Solve the following equations for x.
A. 7(x)^3=243
B. 5(x)^4+7=42
The values of x given the following expression are ∛243/7 and 7^1/4
Indices expressionGiven the following expression
7x³ =243
x³ = 243/7
x = ∛243/7
For the expression
5x⁴ + 7 = 42
5x⁴ = 42 - 7
5x⁴ = 35
x⁴ = 7
x = 7^1/4
Hence the values of x given the following expression are ∛243/7 and 7^1/4
Learn more on indices here: https://brainly.com/question/8952483
#SPJ1
What is the y-intercept of the line 15 - 3y = x?
The y-intercept of the line 15 - 3y = x is ( 0 , 5 )
Sure hope this helps you
Find f(-3) for f(x) = 4(2)^x.
ОА. 1/8
O B. -32
O C. -24
OD. 1/2
Answer:
D
Step-by-step explanation:
using the rule of exponents
[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
substitute x = - 3 into f(x)
f(- 3) = 4([tex](2)^{-3}[/tex] = 4 × [tex]\frac{1}{2^{3} }[/tex] = 4 × [tex]\frac{1}{8}[/tex] = [tex]\frac{1}{2}[/tex]
Express 5x²-15x+1 in the form p(x+q)²+r, where p,q,r ate constants
Answer:
[tex] 5\bigg(x-\frac{3}{2}\bigg)^2-\frac{41}{4}[/tex]
Step-by-step explanation:
[tex] 5x^2-15x +1[/tex][tex]= 5\bigg(x^2-3x +\frac{1}{5}\bigg)[/tex][tex] =5\bigg[x^2-2.\frac{3}{2}x +\bigg(\frac{3}{2}\bigg)^2-\bigg(\frac{3}{2}\bigg)^2+\frac{1}{5}\bigg][/tex][tex] =5\bigg[\bigg(x-\frac{3}{2}\bigg)^2+\frac{1}{5}-\frac{9}{4}\bigg][/tex][tex] =5\bigg[\bigg(x-\frac{3}{2}\bigg)^2+\frac{4-45}{20}\bigg][/tex][tex] =5\bigg(x-\frac{3}{2}\bigg)^2-5.\frac{41}{20}[/tex][tex] =5\bigg(x-\frac{3}{2}\bigg)^2-5.\frac{41}{20}[/tex][tex] =5\bigg(x-\frac{3}{2}\bigg)^2-\frac{41}{4}[/tex]A hyperbola has its foci at (1, 7) and (1, –13). a directrix of the hyperbola is y = . what is the equation of the hyperbola?
The equation of the hyperbola is [tex]\frac{(y + 3)^2}{64} -\frac{(x - 1)^2}{36} = 1[/tex]
How to determine the hyperbola equation?The foci are given as:
(1, 7) and (1, -13)
The foci of a hyperbola are represented using: (m, n+p) and (m, n-p)
Where the center of the hyperbola is (n,p)
By comparison, we have:
m = 1
n + p = 7
n - p =13
Where n = ae
The solution to the above system of equations is
m = 1, n = 10 and p = -3
The directrix is given as:
y = 64/10
The directrix is represented as:
y = a/e
So, we have:
a/e = 64/10
Substitute n = ae in n = 10
ae = 10
Solving ae = 10 and a/e = 64/10, we have:
a = 8 and e = 10/8
To calculate b, we make use of:
[tex]b = a\sqrt{(e^2 - 1)[/tex]
So, we have:
[tex]b = 8\sqrt{(\frac{10}{8}^2 - 1)[/tex]
Evaluate
b = 8 * 0.75
b = 6
The equation of the hyperbola is then calculated using:
[tex]\frac{(y - p)^2}{a^2} -\frac{(x - m)^2}{b^2} = 1[/tex]
This gives
[tex]\frac{(y + 3)^2}{8^2} -\frac{(x - 1)^2}{6^2} = 1[/tex]
Evaluate
[tex]\frac{(y + 3)^2}{64} -\frac{(x - 1)^2}{36} = 1[/tex]
Hence, the equation of the hyperbola is [tex]\frac{(y + 3)^2}{64} -\frac{(x - 1)^2}{36} = 1[/tex]
Read more about hyperbola at:
https://brainly.com/question/3405939
#SPJ4
Three times a number decreased by 2 equals forty
Answer:
14
Step-by-step explanation:
40 plus 2 is 42
42 divided by 3 is 14
Each cube in this figure measures 1 centimeter on each side.
What is the volume of this figure?
112 cm³
84 cm³
33 cm³
31 cm³
How do I solve augmented matrices??
Write the coefficients of the x-terms as the numbers down the first column.
Write the coefficients of the y-terms as the numbers down the second column.
If there are z-terms, write the coefficients as the numbers down the third column.
Draw a vertical line and write the constants to the right of the line.
PLEASE HELP ASAP!!!!
A scatter plot is shown below: if you need an image of it look at the bottom
A graph shows numbers from 0 to 10 on the x axis at increments of 1 and the numbers 0 to 15 on the y axis at increments of 1. The ordered pairs 0, 14 and 1, 11 and 2, 9 and 3, 10 and 4, 7 and 5, 7 and 6, 5 and 7, 5 and 8, 3 and 9, 1 and 10, 0 are shown on the graph.
Which two ordered pairs can be joined to best draw the line of best fit for this scatter plot?
(4, 15) and (10, 7)
(1, 6) and (6, 0)
(0, 13) and (10, 11)
(0, 13) and (10, 0)
Reason:
If you were to draw a line through the points mentioned in choice A, the line wouldn't be close to the points since (4,15) isn't close to the points. The same goes for (10,7). So we can rule out choice A. Choices B and C are similar stories.
Choice D on the other hand has its line fairly close to all of the points.
Last option
(0,13)
The point will lie at top(10,0)
The point will lie at bottomSo
both will contain most no of plots so Option D is correct
Help me with this question please /:
Answer:
B) D) E)
Step-by-step explanation:
Basically, the more days missed, the lower their grades are, so it is a negative linear relationship that has no clusters or outliers.
What is the area of a rectangle with a length of 9
centimeters and a width of 4 centimeters?
Sketch: ?
Area: ?
Answer:
We are given a length of 9 cm and a width of 4 cm and we are also told that it our shape is a rectangle. This means that we are able to use the rectangle formula which is [tex]A=l*w[/tex].
Therefore, we can just multiply 9 cm by 4 cm and we get [tex]A = 36\ cm^2[/tex]
Hope this helps! Let me know if you have any questions
The area of one face of a cube is 144 square inches.what is the volume of the cube?
Check the picture below.
[tex](s)(s)=144\implies s^2=144\implies s=\sqrt{144}\implies s=12 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{volume of the cube}}{(s)(s)(s)\implies s^3}\implies 12^3\implies 1728~in^3[/tex]
Answer:
1728 in³
Step-by-step explanation:
Given that,
→ Area = 144 sq in
Then the length will be,
→ a² = 144
→ a = √144
→ [ a = 12 ]
Formula we use,
→ V = a³
Now required volume will be,
→ a³ = 12³
→ 12 × 12 × 12
→ 1728 in³
Hence, the volume is 1728 in³.
Football boot sizes of a football team continuous or discrete
Answer:
discrete?
according to probability of basic things we know that there are more people different than same so there is more than enough probability of those sizes being discrete.
The diameter of a volleyball is 8.4 in. what is the approximate volume of the volleyball? a. 222 in.3 b. 233 in.3 c. 296 in.3 d. 310 in.3
Answer:
C.
Step-by-step explanation:
According to the volume equation of a sphere (V=4/3πr³)
8.4/2 equals a radius of 4.2, which when cubed equals 74.088 (base area). You then multiply your base area by the numerator of 4/3, giving you 296 when rounded or 296.352 when not rounded. Giving you the answer of C.
Select all the expressions equal to sin (30°). *
sin 2/3
cos 5m/3
tan π/6
sin 5/6
cos 60°
cos 11π/6
Solve: log (15x+10) = 2*
The trigonometric expression sin 30° will be equal to cos 60°. Then the correct option is E.
How to convert the sine of an angle to some angle of cosine?We can use the fact that:
sin(θ) = cos(90 - θ)
To convert the sine to cosine (but the angles won't stay the same unless it's 45 degrees).
The trigonometric expression sin 30° will be equal to
The sin 30° can be written as
sin 30° = cos(90° - 30)
sin 30° = cos 60°
Then the correct option is E.
Learn more about sine to cosine conversion here:
https://brainly.com/question/1421592
#SPJ1
Write 9.30 in scientific notation
Please help :)
I’ll give brainliest to whoever comments first and gets it right!
Answer:
9.30 × 10⁰ bro that was so easy
Which expression shows the distance on the number line between −14 and −5?
∣∣−5−14∣∣
∣∣−14−(−5)∣∣
∣∣−14−5∣∣
∣∣−14+(−5)∣∣
Answer:
||−14+(−5)||
Step-by-step explanation:
What is the measure of ZEKY in this figure?
O 104°
O 115°
O 129°
O I don't know.
Please answer fast!
Answer: 104 degrees
Step-by-step explanation:
Which value of x solves the equation below?
10(x - 1) = 8x - 2
x = 5
X= 6
th
x=2
X= 4
Answer:
x = 4
Step-by-step explanation:
10(x - 1) = 8x - 2
10x - 10 = 8x - 2
10x = 8x + 8
2x = 8
x = 4
Which could be the missing data item for the given set of data if the median of the complete data set is 50?
21 23 60 60 50 54 54 59 26 15 43 15
A. 18
B. 24
C. 45
D. 57
Answer:
D. 57
PLEASE GIVE BRAINLIEST THANK YOU!!!
item 3 lamar gives his dog a pill once each day. each pill contains 3.6 milligrams of medicine. how many grams of medicine does lamar's dog get after one week? item 3 lamar gives his dog a pill once each day. each pill contains 3.6 milligrams of medicine. how many grams of medicine does lamar's dog get after one week?
Multiplication is the process of multiplying. The amount of medicine that Lamar's dog will have in one week is 25.2 milligrams.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
Given a medicine provides 3.6 milligrams of medicine. Therefore, the amount of medicine the dog will have in a week is,
The amount of medicine = 3.6milligrams × 7 = 25.2 milligrams
Hence, the amount of medicine that Lamar's dog will have in one week is 25.2 milligrams.
Learn more about Multiplication:
https://brainly.com/question/14059007
#SPJ1
7 UNIT 2(CALCULATOR 7 OF S
Part A
The first type of cup the manager ordered is in the shape of a right circular cone with the dimensions, in centimeters (cm), as shown in the
figure.
-7 cm
9 cm
What is the volume, in cubic centimeters, of each cup?
O A 110.25m
OB. 47.25T
OC. 36.75m
OD. 10.5m
Part B
Answer:
Volume of Cone=1/3πd²/4×h
= 1/3π×7²/4×9
= 36.75cm³
Can the sides of a triangle have lengths 3, 4, and 19?
NEED HELP ASAP!!! What is the sum of the geometric sequence -4, 24, -144, ... if there are 8 terms?
A. -959,781
B. 29,637
C. 26,661
D. 959,780
Answer:
D
Step-by-step explanation:
the sum to n terms of a geometric sequence is
[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^{n}-1) }{r-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = - 4 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{24}{-4}[/tex] = - 6 , then
S₈ = [tex]\frac{-4((-6)^{8}-1) }{-6-1}[/tex]
= [tex]\frac{-4(1679616-1)}{-6-1}[/tex]
= [tex]\frac{-4(1679615)}{-7}[/tex]
= [tex]\frac{-6718460}{-7}[/tex]
= 959,780
You plan to move to San Antonio. You earn a salary of $42,000 here in McAllen. How much more must you earn in San Antonio if the cost of living is 15% higher?
awnser okease quicxkly
Answer:
P': (-9,10)
Q': (-2,10)
R':(-2,0)
S':(-9,0)
Answer:
the answer for all of this question should be.
P=(-9,-10)
Q=(-2,-10)
R=(-2,0)
S=(-9, 0)
so hopefully those are the correct answers and sorry if i get them wrong because i tried my best i could as possible to get them right so have a great day.
Step-by-step explanation:
Spencer took $21 with him to the mall. At the music store he spent 2/3 of his money on a DVD. He spent ¼ of what he had left on a drink. How much money did Spencer have left after he bought the drink?
Answer:
$10.50
Step-by-step explanation:
2/3 of $21 = $14
1/4 of $14 = $3.50
$14 - $3.5 = $10.50
can you help me with this
Answer:
c
Step-by-step explanation:
6 worker can construct 10 m long wall in 4 days . in how many days 2 worker can contruct 15 m long wall ?
Answer:
it should take the workers 18 days to finish
Step-by-step explanation:
Solve 2x2 + 3x − 5 = 0 by factoring.
x=1, 52
x=1, −52
x=1
x=−52