3(4x + 2)
= 3 . 2(2x + 1)
= 6(2x + 1)
proof
• 3(4x + 2)
= 3(4(2) + 2)
= 30
• 6(2x + 1)
= 6(2(2) + 1)
= 30
What is the sum of the interior angles of the polygon shown?
The sum of the interior angles of the polygon shown is 540 degrees
Solution:
The sum of the measures of the interior angles of a polygon with n sides is:
[tex]Sum = (n -2) \times 180[/tex]
From given figure in question,
Number of sides in polygon = 5 ( which is a pentagon )
Therefore,
n = 5
Thus the sum of measures of interior angles is:
[tex]Sum = (5-2) \times 180\\\\Sum = 3 \times 180\\\\Sum = 540[/tex]
Thus the sum of the interior angles of the polygon shown is 540 degrees
Forty percent of students at pine crest middle school have a school sweatshirt. There are 560 students at the school.
How many students have a school sweatshirt.
Answer: 224 students own a school sweatshirt.
Step-by-step explanation:
40% of 560 means 60% do not have one
0.60 is 60% as a decimal
560 x 0.60 = 336 students without a sweatshirt
560 - 336 = 224
The walking track at one fitness center is a 2/5 mile loop. If Kara walks around the track 8 1/2 times, how many miles does Kara walk? A 3 2/5 miles B 4/85 miles C 8 9/10 miles D 21 1/4 miles
Kara walks A. 3 2/5 miles
Step-by-step explanation:
Step 1; We must calculate how much 2/5 miles is. 2/5 miles equals 0.40 miles. Kara walks this distance times 8 1/2. 8 1/2 times equals 8.5 times. So the distance she walked is the number of loops walked × distance of each loop.
Total distance walked = Number of loops walked × distance of each loop
= 8.5 loops × 0.20 miles = 3.4 miles
Step 2; In order to check which option this is, we must know what values all the given options are equal to
A. 3 2/5 miles equals 3 miles + 2/5 miles = 3 + 0.20 = 3.20 miles.
B 4/85 miles equals 0.047 miles which is lesser than one loops distance.
C. 8 9/10 miles equals 8 miles + 9/10 miles = 8 + 0.90 = 8.90 miles
D. 21 1/4 miles equals 21 miles + 1/4 miles = 21 + 0.25 = 21.25 miles.
So the answer is option A.
Does the denominator represents the part or the whole of a fraction ? Yes or no
Answer:
The whole of a fraction
Answer:
it represents the whole fraction
Step-by-step explanation:
because a fraction is one number, like a decimal but stacked kindA
PLEASE MARK BRAINLIEST IF THIS HELPED
Which equation is the inverse of 5 y + 4 = (x + 3) squared + one-half?
y = one-fifth x squared + six-fifths x + eleven-tenths
y = 3 plus-or-minus StartRoot 5 x + seven-halves EndRoot
Negative 5 y minus 4 = negative (x + 3) squared minus one-half
y = negative 3 plus-or-minus StartRoot 5 x + seven-halves EndRoot
Answer:
The correct option is the last option d.) y = negative 3 plus-or-minus StartRoot 5 x + seven-halves EndRoot
Step-by-step explanation:
the given equation is [tex]5y + 4 =(x+3)^{2} + \frac{1}{2}[/tex]
Therefore we can write [tex]5y\hspace{0.1cm} = (x+3)^{2} + \frac{1}{2} - 4 \hspace{0.3cm} \Rightarrow \hspace{0.2cm} 5y = (x+3)^{2} - \frac{7}{2} \hspace{0.3cm} \Rightarrow \hspace{0.3cm} y = \frac{(x+3)^{2}}{5} - \frac{7}{10}[/tex]
To find the inverse of the above function let us replace x with y and y with x.
Therefore we get
[tex]x = \frac{(y+3)^{2}}{5} - \frac{7}{10}[/tex]
Now we write the above equation with only y on the Left hand side and we will obtain the inverse of the given function
[tex]y = \pm \sqrt{5 (x + \frac{7}{10} )} \hspace{0.1cm} - \hspace{0.1cm} 3 \hspace{0.1cm} \Rightarrow\hspace{0.1cm} y = \pm \sqrt{5x + \frac{7}{2} } - \hspace{0.1cm} 3 \hspace{0.1cm}[/tex]
Therefore the correct option is the last option d.) y = negative 3 plus-or-minus StartRoot 5 x + seven-halves EndRoot , [tex]y = \pm \sqrt{5x + \frac{7}{2} } - \hspace{0.1cm} 3 \hspace{0.1cm}[/tex]
Answer:
y = negative 3 plus-or-minus StartRoot 5 x + seven-halves EndRoot
Step-by-step explanation:
For which pairs of functions is (f•g)(x)=x of functions is (f•g)(x)=x
Answer:
Option A
Step-by-step explanation:
The complete question is shown in the attachment.
Note that: [tex](f\cdot g)(x)=f(x)\cdot g(x)[/tex]
We need to multiply all the functions to see which of them satisfy the given criteria.
Option A
[tex]x^2\cdot \frac{1}{x} =\frac{x^2}{x}=x[/tex]
Option B
[tex]\frac{2}{x} \cdot \frac{2}{c} =\frac{4}{cx}[/tex]
Option C
[tex]\frac{x-2}{3} \cdot 2-3x =\frac{-3x^2+8x-4}{3}[/tex]
Option D
[tex]\frac{1}{2x-2} \cdot \frac{1}{2x+2} =\frac{1}{4(x^2-1)}[/tex]
The correct choice is A
Please help I don't understand how to do this
Answer:
m<B=m<K=100
m<A=m<J=133
m<L=m<C=41
m<M=m<D=86
Step-by-step explanation:
Since [tex]ABCD\cong JKLM[/tex], the corresponding angles are congruent.
This implies that:
[tex]m\angle A=133=m\angle J[/tex]
m<L=41=m<C
m<M=86=m<D
The sum of angles in a quadrilateral is 360 degrees.
m<B+133+41+86=360
m<B+260=360
m<B=360-260
m<B=m<K=100
At the same time a 12 foot adult elephant cast a 4.8 foot shadow a baby elephant casts a 2 foot shadow how tall is the baby elephant?
Which radian measure is equivalent to −15°?
Answer:
Step-by-step explanation:
to convert degree to radians multiply with π/180
therefore -15° =-(15 ×π/180) = -π/12
Yo sup??
To convert any given angle into radian, just multiply it with π/180
therefore
-15° =-(15 *π/180)
=-π/12
You can also solve this question by applying unitary method.
Hope this helps.
After every score in a sample is multiplied by 5, the mean is found to be M = 40. What was the value for the original mean?
Answer:
M=8
Step-by-step explanation:
We have that every score in a sample is multiplied by 5, and the mean is found to be M = 40.
We want to find the original mean.
Since each of the data value is multiplied by 5, the new mean will be 5 times the original mean.
To get the original mean, we need to divide by 5;
Therefore the original mean is [tex]\frac{40}{5}=8[/tex]
To find the original mean, divide the new mean by the multiplying factor.
Explanation:To find the original mean, we need to undo the multiplication by dividing the new mean by the multiplying factor. Since every score was multiplied by 5, we divide the new mean by 5 to get the original mean.
Original Mean = New Mean / Multiplying factor
Original Mean = 40 / 5
Original Mean = 8
Learn more about Finding Original Mean here:https://brainly.com/question/32902609
#SPJ3
what is the answer to 6m + 7(7m + 9)
Answer:
55m+63
Step-by-step explanation:
6m+7(7m+9)
6m+49m+63
55m+63
calculate the length of the circumference of a circle with a radius of 3cm
Answer:
[tex]6\pi[/tex]
Step-by-step explanation:
use the formula [tex]C=2\pi r[/tex]
r = radius
plug in numbers into the equation to get
[tex]2\pi (3)[/tex] which equals [tex]6\pi[/tex]
Answer:
The answer was 9.42 units
Step-by-step explanation:
a baseball has a diameter of 3 inches.Calculate the volume
Answer:
14.14 in3
Step-by-step explanation:
Please help me don’t ignore. Due today at 1:00. Just these three questions, please show your work and give me the correct answer. Like you doing the math on paper. Thank you!
Answer:
Step-by-step explanation:
I would be happy to answer them but I do not see the 3 questions.
3(x-6)+(4x+12)-6x simplify
Answer:
x-6
Step-by-step explanation:
Answer:
x - 30
Step-by-step explanation:
[tex]3(x - 6) + (4x + 12) - 6x \\ 3x - 18 + 4x + 12 - 6x \\ 3x + 4x - 6x - 18 - 12 \\ x - 30[/tex]
Jason and his family travel 160 miles in 3.2 hours. If they continue at this constant speed, how long will it take them to travel 300 miles? Complete the table
It will take them 6 hours to travel 300 miles. How I got my answer: 160 divided by 3.2 = 50 miles per hour, 300 divided by 50 = 6 hours. Hope I could help! :D
Answer:
t = 6hrs
Step-by-step explanation:
Speed = distance/time
Speed at 160miles in 3.2hrs will be = 160/3.2= 50
At the constant speed of 50, time taken to travel 300miles
Is speed = distance / time
50 =300/t
Cross multiply
50t =300
Divide both sides by 50
t = 300/50
t = 6hrs
Is 5/20 equal to 4/12
Answer:
No, it's not
Step-by-step explanation:
Lets simplify the two fractions to the lowest term
for 5/20 we'll divide the numerator and denominator by 5 (the HCF of the two)
it then becomes 1/4
For 4/12 we'll divide the numerator and denominator by 4 (the HCF of the two)
it then becomes 1/3
1/4 = 0.25
1/3 = 0.33
therefore 5/20 is not equal to 4/12
In ΔXYZ, x = 5.9 meters, y = 8.9 meters, and z = 5.8 meters. Find the remaining measurements of the triangle, and round your answers to the nearest tenth.
Answer:
Angles: 40.9°, 99.05°, 40.05°
Step-by-step explanation:
Triangles
When we are given the lengths of the 3 sides of a triangle, we can easily compute all the internal angles by using the cosine's law or formula. Being x,y and z the sides of a triangle, and \alpha, \beta , \gamma the three opposite angles respectively, then
[tex]x^2=y^2+z^2-2yzcos\alpha[/tex]
[tex]y^2=x^2+z^2-2xzcos\beta[/tex]
[tex]z^2=x^2+y^2-2xycos\gamma[/tex]
We have x=5.9, y=8.9, z=5.8, then from
[tex]x^2=y^2+z^2-2yzcos\alpha[/tex]
We solve for [tex]\alpha[/tex]
[tex]\displaystyle cos\alpha=\frac{y^2+z^2-x^2}{2yz}[/tex]
[tex]\displaystyle cos\alpha=\frac{8.9^2+5.8^2-5.9^2}{2\times 8.9\times 5.8}[/tex]
[tex]cos \alpha=0.756[/tex]
[tex]\alpha=40.9 ^o[/tex]
Similarly
[tex]\displaystyle cos\beta=\frac{x^2+z^2-y^2}{2xz}[/tex]
[tex]\displaystyle cos\beta=\frac{5.9^2+5.8^2-8.9^2}{2\times 5.9\times 5.8}[/tex]
[tex]cos\beta=-0.157[/tex]
[tex]\beta=99.05^o[/tex]
Finally
[tex]\displaystyle cos\gamma=\frac{5.9^2+8.9^2-5.8^2}{2\times 5.9\times 8.9}[/tex]
[tex]cos\gamma=0.765[/tex]
[tex]\gamma=40.05^o[/tex]
Answer:
Answer is D
Step-by-step explanation:
If 12 horses eat 96 bales of hay per week, how many 18 horses eat in a week.
Answer:
144
Step-by-step explanation:
If 12 horses eat 96 bales of hay per week
Than one horse eats 96÷12 bales of hay per week
One horse eats 8 bales of hay per week
Than 18 horses will eat 8 × 18 bales of hay per week
18 horses will eat 144 bales of hay per week
Which equation is parallel to the line LaTeX: y=\frac{1}{2}x+3y = 1 2 x + 3and passes through the point (10, -5)?
Group of answer choices
Plz help asap thank you!!
Answer:
[tex]Equation\ of\ line:\ y=\frac{1}{2}x-10[/tex]
Step-by-step explanation:
[tex]Let\ the\ required\ equation\ is\ y=mx+c\\\\where\ m\ is\ the\ slope\ of\ the\ equation\ and\ c\ is\ y-intercept\\\\It\ is\ parallel\ to\ the\ equation\ y=\frac{1}{2}x+3\\\\Hence\ slope\ of\ these\ two\ lines\ will\ be\ same.\\\\Slope\ of\ y=\frac{1}{2}x+3\ is\ \frac{1}{2}\\\\Hence\ slope\ of\ y=mx+c\ is\ \frac{1}{2}\Rightarrow m=\frac{1}{2}\\\\Equation:y=\frac{1}{2}x+c\\\\Line\ passes\ through\ (10,-5).\ Hence\ this\ point\ satisfies\ the\ equation\ of\ line.\\\\-5=\frac{1}{2}\times 10+c[/tex]
[tex]-5=-5+c\\\\c=-10[/tex]
[tex]Equation\ of\ line:\ y=\frac{1}{2}x-10[/tex]
if I have a 100 gallon water tank and use 5 gallons per minute while feeding it 2.5 gallons per minute will that tank run out of water
The dimensions of a 4-in. square are multiplied
by 3. How is the area affected?
Answer:
The area is multiplied by 9.
Step-by-step explanation:
The original square has an area of ...
A = (4 in)² = 16 in²
The larger square has an area of ...
A = (3·4 in)² = (3²)(4²) in² = 9·16 in² . . . . . 9 times the original area
The area is multiplied by the square of the scale factor: 9.
Choose the graph that matches the situation.
Answer:
1. A 2.A
Step-by-step explanation:
A for number 1 shows how the level of the pot slowly increases as things are added, while cooking the level stays consistent then as one dish is served it decreases a level then stays a bit and keeps repeating that.
A for number 2 shows how the bus speeds up then stays a consistent 25 mph and slows down for two stops then speeds up and stays 25 mph.
How to solve 45degrees 45degrees 90degrees triangles
Answer: You're given one leg. Because you know both legs are equal, you know the length of both the legs.
Step-by-step explanation:
You're given the hypotenuse. Divide the hypotenuse by the square root of 2 to find the legs (which are equal).
0.7(3x-5)+3.9=14.5
What is the value of x?
Answer:
srry that was my lil bro
Step-by-step explanation:
ASAP I NEED THIS ANSWERED
The rectangle shown has a perimeter of 86 cm and the given area. Its length is 7 more than three times its width. Write and solve a system of equations to find the dimensions of the rectangle
The width of the rectangle is 9 cm.
The length of the rectangle is 34 cm.
Step-by-step explanation:
step 1 :
Let width of the rectangle be 'x'
The length of the rectangle = 7 + 3x
step 2 :
Perimeter of the rectangle = 2 (length + width)
⇒ 86 = 2 (7 + 3x + x)
⇒ 86 = 2 (7 + 4x)
⇒ 86 = 14 + 8x
⇒ 72 = 8x
x = 72/8
x = 9
∴ The width of the rectangle is 9 cm
step 3 :
The length of the rectangle = 7 + 3x
= 7 + 3(9)
= 7+27 = 34 cm
(-6,5) and (4,-1) equation
Answer:
[tex]y=-\frac{3}{5}x+\frac{7}{5}[/tex]
Step-by-step explanation:
The correct question is
Write an equation for the line passing through (-6,5) and (4,-1)
step 1
Find the slope
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
(-6,5) and (4,-1)
substitute
[tex]m=\frac{-1-5}{4+6}[/tex]
[tex]m=\frac{-6}{10}[/tex]
[tex]m=-\frac{3}{5}[/tex]
step 2
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{3}{5}[/tex]
[tex]point\ (-6,5)[/tex]
substitute
[tex]y-5=-\frac{3}{5}(x+6)[/tex]
step 3
Convert to slope intercept form
[tex]y=mx+b[/tex]
Isolate the variable y
[tex]y-5=-\frac{3}{5}x-\frac{18}{5}[/tex]
[tex]y=-\frac{3}{5}x-\frac{18}{5}+5[/tex]
[tex]y=-\frac{3}{5}x+\frac{7}{5}[/tex]
What are the equations of the asymptotes of the graph of the function f (x) = StartFraction 3 x squared minus 2 x minus 1 Over x squared + 3 x minus 10 EndFraction?
Answer:
A on E2020 (x = -5, x = 2, y = 3)
Step-by-step explanation:
By looking at the equation, we know that the horizontal asymptote can be found by using [tex]y=\frac{a}{b}[/tex], where [tex]a[/tex] and [tex]b[/tex] are the leading coefficients of the variables in the numerator and denominator.
In the equation, [tex]a=3[/tex] and [tex]b=1[/tex]. So, the horizontal asymptote is 3, meaning [tex]y=3[/tex].
To find the vertical asymptotes, we must simplify the denominator by factoring. We will then get [tex](x+5)(x-2)[/tex] in the denominator. So, [tex]x=-5[/tex] and [tex]x=2[/tex].
Therefore, the answer is option A.
Answer:
A Edge 2021
I got 100%
List the next four multiples of the unit fraction 1/2 4th grade
Step-by-step explanation:
We have:
The unit fraction = [tex]\dfrac{1}{2}[/tex]
To find, the next four multiples of the unit fraction [tex]\dfrac{1}{2}[/tex] = ?
∴ The next four multiples of the unit fraction [tex]\dfrac{1}{2}[/tex]
The first multiple = [tex]\dfrac{1}{2}\times 2= \dfrac{2}{2} =1[/tex]
The second multiple = [tex]\dfrac{1}{2}\times 3= \dfrac{3}{2}[/tex]
The third multiple = [tex]\dfrac{1}{2}\times 4= \dfrac{4}{2} =2[/tex]
The fourth multiple = [tex]\dfrac{1}{2}\times 5= \dfrac{5}{2}[/tex]
∴ The next four multiples of the unit fraction [tex]\dfrac{1}{2}[/tex] are
[tex]\dfrac{2}{2}[/tex] ( 1), [tex]\dfrac{3}{2}[/tex], [tex]\dfrac{4}{2}[/tex] (2) and [tex]\dfrac{5}{2}[/tex].
The first four multiples: [tex]\frac{1}{2}, 1, \frac{3}{2}, 2[/tex]. A multiple of a fraction is found by multiplying that fraction by whole numbers.
To find the next four multiples of the unit fraction [tex]\frac{1}{2}[/tex], we can begin by understanding what a multiple of a fraction means.
Let's calculate the first four multiples of [tex]\frac{1}{2}[/tex]:
First multiple: [tex]1 \times \frac{1}{2} = \frac{1}{2}[/tex]
Second multiple: [tex]2 \times \frac{1}{2} = \frac{2}{2} = 1[/tex]
Third multiple: [tex]3 \times \frac{1}{2} = \frac{3}{2}[/tex]
Fourth multiple: [tex]4 \times \frac{1}{2} = \frac{4}{2} = 2[/tex]
Fill in the blank so that the ordered pair is a solution of y=12x+2.
(
, 14)
Answer:
x=1
Step-by-step explanation:
14=12x+2
subtract 2 from both sides
12=12x
divide both sides by 12 and you get x=1