In this case, we are given the value of one angle and told to find the value of angle x. To do so, we will try to relate them based on the position they have in the diagram.
Notice that the two parallel lines split the space into two. One space is in between the lines, and the other space is outside the lines. We can see that both angles are located outside of the parallel lines.
Now, see that the third line splits the space into two. One space is on the left of the third line, and the other one is on the right of the third line. From the diagram, we can tell that each angle is on an opposite side of the third line.
This two relations between these angles (being outside the parallel lines and on opposite sides of third line) gives them the name of alternate outer angles. This angles have the property that they have the same measure.
So, we have the following
[tex]x=56[/tex]so the measure of x, in degrees, is 56°.
WILL MARK BRAINLIEST. Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it
Answer:
The axis of symmetry is -4 because the axis of symmetry is equal to h, in the vertex form!
— 3х + 2 = -4х + 4 need help
Given the following equation:
[tex]-3x+2=-4x+4[/tex]You need to solve for "x" in order to find its value and solve the equation. To do this, you can follow the steps shown below:
1. You need to apply the Subtraction property of equality by subtracting 2 from both sides of the equation:
[tex]\begin{gathered} -3x+2-(2)=-4x+4-(2) \\ -3x=-4x+2 \end{gathered}[/tex]2. Now you can apply the Additio property of equality by adding "4x" to both sides of the equation:
[tex]\begin{gathered} -3x+(4x)=-4x+2+(4x) \\ x=2 \end{gathered}[/tex]Therefore, you get that the solution is:
[tex]x=2[/tex]A school offers band and chorus classes. The table shows the percents of the 1200 students in the school who are enrolled in band, chorus, or neither class. How many students are enrolled in both classes?
Class Enrollment
Band 34%
Chorus 28%
Neither 42%
168 students are enrolled in both classes.
This is a problem from set theory. We can solve this problem by following a few steps easily.
First of all, we have to calculate the students present in both classes.
Student present in both classes = the total student - the student not enrolled in both classes.
So the percentage of the students enrolled in both classes or any of one class is ( 100% - 42% ) = 58%.
Now, the students only enrolled in chorus class is ( 58% - 34%) = 24%
So, the students who joined both classes is ( 28%- 24%)= 4%
The total student is 1200, then 4% of the total student is
( 1200 × 14 )/100 = 168 students.
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Juan took out a $5000 loan for 292 days and was charged simple interest.
The total interest he paid on the loan was $336 As a percentage, what was the annual interest rate of Juan's loan?
Assume that there are 365 days in a year
Since the total interest he paid on the loan was $336. Then, The annual interest rate of Juan's loan if there are 365 days in a year will be as at 8.4%.
What is Simple Interest?Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.
For example, when a person takes a loan of Rs. 5000, at a rate of 10 p.a. for two years, the person's interest for two years will be S.I. on the borrowed money.
The formula of simple interest is given as:
S.I = PRT
Where:
P = principalR = rateT = timeSubstituting the values and solving for the rate on the loan
r = {A} {PT}\r
= {5336} {5000*292}
r = 8.4 %
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On average, Peter goes through three fish hooks in order to catch 7 fish. How many hooks can he expect to use if he needs to catch 189 fish?
By solving a proportional relation, we conclude that he needs 81 hooks to catch 189 fish.
How many hooks can he expect to use if he needs to catch 189 fish?We assume there is a proportional relationship of the form:
F = k*H
where:
F = number of fish.k = constant of proportionality.H = number of hooks.We know that with 3 hooks he catches 7 fish, then we can replace that:
7= k*3
7/3 = k
So the proportional relation is:
y = (7/3)*x
Then if he wants to get 189 fish we can write:
189 = (7/3)*x
And solve this for x:
189*(3/7) = x =81
He will need 81 hooks.
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Rewrite the decimal fraction as a decimal number.
14 25
100
The decimal number of the fraction [tex]14\frac{25}{100}[/tex] is 14.25
The given mixed fraction = [tex]14\frac{25}{100}[/tex]
The mixed fraction is the fraction that consist of one whole number and the simple fraction.
