Answer:
False
Step-by-step explanation
Let's take the example starting number as 100
15% off of 100 gives us 85.
25% off of 85 is 63.45
40% off of 100 would be 60.
please help me outttt
Answer:
(-1, 4) and (2, 7)
Step-by-step explanation:
Graphs f(x) & g (x) are intersecting each other.-> f(x) = g(x)[tex]\implies x^2+3 =x + 5[/tex][tex]\implies x^2+3 -x -5=0[/tex][tex]\implies x^2 -x -2=0[/tex][tex]\implies x^2 -2x +x-2=0[/tex][tex]\implies x(x -2) +1(x-2)=0[/tex][tex]\implies (x -2)(x+1)=0[/tex][tex]\implies (x -2)=0,\:\: (x+1)=0[/tex][tex]\implies x=2\:\: x=-1[/tex][tex]\implies x=-1,\:\:2[/tex]When x = -1[tex]f(x) = (-1)^2+3 = 1 +3 = 4 [/tex]-> (x, f(x)) = (-1, 4) & When x = 2[tex]f(x) = (2)^2+3 = 4 +3 = 7 [/tex]-> (x, f(x)) = (2, 7) Thus, the points of intersection of the functions f(x) and g(x) are (-1, 4) and (2, 7)The base of a ladder is placed 2.8m away from a tree that is 4.5m tall. The end of the ladder touches the top of the tree. Calculate the length of the ladder.
Answer:
The length is 7.3m
Step-by-step explanation:
The end of the ladder touches the top of the tree when kept at 2.8m away from the tree.
The Tree is 4.5m tall
The length of the ladder will be: 2.8+4.5 = 7.3
pleaseee helpp meeee
Answer:
9 sides
Step-by-step explanation:
Formula for finding interior angles of all polygons : 180 ( n - 2) / n = A
(n being the amount of sides it has)
This information is important so you can plug in the numbers that you already know
We know that the interior angle measures to 140 degrees
180 (n - 2) / n = 140
multiply both sides by "n"
(n - 2) x 180 = 140n
Distribute 180 to what's inside the parenthesis
180n - 360 = 140n
Subtract 140n and add 360 to each side (which just moves 360 to the other side of the "="
40n = 360
Divide 40 by both sides
n = 9
hope this helps :)
Work out
the area of this circle. Take
(Pi) to be
3.142 and give your answer to
2 decimal places.
11.2cm
Helpppppppppppppppp please
As there is the highest degree 4 there are four zeros .
Using calculator
the roots are(attached)
The graph is also attached
Answer:
a) 4 roots
b) x = 1 and x = -3
[tex]\textsf{c)} \quad x=1, \quad x=-3, \quad x=\dfrac{-1 + \sqrt{3}i}{2}, \quad x=\dfrac{-1 - \sqrt{3}i}{2}[/tex]
d) see attached
Step-by-step explanation:
Given function:
[tex]f(x)=x^4+3x^3-x-3[/tex]
Part (a)
From inspection of the function, the highest exponent of the polynomial is 4. Therefore, it is expected that the polynomial will have 4 roots.
Part (b)
To find the rational roots, find values of x where [tex]f(x)=0[/tex]
[tex]f(1)=(1)^4+3(1)^3-1-3=0[/tex]
[tex]f(-3)=(-3)^4+3(-3)^3-(-3)-3=0[/tex]
Therefore, the rational roots are: x = 1 and x = -3
Part (c)
As there are only 2 rational roots, the other 2 roots must be complex roots. To find these, first factor the polynomial using the 2 rational roots found in part (b):
[tex]\implies f(x)=(x-1)(x+3)(x^2+bx+1)[/tex]
[tex]\implies f(x)=(x^2+2x-3)(x^2+bx+1)[/tex]
[tex]\implies f(x)=x^4+bx^3+x^2+2x^3+2bx^2+2x-3x^2-3bx-3[/tex]
[tex]\implies f(x)=x^4+(2+b)x^3+(2b-2)x^2+(2-3b)-3[/tex]
Compare coefficients to find b:
[tex]\implies (2+b)x^3=3x^3[/tex]
[tex]\implies b=1[/tex]
Therefore the fully factored function is:
[tex]\implies f\:\!(x)=(x-1)(x+3)(x^2+x+1)[/tex]
Therefore:
[tex](x^2+x+1)=0[/tex]
To find the complex roots, use the quadratic formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
[tex]\implies x=\dfrac{-1 \pm \sqrt{1^2-4(1)(1)}}{2(1)}[/tex]
[tex]\implies x=\dfrac{-1 \pm \sqrt{-3}}{2}[/tex]
[tex]\implies x=\dfrac{-1 \pm \sqrt{3}\sqrt{-1}}{2}[/tex]
[tex]\implies x=\dfrac{-1 \pm \sqrt{3}i}{2}[/tex]
Therefore, all the roots of the function are:
[tex]x=1, \quad x=-3, \quad x=\dfrac{-1 + \sqrt{3}i}{2}, \quad x=\dfrac{-1 - \sqrt{3}i}{2}[/tex]
Part (d)
End behaviors:
As the degree of the function is even and the leading coefficient is positive, the end behaviors are:
[tex]\textsf{As } x \rightarrow - \infty, \:\: f(x) \rightarrow + \infty[/tex]
[tex]\textsf{As } x \rightarrow + \infty, \:\: f(x) \rightarrow + \infty[/tex]
y-intercept
Substitute x = 0 into the function:
[tex]f\:\!(0)=(0)^4+3(0)^3-(0)-3=-3[/tex]
Therefore, the y-intercept is (0, -3)
To find the approximate x-coordinates of the turning points (stationary points), differentiate the function, set it to zero, then solve for x:
[tex]f'\:(x)=4x^3+9x^2-1[/tex]
[tex]\implies 4x^3+9x^2-1=0[/tex]
Using a calculator, x ≈ -2.2, x ≈ -0.4, x ≈ 0.3
Therefore the approximate coordinates of the turning points are:
(-2.2, -9.3), (-0.4, -2.7) and (0.3, -3.2)
We don't need to plot these points, they merely help us with the approximate shape of the curve.
Consider the following function f(x) = x² + 5.
Part A: Write a function, in vertex form, that shifts f(x) right 3 units.
Part B: Write a function, in vertex form, that shifts f(x) left 10 units.
Part A
To shift the curve 3 units to the right, we'll replace x with x-3. What this does is move the xy axis 3 units to the left. If we held the curve in place as the axis moves, then it gives the illusion the curve is moving 3 units to the right.
[tex]f(x) = x^2 + 5\\\\f(x-3) = (x-3)^2 + 5\\\\g(x) = (x-3)^2 + 5\\\\[/tex]
Do not expand out the (x-3)^2 term, because you want to keep the function in vertex form. The old vertex of (0,5) moves three units to the right to arrive at (3,5)
Answer: [tex]g(x) = (x-3)^2 + 5[/tex]==============================================================
Part B
We use the same idea as before. This time we're moving the curve 10 units to the left, so we'll replace x with x+10
[tex]f(x) = x^2 + 5\\\\f(x+10) = (x+10)^2 + 5\\\\g(x) = (x+10)^2 + 5\\\\[/tex]
In ΔABC, m∠B = 90°, cos(C) = , and AB = 16 units.
Based on this information, m∠A =
°, m∠C =
°, and AC =
units.
Note that the angle measures are rounded to the nearest degree.
The sides and angles of the right triangle area as follows:
m∠C = 28°
m∠A = 62°
AC = 17 units
How to find the sides and angles of a right angle triangle?Using trigonometric ratios,
cos C = 15 / 17
m∠C = cos⁻¹ 0.88235294117
m∠C = 28.0726015272
m∠C = 28°
m∠A = 180 - 28 - 90 = 62°
AC = 17 units
AC is the hypotenuse of the right angle triangle.
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You invest $2000 compounded monthly at 9%, how much money do you have in 10 years?
Answer: The final balance is $4,734.73
Tajiq spent $75 on clothes they bought a shirt and three pants. If the shirt cost $15 how much was each pair of pants if they all were the same price? Show your work
Answer:
each pair of pants was $20 each
Step-by-step explanation:
75-15=60
60/3=20
The area of undeveloped land in a suburban town is decreasing at a rate of 17.3% annually. in 2016, there were 3,400 acres of undeveloped land. if t represents the number of years since 2016, which equation can be used to determine after how many years the town will have 900 acres of undeveloped land remaining?
Based on the rate of decrease and the acres of undeveloped land, the equation to determine the number of years till 900 acres is remaining is B)900 = 3,400(0.827)^t.
Which equation shows the number of years till 900 acres are remaining?As 900 acres is the target number of acres to remain, this will be on the left side of the equation as the y value.
The right side of the equation would be:
= Current number of acres remaining x ( 1 - rate of decrease) ^ number of years
= 3,400 x ( 1 - 17.3%) ^ number of years
Putting them together:
900 = 3,400(0.827)^t.
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Look at the image!
iready
a =80 vertically oposite angle
a+b=180 angle of the same side of transversal are 180 degree
so b=180-80
=100
c=b vertically oposite angle
b=100=c
c= 100
I hope it's helpful for you
Answer:
a=80, b=100, c=100
Step-by-step explanation:
Because A is directly across from 80 degrees, A is also 80 degrees. They are alternate angles, and so they equal the same thing. B is 100, because it is on the same line as 80, and a line equals 180 degrees. C is also 100 degrees, because it is across from B and on the same line as A, which is 80 degrees.
Hope this helps!
Which shapes contain at least one right angle?
Select each correct answer.
Answer:
in the picture
Step-by-step explanation:
the sign you see at the corners with arrows (see drawing) indicate a right angle
30 points!! What is the equation of this line?
Answer:
y = - 2x
Step-by-step explanation:
the equation of a line passing through the origin is
y = mx ( m is the slope )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (- 1, 2) ← 2 points on the line
m = [tex]\frac{2-0}{-1-0}[/tex] = [tex]\frac{2}{-1}[/tex] = - 2 , then
y = - 2x ← equation of line
The four 4's chalenge, 1-20
1/4 of the students in guitar class attended class today. Only 3/4 of the students share guitars. What fraction of the class shares guitars?
Answer:
3/16 of the class share guitars today.
Step-by-step explanation:
1/4 x 3/4 = 3/16! :)
Hoping to increase pizza sales on Tuesdays, a new pizza restaurant prints and disperses the following coupon through email and fliers in a neighborhood marketing magazine
After ten weeks of the coupon offer, the owner of the restaurant needs to decide if the restaurant should continue to run the same special or offer a new one. Use the data collected in the table to determine whether or not the coupon appears to be generating sales for the restaurant.
Week Total
Sales
1 $859
2 $1,176
3 $1,480
4 $1,365
5 $1,576
6 $1,498
7 $1,180
8 $1,964
9 $1,634
10 $1,580
Part A: don’t answer
Part B: Use the total sales for weeks 4 and 9 to write an equation for the line of best fit. In your final answer, include all of your calculations.
Part C: in terms of the slope of the equation for the line of best fit, explain whether or not you think the coupon is responsible for the restaurant's increase or decrease in pizza sales on Tuesdays. Use complete sentences in your answer.
Part D: Assuming that the pizza restaurant wishes to continue the coupon for an additional five weeks, use the equation for the line of best fit to predict the restaurant's sales for the Tuesday of the 15th week.
—
B) y = 53.8x + 1149.8
C) Total Sales increase from one week to the next by $53.8.
Therefore, it is true to say that the paid advertisement is responsible for the restaurant's increase in pizza sales during the first quarter.
D) The restaurant's sales for the Monday of the 15th week is expected to be $1956.8
What is equation of line?The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term.
B) As by scatter plot,
The total sales for week 4 is given as 1,365 while that of week 9 is 1,634.
Therefore, we shall determine the equation for the line of best fit using the points;
( 4, 1365) and ( 9, 1634)
The first step would be to determine the slope of this line;
slope = (1634 - 1365)/ (9 - 4)
= 53.8
The equation of the line in slope-intercept form is thus;
Sales = 53.8(Week) + c
We need to determine c, the y-intercept. We can use the point ( 4, 1365);
1365= 53.8(4) + c
c = 1365-215.2
c = 1149.8
The equation of the line of best fit is thus;
y = 53.8x + 1149.8
C) The slope of the equation for the lines of best fit was found to be 53.8.
This value is positive which implies
Total Sales increase from one week to the next by $53.8.
The slope in regression is defined as the change in y for every unit change in x.
Therefore, it is true to say that the paid advertisement is responsible for the restaurant's increase in pizza sales during the first quarter.
D) The equation for the line of best fit was found to be;
y = 53.8x+ 1149.8
where y denotes the total sales and x the corresponding week. We are required to determine y when x is 15;
y = 53.8(15) + 1149.8
y = 1956.8
Therefore, the restaurant's sales for the Monday of the 15th week is expected to be $1956.8.
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Cube: Find the surface area of a cube with side 5 inches.
Answer:
We are given the dimension of the side being 5 inches and it states that we need to determine the surface area. The first step that we must do is find the area of one side and then we multiply it by 6 because we have 6 same sides.
[tex]A = s^2[/tex]
[tex]A = (5\ in)^2[/tex]
[tex]A = 25\ in^2[/tex]
Now that we have the area of one side we can multiply it by 6 to get the total surface area.
[tex]A = 25\ in^2 * 6[/tex]
[tex]A = 150\ in^2[/tex]
Therefore, our final answer is that the surface area is 150 inches squared
Hope this helps!
Answer:
150 square inches
Step-by-step explanation:
find the area of 1 square face
5*5=25
multiply by 6 faces
25*6=150
Which equation can be used to find A, the area of the parallelogram shown?
Explanation:
The area of a parallelogram is equal to base times height.
The base and height are always perpendicular to one another. Usually the base is horizontal along the ground (if not then you'd need to rotate your paper until it is, but that step is optional).
The base is 6 meters and the height is 7 meters.
Therefore, area = base x height = 6 x 7
The side of 11 meters is not used at all. It's likely put in there as a distraction.
Answer:
A = 6 * 7
Step-by-step explanation:
A parallelogram follows the same rules as a regular quadrilateral, as the only difference is that both its sides have been moved along.
If no digit can be used more than once, find how many numbers that can be formed from the digits 3, 4, 5, 6, 7, 8 are greater than 7000.
Answer:
1 560
Step-by-step explanation:
If no digit (from the digits 3, 4, 5, 6, 7, 8) can be used more than once :
we can form 6P5 = 720 (five-digit numbers) and they are all > 7000
we can form 6P6 = 720 (six-digit numbers) and they are all > 7000
if our number has four digits ,then the digit in the ten-thousands place of it must be 7 or 8 :
In this case :
we can form 5P3=60 number where the digit in the ten-thousands place of it is 7.
and we can form 5P3=60 number where the digit in the ten-thousands place of it is 8.
Final answer :
We can form 720+720+60+60 = 1 560 number greater than 7000
ANSWER ASAP FOR BRAINLIEST
Dimitar puts only dimes and quarters into his piggy bank. Right now, it contains five more dimes than quarters, and their total value is exactly $74. How many quarters and how many dimes are in Dimitar's piggy bank?
0.35x=73.85, comgining moving terms
divide both sides by 0.35
x=211 quarters, which is $52.75 ANSWER
x+5=216 dimes, which is $21.60 ANSWER
That total is $74.35
Answer:
the answer is 210 quarters and 215 dimes
Step-by-step explanation:
A farm has an area of 5 km²
The farmer must pay 1p tax for each m² of land he owns.
Find the amount of tax the farmer must pay.
Step-by-step explanation:
1 km² = 1km×1km = 1000m × 1000m = 1000000 m²
5 km² = 5000000 m²
so, he has to pay 5000000p as tax.
The amount of tax the farmer must pay is 50000 Rupees.
What is tax ?A compulsory contribution the government has levied on people's income is called the tax , It is of various types and the money accumulated from that is used for the development of the nation.
It is given that the farmer has an area of 5 km²
The farmer must pay 1p tax for each m² of land he owns.
5km² = 5 * (1000)² m²
Area = 5 *10⁶ m²
The amount of tax the farmer needs to pay is
= 1* 5* 10⁶
= 5000000 p
100p = 1 rupees
= 50000 Rupees
Therefore the amount of tax the farmer must pay is 50000 Rupees.
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Each point on the edge of a circle is equidistant from the center of the circle. The center of a circle is located at (6, 3). Which point on the y-axis could be on the edge of the circle if the distance from the center of the circle to the edge is 10 units?
(0, –1)
(0, 1)
(0, 5)
(0, –5)
Answer: (0, –5)
Step-by-step explanation:
Don’t worry the other person is right
Step-by-step explanation:
Need help with my Study Island math. Wh I can help?
Step-by-step explanation:
scientific notation is
a.b × 10^c
with a being <> 0.
0.0002 cm = 2.0×10^-4 cm (the "2" moves 4 positions to the right for the actual number).
so, this is between 1.0×10^-4 cm and 1.0×10^-3 cm.
0.02 cm = 2.0×10^-2 cm (the "2" only need to move 2 positions to the right for the actual number).
so, this is between 1.0×10-2 cm and 1.0×10^-1 cm.
200 cm = 2.0×10² cm (now the "2" needs to move 2 positions to the left for the actual number).
so, this is between 1.0×10² cm and 1.0×10³ cm.
20,000 cm = 2.0×10⁴ cm (the "2" has to move 4 positions to the left for the actual number).
so, this is between 1.0×10⁴ cm and 1.0×10⁵ cm.
Evaluate the following expression. 7^0=?
Answer:
1
Step-by-step explanation:
7^0 = 1
Note : -
( Any number )^0 = 1
9. Which function's graph is a translation of the graph of f(x) = x shifted 7 units to the left?
Answer:
b) g(x) = x + 7
it may seem like its x - 7, but it's actually x + 7 since it shifts up the graph 7 units.
Help asap.
Given the expression: 5x^10 − 80x^2
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
Part B:Factor the entire expression completely. Show the steps of your work. (6 points)
Answer:
5x² ( x² - 2x + 2 ) ( x² + 2x + 2 ) ( x² + 2 ) ( x² - 2 )
Step-by-step explanation:
→ Find the highest common factor from 5 and 80
5
→ Find the highest common factor of x¹⁰ and x²
x²
→ Write the partially factored form
5x² ( x⁸ - 16 )
→ Factor down ( x⁸ - 16 )
( x⁴ + 4 ) ( x⁴ - 4 )
→ Factor down ( x⁴ + 4 ) ( x⁴ - 4 )
( x² - 2x + 2 ) ( x² + 2x + 2 ) ( x² + 2 ) ( x² - 2 )
Answer:
5x^2(x^8 -16)5x^2(x^2 +2x +2)(x^2 -2x +2)(x^2 +2)(x^2 -2)Step-by-step explanation:
The greatest common factor is that factor that includes every prime factor that is found in both expressions. Once that is removed, the formula for the factorization of the difference of squares is needed.
__
AEach expression factors as ...
5x^10 = 5·x^2·x^8
80x^2 = 5·x^2·16
The common factors in these expressions are 5, x^2, so the expression with the greatest common factor factored out is ...
5x^2(x^8 -16)
__
BThe remaining factor is the difference of squares, which factors as ...
a² -b² = (a -b)(a +b)
Here, we have a=x^4 and b=2^2, so the factors of the difference are ...
x^8 -16 = (x^4 -4)(x^4 +4)
The first of these factors is also recognizable as a difference of squares, so it can be factored further:
x^4 -4 = (x^2 -2)(x^2 +2)
The second factor can also be cast as the difference of squares, allowing it to be factored further:
x^4 +4 = (x^4 +4x^2 +4) -(4x^2) = (x^2 +2)^ -(2x)^2
= (x^2 +2x +2)(x^2 -2x +2)
So, the complete factorization of the original expression is ...
5x^10 -80x^2 = 5x^2(x^2 +2x +2)(x^2 -2x +2)(x^2 +2)(x^2 -2)
_____
Additional comment
We could factor to linear terms if we wanted to use radicals and complex numbers. This is the factorization in integers.
Alexa danced for 3 2/4 hours on Saturday. Sherlyn swam 1/5 of that time. How many
hours did Sherlyn swim on Saturday?
Answer:
Sherlyn swam 42 minutes on Saturday
Step-by-step explanation:
danced for 3 2/4 hours on Saturday
3 2/4 hours is equivalent to 3.5 hours
1 / 5 of (that time) 3.5 hours is (1 / 5) * 3.5 = 0.7 hours
Because one hour is equal to sixty minutes, in order to change the units you have to multiply the number of hours, 0.7, by 60.
0.7 x 60 = 42 minutes
Let me know if you have any questions !
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△ABC ≅ △DEF.
Find the measures of the given angles or the lengths of the given angles.
1). m∠B=3y, m∠E=6y-12
2). AC=7a+5, DF=5a+9
The measures for the given angles B and E are 12° .
Similarity TriangleTriangles are similar when the correspondent angles and the ratio of correspondent sides are equal. Also, it must present the same shape, but it is not mandatory the same dimension.
Like the triangles are similar, ∠B=∠E. Then,
∠B=∠E
3y=6y-12
3y-6y=-12
-3y=-12
y=4
You can write too:
AC=DF
7a+5=5a+9
7a-5a=9-5
2a=4
a=2
Therefore,
∠B=3y= 3* 4 =12
m∠E=6y-12=6*4-12=21-12=12
AC=7a+5= 7*2+5=14+5=19
DF=5a+9=5*2+9=10+9=19
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Find (a) arc length and (b) Area of a sector.
Answer:
a) 19.63 mm (2 dp)
b) 245.44 mm² (2 dp)
Step-by-step explanation:
Formula
[tex]\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right)[/tex]
[tex]\textsf{Area of a sector}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2[/tex]
[tex]\quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in degrees)}[/tex]
Calculation
Given:
[tex]\theta[/tex] = 45°r = 25 mm[tex]\begin{aligned}\implies \textsf{Arc length} &=2 \pi (25)\left(\dfrac{45^{\circ}}{360^{\circ}}\right)\\ & = 50 \pi \left(\dfrac{1}{8}\right)\\ & = \dfrac{25}{4} \pi \\ & = 19.63\: \sf mm \:(2\:dp)\end{aligned}[/tex]
[tex]\begin{aligned} \implies \textsf{Area of a sector}& =\left(\dfrac{45^{\circ}}{360^{\circ}}\right) \pi (25)^2\\& = \left(\dfrac{1}{8}\right)\pi \cdot 625\\& = \dfrac{625}{8} \pi\\& = 245.44\: \sf mm^2 \:(2\:dp)\end{aligned}[/tex]
Please note: As you have not specified if π should be approximated, I have not used an approximation for π.
How do I draw a 50 degree angle ?
To draw a 50 degree angle with a protactor, proceed as follows :
Draw a straight line (i.e. an arm of the angle).Place a dot at one end of the arm. This dot represents the vertex of the angle.Place the centre of the protractor at the vertex dot and the baseline of the protractor along the arm of the angle.Find 50 degree angle on the scale and then mark a small dot at the edge of the protractor.Join the small dot to the vertex with a ruler to form the second arm of the angle.Label the angle with capital letters.Remember that 50 degree angle cannot be constructed using compass.