Solve the equation without using a calculator
[tex]\bf\\\\log^2x+log^2(x+10)=log^211\\\\log(x+10)\neq 0[/tex]
[tex]\bf\\(\ lgx=log_{10}x=logx\ )[/tex]
![Solve The Equation Without Using A Calculator[tex]\bf\\\\log^2x+log^2(x+10)=log^211\\\\log(x+10)\neq](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/FhSXHFE0NuN0XP5Wm13B1JWwkChLxEsO.png)
Answers
The solution to the logarithmic expression log²x + log²(x + 10) = log²11 is;
x = -11 and 1
How to solve logarithm expressions?We are given the logarithmic expression as;
log²x + log²(x + 10) = log²11
By the power rule of logarithm, we know that; log²x = 2log x
Thus;
log²x + log²(x + 10) = log²11 can be expressed as;
2log x + 2log (x + 10) = 2log 11
Divide through by 2 to get;
log x + log (x + 10) = log 11
We know from product rule of logarithm that log (ab) = log a + log b. Thus; log x + log (x + 10) = log 11 is;
log x(x + 10) = log 11
Log cancels out to get;
x² + 10x - 11 = 0
Using quadratic equation calculator gives;
x = -11 and 1
Read more about Logarithm Expressions at; https://brainly.com/question/28041634
#SPJ1
Related Questions
McKenna was asked to write the following expression in standard form.
When writing the expression in standard form, McKenna made a mistake.
a. McKenna made her first mistake in .
b. The correct expression in standard form is .
3 − 5(3a + 6)
3 − 5(3a + 6)
3 + (−5)(3a + 6)
−2(3a + 6)
−6a + (−12)
−6a − 12
Step 1
Step 2
Step 3
Step 4
Answers
a) The step in which McKenna made her first mistake is given as follows: Step 4.
b) The correct simplified expression in standard form is given as follows: -15a - 15.
How to simplify the expression?The expression in this problem is defined as follows:
3 − 5(3a + 6)
On the third step, the expression is given as follows:
3 + (−5)(3a + 6)
And on the fourth step, the expression is given as follows:
−2(3a + 6).
This is where the mistake happened, as the multiplication takes precedence over the subtraction.
Then to obtain the correct expression the first step is applying the distributive property, as follows:
3 − 5(3a + 6) = 3 - 15a - 18.
Then the like terms 3 and -18 are combined to obtain the correct simplified expression, as follows:
3 - 15a - 18 = -15a - 15.
More can be learned about the simplification of expressions at https://brainly.com/question/723406
#SPJ1
Find sin2x,cos2x, and tan2x if sin x=-3/√13 and x terminates in quadrant IV.
sin2x=
cos2x=
tan2x=
Answers
Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
Given:
sin x= -3/√13
So, B = √13 - 9 = √4 =2
cos x= 2/ √13
So, sin 2x= 2 sin x cos x =2 (-3/√13 )(2/√13 ) = -12/√13
and, cos 2x= 1- 2 sin²x
= 1- 2( -3/ √13 )²
= -5/ √13
and, tan 2x = sin 2x/ cos 2x = 5/12
Learn more about trigonometry here:
https://brainly.com/question/26719838
#SPJ1
Marco uses 2 gallons of water while brushing his teeth. He uses 10 gallons of water to wash clothes. How many more cups of water does Marco use while washing his clothes than brushing his teeth? there’s are 16 cups in 1 gallon
Answers
Answer: 192 cups
Step-by-step explanation: there's 16 cups in 1 gallon so you would do 2×16=32 to get 32 cups. Then you would do 10×16=160 to get 160 cups. Now add 32+160=192 cups.
"Use the formula A=P(1+r/n)ⁿt to solve the compound interest problem
Find how long it takes a $ 1700 investment to earn $ 500 interest if it is invested at 2 % interest compounded quarterly.
$ 500 interest will be earned in approximately years. (Round to the nearest tenth.)"
Answers
The compound interest is 61.342 years
What is compound interest ?
The interest you earn on interest is known as compound interest. Simple math may be used to demonstrate this: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year. You will wind up with $110.25 at the conclusion of the second year.
Formulas for Compound Interest
Formula for Monthly Compound Interest.
Compounded Quarterly Formula: Interest compounded monthly is calculated 12 times a year. Four times a year are used to calculate interest that is compounded quarterly.
Formulas for compound interest are available on a daily, annual, and other basis.
A = 1700
P = 500
r = 2%
n = 4
r = R/100
r = 2/100
r = 0.02 per year,
Then, solve the equation for t
t = ln(A/P) / n[ln(1 + r/n)]
t = ln(1,700.00/500.00) / ( 4 × [ln(1 + 0.02/4)] )
t = ln(1,700.00/500.00) / ( 4 × [ln(1 + 0.005)] )
t = 61.342 years
To learn more about compound interest from the given link
https://brainly.com/question/24274034
#SPJ4
8 An electricity company charges the same fixed amount for each unit of electricity used. David uses this graph to work out the total cost of the electricity he has used.
(a) Work out the gradient of the straight line.
(b) What does the gradient of this line represent?
Answers
The gradient of the line is 4/30 and it means that the amount for each unit of electricity used is 4/30
(a) How to determine the gradient of the straight line.From the question, we have the graph that can be used in our computation:
From the graph, we have the following ordered pairs
(0, 0) and (30, 4)
Rewrite the above points properly
So, we have the following ordered pairs
(x, y) = (0, 0) and (30, 4)
The gradient of the line is then calculated using the following slope equation
gradient = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (0, 0) and (30, 4)
Substitute the known values in the above equation
So, we have the following equation
gradient = (4 - 0)/(30 - 0)
Evaluate
gradient = 4/30
Hence, the gradient of the line is 4/30
(b) What does the gradient of this line represent?Generally, slope or gradient means rate
This means that the gradient of this line represent the rate
i.e. the amount for each unit is 4/30
Read more about slope at
https://brainly.com/question/3493733
#SPJ1
The following data represent the monthly cell phone bill for a person's phone for six randomly selected months.
$35.34, $42.09, $39.43, $38.87, $43.39, $49.26
Compute the mean, median, and mode phone bill. (Round to the nearest cent as needed)
Answers
The mean of the data is x(bar) = 41.396
The Median of the data is $40.76
The mode of all the values are appearing once and therefore there is no mode for the phone bill.
Now, According to the question:
Given the data:
$35.34, $42.09, $39.43, $38.87, $43.39, $49.26
Mean is the average of the data computed as x(bar) = Σ[tex]x_i[/tex] /n where [tex]x_i[/tex]
are the data points and n is the number of data points
x(bar) = 35.34 + 42.09 + 39.43 +38.87 +43.39 + 49.26 / 6
x(bar) = 248.38 /6
x(bar) = 41.396
The median is the data point that lies in the middle of the data set when the data is arranged in ascending or descending order.
Thus,
Ascending order:
$35.34, $38.87, $39.43, $42.09, $43.39, $49.26
The median lies between $39.43 and $42.09 and to get it, we find the average of the two numbers
Median = (39.43 + 42.09)/ 2
Median = $40.76
→ Mode is the value in a data set that is repeated most frequently. In the given data, all the values are appearing once and therefore there is no mode for the phone bill.
Hence, The mean of the data is x(bar) = 41.396
The Median of the data is $40.76
The mode of all the values are appearing once and therefore there is no mode for the phone bill.
Learn more about Mean , Median , Mode at:
https://brainly.com/question/15323584
#SPJ4
Pam bought different drinks for a party she was throwing. After the party, she had the following drink amounts left over.
\dfrac1{2}
2
1
start fraction, 1, divided by, 2, end fraction liter of soda
\dfrac15
5
1
start fraction, 1, divided by, 5, end fraction liter of water
\dfrac8{10}
10
8
start fraction, 8, divided by, 10, end fraction liter of apple juice
Which statement correctly compares the amounts of 2 left over drinks?
Choose 1 answer:
(Choice A)
A
Pam had less water left over than apple juice.
(Choice B)
B
Pam had more soda left over than apple juice.
(Choice C)
C
Pam had less soda left over than water.
Answers
Answer:
A) Pam had less water left over than apple juice.
Step-by-step explanation:
Given amounts of drinks left over:
[tex]\dfrac{1}{2}\; \sf liter \;of \;soda[/tex][tex]\dfrac{1}{5}\; \sf liter \;of \;water[/tex][tex]\dfrac{8}{10}\; \sf liter \;of \;apple\;juice[/tex]To compare the amounts of drinks left over, convert the fractions into equivalent fractions that have the same denominator.
The denominators of the three fractions are 2, 5 and 10.
The lowest common multiple of the denominators is 10.
Therefore, rewrite the first two fractions so that their denominators are also 10.
[tex]\textsf{Soda}: \quad \dfrac{1}{2}=\dfrac{1 \cdot 5}{2 \cdot 5}=\dfrac{5}{10}[/tex]
[tex]\textsf{Water}: \quad \dfrac{1}{5}=\dfrac{1 \cdot 2}{5 \cdot 2}=\dfrac{2}{10}[/tex]
Therefore, as:
[tex]\dfrac{2}{10} < \dfrac{5}{10} < \dfrac{8}{10}[/tex]then:
water < soda < apple juiceTherefore, Pam had less water left over than apple juice.
Answer:
a) Pam had less water than apple juice.
★ Water < Soda < Apple juice
Step-by-step explanation:
Converting the fraction into decimals,
→ Soda left = 1/2 = 0.5 litres
→ Water left = 1/5 = 0.2 litres
→ Apple juice left = 8/10 = 0.8 litres
Let's order them in ascending order,
→ 0.2 < 0.5 < 0.8
→ 1/5 < 1/2 < 8/10
→ Water left < Soda left < Apple juice left
Now the applicable options is,
→ Pam had less water than apple juice.
Hence, option (a) is correct answer.
Determine whether each statement implies correlation or causation between two variables. Drag the items on the left to the correct location on the right.
Watching more TV increases the bill for electricity.
Drinking water helps flush out toxins.
Students with high scores in physics also got high scores in chemistry.
A survey shows that people who own a TV also own an automobile.
Vaccination reduces the chance of getting infected by the disease.
Answers
Determining whether each statement implies correlation or causation between two variables is as follows:
Correlation:Students with high scores in physics also got high scores in chemistry.A survey shows that people who own a TV also own an automobile.Causation:Watching more TV increases the bill for electricity.Drinking water helps flush out toxins.Vaccination reduces the chance of getting infected by the disease.How is correlation different from causation?Correlation indicates that one independent variable causes another dependent variable to change.
Causation indicates that one dependent variable or event is the direct result of the occurrence of the other event or independent variable.
Causation shows cause and effect - unlike correlation which points out two events simultaneously occur or two variables change at the same time.
Thus, correlation is a test of association in relationship, while causation focuses on cause and effect.
Learn more about correlation and causation at ttps://brainly.com/question/12479370
#SPJ1
there are 12 levels in Zoe new video game suppose she plays the same number of levels each day what are all the possibilities for the number of days Zoe could play the game show your work. Its about multiples and factors
Answers
Let no of level in one day is x. So, Zoe can play x= 12 level in a day.
What is probability?The likelihood might be between 0 and 1, with 0 denoting impossibility and 1 denoting certainty. In a sample space, each occurrence has a probability of one overall. the possibility that two or more events will follow one another. Since there are two or more of them, the events are either dependent or independent events. A dependent event—also referred to as a conditional event—is one in which the occurrence of the first event affects the occurrences that follow. The total number of outcomes will differ.
