The rectangle with a length of 7 units and a width of 4 units, and with one vertex at the origin (0,0), has been successfully created using the segment tool.
Open the drawing tool or any software that allows you to draw shapes and use the segment tool to begin the construction.
First, mark the origin (0,0) on the canvas as one of the vertices of the rectangle.
Now, move the cursor 7 units to the right from the origin along the x-axis and place a point. This point represents the opposite vertex of the rectangle on the right side.
Next, move the cursor 4 units up from the origin along the y-axis and place another point. This point represents the opposite vertex of the rectangle on the top side.
To complete the rectangle, draw straight lines connecting the following points: (0,0) with (7,0), (7,0) with (7,4), (7,4) with (0,4), and finally, (0,4) back to (0,0).
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-13m = 1 - 14m what is the answer
Answer:
m = 1
Step-by-step explanation:
Step 1: Add 14m to both sides
-13m + 14m = 1 - 14m + 14m
m = 1
Answer: m = 1
A candy store makes a 10-lb mixture of gummy worms, candy corn, and sourballs. The cost of gummy worms is $1.00 per pound, candy corn cost $3.00 per pound, and sourballs cost $1.50 per pound. The mixture calls for three times as many gummy worms as candy corn. The total cost of the mixture is $15.00. How much of each ingredient did the store use?
Answer:
6 grams of gummy worms, 2 grams of candy corn and 2 grams of sourballs.
Step-by-step explanation:
Let the number of pounds of each ingredient be as follows:
Gummy Worms = x pounds
Candy Corn = y pounds
Sourballs = z pounds
The store makes a mixtures of 10 pounds. This means the sum of x, y and z would be 10. Setting up the equation:
[tex]x + y +z = 10[/tex] (Equation 1)
The mixture calls for 3 times as many gummy worms as candy corn. This means amount of gummy worm will be 3 times the candy corn. Setting up the Equation:
[tex]x=3y[/tex] (Equation 2)
Cost of gummy worms is $1.00 per pound, candy corn cost $3.00 per pound, and sourballs cost $1.50 per pound. So cost of x, y and z pounds would be:
1x , 3y and 1.5z, respectively. The total cost of mixture is $15. So we can set up the Equation as:
[tex]x+3y+1.5z=15[/tex] (Equation 3)
Using the value of x from Equation 2, in Equations 1 and 3 give us following two equations:
[tex]4y+z=10[/tex] By substitution in Equation 1. (Equation 4)[tex]6y+1.5z=15[/tex] By substitution in Equation 3. (Equation 5)
Multiplying the Equation 4 by 1.5 and subtracting from Equation 5 gives us:
[tex]6y +1.5z-1.5(4y+z)=15-1.5(10)\\\\ 6y+1.5z-6y-1.5z=15-15\\\\ 0=0[/tex]
When two sides of equations turn into something that is always positive, we conclude that there are infinite number of solutions. In such cases, we fix a variable and give different values to it, to find corresponding values of other variables. Lets re-write the solution in terms of z.
From Equation 4, we have:
[tex]y=\frac{10-z}{4}[/tex]
From Equation 2, we have:
[tex]x=3(\frac{10-z}{4} )[/tex]
Therefore, the solution set will be:
[tex](3(\frac{10-z}{4} ), \frac{10-z}{4} , z)[/tex]
Now in order to find any combination of ingredient, we give any value to z. Let, z is equal to 2 grams.
So,
x would be = 6 grams
y would be = 2 grams
So, one of the possible amount of ingredients that store can use is:
6 grams of gummy worms, 2 grams of candy corn and 2 grams of sourballs.
What is 5x-2.5+6x-3 equivalent to
Answer:
It is equal to
11x-2.5-3e
Answer:
11x-5.5
Step-by-step explanation:
If you combine like terms it will be equivalent still.
5x and 6x can be added together which is 11x
you can also combine -2.5 and -3 which is -5.5
So the product will be 11x-5.5
Hope this helped :)
A paddock contains ducks and sheep. There are total of 42 heads and 96 feet in the paddock. How many ducks and how many sheep are in the paddock
8 bags of potato chips ,5 bags of popcorn, 2bags of pretzels and 1 bag of cheese puffs if a student selects 1 bag at random find the probability that it it is a bag of potato chips or a bag of pretzels
Answer:
10/16
Step-by-step explanation:
Simplified: 5/8
A student selects 1 bag at random, then the probability that it is a bag of potato chips or a bag of pretzels is 0.625.
