Answer:
21 students
Step-by-step explanation:
Let c = number of students in class
c* 2/7 = 6
Multiply each side by 7/2
c * 2/7 *7/2 = 6 *7/2
c = 21
There are 21 students in the class
Match the terms to their definition.
1. corresponding parts
having the same exact size and
shape
2. congruent
3. Similar figures
figures that have the same shape
but not necessarily the same size
the ratio between the lengths of
corresponding sides in similar figures
angles or sides in the same position
on similar figures
figures that have the same size and
4. congruent figures
5. scale factor
shape
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Answer:
------->
Step-by-step explanation:
corresponding parts - angles or sides in the same position on similar figures
congruent - having the same exact size and shape
similar figures - figures that have the same shape but not necessarily the same size
congruent figures - figures that have the same size and shape
scale factor - the ratio between the lengths of corresponding sides in similar figures
what is x? please answer asap thanks!
==================================================
Work Shown:
Straight lines DF and EC intersect at point A. Because of this, angle DAF is a 180 degree angle.
Angles DAB, BAC, and CAF all combine to form a straight 180 degree angle.
Add up the angles mentioned, set the sum equal to 180, and solve for x
-----------
(angle DAB) + (angle BAC) + (angle CAF) = 180
x + 80 + 60 = 180
x + 140 = 180
x + 140-140 = 180-140 ... subtract 140 from both sides
x = 40
Answer:
[tex]\Huge \boxed{x=40\°}[/tex]
Step-by-step explanation:
Angles on a straight line add up to 180 degrees.
We can create an equation and solve for x.
x + 80 + 60 = 180
Add the numbers on the left side.
x + 140 = 180
Subtract 140 from both sides.
x + 140 - 140 = 180 - 140
x = 40
please help ٩(๑òωó๑)۶
Answer:
Height of the cliff = 13.66 m
Step-by-step explanation:
Let the height of the cliff is 'x' m and distance between the base of the cliff and the boat is 'y' m.
From right triangle AOC,
tan 30° = [tex]\frac{\text{Opposite triangle}}{\text{Adjacent side}}[/tex]
[tex]\frac{1}{\sqrt{3}}=\frac{x}{y}[/tex]
y = [tex]x\sqrt{3}[/tex] ------(1)
From right angle triangle BOC,
tan 45° = [tex]\frac{x}{y-10}[/tex]
[tex]1=\frac{x}{y-10}[/tex]
x = y - 10
y = x + 10 -------(2)
From equations (1) and (2),
[tex]x\sqrt{3}=x+10[/tex]
[tex]x(\sqrt{3}-1)=10[/tex]
[tex]x=\frac{10}{\sqrt{3}-1 }[/tex]
x = 13.66 m
Therefore, height of the cliff is 13.66 m.
A shed can hold up to 1620 cubic feet. Items totaling 1180 cubic feet are put
into the shed. If the variable v stands for the amount of additional volume the
shed can hold, which would be a reasonable value for ?
A.) 12 cubic feet
B.) 2800 cubic feet
C.) 0.4 cubic feet
D.) 400 cubic feet
Answer:
c is the answer
Step-by-step explanation:
Answer:
D. 400 cu ft/
Step-by-step explanation:
1620 - 1180
= 440.
La siguiente figura representa una torre de transmisión de energía eléctrica: ¿Mediante cual razón trigonométrica se puede determinar la altura de la torre? Dejar procedimiento o justificación. A. Sen α = BC/c B. Sen α = BC/b C. Sen α = c/b D. Sen α = b/c
Answer:
B. Sen α = BC/b
Step-by-step explanation:
Para un ángulo recto, el lado opuesto es el lado opuesto al ángulo, el lado adyacente es el lado entre el ángulo y el ángulo recto y la hipotenusa es el lado más largo (el lado opuesto al ángulo recto).