Write formula for the probability.Probability = Possible outcomes/total outcomes
Factors of 12 can be written as:
1 * 12 = 12
2 * 6 = 12
3 * 4 = 12
For this question look for factors of 12-These would be
1 and 12 (1 x 12 = 12)
2 and 6 (2 x 6 = 12)
3 and 4 (3 x 4 = 12)
Hence Zoe could either play
1 level each day for 12 days
2 levels each day for 6 days
3 levels each day for 4 days
4 levels each day for 3 days
Or...
12 levels in one day
To learn more about probability visit the link:
https://brainly.com/question/16722133
#SPJ1
HELP ME ASAP!!!!
I NEED THIS ANSWERED RIGHT NOW!!!!!!
Answers
Answer: The bisector of [tex]\angle BAC[/tex]
Step-by-step explanation:
This is a standard construction.
CAN SOMEONE HELP WITH THIS QUESTION?✨
Answers
The value of P = $7,000,r = 3.2%, n = 4, and money after 7 years will be $8749.6954.
What is compound interest?Compound interest is applicable when there will be a change in principal amount after the given time period.
For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.
(A)
As per the given,
Principle amount P = $7,000
Rate of interest r = 3.2%
Number of times interest applied per time period n = 4 (Quarterly)
(B)
Time period T = 7 year
Total amount S(7) = 7,000(1 + 0.032/4)^(4 x 7)
S(7) = $8749.6954
Hence "The value of P = $7,000,r = 3.2%, n = 4, and money after 7 years will be $8749.6954".
For more information about compound interest,
brainly.com/question/26457073
#SPJ1
If the monthly payment is $8,750.00 for a 25-year fully amortizing mortgage that has an annual interest rate of 5.50%, what is the initial loan amount? Group of answer choices
Answers
Using monthly payment formula, the principal of the facility paying a monthly payment of $8750 for 25 years at a rate of 5.50% is $1,424,878.39
Monthly PaymentThe monthly payment is the amount paid per month to pay off the loan in the time period of the loan. When a loan is taken out it isn't only the principal amount, or the original amount loaned out, that needs to be repaid, but also the interest that accumulates.
The formula to calculate the monthly payment of a facility is;
A = P[(r(1 + r)ⁿ] / [(1 + r)ⁿ - 1]
Monthly payment (MP) = 8750time (t) = 25 yearsRate (r) = 5.50%Principal (P) = ?Number of payment (n) = number of months in a year * time of facilitySubstituting the values into the formula and solving for p
P = $1,424,878.39
Learn more on monthly payment here;
https://brainly.com/question/25599836
#SPJ1
Using the preimage below, find the image coordinates after a dilation by a
scale factor of k = 1/3
a. G'(9, 9), H'(9, 27), J'(36, 9)
b. G'(9, 3), H'(9, 9), J'(36,3)
c. G'(1, 1), H'(1, 3), J'(4, 1)
d. G'(3, 3), H'(3,9), J'(12, 3)
Answers
Answer: C
Step-by-step explanation:
4 cars need a new paint job. A body shop offers 15 different colors of paint. All the cars can be painted at the same time. Some cars may have the same color paint. How many possible paint jobs can be done on the 4 cars?
Group of answer choices
a) 15^4
b) P(15, 4)
c) (15-4)!
d) C(15, 4)
Answers
The number of possible paint jobs that can be done on the 4 cars can be determined by permutation (15,4). That is option B.
What is permutation?Permutation is defined as the various number of ways a data set can be arranged to arrive at a definite value.
the number of colours offered by the paint shop = 15
The number of cars the need a new paint job = 4
To find the possible number of colour that can be used permutation (15,4) is carried out.
That is,
= 15!/(15-4)!
= 15!/11!
= 15×14×13×12×11×10×9×8×7×6×5×4×3×2×1/11×10×9×8×7×6×5×4×3×2×1
or 15×14×13×12×11!/11!
= 15×14×13×12
= 32,760
Therefore, there would be 32,760 possible paint jobs that can be carried out on the 4 cars.
Learn more about permutation here:
https://brainly.com/question/28443757
#SPJ1
Identify all of the terms in the expression: 4x³ + x² + 3x + 6.
OA 6
OB 4, 3, 6
OC x³, x², x
OD 4x³, x², 3x, 6
Please help me
Answers
Answer:
OD 4x³, x², 3x, 6
Step-by-step explanation:
Factor the expression completely
54a⁶b²+ 9ab²
Answers
To factor the expression 54a⁶b²+ 9ab², you can use the fact that a common factor of 54a⁶b² and 9ab² is ab².
Thus, you can rewrite the expression as:
ab²(54a⁶ + 9)
You can then factor the expression inside the parentheses using the fact that 3 is a common factor of both 54 and 9:
ab²(3 * 18a⁶ + 3 * 3)
This can be simplified as:
ab²(6a⁶ + 9)
This expression is completely factored and cannot be further simplified. Therefore, the completely factored form of the expression is:
ab²(6a⁶ + 9)
Find using Function Notation
Given the f(x) graph below, find the value of each expression.
Find f(0)
Find f(x) = -3
Answers
The values of x where f(x) is 0 to determine a function's zeros.
How can determine from a graph that f/x)?The set of all x for which the f(x) graph crosses the x-axis is the solution of f(x) = 0. The set of all x for which the graph of f is strictly above the x-axis is the solution of f(x) > 0
In general, finding the zeros of the function f(x) involves setting the function to zero. The zeroes of the function are the values of x that correspond to the set equation. Find the values of x where f(x) = 0 to determine a function's zeros.
f ( x)=- 3 is a horizontal line that connects to the x-axis, hence there is no x-intercept and the y-intercept is ( 0, -3).
The y-intercept is ( 0, -3)
To learn more about function f(x) refer to:
https://brainly.com/question/24748644
#SPJ1
Please help this is for a quiz!
A baby weighed only 14.4 ounces at birth. How much lighter was she than an average baby, who weighs about 7lbs 8 ounces?
Answers
The baby is 105.6 ounces or 6.96 pounds lighter than an average baby.
What is weight ?Weight is the measurement of Gravitational force on an object. It can be zero as in the space.
We are given in the question that A baby weighed only 14.4 ounces at birth the weight of an average baby is 7lb 8 ounces.
1 lb = 16 ounce
Therefore an average baby weight = 7 x 16 + 8 = 120 ounces
The baby weight is just 14.4 ounces
Hence, the baby is 120 - 14.4 = 105.6 ounces lighter than an average baby.
To know more about weight;
brainly.com/question/10069252
#SPJ1
Can you help me factor and solve x^2-14x-142=22 ?
Answers
Step-by-step explanation:
[tex] {x}^{2} - 14x = 164[/tex]
[tex] {x}^{2} - 14x + 49 = 213[/tex]
[tex](x - 7) {}^{2} = 213[/tex]
[tex](x - 7) = \sqrt{213} [/tex]
[tex](x - 7) = - \sqrt{213} [/tex]
[tex]x = 7 + \sqrt{213} [/tex]
[tex]x = 7 - \sqrt{213} [/tex]
Please help me I just look at the photo I am so confused
Answers
Answer:
Step-by-step explanation:
1:Pl 2:Th 3:Th 4:P 5:P 6:Pl 7:Pl 8:Th 9:Th 10:Th 11:Pl 12:P
There you go, the numbers go down. So Iowa is 1 and so on, I don't know if they are all right but I did my best.
Round to the nearest tenth.
The population of Laredo, Texas, was about 215,000 in 2007. It was about 123,000 in 1990. If we assume that the
population growth is constant and y represents the number of years after 1990, write a linear equation to find p,
Laredo's population for any year after 1990.
Answers
A linear equation to find p, Laredo's population for any year after 1990 is 5441t + 123000.
What is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Here, we have
Given:
t = the number of years after 1990.
So, for 1990, t = 0. So the coordinate is (0, 123000).
For 2007, t = 17. So the coordinate is (17, 215500).
Slope = (215500 - 123000)/17
Slope = 5441
P = 5441t + b,
b = 123000
P = 5441t + 123000
Hence, a linear equation to find p, Laredo's population for any year after 1990 is 5441t + 123000.
