For this case we must raise an inequality.
We have "d" dollars initially and they are spent 12. Then:
[tex]d-12[/tex]
At least 51 dollars remain, then, the sign of inequality is greater or equal in favor of the expression[tex]d-12[/tex], that is:
[tex]d-12\geq 51[/tex]
Resolving:
[tex]d\geq 51 + 12\\d\geq 63[/tex]
There are at least 63 dollars left in the account.
Answer:
[tex]d-12\geq 51\\d\geq 63[/tex]
Which equation yields the solutions x=−3 and x=−4?
a)2x2+14x+24=0
b)x2−6x+5=0
c)3x2+30x+48=0
d)−3x2−12x+15=0
Answer:
a) 2x² + 14x + 24 = 0
Step-by-step explanation:
a)
2x² + 14x + 24 = 0
2(x + 4) (x + 3) = 0
x = -4 or x = -3
b)
x² - 6x + 5 = 0
(x - 1)(x - 5) = 0
x = 1 or x = 5
c)
3x² + 30x + 48 = 0
3 (x + 8) (x + 2) = 0
x = -8 or x = -2
d)
-3x² - 12x + 15 = 0
-3 (x + 5) (x - 1) = 0
x = -5 or x = 1
Final answer:
The equation which yields the solutions x=-3 and x=-4 is a. 2x² + 14x + 24 = 0.
Explanation:
To find which equation yields the solutions x=-3 and x=-4, we need to determine which equation, when factored, gives these roots. If an equation has roots x = -3 and x = -4, then it can be written in factorized form as:
(x + 3)(x + 4) = 0
Expanding this, we get:
x² + 4x + 3x + 12 = 0
x² + 7x + 12 = 0
Looking at the given options, we notice that none of them exactly match this equation. However, if we multiply our equation by 2, we get:
2x² + 14x + 24 = 0
This matches option (a). Therefore, the correct equation is:
2x² + 14x + 24 = 0
Tara read 3 1/2 pages in 2 1/2 minutes. Which rate is equivalent to Tara’s unit rate
Tara's unit rate of reading is 1.4 pages per minute, which means an equivalent rate is 2.8 pages per 2 minutes.
The question involves calculating an equivalent rate to Tara's unit rate of reading pages per minute. To find Tara's unit rate, we first need to determine how many pages she reads in one minute. Since Tara reads 3 1/2 pages in 2 1/2 minutes, we divide the number of pages by the number of minutes to find the unit rate:
3 1/2 pages / 2 1/2 minutes = 7/2 pages / 5/2 minutes = 7/2 * 2/5 pages per minuteThis simplifies to 7/5 pages per minute or 1.4 pages per minute.To find an equivalent rate, we can multiply both the numerator and the denominator by the same number to get a rate with different terms but the same value. For example, multiplying by 2 would give us:
(7/5) * 2 pages per (1) * 2 minutes = 14/5 pages per 2 minutes = 2.8 pages per 2 minutesTherefore, an equivalent rate to Tara's reading speed would be 2.8 pages per 2 minutes.
A rectangular sheep pen measures 5 m long and 9 m wide. The perimeter of the cow pen is double the perimeter of the sheep pen what is the perimeter of the cow pen?
Answer:
56m
Step-by-step explanation:
First calculate the perimeter of the sheep pen.
The perimeter is all the side lengths added together.
The rectangle has two sides that are 5m long and two sides that are 9m long.
5 + 5 + 9 + 9 = 28m
Now that you know the perimeter of the sheep pen you can double it by multiplying by 2 to find tha perimeter of the cow pen.
28 * 2 = 56m
Answer:
56
Step-by-step explanation:
5×2 +9×2=28
28 × 2 =56
Please explain your answer as well, THANKS!!!
Answer:
11,232,000
Step-by-step explanation:
The key to this problem is knowing "repetition is NOT ALLOWED".
For the first 3 letters slot:
For the 1st slot, we can pick any of the 26 alphabets
For the 2nd slot, we can pick any of the 25 remaining alphabets (since 1 is already taken)
For the 3rd slot, we can pick any of the 24 remaining letters (since 2 is already taken)
For the three digits slot:
For the 1st slot, we can pick any one of the 10 digits
For the 2nd slot, we can pick any one of the 9 digits left, since 1 is taken already
For the 3rd slot, we can pick any one of the 8 digits left, since 2 is already taken
The number of license plates, thus, would be all of these multiplied together:
26 * 25 * 24 * 10 * 9 * 8 = 11,232,000
A worker at the zoo calculates the amount of fish, in pounds, needed in the weekly diet of an eagle and a bear.
The eagle eats 6 pounds of food each week, and 60% of that weight must be fish.
The bear eats 105 pounds of food each week, and 25% of that weight must be fish.
The zoo increases the amount of food that the bear eats each week to 115 pounds. What is the percent increase in the amount of food that the bear eats each week? Round your answer to the nearest tenth of a percent.
____________________________________________________
Answer:
Your answer would be a 9.5% increase.
____________________________________________________
Step-by-step explanation:
In order to find the answer to your question, we would need to get the amount it's changing by, divide it by it's original, and multiply it by 100.
Your equation should look like this:
[tex]Change/Original * 100[/tex]
Important information in the question:
105 pounds
115 pounds (increase in amount of food that bear eats)
With the information above,we can plug those numbers into our equation.
Since we need to find the change, we would subtract 115 and 105 to get 10. 10 is our change in this scenario.
Our original started at 105, so that'll be our original in our equation.
When you plug in the information, your equation should look like this:
[tex]10/105*100[/tex]
Now you solve:
[tex]10/105*100\\\\0.0952 * 100\\\\=9.523[/tex]
We have to round to the nearest tenth, and the tenth place is the number right after the decimal place.
Since 2 is not a big enough number to round the 5, we would keep the number as 5. Therefore, your answer would be 9.5
Your FINAL answer would be 9.5%
____________________________________________________
The number of license plates on a car is measured in the __. A.ones B.thousands C.hundreds D.tens
Answer:
A.ones
Step-by-step explanation:
Depending on the state and country, cars can have 1 or 2 license plates on them. The one mandatory is in the back. In some places, the cars also have a license plate in the front of the car.
So, since the answer is either 1 or 2, the range for that answer is under 10... so it's a single digit... making it a measure in ones.
The number of tires on a car is also measured in ones.
Pencils cost 25p each. Mr smith spends £15 on pencils. Work out the number of pencils he gets.
Answer:
Step-by-step explanation:
Which of the following best describes the relationship between the data displayed in the scatter plot below?
A Positive linear association
B Negative linear association
C no association
D Quadratic association
Answer: No association
a circle has a radius of 9. An arc in this circle has a central angle of 120°. What is the length of the arc?
Answer:
6pi or about 18.8 units
Step-by-step explanation:
See attached file
To calculate the arc length of a circle with a 120° central angle and a 9-unit radius, multiply the fraction of the circle (1/3) by the circle's circumference (2πr) to find the arc length is 6π units.
Explanation:To find the length of an arc with a central angle of 120° in a circle with a radius of 9, we use the formula for arc length. The arc length (As) is proportional to the angle of rotation, which in this case is 120° or θ = 120° ÷ 360°.
The circumference (C) of a circle is given by the formula 2πr, where r is the radius. For a full revolution (360°), the arc length is equal to the circumference. For an angle θ, the arc length is given by:
As = (θ/360°) × 2πr
Using the radius r = 9 and θ = 120°, we calculate:
As = (120°/360°) × 2π(9)
As = (1/3) × 18π
As = 6π
The arc length is 6π units, which is slightly less than 19, as π is approximately 3.14159.
Learn more about Arc Length Calculation here:
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tina baked 955 cookies for a big super bowl party she had to put the cookies on 8 different tables in the party room if she spit the cookies evenly how many cookies did tina put on each tables how many cookies were left over?
Answer:
119 cookies on each plate and 3 cookies leftover
Step-by-step explanation:
Cookies on each plate:
955 divided by 8 is 119.375 but round it to 119.
Cookies leftover:
Do 119x8 and you will get 952. Then, minus 952 from 955 and your answer is 3 cookies.
i really hope this helps! :)
Can y’all help me lol (picture)
Answer:
2. 13/100.
3. 4/25.
4. 19/100.
5. 3/5.
Step-by-step explanation:
These are all of the correct answers to the questions.
Hope this helps!!!
Kyle.
Here is the picture i'm mostly trying to understand how to solve these type of problems.
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{25\% of "h"}}{\left( \cfrac{25}{100} \right)h}\implies 0.25h \\\\\\ \stackrel{\textit{Rob spent then}}{\stackrel{\textit{planned hours}}{h}+\stackrel{\textit{extra hours}}{0.25h}}\implies h+0.25h\implies \stackrel{\textit{common factor}}{h(1+0.25)}\implies 1.25h[/tex]
Simplify the expression 7√5 - 3√80
A) -5√5
B) -4√75
C) -5
D) 4√-75
Answer:
A.) -5 √5
Step-by-step explanation:
if you solve the problem above, and solve each answer choice, you can ind a match
Hope this helped! ^_^
The expression 7√5 - 3√80 is simplified as negative 5√5. Then the correct option is A.
What is simplification?Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The expression is given below.
⇒ 7√5 - 3√80
Then the expression is simplified as
⇒ 7√5 - 3√(16 x 5)
⇒ 7√5 - 3 x 4√5
⇒ 7√5 - 12√5
⇒ -5√5
Then the correct option is A.
More about the simplification link is given below.
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please explain this to me. so i came across this act question. the book explains the answer but i dont understand (answer is B)
we know line P is y = 3x.
parallel lines have the same slope but different y-intercept, where the graph touches the y-axis. So then parallel lines is the same equation but shifted some either upwards or downwards or sideways.
so then line Q must be the same as P, y = 3x + "some change", well, we notice that the perpendicular distance from each other is 3 units, so then, the y-intercept of P is at (0, 0), thus the y-intercept of Q must be 3 units downwards, at (0, -3), since Q is shifted downwards, thus Q is y = 3x - 3.
Subtract 5x−2 from −3x+4 . What is the answer? −8x+6 −8x+2 8x−6 2x + 2
Answer:
-8x + 6
Step-by-step explanation:
Subtract "5x-2" from "-3x + 4". Set the equation.
(-3x + 4) - (5x - 2) = Answer (A)
First, distribute -1 to all terms within the second parenthesis.
-3x + 4 - 5x + 2 = A
A = -5x - 3x + 4 + 2
Simplify. Combine like terms (terms with the same amount of variables).
A = (-5x - 3x) + (4 + 2)
A = -8x + 6
-8x + 6 is your answer, or the first answer choice.
~
what is the negative reciprocal of 3
1÷3=13.
Step-by-step explanation:
To find the reciprocal of any number simply take 1 and divide it by that number, so the reciprocal of 3 is 1÷3=1/3. We can check that this is the multiplicative inverse of 3 by multiplying those two numbers together and seeing if we get 1: so 3×1/3=3×1/3=1. Where it says =3 you put a line through that 3.
What is the measure of Z if W equals to 116*
Answer:
Z is also 116*
Step-by-step explanation:
The reason for them being the same is because of something called alternating angles. This process allows you to find two angle measurements by just finding one.
simplify square root. of 228- square foot of 50
Answer:
[tex]\large\boxed{\sqrt{228}-\sqrt{50}=2\sqrt{57}-5\sqrt2}[/tex]
Step-by-step explanation:
[tex]\sqrt{228}-\sqrt{50}=\sqrt{4\cdot57}-\sqrt{25\cdot2}\\\\\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt4\cdot\sqrt{57}-\sqrt{25}\cdot\sqrt2\\\\=2\sqrt{57}-5\sqrt2[/tex]
Select the simplification that accurately explains the following statement.
Answer:
D
Step-by-step explanation:
1. Use property of exponents:
[tex](a^b)^c=a^b\cdot ... \cdot a^b\ [\text{ take }c \text{ times } a^b][/tex]
Hence
[tex](7^{\frac{1}{3}})^3=7^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}[/tex]
2. Use multiplication property of exponents:
[tex]a^b\cdot a^c=a^{b+c}[/tex]
Thus,
[tex]7^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}=7^{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}}[/tex]
3. Since
[tex]\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=\frac{3}{3}=1,[/tex]
we have that
[tex]7^{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}}=7^1=7[/tex]
What is 5 1/2 as a Demical
Answer: 5.5
Step-by-step explanation: Converting This To A Decimal Would Be 5.5
to make it into a decimal you would convert the fraction into a decimal which would be .5 then you would take the 5 and make it 5.5
For this case we have the following mixed number:
[tex]5 \frac {1} {2}[/tex]
We move to fraction, then we have to:
[tex]5 \frac {1} {2} = \frac {5 * 2 + 1 * 1} {2} = \frac {10 + 1} {2} = \frac {11} {2}[/tex]
Dividing we have to:
[tex]\frac {11} {2} = 5.5[/tex]
Answer:
[tex]5 \frac {1} {2} = 5.5[/tex]
Rewrite the radical expression as an expression with rational exponents.
5 square root of x to the 7th power
Hello!
5 √ x^7
(^7) means smaller 7 exponent
Hope I helped!
~ Destiny ^_^
Final answer:
To rewrite the radical expression 5 square root of x to the 7th power with rational exponents, express it as 5x7/2.
Explanation:
To rewrite the radical expression as an expression with rational exponents, we can use the property that the square root is equivalent to raising to the power of 1/2. Thus, 5√x7 = 5x7/2.
Which of the following statements best represents the relationship between a relation and function ?
Answer:
First Option
Step-by-step explanation:
A relation is an association or correspondence between two sets, where each element of the Domain Set corresponds to at least one element of the Range set.
The function definition says that:
A relation is a function if and only if, for each input value x, there is only one output value y. In other words, a relation is a function if each value of the Domain set has only one value associated with the Range set.
Therefore, not all relationships are functions, but all functions are relations.
The correct option is the first
6) Solve for x. 2/3 (x + 7) = 10
A)22
B)8
C)- 1 /3
D)41/ 3
For this case we must find the value of the variable "x" of the following equation:
[tex]\frac {2} {3} (x + 7) = 10[/tex]
We multiply by 3 on both sides of the equation:
[tex]2 (x + 7) = 30[/tex]
We divide between 2 on both sides of the equation:
[tex](x + 7) = 15\\x + 7 = 15[/tex]
We subtract 7 on both sides of the equation:
[tex]x = 8[/tex]
Answer:
Option B
What is the slope of the line (7,6) and (3,2)
Answer:
1
Step-by-step explanation:
Answer:
slope = 1
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (7, 6) and (x₂, y₂ ) = (3, 2)
m = [tex]\frac{2-6}{3-7}[/tex] = [tex]\frac{-4}{-4}[/tex] = 1
Find the measure of the missing angle (solve for x)
IN the given figure.
angle A + angle B + angle C = 180°
( angle sum property of Δ)
58°+47°+ x = 180°
105°+ x =180°
x = 180° - 105°
x = 75°thus correct option is (d)
hope this will help u!!
What is the mean of the data displayed in the line plot below?
A. 2
B. 4
C. 5
D. 6
The mean is the average.
Total the numbers and divide by the quantity of numbers.
2 +2 + 3 + 3 +4 +4 +4 +5 +5 +5 +5 + 6 = 48
48 / 12 = 4
The answer is B.4
Answer: The answer is B (or 4)
4,11,6,9,23,34,6,9
What is the median for this set of numbers
A. 6
B.10
C.14
D.16
Answer:
The Median is 9
Step-by-step explanation:
To calculate the median of a data set the first step is to sort the data from least to greatest
4,11,6,9,23,34,6,9
4, 6, 6, 9, 9, 11, 23, 34
The second step is to locate the central value. If the total amount of data is an even number then locate the two central data and the median will be the average of both. In this case we have 8 data. Then the central values will be the data number 4 and the data number 5
4, 6, 6, [9, 9], 11, 23, 34
[tex]Median = \frac{9+9}{2}=9[/tex]
PLEASE HELP
which function rule would help you find the values in the table
p 2, 4, 6, 8
q -14, -28, -42, -56
A. q = -7p
B. q = p - 7
C. q = - 14p
D. q = p - 14
ANSWER
[tex]q = - 7p[/tex]
EXPLANATION
The constant difference of p values is
4-2=2
The constant difference of the 'q' values is
-28--14=-14
The function is of the form:
[tex]q = m(p - p_1) + q_1[/tex]
where
[tex]m = \frac{change \: in \:q }{change \: in \: p} [/tex]
[tex]m = \frac{ - 14}{2} = - 7[/tex]
We plug in the values to get;
[tex]q = - 7(p - 2) + - 14[/tex]
Expand:
[tex]q = - 7p + 14+ - 14[/tex]
Simplify:
[tex]q = - 7p[/tex]
two lenghts are in the ratio 7:8. if the first lenght is 273m, what amount is the second lenght
Answer:
312 m
Step-by-step explanation:
Write and solve an equation of ratios:
7 273 m
----- = ------------
8 x
Then 7x = 8(273 m) = 2184 m
and x = 2184 m / 7 = 312 m
The second length in the given ratio of 7:8, when the first length is 273m, is calculated to be 312m.
Explanation:The given question is about ratios, particularly the ratio between two lengths, where one of them is given as 273 meters and the ratio is 7:8. The ratio tells us that for every 7 units of the first length, there are 8 units of the second length. To calculate the second length, first find the value of one ratio unit by dividing the given length by its ratio (273m / 7), then multiply your result by 8.
Steps:
1. 273m / 7 = 39m (This is one ratio unit)
2. 39m * 8 = 312m (This is the second length).
Therefore, the length of the second line is 312 m.
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x 0 4 9 10 y 3 2 7 -1 Graph the relation and its inverse. Use open circles to graph the points of the inverse.
Answer:
Observe the attached image
Step-by-step explanation:
If we have a function f(x), the inverse of the function denoted [tex]f ^{- 1} (x)[/tex] will have as domain the range of f(x) and its rank will be the domain of the function f(x) this means that if f(x) is given by the following ordered pairs:
x: 0, 4, 9, 10; and: 3, 2, 7, -1
(0, 3) (4, 2) (9, 7) (10, -1)
Then [tex]f ^{- 1}(x)[/tex] will have the following ordered pairs
x: 3, 2, 7, -1 and: 0, 4, 9, 10
(3, 0) (2, 4) (7, 9) (-1, 10)
Observe the attached image
The blue dots are the ordered pairs of the relationship
The red open dots are the ordered pairs of the inverse of the relationship