Given:
The expression is [tex](x+4y)^2[/tex].
The expression [tex]ax(2x+y-5)[/tex] simplifies to [tex]6x^2+3xy-15x[/tex].
To find:
The equivalent expression.
The value of a.
Solution:
The expression is
[tex](x+4y)^2[/tex]
Using [tex](a+b)^2=a^2+2ab+b^2[/tex], we get
[tex](x+4y)^2=x^2+2(x)(4y)+(4y)^2[/tex]
[tex](x+4y)^2=x^2+8xy+16y^2[/tex]
Therefore, the correct option is A.
The expression [tex]ax(2x+y-5)[/tex] simplifies to [tex]6x^2+3xy-15x[/tex]. So,
[tex]ax(2x+y-5)=6x^2+3xy-15x[/tex]
[tex]2ax^2+axy-5ax=6x^2+3xy-15x[/tex]
On comparing the coefficient of [tex]x^2[/tex],, we get
[tex]2a=6[/tex]
Divide both sides by 2.
[tex]a=3[/tex]
Therefore, the value of a is 3.
Find the value of x in the equation without evaluating the power
Step-by-step explanation:
a)2^8=256
2^5*2^x=2^8
5+x=8
x=8-5
x=3
b)(1/3)^6
(1/3)^2*(1/3)^x=(1/3)^6
2+x=6
x=6-2
x=4
therefore the value of x in a is 3
and the value of x in b is 4
hope it helps u...pls mark it as the brainliest answer..
a) The value of x is 3
b) The value of x is 5
Powers and indicesGiven the expression [tex]2^5\cdot 2^x = 256[/tex]
Using the law of indices, the equation becomes;
[tex]2^{5+x} = 2^8\\5 + x = 8\\x = 8 -5 \\x = 3[/tex]
Hence the value of x is 3
b)
[tex](\frac{1}{3})^2 \cdot (\frac{1}{3})^x = (\frac{1}{729})\\(\frac{1}{3})^{2+x} =(\frac{1}{729}) \\(\frac{1}{3})^{2+x} =(\frac{1}{3^7}) \\3^{-(2+x)}=3^{-7}\\-2-x = -7\\x = 5[/tex]
Hence the value of x is 5
Learn more on indices here: https://brainly.com/question/10339517
parallel to the line x-2y=-5 containing the point (0,4)
Answer:
y = x/2 + 4
Step-by-step explanation:
When you are trying to find the line which is parallel to the first line, remember that the second line would have the SAME GRADIENT as the first line.
The magnitude $M$ of an earthquake is measured using the formula $M=\log(\frac{x}{c})$ , where $x$ is the measured amplitude of a seismic wave and $c$ is the reference amplitude of one micron. Two earthquakes are measured. The amplitude of a seismic wave in the first earthquake is 15 times the amplitude of a seismic wave in the second earthquake. How much greater is the magnitude of the first earthquake than the second earthquake? Round your answer to the nearest hundredth.
Answer:
1.18
Step-by-step explanation:
Given the Magnitude of an earth quake model :
M = log(x/c)
x = measured amplitude ; c = reference amplitude
Amplitude of seismic wave in first earthquake = 15 amplitude of seismic wave in second
Let amplitude of seismic wave in first earthquake = x1
amplitude of seismic wave in second earthquake = x2
x1 = 15 * x2 = 15x2
Hence ;
1st earthquake magnitude :
M1 = log(a/c)
2nd earthquake magnitude :
M2 = log(15a/c)
M1 - M2
Log(x1/c) - log(x2/c)
Using the quotient rule
Log(x1) - log(c) - [log(x2) - log(c)]
Log(x1) - log(c) - log(x2) + log(c)
Log(x1) - log(x2)
Substituting x1 = 15x2
Log(x1) = log(15x2)
Seperating using product rule:
Log(x1) = log(15*x2) = log(15) + log(x2)
Hence,
log(15) + log(x2) - log(x2)
Log(15) - 0
= 1.1760
= 1.18 (nearest hundredth)
Evaluate the expression.
17 * (-12 + 10)?
Answer:
-34
Step-by-step explanation:
6^4*6^3 equivalent equation
Equation Given:
6⁴×6³
Step by step explanation:
Step 1:
[tex] {6}^{4} \times {6}^{3} [/tex]
Step 2:
[tex] = 1296 \times 216[/tex]
Step 3:
[tex] = 279936✓[/tex]
Answer:
[tex]{\huge{\pink{\underline{\underline{Question:}}}}}[/tex]
[tex]{6}^{4} \times {6}^{3} [/tex]
[tex]{\huge{\pink{\underline{\underline{Solution:}}}}}[/tex]
[tex] {6}^{4} \times {6}^{3}\\
=>{6}^{(4 + 3)} \\
=>{6}^{7}\\
=>6×6×6×6×6×6×6\\
=>36×36×36×6\\
=>279936\ is\ answer..[/tex]
44% of ten is what number
Answer:
4.4
Step-by-step explanation:
You have to turn 44% into a decimal which will be 0.44
Then multiply 0.44 by 10
0.44*10
4.4
Suppose a group of dancers performed the Round Dance at an Indigenous Peoples' Day
celebration. If the circumference of the circle was 44 feet, what was the diameter of the circle?
Answer:
4.27 meters
Step-by-step explanation:
Gabriel is raising money for a school trip by selling lollipops and bags of chips. The
price of each lollipop is $1 and the price of each bag of chips is $1.50. Yesterday
Gabriel made $30 from selling a total of 26 lollipops and bags of chips. Graphically
solve a system of equations in order to determine the number of lollipops sold, 2,
and the number of bags of chips sold, y.
Answer:
There will be 2 bags of chips sold
Step-by-step explanation:
A system of equation is a collection of one or more equation involving the same variables.
Now , according to question :
since , he had sold 26 lollipop , then total money he made from lollipop is : 26 * $1 = $26
Let us assume he sold x number of chips
money made from chips = $ 1.50 * x
Total money made : $30 (Given )
equation according to question will be
26 + 1.50 x = 30
x= 2.7
Since , number of packets can never be in decimal hence, rounding off to 2 packets
x= 2
Learn more about system of equation:
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#SPJ2
Determine 2 additional fractions that would reduce to one fourth?
Answer:
2/8, 4,16
Step-by-step explanation:
eh what is 2(h + 1) =5h - 7
Answer:
h=3
Step-by-step explanation:
numbers are (-20,10) and (40,-50)
The area of a rectangular garden is 105 ft^2. Find the length if the width is 7ft.
Answer:
[tex] \huge{ \bold{ \boxed{ \tt{15 \: ft}}}}[/tex]
Step-by-step explanation:
[tex] \text{Given} : [/tex]
[tex] \rm{Area \: of \: a \: rectangular \: garden \: = 105 \: {ft}^{2} }[/tex]
[tex] \rm{Width\: of \: a \: rectangular \: garden \: = \: 7 \: ft}[/tex]
[tex] \underline{ \rm{Finding \: the \: length \: of \: a \: rectangular \: garden}} : [/tex]
[tex] \boxed{ \rm{Area \: of \: a \: rectangle \: = \: Length \: \times \: Width}}[/tex]
[tex] \rm{➳ \: 105 = 7 \: Length}[/tex]
[tex] \rm{➳ \: 7 \: Length \: = 105}[/tex]
[tex] \rm{➳ \: \frac{7 \:Length}{7} = \frac{105}{7} }[/tex]
[tex] ➳ \boxed{ \rm{ \: Length \: = \: 15 \: ft}}[/tex]
[tex] \text{The \: Length \: of \: a \: rectangular \: garden \: is \boxed{ \rm15 \: ft}}.[/tex]
[tex] \text{Hope \: I\: helped!}[/tex]
[tex] \rm{Best \: regards!}[/tex]
~[tex] \text{TheAnimeGirl}[/tex]
Onya selected a pair of shoes for the regular price of $80. How much money will she save by using the 20% off coupon? Justify your answer using equations, models, and/or words to explain your mathematical reasoning. Part B: Katie selected a pair of shoes for the regular price of $120. After the 20% off discount is applied, what will be the discounted cost of the shoes (before tax)? Justify your answer using equations, models, and/or words to explain your mathematical reasoning.
Answer:
a. [tex]Savings = \$16[/tex]
b. [tex]Price = \$96[/tex]
Step-by-step explanation:
Solving (a):
[tex]Price = \$80[/tex]
[tex]Coupon = 20\%[/tex]
Required
Determine her savings.
[tex]Savings = Coupon * Price[/tex]
[tex]Savings = 20\% * \$80[/tex]
[tex]Savings = \$16[/tex]
Solving (a):
[tex]Price = \$120[/tex]
[tex]Coupon = 20\%[/tex]
Required
Determine the price before tax
First, we need to determine her savings
[tex]Savings = Coupon * Price[/tex]
[tex]Savings = 20\% * \$120[/tex]
[tex]Savings = \$24[/tex]
The price before tax is calculated as follows:
[tex]Price = \$120 - \$24[/tex]
[tex]Price = \$96[/tex]
-5 2/3 - 1/6 please help
Answer:
-5 5/6
Step-by-step explanation:
I just used my calculator.
You have five quarts of paint it takes 5/8 quarts to paint each chair you are asked to paint how many chairs can u paint
Answer:
8 chairs
Step-by-step explanation:
5 quarts= 40/8 quarts
1 chair= 5/8 quarts
40/8-5/8x=0
(-40/8)/(-5/8)=x
8 chairs
PLEASE HELP AND EXPLAIN!! I will mark brainliest <3
Answer: AB is 40
Step-by-step explanation: CD=CE+ED ED is 5 and it is also the midpoint meaning it is 1/2 of the value of the line. Therefore CD is 10, BC=BD+CD CD as we know is 10 and D is the mid point meaning it is also 1/2 of the value of BC. 10+10=20, AB=AC+BC, BC is 20 so AC must also be 20;therefore AB is 40
Alvin and Simon shared £540 in the ratio 4:5. Alvin gave half of his share to Theo. Simon gave a tenth of his share to Theo. What fraction of the £540 did Theo receive.
Answer:
[tex]\frac{5}{18}[/tex]
Step-by-step explanation:
sum the parts of the ratio, 4 + 5 = 9 parts
Divide the amount by 9 to find the value of one part of the ratio
£540 ÷ 9 = £60 ← value of 1 part of the ratio , thus
4 parts = 4 × £60 = £240 ← Alvin's share
5 parts = 5 × £60 = £300 ← Simon's share
[tex]\frac{1}{2}[/tex] × £240 = £120
[tex]\frac{1}{10}[/tex] × £300 = £30
Theo receives £120 + £30 = £150 , which as a fraction is
[tex]\frac{150}{540}[/tex] ( divide numerator/ denominator by 30 )
= [tex]\frac{5}{18}[/tex] ← in simplest form
A researcher found that 55% of families in the United States have one child under the age of 21, 22% have two children under the age of 21, 15% have three children under the age of 21, 5% have 4 children under the age of 21and 3% have 5 or more children under the age of 21. If a family is selected at random, what is the probability the family has 1 or 3 children under the age of 21?
Answer:
67% or 0.67
Step-by-step explanation:
Given that:
P(1 child under age 21) = 55%
P(2 children under age 21) = 22%
P(3 children under age 21) = 15%
P(4 children under age 21) = 5%
P(5 or more children under age 21) = 3%
If a family is selected at random, what is the probability the family has 1 or 3 children under the age of 21?
P(1 or 3 children under age 21):
Either the selected family has 1 child under 21 years of age OR the selected family has 3 children under 21 years of age ;
P(1 child under age 21) + P(3 children under age 21)
= 55% + 15%
= 67% = 0.67
The table of values below represents a linear function and shows the amount of money in Juanita’s savings account since she began her part-time job. What is her monthly rate of savings?
Amount in Juanita’s Savings Account
Number of Months Working at Part-Time Job
0
2
4
6
8
Amount in Savings Account (in dollars)
$36
$60
$84
$108
$132
a.$12 per month
b.$18 per month
c.$24 per month
d.$36 per month
Answer:
The answer is C., $24 per month.
Answer:
A $12
Step-by-step explanation:
she has saved $36 before she gets a part time job, after 2 months, her savings have increased from 36 to 60. 2 months = 60 - 36, 2 months = 24. now we divide 24 by 2, and the answer is 12. option A is correct.
In the figure below, OS=ST and the coordinates of T are (k, 5). What is the value of K?
F. -5
G. -3
H. - 2
J. 0
K. 5
SHOW EXPLANATION
Answer:
Option (K)
Step-by-step explanation:
From the figure attached,
Coordinates of the point T(x, y),
x-coordinate shows the distance (ST) of point T horizontally from origin and y-coordinate show the vertical distance (OS) of point T from the origin.
If OS = ST, x and y coordinates should be same in measure.
For the point (k, 5),
OS = 5 and ST = k
Since, OS = ST,
Therefore, k = 5
Option (K) will be the correct option.
Two points are plotted on the number line.
Answer:
-2/3+1/3= - 1/3
Step-by-step explanation:
if you look at the number line you just go once to the right
PLEASE HELP! I WILL MAKE YOU BRAINLIST!
Answer:
micro organism
Step-by-step explanation:
Please help!! ASAP!! Math Help!k
[tex]f(x) = 4x^3 + Ax^2 + 2x - 5[/tex]
[tex]f(2) = 5[/tex]
[tex]5 = 4 \cdot 2^3 + A \cdot 2^2 + 2 \cdot 2 - 5\\5 = 4 \cdot 8 + 4A + 4 - 5\\5 = 32 + 4A + 4 - 5\\5 - 32 - 4 + 5 = 4A\\-26 = 4A\\A = \frac{-26}{4} = -\frac{13}{2} = -6.5[/tex]
-4/5 + 33/10 Write your answer as a mixed number in simplest form.
Answer:
2 1/2
Step-by-step explanation:
−45+3310=?
The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD(-4/5, 33/10) = 10
Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.
(−45×22)+(33/10×11)=?
Complete the multiplication and the equation becomes
−8/10+33/10=?
The two fractions now have like denominators so you can add the numerators.
Then:
−8+33/10=25/10
This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 25 and 10 using
GCF(25,10) = 5
25÷5/10÷5=5/2
The fraction
52
is the same as
5÷2
Convert to a mixed number using
long division for 5 ÷ 2 = 2R1, so
52=212
Therefore:
−4/5+33/10= 2 1/2
FIRST ANSWER GETS BRAINLIEST! PLEASE HURRY!
The area of a rectangle is 45 square units. The length is 15 units and the width is z units.
Area = length x width
What is the value of z?
Answer:
z = 3 units
Step-by-step explanation:
45 ÷ 15 = 3
Step-by-step explanation:
A is wl
45 = 15 x z
45 = 15z
3 = z
A slope of 2/3 and a y-intercept of -9/7?
Answer:
Slope intercept form:
[tex]y = \frac{2}{3}x - \frac{9}{7}[/tex]
Answer:
y = 2/3x - 9/7
Step-by-step explanation:
If you want the slope intercept form:
y = 2/3x - 9/7
^ ^
slope y-intercept
What is the slope between the points (3,2) and (-1,10)?
Will mark brainliest
Answer:
m = slope = -2
Step-by-step explanation:
[tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} } =\frac{10-2}{-1-3} = \frac{8}{-4} = -2[/tex]
Hope this helped! :)
A package of 6 insulated gloves cost $50.94. what is the unit price of the pair of gloves.
Answer:
i think your answer would be $8.49 for a pair of gloves.
Step-by-step explanation:
50.94 / 6 = 8.49
Triangle R S Q is shown. Angle R S Q is cut by perpendicular bisector l through point S and through midpoint T. The length of line segment R T is x, the length of line segment T Q is 8, the length of line segment Q S is 10, and the length of line segment R S is 10. What is the length of segment TR?
Answer:
RT = 8
Step-by-step explanation:
The given parameters for the triangle are;
The vertices of the given triangle = RSQ
The point on the perpendicular bisector = Pont S and T
The length of the line segment RT = x
The length of the line segment TQ = 8
The length of the line segment QS = 10
The length of the line segment RS = 10
Given that I is a perpendicular bisector that passes through the vertex S, we have;
The line I bisects the segment RQ at point T into equal segments TQ and TR
Therefore, TQ ≅ TR and we have TQ = TR = 8
TR = 8
TR = RT (reflexive property)
Therefore; RT = 8.
Answer:
RS = 12
Step-by-step explanation:
if your question is asking for RS
On a coordinate plane, Broadway is 4 units to the right and 4 units up. Empire State Building is 1.50 units to the right and 1 unit up. Brooklyn Bridge is 5 units to the left and 4.5 units down. Statue of Liberty is 4 units to the left and 3.5 units up. Which ordered pairs show the location of the Empire State Building? Check all that apply. (1 and one-half, 1) (1, 1 and one-half) (–1.5, –1.0) (1.5, 1.0) (1.0, 1.0)
Answer:
upove is correct
Step-by-step explanation:
hehe