The area of a circle with a radius of 7.5 cm is 176.81 cm² to two decimal places, and the area of a semicircle with a radius of 8.2 cm is 104.8 cm² to one decimal place.
Explanation:Calculating the Area of a Circle and SemicircleTo work out the area of a circle with a radius of 7.5 cm using π (pi) as 3.142, we use the formula A = πr².
First, square the radius: 7.5 cm × 7.5 cm = 56.25 cm².
Then multiply by π: 56.25 cm² × 3.142 = 176.8125 cm².
The area to 2 decimal places is 176.81 cm².
For the area of a semicircle with radius 8.2 cm, we first calculate the area of a full circle and then divide by 2.
Full circle area: 8.2 cm × 8.2 cm × 3.142 = 209.5852 cm².
Area of the semicircle: 209.5852 cm² ÷ 2 = 104.7926 cm², which rounds to 104.8 cm² to 1 decimal place.
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The area of the circle is [tex]177.16[/tex] [tex]cm^2[/tex] and the area of semicircle is [tex]105.0[/tex] [tex]cm^2[/tex].
The area of a circle is given by the formula [tex]\( A = \pi r^2 \)[/tex], where [tex]\( r \)[/tex] is the radius of the circle.
1. For the first question, the radius [tex]\( r \)[/tex] is given as 7.5 cm. Using the formula for the area of a circle:
[tex]\[ A = \pi r^2 \][/tex]
[tex]\[ A = 3.142 \times (7.5 \text{ cm})^2 \][/tex]
[tex]\[ A = 3.142 \times 56.25 \text{ cm}^2 \][/tex]
[tex]\[ A = 177.1625 \text{ cm}^2 \][/tex]
Rounded to two decimal places, the area of the circle is [tex]\( A = 177.16 \text{ cm}^2 \)[/tex].
2. For the second question, the figure is a semicircle with a radius of 8.2 cm. The area of a semicircle is half the area of a full circle.
Therefore, using the formula for the area of a circle and then dividing by 2:
[tex]\[ A_{\text{semi}} = \frac{1}{2} \pi r^2 \][/tex]
[tex]\[ A_{\text{semi}} = \frac{1}{2} \times 3.142 \times (8.2 \text{ cm})^2 \][/tex]
[tex]\[ A_{\text{semi}} = \frac{1}{2} \times 3.142 \times 67.24 \text{ cm}^2 \][/tex]
[tex]\[ A_{\text{semi}} = \frac{1}{2} \times 210.0944 \text{ cm}^2 \][/tex]
[tex]\[ A_{\text{semi}} = 105.0472 \text{ cm}^2 \][/tex]
Rounded to one decimal place, the area of the semicircle [tex]\( A_{\text{semi}} = 105.0 \text{ cm}^2 \)[/tex].
Jordan bought 6 apples priced 3 for $2.89 and 5 pears priced 5 for $4.50 how much did he pay in all
A certain hybrid car can travel 1 4/11 times as far as a similar non hybrid car can, each on one gallon of gasoline. If the non hybrid car can travel 33 miles per gallon of gasoline how far can the hybrid travel on 4/5 gallon of gasoline?
Answer:
On 4/5 gallon of gasoline, hybrid car will travel 36 miles of distance.
Step-by-step explanation:
Suppose, non hybrid car travel "x" distance in 1 gallon of gasoline
then, hybrid will travel " 1 4/11* x" distance in 1 gallon of gasoline
Given that, non hybrid car travel, x = 33 miles per gallon
Then, hybrid car travel, 1 4/11*x = 1 4/11* 33 = 45 miles per gallon
On 1 gallon of gasoline hybrid car travel= 45 miles
On 4/5 gallon of gasoline hybrid car will travel= 4/5*45= 36 miles
On 4/5 gallon of gasoline, hybrid car will travel 36 miles of distance.
Find the slope of the line passing through the two points.
a.)(–1, –8), (–7, –4)
b.)(2.1, 3.8), (3.1, 7.6)
The fromula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
a) (-1, -8), (-7, -4)
substitute
[tex]m=\dfrac{-4-(-8)}{-7-(-1)}=\dfrac{-4+8}{-7+1}=\dfrac{4}{-6}=-\dfrac{2}{3}[/tex]
b) (2.1, 3.8), (3.1, 7.6)
substitute
[tex]m=\dfrac{7.6-3.8}{3.1-2.1}=\dfrac{3.8}{1}=3.8[/tex]
The registration period for the race is under way, and as the word is getting out, the number of participants registering is growing exponentially. The numbers from the first two days of registration are shown in the table.
Use the data in the table and the general form of an exponential growth equation, y= a(1 +r)^x, to write an equation modeling the exponential growth of registrations, where x is the number of days since registration opened, a is the initial number of registrations, r is the rate of growth of registrations per day, and y is the total number of registrations.
y = a(1 + r)ˣ
a = 15 "initial" means what you started with on the first day
r = 6 the rate it increased is the slope ([tex](\frac{21 - 15}{2 - 1})[/tex]
y = 15(1 + 6)ˣ
Answer: y = 15(7)ˣ
What is the solution set of the following equation?
-8x + x + 15 = -7x + 12
Ø
{1/7}
{all reals}
[tex]-8x + x + 15 = -7x + 12\\\\-8x+x+7x=12-15\\\\0=-3\\\\x\in\emptyset[/tex]
There are no solutions to this equation. Hence, the solution to the given linear equation is the empty set (Ø) because simplification results in an untrue statement.
Explanation:This is a linear equation, and we can solve it step by step. The first step is to simplify the equation. If we combine similar terms, we get -7x + 15 = -7x + 12. Then we can cancel the -7x from both sides of the equation, which gives us 15 = 12.
However, this statement is not true. Therefore, there are no solutions to this equation, making the solution set Ø (empty set).
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Find the value of Q in the following system so that the system to the solution is {(x,y) : x-3y=4}
x-3y=4
2x-6y=Q
Here, we are required to find the value of Q in the following system so that the system to the solution is {(x,y) : x-3y=4}
x-3y=4
2x-6y=Q
Therefore, Q = 8.
By comparison between equations: x-3y=4 and 2x - 6y = Q.
We need to multiply equation x - 3y = 4 by 2 so that it somewhat resembles 2x-6y=Q;
Ultimately, we have;
2x - 6y = 8 and 2x - 6y = QTherefore, the two equations now resemble one another and therefore, Q = 8
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The value of Q that makes the system have the same solution as {(x, y) : x - 3y = 4} is Q = 8.
To find the value of Q in the given system so that the solution is {(x, y) : x - 3y = 4}, you need to make sure that the second equation, 2x - 6y = Q, is equivalent to the first equation, x - 3y = 4.
This means that the two equations have the same solution.
To do this, we can start by simplifying the second equation to be equivalent to the first one:
2x - 6y = Q
We can simplify this equation by dividing both sides by 2:
x - 3y = Q/2
Now, we want this equation to be the same as the first equation, x - 3y = 4.
To make them equal, we need to have Q/2 equal to 4.
Therefore:
Q/2 = 4
To solve for Q, multiply both sides of the equation by 2:
Q = 2 * 4
Q = 8
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EXTREMELY IMPORTANT!!!
99 PTS!!!
LOTS AND LOTS OF PTS!!!
PLZ HELP FAST!!!
Seth and Karen are college students who take on different jobs for income. Seth needs $750 for expenses and savings each month; Karen needs $700.
Seth has a part-time job where he earns $7.50 per hour. He also mows lawns and earns $15 per lawn that he mows. His monthly earnings can be expressed with the equation 7.50x + 15y = 750, where x is the number of hours Seth works and y is the number of lawns he mows.
Karen has a part-time job babysitting, where she earns $6 per hour. She also walks dogs and earns $4 per dog that she walks. Her monthly earnings can be expressed with the equation 6x + 4y = 700, where x is the number of hours Karen works and y is the number of dogs she walks.
Part A: Each partner now has an equation, function, and graph that represent the combinations of activities resulting in the income needed for each student. Compare these items and answer the following questions:
Which student, Seth or Karen, has the higher slope when the graphs of their earnings are compared? How can you tell?
