Assuming it's [tex]\sqrt{x^{14}}[/tex]
[tex]\sqrt{x^{14}}=\sqrt{(x^7)^2}=|x^7|[/tex]
Find the volume of the figure on the left
the volume is 408
l times w times h
The height of a baseball thrown from the catcher to first base is modeled by the function h(t) = –0.09t2 + 0.72t + 6, where h is the height of the ball measured in feet and t is the time since being thrown, measured in seconds. The ball is in the air for 10 seconds before being caught. What's the height of the ball at 10 seconds?
The height of a baseball thrown from the catcher to first base is modeled by the function [tex]h(t) = -0.09t^2 + 0.72t + 6[/tex], where h is the height of the ball measured in feet and t is the time since being thrown, measured in seconds
To find out height of the ball at 10 seconds, we plug in 10 for t
[tex]h(t) = -0.09t^2 + 0.72t + 6[/tex]
[tex]h(10) = -0.09(10)^2 + 0.72(10) + 6[/tex]
h(10)=4.2 feet
the height of the ball at 10 seconds= 4.2 feet
plz help. 99 pts
Graph f(x)=−34x−4 . Use the line tool and select two points to graph the line.
Answer:
In the picture
Step-by-step explanation:
Mary mixes 11/12 oz of red paint with 1 3/4 oz of white paint.
How many ounces of paint does Mary mix?
A. 123 oz
B .156 oz
C. 178 oz
D .223 oz
Im assuming that to be the case, so:-
11/12 + 1 3/4
= 11/12 + 7/4
= 11/2 + 21 / 12
= 32 / 12
= 2 2/3 OZ. (Choice D).
Mary mixed Quatities of 2 2/3 ounces of paint by adding 11/12 oz of red paint and 1 3/4 oz of white paint.
Explanation:To find out how many ounces of paint Mary mixed, we need to add the amounts of red and white paint.
First, let's add the red paint: 11/12 oz.
Next, let's add the white paint: 1 3/4 oz.
To add fractions, we need a common denominator. In this case, the common denominator is 12, so we can rewrite 1 3/4 as 7/4: 7/4 oz.
Now, let's add the two amounts: 11/12 + 7/4.
To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 12. Multiply the numerator and denominator of the first fraction by 1 (12/12) and the numerator and denominator of the second fraction by 3 (3/3).
So, 11/12 + 7/4 is equal to (11/12) + (21/12) = 32/12.
We can simplify 32/12 to 2 8/12, and further simplify it to 2 2/3 oz.
Therefore, Mary mixed 2 2/3 ounces of paint.
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The equation x^2-9=0 has how many real solutions
So remember that the degree of the polynomial will indicate how many solutions there are, real or complex. Since the degree of the polynomial is 2, this means that there is a maximum of 2 real solutions in this equation.
Next, we are going to apply the difference of squares rule to this polynomial, which is [tex]x^2-y^2=(x+y)(x-y)[/tex] . In this case:
[tex]x^2-9=(x+3)(x-3)\\(x+3)(x-3)=0[/tex]
Now, we are going to apply the Zero Product Property, which states that if a × b = 0, this means that either a or b = 0 or a and b = 0. In this case, a = x + 3 and b = x - 3. Solve each as such:
[tex]x+3=0\\x=-3\\\\x-3=0\\x=3[/tex]
In short, there are 2 real solutions: x = 3 and x = -3.
The equation [tex]x^2-9=0[/tex] has two real solutions which are x=3 and x=-3. The solutions are obtained by applying the quadratic formula, which indicates that every equation containing an unknown squared will have two solutions.
Explanation:The equation[tex]x^2-9=0[/tex] is a quadratic equation. For any quadratic equation in the form ax²+bx+c = 0, the solutions or roots can be calculated using the quadratic formula: -b ± √(b² - 4ac) / 2a.
In this specific equation, [tex]x^2-9=0[/tex]can be rewritten as x²-9+9 = 9, which simplifies to x² = 9. The solutions can then be obtained using the principal square root or the negative square root, resulting in x = ± √9. Therefore, the two real solutions are x = 3 and x = -3.
It's important to note that every equation containing an unknown squared will have two solutions, which can be both meaningful or only one of them can be reasonable depending on the context of the problem.
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The function p is defined as p(x)=x2+4x-12
Part A
Write an expression that defines p(x-6)+5
Part B
Describe the transformations that map the graph of p(x) to p(x-6)+5. Justify your answer algebraically or by using key features of the graph.
Given the function [tex]p(x)=x^2+4x-12.[/tex]
Part A.
To write the expression that defines [tex]p(x-6)+5,[/tex] you have to substitute x-6 instead of x into the function expression and then add 5 to the function:
[tex]p(x-6)+5=((x-6)^2+4(x-6)+12)+5,\\\\p(x-6)+5=x^2-12x+36+4x-24+12+5,\\\\p(x-6)+5=x^2-8x+29.[/tex]
Part B.
1 transformation is translation 6 units to the right (p(x-6) determines this transfromation).
2 transformation is translation 5 units up (+5 determines this transformation).
Which ordered pairs are solutions to the inequality 2x+y>−4?
Select each correct answer.
(5, −12)
(−3, 0)
(−1, −1)
(0, 1)
(4, −12)
Why does dividing by 10 shift each digit one place to the right?
Answer:
Step-by-step explanation:
As we move up the list -- as we push the digits one place right -- the number has been divided by 10 because each place to the right is worth 10 times less. ... As we move down the list -- as we push the digits to the left through the decimal point -- each number has been multiplied by 10
Dividing by 10 shifts each digit one place to the right due to our base-ten counting system. Each time we divide by 10, the number is broken into 10 equal parts, thereby moving its digits one place to the right. The same principle applies when dealing with larger powers of 10 and is often employed in scientific notation.
Explanation:The reason why dividing by 10 shifts each digit one place to the right relates directly to the base-ten number system we use, which relies on powers of ten. Whenever we divide by 10, we are asking how many times the number can be broken into 10 equal parts, thus moving its digits one place to the right.
For instance, if we take the number 250 and divide it by 10, the result is 25. We've essentially shifted the digits one place right. Similar to this when we are dealing with decimal numbers, the shift occurs with the decimal point. If we had 25.0 and divided by 10, the result would be 2.5
The same principle applies to larger powers of 10. If you divide by 100 (which is 10^2), you shift each digit two places to the right, and so on.
Another way to consider it is using scientific notation, which often uses powers of 10 to simplify large or small numbers. A number like 1,230,000,000 is written as 1.23 × 10⁹ in scientific notation. When we divide this number by 10, the exponent decreases by 1 to become 1.23 × 10⁸, effectively shifting each digit one place to the right.
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Solve for t.
−5t≥70
Help Please
A. is this answer to this question.
The value of inequality is t ≤ -14 which means t will have all value less then and equals to -14 In number line.
What is number line ?
Number line is virtual representation of numbers along with coordinates axis with number equally spaced with equal number of interval.
Here the given inequality is :
−5t ≥ 70
Now, to solve for t we divide both side by -5 :
−5t/-5 ≥ 70/-5
t ≤ -14
It should be noted that negative -5 reverse the inequality sign.
Therefore, the value of inequality is t ≤ -14 which means t will have all value less then and equals to -14 In number line.
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Michael has $550 in his savings account he took out $30.75 every month for one year what is the net change in Michael's account balance following these withdrawals
First You do 30.75 x 12 This is because he said every month for a year and a year has 12 months The answer to 30.75 x 12 is 369 Now all you have to do is 550 - 369 = 181.
Hope this helps :D
eight is greater than or equal to the sum of a number and 3
For the past three months Grace used her cell phone for 42 minutes,62 minutes and 57 minutes. How many minutes would she have to use her cell phone this month for the average usage over the four months to be 55 minutes
This is A Math Problem
Answer:
The amount of minutes Grace has to use her cell phone this month is 59 minutes
Step-by-step explanation:
Let
x -----> amount of minutes Grace has to use her cell phone this month
we know that
The average usage during the four months is equal to the sum of the minutes used in the four months divided by four (the number of months)
so
[tex]55=\frac{42+62+57+x}{4}[/tex]
Solve for x
Multiply by 4 both sides to remove the fraction
[tex]55(4)=(42+62+57+x)[/tex]
[tex]220=(161+x)[/tex]
[tex]x=220-161[/tex]
[tex]x=59\ min[/tex]
therefore
The amount of minutes Grace has to use her cell phone this month is 59 minutes
Simplify. 3/5+(-1/4)÷7/10
Enter your answer, in simplest form, in the boxes.
Please help, look down below at the attachment cuz Im not sure I set the problem up right!
Answer:
1/10
Step-by-step explanation:
There are three simple fractions in this problem: 3/5, -1/4 and 7/10. Rules of order require that the division (-1/4) divided by 7/10 be carried out first; the correct product is -10/28, or -5/14. Then we have 3/5 + (-5/14).
Here the LCD is 70. Then 3/5 + (-5/14) becomes 42/70 - 35/70, which simplifies to 1/10.
Answer:
1/10
Step-by-step explanation:
What is (-6,1) when it is reflected over y=x
ANSWER
The image point is [tex](1,-6)[/tex].
EXPLANATION
For a reflection in then line [tex]y=x[/tex], we simply swap the x and y coordinates.
Thus, in general the mapping for the reflection in the line [tex]y=x[/tex], is
[tex]P(x,y)\rightarrow P'(y,x)[/tex].
Hence,
[tex]P(-6,1)\rightarrow P'(1,-6)[/tex].
See graph.
The reflection of the point (-6,1) over the line y=x results in the point (1,-6).
Explanation:In the context of coordinate geometry, reflection over a line, specifically y=x, requires that we swap the x and y coordinates of a given point. So, when we have the point (-6,1), it is reflected to become (1,-6) over the line y=x. Hence, "this operation fundamentally changes the position of the point".
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A box contains 4 red and 3 blue poker chips. Three chips are pulled random. What is the probability that all are red with a replacement
No. If red balls = 4, Total no. Of balls = 7
Prob of getting first red = 4/7
Second red = 4/7
Third red = 4/7
As all balls are taken out with replacement ,therefore total no. Of red balls remain same
Probability of drawing all red = 4/7×4/7×4/7
=64/343
Wich term best describes a figure formed by three segments connecting three noncollinear points ?
A triangle is the answer.
Answer:
ok the answer is
Step-by-step explanation:
69 gooba, go watch it NOW
Box A contains 53 cubes and has a mass of 1760 grams. Box B contains 18 cubes and has a mass of 1620 grams. The mass of box A is the same as the mass of box B. Every cube has the same mass.
To find the mass of each cube, divide the total mass of the box by the number of cubes. The mass of each cube in Box A is 33.21 grams, while the mass of each cube in Box B is 90 grams.
Explanation:To determine the mass of each cube, we need to divide the total mass of the box by the number of cubes.
Mass of each cube in Box A = Total mass of Box A / Number of cubes in Box A = 1760 grams / 53 cubes = 33.21 grams per cube.
Mass of each cube in Box B = Total mass of Box B / Number of cubes in Box B = 1620 grams / 18 cubes = 90 grams per cube.
Bob is making mini fondant cakes for next bake sale each cake costs bob $1.80 to make if he sells the cakes for $3.00 each how many will he have to sell to make a profit of exactly $36.00 please help me answer
Answer:
he would have to sell 30 cakes
Step-by-step explanation:
if you take the amount it actually cost to make it and the amount he is selling them for you would first do
1.80 - 3.00 = 1.20$
after you get 1 dollar and 20 cents you would divide it by 36 dollars to get 30
to check your answer do 30 x 1.20 = 36.00
four times the sum of some number plus 1 is equal 12 times the difference of the number and 3. Find the number
4(x + 1) = 12(3 - x)
Distributive property on both sides.
4x + 4 = 36 - 12x
Add 12x to both sides.
16x + 4 = 36
Subtract both sides by 4.
16x = 32
Divide both sides by 16.
x = 2
a company rents out 15 food. booths and 20 games booths at the county fair.the fee for a food booths is 100 plus 5 per day the. fee for game booths is 50 plus 7per day the fair lests for d day and all the booths are rented for the entire time write and simplify and expression for the amount in dollars that the company is paid
Answer:
2500 + 215d
Step-by-step explanation:
Total revenue from all booths is the sum of the revenue from the food booths and from the games booths. The food booth revenue for each booth is 100 + 5d, where d is the number of days the fair lasts. There are 15 food booths, so the total revenue from them is ...
... (food booth revenue) = 15(100 +5d)
The games booth revenue for each booth is 50 + 7d, where d is the number of days the fair lasts. There are 20 games booths, so the total revenue from them is ...
... (games booth revenue) = 20(50 +7d)
Then the total revenue is
... total revenue = (food booth revenue) + (games booth revenue)
... = 15(100 +5d) + 20(50 +7d) . . . . . . use the expression for revenue from each
... = 1500 +75d + 1000 +140d . . . . . . eliminate parentheses
... = 2500 + 215d . . . . . . . . . . . . . . . . collect terms
What is the value of k?