What is the probability?The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.
Given:
There are 8 bags of potato chips, 5 bags of popcorn, 2 bags of pretzels and 1 bag of cheese puffs.
The number of bag of potato chips and bag of pretzels,
= 8 + 2
= 10
If a student selects 1 bag at random, then the probability that it is a bag of potato chips or a bag of pretzels:
The probability = number of favorable outcomes / total outcomes
The probability = 10 / 16
The probability = 5/8
The probability = 0.625
Therefore, the probability is 0.625.
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Which equation is equivalent to 2x + 6y = 12?
Answer:
Option C, y = -1/3x + 2
Step-by-step explanation:
2x + 6y = 12
Step 1: Solve for y
2x + 6y - 2x = 12 - 2x
6y / 6 = (12 - 2x) / 6
y = 2 - 1/3x
Answer: Option C, y = -1/3x + 2
Answer:
y = (1/3)x + 2
Step-by-step explanation:
2x + 6y = 12 can be reduced by dividing all three terms by 2; we get:
1x + 3y = 6.
We solve for y. First, subtract 1x from both sides, obtaining:
3y = -1x + 6.
Next, divide all three terms by 3. We get
y = (1/3)x + 2
Ella is checking roof frames to make sure that they are right triangles. Which of the following measures form right triangles? Select all that apply. 10, 24, 26 8, StartRoot 20 EndRoot, 25 8, StartRoot 161 EndRoot, 15 20, 21, 29 39, 80, 89
Answer:
A; C; D; E
Step-by-step explanation:
The answer is A, C, D, and E
A: 10, 24, 26
C: 8, StartRoot 161 EndRoot, 15
D: 20, 21, 29
E: 39, 80, 89
Answer:
A, C, D, E
Step-by-step explanation:
It's correct
Sides KM and FH in the triangles below will be placed together to form a quadrilateral.
Which best describes the quadrilateral that will be formed?
parallelogram
rectangle
rhombus
trapezoid
Any polygon that has exactly 3 sides is called a triangle. Here you haven't provided any figure, so I'll assume that we have two triangles as indicated in the figure below. As you can see, we have two sides:
[tex]KM \ and \ FH[/tex]
When placing together we realize that those sides measures the same, so:
[tex]KM=FH[/tex]
So [tex]KM/FH[/tex] is the diagonal of the shape. From the figure we also know that opposite sides are equal and parallel, therefore, this shape represents a parallelogram. Remember that a parallelogram is a quadrilateral where both pairs of opposite sides are parallel.
So correct option is:
Parallelogram
Answer:
The correct answer is A. parallelogram
Step-by-step explanation:
Right on ED2021, goodluck!
What is the distance between -45 and -98 on a number line?
A) -67
B) 53
Eliminate
C) 67
D) 133
The distance between -45 and -98 on a number line is 53 units.
Explanation:The distance between -45 and -98 on a number line can be determined by subtracting the smaller number from the larger number:
-98 - (-45) = -98 + 45 = -53
The distance between -45 and -98 is 53 units.
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Question 2:
Describe the relationship between the following expressions:
3(25 x 25) and (25 x 25)
The relationship between the expressions 3(25 x 25) and (25 x 25) is that the first expression is 3 times greater than the second one.
Describe the relationship between the following expressions:
3 (25 x 25): This expression means 3 multiplied by the result of 25 multiplied by 25, which is 1875.
(25 x 25): This expression represents the result of multiplying 25 by 25, which is 625.
The relationship between these expressions is that the first expression is 3 times greater than the second expression.
Helpppppppppppppppppp
Option A:
[tex]\left(x^{4}\right)\left(3 x^{3}-2\right)\left(4 x^{2}+5 x\right)=12 x^{9} +15 x^{8} - 8 x^{6}-10 x^{5}[/tex]
Solution:
Given expression [tex]\left(x^{4}\right)\left(3 x^{3}-2\right)\left(4 x^{2}+5 x\right)[/tex].
To find the product of the above expression:
[tex]\left(x^{4}\right)\left(3 x^{3}-2\right)\left(4 x^{2}+5 x\right)[/tex]
First multiply first two factors with each term.
[tex]=(x^{4} \times 3 x^{3}- x^{4} \times 2 ) \left(4 x^{2}+5 x\right)[/tex]
Using exponent rule: [tex]a^m \cdot a^n=a^{m+n}[/tex]
[tex]=(3 x^{7}- 2x^{4} ) \left(4 x^{2}+5 x\right)[/tex]
Now multiply these two factors with each term.
[tex]=3 x^{7} (4 x^{2}+5 x)- 2x^{4} \left(4 x^{2}+5 x\right)[/tex]
[tex]=(4 x^{2} \times 3 x^{7} +5 x \times 3 x^{7} )- \left(4 x^{2} \times 2x^{4}+5 x \times 2x^{4}\right)[/tex]
Using exponent rule: [tex]a^m \cdot a^n=a^{m+n}[/tex]
[tex]=(12 x^{9} +15 x^{8} )- (8 x^{6}+10 x^{5})[/tex]
[tex]=12 x^{9} +15 x^{8} - 8 x^{6}-10 x^{5}[/tex]
[tex]\left(x^{4}\right)\left(3 x^{3}-2\right)\left(4 x^{2}+5 x\right)=12 x^{9} +15 x^{8} - 8 x^{6}-10 x^{5}[/tex]
Hence option A is the correct answer.
Joesfina works between 10 and 30 hours per week at a pizzeria. She earns $8.50 an hour, but can earn tips when she delivers pizzas. Write a system of inequalities to represent the dollars d she could earn for working h hours in a week. {please help me}
Answer:
85 + z <= x <= 255 + z
Step-by-step explanation:
An inequality system will be given by a lower limit and an upper limit, therefore it is only necessary to raise an equation for each case, h being the hours worked and z the extra money you can earn by delivering the pizzas:
For the lower limit:
8.5 * h + z, knowing that in this case it is 10 hours.
85 + z would be the lower limit value
For the upper limit:
8.5 * h + z, knowing that in this case it is 30 hours.
225 + z would be the upper limit value
Therefore the inequality system would be as follows, let x be the money earned:
85 + z <= x <= 255 + z
Which means that the money earned will be determined by the previous inequality.
There are 4 students in a small class. To make a team, the names of 2 of them will be drawn from a hat. How many different teams of 2nstudents are possible?
Answer:
3
Step-by-step explanation:
List all the different teams:
A+B, C+D
A+C, B+D
A+D, B+C
There are 3.
Answer:
3
Step-by-step explanation:
2*2 - 1 = 3
5) What is the solution to the system of equations?
y=-2x+1 and y=-4/7x +1
A) (0,1)
B) (1,0)
C) (-2,1)
D) (-2, -4/7)
Answer:
-2x + 1 = -4/7x + 1
-14/7x + 1 = -4/7x + 1
-10/7x = 0
x = 0
y = -2(0) + 1
y = 1
(0,1)
answer is a
Which is the solution to the inequality? y + 15 less-than 3
A.) y less-than negative 12
B.) y greater-than negative 12
C.) y less-than 18
D>) y greater-than 18
Answer:
Option A.) y less-than negative 12
Step-by-step explanation:
we have
[tex]y+15<3[/tex]
solve for y
subtract 15 both sides
[tex]y+15-15<3-15[/tex]
[tex]y<3-15\\y<-12[/tex]
therefore
y less-than negative 12
Answer:
A
Step-by-step explanation:
can someone show me how to solve this? the lesson didnt show me how to do it.[tex]\frac{x^{2} }{2} -32 = 0[/tex]
Answer:
x=-8,8
Step-by-step explanation:
[tex]\frac{x^2}{2} -32=0\\multiply ~by~2\\x^2-64=0\\x^2-8^2=0\\(x+8)(x-8)=0\\ether~ x=-8\\or~x-8=0\\x=8\\x=-8,8x=-8[/tex]
missing either x+8=0
x=-8
Company A is offering $6,000 for the first month's salary and will increase the amount each month by $5,000. Company B is offering $700 or the first month and will double the pay each month.
Use the given table to determine for which month Company B's payment will first exceed Company A's payment?
A) Month 4
B) Month 6
C) Month 7
D) Month 9
The month in which Company B's payment will first exceed Company A's payment is C) Month 7.
Step-by-step explanation:
Step 1:
Company A offers $6,000 for the first month and increases the salary each month by $5,000.
Company B offers $700 for the first month but doubles the payments each month.
We need to determine which month company B's payment is greater than company A's payment.
Step 2:
According to the table, at month 6 company A pays $31,000 while company B pays $22,400.
However after this month, in the seventh-month company A pays $36,000 while company B pays $44,800, which is higher than company A's salary.
So The month in which Company B's payment will first exceed Company A's payment is C) Month 7.
how many degreese are in 1/9
angle
Answer:
10 degrees
Step-by-step explanation:
1/9 of 90 = 1/9 x 90 = 90/9 = 10
The correct answer is (b) [tex]$40^\circ$[/tex].
To find out how many degrees are in [tex]$\frac{1}{9}$[/tex] of a circle, we first need to understand that a full circle has [tex]$360^\circ$[/tex].
To find [tex]$\frac{1}{9}$[/tex] of a circle, we need to divide [tex]$360^\circ$[/tex] by 9.
So, [tex]$\frac{360^\circ}{9} = 40^\circ$[/tex].
Therefore, [tex]$\frac{1}{9}$[/tex] of a circle is [tex]$40^\circ$[/tex].
Complete Question:
How many degrees are in [tex]$\frac{1}{9}$[/tex] of a circle?
a. [tex]$90^{\circ}$[/tex]
b. [tex]$40^{\circ}$[/tex]
c. [tex]$42^{\circ}$[/tex]
d. [tex]$65^{\circ}$[/tex]
Guy decides to get in shape by running. The first day, he runs 1 mile in 12 minutes. Two months later he has decreased
his mile time by 25%. What is his mile time now?
Step-by-step explanation:
in two months
Decrease of 25%
so you need to do
25%*12 is 3 minutes
Find the difference from 12 minutes
12-3 is 9 minutes.
therefore, his mile time is 9 minutes in two months
After improving his running speed by 25%, Guy would now run a mile time 9 minutes.
It would take for Guy to run a mile after improving his running speed by 25%. Guy's original mile time was 12 minutes. To find his new mile time, we calculate 25% of 12 minutes, which is 3 minutes.
Then, we subtract that from the original 12 minutes: 12 minutes - 3 minutes = 9 minutes. Therefore, Guy's new mile time, after reducing it by 25%, is 9 minutes.
Find the value of x.
log x 8 = 0.5
O A. 4
OB. 16
C. 32
Answer:
c. 4 4÷2 =8 hope it helps
4b-4=3b+4
solve for b
Answer:
4b-3b=4+4
b=8
Step-by-step explanation:
Hence, the value of b is 8
#hope it helps
Answer:
b=8
Step-by-step explanation:
4b-4=3b+4
You have to add 4 to both sides so that all the like terms are together
4b=3b+8
Then you subtract 3b from each side so that the like terms are all together
b=8
Identify the slope and y-intercept of the line y=5x/3+1.
Answer:
slope: 5x/3 and y-intercept: 1
Answer:
5/3 is slope
(0, 1) or 1 is y-int
Step-by-step explanation:
y = mx + b
m is slope
b is y-int
y = 5 x/3 + 1
y = 5/3x + 1
5/3 is slope
(0, 1) or 1 is y-int
A circular path 2 feet wide has an inner diameter of 950 feet. How much farther is it around the outer
edge of the path than around the inner edge? Round to nearest hundredth. Use 3.14 for it.
The outer edge of the path is
feet farther around than the inner edge.
Answer: 12.56 feet
Step-by-step explanation:
Given: The width of the circular path= 2 feet
The inner diameter of circular path= 150 feet
Therefore, the inner radius of circular path=
Now, the outer radius= 75+2=77 feet
We know that the circumference=
Inner circumference=
Outer circumference=
The difference=
Hence, the outer edge of the path is 12.56 feet farther than the inner edge
The value of a car is $30,000. It loses 6.5% of its value each year. What will the value of the car be after 5 years?
The value of a car that costs $30,000 and depreciates at 6.5% annually will be $22,530 after 5 years, calculated using exponential decay.