The simple fraction is the fraction that consist of numerator and denominator as whole number. The top term of the simple fraction is called numerator and bottom term is called denominator
The decimal number is a number that consist of one whole number and the fractional part. The fractional parts are separated by a decimal point.
The number is [tex]14\frac{25}{100}[/tex]
Convert the mixed fraction to simple fraction
[tex]14\frac{25}{100}[/tex] = (100×14+25)/100
= 57/4
Convert the simple fraction to decimal number
57/4 = 14.25
Hence, the decimal number of the fraction [tex]14\frac{25}{100}[/tex] is 14.25
The complete question is:
Rewrite the decimal fraction as a decimal number.
[tex]14\frac{25}{100}[/tex]
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Given the right △△DEF, DE = 30, EF = 72 and DF = 78. Find the cos F=
see the figure below to better understand the problem
cos(F)=EF/DF --------> by CAH
substitute given values
cos(F)=72/78
simplify
cos(F)=12/13Option C64x power 9 as a cube of a monomial
Answer:21
Step-by-step explanation:
What is the surface area of the cube below?
A. 96 units²
B. 120 units²
C. 64 units²
D. 80 units²
Answer:
C. 64 units squared
Step-by-step explanation:
do 4•4•4 so 4 • 4 = 16 then 16 • 4 = 64 and since its surface area square it. so the answer would actually be 4096 units
twice a number increased by twenty is at least eighty-five. select all possible value of the number.
31
35
32
30
33
40
20
34
The number when increased by twenty is at least 85, the possible values of the numbers for this are: 35, 33, 40 and 34.
Given, according to the statement in the question, frame the equation:
2x+20 ≥ 85
⇒ 2x + 20 ≥ 85
⇒ 2x ≥ 85 - 20
⇒ 2x ≥ 65
⇒ x ≥ 65/2
⇒ x ≥ 32.5
hence the numbers greater than or equal to 32.5 are 35, 33, 40 and 34.
Hence the possible values of the number are 35, 33, 40 and 34.
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Gross Income 3 Ted gets paid a monthly salary of $5,000 and receives 6% commission on all sales over $8000. 1 point Which of the following is an equation that can be gross income? y = 5000+ 6(x - 8000) y = 5000+.06 (x - 8000) y = 8000 +.06 (x - 5000) O y = 5000+.06 (8000 - 2) Previous 3 4
Given that,
base salary = b = 5000$
Comission rate = 6% = 0.06
Let's say, the sales are = x
As given in the question, he receives 6% commission on all sales over $8000.
Hence, the commissionable amount is (x - 8000) '.' x - 8000 shows the amount greater than 8000, which receives a commission.
hence, gross income will be
base salary + commission * (commisonable amount)
=> 5000 + 0.06 * (x - 8000)
What is the P(A and B) if P(A) = 1/2 and P(B) = 2/7, where A and B are independent events?5/81/71/121/2
EXPLANATION:
To calculate the number of independent events that occur, the product of the probabilities of the individual events occurring must be calculated.
Therefore if A and B are independent events then:
P (A and B) = P (A) • P (B)
The exercise is as follows:
[tex]\begin{gathered} \frac{1}{2}\times\frac{2}{7}=\frac{2}{14};\text{ Now }we\text{ must take }square\text{ r}oot; \\ \frac{2}{14}=\frac{1}{7} \\ \text{ANSWER: }\frac{1}{7} \end{gathered}[/tex]NOTE:
To obtain the product of two fractions, the numerators must be multiplied with each other and the denominators must also be multiplied with each other.
What is the square root of 225As I am new to thisPlease answer step by step in the easiest form possible
Given:
[tex]225[/tex]To Determine: The square root of the given number
Solution
Step 1: Express 225 as the product pf its prime factors of 225
[tex]\begin{gathered} 225=3\times3\times5\times5 \\ 225=3^2\times5^2 \end{gathered}[/tex]Step 2: Separate the factors into their own square root
[tex]\begin{gathered} \sqrt{225}=\sqrt{3^2\times5^2} \\ \sqrt{225}=\sqrt{3^2}\times\sqrt{5^2} \end{gathered}[/tex]Step 3: Solve the individual's squares
[tex]\begin{gathered} \sqrt{225}=\sqrt{3^2}\times\sqrt{5^2} \\ \sqrt{225}=3\times5=15 \end{gathered}[/tex]Hence, the square root of 225 is 15
Find a solution for the equation. x^2-6x-8=0
Given:
[tex]x^2-6x-8=0[/tex]Required:
To find the solution of the given equation.
Explanation:
From the given equation,
[tex]\begin{gathered} a=1 \\ b=-6 \\ c=-8 \end{gathered}[/tex]Now
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Therefore,
[tex]x=\frac{-(-6)\pm\sqrt{(-6)^2-4(1)(-8)}}{2(1)}[/tex][tex]\begin{gathered} x=\frac{6\pm\sqrt{36+32}}{2} \\ \\ =\frac{6\pm\sqrt{68}}{2} \\ \\ =\frac{6\pm2\sqrt{17}}{2} \\ \\ =\frac{2(3\pm\sqrt{17)}}{2} \\ \\ =3\pm\sqrt{17} \end{gathered}[/tex]Final Answer:
The solutions are
[tex]x=3+\sqrt{17},3-\sqrt{17}[/tex]daryl has 1/4 of a pound of chocolate he wants to divide it into 2 equal parts for his siblings how much will each sibling get
To divide the 1/4 of a pound into two equal parts, it is necessary to divide 1/4 by 2, as follow:
(1/4)/2
if 2 is written as 2/1, the previous quotient can be written as a product:
(1/4) (1/2) = 1/8
Now, to write a general expression that takes into account the number of siblings, you name the number of siblings as x. Thus, you have:
(1/4)/(x) = 1/(4x)
Write the point slope form of the line satisfying the given conditions. Then use the point slope form of the equation to write the slope intercept form of the equation. Slope=7Passing through (-6,1)
Ok, so
The point slope form of the line is given by the following formula:
[tex](y-y_1)=m(x-x_1)[/tex]Where
[tex](x_1,y_1)[/tex]Is a point of the line, and m is the slope.
If we replace our values:
Slope = 7
Point = (-6, 1)
We obtain that the equation is:
[tex]\begin{gathered} (y-1)=7(x-(-6)) \\ (y-1)=7(x+6) \end{gathered}[/tex]To find the slope intercept form of the equation, we distribute in the brackets:
[tex]\begin{gathered} y-1=7x+42 \\ y=7x+43 \end{gathered}[/tex]And the equation of our line in the slope intercept form will be:
y=7x+43
Write the equation of the line, with the given properties, in slope intercept form. Slope = -7, through (-6,8)
Given:
The slopr of line is m = -7.
The line passes through point (-6,8).
Explanation:
The equation of line in slope-intercept form is,
[tex]y=mx+c[/tex]Substitute the valus in the equation to determine the value of c.
[tex]\begin{gathered} 8=-7\cdot(-6)+c \\ c=8-42 \\ =-34 \end{gathered}[/tex]So equation of line is y = -7x - 34.
The height, h (in meters above ground), of a projectile at any time, t (in seconds), after the launch is defined by the function h(t) = −5t2 + 13t + 6. The graph of this function is shown below. When rounded to the nearest tenth, what is the maximum height reached by the projectile, how long did it take to reach its maximum height, and when did the projectile hit the ground?
As we can se from the graph, the maximum value of the function is almost 15 meters, it is reached between t=1s and t=2s, and the height is 0 again when the time is approximately 3 seconds.
We can find the exact values by using the equation.
First, find the zeroes of the function by setting h(t)=0 and solving the quadratic equation for t:
[tex]\begin{gathered} h(t)=-5t^2+13t+6=0 \\ \Rightarrow t=\frac{-13\pm\sqrt[]{13^2-4(6)(-5)}}{2(-5)} \\ \Rightarrow t_1=-0.4;t_2=3 \end{gathered}[/tex]Then, the projectile hits the ground at t=3s.
To find the time at which the projectile reaches its maximum height, find the average between both zeroes:
[tex]t_{\max }=\frac{t_1+t_2}{2}=\frac{-0.4s+3s}{2}=1.3s[/tex]To find the maximum height, evaluate h at t=1.3s:
[tex]h(1.3s)=-5(1.3)^2+13(1.3)+6=14.45[/tex]Therefore, to the nearest tenth, the projectile reached a maximum height of 14.5 meters in 1.3 seconds and it took 3.0 seconds for it to hit the ground.
The correct option is the second one.
1 ptsQuestion 22The point A(8,-6) has been transformed using the composition T-15) • r(180,0). Where is A?0 (71)o 17, -1)0 (-7,1)0 (-7, -1)+ Previous
You have to perform two transformations the first one is a 180º rotation with respect to the origin r(180º,O) and the second one is a translation of one unit left and 5 units up T(-1,5)
Given point A(8,-6)
To make a 180º rotation you have to invert the signs of both coordinates, following the rule:
[tex](x,y)\to(-x,-y)[/tex]For point A, the rotation is the following:
[tex]A(8,-6)\to A^{\prime}(-8,--6)=(-8,6)[/tex]Once you rotate the point, you have to perform the translation T(-1,5). The rule for the translation can be expressed as follows
[tex](x,y)\to(x-1,y+5)[/tex]So, the translation of point (-8,6) is:
[tex]A^{\prime}(-8,6)\to A^{\doubleprime}(-8-1,6+5)=(-9,11)[/tex]Can you teach me how to divide fractions?
We illustrate the division of fractions by taking the example below.
[tex]\frac{5}{7}\div\frac{25}{14}[/tex]The first step is to change the division sign to multiplication by changing the fraction after the division sign.
[tex]=\frac{5}{7}\times\frac{14}{25}[/tex]Next, we multiply the numerators together and the denominators together.
[tex]=\frac{5\times14}{7\times25}[/tex]You then simplify by dividing common factors.
[tex]\begin{gathered} \\ =\frac{5}{25}\times\frac{14}{7} \\ =\frac{1}{5}\times2 \\ =\frac{2}{5} \end{gathered}[/tex]What bearing and airspeed are required for a plane to fly 360 miles due north in 2.0 hours if the wind is blowing from a direction of 331 degrees at 15 mph?
Using the vector form of velocity, it is possible to calculate the airspeed and bearing, which are 165.33 mph and 0.7 degrees respectively.
Given:
A plane may go 360 miles straight north in 2.0 hours if the wind is blowing at 15 mph and 331 degrees from the north.
You can use the following formula to calculate airspeed.
[tex]V^{2} =V_{x} ^{2} + V_{y} ^{2}- 2v_{x} v_{y}cos\beta \\[/tex] ...........equation (1)
[tex]v_{x}[/tex] is the velocity of the wind and [tex]v_{y}[/tex] is the velocity of the plane.
[tex]\beta = 331-180 = 151 degree[/tex]
Putting [tex]v_{x}, v_{y} , \beta[/tex] in equation (1)
[tex]V^{2}= 15^{2} +180^{2} -2*15*180*cos151\\ V^{2} = 225 + 32400 - 5400*cos151\\V^{2} = 27336.49\\V = 165.33[/tex]
Hence, The airspeed of the plane is 165.33 mph
Now,
[tex]\frac{sin\alpha }{v_{x} } =\frac{sin\beta }{V} \\\frac{sin\alpha }{15 } =\frac{sin151 }{165.33} \\\\sin\alpha = 10*0.00122\\\alpha = 0.7[/tex]
Hence bearing required is 0.7 degrees.
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2) The Allen's rectangular backyard has a
perimeter of 144 feet. If the backyard is 40
feet wide, what is the area of their yard?
Answer:
1280 ft²
Step-by-step explanation:
Perimeter is the addition of all sides of the shape added together. Therefore, if the backyard is the rectangular shape you know that two of the sides are 40 feet wide. By adding both sides you get a total of 80 feet. Subtract the total from the perimeter in order to get the total of the unknown sides. 144 minus 80 is equivalent to 64. Now that you have the total of the unknown sides, divide by two in order to get the single unknown length. So, 64 divided by 2 is equal to 32. The area is the multiplication of two sides with quadrilaterals. Therefore, 40 times 32 equals an area of 1280 feet squared.
PLEASE HELP ITS DUE SOON! I DONT GET ANY OF THIS! HELP WOULD BE MUCH APPRECIATED! NEED THIS DONE BEEN STUCK ON THIS FOR WAY TO LONG!
YOU WILL GET 100 POINTS IF YOU HELP! QUESTION DOWN BELOW!!!!!
THIS IS MY LAST QUESTION!!
Answer:
Step-by-step explanation:
statement:
1 = 2
reason:
since 1 and 4 are equal to each other and because lines AB and CD are parallel, any line crossing both lines will create the same angles in the same areas, thus connecting 4 and 2 together. And since 4 is equal to 1, it is also equal to 2.
I hope this helps!
Answer:
statement is 1=2
reason: since 1 and 4 are eqaul to eachothers and beacause lines AB CD are parelle, any line crossing both lines will create the same angels and same area
Where X in the age of the baby in months according to this model what is the weight in pounds of a baby At age 5 months
The given function is:
f(x) = 1.5x + 7
Then, since x represents the age of the baby, in months, in order to find its weight with 5 months, that is, f(5), we need to replace x by 5 in the above equation:
f(5) = 1.5 * 5 + 7 = 7.5 + 7 = 14.5
Therefore, the last option is correct.
how can i find x and y in a triangle?
Using the sine formula;
sin 60 / x = sin 90 / 16
cross-multiply
x sin 90 = 16 sin 60
Divide both-side of the equation by sin 90
x = 16 sin 60 /sin 90
x= 13.86
To find y, we can simply use the Pythagoras theorem
opp² + adj² = hyp²
13.86² + y² = 16²
192.0996 + y² =256
subtract 192.0996 from both-side of the equation
y² = 256 - 192.0996
y² = 63.9004
Take the square root of both-side
y = 7.99
6+4×2+11+10÷2 order
To solve the following calculation
[tex]6+4\cdot2+11+10\div2[/tex]You have to keep in mind the order of operations. Which states that multiplications and divisions are to be solved before additions or subtractions.
So the first step is to solve the multiplication "4*2" and the division "10÷2"
[tex]6+8+11+5[/tex]Now all that is left is to add the numbers when you have to perform the same operation several times, you have to solve them from lef
please Solve for brainliest and 20 points
Answer:
g=30
Step-by-step explanation:
Answer:
g = 28
Step-by-step explanation:
( n - 2 ) × 180
( 30 - 2 ) × 180
( 28 ) × 180 = 5040
6g × 30 = 180g
5040 = 180g
÷180 ÷180
--------------------
28 = g
I hope this helps!
An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was 245ft. Use the formula s=24d−−−√ to find the speed of the vehicle before the brakes were applied. Round your answer to the nearest tenth.
The vehicle speed is 53 units if s = 24d and d = 245ft
Given the formula for speed is = √24 d
s denotes the vehicle's speed.
d = the length of the skid marks
We need to find the speed of the vehicle.
We know that the displacement d is 117 ft
d = 117 ft
And also it is mentioned in the question to use the below-given formula.
s = √24d
Now substituting the value of displacement in the formula we get
=> s = √24 x 117
=> s = √2808
=> s = 52.99
Now approximating to the nearest value of the decimal, we get.
=> s = 53
Therefore the speed of the vehicle is 53 units.
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Ronny is selling coffee mugs for $4.00. So far, he has earned $344.00. Ronny needs to earn more than $392.00 in order to meet his sales goal. How many more coffee mugs, x, does Ronny need to sell in order to reach his sales goal?
Answer:
25 more cups
Step-by-step explanation:
1. You need more than $636.00, but you already have $492.00. To find the needed amount of cups needed to sell, you need to find the difference of the two prices first. In other words, you need to subtract the total needed by the amount already raised.
2. You can get the equation, 636 - 492 = 144
3. Now that you have the amount needed, you can divide the number that you got (144) by 6. You divide it by 6 because that is the amount each cup costs.
4. After dividing 144 by 6, you should get 24. This gives your answer for getting EXACTLY 636. However, in this case, you need more to reach your goal. Since you cannot sell fractions of a cup, just raising it by one can reach your goal. We can add one to 24, making it 25.
In conclusion, you need to sell 25 more cups to reach your goal.
Translate the following sentence into an equation.
Twelve minus three times x equals fourteen.
Answer:
12-3x=14
Step-by-step explanation: