Answer:
Option D is correct
[tex]y =-\frac{1}{4}x+10[/tex]
Step-by-step explanation:
Slope intercept form:
The equation of line is given by:
[tex]y=mx+c[/tex] .....[1]
where, m is the rate or slope and c is the y-intercept or initial value.
As per the statement:
Here, y represents the distance in kilometer and x represents the time in minutes.
A student is running a 10-kilometer race
⇒y(0) = b = 10 km
It is also given that he runs 1 kilometer every 4 minutes.
Now, with each passing minute the student is getting closer and closer to the finish line which was 10 kilometers away when the race started. Thus, as the race progresses, the distance between the student and the finish line will decrease.
[tex]m =-\frac{1}{4}[/tex]
Substitute these in [1] we have;
[tex]y = -\frac{1}{4}x+10[/tex]
Therefore, the function that describes his distance from the finish line is, [tex]y = -\frac{1}{4}x+10[/tex]
Jordan’s job is located 67 miles from his home. His car’s gas mileage is 21 miles to the gallon. Approximately how many gallons of gasoline does Jordan need each day?
I think the answer is 6.381 gallons or 3.2?
The number of gallons of gasoline Jordan need each day is:
3.190476 gallons.
Step-by-step explanation:It is given that:
Jordan’s job is located 67 miles from his home.
His car’s gas mileage is 21 miles to the gallon.
i.e. for 21 miles he need 1 gallon of gas.
This means in order to cover 1 mile he needs 1/21 gallon of gas.
Hence,
In order to cover 67 miles he needs 67/21 gallon of gas
i.e.
for 67 miles he needs 3.190476 gallons of gas.
If 7 units represent 98 liters find the value of 15 units
Final answer:
To find the value of 15 units when 7 units represent 98 liters, set up a proportion, cross multiply, and divide to find the value of 15 units, which is 210 liters.
Explanation:
To find the value of 15 units when 7 units represent 98 liters:
Set up a proportion: 7 units = 98 liters and determine the value of 15 units.Cross multiply to solve for the unknown value: 7 units * x liters = 15 units * 98 liters.Divide to find the value of 15 units: x = (15 * 98) / 7 = 210 liters.Decide whether y is a function of x.
y=-3x-4
Plane ABC and plane BCE ____ be the same plane.
A. must
B. may
C. cannot
A 16-inch cheese pizza at Fine Dough Pizza costs $10.00 and each additional topping is $1.50. The same size pizza at Johnson's Pizza costs $8.00 and each additional topping is $2.00. After how many toppings do the pizzas cost the same? Which pizza costs more with additional toppings?
To find the number of toppings at which the pizzas cost the same, we can set the total cost expressions for both pizzas equal to each other and solve for 'x'. After 4 additional toppings, the pizzas will cost the same. With 5 additional toppings, Johnson's Pizza costs more.
Explanation:To find the point at which the pizzas cost the same, we need to determine the number of toppings that will make the total cost equal for both pizzas. Let's denote the number of additional toppings as 'x', and the cost of each additional topping at Fine Dough Pizza as $1.50, and at Johnson's Pizza as $2.00. The total cost for Fine Dough Pizza will be $10.00 + $1.50x, and the total cost for Johnson's Pizza will be $8.00 + $2.00x. To find the number of toppings at which the pizzas cost the same, we can set the two total cost expressions equal to each other and solve for 'x':
$10.00 + $1.50x = $8.00 + $2.00x
To solve the equation, we can subtract $1.50x from both sides:
$10.00 = $8.00 + $0.50x
Next, we subtract $8.00 from both sides:
$2.00 = $0.50x
To isolate 'x', we divide both sides by $0.50:
x = 4
Therefore, after 4 additional toppings, the pizzas will cost the same.
To determine which pizza costs more with additional toppings, we can compare the total cost expressions for both pizzas for a specific number of toppings. For example, let's consider 5 additional toppings:
Total cost at Fine Dough Pizza = $10.00 + $1.50(5) = $10.00 + $7.50 = $17.50
Total cost at Johnson's Pizza = $8.00 + $2.00(5) = $8.00 + $10.00 = $18.00
Therefore, with 5 additional toppings, Johnson's Pizza costs more.
Alberto is making a budget. He owes a cell phone bill of $60 per month for 23 more months, plus the fees for any extra usage such as text messaging or extra minutes. Which of the following is the correct category for this expense?
a.
Essential (flexible) expense
b.
Emergency fund
c.
Essential (fixed) expense
d.
Non-essential expense
Answer:
a. Essential (flexible) expense
Step-by-step explanation:
Most people consider a cell phone an essential expense, since they are used in power outages or emergencies while traveling.
This is a flexible expense, since there are extra fees for extra usage.
The phone bill expense is an Essential (flexible) expense so option (A) will be correct.
What is the reasoning?The procedure of utilizing logical reasoning to analyze a condition to determine the best problem-solving approach for a particular issue, then using this approach to create and explain a resolution.
In another word, reasoning is a tricky but interesting problem in mathematics that required relations of variables to solve.
The mobile cost is an essential cost because it is can be used in an emergency situation or it is very useful for calling massaging or video calling.
Since the plan for mobile recharge varies higher or lower according to benefits so it will be a flexible expense.
Hence "The phone bill expense is an Essential (flexible) expense".
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Find the circumference of the circle if the square has an area of 144 m2. Give your answer to the nearest tenth. Use 3.14 form
The circumference of the circle is found by first determining the side length of the square, then using that to calculate the diameter and radius of the circle. Using 3.14 as an approximation for pi, the circumference is calculated to be 37.7 meters when rounded to the nearest tenth.
To find the circumference of the circle when the square has an area of 144 m², we first determine the side length of the square using the formula for the area of a square, A = a², where A is the area and a is the side length.
A = 144m²
a = 12m
Since the area is 144 m², the side length of the square is "12 m (since 12 x 12 = 144).
Since the circle fits perfectly within the square, the diameter D of the circle is equal to the side length of the square. Therefore, D = 12 m. The radius r is half the diameter, so in this case, r = 6 m.
The formula for the circumference C of a circle is C = 2πr.
C = 2 x 3.14 x 6 m = 37.68 m
The circumference is 37.7 m.
What is the coefficient of the term 43yz ? A. 1/3 B.4 C.4/3 D.4yz
Using the rule of thirds to evaluate the composition of a well-crafted painting, the eye should be attracted to A. one or more points of interest. B. the top of the painting. C. the lighter values in the painting. D. the midpoint of the composition.
Answer: A: one or more points of interest.
Step-by-step explanation:
The rule says that an image should be divided into 9 equal squares by two horizontal and two vertical lines and that the important objects of the image should be placed between the lines (in the centers of the squares) or in the intersections of the lines.
In this way, the eye is dragged to the different points that the artist wants the viewer to focus on the image, then the correct option is option A: one or more points of interest.
How to factorise 4b squared + 19b
Before 1995, three-digit area codes for the united states had the following restrictions:
(a) neither 0 nor 1 could be used as the first digit.
(b) 0 or 1 had to be used for the second digit.
(c) there were no restrictions on the third digit.
How many different area codes were possible?
If the altitude of an isosceles right triangle has a length of x units, what is the length of one leg of the large right triangle in terms of x? x units x units x units 2x units
the picture in the attached figure
we know that
if ABC is an isosceles triangle
then
AB=BC
angle A=angle C=45 degrees
and
triangle ABD and triangle BDC also are isosceles triangles
AD=BD=x
DC=BD=x
the hypotenuse AC is equal to
[tex] AC=AD+DC\\ AC=x+x\\ AC=2x [/tex]
To find the length AB applying the Pythagorean Theorem
[tex] AC^{2} =AB^{2} +BC^{2} [/tex]
remember that AB=BC
[tex] AC^{2} =2AB^{2} [/tex]
[tex] AC^{2} =2AB^{2}\\\\ AB=\frac{AC}{\sqrt{2}}\\\\ AB=\frac{2x}{\sqrt{2}}\\\\ AB=x\sqrt{2} [/tex]
therefore
the answer is
the length of one leg of the large right triangle in terms of x is equal to [tex] x\sqrt{2} [/tex]
Answer:
b)x/2
Step-by-step explanation:
took the test
write 33/72 in simplest form
11/72
33/24
33/72
11/24
please explain ...?
Simplify as an Exponent: 10 •10• 3 • 3 • 3 =
Consider a triangle where A=30 degrees, a=1.5cm and b=2cm
How many possible triangles have the above properties? Write either 0 or 1 or 2.
I don't understand this question at all. ...?
With the given conditions of angle A being 30 degrees, side a being 1.5 cm, and side b being 2 cm in a triangle, only one possible triangle satisfies these properties according to the Law of Sines.
Explanation:The question relates to determining the number of possible triangles given certain conditions. Specifically, it refers to a triangle with an angle A of 30 degrees, a side a of 1.5 cm opposite to A, and another side b of 2 cm. To decide the number of possible triangles that fit these criteria, we make use of the Law of Sines. This law states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.
In the given scenario, since side a (1.5 cm), opposite to angle A (30 degrees), is shorter than side b (2 cm), it is possible that two different triangles could exist, often referred to as the ambiguous case in the Law of Sines. However, the fact that side a is shorter than side b coupled with angle A being acute (30 degrees) leaves us with only one possible triangle. This is because the side opposite the smallest angle (A) cannot form a valid triangle if it's longer than the other given side. Therefore, there is just one solution to this problem.
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For the function f(x) = x2 -12, find (f o f-1)(4)
15 is what percent of 56
If t = -2π/3, evaluate (if possible) sin t, cos t, tan t
The diagram below shows a square inside a regular octagon. The apothem of the octagon is 13.28 units. To the nearest square unit, what is the area of the shaded region?
Area of shaded region is 463 square units.
What is area of octagon?Area of octagon = [tex]\frac{1}{2}[/tex] × [tex]8[/tex] × base × height
What is apothem of octagon?The apothem of any polygon is equal to the line that connects the center of the polygon with one of its sides perpendicularly. Using the apothem, we can calculate the area of the polygons in an easier way.
Given
Apothem of the octagon = 13.28 units
Base of octagon = 11 units
Area of octagon = [tex]\frac{1}{2}[/tex] × [tex]8[/tex] × base × height
= [tex]\frac{1}{2}[/tex] × [tex]11[/tex] × [tex]13.28[/tex] × [tex]8[/tex]
= 584.32
Area of square = side × side
= 11 × 11
= 121
Area of shaded region = Area of octagon - Area of square
= 84.32 - 121
= 463.32
≅ 463 square units.
Hence, area of shaded region is 463 square units.
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Solve for b. ab + c = d b = a + c/d b = a/(c - d) b = (d - c)/a
Answer: im sorry if im wrong but i think the answer is 0.3
Step-by-step explanation:
From net earnings of $740 per month for the rent on an apartment she says the two friends what percent of income is her rent payment
Factor completely: 5ab(x + 6) − 4(x + 6) ...?
Answer:
D is your answer :)
Step-by-step explanation:
In 5 years, Dad will be three times as old as his daughter Jill will be then. If the sum of their present ages is 50, how old are they now?
If x + 5 is Jill's age five years from now, which of the following equations could be used to solve the problem?
a.3x + 5 = 55 - x
b.3x + 15 = 55 - x
c.3x + 15 = 45 - x ...?
The height of a cone is two times its base diameter. What is the volume of the cone in terms of its base radius r?
I will Upvote!
A bicyclist rides 14 miles in 112 minutes. If she continues at this speed, how long will it take her to travel 35 miles?
A) 43 minutes
B) 45 minutes
C) 280 minutes
D) 602 minutes
8y + 9
What is the variable term in the expression?
Answer:
8y
Step-by-step explanation:I took the test
8y contain the variable term where the variable is 'y'.
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
expression: 8y + 9
As, we know a symbol without a set value is referred to as a variable.
So, 8y contain the variable term where the variable is 'y'.
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A convention center rents a meeting room for $250 per day. There is a $30 one-time fee to make a reservation.
What function equation represents the total cost to rent a meeting room for d days?
A. c(d) = 250d + 30
B. c(d) = 30d − 250
C. c(d) = 30d + 250
D. c(d) = 250d − 30
The price of a gallon of milk is 3.70 5 dollars what is the price that is rounded to the nearest dollar
solve.
5m + 7/2 = -2m + 5/2
P is the midpoint of QN, MP is perpendicular to to QN prove rectangle MRQ is congruent to rectangle MRN
By using the rules of geometry, we can determine that if P is the midpoint of QN and MP is perpendicular to QN, then rectangles MRQ and MRN are congruent. The congruency is due to the properties of rectangles, triangles, midpoints, and the Hypotenuse-Leg Theorem.
Explanation:The proof of the congruence of rectangles MRQ and MRN involves geometry rules, particularly the properties of rectangles, triangles, and midpoints. Let's consider rectangle MRQ and MRN. We know that in a rectangle, diagonals are congruent. If P is the midpoint of QN, that means QP = PN. Additionally, if MP is perpendicular to QN, PMQR and PMNR are right triangles with the same hypotenuse.
Using the properties of triangles, we can say that if two right triangles have a congruent hypotenuse and one leg (which is MP in both cases), then these triangles are congruent. Therefore, ∆PMQR is congruent to ∆ PMNR by the Hypotenuse-Leg (HL) Theorem.
Considering that ∆ PMQR ≅ ∆ PMNR and QP = PN, we can say that quadrilaterals MRQN and MRNP are each a parallelogram. Additionally, since MP is perpendicular to QN, quadrilaterals MRQN and MRNP are actually rectangles based on the definition of a rectangle (a parallelogram with a right angle). Therefore, rectangle MRQ is congruent to rectangle MRN.
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