Part B: Whose graph, Seth's or Karen's, has a greater y-intercept? What does that mean for this person?
Part C: If both students work 80 hours for the month, is the number of lawns Seth has to mow greater than or less than the number of dogs Karen has to walk? Justify your answer.
Part D: Karen begins charging $8 per hour for babysitting and Seth begins earning $8 per hour. How does this change affect their graphs if everything else remains the same?
P.S. Those who answer wrong answers on purpose will be reported. (Has happened too many times by the same person. You know who you are.) This is very important, so the faster I get the correct answer for each part, the better. Thank you for those who help!!! I will be in your debt!
Seth:
Equation 7.50x + 15y = 750, where x is the number of hours Seth works and y is the number of lawns he mows.
Karen:
Equation 6x + 4y = 700, where x is the number of hours Karen works and y is the number of dogs she walks.
Part A: Converting it in function for by solving for y first.
Solving 7.50x + 15y = 750, equation we get
7.50x + 15y = 750
15y = -7.50x + 750
y = -1/2x + 50Solving 6x + 4y = 700 for y, we get
6x + 4y = 700
4y = -6x + 700
y= -3/2x + 175.On comaring with slope-intercept form y=mx+b, we got slope for Seth equation is -1/2 and slope for Karen is -3/2.
If we take absolute of those -1/2 and -3/2 we get 1/2 and 3/2.
Therefore, Karen has the higher slope. We can see the graph that blue line has greater slope as it's increasing/decreasing with greater rate.
In function form we could write equation as
f(x) = -1/2x + 50 andf(x) = -3/2x + 175.Part B : y-intercept of Karen equation is 175 and y-intercept of Seth equation is 50.
Therefore, Karen has greater y-intercept.This means Karen earns $175 by just walking dogs.Part C: If both students work 80 hours for the month.
Let us plug x =80 in each of the equations.
y = -1/2x + 50 => y = -1/2(80) + 50 = -40 +50 = $10.Seth would earn $10 from mowing lawn.
Therefore, the number of lawns Seth has to mow = 10/15 = 0.67 that is approximately 1 lawn.
y = -3/2x + 175 => y = -3/2(80) + 175 = -120 +175 = $55.Karen would earn $50 from walking dog.
So, the number of dogs Karne has to walk = 55/4 = 13.75 that ia approximately 14 dogs.
Therefore, the number of lawns Seth has to mow is less than the number of dogs Karen has to walk.Part D: If Karen begins charging $8 per hour for babysitting and Seth begins earning $8 per hour.
The equations would become : 8x + 15y = 750, 8x + 4y = 700.
It would not effect the graph much. Even the y-intercepts would remain same.There would be a slightly change in slopes.Answer:
Seth:
Equation 7.50x + 15y = 750, where x is the number of hours Seth works and y is the number of lawns he mows.
Karen:
Equation 6x + 4y = 700, where x is the number of hours Karen works and y is the number of dogs she walks.
Part A: Converting it in function for by solving for y first.
Solving 7.50x + 15y = 750, equation we get
7.50x + 15y = 750
15y = -7.50x + 750
y = -1/2x + 50
Solving 6x + 4y = 700 for y, we get
6x + 4y = 700
4y = -6x + 700
y= -3/2x + 175.
On comaring with slope-intercept form y=mx+b, we got slope for Seth equation is -1/2 and slope for Karen is -3/2.
If we take absolute of those -1/2 and -3/2 we get 1/2 and 3/2.
Therefore, Karen has the higher slope. We can see the graph that blue line has greater slope as it's increasing/decreasing with greater rate.
In function form we could write equation as
f(x) = -1/2x + 50 and
f(x) = -3/2x + 175.
Part B : y-intercept of Karen equation is 175 and y-intercept of Seth equation is 50.
Therefore, Karen has greater y-intercept.
This means Karen earns $175 by just walking dogs.
Part C: If both students work 80 hours for the month.
Let us plug x =80 in each of the equations.
y = -1/2x + 50 => y = -1/2(80) + 50 = -40 +50 = $10.
Seth would earn $10 from mowing lawn.
Therefore, the number of lawns Seth has to mow = 10/15 = 0.67 that is approximately 1 lawn.
y = -3/2x + 175 => y = -3/2(80) + 175 = -120 +175 = $55.
Karen would earn $50 from walking dog.
So, the number of dogs Karne has to walk = 55/4 = 13.75 that ia approximately 14 dogs.
Therefore, the number of lawns Seth has to mow is less than the number of dogs Karen has to walk.
Part D: If Karen begins charging $8 per hour for babysitting and Seth begins earning $8 per hour.
The equations would become : 8x + 15y = 750, 8x + 4y = 700.
It would not effect the graph much. Even the y-intercepts would remain same.
There would be a slightly change in slopes.
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Step-by-step explanation:
Solve.
x + 3/5=2
A) -5
B) -3
C) 7
D) 13
Answer:
Option C: x=7
Step-by-step explanation:
We are given an equation in x and asked to solve for x
The given equation is
[tex]\frac{x+3}{5} =2[/tex]
To solve for x, we have to have only x on the left side.
So multiply the equation both sides by 5 first
We get x+3 =2(5) =10
Subtract 3 to get
x =10-3 =7
Hence 7 is the answer.
We can verify the answer by substituting for x in the given equation.
Substitute x=7 we get (7+3)/5 = 2
Thus answer is right.
Which is the best estimate for the number of items that customers bought during a trip to the grocery store one day?
The histogram shows the number of items that customers bought during a trip to the grocery store one day. Four hundred customers took a trip to the grocery store that day.
Options are:
15 (I think it is this one)
20
34
65
The answer is 65! Just took the test
How many hats did the knitter who sold 5 scarves sell?
Without additional information correlating the number of hats sold to the number of scarves sold, it is impossible to determine how many hats the knitter sold.
Explanation:Based on the question, there isn't enough information provided to determine how many hats the knitter sold. The information given tells us only about the number of scarves sold, which is 5. If any relationship between the number of hats and scarves sold was provided, then the solution could be possible. For example if the knitter sells an equal amount of hats and scarves then we could say she sold 5 hats. However, without any such information, it is impossible to ascertain the number of hats sold.
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How many side pieces 8 1/4 inches long and 6 3/4 inches wide can mr. Penny cut from a wooden plank 9 5/8 feet long and 9/16 foot wide
Answer:Total number of side pieces [tex] = 14[/tex]
Step-by-step explanation:
To find the number of side pieces we use formula = [tex] \frac{Area of wooden plank}{Area of 1 side piece} [/tex]
Area of wooden plank [tex]= length \times width[/tex]
Length of wooden plank [tex] =\frac{77}{8}feet =\frac{77}{8} \times 12 [/tex] inches
Length [tex] = \frac{231}{2} [/tex] inches
Width of plank [tex] = \frac{9}{16} foot = \frac{9}{16} \times 12 =\frac{27}{4}[/tex] inches
Area of plank[tex]= \frac{231}{2} \times \frac{27}{4} [/tex] sq inches
Area of 1 side piece [tex]= \frac{33}{4} \times \frac{27}{4}[/tex] sq inches
Now using formula
Number of pieces [tex]= \frac{Area wooden plank}{Area of 1 side piece} [/tex]
[tex] =(\frac{231}{2} \times \frac{27}{4} )\div (\frac{33}{4} \times \frac{27}{4}) [/tex]
Converting division into multiplication we get,
[tex] =(\frac{231}{2} \times \frac{27}{4} )\times (\frac{4}{27} \times \frac{4}{33} )[/tex]
On solving we get
[tex]= 14[/tex]
Total number of side pieces [tex] = 14[/tex]
Choose all the postulates and theorems that can prove to a triangles are congruent A. side side side B. side angle side C.angle angle side D. Angle side angle E.HL Leg
There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL.
1. SSS (side, side, side)
SSS Triangle
SSS stands for "side, side, side" and means that we have two triangles with all three sides equal.
For example:
triangle is congruent to: triangle
(See Solving SSS Triangles to find out more)
If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
2. SAS (side, angle, side)
SAS Triangle
SAS stands for "side, angle, side" and means that we have two triangles where we know two sides and the included angle are equal.
For example:
triangle is congruent to: triangle
(See Solving SAS Triangles to find out more)
If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.
3. ASA (angle, side, angle)
ASA Triangle
ASA stands for "angle, side, angle" and means that we have two triangles where we know two angles and the included side are equal.
For example:
triangle is congruent to: triangle
(See Solving ASA Triangles to find out more)
If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.
4. AAS (angle, angle, side)
AAS Triangle
AAS stands for "angle, angle, side" and means that we have two triangles where we know two angles and the non-included side are equal.
For example:
triangle is congruent to: triangle
(See Solving AAS Triangles to find out more)
If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.
5. HL (hypotenuse, leg)
This one applies only to right angled-triangles!
triangle HL or triangle HL
HL stands for "Hypotenuse, Leg" (the longest side of a right-angled triangle is called the "hypotenuse", the other two sides are called "legs")
It means we have two right-angled triangles with
the same length of hypotenuse and
the same length for one of the other two legs.
It doesn't matter which leg since the triangles could be rotated.
For example:
triangle is congruent to: triangle
(See Pythagoras' Theorem to find out more)
If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent.
Caution! Don't Use "AAA"
AAA means we are given all three angles of a triangle, but no sides.
AAA Triangle
This is not enough information to decide if two triangles are congruent!
Because the triangles can have the same angles but be different sizes:
triangle is not congruent to: triangle
Without knowing at least one side, we can't be sure if two triangles are congruent.
The five postulates and theorems that can prove triangles are congruent are Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Angle-Side (AAS), Angle-Side-Angle (ASA), and Hypotenuse-Leg (HL). These are based on comparing angles and sides of the triangles.
Explanation:In geometry, congruent triangles are triangles that have the same size and shape, meaning they have equal side lengths and angles. There are several postulates and theorems that can be used to prove that triangles are congruent. They include:
Side-Side-Side (SSS): If all three sides of one triangle are congruent to the corresponding sides of another triangle, the triangles are congruent. Side-Angle-Side (SAS): If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent. Angle-Angle-Side (AAS): If two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, the triangles are congruent. Angle-Side-Angle (ASA): If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent. Hypotenuse-Leg (HL): In right triangles, if the hypotenuse and one leg of one triangle are congruent to the hypotenuse and one leg of another triangle, the triangles are congruent. Learn more about Congruent Triangles here:https://brainly.com/question/31700817
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The amount of a person’s paycheck p varies directly with the number of hours worked t . For 10 hours of work, the paycheck is $57.50. Write an equation for the relationship between hours of work and pay. p = 5.75t p = t + 5.75 p = 57.50t p = t + 57.50
Answer:
the answer is p=5.75t
Step-by-step explanation:
Cameron adds 4 new hats to his collection each year. He started with only 3. Find slope and the y intercept.
The slope is 4. The y intercept is 3.
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please help asap 25 pts
The answer is B: 4.5 cm, 7.5 cm
Here's why: 7.5 is 3 cm more than 4.5, and when added together, 7.5 + 7.5 + 4.5 + 4.5 = 24.
The formula of a perimeter of a rectangle: P = 2(w + l)
w - width, l - length
We have:
P = 24cm and l = (w + 3)cm
Substitute:
24 = 2(w + w + 3)
24 = 2(2w + 3) |use distributive property
24 = (2)(2w) + (2)(3)
24 = 4w + 6 |subtract 6 from both sides
18 = 4w |divide both sides by 4
w = 18/4
w = 9/2
w = 4.5 cm
l = 4.5 + 3 = 7.5cm
Answer: b. 4.5 cm, 7.5 cm.a page of school yearbook is 8 1/2 inches wide. The left and right margins are 1 inch and 2 1/2 inches respectively. The space between each picture is 1/4 inch. To fit 5 pictures across the page , how wide should each picture be ? \ NEEED HELPP!
6 pounds of raisins cost 12$, what is the price per pound of raisins?
What is the GCF of the following terms?
Factor each one to see what they have in common:
15x² = 3 * 5 * x * x
42x³ = 2 * 3 * 7 * x * x * x
They both have: 3, x, x
When multiplied together, 3 * x * x = 3x²
Answer: 3x²
Which number produces a rational number when add to 0.6
Any rational number added to 0.6 will produce a rational number.
Adding any rational number to 0.6 will produce a rational number. Rational numbers include whole numbers, fractions, and terminating or repeating decimals.
The question asks which number, when added to 0.6, produces a rational number. A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero. Since 0.6 is already a rational number (it can be expressed as 6/10 or 3/5), adding any other rational number to it will also produce a rational number. Examples of rational numbers include whole numbers, fractions, and terminating or repeating decimals.
Therefore, any number that is rational (such as 0, 1/2, 3, 4.5, etc.) will produce a rational number when added to 0.6.
Which explanation correctly solves this problem? A golf club has 85 golfers in a golf tournament. The golfers will ride in golf carts. Each cart holds 4 golfers. How many golf carts will the club need for all the golfers? 85 ÷ 4 = 21 with 1 left over. They will need 22 golf carts. 85 ÷ 4 = 21 with 1 left over. They will need 21 golf carts. 85 ÷ 4 = 21 with 1 left over. They will need 21142114 golf carts.
The answer is A. 85/4=21 with 1 left over. They will need 22 golf carts.
Mental math 5×395=5×(_ - _)step by step how do you solve this problem?
You want to use the distributive property, i.e. the possibility to distribute a multiplication to both terms of an sum/subtraction.
In this case, if you think of 395 as of 400-5, you have
[tex] 5 \times 395 = 5 \times (400-5) [/tex]
And you can use the distributive property to write
[tex] 5 \times (400-5) = 5\times 400 - 5\times 5[/tex]
Both of these multiplications are easy to perform in your mind:
[tex] 5\times 400 - 5\times 5 = 2000 - 25 = 1975[/tex]
The solution to 5×395=5×(_ - _) is found by calculating the multiplication, 5 x 395 = 1975. Then we find two numbers that result in 1975 when multiplied by 5 and subtracted; one example could be 396 and 1. Thus, the equation can be 5×395=5×(396 - 1).
Explanation:In order to solve the problem 5×395=5×(_ - _) using mental math, we first compute the multiplication of 5 and 395, which is 1975. Now, we need to find two numbers that, when multiplied by 5 and subtracted, give us 1975. As there can be multiple possible pairs, one potential solution could be 5×(395+1) = 5×396 = 1980. So, the two numbers are 396 and 1, and the complete equation would be 5×395=5×(396 - 1).
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Gayle is saving to buy a bicycle. The bicycle costs $119.90 she has saved 0.7 of what she needs how much has she saved so far?
Let the amount saved by Gayle be = x
Cost of the bicycle = $119.90
Gayle's saving till now = 0.7% of 119.90
[tex]\frac{0.7}{100}\times119.90=x[/tex]
[tex]x=0.83[/tex]
Hence, Gayle has saved $0.83 so far.
Answer:
She has saved $83.93.
Step-by-step explanation:
Gayle is saving to buy a bicycle.
The cost of bicycle = $119.90
She has saved = 0.7 of $119.90
= 0.7 × 119.90
= $83.93
The amount she needs more = 119.90 - 83.93
= $35.97
She has saved $83.93.
Question 3solve the problem.a moving firm charges a flat fee of $45 plus $40 per hour. Let y be the cost in dollars of using the moving firm for x hours. Find the slope-intercept form of the equation. ay = 40x + 45 by = 40x - 45 cy = 45x - 40 dy = 45x + 40
slope (m) = rate. $40 per hour is the rate, so m = 45
y-intercept (b) = one time fee. $45 is the flat rate which is the one time fee, so b = 45
y = mx + b
y = 40x + 45
Answer: A
Given the two figures are similar, calculate the value of w
2 : 2.5 = 3 : w
w = 2.5 * 3 : 2
w = 3.75
Which statement is true? A.27/19<11/30 b.17/31>19/14 c.16/26>30/31 d.35/30<22/12
is this true 27/19<11/30
In order to check if a comparison such as this is true, you can use this logical equivalence:
[tex] \dfrac{a}{b} > \dfrac{c}{d} \iff ad > bc,\quad \dfrac{a}{b} < \dfrac{c}{d} \iff ad < bc [/tex]
Anyway, it's not always necessary to make this check. We know that every proper fraction represents a number between 0 and 1, and any improper fraction represents a number greater than 1. So, every proper fraction is less than every improper fraction.
