To find Ben's age, we establish an equation based on the given information that Ben is three times as old as Daniel and four years older. Solving this equation reveals that Daniel is 2 years old, therefore, Ben is 6 years old.
Explanation:The question states that Ben is 3 times as old as Daniel and also 4 years older than Daniel. To solve for Ben's age, let's assign the variable D to represent Daniel's age. Therefore, Ben's age can be expressed as 3D. It's also stated that Ben is 4 years older than Daniel, which gives us another equation, Ben's age equals Daniel's age plus 4 (D + 4).
Setting these two expressions for Ben's age equal to each other gives us: 3D = D + 4. By solving this equation, we subtract D from both sides to get 2D = 4. Dividing both sides by 2 gives us D = 2, which is Daniel’s age.
To find Ben's age, we multiply Daniel’s age by 3, as Ben is three times older than Daniel. So, Ben's age is 3 * 2 = 6 years old.
In account is gaining value at a rate of 4.9% per year that account held $150 and it's first year how much will be in the account after 10 years
Answer:
$242
Step-by-step explanation:
You will need to use the compound interest formula for this.
[tex]P(1+\frac{r}{n} )^{nt}[/tex]
P = initial balance
r = interest rate
n = number of times compounded annually
t = time
Your equation will look like this:
[tex]150(1+\frac{.049}{1} )^{10}[/tex] = $242
Your answer is: $242
Identify the graph of g(x) = –x2 + 9x – 20 from the choices below.
The graph of the quadratic function g(x) = -x^2 + 9x - 20 will be a downward opening parabola with vertex at (4.5, 0.25), x-intercepts at (4, 0) and (5, 0), and a y-intercept at (0, -20). To graph it, label the axes as 'f(x)' and 'x' and scale them to include these critical points.
Explanation:The student wants to identify the graph of the quadratic function g(x) = –x2 + 9x – 20. To do this, first note that the standard form of a quadratic function is ax2 + bx + c, where a, b, and c are constants.
In this case, a = -1 (which makes the parabola open downward), b = 9, and c = -20.
The vertex form of a quadratic function is f(x) = a(x - h)2 + k, where (h, k) is the vertex of the parabola. To find the vertex, we can use the formula h = -b/(2a).
For g(x), this gives h = -9/(2 * -1) = 4.5.
We can then find the value of k by substituting h back into g(x), which gives us k = -4.52 + 9(4.5) - 20.
Therefore, k = 0.25.
The vertex of the parabola is at (4.5, 0.25), and because a is negative, the parabola opens downward. The x-intercepts (or roots) of the parabola can be found by factoring the quadratic equation or using the quadratic formula. In this case, the x-intercepts are (4, 0) and (5, 0). Lastly, the y-intercept occurs when x = 0, which for g(x) is -20.
To label the graph, we'd use 'f(x)' for the vertical axis and 'x' for the horizontal axis. The scale of the axes depends on the maximum and minimum x and y values of the graph, which in this instance would include at least the vertex, x-intercepts, and y-intercept.
Need help!!!!!!
This is so confusing
Answer:
Omar
Step-by-step explanation:
to find the base, which i am to assume they want to find the triangle base based on the formula they are using,
you should multiply base * height, then divide by 2, since it is a triangle, you not solving for a rectangle.
dividing by 2 and multiplying by 1/2 is the same thing!
so,
1/2 (7* 24) is the right answer to finding the base!
Kari looked at he direct base of 7*28, however, that shape is actually a rectangle... so Kari is wrong because he multiplied that dimension by 1/2, which is the formula for a triangle.
Omar is correct because he chose the dimensions of a triangle, and properly used the triangle formula!
i hope this helped you out!
stay safe!
:)
A transit train from Boston to New York and a passenger train from New York to Boston departed at the same time, at 3:00 PM. The distance between New York station and Boston station is 280 miles. The speed of the transit train was 80 miles per hour. The speed of the passenger train was 60 miles per hour.
Chapter Reference
At what time will the trains pass each other?
The transit and passenger trains will pass each other at 5:00 PM, considering their combined speed and the distance between New York and Boston.
The question involves using relative speed to determine the time at which two trains traveling towards each other will meet. The transit train travels from Boston to New York at a speed of 80 mph, and the passenger train travels from New York to Boston at a speed of 60 mph. Since both trains start at the same time and move towards each other, their combined speed is the sum of their individual speeds, which is 80 mph + 60 mph = 140 mph. To find the time taken for the trains to meet, we divide the total distance by their combined speed.
The distance between New York and Boston is 280 miles. Therefore, the time taken to meet is calculated by dividing the distance by the combined speed, which is 280 miles / 140 mph = 2 hours. Given that they departed at 3:00 PM, they will pass each other at 3:00 PM + 2 hours = 5:00 PM.
What area is 20 and perimeter 18
Answer:
Width 4 Length 5
Step-by-step explanation:
4+4+5+5=18
4*5=20
Answer:if your talking about a square or rectangle then two sides would 5 and the other two four
Step-by-step explanation:area equals base times height
Base=5
Height=4
5*4=20 which is area
5+5+4+4=18 which is perimeter
What is the answer to this question
Answer:
A
Step-by-step explanation:
Given the exponential function
f(t) = 228[tex](0.975)^{t}[/tex] ← where t is time in years
Substitute t = 20 into f(t), that is
f(20) = 228 × [tex](0.975)^{20}[/tex] = 228 × 0.60268.... ≈ 137 → A
if 3300 equals 4.5 percent what is the price of 100%
Answer:
73333.333
Step-by-step explanation:
100/4.5= 22.222
3300*22.222= 73333.333
Express your answer exactly
Answer:
sin(θ) = [tex]\frac{\sqrt{55} }{8}[/tex]
Step-by-step explanation:
See the attachment.
Cosine is adjacent over hypotenuse, so since cos(θ) = 3/8, then the adjacent side of the triangle is 3 and the hypotenuse is 8.
Since is opposite divided by hypotenuse. To find the opposite side, which is the unlabelled side on the graph, we need to use the Pythagorean Theorem:
x = [tex]\sqrt{8^2-3^2} =\sqrt{64-9} =\sqrt{55}[/tex]
So, sin(θ) = [tex]\frac{\sqrt{55} }{8}[/tex].
Hope this helps!
4x-2 >-18
what is the answer?!
Hope this will help u....
Six more than the product of 24 and Vidya’s age
If we use v for Vidya's age, then the expression (24v)+6
What is the perimeter of the rhombus below?
Answer:
16
Step-by-step explanation:
the perimeter of the given rhombus is 8√5.
To find the perimeter of a rhombus, we need to calculate the sum of the lengths of all four sides.
Given the coordinates of the points touching the graph: (-5,-3), (-1,-1), (3,-3), and (-1,-5), we can calculate the distances between these points to find the lengths of the sides.
Let's calculate the lengths of the sides:
1. Side 1: Distance between (-5,-3) and (-1,-1)
Length = √[(x2 - x1)^2 + (y2 - y1)^2]
Length = √[(-1 - (-5))^2 + (-1 - (-3))^2]
Length = √[4^2 + 2^2]
Length = √[16 + 4]
Length = √20
Length = 2√5
2. Side 2: Distance between (-1,-1) and (3,-3)
Length = √[(x2 - x1)^2 + (y2 - y1)^2]
Length = √[(3 - (-1))^2 + (-3 - (-1))^2]
Length = √[4^2 + (-2)^2]
Length = √[16 + 4]
Length = √20
Length = 2√5
3. Side 3: Distance between (3,-3) and (-1,-5)
Length = √[(x2 - x1)^2 + (y2 - y1)^2]
Length = √[(-1 - 3)^2 + (-5 - (-3))^2]
Length = √[(-4)^2 + (-2)^2]
Length = √[16 + 4]
Length = √20
Length = 2√5
4. Side 4: Distance between (-1,-5) and (-5,-3)
Length = √[(x2 - x1)^2 + (y2 - y1)^2]
Length = √[(-5 - (-1))^2 + (-3 - (-5))^2]
Length = √[(-4)^2 + 2^2]
Length = √[16 + 4]
Length = √20
Length = 2√5
Now, we can calculate the perimeter by adding the lengths of all four sides:
Perimeter = Side 1 + Side 2 + Side 3 + Side 4
Perimeter = 2√5 + 2√5 + 2√5 + 2√5
Perimeter = 8√5
Therefore, the perimeter of the given rhombus is 8√5.
What is the circumference of the circle? Use 3.14 for pi
r = 6.4 cm
20 096 cm
40 192 cm
200 96 cm
401 92 cm
Answer:
its
40 192 cm
Step-by-step explanation:
Answer:
40.192cm
Step-by-step explanation:
the circumference of a circle = ?
radius = 6.4cm
recall that,
circumference of a circle = 2πr
circumference of a circle = 2 x 3.14 x 6.4cm
circumference of a circle = 40.192cm
therefore the circumference of a circle whose radius is 6.4cm is evaluated to be equals to 40.192cm.
the answer to your question is option B 40.192cm
Similar triangles are two triangles with equal ____ angles.
a. vertical
b. corresponding
angles.
c. horizontal
d. elliptical
Similar triangles are defined as two triangles having equal B. corresponding angles, shown by the congruence of vertical angles, alternate interior angles, and the application of the AAA theorem.
Similar triangles are two triangles with equal corresponding angles. According to the question, in the figure, two triangles named triangle ABC and triangle FCE are observed to be similar because they have three sets of congruent angles - vertical angles (Angle ACB \\<=\ Angle FCE), alternate interior angles (Angle CAB \\<=\ Angle CFE), and another set of alternate interior angles (Angle CBA \\<=\ Angle CEF).
This is summed up by the AAA (Angle Angle Angle) theorem which states that two triangles are similar if all their corresponding angles are congruent. An example will be two right triangles which are equal when the hypotenuse and an acute angle of one are equal, respectively, to the hypotenuse and an acute angle of the other. These principles help us understand the similarity of triangles in geometry.
This graph shows a car moving at a
constant speed. For example, in 8 hours
the car travels 400 miles.
Which equation shows the line on the
graph?
A y = 2x
B y = 50x
C y = 400x
Answer:
B
Step-by-step explanation:
If you set x to hours and y to the amount of miles, you can multiply the hours to the numbers and equal out your miles. So, if 8 hours is multiplied to 50, it equals out the 400 miles.
which expression is equivalent to 9x2 − 16
Answer:
[tex]9 \times 2 - 16 \\ 18 - 16 = 2[/tex]
First one that knows the answer
wins brainliest
Answer:
The bakery made a profit of $8,013 during the summer months
Step-by-step explanation:
A profit is made when income is greater than expenses while a loss is made when expenses are greater than income
A loss is a negative profit
In June
Income = $750
Expense:
rent = $890
Operating costs = $975
Total expense = $1,865
Profit = income - expense
profit = $750 - $1865
= -$1115
Therefore, a loss of $1115 was made in June
July
Income = $ 925
Expenses:
Rent = $890
Operating costs = $721
Total expenses = 1611
Profit = $925 - $1611
= -$686
A loss of $686 was made in July
August
Income = $11,250
Expenses:
Rent = $890
Operating costs= $546
Total expense = $1436
Profit = $11,250 - $1436
= $9,814
A profit of $9,814 was made in August
Now let's find the difference between the profit and losses that were made during the summer months. This will be the addition of the profit and losses of all three months
Remember that losses carry a negative sign
$9,814 -$686 -$1115 = $8,013
Therefore, the bakery made a profit of $8,013 during the summer months
A shop owner bought some T-shirts and purses.
Each T-shirt cost $8 and each purse cost $5
She bought a total of 28 T-shirts and purses.
She spent $161 altogether.
How many T-shirts did she buy? [3 marks]
Answer:
20 t shirt
Step-by-step explanation:
Can someone please explain how to solve this question? I will give thanks and 5 stars! Whoever answers, thank you!
Answer:
33 1/3%
Step-by-step explanation:
When you roll a die, the possible outcomes are 1,2,3,4,5,6
getting a number less than 5: 1,2,3,4
P( getting a number less than 5)
= number of outcomes that meet conditions / total outcomes
=4/6
= 2/3
Then we flip a coin heads or tails
We want heads
P (heads) = number of outcomes that meet conditions / total outcomes
= 1/2
Since the event outcomes do not depend on each other
P( getting a number less than 5) *P (heads) = 2/3 * 1/2 = 1/3
as a percent
= 33 1/3%
66 times 26 times 60 then multiply 1/2
Answer:
Step-by-step explanation:
51,480 is the answer.
Answer:
51,480
Step-by-step explanation:
66 x 26 = 1,716
1,716 x 60 = 102,960
102,960 x 1/2 = 51,480
29+5x=44 whats the valué of x
Answer:
x=3
Step-by-step explanation:
44-29=15
5*3=15
The value of x in the equation 29 + 5x = 44 is solved by isolating x to find that x = 3.
Explanation:To solve the equation 29 + 5x = 44 for x, you should start by isolating the variable on one side. Here's a step-by-step process:
Subtract 29 from both sides of the equation to get 5x = 44 - 29.This simplifies to 5x = 15.To find the value of , divide both sides by 5, leading to .Finally, you get the solution x = 3.Therefore, the value of x in the given equation is 3.
convert 20 miles to km
Answer:
32.1869
Step-by-step explanation:
multiply 20 by 1.609
multiplying miles by 1.609 will give you the answer
Answer:
20 miles =32.1869
Step-by-step explanation:
For an approximate result multiply the length value by 1.609.
The coordinates of trapezoid ABCD are A (-6,3) B (-3,6) C (9,6) and D (-5,-8). Find the coordinates of trapezoid A’ B’ C’ D’ after the translation whose rule is T 3,4.
Answer:
A' (-3,7)
B' (0,10)
C' (12,10)
D' (-2,-4)
Step-by-step explanation:
A' (-6+3 , 3+4) = (-3,7)
B' (-3+3 , 6+4) = (0,10)
C' (9+3 , 6+4) = (12,10)
D' (-5+3 , -8+4) = (-2,-4)
Find the measure of Arc JN
Find the measure of arcJN=
Find the m
Step-by-step explanation:
[tex]m(arc \: JN) = 360 \degree - (60 \degree + 150 \degree) \\ \hspace{57pt}= 360 \degree - 210 \degree \\ \hspace{57pt} = 150\degree \\ \\ m \angle K = \frac{1}{2} \times m(arc \: JN) \\ \hspace{30pt}= \frac{1}{2} \times 150\degree \\ \hspace{30pt} = 75\degree \\ [/tex]
Solve the equation log(x−7)=2
Answer:
x=107
Step-by-step explanation:
If y = 11 inches, z = 14 inches, h = 7 inches, and w = 3 inches, what is the area of the object?
The information given, y = 11 inches, z = 14 inches, h = 7 inches, and w = 3 inches, is not enough to calculate the area of an object unless its shape is known. If it's a rectangular prism, the volume can be calculated. But without further information, we cannot provide a specific area calculation.
Explanation:The type of area an object will have depends on its shape. For example, the area of a rectangle is given by width times height (w * h). Similarly, the volume of a rectangular prism would be length times width times height (l * w * h). However, the given dimensions in the question (y = 11 inches, z = 14 inches, h = 7 inches, and w = 3 inches) are not enough to determine the shape of the object. We need additional information on how these dimensions are related to the shape of the object before we can calculate the area.
If for instance, this object is a rectangular prism, then we could calculate its volume. That volume would be y (depth) * z (width) * h (height). In this case with the provided values, the volume would be 11 inches * 14 inches * 7 inches = 1078 cubic inches.
Without more information on the object’s shape, we can’t make assumptions and provide a definitive calculation of the area.
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1.
What is the mean for the following scores: 2, 5, 4, 1, 8?
A. 3
B. 4
c. 5
20
Answer to your question is:
B. 4
Explanation:
2 + 5 + 4 + 1 + 8 = 20
20 ÷ 5 = 4
The mean is found out by adding the scores given and dividing the total by the number of scores.
In the given question the mean of the scores is 4.
The mean is calculated to get an average about something that is given.
Here
n= number of scores= 5
Sum of scores = ∑x= 2+5+4+1+8= 20
Mean = x bar= ∑x/n= 20/5= 4
For different distributions mean may or may not be the middle value.
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The box-and-whisker plot shows the average temperatures in Orlando, Florida in January.
51,54,57,60,63,66,69,72,75,78,81,84
Which statement about the temperatures in Orlando must be true?
A. About half of the days in January had average temperatures above 75 degrees.
B. About 50% of the days in January had average temperatures between 66 and 75 degrees.
C. The coldest day in January was 66 degrees.
D. The hottest day in December was 75 degrees.
Answer:
B. About 50% of the days in January had average temperatures between 66 and 75 degrees.
The box ranges from 66 to 75... meaning that most of the days were in those temperatures.
The lines mean that there were only a few days that were in those temperatures.
You're welcome if I'm correct.
The correct answer is about 50% of the days in January had average temperatures between 66 and 75 degrees.
What is the box and whisker plot?A Box and Whisker Plot (also known as a Box Plot) is a visual representation of data distribution through quartiles.
The maximum and minimum value of the function is plotted at the ends of a box and whisker plot.The box in the middle displays the interquartile range, which means that about 50% of values when the data is arranged in ascending or descending order.In the graph given in the question we can clearly see that the interquartile range of the data is lying between the temperatures 66° to 75°, which means that 50% of days in January had the temperature between 66 to 75 degrees.
Hence, Option(c) is correct for the given question.
Learn more about quartiles on:
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If a-b = 4 and ab = 60, what is the value of a + b?
Answer:
a + b = 16 or -16.
Step-by-step explanation:
a - b = 4
ab = 60 so a = 60/b
Substituting for a in the first equation:
60/b - b = 4
60 - b^2 = 4b
b^2 + 4b - 60 = 0
(b + 10)b - 6) = 0
b = 6, -10.
Therefore, from the first equation:
When b = -10 . a + 10 =4 giving a = -6 or
When b = 6, a - 6 = 4 giving a = 10.
So when a = -6, b = -10 and
when a = 10, b = 6.
So a + b is either 16 or -16.
please solve this question
Given:
Number of mice and frequency
Mean = 7
To find:
The value of x.
Solution:
Number of mice = X
Frequency = Y
XY = Multiply X and Y values.
X Y XY
5 4 20
6 13 78
7 16 112
8 x 8x
9 6 54
Sum of Y = 4 + 13 + 16 + x + 6
= 39 + x
Sum of XY = 20 + 78 + 112 + 8x + 54
= 8x + 264
Mean formula:
[tex]$Mean = \frac{\Sigma XY }{\Sigma Y}[/tex]
[tex]$7=\frac{8x+264}{39+x}[/tex]
Do cross multiplication.
[tex]7(39+x)=(8x+264)[/tex]
[tex]273+7x=8x+264[/tex]
Subtract 264 from both sides, we get
[tex]9+7x=8x[/tex]
Subtract 7x from both sides, we get
[tex]9=x[/tex]
The value of x is 9.
Vicky works in retail. Her annual gross salary is $24,000. From this, she must pay 15% income tax. In addition, she must repay a loan at a rate of $120 per month. The loan amount is taken out of her post-tax pay (i.e. after the tax has been calculated). What is Vicky's take home pay per month?
Answer:
Vicky's take home pay per month will be $1,580
Step-by-step explanation:
Given that her salary per annual i.e salary for the year = $24,000
Therefore salary per month would be $24,000/12 = $2,000.
From this, she must pay 15% income tax.
i.e 15% of salary
15/100 * 2000
= 0.15*2000
= $300.
Salary after paying tax = $2,000 - $300= $1,700.
Since, she must repay a loan at a rate of $120 per month we will reduct the loan from her salary,
$1,700 - $120 = $1,580
Vicky's take home pay per month will be $1,580
Answer: Vicky's take home pay per month is $1,580
Step-by-step explanation: If Vicky's annual gross salary (salary before any deductions) is given as 24000, then her monthly gross salary is derived as;
Salary Per month = 24000/12
Salary per month = 2000
She must pay 15 percent income tax and this derived as follows;
Income tax = 2000 x 0.15
Income tax = 300
Therefore her salary after tax deduction is derived as follows;
Salary after tax = 2000 - 300
Salary after tax = 1700
However, she must repay a loan (after tax deduction) at a rate of 120 per month, which is now derived as follows;
Salary after loan repayment = 1700 - 120
Salary after loan repayment = 1580
Therefore the calculations show that her take home pay after all adjustments comes down to $1,580 per month.