point Given the information belowhat is the value of x? Be careful identifying each angle.
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6
Explanation
Step 1
Let
[tex]\begin{gathered} \measuredangle QRS=7x-2(\text{blue)} \\ \measuredangle QRT=9x+1(\text{red)} \\ \measuredangle SRT=15\text{ (green)} \end{gathered}[/tex]then
blue +green = red
[tex]\measuredangle QRS+\measuredangle SRT=\measuredangle\text{QRT}[/tex]Step 2
replace and solve for x
[tex]\begin{gathered} \measuredangle QRS+\measuredangle SRT=\measuredangle\text{QRT} \\ (7x-2)+15=9x+1 \\ 7x-2+15=9x+1 \\ 7x+13=9x+1 \\ 7x-9x=1-13 \\ -2x=-12 \\ x=\frac{-12}{-2} \\ x=6 \end{gathered}[/tex]I hope this helps you
Related Questions
Find the volume of the following shape. Round to the tenths place.
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To answer this question we will use the following formula to compute the volume of a cone:
[tex]V=\frac{\pi r^2h}{3}.[/tex]Substituting r=9cm and h=10cm in the above equation we get:
[tex]V=\frac{\pi(9cm)^2(10cm)}{3}=\frac{810\pi cm^3}{3}=270\pi cm^3\approx848.2cm^3.[/tex]Answer: 848.2cm³
Hi, can you help me to solve this exercise please!!
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Trigonometric Functions
The basic trigonometric functions (sine and cosine) are related by the equation:
[tex]\sin ^2\theta+\cos ^2\theta=1[/tex]In θ lies on the quadrant III (170
Determine if the following side lengths could form a triangle. Prove your answer with an inequality 28,50,22
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Remember that
The Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than the measure of the third side
You only need to see that the two smaller sides are greater than the largest side
In this problem
we have
28,50,22
so
28+22 > 50
50 > 50 -----> is not true
therefore
the following side lengths not form a triangleIf f(x) = x2 is reflected over the x-axis and then shifted 3 units down, what isthe equation of the new function, g(x)?O A. g(x) = (- x)2 + 3O B. g(x) = -x - 3O C. g(x) = - x2 + 3O D. g(x) = (- x)2 – 3
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Hello!
First, let me show you the graph of the function f(x) = x²:
The exercise informs that this graph was shifted 3 units down. It means that the parabola must be the same, it just has to pass the y-axis at point -3, because now it passes when y = 0.
So, as we want that function remains the same and only the interception on the Y-axis to be different, the correct alternative is the letter D. g(x) = (- x)² – 3.
Look at the graph of g(x) = (- x)² – 3 below:
what digit is in the
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We must solve for x using the addition principle, the equation is as follows
[tex]\begin{gathered} x+16=-6 \\ x=-6-16 \\ x=-22 \end{gathered}[/tex]In conclusion, the answer is x = -22
The dimensions of a rectangle are 5x+3 and 4x - 6. Write an expression that represents the area of the rectangle.
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Area of a rectangle is given by the formula;
[tex]A=l\times w[/tex]From the question:
l=5x + 3 and w=4x-6
substitute the values into the formula
[tex]A=(5x+3)(4x-6)[/tex]we can open the parenthesis
[tex]A=\text{ 5x(4x-6)+3(4x-6)}[/tex][tex]A=20x^2\text{ -30x + 12x - 18}[/tex][tex]A=20x^2-18x-18[/tex]Hence, the area of the rectangle can be represented by the expression above
how do I find how many circles would be in the 5th term
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You can notice that in the first term there is one circle, in the second term there are three cricles and in the third term are six circles.
Each of the previous term can be expressed as follow:
first term:
[tex]2^0+0=1[/tex]second term:
[tex]2^1+1=3[/tex]third term:
[tex]2^2+2=6[/tex]In gereral, you can write for the (n + 1)th term:
[tex]2^n+n[/tex]Thus, each term of the series can be expressed as the previoues expression indicates. The fourth term is the result for n=3 and the fifth term is the result for n=4. You replace and you obtain:
fifth term:
[tex]2^4+4=16+4=20[/tex]Hence, the fifth term will have 20 circles.
