Clay soil = 1/5
bale of straw = 1/8
Clay soil needed = x
Bale of straw needed = 1
Clay soil : Bale of straw (rate)
1/5 : 1/8 = x : 1
1/5 ÷ 1/8 = x / 1
1/5 × 8/1 = x / 1
8/5 = x / 1
Cross product
8 * 1 = 5 * x
8 = 5x
Divide both sides by 5
x = 8/5
6.[–/1 Points]DETAILSALEXGEOM7 8.3.006.MY NOTESASK YOUR TEACHERIn a regular polygon, each interior angle measures 120°. If each side of the regular polygon measures 4.6 cm, find the perimeter of the polygon in centimeters. cm
Given:
Measure of each interior angle = 120 degrees
Length of each side = 4.6 cm
Let's find the perimeter of the polygon.
Since the measure of each interior angle is 120 degrees, let's find the number of sides of the polygon using the formula below:
[tex]120=\frac{(n-2)*180}{n}[/tex]Let's solve for n.
We have:
[tex]\begin{gathered} 120n=(n-2)*180 \\ \\ 120n=180n-180(2) \\ \\ 120n=180n-360 \\ \\ 180n-120n=360 \\ \\ 60n=360 \end{gathered}[/tex]Divide both sides by 60:
[tex]\begin{gathered} \frac{60n}{60}=\frac{360}{60} \\ \\ n=6 \end{gathered}[/tex]Therefore, the polygon has 6 sides.
To find the perimeter, apply the formula:
Perimeter = number of sides x length of each side
Perimeter = 6 x 4.6
Perimeter = 27.6 cm
Therefore, the perimeter of the polygon is 27.6 cm
ANSWER:
27.6 cm
Give the domain and range of a quadratic function whose graph as described. The vertex is (-5,-6) and the parabola opens up. The domain of f is ___
We will have that it's domain goes from -infinity to infinity.
It's range, goes from infinity to -6.
Michelle sells new and used kayaks. She makes a 10.5% commission on every kayak she sells and she also gets paid $495.50 per week. a) Develop an equation for the way Michelle is paid. b) Last month, the total value of the kayaks she sold was $19 425. Use the equation you’ve developed to find out how much Michelle was paid for that month.
Michelle was paid for that month is $ 4021.625
A linear equation is an algebraic equation of the form y=mx+b. regarding only a regular and a first-order (linear) time period, in which m is the slope and b is the y-intercept. on occasion, the above is called a "linear equation of two variables," where y and x are the variables.
Calculation:-
Percentage of commission = 10.5%
per week paid = $495.50
a. Equation of Michelle paid = 10.5/100X + 495.50
b. The total value of the kayaks she sold was $19 425.
Michelle was paid for that month = 19 425 × 10.5/100 + 4 × 495.50
= 2039.625 + 1982
= $ 4021.625
A linear equation bureaucracy is an immediate line on a graph. A nonlinear equation paperwork an S-curve, bell curve, or any other nonlinear form on a graph. experts in mathematics and physics view linear equations as simple. specialists in mathematics and physics view nonlinear equations as complex.
A linear equation in a single variable is an equation wherein there is handiest one variable present. it is of the form Ax + B = 0, wherein A and B are any real numbers and x is an unknown variable that has the handiest one answer. for instance, 9x + 78 = 18 is a linear equation in one variable.
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I need help with 3 , 7 ,4 and 8
Solution:
Question 3:
The image below gives a vivid explanation of the question
Concept:
The sum of angles in a triangle is
[tex]=180^0[/tex][tex]\begin{gathered} \angle A+\angle B+\angle C=180^0 \\ \angle A=61^0 \\ \angle B=90^0 \\ \angle C=4f+1 \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \angle A+\angle B+\angle C=180^0 \\ 61^0+90^0+4f+1=180^0 \\ \text{collect similar terms, we will have} \\ 61+90+1+4f=180^0 \\ 152^0+4f=180^0 \\ 4f=180-152^0 \\ 4f=28^0 \\ \text{Divide both sides by 4} \\ \frac{4f}{4}=\frac{28}{4} \\ f=7^0 \end{gathered}[/tex]Hence,
The final answer is f = 7°
What are the roots for the trinomial below? *x2 – 2x – 15O x=-5,x=-3Ox=5,x=-3Ox=3,x=5O x=-5,x=3
ANSWER:
[tex]x=5,=-3[/tex]STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]x^2-2x-15[/tex]We solve by factoring. We look for two numbers that product -15 and the sum is equal to -2:
[tex]\begin{gathered} 3\cdot-5=-15 \\ 3+(-5)=-2 \\ \text{Therefore:} \\ (x+3)\cdot(x-5)=0 \\ x+3=0\rightarrow x=-3 \\ x-5=0\rightarrow x=5 \end{gathered}[/tex]find the prime factorization ofa) 2205 and b)2525
(a) 2205.
The prime factorization consist in finding prime numbers which multiplication gives the initial number, to find those prime numbers, we divide the number by 2, 3, or 5, depending on the case. Let's do it.
2205 | 5
441 | 3
147 | 3
49 | 7
7 | 7
1
So, the prime factorization is
[tex]2205=5\times3\times3\times7\times7[/tex](b) 2525.
Let's repeat the process as we did with (a).
2525 | 5
505 | 5
101 | 101
1
So, the prime factorization is
[tex]2525=5\times5\times101[/tex]00:00Drag a tile to each number to classify it as rational or irrational.rationalirrational9.682.010010001...✓ 64-57
the numbers are
[tex]undefined[/tex]A department store is having a clothing sale. If a $35.00 pair of pants has a discount tag of 25% off, what is the sale price?
Given Data:
The prise of the pair of the pant is: p= 35
the percentage of discount is: 25%
The expression to calculate the discount sale price is,
[tex]d=p\times\frac{25}{100}[/tex]Substitute values in the above expression.
[tex]\begin{gathered} d=35\times\frac{25}{100} \\ =35\times0.25 \\ =8.75\text{ } \end{gathered}[/tex]Thus, the discount price of the pant is $8.75.
Which of the following describes the graph of h(x)= -2^(x+3)-4. Thanks for the help!
SOLUTION:
Case: Graphs
Method:
The equation:
[tex]h(x)=-2^{(x+3)}-4[/tex]We will plug in several values of x
(-3, ?), (0, ?)
[tex]\begin{gathered} (-5,?) \\ h(-3)=-2^{(-3+3)}-4 \\ h(-3)=-2^0-4 \\ h(-3)=-1-4 \\ h(-3)=-5 \\ (-3,-5) \end{gathered}[/tex]And
[tex]\begin{gathered} (0,?) \\ h(0)=-2^{(0+3)}-4 \\ h(0)=-2^3-4 \\ h(0)=-8-4 \\ h(0)=-12 \\ (0,-12) \end{gathered}[/tex]Final answer: 3rd Option
The graph:
[tex] \frac{1}{2} {x}^{2} + 1 = 2 \times - 1[/tex]Solve the equation
Solve the system of equations:
4x-2y=10 (1)
y=2x-5 (2)
We can substitute 2 in 1:
4x-2(2x-5)=10
4x-4x+10=10
0=0
Since the solution of the system of equation is 0=0 we can say that it has infinite solutions.
graph the inequality x-2y less than or equal to 0
To graph the inequality, we can do the following steps.
Step 1: We rearrange the equation so y is on the left and everything else is on the right.
[tex]\begin{gathered} x-2y\le0 \\ \text{ Subtract x from both sides} \\ x-2y-x\le0-x \\ -2y\le-x \\ \text{ Divide by -2 from both sides} \\ \frac{-2y}{-2}\le\frac{-x}{-2} \\ y\ge\frac{x}{2} \end{gathered}[/tex]Step 2: We plot the line associated with the inequality. For this, we choose two values of x and replace them in the below equation.
