Answer:
-22/3
Step-by-step explanation:
Multiply the whole number by the denominator, and then add the numerator to get the improper fraction.
Solve for x.
[tex]\frac{2x}{9}[/tex] = -65
x = -292 [tex]\frac{1}{2}[/tex]
x = -14 [tex]\frac{4}{9}[/tex]
x = 292 [tex]\frac{1}{2}[/tex]
The correct answer is:
[tex]x = -292 \frac{1}{2}[/tex]
Let's solve the equation step-by-step to find the value of [tex]x[/tex]:
The given equation is:
[tex]\frac{2x}{9} = -65[/tex]
First, we need to isolate [tex]x[/tex]. We can do this by multiplying both sides of the equation by 9, which is the denominator on the left side:
[tex]9 \times \frac{2x}{9} = 9 \times -65[/tex]
This simplifies to:
[tex]2x = -585[/tex]
Next, we need to get [tex]x[/tex] by itself, so we divide both sides by 2:
[tex]\frac{2x}{2} = \frac{-585}{2}[/tex]
This simplifies to:
[tex]x = -292.5[/tex]
So, [tex]x = -292.5[/tex] or [tex]x = -292 \frac{1}{2}[/tex].
The manager at a pizza restaurant keeps track of the number of large pizzas and small pizzas sold each day and the total money received. On Monday, a total of 63 pizzas were sold, and the money collected was $989. If large pizzas are sold for $18 and small pizzas are sold for $13, how many large pizzas and small pizzas were sold?
34x18 = 612
29x13=377
377+612 = 989
34 large 29 small
The number of large pizza is 34 and the number of small pizza is 29.
How to find the number of small and large pizza in the problem given ?It is given that a total of 63 pizzas were sold.
Also, the money collected was $989.
Moreover, large pizzas are sold for $18 and small pizzas are sold for $13.
Let the number of large pizzas be x and the number of smaller pizzas be y.
From the problem statement , x + y = 63.
The total cost for large pizza is $18x and the total cost for small pizza is $13y . Now this sum is the total money collected.
∴ 18x + 13y = 989.
We have two equations ,
x + y = 63 and 18x + 13y = 989.
Substituting the value of x from first and putting it to second,
⇒ 1134 - 18y + 13y = 989.
⇒ -5y = -145
∴ y = 29 .
Putting value of y in the first equation, we have x = 34.
Therefore the number of large pizza is 34 and the number of small pizza is 29.
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What are the steps to solve this inequality?
-9.5 + 6x > 42.1
> is the greater than symbol. So it has to be greater than 42.1
x = 8.6 (at least)
6x4=8xN
how do i solve this equation
Answer:
n = 3
Step-by-step explanation:
find multiples of the product of 24 that comes from 6*4
Square root of xy squared multiply by the square root of x cubed and y to the seventh power
Answer:
=[tex]x^{2} y^{9}\sqrt{x}[/tex]
Step-by-step explanation:
[tex]xy^{2}[/tex] multiplyed by [tex]\sqrt{x^{3} }[/tex]multiplyed by [tex]y^{7}[/tex]
=[tex]x^{2} y^{9}\sqrt{x}[/tex]
Have a nice day!!!!!!!!!!! :-)
KA
The expression with square roots simplifies to x squared times y to the 4.5th power, or x squared times y to the 4th power times the square root of y, applying the rules for multiplying exponents and expressing square roots as fractional powers.
Explanation:To solve the expression involving square roots and variables raised to different powers, we apply the rules of exponents and radical expressions. The student asks about the square root of xy2 multiplied by the square root of x3y7. First, we express the square roots as fractional powers, and then we use the rule of multiplication of exponents.
For square roots, the rule is that the square root of x can be rewritten as x raised to the 1/2 power. As in the examples provided, the rule for raising a number to a power (xp) and then multiplying it by the same base raised to another power (xq) is to add the exponents, resulting in xp+q. Finally, the cube of an exponential involves cubing the digit term and multiplying the exponent by 3.
In this case:
Square root of xy2 is x1/2ySquare root of x3y7 is x3/2y7/2When we multiply these together:
(x1/2y) * (x3/2y7/2) = x1/2+3/2y1+7/2 = x2y9/2
This expression simplifies to x2y4.5 or x2y4√y.
f (x) = (2x – 5) ^2 then evaluate f (-4)
Hello ;w;
-------------------------------------------------------------------
f=
x=(2x - 5)^2
f=
-4 = -4
I believe your answer is -4, sorry if I'm wrong, have a great day.❤
Rearrange to make x the subject
P=hx/5. Pls help
Answer:
x = [tex]\frac{5P}{h}[/tex]
Step-by-step explanation:
Given
P = [tex]\frac{hx}{5}[/tex] ( multiply both sides by 5 )
5P = hx ( divide both sides by h )
x = [tex]\frac{5P}{h}[/tex]
The given equation P = hx/5 can be rearranged to x = 5P/h, by first multiplying both sides by 5, and then dividing both sides by h
Explanation:The current equation P = hx/5 can be rearranged to isolate x by employing algebraic steps. We first need to get rid of the division by 5 from the right side of the equation to leave hx isolated. We achieve this by performing the opposite operation, that is multiplication on both sides of the equation by 5:
5P = 5*(hx/5)
This simplifies to 5P = hx.
Finally, to obtain x by itself, we want to get rid of the multiplication by h in the equation. We do so by dividing both sides of the equation by h:
(5P)/h = hx/h
Which simplifies to: x = 5P/h
This is the final rearranged equation with x isolated.
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Simplify the expression -|15|
The simplified form of the given expression -|15| is -15.
Use the concept of modulus defined as:
A modulus function is a function that determines a number or variable's absolute value. It generates the size of the variable count.
A function with absolute values is another name for it. No matter what input was provided to this function, the output is always favorable.
The given expression is -|15|
Since we know that,
|x| = x when x > 0
|x| = 0 when x = 0
|x| = -x when x<0
And here 15 > 0
Therefore,
|15| = 15
then -|15| = -15
Hence,
The simplified form of the given expression is -15.
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A classmate plotted the following points:
A(-3, 2), B(-1, 4), and C(1, 2).
Where should the classmate plot point
D so that the quadrilateral formed has
perpendicular sides?
Answer:
D(-1,0)
Step-by-step explanation:
Plot points A(-3, 2), B(-1, 4), and C(1, 2) on the coordinate plane (see attached diagram).
Two sides AB and BC are of equal length and are perpendicular, because
[tex]AB=\sqrt{(-3-(-1))^2+(2-4)^2}=\sart{(-2)^2+(-2)^2}=\sqrt{4+4}=2\sqrt{2}\ units\\ \\BC=\sqrt{(-1-1)^2+(4-2)^2}=\sart{(-2)^2+2^2}=\sqrt{4+4}=2\sqrt{2}\ units\\ \\\text{Slope AB}=\dfrac{4-2}{-1-(-3)}=\dfrac{2}{2}=1\\ \\\text{Slope BC}=\dfrac{2-4}{1-(-1)}=\dfrac{-2}{2}=-1\\ \\\text{Slope AB}\cdot \text{Slope BC}=1\cdot (-1)=-1\Rightarrow \text{lines AB and BC are perpendicular}[/tex]
If the quadrilateral ABCD has all sides perpendicular, then ABCD is a square. The diagonals of the square bisects each other. Find the coordinates of the point of intersection of these diagonals. This is the midpoint of segment AC:
[tex]x=\dfrac{-3+1}{2}=-1\\ \\y=\dfrac{2+2}{2}=2[/tex]
If point O(-1,2) is the point of intersection of diagonals, then it is the midpoint of the diagonal BD. Find coordinates of point D:
[tex]x_O=\dfrac{x_B+x_D}{2}\Rightarrow -1=\dfrac{-1+x_D}{2},\ -1+x_D=-2,\ x_D=-1\\ \\y_O=\dfrac{y_B+y_D}{2}\Rightarrow 2=\dfrac{4+y_D}{2}, 4+y_D=4,\ y_D=0[/tex]
Thus, D(-1,0)
What is the expanded form for 6 * 532?
Answer:
(6*500)+(6*30)+(6*2)=3192
Step-by-step explanation:
532 is 500+30+2. By expanding this number to its components and multiplying each by 6, you can solve this problem significantly faster without the use of a calculator.
Compare the expressions using <, >, or =. Show all your work.
(18 – 3) ÷ (6 - 1) _____ 4 • (10 – 3) – 4 • 2
Answer:
The answer would be <
Step-by-step explanation:
(18-3)÷(6-1)
18-3=15
6-1=5
15÷5=3
________
4×(10-3)-4×2
10-3=7
4×7-4×2
28-8=20
When can a trapezoid also be called a parallelogram?
Answer:
Yes, because it has one pair of parallel sides.
Step-by-step explanation:
Answer:
Explained
Step-by-step explanation:
In trapezoid only one pair of side is parallel to each other whereas in A parallelogram both pair of sides are parallel to each other. Although both are quadrilaterals with four sides. But according to above stated condition A a trapezoid can not be called a parallelogram.
hope you got the point and ask your doubts in comments
3x+15=8x+25 i need x
Answer: -2 = X
Step-by-step explanation:
3x +15 = 8x +25
-3x -3x *Make sure you do it to both sides
15 = 5x + 25
-25 -25 *Your goal is to get X on one side
-10/5 = 5x/5
-2 = X
X=-2
3x+15=8x+25
-8x. -8x
-5x+15=24
-15
-5x=10
-5x/5 -10/5
X=-2
Ratios 24 dollars for 9 books how much is worth one book
Answer: 2.7
Step-by-step explanation:
24÷9=2.7
Final answer:
To find the cost of one book when 24 dollars buy 9 books, divide the total cost by the total number of books. This gives a cost of 2.67 dollars per book.
Explanation:
The question asks how much one book is worth if 24 dollars can buy 9 books. This is a basic arithmetic problem involving the concept of ratios and unit rates. To find the cost of one book, we divide the total cost by the total number of books.
Step-by-Step Solution:
Total cost for 9 books = 24 dollars.
Divide the total cost by the number of books to find the cost per book: 24 dollars ÷ 9 books = 2.67 dollars per book.
Therefore, the cost of one book is 2.67 dollars.
10. The values of x and y vary directly, and
when x = 48, y = 36. Find the value of x when
y = 18.
Answer:the answer is 24
Step-by-step explanation:
Because when 18 is the half of 36 so 24 is the half of 48
Given x and y vary directly with constant ratio 1.33, the value of x when y equals 18 is 23.94.
Explanation:The subject question deals with direct variation, a concept in Mathematics. When two variables vary directly, a change in one variable results in a proportionate change in the other variable. If x and y vary directly, it means the ratio of x to y is constant.
From the problem, x = 48 when y = 36. Therefore, the ratio of x to y is 48/36 = 1.33.
To find the value of x when y = 18, simply multiply the constant ratio (1.33) by the new value of y.
So, x = 1.33 * 18 = 23.94
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What is the real interest rate for a savings account that has a nominal interest rate of 1% when the rate of inflation is 1% ?
A.) -2%
B.) 0%
C.) 1%
D.) 2%
The real interest rate of a savings account that has a nominal interest rate of 1% when the rate of inflation is 1% is B.) 0%
How to find the real interest rate ?The real interest rate is the interest rate that is adjusted for inflation. It is calculated by subtracting the inflation rate from the nominal interest rate. In this case, the nominal interest rate is 1% and the inflation rate is also 1%.
So, the real interest rate is:
= 1% - 1%
= 0%
In other words, if you deposit $100 in a savings account with a nominal interest rate of 1%, you will earn $1 in interest after one year. However, because inflation is also 1%, the purchasing power of your $100 will decrease by $1. So, the real value of your savings will not change.
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Final answer:
The real interest rate for a savings account with a nominal interest rate of 1% and an inflation rate of 1% is 0%. This is found by subtracting the inflation rate from the nominal interest rate.
Explanation:
The real interest rate is calculated by taking the nominal interest rate and subtracting the rate of inflation. In this case, if you have a nominal interest rate of 1% and an inflation rate of 1%, the real interest rate would be calculated as follows:
Real interest rate = Nominal interest rate - Inflation rate
Real interest rate = 1% - 1% = 0%
Therefore, the real interest rate for the savings account is 0%. This means that the purchasing power of the money in the savings account is essentially staying the same. The correct answer is B.) 0%.
For the given exercises:
If the nominal interest rate is 5 percent and the inflation rate is 3 percent, the real interest rate is 2 percent.Yes, the real interest rate can be negative if inflation rate exceeds the nominal interest rate.Risks involved in investing in a foreign bank include exchange rate risk, political risk, and differing levels of financial regulationIndicate whether each of the following numbers is divisible by 4.
Answer yes or no.
a. 124
b. 289
c. 304
d. 222
Answer:
a.yes
b.no
c.yes
d.no
Step-by-step explanation:
4×31=124
4×56=304
find the product 3(x + 4 )( x - 5)
Answer:
[tex]3x^2-3x-60[/tex]
Step-by-step explanation:
Given: [tex]3(x+4)(x-5)[/tex]
Let's use the distributive property to multiply [tex](x+4)(x-5)[/tex] together since they are right next to each other. We can use the FOIL method.
[tex](x+4)(x-5)\\x^2-5x+4x-20\\x^2-x-20[/tex]
Now that we simplified that, we still have to multiply everything by the value of [tex]3.[/tex]
[tex]3(x^2-x-20)\\3x^2-3x-60[/tex]
Now, you could have left the answer as [tex]3(x^2-x-20)[/tex] since it is factored, but the problem wants us to find the product, so we need to completely simplify.
Help please D: If you answer I will give you brainliest
Step-by-step explanation:
Write the population of florida in expanded form using exponents
floride population = 18,801,310
Expanded form ;
1x10^{7} + 8x10^{6} + 8x10^{5} + 0x10^{4} + 1x10^{3} + 3x10^{2} + 1x10^{1} + 0x10^{0}
Thirty-six is at least one half of a number.
What is the area of a rectangle with a base of 12 mm and a height of 1.4 mm? A. 13.4mm2 B. 16.8 mm2, C. 134 mm2, 168 mm 2
Answer:
D. 168 mm²Step-by-step explanation:
The formula of an area of a rectangle:
[tex]A=l\cdot w[/tex]
l - length (base)
w - width (height)
We have l = 12mm, h = 14mm.
Substitute:
[tex]A=(12)(14)=168\ (mm^2)[/tex]
In 35 ÷ 7 = 5, what is the 35 called?
Answer: The dividend
Step-by-step explanation:
Answer: in that equation the 35 is called the dividend.
Step-by-step explanation: the 7 is the divisor and the 5 is the quotient
What is the initial value of the exponential function represented by the table? A.1/8 B.1/4 C.1/2 D.1
Answer:no, The answer is 1/2.
Step-by-step explanation:
Answer:
C.
Step-by-step explanation:
Find the average:
-1,5, 4, 5, 1, -4
Answer:
1 [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
you have to add all the values together and divide the total by the number of values you added together. In this situation, there is 6 values
-1 + 5 + 4 + 5 + 1 - 4 = 10
10 ÷ 6 = 1 [tex]\frac{2}{3}[/tex]
The student travel to the zoo in three buses. One bus had 47 students. The second has 38 students. The third bus had 43 students. How many students are there in total in the 3 buses
If a number is not a whole number then it is not a natural number
Answer:
false
Step-by-step explanation:
a natural number is a number you count by, you wouldn't cound by decimals or fractions
Look at this diagram:
Which diagram shows AABC rotated 120° counterclockwise about B?
Answer:
second one diagram rotated 120
In a 120° counterclockwise rotation about point B, diagram AABC would shift each point along a circular path 120° in a counterclockwise direction around point B. The positions of points A and C would change, while point B would stay as it is. The correct diagram would reflect these changes.
Explanation:Without a specific diagram to refer to, I can provide only a general explanation of how to determine the diagram that represents AABC rotated 120° counterclockwise about point B.
Rotations in a plane are performed counterclockwise with a positive degree measure. So, a 120° counterclockwise rotation about a fixed point B would take every point on triangle AABC and shift it along a circular path 120° in a counterclockwise direction around point B. The result would be a new triangle A'B'C'. If point B is the origin of rotation, it would remain unchanged. However, points A and C would change their positions after the rotation.
To determine the correct diagram, you would look for a triangle that has been shifted around point B in a counterclockwise direction with positions of points A and C reflecting a 120° rotation.
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Solve the equation for x.
6(4x − 10) = 84
A) 2
B) 3
C) 4
D) 6
Hey!
----------------------------------------
Solution:
6(4x - 10) = 84
24x - 60 = 84
24x + (-60) = 84
24x + (-60) + 60 = 84 + 60
24x = 144
24x/24 = 144/24
x = 6
----------------------------------------
Answer:
x = 6
----------------------------------------
Hope This Helped! Good Luck!
The solution of expression is,
⇒ x = 6
We have to given that;
Expression is,
⇒ 6(4x − 10) = 84
Now, We can simplify as;
6(4x - 10) = 84
24x - 60 = 84
24x + (-60) = 84
24x - 60 + 60 = 84 + 60
24x = 144
24x/24 = 144/24
x = 6
Therefore, Solution is,
⇒ x = 6
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Ayodele received a raise in her hourly pay, from $24.50 to $25.48. Find the percent change.
Answer:
4%
Step-by-step explanation:
The raise in her hourly pay is
$25.48-$24.50 =$0.98
Cross multiplying (rule of three)
24.50------100%
0.98--------x%
and so, x= 0.98*100/24.5 = 4%
Answer: The required percent change is 4%.
Step-by-step explanation: Given that Ayodele received a raise in her hourly pay, from $24.50 to $25.48.
We are to find the percent change.
The percent change is given by
[tex]p=\dfrac{\textup{increse in the amount}}{\textup{original amount}}\times100\%.[/tex]
In the given situation, we have
[tex]\textup{increase in the amount}=\$(25.48-24.50)=\$0.98.[/tex]
Therefore, the percent change is given by
[tex]p=\dfrac{0.98}{24.50}\times100\%=\dfrac{98}{24.50}\%=4\%.[/tex]
Thus, the required percent change is 4%.
What is the value of (g o f)(-6)
F(x)=2x+7; g(x)=3x+12
Answer:
(g o f)(-6) = -3
Step-by-step explanation:
f(x)=2x+7; g(x)=3x+12
(g o f)(-6) = g(f(-6))
but f(-5) = 2(-6)+7 = -5
(g o f)(-6) = g(f(-6)) = g(-5) = 3(-5)+12 = - 3