So, the first two options are surely wrong, because they ask for a proper fraction to be more than an improper fraction.
The third option compares two proper fractions, so we actually have to check:
[tex] \dfrac{16}{26}>\dfrac{30}{31} \iff 16 \cdot 31 > 26 \cdot 30 \iff 496 > 780[/tex]
which is false.
Last option:
[tex] \dfrac{35}{30}<\dfrac{22}{12} \iff 35 \cdot 12 < 30 \cdot 22 \iff 420 < 660[/tex]
Which is true.
Solve the equation for x. -2-3/4x=10a.) -16b.) 0c.) 16d.) -32/3
[tex]-2-\dfrac{3}{4}x=10\ \ \ \ |+2\\\\-\dfrac{3}{4}x=12\ \ \ \ |\cdot(-4)\\\\3x=-48\ \ \ \ |:3\\\\\boxed{x=-16}\\\\Answer:\ a.)\ -16[/tex]
Final answer:
To solve the equation -2 - 3/4x = 10, you first add 2 to both sides of the equation, then multiply both sides by -4/3 to get x alone. The solution to the equation is x = -16, which is option (a).
Explanation:
To solve the equation −2 − 3/4x = 10, we need to isolate x. First, we can add 2 to both sides of the equation:
−3/4x = 10 + 2
−3/4x = 12
Next, we multiply both sides by the reciprocal of −3/4, which is −4/3 to get x alone:
(−4/3)*(−3/4)x = 12(−4/3)
x = −16
Therefore, the solution is −16, which corresponds to option (a) −16.
What is the equation in point−slope form of the line passing through (0, 6) and (1, 3)? (5 points)
The slope-point formula:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have (0, 6) and (1, 3),
Substitute:
[tex]m=\dfrac{3-6}{1-0}=\dfrac{-3}{1}=-3\\\\y-6=-3(x-0)[/tex]
Two angles that are adjacent and form a straight angle (line) together are called ______ ______. (Two Words)
The answer I believe is Linear Pair
Answer: Linear Pair
Two angles that are adjacent and supplementary form a linear pair.
A toy store owner gives 47 balloons to his customers. He has 7 balloons left. How many balloons did he start with?
Answer:
Step-by-step explanation:
As per the problem, we are given that
Toy store owner gave 47 balloons to his customers.
And there are 7 balloons left.
So we can find the total number of balloons the Toy store owner start with by adding the given numbers.
Hence total number of balloons the Toy store owner start with[tex]=47+7=54[/tex]
Final answer:
The toy store owner had 54 balloons originally. This is found by adding the 7 balloons left to the 47 given away.
Explanation:
The question is asking to find the total number of balloons the toy store owner originally had. To solve this, we use simple addition. If the owner gave away 47 balloons and has 7 left, you would add the two numbers together to find the original amount.
Step-by-Step Explanation:
Start with the number of balloons the owner has left, which is 7.Add the number of balloons given to customers, which is 47.7 balloons left + 47 balloons given away = 54 balloons originally had.Therefore, the toy store owner originally had 54 balloons.
During the summer, payton and James mow the lawns in their subdivision. On each lawn they spend $3.50 on gas and $1.20 on leaf bags. If they charge $22.00 for each lawn ,how much profit do they make?
Answer:
17.30 dollars
Step-by-step explanation:
Given that Payton and James mow the lawns.
They do this during summer.
The amount they spend are:
Gas cost = 3.50
Leaf bags = 1.20
Add these to get total costs
Total cost = 4.70
Charge they get per lawn = 22.00
Profit = Revenue - cost
Here revenue per lawn = 22 and cost per lawn = 4.70
Hence profit = 22-4.70 = 17.30 dollars.
Answer is they make 17.30 dollars per lawn.
Answer:
The answer is B
Step-by-step explanation: