I guess the annual retreat of the glacier is linear, and two points in the line are
[tex](0,1000),(15,745)[/tex]Where x is in years and y in meters.
We can find the equation of a line given two points by using the formula below
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]In our case,
[tex]\begin{gathered} y-1000=\frac{745-1000}{15-0}(x-0) \\ \Rightarrow y-1000=-17x \\ \Rightarrow y=-17x+1000 \end{gathered}[/tex]2) Suppose that x=0 corresponds to the year 2010. Then, the information in the table is:
[tex]\begin{gathered} 2010\to-17(0)+1000=1000 \\ 2020\to-17(10)+1000=830 \\ 2030\to-17(20)+1000=660 \\ 2040\to-17(30)+1000=490 \\ 2050\to-17(40)+1000=320 \end{gathered}[/tex]The answers are 1000,830,660,490,320 to to bottom
c)
We already obtained the equation we are asked for in this part of the problem. Remember that we used the points (0,1000) and (15,745)
The equation is:
[tex]y=-17x+1000[/tex]y=-17x+1000
Factor 3x² + 10x + 8 using earmuff method.
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).
Hello I need help with this please , I was studying it I don’t get this
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.POSThe expression(-4)(x) is equivalent to the expression x”. What is the value of n?n =
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]in the diagram below, line CD and BC intersect at a. Which of the following rigid motions could be used to show that
The only rigid motion that could be used to show that angle BAE is congruent to the angle DAC is D.
Because if we do the rotation of 180° clockwise about A we will obtain the same Figure.
This is the original figure
As we can see making the rotation we obtain same figure
Solve the following inequality for kk. Write your answer in the simplest form.8k - 3 > 9k + 10
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]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*
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.
g(x)= 6/x find (g°g). and domain in set notation.
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.
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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
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
3. Determine - f(a) for f(x) =2x/x-1 and simplify.
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]which does not name an integer a.-35 b. 0 c. 3/15d. 10/2
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
Steve made a business trip of 200.5 miles. He averaged 51 mph for the first part of the trip and 62 mph for the second part. If the trip took 3.5 hours, how long did hetravel at each rate?
Let t = time traveled at 51 mph
The total time is given as 3.5 hours
So (3.5- t )= time traveled at 62 mph
We are going to use the distance formula:
distance = speed* time
51t + 62(3.5-t) = 200.5
51t + 62*3.5 - 62*t = 200.5
51t + 217 - 62t = 200.5
Solve the equal terms
51t - 62t = 200.5 - 217
-11t = -16.5
t = -16.5/-11
t = 1.5
Then he took 1.5 at 51mph
and (3.5- t ) = (3.5-1.5) = 2h at 62 mph
To confirm these results, find the actual speed of each speed:
speed* time = distance
51*1.5 = 76.5miles
62*2. = 124 miles
76.5miles + 124 miles = 200.5miles
A right triangle has legs that are 5 cm and 7 cm long what is the length of the hypotenuse 1.√122.√243.√74 4.√144
Answer:
3. √74
Explanation:
By the Pythagorean theorem, the length of the hypotenuse can be calculated as:
[tex]c=\sqrt[]{a^2+b^2}[/tex]Where c is the hypotenuse and a and b are the lengths of the legs.
So, replacing a by 5 and b by 7, we get:
[tex]\begin{gathered} c=\sqrt[]{5^2+7^2} \\ c=\sqrt[]{25+49} \\ c=\sqrt[]{74} \end{gathered}[/tex]Therefore, the answer is 3. √74
Given:• ABCD is a parallelogram.• DE=3z-3• EB=2+11• EC = 5x + 7What is the value of x?44.507
To answer this question, we need to recall that: "the diagonals of a parallelogram bisect each other"
Thus, we can say that:
[tex]DE=EB[/tex]And since: DE = 3x - 3 , and EB = x + 11, we have tha:
[tex]\begin{gathered} DE=EB \\ \Rightarrow3x-3=x+11 \end{gathered}[/tex]we now solve the above equation to find x, as follows:
[tex]\begin{gathered} \Rightarrow3x-3=x+11 \\ \Rightarrow3x-x=11+3 \\ \Rightarrow2x=14 \\ \Rightarrow x=\frac{14}{2}=7 \\ \Rightarrow x=7 \end{gathered}[/tex]Therefore, the correct answer is: option D
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.)
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]I’m not sure how to solve it please help me!
ANSWER:
33.5%
STEP-BY-STEP EXPLANATION:
We have the amount in 2003 in 5799 fish and in 2014 there are there are 1943 less fish.
The percentage of change would be the difference in fish between these years divided by the initial amount of fish, just like this:
[tex]\begin{gathered} p=\frac{5799-(5799-1943)}{5799}\cdot100 \\ \\ p=\:\frac{1943}{5799}\cdot100\: \\ \\ p=33.505\cong33.5\% \end{gathered}[/tex]This means that the percentage of change is negative since the population has decreased by 33.5%.
10.Find the approximated circumference of a circle whose area is 136.46
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
my work is saying solve for the value of a
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]What is a formula for the nth term of the given sequence?135, -225,375...
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
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
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
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 .
The first answer is: definition of complementary angles.
The second is: of the triangle sum theorem.
The third one is: substraction property
What should your brain immediatelythink when it sees5(11 + 4y)
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.
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.
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.
I need help knowing the range of this function. the graph of it is[tex]y = {x}^{2} - 2x - 8[/tex]
Given the function:
[tex]y=x^2-2x-8[/tex]Let's determine the range of the function using the graph.
The range of a function is the set of all possible y-values which define the function.
From the graph shown, the value of y starts from the vertex at y = -9 and goes upward.
Therefore, the range of the function is all values of y greater than or equal to -9.
{y|y ≥ - 9}
Hence, in interval notation is:
[tex][-9,\infty)[/tex]ANSWER:
[tex][-9,\infty)[/tex]distance is a direct variation of time if the distance
Explanation
In order to be able to predict the time, it will take to cover 220 miles, we will have to get the relationship
The relationship between distance and the time can be obtained as follow:
When the distance is 80 miles, the time taken is 2 hours
So when the distance is 220 miles, the time taken will be
[tex]x=\frac{220\times2}{80}=5.5[/tex]Therefore, it will take 5.5 hours to cover a distance of 220 miles
Therefore, the answer is 5.5 hours
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
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.
Which of the following transformations, when performed on Figure Q, will result in Figure R?A.) a reflection over the y-axis followed by a translation of 1 unit to the rightB.) a translation of 7 units to the rightC.) a rotation of 270 degrees counterclockwise about the originD.) a rotation of 90 degrees clockwise about the origin
Given:
Given that a figure Q and its transformation R.
Required:
To choose the correct transformation of the given figure.
Explanation:
The figure R is 7 unit right to the figure Q.
Therefore the option B is correct.
Final Answer:
(B) A translation of 7 units to the right.
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.
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]
The sum of a number and -2 is no more than 6.
Answer: 8
Step-by-step explanation: if you add -2 and 8 you get 6. :) pls give me brainliest
How do you write 476 in scientific notation?
Answer:
[tex]undefined[/tex]How to write 476 in scientific notation.
To write a number in scientific notation, express the number in the form:
[tex]m\text{ }\times10^n[/tex]Where m is a number that has a unit place value. (That is a number less than 10 but greater than 1)
In the case of 476, you put a point after 4, you would see that there are two digits after 4 ( 7 and 6)
The scientific notation of 476 is therefore:
[tex]4.76\times10^2[/tex]Julia rides her bike 14 miles in 2 hours. If she rides at a constant speed, select the answers below that are equivalent ratiosto the speed she rides. Select all ratios that are equivalent,
Divide the distance over the total time to find the distance Julia rides in one hour:
[tex]\frac{14\text{ miles}}{2\text{ hours}}=7\text{ miles per hour}[/tex]Do the same for each option to find whether or not they represent the same speed:
A)
[tex]\frac{35\text{ miles}}{6\text{ hours}}=5.83\text{ miles per hour}[/tex]B)
[tex]\frac{7\text{ miles}}{1\text{ hour}}=7\text{ miles per hour}[/tex]C)
[tex]\frac{28\text{ miles}}{4\text{ hours}}=7\text{ miles per hour}[/tex]D)
[tex]\frac{42\text{ miles}}{7\text{ hours}}=6\text{ miles per hour}[/tex]Therefore, only options B and C represent the same ratio.