Answer:
a=4Step-by-step explanation:
Simplify both sides of the equation:
4 (2 + a) = 24
( 4 )( 2 ) + ( 4 )( a ) = 24 (Distribute)
8 + 4a = 24
4a + 8 = 24
subtract 8 from both sides:
4a + 8 − 8 = 24 − 8
4a = 16
Divide both sides by 4:
4 a/4 = 16/4
a = 4
Multiple bracket out first:
4 x 2 =8
4 x a = 4a
8 +4a = 24
-8
4a. = 16
÷4
a = 4
Hope this helps!
Given the triangle below, which of the following is a correct sta
A
LO
5
B
6
○ cot < B = 1/2
O
5
○ csc 2 C = 2²/04
3
O
8
O
○ cot / C = ²/3
5
6
4
○ csc ≤ B = 1/3
O
8
C
Among all the statements the correct statement is cosec B=4/3 which is last statement.
Given a triangle in which angles are different.
We are required to find the correct statement among the given statements.
We have to take statements one by one and find the trigonometric ratios.
Trigonometric ratios are the ratios which expresses the ratios of the sides of a right angled triangle.
Sin Θ=P/H
Cos Θ=B/H
Tan Θ=P/B
Cosec Θ=H/P
Sec Θ=H/B
Cot Θ=B/P
First statement: cot B=6/5When we take angle B then we can find that cot B=5/6.
So the first statement is wrong.
Second statement: Cosec C=3/4When we take angle C then we can find that cosec C=8/5.
So the second statement is also wrong.
Third statement: Cot C=8/5.When we take angle C then we can find that cot C=6/5.
So the third statement is also wrong.
Fourth statement: Cosec B=4/3When we take angle B then we can find that Cosec B=8/6=4/3
So the fourth statement is correct.
Hence among all the statements the correct statement is cosec B=4/3 which is last statement.
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Drag each length to the correct location on the image. Each length can be used more than once, but not all lengths will be used.
What are the missing segment lengths shown in the image?
By applying Pythagoras theorem, the missing segment lengths of this triangles include:
CD = 10√2AC = 10√2BC = 10AB = 10How to find the missing segment lengths?Since triangle ACD is a right-angle triangle, we would use Pythagoras theorem to find the missing segment lengths of this triangles as follows:
c² = a² + b² ≡ AD² = CD² + AC²
Next, we would use cos trigonometric ratio to find side CD,
cos45 = adjacent/hypotenuse
cos 45 = CD/20
1/√2 = CD/20
CD = 1/√2 × 20
CD = (20√2)/2
CD = 10√2
For side AC, we have:
AD² = CD² + AC²
AC² = AD² - CD²
AC² = 20² - (10√2)²
AC² = 400 - 100(2)
AC = √200
AC = 10√2
From triangle ABC, we have:
cos45 = BC/10√2
BC = 10√2 × cos45
BC = 10√2 × 1/√2
BC = (10√2)/√2
BC = 10
For side AB, we have:
AB² = (10√2)² - 10²
AB² = 200 - 100
AB² = 100
AB = 10.
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List the sides in order from the smallest to the largest 83 56 41
the order from smallest to largest is:
41, 56, 83.
How to list from smallest to largest?
Here we have 3 values, that are:
{83, 56, 41}
To list it from smallest to largest, we first need to write the smallest number, which we can identify is 41.
Then the middle number. Which is 56, that is larger than 41 and smaller than 83.
Finally, the largest number, which is 83.
Then the order is:
41, 56, 83.
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Find the area of a triangle with base of 10 inches and altitude to the base of 16 inches. 135 in 2 160 in 2 80 in 2
For a triangle with base of 10 inches and altitude of 16 inches, its area will be 80 in² (third option).
Calculation For the Area of the Triangle:
It is given that,
The base of the triangle, B = 10 inches
The altitude from the base of the triangle or height, H = 16 inches
Now, the formula used for finding the area of a triangle is given as follows,
Area, A = (1/2) × B × H
Substituting the given values of B and H in the above formula for area, we get,
A = (1/2) × (10 inches) × (16 inches)
A = 5 × 16 inches²
A = 80 inches²
Thus, the area of the triangle have base 10 inches and altitude 16 inches is 80 square inches.
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The roots of the quadratic equation x 2 − 51x + k = 0 differ by 75, where k is a real number. Determine the sum of the squares of the roots
The sum of the squares of the root is 4113
In a quadratic equation ax² + bx + c , the sum of the roots is -b/a and the product of the roots is c/a
Let m, n be roots of the given equation.
So,
m - n = 75 -1)
m + n = 51 (as sum of roots of a quadratic equation is -b/a) -2)
adding both equations 1) and 2)
2m = 75 + 51
2m = 126
m = 63
substituting value of m in equation 1 we get
63 - n = 75
n = -12
So the sum of squares of the roots of the equation is = 63² + -12²
= 3969 + 144
= 4113
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A bag contains blue, orange and red jelly beans only there are 6x blue jelly beans, 2x-3 orange jelly beans and 15-x red jelly beans there are a total of 54 jelly beans in the bag.
a) how many orange jelly beans are there in the bag?
b) how many blue jelly beans are there in the bag?
Answer:
a.9
b.36
Step-by-step explanation:
Blue beans + orange beans + red beans = 54
6x + 2x-3 + 15-x = 54
6x+2x-x=54+3-15
7x=42
divide both sides by 7
x=6
a. orange beans = 2x-3
but x=6
2(6)-3
12-3
=9
b.blue beans =6x
6(6)
=36
7. [Decimal +,-]
16
9.74
+2 6.80
Answer:
169.74+26.80
= 196.54
the correct decimal answer is 196.54
The length of plot is 8 meters more than its breath. If its perimeter is 80 metres, find its length and breath.
Answer:
length = 24 meters
breadth = 16 meters
Step-by-step explanation:
Let L be length and B be breadth
From the first fact we get the equation
L = B + 8 (1)
We know that perimeter = 2(L+B) and this is given as 80
So 2(L+B) = 80
L + B = 80/2 = 40
or
L = 40 - B (2)
If we add equations (1) and (2) we can eliminate B
We get 2L = B + 8 + 40 - B =48
L = 48/2 = 24
Substituting for L in equation (1) we get
24 = B + 8 ==>
B = 24-8 =16
Cross-check
Perimeter = 2 (L+B) = 2(24 + 16) = 2(40) = 80
Hence check OK
Which unit rate is the lowest price per ounce
Choice a: 10 ounces of chocolate chips for $1.66
Choice b: 20 ounces of chocolate chips for $3.22
1: choice a
2: choice b
3:unit rates are equal
4:Cannot be determined
Answer:
2: choice b
Step-by-step explanation:
a: $1.66 / 10 oz = $0.166/oz
b: $3.22 / 20 oz = $0.161/oz
Answer: 2: choice b
Look at the equation shown below. 19 - 5 = 3 z - 11 Which of these expressions gives the value of Z
If the equation is 19-5=3z-11 then the value of z is 15/3.
Given an equation in terms of z is 19-5=3z-11.
We are required to find the value of variable z which exist in equation.
Equation is like a relationship between two or more variables expressed in equal to form. Equations of two or more variables look like ax+by=c. It may be linear equation, quadratic equation,cubic equation,or many more depending on power of the variable.
The value of z can be find as under:
19-5=3z-11
4=3z-11
3z=4+11
3z=15
z=15/3
Hence if the equation is 19-5=3z-11 then the value of variable z is 15/3.
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What is the solution to this inequality?
7x+18>−3
x>−3
, , x greater than negative 3, ,
x<−3
, , , , x less than negative 3, , , ,
x>3
, , x greater than 3, ,
x<3
Answer:
x>-3
Step-by-step explanation:
7x+18>-3
transpose 18 to the other side to group the like terms
7x>-3-18
7x>-21
You divide bother sides by a 7 to get the value of x
7x/7>-21/7
therefore x>-3
2 plus 0.5x if x is equal to 5
Answer: 4.5
Step-by-step explanation:
2 + 0.5x
x = 5
2 + 0.5 ( 5 )
2 + 2.5
2 + 2.5 = 4.5
Hope this helps!
In how many ways can you select five people from a group of ten if the order of selection is important?
There are 30240 ways in which we can select five people from a group of ten if the order of selection is important.
Given that there are 10 total number of people.
We are required to find the number of ways in which 5 people can be selected from 10 people.
Permutations is basically the number of arrangements that can be possible with the number of things , people, etc. It is denoted as [tex]nP_{r}[/tex]=n!/(n-r)!.
We have 10 people and we have to select 5 people from them then the number of ways can be find out by [tex]10P_{5}[/tex].
We have to expand this permutation.
=10!/(10-5)!
=10!/5!
=10*9*8*7*6*5!/5!
=10*9*8*7*6
=30240 ways
Hence there are 30240 ways in which we can select five people from a group of ten if the order of selection is important.
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magan wants to ride his bicycle 30.4 miles this week. he has already ridden 4 miles if he rides for 4 more days what is the average number of miles he would have to ride each day to meet his goal?
The average number of miles he will ride each day to meet his goal is 6.6 miles
How to find the average number of miles she will ride?He wants to ride his bicycle 30.4 miles this week.
He has already ridden 4 miles.
He rides 4 more days.
Therefore, the average number of miles he would have to ride each day to meet his goal can be calculated as follows:
let
x = number of miles driven
Hence, the equation can be represented as follows;
4x + 4 = 30.4
Therefore,
4x + 4 = 30.4
4x + 4 - 4 = 30.4 - 4
4x = 26.4
x = 26.4 / 4
x = 6.6
Therefore, the average number of miles he will ride each day to meet his goal is 6.6 miles
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Can anyone help me with this? I'm not very good at math... =.=
The motion of an object was recorded by measuring the velocity of the object in meters per second at various times, as shown in the table. The scatterplot below was graphed from the data in the table, where t represents the time, and v represents the velocity. Based on the scatterplot, which equation BEST represents the relationship between velocity and time?
Based on the scatterplot, the equation that BEST represents the relationship between velocity and time is y = 2.2x + 6
How to determine the line of best fit?The line of best fit is the line that best represents the relationship between 2 variables. The equation of a line in slope-intercept form is expressed as:
y = mx + b
where
m is the slope
b is the intercept
Using the coordinate points on the plane (0, 6) and (10, 28)
Determine the slope
Slope = 28-6/10-0
Slope = 22/10
Slope = 2.2
Determine the y-intercept
6 = 2.2(0) + b
b = 6
Determine the equation of aline of best fit.
y = 2.2x + 6
Hence based on the scatterplot, the equation that BEST represents the relationship between velocity and time is y = 2.2x + 6
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In which order do these stages occur? 4, 3, 2, 1, 3 3, 2, 1, 3, 4 4, 3, 2, 3, 1 4, 2, 3, 1, 3
The order of the stages of recession will be 4, 2, 3, 1, 3.
What happens in a recession?
This is the first stage, and it's characterized by a decrease in activity throughout the economy. This can manifest itself in different ways, like lower production levels, fewer jobs, and less spending by consumers and businesses.Who benefits in a recession?
Rental agents, landlords, and property management companies can thrive during a recession when renting is likely to become a more appealing option, if not the only one available.
So, these stages are occur -
4. peak production
2. falling production
3. falling demand (occurs twice)
1. job loss
3. falling demand (occurs twice)
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The complete question is-
There are five stages in a recession.
1. job loss
2. falling production
3. falling demand (occurs twice)
4. peak production
In which order do these stages occur?
4, 3, 2, 1, 3
3, 2, 1, 3, 4
4, 3, 2, 3, 1
4, 2, 3, 1, 3
4, 2, 3, 1, 3.Answer:4, 2, 3, 1, 3.
4, 2, 3, 1, 3.Step-by-step explanation:4, 2, 3, 1, 3.
A company reduced the prices of its goals by 13% during a promotional sale. A product was sold for 435.00 during the promotional sales. What was the price before the promotional sales?
The price of the product before promotional sales was 500,000.
How to find out what the previous price was?To find what the previous price of the product was, we must take into account that we know that 87% of the value is equal to 435,000. So to find out how much the 13% (discount) that the product had is equivalent to, we do the following operation:
435,000 × 100 ÷ 87 = 500,000
So we know that the 13% discount was 65,000
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Mia, Keela And Michelle are selling girl scout cookies.In all they have sold $800 worth of cookies. Mia sold 57 boxes, Keela sold 28 boxes and Michelle sold 15 boxes. How should the girls split the money so that they earn the same fraction as the boxes of cookies that they sold? Should Mia and Michelle get the same amount of money? Why Or Why not?
Answer:
the money should be split as per each girl sold. total boxes sold is 100.
Step-by-step explanation:
total boxes sold is 100. Mia sold 57/100 keela 28/100 and Michelle 15/100.
mia=456$
keela=224$
michelle=120$
calculated as boxes sold/100 x 800$
Akira and her puppy are both dressing up as superheroes for Halloween this year. Akira needs 1 yard of cloth for her cape. She also needs 1 foot of cloth for her puppy's cape. How many feet of cloth should she buy for their capes?
The feet of cloth that she should buy for the capes is 4 feet.
How many feet should she buy?
The mathematical operations that would be used to determine the answer are addition and multiplication.
Addition is the process of summing two or more numbers together. Multiplication is the process of determining the product of two or more numbers.
The first step is to convert yard to feet
According to the unit of conversion : 1 yard = 3 feet
1 x 3 = 3 feet
The second step is to add the feet needed for Akira's cape with the foot needed for the puppy's cape
Total feet needed = 3 + 1 = 4 feet
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A local smallholder is putting animals in different fields. She put them in different ratios. 50 POINTS AND BRAINLIEST!!
She spilt the 54 pigs in the ratio 1:2:3. How many are in each field as a ratio? __:__:__
She split the 154 chikens in the ratio 2:3:6. How many are in each field? __:__:__
Answer:
Part 1: 9:18:27
Part 2: 28:42:84
Step-by-step explanation:
Part 1:
54 pigs are split into the ratio 1:2:3. Treating a "1" ratio as x, we have x:2x:3x is 54 pigs. We can add up all parts of the ratio to become the whole. x+2x+3x=54. Solving, x=9. Substituting, our ratio is 9:18:27.
Part 2:
Similar to part 1, we treat a "1" ratio as y. Our ratio is 2y:3y:6y for a total of 154 chickens. Adding all the parts, we have 2y+3y+6y=154, so y=14. Substituting, our ratio is 28:42:84.
solve for x: 5^x/5^14=1/5^5
Answer:
[tex] \frac{1 \\ }{3125} [/tex]
Answer:
x = 9
Step-by-step explanation:
Law of exponents:[tex]\sf \dfrac{a^m}{a^n}=a^{m-n}\\\\\\ \dfrac{1}{a^m}=a^{-m}[/tex]
[tex]\sf \dfrac{5^x}{5^{14}}=\dfrac{1}{5^5}\\\\5^{x -14} = 5^{-5}[/tex]
Base are same. Compare the exponents.
x - 14 = -5
x = -5 + 14 {Addition property of equality}
x = 9
5. Mr. Griffin asked the students to form the number eighty-four million, five
hundred thirty thousand, two hundred sixteen. Ben still had the number card
with the 3. In what place was Ben standing? Show your work in the space
below. Remember to check your solution
Answer:
Ben was standing in the
Step-by-step explanation:
84 000 000
+ 00 530 000
+ 00 000 216
_________________
84 530 216
From this u can see that the 3 is in the ten thousands place
Joseph paid $105,000 for his home twenty years ago. since then, his house has increased its property value by 2.0% every year. in addition, joseph has made renovations and improvements to the house which will increase its sale value by $28,700. if joseph sells his home, how much profit will he make, to the nearest hundred dollars? a. $79,700 b. $84,700 c. $93,700 d. $122,400
If joseph sells his home, profit will he make = (a) $79720
What is profit and its example?
Profit is a term that often describes the financial gain a business receives when revenue surpasses costs and expenses. For example, a child at a lemonade stand spends one quarter to create one cup of lemonade. She then sells the drink for $2. Her profit on the cup of lemonade amounts to $1.75.Profit earned on the house if he sells = $79720
Amount paid by Joseph for his home = $105000
His house has increased its property value by 2.0% every year
So, Property cost after 20 years :
[tex]Cost = 105000 * (1.02)^{20}[/tex]
Cost = 105000 × 1.4859
Cost = 156020
Also, Due to renovations and improvements to the house, the property cost is increased by $28700
So, Total cost of the house after 20 years = 156020 + 28700
= $184720
So, Profit earned on the house if he sells = 184720 - 105000
= $79720
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Answer:a) $79720
Step-by-step explanation:edge
A fountains pool is enclosed by a circular plastic tank. The distance from the center of the pool to the wall of the tank is 10 feet. How long is the wall of the tank in feet?
The length of the wall of the tank in feet is 62.8 feet.
How to solve circumference?Circumference is the perimeter of a circular object. Therefore,
circumference = 2πr
where
r = radiusThe fountains pool is enclosed by a circular plastic tank.
The distance from the centre of the pool to the wall of the tank is 10 feet. This is the radius of the circle
Hence,
length of the tank = 2πr
length of the tank = 2 × 3.14 × 10
length of the tank = 20 × 3.14
length of the tank = 62.8 feet.
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Given a point A(-2,5), find the coordinates of a point B so that the line segment AB has each slope.
a) 2/3
b) -2/3
c) 4
d) -3
e) 0
f) undefined
Step-by-step explanation:
I understand this that we need to find a point B for each of a) to f).
remember, the slope is the (y coordinate difference / x coordinate difference) when going from one point on the line to the other.
a)
the slope 2/3 means that when going to B x has to increase by 3, and y has to increase by 2.
so, B = (-2 + 3, 5 + 2) = (1, 7)
b)
-2/3 means that either x or y have to decrease and the other to increase.
e.g. x increases by 3, y decreases by 2.
so, B = (-2 + 3, 5 - 2) = (1, 3)
c)
4 stands for 4/1.
so, x increases by 1, y increases by 4.
B = (-2 + 1, 5 + 4) = (-1, 9)
d)
similar to c) -3 stands for -3/1.
and similar to b) either x or y has to decrease and the other to increase.
e.g. x increases by 1, y decreases by 3.
B = (-2 + 1, 5 - 3) = (-1, 2)
e)
that means the y difference is 0. B has the same y coordinate.
e.g. B = (3, 5)
x can be any value.
the line is a horizontal line going through y = 5 or (0, 5) on the y-axis.
f)
that means the x difference is 0. B has the same x coordinate.
e.g. B = (-2, 9)
y can be any value.
the line is a vertical line going through x = -2 or (-2, 0) on the x-axis.
Find the average rate of change of the function a(x) = πx2 where a is the area of a circle with radius x as the radius changes from x=4 to x=6.
The average rate of change of the given function is 10π.
Given function
a = πx^2
Where a is the area of a circle with radius x
The radius changes from x = 4 to x = 6.
Calculating the average rate of change of function:
The method of finding the average rate between the function value over a certain interval is called the average rate of change.
The formula is given by :
Average = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
Where f(a) and f(b) are the function value over the limit a and b.
Average = [tex]\frac{f(6)-f(4)}{6-4}[/tex]
= [tex]\frac{\pi (6)^{2} -\pi (4)^{2} }{6-4}[/tex]
= [tex]\frac{\pi (36-16)}{2}[/tex]
= [tex]\frac{20\pi }{2}[/tex]
= 10π
The average rate of change of the given function is 10π.
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The following are the ages of 13 history teachers in a school district. 24, 27, 29, 29, 35, 39, 43, 45, 46, 49, 51, 51, 56 Notice that the ages are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum: Interquartile range:
The Five number summary for the given data:
Minimum: 24
Lower quartile: Q1 = 29
Median: 43
Upper quartile: Q3 = 50
Maximum: 56
Interquartile range: IQR = 21
What is the interquartile range?The interquartile range is calculated by
IQR = Q3 - Q1
Where Q3 - upper quartile and Q1 - lower quartile
Q3 = 3/4(n + 1) th term
Q1 = 1/4(n + 1) th term
Calculation:The given data points are
24, 27, 29, 29, 35, 39, 43, 45, 46, 49, 51, 51, 56
where n = 13
Maximum data value = 56
Minimum data value = 24
Calculating Median:
Median = (n+1)/2 th term
⇒ Median = (13 + 1)/2 = 7th term
∴ Median = 43
Calculating the quartiles:
Upper quartile Q3 = 3/4(n + 1)th term
⇒ Q3 = 3/4(13 + 1) = 10.5
⇒ Q3 = 10th term + 1/2(11th term - 10th term)
⇒ Q3 = 49 + 1/2(51 - 49)
⇒ Q3 = 49 + 1
∴ Q = 50
Lower quartile Q1 = 1/4(n + 1)th term
⇒ Q1 = 1/4(13 + 1) = 3.5
⇒ Q1 = 3rd term + 1/2(4th term - 3rd term)
⇒ Q1 = 29 + 1/2(29 - 29)
∴ Q1 = 29
Calculating the IQR:
IQR = Q3 - Q1
= 50 - 29
= 21
Thus, the interquartile range is 21.
Therefore, the five-number summary for the given data:
Minimum: 24
Lower quartile: Q1 = 29
Median: 43
Upper quartile: Q3 = 50
Maximum: 56
Interquartile range: IQR = 21
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A circle with center O. Two tangents to the circle from the point C meet the circle at points A, and B. Two lines O B, and O C forms an exterior angle of 250 degrees. Two lines B D, and A D are drawn from a point D on the circle.
In this figure, m∠BDA =
° and m∠BCA =
°.
Based on the calculations, the measure of m∠BDA and m∠BCA are 55° and 70° respectively.
What is a tangent?In geometry, a tangent is also referred to as a tangent line and it can be defined as a straight line that touches a plane curve at a specific point.
What is a circle?A circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Also, a circle simply refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).
First of all, we would determine angle BOA:
∠BOA + ∠BOA = 360° (Angles at a point)
∠BOA + 250° = 360°
∠BOA = 360° - 250°
∠BOA = 110°
Next, we would determine angle BDA:
2 × m∠BDA = ∠BOA (Angle inscribed at the center is twice the angle at the circumference)
2 × m∠BDA = 110°
m∠BDA = 110°/2
m∠BDA = 55°.
What is the theorem of intersecting secants?The theorem of intersecting secants states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.
By applying the theorem of intersecting secants, angle BCA will be given by this formula:
m∠BCA = ½ × (m<AO - m<BO)
Substituting the given parameters into the formula, we have;
m∠BCA = ½ × (250 - 110)
m∠BCA = ½ × 140
m∠BCA = 70°.
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Answer:
70
Step-by-step explanation:
18 PTS!! What is the 400th term of the sequence below when using the explicit formula
aₙ=a₁+(n-1)•d?
79, 82, 85, 88,...
A. 1273
B. 1279
C. 1276
D. 1282
Answer:
[tex]\huge\boxed{\sf a_{400}=1276}[/tex]
Step-by-step explanation:
Sequence:79, 82, 85, 88, ....
Explicit formula:[tex]a_n=a_1+(n-1)d[/tex]
Where,
[tex]a_n = a_{400[/tex] (the term that is to be found)[tex]a_1 = 79[/tex] (the first term)[tex]n = 400[/tex][tex]d = 3[/tex] (difference between first and second term)Put the givens in the above formula
[tex]a_{400}=79 +(400-1)3\\\\a_{400}=79 + 399\times3\\\\a_{400}=79+ 1197\\\\a_{400}=1276\\\\\rule[225]{225}{2}[/tex]