Answers
Answer:
x = 2
Step-by-step explanation:
(x² logₓ27) log₉x = x + 4
Use change of base formula.
x² (log 27 / log x) (log x / log 9) = x + 4
Simplify.
x² (log 27 / log 9) = x + 4
x² (log 3³ / log 3²) = x + 4
x² (3 log 3 / (2 log 3)) = x + 4
x² (3 / 2) = x + 4
3x² = 2x + 8
3x² − 2x − 8 = 0
(x − 2) (3x + 4) = 0
x = 2 or -4/3
Since x > 0, x = 2.
Related Questions
Which of the following sets of points are vertices of a right triangle?
1) A(-1, -3), B(4, -3), C(2, -1)
2) A(-2, 2), B(1, -4), C(4, 2)
3) A(-1, 1), B(3, 5), C(4, -4)
4) A(-1, 3), B(-4, -3), C(-4, 1)
Answers
I scanned for a pair of x coordinates that match and a pair of y coordinates that match. That would be a right triangle whose sides are parallel to the axes. It's possible our right triangle is more complicated, but let's start here.
Nope, it doesn't look like our right triangle is oriented to the axes. Let's do the Pythagorean Theorem.
1) A(-1, -3), B(4, -3), C(2, -1)
AB² = (4 - -1)² + (-3 - -3)² = 25
AC²= (2 - -1)² + (-1 - -3)² = 9 + 4 = 13
BC²= (2 - 4)² + (-1 - -3)² = 4 + 4 = 8
25 ≠ 13 + 8, not a right triangle
2) A(-2, 2), B(1, -4), C(4, 2)
AB² = (-2 - 1)² + (-4 - 2)² = 9 + 36 = 45
AC²= (4 - -2)² + (2 - 2)² = 36
BC²= (4 - 1)² + (2 - -4)² = 9 + 36 = 45
not a right triangle, but isosceles
3) A(-1, 1), B(3, 5), C(4, -4)
AB² = 4² + 4² = 32
AC²= 5² + 5² = 50
BC²= 1² + 9² = 82
BC² = AC² + AB², THIS IS A RIGHT TRIANGLE
4) A(-1, 3), B(-4, -3), C(-4, 1)
AB² = 3² + 6² = 45
AC²= 3² + 2² = 13
BC²= 0² + 4² = 16
not a right triangle
Answer: 3) A(-1, 1), B(3, 5), C(4, -4)
please help i give ponts
Answers
Answer:
x+5+2/x+2
Step-by-step explanation:
Using polynomial division you can simplify the expression to find the above numerical answer
Answer:
x+5+2/x+2
Step-by-step explanation:
How many times greater is the value of the 4 in 42,672 than the value of the 4 in
37,426?
Answers
Answer:
Step-by-step explanation:
Value of 4 in 42,672 = 40,000
Value of 4 in 37,426 = 400
40,000 ÷ 400 =100
Value of 4 in 42,672 is 100 times greater than value of 4 in 37,426
Kim works at an ice-cream store. She wants to calculate how much ice-cream one cone can hold. If the cone is 6 inches tall and the circular opening at the top is 2.5 inches across, how much can the cone hold? Round to the nearest tenth at the end.
Answers
Answer:
The cone holds 9.8 cubic inches ice cream
Step-by-step explanation:
Height of cone = 6 inches
The circular opening at the top is 2.5 inches across
Diameter of cone = 2.5 inches
Radius of cone = [tex]\frac{2.5}{2}=1.25[/tex]
Volume of cone = [tex]\frac{1}{3} \pi r^2 h[/tex]
Volume of cone = [tex]\frac{1}{3} \times 3.14 \times 1.25^2 \times 6[/tex]
Volume of cone = [tex]9.8125 in^3[/tex]
Hence the cone holds 9.8 cubic inches ice cream.
