Nancy has 8 meters of rope. How many pieces of rope of length 1/2 meter can she cut from it
Answer:
16
Step-by-step explanation:
8 divided by 1/2 is
8 times 2
which is
16
Which expression is equal to (screenshot)
Answer:
D. 6x + 4 / x² + 5x
Step-by-step explanation:
Dividing a fraction is same as multiplying its inverse.
Therefore,
(3x + 2)/(4x) × 8/(x + 5)(3x + 2)/x × 2/(x + 5)2(3x + 2)/x(x + 5)6x + 4 / x² + 5xOption DAnswer:
[tex]\textsf{D.} \quad \dfrac{6x+4}{x^2+5}[/tex]
Step-by-step explanation:
When dividing fractions, multiply the first fraction by the reciprocal of the second fraction:
[tex]\begin{aligned}\left(\dfrac{3x+2}{4x}\right) \div \left(\dfrac{x+5}{8}\right) & =\left(\dfrac{3x+2}{4x}\right) \times \left(\dfrac{8}{x+5}\right)\\\\& = \dfrac{(3x+2) \times 8}{4x \times (x+5)}\\\\& = \dfrac{8(3x+2)}{4x(x+5)}\\\\& = \dfrac{2(3x+2)}{x(x+5)}\\\\& = \dfrac{6x+4}{x^2+5}\\\end{aligned}[/tex]
If y varies directly with x and y = 87 when x = 3, find y when x = 5. Write and solve a direct variation equation to find the answer
Answer:
145
Step-by-step explanation:
y=kx
87=3k
k= 87/3
k= 29
y=29×5
y= 145
What line is perpendicular to y−7=4/5(x+3)?
A. y= −5/4x+1
B. y= 5/4x+1
C. y= 4/5x+1
D. y= −4/5x+1
Answer: The correct answer would be C. y= 4/5x+1
Step-by-step explanation:
[tex]y-intercept=\frac{47}{5}[/tex]
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
y-7-(4/5*(x+3))=0
STEP
1
:
4
Simplify —
5
Equation at the end of step
1
:
4
(y - 7) - (— • (x + 3)) = 0
5
STEP
2
:
Equation at the end of step 2
4 • (x + 3)
(y - 7) - ——————————— = 0
5
STEP
3
:
Rewriting the whole as an Equivalent Fraction
3.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 5 as the denominator :
y - 7 (y - 7) • 5
y - 7 = ————— = ———————————
1 5
Equivalent fraction: The fraction thus generated looks different but has the same value as the whole
Common denominator: The equivalent fraction and the other fraction involved in the calculation share the same denominator
3.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
(y-7) • 5 - (4 • (x+3)) 5y - 4x - 47
——————————————————————— = ————————————
5 5
Equation at the end of step
3
:
5y - 4x - 47
———————————— = 0
5
STEP
4
:
When a fraction equals zero :
4.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now, to get rid of the denominator, I multiply both sides of the equation by the denominator.
Here's how:
5y-4x-47
———————— • 5 = 0 • 5
5
Now, on the left hand side, the 5 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
5y-4x-47 = 0
Equation of a Straight Line
4.2 Solve 5y-4x-47 = 0
CalderonJ recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx + b" is the formula of a straight line drawn on a Cartesian coordinate system in which "y" is the vertical axis and "x" is the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 5y-4x-47 = 0 and calculate its properties
Notice that when x = 0 the value of y is 47/5 so this line "cuts" the y axis at y= 9.40000
y-intercept = 47/5 = 9.40000
Calculate the X-Intercept :
When y = 0 the value of x is 47/-4 Our line therefore "cuts" the x axis at x=-11.75000
x-intercept = 47/-4 = -11.75000
Calculate the Slope :
The slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 9.400 and for x=2.000, the value of y is 11.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 11.000 - 9.400 = 1.600 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 1.600/2.000 = 0.800
Whats the area of this shape?
The area of the shape shown in the image which is in the shape of kite figure is 168 squared centimeters.
What is the area of the kite figure?The area of the kite figure is half of the product of its diagonals. Area of kite figure can be find out using the following formula.
[tex]A=\dfrac{pq}{2}[/tex]
Here, p and q are the diagonals of the kite.
The length of the first diagonal of the kite figure is,
p=6+15
p=21 cm
The length of the second diagonal of the kite figure is,
q=8+8
q=16 cm
Thus, the area of kite figure is:
[tex]A=\dfrac{21\times16}{2}\\A=\dfrac{21\times16}{2}\\A=168\rm\; cm^2[/tex]
Thus, the area of the shape shown in the image which is in the shape of kite figure is 168 squared centimeters.
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What does X= and what is the angle
A. Corresponding
B.same side interior
C. Alternate interior
D.Alternate exterior
Please help fghgbvnghgbvhgghg
Answer:
x=326
Step-by-step explanation:
0.3x - 34 + 0.2x -39 = 90.
Simplify this equation.
0.5x = 163
x = 326
A wheel on Aldo's bicycle is 0.3m in diameter. Aldo rides the bicycle in a race, and the wheel turns 45 times during the course of the race. How long is the race?
Use the value 3.14 for pi. Round your answer to the nearest tenth. Do not round any intermediate steps.
Answer:
42.39m Please round it to nearest tenth.I haven't rounded it
So confused! Anyone good at this?
Answer:
x = 90 degrees.
Step-by-step explanation:
These are all regular octagons and the value of x = 2 * external angle of an octagon.
The sum of external angles of a polygon sum to 360 degrees and in the case of an octagon each external angle = 360/8 = 45 dgrees,
So angle x = 2*45 = 90 degrees.
split 54 between 4 people
Answer:
your answer is 13.2
Step-by-step explanation:
The sum of the digits of a two - digit number is 15. if the the digits were reversed , the number increases by 9 . Find the number .
Stay away if u don't know the ans.
Well explained ans needed :)
Answer:
78
Step-by-step explanation:
Let the two-digit number have the digits a and b.
It mentions that they add up to 15.
Then the possible numbers are :
69 (6 + 9 = 15)78 (7 + 8 = 15)=============================================================
Let's reverse the numbers :
69
69 ⇔ 9696 - 69 = 27Not the right number ×78
78 ⇔ 8787 - 78 = 9This is correct √=============================================================
Solution :
Hence, the number needed is 78
Step-by-step explanation:
no. 10y+x
no. formed by reversing the digits = 10x+ y
ATQ
EQ(1)= x+y=15
EQ (2)=10x+y+9=10y +x ( Digits are reversed)
9x-9y=-9
x-y=-1
x+y=15 ( given)
2x=14,x=7
and y=15–7=8
thus the number=78
what is the length of the leg in a 45-45-90 triangle with a hypotenuse of 1?
Answer:
√2 / 2
Step-by-step explanation:
In a 45-45-90 triangle, the length of a leg is equal to the hypotenuse / √2
Therefore, the length of a leg is 1 / √2
Rationalize by multiplying the numerator and denominator by √2, and this becomes √2 / 2
in need of help please :)
Answer:
okay let's start
Step-by-step explanation:
[tex]number \: 1 \\ cos \: b = \frac{adjacent}{hypotenuse} \\ cos \: b = \frac{ac}{cb} \\ \: \ cos \: b = \frac{12}{13} \\ [/tex]
Determine the sum of the terms in the series 25 + 30 + 35 + ⋯ + 245. Show your work.
Answer:
6075
Step-by-step explanation:
Given series is: 25 + 30 + 35 + ⋯ + 245.Here, first term (a) = 25Common difference (d) = 5Last term [tex](a_n) = 245[/tex]First we find the number of terms that this series has by the following formula:[tex]a_n = a+(n-1)d[/tex]Plugging the values of a, d and [tex]a_n[/tex], we find.[tex]245 = 25+(n-1)5[/tex][tex]\implies 245 - 25=(n-1)5[/tex][tex]\implies 220=(n-1)5[/tex][tex]\implies \frac{220}{5}=n-1[/tex][tex]\implies 44=n-1[/tex][tex]\implies 44+1=n[/tex][tex]\implies\red{\bold{ n=45}}[/tex]Thus, the given series contains 45 terms.Next, we find the sum of the given series using the formula given below.[tex]S_n = \frac{n}{2}(a+a_n)[/tex][tex]\implies S_{45}= \frac{45}{2}(25+245)[/tex][tex]\implies S_{45}= \frac{45}{2}(270)[/tex][tex]\implies S_{45}=45*135[/tex][tex]\implies\orange{\boxed{\boxed{\boxed{\bold{ S_{45}=6075}}}}}[/tex]Dylan has a total of 25 marbles. He gives ! marbles to his sister, Jane. What fraction
of marbles did Jane receive?
The Dylan sister Jane received 1/5 marbles, which is a part of 25 if the Dylan has a total of 25 marbles.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The total number of marbles Dylan has = 25
The total number of marbles Dylan gave to his sister = 5
If we choose one marble out of 25 = 1/25
If we choose 5 marbles = 5(1/25) = 1/5
Thus, the Dylan sister Jane received 1/5 marbles, which is a part of 25 if the Dylan has a total of 25 marbles.
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if v1 = (3,7) and v2 = (2,4), then v1 v2 is equal to which of the following
Answer:
If it is dot product, then 32.
Step-by-step explanation:
3*2+7*4
6+28
32
There are 20 boys and 18 girls in a class find the percentage of {1} boys {2} girls, in the class
Answer:
1. 52.63% 2. 47.36%
Step-by-step explanation:
20 + 18 = 38 total people
20 divided by 38 = 0.5263 to 52.63%
18 divided by 38 = 0.4736 to 47.36%
Hope this helps!
Which is the equation of a hyperbola with directrices at x = ±2 and foci at (6, 0) and (−6, 0)?
Answer:
[tex]\displaystyle \frac{x^2}{12}-\frac{y^2}{24}=1[/tex]
Step-by-step explanation:
Since the directrices are vertical lines:
Use the hyperbola equation [tex]\displaystyle \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex] Foci are [tex](\pm c,0)[/tex][tex]a^2+b^2=c^2[/tex][tex]a[/tex] and [tex]b[/tex] are half the lengths of the tranverse and conjugate axes respectivelyDirectrices are located at the lines [tex]\displaystyle x=\pm\frac{a^2}{c}[/tex]We assume the center to be [tex](h,k)\rightarrow(0,0)[/tex]Since we already know our directrices are at the lines [tex]x=\pm2[/tex] and we know that [tex]c=\pm6[/tex] from our foci, we can solve for the value of [tex]a^2[/tex]:
[tex]x=\frac{a^2}{c}\\\\2=\frac{a^2}{6}\\\\12=a^2[/tex]
This allows us to solve for the value of [tex]b^2[/tex]:
[tex]a^2+b^2=c^2\\\\12+b^2=6^2\\\\12+b^2=36\\\\b^2=24[/tex]
Thus, our equation for the hyperbola is [tex]\displaystyle \frac{x^2}{12}-\frac{y^2}{24}=1[/tex].
Which function best models the data in the graph? y = 10.1x 101 y = x2 101 y = 101(2x) y = 1.01x2 101
Based on the calculations, the function which best models the data in the graph is y = 10.1x + 101.
How to determine the function?Mathematically, the equation of a line in standard form is given by this formula:
y - y₁ = m(x - x₁)
Where:
m is the slope.y is the point on the horizontal axis.x is the point on the vertical axis.In order to determine the function which best models the data in the graph shown in the image attached below, we would calculate the slope of the data by using this formula:
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}\\\\Slope = \frac{202\;-\;101}{10\;-\;0}\\\\Slope = \frac{101}{10}[/tex]
Slope = 10.1.
For the function, we have:
y - y₁ = m(x - x₁)
y = 10.1(x - 0) + 101
y = 10.1x + 101.
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The next part is D then C
Step-by-step explanation:
What is the mode?
9 4 6 3 9 3 10 4 6 4
Answer:
4
Explanation:
The mode is what number occurs most often
The mode for this question is 4
Mode
In a set of numbers, the mode is the number that occurs most often. In other words, it measures how frequently a particular number occurs within a set of numbers. It is a type of average, like its counterparts, the median and mean.
To find the mode of a set of numbers,
List the set of numbers in ascending or descending order, including any duplicatesCount the number of times each number in the set of numbers occurs. The number that occurs the highest number of times is the mode of the set of data5х + 15 + 3xy +9y factor it
Answer:
(5+3y) (x+3)
first of all you bracket by (5x+15)(3xy+9y). and you start fact as follows by 5(x+3y) 3y(x+3)after here you take (5+3y) (x+3)
Answer:
(x+3)+(5+3y)
Step-by-step explanation: In the equation, when you have four terms you group like terms. So 5x+15 by itself and work it out which you will get 5(x+3) and do the same for 3xy+9y answer is 3y(x+3).
Then you will say 5(x+3)+3y(x+3) and then you'll
5(x+3)/(x+3)=5 because you will cancel the (x+3) so the answer would be 5
You will do the same for 3y(x+3)/(x+3)
you will get 3y
Finally, you will take the first equation which is (x+3), and then you'll use the last equation which is (5+3y)
So that's how you will get (x+3)+(5+3y)
Select the best description for the sum of the expression below.
√10 + √26
A. rational
B. neither rational nor irrational
C. both rational and irrational
D. irrational
Answer:
D.irrational
Step-by-step explanation:
√10 +√26= 8.261279174
is has decimal at the end therefore it is irrational
billy has 2.4m of ribbon for crafts. he wants to share it evenly with 12 friends. how many centimeters of ribbon would 7 friends get
Answer:
140cm
Step-by-step explanation:
We first have to change 2.4 meters into centimeters. And the formula for that is (x)m = (x)cm x 100.
So 2.4 x 100 = (x)m. We can solve this by moving the "." two times to the right and we will get 2.4m = 240cm.
The next step is to divide it by twelve because Billy wants to share it with 12 friends. 240cm/12 = 20cm per person.
Then we have to multiply 20 with 7 to see how many centimeters 7 friends would get.
20*7 = 140. So the answer is 140cm.
[6m² x 6n² ÷ 9mn ÷ 2m]² ??
I need to simplify this expression
please help with working out so I can understand. Thanks!
Answer:
4n^2.
Step-by-step explanation:
Working from left to right in the square parentheses:-
[6m² x 6n² ÷ 9mn ÷ 2m]²
= [(36m^2n^2 / 9mn) / 2m]^2
= (4mn / 2m)^2
= (2n)^2
= 4n^2.
[6m² x 6n² ÷ 9mn ÷ 2m]²
to find:the simplest form.
solution:[tex] (\frac{6 {m}^{2} \times (6 {n}^{2} ) \div 9mn {}^{} }{2m} ) {}^{2} [/tex]
[tex] = \binom{ \frac{2 {m}^{2} \times (6 {n}^{2}) }{3mn} }{2m} {}^{2} [/tex]
[tex] = \binom{ \frac{2m \times (2 {n}^{2}) }{n} }{2m} {}^{2} [/tex]
[tex] = ( \frac{m \times (2n)}{m} ) {}^{2} [/tex]
[tex] = (2n {)}^{2} [/tex]
[tex] = 4 {n}^{2} [/tex]
F is directly proportional to A. If F=36 when A=9 find, F when A=4
Answer:
16
Step-by-step explanation:
f=ka
36=9k
k=4
f=4×4
f=16
Probability & Sampling:Question 8
Mr. Evans wanted to compare the math grades of his 6th
grade students and 7th grade students. He displayed the
data on dot plots.
The conclusion that Mr. Evans can make is that On average, students in 6th Grade have lower grades than students in 7th Grade.
What is a dot plot?This is also known to be a dot chart. It is said to be a statistical chart that is made up of data points which are known to be plotted on a little and simple scale.
Note that based on the dotted plot of the student's grade, the conclusion that can be drawn or the one that Mr. Evans can make is that On average, students in 6th Grade have lower grades than students in 7th Grade.
See full question below
What conclusion can Mr. Evans make? Hint: Find the mean
answer choices
On average, students in 6th Grade have lower grades than students in 7th Grade.
On average, students in 6th Grade have higher grades than students in 7th Grade.
Students will always have a lower math grade in 6th Grade than 7th Grade.
On average, students in 6th Grade and 7th Grade have about the same grade
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It's seventh grade social studies the question is written thanks!!
Answer:
Slavery caused the Civil War because colored people were being treated unfairly by the South and the North didn't like that. States rights is when a state abides by its own rules. Missouri was allowed to enter the Union as a slave state. California had to decide if they were going to be a slave state or a free state.
Step-by-step explanation:
Slavery was the root of the Civil War in the United States. Following the election of Republican and abolitionist Abraham Lincoln in 1861, southern governments grew fearful of his political beliefs. His victory sparked heated debate in the slave-dependent southern states. Because of the incoming president's future activities, states were planning to secede. These republics were heavily reliant on agriculture, therefore ending slavery would be disastrous. After Lincoln rejected their judgment, the Union and Confederacy declared war on one other. The Confederacy battled and killed to keep slavery alive, but the union won four years later. Abraham Lincoln fought for black people's freedom and human rights while simultaneously fighting to keep the Unified States united. This battle not only ended slavery, but it also brought the states together and preserved a strong country developing together.In the 1860 presidential election, Abraham Lincoln campaigned for president and won, becoming the first republican candidate to do so. His election, on the other hand, brought terrible news to the southern states, which were heavily reliant on agricultural and used slavery to increase revenues. "By and large," according to the book America Past and Present, "By and large, by and large, by and large, by and The civil war began in April 1861, when Southern states attempted to secede from the nation after Abraham Lincoln's election, and concluded in 1865, when the northerners (the Union) triumphed. However, the most crucial reason for the outbreak of the war was that Republican Abraham Lincoln won the election of 1860, and his views on slavery were diametrically opposed to those of the southerners. His election sparked such outrage in the southern states that the possibility of going to war to avoid being linked with his political ideals was floated.
Six sophomores and 14 freshmen are competing for two alternate positions on the debate team.
Which expression represents the probability that both students chosen are sophomores?
I think the answer is B<==
Permutation helps us to know the number of ways an object can be arranged in a particular manner. The correct option is B.
What are Permutation and Combination?Permutation helps us to know the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.
The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.
[tex]^nC_r = \dfrac{n!}{(n-r)!r!}\ , \ \ ^nP_r = \dfrac{n!}{(n-r)!}[/tex]
where,
n is the number of choices available,
r is the choices to be made.
The probability that both students have chosen are sophomores is,
(6/20) × (5/19) = 30/380
Similarly, The expression that represents the probability that both students have chosen are sophomores is,
(⁶P₁ × ⁵P₁)/(²⁰P₂) = 30/380
Hence, the correct option is B.
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Sarah is going on a trip. she drives for 2 hours and 45 minutes, rests for 35 minutes and drives
for another 2 hours 50 minutes.
what is her total travel time in hours and minutes
Answer:
5 hours and 35 minutes
Step-by-step explanation:
If you add the 45 and 50 minutes, you get 95 minutes, but an hour is only 60 minutes. So you subtract 60 and you're left with 35 minutes. You add the new hour onto the other 4 hours and you get 5 hours total.
Answer: 5 hours and 35 minutes
Step-by-step explanation: 2 + 2 = 4 45 + 50 = 95 95- 60 = 35
Volleyball players are randomly placed on teams by spinning a spinner with four congruent, colored sections. They are assigned positions on the team by rolling a six-sided die. The team colors are red, black, green, and purple.
What is the conditional probability of rolling a 5 given that the spinner landed on black?
A. 1/6
B. 1/24
C. 2/5
D. 1/4
