Answer:
The domain is all real numbers. The range is {y|y ≤ 16}
Step-by-step explanation:
we have
[tex]f(x)=-x^{2}-2x+15[/tex]
This is the equation of a vertical parabola open downward
The vertex is a maximum
Find the vertex of the quadratic equation
[tex]f(x)-15=-x^{2}-2x[/tex]
[tex]f(x)-15=-(x^{2}+2x)[/tex]
[tex]f(x)-15-1=-(x^{2}+2x+1)[/tex]
[tex]f(x)-15-1=-(x^{2}+2x+1)[/tex]
[tex]f(x)-16=-(x^{2}+2x+1)[/tex]
[tex]f(x)-16=-(x+1)^{2}[/tex]
[tex]f(x)=-(x+1)^{2}+16[/tex] -----> equation in vertex form
The vertex is the point (-1,16)
therefore
The domain is the interval ----> (-∞,∞) All real numbers
The range is the interval ----> (-∞,16] All real numbers less than or equal to 16
Answer:
The Answer Is B
Step-by-step explanation:
domain is all real numbers. The range is {y|y ≤ 16}.
Which expression is equivalent to(8w 7x-5y3z-9)-2/3
Answer:
[tex]56wx - 15yz - \frac{29}{3} [/tex]
Step-by-step explanation:
[tex]1. \: 56wx - 5y \times 3z - 9 - \frac{2}{3} \\ 2. \: 56wx - 15yz - 9 - \frac{2}{3} \\ 3. \: 56wx - 15yz + ( - 9 - \frac{2}{3} )[/tex]
The expression equivalent to given condition is 56wx - 15yz - 29/3.
What is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given expression,
(8w.7x - 5y.3z - 9) - 2/3
since variables are in the product, so their constants are multiplied,
8w.7x = 56wx
5y.3z = 15yz
the equation can be written as,
56wx - 15yz - 9 - 2/3
and - 9 - 2/3 = (-27 - 2)/3 = -29/3
=> 56wx - 15yz - 29/3
Therefore, the equivalent form of the equation is 56wx - 15yz - 29/3.
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Assuming that there are 20. drops in 1.0 mL, how many drops are in 3.9 gallons?
drops
Answer:
295261.98 or just 295.2962 (rounded).
Step-by-step explanation:
You have to figure out how many ml are in a gallon. Then multiply that by 3.9 gallons.
Find the surface area of a sphere with a diameter of 4 units in terms of pi
Answer:
16π
Step-by-step explanation:
The surface area of a sphere is:
A = 4πr²
where r is the radius, or half the diameter.
If the diameter is 4 units, then the radius is 2 units:
A = 4π (2)²
A = 16π
The surface area is 16π square units.
Each month, Anna pays $630 in rent. How much rent does she pay over the course of 18 months?
Answer:
$11,340
Step-by-step explanation:
1 month: 630
18 months: 18×630=11,340
Anna pays a total of $11,340 in rent over the course of 18 months by multiplying her monthly rent of $630 by 18.
To find out how much rent Anna pays over the course of 18 months, we need to multiply her monthly rent by the number of months. Anna pays $630 each month, so over 18 months, she would pay:
$630 times 18 = $11,340.
Therefore, Anna pays a total of $11,340 in rent over the course of 18 months.
On Ms. Smith's last math test, 80% of her 25 students earned an 83% or better. How many of Ms. Smith's students earned an 83% or better on the last math test?
Answer:
20 students
Step-by-step explanation:
It says 80% of 25 students got 83%+.
This means the number of students that got 83%+ is 80% of 25, or 25*0.8.
25*0.8 is 20, so 20 students got 83%+.
Answer:
20 students earned 83% or better in last maths test.
Step-by-step explanation:
We are given that on Ms. Smith's last math test, 80% of her 25 students earned an 83% or better.
We are to find the number of students who earned 83% or better on the test.
Number of students who earned 83% or more = 80% × 25 = [tex] \frac { 8 0 }{ 1 0 0 } \times 2 5[/tex] = 20
In a bouquet of 24 roses, sixteen are red and the rest are pink. What is the ratio of pink to red roses?
Answer: 1:2 ratio
Step-by-step explanation:
Total-red roses=pink roses
24-16=8
8:16
GCF: 8
16/8=2
8/8=1
1:2 ratio
pink:red
The ratio of pink to red roses 1:2 ratio
Total-red roses=pink roses
24-16= 8
8:16
GCF: 8
16/8=2
8/8=1
1:2 ratio
pink : red
A ratio indicates how many times one number contains another.
The numbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc. In most contexts, both numbers are restricted to be positive.
ReductionRatios can be reduced (as fractions are) by dividing each quantity by the common factors of all the quantities. As for fractions, the simplest form is considered that in which the numbers in the ratio are the smallest possible integers.
Thus, the ratio 40:60 is equivalent in meaning to the ratio 2:3, the latter being obtained from the former by dividing both quantities by 20. Mathematically, we write 40:60 = 2:3, or equivalently 40:60∷2:3. The verbal equivalent is "40 is to 60 as 2 is to 3."
Irrational ratiosRatios may also be established between incommensurable quantities (quantities whose ratio, as the value of a fraction, amounts to an irrational number). The earliest discovered example, found by the Pythagoreans, is the ratio of the length of the diagonal d to the length of a side s of a square, which is the square root of 2, formally.
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What are the roots, in simplest form, of the equation 4x2 + 98= 0
Answer:
x = ±√ 24.500 = ± 4.94975
Step-by-step explanation:
: (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Step-by-step explanation:
4x² + 98 = 0
2x² + 49 = 0
2x² = -49
x² = -49/2
x = ±√(-49/2)
x = ±7i√(1/2)
x = (±7i√2) / 2
Over the set of integers, factor the expression x^4– 4x^2 – 12.
Step-by-step explanation:
problem answer in picture
The value of the expression after factorization is (x² + 2)(x² - 6)
What is Factorization?'In math, factorization is when you break a number down into smaller numbers that, multiplied together, give you that original number.'
According to the given problem,
[tex]x^{4} - 4x^{2} - 12\\[/tex]
⇒ [tex]x^{4} + 2x^{2} - 6x^{2} - 12\\[/tex]
⇒ [tex]x^{2} (x^{2} +2) -6(x^{2} +2)[/tex]
⇒ [tex](x^{2} +2)(x^{2} -6)[/tex]
Hence, we can conclude the value of the given expression after factorization is [tex](x^{2} +2)(x^{2} -6)[/tex].
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Find -x + 10 subtracted from 0.
-* +10
0X-10
Answer:
x-10
Step-by-step explanation:
we know that
(-x+10) subtracted from 0 is equal to
0 minus (-x+10)
so
0-(-x+10)=0+x-10
=x-10
Answer:
x-10
Step-by-step explanation:
If s(x) = 2 – x^2 and t(x) = 3x, which value is equivalent to (s•t)(-7)?
Answer:
[tex]-439[/tex]
Step-by-step explanation:
we have
[tex]s(x)=2-x^{2}[/tex]
[tex]t(x)=3x[/tex]
we know that
[tex](sot)(x)=2-(3x)^{2}[/tex]
[tex](sot)(x)=2-9x^{2}[/tex]
For x=-7
substitute
[tex](sot)(-7)=2-9(-7)^{2}[/tex]
[tex](sot)(-7)=2-441[/tex]
[tex](sot)(-7)=-439[/tex]
please help me with this question.
Answer:
1344 ft²Step-by-step explanation:
From the picture we have:
4w = 3l
If w = 12 ft, then
3l = 4(12)
3l = 48 divide both sides by 3
l = 16 ft
The dimensions of rectangular floor are 4w × (l + w).
