Answer:
The length of a is 36 mm.
Step-by-step explanation:
Similar rectangles have the same shape, but can have different sizes. The ratio of the lengths of corresponding sides of similar rectangles is always the same.
Given that b = 18 mm, c = 24 mm, and d = 36 mm, the ratio of the lengths of corresponding sides of the two rectangles is c/d = 24/36 = 2/3.
So, the length of a is equal to b * (c/d) = 18 * (2/3) = 36 mm.
Mayra's brother is driving back from college to visit. His college is 330 miles away. After an hour of
driving, he still has 275 miles to go. If the roads are clear, he'll be able to keep up that pace for the
whole drive. Write a linear function to model how much further he'll have to go over time.
The linear function to model how much further he'll have to go over time is h(t) = 330 - 55t
How to write a linear function?Total distance between home and college= 330 miles
Distance remaining to cover= 275 miles
Distance covered= Total distance between home and college - Distance remaining to cover
= 330 miles - 275 miles
= 55 miles
Time taken to cover 55 miles= 1 hour
h(t) = 330 - 55t
Where,
h = distance remaining to cover
t = time
Ultimately, h(t) = 330 - 55t is the linear function which represents how much further he'll have to go over time.
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Write the ratio in unit rate form. There are 25 runners on a cross country team. 5 of the runners are boys. Write the unit rate comparing all runners to boys.
The ratio the unit rate comparing all runners to boys is 5:1.
What is the unit rate formula?How to Calculate Unit Rate The denominator of a unit rate is always 1. Therefore, divide the denominator by the numerator so that the denominator equals one in order to determine the unit rate. The unit rate is 50km/5.5 hours = 9.09 km/hour, for instance, if 50km are travelled in 5.5 hours.
What does a typical unit rate mean?A unique form of ratio called a unit rate has a denominator (second number) of one. You are comparing a quantity to one when using a unit rate. Miles per gallon, price per pound, and pay rate per hour are a few examples of popular unit rates.
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The distance between Jenna's school and the park is 1 4/5 miles. Jenna leaves the school and walks 7/10 mile toward the park and stops for a break. How far, in miles, is Jenna from the park when she stops?
The distance between where Jenna stopped and the park is 1 1/10 miles
What is word problem?A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.
The word problems are interpreted into mathematics equation.
The distance between Jena's school and the park is 1⅘ miles = 9/5 miles
He stopped after walking for 7/10 miles .
The distance left to the park from where he stopped = 9/5 - 7/10
= (18-7)/10
= 11/10 miles
= 1 1/10 miles
Therefore Jena is 1 1/10 miles away from the park when she stopped.
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Topic 21 Angles of Triangles
3.
88 1
180'
姐
5.
(8x-35)
For questions 3 and 4, find the measure of each missing angle.
11 180
ई
-64
(3x-1)
(6r-5)
6.5
642
•92⁰
m22 = 24
m21 =
m23-
m24 =
m25=
80
For questions 5 and 6, find the value of x.
6.
(i=11)
2x+20)
(11X-63)
mel-
m/2=
m23-
m24
m25-
m26-
m47 =
The value of x is 13 and the angles in the triangle are 38,69 and 73 respectively.
What is triangle ?
Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.
From the given figure,
In the given triangle ,
The triangles are 3x - 1 , 8x - 35 and 6x - 5
The sum of all angles is always is 180 degrees.
so,
we get,
3x - 1 + 8x - 35 + 6x - 5 = 180
17x - 41 = 180
17x = 180 + 41
17x = 221
x = 221 / 17
x = 13
so,
3x - 1 = 3*13 - 1 = 38
8x - 35 = 8* 13 - 35 = 104 - 35 = 69
6x - 5 = 6*13 - 5 = 78 - 5 = 73
Therefore, The value of x is 13 and the angles in the triangle are 38,69 and 73 respectively.
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The vertices of a right-angled triangle are A(1, 0), B(7, 0) and C(1,8). Plot the points A, B and C on a sheet of graph paper. Hence, find the area of triangle ABC. (05)
Answer:24 sq. units
Step-by-step explanation:
The length of the base is (7-1)= 6 units. The height is 8 units.
Area =1/2*l*b=24
Why do colleges look at your standardized test scores?
determine whether or not the function f(x)= x^2 +2x if x<0 x^3-2x if x>0 is continuous at x=0
The given function f(x) = x² + 2x when x <0 and f(x) = x³ - 2x when x > 0 is continuous at x=0
What is continuity ?In mathematics, The function is called as continuous at the particular value of x, if right hand limit, left hand limit and the value of function at x all are equal.
RHL = LHL = F(x)
Limit exist and continuous
Given that,
F(x) = x² + 2x {x ≤ 0}
= x³ - 2x { x > 0}
To check whether it is continuous at x = 0
First taking LHL,
F(0) = 0² + 2x0
= 0
Now, taking RHL
F(0) = 0³ - 2x0
At x = 0
F(0) = 0² + 2x0
= 0
RHL = LHL = F(0)
Hence, the given function is continuous at x =0
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fraction that is equivalent to 3/9 and has a denominator of 3."
, The fraction equivalent to 3/9 with denominator 3 is the proper fraction p=1/3
What is a fraction in math?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
Given here: The fraction 3/9
Now we can simplify the fraction further by dividing both the numerator and denominator by 3
let p=3/9
then p=3/3 / 9/3
p= 1/3
Hence, The fraction equivalent to 3/9 with denominator 3 is the proper fraction p=1/3
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Cody purchased a bag of carrots costing $1.54. If Cody received $4.41 in change, how much money did he give to the cashier?
Answer: Cody gave the cashier $2.87.
Step-by-step explanation:
To determine the amount of money Cody gave to the cashier, you can subtract the amount of change he received from the cost of the carrots.
$4.41 (change) - $1.54 (cost of carrots) = $2.87
So, Cody gave the cashier $2.87.
Two different workers are producing a specialized part for a machine. The number of parts produced per hour by the workers are as follows:
Worker A: 5, 4, 4, 6, 7, 5, 6, 3
Worker B: 4, 8, 1, 9, 2, 9, 4, 3
Both workers averaged 5 parts per hour. Which worker has the higher variance and standard deviation?
The worker B has a higher variance of σ² = 9 and standard deviation of 3
What is Standard Deviation?The standard deviation refers to a measurement of the data dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Standard Deviation is calculated by
Each number's deviation from the mean must be determined, and then squared.
Next, add up all of these values.
Divide the result by the quantity of numbers.
Then calculate its square root.
Given data ,
Let the data of worker A = { 5, 4, 4, 6, 7, 5, 6, 3 }
Let the data of worker B = { 4, 8, 1, 9, 2, 9, 4, 3 }
Now , the mean of worker A = 5
The mean of worker B = 5
So , the standard deviation of worker A is calculated as
The sum of the difference of the data from mean is
SD = √ ( 5 - 5 )² + ( 5 - 4 )² + ( 5 - 4 )² + ( 5 - 6 )² + ( 5 - 7 )² + ( 5 - 5 )² + ( 5 - 6)² + ( 5 - 3 )² / 8
On simplifying the equation , we get
SD = √ ( 12/8 )
SD = √1.5
Standard deviation σ = 1.2247449
And , the variance of worker A is σ² = 1.5
Now ,
The standard deviation of worker B is calculated as
The sum of the difference of the data from mean is
SD = √ ( 5 - 4 )² + ( 5 - 8 )² + ( 5 - 1 )² + ( 5 - 9 )² + ( 5 - 2 )² + ( 5 - 9 )² + ( 5 - 4)² + ( 5 - 3 )² / 8
On simplifying the equation , we get
SD = √ ( 72/8 )
SD = √9
Standard deviation σ = 3
And , the variance of worker A is σ² = 9
Hence , the worker B has higher standard deviation
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Please help. I don’t know how to work it out and need somebody to show me
The distance of AB is 117.992 meters.
What is Law of Sines?Law of sines is a law in trigonometry which states that the ratios of the angle to the opposite side of a triangle are equal.
For triangle ABC,
sin A / a = sin B / b = sin C / c
where a, b and c are the sides opposite to the angles A, B and C respectively.
Here,
∠B = 112° 10' = 112° + 0.167° = 112.167°
∠C = 15° 20' = 15° + 0.333° = 15.333°
By the angle sum property of triangle,
∠A = 180° - (∠B + ∠C)
∠A = 180° - (112.167° + 15.333°)
= 52.5°
Using law of sines,
sin A / BC = sin C / AB
sin (52.5°) / 354 = sin (15.333°) / AB
AB = [354 × sin (15.333°)] / [sin (52.5°)]
AB = [354 × 0.264] / [0.793]
AB = 117.992 meters
Hence the distance across the river is 117.992 meters.
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Complete the description of the piecewise function graphed below.
The required description of the given piecewise function is graphed below.
f(x) = 3 if [-5, -2]; f(x) = -3 if (-2, 3]; and f(x) = 3 if (3, 4]
What is a piecewise function?A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).
The graph is given in the question, as shown
f(x) = 3 if [-5, -2]
This the sub-function define between the interval [-5, -2].
f(x) = -3 if (-2, 3]
This the sub-function define between the interval (-2, 3].
f(x) = 3 if (3, 4]
This the sub-function define between the interval (3, 4].
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|60| ___ |-60|
>
=
<
can you help me about that problem
Answer:
the correct answer to this equation would be: >
inverse function of f(x) = (x^2+1)^2 step by step
The inverse function of f(x) = (x^2+1)^2 step by step is given below.
The inverse of f(x) is √(√x - 1).
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = (x² + 1)²
The steps for finding the inverse of a function.
Step 1:
Keep y = f(x)
y = (x² + 1)²
Step 2:
Interchange x and y.
x = (y² + 1)²
Step 3:
Solve for y.
x = (y² + 1)²
Square root on both sides.
√x = y² + 1
(√x - 1) = y²
Square root on both sides.
y = √(√x - 1)
Thus,
The inverse of f(x) is √(√x - 1).
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Originally, a department store bought a set of dishes at a cost of $57.68 and marked it up 125%. After a month, the set of dishes had not sold, so the store marked it down 50%. What was the discounted price?
$
The discounted price of the set of dishes would be = $63.89
How to calculate the discounted price?The original cost of the dishes = $57.68
The percentage increase of the cost of the dishes = 125%
That is,
= 125/100 × 57.68
= 7210/100 = $72.10+57.68 = $129.78
After one month, the store marked it down by 50%, therefore the discounted price;
= 50/100 × 129.78/1
= 6489/100
= $65.89
= 129.78-65.89 = $63.89
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The discounted price is $64.89
What was the discounted price?From the question, we have the following parameters that can be used in our computation:
Cost = $57.68
Mark up = 125%
Mark down = 50%
The discounted price is then calculated as
price = cost * (1 + mark up) * (1 - mark down)
So, we have
price = 57.68 * (1 + 125%) * (1 - 50%)
Evaluate
price = 64.89
Hence, the price is 64.89
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You want to buy a pet iguana. You already have $12 and plan to save $9 per week.
A. If w represents the number of weeks until you enough Mooney to buy the iguana, what equation represents your plan to afford the iguana?
B. Explain how you could set up an equation to find the amount of money you should save each week to buy the iguana in 6 weeks.
A) An equation to represents your plan to afford the iguana is,
⇒ y = $12 + $9w
Where, y is total money after w weeks.
B) The amount of money you should save each week to buy the iguana in 6 weeks is, $66.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
You want to buy a pet iguana. You already have $12 and plan to save $9 per week.
Let w represents the number of weeks until you enough Money to buy the iguana.
Hence, An equation to represents your plan to afford the iguana is,
⇒ y = $12 + $9w
Where, y is total money after w weeks.
And, The amount of money you should save each week to buy the iguana in 6 weeks is,
⇒ y = $12 + $9w
⇒ y = $12 + $9 × 6
⇒ y = $12 + $54
⇒ y = $66
Thus, A) An equation to represents your plan to afford the iguana is,
⇒ y = $12 + $9w
Where, y is total money after w weeks.
B) The amount of money you should save each week to buy the iguana in 6 weeks is, $66.
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DIRECTIONS: Use this information to answer Parts A and B. −5=−y−3x Question 1 Part A Write the equation in slope-intercept form. Enter the correct equation in the box.
Slope intercept form of equation is y = -3x + 5.
What is slope intercept form of equation?The graph of the linear equation y = mx + c is a line with m as slope and c as the y-intercept. This form of the linear equation is called the slope-intercept form, and the values of m and c are real numbers.
Given equation,
-5 = -y - 3x
Standard Slope intercept form of equation y = mx + c
Given equation can be written as
y = -3x + 5
Hence, y = -3x + 5 is the slope intercept form of given equation
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The required equation in the slope-intercept form is given as y = -3x + 5.
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
The equation of line passes through points (x, y) and has a slope and intercept of m and c respectively is given as,
y = mx + c
The above expression is the standard slope intercept form of a line.
Trasform the given equation,
-5 = -y - 3x
y - 5 = -3x
y = -3x + 5
Thus, the required equation in the slope-intercept form is given as y = -3x + 5.
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If P is the circumcenter of ABC, AD = 7x - 6; DB = 5x + 8, and PC = 35, find DP.
If P is the circumcenter of ABC, the DP is 13.27 units.
What is the value of DP?
The value of DP is calculated by applying the following method as shown below.
Based on the given figure, D is the midpoint of AB
Line AD = BD, so line DP is perpendicular to line AB and the following equation can be formed to determine value of x.
7x - 6 = 5x + 8
2x = 14
x = 14/2
x = 7
DB = 7x - 6
DB = (7 x 7 ) - 6 = 43
Let PC = 45
PC = PB = 45
Apply Pythagoras theorem to determine DP;
DP² = PB² - DB²
DP² = 45² - 43²
DP² = 176
DP = √176
DP = 13.27 units
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20.
Solve the equation. Round the result to the nearest hundredth.
-15x + 73 = 26
21.
Solve the equation. Round the result to the nearest hundredth.
1.5x + 7.4 = -1.8x - 6.9
22.
Solve the equation. Round the result to the nearest hundredth.
14.1 - 0.3x = 1.3x - 4.2
23.
Multiply the equation by a power of 10 to write an equivalent
equation with integer coefficients.
6.2x + 4.5 = 3.8x + 7.9
24.
Multiply the equation by a power of 10 to write an equivalent
equation with integer coefficients.
4.603y - 1.842 = -3.651y
25.
Find the percent. Round to the nearest whole percent.
159 people in favor out of 350 people surveyed.
The solution to the linear equations are;
20. x = 3. 200
21. x = 4. 333
22. x = 11. 438
23. x = 1.417
24. y = 0. 223
25. 45%
How to simply the expressionFrom the information given, we have to solve the linear equations, we have;
20. -15x + 73 = 26
collect like terms
-15x = 26 - 74
-15x = -48
Make 'x' the subject
x = 3. 200
21. 1.5x + 7.4 = -1.8x - 6.9
collect the like terms
3.3x = 14.3
Make 'x' the subject
x = 4. 333
22. 14.1 - 0.3x = 1.3x - 4.2
collect like terms
1.6x = 18.3
Make 'x' the subject
x = 11. 438
23. 6.2x + 4.5 = 3.8x + 7.9
collect like terms
2.4x = 3.4
Make 'x' the subject
x = 1.417
24. 4.603y - 1.842 = -3.651y
collect like terms
8.254y = 1.842
Make 'y' the subject
y = 0. 223
25. The percentage is given as;
159/350 × 100/1
45%
Hence, the values are x = 3. 200, x = 11. 438, x = 1.417, y = 0. 223 and 45%
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What is 70% of 90 as a number thank you
Answer:
70 percent of what number is 90?
90 is 70% of 128.57
Steps to solve "90 is 70 percent of what number?"
We have, 70% × x = 90
or,
70
100
× x = 90
Multiplying both sides by 100 and dividing both sides by 70,
we have x = 90 ×
100
70
x = 128.57
If you are using a calculator, simply enter 90×100÷70, which will give you the answer.
Answer: 70 % of 90 = 63
Step-by-step explanation:
70 % x 90.
= (70/100) x 90
= (70*90)/100
= 6300/100
= 63
I need help, please.
Note that where Will C. Lowe wishes to purchase an ordinary whole life insurance policy with a face value Of $50,000, his annual premium, if his age for insurance purposes is thirty-one is: $7,665.
What is premium?The insured pays a premium to the insurer on a regular basis to cover his risk. The risk is transferred from the insured to the insurer under an insurance arrangement. The premium is the amount charged by the insurer for accepting this risk.
To compute the Premium Payable, you must apply the stipulated rate against the sum insured.
Since the Sum assured is $50,000; and
The applicable rate for a 31-year-old is 15.33%
Thus the Insurance Premium for an Ordinary Whole Life Insurance Policy is:
(50,000 * 15.33)/100
= 766500/100
= $7,665.
Thus Lowe to be entitled to an annual Life Insurance cover of $50,000 must pay $ $7,665 every year.
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let use the divisibility test and write which of the following numbers are exactly divisible by 7 a) 525 b)798 c)836 d) 3696 e) 5706
The numbers that are exactly divisible by 7 are;
a) 525
b) 798
d) 3696
How to use the rules of divisibility?To solve this, what we will do is to quote the divisibility rule for 7 here which is that;
For a 3 digit number abc to be divisible by 7 then it means that ab - 2c must be divisible by 7. Thus;
A) 525;
52 - 2(5)
= 52 - 10
= 42
42 is divisible by 7 and as such 525 is divisible by 7
B) 798;
79 - 2(8)
= 63
63 is divisible by 7 and as such 79 is divisible by 7
C) 836;
83 - 2(6)
= 83 - 12
= 71
71 is not divisible by 7 and as such 836 is not divisible by 7
D) 3696;
369 - 2(6)
= 357
35 - 2(7)
= 21
21 is divisible by 7 and as such 3696 is divisible by 7
E) 5706;
570 - 2(6)
= 558
55 - 2(8)
= 39
It's not divisible by 7 and so 5706 is not divisible by 7
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3. The marginal cost of producing a certain product is GHe 12 per unit, while the cost to produce
100units is GH¢1,500.
a) Find the cost function, C(x), given that it is linear.
b) Find the average cost per item to produce 50 units and 300 units.
Answer:
a) GH¢15x
b) GH¢15
Step-by-step explanation:
a) To find the cost function, C(x), given that it is linear, we need to find the slope and y-intercept of the line that represents the cost to produce x units of the product. We can use the point-slope form of a line to find the cost function: C(x) = mx + b, where m is the slope and b is the y-intercept.
We have two points: (100, GH¢1,500) and (0, GH¢0), which represents the cost to produce 100 units and 0 units, respectively. The slope can be found by dividing the change in y by the change in x:
m = (GH¢1,500 - GH¢0) / (100 - 0) = GH¢15
The y-intercept can be found by plugging in one of the points and solving for b:
GH¢1,500 = (GH¢15)(100) + b
GH¢1,500 = GH¢1,500 + b
b = GH¢0
So the cost function is C(x) = GH¢15x + GH¢0.
b) To find the average cost per item to produce 50 units and 300 units, we need to divide the total cost by the number of units produced.
For 50 units:
C(50) = GH¢15 * 50 + GH¢0 = GH¢750
Average cost = C(50) / 50 = GH¢15
For 300 units:
C(300) = GH¢15 * 300 + GH¢0 = GH¢4,500
Average cost = C(300) / 300 = GH¢15
Consider the function shown on the graph. Which function does the graph represent? f(x) = (x + 3)(x + 7) f(x) = (x – 3)(x – 7) f(x) = 3(x – 3)(x – 7) f(x) = 11(x + 3)(x + 7)
The solution is Option C.
The value of the function is f ( x ) = 3 ( x - 3 ) ( x - 7 )
What is Equation of Graph of Polynomials?Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.
Identify the even and odd multiplicities of the polynomial functions' zeros.
Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.
The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = 3 ( x - 3 ) ( x - 7 ) be equation (1)
On simplifying the equation , we get
y = 3 ( x - 3 ) ( x - 7 )
And , the point ( 8 , 15 ) lies on the graph
Substituting the values in the equation , we get
when x = 8
y = 3 ( 8 - 3 ) ( 8 - 7 )
y = 3 ( 5 )
y = 15
Therefore , the point P ( 8 , 15 ) lies on the graph of the function
And , the graph has two zeros at (3,0) and (7,0)
Hence , the graph of the function is f ( x ) = 3 ( x - 3 ) ( x - 7 )
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Answer:
c
Step-by-step explanation:
c
EASY POINTS!
Winter has just begun. After one week, the temperature decreased by 46.8° with a
percent change of 72%. What was the temperature at the beginning of the week and
what is the temperature now?
Answer:Can somebody also help me with this. i'm confused please hurry!
Step-by-step explanation:
PLS HELP !
solve the inequality 
3/4 |1/3 + 2| < 6
a. x > -8 and x < -4
b. x > -30 and x < 2
c. x < -30 and x < 18
d. x > -30 and x < 18
The solutions of the equation are x < 18 and x < - 30.
Solution on inequalities:Solutions of equations are the numerical values of the variables that will satisfy the condition in the given equation. Similarly, the solutions of inequalities are the values of variables that can satisfy the given inequality.
We can solve an inequality by adding or subtracting the same integer on both sides, or we can multiply or divide by the same number on both sides until we get the value of 'x'.
Here we have
3/4 |1/3x + 2| < 6
We can solve the above equation as follows
3/4 |1/3x + 2| < 6
Multiply by 4 on both sides
=> 4 [ 3/4 |1/3x + 2| ] < 4 × 6
=> 3 |1/3x + 2| < 24
=> | x + 6| < 24
=> x + 6 < ± 24
=> x + 6 < 24 and x + 6 < - 24
Subtract - 6 on both sides
=> x + 6 - 6 < 24 - 6 and x + 6 - 6 < - 24 - 6
=> x < 18 and x < - 30
Therefore,
The solutions of the equation are x < 18 and x < - 30.
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Someone help me with this math problem.
From the graph, she walked at a rate of [tex]\frac{25-10}{5-2}=5 \text{ ft/s}[/tex].
Therefore, she walked faster on her next three walks compared to her first two walks.
The product of 2 and the difference between 1 is 14
The expression from the statement is 2x - 1 = 14
How to determine the expressionFrom the question, we have the following parameters that can be used in our computation:
The product of 2 and the difference between 1 is 14
Represent the variable with x
So, we have
2x and the difference between 1 is 14
When the difference is expressed as an expression, we have
2x - 1 is 14
So, we have
2x - 1 = 14
Hence, the expression is 2x - 1 = 14
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I know this looks easy but to me is hard will mark u brainliest!!!
Answer:
14q/25
Step-by-step explanation:
14q/25
what is the slope of the line passing through the points (-3, 4) and (2, -1)
Answer:
-1
Step-by-step explanation:
You want the slope of the line through the points (-3, 4) and (2, -1).
SlopeThe slope is given by the formula ...
m = (y2 -y1)/(x2 -x1)
Using the given points, we find the slope to be ...
m = (-1 -4)/(2 -(-3)) = -5/5 = -1
The slope of the line through the given points is -1.