De identidades trigonométricas:
[tex]sen\ \alpha=\frac{opuesto}{hipotenusa}[/tex]
De la figura, el lado opuesto = altura = BC y la hipotenusa = b. Por lo tanto:
[tex]sen\ \alpha=\frac{opuesto}{hipotenusa}\\\\sen\ \alpha=\frac{BC}{b}[/tex]
(3 + 2i) + (-5 + 7i) Add or subtract the complex numbers as needed and write your answer in the simplest a+bi form.
Answer:
-2 + 9i
Step-by-step explanation:
( 3 + 2i ) + ( -5 + 7i )
→ Remove brackets
3 + 2i +- 5 + 7i
→ Remember that the negative cancels out the plus
3 + 2i - 5 + 7i
→ Add the whole numbers together
-2 + 2i + 7i
→ Add the i values together
-2 + 9i
Answer:
[tex]\huge\boxed{-2 + 9i}[/tex]
Step-by-step explanation:
[tex]\sf (3+2i)+(-5+7i)\\Expanding \ Parenthsis\\3+2i -5 +7i\\Combining \ like \ terms\\3-5 + 2i+7i\\-2 + 9i[/tex]
This is the required answer in the form a + b i
Two sums of money are in the ratio 5:1.If the Smaller amount is 15 kobo.What is the largest?
(a) 35k (b) 45k (c)55k (d)65K (e) 75K
Answer:
[tex]\huge\boxed{ x = 75 k}[/tex]
Step-by-step explanation:
The given ratio is:
=> 5 : 1
Given that the smallest one is 15k
So, Let's built a proportion:
=> 5 : 1 = x : 15 [Where x is the unknown one]
Product of Means = Product of Extremes
x = 5 * 15
=> x = 75 k
Determine whether the following sequence is arithmetic, geometric, or neither.
-7, -14, -28, -56,
===============================================
Explanation:
To go from term to term, we are multiplying by 2
-7 * 2 = -14
-14 * 2 = -28
-28 * 2 = -56
This means the common ratio is 2 and this sequence is geometric.
---------
Alternatively, you can divide each term by its prior term
-56/(-28) = 2
-28/(-14) = 2
-14/(-7) = 2
Each time we get the same result showing the common ratio is 2.
Answer:
Geometric
Step-by-step explanation:
It multiplies by two each time
|9-(-1)|= simplify the expression
Answer:
10
Step-by-step explanation:
Remove parentheses.
|9+1|
Simplify 9+1 to 10.
|10|
simplify
10
make m the subject of the formula. r=5m^2-n
Answer:
The answer is
[tex]m = \sqrt{ \frac{r + n}{5} } [/tex]Step-by-step explanation:
[tex]r = 5 {m}^{2} - n[/tex]To make m the subject send n to the left side of the equation
That's
[tex] {5m}^{2} = r + n[/tex]Divide both sides by 5
We have
[tex] \frac{ {5m}^{2} }{5} = \frac{r + n}{5} [/tex][tex] {m}^{2} = \frac{r + n}{5} [/tex]Find the square root of both sides to make m stand alone
That's
[tex] \sqrt{ {m}^{2} } = \sqrt{ \frac{r + n}{5} } [/tex]We have the final answer as
[tex]m = \sqrt{ \frac{r + n}{5} } [/tex]Hope this helps you
Answer:
Step-by-step explanation:
r = 5m² - n
Add n to both sides
r + n = 5m² - n +n
r + n = 5m²
Divide both sides by 5
(r+n)/5 = 5m²/5
(r + n)/5 = m²
Take square root ,
[tex]\sqrt{\frac{r + n}{5}} =\sqrt{m^{2}} \\\\\sqrt{\frac{r + n}{5}}=m\\\\\\m=\sqrt{\frac{r + n}{5}}[/tex]
Simplify the expression 8x² + x - 5 + (2x² - 9x + 13)
A. 10x² - 8x + 8
B. 10x²
C. 10x² + 8x - 8
D. 10x² - 8x - 8
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{10 {x}^{2} - 8x + 8}}}}}[/tex]
Option A is the correct option
Step-by-step explanation:
[tex] \sf{8 {x}^{2} + x - 5 + (2 {x}^{2} - 9x + 13)}[/tex]
When there is a ( + ) in front of an expression in parentheses , there is no need to change the sign of each term.