What part of a gallon is 2 qt. 1 pt.?
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SOLUTION
This questions means what is the fraction of 2 quarts 1 pint to gallon.
This means we will convert 2 quarts to pint, then add to 1 pint, then covert the total pint to gallon.
1 quart = 2 pint.
So 2 quarts = 4 pint
Therefore 2 quarts 1 pint = 5 pints.
Also 1 gallon = 8 pints . This means
[tex]1\text{ pint =}\frac{1}{8}\text{ gallons}[/tex]Therefore 5 pints becomes
[tex]\frac{5}{8}\text{ gallons }[/tex]So the answer is
[tex]\frac{5}{8}[/tex]Option D
What is the equation for the nth term of the arithmetic sequence where a1 = 30 and d = –9? an = 30 – 9n an = 30 – 9(n – 1) an = 30 + 9n an = 30 + 9(n – 1)
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Given:
[tex]a_1=30\text{ and d=-9}[/tex][tex]a_n=a_1+(n-1)d[/tex][tex]a_n=30_{}+(n-1)(-9)[/tex][tex]a_n=30_{}-9(n-1)[/tex]I need some help with these three right here, last tutor I had gave me an explanation but didn't actually help me with the answers
Answers
at 1st triangle: all three sides are not similar
second triangle:only two sides are similar
at third triangle all the three sides are similar
X is a normally distributed random variable with mean 52 and standard deviation 7.What is the probability that X is between 45 and 59?Use the 0.68-0.95-0.997 rule and write your answer as a decimal.
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We know that
[tex]\begin{gathered} \mu=52 \\ \sigma=7 \end{gathered}[/tex]If X is a normally distributed random variable with mean 52 and standard desviation 7, the probability that X is between 45 and 59 is represented as
[tex]P(45Then, we must write 45 and 59 as the mean 52 plus or minus a multiple k of the standard desviation 7[tex]\begin{gathered} 45=\mu+\sigma k \\ 45=52+7k \\ 7k=45-52 \\ k=-1 \end{gathered}[/tex]So,
[tex]45=\mu-\sigma[/tex]By a similar calculation
[tex]59=\mu+\sigma[/tex]This means
[tex]P(45taking into account that X is normally distributed and using the 0.68-0.95-0.997 rule[tex]P(\mu-\sigmaSo, P (45 < X < 59) = 0.68Two times a number decreased by four is between -14 and 32.Find the interval for valid values. (The answer should be in interval notation.)
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Since two times a number decreased by four is between -14 and 32, we need to solve the following compound inequality:
[tex]-14<2x-4<32[/tex]In order to solve it, we can apply the same operations on all the parts of the inequality, until we isolate the variable x and find its value.
We obtain:
[tex]\begin{gathered} -14+4<2x-4+4<32+4 \\ \\ -10<2x<36 \\ \\ -\frac{10}{2}<\frac{2x}{2}<\frac{36}{2} \\ \\ -5Now, we need to write the answer using interval notation. Since x can't be -5 nor 18, only the values between them, the interval of valid values is:[tex](-5,18)[/tex]Simplify: 2/5÷2 3/4
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Solution
Solution
[tex]\begin{gathered} \frac{2}{5}\text{ }\div\text{ 2}\frac{3}{4} \\ \\ \frac{2}{5}\text{ }\div\text{ }\frac{11}{4} \\ \\ \frac{2}{5}\text{ }\times\text{ }\frac{4}{11} \\ \\ \frac{8}{55} \end{gathered}[/tex]Final answer
[tex]\frac{8}{55}[/tex]Zу412Which of the following represents the values of x, y, and z?
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The figure for the triangle is,
Consider the triangle ABC and triangle ABD.
[tex]\begin{gathered} \angle ABD=\angle\text{ABC (Common angle)} \\ \angle ADB=\angle BAC\text{ (Each angle 90 degr}e\text{)} \\ \Delta ABD\cong\Delta CBA \end{gathered}[/tex]So ratio of corresponding side is equal.
[tex]\frac{AB}{CB}=\frac{BD}{BA}=\frac{AD}{CA}[/tex]Determine the measure of side AB by using the sides ratio.
[tex]\begin{gathered} \frac{AB}{12}=\frac{12-4}{BA} \\ (BA)^2=12\cdot8 \\ (x)^2=96 \\ x=\sqrt[]{96} \\ =4\sqrt[]{6} \end{gathered}[/tex]Determine the measure of side y.
[tex]\begin{gathered} y^2=x^2-(8)^2 \\ =96-64 \\ =32 \\ y=\sqrt[]{32} \\ =4\sqrt[]{2} \end{gathered}[/tex]Determine the mesure of side z.
[tex]\begin{gathered} z^2=y^2+(4)^2 \\ =32+16 \\ z=\sqrt[]{48} \\ =4\sqrt[]{3} \end{gathered}[/tex]Thus option B is correct.
The Shake Shop sells their drinks in cone-shaped cups that are 7 inches tall. The small size has a diameter of 3 inches, and the large size has a diameter of 5 inches Use 3.14 for it
Answers
We get that the volume of the small cup is:
[tex]V=\frac{1}{3}\cdot\pi\cdot r^2\cdot h=\frac{1}{3}\cdot3.14\cdot(\frac{3}{2})^2\cdot7\approx16.5in^3[/tex]how to solve the area of the box as a product and sum
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From the box we know that the area as a product is given by:
[tex]3x(6x^2-x+9)[/tex]And the result as a sum is given by:
[tex]18x^3-3x^2+27x[/tex]Then:
[tex]3x(6x^2-x+9)=18x^3-3x^2+27x[/tex]1.1.4QueName the segments in the figure below.RSelect all that apply.DASTB. TUC. SRE. QUOGOSDIOTD. RSOF OTH.RSJ. TOL. RSNOTOK RTM. QR
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In my opinion the names are just
QT, QS, QR, RT, RS, ST
Hi I need help I don’t understand and the example bottom doesn’t work
Answers
The vertex of the parabola given is (0,0)
Given the formula for the nth term, state the first 5 terms of each sequence.tn=1/2(2)^n-1
Answers
Given,
The expression is,
[tex]t_n=\frac{1}{2}(2)^{n-1}[/tex]Required
The first five term of the sequence.
Taking n= 1 then,
[tex]t_1=\frac{1}{2}(2)^{1-1}=\frac{1}{2}[/tex]Taking n= 2 then,
[tex]t_2=\frac{1}{2}(2)^{2-1}=\frac{1}{2}\times2=1[/tex]Taking n= 3 then,
[tex]t_3=\frac{1}{2}(2)^{3-1}=\frac{1}{2}\times4=2[/tex]Taking n= 4 then,
[tex]t_4=\frac{1}{2}(2)^{4-1}=\frac{1}{2}\times8=4[/tex]Taking n= 5 then,
[tex]t_5=\frac{1}{2}(2)^{5-1}=\frac{1}{2}\times16=8[/tex]Hence, the first five term of the sequence is 1/2, 1,2, 4, 8.
Point P is the image of P (5,-5) under translation by two units to the left and five units up
Answers
The coordinate of P' = (3, 0)
Explanation:Given:
Point P coordinate = (5, -5)
Point P was translated by 2 units left and 5 units up to get P'
To find:
The coordinates of the image which is P'
To get the coordinate of P', we will move the point P by 2 units to the left (subtract 2 units from the x coordinate) and add 5 units to the y coordinate
[tex]\begin{gathered} Translation\text{ rule:} \\ translation\text{ to the left: \lparen x, y\rparen}\rightarrow\text{ \lparen x-a, y\rparen} \\ where\text{ a is the number of units moved left} \\ \\ translation\text{ up: \lparen x, y\rparen}\rightarrow(x,\text{ y + b\rparen} \\ b\text{ is the number of units moved up} \end{gathered}[/tex][tex]\begin{gathered} Applying\text{ the translation:} \\ a\text{ = 2 units and b = 5 units} \\ (5,\text{ -5\rparen }\rightarrow\text{ \lparen5 - 2, -5 +5\rparen} \\ =\text{ \lparen3, 0\rparen} \\ \\ The\text{ coordinate of P' = \lparen3, 0\rparen} \end{gathered}[/tex]20. In a volleyball game, Caroline served the ball over the net 16 out of 20 times. Whatpercent did she not make her serve over the net?lo
Answers
Given:
Number of times Caroline served the ball over the net out of 20 times = 16
Required: Percentage of Caroline did not make her serve over the net
Explanation:
Number of times Caroline not served the ball over the net out of 20 times
[tex]\begin{gathered} =20-16 \\ =4 \end{gathered}[/tex]Percentage of Caroline did not make her serve over the net
[tex]\begin{gathered} =\frac{4}{20}\cdot100\% \\ =20\% \end{gathered}[/tex]Final Answer: Percentage of Caroline did not make her serve over the net is 20%.
lent/Dependent Variables Lesson 22 WHITBY (Block5-6th Grade MATH-Whitby) CTABLO [GRAPTO PROCESS 5 5 [EQUATION (VARIABLES] [VERBAL DESCRIPTION) Independent variable: A baker con produco 40 cookios (0) every hour (h). Dependent variable: What is the DEPENDANT variable in this problem? * (1 Point) O number of hours Activate Wing Go to Settings to total number of cookies a
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In the problem, the number of cookies depend upon the number of hours, as increase in number of hours increase number of cookies and decrease in number of hours decrease the number of cookies.
So cookies is dependent variable and number of hours is independent variable.
Thus, dependent variable is number of cookies.
If P={1,3,6,7,9} and Q={1,2,4,5,6,7,8), find P n Q.{}{1, 2, 3, 4, 5, 6, 7, 8, 9}{1, 6, 7}{2, 3, 4, 5, 8, 9}
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Given:
P={1,3,6,7,9}
Q={1,2,4,5,6,7,8)
We have to find P ∩ Q.
The symbol ∩ insdicates intersection. So, P ∩ Q indicates the intersection of P and Q.
The intersection of two sets P and Q is the set of all elements that are common in both P and Q.
The elements common in both P and Q are 1, 6, 7.
Therefore, P ∩ Q={1, 6,7}.
P= a+b+c. Solve for b
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We are given
[tex]P=a+b+c[/tex]We are to solve for b
This simply means we are to make b the subject
Hence we have
[tex]\begin{gathered} P-a-c=b \\ b=P-a-c \end{gathered}[/tex]Therefore, the solution is
[tex]b=P-a-c[/tex]Ivanna bought some books. She spent a total of $71 after a discount of $5 off of her total purchase. Each book cost $4. How many books did she buy?Write an equation that could be used to answer the question above.
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Answer:
19 books
Explanation:
Let the amount of books bought be x
If she spent a total of $71 after a discount of $5, the total amounshe spend on the books will be $76
If each book costs $4,
x books will cost $76
Cross multiply
1 * 76 = x * 4
76 = 4x
Rearrange
4x = 76
Divide both sides by 4
4x/4 = 76/4
x = 19
Hence she bought 19 books
Simplify 110011two × 101 two
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SOLUTION:
We want to multiply the following binary numbers;
[tex]110011_2\times101_2[/tex]It would be really convenient to convert this to base ten, multiplying and then reconverting to base 2;
[tex]\begin{gathered} 110011_2=51_{10} \\ 101_2=5_{10} \end{gathered}[/tex]Thus, the multiplication gives;
[tex]51\times5=255_{10}[/tex]Converting this back to binary we have the result;
[tex]110011_2\times101_2=11111111_2[/tex](9) If an angle is 26° greater than its supplement, find the measure of the angle.
Answers
Answer: 103°
Step-by-step explanation:
Let the angle be x
Angle 26° greater than x is x + 26
sum of two supplementary angles is 180°
Now,
x + x + 26 = 180
⇒ 2x + 26 = 180
⇒ 2x = 154
⇒ x = 77
So required angle = 77 + 26 = 103°
Rewrite in simplest terms: 5w 9( 6W + 9)
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we multiply each term of the parenthesis by -9
[tex]\begin{gathered} 5w+(6w\times-9)+(9\times-9) \\ 5w-54w-81 \end{gathered}[/tex]simplify doing the subtract between terms with w
[tex]\begin{gathered} (5-54)w-81 \\ -49w-81 \end{gathered}[/tex]Solution
[tex]-49w-81[/tex]Loretta has a patio in the shapea trapezoid. The floor of the patio is shown in the sketch below.12 feet5 feetWood PlanksBrick15 feetLoretta wants to put trim around the edge of the floor of the patio that is wood planks that does notshare an edge with the brick part. How many feet of trim will she need?
Answers
We can calculate the width of the rectangle patio with pythagorean theorem:
[tex]\begin{gathered} \text{Base of triangle=15-12=3} \\ c^2=a^2+b^2 \\ 5^2=3^2+b^2 \\ b=\sqrt[]{25-9} \\ b=\sqrt[]{16} \\ b=4 \end{gathered}[/tex]Then, she need to put trim on the edge of the floow of the patio that is wood planks and DOES NOT share and edge with the brick part:
[tex]\begin{gathered} T=12+4+12 \\ T=28\text{ feet} \end{gathered}[/tex]Loretta need to put 28 feet of trim.
Simplify and state restrictions. Show the factors before cancelling. 2x2-6x x2-9 . 4x3+28x2 x2+8x+15
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Solution:
Given:
[tex]\frac{2x^2-6x}{x^2-9}\div\frac{4x^3+28x^2}{x^2+8x+15}[/tex][tex]\begin{gathered} \frac{2x^2-6x}{x^2-9}\times\frac{x^2+8x+15}{4x^3+28x^2} \\ \\ To\text{ simplify the expression, we n}eed\text{ to factorize each expression and cancel them out.} \\ \text{Hence,} \\ \frac{2x(x-3)}{(x-3)(x+3)}\times\frac{(x+3)(x+5)}{4x^2(x+7)} \end{gathered}[/tex]Canceling out the common factors,
[tex]\begin{gathered} \frac{2x(x-3)}{(x-3)(x+3)}\times\frac{(x+3)(x+5)}{4x^2(x+7)} \\ \frac{(x+5)}{2x(x+7)} \end{gathered}[/tex]Thus,
[tex]\frac{2x^2-6x}{x^2-9}\div\frac{4x^3+28x^2}{x^2+8x+15}=\frac{(x+5)}{2x(x+7)}[/tex]The restrictions will occur for the expression to be undefined.
The expression will be undefined when the denominator is zero.
[tex]\begin{gathered} \frac{(x+5)}{2x(x+7)} \\ \text{Hence,} \\ 2x(x+7)=0 \\ 2x=0\text{ OR x + 7 = 0} \\ x=\frac{0}{2}\text{ OR x = 0 - 7} \\ x=0\text{ OR x = -7} \\ \\ \text{Hence, there are restrictions at x = 0 and x = -7 because the expression will be undefined at these two points} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \frac{(x+5)}{2x(x+7)}\text{ will have the following restrictions,} \\ x\ne0\text{ and x }\ne-7 \end{gathered}[/tex]