Answer:
[tex]x = 16[/tex]
Step-by-step explanation:
Given
[tex]log_{16}(x) + log_4(x) + log_2(x) = 7[/tex]
Required
Solve for x
[tex]log_{16}(x) + log_4(x) + log_2(x) = 7[/tex]
Change base of 16 and base of 4 to base 2
[tex]\frac{log_2(x)}{log_2(16)} + \frac{log_2(x)}{log_2(4)} + log_2(x) = 7[/tex]
Express 16 and 4 as 2^4 and 2^2 respectively
[tex]\frac{log_2(x)}{log_2(2^4)} + \frac{log_2(x)}{log_2(2^2)} + log_2(x) = 7[/tex]
The above can be rewritten as:
[tex]\frac{log_2(x)}{4log_22} + \frac{log_2(x)}{2log_22} + log_2(x) = 7[/tex]
[tex]log_22 = 1[/tex]
So, we have:
[tex]\frac{log_2(x)}{4*1} + \frac{log_2(x)}{2*1} + log_2(x) = 7[/tex]
[tex]\frac{1}{4}log_2(x) + \frac{1}{2}log_2(x) + log_2(x) = 7[/tex]
Multiply through by 4
[tex]4(\frac{1}{4}log_2(x) + \frac{1}{2}log_2(x) + log_2(x)) = 7 * 4[/tex]
[tex]log_2(x) + 2}log_2(x) + 4log_2(x) = 28[/tex]
[tex]7log_2(x) = 28[/tex]
Divide through by 7
[tex]\frac{7log_2(x)}{7} = \frac{28}{7}[/tex]
[tex]log_2(x) = 4[/tex]
Apply the following law of logarithm:
If [tex]log_ab = c[/tex] Then [tex]b = a^c[/tex]
So, we have:
[tex]x = 2^4[/tex]
[tex]x = 16[/tex]
Find the measure of the exterior angle.
add the two angles withen the triangle and make that equal to the exterior angle
The price of an item has been reduced by 45%. The original price was $85.
Answer:
$38.25
Step-by-step explanation:
Answer:
Sale Price: $85 * 0.55 = $46.75
Step-by-step explanation:
Maria Invests $600 in a bank account that earns simple interest. She earns $30 at the end of 12 months . Janae invest $350 at the same rate of interest for 12 months
Answer:
Interest = $1.75
Step-by-step explanation:
Maria invest $600, and receives interest of $30 per year
We know that PRT/100= INTEREST
R=( 100*INTEREST)/(PT)
R = (100*30)/(600*1)
R= 3000/600
R= 5%
Jane invest $350 at Sam rate with Maria , that is 5% , for a year, her interest
Interest= 350*5*1/100
Interest = $1.75
2/10 (4/5)-(5/2)+ (10)
Answer:
2/10 (4/5)-(5/2)+ (10)=7.66
Answer:
[tex]\frac{383}{50} = 7.66[/tex]
Step-by-step explanation:
[tex]\frac{2}{10}(\frac{4}{5})-(\frac{5}{2})+10[/tex]
[tex]= \frac{4}{25} -\frac{5}{2}+10[/tex]
[tex]=\frac{383}{50} = 7.66[/tex]
please help :)
translate the sentence into an inequality.
two subtracted by Y is less than or equal to -22
17 increased by twice Greg's height
Answer:25
Step-by-step explanation:
During the election for class president, 35% of students voted for Leandro and the rest voted for Gerardo. If 70 students voted for Leandro, how many voted for Gerardo? Someone answer it's due tmrw
Answer:
130 studentsStep-by-step explanation:
Out of the whole class, if 35% of students voted for Leandro voted for Leonardo , this means that 64% of the class voted for Gerardo.
Let the total number of people in the class be x;
If 70 students voted for Leandro, then;
35% of x = 70
0.35x = 70
x = 70/0.35
x = 200
The total number of people that voted for Gerardo will be 200 - 70 = 130
Hence 130 voted for Gerardo
Solve the inequality. 4(x + 3) − 7 ≥ x + 3(x + 1)
Answer:
if want to know is true or flas. this is true
Step-by-step explanation:
Sandra's Bike Club had 360 members last month. Each member pays a $12 membership fee per month.
This month, 27 new members joined and 34 members left the club. How much money will Sandra collect
this month in membership fees?
