Answer:
-2
Explanation:
By properties of logarithms, the logarithm of a fraction is equal to the difference of logarithms, so
[tex]\log _6(\frac{1}{36})=\log _61-\log _636[/tex]Now, log₆(1) = 0 and log₆36 = 2, so
[tex]\begin{gathered} \log _6(\frac{1}{36})=0-2 \\ \log _6(\frac{1}{36})=-2 \end{gathered}[/tex]Therefore, the answer is -2
Given f(x), find g(x) and h(x) such that f(x)= g(h(x)) and neither g(x) nor h(x) is solely x.
Given:
[tex]\begin{gathered} f(x)=g(h(x)) \\ f(x)=\sqrt[]{-4x^2-3}+2 \end{gathered}[/tex]Solve :
[tex]g(h(x)=\sqrt[]{-4x^2-3}+2[/tex]The function g(x) convert then x is equal to h(x) then:
[tex]\begin{gathered} h(x)=-4x^2 \\ g(x)=\sqrt[]{x-3}+2 \end{gathered}[/tex]Triangle Inequality TheoremDetermine if a triangle can be formed with the given lengths. If so, classify the triangle by its angle.YESorNO
Given:-
[tex]7,20,12[/tex]To find:-
Wheather the given sides form a valid triangle.
So now let,
[tex]A=7,B=20,C=12[/tex]To check we use the condition,
[tex]A+B>C,B+C>A,C+A>B[/tex]Substituting the values we get,
[tex]7+20>12,20+12>7,12+7>20[/tex]In the above condition 12+7>20 is wrong.
So the condition fails and the given sides doesnt form a triangle.
i need help, im confused
Answer:
2
Step-by-step explanation:
Find R on line segment NM that is 1/4 the distance from N(-3,-3) toM(2, 3).R(x, y) =
The distance on the x-coordinate from N to M is:
distance = 2 - (-3) = 2 + 3 = 5
Because 2 is the x-coordinate of M and -3 is the x-coordinate of N
Then, 1/4 of the distance is:
1/4*distance = (1/4)*5 = 5/4 = 1.25
So, the x-coordinate of R is:
(x-coordinate of N) + (1/4*distance) = -3 + 1.25 = -7/4 = -1.75
At the same way, the distance on the y-coordinae from N to M is:
distance = 3 - (-3) = 3 + 3 = 6
Then, 1/4 of the distance is:
1/4*distance = (1/4)*6 = 6/4 = 1.5
So, the y-coordinate of R is:
(y-coordinate of N) + (1/4*distance) = -3 + 1.5 = -1.5
Answer: R(x, y) = (-1.75, -1.5)
Miles east of 100 80 60 40 20 1 2 3 4 5 6 7 8 9 10 Time (hours) Where were the two cars in relation to each other when they began traveling? O A. Car B was 5 miles east of car A. O B. Car B was 20 miles east of car A. O C. Car Awas 15 miles east of car B. D. Car A was 5 miles east of car B. < PREVIOUS
Car B was 5 miles east of car A, Option A
Part A. 150% of what number is 156 Part B. 4.4 is 5.5% of what number
EXPLANATION
Since 150% represents a percentage bigger than 156, the appropiate relationship would be as follows:
[tex]Part\text{=}\frac{\text{Percentage}}{100}\cdot\text{Whole}[/tex]Where the whole number is 156 and the percentage is 150%:
[tex]\text{Part}=\frac{150}{100}\cdot156[/tex][tex]\text{Part}=1.5\cdot156=234[/tex]In conclusion, the solution is 234
Solve the inequalities|4x + 5| + 2 > 10
We have to solve this inequality:
[tex]\begin{gathered} |4x+5|+2>10 \\ |4x+5|>10-2 \\ |4x+5|>8 \end{gathered}[/tex]We now use the properties of the absolute value. We will have two boundaries: one corresponding to when 4x+5 is negative and the other is when 4x+5 is positive.
When 4x+5 is negative, the absolute value function will change the sign of the expression, so we will have:
[tex]\begin{gathered} -(4x+5)>8 \\ -4x-5>8 \\ -4x>8+5 \\ -4x>13 \\ x<\frac{13}{-4} \\ x<-3.25 \end{gathered}[/tex]The other interval will be defined when 4x+5 is positive. In this case, the absolute function does not change the sign and we get:
[tex]\begin{gathered} 4x+5>8 \\ 4x>8-5 \\ 4x>3 \\ x>\frac{3}{4} \\ x>0.75 \end{gathered}[/tex]Then, the solution set is the union of the intervals x < -3.25 and x > 0.75.
We can express the interval as (-∞, -3.25) ∪ (0.75, ∞).
Answer: (-∞, -3.25) ∪ (0.75, ∞)
3: Select the correct equation for the given situation. Then, select the solution for that equation. Two research submarines start to rise vertically toward the ocean surface. The Tri-I sub is at 4,863 feet below sea level (or -4,863 feet) and is ascending 81.1 feet per minute. The Quad-II sub is at 3,645 feet below sea level (or -3,645 feet) and is ascending 76.9 feet per minute. If the ocean surface is at 0 feet, how many minutes (m) must elapse for the two submarines to reach the same depth? m = 290 minutes m = 145 minutes m = 53.8 minutes 4,863 - 76.9m = 3,645 - 81.1m O -4,863 + 81.1m = - 3,645 + 76.9m 0 - 4, 863 + 76.9m = -3, 645 + 81.1m – 4, 863 – 81.2m 2 – 3, 645 + 76.9m Om < 53.8 minutes
Unknown, the correct equation is:
- 4,863 + 81.1m = - 3,645 + 76.9m
And to solve for m, you use the standard form:
Like terms:
81.1m - 76.9m = -3,645 + 4,863
4.2m = 1,218
Answer:Nuts
Step-by-step explanation:
green on green
пеу Fabric Sale At a fabric store, fabrics are sold by the yard. A dressmaker spent $46 on 5 yards of silk and cotton fabrics for a dress. 1 x + y = 5 117x + 4y = 46) Silk is $17 per yard and cotton is $4 per yard. Here is a system of equations that represent the constraints in the situation. What does the solution to the system represent?
It is said that the dressmaker bought 5 yards of cotton and silk. Let's see the first equation of the system:
[tex]x+y=5[/tex]And that he spent $46 on those 5 yards. Also, it is said that silk costs $17 per yard and cotton $4 per yard. Let's see the second equation of the system:
[tex]17x+4y=46[/tex]If 46 is how much the dressmaker spent, and 17 and 4 represent how much silk and cotton cost PER YARD then we know that x and y represent how much of each fabric did the dressmaker bought. Also, in the first equation you see that the total is 5 yards. So, if you solve this system you will find that 'x' is how many yards of silk the dressmaker bought and 'y' is how many yards of cotton he bought.
In summary, the solution of this system represents how may yards of silk (x) and cotton (y) the dressmaker bought.
If cos A = 3/√13 and angle A is not in quadrant I, determine the exact value of sin A.
To determine the exact value of sin A we get -2/√13
What is determinant?
the determinant is a scalar of value that is a function of to the entries of a square matrix. It is allows characterizing of some properties of to the matrix and the linear map of represented by the matrix.
It is a scalar value which is associated with the square matrix.
Sol-Cos A =3/√13
angle A is not in quadrant I
So angle A is in quadrant IV
Thus,
Sin A =-√(√13)^2-3^2/√13
=-√13-9/√13
=-√4/√13
=-2/√13
Thus the answer is -2/√13.
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riangle QRS has vertices Q(8, −4), R(−1, 2), and S(3, 7). What are the coordinates of vertex Q after the triangle is reflected across the y-axiriangle QRS has vertices Q(8, −4), R(−1, 2), and S(3, 7). What are the coordinates of vertex Q after the triangle is reflected across the y-axi
simplify 3^5×3^4.a. 3×20b. 3^9c. 6^9d. 3^20I think its b but I am unsure.
Recalling the laws of exponents:
[tex]a^m\cdot a^n=a^{m+n}[/tex]So, for the number 3^5 times 3^4, we have:
[tex]3^5\cdot3^4=3^{5+4}=3^9[/tex]Therefore, the answer is the option b) 3^9.
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS!!!!!!!!
Answer:
Option 2
Step-by-step explanation:
hope this helps
The formula k=5/9(f-32)+273.15 converts temperature of the object in a laboratory is cooled to 1.5 kelvin. What is the temperature of the object in degrees fahrenheit?
The temperature of the object is -456.97 degrees
What is the average rate of change from f(-1) to f(1)?Type the numerical value for your answer as a whole number, decimal or fractionMake sure answers are completely simplified
The average rate of change of the function is the average rate at which one quantity is changing with respect to another.
Average rate of change = (y2 - y1)/(x2 - x1)
y represents the output values and it is also called f(x)
x represents the input values
For the given interval,
for f(- 1), x = -1 and f(x) = 8
For f(1), x = 1, f(x) = 4
Average rate of change = (4 - 8)/1 - - 1) = - 4/(1 + 1) = - 4/2
Average rate of change = - 2
Find the Value of interval [0,2pie] such as that tan s= -radical3/3
The values of s in the interval [0, 2π) such that tan s = -(√3)/3 are 5π/6 and 11π/6.
What is trigonometry and how is it assessed?
Simply put, trigonometric functions—also referred to as circular functions: are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions. Numerous trigonometric identities and formulas indicate the relationship between the functions and aid in determining the triangle's angles.
The quadrants determine the values of the trigonometric functions.
Given, tan s = -(√3)/3 ⇒ tan s = -(√3)/(√3)² ⇒ tan s = (-1)/(√3)
Therefore, the simplified value of tangent of s is tan s = (-1)/(√3)
Again the interval of the function is [0, 2π), so only the second and fourth quadrants can contain the given value of tangent being negative.
For the value of s in second quadrant, we have:
tan s = (-1)/(√3) ⇒ tan s = tan (π - (π/6)) ⇒ tan s = tan (5π/6) ⇒ s = 5π/6
For the value of s in the fourth quadrant, we have:
tan s = (-1)/(√3) ⇒ tan s = tan (2π - (π/6)) ⇒ tan s = tan (11π/6) ⇒ s = 11π/6
Thus, the values of s in the interval [0, 2π) such that tan s = -(√3)/3 are 5π/6 and 11π/6.
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Evalue each expression for the given value(s) of the variable(s)exponents
Any number raised to the power of zero equals 1, then
[tex]r^0s^{-2}=1\cdot s^{-2}=s^{-2}[/tex]then, we need to substitute the value 10 in the variable s. It yields,
[tex]s^{-2}=\frac{1}{s^2}\Rightarrow\frac{1}{10^2}=\frac{1}{100}[/tex]Then, the answer is
[tex]r^0s^{-2}=\frac{1}{s^2}\Rightarrow\frac{1}{100}[/tex]that is, 1 / 100.
Please help me don't understand
Answer:
x=13
Step-by-step explanation:
50+3x=89
89-50=3x
39=3x
13=x
Find the measure of the arc or central angle indicated. Assume that lines which appear to bediameters are actual diameters.
From the given circle, the measure of the arc or the central angle indicated is as shown at the center of the circle is subtended by the arc
Hence, the measure of the arc or central angle indicated is 65° ,Option B
Which is the upper left quadrant on the coordinate plane?A coordinate plane.Quadrant IQuadrant IIQuadrant IIIQuadrant IV
The quadrants on the coordinate plane are the following:
then, we have that the upper left quadrant is quadrant II
10) f(x) = x5 - 10x4 + 42x3 -124 x2 + 297x - 306; zero: 3i ? A) 2, -3i, -4 - i, -4 + i C) 2, -3i, 4 - i, 4 + i B) -2, -3i, -4 -i, -4 + i D) -2, -3i, 4-i, 4 + i
Answer
Option C is correct.
The roots of the given function include
2, -3i, (4 + i), (4 - i)
Explanation
To solve this, we would put the given roots of the solution into the place of x. The ones that give 0 are the roots of the expression
The expression is
f(x) = x⁵ - 10x⁴ + 42x³ - 124x² + 297x - 306
Starting with 2
f(x) = x⁵ - 10x⁴ + 42x³ - 124x² + 297x - 306
f(2) = 2⁵ - 10(2)⁴ + 42(2)³ - 124(2)² + 297(2) - 306
= 32 - 160 + 336 - 496 + 594 - 306
= 0
So, 2 is a root
-3i
f(x) = x⁵ - 10x⁴ + 42x³ - 124x² + 297x - 306
f(-3i) = (-3i)⁵ - 10(-3i)⁴ + 42(-3i)³ - 124(-3i)² + 297(-3i) - 306
= -243i - 810 + 1134i - 1116 - 891i - 306
= 0
So, -3i is also a root
4 + i
f(x) = x⁵ - 10x⁴ + 42x³ - 124x² + 297x - 306
f(4 + i) = (4 + i)⁵ - 10(4 + i)⁴ + 42(4 + i)³ - 124(4 + i)² + 297(4 + i) - 306
= 0
So, we know that the right root, when inserted and expanded will reduce the expression to 0.
4 - i
f(x) = x⁵ - 10x⁴ + 42x³ - 124x² + 297x - 306
f(4 - i) = (4 - i)⁵ - 10(4 - i)⁴ + 42(4 - i)³ - 124(4 - i)² + 297(4 - i) - 306
= 0
Inserting any of the other answers will result in answers other than 0 and show that they aren't roots/zeros for this expression.
Hope this Helps!!!
So ABC and DEF are the same triangle, this question is asking me to write an equation between the relationships of DEF. How do I write that?
Explanation
The first step is to draw a representation of the given parameters.
Since this is a right-angle triangle, the Pythagorean theorem applies. This can be seen below;
[tex]\text{Longest Leg}^2=sum\text{ of the square of the short legs}[/tex]We can then apply it to the sides of the triangle.
DF is the longest side. Therefore,
Answer
[tex]DF^2=DE^2+EF^2[/tex]12.Work backwards to write a quadratic equation that will have solutions of x = -1/2 and x = 4. (Your equation must only have integer coefficients, meaning no fractions or decimals.)
In general, a quadratic equation can be written in terms of its solutions:
[tex]y=(x-a)(x-b).[/tex]Now, notice that:
[tex]x+\frac{1}{2}=0\text{ }[/tex]when x= -1/2, and it is equivalent to:
[tex]2x+1=0.[/tex]Therefore, you can write the quadratic equation as:
[tex]y=(2x+1)(x-4).[/tex]Computing the above multiplication, you get:
[tex]y=2x^2-8x+x-4.[/tex]Simplifying the above equation you get:
[tex]y=2x^2-7x-4.[/tex]Answer: [tex]y=2x^{2}-7x-4[/tex]You need 30 ounces of chocolate chips to bake some cooldes. You already have 8 ounces of chocolate chips at home. Write an inequality that could beused to find how many ounces of chocolate chips you need to buy.whats the inequality:
Given:
Amount of chocolate chips needed = 30 ounces
Amount of chocolate you have already = 8 ounces
Let's find the inequality that can be used to find the ounces of chocolate chips you need to buy.
To write the inequality, we have:
8 + x ≥ 30
Where x represents the ounces of chocolate chips you need to buy.
Therefore, the inequality that could be used to fid how many ounces of chocolate chips needed is:
8 + x ≥ 30
ANSWER:
8 + x ≥ 30
Write an exponential expression: Let 10 be the base and an even number between 1 and 10 be the exponent.
Then write the exponential expression in expanded form and standard form.
The exponential expression as required to be chosen is; 10⁴.
The expanded form of the expression is; 10 × 10 × 10 × 10.
The standard form of the expression is; 10,000.
Exponential expressions in expanded form and Standard form.It follows from the task content that the exponential expression is to be written in expanded and standard form.
Since the exponential expression must have 10 as the base and an even number between 1 and 10 as the exponent.
An example of such exponential expression is therefore;
10⁴.
Hence, to write the expression in expanded form; it is written as a product of factors as follows;
10 × 10 × 10 × 10
Also, the expression can be written in standard form as the result of the multiplication above;
= 10,000.
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Classify each set of measures as AAS, ASA, SSA, SAS, or SSS. Then find the indicated length or angle measure (to the nearest tenth).
Hello there. To solve this question, we'll have to remember some properties about triangles.
Given the triangle:
Notice in this case we have two consecutive angles and a side between them. This is a case of ASA (angle-side-angle).
With respect to the side with measure x, we have two consecutive angles then the side, hence AAS.
To find x, we'll have to apply the law of sines:
[tex]\dfrac{A}{\sin(\alpha)}=\dfrac{B}{\sin(\beta)}=\dfrac{C}{\sin(\gamma)}=2R[/tex]In this case, the angle opposite to x measures 73º and the angle opposite to 4 measures 85º, hence:
[tex]\dfrac{x}{\sin(73^{\circ})}=\dfrac{4}{\sin(85^{\circ})}[/tex]Multiply both sides by a factor of sin(73º)
[tex]x=\dfrac{4\sin(73^{\circ})}{\sin(85^{\circ})}[/tex]Using a calculator, we get the following approximation (rounding to the nearest tenth):
[tex]x\approx3.8[/tex]This is the measure of x we're looking for.
A person standing 306 feet from the base of a church observed the angle of elevation to the church’s steeple to be 20°. How tall is the church. Give answer to the nearest whole number
Solution
- The solution steps are given below:
[tex]\begin{gathered} \text{ Applying SOHCAHTOA, we have:} \\ \frac{h}{306}=\tan20 \\ h=306\tan20 \\ \\ h=111.374...ft\approx111ft\text{ \lparen To the nearest whole number\rparen} \end{gathered}[/tex]Final Answer
111 ft
Find the mzEFH, given that mzEFG = 50°. F E G . I
By theorem, we will have that m
m
=> m
=>2m
Then, we replace values and solve:
2m m
So, we have that m
ratio problems that I am struggling with
7 out of every 500 Americans are aged 13-17 years generation are vegetarian
Thus the ratio of the vegetarian is 7 : 500
In a group of 350,
Let x be the number of people who are vegetarian
So, the ratio out of 350 who are vegetarian are : x : 350
SInce the ratio is same so:
[tex]\begin{gathered} 7\text{ : 500=x:250} \\ \frac{7}{500}=\frac{x}{250} \\ \text{ Simplify for x,} \\ x=\frac{7}{500}\times250 \\ x=\frac{7}{2} \\ x=3.5 \\ x\approx4 \end{gathered}[/tex]So, the number of people who are vegetarian out of 350 people is 4 people
A genetic experiment with
peas resulted in one sample of offspring that consisted of 447 green peas and 169 yellow peas.
a. Construct a 90% confidence interval to estimate of the percentage of yellow peas.
b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow?
a. Construct a 90% confidence interval. Express the percentages in decimal form.
L s p< (Round to three decimal places as needed.)
b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow?
O
No, the confidence interval includes 0.25, so the true percentage could easily equal 25%
L
O Yes, the confidence interval does not include 0.25, SO the true percentage could not equal 25%
Using the z-distribution, it is found that:
a. The 90% confidence interval to estimate of the percentage of yellow peas is: (34.04%, 41.58%).
b. The correct option is: Yes, the confidence interval does not include 0.25, so the true percentage could not equal 25%.
What is a confidence interval of proportions?The bounds of a confidence interval of proportions is given according to the equation presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the parameters are described as follows:
[tex]\pi[/tex] is the sample proportion.z is the critical value of the distribution.n is the sample size, from which the estimate was builtThe confidence level is of 90%, hence the critical value is z = 1.645, using a z-distribution calculator.
The values of the sample size and of the estimate are given as follows:
[tex]n = 447, \pi = \frac{169}{447} = 0.3781[/tex]
Hence the lower bound of the interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3781 - 1.645\sqrt{\frac{0.3781(0.6219)}{447}} = 0.3404[/tex]
The upper bound is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3781 + 1.645\sqrt{\frac{0.3781(0.6219)}{447}} = 0.4158[/tex]
As a percentage, the interval is given as follows: (34.04%, 41.58%).
The confidence interval does not contain 0.25, hence the true percentage would not be equal to 25%, contradicting the expectation.
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