Answer:
16
Step-by-step explanation:
We use the completing square method to find make the expression a perfect square.
(b/2)²=ac where a and b are coefficients of x² and x respectively while c is a constant.
= (-8/2)²=16
We add 16 to both sides and the expression becomes a perfect square.
use distributive property to rewrite the expression without parentheses
(y+6)9
Answer:
9y + 54
Step-by-step explanation:
Multiply 9 both terms inside the parentheses
y*9 + 6*9
9y + 54
What is the solution to the system of equations below?
2x+3y = 17
3x+6y= 30
Answer:
x = 4, y = 3 → (4, 3)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}2x+3y=17&\text{multiply both sides by (-2)}\\3x+6y=30\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-4x-6y=-34\\3x+6y=30\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-x=-4\qquad\text{change the signs}\\.\qquad x=4\\\\\text{put the value of x to the first equation:}\\\\2(4)+3y=17\\8+3y=17\qquad\text{subtract 8 from both sides}\\3y=9\qquad\text{divide both sides by 3}\\y=3[/tex]
Tom travels between the two mile markers shown and then finds his average speed in miles per hour. Select the three equations that represent this situation.
Answer:
1.5 hours is the correct answer !
Step-by-step explanation:
Speed is the rate of distance over time.
The equations are:
[tex]\mathbf{Speed = \frac{195\ miles}{3\ hours}}[/tex][tex]\mathbf{3\ hours \times Speed = 195\ miles}[/tex][tex]\mathbf{3\ hours = \frac{195\ miles}{Speed}}[/tex]The given parameters are:
[tex]\mathbf{(t_1,d_1) = (1:30pm,35miles)}[/tex]
[tex]\mathbf{(t_2,d_2) = (4:30pm,230miles)}[/tex]
So, the time difference is:
[tex]\mathbf{t=4:30pm - 1:30pm}[/tex]
[tex]\mathbf{t=3\ hours}[/tex]
The distance traveled is:
[tex]\mathbf{d = 230miles - 35miles}[/tex]
[tex]\mathbf{d = 195miles}[/tex]
Speed is calculated as:
[tex]\mathbf{Speed = \frac{Distance}{Time}}[/tex]
So, we have:
[tex]\mathbf{Speed = \frac{195\ miles}{3\ hours}}[/tex]
Multiply both sides by 3 hours
[tex]\mathbf{3\ hours \times Speed = 195\ miles}[/tex]
Divide both sides by Speed
[tex]\mathbf{3\ hours = \frac{195\ miles}{Speed}}[/tex]
Hence, the equations are:
[tex]\mathbf{Speed = \frac{195\ miles}{3\ hours}}[/tex]
[tex]\mathbf{3\ hours \times Speed = 195\ miles}[/tex]
[tex]\mathbf{3\ hours = \frac{195\ miles}{Speed}}[/tex]
Read more about speed and rates at:
https://brainly.com/question/359790
Which is the end point of a ray
Answer:
A ray has an endpoint at one end, and goes on infinitely in the other direction. An endpoint is shown with a point (usually including a label that is typically a single letter), and the infinite direction is shown with an arrow.
a survey of 2000 doctors showed that an average of 3 out of 5 doctors used brand x aspirin. how many doctors use brand x aspirin (solve for x)
Answer:
1,200 doctors use brand X aspirin
Step-by-step explanation:
Out of the 2,000 doctors, the survey showed that 3 out of 5 use brand X. So that means [tex]\frac{3}{5}[/tex] of 2000 doctors use Brand X. So the proportion will then be lke this:
[tex]\dfrac{3}{5} = \dfrac{x}{2000}[/tex]
So we can now solve for x using this equation:
[tex]\dfrac{3}{5} = \dfrac{x}{2000}\\\\\dfrac{(2000)(3)}{5} = x\\\\\dfrac{6000}{5} = x\\\\1200 = x[/tex]
Which phrase matches the expression k - 5
A.) 5 less than k
B.) half of k
C.) k less than 5
D.) the k power or 5
Answer:
A
Step-by-step explanation:
If you choose any number 'k', then the result of subtracting 5 will be '5 less than k'.
Example: If k=6, k-5 is 1.
1 is 5 less than k=6.
The expression is also written as k less than 5. Then the correct option is C.
What is an equivalent expression?The equivalent is the expressions that are in different forms but are equal to the same value.
The expression is given as (k – 5).
The expression is also written as k less than 5.
Then the correct option is C.
More about the equivalent link is given below.
https://brainly.com/question/889935
#SPJ2
Which of the following is the equation of a circle with center (5, - 2) and a radius of 3?
a.(x-5)^2+(y+2)^2=9
b.(x+5)^2+(y-2)^2=9
c.(x-5)^2+(y+2)^2=3
d.(x+5)^2+(y-2)^2=3
Answer:
option a
Step-by-step explanation:
we know the equation of a circle is:
(x-x1)^2 +(y-y2)^2= r^2
center= (x1,y2)
radius =r
in this case we have:
center= (5,-2)
r=3
so we have:
(x-5)^2 +(y-(-2))^2=9
finally we have:
(x-5)^2 +(y+2)^2=9
prove that cos^2(45º – A ) - sin^2 (45º – A) = Sin2A
Answer:
see explanation
Step-by-step explanation:
Using the addition identity for sine
sin(x + y) = sinxcosy - cosxsiny
Consider the left side
cos²(45 - A) - sin²(45 - A)
cos²(45 - A) = 1 - sin²(45 - A), thus
1 - sin²(45 - A) - sin²(45 - A)
= 1 - 2sin²(45 - A) ← expand sin(45 - A)
= 1 - 2(sin45cosA - cos45sinA)²
= 1 - 2([tex]\frac{\sqrt{2} }{2}[/tex]cosA - [tex]\frac{\sqrt{2} }{2}[/tex]sinA)²
= 1 - 2([tex]\frac{1}{2}[/tex]cos²A - sinAcosA + [tex]\frac{1}{2}[/tex]sin²A)
= 1 - cos²A + 2sinAcosA - sin²A
= sin²A + 2sinAcosA - sin²A
= 2sinAcosA
= sin2A = right side ⇒ verified
By Using the addition identity for sine; sin(x + y) = sinx cosy - cosx siny.
It is proved that cos²(45 - A) - sin²(45 - A)= Sin2A.
How to convert the sine of an angle to some angle of cosine?We can use the fact that:
[tex]\sin(\theta ^\circ) = \cos(90 - \theta^\circ)[/tex]
To convert the sine to cosine (but the angles won't stay the same unless it's 45 degrees).
Using the addition identity for sine
sin(x + y) = sinx cosy - cosx siny
Now,
cos²(45 - A) - sin²(45 - A)
cos²(45 - A) = 1 - sin²(45 - A),
1 - sin²(45 - A) - sin²(45 - A)
= 1 - 2sin²(45 - A)
Expand sin(45 - A)
= 1 - 2(sin45cosA - cos45sinA)²
= 1 - 2(√2/2 cosA - √2/2 sinA)²
= 1 - 2(1/2 cos²A - sinAcosA + 1/2 sin²A)
= 1 - cos²A + 2sinAcosA - sin²A
= sin²A + 2sinAcosA - sin²A
= 2sinAcosA
cos²(45 - A) - sin²(45 - A) = sin2A = right side
Hence, it is verified.
Learn more about sine to cosine conversion here:
https://brainly.com/question/1421592
#SPJ2
Given: x - 7>-2.
Choose the solution set.
O fxIXER, x>-9)
O fxIXER, x>-5)
OxIXER,x>5)
OxIXER, x> 14)
Help me please
Answer:
C) {xIx=R (all real #'s) , x>5}
Step-by-step explanation:
If I am reading the options correctly it should be c since after u add 7 to both sides you get x>5
(pls give brainliest)
Solve for m
5m - 10m = 20
can anyone help me out?
Answer:
m=-4
Step-by-step explanation:
5m-10m=-10m+5m=-(10m-5m)=-5m=20
divide by 5 on both sides, -m=4
miltiply by -1 on both sides, m=-4
Answer:
m = - 4
Step-by-step explanation:
Given
5m - 10m = 20 ← simplify left side by combining terms
- 5m = 20 ( divide both sides by - 5 )
m = - 4
Three ounces of cinnamon cost $2.40. If there are 16 ounces in 1 pound, how much does cinnamon cost per pound?
Jackrabbits are capable of reaching speeds up to 40 miles per hour. How fast is this in feet per second? (Round to the nearest whole number.)
5,280 feet = 1 mile
Answer:
80¢\lb.; 58 667\1000 ft.\sec.
Step-by-step explanation:
Divide the cost by three; multiply 40 by 1.466675.
What is the domain of the function y=in(x+2) x<-2 x>-2 x<2 x> x<-2 x>-2 x<2 x>2
For this case we must find the domain of the following function:
[tex]y = ln (x + 2)[/tex]
By definition, the domain of a function is given by all the values for which the function is defined.
In this case, the argument of the expression must be greater than 0 to be defined.
[tex]x + 2> 0\\x> -2[/tex]
Thus, the domain of the function is given by all the values of x greater than -2.
Answer:
Domain: [tex]x> -2[/tex]
A cylindrical container has a height of 24 inches. Currently, the container is filled with water to a height of 18 inches. A leaky
faucet drips into the container, causing the height of the water in the container to increase by 2 inches per hour. The equation
below can be used to find t, the number of hours it would take to fill the container.
18 + ?t = 24
What number should be the coefficient of t?
Answer:
2
Step-by-step explanation:
The rate at which the height increases is 2 inches per hour. That is the slope of the equation.
18 + 2t = 24
The coefficient of t is 2.
Answer:
2
Step-by-step explanation:
We are given that a cylinder container has a height of 24 inches.
Currently, the container filled with water to a height=18 inches
If the height of the water in the container increase by 2 inches per hour
We are given that an equation which can be used to find the t in number of hours it would take to fill the container
We have to find the coefficient of t
In one hour, height increase=2 inches
In t hours, height increase=2t
According to question
[tex]18+2t=24[/tex]
Therefore, the coefficient of t is 2.
Hence, the number should be the coefficient of t=2
Please help me someone
Answer:
The correct answer option is D. He multiplied the divisor by 100 and dividend by 10.
Step-by-step explanation:
We are given that Miguel completed the division where initially he had to divide 754 by 0.52.
To make it easier, he multiplied both the divisor and the dividend by the same number to get rid of the decimal in the divisor.
If he multiplied the divisor by 100, he should have multiplied the dividend by 100 too. But instead, he mistakenly multiplied the divisor by 100 and dividend by 10.
Are the equations lxl – 3 = 7 and [x] = 10 equivalent?
They're not equivalent.
[tex]|x|[/tex] (vertical bars) represents the absolute value of x. How it works is that it turns negative numbers positive but leaves 0 and positive numbers alone (hence it gets a number's distance from 0 on the number line).
[tex][x][/tex] (square brackets) usually represents the floor function, which returns the largest integer that is less than or equal to x. (The floor of x can also be written as [tex]\lfloor x \rfloor[/tex] --- it depends on what your textbook/source says).
To solve [tex]|x| - 3 = 7[/tex], you first transform it into the equivalent equation [tex]|x| = 10[/tex]. Then by definition of absolute value, there are only two solutions for the first equation: x = 10 or x = -10.
[x] = 10 has infinitely many solutions. For example, the floor of 10 is 10, so [tex][10] = 10[/tex], thus a solution for the second equation is x = 10
The floor of 10.1 is 10, so [tex][10.1] = 10[/tex], thus another solution for the second equation is x = 10.1.
The two equations do not have the same solution set (as x = 10.1 does not solve |x| - 3 = 7 but solves [x] = 10), so they're not equivalent.
Yvette earns a $45,000 salary plus a 12% commission on any sales over $10,000. Last year Yvette made $30,000 in sales. How much did Yvette earn in salary plus commission ?
She earns commission on the amount of sales over $10,000
Subtract 10,000 from her sales to get the amount she earns commission on:
30,000 - 10,000 = 20,000.
multiply that by the percent:
20,000 x 0.12 = 2400
She earned $2,400 in commission.
Now add that to her salary to find her total pay:
45,000 + 2,400 = $47,400
Answer:
$47,400.
Step-by-step explanation:
We have been given that Yvette earns 12% commission on any sales over $10,000. Last year Yvette made $30,000 in sales.
The amount on which Yvette will get commission would be [tex]\$30,000-\$10,000=\$20,000[/tex].
Since Yvette gets 12% commission, so amount earned as commission would be 12% of $20,000.
[tex]\text{Commission}=\$20,000\times \frac{12}{100}[/tex]
[tex]\text{Commission}=\$20,000\times 0.12[/tex]
[tex]\text{Commission}=\$2,400[/tex]
Yvette also gets a salary of $45,000, so Yvette's total earnings would be $45,000 plus $2,400.
[tex]\text{Yvette's total earnings}=\$45,000+\$2,400[/tex]
[tex]\text{Yvette's total earnings}=\$47,400[/tex]
Therefore, Yvette's earned $47,400 in salary plus commission.
What is an statistics
Hello There!
Statistics is a tool used to help people process, summarize, analyze and interpret data for making better decisions.
It helps us with future events if we know what has happened in past.
Helps us make better decisions.
The better we know about the future of an outcome, the more possibility we have to work around it.
Answer:
Statistic is the art or science of collecting,analysing ,summarising and presenting data by using numbers.
A package of bacon holds 15 strips of bacon. The pancake house uses 17 packages of bacon in the morning and 21 packages in the afternoon. How many more strips were used in the afternoon than the morning?
Answer:
60 more strips were used in the afternoon
Step-by-step explanation:
Bacon used in the morning
17 packages * 15 strips/ package = 255 strips
Bacon used in the afternoon
21 packages * 15 strips/package = 315
Difference = 315-255 =60
60 more were used in the afternoon
Help me I need to pass so I can go on to the next thing plz someone help me. Will give brainliest!!
Mr and mrs Wilson hosted their daughter wedding they paid $575 to rent a banquet hall and $13 per person for a catered dinner in all there were 118 people at the wedding how much did the Wilson’s pay for the hall and the food use inverse operation to check your answer
Answer:
$2109
Step-by-step explanation:
We are given that Mr and Mrs Wilson payed a rent of $575 for the banquet hall and a per head of $13 for the catering dinner for their daughter's wedding.
We are to find the total amount they paid.
Amount paid for dinner for 118 people = [tex]118 \times 13[/tex] = $1534
Total amount payed by Mr and Mrs Wilson = $1534 + $575 = $2109
Inverse check:
2109 - 575 = 1534
1534/118 = 13
25POINTS!!Which expression is equivalent to 3 x 5 x 5 x 5 x 5 X 5 X 5?
15^6
15^7
3(5)^6
3(5)^7
Answer:
the third one
Step-by-step explanation:
count your factors of 5... I count 6
so the only answer that says you have a factor of 3 and 6 factors of 5 is the third one
Which equation has x=4 as the solution? A) ^log 4 (3x+4)=2 B) ^log 3 (2x-5)=2 C) ^log x 64=4 D) ^log x 16=4
ANSWER
[tex] \log_{4}(3x + 4) = 2[/tex]
EXPLANATION
Consider the equation:
[tex] \log_{4}(3x + 4) = 2[/tex]
When we rewrite this logarithmic equation in the exponential form, we obtain:
[tex]3x + 4= {4}^{2} [/tex]
Note that to write a logarithmic equation in exponential form, the base of the logarithm is still the base in the exponential form.
We now simplify the RHS.
[tex]3x + 4 = 16[/tex]
Group like terms
[tex]3x = 16 - 4[/tex]
This implies that
[tex]3x = 12[/tex]
Divide both sides by 3
[tex] \frac{3x}{3} = \frac{12}{3} [/tex]
Simplify to get;
[tex]x = 4[/tex]
Hence the equation that has x=4 as a solution is
[tex] \log_{4}(3x + 4) = 2[/tex]
Another way to do this is to substitute x=4 into each equation. The equation that is satisfied is the correct choice.
Answer:
(A)
Step-by-step explanation:
on edg 2021
The slope of a line is 5/8,(5 on he top and 8 on the bottom) and the line passes through the point .(−8,−4).
What is the slope-intercept form of the equation for this line?
Answer:
y=5/8 x+1
Step-by-step explanation:
so not 58 but 5/8 is the slope, okay... Did you try looking at your last question as an example for this one?
y=mx+b
we are given m=5/8 so plug in
y=5/8 x+b
You are given an (x,y) on the line which is (-8,-4) so plug in and find b
-4=5/8 (-8)+b
-4=-5+b
1=b
So the line y=5/8 x+1
Circle O has a circumference of 887 cm.
What is the length of the radius of the circle?
cm
Answer:
44cm
Step-by-step explanation:
Formula for circumference, C = 2πr
where r is the radius
r = C / 2π
= [tex]\frac{88\pi }{2\pi }[/tex]
=44 cm
Answer:
approximately 44 cm
Step-by-step explanation:
The formula for circumference of a circle of radius r is C = 2π·r. Solving for r, we get:
C
r = ------------
2π
and in this instance, r = 88π cm / 2π, or 44 cm
Which statement is true about the sum of two rational numbers?
Answer:
So, adding two rationals is the same as adding two such fractions, which will result in another fraction of this same form since integers are closed under addition and multiplication. Thus, adding two rational numbers produces another rational number. Proof: "The product of two rational numbers is rational."
Sum of two rational numbers is always a rational number is always true .
What are rational numbers?A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. For example, −3/7 is a rational number, as is every integer
According to the question
The sum of two rational numbers :
Case 1: Consider rational numbers with different denominator : [tex]\frac{4}{5} , \frac{2}{3}[/tex]
Sum of both rational numbers
= [tex]\frac{4}{5} + \frac{2}{3}[/tex]
= [tex]\frac{12 + 10 }{15}[/tex]
= [tex]\frac{22}{15}[/tex]
Case 2:Consider rational numbers with same denominator : [tex]\frac{4}{5} , \frac{1}{5}[/tex]
= [tex]\frac{4}{5} + \frac{1}{5}[/tex]
= [tex]\frac{5}{5}[/tex]
= [tex]\frac{1}{1}[/tex]
= 1
Sum in both cases are rational numbers
Hence, Sum of two rational numbers is always a rational number is always true .
To know more about rational number here:
https://brainly.com/question/17450097
#SPJ2
If m<M=4x, m<L=5x, and m<MKL=6x. find m<JKM.
((72
((132
((108
((120
Thank you so much!!
Answer:
The measure of angle JKM is 108°
Step-by-step explanation:
step 1
Find the value of x
we know that
The sum of the interior angles of a triangle must be equal to 180 degrees
so
∠M+∠L+∠MKL=180°
substitute the given values
4x+5x+6x=180°
15x=180°
x=12°
step 2
Find the measure of angle JKM
we know that
Angles MKL and JKM are supplementary angles
so
∠MKL+∠JKM=180°
6x+∠JKM=180°
substitute the value of x
6(12)+∠JKM=180°
∠JKM=180°-72°=108°
Answer:
108
Step-by-step explanation:
We know sum of all the 3 angles in a triangle is equal to 180. We can set up an equation for the triangle KML using the information given:
[tex]4x+5x+6x=180\\15x=180\\x=\frac{180}{15}=12[/tex]
So measure of Angle MKL is 6x, or 6(12) = 72
Now, we know Angle JKM + Angle MKL = 180 (straight line). Thus,
Angle JKM + 72 = 180
Angle JKM = 180 - 72 = 108
what is 1/2 to the power of -2
Answer:
4
Step-by-step explanation:
=(1/2)^-2
=(2/1)^2
=2^2
=4
least to greatest -3, 3 1⁄3, -3 3⁄4, 3 1⁄10
Answer:
-3 3/4, -3, 3 1/10, 3 1/3
Step-by-step explanation:
in negative numbers bigger number is always smaller in value and in fractions bigger numbers yet again if in a small portion is a smaller value
9 to the third power
Answer:
729
Step-by-step explanation:
9 x 9 x 9
Answer:729
Step-by-step explanation:
third power means squared, and that means that you multiply the number by it's self three times, 9*9=81, that's once. then again 81*9 =728
PLEASE HELP ME RIGHT NOW!! 40 PTS.
The ceiling of Katie’s living room is a square that is 12 ft long on each side. To decorate for a party, she plans to hang crepe paper around the perimeter of the ceiling and then from each corner to the opposite corner. Katie can buy rolls that each contain 10 ft of crepe paper. What is the minimum number of rolls she should buy? Show your work.
Show work Please.
CREDIT BELONGS TO Sage24
I think that 3 rolls is wrong and that 6 rolls is right. If you create a 15 by 15 square and draw two lines through the center that connect to the opposite corner, you'll be able to use the Pythagorean Theorem.
Perimeter: 15+15+15+15=60ft.
Length of Line from Corner to Corner:
(15)(15)+(15)(15)=C^2
225+225=C^2
450=C^2
21.2=C
21.2(2)= 42.4ft.
42.4ft.+60ft.= 102.4ft.
102.4ft. divided by 20ft. = 5.12 = 6 rolls
Read more on Brainly.com - https://brainly.com/question/3713544#readmore