Answer:
k=2
Step-by-step explanation:
We have got a right triangle LNO with sides = m,4 and 8
By Pythagorean theorem
m^2=4^2 +8^2
Or m^2 = 80 ... i
IN triangle NOM, 4^2 +k^2 = l^2
i.e. 16+k^2 = l^2... i
In triangle LNM, m^2+l^2 = (8+k)^2
Substitute for m^2 as 80,
i.e. 80+l^2 = 64+k^2 +16k ... iii
From i, l^2 = 16+k^2
Substitute in iii
80+16+k^2 = 64+k^2 +16k
16k = 32 or k =2
-1(2x +3) -2(2x-1) simplified
- 6x - 1
distribute parenthesis and collect like terms
- 2x - 3 - 4x + 2
= (- 2x - 4x) + (-3 + 2) = - 6x - 1
A jet ski rental company charges a $100 rental fee, plus $20 per hour. Write and dole an equation to determine how many hours you can rent the jet ski for it if you have a budget of $175.
Solve the word problem
3 hours because if u have 175 dollers and u spend 100 so now u have 75. 75 -20 is 55. then 55 - 20 is 35. then 35 - 20 is 15 so then you have 15 dollers to spare. so 3
You can represent this problem as a linear equation 100 + 20x = 175. Solving for x gives you 3.75, hence with $175, you can rent the jet ski for 3.75 hours.
Explanation:To solve this problem, you need to set up a linear equation. Let's represent the number of hours of the jet ski rental as x. The jet ski rental company charges a $100 rental fee plus $20 per hour, so we can write this as a equation: 100 + 20x = 175.
Next, we need to solve for x. First, subtract 100 from each side of the equation, you obtain 20x = 75. Then, divide each side by 20 to solve for x. You'll find that x = 3.75. Therefore, with $175, you can rent the jet ski for 3.75 hours.
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Please anyone help fast
For 20 points
Simplify: 9(3 + 4)
simplify 9[3+4}
using bodmass
=9{7}
63
In the past two weeks, Sue earned $513 at her part-time job. She worked a total of 54 hours. About how much did Sue earn per hour?
I think the answer you're looking for is $9.50.
513 / 54 = 9.5
Sue made $9.50 an hour.
divide sh.6300 in the ratio 3:4. how much is each share?
3 : 4 = 2700 : 3600
sum the parts of the ratio : 3 + 4 = 7
divide 6300 by 7 to obtain 1 part
[tex]\frac{6300}{7}[/tex] = 900 ← 1 part
3 parts = 3 × 900 = 2700
4 parts = 4 × 900 = 3600
note that 2700 + 3600 = 6300
Ten times a number decreased by seven equals 101 plus that number. Find the number
Final answer:
A student's math problem involving an algebraic equation to find a number has been solved by isolating and solving variables, resulting in the number 12.
Explanation:
To solve the equation where ten times a number decreased by seven equals 101 plus that same number, we would set up the following equation:
10x - 7 = 101 + x
Now, we solve for x:
First, subtract x from both sides of the equation to get all the x terms on one side:
9x - 7 = 101
Next, add 7 to both sides of the equation to isolate the term with x:
9x = 108
Finally, divide both sides by 9 to solve for x:
x = 12
Hence, the number we are looking for is 12.
The bottom and top of a box are rectangles twice as long as they are wide. Find the volume of the box if it is four feet high and has a total surface area of 220 feet squared.
Let x = the width
then
2x = the length
:
The box dimensions: 2x by x by 4
Given the surface area:
2(2x*x) + 2(2x*4) + 2(x*4) = 220
:
4x^2 + 16x + 8x = 220
A quadratic equation:
4x^2 + 24x - 220 = 0
simplify, divide by 4
x^2 + 6x - 55 = 0
Factor
(x+11)(x-5) = 0
The positive solution is what we want here:
x = 5 ft is the width
then
2(5) = 10 ft is the length
:
Find the volume
10 * 5 * 4 = 200 cu/ft is the volume
Final answer:
The volume of the box is 192 cubic feet, calculated using the dimensions provided in the question.
Explanation:
The volume of the box is 192 cubic feet.
To find the volume, we need to calculate the dimensions of the base rectangle. Since the base and top are twice as long as they are wide, the larger square will have sides of 8 feet. With a height of 4 feet, the volume can be calculated as V = length*width*height. Plugging in the values, we get V = 8*4*4 = 192 cubic feet.
if ∠2 and ∠3 are supplementary angles, then ∠2 and ∠3 form a linear pair true or false
Answer:
True ,if they are adjacent and share a vertex and one side
When a figure is translated, its orientation (blank) and the measures of its angles (blank).
Answer:
Its orientation may change and the measures of its angles stay the same.
Step-by-step explanation:
Answer:
When a figure is translated its orientation may change and the measures of its angles keeps the same measure.
Step-by-step explanation:
Whenever we translate a figure, we move a figure into some orientation given by this same vector. But the angles will remain the same since there is no distortion.
Just as the picture below