FILL IN THE BLANK 1. x-7>10 X>______ 2. 3x ≤ 21 x ≤_____ 3. 5a-2<18 a<_____ 4. 2t + 8 ≥ -4(t+1) t≥______
Answer with Step-by-step explanation:
1. x-7>10
Adding 7 on both sides,we get
x>17
2. 3x ≤ 21
Dividing both sides by 3,we get
x≤7
3. 5a-2<18
Adding 2 on both sides, we get
5a<20
Dividing both sides by 5,we get
a<4
4. 2t + 8 ≥ -4(t+1)
Distributing -4 on right hand side of inequality
2t+8 ≥ -4t-4
2t+4t ≥ -4-8
6t ≥ -12
Dividing both sides by 6, we get
t ≥ -2
Which ordered pair represents a point on the line y = 2x + 1?
A. (0, 3)
B. (2, 1)
C. (-1, -1)
D. (1, 2)
Answer:
C.
Step-by-step explanation:
The ordered pair which represents the point on the line y = 2x + 1 is C. (-1, -1).
What are the Coordinates?Coordinates are the set of points in a geometrical plane or space, which is used to denote the exact point in the coordinate plane or space.
Given equation is y = 2x + 1.
We have to substitute each of the points in the line if the equation holds or not.
A. (0, 3)
2x + 1 = 0 + 1 = 1 ≠ 3
B. (2, 1)
2x + 1 = 4 + 1 = 5 ≠ 1
C. (-1, -1)
2x + 1 = -2 + 1 = -1
D. (1, 2)
2x + 1 = 2 + 1 = 3 ≠ 2
Hence the point on the line is C. (-1, -1).
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Max's bill at a restaurant is $8.67. He uses the following method to figure out a tip of about 15%. Round the amount of the bill to the nearest ten cents. Move the decimal point one place to the left. Then find half of the result. Add the last two answers and round to the nearest five cents. How much will the tip be for the bill? Why does Max's method work?
how do you do a 4 pound bag of sugar contains 454 one teaspoon servings and cost 3.49. A batch of muffins uses 3/4 cups of sugar. How many batches can you make if you use all the sugar what is the cost of sugar each
The number of batches you can make if you use all the sugar is 12.61 batches.
The cost of sugar used per batch is $0.28.
How many batches can you make if you use all the sugar?A 4-pound bag of sugar = 454 one-teaspoon
Sugar used for a batch of muffins = ¾ cup
If 1 cup = 48 teaspoons
3/4 cup = 3/4 × 48
= 36 teaspoons
Number of batches to make = 454 one-teaspoon / 36 teaspoons
= 12.61 batches
Cost of sugar teaspoons= 3.49/454
= $0.007687224669603 per teaspoon
Cost of sugar per batch = 0.007687224669603 × 36
= $0.276740088105726 per batch
Hence, the cost of sugar used per batch is approximately $0.28
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A 4-pound bag of sugar contains 454 one-teaspoon servings and costs $3.49. A batch of muffins uses ¾ cup of sugar. How many batches can you make if you use all the sugar? What is the cost of sugar for each batch? (1 cup = 48 teaspoons)
To find out how many batches of muffins can be made and the cost per batch, convert the total servings of sugar to cups, then divide by the amount of sugar used per batch, and finally, divide the total cost by the number of batches. which results in approximately $0.29 per batch.
The subject of this question is Mathematics, and it appears to be at the High School level due to the application of ratios, conversions, and basic algebraic skills to solve real-world problems.
Calculating Batches of Muffins from a Sugar Bag
Firstly, we determine the total amount of sugar in the bag in terms of cups. Since 1 teaspoon is equivalent to 4 grams of sugar, and we have 454 servings, we multiply 454 by 4g to get 1816g of sugar in total. To convert grams to cups (given 1 cup of sugar is 200g), we divide 1816g by 200g/cup, which gives us 9.08 cups.
Since a batch of muffins uses 3/4 cup of sugar, we divide the total cups of sugar by 3/4 to find the number of batches. 9.08 cups divided by 3/4 cups per batch results in approximately 12.1 batches; however, since you can't make a partial batch with the remaining sugar, it is safe to say you can make 12 full batches. To find the cost per batch, divide the total cost of the bag ($3.49) by the number of batches (12), which results in approximately $0.29 per batch.
Sharon called 3 friends on Friday. On Saturday, each of those 3 friends called 3 different friends. On Sunday, each person who was called on Saturday called 3 different people.
How many friends were called on Sunday?
The number of friends that were called on Sunday are 27 friends.
On Friday, the number of friends Sharon called = 3 friends
On Saturday, the number of each of those 3 friends called 3 different friends.
Therefore the number of friends on Saturday = 3×3
= 9
The number of friends called on Sunday = 9 × 3
= 27
Therefore the number of friends called on Sunday= 27
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Use properties of equality to solve these equations. Identify the properties used and describe how you used them.
(–5 • 7)25 = x(7 • 25)
PLEASE HELP.
Jessica is filling glasses with water. Each glass holds 3/5 cup of water. She pours 4 1/5 cups of water into the glasses.
How many glasses does she fill with water?
7 cups
4 1/5= 21/5
3+3+3+3+3+3+3= 21
7
Jessica can fill 7 glasses with water, by dividing the total amount of water ([tex]4\frac{1}{5}[/tex] cups) by the amount that each glass holds ([tex]\frac{3}{5}[/tex] cup).
The question asks us to determine how many glasses Jessica can fill with water when each glass holds [tex]\frac{3}{5}[/tex] cup of water and she has 4 1/5 cups of water in total. To solve this, we need to divide the total amount of water by the amount each glass holds.
Firstly, we need to convert the mixed number 4 1/5 cups to an improper fraction. This is done by multiplying the whole number by the denominator and adding the numerator, like this: (4 times 5) + 1 = 21, so 4 1/5 cups is the same as [tex]\frac{21}{5}[/tex]cups.
Next, we divide the total amount of water (21/5 cups) by the amount each glass holds ([tex]\frac{3}{5}[/tex] cup), which can be written as a fraction division problem:
[tex]\frac{\frac{21}{5} }{\frac{3}{5} }[/tex] = [tex]\frac{21}{5}[/tex] x [tex]\frac{5}{3}[/tex] = [tex]\frac{21}{3}[/tex] = 7
So, Jessica can fill 7 glasses with water.
Product of nine and the sum of a number Z and four
The product of nine and the sum of a number Z and four can be written as 9(Z + 4). For example, if Z = 5, then the expression becomes 9(5 + 4), which equals 81.
Explanation:The product of nine and the sum of a number Z and four can be written as 9(Z + 4).
For example, if Z = 5, then the expression becomes 9(5 + 4), which equals 9(9) = 81.
So, the product of nine and the sum of a number Z and four is 9(Z + 4), where Z represents any number.
3ax+2b/c=4d solve x answer
your dog's water bowl is 3/4 full. After taking a drink, the water bowl is 1/3 full. what fraction of the bowl did your dog drink?
Let amount of water that , my dog's water bowl can hold=x cubic unit
Level of water upto which my dog's water bowl is filled
[tex]=\frac{3x}{4} \text{Cubic unit}[/tex]
Let amount of water drank by my Dog in a drink=y cubic unit
Writing the statement in terms of equation
[tex]\frac{3x}{4}-y=\frac{x}{3}\\\\y=\frac{3x}{4}-\frac{x}{3}\\\\y=\frac{9x-4x}{4 \times 3}\\\\y=\frac{5x}{12}[/tex]
Fraction of the bowl did my dog drank is equal to [tex]\frac{5}{12}[/tex]
m=1/2 (d1+d2) solve for d1
Answer: The required solution for [tex]d_1[/tex] is [tex]d_1=2m-d_2.[/tex]
Step-by-step explanation: We are given to solve the following equation for [tex]d_1:[/tex]
[tex]m=\dfrac{1}{2}(d_1+d_2)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To solve the given equation for [tex]d_1,[/tex] we must take all the other terms on the right side of the equation.
From equation (i), we get
[tex]m=\dfrac{1}{2}(d_1+d_2)\\\\\\\Rightarrow 2m=d_1+d_2\\\\\Rightarrow d_1=2m-d_2.[/tex]
Thus, the required solution for [tex]d_1[/tex] is [tex]d_1=2m-d_2.[/tex]
If parallelogram ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°, where would point A' lie?
[Hint: Place your coordinates in the blank with no parentheses and a space after the comma in the form: x, y]
Answer:
The point A' lie at (-4,1).
Step-by-step explanation:
From the given figure it is clear that the coordinates of A are (-4,1).
If parallelogram ABCD was reflected over the y-axis, then
[tex](x,y)\rightarrow (-x,y)[/tex]
[tex]A(-4,1)\rightarrow A_1(4,1)[/tex]
Then it reflected over the x-axis,
[tex](x,y)\rightarrow (x,-y)[/tex]
[tex]A_1(4,1)\rightarrow A_2(4,-1)[/tex]
After that, it rotated 180° about the origin,
[tex](x,y)\rightarrow (-x,-y)[/tex]
[tex]A_2(4,-1)\rightarrow A'(-4,1)[/tex]
Therefore the point A' lie at (-4,1).
The main difference between a prototype and other kinds of models is that a prototype .... (A) uses much more advanced technology (B) is a comparison between two different things (C) uses complex calculation to answer a question (D)is designed to have some features that work like the real thing ?????
A prototype is unique in that it is designed to have functional features similar to the final product, allowing designers and engineers to test and refine the design. Option D.
A prototype often includes functional elements that mimic the final product to test specific aspects of its design. Unlike other models that may only represent the appearance or structure, prototypes are used by designers and engineers to identify potential improvements before initiating full-scale manufacturing.The main difference between a prototype and other kinds of models is that a prototype is designed to have some features that work like the real thing (Option D).
At 5 a.m., the temperature at an airport was −9.4°F . Six hours later, the temperature was 2.8°F . Which expression represents the total temperature change over the six hours?
|2.8−(−9.4)|
−9.4+2.8
|−9.4+2.8|
|2.8+(−9.4)|
Answer:
Your answer is B
What is the estimat of 1,537×242 need answer aspA
if a snail travels 200 inches in 2 hours, how long will it take for the snail to travel 50 inches?
Tony is the best pizza delivery man in the city. He has been offered a job from Pizza Tent, which has given tony his pay options in the following function. S represents Tonys salary, and p represents the number of pizzas he delivers. S= 2.75 + 52
Convert 18532.6 into scientific notation
move the decimal point 4 places to the left to get
1.85326 x 10^4
Max makes and sells posters. The function p(x)= -10x^2 +200x -250, graphed below, indicates how much profit he makes in a month if he sells the posters for 20-x dollars each. (Picture in comments) What should Max charge per poster to make the maximum profit, and what is the maximum profit he can make in a month? A: $800 at $10 per poster B: $800 at $5 per poster C: $750 at $10 per poster D: $750 at $5 per poster
Answer:
$750 at $10 per poster
Step-by-step explanation:
How to add 3/5 and 1/10 in simplest form
What's the answer and work of 42.3-(-18.7)
1. Refer to the equation 2x − 6y = 12.
(a) Create a table of values for at least 4 points. Show your work.
(b) Use the table of values to graph the line.
Mariah borrowed 15 books from the library last month. She's already read 2/5 of them. How many of the 15 books has she read?
given the number, two-fifths,generate its equivalents forms as a fraction, a decimal, and a percent. in addition, give a real world example in which each form might be used
Melvin and Sylvia are married with no children, and they're filing their federal income tax return. Melvin had a gross income of $44,500 last year, while Sylvia had a gross income of $51,200, and they plan to use the standard deduction. They're trying to decide whether to file their return jointly or separately, so they want to calculate how much less they would pay in federal income taxes if they filed jointly rather than separately.
Part I: When filing separately, both Melvin and Sylvia have a standard deduction of $5700, and each can claim him/herself as an exemption for $3650. Neither has any additional adjustments to income. What is Melvin's taxable income? How about Sylvia's taxable income?
add standard deduction and exemption: 5700 + 3650 = 9350
subtract from each of their incomes and that will be the taxable income:
Melvin: 44500 - 9350 = 35150 taxable income
Sylvia: 51200 - 9350 = 41850 taxable income
Melvin's taxable income is $34,150 and Sylvia's taxable income is $42,850.
Explanation:To calculate Melvin's taxable income, we need to subtract his standard deduction and exemption from his gross income. Melvin's gross income was $44,500 and his standard deduction is $5700. He can also claim himself as an exemption for $3650. Therefore, Melvin's taxable income would be $44,500 - ($5700 + $3650) = $34,150.
In a similar way, to calculate Sylvia's taxable income, we subtract her standard deduction and exemption from her gross income. Sylvia's gross income was $51,200 and her standard deduction is $5700. She can also claim herself as an exemption for $3650. Therefore, Sylvia's taxable income would be $51,200 - ($5700 + $3650) = $42,850.
776 DIVIDED BY 28 COMPATIBLE NUMBERS
Answer:
27.7 or 28
Step-by-step explanation:
The table shows the low temperatures in Alto for 5 days.What is the average low tempreature
Graph y−2=−34(x−6) using the point and slope given in the equation.
Use the line tool and select two points on the line.
Answer:
Point-slope form: An equation of a straight line in the form [tex]y -y_1 = m(x -x_1)[/tex];
where
m is the slope of the line and [tex](x_1, y_1)[/tex] are the coordinates of a given point on the line.
Given the equation: [tex]y-2=-\frac{3}{4}(x-6)[/tex] ......[1]
On comparing with Point slope form equation we have;
m = [tex]-\frac{3}{4}[/tex] and point (6 , 2)
Now, find the Intercept of the given equation:
x-intercept: The graph crosses the the x-axis i.e,
Substitute y =0 in [1] and solve for x;
[tex]0-2=-\frac{3}{4}(x-6)[/tex]
[tex]-2=-\frac{3}{4}(x-6)[/tex]
Using distributive property: [tex]a\cdot(b+c) = a\cdot b +a\cdot c[/tex]
[tex]-2 = -\frac{3}{4}x + \frac{18}{4}[/tex]
Subtract [tex]\frac{18}{4}[/tex] on both sides we get;
[tex]-2-\frac{18}{4}= -\frac{3}{4}x + \frac{18}{4} -\frac{18}{4} [/tex]
Simplify:
[tex]-\frac{26}{4} = -\frac{3}{4}x[/tex]
or
-26 = -3x
Divide both sides by -3 we get;
x = 8.667
x-intercept: (8.667, 0)
Similarly, for
y-intercept:
Substitute x = 0 in [1] and solve for y;
[tex]y-2=-\frac{3}{4}(0-6)[/tex]
[tex]y-2=\frac{18}{4}[/tex]
Add 2 on both sides we get;
[tex]y-2+2=\frac{18}{4}+2[/tex]
Simplify:
[tex]y=\frac{26}{4} =6.5[/tex]
y-intercept: (0, 6.5)
Now, using these two points (8.667, 0) and (0, 6.5) you can plot the graph using line tool as shown below.
Jeremy earns $234 for 36 hours of work. Miguel earns $288 for 40 hours of work . Are the pay rates of these two people proportional?
Vince has 16 beads. How many different arrays can Vince draw to represent the total number of beads he has? List the sizes of the arrays.
There are 36 different arrays that Vince can draw to represent the total number of beads he has. The sizes of the arrays range from 1 to 16 beads.
To find the different arrays Vince can draw to represent the total number of beads he has, we need to consider all the possible ways he can arrange the beads. Essentially, we are looking for all the possible partitions of 16.
A partition of a number represents the different ways it can be expressed as a sum of positive integers. In this case, we want to find all the partitions of 16.
To do this, we can list all the possible sizes of arrays that Vince can draw. Here are the possible sizes:
16
15 + 1
14 + 2
13 + 3
12 + 4
11 + 5
10 + 6
9 + 7
8 + 8
14 + 1 + 1
13 + 2 + 1
12 + 3 + 1
11 + 4 + 1
10 + 5 + 1
9 + 6 + 1
8 + 7 + 1
12 + 2 + 2
11 + 3 + 2
10 + 4 + 2
9 + 5 + 2
8 + 6 + 2
7 + 7 + 2
10 + 3 + 3
9 + 4 + 3
8 + 5 + 3
7 + 6 + 3
6 + 6 + 4
9 + 3 + 3 + 1
8 + 4 + 3 + 1
7 + 5 + 3 + 1
6 + 6 + 3 + 1
8 + 3 + 3 + 2
7 + 4 + 3 + 2
6 + 5 + 3 + 2
5 + 5 + 4 + 2
7 + 3 + 3 + 3
6 + 4 + 3 + 3
5 + 5 + 3 + 3
4 + 4 + 4 + 4
So, there are 36 different arrays that Vince can draw to represent the total number of beads he has. The sizes of the arrays range from 1 to 16 beads.
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