That means, the expression remains the same.
Also, Remove the unnecessary bracket
⇒[tex] \sf{8 {x}^{2} + x - 5 + 2 {x}^{2} - 9x + 13}[/tex]
Collect like terms
⇒[tex] \sf{8 {x}^{2} + 2 {x}^{2} + x - 9x - 5 + 13}[/tex]
⇒[tex] \sf{10 {x}^{2} - 8x - 5 + 13}[/tex]
Calculate
⇒[tex] \sf{10 {x}^{2} - 8x + 8}[/tex]
Hope I helped!
Best regards!!
The ratio of the number of boys to the number of girls at Liam's school is 4:5. There are 270 students at his school. Statement 1: The number of boys at school is 4/5 the number of girls.
Answer:
"statement 1: The number of boys at the school is [tex]\frac{4}5[/tex] of the number of girls." is true.
Step-by-step explanation:
Given:
Ratio of Number of boys to the number of girls = 4 : 5
Total number of students = 270
To find:
Number of boys in terms of number of girls = ?
Solution:
As per given statement,
Let, Number of boys = [tex]4x[/tex]
Let, Number of girls = [tex]5x[/tex]
Total number of students = Number of boys + Number of girls = 270
[tex]\Rightarrow 4x+5x =270\\\Rightarrow 9x=270\\\Rightarrow \bold{x = 30}[/tex]
Therefore, number of boys = 4 [tex]\times[/tex] 30 = 120
And, number of girls = 5 [tex]\times[/tex] 30 = 150
As per Statement 1:
Finding [tex]\frac{4}5[/tex] of the number of girls:
[tex]\dfrac{4}{5}\times 150 = 4 \times 30 = 120[/tex] = Number of boys.
Finding [tex]\frac{4}9[/tex] of the total number of students:
[tex]\frac{4}{9}\times 270= 4 \times 30 = 120[/tex] = Number of boys.
Number of boys is equal to [tex]\frac{4}9[/tex] of total number of students.
So, "statement 1: The number of boys at the school is [tex]\frac{4}5[/tex] of the number of girls." is true.
I really need help with this, ill give brainliest if its right :)
Am I right to try and prove that ΔABC ≅ ΔGFE by ASA? it was given that ∠B ≅ ∠F and I proved that ∠ACB ≅ ∠GEF but i cant figure out which side to prove or how to prove it?
Answer:
maybe
Step-by-step explanation:
To use ASA, you need to show the side between the angles is congruent to the corresponding side. In ΔACB, you have shown that angles B and C are congruent to their counterparts. The side between angles B and C is BC.
To use ASA, you must show BC ≅ FE.
__
Not enough information is given here for us to tell how one might prove congruence of the triangles. Hence your approach may work, or it may not--depending on the given information.
Solve for x 2/3x-5=21
Answer:
2x/3 - 5 = 21
2x/3 = 26
2x = 78
x = 39
Step-by-step explanation:
Answer:
x = 39
Step-by-step explanation:
URGENT!!!!!!! Find all seventh roots of unity and sketch them on the axes below.
Answer:
The 7th roots are : [tex]$ 1, \frac{2 \pi}{7}, \frac{4 \pi}{7}, \frac{6 \pi}{7}, \frac{8 \pi}{7}, \frac{10 \pi}{7}, \frac{12 \pi}{7}$[/tex]
Step-by-step explanation:
The roots of unity are evenly spread around the unit circle.
The roots of unity can be find by using the relation
[tex]$ 1= 1 ( \cos 0 ^\circ +i \sin ^\circ )$[/tex]
[tex]$\sqrt[n]{1} = 1 [\cos (\frac{2k \pi}{n}})+ i \sin (\frac{2k \pi}{n}) ] $[/tex]
Now z be a polynomial.
[tex]$z^7=1 \Rightarrow z = 1^{\frac{1}{7}}$[/tex]
therefore, cos 0 = 1.
[tex]$ z = \cos (2k \pi)^{\frac{1}{7}}$[/tex] [tex]$ (\cos \theta)^n = \cos n \theta $[/tex]
[tex]$ z = \cos \frac{2k \pi}{7} $[/tex]
Now, for k=0, z = 1
[tex]$ k=1 \Rightarrow z = \cos \frac{2 \pi}{7} = \cos 3 \frac{2 \pi}{7}+ i \sin \frac{2 \pi}{7}$[/tex]
[tex]$ k=2 \Rightarrow z = \cos \frac{4 \pi}{7} = \cos \frac{4 \pi}{7}+ i \sin \frac{4 \pi}{7}$[/tex]
[tex]$ k=3 \Rightarrow z = \cos \frac{6 \pi}{7} = \cos \frac{6 \pi}{7}+ i \sin \frac{6 \pi}{7}$[/tex]
[tex]$ k=4 \Rightarrow z = \cos \frac{8 \pi}{7} = \cos \frac{8 \pi}{7}+ i \sin \frac{8 \pi}{7}$[/tex]
[tex]$ k=5 \Rightarrow z = \cos \frac{10 \pi}{7} = \cos \frac{10 \pi}{7}+ i \sin \frac{10 \pi}{7}$[/tex]
[tex]$ k=6 \Rightarrow z = \cos \frac{12 \pi}{7} = \cos \frac{12 \pi}{7}+ i \sin \frac{12 \pi}{7}$[/tex]
[tex]$ k=7 \Rightarrow z = \cos \frac{14 \pi}{7} = \cos \frac{14 \pi}{7}+ i \sin \frac{14 \pi}{7}$[/tex]
Then the 7th roots are : [tex]$ 1, \frac{2 \pi}{7}, \frac{4 \pi}{7}, \frac{6 \pi}{7}, \frac{8 \pi}{7}, \frac{10 \pi}{7}, \frac{12 \pi}{7}$[/tex]
Find an equation of a line that goes through (4,1) and is perpendicular to the line x - 3y = 9. DO NOT USE THE POINT SLOPE METHOD, use the Slope Intercept method demonstrated.
Answer:
y = -3x + 13
Step-by-step explanation:
For slope-intercept form, you need the slope and the y-intercept. To find the slope, you need to rearrange the given equation to slope-intercept form.
x - 3y = 9
-3y = -x + 9
y = 1/3x - 3
The slope for the given equation is 1/3. The slope of a perpendicular line will be the negative reciprocal. This means that the slope of the perpendicular line will be -3.
You can now solve for the y-intercept (b) using the slope (m) and the given point in slope-intercept form.
y = mx + b
1 = (-3)(4) + b
1 = -12 + b
13 = b
b = 13
Now that you have both the slope and y-intercept, you can find the equation.
y = -3x + 13
The equation of the line is y = -3x + 13
What is an equation of a line?The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system.
The slope intercept form is given by:
y = mx + b
m = slope and b = y-intercept
We have,
A line perpendicular to line x - 3y = 9 and the line passes through the point (4, 1).
Make the line x - 3y = 9 in slope-intercept form.
-3y = 9 - x
y = (9 - x) / -3
y = (1/3)x - 3
The slope of the line x - 3y = 9 is:
m1= 1/3
Since the line required to find is perpendicular to the line x - 3y = 9
Let the required line slope be m2
m1 x m2 = -1
m2 = -1 / (1/3) = -3
The required line passes through the point (4, 1).
Let the required line be y = mx + b
we have,
1 = (-3)4 + b
1 = -12 + b
b = 13
We can write as:
y = -3x + 13
Thus the equation of the line is y = -3x + 13
Learn more about the equation of a line here:
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pls help asp [(4+3)⋅5−6]⋅2
23
24
29
58
Can you help me with this please this is my first time using the app
Answer:
A
Step-by-step explanation:
Determine whether the fractions 3/6 and 4/8 are equivalent.
Answer:
they are equivalent
Step-by-step explanation:
[tex]\frac{3}{6} = \frac{1}{2} (both \: can \: be \: divide \: by \: 3)[/tex]
[tex] \frac{4}{8} = \frac{1}{2} (both \: can \: be \: divide \: by \: 4)[/tex]
The two (2) fractions are equivalent.
In this exercise, you're required to determine whether or not given fractions are equivalent (equal). In order to do this, we would reduce the fractions to the lowest term.
Given the following fractions;
Fraction A = [tex]\frac{3}{6}[/tex]Fraction B = [tex]\frac{4}{8}[/tex]For Fraction A, we would divide both the numerator and the denominator by 3 because it's common to both them.
Fraction A = [tex]\frac{3}{6} = \frac{1}{2}[/tex]
Simplifying Fraction B, we have;
Fraction B = [tex]\frac{4}{8} = \frac{1}{2}[/tex]
Also, for two (2) fractions to be equivalent, their sums must be equal to one (1).
[tex]Fraction \;A + Fraction \;B = 1[/tex]
[tex]\frac{1}{2} + \frac{1}{2} = 1[/tex]
Therefore, we can deduce from the calculations that the two (2) fractions are equivalent.
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find the diameter of the circle whose circumference are 198cm
Answer:
63.057
Step-by-step explanation:
circumference= πd
Answer:
[tex] \boxed{ \boxed{ \bold{ \sf{63.05 cm}}}}[/tex]
Step-by-step explanation:
Given,
Circumference ( C ) = 198 cm
Diameter ( d ) = ?
Now, let's find the diameter of the circle :
We have,
[tex] \sf{c \: = \: \pi \: d}[/tex]
plug the values
⇒[tex] \sf{198 = 3.14 \: d}[/tex]
Swap the sides of the equation
⇒[tex] \sf{3.14 \: d \: = 198}[/tex]
Divide both sides of the equation by 3.14
⇒[tex] \sf{ \frac{3.14 \: d}{3.14} = \frac{198}{3.14} }[/tex]
Calculate
⇒[tex] \sf{d = 63.05}[/tex] cm
[tex] \underline{ \underline{ \sf{ \bold{ \blue{further \: more \: information}}}}}[/tex]
▪️[tex] \sf{ \bold{ Circumference}}[/tex]
⇒The perimeter of a circle is called it's circumference. It is the total length of the curved line of the circle.
▪️[tex] \sf{ \bold{ Radius}}[/tex]
⇒It is the line segment that joins the center of a circle and any point on its circumference.
▪️[tex] \sf{ \bold{Diameter}}[/tex]
⇒A line segment that passes through the centre of a circle and joins ant two points on its circumference is called the diameter of the circle. The length of a diameter is two times radius.
Hope I helped!
Best regards!!
Find the value of 2 √ + 1 = 11
Answer:
√ is 10
Step-by-step explanation:
Amira has a bag of cat food her cat eats 1/10 of a bag per week how many weeks will the food last ?.
Answer:
10 weeks
Step-by-step explanation:
f(x) = 9-3x
g(x) = 5x-7
Find f(x)+g(x).
Answer:
In the problem, the sum of the two functions is 2x + 2
Step-by-step explanation:
For this problem, we have to add together f(x) and g(x).
f(x) = 9 - 3x
g(x) = 5x - 7
(f + g)(x) = (9 - 3x) + (5x - 7)
Combine like terms.
(f + g)(x) = 2x + 2
So, when you combine the two functions together, you will get 2x + 2.
The value of f(x)+g(x) according to the question given is; 2x + 2.
To evaluate the sum of functions f(x) and g(x); we have;
f(x) = 9-3x andg(x) = 5x-7Therefore;
f(x)+g(x) = 9-3x + 5x -7f(x)+g(x) = 2x + 2.Read more on addition:
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Solve the equation
(If possible please show work)
squared 3x times squared 49x
Answer:
9xx2401x=21609x
Step-by-step explanation: 3x3=9. 40x40=1600, 40x9=360x2 because there are 2 of the same problem because the number is the same. 9x9=81.
Now we add them up. 1600+720+81=2401. 2401x9=21609
But don't forget to add the x at the end or the answer is wrong!!!
How many pennies could you have if:
When you break the pennies into groups of 2, you have
1 penny left over, AND when you break the pennies into
groups of 3, you have 1 penny left over, AND when you
break the pennies into groups of 5, you have 1 penny
left over, AND when you break the pennies into groups
of 7, you have NO pennies left over?
Answer:
The number of pennies are 91 pennies
Step-by-step explanation:
The given parameters are
When we split the pennies in twos the number left = 1
When the pennies are split in 3s the number left = 1
When the pennies are split in 5s the number left = 1
When the pennies are split in 7 the number left = 0
Therefore, 7 is a factor of the number
Given that when the pennies are split in 5s the number left = 1, the number ends with a 1
We have the products of 7 ending with 1 from Excel as 21 and 91, 161...
We check 91 given 21 is directly divisible by 3 as follows;
91/2 = 45 remainder 1
91/3 = 30 remainder 1
91/5 = 18 remainder 1
91/7 = 13 remainder 0
Therefore, the number of pennies are 91 pennies.
On Monday, Brian counted 28 ducks and Cathy counted 15 ducks. On Tuesday,
they counted 37 ducks altogether. How many more ducks did they count on
Monday than Tuesday?
Answer:
6 ducks
Step-by-step explanation:
Monday, Brian counted 28 ducks and Cathy counted 15 ducks
= 28+15 =43
Tuesday, they counted 37
Monday count - Tuesday count
43 - 37 =6
-2/3 divided by 2 1/4 simplified
Answer:
(-8)/27
Step-by-step explanation:
Simplify the following:
(-2)/(3 (2 + 1/4))
Put 2 + 1/4 over the common denominator 4. 2 + 1/4 = (4×2)/4 + 1/4:
(-2)/(3 (4×2)/4 + 1/4)
4×2 = 8:
(-2)/(3 (8/4 + 1/4))
8/4 + 1/4 = (8 + 1)/4:
(-2)/(3 (8 + 1)/4)
8 + 1 = 9:
((-2)/3)/(9/4)
Multiply the numerator by the reciprocal of the denominator, ((-2)/3)/(9/4) = (-2)/3×4/9:
(-2×4)/(3×9)
3×9 = 27:
(-2×4)/27
-2×4 = -8:
Answer: (-8)/27
Answer:
-8/27
Step-by-step explanation:
-2/3 ÷ 2 1/4
Change to an improper fraction
-2/3 ÷ ( 4*2+1)/4
-2/3 ÷9/4
Copy dot flip
-2/3 * 4/9
-8/27
What is the slope of the line?
Answer: 1/4
Step-by-step explanation: In algebra, we use the word slope to describe how steep a line is and slope can be found using the ratio rise/run between any two points that are on that line.
So for the line you see here, let's use these two points to find its slope.
Let's go from left to right.
To get from the point that has the coordinates (0,1) to (4,2),
we rise 1 unit and run 4 units to the right and we end up the other point.
So the slope of this line is 1/4.
A jar of peanut butter contains 454 g with a standard deviation of 10.2 g. Find the probability that a jar contains more than 466 g. Assume a normal distribution. Use a z-score rounded to 2 decimal places.
Answer:
The probability that a jar contains more than 466 g is 0.119.
Step-by-step explanation:
We are given that a jar of peanut butter contains a mean of 454 g with a standard deviation of 10.2 g.
Let X = Amount of peanut butter in a jar
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean = 454 g
[tex]\sigma[/tex] = standard deviation = 10.2 g
So, X ~ Normal([tex]\mu=454 , \sigma^{2} = 10.2^{2}[/tex])
Now, the probability that a jar contains more than 466 g is given by = P(X > 466 g)
P(X > 466 g) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{466-454}{10.2}[/tex] ) = P(Z > 1.18) = 1 - P(Z [tex]\leq[/tex] 1.18)
= 1 - 0.881 = 0.119
The above probability is calculated by looking at the value of x = 1.18 in the z table which has an area of 0.881.