The inequality that represents the greatest number of rides that Daniel can go is 1.50x + 10 ≤ 40
How to solve for the inequalityFrom the question we would have the inequality that would be written as
1.50x + 10 ≤ 40
admission is 10 dollars
cost of rides is 1.50 dollars
So, the equation would be -
1.50x + 10 ≤ 40
we are to solve for the value of x. Such that we would have
1.5x ≤ 40 - 10
1.5x ≤ 30
divide through by 1.5
x = 30 / 1.5
x = 20
Proof
Hence we would have
1.5 * 20 = 30 + 10 = 40
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What is the equation of this line in slope intercept form?
y = mx + b
m = slope
b = y-intercept
The equation of the line in slope intercept form is y = -4x + 1.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
Intercept of a line is the point where the line touches with one of the axis.
The general equation of a line in slope intercept form is,
y = mx + d, where m is the slope and d is the y intercept.
y intercept point touches the y axis.
Take any two points from the line.
Let it be (0, 1) and (-1, 5).
Slope = (5 - 1) / (-1 - 0) = 4 / (-1) = -4
m = -4
We have the point (0, 1), where the line touches the Y axis.
y intercept, d = 1.
Equation of the line is,
y = -4x + 1
Hence the equation of the line is y = -4x + 1, when slope is -4 and y intercept is 1.
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Find the missing side length. Tell if the side lengths form a Pythagorean triple. Also, identify the correct explanation.
The missing side length is 17 and the side lengths 8, 15, and 17 form a Pythagorean triple.
Side lengths: 8, 15
Missing side length: 17
Yes, the side lengths form a Pythagorean triple. The side lengths 8, 15, and 17 form a Pythagorean triple because 8^2 + 15^2 = 17^2.
To answer this question, we first need to determine if the side lengths 8, 15 and the missing side length form a Pythagorean triple. To do this, we use the Pythagorean theorem which states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side. If this is true, then the side lengths form a Pythagorean triple.
In this case, we can plug in the side lengths 8 and 15 into the Pythagorean theorem. 8^2 + 15^2 = 17^2. Since the equation is true, this means that the side lengths 8, 15 and 17 form a Pythagorean triple. Therefore, the missing side length is 17.
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A student solved the following problem and made an error:
Triangles ABC and DEF. Angles A and F are congruent and measure 135 degrees. The coordinates for the vertices are at A 0, 2 and B 2, 4 and C 0, 0 and D 2, 0 and E 4, 4 and F 4, 2.
Line 1 segment AC equals 2, segment DF equals 2, segment AC is congruent to segment DF
Line 2 ∠A ≅ ∠F
Line 3 Length of segment AB.
A (0, 2)
B (2, 4)
d equals square root of quantity x sub 1 minus x sub 2 squared plus quantity y sub 1 minus y sub 2 squared, then d equals the square root of quantity 0 minus 2 all squared plus quantity 2 minus 4 all squared, then d equals the square root of negative 2 squared plus negative 2 squared, then d equals the square root of 4 plus 4, then d equals the square root of 8
segment AB = 2.83
Line 4 Length of segment FD.
D (2, 0)
F (4, 2)
d equals the square root of quantity x sub 1 minus x sub 2 squared plus quantity y sub 1 minus y sub 2 squared then d equals the square root of quantity 2 minus 4 all squared plus quantity 0 minus 2 all squared, then d equals the square root of negative 2 squared plus negative 2 squared, then d equals the square root of 4 plus 4, then d equals the square root of 8
segment FD = 2.83
Line 5 segment AC is congruent to segment FD
Line 6 triangle ABC is congruent to triangle FDE by SAS
In which line did the student make the first mistake?
Triangle ABC is congruent to triangle FDE by SAS congruence. Therefore, students did mistake in line 1.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
Given that, in triangles ABC and DEF
∠A≅∠F=135°
The coordinates for the vertices are at A(0, 2), B(2, 4) and C(0, 0)
In triangle DEF, we have D(2, 0), E(4, 4) and F(4, 2)
AC= 2 units and DF= 2 units
AC≅DF
Length of segment AB.
A (0, 2) and B (2, 4)
Here, d=√[(x₂-x₁)²+(y₂-y₁)²]
= √[(2-0)²+(4-2)²]
= √8
AB = 2.83
Length of segment FD.
D (2, 0)
F (4, 2)
Here, d=√[(4-2)²+(2-0)²]
FD= = 2.83
AC≅FD
Triangle ABC is congruent to triangle FDE by SAS congruence
Hence, students did mistake in line 1.
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Need help ASAP……………..
Answer:
5
Step-by-step explanation:
diameter = 4 so radius =2
open up the cylinder so its top & bottom circle's circumference = 2πr =4π
top & bottom circle's area = πr² = 4π each, 8π for both
total surface = 28π
so lateral surface = 28π - 8π = 20π
so 20π = 4π* height
so height is 5
What was the principal for continuously compounded account earning 3.9% for 15 years that
now has a balance of $2,656,586.66?
$4,768,549.11
$1,496,548.42
$1,480,000
This problem is related to the concept of continuous compounding, which is a method of calculating the interest earned on an account over a certain period of time. The formula for calculating the principal amount for a continuously compounded account earning 3.9% for 15 years is as follows:
P = A/ (1 + r)^t
Where P is the principal, A is the balance after 15 years, r is the rate of interest and t is the number of years.
In this problem, P = $4,768,549.11, A = $2,656,586.66, r = 3.9% and t = 15.
Therefore, the principal for the continuously compounded account earning 3.9% for 15 years is $4,768,549.11
If the length of each side of a square is represented by 3x + 5, which expression represents the perimeter?
(1)
2)
3)
4) 9x² + 6x + 25
6x +10
12x + 20
12x² + 20
The expression that represents the perimeter is 12x+20 the correct option is C
What is perimeter?Perimeter is the sum of length of the sides used to made the given figure. A regular figure with n-sides has n equal sides in it, and they are the only parts of it(that means, nothing more than those of equal length n sides).
Given;
The length of each side of square= 3x+5
Perimeter of square= 4a
where, a is the length of each side
So,
perimeter= 4 x (3x+5)
= (4 x 3x) + (4 x 5)
= 12x +20
Therefore, the perimeter will be12x+20
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Is my birthday divisible by 3?
Yes, your birthday is divisible by 3.
To check if a number is divisible by 3, the sum of its digits must be divisible by 3. To determine the sum of the digits of your birthday, we can use the formula:
Birthday = abc
Sum of digits = a + b + c
For example, if your birthday is the 7th of December, 2020:
Birthday = 07122020
Sum of digits = 0 + 7 + 1 + 2 + 2 + 0 + 2 + 0 = 14
Since 14 is divisible by 3, your birthday is divisible by 3.
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Quarter 2 Assessment
The line models the temperature on a certain winter day since sunrise. What is the y-intercept of the
line? What does the y-intercept represent?
Temperature (degrees Celsius)
10-
6
4
0
Temperature Since Sunrise
2
6
4
Hours after Sunrise
00-
8
10
I
The y-intercept is
What does the y-intercept represent?
O
O
O
O
The rate the temperature increases
The temperature at sunrise
The temperature at sunset
The rate the temperature decreases
The point on a line where it crosses the y-axis is known as the y-intercept.
Graphs and charts are useful visual aids because they make information accessible and quick to understand. Therefore, it is not unexpected that print and electronic media frequently use graphs. When data is displayed as a graph rather than a table, it can often be easier to understand because the graph might show a pattern or comparison.
The temperature initially climbs to 5 degrees Celsius.
formula for a line
A line's y-intercept, also known as the point where the x-coordinate equals zero, is where the line intersects the y-axis.
You can see from the graph that the line intersects the y-axis at y = 5. This demonstrates that the temperature initially increases to 5 degrees Celsius.
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Complete question -
The total charge on 4 particles is −36 units. All the particles have the same charge. What is the charge on each particle? (3 points) a −9 units b −8 units c 8 units d 9 units
HELPPP AGAIN PLEASEE. What is the equation of the line that passes through the point (-6,5) and has a slope of -3/2?
Answer:
y - y1 = m(x - x1)
y - 5 = -3/2 [x - (-6) ]
2 (y - 5) = 2 × -3/2 [x - (-6) ]
2y - 10 = -3 [x + 6]
2y - 10 = -3x - 18
2y- 10 + 3x + 18 = 0
2y + 3x -10 + 18 = 0
2y + 3x + 8 = 0
Step-by-step explanation:
I stated the formula to find the equation of the line . Then replaced the y1 and x1 with -6 and 5 respectively. I multiplied the whole equation by the LCM, which is 2. Group the whole equation to the left and equate it to 0. Then group like terms and solve. The final answer is the equation of the line
what is y=x-1 if y=x+5
Answer:
I think your question is incorrect
Do the segments 15 12 and 9 form a right triangle?
It is possible to construct a triangle whose sides are 15 cm 12 cm and 9 cm because the sum of two sides are greater than three sides.
In the given question, we have to check that it is possible to construct a triangle whose sides are 15 cm 12 cm and 9 cm.
The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.
To check this we firstly add the 15 and 12
15 + 12 > 9
27 > 9
Now we add 15 and 9
15 + 9 > 12
24 > 12
Now we add 12 and 9
12 + 9 > 15
21 > 15
It is possible to construct a triangle whose sides are 15 cm 12 cm and 9 cm because the sum of two sides are greater than three sides.
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Is it possible to have a triangle with the following sides 3cm 5cm 7cm?
One can create a triangle with the sides 3 cm, 5 cm and 7 cm.
We can check the possibility of constructing a triangle through side-side-side. It states that the sum of any two sides of triangle should be greater than third side of the triangle. Therefore, let us say 3 cm is side a, 5 cm is side b and 7 cm is side c.
Now, checking the rule.
Side a + side b > side c
3 + 5 > 7
Add the digits on left
8 > 7
Side b + side c > side a
5 + 7 > 8
Add the digits on left
12 > 8
side c + side a > side b
8 + 5 > 7
Add the digits on left
13 > 7
The side-side-side rule of triangle is followed in all the cases, and hence triangle formation is possible.
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Draw any line egment pq take any point r on it. Through R draw a perpendicular to pq
Perpendicular drawn through point R on the given line segment PQ.
Constructed figure is attached.
Step of construction :
Constructed figure is attached.
Draw a line segment PQ of any measurement.Take a point R on the line segment PQ.Draw an arc through point R on line segment PQ such that it intersect PQ at point A and B.Now take more than half the measure of arc AB .Take A as center and draw an arc in the upper half plane of line segment PQ.Take B as center and with the same measure draw an arc in the upper half plane of line segment PQ such that it intersect the previous arc and name it C.Join RC which represent the perpendicular drawn through point R on line segment PQ.Therefore, perpendicular line drawn through point R on line segment PQ using above steps of construction.
The above question is incomplete , the complete question is :
Draw any line segment PQ take any point R on it. Through R draw a perpendicular to PQ.
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24. Mr. Karbon is 35 years old and his heart beats on average 62 beats per minute.
How many times has his heart been beating during his life? (assume there are no leap
years)
Mr. Karbon 1,14,05,52,000 times has his heart been beating during his life.
Adults typically have a resting heart rate between 60 and 100 beats per minute. A lower resting heart rate typically indicates improved cardiovascular fitness and more effective cardiac function. A well-trained athlete, for instance, might have a typical resting heart rate that is closer to 40 beats per minute.
Based on your age, you may calculate your maximum heart rate. Subtract your age from 220 to get a ballpark idea of your maximal age-related heart rate. For instance, the predicted maximum age-related heart rate for a 50-year-old person would be computed as 220 - 50 years = 170 beats per minute (bpm).
There are total 60 minutes in an hour,
1440 minutes in a day,
There are 365 days in a year,
and Mr. Karbon has lived for 35 years.
his heart beats on average 62 beats per minute.
His heart has beaten for 35 × 365 × 1440 × 62
1,14,05,52,000 times has his heart been beating during his life.
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621 x 99 = 621 x ----- - 621 x ---------(1 Point)
a) 90 ,9
b) 100 ,1
c) 98 ,1
d) 0 ,100
621 × 99 = 621 × 100 - 621 x 1
option b is correct.
6(x + 3) = -84
Show work
Answer: -14
Step-by-step explanation:
1) Distribute
6(x+3) =-84
6*x + 6*3 =-84
6x + 18 = -84
2) Addition/Subtraction Inverse
6x + 18 =-84
-18. -18
3) Divide/Multiply Inverse
6x = -84
-84/6x = -14
Answer:
x = -17
Step-by-step explanation:
6(x + 3) = -84
6x + 18 = -84
6x = -84 - 18
6x = -102
x = -102 : 6
x = -17
------------------------------------
check6(-17 + 3) = -84
-102 + 18 = -84
-102 = -84 - 18
-102 = -102
the answer is good
how to find the acute angle of each angle in a triangle if the given angles are in the form of an equation
To find the acute angle of each angle in a triangle if the given angles are in the form of an equation follow the steps in the main answer part
What is the acute angle?To find the acute angles of a triangle given the angles in the form of an equation, you can use the following steps:
Write down the equation for the triangle's angles, typically in the form of "angle A + angle B + angle C = 180 degrees".Use the equation to solve for one of the angles. For example, if the equation is "angle A + angle B + angle C = 180 degrees", you can solve for angle A by subtracting angle B and angle C from 180 degrees.Repeat step 2 for the other angles.Check if the angles are acute or not. An acute angle is an angle that measures less than 90 degrees.If an angle is not acute, use the property of the triangle that the sum of all the angles is 180° and subtract the angle from 180° to get the acute angle.Example: Let's say you are given an equation,
A+B+C = 180°
If
A = 70°
B = 70° then
C = 40°
C is not acute, so subtract it from 180° to get C= 140°
Now you have A = 70° and C = 140° which are acute angles.
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Do sides 7cm 24cm 25cm form a right angled triangle *?
Given, sides of the triangle are 7 cm, 24 cm, and 25 cm. Squaring the lengths of the sides of the, we will get 49, 576, and 625. Therefore, the above equation satisfies, Pythagoras theorem. Hence, it is right angled triangle.
Which are side of a right triangle 7 24 and 25?Yes, 7, 24, 25 is a Pythagorean Triple and sides of a right triangle. Yes, 9, 40, 41 is a Pythagorean Triple and sides of a right triangle. No, 11, 56, 57 do not represent the sides of a right triangle.The triangle is therefore not acute. Thirteen plus seven equals twenty, and twenty is more than nine. The Triangle Inequality Theorem is satisfied by this set of side lengths. A triangle is formed by these lengths. No, not in the traditional sense of the word (Euclidean geometry). A "degenerate triangle" is possible, but it isn't exactly a triangle in the sense that we often think of triangle 8 + 7 = 15 the length of any two sides added together.To learn more about side of a right triangle refer to:
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6. Keith's charge account uses the unpaid-balance method to compute the finance charge
at a monthly periodic rate of 1.5%. His previous balance was $200. During the month,
he charged $178.62, made a $200 payment.
a. What is Kieth's unpaid balance?
b. What is Kieth's finance charge?
c. What is Kieth's new balance?
Keith's unpaid balance is $178.62, finance charge is $2.6795 and new balance is $181.2995
Kieth's unpaid balanceTo find Keith's unpaid balance, we need to find the difference between the previous balance and the payments made during the month.
Keith's previous balance was $200.
During the month, he charged $178.62, made a $200 payment.
So, Keith's unpaid balance is:
$200 (previous balance) - $200 (payment) + $178.62 (charges) = $178.62
Finance chargeTo find Keith's finance charge, we need to multiply the unpaid balance by the monthly periodic rate (1.5% in this case).
Keith's finance charge is:
$178.62 (unpaid balance) * 0.015 (monthly periodic rate) = $2.6795
New balanceTo find Keith's new balance, we need to add the finance charge to the unpaid balance.
Keith's new balance is:
$178.62 (unpaid balance) + $2.6795 (finance charge) = $181.2995
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What is the quotient of 2.506 × 108 and 8.95 × 104
* expressed in scientific
notation?
The quotient of 2.506 × 10^8 and 8.95 × 10^4 expressed in scientific
notation is 2.8 x 10^3.
What is the quotient?
Quotient is the result of the division process. Scientific notation is a method that is used to compress larger numbers into smaller numbers. In order to write a number in scientific notation, the number is expressed as a power of 10. For example, 1000 in scientific notation is 1 x 10³.
(2.506 x 10^8) ÷ (8.95 x 10^4)
= (2.506 / 8.95) x 10^8 - 4
0.28 x 10^4
2.8 x 10^4 - 1
= 2.8 x 10^3
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52.8% as fraction in simplest form
Answer:
66/125
Step-by-step explanation:
%52.8 = 52.8/100
= 0.528
0.528/1 x 1000/1000
=528/1000
=66/125
i need help on question 7 please!!!
For a single serving, 1 4/5 pounds of chicken is needed.
What is the fraction?
A fraction is a way of representing a part of a whole. It consists of two parts: the numerator and the denominator. The numerator represents the number of parts being considered, and the denominator represents the number of parts in the whole.
To find out how many pounds of chicken will be needed for a single serving, we need to divide the amount of chicken needed for 4 servings by the number of servings.
The amount of chicken needed for 4 servings is 4 4/5 pounds. To convert it to a single serving we will divide it by 4.
(4 4/5) / 4 = (4 + 4/5) / 4 = 4/4 + 4/5*4/4 = 1 + 4/5 = 1 4/5 pounds
Hence, for a single serving, 1 4/5 pounds of chicken is needed.
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Assignment is due tonight!!!! Please help
Erik and Nita are playing a game with numbers. In the game, they each think of a random number from 0 to 20. If the difference between their two numbers is less than 10, then Erik wins. If the difference between their two numbers is greater than 10, then Nita wins. Use the information in the interactive and what you know about absolute value inequalities to better understand the game.
The inequality for Erik to win is
|x- y| ≤ 10
And for Nita to win
|x- y| ≥ 10
What is Inequality ?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), larger than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Inequalities define the connection between two values that are not equal. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than. The different inequality symbols, characteristics, and methods for resolving linear inequalities in one variable and two variables will all be covered in this article along with examples.
In the problem let the number chosen by Erik and Nita be x and y respectively .
here both x,y ≤ 20
so the inequality for Erik to win is
|x- y| ≤ 10
And for Nita to win
|x- y| ≥ 10
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ASAP
If f(x)= 3x-4, which of these is the inverse of f(x)?
O A. f-¹(x)=X-4/3
B. f¹(x)=x+4/3
OC. F¹(x) = x/3+4
OD. ¹(x)=x/3-4
Answer:
Step-by-step explanation:
f(x)=−3x−4
f
(x)=−3x−4 as an equation.
y=−3x−4 Interchange the variables.
x=−3y−4 Solve for y
y=−x3−4
3 Replace y with f−1(x) to show the final answer.
f−1(x)=−x3−43 Verify if f−1(x)=−x3−43
is the inverse of (x)=−3x−4.
F−1(x)=−x3−43
Use the origin as the center of dilation and the given scale factor to find the coordinates of the vertices of the image of the polygon.
k = 2
The coordinates of the points after dilation is P'(6,10), Q'(8,0), and R'(2,2).
What is dilation?Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.
Given that the scale factor is 2. The coordinates of the points after dilation is,
P(3,5) = P'(6,10)
Q(4,0) = Q'(8,0)
R(1,1) = R'(2,2)
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one more than the difference between 18 and 7 times a number is -9
eight times a number plus 6 less than twice the number is 34
twelve less than the quotient of a number and 8 is -1
i don't think they're supposed to be fractions as going over the others in class didn't and tried checking over my work
Answer:
The difference between 18 and seven times a number: 18 - 7x
Step-by-step explanation:
(ii) One more than the difference between 18 and seven times a number:
Add 1 to the expression from step (i) and get
1 + (18 - 7x)
(iii) One more than the difference between 18 and seven times a number is -9:
Set expression from step (ii) equal to -9 and get
1 + (18 - 7x) = -9
You can simplify and solve for x.
If mary had 456 apple, and her iter had half of mary apple, and they both give half of their apple to their mom, nhow many apple doe the girl till have?
Answer:
Mary:228
iter:114
Step-by-step explanation:
Mary's "iter" would have 228 apples (half of what mary has) and would be left with 114 after giving half to her mother.
Mary would be left with 228 apples because 456/2=228.
He tax rate a a percent, r, charged on an item can be determined uing the formula StartFraction c Over p EndFraction minu 1 equal r. – 1 = r, where c i the final cot of the item and p i the price of the item before tax. Louie rewrite the equation to olve for the final cot of the item: c = p(1 ). What i the final cot of a $40 item after an 8% tax i applied?
A $40 item will ultimately cost $43.2 when an 8% tax is included.
The formula Lousie used is:
c = p(1 + r)
We will solve this problem with the help of percentages.
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
We are given that the price of the item is $40
r = 8% .
Therefore,
c = 40(1 + 8%)
c = 40 (1 + 8/100)
c = 40 ((100+8)/100)
c = 40 (108/100)
c = 40 * 1.08 = 43.2
Final cost = $43.2
Therefore the final cost of the $40 item after an 8% tax is applied will be $43.2.
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Melissa is planning a rectangular vegetable garden with a square patch for tomatoes. She wants the length of the garden to exceed three times the length of the tomato patch by 2 feet. She also wants the garden’s width to exceed the width of the tomato patch by 5 feet.
Let x represent the length, in feet, of the square tomato patch.
Write expressions to represent the length and width of Melissa’s vegetable garden in terms of x.
Enter the correct answer in the box.
y = ____
The expressions to represent the length and width of Melissa’s vegetable garden in terms of x include the following:
y = 3x + 2.
y = x + 5
How to write the required expressions?In order to write the expressions representing the length and width of Melissa’s vegetable garden, we would assign variables to its dimensions as follows;
Let the variable x represent the length of the tomato square patch.Let the variable y represent the length of the rectangular vegetable garden.Since Melissa wants the length of her rectangular vegetable garden to exceed three (3) times the length of the tomato square patch by 2 feet, the length of the rectangular vegetable garden with respect to its length is given by:
y = 3x + 2.
For the width, an expression for the rectangular vegetable garden's width with respect to the width of the tomato square patch is given by:
y = x + 5
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