A 2-year loan of $500 is made with 4% simple interest. Find the interest earned. Please state the answer with a dollar sign followed by a whole number. Example: $32
Answers
Answer:
$10
Step-by-step explanation:
4% of 500 is 5 dollars and two years is 10
I Used the equation I=Prt
Find the value of x and the value of y.
Answers
Answer:
B.
Step-by-step explanation:
If you extend the middle line, you will find that the two angles that the line makes are 60° and 40° by alternate interior angles.
Then, you can just make an equation:
2x + 2x - y + y + 60 + 40 = 360
4x = 260
x = 65°
Now you can use same side interior angles to make another equation:
2x - y + 60 = 180
130 + 60 - y = 180
y = 10
PLEASE HELP, ILL GIVE BRAINLIEST.
URGENT.
Answers
Answer:
y=1/2x+0
Step-by-step explanation:
slope is 1/2
y=1/2x+b
plug in (0,0)
b=0
y=1/2x+0
Answer:
Equation: y=1/2x
Step-by-step explanation:
The equation's formula is: y=mx+b
m is slope b is y-intercept
Please mark brainliest! Hope this helps :)
Please help! Choose all that apply.
Answers
Answer:
I believe that the answers are B & C
Step-by-step explanation:
Hope this helps! Please pick me as brainliest!
need help quick plz
Answers
this is the other part! please help!
Answers
Answer:
Line B
Step-by-step explanation:
Line b is the the correct answer because the line has the most dots near or on it
Create a list of steps, in order, that will solve the following equation.
3(x+2)^2=48
Answers
Answer:
Start with the given equation.
%28x-2%29%5E2=%2848%29%2F%283%29 Divide both sides by 3.
%28x-2%29%5E2=16 Reduce.
x-2=%22%22%2B-sqrt%2816%29 Take the square root of both sides.
x-2=sqrt%2816%29 or x-2=-sqrt%2816%29 Break up the "plus/minus" to form two equations.
x-2=4 or x-2=-4 Take the square root of 16 to get 4.
x=2%2B4 or x=2-4 Add 2 to both sides.
x=6 or x=-2 Combine like terms.
Step-by-step explanation:
Steps: Divide both sides by 3
- Then take square root of both sides
- Separate the equation like this:
x+2= -4
x+2= 4
- Solve for x:
To get -6 subtract -4 and 2
To get 2 subtract 4 and 2
x= -6
x= 2
Data was collected on the weight of a male laboratory rat for the first 25 weeks
after its birth. The linear regression equation is y= 40x+100, where x is number of
weeks and y is weight in grams.
What does the y-intercept mean in context of the problem?
The predicted weight of the rat in year 0.
The current weight of the rat.
The predicted weight of the rat at birth
The average increase in the rat's weight
Answers
Answer:
[tex] y = 40x +100[/tex]
where x is number of weeks and y is weight in grams.
For this case the y intercept is the value 100 and represent the initial weight for 0 weeks and the best interpretation for this case is given by:
The predicted weight of the rat at birth
And the reason is because the starting value for the weigth represent the weight for the birth
Step-by-step explanation:
For this case we have the following equation given:
[tex] y = 40x +100[/tex]
where x is number of weeks and y is weight in grams.
For this case the y intercept is the value 100 and represent the initial weight for 0 weeks and the best interpretation for this case is given by:
The predicted weight of the rat at birth
And the reason is because the starting value for the weigth represent the weight for the birth
how many twentieths equal three-fifths
Answers
Answer:
12
Step-by-step explanation:
It takes twelve 1/20 tiles to exactly cover three 1/5 tiles, so 35=12/20.
The number of twentieths required to make three fifths is required.
Twelve twentieths equal to three-fifths
The question can be rephrased as "How many times do you have to add [tex]\dfrac{1}{20}[/tex] to get [tex]\dfrac{3}{5}[/tex]"
The end result should be [tex]\dfrac{3}{5}[/tex]
Let the number of times be [tex]x[/tex]
[tex]x\times \dfrac{1}{20}=\dfrac{3}{5}\\\Rightarrow x=\dfrac{3}{5}\times 20\\\Rightarrow x=12[/tex]
So, twelve twentieths equal to three-fifths.