Answer:
$4,236
Step-by-step explanation:
34-27=7
360-7=353
353(12)=4,236
A student forgets to study for an exam consisting of ten multiple choice questions, each with three possible answers. Instead, the student will have to randomly guess, so that there is a 1 3 probability of getting any arbitrary question right. If 6 or more correct answers is a passing score, what
Complete question :
A student forgets to study for an exam consisting of ten multiple choice questions, each with three possible answers. Instead, the student will have to randomly guess, so that there is a 1 3 probability of getting any arbitrary question right. If 6 or more correct answers is a passing score, what is the probability of passing
Answer:
0.07656
Step-by-step explanation:
Given that:
P(correct guess) = 1/3 ; p= 0.33333
Number of questions /trials = 10
P(x ≥ 6) = p(6) + p(7) + p(8) +... + p(10)
This is the sum of the probabilities of getting exactly 6, 7, 8, 9 or 10 questions.
Using the binomial probability calculator to save computation time :
P(x ≥ 6) = 0.07656
10 is 25% of what number?
Answer:
40
Step-by-step explanation:
It costs $6 to buy 3 bags of chips. How much do 24 bags of chips cost?
Answer:
$48
Step-by-step explanation:
24/3 = 8
8 x 6 = $48
Answer:
48
Step-by-step explanation:
because butterfly method 6 time 24 =144 and didved 144 by 3 which gives you 48
Please help my sister is being super mean and my parents are working please help
Which statement is true about the points shown on the number line?
A)-3.8 1.5, and -3.8 is located to the right of 1.5.
D)-3.8 > 1.5, and -3.8 is located to the left of 1.5.
Answer:
2nd option on the top right
Step-by-step explanation:
A store is on sale for 75% less than it’s original price of $24
Answer:
So wouldn't it be like $6 as the actual price now.
Step-by-step explanation:
Hope this helps if not let me know.
Sorry if it is wrong,
The fraction 7/8 produces a repeating decimal.
0.875
O A. True
O B. False
Answer:
b
Step-by-step explanation:
the answer to 7/8 is 0.875 it is not recurring as it has no dot at the top
What is the common difference between successive terms in the sequence?
2, 8, 14, 20, 26, ...
-6
-4
4
6
What is the measure of eg?
Which statement is not true about the pattern sown?
Answer:each fraction is greater than the one before it is not true
Source:trust me bro
The one that is highlighted
5. If AABC = ADEF, find the measure of
Can someone explain me?
Answer:
Option A) angle B = 67°
Step-by-step explanation:
I'll use " [ " symbol for saying angle.
Alright so ...
since triangle ABC and triangle DEF are congruent
it means [ A = [ D
[ B = [ E
[ C = [ F
here [ A = 78° (which means [ D is also 78°)
and ..[ F = 35° (which means [ C is also 35°)
-->So now all you need to know to find [ B is to know the other two angles in the triangle. and thats where ..
you write.. [ A + [ B + [ C = 180° (angle sum property)
78° + [ B + 35° = 180°
113° + [ B = 180°
[ B = 180 - 113
= 67°
I hope that clears the concept , if you have any questions regarding it I'd love to help .
1. Explain the difference between circumscribed angles and inscribed angles in relationship to a circle.
2. Explain, in your own words, the steps required to convert any equation of a circle into standard form be completing the square.
3. Explain/define the following terms, or draw a picture and label the terms.
a. radius
b. diameter
c. chord
d. secant
e. tangent
f. point of tangency
9514 1404 393
Explanation:
1. Consider the attachment. Angle CDF is a circumscribed angle. It is formed at the intersection of two tangents to the circle. Angles BCE, CBE, and BEC are inscribed angles. Their vertices are on the circle, and they are formed by two chords.
If a chord degenerates to zero length, the ray it represents with respect to an inscribed angle becomes a tangent. That is, angles BCD and ECD can also be considered to be inscribed angles. Similarly, straight angle DFG at tangent point F can be considered to be a degenerate case of both an inscribed angle and a circumscribed angle. (Some authors may not include degenerate cases in their definitions. YMMV)
__
2. The general form of the equation of a circle is ...
Ax² +Ay² +Dx +Ey +F = 0
Any equation of a circle can be put in this form. If we divide by A, this can be written as ...
x² +y² -2hx -2ky +c = 0 . . . . where h = -D/(2A), k = -E/(2A), c = F/A
and the equation can be further transformed to the standard form ...
(x -h)² +(y -k)² = r² . . . . . where r² = h² +k² -c
The last equation is the result of "completing the square" by adding h² and k² to both sides of the second equation shown. The values of h and k are as shown above, given the coefficients of the general form equation.
__
3. Again refer to the attached diagram.
a) a radius is a line segment with the circle center at one end and a point on the circle at the other end. AB and AC are radii.
b) A diameter is a line segment whose ends are on the circle and whose midpoint is the center of the circle. BC is a diameter.
c) A chord is a line segment whose end points lie on the circle. BC, BE, and CE are chords.
d) A secant is a line containing two points of the circle. Lines CG and CE are secants.
e) A tangent is a degenerate case of a secant in which the two points of intersection merge to one point of intersection. It is a line that touches the circle at exactly one point, the point of tangency. DG and DC are tangents.
f) The point of tangency is the single point where a tangent intersects a circle. A radius to the point of tangency (such as AC) is always perpendicular to the tangent line (DC).
Is a triangle whose sides measure 6 10 and 8 a right triangle?
Answer:
Step-by-step explanation:
They are equal, and thus, the triangle is a right triangle. ... These sides are 6: 8: 10, then the triangle is a right one.
The discrimination of a quadratic function is 13. Which is a true statement about the roots of the function?
Answer:
If the discrimination of a quadratic function is 13, then the function will have two distinct real roots.
Step-by-step explanation:
Given the quadratic function
[tex]y=ax^2+bx+c[/tex]
where D = b²-4ac is called the discrimination of a quadratic function.
The discriminant D=b²-4ac indicates the type of roots the equation may have.
If D > 0, then the equation has two distinct real roots.
Given that the discrimination of a quadratic function is 13.
i.e. D = 13
As D > 0, so the function will have two distinct real roots.Thus, we conclude that if the discrimination of a quadratic function is 13, then the function will have two distinct real roots.
Answer the question for brainliest.
(Simplify Please)
[tex]1 \frac{2}{5} m - \frac{3}{5} ( \frac{2}{3} m + 1)[/tex]
[tex]\frac{7}{5} m - \frac{6}{15} m - \frac{3}{5} [/tex]
[tex] \frac{21}{15} m - \frac{6}{15} m - \frac{3}{5} [/tex]
[tex]( \frac{(21 - 6)m}{15} ) - \frac{3}{5} [/tex]
[tex] \frac{15}{15} m - \frac{3}{5} [/tex]
[tex]1m - \frac{3}{5} [/tex]
[tex]m - \frac{3}{5} [/tex]
What is 6/7 divided by 2/7
Answer:
3
Step-by-step explanation:
6/7 divided by 2/7
=
6/7 divide 7/2 (cancel out 7)
=
6 multiply 1/2 (reduce)
=
3
What is the zero of the function below?
A. x = -3
B. x = 1
C. x = -1
D. x = 9
Which of the following
Answer:
A
Step-by-step explanation:
(Giving brainliest!!)
Terrance packs two boxes inside a crate. The total weight of the crate and two boxes is 98.45 pounds. One box weighs 32.8 pounds, and the other box weighs 39.34 pounds. How much does the crate weigh?
A) 72.14 pounds
B) 59.11 pounds
D) 26.31 pounds
Answer:
the crate weighs 26.31
Step-by-step explanation:
add 32.8 and 39.34 together and then subtract 98.45 from the sum. ^^
Answer:
the crate weighs 26.31
Step-by-step explanation:
add 32.8 and 39.34 together and then subtract 98.45 from the sum. ^^
Step-by-step explanation:
Priving all night. Kathryn drove her rig 5 hours before
dawn and 6 hours after dawn. If her average speed was
5 miles per hour more in the dark and she covered
630 miles altogether, then what was her speed after dawn?
Answer:
yes
Step-by-step explanation:
Answer: x=16
Step-by-step explanation:
shown in screenshot below
On a coordinate plane, a triangle has points A (negative 5, 3), B (negative 2, 4), C (negative 2, 2).
Triangle ABC is shown on the graph. What are the coordinates of the image of point B after the triangle is rotated 270° about the origin?
(4, 2)
(2, 4)
(–4, –2)
(–2, –4)
In the diagram, the length of segment QV is 15 units.
Line m is a perpendicular bisector of line segment S Q. It intersects line segment S Q at point R. Line m also contains points T and V. Line segment T S is 3 x + 2. Line segment S V is 4 x minus 1.
What is the length of segment TQ?
4 units
11 units
14 units
15 units
Please help me with this.