There are 7 possible positive integers that satisfy the inequality.
InequalityIn Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.
We can find the positive values of x in the given inequality.
2x + 8 < 22
2x < 22 - 8
2x < 14
x < 7
The solution shows that x < 7
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Which expression is equivalent to the algebraic expression 3^(2t+3)
An equivalent expression for 3^(2 · t + 3) is given by the use of algebra properties for power expressions: 27 · 9^t.
How to find an equivalent algebraic expression by power propertiesIn this problem we find a power expression whose exponent is the sum of two numbers and we are asked to determine an equivalent form by using the following properties for power expressions:
1) Product of two powers of same base
a^m · a^n = a^(m + n)
2) Power of a power
(a^m)^n = a^(m \cdot n)
First, write the expression introduced in the statement of this question:
3^(2 · t + 3)
Second, use the algebra property for the product of two powers of same base in the expression:
3^(2 · t) · 3³
27 · 3^(2 · t)
Third, use the algebra property for the power of a power in the expression:
27 · (3²)^t
27 · 9^t
Fourth, write the resulting expression after applying algebra properties:
27 · 9^t
According to algebra properties, an equivalent expression is 27 · 9^t.
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Write the point-slope form of the equation of the line with slope 9 that passes through the point(−4, −6).
y – 6 = 9(x − 4)
x – 4 = 9(y − 6)
y + 6 = 9(x + 4)
y + 4 = 9(x + 6)
Answer:
y+6=9(x+4)
Step-by-step explanation:
point slope form is y-y1=m(X-x1)
y1 is -6
x1 is -4
And the slope or m is 9 so we can fill it in
y-(-6)=9(x-(-4))
y+6=9(x+4)
we can fill the equation out to see if it’s true
-6+6=9(-4+4)
0=9(0)
0=0
It is true
Hopes this helps please mark brainliest
One leg of a right triangle is 8 units long, and its hypotenuse is 14 units long. what is the length of the other leg? round to the nearest whole number. 11 units 13 units 18 units 22 units
Answer:
Step-by-step explanation:
The answer is C
Solve 8 + 10ƒ > 14 – 2ƒ.
Answer:
f>1/2
Step-by-step explanation:
8 + 10ƒ > 14 – 2ƒ.
-8 +2f
12f > 6
/12 /12
f>1/2
600 can be written as 2ª × b × cº
X
where a, b, c and d are all prime numbers.
Find the values of a, b, c and d.
For the given expression, the values are a = 3, b = 3, c = 5 and d=2
What are prime number?
A whole number higher than 1 whose only elements are 1 and itself is referred to as a prime number. A whole number that can be divided evenly into another number is referred to as a factor. 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29 are the first few prime numbers. Composite numbers are those that have more than two factors.What is prime factorization?
The technique of expressing all numbers as the product of primes is known as prime factorization. So, let's take something like the number 20 as an example. That can be divided into two components. "Well, that's 4 times 5," we can respond. Observe that 5 is a prime number.The prime factorization of 600 is given by
600 = 2 * 2 * 2 * 3 * 5 * 5
= 2³ * 3 * 5²
Compare this to the given expression.
Hence, the values are a = 3, b = 3, c = 5 and d=2
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Select the correct answer. Cole’s age is 3 years less than his sister Tina’s age, t. If Cole is 18, which equation represents this situation, and how old is Tina? A. The equation that represents this situation is t − 3 = 18. Tina is 21. B. The equation that represents this situation is t + 3 = 18. Tina is 15. C. The equation that represents this situation is 3 − t = 18. Tina is 21. D. The equation that represents this situation is -3 − t = 18. Tina is 15.
Answer: A
Step-by-step explanation:
a 16-step path is to go from to with each step increasing either the -coordinate or the -coordinate by . how many such paths stay outside or on the boundary of the square , at each step?
The paths that will stay outside or on the boundary of the square-2≤ x≤2, -2≤y ≤2 at each step will be 1698
We'll make advantage of the complementary counting idea. If you enter the square, you must exit by the boundaries and by the designated points because otherwise, you would touch another point in one of the sets of points in the connection (Call it S). Since y=x is symmetric, we simply need to take into account (1,-1), (1,0), and (1,1). We can only investigate one scenario and multiply it by two since (1,1) can cross the barrier in two different ways. We may just multiply (1,0) by two and (1,-1) by two. Therefore, we count the routes from (-4,4) to each of these sites and multiply that number by the total number of routes from the starting position.
[tex](\left {{16} \atop {8}} \right.) -2[(\left {{8} \atop {3}} \right.) (\left {{7} \atop {2}} \right.) +(\left {{9} \atop {4}} \right.) (\left {{6} \atop {2}} \right.) +(\left {{10} \atop {5}} \right.) (\left {{5} \atop {2}} \right.)] =1698[/tex]
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Your question is incomplete, but most probably, the full question was:
A 16-step path is to go from (-4,-4) to (4,4) with each step increasing either the x-coordinate or the y-coordinate by 1. How many such paths stay outside or on the boundary of the square -2≤ x≤2, -2≤y ≤2 at each step?
A.92
B.144
C.1568
D.1698
E.12800
oint c is the center of the circle above. what fraction of the area of the circle is the area of the shaded regio
Fraction of the area of the circle is the area of the shaded region is 5/18.
From the figure:
The shaded region has angle = 100
In the circle the total angle is 360.
Fraction = 100/360
= 50/180
= 25/90
= 5/18
Therefore fraction of the area of the circle is the area of the shaded region is 5/18.
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PLEASE HELP I’m really struggling on these
What is the slope of a line perpendicular to the line whose equation is 5x+y=-4. Fully simplify your answer.
Answer:
-5
Step-by-step explanation:
5x+y=-4
-5x -5x
y=-5x-4
slope intercept form = y=mx+b, where m=slope
and a line parallel to this line would have the same slope right
so i assume the answer to be -5
If the fdic has an insurance fund of $67. 8 billion and must use 7. 6% of it to cover several failed banks, approximately how much money is left in the fund? a. $5,153 million b. $57. 49 billion c. $72. 95 billion d. $62. 65 billion.
There is currently $62.65 billion in the fund.
Given that;
If the FDIC must use 7.6% of its $67.8 billion insurance reserve to pay for several bankrupt banks,
To get how much money is left in the fund, we need to;
The total insurance fund = $67.8 billion
To cover several failed banks = 7.6% = 0.076
Therefore, the money left = $67.8 * 0.076
= $5.15
So, the final amount left in the fund = $67.8 - $5.15
= $62.65
Hence, the money left in the fund is $62.65 billion.
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A car detailing shop charges $30 for materials, plus $50 per hour for labor to paint pinstripes on a car. Which function can be used to find the total cost c(h) to get pinstriping that requires h hours to complete?.
Answer:
Step-by-step explanation:
ii
Answer: c(h) = 30 + 50h
The cost to join a gym includes a one-time membership fee, plus a monthly
fee.
John joined the gym and paid $325 for 6 months.
• Abigail joined the gym and paid $475 for 9 months.
.
.
Claribel wants to join the gym for 17 months. How much will the gym
charge Claribel for 17 months?
O $650
O $875
O $775
O $950
Claribel needs to pay $875 for 17 months to gym, $25 for one time membership fee and $50 for 17 months.
What is System of Linear Equations?A set or group of equations that you solve all at once is referred to as a "system" of equations. A linear equation can be represented as Ax + By +C = 0, Where A, B are coefficient and C is the constant. Linear equations (those that graph as straight lines) are easier to understand than non-linear ones.
To find the amount for Claribel, we have to find the monthly fee and one time membership fee for the gym.
Let x be one time membership fee for the gym and y be the monthly fees, so the system of equations will be,
x + 6y = 325
x + 9y = 475
Now, subtracting the above equations, we get
3y = 150
y = 50
Now, putting the value of y in first equation, we get
x + 6(50) = 325
x+300 = 325
x = 25
Now, finding the amount for Claribel,
One time membership fee + 17(Monthly Fee) = Total Amount
Putting the values,
Total Amount = 25 + 17(50)
= 25 + 850
=$ 875
Therefore, Claribel needs to pay $875 for 17 months to gym.
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The carving of George Washington’s face is 60 feet tall. The height of Washington’s face is 100 feet less than 4 times its width.
The equation to find the width of Washington’s face, using the variable f, is
4f - 100 = 60
Solve the equation given to find the width of Washington's face.
f =
feet
The width of George Washington's face would be f = 40
How to solve for the equationThe question tells us to find the width of Washington’s face, using the variable f. The equation that we are to use in order to find this is given as 4f - 100 = 60
The next thing would be for us to take the like terms of the equation
4f - 100 = 60
4f = 60 + 100
The sign next to 100 changed to positive because it went over the equal to sign
4f = 160
divide through by 4
f = 160 / 4
f = 40
Hence the width of the face of George Washington is given as 40 ft
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2. Manny's dog spent 4 days in a veterinary hospital.
Manny paid $1585 for the surgery, $16.25 a day for board, and $49.75 for
medicine. What was Manny's total bill?
Manny's total bill is $1699.75 when the dog spent 4 days in veterinary hospital.
According to the question,
We have the following information:
Manny's dog spent 4 days in a veterinary hospital. Manny paid $1585 for the surgery, $16.25 a day for board, and $49.75 for medicine.
Now, for 4 days, we will first find the bill for boarding using multiplication.
Bill for 4 days of boarding = 16.25*4
Bill for 4 days of boarding = $65
Now, in order to find the total bill of 4 days, we will add all the given bills.
Total bill = 1585+65+49.75
Total bill = $1699.75
Hence, Manny's total bill is $1699.75 when the dog spent 4 days in veterinary hospital.
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Pedro made a quilt for his cousin's doll. The quilt had a 7 × 7 array of different color square patches. If each patch is 3 1/2
in long, what is the area of the whole quilt?
If Pedro made a quilt for his cousin's doll. The quilt had a 7 × 7 array of different color square patches. If each patch is 3 1/2 in long, then the area of the whole quilt is 600.25 in²
What is Square?Square is a regular quadrilateral, which has all the four sides of equal length and all four angles are also equal.
Pedro made a quilt for his cousin's doll.
This shows that there are seven rows and there are seven columns.
So, the total quilt is
7 × 7 = 49 squares patches
We are told that each of this square patches are 3½ in long
Then, since it is a square patch, it's area is
A = S² = 3½ × 3½ = 12¼ in²
So, each square patch has an area of 12¼in²,
Then, for 49 square patches
The total area of 49 Square patches is
A = 49 × 12¼ = 600.25 in²
Hence, the area of the whole quilt is 600.25 in²
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Factor 1/3x−1/3 . If the expression cannot be factored, write cannot be factored.
The factorization of the given expression ¹/₃x - ¹/₃ gives; ¹/₃(x - 1)
How to factorize algebraic expressions?When we want to factorize an algebraic expression, it means that the highest common factors of the terms seen in given algebraic expression will be determined after which we group the terms accordingly.
We are given the algebraic expression as;
¹/₃x - ¹/₃
Now, looking at the above algebraic expression, we can see that the highest common factor between the two values is ¹/₃.
Thus, the complete factorization of the expression is;
¹/₃(x - 1)
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$
First try was incorrect
Every day, a local coffee shop sells 29 more hot coffee items than iced
coffee items.
Let h represent the number of hot coffee items sold and let c
represent the number of iced coffee items sold.
Write an equation that represents the relationship between h and c.
The equation that represents the relationship between h and c is given by h = c + 29.
It is given to us that -
The local coffee shop sells 29 more hot coffee items than iced coffee items
Let h represent the number of hot coffee items sold
Let c represent the number of iced coffee items sold
We have to write an equation that represents the relationship between h and c.
According to the given information, the local coffee shop sells 29 more hot coffee items than iced coffee items
=> h = c + 29
The equation that represents the relationship between h and c is given by h = c + 29.
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Which equation represents the same line as the points in the table?
y=4x+6y is equal to 4 x plus 6
y=2/3x−4y is equal to 2 thirds x minus 4
y= −2x+6y is equal to negative 2 x plus 6
y= −4x+2/3
Answer:
y=-4x+2/3.,......,....................,-
change this root into a power
Five customers buy 10, 15, 20, 25, 30 toffees respectively from one shop. But the person who bought 20 toffees forgot to pay. If the shopkeeper makes 20% profit, what will be his profit or loss from these five customers if the person who forgot to pay had paid his amount?.
If the person who had forgot to pay had paid, the shopkeeper would have earned a 20% profit.
It is given that 5 customers bought 10, 15, 20, 25, and 30 toffees from a shop.
Therefore, the total number of toffees bought is
10 + 15 + 20 + 25 + 30 toffees
= 100 toffees.
Let the cost of one toffee be $x.
Hence the cost of 100 toffees is $100x
It is said that we need to consider the customer who had forgotten to pay has actually paid.
Therefore,
the shopkeeper has received money for 100 toffees.
Now, he makes a 20% profit on each toffee
Therefore the selling price of each toffee is-
20% of x + x
= 0.2x + x
= $1.2x
Hence for 100 toffees, he receives
$120x
Therefore, the profit made on those toffees is
$120x - $100x
$20x
Therefore profit percentage
= Profit/Cost Price X 100
= 20x/100x X 100
= 20%
Hence, he would have made a 20% profit.
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40 POINTS PLEASE HELP ASAP
Regarding the data from the table, it is found that:
a) The percentage of students who failed, given that they completed the review, is of 15.38%.
b) The percentage of students who failed, given that they did not complete the review, is of 42.86%.
c) There is an inverse association between failing the exam and completing the exam review.
How to calculate a percentage?A percentage is calculated applying proportions, as it is a fraction of a total amount, obtained as the division of the number of desired outcomes by the number of total outcomes and multiplied by 100%.
For item a, the outcomes are given as follows:
Total outcomes: 65% completed the review.Desired outcomes: 10% failed the exam and completed the review.Hence the percentage is:
p = 10/65 x 100% = 15.38%.
For item b, the outcomes are given as follows:
Total outcomes: 35% did not complete the review.Desired outcomes: 15% failed the exam and did not complete the review.Hence the percentage is:
p = 15/35 x 100% = 42.86%.
Regarding the association between failing the exam and completing the exam review, it is an inverse association, as the percentage of those who failed completing the review is way less than the percentage of those who failed without completing the review.
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HELP!! PLEASE!!!! ASAP!!
The milligrams of the vitamin in the drink are 80 mg,
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
We have been given that A new health drink has 160% of the recommended daily allowance (RDA) for a certain vitamin. The RDA for this vitamin is 50 mg.
Therefore, we can say that 50 = 100%,
Now; 60% of 50
0.60 x 50 = 30
Then we have to add;
30 + 50 = 80 mg
Hence, The milligrams of the vitamin in the drink are 80 mg,
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PLEASE HURRY!!
The two figures are similar. Find the ratios (shaded to nonshaded) of the perimeters and of the areas.
The ratio of the perimeters is 8:3 and the ratio of the area of the shaded to the non-shaded is 64 : 9 .
We know that when two figures are similar then the ratio of all the corresponding sides of the two figures are the same.
1) Given the ratio of the sides of shaded : non-shaded = 8 : 3
Therefore the perimeter of the shaded figure : perimeter of non shaded rectangle= 8 : 3
Again ratio of areas = ratio of the square of corresponding sides.
Area of shaded : area of non -shaded = 8² : 3² = 64 : 9
2) ratio of perimeter of shaded to non shaded trapezium
ratio = 6 : 10 = 3: 5
ratio of areas = 3² : 5² = 9 : 25
3) From the property of similarity of triangle :
8/10 = 3/ x
or, x = 30/8 = 3.75
4) From the property of similarity:
x/7=12/5
or, x = 16.8
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Timothy is preparing a stuffed Tofurky while Robert is preparing drummettes. It takes two minutes to cook the drummettes in the
microwave or eighteen minutes in the oven. It takes three times longer to cook the Tofurky than to cook the drummettes in the oven. Robert decided to use the oven and was done cooking the drummettes at 5:12 p.m. If Timothy started to cook the Tofurky at the same time as Robert started to cook the drummettes, what time will Timothy take the Tofurky out of the oven? (explain your answer)
Answer:
45 minutes
Step-by-step explanation:
the reason is because if you leave it at 5:12 add 33 more minutes you get 5:45
(5,-4) & (-15,16)
Find the slope
The slope by the given point is m = -1.
What is slope?
Slope is a value that describes the steepness and direction of a line. In variable format, it is commonly represented by the letter m. The slope of a line is also called its gradient or rate of change. The slope formula is the vertical change in y divided by the horizontal change in x, sometimes called rise over run.
The formula to find the slope = (y2-y1)/(x2-x1)
here the points are (5,-4) and (-15,16)
m = 16+4/-15-5
m = 20/-20
m = -1
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Can you solve this sum?
If you can show me how to made it step by step.
Step-by-step explanation:
counting numbers means whole numbers.
these divisible rules mean numbers that are divisible by 4 and by 3 and by 5.
4 = 2×2
so, everything that is divisible by 4 is also divisible by 2.
6 = 2×3
everything that is divisible by 2 and by 3 is also divisible by 6. therefore everything that is divisible by 4 and by 3 is also divisible by 6.
5 is a prime number on its own.
so, we are looking for all numbers that are divisible by
3×4×5 = 60
the smallest common multiple of 2, 3, 4, 5 and 6.
formally we get this by the combination of the longest chains of the prime factors :
2 = 2
3 = 3
4 = 2×2
5 = 5
6 = 2×3
the longest chain of 2 is 2×2.
the longest chain of 3 is 3.
the longest chain of 5 is 5.
so, 2×2×3×5 = 60
therefore, our solution is all numbers divisible by 60.
that means all multiples of 60 between 200 and 500.
what is the lowest number for that ?
3×60 = 180 too low
4×60 = 240 ok
what is the highest number ?
8×60 = 480 ok
9×60 = 540 too high
so, we only have
4×60 = 240
5×60 = 300
6×60 = 360
7×60 = 420
8×60 = 480
we have 5 numbers between 200 and 500 that are divisible by all of 2, 3, 4, 5 and 6.
Examples of a unit rate
The examples of unit rates include miles per hour, blinks per second, calories per serving, and steps per day.
What is a unit rate?A unit rate is the price for one unit of something. This is written as a ratio with a denominator of one. For instance, if you ran 70 yards in 10 seconds, you averaged 7 yards per second. Both ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but only the latter is a unit rate.
The denominator of a unit rate is always 1. To find the unit rate, divide the denominator by the numerator so that the denominator equals 1.
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what is the equation in slope intercept form of the line that passes through the point (-0.5,7) and is parallel to the graph of y=-8x-27
Answer:
y =-8x + 3
Step-by-step explanation:
Parallel lines have to have the same slope, and by plugging in the coordinates into the slope-intercept form of y = -8x -27, you get the answer above.
Answer:
Y= 8x +3
Step-by-step explanation:
Slope intercept form = y=mx + c
Where m= gradient
Parallel lines have equal gradients
By comparison,M= -8
Equation of a line
Y - Y1 = m(x- x1)
Y-7=-8(x- (-0.5)0
y-7 = 8(x +0.5)
y-7=8x -4
y=8x+7-4
y= 8x +3
How are rigid transformations used to justify the SAS congruence theorem?
(Need it right now fr fr)
Answer:
When a shape is transformed by rigid transformation, the sides lengths and angles remain unchanged.
Rigid transformation justifies the SAS congruence theorem by keeping the side lengths and angle, after transformation.
Assume two sides of a triangle are:
And the angle between the two sides is:
When the triangle is transformed by a rigid transformation (such as translation, rotation or reflection), the corresponding side lengths and angle would be:
Notice that the sides and angles do not change.
Hence, rigid transformation justifies the SAS congruence theorem by keeping the side lengths and angle, after transformation.
Step-by-step explanation: