In a rectangle of area 50 the value of x is 5
How to solve for xArea of a rectangle is given by multiplication of the length and the width
Area was given as 50
length = x + 10
width = x
Area = L * w
50 = (x + 10) * x
50 = x^2 + 10x
rearranging the equation
x^2 + 10x - 50
factorizing gives
x - 5x + 10x - 50
x(x- 5) + 10(x - 5)
(x - 5)(x + 10)
therefore
x = 5 or x = -10
taking the positive value
x = 5
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Question
The area of a rectangle is 50 the length is x+10 and the width is x
solve for x.
I'll send the pic in the session
The Slope-Intercept form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
In this case you know that "y" represents the number of books in Himanshu's home library and "x" represents the number of weeks.
In the graph you can identify that:
[tex]b=6[/tex]And you can also identify this point on the line:
[tex]\mleft(2,8\mright)[/tex]Where:
[tex]\begin{gathered} x=2 \\ y=8 \end{gathered}[/tex]Substitute these values into the equation
[tex]y=mx+b[/tex]and solve for "m" in order to find the slope:
[tex]\begin{gathered} 8=(m)(2)+6 \\ 8-6=2m \\ \\ \frac{2}{2}=m \\ \\ m=1 \end{gathered}[/tex]Then, the equation of this line is:
[tex]y=x+6[/tex]Based on the explained above, you can conclude that he had 6 books in his library and then he started adding 1 book each week.
To find the number of books he has after 4 weeks, you can make:
[tex]x=4[/tex]Substitute this value into the equation and evaluate. Then:
[tex]y=(4)+6=10[/tex]The answer is: Option A and Option F.
California Chinese Shar Pei Rescue buys 1,898 lbs of dog food. They plan to split it equally among their 26 dogs. How much dog food will each dog receive (this is not per day FYI)?
Answer:
The answer is 73 i hope it helps
Problem 2: Solve the matrix equation for "x" and "y" 8 -X 2 13 4 1- [ 3 -9 10 -4y 5 6 [ 0 16
Solve the operation of the matrix
[tex]\begin{gathered} 2\begin{bmatrix}{8} & {-x} & {} \\ {5} & {6} & {} \\ & {} & {}\end{bmatrix}{}-\begin{bmatrix}{3} & {-9} & {} \\ {10} & {-4y} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{13} & {4} & {} \\ {0} & {16} & {} \\ {} & {} & {}\end{bmatrix} \\ \begin{bmatrix}{16} & {-2x} & {} \\ {10} & {12} & {} \\ {} & & {}\end{bmatrix}-\begin{bmatrix}{3} & {-9} & {} \\ {10} & {-4y} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{13} & {4} & {} \\ {0} & {16} & {} \\ {} & {} & {}\end{bmatrix} \\ \begin{bmatrix}{13} & {-2x+9} & {} \\ {0} & {12+4y} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{13} & {4} & {} \\ {0} & {16} & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}[/tex]From this result we know that
[tex]\begin{gathered} -2x+9=4 \\ 12+4y=16 \end{gathered}[/tex]Now clear x and y from the equations
[tex]\begin{gathered} -2x+9=4 \\ -2x=-5 \\ x=-\frac{5}{-2} \\ x=\frac{5}{2} \end{gathered}[/tex][tex]\begin{gathered} 12+4y=16 \\ 4y=4 \\ y=\frac{4}{4} \\ y=1 \end{gathered}[/tex]x is 5/2 and y is 1
Find the range and standard deviation of the set of data.230, 232, 234, 236, 238, 240, 242
The data given is ,230, 232, 234, 236, 238, 240, 242.
The range of the data is defined the difference of largest number from smallest number.
The largest number in the data is, 242.
The smallest number in the data is, 230.
Therefore, the range is determined as
[tex]R=242-230[/tex][tex]R=12.[/tex]The range of the set of data is 12.
To determine the standard deviation,
First determine the mean of the data,
[tex]E(x)=\frac{230+232+234+236+238+240+242}{7}[/tex][tex]E(x)=\frac{1652}{7}[/tex][tex]E(x)=236[/tex]The value of
[tex]E(x^2)=(230-236)^2+(232-236)^2+(234-236)^2+(236-236)^2+(238-236)^2+(240-236)^2+(242-236)^2[/tex][tex]E(x^2)=36+16+4+0+4+16+36[/tex][tex]E(x^2)=112[/tex]The standard deviation is determined as,
[tex]SD=\sqrt[]{v}[/tex]Here v denotes the variance.
