of markers 56 coloring books and 72 packages of modeling claywhich of the following are possible answers for the greatest number of backpacks they can fill if the markers books and clay are equally distributed
we have that
they have 24 boxes of markers 56 coloring books and 72 packages of modeling clay
so
24=(2^3)(3)
56=(2^3)(7)
72=(2^3)(3^2)
24/8=3
56/8=7
72/8=9
the number of backpacks is 8
therefore
teh answer is option B
2) y = -5 +4V7-2 A) Domain: { All real numbers. } Range: { All real numbers. } B) Domain: x 22 Range: y 2-5 + C) Domain: 'x z 2 Range: ys-5 D) Domain: x 2-2 Range: y z 5
Looking at the restrictions over the variable x, we know that the domain is:
[tex]x\ge2[/tex]To find the range, notice that:
[tex]\sqrt[]{x-2}\ge0[/tex]On the other hand, the function:
[tex]y=\sqrt[]{x-2}[/tex]is an increasing function (its value grows when x grows), and can get as large as we want provided a sufficiently large value for x. Then, the range of such a function would be:
[tex]y\ge0[/tex]Which does not get altered when we multiply the square root of (x-2) by 4.
Since the function:
[tex]y=-5+4\sqrt[]{x-2}[/tex]is a 5-units shift downwards, then the variable y can take any value from -5 onwards.
Then, the range of the function is:
[tex]y\ge-5[/tex]Another way to find the range is to isolate x from the equation:
[tex]\begin{gathered} y=-5+4\sqrt[]{x-2} \\ \Rightarrow y+5=4\sqrt[]{x-2} \\ \Rightarrow\frac{y+5}{4}=\sqrt[]{x-2} \\ \Rightarrow(\frac{y+5}{4})^2=x-2 \\ \Rightarrow x-2=(\frac{y+5}{4})^2 \\ \Rightarrow x=(\frac{y+5}{4})^2+2 \end{gathered}[/tex]Since we already know that x must be greater than 2, then:
[tex]\begin{gathered} 2\le x \\ \Rightarrow2\le(\frac{y+5}{4})^2+2 \\ \Rightarrow0\le(\frac{y+5}{4})^2 \\ \Rightarrow0\le|\frac{y+5}{4}| \\ \Rightarrow0\le|y+5| \end{gathered}[/tex]From here, there are two options:
[tex]\begin{gathered} 0\le y+5 \\ \Rightarrow-5\le y \\ \text{ Or} \\ 0\le-y-5 \\ \Rightarrow y\le-5 \end{gathered}[/tex]Since we know an equation for y, then:
[tex]\begin{gathered} -5\le-5+4\sqrt[]{x-2} \\ \Rightarrow0\le4\sqrt[]{x-2} \end{gathered}[/tex]Or:
[tex]\begin{gathered} -5+4\sqrt[]{x-2}\le-5 \\ \Rightarrow4\sqrt[]{x-2}\le0 \end{gathered}[/tex]The second case is not true for every x.
Therefore:
[tex]-5\le y[/tex]Therefore:
[tex]\begin{gathered} \text{Domain: }x\ge2 \\ \text{Range: }y\ge-5 \end{gathered}[/tex]what is the polar form of -3+sqrt3i
Solution
For this case we have the following number given:
[tex]-3+\sqrt[]{3}i[/tex]We can see that x = -3 and y = - sqrt(3)
The angle is given by:
[tex]\arctan (\frac{-\sqrt[]{3}}{3})=-30=-\frac{\pi}{6}[/tex]The radius would be:
[tex]r=\sqrt[]{(3)^2+(-\sqrt[]{3})^2}=\sqrt[]{12}[/tex]And the polar form would be given by:
[tex]z=\sqrt[]{12}(\cos (-\frac{\pi}{6})+i\sin (-\frac{\pi}{6}))\text{ }[/tex]Answer:
The answer is D!!
Step-by-step explanation:
Right on edg 2022
Interpret parts of the algebraic expression to describe the real-world scenario.
Answer:
Given equation is, (Dollar value of a sandwich shop of a tip jar)
[tex]0.65h+1.25[/tex]h is the number of hours since the shop opened.
a) To find the value where the tip jar increasing per hour.
we know that,
A slope of a line is the change in y coordinate with respect to the change in x coordinate.
The slope or gradient of a line is a number that describes both the direction and the steepness of the line. That gives the value of the rate of y with respect to x.
The equation of a line with slope and intercept is,
y=mx+c
where m is the slope.
The increasing value of a tip jar per hour is the slope of the given equation.
The slope of the ginen equation is,
[tex]0.65[/tex]we get,
$0.65 is value of the tip jar increasing per hour
Answer is: $0.65 is value of the tip jar increasing per hour.
b) To find the initial value of the tip jar when the shop opens.
Given equation is, (Dollar value of a sandwich shop of a tip jar)
[tex]0.65h+1.25[/tex]h is the number of hours since the shop opened.
When the shop opens, we get that h=0
Substitute h=0 in the given equation we get,
[tex]1.25[/tex]Therefore, the initial value of the tip jar when the shop opens is $1.25.
Answer is: Therefore, the initial value of the tip jar when the shop opens is $1.25.
Relate decimals and fractionsOf the 100 students in the fourth grade, 70 students are girls.Write a fraction in tenths and a fraction in hundredths to tell what fraction of the fourth-grade students are girls Question 5 Write a fraction in tenths and a fraction in the hundredths to tell what fraction of the fourth-grade students are boys
Step 1. Gather all of the information.
Out of 100 students, 70 students are girls. This also means that the other 30 students are boys:
--> 70 girls, and 30 boys for every 100 students.
Step 2. Write a fraction in tenths and a fraction in hundredths to tell what fraction of the fourth-grade students are girls.
The fraction in hundredths:
[tex]\frac{70}{100}[/tex]To find the fraction in tenths, we simplify the previous fraction by dividing both numbers by 10, and the resulting numbers are 7 and 10.
The fraction in tenths:
[tex]\frac{7}{10}[/tex]Step 3. Write a fraction in tenths and a fraction in the hundredths to tell what fraction of the fourth-grade students are boys.
In this case, we use 30 instead of 70 because now we are talking about the number of boys.
The fraction in hundredths:
[tex]\frac{30}{100}[/tex]We do the same as we did in step 2 to find the fraction tenths, divide both numbers by 10, the result is 3 and 10.
The fraction in tenths:
[tex]\frac{3}{10}[/tex]Answer:
Write a fraction in tenths and a fraction in hundredths to tell what fraction of the fourth-grade students are girls
[tex]\frac{7}{10}\text{ and }\frac{70}{100}[/tex]Write a fraction in tenths and a fraction in the hundredths to tell what fraction of the fourth-grade students are boys
[tex]\frac{3}{10}\text{ and }\frac{30}{100}[/tex]
QUESTION 4 of 10: A "direct response" social media advertisement offers a 50% discount at your restaurant for one of two people diningtogether as a couple on Valentine's Day. The discount will apply to the lower priced meal. One meal will cost $24.77 and the other costs$22.56. What will the total cost of the check be with the discount?a) $24.77b) $34.95c) $36.05d) $47.33Submit
QUESTION 4 of 10: A "direct response" social media advertisement offers a 50% discount at your restaurant for one of two people dining
together as a couple on Valentine's Day. The discount will apply to the lower priced meal. One meal will cost $24.77 and the other costs
$22.56. What will the total cost of the check be with the discount?
a) $24.77
b) $34.95
c) $36.05
d) $47.33
step 1
apply discount to the lowe price
so
the lower price is $22.56
50%=50/100=0.50
0.50(22.56)=$11.28step 2
step 2
adds the costs
11.28+24.77=$36.05
therefore
answer C
3x +5= 2x +7How will the equation look if you subtract 2xfrom both sides?Click on the correct answer.5x +5= 7x+5=73x +5=7
If you subtract 2x from both sides of the equation you have:
[tex]\begin{gathered} 3x+5=2x+7 \\ 3x+5-2x=2x+7-2x \\ \text{ Operate similar terms} \\ x+5=7 \end{gathered}[/tex]Therefore, if you subtract 2x both sides, the equation will look like
[tex]x+5=7[/tex]What strategies can be used to find solutions for equations such as 2,000 = 20x + 10y?
The strategies you can use to solve the equation 2000 = 20x + 10y are
1. if you have information on the values of y and x.
2. By establishing another relationship of y and x values. This relationship can now be solved simultaneously using substitution method or elimination method. Graphing can also be used to solve the equation.
5(y + 1) = 10 Submit Answer
1) Two integers have a sum of 47 and a difference of 23. Find the product of the numbers.
Given:
Two intergers have a sum of 47 and a difference of 23.
Let's find the product of the two numbers.
Let x and y represent the numbers.
We have:
Two integers have a sum of 47: x + y = 47
Two integers have a difference of 23: x - y = 23
We gave the system of equations:
x + y = 47.......................equation 1
x - y = 23.......................equation 2
Let's solve the system simultaneously using substitution method.
Rewrite equation 1 for x:
x = 47 - y
Substitute (47 - y) for x in equation 2:
(47 - y) - y = 23
47 - y - y = 23
47 - 2y = 23
Subtract 47 from both sides:
47 - 47 - 2y = 23 - 47
-2y = -24
Divide both sides of the equation by -2:
[tex]\begin{gathered} \frac{-2y}{-2}=\frac{-24}{-2} \\ \\ y=12 \end{gathered}[/tex]Now, substitute 12 for y in either of the equations.
Let's take equation 1.
x + y = 47
x + 12 = 47
Subtract 12 from both sides:
x + 12 - 12 = 47 - 12
x = 35
Therefore, we have:
x = 35, y = 12
The numbers are 35 and 12.
To find the product of the numbers, let's multiply the numbers:
35 x 12 = 420
Therefore, the product of the numbers is 420.
ANSWER:
420
Find intervals of concavity and points of inflection of function y = x^4 - 6x + 2
SOLUTION:
Step 1:
In the question, we are given the following:
Find intervals of concavity and points of inflection of function
[tex]y\text{ = x }^4\text{ - 6 x + 2}[/tex]Step 2:
The details of the solution are as follows:
PART A:
Find intervals of concavity of function:
[tex]y\text{ = x}^4\text{ - 6 x + 2}[/tex]PART B:
Find the points of inflection of the function:
[tex]y\text{ = x}^4\text{ - 6 x + 2}[/tex]
11 divided by 2014
(Lond division answer)
Answer:
0.005461767627
Step-by-step explanation:
0.005461767627
filling in to send
hi how are you I need help with this question.
Hello
Question one requires us to find the value of the angle
Using trigonometric ratios
SOHCAHTOA
[tex]\begin{gathered} \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \\ \text{opposite}=8 \\ \text{adjacent}=10 \\ \tan \theta=\frac{8}{10} \\ \tan \theta=0.8 \\ \theta=\tan ^{-1}0.8 \\ \theta=38.66\approx38.7^0 \end{gathered}[/tex]For question b, we can use trigonometric ratio to find the value of the missing side or use pythagoran's theorem
I would use pythagoran's theorem here because we would arriave at our answer faster
[tex]\begin{gathered} x^2=y^2+z^2 \\ x^2=8^2+10^2 \\ x^2=64+100 \\ x^2=164 \\ \text{take the square root of both sides} \\ x=\sqrt[]{164} \\ x=12.81\approx12.8 \end{gathered}[/tex]From the calculations above, the value of the angle is 38.7 degree and the missing side is 12.8 units