[tex]\begin{gathered} x=2 \\ $$\boldsymbol{y=\frac{x}{2}}$$ \\ y=\frac{2}{2} \\ y=1 \\ \text{ Then, the lines passes through the point (2,1).} \end{gathered}[/tex][tex]\begin{gathered} x=4 \\ y=\frac{x}{2} \\ y=\frac{4}{2} \\ y=2 \\ \text{ Then, the lines passes through the point (4,2).} \end{gathered}[/tex]Since inequality has the symbol ≥, we make a solid line.
Step 3: Since inequality has the symbol ≥, we shade above the line. Therefore, the graph of the inequality is:
Look at the graphs and their equations below. Then in the information about the ABCand D
Given:
Given a graph and their equations. Then in the information about the A,B, Cand D
Required:
To fill the blanks.
Explanation:
(a) For each coefficient choose whether it is positive or negative :
A : It has positive coefficient.
B : It has positive coefficient.
C : It has negative coefficient.
D : It has negative coefficient.
(b) Choose the coefficient with the least value:
The graph D.
(c)
Find the measure of angle A associated with the following ratios and round to the nearest degree.
For, CosA = 0.2785 value of angle m∠A = 73.8293° ≈ 74°
Inverse Cosine function:
The inverse cosine function is written as cos^-1(x) or arccos(x).
CosA = 0.2785
A = [tex]Cos^{-1}[/tex](0.2785)
A = 73.8293°
thus by calculation we can say,
m∠A = 73.8293°
≈ 74°
Thus,
For, CosA = 0.2785 value of angle m∠A = 73.8293°
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Solve for x.
11x=2=8x+26
Answer:
X=8
Step-by-step explanation:
11x=2=8x=+26
11x -8x = -2 +26
3x=24
X=8
What is the area of rectangle with a length of 24 meters and a height of 7 meters?A84 square meters84 square metersB600 square meters600 square metersC168 square meters168 square metersD300 square meters
Answer: C. 168 m²
Explanation
The area of a rectangle (A) is given by:
[tex]A=l\cdot h[/tex]where l represents the length and h represents the height.
Then, in our case, l = 24m and h = 7m. By replacing the values and simplifying we get:
[tex]A=24m\cdot7m[/tex][tex]A=168m^2[/tex]would the answer be written as 47 ¹¹⁰/¹⁷³? my daughter has to write the answer as the remainder as a fraction. 8241 ÷ 173
8241 ÷ 173
173 will go into 8241 47 times an we will have a remainder of 110
So, it will be written as;
8241 ÷ 173
[tex]=47\text{ }\frac{110}{173}[/tex]Joe’s parents are making sandwiches for the class picnic they have 7230 size is 48 two slices and 96 tomato sauce is Y
We have to calculate the maximum common divisor of these 3 numbers in order to know what is the maximum ammount of sandwiches they can make.
We can list the factors of each number:
72: 1, 2, 3, 4, 6, 8, 12, 18, 24, 36, 72.
48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 96.
To calculate this factors, we start by dividing by 2 and 3, and so on, and checking if the result is a whole number. If it is, the denominator is a factor.
The maximum common divisor is 24, so they can make 24 sandwichs, each one with 72/24=3 slices of turkey, 48/24=2 slices of cheese and 96/24=4 slices of tomatoes.
George's boxes
He has bought boxes at different prices.
3 boxes at $3.50 and 4 boxes at $3.00.
The cost of the first group of boxes is 3 boxes x 3.50 $/boxes = $10.50.
The cost of the second group is 4 boxes x 3.00 $/boxes = $12.
Then, if we add the cost, it is 10.50 + 12 = $22.50.
If we write it in the blanks we have:
3 boxes * 3.50 = 3 * 3.50
4 boxes * 3.00 = 4 * 3.00
(3 * 3.50) + (4 * 3.00) = 22.50
(underlined is what goes in the blanks)
Let X represent number of sundaes sold and y represent the number of banana splits sold.Sundaes are sold for $2 each and banana splits for $3 each. They made a total of $150. Equation____________The number of sundaes sold is 5 times more than the number of banana splits sold. Equation________Solve the system of problem questions by substitution
Given that the total income was $150 by selling 'x' sundaes and 'y' banana splits,
[tex]\begin{gathered} \text{Total Cost}=\text{ Cost per sundae}\cdot\text{ Number of sundae}+\text{ Cost per banana splits}\cdot\text{ Number of banana splits} \\ 150=2x+3y \\ 2x+3y=150\ldots(1) \end{gathered}[/tex]Also given that the number of sundaes sold is 5 times more than the number of banana splits sold,
[tex]\begin{gathered} x=y+5y \\ x=6y\ldots(2) \end{gathered}[/tex]Substitute this value in equation (1),
[tex]\begin{gathered} 2(6y)+3y=150 \\ 12y+3y=150 \\ 15y=150 \\ y=10 \end{gathered}[/tex]The corresponding value of 'x' is calculated by using equation (2) as,
[tex]\begin{gathered} x=6(10) \\ x=60 \end{gathered}[/tex]Thus, the solution to the system of problem
-8x+3y= 313x-3y= -18x=y=
Given the pair of simultaneous equation;
[tex]\begin{gathered} -8x+3y=3 \\ 13x-3y=-18 \end{gathered}[/tex]We are going to use the method of elimination to solve this.
We will be eliminating the variable y first, since it has the same co-efficient in the two(2) equations.
Thus, we have:
[tex]\begin{gathered} -8x+13x=3-18 \\ 5x=-15 \\ x=-\frac{15}{5} \\ x=-3 \end{gathered}[/tex]To solve for y, we are going to substitute for x = -3 into any of the two(2) equations.
Thus, we have:
[tex]\begin{gathered} \text{from equation i}i) \\ 13x-3y=-18 \\ 13(-3)-3y=-18 \\ -39-3y=-18 \\ -3y=-18+39 \\ -3y=21 \\ y=-\frac{21}{3} \\ y=-7 \end{gathered}[/tex]5 + kx = 17Solve for x
1) To solve for x, is to leave the x on the left side the other variables on the right along with the constants, like this
[tex]\begin{gathered} 5\text{ +kx =17} \\ kx\text{ =17-5} \\ x=\frac{17-5}{k} \end{gathered}[/tex]Note that, we subtracted 5 and then divided by x.
Answer:
5+kx=17
kx=17-5
kx=12
x= 12/k
1. A function is given by the set of ordered pairs {(2,5),(4,9), (6,13), (8,17)). Write its domain and rangein roster form.Domain:Range:
The domains are:
{2, 4, 6, and 8}
The range are {5, 9, 13 and 17}
EXPLANATION
Given:
{(2,5),(4,9), (6,13), (8,17))
The above is given in the form (x, y)
where x is the domain and y is the range.
The domains are:
{2, 4, 6, and 8}
The range are {5, 9, 13 and 17}
2. A blanket is 4 feet wide. It is 3 times as long as it is wide. Draw a diagram of the blanket, and label its dimensions. b. Find the perimeter and area of the blanket.
the width of the blanket is 4 ft
it is given that length is 3 times of width so the length is 3 * 4 = 12 ft
part b)
so the blanket is rectangular.
the perimeter of the blanket is
2(4+12) = 32
area of the blanket is
length x width
12 x 4 = 48 square ft
part a)
the diagram of the blanket is given as follows,
How many different 5 card hands can be dealt from a deck of 52 cards if the hand consists of exactly 2 aces?
Solution
We need to remember that in a standard deck we have 4 aces and 48 other types of cards
For this case we can solve the problem with the follwoing operation:
[tex](4C2)\cdot(48C3)=\frac{4!}{2!2!}\cdot\frac{48!}{45!3!}=6\cdot17296=103776[/tex]So then we have 103776 ways to create the combination required
If we start with 5 people that have the coronavirus, and the number of cases increases by 26% each week. How many cases of coronavirus will there be
in 36 weeks?
Answer:
6600 new cases
Step-by-step explanation:
Figure 2 is the image of Figure 1. What is the scale factor?
Answer
Scale factor = (2/5)
Explanation
The scale factor shows the extent to which the original image has been dilated (enlarged or reduced). It is given mathematically as
[tex]\text{Scale factor = }\frac{Length\text{ of a side of the image}}{Length\text{ of the corresponding side of the original figure}}[/tex]From the image attached we can see that
Length of a side of the image = 4 dots
Length of the corresponding side of the original image = 10 dots
Scale factor = (4/10) = (2/5)
Hope this Helps!!!
A garden table and a bench cost $669 combined. The garden table costs $81 less than the bench. What is the cost of the bench?
Given:
The cost of garden table and bench is, 669.
The garden table costs 81 less than bench.
Let us take x as the cost of the bench and y as the cost of the table. Then we have,
[tex]\begin{gathered} x+y=669\ldots\text{.}.(1) \\ y=x-81\ldots.(2) \end{gathered}[/tex]Now, substituting the value of y in equation 1, we get,
[tex]\begin{gathered} x+x-81=669 \\ 2x=669+81 \\ 2x=750 \\ x=\frac{750}{2}=375 \end{gathered}[/tex]Thus, the cost of bench is 375.
Find the volume of this right rectangularprism.3 ft15 ft10 ft[? ]ft3
Given the following question:
[tex]\begin{gathered} volume=l\times b\times h \\ l=15 \\ b=10 \\ h=3 \end{gathered}[/tex][tex]\begin{gathered} volume=l\times b\times h \\ volume=15\times10\times3 \\ 15\times10=150 \\ 150\times3=450 \\ v=450ft^3 \end{gathered}[/tex]Volume is equal to 450 feet^3.
If the scale factor is 5:8, and the actual width of the model is 20 feet, what is the model width?
If the scale factor is 5:8, it is the same as 5/8.
In order to calculate the width of the model, just multiply its actual width by the scale factor, as follow:
width of the model = (20 ft)(5/8) = 12.5 feet
Hence, the width of the model is 12.5 feet
Max is scuba diving at elevation of -64.5 feet, when friend signals to come higher. Max makes 2 ascents, each an equal distance to reach an elevation of -21.4 feet, where his friend is located. What was max’s elevation after his first ascent?I come up with -43.1
Answer: - 42.95 feet
Explanation:
Let each ascent be x. Thus,
2 equal ascents = 2x
From the information given,
initial position = - 64.5 feet
Final position after 2 ascents = - 21.4 feet
This means that
- 64.5 + 2x = - 21.4
2x = - 21.4 + 64.5
2x = 43.1
x = 43.1/2
x = 21.55
Thus, Max's elevation after the first ascent is
- 64.5 + 21.55
= - 42.95 feet
17 people fit comfortably in a 7 feet by 7 feet area. Use this value to estimate the size of a crowd that is 21 feet deep on both sides of the street along a 3-mile section of a parade route. (Hint: 1mile= 5,280ft) Draw a diagram
In order to estimate the size of the crowd, let's find the area of the parade route.
The length is 3 miles, that is, 3 * 5280 = 15840 ft.
The width is 2 times 21, so 42 ft.
Therefore the area is:
[tex]A=15840\cdot42=665280[/tex]Now, to estimate the size of the crowd, let's use a rule of three, knowing that the area for 17 people is 7 * 7 = 49 ft²:
[tex]\begin{gathered} 17\text{ people}\to49\text{ ft}^2 \\ x\text{ people}\to665280\text{ ft}^2 \\ \\ \frac{17}{x}=\frac{49}{665280} \\ x=\frac{665280\cdot17}{49} \\ x=230811.43 \end{gathered}[/tex]Rounding to the nearest integer, we have 230,881 people.