To learn more bout the linear equation from the given link
https://brainly.com/question/14323743
#SPJ1
car is traveling at a steady speed It travels 1 1/2 miles in 2 1/4 minutes How far will it travel in 23 minutes? In ?
Answers
Answer:
15 1/3 miles in 23 minutes
(2/3)x in x minutes
Step-by-step explanation:
1 1/2=1.5
2 1/4=2.25
Convert to unit ratio
[tex]1.5/2.25=(2/3)/1[/tex]
2/3*23=46/3
Simplify
15 1/3 miles in 23 minutes
(2/3)x in x minutes
Figure HEFG below is a parallelogram. If UH=19 and FH= 5x-7, find X
Answers
A parallelogram is a quadrilateral that has two pairs of parallel sides.
In a parallelogram, opposite sides and angles are equal.
The adjacent angles add up to 180 degrees.
The value of x is 5.2.
What is a parallelogram?
A parallelogram is a quadrilateral that has two pairs of parallel sides.
In a parallelogram, opposite sides and angles are equal.
The adjacent angles add up to 180 degrees.
We have,
UH and FH are the two sides of the diagonal.
UH and FH are equal.
UH = FH
19 = 5x - 7
19 + 7 = 5x
5x = 26
x = 5.2
Thus,
The value of x is 5.2.
Learn more about parallelograms here:
https://brainly.com/question/1563728
#SPJ1
Look at photo for problem
Just need chart filled out
4. y=-2(x+2)²-3
Answers
Following values can be filled in the table:
(0,-3), (-1,0), (1,-8), (-2,1), (2,-15)
It can be solved using the concept of graph plotting and function.
What is graph?
When a set of points are connected together to form a strcture then the structure is known as graph. The set of ponts is known as ordered pair.
Consider the eqution.
[tex]y=-2(x+2)^2-3[/tex]
Substitute the simplest value x = 0 and find the value of y.
[tex]y=-2(0+2)^2-3\\=-11\\[/tex]
Now, substitute x = -1 and find the value of y.
[tex]y=-2(-1+2)^2-3\\=-5\\[/tex]
Now, substitute x = 1 and find the value of y.
[tex]y=-2(1+2)^2-3\\=-21\\[/tex]
Now, substitute x = -2 and find the value of y.
[tex]y=-2(-2+2)^2-3\\=-3\\[/tex]
Now, substitute x = 2 and find the value of y.
[tex]y=-2(2+2)^2-3\\=-35\\[/tex]
Hence, following values can be filled in the table:
(0,-11), (-1,-5), (1,-21), (-2,-3), (2,-35)
It can be solved using the concept of graph plotting.
Learn more about the graph plotting form the following link:
https://brainly.com/question/25020119
#SPJ4
15) How many terminal zeros does the integer equal to
80 power to the 16 times 75 power 8 have?
Answers
75=(5)2*3 so you have 16 (5) so 16 zero
I need a answer using the race method (high school level)
and i will make it worth your time
What do you think you could do to show this statement is true?
How could you manipulate this equation to allow you to state this.
Answers
Answer:
Step-by-step explanation:
Well, there are the same amount of numbers in each equation. You can take the a from both equations, raise it to the second power, then do the same to the b. The addition sign will automatically disappear because you've added the two components together. You'll use subtraction to get your answer. I think.
Hi can you guys please help me create an ppt presentation on excel these are what it should include.
A bar graph
A line graph
A pie chart
Payslip
Table with all the employees names and position.
These should be connected to one topic. All illustration should be connected.
There should also be the meaning of Excel
And you can also add in information if you'd like or fun facts about excel
100/_
Answers
You can make a chart in PowerPoint or Excel. If you have lots of data to chart, create your chart in Excel, and then copy it into your presentation. This is also the best way if your data changes regularly and you want your chart to always reflect the latest numbers. In that case, when you copy and paste the chart, keep it linked to the original Excel file.
To create a simple chart from scratch in PowerPoint, click Insert > Chart and pick the chart you want.
1. Click Insert > Chart.
2.Click the chart type and then double-click the chart you want.
3.In the worksheet that appears, replace the placeholder data with your own information.
4.When you insert a chart, small buttons appear next to its upper-right corner. Use the Chart Elements Chart Elements button button to show, hide, or format things like axis titles or data labels. Or use the Chart Styles Customize the Look of Your Chart button button to quickly change the color or style of the chart.
What is excel ?
Excel is a spreadsheet program from Microsoft and a component of its Office product group for business applications. Microsoft Excel enables users to format, organize and calculate data in a spreadsheet.
The main uses of Excel include: Data entry. Data management. Accounting.
To learn more about excel visit :
https://brainly.com/question/3441128
#SPJ1
"Find the slope of the line that passes through all of the points
Find the stope of the line that passes through all of the points on the table."
Answers
By using the formula for slope, it can be calculated that
The slope of the given line is 10
What is slope of a line?
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan \theta[/tex]
If the line passes through [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex], slope is calculated by the formula
Slope = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here, the line passes through (2, 3) and (3, 13)
Slope = [tex]\frac{13 - 3}{3-2}[/tex]
Slope = 10
So the slope of the given line is 10
To learn more about slope of a line, refer to the link-
https://brainly.com/question/3493733
#SPJ4
A light is on the top of a 12 ft tall pole and a 5’6’’ tall person is walking away from the pole at a rate of 2 ft/sec At what rate is the tip of the shadow moving away from the pole when the person is 25 ft from the pole? At what rate is the tip of the shadow moving away from the person when the person is 25 ft from the pole? please give all solutions
Answers
Part a: the rate at which the shadow's tip moves away from the pole while the subject is 25 feet distant is 48/13 ft/sec.
Part b: the speed of the shadow from the speed of the man is 22/13 ft/sec.
Explain the term rate of change?Rate of Change: How quickly a parameter changes over a predetermined amount of time. It is frequently used while discussing momentum and is typically expressed as a proportion of one variable's change to another's corresponding change.A 5 feet 6 inch tall individual is going away from a 12 foot tall pole with a light on top at a 2 foot per second pace.
A) the speed at which the shadow's tip moves away from the pole while the subject is 25 feet distant;
Similar triangles allow us to say:
12/L = 55/(L - x)
Simpllifying,
12(l - x) = 5.5l
12l - 12x = 5.5l
6.5l = 12x
x = (6.5/12)l
Differentiate with respect to time;
dx/dt = (6.5/12)dl/dt or
dl/dt = (12/6.5)(dx/dt)
As, dx/dt = 2
dl/dt = (12/6.5)(2)
dl/dt = 24/6.5
dl/dt = 48/13 ft/sec
B: When a person is 25 feet from a pole, the point of the shadow travelling away from them at:
Subtract the speed of the shadow from the speed of the man.
Therefore,
48/13 - 2 = 22/13 ft/sec.
Thus, the speed of shadow from the speed of the man is 22/13 ft/sec.
To know more about the rate of change, here
https://brainly.com/question/8728504
#SPJ4
Solve the systems of equations
5x - 4y = -10
-4x + 5y = 8
x =
y =
Answers
The solution of the system of equation are;
⇒ x = - 2
⇒ y = 0
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The system of equation are,
⇒ 5x - 4y = - 10
⇒ - 4x + 5y = 8
Now,
Find the solution as;
The system of equation are,
⇒ 5x - 4y = - 10 ..(i)
⇒ - 4x + 5y = 8 ..(ii)
Multiply by 4 in equation (i) + Multiply by 5 in equation (ii);
⇒ 20x - 16y + (- 20x + 25y) = - 40 + 40
⇒ 9y = 0
⇒ y = 0
And, - 4x + 5y = 8
⇒ - 4x + 0 = 8
⇒ x = - 2
Thus, The solution of the system of equation are;
⇒ x = - 2
⇒ y = 0
Learn more about the system of equation visit:
https://brainly.com/question/12933204
#SPJ1