Answer:
done same as before put value and do process like simplify
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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-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
Can you help me with this please this is my first time using the app
Answer:
A
Step-by-step explanation:
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!!
(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
|9-(-1)|= simplify the expression
Answer:
10
Step-by-step explanation:
Remove parentheses.
|9+1|
Simplify 9+1 to 10.
|10|
simplify
10
Aneesha travels at a rate of 50 miles per hour. Morris is traveling 3 feet per second less than Aneesha. Which is the best estimate of the speed Morris is traveling? algebra
Answer:
50 miles per hour =73.33 feet per second (the conversion rate)
now if Morris is travelling 3 feet per second less than Aneesha so, the speed of Morris is 70.33 feet per second;
if we convert this to Miles per hour;
70.33 feet per second= 48 miles per hour (approximately)
so here the last last option is the right
48 miles per hour
Answer:
48 miles per hour
Step-by-step explanation:
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.
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.
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.
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]
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!!!
Write the given number in the form a × 10 n , where a is a real number such that 1 ≤ |a| < 10 and n is an integer. 230,000,000,000 = 2.3 × 100,000,000,000 = 2.3 × 10 11
Answer:
2.3 x 10^11.
Step-by-step explanation:
There are 11 digits after the first digit (2).
The answer is 2.3 x 10^11.
This is called scientific notation.
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:
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]
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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a) x² - y² - x + y Factorize
Answer:
(x - y) (x+y -1)
Step-by-step explanation:
See steps of factorization:
x² - y² - x + y =(x² - y²) - (x - y) = (x - y) (x + y) - (x- y) =(x - y) (x+y -1)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.
Lin created a scaled copy of Triangle A with an area of 72 square units. How many times larger is the area of the scaled copy compared to that of Triangle A
Answer:
The question is not complete, here is a possible match to the complete question:
Here is Triangle A. Lin created a scaled copy of Triangle A with an area of 72 square units. What scale factor did Lin apply to the Triangle A to create the copy? Remember: A=1/2bh
a) 4
b) 8
c) 16
Answer:
Scale factor = 16
Step-by-step explanation:
From the diagram attached to this solution, the triangle was plotted on a graph sheet, and each grid on the graph represents 1 unit. hence the dimensions of Triangle A from the diagram is as follows:
Base = 3 units
Height = 3 units
Next, in order to determine the scale factor of the area of the triangle after scaling, let us calculate the area of the unscaled triangle.
Area of Triangle = 1/2 (base × height)
Area or Triangle = 0.5 × 3 × 3 = 4.5 square units
Therefore,
Area of unscaled triangle = 4.5 squared units
Area of scaled triangle = 72 squared units
since the area of the scaled triangle is larger than the unscaled triangle, the scale factor is simply the number of times by which the scaled triangle was enlarged, compared to the unscaled triangle. This can be calculated by dividing the scaled triangle by the unscaled triangle as follows:
Scale factor =(scaled triangle) ÷ (unscaled triangle)
Scale factor = 72 ÷ 4.5 = 16
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]
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.
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!!
What’s the area of this shape?
Answer:
212 m²
Step-by-step explanation:
Break it down into 3 rectangles.
10x8=80
4x13=52
16x5=80
80+52+80=212
Solve the equation
(If possible please show work)
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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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.
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
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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TURN IT IN
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
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