Answers
The y co-ordinate of the point C is 13.
Given, the points are :
A (2,4) = (x₁,y₁)
B (10,10) = (x₂,y₂)
Ratio of the length AC to CB is 3:1.
⇒ 3:1 = m:n
⇒ section formula C = (mx₂-nx₁/m-n) , my₂-ny₁/m-n)
substitute the values.
⇒ C = (3(10)-1(2)/3-1 , 3(10)-1(4)/3-1)
⇒ C = (30-2/2 , 30-4/2)
⇒ C = (28/2 , 26/2)
⇒ C = (14 , 13)
Hence the y coordinate of C is 13.
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Related Questions
10.Find the approximated circumference of a circle whose area is 136.46
Answers
The area of a circle is given by the following formula:
[tex]A=\pi r^2[/tex]Where r is the radius.
We know the area of the circle, then we can replace it in the formula and find r:
[tex]\begin{gathered} 136.46=\pi\cdot r^2 \\ r^2=\frac{136.46}{\pi} \\ r^2=43.44 \\ r=\sqrt[]{43.44} \\ r=6.59 \end{gathered}[/tex]The circumference of a circle is given by the formula:
[tex]C=2\pi r[/tex]By replacing the r-value that we found, we can solve for C:
[tex]\begin{gathered} C=2\cdot\pi\cdot6.59 \\ C=41.41 \end{gathered}[/tex]The approximated circumference of the circle is 41.41
The following two-way table describes student'safter school activities. Find the probability that arandomly selected student is in sports.GradeMusic/DramaWorkSports20Sophomore73Junior2013255SeniorP(Sports) = [? ]%25
Answers
Solution
The Probability that a random selected students is in sports is
[tex]P(Sports)=\frac{65}{Total}=\frac{65}{20+20+25+7+13+5+3+2+5}=0.65=65\%[/tex]The answer is 65%
A couple plans to save for their child's college education. What principal must be deposited by the parents when their child is born in order to have $37,000 when the child reaches the age of 18? Assume the money earns 9% interest, compounded quarterly. (Round your answer to two decimal places.)
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We can use the compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where:
A = Amount = $37000
P = Principal
r = Interest rate = 9% = 0.09
n = Number of times interest is compounded per unit of time = 4 (Since it is compounded quarterly)
t = time = 18
Therefore:
[tex]37000=P(1+\frac{0.09}{4})^{18*4}[/tex]Solve for P:
[tex]\begin{gathered} P=\frac{37000}{4.963165999} \\ P=7454.918 \end{gathered}[/tex]Data: x y 4 1 5 2 6 3 7 4 y = x - ?
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
x y
4 1
5 2
6 3
7 4
y = x - ?
Step 02:
equation of the line:
y = x - ?
y = mx + b
m = slope = 1
point ( 4 , 1)
Point-slope form of the line
(y - y1) = m (x - x1)
(y - 1) = 1 (x - 4)
y - 1 = x - 4
y = x - 4 + 1
y = x - 3
The answer is:
y = x - 3
On his way home from school board meeting , Keith fills up his car. He like the idea of using gasoline with ethanol , but think his car only handle 40% ethanol. At the gas station , he can use regular gas with 10% ethanol or E85 fuel with 85% ethanol. How many gallons of each type of fuel should Keith use if he wants to fill up his car with 10 gallons of fuel containing 40% ethanol ?
Answers
ANSWER:
6 gallons regular gas with 10% ethanol and 4 gallons E85 fuel with 85% ethanol
STEP-BY-STEP EXPLANATION:
In this case, we must test with values for each fuel class to arrive at the correct answer.
For example, 6 gallons of 10% ethanol and 4 gallons of 85% ethanol:
[tex]\begin{gathered} 10\text{\% of 6 =}\frac{10}{100}\cdot6=0.6\text{ gallons of ethanol in it} \\ 85\text{\% of 4 =}\frac{85}{100}\cdot4=3.4\text{ gallons of ethanol in it} \\ \text{ Total ethanol in 10 gallons is 0.6 + 3.4 = 4 gallons }\rightarrow\text{ 4 gallons is 40\% of 10} \\ \text{Therefore, we have 10 gallons of fuel containing 40\% ethanol } \end{gathered}[/tex]Solve the inequality: 4x + 8 - 5x > 13
Answers
4x+8-5x > 13
Combine like terms
4x-5x+8> 13
-x +8 > 13
Subtract 8 from both sides:
-x+8-8 > 13-8
-x > 5
Multiply both sides by -1
x < -5
The figure below is a net for a right rectangular prism. Its surface area is 432 m2 andthe area of some of the faces are filled in below. Find the area of the missing faces,and the missing dimension.
Answers
The surface area is the sum of all the areas in the given prims, then we have:
[tex]SA=72+72+48+48+2A[/tex]Plugging the value for the surface area and silving for A we have:
[tex]\begin{gathered} 432=72+72+48+48+2A \\ 432=240+2A \\ 2A=432-240 \\ 2A=192 \\ A=\frac{192}{2} \\ A=96 \end{gathered}[/tex]Now that we know the missing area we can know the missing dimension:
[tex]\begin{gathered} 96=8x \\ x=\frac{96}{8} \\ x=12 \end{gathered}[/tex]Therefore the missing length is 12.
A community boating center had $12,500. It bought 3 surf skis and 1 keelboat and had $265 left over. The keelboat cost $6,455 more than a surf ski. How much did the keelboat cost?
Answers
The cost of one keelboat is $7950
Given, A community boating center had $12,500.
It bought 3 surf skis and 1 keelboat and had $265 left over.
The keelboat cost $6,455 more than a surf ski.
Let the cost of one surf ski be x,
According to question,
cost of one keelboat = x + 6455
also, 3x + (x + 6455) + 265 = 12500
4x + 6520 = 12500
4x = 5980
x = 1495
So, the cost of one surf ski is $1495
and the cost of one keelboat is 1495 + 6455
= $7950
Hence, the cost of one keelboat is $7950
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Tank (#1) Capacitybarrels per Ft: 62.50Barrels per inch: 5.21.Convert Barrels to Feet, and inches with the information given.If you deposited 190 barrels of water into tank #1. What would be the total amount deposited (feet) and (inches).*remember there are only 12 inches in a foot*
Answers
To answer this question, we have to convert the given amount of barrels to feet and to inches using the conversion factors shown.
Barrels to feet:
[tex]190barrels\cdot\frac{1ft}{62.50barrel}=3.04ft[/tex]Barrels to inches:
[tex]190barrels\cdot\frac{1in}{5.21barrel}=36.47in[/tex]It means that the total amount deposited would be 3.04 ft or 36.47 in.
my work is saying solve for the value of a
Answers
Using the definition of suplementary angles we know that the angle that contains a and the 75° added together are 180°
[tex]75+(9a+6)=180[/tex]solve the equation for a
[tex]\begin{gathered} 81+9a=180 \\ 9a=180-81 \\ 9a=99 \\ a=\frac{99}{9} \\ a=11 \end{gathered}[/tex]which does not name an integer a.-35 b. 0 c. 3/15d. 10/2
Answers
The integer numbers are the whole numbers or the numbers that are not written as a/b
For the given question
-35 is an integer number
0 is an integer number
10/2 = 5 is an integer number
3/15 = 1/5 is not an integer number
So, the answer will be option c. 3/15
Factor 3x² + 10x + 8 using earmuff method.
Answers
To factor the above quadratic equation using Earmuff Method, here are the steps:
1. Multiply the numerical coefficient of the degree 2 with the constant term.
[tex]3\times8=24[/tex]2. Find the factors of 24 that when added will result to the middle term 10.
1 and 24 = 25
2 and 12 = 14
3 and 8 = 11
6 and 4 = 10
Upon going over the factors, we will find that 6 and 4 are factors of 24 and results to 10 when added.
3. Add "x" on the factors 6 and 4. We will get 6x and 4x.
4. Replace 10x in the original equation with 6x and 4x.
[tex]3x^2+6x+4x+8[/tex]5. Separate the equation into two groups.
[tex](3x^2+6x)+(4x+8)[/tex]6. Factor each group.
[tex]3x(x+2)+4(x+2)_{}[/tex]7. Since (x + 2) is a common factor, we can rewrite the equation into:
[tex](3x+4)(x+2)[/tex]Hence, the factors of the quadratic equation are (3x + 4) and (x + 2).
Another way of factoring quadratic equation is what we call Slide and Divide Method. Here are the steps.
[tex]3x^2+10x+8[/tex]1. Slide the numerical coefficient of the degree 2 to the constant term by multiplying them. The equation becomes:
[tex]\begin{gathered} 3\times8=24 \\ x^2+10x+24 \end{gathered}[/tex]2. Find the factors of 24 that results to 10 when added. In the previous method, we already found out that 6 and 4 are factors of 24 that results to 10 upon adding. So, we can say that the factors of the new equation we got in step 1 is:
[tex](x+6)(x+4)[/tex]3. Since we slide "3" to the constant term, divide the factors 6 and 4 by 3.
[tex]\begin{gathered} =(x+\frac{6}{3})(x+\frac{4}{3}) \\ =(x+2)(x+\frac{4}{3}) \end{gathered}[/tex]4. Since we can't have a fraction as a factor, slide back the denominator 3 to the term x in the same factor.
[tex](x+2)(3x+4)_{}[/tex]Similarly, we got the same factors of the given quadratic equation and these are (x + 2) and (3x + 4).
7. Zak buys 6 gallons of fruit punch. He hascoupons for $0.55 off the regular price ofeach gallon of fruit punch. After using thecoupons, the total cost of the fruit punch is$8.70. Find the regular price of a gallon offruit punch. (Example 2)
Answers
Zak buys 6 gallons of fruit punch.
He has coupons for $0.55 off the regular price of each gallon of fruit punch.
This means that $0.55 will be subtracted from the regular price of each gallon.
After using the coupons, the total cost of the fruit punch is $8.70.
Let x be the regular price of each gallon of fruit punch.
[tex](x-\$0.55)\times6=\$8.70[/tex]Now let us solve this equation for x.
[tex]\begin{gathered} (x-\$0.55)\times6=\$8.70 \\ 6x-\$3.3=\$8.70 \\ 6x=\$8.70+\$3.3 \\ 6x=\$12 \\ x=\frac{\$12}{6} \\ x=\$2 \end{gathered}[/tex]Therefore, the regular price of each gallon of fruit punch is $2
change to y=mx+b form 3x-y=6
Answers
Starting with the equation:
[tex]3x-y=6[/tex]Isolate the variable y. Substract 3x from both sides of the equation:
[tex]-y=6-3x[/tex]Multiply both sides of the equation by -1:
[tex]y=-6+3x[/tex]Use the commutative property of the sum to rewrite the right hand side of the equation:
[tex]y=3x-6[/tex]This equation is written in the form y=mx+b.
What is the total area patty can reach? What is the total grazing area?
Answers
as patty can not reach the square, we have that she can reach 3/4 parts of a circle with radius equal to 12 feet. Therefore the area she can reach is :
[tex]A_p=\frac{3}{4}\pi\cdot r^2=\frac{3}{4}\pi\cdot144=108\pi\approx339.3[/tex]and the gazzing area is the area of the square so we get:
[tex]A_g=12^2=144[/tex]the total amounts of rainfall at various points And time during a thunderstorm are shown in the table. time(hours) 0.4 | 1.1 | 2.9 | 3.2 | 3.7 | 4.4Rainfall(cm) 0.3 | 0.6 | 1.8 | 2.0 | 2.2 | 2.6According to a regression calculator, what is the equation of the line of best fit for the data?answers: a y= 0.06x+0.03 | b y= 0.06x+0.29 | c y=0.59x+0.03 | d y= 0.59x+0.29Please help!
Answers
Hello I need help with this please , I was studying it I don’t get this
Answers
Given that
The Pythagoras theorem is true for all right triangles or not.
Explanation -
For each and every right-angled triangle the Pythagoras theorem can be used.
So the final answer is True.
The sum of a number and -2 is no more than 6.
Answers
Answer: 8
Step-by-step explanation: if you add -2 and 8 you get 6. :) pls give me brainliest
What should your brain immediatelythink when it sees5(11 + 4y)
Answers
Distributive Property , I need to multiply!
Explanation
[tex]5(11+4y)[/tex]
Step 1
to find the value of y, you need isolate it
to do that, you will have to eliminate the parenthesis, you can remove it using
THE DISTRIBUTIVE PROPERTY
[tex]\begin{gathered} a(b+c)=ab+ac \\ \end{gathered}[/tex]Step 2
then
[tex]5(11+4y)=5\cdot11+5\cdot4y=55+20y[/tex]I hope this helps you.
use the equation of a parabola in standard form having a vertex at (0, 0), x^2= 8y.Solve the equation for "p" and then describe the focus (0, p), the directrix, and the 2 focal chord endpoints.
Answers
Solution
We have the following equation:
[tex]x^2=8y[/tex]the general formula for a parabola is given by:
[tex](x-h)^2=4p(y-k)[/tex]Where (h,k) =(0,0) represent the vertex, so then our equation is:
[tex]x^2=4py[/tex]By direct comparison we have this:
4p= 8
p = 2
Then the focus is given by:
(0,p) = (0,2)
the directrix is given by:
y= 0-p = 0-2= -2
y=-2
And finally the 2 focal chord endpoints are:
[tex](|2p|,p)=(4,2),(-|2p|,p)=(-4,2)[/tex]Can you hello me with number 2 using 3.14 and I have to round to the answer to the nearest tenth as well thanks
Answers
Given data:
Radius of the circle = 10in.
To find:
The circumference of the circle.
The formula to find the cicumference of the circle is,
[tex]C=2\pi r[/tex]subsitute the values of,
[tex]\begin{gathered} r=\text{ 10in} \\ \pi=3.14 \end{gathered}[/tex]we get,
[tex]\begin{gathered} C=2\cdot3.14\cdot10 \\ =62.8 \end{gathered}[/tex]THE CIRCUMFERENCE OF THE CIRCLE IS 62.8 IN
Find the x and y intercept then use them to graph the line
Answers
The x-intercept = (7, 0)
The y-intercept = (0, -3.5)
Explanation:The given equation is:
-2x + 4y = -14
Find the x-intercept by setting y = 0
-2x + 4(0) = -14
-2x + 0 = -14
-2x = -14
x = -14/-2
x = 7
Therefore, the x-intercept = (7, 0)
Find the y-intercept by setting x = 0
-2(0) + 4y = -14
0 + 4y = -14
4y = -14
y = -14/4
y = -3.5
Therefore, the y-intercept = (0, -3.5)
Considering the x and y-intercepts, the graph is plotted
Bruce owns a small grocery store and darges per pound et produce Ir a customer orders S pounds of prodeer, om zich das Bruxe charge the castomert function
Answers
bruce will charge the customer $23.75
Explanation:
Amount charged per pound = $4.75
Let the number of pounds of produce = x
Total cost per number of pounds = $4.75 × x
Let the total cost of produce = y
y = 4.75x
If the number of pounds of produce = x = 5
y = 4.75 (5)
y = $23.75
Therefore, bruce will charge the customer $23.75
POSThe expression(-4)(x) is equivalent to the expression x”. What is the value of n?n =
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given expression:
[tex]\mleft(-4\mright)\mleft(x\mright)=x^n[/tex]To find the value of n.
[tex]\begin{gathered} \ln \mleft(\mleft(-4\mright)x\mright)=n\ln \mleft(x\mright) \\ n=\frac{\ln\left(-4x\right)}{\ln\left(x\right)} \end{gathered}[/tex]3. Determine - f(a) for f(x) =2x/x-1 and simplify.
Answers
Substitute a for x
[tex]-f\text{ (x ) = - f (a) = - }\frac{2a}{a-1}[/tex]Determine - f(a) for f(x) =2x/x-1 and simplify.
Thus, the solution becomes:
[tex]-\frac{2a}{a-1}\text{ or }\frac{2a}{1-a}[/tex]g(x)= 6/x find (g°g). and domain in set notation.
Answers
We have to find the expression for the composition
[tex]g\circ\text{ g\lparen x\rparen}[/tex]Where
[tex]g(x)=\frac{6}{x}[/tex]And express its domain in set notation. We will start by finding the expression for the composition
[tex]g\circ\text{ }g(x)=g(g(x))=g(\frac{6}{x})[/tex]that is we firsts evaluate the inner functions that in this case is g, now taking as argument y=6/x, we evaluate the outer function that in this case also is g, as follows:
[tex]g\text{ \lparen }\frac{6}{x})=\frac{6}{\frac{6}{x}}=\frac{6}{6}=x[/tex]That is, the composition g*g is equal to x, the identity.
