In this expression, we have the same value on the left side is equal to the same amount on the right side.
So, let's start operating it to simplify it
6(_+x) -8(-3+8x)=30-58x
6(_+x)+24-64x=30-58x
6( ) +6x +24 -64x =30 -58x
6( ) -58x+24=30-58x
6( )-58x +58x=30-24
6( ) =14 DIviding both sides by six
( ) =7/3
Testing:
6(7/3 +x) -8(-3+8x)=30-58x
14+6x +24 -64x =30-58x
38
Grayson needs to order some new supplies for the restaurant where he works. The restaurant needs at least 261 forks. There are currently 205 forks. If each set on sale contains 10 forks, which inequality can be used to determine the minimum number of sets of forks Grayson should buy?
ANSWER
[tex]10x\ge56[/tex]EXPLANATION
We have that the restaurant needs at least 261 forks.
There are currently 205 forks.
First, we have to find the number of forks that the restaurant currently needs.
We do that by finding the difference between the number of forks they have from the number of forks they need:
261 - 205 = 56 forks
They need at least 56 forks.
We have that each set of forks on sale has 10 forks each.
Let the number of sets they need be x.
This means that the amount of forks they should buy must be greater than or equal to 56. That is:
[tex]\begin{gathered} x\cdot10\ge56 \\ \Rightarrow10x\ge56 \end{gathered}[/tex]That is the inequality that can be used to determine the minimum number of sets of forks Grayson should buy.
22% 38% 1/4 21/10 three 5/10 and 3/8 from least to greatest value
The ascending order for the given values will be 22%<1/4<3/8<38%<21/10<3 5/10 as the definition of ascending order will be "When numbers are arranged in ascending order, they are done so from smallest to largest."
What is ascending order?When numbers are arranged in ascending order, they are done so from smallest to largest. Ascending order, also known as increasing order of importance, is the exact opposite of descending order. The order of the items is lowest to highest value. The smallest value is placed first in the order, and the biggest value is placed last. As a result, if you were to put the numbers from the previous section in ascending order, they would be as follows: 11, 20, 49, 80, 56, and so on. The first number is always the smallest, in this case 11. The last number is always the largest, in this case 80.
Here,
22%=0.22
38%=0.38
1/4=0.25
21/10=2.1
3 5/10=3.5
3/8=0.375
22%<1/4<3/8<38%<21/10<3 5/10
According to the definition of ascending order, the given values will be in ascending order as follows: 22%<1/4<3/8<38%<21/10<3 5/10 "Numbers are arranged from smallest to largest when they are arranged in ascending order."
To know more about ascending order,
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a cake is in the room, 5he first person takes 1/3 and then the second person takes 1/3 of what is left and so on, c(n) represents the amount of cake left each time find out how much cake there is after 5 people
Let the full cake represent,
[tex]c(1)=1[/tex]Therfore, the given problem is in the form of an arithmetic sequence,
[tex]1,\frac{2}{3},\ldots.[/tex]Here, n=5, d=-1/3, c(1)=1
[tex]c(5)=c(1)+(5-1)\times-\frac{1}{3}[/tex]Therefore,
[tex]\begin{gathered} c(5)=1-\frac{4}{3} \\ =-\frac{1}{3} \end{gathered}[/tex]So, the remaining amount of cake is -1/3.
After a 30% discount, the price of a t-shirt was $14. What was the price BEFORE the discount?
Price after discount = $14
discount = 30%
x (1-30/100) = 14
x (1-0.3) = 14
x 0.7 = 14
Solve for x (original price )
x = 14/0.7
x = 20
is( 1,9)a solution to the equation y=x
is( 1,9) a solution to the equation y=x
answer is
is not a solutionbecause y=x means
the value of x is equal to the value of y
and 1 is not equal to 9
What numeric value of b would make the following two expressions equivalent? bx +2.4 and 6(2x+0.4) + 3x
For the two expressions to be equivalent, then we would have;
[tex]bx+2.4=6(2x+0.4)+3x[/tex]We solve the right hand side and we'll now have;
[tex]\begin{gathered} bx+2.4=12x+2.4+3x \\ bx+2.4=15x+2.4 \\ \text{Collect all like terms and you'll have} \\ 2.4-2.4=15x-bx \\ 0=15x-bx \\ Add\text{ bx to both sides of the equation} \\ 0+bx=15x-bx+bx \\ bx=15x \\ \text{Divide both sides by x} \\ \frac{bx}{x}=\frac{15x}{x} \\ b=15 \end{gathered}[/tex]The first option is the correct one.
b = 15
Three values on a number line ate labeled f, g and h.
• f = -4
,• g = -g
,• h = -f
ExplanationLet us find the values of g and h.
• Since we know the value of, we can find the value of h.
[tex]\begin{gathered} h=-f \\ h=-(-4) \\ h=4 \end{gathered}[/tex]• We solve the given equation for g.
[tex]\begin{gathered} g=-g \\ \text{ Add g from both sides} \\ g+g=-g+g \\ 2g=0 \\ \text{ Divide by 2 from both sides} \\ \frac{2g}{2}=\frac{0}{2} \\ g=0 \end{gathered}[/tex]AnswerTherefore, the number line that shows correctly the values of f,g, and h is the one in option c.
Robert moved 4 cards that are worth -10 points each. How did thier score change.
We have the following:
Since there are 4 cards and each one has a value of -10 points, we have
[tex]4\cdot-10=-40[/tex]Which means that the score changed by -40 points
how would you graph a figure that is translated by (x-4, y+2
Is 8.012 greater or less than 8.03
In order to compare the numbers, we need to check each pair of digits that are in the same position before and after the decimal point.
We start from the left to the right. If the result of one number is greater, than this number is greater than the other number. If the digits of both numbers are the same, we move to the next digit and compare them.
So we have:
Unit position: 8 and 8
Equal results, so let's check the next digit.
Tenth position: 0 and 0.
Equal results, so let's check the next digit.
Hundredth position: 1 and 3.
3 is greater than 1, so the second number is greater than the first one.
Therefore 8.012 is less than 8.03.
2x - 1 if x < 0Evaluate g (4) for g(x)for g(x) = x²W√xif 0 ≤ x ≤ 5.if x > 5
Solution
Question A:
[tex]\begin{gathered} \text{ To find the rate we compare with the equation below:} \\ A=P(1+r)^t \\ \\ \text{ Thus, } \\ 1+r=0.9 \\ \text{ Subtract 1 from both sides} \\ r=0.9-1 \\ r=-0.1 \end{gathered}[/tex]- Rate of depreciation is 10%
Question B:
[tex]\begin{gathered} v=34000(0.9)^t \\ \text{ when } \\ v=\frac{34000}{2}=17000 \\ \\ 17000=34000(0.9)^t \\ \text{ Divide both sides by 34000} \\ 0.5=(0.9)^t \\ \text{ Take the natural log of both sides} \\ \ln0.5=t\ln0.9 \\ \\ \therefore t=\frac{\ln0.5}{\ln0.9} \\ \\ t=6.578813...\approx6.58years \end{gathered}[/tex]- The number of years is 6.58years
find the correct area
The figure consist of trapezium and rectangle.
Determine the area of figure.
[tex]\begin{gathered} A=\frac{13+24}{2}\cdot4+24\cdot7 \\ =37\cdot2+168 \\ =74+168 \\ =242 \end{gathered}[/tex]Thus area of the figure is 242 inch square.
Topic 4,: Graphing Proportional relationships.Note: A way to determine whether two quantities are proportional is to graph themon a coordinate plane. If the graph is a straight line through the origin, then the twoquanti1lies are proportional.Ex 4. Determine whether the number of calories burned is proportional to thenumber of minutes played
Given
Table:
Time: 0, 1, 2, 3, 4
Calories: 0, 7, 14, 21, 28
Procedure
Let's plot the points shown
We can see that the points fall on a straight line. Therefore time and calories are two proportional quantities.
What number makes the equation true? Enter the answer in the box.+5= 9
The complete information for the question was not provided by the student, however we can assume that the box is either to the left or to the right of the equal sign:
If it's to the left, we have:
Box + 5 = 9
Box = 9 - 5
Box = 4
If it's to the right, we have:
5 = 9 - Box
5 - 9 = - Box
-4 = - Box
4 = Box
Answer: No matter if the box is to the left or to the right of the equal sign, the number in the box that makes the equation true is 4
The plastic lid of a cylindrical container is a circle. The lid has a radius of 9centimeters. What is the circumference of the lid?
We are asked to determine the circumference of a 9 cm radius circle. To do that we will use the following formula:
[tex]S=2\pi r[/tex]Where:
[tex]\begin{gathered} S=\text{ circumference} \\ r=\text{ radius} \end{gathered}[/tex]Now, we substitute the value of the radius:
[tex]S=2\pi(9cm)[/tex]Solving the operations:
[tex]S=18\pi=56.55cm[/tex]Therefore, the circumference is 56.55 cm.
A recipe calls for 1/2 cup sugar, a cup of flour and 1/3 cup of milk. I need to make 3 batches. How much of each ingredient will I need?
The recipe calls for
1/2 cup of sugar : 1 cup of flour : 1/3 cup of milk for 1 batche
We need to make 3 batches, so
Multiply each ingredient bu 3
Sugar = 1/2 * 3 = 3/2 cups
Flour = 1 * 3 = 3 cups
Milk = 1/3 * 3 = 1 cup
3/2 cups of sugar : 3 cups of flour : 1 cup of milk
At the grocery store, halibut costs $20 per pound and salmon costs $17 per pound. Which of the following situations can be modeled by the equation below? 20(x-5) = 17xA) The cost of x pounds of salmon is $5 less than the cost of x pounds of halibutt B) The cost of x pounds of halibut is $5 less than the cost of x pounds of salmon C) The cost of pounds of salmon is the same as the cost of x-5 pounds of halibutD) The cost of x pounds of halibut is the same as the cost of x-5 pounds of salmon.
Answer: C.
The cost of x pounds of salmon is the same as the cost of x-5 pounds of halibut
[tex]\begin{gathered} \text{halibut }\rightarrow\text{ \$20 and (x-5) pounds} \\ \text{salmon }\rightarrow\text{ \$17 and x pounds} \end{gathered}[/tex]Explanation:
Given the model;
[tex]20(x-5)=17x[/tex]where x is the number of pounds.
The cost per pound of Halibut is;
[tex]\text{ \$20}[/tex]So, the corresponding number of pounds of Halibut on the model is;
[tex]x-5[/tex]Also, the cost per pound of Salman is;
[tex]\text{ \$17}[/tex]the corresponding number of pounds of Salmon on the model is;
[tex]x[/tex]Since they are equal to each other, then the cost of x pounds of salmon is the same as the cost of x-5 pounds of halibut
[tex]\begin{gathered} \text{hailbut }\rightarrow\text{ \$20 and (x-5) pounds} \\ \text{salmon }\rightarrow\text{ \$17 and x pounds} \end{gathered}[/tex]Name:Date:6. The table shows the postage charges for sending letters to Country A.How much does it cost to send a letter weighing 80 ounces to Country A?First 30 Ounces60For Every Additional 10 Ounces35
The first 30 ounces costs 60¢.
For every additional 10 ounces the cost increases in 35¢.
From the given 80 ounces, the first 30 costs 60¢ and the other 50 ounces, by considering it is 5 times 10 ounces, cost 5*(35¢) = 175¢.
Then, the total cost is:
total = 60¢ + 175¢ = 235¢
The ratio of 8th graders in a chess club to the total number of members is 0.45.What is the decimal in fraction form?Enter the correct answers in the boxes.
The ratio of 8th graders in a chess club to the total number of members is 0.454545...
This is called a repeating decimal.
Let us convert this decimal into a fraction.
[tex]x=0.4545\ldots[/tex]Step 1:
Multiply by 100
[tex]\begin{gathered} 100\times x=100\times0.4545\ldots \\ 100x=45.45\ldots \end{gathered}[/tex]Step 2:
Subtract x
[tex]\begin{gathered} 100x-x=45.45\ldots-0.4545 \\ 99x=45 \end{gathered}[/tex]Step 3:
Finally, divide by 99
[tex]\begin{gathered} \frac{99x}{99}=\frac{45}{99} \\ x=\frac{45}{99} \end{gathered}[/tex]Therefore, the fraction form is
[tex]x=\frac{45}{99}[/tex]apple trees need to be planted in an orchard this process takes two hours per tree
the fact that we can not plant the half of tree imples that there is no line between the points of the graph. So the answer is letter B
Your lacrosse team wins 4 of the games that it plays. Describe huikelihood of winning.
the statement say us the rate of winning is 3/4 then the probability is the same
but performance it on decimals
[tex]\frac{3}{4}=0.75[/tex]probability is 0.75
NO LINKS!! Use the method of substitution to solve the system. (If there's no solution, enter no solution). Part 9z
Answer:
(-3, 2)(1, 0)=====================
Given systemy² = 1 - x x + 2y = 1Rearrange the first equationx = 1 - y² Substitute the value of x into second equation1 - y² + 2y = 1y² - 2y = 0y(y - 2) = 0y = 0 and y = 2Find the value of xy = 0 ⇒ x = 1 - 0² = 1y = 2 ⇒ x = 1 - 2² = -3Answer:
[tex](x,y)=\left(\; \boxed{-3,2} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{1,0} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}\;\;\;\;\;\;\;y^2=1-x\\x+2y=1\end{cases}[/tex]
To solve by the method of substitution, rearrange the second equation to make x the subject:
[tex]\implies x=1-2y[/tex]
Substitute the found expression for x into the first equation and rearrange so that the equation equals zero:
[tex]\begin{aligned}x=1-2y \implies y^2&=1-(1-2y)\\y^2&=1-1+2y\\y^2&=2y\\y^2-2y&=0\end{aligned}[/tex]
Factor the equation:
[tex]\begin{aligned}\implies y^2-2y&=0\\y(y-2)&=0\end{aligned}[/tex]
Apply the zero-product property and solve for y:
[tex]\implies y=0[/tex]
[tex]\implies y-2=0 \implies y=2[/tex]
Substitute the found values of y into the second equation and solve for x:
[tex]\begin{aligned}y=0 \implies x+2(0)&=1\\x&=1\end{aligned}[/tex]
[tex]\begin{aligned}y=2 \implies x+2(2)&=1\\x+4&=1\\x&=-3\end{aligned}[/tex]
Therefore, the solutions are:
[tex](x,y)=\left(\; \boxed{-3,2} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{1,0} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
The circle has center O. Its radius is 3 m, and the central angle a measures 60°. What is the area of the shaded region?Give the exact answer in terms of pi, and be sure to include the correct unit in your answer
Explanation
The area of a portion of a circle with radius 'r' and angle 'a' (in radians) is:
[tex]A_{\text{portion}}=\frac{1}{2}\cdot r^2\cdot a[/tex]In this problem r = 3m, a = 60º.
First we have to express the angle in radians:
[tex]a=60º\cdot\frac{\pi}{180º}=\frac{1}{3}\pi[/tex]The area of the shaded region is:
[tex]\begin{gathered} A=\frac{1}{2}\cdot(3m)^2\cdot\frac{1}{3}\pi \\ A=\frac{1}{2}\cdot9m^2\cdot\frac{1}{3}\pi=\frac{3}{2}\pi \end{gathered}[/tex]Answer
The area is:
[tex]A=\frac{3}{2}\pi[/tex]how would you write this as an expression.
The quotient of 29 and the product of a number and −5.
ANSWER
[tex]\frac{29}{-5x}[/tex]EXPLANATION
Let 'x' be a number. The product of a number and -5 is: -5x
Then the quotient of 29 and something is: 29/something
Now, that something is the product -5x so, the quotient of 29 and the product of a number and -5 is:
[tex]\frac{29}{-5x}[/tex]Help Curtis round 37,254,503 to the nearest hundred thousand for his report.
the answer is:
37, 300, 000
Answer:
37,300,500
Step-by-step explanation:
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
The population of a city was 136 thousand in 1992. The exponential growth rate was 1.7% per year.a) Find the exponential growth function in terms of t, where t is the number of years since 1992.P(t) = 136,000 e 0.0177
We will have that the expression will be:
[tex]p(t)=136000(1+0.017)^t[/tex]I need help with this please and thank you im just really confused
To find the values of x and z, apply the opposite angles theorem.
Opposite angles are angles that can be said to be non-adjacent angles formed by two intersecting lines.
Opposite angles are congruent.
• Measure of angle Z:
∠z and 110 are opposite angles.
Thus, we have:
m∠z = 110°
• Value of x:
Given that total measure of angles = 360
We have:
[tex](5x-20)=\frac{360-110-110}{2}[/tex]Let's solve for x:
[tex]\begin{gathered} 5x-20=\frac{140}{2} \\ \\ 5x-20=70 \\ \\ \text{Add 20 to both sides:} \\ 5x-20+20=70+20 \\ \\ 5x=90 \end{gathered}[/tex]Divide both sides by 5:
[tex]\begin{gathered} \frac{5x}{5}=\frac{90}{5} \\ \\ x=18 \end{gathered}[/tex]ANSWER:
x = 18
z = 110°
Someone please help me with this problem in the most simple easy way possible no long explanation needed.
ANSWER:
2797.74 cubic inches
EXPLANATION:
Given:
Height of the cylinder(h) = 11 inches
Radius of the cylinder(r) = 9 inches
Pi = 3.14
To find:
The volume(V) of the cylinder
We'll go ahead and determine the volume(V) of the cylinder using the below formula;
[tex]\begin{gathered} V=\pi r^2h \\ =3.14*9^2*11 \\ =31.4*81*11 \\ =2797.74\text{ cubic inches} \end{gathered}[/tex]So the volume of the cylinder is 2797.74 cubic inches
The highest recorded temperature in Massachusetts was one hundred seven degrees Fahrenheit on August 27, 1975. The average monthly high temperature is 81.7 degrees Fahrenheit. How many degrees hotter than average was the temperature on August 27, 1975?
Answer:
25.3°F
Explanation:
We need to find the difference between the temperature on August 27, 1975, and the average temperature. So, the difference is equal to:
107 °F - 81.7°F = 25.3°F
It means that on August 27, 1975, the temperature was 25.3°F hotter than average.