Substitute the values of w and l:
4w = 4(12) = 48 ft
l + w = 16 + 12 = 28 ft
The formula of an area of a rectangle:
A = width × length
Substitute:
A = (48)(28) = 1344 ft²
1. In a 30-60-90 triangle, the leagoo the hypotenuseis 6. What is the leaga of the shortest
a2
6.3
Answer:
b. 3
Step-by-step explanation:
In a 30°-60°-90° triangle, the short side is ½ the hypotenuse [the long side is double the short side].
30°-60°-90° Triangles
x√3 → long side
x → short side
2x → hypotenuse
45°-45°-90° Triangles
x → two legs
x√2 → hypotenuse
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A mover in a moving truck is suing a rope to pull a 400-pound box up a ramp
that has an incline of 25o. What is the force needed to hold the box in a
stationary position to prevent the box from sliding down the ramp?
Answer:
Step-by-step explanation:
The pulling force
Answer:
F = -52.8 N
Step-by-step explanation:
Given :
Inclination angle : 25°
Weight, W = 400 lb
The force N will push the box against the ramp.
Therefore, Force F will prevent the box from sliding down the ramp.
F = W sin 25°
= 400 x (-0.132)
= -52.8 N ( negative sign shows that the force applied in the opposite direction )
Divide x^4 + 7 by x - 3.
a.) x³ - 3x² - 9x - 27 R 88
b.) x³ + 3x² + 9x - 27 R -74
c.) x³ + 3x² + 9x + 27 R 88
Answer:
c
Step-by-step explanation:
Divide using synthetic division, remembering to place a zero to denote the terms x³, x² and x
Since division by (x - 3) then evaluate using h = 3
3 | 1 0 0 0 7
↓
1 3 9 27 81
----------------------
1 3 9 27 88 ← degree 3 polynomial
quotient = x³ + 3x² + 9x + 27 , remainder = 88 → c
Follow below steps:
To divide x^4 + 7 by x - 3, we will use polynomial long division. This process is similar to the long division we use with numbers. Let's perform the division step by step:
Divide the term with the highest power in the dividend (x^4) by the highest power in the divisor (x) to get x^3.
Multiply the entire divisor by x^3 and subtract the result from the dividend.
The subtraction will give a new polynomial. Repeat the process until the degree of the remainder is less than the degree of the divisor, or until no further division can be carried out.
The correct result for the division of x^4 + 7 by x - 3 is option (a): x^3 - 3x^2 - 9x - 27 R 88.
determine the slope and vertical intercept of the following linear function below
X/-4,-2,0,2,4
Y/-114,-60,-6,48,102
what is the slope & what is the vertical intercept ( as an ordered pair ) ?
to get the slope of it, we simply need two points off the table, say (-4,-114) and (2,48). Recall that the y-intercept, where the graph intercepts the y-axis, when that happens x = 0, so is right there on the table already.
[tex]\bf \begin{array}{rrll} x&y\\ \cline{1-2} -4&-114\\ -2&-60\\ 0&-6&\leftarrow y-intercept\\ 2&48\\ 4&102 \end{array}~\hfill (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-114})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{48})[/tex]
[tex]\bf slope\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{48-(-114)}{2-(-4)}\implies \cfrac{48+114}{2+4}\implies \cfrac{162}{6}\implies 27 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left(\stackrel{slope}{27}~~,~~\stackrel{y-intercept}{-6} \right)~\hfill[/tex]
what is 5 - j = 3 ????
Answer:
j=2
Step-by-step explanation:
First, subtract by 5 from both sides of equation.
5-j-5=3-5
Simplify.
3-5=-2
-j=-2
Divide by -1 from both sides of equation.
-j/-1=-2/-1
Simplify, to find the answer.
-2/-1=2
It change negative to positive.
j=2 is the correct answer.
I hope this helps you, and have a wonderful day!
Answer:
2
/////////////////////////////////////////////////////////////////////////////////
1st step: again, reverse the equation (by flipping the equation around)
2nd step: do the equation ; 5 - 3 = 2
3rd step: (check your answer) ; 3 plus 2 equals 5
therefore, the answer 2 is correct.
What is the following product? 3 sqrt 16x7 . 3 sqrt 12x9
Answer: The required product is [tex]4x^5\sqrt[3]{3x}[/tex]
Step-by-step explanation: We are given to find the following product :
[tex]P=\sqrt[3]{16x^7}\times \sqrt[3]{12x^9}.[/tex]
We will be using the following property of exponents :
[tex](i)~\sqrt[b]{x^a}=x^\frac{a}{b}\\\\(ii)~x^a\times x^b=x^{a+b}\\\\(iii)~x^a\times y^a=(xy)^a.[/tex]
The required multiplication is as follows :
[tex]P\\\\=\sqrt[3]{16x^7}\times \sqrt[3]{12x^9}\\\\=(16x^7)^\frac{1}{3}\times (12x^9)^\frac{1}{3}\\\\=(16\times12\times x^{7+9})^\frac{1}{3}\\\\=(192x^{16})^\frac{1}{3}\\\\=192^\frac{1}{3}x^\frac{16}{3}\\\\=(64\times3)^\frac{1}{3}x^\frac{16}{3}\\\\=4^{3\times\frac{1}{3}}3^\frac{1}{3}x^{5+\frac{1}{3}}\\\\=4\times 3^\frac{1}{3}x^5\times x^\frac{1}{3}\\\\=4x^5\sqrt[3]{3x}.[/tex]
Thus, the required product is [tex]4x^5\sqrt[3]{3x}.[/tex]
Using complete square to slove for x in the equation (x+7) (x-9)=25
Answer:
[tex]x_1=1+\sqrt{89}\\\\x_2=1-\sqrt{89}[/tex]
Step-by-step explanation:
Apply Distributive property:
[tex](x+7)(x-9)=25\\\\x^2-9x+7x-63=25[/tex]
Add like terms and then add 63 to both sides of the equation:
[tex]x^2-2x-63=25\\\\x^2-2x-63+63=25+63\\\\x^2-2x=88[/tex]
Pick the coefficient of the x term, divide it by 2 and square it:
[tex](\frac{2}{2})^2=1[/tex]
Add it to both sides of the equation:
[tex]x^2-2x+1=88+1[/tex]
Rewriting the left side as a squared binomial, we get:
[tex](x-1)^2=89[/tex]
Apply square root to both sides:
[tex]\sqrt{(x-1)^2}=\±\sqrt{89}\\\\x-1=\±\sqrt{89}[/tex]
And finally we need to add 1 to both sides of the equation. Then we get:
[tex]x-1+1=\±\sqrt{89}+1\\\\x=\±\sqrt{89}+1\\\\\\x_1=1+\sqrt{89}\\\\x_2=1-\sqrt{89}[/tex]
Convert 27 feet to inches.
27 feet- inches
(Round to the nearest hundredth as needed.).
Final answer:
To convert 27 feet to inches, multiply 27 by the conversion factor of 12 inches per foot, resulting in 324 inches.
Explanation:
To convert 27 feet to inches, we use the unit equivalence that 1 foot = 12 inches. We multiply the number of feet by the conversion factor to get the measurement in inches.
27 feet × 12 inches/foot = 324 inches.
Therefore, 27 feet is equivalent to 324 inches. This is a straightforward application of unit conversion, which is a fundamental skill in mathematics, especially useful for various applications in science, engineering, and everyday calculations.
Cone A has a surface area of 384 ft2 and Cone B has a surface area of 96 ft?. What is the ratio of their volume?
Answer:
8 : 1
Step-by-step explanation:
Given ratio of sides = a : b, then
ratio of area = a² : b²
ratio of volumes = a³ : b³
Given
ratio of areas = 384 : 96 = 4 : 1 ← in simplest form, then
ratio of sides = [tex]\sqrt{4}[/tex] : [tex]\sqrt{1}[/tex] = 2 : 1
Hence
ratio of volumes = 2³ : 1³ = 8 : 1
John has consumed 1,600 calories so far today. He has also burned off 400 calories at the gym. He would like to keep his daily calorie total to 1,800 calories per day. How many calories does he have left to consume for the day? Is 1,000 a viable solution to this problem?
Answer:
No; 1,000 will cause him to exceed 1,800.
Step-by-step explanation:
Given,
The consumed calories = 1,600,
Burned calories = 400,
Thus, the remaining calories = 1600 - 400 = 1200
Since, 1,800 calories per day would be like to keep,
Also, 1200 < 1800
Hence, remaining calories is less than the required calories,
And, the calories left to consume for the day = Required calories - remaining calories
= 1800 - 1200
= 600
Therefore, 600 is the viable solution to this problem.
Note : If 1,000 a viable solution to this problem then the required calories will be more than 1800 or exceed 1800.
each cookie sells for $0.50 Sam spent $90 on baking supplies and each cookie cost $0.25 to make how many cookies does Sam need to sell before making a profit formula: sales>cost
Answer:he needs to sell 180 cookies or more
Step-by-step explanation:
90.00/.50=180
Which graph represents y=[2] over the domain 3 <_x <_ 6?
Answer:
Top Right
Step-by-step explanation:
First things first, you can eliminate the bottom left option. The domain 3≤x≤6 means that the graph will only show points greater than or equal to 3 and less than or equal to 6. That option shows x = 2, which is not in this domain.
The symbols on either side of the x are known as ceiling functions. It means that y equals whatever whole number is greater than or equal to than x.
Basically, whatever y is, round it up to the nearest whole number to get x.
So, let's do a table from x = 3 to x = 6
x ║ y Now, see which graph best matches these
2.5 ║ 3 coordinates. Keep in mind that to be a function,
3 ║ 3 the points cannot overlap (they have to pass the
3.5 ║ 4 vertical line test). It looks like the best answer is
4 ║ 4 going to be the top right.
4.5 ║ 5
5 ║ 5
5.5 ║ 6
6 ║ 6
Answer:
Top Right Corner
Step-by-step explanation:
The swiftest way to know this is that on each end is a closed circle from 3 [open] to 6 [close]. Bottom left is close, but has an extra line signaling that x is equal to 2, and it is not included, so do not pick this one.
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Which graph represents the function g(x) = |x + 4| + 2? Image for option 1 Image for option 2 Image for option 3 Image for option 4
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]g\left(x\right)=\left|x+4\right|+2[/tex]
The vertex of the function is the point (-4,2)
The y-intercepts is the point (0,6)
using a graphing tool
see the attached figure
Answer:
It is the second graph
Look at the picture that's attached to that is the answer
A cat and a dog have a race. The cat’s strides are 30% shorter than the dog’s but it makes 30% more strides than the dog. Which of them will win the race?
identify an equation in point slope form for the line perpendicular to y=3x+5 that passes through (4,-1)
Answer:
y-4 = (-1/3)(x+1)
Step-by-step explanation:
We need to identify the equation in point slope form.
The standard equation of point slope form is:
(y-y₁) = m (x-x₁)
where m is the slope and x₁ and y₁ are the points
We are given point(4,-1) so,
x₁=4 and y₁=-1
And a perpendicular line: y =3x+5
Which is equal to y = mx+b
where m is slope so, slope m = 3
Since the line is perpendicular, so the slope in negative inverse of actual slope that m = -1/m
i.e, m = -1/3
So, the equation in point slope form is:
y-(-1) = (-1/3)(x-4)
=> y+1 = (-1/3)(x-4)
Answer:
The equation in point slope form for the line perpendicular to y=3x+5 that passes through (4,-1) is y = -⅓x + ⅓
Step-by-step explanation:
Given
Let P represent the lind
Equation of P; y = 3x + 5
Let Q represent the other point.
Coordinates of Q; Q(4,-1)
It is said that the line P is perpendicular to point Q.
So, the first thing to do is to calculate the slope of Q;
Since both lines are perpendicular, then we make use of formula for calculating the condition of perpendicularity
This is given as m1m2 = -1
Where m1 = slope of P
m2 = slope of Q
To get m1;
m1 is the coefficient of x in equation of line P.
