Answer:
Yes, because if you divide the two numbers, you get a whole number which means it is. Also, since the last numbers are 56, 8 can go into 56 so yes.
Step-by-step explanation:
What is the solution to the equation below?A.x = -1B.x = 0C.x = -5D.x = 3
We must solve the following equation for x:
[tex]x+3=\sqrt{3-x}[/tex]We can square both sides of the equation so we can get rid of the radical:
[tex]\begin{gathered} (x+3)^2=(\sqrt{3-x})^2 \\ (x+3)^2=3-x \end{gathered}[/tex]We expand the squared binomial on the left:
[tex]\begin{gathered} (x+3)^2=x^2+6x+9=3-x \\ x^2+6x+9=3-x \end{gathered}[/tex]Then we substract (3-x) from both sides:
[tex]\begin{gathered} x^2+6x+9-(3-x)=x-3-(3-x) \\ x^2+6x+9+x-3=0 \\ x^2+7x+6=0 \end{gathered}[/tex]Then we have to find the solutions to this last equation. Remember that the solutions to an equation of the form ax²+bx+c have the form:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]In our case a=1, b=7 and c=6 so we get:
[tex]\begin{gathered} x=\frac{-7\pm\sqrt{7^2-4\cdot1\cdot6}}{2\cdot1}=\frac{-7\pm\sqrt{49-24}}{2}=\frac{-7\pm\sqrt{25}}{2}=\frac{-7\pm5}{2} \\ x=\frac{-7+5}{2}=-1\text{ and }x=\frac{-7-5}{2}=-6 \end{gathered}[/tex]So we have two potential solutions x=-1 and x=-6. However we should note something important, in the original equation we have the term:
[tex]\sqrt{3-x}[/tex]Remember that the result of the square root is always positive. Then the term in the left of the expression has to be positive or 0. Then we impose a restriction in the value of x:
[tex]x+3\ge0\rightarrow x\ge-3[/tex]From the two possible solutions only x=-1 is greater than or equal to -3 so this is the correct one.
AnswerThen the answer is option A.
use the graph to complete the ordered pair solution (0,_) for f.
we must look the value of the graph when x=0
the graph trought x=0 when y=-1 so, the point is
[tex](0,-1)[/tex]What is 2 2/3 - 3/5? 7/154 4/152 1/15 1 2/5
What would -5/6 be when turned into a decimal?
Answer:
answer is -0.8333
round about -0.834
Step-by-step explanation: I hope this helps.
Answer:
Two cyclists, 108 miles apart, start riding toward each other at the same time. One cycles 2 times asfast as the other. If they meet 4 hours later, what is the speed (in mi/h) of the faster cyclist?
Initial distance: 108 miles
We know that they start riding toward each other, and one of them is 2 times as fast as the other. Then, if the speed of the slowest is v, the speed of the faster cyclist is 2v. The combined speed is:
[tex]v_T=v+2v=3v[/tex]The speed and the distance are related by the equation:
[tex]V=\frac{D}{t}[/tex]They meet 4 hours later, thus:
[tex]\begin{gathered} D=108 \\ t=4 \end{gathered}[/tex]Finally, using the previous equation:
[tex]\begin{gathered} 3v=\frac{108}{4} \\ \Rightarrow v=9\text{ mi/h} \end{gathered}[/tex]The speed of the faster cyclist (2v) is 18 mi/h.
Tank A contains a mixture of 10 gallons of water and 5 gallons of pure alcohol tank b has 12 gallons of what and 3 gallons of alcohol how many gallons should be taken from each tank and combiend in order to obtain 8 gallons of a solution countaning 25% alcohol
The volume from tanks A and B are taken as 3 and 5 gallons respectively.
Here,
Let the volume taken from tank A and tank B be x and y.
According to the question,
x + y = 8 - - - - - (1)
And
Composition of the alcohol in Tank A = 1/3
Composition of the alcohol in tank B = 1 /5
x / 3 + y / 5 = 8 / 4
5x + 3y = 30
From equation 1
5(y8 - y) + 3y = 30
-5y + 40 + 3y = 30
-2y = -10
y = 5
Now, put y in equation 1
x = 8 - 5
x = 3
Thus, the Volume from tanks A and B are taken as 3 and 5 gallons respectively.
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Out of 3500 students at a college 1760 are enrolled in a computer class. What is the per cent of students taking the computer class?
Using percentages we can conclude that 50.2% of students are taking a computer class.
What is the percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.So, the percentage of students taking computer classes:
The total number of students is 3500.The number of students enrolled in a computer class is 1760.Now, calculate as follows:
1760/3500 × 1000.502 × 10050.2Therefore, using percentages we can conclude that 50.2% of students are taking a computer class.
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Event A, Event B, and Event Care provided. Event A and Event B aremutually exclusive. Event A and Event C are not mutually exclusive.P(A) = 0.45P(B) = 0.30P(C) = 0.25What is the probability of the union of A and B?
Given data:
The probability of A is P(A)=0.45.
The probability of B is P(B)=0.30.
The expression for the mutually exclusive events is,
[tex]P(A\cap B)=0[/tex]The expression for the probability of A union B is,
[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ =0.45+0.30-0 \\ =0.75 \end{gathered}[/tex]Thus, the probability of (AUB) is 0.75.
2. I want to find the area of a basketball free throw lane, and I am trying to use this formula:
Area =(6 ft) + (12 ft)(19 ft).
Clearly explain how you can tell this is wrong without knowing any area formulas.
Answer:
Down Here
Step-by-step explanation:
Hello!
Area is measured in units². Here, the units are feet, so the area would be written as feet² (ft²).
Simplifying the expression:
6ft + (12ft)(19ft)6ft + 228ft²You can't simplify this because the units are not the same, and this can't measure area because all units of the area have to be squared. The term 6ft has non-squared units.
if an above ground graden is the shape of triangular pyramid measuring.the base is a right triangle with adjacent lengths measuring 5feet and 8feet. the height of the pyramid is 1.5feet. the organic soil cost $1.20 per cubic foot. how much will it cost to fill the graden fully
Solution
The volume for a triangular pyramid is given by:
[tex]V=\frac{1}{3}Bh[/tex]And the Base is given by:
[tex]B=\frac{1}{2}(5)(8)[/tex]And since h= 1.5 ft we have this:
[tex]V=\frac{1}{6}(5\cdot8)\cdot1.5ft^3=10ft^3[/tex]And then we can find the total cost like this:
[tex]C=10ft^3\cdot\frac{1.2\text{ dollars}}{1ft^3}=12dollars[/tex]Then the final answer would be 12$
I need help with my math homework question please. Plus it has a second part of the question
The given quadratic equation is
y = - x^2 + 25
a) The leading coeffiecient is the coefficient of the term with the highest exponent. Thus, the leading coefficient is the coefficient of x^2.
Leading coefficient = - 1
Since the leading coefficient is negative, the graph would open downwards. Thus, the correct option is
Down
b) The standard form of a quadratic equation is
y = ax^2 + bx + c
By comparing both equations,
a = - 1
b = 0
c = 25
The formula for calculating the x coordinate of the vertex of the graph is
x = - b/2a
By substituting the given values,
x = - 0/2 * - 1 = 0
We would calculate the y coordinate of the vertex by substituting x = 0 into the original equation. We have
y = - 0^2 + 25
y = 25
The coordinate of the vertex is (0, 25)
c) To find the x intercepts, we would equate the original equation to zero and solve for x. We have
- x^2 + 25 = 0
x^2 = 25
Taking the square root of both sides,
x = square root of 25
x = ± 5
Thus, the x intercepts are
(5, - 5)
d) The y intercept is the value of y when x = 0
Substituting x = 0 into the orignal equation,
y = - 0^2 + 25
y = 25
y intercept = (0, 25)
e) We would find another point on the graph. Let us substitute x = 6 into the equation. We have
y = - (6)^2 + 25 = - 36 + 25
y = - 11
We would plot (6, - 11) and (0, 25) on the graph. The graph is shown below
Given f(x)=3x+2 find f(-4)
Step-by-step explanation:
i think it will satisfied you
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Short steps pleaseFind the mean and variance of the binomial experiment in which n 5 and p 0.7. a. Mean b. Variance
Given
n= 5
p = 0.7
Find:
a. mean
b. variance
sol:
Mean d
[tex]\begin{gathered} mean\text{ =n}\times\text{p} \\ \\ \text{ = 5}\times\text{0.7} \\ \\ \text{ =3.5} \end{gathered}[/tex][tex]\begin{gathered} variance=np(1-p) \\ \\ =\text{ }5\times0.7(1-0.7) \\ \\ =3.5(0.3) \\ \\ =1.05 \\ \\ \end{gathered}[/tex]If lines L=4x and M=x are perpendicular, what is the value of x?
Those angles are complementary, therefore, we can conclude:
[tex]\begin{gathered} 4x+x=90 \\ add_{\text{ }}like_{\text{ }}terms: \\ 5x=90 \\ Solve_{\text{ }}for_{\text{ }}x: \\ x=\frac{90}{5} \\ x=18 \end{gathered}[/tex]Answer:
x = 18
can you solve for x and y y=4x-11=x+13
x = 8, y = 21
Explanations:The given equation is:
y = 4x - 11 = x + 13
This can be splitted into two equations as:
y = 4x - 11..........(1)
y = x + 13..........(2)
Substitute equation (1) into equation (2)
4x - 11 = x + 13
4x - x = 13 + 11
3x = 24
x = 24/3
x = 8
Substitute the value of x into equation (1)
y = 4x - 11
y = 4(8) - 11
y = 32 - 11
y = 21
x = 8, y = 21
This table shows the top athletes that play both basketball and track. What is the intersection between the set of basketball players and the set of track athletes? Basketball Track Arnold Berenson Nickerson Eaton Yun Tadesse McDonald Jones Tadesse Nickerson Yang Martin
The intersection between the set of basketball players and the set of track athletes is given by:
{Tadesse, Nickerson}
What is the intersection between two sets?The intersection between two sets is the set containing the elements that belong to both sets which we are calculating the intersection.
In the context of this problem, the sets are given as follows:
List of basketball players: {Arnold, Nickerson, Yun, McDonald, Jones, Tadesse}List of track athletes: {Berenson, Eaton, Tadesse, Nickerson, Yang, Martin}.The intersection is composed by athletes that are both basketball players and track athletes, hence it is given as follows:
{Tadesse, Nickerson}
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2,000 deposit,compound interest,compounded anually,at 6% for 2 years. What is the total balance(A=Principal+Interest)?
Given a principal P, compounded anually at r% for t years. Then the
ind the value of x. Round to the nearest tenth. The diagram is not drawn to scale.
ANSWER
x = 10.2
EXPLANATION
In this problem, we are given a right triangle: one of its non-right interior angles measures 22°. We know that the length of the hypotenuse is 11 units long and we have to find the length of the side adjacent to the given angle, x.
With the given information, we can use the cosine of the angle to find the missing value,
[tex]\cos\theta=\frac{adjacent\text{ }leg}{hypotenuse}[/tex]In this problem,
[tex]\cos22\degree=\frac{x}{11}[/tex]Solving for x,
[tex]x=11\cdot\cos22\degree\approx10.2[/tex]Hence, the value of x is 10.2, rounded to the nearest tenth.
Look at the photograph and if you need anything let me know
Observe that the triangles have one pair of congruent angles, and two pair of congruent sides. This means we can demonstrate the congruence using SAS postulate, that is, Side-Angle-Side.
Therefore, the answer is the first option.
Which of the following is the position vector for a vector that has an initial point of (10, 2) andterminal point of (-8, -7)?
initial point = (10,2)
Terminal point = (-8,-7)
subtract the coordinates of the initial point from the coordinates of the terminal point
Position vector = ( -8-10 , -7-2 ) = <-18,-9>
Describe a situation that can be represented by the expression –15 + 8.
Answer:
-7
Step-by-step explanation:
Tiger Woods was 15 under par after the third round of a golf tournament, but was 8 over par for the fourth round. So, his score for the entire tournament was -15 + 8 = -7 (That is, 7 under par).
Need answer if you could show work would be nice
In the Polynomial function f(x)= [tex]2x^{3} -11x^{2} -12x+36 =0 then[/tex]
So all the zeros of f(x) algebraically
[tex]\mathrm{f}(\mathrm{x}) \ are\ \mathrm{x}=-2, \mathrm{x}=\frac{3}{2}, \mathrm{x}=6$[/tex].
Step: 1
Given[tex]$f(x)=2 x^3-11 x^2-12 x+36$and $f(6)=0 \Rightarrow(x-6)$ is factor of $f(x)$now $f(x)=2 x^3-11 x^2-12 x+36$$$[/tex]
[tex]\begin{aligned}&\Rightarrow \mathrm{f}(\mathrm{x})=\left(2 \mathrm{x}^2-12 \mathrm{x}^2\right)+\left(\mathrm{x}^2-\right. \\&\Rightarrow \mathrm{f}(\mathrm{x})=2 \mathrm{x}^2(\mathrm{x}-6)+(\mathrm{x}-6)^2 \\&\Rightarrow \mathrm{f}(\mathrm{x})=(\mathrm{x}-6)\left(2 \mathrm{x}^2+\mathrm{x}-6\right)\end{aligned}$$[/tex]
Step: 2
Now consider [tex]$2 x^2+x-6=2 x^2+4 x-3 x-6$$$\begin{aligned}&\Rightarrow 2 x(x+2)-3(x+2) \\&\Rightarrow 2 x^2+x-6=(2 x-3)(x+2)\end{aligned}$$[/tex]
[tex]$5 \circ f(x)=(x-6)\left(2 x^2+x-6\right)$$$\Rightarrow \mathrm{f}(\mathrm{x})=(x-6)(2 \mathrm{x}-3)(\mathrm{x}+2)$$[/tex]
Step: 3
so for finding zeros of
[tex]$f(x) \rightarrow f(x)=0$$$\Rightarrow(x-6)(2 x-3)(x+2)=0$$$$\Rightarrow(x-6)=0 ;(2 x-3)=0 ;(x+2)=0$$[/tex]
[tex]$$\Rightarrow x=6, x=\frac{3}{2} ; x=-2$$[/tex]
Explanation: Please refer to solution in this step.
Answer:
So required zeros of
[tex]\mathrm{f}(\mathrm{x}) \ are\ \mathrm{x}=-2, \mathrm{x}=\frac{3}{2}, \mathrm{x}=6$[/tex]
What is polynomial function?A polynomial consists of two words, poly and nominal. "Poly" means many and "nomial" means term, and so when combined, polynomials can be said to be "algebraic expressions with many terms." Let's go ahead and start by defining polynomial functions and their types.
The polynomial function in standard form is:
f(x) = [tex]a_{n}x^{n} +a_{n-1} x^{n-1} +.....a_{2} x^{2} +a_{1} x+a0[/tex]
This algebraic expression is called a polynomial function of the variable x. The name of a polynomial is determined by the number of terms it contains.
The three most common polynomials we usually encounter are
monomial binomial trinomialTo learn more about polynomial function, refer;
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Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth. sin 16° = ___
We have round of to 100th place means up to 3 places
[tex]\sin (16\text{ degre}e)=0.27563[/tex]Now we will reduce the digit from right side upto 3 places
As last digit is 3 which is less than 5 so it will remove directly
[tex]\sin (16\text{ degr}e)=0.2756[/tex]Now the last digit is 6 which is greater than 5. So and is even so change we will simply remove this
[tex]\sin (16\text{ degre}e)=0.275[/tex]A number cube is rolled once, {1,2,3,4,5,6)Determine the likelihood of each situation,Column AColumn B1.rolling an even numbera. unlikely2.rolling a 7b. impossible3.rolling a number greater than 0Ccertain4.rolling a number that is greater than 2d. likely5.rolling a 2 or 3e equally likely
The likelihood of the following situations:
1. rolling an even number is likely.
2. rolling a 7 is impossible.
3. rolling a number greater than 0 is certain.
4. rolling a number that is greater than 2 is likely.
5. rolling a 2 or 3 is equally likely
8 Madison has two plants. She waters the spider plant every 4 days and the cactus every 6 daysShe water bo November 30. What is the next day that she will water both plants?
