Answer:
Step-by-step explanation:
When the base of a logarithm is not specified, it is assumed that the base is 10. Therefore we have:
[tex]log_1_0(x^2-15)=log_1_0(2x)[/tex]
Intuitively you can see that if the two arguments inside of the logarithm equal each other, then both sides will be equal to each other. Therefore, you can say the following requirement:
[tex]x^2-15=2x[/tex]
Subtract 2x on both sides to get:
[tex]x^2-2x-15=0[/tex]
Use the quadratic formula to solve for 'x' to get:
[tex]x=(-b+\sqrt{b^2-4ac} )/2a[/tex]
[tex]x=(-b-\sqrt{b^2-4ac} )/2a[/tex]
Beginning with the first solution:
[tex]x=(-(-2)+\sqrt{(-2)^2-4(1)(-15)} )/2(1)[/tex]
[tex]x=2+\sqrt{4+60} )/2[/tex]
[tex]x=(2+\sqrt{64}) /2[/tex]
[tex]x=(2+8)/2[/tex]
[tex]x=5[/tex]
Second solution:
[tex]x=(-(-2)-\sqrt{(-2)^2-4(1)(-15)} )/2(1)[/tex]
[tex]x=(2-\sqrt{4+60} )/2[/tex]
[tex]x=(2-8)/2[/tex]
[tex]x=-6/2[/tex]
[tex]x=-3[/tex]
Since the 'x' value inside of the logarith is squared, the -3 is a valid solution. Ordinarily, the log function cannot take on negative values.
Pls help asap I need step by step pls I’ll give brainliest
Answer:
it would be 12
Step-by-step explanation:
Answer:
area = 100 inches^2
Step-by-step explanation:
width = x
length = 4x
x + x + 4x + 4x = 50
10x = 50
x = 5
width = 5
length = 4 × 5 = 20
area = length x width
= 20 x 5 = 100
On a coordinate plane, line M N goes through points (2, 3) and (negative 3, 2). Point K is at (3, negative 3).
Which point could be on the line that is perpendicular to Line M N and passes through point K?
(0, −12)
(2, 2)
(4, 8)
(5, 13)
Answer:
suitable is (4, 8)
Step-by-step explanation:
slope of MN (y2-y1)/(x2-x1) = (2-3)/(-3-2)= -1/-5 = 1/5
line MN and line K is perpendicular
(1/5)*(m2) = -1
slope of k which is m2 is -5
slope of K (y2-y1)/(x2-x1)= 5
slope of MN (-3-y1)/(3-x1)=5
suitable is (4, 8)
Answer:
2,2 is correct
Step-by-step explanation:
#36
You look up at a drone at an angle of elevation of 23º. Your eyes are 5 feet above the ground, and the distance to
the drone is 210 feet. What is the altitude of the drone? Round your answer to the nnearest tenth.
Altitude: about ___
feet
Using the slope concept, it is found that the height of the drone is of about 94 feet.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
In this problem:
The vertical change is of h - 5, in which h is the altitude of the drone.The horizontal change is of 210 ft.The angle is of 23º.Hence:
[tex]\tan{23^\circ} = \frac{h - 5}{210}[/tex]
[tex]h - 5 = 89[/tex]
[tex]h = 94[/tex]
The height of the drone is of about 94 feet.
More can be learned about the slope concept at https://brainly.com/question/18090623
A mortgage has an initial balance of $150,000 and is charged 5% yearly interest applied monthly. If a person makes a payment of $1000 each month, which of the following is closest to the mortgage balance after 3 months of payments?
(1) $145,165
(2)$147,520
(3)$148,160
(4)$148,870
The first equation in the system models the height in feet, h, of a falling baseball as a function of time, t. the second equation models the height in feet, h, of the glove of a player leaping up to catch the ball as a function of time, t. which statement describes the situation modeled by this system? startlayout enlarged left-brace 1st row h = 35 minus 16 t squared 2nd row h = 6 18 t 16 t squared endlayout the height of the baseball is 18 feet at the moment the player begins to leap. the height of the baseball is 16 feet at the moment the player begins to leap. the height of the baseball is 35 feet at the moment the player begins to leap. the height of the baseball is 6 feet at the moment the player begins to leap.
The height of the baseball is 6 feet at the moment the player begins to leap. Then the correct option is D.
What is a function?The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
The first equation in the system models the height in feet, h, of a falling baseball as a function of time, t. the second equation models the height in feet, h, of the glove of a player leaping up to catch the ball as a function of time, t.
h(t) = 35 - 16t²
h(t) = 6 + 18t + 16t²
At t = 0, Then we have
h(0) = 35 - 16(0)²
h(0) = 35
And
h(0) = 6 + 18(0) + 16(0)²
h(0) = 6
The height of the baseball is 6 feet at the moment the player begins to leap.
More about the function link is given below.
https://brainly.com/question/5245372
Answer:
option 2 or B
Step-by-step explanation:
3/16 x 6 in the simplest form
The fraction 9/8 is the simplest form of the given fraction.
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
The fraction is given in the question, as follows:
3/16 x 6
We have to determine the evaluation of the given fraction
As per the question, we have
3/16 x 6
Apply the multiplication operation,
18/16
Reduce the above fraction into the simplest form, and we get
9/8
Thus, the fraction 9/8 is the simplest form of the given fraction.
Learn more about the fraction here:
brainly.com/question/10354322
#SPJ2
really need help with this math makeup work pleasee
Answer:
A and D would be congruent
Step-by-step explanation:
COngruent angles are angles with the same measurements (same size angles).
Answer:
First Image: ∠G ≅ ∠B, ∠E ≅ ∠D Second Image: ∠1 = 140 ∠2 = 40
Step-by-step explanation:
∠G ≅ ∠B by Alternate exterior angles, ∠E ≅ ∠D by Alternate interior angles ∠1 = 140 by alternate exterior angles and ∠2 = 40 by supplementary angles 180 - 140 = 40
helpp!! Please I appreciate it
Answer:
x < -10
Step-by-step explanation:
Solve the inequality.
-2x + 4 > 24 Subtract 4 from both sides
-2x > 20 Divide both sides by -2
x < -10 We must flip the inequality sign because we divided by a negative number in the last step.
When you graph, draw a number line. Then, draw a circle on top of -10. Since x is less than -10, the arrow goes to the left of -10. Additionally, the circle on top of -10 will be an open circle because the inequality sign is a less than, not a less than or equal to.
I hope this helps and please mark me as brainliest!
Multiply the binomials (4x + 7) and (2x - 8).
es )
A)
8x2 +18x - 56
B)
8x2 - 18x - 56
8x2 - 46x + 56
D)
8x2 - 46x - 56
8x²-18x-56
Solve :
(4x + 7) (2x - 8)apply distributive method
(4x)(2x)+(4x)(-8)+7(2x)+7(-8)simplify the following
8x²-32x+14x-56final outcome
8x²-18x-56Answer:
B) [tex]8x^2-18x-56[/tex]
Step-by-step explanation:
Given expression:
[tex](4x + 7)(2x - 8)[/tex]
Apply the FOIL method: [tex](a+b)(c+d)=ac+ad+bc+bd[/tex]
[tex]\implies (4x \cdot 2x)+(4x \cdot -8)+(7 \cdot 2x) +(7 \cdot -8)[/tex]
[tex]\implies 8x^2-32x+14x-56[/tex]
Combine like terms:
[tex]\implies 8x^2-18x-56[/tex]
List one of the "modes" of the
test scores. (Mode means the
numbers that appear the most
often in a set.)
Test Scores: 100, 75, 40, 90,
80, 100, 92, 88, 80, 84, 81
Answer:
100 & 80
Step-by-step explanation:
100 appears twice...same with 80
10) 192
11) 58
12 120
Which I’m guessing they want the angle that has those ??
Answer:
10: Reflex
11. Acute
12. Obtuse
Step-by-step explanation:
Reflex: Greater than 180 but less than 360
Acute: Less than 90
Obtuse: Greater than 90 and less than 180
Answer:
I believe they want what it looks like, so i have gone ahead and drew those below: its not the best but i tried.
Step-by-step explanation:
how to i put [tex]y^{2} +20x+8y+156=0[/tex] into standard form
Answer:
y=−4+2√5(−x−7)
y=−4−2√5(−x−7)
Do 5.8 and 5.08 have the same value? In a full sentence, explain why or why not?
Answer: 5.8 is correct
Step-by-step explanation: because 5.8 is bigger
Factor 5x² + 8x – 4 using substitution.
Answer:
(
5
x
−
2
)
(
x
+
2
)
is the factorised form of the expression.
Explanation:
5
x
2
+
8
x
−
4
We can Split the Middle Term of this expression to factorise it.
In this technique, if we have to factorise an expression like
a
x
2
+
b
x
+
c
, we need to think of 2 numbers such that:
N
1
⋅
N
2
=
a
⋅
c
=
5
⋅
(
−
4
)
=
−
20
AND
N
1
+
N
2
=
b
=
8
After trying out a few numbers we get
N
1
=
10
and
N
2
=
−
2
10
⋅
(
−
2
)
=
−
20
, and
10
+
(
−
2
)
=
8
5
x
2
+
8
x
−
4
=
5
x
2
+
10
x
−
2
x
−
4
=
5
x
(
x
+
2
)
−
2
(
x
+
2
)
(
x
+
2
)
is a common factor to each of the terms
=
(
5
x
−
2
)
(
x
+
2
)
(
5
x
−
2
)
(
x
+
2
)
is the factorised form of the expression.
A mechanic works on the overhaul of a transmission. He starts at 8:25 AM and finishes
at 4:25 PM, and takes one hour off for lunch. At $18.75 per hour, find out how much the
mechanic earned to the nearest crent.
A line with a slope of 4 passes through (6,11). Complete the equation of this line in point-slope form.
Answer:
y – 11 = 4 (x-6)
Step-by-step explanation:
ttm
solve the pattern to y=-3(x+2)²+4.
Answer:
-8x
Step-by-step explanation:
[tex]-3(x+2)^{2}+4\\-3(2x)^{2}+4\\-12+4\\\ y=-8x[/tex]
Please answer the one you would like. I’m very bad at math :(
Answer:
The answer for question one is 162 cm
b) If you were to roll the dice 100 times, how often would you expect to get doubles?
If you're rolling a single cube, then ...
-- There are 6 possible out comes.
-- One of them (5) is a multiple of 5 .
-- The probability of rolling it is (1/6) = 16-2/3 % .
If everything is acting perfectly random, then ion 100 rolls,
you'd expect to succeed 16 or 17 times.
If you're rolling a pair of cubes, then ...
-- There are (6 x 6) = 36 possible outcomes.
-- There are seven ways to get a multiple of 5.
(1+4), (4+1), (2+3), (3+2), (4+6), (6+4), (5+5)
-- The probability of rolling one of those is
(7/36) = 19-4/9 % .
If everything is acting perfectly random, then in 100 rolls,
you'd expect to succeed 19 or 20 times.
Do number 5 please. Please bots don’t answer I’m just trying to get help!!!! :( please
Answer:
(a) 40 units
Step-by-step explanation:
32/16=2
20 times 2=40
Answer:
A
Step-by-step explanation:
Since square pyramids A and B are similar, they need to have similar lengths.
Pyramid B's lengths are 2 times larger than that of pyramid A.
Pyramid A: 16 units, 16 units, 20 units.
*2 *2 *2
Pyramid B: 32 units, 32 units, ? units
So, the missing side length has to be 20 *2 = 40 units.
Please mark as brainliest!
Please help me
True or false?
I accidentally answered it but
ignore it just please help
Answer:
Step-by-step explanation:
You are correct in saying false
well, the cheap answer is, linear expressions have one variable and some coefficient in front of it, like 3x or 2y + 3, or (1/4)x - 15 or such, however, a LINEar expression when drawn, yields a LINE, not a curve or such, and that only happens if the variable's exponent is 1, not more than 1, if the variable's exponent is higher, then is a curve of kinds,
so such expressions like -13xy, which has the product of two variables, or 7y³ - 2 or 4x⁵ + 9, are curvy lines.
Pls help me
What is the volume of this figure?
Enter your answer in the box.