So, m1 = 3.
Now we can solve for m2
m1.m2 = -1. ---- make m2 the subject of formula
m2 = -1/m1
Substitute 3 for m1
m2 = -1/3
m2 = -⅓
Recall that the coordinates of Q is 4 and -1.
To calculate the equation of Q; we make use of the following
m = (y - y1)/(x - x1)
Where m = m2 = -⅓
x1 = 4 and y1 = -1
By substituton, we have
-⅓ = (y - (-1))/(x - 4)
-⅓ = (y + 1)/(x - 4) --- multiply both sides by 3(x - 4)
-⅓ * 3(x - 4) = 3(x - 4) * (y + 1)/(x - 4)
-(x - 4) = 3(y + 1)
-x + 4 = 3y + 3 --- make y the subject of formula
3y = -x + 4 - 3
3y = -x + 1 --- divide through by 3
3y/3 = (-x + 1)/3
y = -x/3 + 1/3
y = -⅓x + ⅓
Hence, the equation in point slope form for the line perpendicular to y=3x+5 that passes through (4,-1) is y = -⅓x + ⅓
Use the substitution method to solve the system of equations. Choose the
correct ordered pair.
x + 2y = 12
- x = -y-6
A. (7.1)
B. (9,3)
C. (6,0)
D. (8,2)
[tex]\bf \begin{cases} x+2y=12\\ \cline{1-1} -x=-y-6\\ \boxed{x}=y+6 \end{cases}\qquad \qquad \stackrel{\textit{doing some substitution in the 1st equation}}{\boxed{y+6}+2y=12\implies 3y+6=12} \\\\\\ 3y=6\implies y=\cfrac{6}{3}\implies \blacktriangleright y=2 \blacktriangleleft \\\\\\ \stackrel{\textit{since we know that }}{x=y+6\implies }x=(2)+6\implies \blacktriangleright x=8 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (8,2)~\hfill[/tex]
73 m is equal to ____ dm. (Only input whole number answer.)
Numerical Answers please!
Answer:
73 m is equal to 730 dm
Step-by-step explanation:
We Need to convert 73 m into dm
We know that 1 meter is equal to 10 decimeter
We are given 73 m. Multiply it with 10 and we will get value in decimeter
73*10
= 730 decimeter
So, 73 m is equal to 730 dm
Answer:
The correct answer would be 730 dm.
Step-by-step explanation:
M is the abbreviation of Meter and dm is an abbreviation of Decimeter. A meter is a unit of length as prescribed by the international system of units. This unit is used to measure the length. Decimeter is the smaller unit of meter. 10 Decimeter makes one meter, which means 1M equals 10DM. So where there are 73 meters, there would be 73 * 10 Decimeters in it. This is shown as below.
73 m = 73 * 10 = 730 DM
3 times the measure of an angle is 14 less than the measure of its complement. What is the measure of the angle? 19° 57° 71° 76°
Answer:
x = 19°
Step-by-step explanation:
Let The angle be "a"
Now according to the question,
⇒ 3 × a = (90° - a) - 14° (Then remove the brackets)
⇒ 3a = 90° - a - 14°
⇒ 3 + a = 76°
⇒ 40° = 76°
⇒ a = 76/4
Now since you got 76/4 you have to make it into simplest form so it'll be :
19/1
Your answer is : a = 19°
Answer:
A on edg.
Step-by-step explanation:
Factor completely: 2x2 + 10x + 12
[tex]\bf 2x^2+10x+12\implies 2(x^2+5x+6)\implies 2(x+3)(x+2)[/tex]
recall that 3 * 2 = 6, and 3x + 2x = 5x.
Answer:
Step-by-step explanation:
It is a little easier if you take out the two.
2*(x^2 + 5x +6)
The numbers that multiply to 6 and adds to 5 are 3 and 2
2*(x + 3)(x + 2)
So that's how the trinomial factors.