Answer:
YESStep-by-step explanation:
14 - r < 9
Put r = 6 and check inequality:
14 - 6 < 9
8 < 9 TRUE
By substituting r = 6 into the inequality 14 - r < 9, we find that the inequality holds true, indicating that r = 6 is a solution to the inequality.
Explanation:To determine if r = 6 is a solution to the inequality 14 - r < 9, we simply substitute the value of r into the inequality and check the result.
Substituting r = 6 into the inequality gives us:
14 - 6 < 9
Which simplifies to:
8 < 9
Since 8 is less than 9, the inequality holds true,
which means that r = 6 is indeed a solution to the inequality 14 - r < 9.
Frank is going to plant y vegetable seeds in one garden and 4y+9 vegetable seeds in another. How many seeds is frank going to plant
Frank will plant a total of 5y + 9 vegetable seeds across his two gardens.
Frank has two gardens where he plans to plant vegetable seeds. In one garden, he will plant y vegetable seeds. In the other garden, he will plant 4y+9 seeds. To find the total number of seeds Frank is going to plant, we need to add together the number of seeds for each garden.
The total number of seeds is:
Total seeds = y + (4y + 9)
Combine like terms:
Total seeds = y + 4y + 9
Total seeds = 5y + 9
Thus, Frank will plant a total of 5y + 9 vegetable seeds across both gardens.
I NEED SMART STUDENT TO HELP ME PLEASE...ILL GIVE POINTS
Answer:
I believe 27%
Step-by-step explanation:
Total juniors = 8
Total students = 30
So 8 out of 30 as a percentage = 26.67
Hope this helps! :)
Please answer them
This is homework
Answer:
Step-by-step explanation:
31) Y = -3x² + 18 x -25 = -3*x² + -3*-6x -25
= -3(x² -6x) - 25
( (a-b)² =a² - 2ab + b²; here a = x; 2ab = -6x = -2*x*3; and so b = 3)
= -3(x² -6x + 9 - 9) - 25
{ when we add and subtract 9, the equation will not change}
= -3[(x -3)² - 9] -25
= -3(x - 3)² - (-3)*9 - 25
= -3(x - 3)² + 27 -25
= -3(x - 3)² + 2
32) y= -3x² - 18x - 25
= -3 (x² + 6x )-25
= -3 (x² + 6x + 9 - 9) -25
= -3 [ (x+ 3)² - 9] -25
=-3 (x + 3)² - (-3)*9 - 25
= -3(x + 3)² + 27 - 25
= -3(x+3)² +2
If Jose's present age is 3n, how old will he be in 5 years?
Answer:
3n + 5
Step-by-step explanation:
You can't add 5 to 3n. So in 5 years he will 3n + 5.
José's age in 5 years will be 3n + 5, where 3n represents his current age.
Explanation:If José's present age is 3n, and we want to find out how old he will be in 5 years, we need to add 5 to his current age expressed as 3n. This can be done with a simple algebraic expression:
Age in 5 years = Current Age + 5 = 3n + 5
Without the value of n, we can't calculate his exact future age, but we know that in 5 years, his age will be 5 years older than it is now.
In a wildlife park there are 20 gray wolves after a few years they were 38 Greywolf what is the percent increase
The percent increase is 0.53%
The percentage increase in the number of Greywolf is 90% and this can be determined by using the unitary method.
Given :
There are previously 20 Greywolf in a wildlife park.After a few years, the total number of Greywolf is 38.The following steps can be used in order to determine the percentage increase in the number of Greywolf:
Step 1 - The unitary method can be used in order to determine the percentage increase in the number of Greywolf.
Step 2 - According to the given data, there are previously 20 Greywolf in a wildlife park which is 100%.
Step 3 - So, let the percentage of 38 Greywolf be 'x'. So, the value of 'x' can be calculated as:
[tex]x = \dfrac{38}{20}\times 100[/tex]
[tex]x = 190\%[/tex]
Step 4 - So, the percentage increase in the number of Greywolf is:
[tex]{\rm Percentage \; Increase} = 190-100[/tex]
[tex]{\rm Percentage \; Increase} = 90\%[/tex]
The percentage increase in the number of Greywolf is 90%.
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The area of a circle is 28.26 square meters. What is the circle's diameter?
Answer: area for circle is πr² so πr² =28.26 and we can sub 3.14 as pi
3.14*r²=28.26 we can divide by 3.14 to get r² on it's own
r²=28.26/3.14
then we root both sides to get r on it's own
28.26/3.14=9 √9=3
and the diameter is double the radius 3*2=6 so the diameter is 6
Step-by-step explanation:
1: In Rectangle ABCD, AC is 5x - 12, and BD is 2x + 15. Find x.
Answer:
X=9
Step-by-step explanation:
In the picture above.
the health food store wishes to blend peanuts that cost $1.20/ib with raisins that cost $2.10/ib to make 50 pounds of a mixture that cost $1.47/ib how many pounds of peanuts and of raisins are needed
To solve the mixture problem, we set up an equation based on the total weight and another based on the total cost, then solve the system of equations algebraically to find out how many pounds of peanuts and raisins are needed.
Explanation:The question involves creating a cost-based blend of two items, peanuts and raisins, to produce a mixture with a target cost per pound. This is a typical algebraic mixture problem, commonly encountered in high school math. To solve this problem, we want to find out how many pounds of peanuts and raisins are needed to make a 50-pound mixture that costs $1.47 per pound when peanuts cost $1.20 per pound and raisins cost $2.10 per pound.
Let's denote the weight of peanuts as P pounds and the weight of raisins as R pounds. The total weight of the mixture is given as 50 pounds, which gives us the equation:
P + R = 50
Next, we need to consider the total cost of the mixture. The cost of the peanuts is P times $1.20, and the cost of the raisins is R times $2.10. Since the mixture should have an overall cost of $1.47 per pound, our cost equation becomes:
1.20P + 2.10R = 1.47 × 50
From our first equation, we can express R as 50 - P, and substitute it into our second equation to find the value of P. After solving these linear equations, we will obtain the exact quantities of peanuts and raisins required to make the desire mixture.
What fraction is larger 1 1/6 or 1 4/12
Answer:
1 4/12
Step-by-step explanation: What you need to do first is make them improper fractions with the same denominator.
1 1/6 = 7/6 1 4/12 = 16/12. Now you can make them have the same denominator. 7/6 = 14/12 and 16/12. So 1 and 4/12 is bigger.
$250 at 6% for 4 years find the interest
Answer:
I=60
Step-by-step explanation:
So
P=$250
R=6%
T=4
So to get the answer we would need to multiply everything to get the interest so the answer would be 60 because 250 times 6% equals to 15 then we would multiply 15 by 4 and then get out answer of $60 interest.
three and two sevenths plus eight and one third
0.4x3.2
Step by step
Answer:
Step-by-step explanation:
0.4 × 3.2
Convert to fraction
0.4 = 4/10 = 2/5 & 3.2 = 32/10 = 16/5
0.4 × 3.2 = 2/5 × 16/5 = 32/25 = 1.28
Without conversion you press ur calculator and you get 1.28
Dimitri determined that the ordered pair (2, –2) is a solution to the system of linear equations 7x + 9y = –4 and 5x – 2y = 6 as shown. Equation 1: 7 x + 9 y = negative 4. 7 (2) + 9 (negative 2) = negative 4. 14 + (negative 18) = negative 4. Negative 4 = negative 4. Equation 2: 5 x minus 2 y = 6. 5 (2) minus 2 (negative 2) = 6. 10 minus 4 = 6. 6 = 6. What was Dimitri’s mistake? He mixed up the coordinates of the ordered pair when substituting it into the equations 7x + 9y = –4 and 5x – 2y = 6. He checked the equation 7x + 9y = –4 first when he should have checked 5 x minus 2 y = 6 first. He made a mistake in his calculations when substituting the ordered pair into the equation 7x + 9y = –4 and simplifying. He made a mistake in his calculations when substituting the ordered pair into the equation 5x – 2y = 6 and simplifying.
Answer:
The correct answer is He made a mistake in his calculations when substituting the ordered pair into the equation 5x – 2y = 6 and simplifying.
Step-by-step explanation:
I just took the test ;) good luck on yours
Answer:
He made a mistake in his calculations when substituting the ordered pair into the equation 5x – 2y = 6 and simplifying.
Step-by-step explanation:
A series of light brown lines drawn at intervals of 50 feet to designate their respective heights aboveboard sea level are called
Answer:
Contour lines. Hope this helps!
What is 1.3333333333 equal to in fractions
Answer: 1 1/3
Step-by-step explanation: 0.33 repeating and in general is equal to 1/3
What is 6x-6y=-24
Y=3x+14
Answer: x=13
Step-by-step explanation:
Replace u wit y = 3x+14
6x-6(3x+14)=-24
6x-18-84 = -24
6x-102=-24
Add -102 on both sides
6x=78
Divide 6 on both side and have your answer
Answer:
Step-by-step explanation:
I've already answered this question.
A gift basket that contains jars of jam and packages of bread mix costs $45. There are 8 items in the basket. Jars of jam cost $6 each, and packages of bread mix cost $5 each. Write and solve a system of linear equations to find the number of jars of jam and the number of packages of bread mix in the gift basket.
5 jars of jam and 3 packages of bread mix are in gift basket
Solution:
Let "x" be the number of jars of jam
Let "y" the number of packages of bread mix
Cost of 1 jars of jam = $ 6
Cost of 1 package of bead mix = $ 5
There are 8 items in the basket
Therefore,
number of jars of jam + number of packages of bread mix = 8
x + y = 8 ---------- eqn 1
A gift basket that contains jars of jam and packages of bread mix costs $45
Therefore, we frame a equation as:
number of jars of jam x Cost of 1 jars of jam + number of packages of bread mix x Cost of 1 package of bead mix = 45
[tex]x \times 6 + y \times 5 = 45[/tex]
6x + 5y = 45 --------- eqn 2
Let us solve eqn 1 and eqn 2
From eqn 1,
x = 8 - y --------- eqn 3
Substitute eqn 3 in eqn 2
6(8 - y) + 5y = 45
48 - 6y + 5y = 45
y = 48 - 45
y = 3Substitute y = 3 in eqn 3
x = 8 - 3
x = 5Thus 5 jars of jam and 3 packages of bread mix are in gift basket
Maddie earned an 88 on her first test and an 80 on second test. What is her average test score
Answer:
Step-by-step explanation:
the average can be found by adding up all ur numbers and dividing by how many numbers u have
so her average test score is : (88 + 80) / 2 = 168/2 = 84 <==
To find Maddie's average test score, add up her scores (88+80=168) and divide by the number of tests (2). This gives us an average of 84.
Explanation:The subject of this question is Mathematics, specifically the concept of calculating averages. To calculate Maddie's average test score, you'll need to add up the scores she received and then divide the sum by the number of tests she took.
In this case, Maddie earned an 88 on her first test and an 80 on her second test. You would add these two scores together (168), then divide by 2 (since she took 2 tests), which gives us an average of 84.
So, Maddie's average test score is 84.
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Solve the following systems of equations express your answer as an ordered pair in the format (a,b) With no spaces between the numbers or symbols
2x+7y=-7
-4x-3y=19
Answer: 5/11,5
Step-by-step explanation:
Multiply equation one by -4
Multiply equation two by 2
Then, it becomes
-8x - 28y = 28
-8x - 6y = 38
Subtract equation two from equation one .
It becomes -22y = -10
Divide both sides by 22, you have y= 5/11
NOW substitute y=5/11 into equation two to get X.
-4x -3(5/11) =19
-4x = 19 + 15/11
-4x = 20
Divide both sides by -4
X = -5
To solve the system of equations, the elimination method was used, resulting in the solution of the equations as an ordered pair (-6 16/77, 5/11).
To solve the system of equations 2x + 7y = -7 and -4x - 3y = 19, one can use the elimination method. This involves manipulating the two equations to eliminate one of the variables, allowing the other variable to be found. We can multiply the first equation by 2 to align the coefficients of the 'x' terms and then add the equations to cancel out the 'x' terms.
Multiply the first equation by 2: 4x + 14y = -14.
Add this to the second equation: (4x + 14y) + (-4x - 3y) = -14 + 19.
This simplifies to 11y = 5, and solving for 'y' gives y = 5/11.
Substitute 'y' back into the first original equation: 2x + 7(5/11) = -7.
Solve for 'x', which gives x = -6 16/77.
So, the solution to the system of equations, expressed as an ordered pair, is (-6 16/77, 5/11).
Which choice correctly compares the two decimal numbers to hundredths?
A) 73.28 > 74.22
B) 73.47 > 73.52
C) 73.51 < 73.19
D) 74.73 < 74.86
Maricel is programming an archery component of a new video game. In her code, she has created an "auto aim" feature that helps players more easily hit their intended targets. The code works such that if the player is aimed at AAA but instead should be aimed at target TTT, the game will automatically adjust the angle at which the arrow is fired directly at TTT. If AAA and TTT are 151515 meters apart in the example below, how many degrees will Maricel's code adjust the shot? Do not round during your calculations. Round your final answer to the nearest degree.
Maricel's code will adjust the shot by 12º
Answer:
The correct angle will be 12.5 degrees.
What is 7/9 minus 1/3
Answer:
4/9 or 0.444...
Step-by-step explanation:
[tex] \frac{7}{9} - \frac{1 \times 3}{3 \times 3} [/tex]
[tex] \frac{7}{9} - \frac{3}{9} [/tex]
[tex] \frac{4}{9} [/tex]
Answer: 4/9
Step-by-step explanation: Since our denominators in this problem are 9 and 3, and 9 factors as 3 x 3, they have a common factor of 3 so we find their least common denominator by multiplying the 3 that comes from the 3's that match up times the 3 that doesn't match up so we have 3 x 3 or 9.
In order to get a common denominator of 9 for both our fractions, we multiply top and bottom of the the second fraction by 3 and we have 7/9 - 3/9 which simplifies to 4/9. So 7/9 - 1/3 is 4/9.
I have also attached my work in the image provided.
A fruit bowl contains apples, oranges, and bananas. The radius of one of the oranges is 1.35 inches. What is the approximate volume of the orange? Use 3.14 for pi.
Answer:
[tex]10.3\ in^3[/tex]
Step-by-step explanation:
Orange has the shape of a ball.
The volume of a ball with radius r inches is
[tex]V=\dfrac{4}{3}\pi r^3\ in^3[/tex]
The radius of one of the oranges is 1.35 inches.
Hence, its volume is
[tex]V=\dfrac{4}{3}\cdot \pi \cdot (1.35)^3\approx \dfrac{4}{3}\cdot 3.14\cdot 2.460375=10.30077\ in^3 \approx 10.3\ in^3[/tex]
Answer:
10.3 in^3
Step-by-step explanation:
The length of a rectangle is 3 1/6 cm longer than the width. The perimeter of the rectangle is 15 1/3 cm. What are the width and length of this rectangle?
The width of rectangle is [tex]2\frac{1}{4}[/tex] cm and length is [tex]5\frac{5}{12}[/tex] cm.
Step-by-step explanation:
Let,
Width of rectangle = w
Length of rectangle = [tex]w+3\frac{1}{6}=w+\frac{19}{6}[/tex]
Perimeter of rectangle = [tex]15\frac{1}{3}=\frac{46}{3}[/tex] cm
Perimeter = 2(Length + Width)
[tex]\frac{46}{3}=2(w+\frac{19}{6}+w)\\\\\frac{46}{3}=2(2w+\frac{19}{6})\\\\\frac{46}{3}=4w+\frac{19}{3}\\\\4w+\frac{19}{3}=\frac{46}{3}\\\\4w=\frac{46}{3}-\frac{19}{3}\\\\\ 4w=\frac{46-19}{3}\\\\4w=\frac{27}{3}\\\\4w=9[/tex]
Dividing both sides by 4
[tex]\frac{4w}{4}=\frac{9}{4}\\\\w=\frac{9}{4}[/tex]
Width of rectangle = [tex]\frac{9}{4}=2\frac{1}{4}\ cm[/tex]
[tex]Length = w+\frac{19}{6}=\frac{9}{4}+\frac{19}{6}\\\\Length = \frac{27+38}{12}=\frac{65}{12}\\\\Length=5\frac{5}{12}\ cm[/tex]
The width of rectangle is [tex]2\frac{1}{4}[/tex] cm and length is [tex]5\frac{5}{12}[/tex] cm.
Keywords: rectangle, perimeter
Learn more about perimeter at:
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Final answer:
The width of the rectangle is 9.92 cm (approx.) and the length is 13.09 cm, calculated using the given perimeter and the relationship between the width and length, both rounded to three significant figures.
Explanation:
The question asks to find the width and length of a rectangle given that the length is 3 1/6 cm longer than the width and the perimeter is 15 1/3 cm. To solve this, first express the perimeter as an equation involving width (w) and length (l):
Perimeter (P) = 2l + 2w
Since the length is 3 1/6 cm longer than the width, we can express the length as:
l = w + 3 1/6
Substitute the value of l in the perimeter equation:
15 1/3 = 2(w + 3 1/6) + 2w
Convert mixed numbers into improper fractions for easier computation:
46/3 = 2(w + 19/6) + 2w
Expand and solve for w:
46/3 = (4w + 19/3)
3(46) = 4w(3) + 19
138 = 12w + 19
119 = 12w
w = 119/12
w = 9.916666...
To match our significant figures requirement, we report the width of the rectangle as 9.92 cm to three significant figures. Now calculate the length:
l = w + 3 1/6
l = 9.92 + 3.1666...
l = 13.0866...
Again, matching our significant figures requirement, the length is reported as 13.09 cm to three significant figures.
A line passes through the point (10,-1) and has a slope of 3/2. Write an equation in point-slope form for this line.
Answer:
work is shown and pictured
Complete the equation of the line whose slope is -2−2minus, 2 and y-intercept is (0,3)
Answer:
[tex]y=-2x+3[/tex]
Step-by-step explanation:
Given the slope of line [tex]m[/tex] is [tex]-2[/tex].
And y-intercept is [tex](0,3)[/tex]
We can write the equation of line by using the slope-intercept form.
The slope-intercept from is
[tex]y=mx+b[/tex]
Where [tex]m[/tex] is the slope of line. And [tex]b[/tex] is the y-intercept.
In our problem y-intercept is given as [tex]b=3[/tex].
Plugging these we get,
[tex]y=-2x+3[/tex]
How do you Simplify :(2p^-3)^5
Answer:
The final simplification is (32p^-15).
Step-by-step explanation:
Given:
(2p^-3)^5 we have to simplify.
Property to be used:(Power rule)
Power rule states that: [tex](a^x)^y=a^x^y[/tex] ...the exponents were multiplied.
Using power rule.
We have,
⇒[tex](2p^-3)^5[/tex]
⇒[tex](2^5)(p^-3^*5)[/tex] ...taking exponents individually.
⇒[tex]32(p^-^1^5)[/tex] ...[tex]2^5=2*2*2*2*2=32[/tex]
⇒[tex]32p^-^1^5[/tex]
So our final values are 32p^-15
A boat traveled 336 miles downstream and back. The trip downstream took 12 hours. The trip back took 14 hours. What is the speed of the boat in still water? What is the speed of the current?
speed of a boat when it goes downstream is 336/12 = 28 mi/h
speed of a boat when it goes upstream is 336/14 = 24 mi/h
Let v is speed of the boat in still water and x is speed of the current. Then,
v + x = 28
v - x = 24
Solve the system for v and x and get v = 26 mi/h, x = 2 mi/h
Mark as Brainliestwhat is (1/2x-5)^2 simplified?
[tex]\frac{x^2}{4}-\frac{10x}{2}+25[/tex]
Solution:
Given expression is [tex](\frac{1}{2}x-5)^2[/tex].
Simplify the expression using algebraic formula [tex](a-b)^2=a^2-2ab+b^2[/tex]
[tex](\frac{1}{2}x-5)^2=(\frac{x}{2}-5)^2[/tex]
[tex]=(\frac{x}{2})^2-2(\frac{x}{2})5+5^2[/tex]
[tex]=\frac{x^2}{4}-10(\frac{x}{2})+25[/tex]
[tex]=\frac{x^2}{4}-\frac{10x}{2}+25[/tex]
[tex](\frac{1}{2}x-5)^2=\frac{x^2}{4}-\frac{10x}{2}+25[/tex].
Hence, the simplified form of [tex](\frac{1}{2}x-5)^2[/tex] is [tex]\frac{x^2}{4}-\frac{10x}{2}+25[/tex].
An electronics store usually sells computers priced at $1500 each. If the customer orders the computer over the Internet, he has to pay only $1200 for the computer. If p represents the percent decrease in price of the computer, which proportion can be used to calculate p?
Answer:
B is the answer