Answer:
Since both terms are perfect squares, factor using the difference of squares formula,
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
where
a
=
k
2
and
b
=
1
.
9
(
−
36
k
6
+
k
5
−
k
−
2
)
What is the area of the triangle?
3
2
6
Answer:
A = 6 units^2
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh
A = 1/2 (6)(2)
A = 6 units^2
Answer:
6 units^2
Step-by-step explanation:
The area of a triangle can be found using the following formula.
a=(bh)/2
where b is the base and h is the height. In this triangle, we know that 6 units is the base. We also know that 2 units is the height, because the height should form a right angle(little square) with the base.
b=6
h=2
Substitute these values into the formula.
a=(6*2)/2
Multiply 6 and 2 first.
a=12/2
Divide 12 by 2
a=6
Add appropriate units. Area always has the unit squared.
a= 6 units^2
The area of the triangle is 6 square units.
If f(x) = 3/x+2-/x-3, Complete the following statement: The domain of for f(x) is all real numbers _____ than or equal to 3
Answer:
Step-by-step explanation:
Answer:
Greater
Step-by-step explanation:
because Since the radicand is x - 3, the value of x cannot be less than 3 because that would make the value of sqrt (x - 3) an imaginary number.
A city is holding a referendum on increasing property taxes to pay for a new high school. In a survey of 458 likely voters, 254 said that they would vote “yes” on the referendum. Create a 95% confidence interval for the proportion of likely voters who will vote “yes” on the referendum. Use Excel to create the confidence interval, rounding to four decimal places.
Answer:
[tex]\hat p \pm Z*\sqrt{\frac{\hat p\times(1-\hat p)}{n} }[/tex]
[tex]=0.5546\pm1.96*\sqrt{\frac{0.5546\times(1-0.5546)}{458} }[/tex]
[tex]=0.5546\pm1.96*\sqrt{\frac{0.5546\times(0.4454)}{458} }[/tex]
[tex]=0.5546\pm1.96*\sqrt{\frac{0.2470}{458} }[/tex]
[tex]=0.5546\pm1.96*\sqrt{0.00053934}[/tex]
[tex]=(0.5091,0.6001)[/tex]
Lower limit for confidence interval=0.5091
Upper limit for confidence interval=0.6001
Step-by-step explanation:
We have given,
x=254
n=458
Estimate for sample proportion= [tex]\bar p = 0.5546[/tex]
Level of significance is =1-0.95=0.05
Z critical value(using Z table)=1.96
Confidence interval formula is
[tex]\hat p \pm Z*\sqrt{\frac{\hat p\times(1-\hat p)}{n} }[/tex]
[tex]=0.5546\pm1.96*\sqrt{\frac{0.5546\times(1-0.5546)}{458} }[/tex]
[tex]=0.5546\pm1.96*\sqrt{\frac{0.5546\times(0.4454)}{458} }[/tex]
[tex]=0.5546\pm1.96*\sqrt{\frac{0.2470}{458} }[/tex]
[tex]=0.5546\pm1.96*\sqrt{0.00053934}[/tex]
[tex]=(0.5091,0.6001)[/tex]
Lower limit for confidence interval=0.5091
Upper limit for confidence interval=0.6001
What is the opposite integer of -111111111111111111111111111111111111111111111111111111111111111111
Answer:
positive 111111111111111111111111111111111111111111111111111111111111111111
Step-by-step explanation:
Riley and Francesca both commute to work. Riley's commute on the train
1
takes 12 minutes more than as many minutes as Francesca's commute
2
by car. It takes Riley 36 minutes to get to work. Write an equation to
determine how many minutes it takes Francesca to get to work.
36 =
X - 12
2
36 = 2x - 12
36 = 2x + 12
36 = -x + 12
Solve the following equation for x.
7x-3y=-13
Answer:
x = 3/7y - 13/7
Step-by-step explanation:
7x-3y=-13
+3y +3y Add 3y to both sides
7x = 3y - 13 Divide both sides by 7
x = 3/7y - 13/7
Select the correct answer from each drop-down menu. the profit earned by a sporting goods outlet is modeled in the graph below, where x is the number of years since the outlet opened. He recorded profit for the first ten years since the outlet opened. The domain represents the (cost per item, number of years, number of units) for which the outlet will earn a profit. The range of this function is (0,160000,80000 and 0,160000,80000). For this function, the range represents the outlets (number of years since opening,maximum profit, possible annual profits).
Answer:
The answer would be A. 1 1/5
48/40 = 1 8/40
1 8/40 Simplify to 1 1/5
V=4/3pi(r^3)
V=4/3pi(9^3)
V=3,054 inches^3
Hope this helps!!!!!!!!!
Step-by-step explanation:
from the graph attached below:
domain of graph is the value of x for which the given function profit function p(x) is defined.
(a) the domain represents the number of years for which the outlet will earn a profit.
range of profit function defines the lowest to highest value of profit earned.
(b) the range of this function is (0 , 160 ). for this function, the range represents the outlet's profit earned.
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
140 degrees
Step-by-step explanation:
The sum of the angles on a line is 180. Since we know one of the angles is 40, you do 180-40 to figure out the other angle (DCB). The answer is 140.
Answer:
[tex]x = 140 \: \: degrees[/tex]
Step-by-step explanation:
Angels in a straight line = 180°
Let the DCB angle be x
Given that,
ACD angle = 40°
Let's solve now,
[tex]40 + x = 180 \\ x = 180 - 40 \\ x =1 40 \: \: \: degrees[/tex]
hope this helps you
brainliest appreciated
good luck! have a nice day!
In a circle with radius 22, an angle measuring 2\pi2π radians intercepts an arc. Find the length of the arc in simplest form.
Answer:
15
Step-by-step explanation:
The length of the arc in its simplest form will be 138.16 units.
What is the arc length of the sector?Let r is the radius of the sector and θ be the angle subtended by the sector at the center. Then the arc length of the sector of the circle will be
Arc = (θ/2π) 2πr
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
In a circle with a radius of 22, an angle measuring 2π radians intercepts an arc.
Then the length of the arc in the simplest form will be given as,
Arc = (2π/2π) 2π (22)
Arc = 44 x 3.14
Arc = 138.16 units
The length of the arc in its simplest form will be 138.16 units.
More about the arc length of the sector link is given below.
https://brainly.com/question/15955580
#SPJ5
a fireplace contains 54 bricks along its bottom row. if each row above decreases by 3 bricks, what is the function that shows the bricks on the 10th row
Step-by-step explanation:
the fireplace would have 24 bricks on the 10th row
Answer:
27 bricks
Step-by-step explanation:
y= 54- 3(x-1)
y= 57- 3x
is the function, y= number of bricks on the xth row, x= row number above the bottom one
x=10 ⇒ y= 57 - 3*10 ⇒ y= 27 bricks
-4( x^3 + x^2 -3 ) =
please need help I will be MARKING as BRIANILIST. thank you so much.
Answer:
27
Step-by-step explanation:
9(12)/4
9(3)
27
Answer:
Please mark me brainliest and I hope this helped!
D. 27
Step-by-step explanation:
First, we look at the exponents and for 3, 3 to the power of 2 is 3 times 3. The answer to that is 9. Next, we look at 2 to the power of 3. That is 2 times 2 times 2. That equals 8. 8 + 4 = 12. 12 * 9 = 108. The numerator is 108 so now we go to the bottom and 2 to the power of 2 is 2 times 2. So the denominator is 4. 108 divided by 4 is 27 and that's your answer!
if ABC~DEF and the perimeter of ABC is 4 times greater than the
perimeter of DEF, what is the relationship between the areas of the
triangles?
Answer:
The area of triangle ABC is 16 times larger than the area of triangle DEF
Step-by-step explanation:
Step 1: Re-state the input
Given two triangles ABC and DEF are similar with ratio k.
Step 2: Derive the information
Suppose that the triangle ABC is k times larger than triangle DEF.
=> It means that all sides and heights of triangle ABC are k times larger than corresponding sides and heights of triangle DEF.
For example:
AB = k x DE
AC = k x DF
BC = k x EF
=> AB + AC + BC = k x (DE + DF + EF)
=> Perimeter of triangle ABC is k times larger than perimeter of triangle DEF
Step 3: Solve the problem step-by-step
Suppose that AH is the height from vertex A to base BC of triangle ABC and DH' is the height from the vertex D to base EF of triangle DEF.
As the above assumption states:
AH = k x DH'
BC = k x EF
Multiply both sides of the two above equations:
=> AH x BC = DH x EF x k x k
Simplify k components:
=> AH x BC = DH x EF x k^2
Multiply (1/2) to both sides:
=> (1/2) x AH x BC = (1/2) x DH x EF x k^2
Apply the formula to calculate the area of a triangle:
=> Area of triangle ABC = Area of triangle DEF x k^2
In other words:
The area of triangle ABC is (k^2) times larger than area of triangle DEK.
Here, the perimeter of triangle ABC is 4 times larger than the perimeter of triangle DEF => k = 4
Step 4: Make the conclusion
=>The area of triangle ABC is (4^2 = 16) times larger than area of triangle DEK.
Hope this helps!
:)
5. A model of Earth is located 7600 meters from the Globe Arena in Sweden’s solar system model. The volume of the model is approximately 3052.08 cubic centimeters. What is the length of the radius of the
Earth model?
Solve each problem. Use 3.14 for p.
Answer:
the length of the radius of the Earth Model = 9cm
Step-by-step explanation:
The volume of the model of Earth is approximately 3052.08 cubic centimeters.
It has been discovered that the Earth is spherical in shape, hence this model is spherical as well.
The formula for the Volume of a Sphere = 4/3 πr³
Where r = radius or the length of the radius
The Volume of the Earth Model = 3052.08 cm³
We are told to use π = 3.14
To find the length of the radius, we have derive the formula
V = 4/3 × π × r³
V = 4πr³/3
Cross multiply
3V = 4πr³
Divide both side by 4π
3V/4π = r³
We find the cube root of both sides =
∛(3V/4π) = r
Substituting our given values in the question, we have:
∛(3 × 3052.08/ 4 ×3.14) = r
r = ∛9156.24÷12.56
r = ∛729
r = 9cm
Therefore, the length of the radius of the Earth Model = 9cm
What is the slope of the line? 2x+4y=6-y
Answer:
m= -2/5
Step-by-step explanation:
use the slope-intercept form y=mx+b to find the slope m.
Answer:
-2/5
Step-by-step explanation:
plz mark brainliest!
can someone pls help
Answer:
3.6
Step-by-step explanation:
sine theta=3.2/5.1
theta=sine^-1(3.2/5.1)
theta=38.86230987
sine 38.86230987=x/5.7
x=sine 38.86230987(5.7)
x=3.576470588
Rounded to the nearest tenth is 3.6
Marci hiked 15 miles from Park Headquarters to Blue Lake in 5 hours. What was her average speed?
Answer:
3 miles per hour
Step-by-step explanation:
The formula for average speed is: [tex]R = \frac{D_{total} }{T_{total} }[/tex] R being rate, D being distance, T being time. We substitute the values to get [tex]R = \frac{15}{5}[/tex] Simplified 3. Her average speed was 3 miles per hour. Hope this helps!
Answer:
3 miles per hour.
Step-by-step explanation:
15 divided by 5 is 3
each hour he would have covered 3 miles of distance.
What is the equation of the line that is parallel to the line x = -2 and passes through the point (-5, 4)?
y=-6
y = 4
Answer:
x = - 5
Step-by-step explanation:
The line with equation x = - 2 is a vertical line parallel to the y- axis.
A parallel line will also have the equation
x = c
where c is the value opf the x- coordinates the line passes through.
The line passes through (- 5, 4) with x- coordinate - 5, thus
x = - 5 ← equation of parallel line
Explain how the Quotient of Powers Property was used to simplify this expression.
three to the fourth power all over nine equals three squared
By simplifying 9 to 32 to make both powers base three and adding the exponents
By simplifying 9 to 32 to make both powers base three and subtracting the exponents
By finding the quotient of the bases to be one third and simplifying the expression
By finding the quotient of the bases to be one third and cancelling common factors
Answer:
The answer is option 2, by simplifying 9 to 3² to make both powers base 3 and subtracting the exponents.
Step-by-step explanation:
You have to make the expressions into the same base :
[tex] \frac{ {3}^{4} }{9} = \frac{ {3}^{4} }{ {3}^{2} } [/tex]
Next, you have to apply Indices Law :
[tex] {a}^{m} \div {a}^{n} \: ⇒ \: {a}^{m - n} [/tex]
[tex] {3}^{4} \div {3}^{2} [/tex]
[tex] = {3}^{4 - 2} [/tex]
[tex] = {3}^{2} [/tex]
By simplifying 9 to 3² to make both the powers base 3 as well as subtracting the exponents. A further explanation of the given question is below.
According to the question,
The equation will be:
→ [tex]\frac{(3)^4}{9} = \frac{(3)^4}{(3)^2}[/tex]
By applying the Indices law i.e.,
→ [tex]\frac{a^m}{a^n} = a^{m-n}[/tex]
then, we get
→ [tex]\frac{3^4}{3^2}[/tex]
→ [tex]3^{4-2}[/tex]
By subtracting the powers, we get
→ [tex]3^2[/tex]
Thus the above answer i.e., option B) is the correct approach.
Learn more:
https://brainly.com/question/19660607
8. Lilly paid $19.16 for a 1kg apple basket. This amount includes a tax of 3%. What was the cost of the apple before tax?
Answer:
$18.59
Step-by-step explanation:
19.16=100%
0.1916=1%
97(0.1916)
18.59
Answer:
$18.5852
Step-by-step explanation:
A quadrilateral has vertices a(-4 -8) b (-2, 34) c(6,12 and d (10, -30). It undergoes the transformation (x,y) to (x/2,y/2).
What is it's scale factor?
What are the coordinates of the new vertices?
What is a dilatation?
(Will give Brainly)
Answer:
Step-by-step explanation:
scale factor:
1/2
the coordinates of the new vertices are
A (-4/2, -8/2)
A:(-2, -4)
B (-2/2, 34/2)
B: (-1, 17)
C (6/2, 12/2)
C:(3, 6)
D (10/2, -30/2)
D:(5, -15)
I guess the dilation is 2 times bigger?
I’m really confused the question is on shapes
Answer:The polygon has 18 sides.
Step-by-step explanation;since it is a straight line, we get 8x since they said that each interior angle is 8 times the exterior angleso it is 8x =x which is the exterior angle +180 degrees since it is a sraight line.
n:
Answer:
A) Each Interior Angle = 180 degrees - (360 / number sides)
B) Each Exterior Angle = 360 / number of sides
A) = 8 * B)
8 * 360 / # sides = 180 - (360 / #sides)
We'll call # sides as "n".
2,880 / n = [ 180 - (360 / n)]
2,880 = n * [ 180 -(360 / n)]
3,240 = 180n
180n = 3,240
n = 18 sides.
The polygon has 18 sides which is an octadecagon.
Step-by-step explanation:
A picture was marked at $90.00. It was sold at 3/4 of its marked price. What was the sale price?
Answer: $67.50
Step-by-step explanation:
Marked price = $90
It is sold at 3/4 of marked price
3/4 of 90
3*4 x 90 = 135/2
= 67.50 = sale price
Given the speeds of each runner below, determine who runs the fastest.
Adam runs 9 feet per second.
Noah runs 164 feet in 14 seconds.
Jake runs 1 mile in 412 seconds.
Katie runs 845 feet in 1 minute.
Answer:
Katie
Step-by-step explanation:
lets convert all the speeds to ft/1 sec
V adam: 9ft/sec
V noah: 164ft/14sec
164/14=11.7142857143= around 11.7 ft/sec
V jake: 1 mile/412 sec
1 mile= 5280 ft
5280 ft/412 sec=
5280/412=12.8155339806= around 12.8 ft/sec
V katie: 845ft/min
minute=60 sec
845ft/60sec=
845/60=14.0833333333= around 14.1 ft/sec
now lets order the velocities(speeds) from least to greatest:
V adam: 9ft/sec, V noah: 11.7 ft/sec, V jake: 12.8 ft/sec, V katie: 14.1 ft/sec
thus, Katie is the fastest runner
Find the product of (x − 5)2. (1 point)
Answer:
x² - 10x + 25
Step-by-step explanation:
Given
(x - 5)² = (x - 5)(x - 5)
Each term in the second factor is multiplied by each term in the first factor, that is
x(x - 5) - 5(x - 5) ← distribute both parenthesis
= x² - 5x - 5x + 25 ← collect like terms
= x² - 10x + 25
(x+y)^2 (x2+2xy+y2) pleas show all work
Answer:
{x}^{4}+4{x}^{3}y+6{x}^{2}{y}^{2}+4x{y}^{3}+{y}^{4}x
4
+4x
3
y+6x
2
y
2
+4xy
3
+y
4
Step-by-step explanation:
1 Use Square of Sum: {(a+b)}^{2}={a}^{2}+2ab+{b}^{2}(a+b)
2
=a
2
+2ab+b
2
.
({x}^{2}+2xy+{y}^{2})({x}^{2}+2xy+{y}^{2})(x
2
+2xy+y
2
)(x
2
+2xy+y
2
)
2 Expand by distributing sum groups.
{x}^{2}({x}^{2}+2xy+{y}^{2})+2xy({x}^{2}+2xy+{y}^{2})+{y}^{2}({x}^{2}+2xy+{y}^{2})x
2
(x
2
+2xy+y
2
)+2xy(x
2
+2xy+y
2
)+y
2
(x
2
+2xy+y
2
)
3 Expand by distributing terms.
{x}^{4}+2{x}^{3}y+{x}^{2}{y}^{2}+2xy({x}^{2}+2xy+{y}^{2})+{y}^{2}({x}^{2}+2xy+{y}^{2})x
4
+2x
3
y+x
2
y
2
+2xy(x
2
+2xy+y
2
)+y
2
(x
2
+2xy+y
2
)
4 Expand by distributing terms.
{x}^{4}+2{x}^{3}y+{x}^{2}{y}^{2}+2{x}^{3}y+4{x}^{2}{y}^{2}+2x{y}^{3}+{y}^{2}({x}^{2}+2xy+{y}^{2})x
4
+2x
3
y+x
2
y
2
+2x
3
y+4x
2
y
2
+2xy
3
+y
2
(x
2
+2xy+y
2
)
5 Expand by distributing terms.
{x}^{4}+2{x}^{3}y+{x}^{2}{y}^{2}+2{x}^{3}y+4{x}^{2}{y}^{2}+2x{y}^{3}+{y}^{2}{x}^{2}+2{y}^{3}x+{y}^{4}x
4
+2x
3
y+x
2
y
2
+2x
3
y+4x
2
y
2
+2xy
3
+y
2
x
2
+2y
3
x+y
4
6 Collect like terms.
{x}^{4}+(2{x}^{3}y+2{x}^{3}y)+({x}^{2}{y}^{2}+4{x}^{2}{y}^{2}+{x}^{2}{y}^{2})+(2x{y}^{3}+2x{y}^{3})+{y}^{4}x
4
+(2x
3
y+2x
3
y)+(x
2
y
2
+4x
2
y
2
+x
2
y
2
)+(2xy
3
+2xy
3
)+y
4
7 Simplify.
{x}^{4}+4{x}^{3}y+6{x}^{2}{y}^{2}+4x{y}^{3}+{y}^{4}x
4
+4x
3
y+6x
2
y
2
+4xy
3
+y
4
answer: x^4+4x^3 y+6x^2 y^2+4xy^3+y^4
SS
question 6/12
A text message can have a maximum of 160 characters. If Daisy has typed 3 sentences with 45
characters each, then which equation can be solved to find the number of characters she can still
type. Let "c" equal number of Daisy characters left.
Answer:
c = 160 - 3(45)
Step-by-step explanation:
if c = the number of characters left;
160 = maximum number of characters that can be used in a text
3*45 = number of characters in sentences already used. (There are 3 sentences of 45 characters.)
(# of char left) = (max # char) - (# char already used) so:
c = 160 - 3*(45)
c = 160 - 135
c = 25
What is data about?
Answer: the quantities, characters, or symbols on which operations are performed by a computer, being stored and transmitted in the form of electrical signals and recorded on magnetic, optical, or mechanical recording media.
Step-by-step explanation:
Data mainly is about taking note of specific observations in numbers, for reference in the future.
Find the volume of a cone that has a radius of 3 inches and a height of 9 inches.
(Use 3.14 for pi and round the answer to the nearest hundredth.)
Answer:
84.82
Step-by-step explanation:
I rounded it to the decimals hundredth place if I did not it would have been 84.823.
The system of equation y=3/4 and y=-x+3 According to the graph, what is the solution to this system of equations?
(4, -1)
(-1.4)
(4.1)
(1.4)
Answer:
a
Step-by-step explanation:
