Final answer:
To evaluate -6(4 2/3), convert 4 2/3 to an improper fraction, then multiply it by -6 and simplify the result.
Explanation:
To evaluate the expression -6(4 2/3), we need to simplify the expression inside the parentheses first. 4 2/3 can be converted to an improper fraction as follows: (4 * 3 + 2) / 3 = 14 / 3. Then, we multiply -6 by 14/3 to get: -6 * 14/3 = -84/3. The final step is to simplify -84/3, which is -28.
Factor −1/2 out of −1/2x+6.
The factored expression is
Final answer:
To factor −1/2 out of −1/2x+6, we identify the common factor, divide each term by −1/2, and write the expression as −1/2 times the simplified expression. The result is −1/2(x − 12).
Explanation:
To factor −1/2 out of −1/2x+6, we can think of pulling out the −1/2 as a common factor from both terms in the expression. Here's a step-by-step breakdown:
Identify the common factor in both terms. In this case, the common factor is −1/2.Divide each term by −1/2 (which is the same as multiplying by −2).Write the original expression as the product of the common factor and the simplified expression.Applying these steps, we get:
−1/2x divided by −1/2 equals x.6 divided by −1/2 equals −12.The factored expression is then −1/2(x − 12).So, −1/2x+6 factored with −1/2 taken out is −1/2(x − 12).
Mrs. William shops at a store that has an annual membership fee of $30. today she paid her annual membership and bought several fruit baskets costing $15 each as gifts for her co-workers. her total was $105. solve the equation 15b+ 30=105 to find the number of fruit baskets mrs. Williams purchased.
Number of fruit baskets purchased by Mrs. William is 5
Solution:Given that
Annual membership fee of store where Mrs. William shops = $30
Cost of one fruit basket which Mrs. William as gifts for her co-workers = $15
Total amount spent by Mrs. William = $150
Given that "b" represents number of basket purchased
Equation which models the above scenario is as follows
15b+ 30=105 ------ (1)
Where b represents number of fruit basket purchased by Mrs. William
Need to calculate number of fruit basket purchased by Mrs. William
For which we need to solve equation (1) for b
On solving we get
15b+ 30 = 105
On Subtracting 30 from both sides we get
15b + 30 – 30 = 105 – 30
=> 15b = 75
On dividing both sides by 15 we get
[tex]\begin{array}{l}{\frac{15 b}{15}=\frac{75}{15}} \\\\ {=>b=5}\end{array}[/tex]
As variable "b" represents number of basket purchased, hence we can conclude that number of fruit baskets purchased by Mrs. William is 5
The monthly budget for the front of the house is $5,000. You spent 10% of the budget on fresh flowers. How much did you spend on fresh flowers?
Final answer:
To find out how much was spent on fresh flowers, 10% of the monthly budget of $5,000 was calculated, resulting in $500 spent on fresh flowers.
Explanation:
If the monthly budget for the front of the house is $5,000, and you spent 10% of the budget on fresh flowers, you can calculate the amount spent on fresh flowers by finding 10% of $5,000. To do this, you simply multiply the total budget by the percentage (expressed as a decimal).
To express 10% as a decimal, you divide 10 by 100, which gives 0.10. Next, multiply the monthly budget by this decimal:
0.10 × $5,000 = $500
Therefore, you spent $500 on fresh flowers.
25 POINTS HELP ME PLEASE
Answer:D
Step-by-step explanation:
Your first solution is to look at the 10x^2y in order to get 8 from ten you would need to subtract 2x^something y and there is only one answer with that
Answer:
yes its D.
Step-by-step explanation:
use the method of completing the square to solve y²+y-7=0
Answer:
y = sqrt(29)/2 - 1/2 or y = -1/2 - sqrt(29)/2
Step-by-step explanation:
Solve for y:
y^2 + y - 7 = 0
Add 7 to both sides:
y^2 + y = 7
Add 1/4 to both sides:
y^2 + y + 1/4 = 29/4
Write the left hand side as a square:
(y + 1/2)^2 = 29/4
Take the square root of both sides:
y + 1/2 = sqrt(29)/2 or y + 1/2 = -sqrt(29)/2
Subtract 1/2 from both sides:
y = sqrt(29)/2 - 1/2 or y + 1/2 = -sqrt(29)/2
Subtract 1/2 from both sides:
Answer: y = sqrt(29)/2 - 1/2 or y = -1/2 - sqrt(29)/2
Answer:
y=sqrt(29)/2-1/2, -sqrt(29)/2-1/2
Step-by-step explanation:
y^2+y-7=0
completing the square,
(b/2)^2=(1/2)^2=1/4
(y+1/2)^2=7+1/4
(y+1/2)^2=28/4+1/4
(y+1/2)^2=29/4
y+1/2=sqrt(29/4)
y=sqrt(29/4)-1/2
y=sqrt(29)/2-1/2
y=-sqrt(29)/2-1/2
2. One of the most common mutagens in
our environment, that we are exposed
to everyday we are outside in the
sunlight, is
O UV radiation
infrared radiation
Answer:
Ultraviolet (UV) radiation.
Step-by-step explanation:
Mutagen is part of genetics, it is chemical or physical agent which are present in atmosphere and causes changes or mutation in the genetic materials i.e. in DNA (these changes can be permanent as well). Example of mutagen are radioactive substances, ultraviolet radiation, etc.
UV radiation is an electromagnetic radiation which is present in sunlight. It is a strong mutagen which is when absorbed by DNA can cause extreme damage, for example, uncontrolled division of skin cell can cause skin cancer, that's the reason why UV radiation is the most common mutagen to which we are exposed to when we are outside in the sunlight.
What is y+2=⅞(x-3) in standard form?
Answer:
7x - 8y = 37
Explanation:
y+2 = ⅞(x-3) (distribute ⅞ -- x times 7/8, -3 times 7/8)
y+2 = ⅞x - 21/8 (subtract ⅞x from both sides)
y+2-⅞x = -21/8 (subtract 2 from both sides)
y-⅞x = -37/8 <--- result of -21/8 - 2
Multiply both sides by 8 to get ride of fractions
8y - 7x = -37 (rearrange)
-7x + 8y = -37
It's better to have a positive coefficient for x if you can. So multiply both sides by -1. That just means changing the sign of every term on both sides, you get
7x - 8y = 37
Shawn hikes up a mountain, back down the other side, then around the front of the mountain back to his truck. How far did he go if n = 5 and m = 6?
Answer:
The distance Shawn went is 40.
Step-by-step explanation:
Given:
N= 5 and M =6
Mountain hike = N = 5
Back down the other side = 2N+1 = 2×5 + 1 = 10 + 1 =11
From Mountain back to truck = 4M = 4×6 = 24
We need to find the total distance he went and can be calculate by adding Mountain hike with back down the other side and then from Mountain back to truck.
Total distance Shawn went = Mountain hike+ Back down the other side + From Mountain back to truck = 5 + 11 + 24 = 40
Hence Shawn went the distance of 40.
Solving systems by substitution
X=y-11
2x+3y=8
Answer:
x=-5, y=6. (-5, 6).
Step-by-step explanation:
x=y-11
2x+3y=8
--------------
2(y-11)+3y=8
2y-22+3y=8
5y-22=8
5y=8+22
5y=30
y=30/5=6
x=6-11=-5
What value of z makes the equation true? 0.2z -8 =0.4z -7
Answer:
X= -0.4545
Step-by-step explanation:
YOU HAVE TO SUBTRACT .2Z FROM .4Z WHICH GETS YOU .2 ON THE RIGHT SIDE
THAT WOULD MEAN YOU HAVE TO CLEAR OUT THE SEVEN BY ADDING IT ON BOTH SIDES GETTING -1
THEN YOU WOULD HAVE -1=.2Z
THEN DIVIDE BY .2 GETTING YOU A TOTAL OF -0.4545 WHEN YOU FINISH DIVIDING
Diego is 165 cm tall. Andre is 1.7 . tall. Who is taller Diego or Andre?
Answer:
Andre is taller.
Step-by-step explanation:
I assume Andre's height is 1.7 m.
Let's convert Andre's height to cm.
1 m = 100 cm
1.7 m = 1.7 * 1 m = 1.7 * 100 cm = 170 cm
Andre is 170 cm tall. Diego is 165 cm tall.
Since 170 cm > 165 cm, Andre is taller.
1.7 m = 170 cm
170 cm > 165 cm
Andre > Diego
It took a car 5 days to travel 1459 miles. What was this car average speed in miles per hour ?
Answer:
12.1583333333 miles/hr.
Step-by-step explanation:
24 * 5 = 120 hrs
1459/120 = 12.1583333333
Answer:
12.158 miles/hour
Step-by-step explanation:
[tex]\frac{1459 miles}{5 days} = 291.8 miles/day\\\frac{291.8 miles}{1 day} x \frac{1 day}{24 hours} = 12.158 miles/hour[/tex]
Uncle Drew scored 28 points in 5 minutes during a game of basketball.
How many points did he average per minute during that 5-minutes?
points per minute
Uncle Drew averaged 5.6 points per minute during that 5-minute game.
To find the average number of points Uncle Drew scored per minute during the 5-minute game, we divide the total number of points scored by the number of minutes played.
Given that Uncle Drew scored 28 points in 5 minutes, we divide 28 by 5:
[tex]\[ \text{Average points per minute} = \frac{28}{5} \]\[ \text{Average points per minute} = 5.6 \][/tex]
Complete the statement below to explain how this model shows that 2/3÷3/4=8/9
To reciprocal the term for dividing, then multiply both fractions and get the solution to model 2/3 ÷ 3/4 = 8/9.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
The numeral model is given in the question following:
⇒ 2/3 ÷ 3/4 = 8/9
According to the given question, the required solution would be as:
Find the reciprocal in this situation to divide by a fraction:
3/4 divided by 2/3
This would be: 2/3 x 4/3
When you multiply the components, you get 8/9.
Thus, to reciprocal the term for dividing, then multiply both fractions and get the solution.
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Final answer:
To show that 2/3 divided by 3/4 equals 8/9, we multiply 2/3 by the reciprocal of 3/4, which is 4/3, yielding the answer 8/9. This illustrates that division by a fraction involves multiplying by its reciprocal.
Explanation:
To explain how the model shows that 2/3 ÷ 3/4 = 8/9, we need to understand division of fractions and the concept of reciprocals. Division of fractions is the same as multiplying by the reciprocal of the divisor. The reciprocal of 3/4 is 4/3. Therefore, to divide 2/3 by 3/4, we multiply 2/3 by 4/3:
(2/3) × (4/3) = 8/9
This demonstrates that dividing by a fraction is equivalent to multiplying by its reciprocal. We can also use familiar scenarios to rationalize the answer. For instance, we know that half of one half (1/2 × 1/2) equals one quarter (1/4) and this helps us understand the process - we are scaling a number by another when we multiply fractions.
When discussing multiplication and division of fractions, it is useful to remember that these operations are fundamentally linked; division is essentially multiplication by a reciprocal. Hence, dividing 2/3 by 3/4 is the same as multiplying 2/3 by the reciprocal of 3/4, which is 4/3, resulting in 8/9.
What number would x be for 2x+1/3 and 2x be the same equation
Answer:
No solution.
Step-by-step explanation:
2x+1/3=2x
1/3=2x-2x
1/3=0
no solution
6 dollars of 3 cans of tuna in a unit rate
The unit rate is $2 per can.
Step-by-step explanation:
You divide 6 by 3 which then equals 2.
Answer:
$2.00 per can
Step-by-step explanation:
-6(y+5)-24=66 find the value of y
Answer:
y=-20
Step-by-step explanation:
-6(y+5)-24=66
-6y-30-24=66
-6y-54=66
-6y=66+54
-6y=120
y=120/-6=-20
Find the area and circumference of a circle that has a diameter of 17mm
The area of the circle is approximately [tex]\(69.46 \, \text{mm}^2\)[/tex] and the circumference is approximately [tex]\(53.49 \, \text{mm}\).[/tex]
To find the area A and circumference C of a circle given its diameter d, we can use the following formulas:
1. Area A of a circle:
[tex]\[ A = \pi \times \left(\frac{d}{2}\right)^2 \][/tex]
2. Circumference C of a circle:
[tex]\[ C = \pi \times d \][/tex]
Given that the diameter d is 17 mm, we can plug this value into the formulas to find the area and circumference.
1. Area A of the circle:
[tex]\[ A = \pi \times \left(\frac{17}{2}\right)^2 \]\[ A = \pi \times \left(\frac{17}{2}\right) \times \left(\frac{17}{2}\right) \]\[ A = \pi \times \frac{17 \times 17}{4} \]\[ A = \pi \times \frac{289}{4} \]\[ A = \frac{289}{4} \pi \][/tex]
[tex]\[ A \approx 69.46 \, \text{mm}^2 \][/tex]
2. Circumference (\(C\)) of the circle:
[tex]\[ C = \pi \times 17 \]\[ C = 17\pi \][/tex]
[tex]\[ C \approx 53.49 \, \text{mm} \][/tex]
if f(x)=4/x+2 and g is the inverse of f, then g'(10)=
Answer:
The value of g'(10)=[tex]\frac{(-1)}{16}[/tex]
Step-by-step explanation:
Given function is f(x)=[tex]\frac{4}{x} + 2[/tex]
Take f(x)=y
y=[tex]\frac{4}{x} + 2[/tex]
Subtract 2 from both side.
y-2=[tex]\frac{4}{x}[/tex]
x=[tex]\frac{4}{y-2}[/tex]
The inverse of f(x) is written as [tex] \frac{4}{y-2}[/tex]
It is said as g is inverse of f
g(y)=\frac{4}{y-2}[/tex]
g(y)=[tex]\frac{4}{y-2}[/tex]
g(10)=[tex]\frac{4}{10-2}[/tex]
g(10)=[tex]\frac{1}{2}[/tex]
Differentiating both sides we get,
g'(y)=[tex]\frac{4(-1)}{(y-2)^{2}}+0[/tex]
g'(y)=[tex]\frac{(-4)}{(y-2)^{2}}[/tex]
To find g'(10)=[tex]\frac{(-4)}{(10-2)^{2}}[/tex]
g'(10)=[tex]\frac{(-1)}{16}[/tex]
please help. If you answer correctly and give an explanation I'll give you 5 stars, thanks, and brainliest.
solve the equation:
2x + 1-x/4 = 3
or
[tex]2x + \frac{1-x}{4} = 3[/tex]
The solution of the equation is [tex]x=\frac{11}{7}[/tex]
Step-by-step explanation:
To simplify an equation of x
Simplify each side of the equationCollect x in side and the numerical terms in the other sideFind the value of x∵ The equation is [tex]2x + \frac{1-x}{4}=3[/tex]
- Multiply all terms of the equation by 4 to cancel the denominator
of the 2nd term in the left hand side
∵ The equation is [tex]4(2x) +4 (\frac{1-x}{4})=4(3)[/tex]
∴ 8x + (1 - x) = 12
∴ 8x + 1 - x = 12
- Add like terms
∴ (8x - x) + 1 = 12
∴ 7x + 1 = 12
- Subtract 1 from both sides
∴ 7x = 11
- Divide both sides by 7
∴ [tex]x=\frac{11}{7}[/tex]
The solution of the equation is [tex]x=\frac{11}{7}[/tex]
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please answer fast I have been work on it for a week .thank you
Answer:
A) 3x-5=25
I'll try my best on the others
B) x+y^2=18
C)x•6/5=x+4 ????
D).5+x=2-4???
That's all I know :/
Step-by-step explanation:
yeah I'm not sure lol
Over the course of a year, a company goes from 115 employees to 124 employees.
Use the drop-down menus to build an equation that could be used to find the percent change, p, in the number of employees
Answer:
on the top is 124 - 115 whille in the bottom is 115
Step-by-step explanation:
To calculate the percent change in the number of employees, use the formula (Change in Quantity / Original Quantity) × 100. The original number of employees is 115, and it increased to 124, resulting in a change of 9. The percent change is approximately 7.83%.
Explanation:To find the percent change in the number of employees, you can use the following formula:
Percent Change (p) = (Change in Quantity / Original Quantity) × 100
In this case, the Original Quantity is the number of employees at the start of the year (115) and the Change in Quantity is the difference between the number at the end of the year (124) and the number at the start of the year (115).
So, we calculate Change in Quantity as 124 - 115 = 9.
Now, using the formula:
p = (9 / 115) × 100
Calculating this gives us the percentage change:
p = (9 / 115) × 100 ≈ 7.83%
The percent change in the number of employees is approximately 7.83%.
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Thank you! Please do both
Answer:
my 12 inch pito that pito good
What’s 333x333 please I need to know
Answer:
110889
Step-by-step explanation:
Answer:
110,889 is the answer dude..
Calculate the constant of variation if y varies directly as x. PLEASE GIVE EXPLANATION
Answer:
[tex]k = - \frac{3}{2}[/tex]
Step-by-step explanation:
If y varies directly with x, then from the relation of direct variation we can write y ∝ x
Now, converting the variation relation to equation relation,
⇒ y = kx ........... (1) {Where k is the constant of variation}
Now, given that at y = - 3, x = 2 and this solution will satisfy the equation (1).
Hence, - 3 = 2k
⇒ [tex]k = - \frac{3}{2}[/tex] (Answer)
Can somebody help me with the 3 questions?
Answer:
1.
a. 2.75 seconds
b. 169 feet
2. x - 3 is a factor
Other factors: x + 2, 2x + 1, 3x - 4
3. Real zeros: [tex]x = -2[/tex]
Complex zeros: [tex]x_{2,3}=-3\pm 2i[/tex]
Step-by-step explanation:
1. Given equation of parabola
[tex]s(t)=-16t^2+88t+48[/tex]
a) The rocket reaches its maximum height at the vertex of parabola. Find t-coordinate of the vertex:
[tex]t_v=\dfrac{-b}{2a}\\ \\=\dfrac{-88}{2\cdot (-16)}\\ \\=\dfrac{11}{4}\\ \\=2.75\ seconds[/tex]
b) The maximum height is s-coordinate of the vertex. Find it:
[tex]s\left(\dfrac{11}{4}\right)\\ \\=-16\cdot \left(\dfrac{11}{4}\right)^2+88\cdot\left(\dfrac{11}{4}\right)+48\\ \\=-121+22\cdot 11+48\\ \\=169\ feet[/tex]
2. For x – 3 to be a factor of [tex]f(x)=6x^4-11x^3-35x^2+34x+24,[/tex] the Factor Theorem says that x = 3 must be a zero of f(x). Check it (whether f(3)=0):
[tex]f(3)\\ \\=6\cdot 3^4-11\cdot 3^3-35\cdot 3^2+34\cdot 3+24\\ \\=6\cdot 81-11\cdot 27-35\cdot 9+102+24\\ \\=486-297-315+126\\ \\=0[/tex]
So, x = 3 is zero of the function f(x) and x - 3 is the factor of the function f(x). Rewrite the function as follows:
[tex]f(x)\\ \\=6x^4-11x^3-35x^2+34x+24\\ \\=6x^4-18x^3+7x^3-21x^2-14x^2+42x-8x+24\\ \\=6x^3(x-3)+7x^2(x-3)-14x(x-3)-8(x-3)\\ \\=(x-3)(6x^3+7x^2-14x-8)\\ \\=(x-3)(6x^3+12x^2-5x^2-10x-4x-8)\\ \\=(x-3)(6x^2(x+2)-5x(x+2)-4(x+2))=\\ \\=(x-3)(x+2)(6x^2-5x-4)\\ \\=(x-3)(x+2)(6x^2+3x-8x-4)\\ \\=(x-3)(x+2)(3x(2x+1)-4(2x+1))\\ \\=(x-3)(x+2)(2x+1)(3x-4)[/tex]
3. [tex]x=-2[/tex] is a zero of the function [tex]f(x)=x^3+8x^2+25x+26,[/tex] then
[tex]f(x)\\ \\=x^3+8x^2+25x+26\\ \\=x^3+2x^2+6x^2+12x+13x+26\\ \\=x^2(x+2)+6x(x+2)+13(x+2)\\ \\=(x+2)(x^2+6x+13)[/tex]
Find the discriminant of the quadratic polynomial [tex]x^2+6x+13;[/tex]
[tex]D=6^2-4\cdot 1\cdot 13=36-52=-16[/tex]
This expression has no more real zeros (the discriminant is less than 0), it has two complex zeros:
[tex]x_{1,2}=\dfrac{-6\pm \sqrt{-16}}{2\cdot 1}=\dfrac{-6\pm 4i}{2}=-3\pm 2i[/tex]
Rammy has $9.60 to spend on some peaches and a gallon of milk. Peaches
cost $1.20 per pound, and a gallon of milk costs $3.60.
The inequality 1.20x+ 3.60 39.60 models this situation, where x is the
number of pounds of peaches.
HEF
Solve the inequality. How many pounds of peaches can Rammy buy?
Answer:
[tex]\large \boxed{\text{5.00 lb}}[/tex]
Step-by-step explanation:
[tex]\begin{array}{rcl}1.20x + 3.60 & \leq & 9.60\\1.20x & \leq & 6.00\\x &\leq & \mathbf{5.00}\\\end{array}\\\text{Rammy can buy $\large \boxed{\textbf{5.00 lb}}$ of peaches.}[/tex]
Check:
[tex]\begin{array}{rcl}1.20(5.00) + 3.60 & \leq & 9.60\\6.00 + 3.60 & \leq & 9.60\\9.60 & \leq & 9.60\\\end{array}[/tex]
OK.
The number of pounds of peaches that Rammy can buy is 5 pounds.
Based on the information given in the question, the equation to solve the question will be:
1.20x + 3.60 ≤ 9.60
Collect like terms
1.20x ≤ 9.60 - 3.60
1.20x ≤ 6.00
Divide both side by 1.20
1.20x/1.20 ≤ 6.00/1.20
x ≤ 5.00
Therefore, the number of pounds of peaches that Rammy can buy is 5 pounds
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Given: △AKM, KD ⊥ AM , AK = 6, KM = 10, m∠AKM = 93º Find: KD
The length of KD in triangle △AKM, with AK = 6 and KM = 10, and m∠AKM = 93° is 10, since KD is the height of a right triangle and KM is the hypotenuse.
The question asks to find the length of KD in triangle △AKM where KD is perpendicular to AM. Given AK = 6, KM = 10, and m∠AKM = 93º, we can solve for KD using trigonometric ratios.
Since KD ⊥ AM, we have a right triangle △KDM.
We know the hypotenuse KM and angle AKM, so we can use the sine function, where sin(AKM) = opposite/hypotenuse, to find the length of KD. The sine of angle AKM (which is slightly adjusted from 93º to 90º since we are looking for the height in a right triangle) gives us:
sin(90º) = KD/ KM
We know sin(90º) = 1 and KM = 10, so:
1 = KD / 10
Therefore, KD = 10.
The hockey team won 8 out of their first 14 games. At the same rate, how many games should they expect to win out of 84
Answer:
48
Step-by-step explanation:
Answer:
The answer is 48 games out of 84.
Step-by-step explanation:
So first we go through a step by step process.
We have a problem set up that looks something like this.
8/14 = ?/84
Step 1:
So we will first divide 84 by 14, giving us 6.
Step 2:
So 14x6 is equal to 84. Now we have to multiply the top half of the equation by 6. This is 8x6 giving us 48.
Step 3:
Now we substitute the ? with the 48. In the end if playing 84 games the hockey team would win 48 at the rate it was going.
Hope this helped!
A copy machine makes copies at a constant rate. The machine can make 80 copies in 2.5 minutes. Write an equation to represent the number of copies, n, that can be made over any time interval,t. ( PLEASE HELP ANSWER THIS QUICKLY!!!!)