The value of a car is $30,000 and it loses 6.5% of its value each year. To calculate the value of the car after 5 years, we can apply the concept of exponential decay. The value after one year would be the initial value minus 6.5% of the initial value. Mathematically, we can express this as:
V1 = V0 (1 - 0.065),
where V1 is the value after one year and V0 is the initial value. To find the value after 5 years, we would apply this formula iteratively or use the formula for exponential decay:
Vn = V0 x (1 - 0.065)ⁿ,
where Vn is the value after n years. Therefore:
V5 = $30,000 x (1 - 0.065)⁵,
V5 = $30,000 x (0.935)⁵,
V5 = $30,000 x 0.7510,
V5 = $22,530.
After 5 years, the value of the car will be $22,530.
Zack is taking inventory of loaves of bread at the grocery store where he works. There are 20 loaves in a full case, and Zack has 3 partially filled cases: 1 case is 12 full, 1 case is 14 full, and 1 case is 25 full. How many total
Answer:
51 loaves
Step-by-step explanation:
Given that one case contains 20 loaves.
-Sum the number of partially filled cases and divide to get complete cases:
[tex]T_{loaves}=12+14+25\\\\=51[/tex]
#He has a total of 51 loaves:
[tex]20 loaves = 1 case\\51 loaves=x\\\\x=\frac{51}{20}\\\\x=2 \ rem 11[/tex]
Hence, Zack has a total of 51 loaves (2 full cases, 1 partial of 11 loaves)
Johnny thinks that the slope of the line through (5,10) and (4,4) is -1/6. Is he correct? If he is explain why. If he’s not, provide the correct answer and explain what he did wrong.
Answer:
Johnny is incorrect because the slope is actually 6.
Step-by-step explanation:
To find the slope: m = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
Step 1: Plug in the points
m = [tex]\frac{4 - 10}{4 - 5}[/tex]
m = [tex]\frac{-6}{-1}[/tex]
m = 6
Answer: Johnny is incorrect because the slope is actually 6.
What’s the next number in the sequence 72,81,90,99
they are increasing by 9 so next is 108
Maureen has two hollow containers. One is a 5 cm cube and the other is a cylinder of radius 2 cm. She completely fills the cube with water and then pours it into the cylinder.
What is the depth of the water in the cylinder? Give your answer in cm correct to 3 significant figures.
You can assume that the cylinder is tall enough to hold all the water from the cube.
Answer:
it's 9.947
Step-by-step explanation:
for this we need an equation which contain height in it so we used volume in both so we get height
π2^2h=5*5*5
π4h=125
h=9.947
To find the depth of water in the cylinder, calculate the volume of the cube and then use that volume to find the height of the cylinder.
Explanation:To find the depth of water in the cylinder, we need to calculate the volume of the cube and then use that volume to find the height of the cylinder.
The volume of a cube is given by V = s^3, where s is the length of a side.
The volume of the cube is (5 cm)^3 = 125 cm^3.
Now, we can use the formula for the volume of a cylinder, V = πr^2h, where r is the radius and h is the height.
Using the volume of the cube as the volume of the water in the cylinder, we get 125 cm^3 = π(2 cm)^2h. Solving for h, we find h = 9.278 cm.
Therefore, the depth of the water in the cylinder is approximately 9.278 cm.
Find the quotient
-54у^2 + 24/ 9y + 6
Answer:
56
Step-by-step explanation:
Mrs.stevens has award winning rose bushes that grow at a rate of 3/4 foot per week. Her American home rose bush currently measures 5 feet tall, while her camp David Rose bush is 4 1/2 feet tall in two weeks how tall will mrs.stevens American home rose bush measure?
Answer:
The answer would be 6.5 feet.
Pre-Thinking:
Knowing that the rose bushes grow at a rate of 3/4 feet per week, we can turn that into 0.75, a decimal.
Because, we need to know the height of the rose bush in 2 weeks, multiply 0.75 by 2.
0.75 * 2 = 1.5
Working and Stuff:
Because we only need the length of the American Home Rose Bush, which is 5 feet tall, we can discard the other rose bush.
Lastly, add 1.5 to 5.
1.5 + 5 = 6.5 feet
Amazing MS-Paint drawing of a rose bush: