Solve the problem and enter your solution for the variable below. Do notinclude units in your answer.The scale below shows the weight, in grams, of two identical blocks. Howmany grams does one of the blocks weigh?
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Since the scale is balanced, the weight on the left end is equal to the weight on the right end.
Let x be the weight of one of the blocks. We'll have that
[tex]\begin{gathered} x+x=10 \\ \rightarrow2x=10\rightarrow x=\frac{10}{2} \\ \rightarrow x=5 \end{gathered}[/tex]Therefore, the weight of one of the blocks is 5
Related Questions
find the slope of the line that passes through (2,3) and (10,10)
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The slope of a line represents the change in y over the change in x.
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]We are given the points (2,3) and (10,10).
[tex]m=\frac{3-10}{2-10}=\frac{7}{8}=0.875[/tex]15) *15. Last year Ms. Garcia ordered 24 pounds of apples from a local orchard. Thisyear, he plans to order 15 times as many pounds of apples as were ordered3lastyear.Mr. Garcia will use of this order to create fruit baskets. What isthe total amount, in pounds, of apples that Mr. Garcia will use in fruit baskets?Your answer16A) *
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Last year order = 24
This year = 1 (1/2) = 3/2 more
Then we multiply
total amount of apples (in pounds)
A store did $54,000 in sales in 2017, and $67,000 in 2018.(a) Assuming the store's sales are growing linearly, find the growth rate d.(b) Write a linear model of the form Pt=P0+dt to describe this store's sales from 2017 onward.Pt= (c) Predict the store's sales in 2025.$ (d) When do you expect the store's sales to exceed $105,000? Give your answer as a calendar year (ex: 2020).During the year
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Given:
A store did $54,000 in sales in 2017, and $67,000 in 2018.
a)
To find the growth rate:
Since, the store's sales are growing linearly
We can use the formula,
[tex]\begin{gathered} d=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{67,000-54,000}{2018-2017} \\ =13,000 \end{gathered}[/tex]Hence, the growth rate d is 13,000.
b)
To write a linear model of the form Pt=P0+dt to describe this store's sales from 2017 onwards:
So, the linear equation is
[tex]P_t=54,000+13,000t[/tex]c) To predict the store's sales in 2025.
The total number of year from 2017 to 2025 is 8.
Let us substitute t=8 in the above equation we get,
[tex]\begin{gathered} P_t=54,000+13,000t \\ P_8=54,000+13,000(8) \\ =54,000+1,04,000 \\ =1,58,000 \end{gathered}[/tex]Therefore, the store's sales in 2025 is $ 1,58,000.
d) To find the year at which the sales is exceed $1,05,000
Then the linear equation becomes,
[tex]\begin{gathered} 1,05,000=54,000+13,000t \\ 13,000t=1,05,000-54,000 \\ 13,000t=51,000 \\ t=3.923 \end{gathered}[/tex]Therefore, 2017+3.9 Years
We will get, the sales will get exceed in the 2020 itself.
Hence, the sales will get exceed $1,05,000 in the year 2020.
Here is a scatter plot: y 5 4 3 . 2 1 . 0 1 2 3 4 5 X The graph of what linear equation is a good fit for this data? Oy= - 30+ 2 Oy = -x + 6 Oy= 5x +2 o y = 120 + 6
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Take into account that the genereal form of an equation of a line is given by:
y = mx + b
where m is the slope of the line and b the y-intercept.
You can notice that y decreases when x increases. It means that the line has a negative slope.
Moreover, you can notice that the y intercept of the line coudl be b = 2.
Hence, the best linear equation to fit the data is:
y = -1/3 x + 2
because the slope is negative and the y-intercept is 2
tell whether each number is divisible by 2 3 4 5 6 9 or 10 then classify the number as even or odd
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
13. 24
Step 02:
classify the number and divisibility:
classify the number:
24 ===> even number
divisibility:
[tex]\begin{gathered} \frac{24}{2}=\text{ 12 } \\ \\ \frac{24}{3}=\text{ 8} \\ \\ \frac{24}{4}=6 \\ \\ \frac{24}{5}=4.8\text{ \lparen inexact division\rparen} \\ \\ \frac{24}{6}=4 \\ \\ \frac{24}{9}=2.66...\text{ \lparen inexact division\rparen} \\ \\ \frac{24}{10}=2.4\text{ \lparen inexact division\rparen } \\ \end{gathered}[/tex]That is the full solution.
find the reflection of (-1,-2) across the line y=2
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Start by graphing the line y=2 and the point given
since the line y=2 is a straight line, then the reflection will stay on the same x coordinate and the y coordinate will be 4 units above the line.
The reflection will be at point (-1,6)
(x - 5)²Simplify the polynomial expression
Answers
x² - 10x + 25
Explanation:(x - 5)² = (x -5)(x -5)
Simplifying the expression:
x(x -5) -5(x - 5)
x(x) -x(5) -5(x) -5(-5)
Multiplication of same sign gives positive number. Multiplication of opposite signs give negative number.
x²- 5x - 5x + 25
collect like terms:
x² - 10x + 25
Choose the best translation of the English phrase.The radius of a circle with a circumferenceof 10 feet.
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point A is located at ( 3,4). find A'=T<3,5>(A)point A is located at(3,4).find after A has been reflected across the line y=x
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Answer:
A(4,3)
Step-by-step explanation:
When we reflect a point over the line y = x, the values of x and y are exchanged in the point.
We have: Point A(3,4)
After reflection across the line y = x: A(4,3)
13 Rewrite the expression withparentheses to equal thegiven value.(2 + 5)( 4 - 2)value: 12
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We need to rewrite the following expression:
[tex](2+5)\cdot(4-2)[/tex]We need to rewrite the expression to make it equal to 12. This is done below:
[tex](5-3)\cdot(4+2)[/tex]This makes it equal to 12, because:
[tex]\begin{gathered} (5-3)\cdot(4+2) \\ 2\cdot6 \\ 12 \end{gathered}[/tex]Therefore the expression is (5-3)*(4+2).
i need help please this is for my pre calculus class
Answers
To find the vertical asymptotes, we have to find the zeros of the denominator.
[tex]x^2-x-2=0[/tex]We have to find two numbers whose product is 2, and which difference is 1. Those numbers are 2 and 2.
[tex]x^2-x-2=(x-2)(x+1)[/tex]Then, the zeros are
[tex]\begin{gathered} x=2 \\ x=-1 \end{gathered}[/tex]Therefore, the vertical asymptotes are x = -1 and x = 2.Hi, do you think u can solve this for me im kinda in a hurry cause I neednto answer the question soon please.
Answers
Step 1: Calculate the hours worked for the morning and afternoon
[tex]\begin{gathered} M\text{orning }\Rightarrow8\colon15-12\colon50=4\text{hours} \\ A\text{fternoon}\Rightarrow13\colon00-17\colon30=4.5\text{hours} \end{gathered}[/tex]Step 2: Calculate the entire hours worked for the day
[tex]\text{Morning+Afternoon=4+4.5=8.5hours }[/tex]Step 3: Given the wage to be $13.50 per hour, calculate the wage for the combined hours worked
A grocery store received two shipments of watermelon. each watermelon in a shipment was weighed, then a line plot was made of all of the weights in a shipment. what statement about the two plots' disributions is true? Choose EACH correct statement.
Answers
The correct statements are:
• The lightest watermelon in shipment 1 weighs the same amount as the lightest watermelon in shipment 2.
• The range of weighs in shipment 1 is greater than the range of weighs in shipment 2
Explanation:From the given line plots, the following are correct:
The lightest watermelon (16) in shipment 1 weighs the same amount as the lightest watermelon (16) in shipment 2.
The range (10) of weighs in shipment 1 is greater than the range (8) of weighs in shipment 2
125x^3 + 27factor completely
Answers
The given expression is
[tex]125x^3+27[/tex]We can observe that it's a sum of perfect cubes, which can be solved as follows
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]Where
[tex]undefined[/tex]Hello I need help with this question pleaseFind the equation of the line containing the given points (3, -2) and (-4, -8)
Answers
Solution:
To find the equation of a line, the formula is
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]Where
[tex]\begin{gathered} (x_1,y_1)=(3,-2) \\ (x_2,y_2)=(-4,8) \end{gathered}[/tex]Substitute the values of the variable
[tex]\begin{gathered} \frac{y-(-2)}{x-3}=\frac{-8-(-2)}{-4-3} \\ \frac{y+2}{x-3}=\frac{-8+2}{-7} \\ \frac{y+2}{x-3}=\frac{-6}{-7} \end{gathered}[/tex][tex]\begin{gathered} Crossmultiply \\ -7(y+2)=-6(x-3) \\ -7y-14=-6x+18 \\ 6x-7y-18-14=0 \\ 6x-7y-32=0 \end{gathered}[/tex]Hence, the equation is
[tex]6x-7y-32=0[/tex]The midpoint of PQ is M=(1, -5) . One endpoint is P=(6, -8).Find the coordinates of the other endpoint, Q.
Answers
Given:
The midpoint of a line PQ is M = (1,-5).
THe coordinate of point P = (6,-8).
The objective is to find the coordinate of other point Q.
Explanation:
Since, M is the midpoint of PQ, the distance between PM and QM will be equal.
Consider the coordinate of P , M and Q as,
[tex]\begin{gathered} P(x_1,y_1)=P(6,-8) \\ M(x,y)=(1,-5) \\ Q\mleft(x_2,y_2\mright) \end{gathered}[/tex]The general midpoint formula is,
[tex]\begin{gathered} M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ (x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \end{gathered}[/tex]To find the value of x value of point Q:
By equating only the variables of x,
[tex]\begin{gathered} x=\frac{x_1+x_2}{2} \\ 1=\frac{6+x_2}{2} \\ 1(2)=6+x_2_{} \\ x_2=2-6 \\ x_2=-4 \end{gathered}[/tex]To find the value of y value of point Q:
By equating only the variable of y,
[tex]\begin{gathered} y=\frac{y_1+y_2}{2} \\ -5=\frac{-8+y_2}{2} \\ -5(2)=-8+y_2 \\ y_2=-10+8 \\ y_2=-2 \end{gathered}[/tex]Hence, the coordinate of Q is (-4,-2).
Arielle is selling t-shirts online. She spent $500 making the shirts and plans on selling them for $25 each. How many shirts must she sell to make a profit of at least $2500?
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Answer:
120 T-Shirts
Explanation:
Let the number of t-shirts Arielle made = x
• Cost of making x t-shirts = $500
If she is planning to sell each for $25, then:
• Total Income from x t-shirts = 25x
Profit = Income -Expenses
=25x-500
Since she plans to make a profit of at least $2500, then:
[tex]25x-500\ge2500[/tex]We solve the inequality for x.
[tex]\begin{gathered} 25x\ge2500+500 \\ 25x\ge3000 \\ x\ge\frac{3000}{25} \\ x\ge120 \end{gathered}[/tex]She must sell 120 t-shirts.
what is the opposite of 0
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Zero does not have an opposite, because it is in the middle
or I'm thinking in the possibility that it is Infinity
[tex]\infty\text{ This is infinity symbol}[/tex]Find the indicated side of theright triangle.60330X == [?].Enter
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Step 1
State a trigonometric identity that can be used to find the value of x
[tex]\begin{gathered} \text{Toa} \\ \text{where} \\ T\text{ = tan} \\ o=\text{ opposite}=3 \\ a\text{ = adjacent}=x \\ \text{and written as} \\ \text{Tan 30 =}\frac{opposite}{\text{adjacent}} \end{gathered}[/tex]Step 2
Substitute and find the value of x
[tex]\begin{gathered} \text{Tan}30\text{ =}\frac{3}{x} \\ Tan\text{ 30 = }\frac{1}{\sqrt[]{3}} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} \frac{1}{\sqrt[]{3}}=\frac{3}{x} \\ x\text{ = 3}\sqrt[]{3} \end{gathered}[/tex]Therefore x = 3√3
what is the perpendicular slope to the line on the graph?
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This question is confusing need help
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The solution to the system of equations is the ordered pair where the graphs intersect. In this case, the point is at the coordinate (-3, 1).
Therefore:
x = -3
y = 1
Answer: D. x = -3, y = 1
What measure of variance is best to describe Mr. Mack’s 1st period scores.
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Given: A bar chart showing the group data test scores for frst period angainst the frequency
To Determine: What measures of variance is best to describe Mr. Mack's 1st period scores
Solution
In statistics, variance measures variability from the average or mean. It is calculated by taking the differences between each number in the data set and the mean, then squaring the differences to make them positive, and finally dividing the sum of the squares by the number of values in the data set
The following are the four major measures of variance
Range: the difference between the highest and lowest values.
Interquartile range: the range of the middle half of a distribution.
Standard deviation: average distance from the mean.
Variance: average of squared distances from the mean
What is the measure of n?515mnn = 5V[?]Give your answer in simplest form.Enter
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We have the following relation
Therefore, we have
[tex]\begin{gathered} n^2=15\cdot5 \\ \\ n^2=3\cdot5\cdot5 \\ \\ n^2=3\cdot5^2 \\ \\ \sqrt[]{n^2}=\sqrt[]{3\cdot5^2} \\ \\ n=5\, \sqrt[]{3} \end{gathered}[/tex]The number in [?} is 3
Use the figure above and find the Endpoints (two of them from the red arrows). Using the endpoints and the formula find the midpoint of the segment above.
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The two endpoints are (-1,2) and (4,2).
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex][tex](\frac{-1+4}{2},\text{ }\frac{2+2}{2})=(\frac{3}{2},\frac{4}{2})=(\frac{3}{2},2)[/tex]Thank you to whoever helps me I will mark brainlest if correct
Answers
1.
Length = 22 ft
width = w
Perimeter = 74
Perimeter of a rectangle: 2 length + 2 width
Replacing:
74 = 2(22) + 2 w
Solve for w
74 = 44 + 2w
74-44 = 2w
30 = 2w
30/2 = w
w= 15 ft
12 / x equals 6 x equals what
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First equation
[tex]\begin{gathered} \frac{12}{x}=6 \\ 12=\text{ 6x} \\ x=\text{ }\frac{12}{6} \\ x=\text{ 2} \end{gathered}[/tex]The table shows how the number of sit-ups Marla does each day has changed over time. At this rate, how many sit-ups will she do on Day 12? Explain your steps in solving this problem.
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To determine the number sit-ups Marla will do on day 12;
The number is arithmetic sequence;
[tex]\begin{gathered} 17,21,25,29,33 \\ a_1=17,\text{ d=4, n=12 and a}_{12}=? \end{gathered}[/tex][tex]a_n=a_1+(n-1)d[/tex][tex]a_{12}=17+11(4)=17+44=61[/tex]
The answer is 61.
Kenny has $500 in an account. The interest rate is 5% compounded annually.To the nearest cent, how much interest will he earn in 1 year?Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
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Solution:
Using the formula;
[tex]B=p(1+r)^t[/tex]Where;
[tex]\begin{gathered} p=500,r=5\text{ \%}=0.05,t=1 \\ \\ B=500(1+0.05)^1 \\ \\ B=525 \end{gathered}[/tex]CORRECT ANSWER: $525
22. In the figure below, which theorem or postulate can be used to prove TriangleADM=triangleZMD?
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D) AAS
1) Let's sketch this to better grasp it:
As we can see in the sketch above, there is another pair of congruent angles. These are Vertical Angles, therefore we can tell that this falls within the following case, since the congruent side is not between the pair of congruent angles.
[tex]AAS[/tex]Thus, this is the answer.
Find the LCM of 4 and 14
Answers
Answer
28 is the LCM of 4 and 14.
Explanation
We are asked to find the Lowest Common Multiple of 4 and 14. This refers to the lowest number that is a multiple of both 4 and 14.
The multiples of 4 include 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44 etc.
The multiples of 14 include 14, 28, 42, 56, 70 etc.
We can see that the lowest number on both of these lists that is common to both 4 and 14 is 28.
Hence, 28 is the LCM of 4 and 14.
Hope this Helps!!!