The measurement of ∠STU is 20°.
Define Angle
When two rays are connected at their endpoints, they form an angle in geometry. We refer to these rays as the angle's sides or arms.
Components of an Angle
An angle is composed of the arms and the vertex as its two basic components:
The arms of the angle: The arms of the angle are the two rays that combine to form it at a common point.Point of the angle: The two rays share a vertex as a common terminus.Given, ∠STU = [tex](\frac {1}{4} x+8)[/tex]°
∠UTV = x+2°
Given, that the line TV bisects ∠STU,
∠STV = ∠UTV
Substitute their values,
[tex](\frac {1}{4} x+8)[/tex]° = x+2°
Calculating,
[tex]\frac{1}{4}x-x[/tex] = 2-8
[tex]-\frac{3}{4}x[/tex] = -6
x = [tex]-6*(-\frac{4}{3})[/tex]
x = 8
So, we know that:
∠STU = ∠STV + ∠UTV
= [tex](\frac {1}{4} x+8)[/tex]° +( x+2°)
= [tex](\frac {5}{4} x+10)[/tex]
Now, substitute the value of x,
∠STU = [tex](\frac {5}{4} )*8[/tex]°+10°
= 10° + 10°
= 20°
Therefore, the measure of ∠STU is 20°.
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help me out with this question..this is a k11..remember this is a practice question not a graded one
Each flight has a probability of 60% or 0.6 of being on time. This means that its complement, or the probability that the flight isn't on time is:
[tex]\text{\textasciitilde{}P(on time)}=1-0.6=0.4[/tex]It is 40% or 0.4. "~P(on time)" stands for the probability of the flight not being on time.
1. The probability that at least 2 flights are on time is:
To find the probability that 2 or more flights are on time we can fight the probability that "0" or "1" are not on time.
[tex]P(0\text{ on time)}=0.4^9=0.000262144[/tex][tex]\begin{gathered} P(1\text{ on time})=\frac{9!}{1!\cdot(9-1)!}\cdot0.6\cdot(0.4)^8 \\ P(1\text{ on time)}=9\cdot0.6\cdot(0.4)^8=0.003538944 \end{gathered}[/tex][tex]\begin{gathered} P(1\text{ or less on time)}=P(0\text{ on time)}+P(1\text{ on time)} \\ P(1\text{ or less on time)}=0.000262144+0.003538944=0.003801088 \end{gathered}[/tex]The probability of 2 or more flights are on time is:
[tex]P(2\text{ or more on time)}\cdot=1-0.003801088=0.996198912[/tex]The probability of 2 flights or more are on time is 0.996198912
2.
We need to calculate the probabilities of 7,8 and 9 flights are on time and then subtract by 1.
[tex]\begin{gathered} P(7)=\frac{9!}{7!\cdot(9-7)!}\cdot0.6^7\cdot0.4^2 \\ P(7)=36\cdot0.6^7\cdot0.4^2=0.161243136 \end{gathered}[/tex][tex]\begin{gathered} P(8)=\frac{9!}{8!\cdot(9-8)!}\cdot0.6^8\cdot0.4 \\ P(8)=9\cdot0.6^8\cdot0.4=0.060466176 \end{gathered}[/tex][tex]P(9)=0.6^9=0.010077696[/tex]The probability of at most 6 flights are on time is:
[tex]\begin{gathered} P(6\text{ or less on time) = 1 - (}P(7)+P(8)+P(9)) \\ P(6\text{ or less on time) = 1-(0.161243136+0.060466176+0.010077696)=}0.768212992 \end{gathered}[/tex]The probability of 6 or less are on time is 0.768212992.
3.
The probability of exactly 5 flights are on time is:
[tex]\begin{gathered} P(5)=\frac{9!}{5!(9-5)!}0.6^5\cdot0.4^4 \\ P(5)=126\cdot0.6^5\cdot0.4^4=0.250822656 \end{gathered}[/tex]The probability of exactly 5 flights are on time is 0.250822656.
laws exponents multiplication band power to a power simplifymake it small steps please the smallest you can like the minimum steps
Answer:
-64x^12
Explanation:
Given the expression
m = -4x^4
You are to look for m^3 as shown;
[tex]\begin{gathered} m=-4x^4 \\ m^3\text{ = (-4x}^4\text{)}^3 \\ m^3=(-4)^3\times(x^4)^3 \end{gathered}[/tex]Open the bracket:
[tex]\begin{gathered} (-4)^3\text{ }\times(x^4)^3\text{ = (-4}\times-4\times-4\text{)}\times x^{^{12}} \\ (-4)^3\text{ }\times(x^4)^3\text{ = (16}\times-4\text{)}\times x^{^{12}} \\ (-4)^3\text{ }\times(x^4)^3=-64x^{12} \end{gathered}[/tex]THe correct answer is -64x^12
an arithmetic sequence has these properties: a1=2an = an-1 + 5 what are the first four terms of the sequence?
we have that the arithmetic sequence have:
[tex]\begin{gathered} a_1=2 \\ a_n=a_{n-1}+5 \end{gathered}[/tex]so we can replace for n=2,3,and 4 to find the first four terms so:
for n=2
[tex]\begin{gathered} a_2=a_{2-1}+5 \\ a_2=a_1+5 \\ a_2=2+5 \\ a_2=7 \end{gathered}[/tex]for n=3
[tex]\begin{gathered} a_3=a_{3-1}+5 \\ a_3=a_2+5 \\ a_3=7+5 \\ a_3=12 \end{gathered}[/tex]and for n=4
[tex]\begin{gathered} a_4=a_{4-1}+5 \\ a_4=a_3+5 \\ a_4=12+5 \\ a_4=17 \end{gathered}[/tex]So the first four numbers are
[tex]2,7,12,17[/tex]Complete the similarity statement relating the three triangles in the diagram. Show work.
Answer:
[tex]\Delta JKM\approx\Delta MKL\approx\Delta JML[/tex]Explanation:
There are three right angled triangles are in the diagram of three different sizes.
Identify the right angles.
In the first triangle, the right angle is angle M. In the second one, the right angle is angle K and in the third triangle, it is angle K.
Now, identify the shortest sides of each.
The shortest side in the first triangle is MJ, in the second triangle, it is JK and in the third triangle, it is MK.
In the given triangle JKM, notice that JK is the shortest side and angle K is the right angle. Write the other two tringles also in the similar form with the first two letters gives the short side and middle letter represents the right angle.
So, the similarity statement is
[tex]\Delta JKM\approx\Delta MKL\approx\Delta JML[/tex]point(10) On Myra's family vacation, her mom drove on the highway at aconstant speed of 60 miles per hour. Based on this rate, which of thefollowing times and miles driven are correct? Select all that apply. GRP.30190 miles driven in 3 hours150 miles driven in 2.5 hours30 miles driven in 30 minutes
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 19.6 feet
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]
The area of circular pound is 21.5 m2. Work out the diameter of the circle. Give your answer correct to the nearest centimetre.
The diameter of the circle is 5.2m.
The area of circular pond is 21.5 m2
area of a circle is given by the formula
area = πr²
21.5 = 3.14 r²
r² = 6.84
r = ±2.6
r is a length and it cannot be negative
So, r = 2.6
Diameter is twice of radius
d = 2r
d = 2(2.6)
d = 5.2
Therefore, the diameter of the circle is 5.2m.
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6. Chester paid a $30 membership fee to a toddler gym and $8 for each of 6 tumbling
classes for his son. The expression 30 + 8 x 6 can be used to evaluate the total cost
of the program. Is the cost $228 or $78? Explain.
Answer:
$78
Step-by-step explanation:
pemdas says we multiply then add
8x6+30
48+30
78
It is $78 and not $228 because we do not add first when doing order of operations and when we multiply first we get 78 also it’s each tumbling is 8 dollars and there were 6 of them so we just multiply the cost by each tumbling and add the membership fee after.
Hopes this helps please mark brainliest
What number is in the hundreds place after
simplifying?
(21 × 10¹)+(3×
X
10²) + (9 × 10²)
a) 4
b) 1
c) 3
d) 7
The digit in the hundreds place is 4
From the question, we have
(21 × 10¹)+(3×10²) + (9 × 10²)
=210+300+900
=1410
The digit in the hundreds place is 4 and the value is 400.
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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ſ x - 5y = -9( 4x + 4y = - 12Step 1 of 2: Determine if the point (-4,1) lies on both of the lines in the system of equations by substituting theordered pair into both equations.
Given:
[tex]\begin{gathered} x-5y=-9\ldots\ldots(1) \\ 4x+4y=-12\ldots\text{.}\mathrm{}(2) \end{gathered}[/tex]The given point is (-4,1)
Let's check the ordered pair (-4,1) in the first equation
[tex]\begin{gathered} x-5y=-9 \\ (-4)-5(1)=-9 \\ -4-5=-9 \\ -9=-9 \end{gathered}[/tex]Hence, (-4,1) is a solution of the first equation x-5y=-9.
Now, let's check (-4,1) in the second equation.
[tex]\begin{gathered} 4x+4y=-12 \\ 4(-4)+4(1)=-12 \\ -16+4=-12 \\ -12=-12 \end{gathered}[/tex]So, (-4,1) is a solution of the second equation 4x+4y=-12.
Hence, (-4,1) is a solution of both equation in the system, then it is a solution to the overall system.
help meeeeeeeeeeeeeeeeeeee pleaseee rnnnn rn!!!!
The length of short side x is 4.5 units, the length of short side x+5 is 9.5 units and the length of longest side is 10.5 units.
By Pythagorean theorem,
[tex]( Hypotenuse)^{2} = (Base)^{2}+ (Perpendicular)^{2}[/tex]
Let base = x+5
perpendicular = x
Hypotenuse = x+6
[tex](x+6)^{2} = x^{2} +(x+5)^{2}[/tex]
[tex]x^{2} +12x+36 = x^{2} +x^{2}+10x+25[/tex][tex]2x^{2} +10x+25-x^{2} -12x-36=0[/tex]
[tex]x^{2} -2x-11=0[/tex]
[tex]x = \frac{-(-2) + \sqrt{4 - 4(1)(-11)} }{2*1}[/tex] or [tex]\frac{-(-2) - \sqrt{4 - 4(1)(-11)} }{2*1}[/tex]
[tex]x=\frac{2 + \sqrt{4 +44} }{2}[/tex] or [tex]\frac{2 - \sqrt{4 +44} }{2}[/tex]
[tex]x = \frac{2 + \sqrt{48} }{2}[/tex] or [tex]\frac{2 - \sqrt{48} }{2}[/tex]
[tex]x = \frac{2+2\sqrt{12} }{2}[/tex] or [tex]\frac{2-2\sqrt{12} }{2}[/tex]
[tex]x = 1+\sqrt{12}[/tex] or [tex]1-\sqrt{12}[/tex]
[tex]x = 1+3.5[/tex] or [tex]1-3.5[/tex]
[tex]x = 4.5[/tex] or [tex]-2.5[/tex]
As, length can't be negative, we will take x = 4.5
Therefore, x = 4.5
x + 5 = 4.5 + 5
= 9.5
x + 6 = 4.5 + 6
= 10.5
Hence, the length of short side x is 4.5 units, the length of short side x+5 is 9.5 units and the length of longest side is 10.5 units.
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Charlotte states that (43)3
can be rewritten as 218
. Which of the following explains how she is correct? Select all that apply.
The statement that explains why Charlotte's submission is correct is that (4³)³ simplifies to (4⁹) and (4⁹) simplifies to 2¹⁸
How to determine why Charlotte's submission is correct?From the question, the expression is given as
(43)3
Rewrite the expression properly
So, we have the following representation
(4³)³
Apply the law of indices to rewrite the exponents in the expression properly
So, we have
(4³)³ = 4³*³
Next, we evaluate the products
So, we have the following notation
(4³)³ = 4⁹
Solving further, we need to express 4 as the square of 2
So, we have
(4³)³ = (2²)⁹
Apply the law of indices to rewrite the exponents in the expression properly
So, we have
(4³)³ = 2²*⁹
Next, we evaluate the products
So, we have the following notation
(4³)³ = 2¹⁸
Hence, Charlotte's expression is correct
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Possible question
Charlotte states that (4³)³ can be rewritten as 2¹⁸. Which of the following explains how she is correct? Select all that apply.
Help
In 1846 the depth of the river was 5 feet deep.
In 1847 it dropped to 3.8 feet.
This year, 1848, it rose to 6.4 feet.
Find the percent change in river depth & complete the table.
The percent change in river depth is 52%
How to calculate the percentage?From the information, the depth of the river was 5 feet deep, it dropped to 3.8 feet and in 1848, it rose to 6.4 feet. The new feet will be:
= -5 - 3.8 + 6.4
= 2.4
Therefore, the percentage change will be:
= New feet / Initial feet × 100
= (5 - 2.4) / 5 × 100
= 2.6 / 5 × 100
= 52%
Note that there was no table given.
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1. Mr. Z's class has 18 boys and 22 girls. What is the ratio of girls to boys?
2. What is the ratio of boys to total students?
3. What is the ratio of girls to total students?
while shopping for clothes, Daniel spent $26 less than 2 times what curtis spent. Daniel spent $10. write and solve an equation to find how much curtis spent. let x represent how much curtis spent
while shopping for clothes, Daniel spent $26 less than 2 times what curtis spent. Daniel spent $10. write and solve an equation to find how much curtis spent. let x represent how much curtis spent
Let
x ------> amount that Curtis spent
we have that
10=2x-26 ------> equation that represent this situation
solve for x
2x=10+26
2x=36
x=$18
therefore
Curtis spent $18……………………………………………………..
?
Please type what you are trying to solve or any questions that you would like answers for.
solveeeeeeeeeeeee for x
Answer:
7.5/3
Step-by-step explanation:
set AC and BD equal to eachother because they are equal and solve
Type the correct answer in each box. Use numerals instead of words. This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form? Graph shows upward parabola plotted on a coordinate plane. The parabola has vertex at (2, minus 8) with the left slope at (0, 0) and the right slope at (4, 0).
The function’s equation written in factored form and in vertex form are respectively;
f(x) = 2x(x - 4)
f(x) = 2(x - 2)² - 8
How to Interpret Quadratic Graphs?The factored form of a quadratic function is;
f(x) = a(x - p)(x - q)
where:
p and q are the x-intercepts
a is a constant
Now, we are given x-intercepts as; (0, 0) and (4, 0)
Thus;
f(x) = a(x - 0)(x - 4)
f(x) = ax(x - 4)
To find a, substitute the given vertex (2, -8) into the equation and solve for a:
2a(2 - 4) = -8
-4a = -8
a = 2
Thus;
f(x) = 2x(x - 4)
The vertex form of a quadratic equation is;
f(x) = a(x - h)² + k
where:
(h, k) is the vertex
a is constant
Since vertex is (2, -8), then we have;
f(x) = a(x - 2)² - 8
Put the coordinate (0, 0) to find a;
0 = a(0 - 2)² - 8
4a = 8
a = 2
Thus;
f(x) = 2(x - 2)² - 8
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Use the elimination method to solve the system of equations.3x + 4y = 8x - y = 12
Answer:
We have to use to elimination method to solve the provided system of equations, this method essentially involves eliminating one of the variables in the first equation by adding or subtracting a multiple of the second equation:
[tex]\begin{gathered} 3x+4y=8\rightarrow(1) \\ \\ x-y=12\rightarrow(2) \end{gathered}[/tex]The elimination of the variable y in equation (1) is achieved by adding the 4 times the equation 2 into the equation (1), the steps of the process are as follows:
[tex]\begin{gathered} 3x+4y=8 \\ \\ + \\ \\ 4\times(x-y)=4\times12 \\ \\ ------------------------------- \\ \\ 3x+4x=8+48 \\ \\ \\ 7x=56 \\ \\ \\ x=8 \end{gathered}[/tex]We have found the x value, the last step is to plug in the variable x value in any of the (1) or (2) equations, and solve for the y variable, the steps are as follows:
[tex]\begin{gathered} x-y=12 \\ \\ x=8 \\ \\ \therefore\Rightarrow \\ \\ 8-y=12\rightarrow y=8-12=-4 \\ \\ y=-4 \end{gathered}[/tex]The final answer is as follows:
[tex](8,-4)\Rightarrow\text{ Option \lparen B\rparen}[/tex]Therefore the answer is Option(B).
Solve for z in -3 < z-1 < 3.Give the result in the interval notation and graph on a number line
Answer:
(-2,4)
Explanation:
Given the inequality:
[tex]-3First, we add 1 to all parts of the inequality.[tex]\begin{gathered} -3+1We can represent this in interval notation as:[tex](-2,4)[/tex]The solution set is graphed on the number line below:
Suppose that h(x) varies inversely with x and h(x)=50 when x = 0. 25. What is h(x) when x = 2?.
If h(x) varies inversely with x , then the value of h(x) is 6.25 , when x = 2 .
In the question ,
it is given that ,
the function h(x) varies inversely with x ,
that means h(x) ∝ 1/x ,
to remove the proportionality sign , we write the constant of proportionality "k",
h(x) = k*(1/x)
given , that h(x)=50 when x = 0. 25
Substituting the values we get
50 = k*(1/0.25)
50 = k/0.25
k = 50×0.25
k = 12.5
So , the equation becomes
h(x) = 12.5/x
to find the value of h(x) when x = 2, we put x = 2 , in the equation ,
h(2) = 12.5/2
= 6.25
Therefore , If h(x) varies inversely with x , then the value of h(x) is 6.25 , when x = 2 .
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Solve. −45 = −2b + 3 + 8b
Answer:
b= -8
Step-by-step explanation:
just trust me dude. I know what I'm doing
Which expression is a factored form of −32m+96 −8(4m+12) 32(−m−3) 16(−2m+6) 32(−m+3)
Answer:
32(−m+3)
Step-by-step explanation:
1. Find the greatest common factor.
32 is the GCF
2. Factor.
32(-m + 3) -- you can check with distrubutive property.
Solve the equations.a) 4t^2 - 5t = 0d) (y + 6)(y - 6) = - (y + 6)^2h) h) (u - 4)(u + 4) = (u + 2)(u - 2).
The equations are given
a) 4t^2 - 5t = 0
d) (y + 6)(y - 6) = - (y + 6)^2
h) (u - 4)(u + 4) = (u + 2)(u - 2).
Explanationa. 4t^2 - 5t = 0
[tex]\begin{gathered} t(4t-5)=0 \\ t=0,4t-5=0 \\ t=0,t=\frac{5}{4}=1.25 \end{gathered}[/tex]d. (y + 6)(y - 6) = - (y + 6)^2
[tex]\begin{gathered} y^2-6y+6y-36=-(y^2+36+12y) \\ y^2-36=-y^2-36-12y \\ y^2+y^2+36-36+12y=0 \\ 2y^2+12y=0 \\ 2y(y+6)=0 \\ y=0,y=-6 \end{gathered}[/tex]h. (u - 4)(u + 4) = (u + 2)(u - 2).
[tex]\begin{gathered} u^2+4u-4u-16=u^2-2u+2u-4 \\ u^2-16=u^2-4 \\ u^2-16-u^2+4=0 \\ -12\ne0 \end{gathered}[/tex]Answer
Hence the solution to the equations are
[tex]\begin{gathered} a.t=0,1.25 \\ d.\text{ y=0,-6} \\ h.\text{ no solution} \end{gathered}[/tex]If ABCD is dilated by a factor of 2, thecoordinate of B' would be:543С2B1-8 -7-6-5-4-3-2-1 012.34567891011-1A-2D-3B' = ([?], [ ]=4Cotor
We have a figure ABCD that is dilated by a factor of 2.
We have to find the coordinate of the image point B'.
If the center of dilation is the origin (0,0) and the factor is k = 2, we can write the rule:
[tex](x,y)\longrightarrow(2x,2y)[/tex]Then, for B(-1,1), we will get:
[tex]B=(-1,1)\longrightarrow B^{\prime}=(2\cdot(-1),2\cdot1)=(-2,2)[/tex]Answer: B' = (-2,2)
the product of 5 - 2i and i is
Answer:
5i + 2
Step-by-step explanation:
(5-2i)(i)
5i - 2i^2
i^2= -1
5i -2(-1)
= 5i + 2
Hello, I need help solving is and finding the checkpoints
161 feet lower
166 feet
Explanationsa) Given the following parameters
Distance of checkpoint 3 above the sea = -197 feet
Distance of checkpoint 5 above the sea = -36 feet
Determine the distance between the checkpoints
Distance = checkpoint 5 - (checkpoint 3)
Distance = -36 - (-197)
Distance = -36 + 197
Distance = 161feet
Hence checkpoint 3 is 161 feet lower than checkpoint 5
b) If the top of the hill is 363feet above check point 3, the altitude of the top of the hill is given as:
Altitude = -197 + 363
Altitude = 166feet
Hence the altitude of the top of the hills is 166feet
6. Find the are of the Rectangle
776
in
13
in
Answer:
about 3.09
Step-by-step explanation:
A = l x w
A = 13/7 x 7/6
A = 1.857 x 1.666
A = 3.09
Hope it helps!
Which of the following equation has one solution?
Responses
4x + 2x = 6x - 4
3 (2x + 4) = 2 (2x - 4)
5(x - 3) = 5x - 3
2x = 2x + 4
a) 4x + 2x = 6x - 4
= 6x = 6x - 4
cannot be solved further.
b) 3(2x + 4) = 2(2x - 4)
= 6x + 12 = 4x - 4
(bring the numbers and variables on one side)
= 6x + 4x = 12 - 4
10x = 8
x = 8/10 = 4/5
can be solved.
c) 5(x - 3) = 5x - 3
= 5x - 15 = 5x - 3
= (bring the variables and numbers on one side)
5x + 5x = -15 - 3
= 10x = -18
x = -18/10 = 9/5
can be solved
d) 2x = 2x + 4
= 2x + 2x = 4
= 4x = 4
x = 4/4 OR 1.
THUS, (B, (C AND (D CAN BE SOLVED WITH ONE SOLUTION.find 3 consecutive odd integers when the sum of the first and third integer is 26
Let's call the first odd number x.
The next odd number will be x + 2, and the last one will be x + 4.
If the sum of the first number and the last one is 26, we have that:
[tex]\begin{gathered} x+x+4=26 \\ 2x+4=26 \\ 2x=22 \\ x=\frac{22}{2}=11 \end{gathered}[/tex]So the numbers are:
[tex]\begin{gathered} x\to11 \\ x+2\to13 \\ x+4\to15 \end{gathered}[/tex]11, 13 and 15.