Answers
We are asked to find the value of x.
As you can see, the two sides are parallel and when these parallel sides intersect sides of overlapping triangles then the intercepted segments are proportional.
So, we can set up the following proportion.
[tex]\frac{15}{6}=\frac{(3x+10)-8}{8}[/tex]Let us solve the above equation for x.
[tex]\begin{gathered} \frac{15}{6}=\frac{3x+10-8}{8} \\ \frac{15}{6}=\frac{3x+2}{8} \\ 15\cdot8=6\cdot(3x+2) \\ 120=18x+12 \\ 120-12=18x \\ 108=18x \\ \frac{108}{18}=x \\ 6=x \\ x=6 \end{gathered}[/tex]Therefore, the value of x is 6
Related Questions
a sofa is on sale for $289, which is 32% less than the regular price what is the regular price
Answers
6149488990ay, this is the solution:
Let's use the Direct Rule of Three for answering this problem, this way:
Price Percentage
289 68
x 100
___________________
28,900 = 68x
68x/68 = 28,900/68
x = 425
The regular price of the sofa is $ 425, and you will save $ 136 if you buy it on sale.
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the ferris wheel is drawn on a coordinate plane so that the first car is located at the point ( 0, 80). what are the coordinates of the first car after a 270° counterclockwise about the originthe coordinate of the first car are........ after a rotation of 270° about the origin
Answers
We can draw the following picture:
That is, the coordinates are (80,0)
Identify the prime factorization for 75A 25x3B25x 3C 52x3
Answers
Given the number below;
[tex]75[/tex]We are asked to find the prime factorization of the number.
Step 1: Definition
"Prime Factorization" is finding which prime numbers multiply together to make the original number.
Step 2: We will use prime numbers to go through the given value until we can not divide further.
Since 75 is an odd number we will start with 3.
We can find above all the prime factors used to divide 75. Therefore;
[tex]75=3\times5\times5=3\times25^{}[/tex]Answer:
[tex]3\times25[/tex]Expand the expression.3(x - 5)
Answers
solve for x
[tex]\begin{gathered} 3x=15 \\ \frac{3x}{3}=\frac{15}{3} \\ x=5 \end{gathered}[/tex]Find the 5 number summary for the data shownx2.72.97.27.58.511.215.418.3
Answers
2.7 ,2.9, 7.2, 7.5, 8.5, 11.2,15.4, 18.3
The minimum is the smallest number in the data : 2.7
The maximum is the largest number in the data : 18.3
Next, we find the median, which is the middle number in the data when arranged from smallest to largest. There are 8 numbers, so we will average the middle 2 numbers
2.7 ,2.9, 7.2, 7.5, 8.5, 11.2,15.4, 18.3
The middle is between the 4th and 5th numbers
( 7.5 + 8.5) / 2 = 16/2 = 8
The median(Q2) is 8
To find Q1 ( the 1st quartile), we take the numbers below the mean
2.7 ,2.9, 7.2, 7.5,
and find the median of these numbers
There are 4 numbers so the middle is between the 2nd and 3rd numbers
2.7 , 2.9, 7.2, 7.5,
(2.9+7.2) /2 =5.05
Q1 = 5.05
We will do the same process for Q3, which is the third quartile. We will use the numbers above the median
8.5, 11.2,15.4, 18.3
( 11.2 + 15.4) /2 =13.3
Q3 = 13.3
Weight: How many grams does a 5 lb 8 oz roast weigh?The roast weighs ? grams.
Answers
Solution
For this case we have the following weight:
5 lb and 8 oz
Using the following conversion ratios
1lb = 453.592 gr
1 oz = 28.3495 gr
We need to convert into grams so we can do this:
[tex]5lb\cdot\frac{453.592gr}{1lb}=2267.96gr[/tex][tex]8oz\cdot\frac{28.3495gr}{1oz}=226.796gr[/tex]Then adding the two values we have:
2267.96gr + 226.796gr = 2494.756 gr
convert 2.5 years into hours
Answers
We are asked to convert 2.5 years into hours.
Step 1:
There are 365 days in a year so 2.5 years will have
[tex]2.5\cdot365=912.5\text{ days}[/tex]Step 2:
There are 24 hours in a day so 912.5 days will have
[tex]912.5\cdot24=21900\text{ hours}[/tex]Therefore, 2.5 years will have 21900 hours.
Solve for R in I=PRTa.) What is the variable?b.) What is happing to the variable? (list the operations from the first thing to the last thing)c.) What is the inverse (opposite) of the last thing that happened to the variable. (Make a list of the steps to solve)
Answers
a) R is the variable
b) a product, the variable is being multiplied
[tex]R=\frac{I}{PT}[/tex]Explanation
Step 1
[tex]I=\text{PRT}[/tex]the value for I depends on the value for R, it means, that I depends on the value for R
so, R is the variable
Step 2
when you have
[tex]\begin{gathered} I=\text{PRT} \\ is\text{ equal to} \\ I=P\cdot R\cdot T \end{gathered}[/tex]it is a multiplication between P, R and T,the variable is being multiplied
Step 2
solve for R
[tex]\begin{gathered} I=\text{PRT} \\ \text{you n}eed\text{ to do the inverse operation } \\ \text{Multiplication}\Rightarrow opposite\Rightarrow Division \end{gathered}[/tex]then, opposite operation is division, divide both sides by PT
[tex]\begin{gathered} \frac{I}{PT}=\frac{PRT}{PT} \\ \frac{I}{PT}=R \\ R=\frac{I}{PT} \end{gathered}[/tex]I hope this helps you
proportional relationship. Vivian says that cannot be true because the constants ofMindy says that the equations p =1.59 and {o= q both represent the sameproportionality are different. Which student do you agree with? Explain.
Answers
We have two equations:
[tex]\begin{gathered} p=1.5q \\ \frac{2}{3}p=q \end{gathered}[/tex]We would like to know if those represent the same proportional relationship or don't.
For doing so, we remember that a constant of proportionality
A line passes through the point (-1,-13) and has a slope of 6. An equation of the line is
Answers
Recall that 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.
To take the given equation to its slope-intercept form, first, we multiply it by x+1 and get:
[tex]\begin{gathered} y+13=6(x+1), \\ y+13=6x+6. \end{gathered}[/tex]Subtracting 13, we get:
[tex]\begin{gathered} y=6x+6-13, \\ y=6x-7. \end{gathered}[/tex]Answer:
[tex]y=6x-7.[/tex]The function h(x) = 1/x-7 can be expressed in the form f(g(x)), where g(x) = x-7), and f(x) is defined as:f(x) =
Answers
Answer:
f(x) = 1 /x
Explanation:
We know that
[tex]h(x)=f(g(x))=\frac{1}{x-7}[/tex]and
[tex]g(x)=x-7[/tex]Now, what must be the form of f(x)?
Let us guess.
If we said
[tex]f(x)=\frac{1}{x}[/tex]then what would be f(g(x)) in this case?
To find out we simply replace x with g(x). This gives
[tex]f(g(x))=\frac{1}{g(x)}[/tex][tex]\Rightarrow f(g(x))=\frac{1}{x-7}[/tex]which is exactly the form we are told f(g(x)) take! This means our guess was correct and
[tex]\boxed{f(x)=\frac{1}{x}\text{.}}[/tex]HELP MEEEEisolate the variable to solve 4x + 4 > -20. what number line shows the solution set?
Answers
Given,
The expression is,
[tex]4x+4>-20[/tex]Required
The solution of the inequality.
Taking the given expression as,
[tex]\begin{gathered} 4x+4>-20 \\ 4x+4-4>-20-4 \\ 4x>-24 \\ \frac{4x}{4}>-\frac{24}{4} \\ x>-6 \end{gathered}[/tex]So, the solution of the inequality is x > -6.
Hence, option B is correct.
Find the quadratic equation using the points given (-1,2), (0,1) and (-2,5).
Answers
The general equation for a quadratic equation is,
[tex]y=ax^2+bx+c[/tex]Substititute the values to obtain the equations for the coefficients.
[tex]\begin{gathered} 2=a(-1)^2+(-1)b+c \\ a-b+c=2 \end{gathered}[/tex][tex]\begin{gathered} 1=a(0)^2+b(0)+c \\ c=1 \end{gathered}[/tex]and
[tex]\begin{gathered} 5=a(-2)^2+b(-2)+c \\ 4a-2b+c=5 \end{gathered}[/tex]Substitute the value of c in the equation a-b+c=2 to obtain the equation for a and b.
[tex]\begin{gathered} a-b+1=2 \\ a=1+b \end{gathered}[/tex]Substitute the value of a and c in the equation 4a-2b+c=5 to obtain the value of b.
[tex]\begin{gathered} 4(1+b)-2b+1=5 \\ 4-2b+1=5 \\ 2b=0 \\ b=0 \end{gathered}[/tex]Substitute the value of b in the equation a=1+b to obtain the value of a.
[tex]\begin{gathered} a=1+0 \\ a=1 \end{gathered}[/tex]So quadratic equation for a=1, b=0 and c=1 is,
[tex]y=x^2+1[/tex]Find the volume of this object.Use 3 for a.Volume of a CylinderV=Tir2h4 cm7 cm8 cm]1 cm V ~ [?]cm31
Answers
Explanation
The volume of the object is the sum of the volumes of the composite solids that make up the object. Since each solid is a cylinder, we will make use of the formula below.
[tex]\text{Volume of a cylinder =}\pi r^2h[/tex]The question gives the following parameters for the solids
[tex]\begin{gathered} \text{Solid 1 }\mleft\lbrace r=\frac{4}{2}=2;h=7\mright\rbrace \\ Solid\text{ 2 }\mleft\lbrace r=\frac{8}{2}=4;h=1\mright\rbrace \\ \text{where }\pi=3 \end{gathered}[/tex]We can substitute the parameters into the formula.
[tex]\begin{gathered} \text{Volume of solid 1=}3\times2^2\times7=84\operatorname{cm}^3 \\ \text{Volume of solid 2 = }3\times4^2\times1=48cm^3 \end{gathered}[/tex]Therefore;
[tex]\text{Volume of the object }=84+48=132\operatorname{cm}^3[/tex]Answer:
[tex]132\operatorname{cm}^3[/tex]Evaluate the expression −2ln(e^2 −12)+8
Answers
Solve
[tex]\begin{gathered} -2\ln (e^2-12)+18 \\ -2\ln (7.389-12)+18 \\ -2\ln (-4.611)+18 \end{gathered}[/tex]Answer: Undefined solution
simply 3 (sqrt(c^2)) if c is > or equal to 0I can upload a picture
Answers
Recall that:
[tex]\begin{gathered} \text{For all x}\in\R \\ \sqrt[]{x^2}=|x|\text{.} \end{gathered}[/tex]Therefore:
[tex]3\sqrt[]{c^2}=3|c|\text{.}[/tex]Now, since c≥0, we get that:
[tex]|c|=c\text{.}[/tex]Substituting the above result in 3|c| we get:
[tex]3\sqrt[]{c^2}=3c\text{.}[/tex]Answer:
[tex]3c\text{.}[/tex]find the slope of the line through the giving points-1 -5 and 1 -1
Answers
the given points are
(x1 , y1) = (-1 , -5) and ()x2, y2) = (1 , -1)
the slope of the line is given as follows,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\begin{gathered} m=\frac{-1-(-5)}{1-(-1)} \\ m=\frac{-1+5}{1+1}=\frac{4}{2}=2 \end{gathered}[/tex]so the slope is m = 2
Mr. Weinberg harvests apples from his apple tree each autumn. As the tree has matured since it's first crop, the weight in lbs, W, of the apple harvest has increased exponentially by 60% every 4 years according to the function W (t)=80(1.6)^ t/4, where the t is the number of years since the first crop.Based on this model, which is the best estimate for the percent change in the weight of the apple harvest from year to year?-26.5%-15.0%-40.0%-8.8%-12.5%
Answers
Answer:
12.5%
Explanation:
To know the percent of change from year to year, we will calculate the Weight for 2 consecutive years.
So, when t = 0, we get that W is equal to:
[tex]\begin{gathered} W_0=80(1.6)^{\text{ t/4}} \\ W_0=80(1.6)^{\text{ 0/4}} \\ W_0=80 \end{gathered}[/tex]Then, when t = 1, we get:
[tex]\begin{gathered} W_1=80(1.6)^{\text{ t/4}} \\ W_1=80(1.6)^{\text{ 1/4}} \\ W_1=89.97 \end{gathered}[/tex]Now, we can calculate the percentage of change as:
[tex]\frac{W_1-W_0}{W_0}\times100=\frac{89.97-80}{80}\times100=12.47\text{ \%}[/tex]Therefore, the best estimate is 12.5%
If the coefficient of determination is 0.233, what percentage of the variation in the data about the regression line is explained?5.43%76.7%23.3%46.6%
Answers
We need the coefficient of determination definition
The coefficient of determination (R²) is a number between 0 and 1 that measures how well a statistical model predicts an outcome. You can interpret the R² as the proportion of variation in the dependent variable that is predicted by the statistical model
So if we have a coefficient of determination of 0.233 we multiply by 100 to get the percentage
Answer: 23.3%
If PN = 2x + 5 ON =x + 3 and OS = 3x - 2. Solve for ps
Answers
Remember that
In a rectangle
opposite sides are parallel and congruent and the measure of the interior angles are 90 degrees
The diagonals are congruent
so
PS=ON
PO=SN
PN=OS
equate the equations of diagonals
PN=2x+5
OS=3x-2
2x+5=3x-2
solve for x
3x-2x=5+2
x=7
Find out PS
Remember that
PS=ON=x+3
substitute the value of x
PS=7+3
Ps=10 unitsThe triangle is a 45°-45°-90° triangle.x√2 = 66²36X =(√2)²x = 18Did not multiply the numerator by the radicalShould have squared the denominator only.No ErrorShould have squared the numerator onlyJUN1O6V2=82
Answers
Answer:
Did not multiply the numerator by the radical
Explanation:
The hypotenuse of a 45-45-90 triangle is equal to the leg times √2.
In this case, the leg is x and the hypotenuse is 6, so we have the following equation
hypotenuse = leg √2
6 = x √2
To solve for x, we get
[tex]\begin{gathered} x\sqrt{2}=6 \\ \\ x=\frac{6}{\sqrt{2}} \end{gathered}[/tex]Then, we need to multiply the numerator and denominator by √2, so
[tex]x=\frac{6}{\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}}=\frac{6\sqrt{2}}{(\sqrt{2})^2}[/tex]Therefore, the solution is equal to
[tex]x=\frac{6\sqrt{2}}{2}=3\sqrt{2}[/tex]Therefore, the error in the process was that they did not multiply the numerator by the radical
the winner in a recent Los Angeles marathon ran the 26-mile race in 2.23 hours. How many yards per minute did he run? Round to the nearest hundredth
Answers
Distance = 26 miles
Time = 2.23 hours
1 mile = 1760 yards
26 m = 26 x 1760 = 45760 yards
1 hours = 60 minutes
2.23 h = 2.23 x 60 = 133.8 minutes
Speed rate = distance / time
Replacing:
S = 45760 y / 133.8 m = 342 yards per minute
Find the approximated area of a circle whose circumference is 7.85.
Answers
The formula of the circumference of a circle is given by:
[tex]C=2\pi r[/tex]Where r is the radius.
By replacing the C-value, we can solve for r:
[tex]\begin{gathered} 7.85=2\pi r \\ r=\frac{7.85}{2\pi} \\ r=1.25 \end{gathered}[/tex]Now, the formula of the area is given by:
[tex]A=\pi r^2[/tex]Replace the r-value and solve for A:
[tex]\begin{gathered} A=\pi(1.25)^2 \\ A=\pi\cdot1.56 \\ A=4.91 \end{gathered}[/tex]The area of the circle is 4.91
A market analyst has projected that the cost of producing d dog leashes will be given by the polynomial10,500 + 3,9d, The revenue generated from the sale of d dog leashes will be given by the polynomial.d14,5 - 0,000030), Find a polynomial expression for the profit earned from producing and selling d dogleashes, Evaluate the expression for da 30,000.© $514,500© $295,650© $280,500© $535,500
Answers
Note that Profit = Revenue - Cost
From the problem, we have :
Revenue = d(14.5 - 0.00003d)
and
Cost = 10,500 + 3.9d
The profit function will be :
[tex]\begin{gathered} \text{Profit}=\text{Revenue}-\text{Cost} \\ \text{Profit}=d(14.5-0.00003d)-(10500+3.9d) \\ \text{Profit}=14.5d-0.00003d^2-10500-3.9d \\ \text{Profit}=-10500+10.6d-0.00003d^2 \end{gathered}[/tex]Substitute d = 30,000
[tex]\begin{gathered} \text{Profit}=-10500+10.6d-0.00003d^2 \\ \Rightarrow-10500+10.6(30000)-0.00003(30000)^2 \\ \Rightarrow280500 \end{gathered}[/tex]Answer :
C. $280,500
Hi, can you help me answer this question please, thank you
Answers
The test statistic, z, is computed as follows:
[tex]z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt[]{n}}}[/tex]where:
x: sample mean
μ: population mean
σ: standard deviation
n: number of samples
Substituting with x = 89.7, μ = 84.9, σ = 13.9, and n = 61, we get:
[tex]\begin{gathered} z=\frac{\bar{89.7}-84.9}{\frac{13.9}{\sqrt[]{61}}} \\ z=2.697 \end{gathered}[/tex]How to find the domain of y=5√(2x-7) +10?
Answers
To find the domain for this function, we can see that the restriction we need to take into account is that the values in the radical must be values equal or greater than zero, so this function can have values in the Real set of numbers. Then, we have:
[tex]y=5\sqrt[]{2x-7}+10[/tex]We need to evaluate:
[tex]2x-7\ge0[/tex]Then, add 7 to both sides of the inequality, and then dividing the inequality by 2 (at both sides again) we have:
[tex]2x-7+7\ge0+7\Rightarrow2x+0\ge7\Rightarrow2x\ge7\Rightarrow\frac{2}{2}x\ge\frac{7}{2}_{}\Rightarrow x\ge\frac{7}{2}[/tex]We have that the values for the domain of this function are those for which are equal or greater than 7/2.
We can write the domain of this function in interval notation as follows:
[tex]D=\lbrack\frac{7}{2},\infty)[/tex]The important fact here is that for this function to have a domain and a range in the Real set, we need to have this restriction for this function.
The values of 5 and 10 are 'displacements' of a parent function and do not affect the values for this function to be in the Real Set of numbers.
For example, the value of 5 multiply the function, and the values for the range are greater (for x values) if the function was not multiplied by 5 ( and this does not affect, however, the values for the domain).
The value of 10 makes the function to be shifted 10 units above in the y-axis (and it does not affect the most important restriction found above). However, it does affect the values for the range in the function.
Find the volume of the solid who’s base is the region in the first quadrant bounded by y=x^3, y=1, and the y-acid and who’s cross sections perpendicular to the y axis are equilateral triangles
Answers
The given parameters are:
y=x^3, y=1
From the question,
Use the following equation to solve for xf(x) = 2x-8f(6) =
Answers
I need to figure out how or where to find the standard deviation and mean for this problemGiven that z is a standard normal random variable, compute the following probabilities.a. P(z≤−1.0)b. P(z≥−1)c. P(z≥−1.5)d. P(−2.5≤z)e. P(−3
Answers
a.
P(z≤−1.0)
Using the z - score table, that gives the probabilities to the left side of the z score:
P ( z ≤−1.0) = 0.1587
b. P(z≥−1)
1 - P ( z ≤−1.0) = 1 - 0.1587 = 0.8413
c. P(z≥−1.5)
1 - P(z≤−1.5) = 1 -0.0668 = 0.9332
d. P(−2.5≤z)
P (z ≥ -2.5)
1 - P (z ≤-2.5) = 1 - 0.0062 = 0.9938
e. P(−3
P ( z≤0 ) = 0.5
P ( z ≤ -3 ) = 0.0013
P ( z ≤ 0 ) -P (z < -3) = 0.5 - 0.0013 = 0.4987
need help on value of f(5) for function[tex]f(x) = \frac{1}{4} \times {2}^{x} [/tex]
Answers
Given
The function,
[tex]f(x)=\frac{1}{4}\times2^x[/tex]To find:
The value of f(5).
Explanation:
It is given that,
[tex]f(x)=\frac{1}{4}\times2^x[/tex]Then,
For x=5,
[tex]\begin{gathered} f(5)=\frac{1}{4}\times2^5 \\ f(5)=\frac{1}{4}\times32 \\ f(5)=8 \end{gathered}[/tex]Hence, the value of f(5) is 8.