[tex]v=\frac{112}{7-1}[/tex][tex]v=\frac{112}{6}[/tex][tex]v=18.66[/tex]The standard deviation is given as,
[tex]SD=\sqrt[]{18.66}[/tex][tex]SD=4.32[/tex]Two consecutive terms in an ARITHMETIC sequence are given. Find the recursive function.
An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
The recursive formula have the following format:
[tex]a_{n+1}=a_n+d[/tex]Where 'd' is the common difference between each term.
From the text, we know that
[tex]\begin{gathered} a_3=5 \\ a_4=8 \end{gathered}[/tex]Plugging those values in our formula, we find that the common difference between our terms is 3.
This gives us the following recursive function:
[tex]f(n+1)=f(n)+3[/tex]Evaluating the function at '5' and '6', we get the following:
[tex]\begin{gathered} f(5)=f(4)+3=8+3=11 \\ f(6)=f(5)+3=11+3=14 \end{gathered}[/tex]If Ashley had 4 yards of yarn and Ramon had 11 feet of yarn, who had more yarn?
Answer:
Step-by-step explanation:
Ashley had more yarn, 1 yard = 3 ft 3 times 4 = 12 so 3 yards is 12 feet.
Answer:
Ashley has more yarn than Ramon.
Step-by-step explanation:
1 yard is 3 feet, so thats 4 (yards) time 3 (feet per yard) is 12. Ashley has 12 feet of yarn. Ramon has 11. 12 is greater than 11, so Ashley has more yarn.
HELP HELP HELP MEEEEEEEEE PLEASEEEEEEEEE
Answer:
see explanation
Step-by-step explanation:
the domain is the x- coordinates (input) of the ordered pairs, note repeated values are only listed once , then
domain { - 3, 0, 1, 2 }
the range is the y- coordinates (output) of the ordered pairs , note repeated values are only listed once, then
range { 1, 2, 4, 5 }
For the relation to be a function then each value of x must map to one unique value of y.
here - 3 → 1 and 2 → 1
Thus the relation is not a function
how many bites have their second, third and fourth digit equal to 0
How many bytes have their second, third, and fourth digit equal to 0.
If we refer to 8-bits, we would have a value from 00000000 to 11111111, there would be a total of 256 values.
[tex]2^8=256[/tex]Considering that we only need it to have its second, third and fourth digit equal to 0, we can add the values from 2^0 up until 2^4
[tex]2^0+2^1+2^2+2^3+2^4=1+2+4+8+16=31[/tex]That would be equal to 31 bytes.
Mrs.smith deposits $980 in a saving account that pays 3.1% interest compounded daily
The amount at the end of 30 days, when interest compounded daily is found as $982.53.
What is referred as the compound interest?Compound interest is investment determined on the preliminary principal plus all previous periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest could be compounded at any time, from continuously to everyday to annually.The formula for calculating the compound interest is;
A = P(1 + r/100n)∧nt
Where,
CI = compound interestP = principal amount = $980r = rate of interest = 3.1%n = number of time interest compounded = 30 dayst = time in years = 1 months; 1/12 year.A = amount after given time.Now put the values in the formula.
A = 980(1 + 3.1/3000)∧30(1/12)
A = 980(1.0025)
A= 982.53
Thus, the amount at the end of 30 days, when interest compounded daily is found as $982.53.
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The complete question is-
Mrs.smith deposits $980 in a saving account that pays 3.1% interest compounded daily. Calculate the total amount for 30 days.
Edmond, an NFL running back, rushed for an average of 148 yards per game this season, which is 85% higher than his average was last season. What was his average then?
Edmond average then was 174.12 , by using the given percentage.
What do you mean by percentage?
A ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
It is given that Edmond rushed for an average of 148 yards per game this season.
Let the average of Edmond last year be x
According to question, 148 yards per game is 85% of x
85% of x = 148
85/100 × x = 148
x = 148 ÷ (85/100) = 148 × (100/85) = 14800/85 = 174.12
Thereofore, Edmond average then was 174.12
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this is a 4 question part which price has the lowest unit per ounce choice a 6 ounces of chocolate chips for $ 2.49 choice b 8 ounces of chocolate chips for $ 3.32 I will ask the other 3 questions soon
For choice (a);
[tex]\begin{gathered} 6\text{ ounces of chocolate for 2.49} \\ \text{Per ounce=}\frac{2.49}{6} \\ \text{Per ounce=\$0.415} \end{gathered}[/tex]For choice (b);
[tex]\begin{gathered} 8\text{ ounces of chocolate for 3.32} \\ \text{Per ounce=}\frac{3.32}{8} \\ \text{Per ounce=\$0.415} \end{gathered}[/tex]Both options (a) and (b) have the same price per ounce which is $0.415.
Therefore, none of them is a cheaper option.
(3x-3) = 48 Find the value of X
Answer:
17
Step-by-step explanation:
3x-3=48
3x = 48+3
3x= 51
x= 51/3 = 17
Two machines worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. Together they charge a total of $2250. What was the rate charged per hour by each mechanic if the sum of the two rates was $125 per hour?
Solution:
Let's make,
mechanic #1's rate = x
mechanic #2's rate = y
Note that their rate is dollars per hour.
Now, mechanic #1 worked for 20 hours. Then, we get the following equation:
20x = money earned by mechanic #1
On the other hand, mechanic #2 worked for 15 hours. Then, we get the following equation:
15y = money earned by mechanic #2
together they charged a total of $2250. So the amount of money earned by both mechanics is:
20x + 15y = 2250 EQUATION 1
On the other hand, the sum of the two rates was:
x + y = 125 EQUATION 2
From the equation, if we solve for x, we get:
x = 125-y EQUATION 3
plug (125-y) in for "x" in equation 1 to get everything in terms of one variable:
20(125-y)+15y = 2250
this is equivalent to
2500-20y +15y = 2250
this is equivalent to
2500 -5y = 2250
this is equivalent to
-5y = 2250 -2500
this is equivalent to:
-5y = -250
or
5y = 250
solving for y, we get:
[tex]y\text{ =}\frac{250}{5}=50[/tex]now, replacing this into equation 3, we get:
x = 125-y = 125 - (50) = 75
so that, we can conclude that the correct answer is:
mechanic #1 charged 75 $/hr
mechanic #2 charged 50 $/hr
x = y + 3
(2y + x = 12
Answer:
X is 6, Y is 3
Step-by-step explanation:
The first equation states that x=y+3, so we can substitute x for y+3 in the second equation. We get 2y+y+3=12.
Combine like terms: 3y+3=12
Subtract 3: 3y=9
Divide by 3: y=3
Substitute y=3 into the first equation: x=3+3
Simplify: x=6
Answer:
first one is
x= 6
second one is
y = 3
Step-by-step explanation:
just use the solving eqautions method- I will give you a chart on how
Apr 20, 11:27:10 AMA series of coins are stacked to represent a right circular cylinder (on the left). Thecoins are then "slid" to represent a distorted cylinder (on the right). The samenumber of congruent coins was used in each stack. Which of the following statementswill be TRUE regarding these stacks of coins?
The picture provides to stacks of coins and the number of coins used in both stacks are the same. One stack is straight while the other has been slightly distorted. Nonetheless, since the stacks of coins are congruent, the volume would be the same.
Find the least common denominator for thesetwo rational expressions.x3-3x2 – 2x + 1 x2 + 6x - 7-Enter the correct answer.000DONEClear all02 ?
Solution
Given
[tex]\begin{gathered} \frac{x^3}{x^2-2x+1}=\frac{x^3}{(x-1)^2} \\ \\ \frac{-3}{x^2+6x-7}=-\frac{3}{(x-1)(x+7)} \\ \end{gathered}[/tex]Hence the LCM is
[tex](x-1)^2(x+7)[/tex]
Write the coordinates of the vertices after a rotation 90° counterclockwise around the origin.
Q=
R=
S=
T=
Check the picture below.
how do I translate six more than four times a number z into a variable expression
For the relationship, two variables are needed.
One of the variable is given as 'z'. Let the other one be 'x'.
Then you need to translate that 'x' is six more than four times a number 'z'.
This can be expressed as,
[tex]x=6+4z[/tex]Thus, the right side of the expression represents the relationship "six more than four times a number z".
1). preises 12,4 the following: Find the intercepts and domain and perform the symmetry test on each parabola with equation: Graph the vertex, focus, and endpoints of the latus rectum; then draw the parabola for each ome axes the parol plete (a) y = 87 (c) y = – 4x (b) x2 = 8y (a) x = - 4y
wee have
y^2=8x
this is a horizontal parabola open to the right
the vertex is the origin (0,0)
so
(h,k)=(0,0) ------> vertex of the parabola
If f(x) = x - 3, g(x) = 3x - 9, and h(x) = x^2-6x+9, then (gf)(2)=
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given functions
[tex]\begin{gathered} f(x)=x-3 \\ g(x)=3x-9 \\ h(x)=x^2-6x+9 \end{gathered}[/tex]STEP 2: Find the gf(2)
[tex]\begin{gathered} \left(gf\right)\left(x\right)=g\left(x\right)f\left(x\right) \\ =g\left(2\right)f\left(2\right) \end{gathered}[/tex]Find g(2)
[tex]\begin{gathered} x=2 \\ By\text{ substitution,} \\ g(2)=3(2)-9=6-9=-3 \end{gathered}[/tex]Find f(2)
[tex]\begin{gathered} x=2 \\ By\text{ subsitution,} \\ f(2)=2-3=-1 \end{gathered}[/tex]Find gf(2)
[tex]\begin{gathered} By\text{ multiplication,} \\ =-3\cdot-1=3 \end{gathered}[/tex]Hence, the answer is 3
I need help with this practice problem *you can pick more than one answer
Solution:
Consider the following trigonometric equation:
[tex]3\cot (\theta)=-\sqrt[]{3}[/tex]This is equivalent to:
[tex]\cot (\theta)=-\frac{\sqrt[]{3}}{3}[/tex]now, consider the following trigonometric circle and the above equation:
According to this trigonometric circle and the definition of the cotangent function, we can conclude that the general solution would be:
[tex]\theta=\frac{2\pi}{3}+\pi n[/tex]Use your answers from #1 and #2 to find the length of each arc between gondola cars. Use 3.14 for pi and round to the nearest hundredth. You must write out all the numbers you are multiplying together, meaning, show your work for full credit.
We have a SkyWheel.
We know that the angle between the gondolas is 360/41 = 8.78°.
The radius of the wheel is 181/2 = 90.5.
We know have to calculate the length of the arc between gondolas.
The length of the arc L can be calculated using proportions: the length of the arc is to the angle between gondolas as the total circumference of the wheel is to 2*pi (or 360°).
We can express this as:
[tex]\frac{L}{\theta}=\frac{C}{2\pi}[/tex]If we rearrange, we can solve for L:
[tex]\begin{gathered} \frac{L}{\theta}=\frac{C}{2\pi} \\ \frac{L}{\theta}=\frac{2\pi r}{2\pi} \\ \frac{L}{\theta}=r \\ L=\theta\cdot r=(\frac{2\pi}{41})\cdot90.5=(\frac{2\cdot3.14}{41})\cdot90.5=13.86ft \end{gathered}[/tex]NOTE: we have to express the angle theta (that is the angle between the gondolas) in radians when we want to calculate a length. That is why this angle is expressed as the total angle of the circle (2*pi) divided the 41 gondolas.
If we use 8.78°, we should express it as:
[tex]L=\theta\cdot r=8.78\degree\cdot(\frac{2\pi}{360\degree})\cdot90.5ft=13.86ft[/tex]With the factor 2pi/360 we are converting the angle in degrees into radians in order to calculate the length.
Answer: the length of the arc between gondolas is 13.86 ft.
Determine the present value P that must be invested to have the future A at simple interest rate r after time t A= $3000.00 r=15,0% t= 9 months Round up to nearest cent as needed
Answer:
$2696.63
Explanation:
The future value A and the present value P are related by the following equation
A = P(1 + rt)
Where r is the interest rate and t is the time.
Now, we need to convert 9 months to years as follows
9 months x 1 year / 12 months = 0.75 years
Then, replacing A = 3000, r = 15% = 0.15 and t = 0.75, we get:
3000 = P(1 + 0.15(0.75))
3000 = P(1 + 0.1125)
3000 = P(1.1125)
Now, we can solve for P
P = 3000/1.1125
P = 2696.63
Therefore, the present value is $2696.63
1. Translate & Solve *20 points"Seven subtracted from the product of a number and -4 is -59."A) n = 13B) n = -13C) n = 26D) n = -26
Seven subtracted from the product of a number and -4 is -59, let me translate it.
[tex]-4x-7=-59[/tex]Let me solve it now (Next).
[tex]\rightarrow4x+7\text{ = 59}\rightarrow x=13[/tex]The sum of two-sevenths of a number and 3 is 9
[tex]\frac{2x}{7}+3=9[/tex]This is the translation, let me solve it next.
[tex]\frac{2x}{7}=6\rightarrow x\text{ = }\frac{42}{2}=21[/tex][tex]x^2-14=50\rightarrow x\text{ = 6}[/tex][tex]\frac{40x}{100}-10\text{ =-4}[/tex][tex]\frac{40x}{100}=6\rightarrow x\text{ = }\frac{600}{40}=15[/tex]The quotient of a number increased by 4 and -3 is 15
[tex]\frac{x}{4}-3=15\rightarrow x=72[/tex]Assume that a sample is used to estimate a population mean . Find the margin of error M.E. that corresponds to a sample of size 5 with a mean of 75.2 and a standard deviation of 21.2 at a confidence level of 98% Report ME accurate to one decimal place because the sample statistics are presented with this accuracy M.E. Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.
We have the following:
[tex]\begin{gathered} df=n-1 \\ =5-1 \\ df=4 \end{gathered}[/tex]therefore:
[tex]\begin{gathered} ME=t_{critical}\cdot\frac{s}{\sqrt{n}} \\ ME=3\text{.}747\cdot\frac{21.2}{\sqrt{5}} \\ ME=35.52 \end{gathered}[/tex]The margin the error that corresponds to a sample of size of 5 with mean 75.2 and a standard deviation of 21.2 at a confidence level of 98% is 35.52
Select the correct answer.
What is the solution to |2x + 3| = 15?
Answer:
6
Step-by-step explanation:
2x+3=15
2x=15_3
2x=12
x=12÷2
x=6
What is (f + g)(x)?f(x) = x + 1g(x) = 3x²Write your answer as a polynomial or a rational function in simplest form.
Given:
f(x) = x + 1
g(x) = 3x²
To find (f + g)(x), sum the like terms of the function.
(f + g)(x) = f(x) + g(x) = x + 1 + 3x²
(f + g)(x) = 3x² + x + 1
Answer: 3x² + x + 1
Is it a
linear function?
Answer:
No
Step-by-step explanation:
Well, by looking at the x factors, none of them repeat so it is a function. To determine if it's linear, you can look to see if the change is consistent. From 0 to 2 is +2, and from 10 to 6 is -4. From 2 to 4 is +2, but from 6 to 4 is -2. Since it doesn't go down the table at a set rate, it isn't linear. So, it is a function, but not a linear function
which is the best estimate for the average rate of change for the quadratic function graph on the interval [tex]0 \leqslant x \leqslant 4[/tex]
The average rate of change of the given quadratic function on the interval
[tex]0\le x\le4[/tex]is the slope of the secant line connecting the points
[tex](0,f(0))\text{ and (4,f(4)}[/tex]In other words, the average rate of change is
[tex]m=\frac{f(4)-f(0)}{4-0}[/tex]From the graph, we can see that f(0)=0 and f(4)=-4. By substituying these values into the last equation, we obtain
[tex]\begin{gathered} m=\frac{-4-0}{4-0} \\ m=-\frac{4}{4} \\ m=-1 \end{gathered}[/tex]Hence the average rate of change for the given quadratic function whose graph is shown on 0≤x≤4 is -1
Can please help mii here
Answer:
the function Is y= -x+5 .........