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What is the value of tan(60°)?
А
O
300
N
V3
B
60°
3
2
6
C
Answers
Answer:
The exact value of tan(60°) is √(3).
Step-by-step explanation:
The value of the trigonometric relation tan ( 60 )° = √3
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the trigonometric relation be represented as A
Now , the value of A is
A = tan ( 60 )°
And , from the trigonometric identities , we get
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
So , the measure of tan ( 60 )° = √3
Hence , the trigonometric relation is solved
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Which best describes the relationship between the
125° angle and angle A?
They are same side interior angles. Angle A
measures 55°
O They are alternate interior angles. Angle A
measures 125°
O They are vertical angles. Angle A measures 125º.
They are corresponding angles. Angle A measures
55°
Answers
Answer:
A. They are same side interior angles. Angle A measures 55°.
Step-by-step explanation:
Got it right on Egd.
Option A.) is correct. They are same side interior angles. Angle A measures 55°.
What is angle?The angle can be defined as the one line inclined over other line.
questions seem to be in incomplete, Although question could be
what would be sum of the interior angles of a quadrilateral.
The sum of the interior angle = 180
A = 180-125
A = 55°
Thus, the required Angle A measures is 55°.
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I really need help and I would greatly appreciate it
Answers
Answer:
a. 15.783/19 × 100% = 15.78
b. 7
12-5 = 7
To find the range, first order the data from least to greatest. Then subtract the smallest value from the largest value in the set.
c. 8
because 8 divides the age group making half the people younger than this age and half are older
2 . a - highest point is 8.7
c . georgina did better then half of the other gymnists which can be seen because the highest point is 8.7 where there are many who 7.7
mark brainliest pls
What is the converse of the following statement ?
If two triangles are congruent, then their corresponding angles are congruent.
Answers
Answer: C
Step-by-step explanation: Converse means the reversed statement
3. If two triangles are not congruent, then their corresponding angles are not congruent. the converse of the following statement is option C.
What is the congruent triangle?Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.
Given statement:
"If two triangles are congruent, then their corresponding angles are congruent."
1. If the corresponding angles of two triangles are congruent, then the triangles are congruent.
This is not the converse of the following statement.
2. If two triangles are congruent, then their corresponding angles are congruent.
This is not the converse of the following statement.
3. If two triangles are not congruent, then their corresponding angles are not congruent.
This is the converse of the following statement.
4. If the corresponding angles of two triangles are not congruent, then the triangles are not congruent This is not the converse of the following statement.
Thus, the converse of the following statement is option C.
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5x+4y= 10
–5x+y = 15
Answers
Answer:
what exactly are we trying to solve for
what is the answer to:
16^3/2
Answers
In my view the answer is 2,048
I am not sure about this answer..so if it is mistake then sorry
Answer:
[tex]16^\frac{3}{2} = 64[/tex]
Step-by-step explanation:
[tex]16^\frac{3}{2}[/tex]
Factor the number: [tex]16 = 4^2[/tex]
[tex]= (4^2)^{\frac{3}{2} }[/tex]
Apply exponent rule: [tex](a^b)^c=a^b^c[/tex]
[tex]\left(4^2\right)^{\frac{3}{2}}=4^{2\cdot \frac{3}{2}}=4^3[/tex]
[tex]= 4^3[/tex]
Refine:
[tex]=64[/tex]
Hope I helped, may I get brainliest and a thanks?
Thank you, have a good day! =)
An owner of a restraint wants to conduct a survey about possible menu changes. Give an example of a sampling method that would produce a valid sample.
Answers
Do you mean restaraunt?
Every 10th customer Every 15th customerSomething like that. I hope this helps.