Two plants
Spider plant 4 days
Cactus plant 6 days
Then find when
4X = 6Y
find m.c.m (minimum common multiple) of 4 and 6
m.c.m (4,6) = 12
SO therefore, if both plants were watered November 30, then
add 12 days to Nov 30
12 days after Nov 30 = December 12
how to find a volume of a cylinder that has a radius of 10 and a base of 4 Khan academy
Question:
Find a volume of a cylinder:
Solution:
Remember that the volume of the cylinder with radius r and height h is given by the following formula:
[tex]V\text{ = }\pi r^2h[/tex]then, replacing the data of the problem into the previous equation, we get:
[tex]V\text{ = }\pi(4^2)(10)\text{ = 3.14 (16)(10) = 502.4}[/tex]thus, we can conclude that the correct answer is:
[tex]V\text{ = 502.4}[/tex]
Which of the following statements are equivalent to "Some politicians are not crooked"? Select all that apply:All politicians are crooked.Some politicians are crooked.Not all politicians are crooked.All politicians are not crooked.
SOLUTION
The given statement is
"Some politicians are not crooked"
The equivalent statement is
Not all politicians are crooked
And
All politicians are not crooked.
The equivalent statement is
Not all politicians are crooked
And
All politicians are not crooked.
Answer: Not all politicians are crooked
It is equivalent to saying that "Some politicians are not crooked". Both are implying that not every politician is crooked and some of them are good.
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4) The half-life of a medication is the amount of time for half of the drug to be eliminated from the body. The half-life of Advil or ibuprofen is represented by the equation 2 ) 5 . 0 ( t M R = , where R is the amount of Advil remaining in the body, M is the initial dosage, and t is time in hours.
Based on the half-life, 35.36 mg will remain at 6:00P PM in the body
The amount of the medication that will remain at 6:00P PM?The details that complete the question are added as an attachment
From the question, we have
Initial dosage = 200 mg
This means that
M = 200
Also, we have
Initial time =1 : 00 pm
This means that the number of hours, is
n = 6pm - 1pm
n = 5
Recall that the function is given as
R = M(0.5)ⁿ/²
So, we have the following equation
R = 200 x (0.5)⁵/²
Evaluate the quotient of the exponents
So, we have the following equation
R = 200 x (0.5)².⁵
Evaluate the products
R = 35.36 mg
Using the above computation as a guide, we have the remaining amount to be 35.36 mg
Hence, the amount of the medication that will remain at 6:00P PM is 35.36 mg
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I only need help for letter b, the question is on the picture
Part B
Remember that
z =(x - μ)/(σ/√n)
where
n=21
we have
μ=1,700
σ=200
For X=1,500
Find out the value of Z1
Z1=(1,500-1,700)/(200/√21)
Z1=-4.5826
For X=1,900
Z2=(1,900-1,700)//(200/√21)
Z2=4.5826
Using a z-score table value
P(1,500therefore
The answer is 21 out of 21
(−1/2x+7/10)−(−3/4x−1/5)
The expression (−1/2x + 7/10) − (−3/4x − 1/5) has a value of 1/4x + 9/10 when simplified
How to evaluate the expression?From the question, the expression is given as
(−1/2x+7/10)−(−3/4x−1/5)
Rewrite the expression properly to make it legible
So, we have
(−1/2x + 7/10) − (−3/4x − 1/5)
Expression the above parameter as an equation
This is represented as
(−1/2x + 7/10) − (−3/4x − 1/5) = (−1/2x + 7/10) − (−3/4x − 1/5)
Open the brackets
So, we have the following equation
(−1/2x + 7/10) − (−3/4x − 1/5) = −1/2x + 7/10 + 3/4x + 1/5
Collect the like terms in the equation
(−1/2x + 7/10) − (−3/4x − 1/5) = 3/4x − 1/2x + 7/10 + 1/5
Evaluate
(−1/2x + 7/10) − (−3/4x − 1/5) = 1/4x + 9/10
The expression cannot be further simplified
Hence, the solution to the expression (−1/2x + 7/10) − (−3/4x − 1/5) is 1/4x + 9/10
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