Now we will find the domain of g*g:
Note that the domain of a composition is an interception, as follows:
[tex]Domain\text{ }g\circ\text{ g=\textbraceleft Domain of }g\text{ \textbraceright }\cap\text{ \textbraceleft Image of }g\text{ \textbraceright}[/tex]Therefore, we have to find the domain and image of g, and intercept both sets. We start with the domain of g_
[tex]Domain\text{ of }g\text{ }=\text{ }\mathbb{R}\text{ - \textbraceleft0\textbraceright}[/tex]That is all the real numbers except the 0. Now note that the image of g is
[tex]Image\text{ g= }\mathbb{R}\text{ - \textbraceleft0\textbraceright}[/tex]Finally, the domain of the composition g*g, can be obtained by the formula above:
[tex]Domain\text{ of }g\circ\text{ g=}\mathbb{R}\text{ -\textbraceleft0\textbraceright }\cap\text{ }\mathbb{R}\text{ - \textbraceleft0\textbraceright= }\mathbb{R}\text{ - \textbraceleft0\textbraceright=}(-\infty\text{ },0)\text{ }\cup\text{ }(0,\infty)\text{ }[/tex]Therefore, the domain of the composition are all the real numbers excluding the 0.
-
What is a formula for the nth term of the given sequence?135, -225,375...
Answers
Step 1: Write out the formula for a geometric sequence
[tex]\begin{gathered} T_n=ar^{n-1} \\ \text{Where} \\ T_n=\text{ the nth term} \\ a=\text{ the first term} \\ r=\text{ the common ratio} \end{gathered}[/tex]Step 2: Write out the given values and find the formula
[tex]\begin{gathered} a=135, \\ r=-\frac{225}{135}=-\frac{5}{3} \end{gathered}[/tex]Therefore the formula is given by
[tex]T_n=135(-\frac{5}{3})^{n-1}[/tex]Hence, the correct choice is the first choice
14 Find the percent increase or decrease for each of the following values (indicate whether each is an increase or a decrease). a. 4x to x/ b. 0.25m to 0.5m 5 c. + 2p to d.y to 0.687 8 р 15 Consider the following relationships. TI. 1
Answers
The percentage increase or decrease is given by
[tex]\frac{final\: \text{amount}-original\: \text{amount}}{original\: \text{amount}}\times100\%[/tex]Let us find the percentage increase or decrease for the given cases.
a) 4x to x
[tex]\begin{gathered} \frac{x-4x}{4x}\times100\% \\ \frac{-3x}{4x}\times100\% \\ -0.75\times100\% \\ -75\% \end{gathered}[/tex]Therefore, it is a percentage decrease (-75%) since it is negative.
b) 0.25m to 0.5m
[tex]\begin{gathered} \frac{0.5m-0.25m}{0.25m}\times100\% \\ \frac{0.25m}{0.25m}\times100\% \\ 1\times100\% \\ 100\% \end{gathered}[/tex]Therefore, it is a percentage increase (100%) since it is positive.
c) 1/2p to 5/8p
[tex]\begin{gathered} \frac{\frac{5}{8}p-\frac{1}{2}p}{\frac{1}{2}p}\times100\% \\ \frac{\frac{1}{8}p}{\frac{1}{2}p}\times100\% \\ \frac{1}{8}\times\frac{2}{1}\times100\% \\ \frac{2}{8}\times100\% \\ \frac{1}{4}\times100\% \\ 25\% \end{gathered}[/tex]Therefore, it is a percentage increase (25%) since it is positive
d) y to 0.68y
[tex]\begin{gathered} \frac{0.68y-y}{0.68y}\times100\% \\ \frac{-0.32y}{0.68y}\times100\% \\ -0.47\times100\% \\ -47\% \end{gathered}[/tex]Therefore, it is a percentage decrease (-47%) since it is negative.
We start with triangle ABC and see that angle ZAB is an exterior angle created by the extension of side AC. Angles ZAB and CAB are a linear pair by definition. We know that m∠ZAB + m∠CAB = 180° by the . We also know m∠CAB + m∠ACB + m∠CBA = 180° because .
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The first answer is: definition of complementary angles.
The second is: of the triangle sum theorem.
The third one is: substraction property
Solve the following inequality for kk. Write your answer in the simplest form.8k - 3 > 9k + 10
Answers
Given:
[tex]8k-3>9k+10[/tex]To solve for k:
Solving we get,
[tex]\begin{gathered} 8k-3>9k+10 \\ 8k-9k>10+3 \\ -k>13 \\ k<-13 \end{gathered}[/tex]Hence, the answer is,
[tex]k<-13[/tex]