Expand and simplify (x + 5) ( x + 6)
Answers
Answer:
x^2 + 11x + 30
Step-by-step explanation:
In the diagram of circle A, what is the measure of ZXYZ?
35
70°
75
140
Answers
The solution is, the value is 35 degrees, is the measure of ZXYZ.
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
here, we have,
from the given diagram, we get,
Using the intersecting secant theorem:
Angle xyz = 1/2( wz- XX)
Xyz = 1/2(175-105)
Xyz = 1/2(70)
Xyz= 35
The solution is, the value is 35 degrees, is the measure of ZXYZ.
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Pls help me on this question !
Answers
2/5 of it is 22.\
I need help PLS
Answers
Answer
55
Step-by-step explanation:
2
5
(22)
=(
2
5
)(
22
1
)
=
(2)(22)
(5)(1)
=
44
5
(Decimal: 8.8)
which will give 55
PLease mark brainllest!!!!!!!
Answer:
2 divided by 5 = 0.4
22/0.4=220/4=55
55 is the number. Hope this helps.
Step-by-step explanation:
What is the exponential form of log4 16 = 2?
Answers
Explenation:
Logarithm
log
b
x
is the exponent of a power with base
b
which gives the number under
log
sign (
x
).
In this example we can say that:
log
4
16
=
2
because:
4
2
=
16
Step-by-step explanation:
The radius of a circle is 12.1 in. Find the circumference \textit{to the nearest tenth}to the nearest tenth.
Answers
Answer:
76.03
Step-by-step explanation:
Answer:
the circumference is 76.027 but it rounded to the nearest tenth is 76.030
Step-by-step explanation:
Graph: y = 12 - 41 + 2
Answers
Step-by-step explanation:
y=-27
...................
Given a cone 10 feet tall with a diameter of 10 feet, determine the radius of the smaller cone created when a horizontal plane passes through the cone at exactly 4 feet from the base.
Answers
Answer:
r=3 ft
Step-by-step explanation:
it is similarity of two triangles
one
perpendicular side=10 ft
base=10/2=5 ft
second
perpendicular side=10-4=6 ft
Base r=?
[tex]\frac{r}{5}=\frac{6}{10}\\r= \frac{6}{10} \times 5=3~ft[/tex]
HELP PLEASE
The volume of this cone is 376.8 cubic feet. What is the radius of this cone? Height is 10ft
Use ≈ 3.14 and round your answer to the nearest hundredth
Answers
Answer:
6.08 ft
Step-by-step explanation:
Volume of cone = [tex]\frac{1}{3}[/tex][tex]\pi[/tex]r²h
Radius = [tex]\sqrt{ \frac{V}{\frac{1}{3}\pi h } }[/tex]
[tex]R = \sqrt{\frac{376.8}{\frac{1}{3} \pi 10} }[/tex]
[tex]R = \sqrt{\frac{376.8}{10.47} }[/tex]
[tex]R = \sqrt{36.98}[/tex]
[tex]R = 6.08[/tex]
Two triangular faces of a rectangular pyramid each have an area of 7.8 cm2 and the other two faces each have an area of 16.5 cm2. If the area of the base is 60 cm2, what is the total surface area of the pyramid? 84.3 cm2 108.6 cm2 157.2 cm2 168.6 cm2
Answers
The total surface area of the rectangular pyramid is the sum of the whole area. Therefore, the total surface area is 108. 6cm²
How to find the surface area of a pyramid?
The surface area of the rectangular pyramid is the sum of the whole areas.
The total surface area is the sum of the whole area.
A rectangular pyramid has 4 triangular faces and a rectangular base.
Therefore,
total surface area = 7.8 cm² + 7.8 cm² + 16.5 cm² + 16.5 cm² + 60 cm²
total surface area = 108.6 cm²
Therefore, the total surface area of the rectangular prism is 108. 6cm²
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