Answer:
Step-by-step explanation:
Volume of the figure = Base area * height
Base area:
Base area = area of trpezium + area of triangle
Trapezium:
a, b area the length of parallel sides and h is the height of trapezium.
a = 8 m ; b = 5 m & h = 3 m
[tex]\boxed{ \text{ Area of trapezium = $\dfrac{(a +b)*h}{2} $}}[/tex]
[tex]=\dfrac{(8+5)*3}{2}\\\\\\=\dfrac{13*3}{2}\\\\\\= \dfrac{39}{2}\\\\\\= 19.5 \ m^{2}[/tex]
Triangle:
height = 4 m & base = 8 m
[tex]\boxed{\text{Area of triangle =$\dfrac{1}{2}*base*height$}}[/tex]
[tex]=\dfrac{1}{2}*8*4\\\\\\= 4*4\\\\= 16 \ m^{2}[/tex]
Base area = 19.5 + 16
= 35.5 m²
Volume of the figure = Base area * height
= 35.5 * 14
= 497 m³
100 PTS!! If line segment AB is dilated with a scale factor 3/2, what is the length of the new line segment A’B’?
A)7.5cm
B)15cm
C)20cm
D)30cm
Length of AB is not given so insufficient info provided
Let's see how to solve then
Scale factor is 3/2 means 3/2 is multiplied with AB to form A'B'
If length of AB is n the. then length of A'B' is 3n/2
If 30% of the 1000 cars on a lot are not hybrids, and 45% are not sedans, how many cars on the lot are hybrid sedans?
The number of cars that are hybrid sedans are = 250 cars
Calculation using a Venn diagramThe value of 30% of 1000 = 30/100× 1000
= 300 cars are not hybrids.
Therefore the number of cars that are hybrids = 300 - x
The value of 45% of 1000 = 45/100 × 1000
= 450 cars are not sedans
Therefore the number of cars that are sedans
= 450 - x
Where X is the cars that are both hybrid and sedans
Using the Venn diagram equation,
1000 = 300 -x + X + 450 - x
1000 = 750 - X
X= 750 - 1000
X = 250 cars
The number of cars that are hybrid is 300 - x where X = 250.
300 - 250 = 50 cars
The number of cars that are sedans is 450 - x. That is,
450 - 250 = 200 cars
Therefore, the cars that are both hybrid and sedans = 250 cars.
Learn more about Venn diagram equation here:
https://brainly.com/question/24581814
The average daily rainfall in Seattle for the
month of June has a mean absolute deviation
of 1.3 inches. What conclusion can you make
about the average daily rainfall in Seattle for
the month of June?
The conclusion regarding the MAD is that the average of the absolute values of the daily difference between the actual and expected rainfall is of 1.3 inches.
What is the mean absolute deviation(MAD) of a data-set?The mean of a data-set is given by the sum of all observations divided by the number of observations.The mean absolute deviation(MAD) of a data-set is the sum of the absolute value of the difference between each observation and the mean, divided by the number of observations.The mean absolute deviation represents the average by which the values differ from the mean.Hence, the mean absolute deviation of 1.3 inches means that the average of the absolute values of the daily difference between the actual rainfall and the expected rainfall is of 1.3 inches.
More can be learned about the mean absolute deviation at https://brainly.com/question/3250070
help please!!!!!11!!!1!!
Answer:
2.1 meters
Step-by-step explanation:
[tex]13.8=2w+2(w+2.7)[/tex]
[tex]13.8=2w+2w+5.4[/tex]
[tex]13.8=4w+5.4[/tex]
[tex]8.4=4w[/tex]
[tex]2.1=w[/tex]
(-9-11)/(-4)divided by -7^2+(11 times 2^2)
Pleaseeeeee helppp!!!!! Will mark brainliest!!
Answer:
the first one (3x-2)(2x-3)
10) Ryan plans to borrow $4,500 from the bank to
purchase a used vehicle. If he borrows the money
at a rate of 4% interest for 2 years, what is the
total amount be will have to pay back to the bank?
Ryan will have to make a monthly payment of $195.41
please help Brianlist Provide the missing reasons for the proof.
Given:
Prove:
Answer:
Answer:
1) given
2) reflexive property
3) corresponding angles theorem
4) AA similarity
5) Corresponding sides of similar triangles are proportional.
