Answer:
1. 80
2. 2400
Step-by-step explanation:
1. what is the change in Dan's total pay for each copy of math is fun he sells?
2. what is Dan's total pay if he doesn't sell any copies of math is fun?
Given
y=80x + 2400
When x=0
y=80(0)+2400
=0+2400
=2400
When x=1
y=80x + 2400
=80(1) + 2400
=80+2400
=2480
change in Dan's total pay for each copy of math is fun he sells is
= 2480 - 2400
=80
2. Dan's total pay if he doesn't sell any copies of math is fun?
y=80x+2400
When x=0
y=80(0)+2400
=0+2400
=2400
Someone please help me!!!!
Answer:
Below.
Step-by-step explanation:
Left side = 2 cos^2 ( π/4 - A/2) - 1
= 2 ( cos π/4 cos A/2 + sin π/4 sin A/2)^2 - 1
Now sin π/4 and cos π/4 = 1 /√2 so:
= 2 ( 1/√2 cos A/2 + 1/√2 sin A/2)^2 - 1
= 2 * 1/2( cos^2 A/2 + sin^2 A/2 + 2 sin A/2 cos A/2) - 1
But cos^2 a/2 + sin^2 A/2 = 1 so we have:
2 * 1/2( 1 + 2sin A/2 cos A/2) - 1
= 1 + 2 sin A/2 cos A/2 - 1
= 2 sin A/2 cos A/2
Using the identity 2 sin A cos A = sin 2A
2 sin A/2 cos A/2 = sin A = right side.
So left side = right side and the identity is proved.
Answer: see proof below
Step-by-step explanation:
Use the Double Angle Identity: cos 2A = 2cos²A - 1
Use the Difference Identity: cos (A - B) = cosA · cosB + sinA · sinB
Use the Unit Circle to evaluate: cos (π/2) = 0 & sin (π/2) = 1
Proof LHS → RHS
[tex]\text{Given:}\qquad \qquad \qquad \qquad 2\cos^2\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)-1\\\\\\\text{Double Angle Identity:}\quad \cos2\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)\\\\\\\text{Simplify:}\qquad \qquad \qquad \quad \cos\bigg(\dfrac{\pi}{2}-A\bigg)\\\\\\\text{Difference Identity:}\qquad \cos\dfrac{\pi}{2}\cdot \cos A+\sin \dfrac{\pi}{2}\cdot \sin A\\\\\\\text{Unit Circle:}\qquad \qquad \qquad 0\cdot \cos A+1\cdot \sin A\\\\\\\text{Simplify:}\qquad \qquad \qquad \qquad \sin A[/tex]
LHS = RHS: sin A = sin A [tex]\checkmark[/tex]
2
A circle has the equation x^2+ y^2 + 6x - 8y + 21 = 0.
a) Find the coordinates of the centre and the radius of the circle.
The point P lies on the circle.
b) Find the greatest distance of P from the origin.
Answer:
a) (-3, 4) and radius = 2.
b) 7 cms.
Step-by-step explanation:
x^2+ y^2 + 6x - 8y + 21 = 0
x^2 + 6x + y^2 - 8y = -21
Completing the square on the x and y terms:
(x + 3)^2 - 9 + (y - 4)^2 - 16 = -21
(x + 3)^2 + (y - 4)^2 = -21 + 9 + 16 = 4
a) So the center is (-3, 4) and the radius = sqrt4 = 2.
Ill come back to you later with the second part.
(b) For the point P to be a maximum distance from the origin the line must pass through the center of the circle:
Distance of the center from origin:
= √(-3 - 0)^2 + (4 -0)^2)
= 5.
So the dsitance of P from the origin is 5 + radius
= 7 cm.
I didn't understand this
Hector is flying a kite. He has let out 86 feet
of string and is holding it 4 feet off the
ground. If the string is at an angle of
elevation of 42°15’30”, how high is the kite?
Answer:
Hector's kite is 61.84 feet from the ground.
Step-by-step explanation:
The angle of elevation of the kite is 42°15’30” when converted to decimals, it is [tex]42.258333^{0}[/tex] ≅ [tex]42.26^{0}[/tex]
Let the height of the kite to the horizontal of angle of elevation be represented as x. Applying the trigonometric function to the sketch of Hector's kite,
Sin θ = [tex]\frac{opposite}{hypotenus}[/tex]
Sin [tex]42.26^{0}[/tex] = [tex]\frac{x}{86}[/tex]
⇒ x = 86 x Sin [tex]42.26^{0}[/tex]
= 86 x 0.6725
= 57.835
x ≅ 57.84 feet
The height of Hector's kite from the ground = x + 4
= 57.84 + 4
= 61.84 feet
find the value of
[tex]3 log_{2}4[/tex]
Answer:
6
Step-by-step explanation:
log ₐ (aˣ) = x
3 log ₂ (4)
3 log ₂ (2²)
3 * 2
6
What is (0,6) after a reflection over the y-axis?
Answer:
Still (0,6)
Step-by-step explanation:
The point is actually on the y-axis. It can't change in a y-axis reflection, only in an x-axis reflection.
Graph the line with slope -3 passing through the point (5,1) .
Answer:
we know that,
y-y1=m(x-x1)
or, y-1=-3(x-5)
or, y-1=15-3x
or 3x+y-16=0 is the required equation
The graph of the line with slope -3 passing through the point (5,1) is attached.
The equation of the line in the slope-intercept form is y = -3x + 16.
The equation of the line in the standard form is 3x + y = 16.
What is the equation of a line?The equation of a line is the representation of a line on a coordinate plane (x-y plane), which shows the relation between x and y, for every point on the particular line.
The standard form of a line is ax + by = c, where x and y are variables and a, b, and c are constants.
The slope-intercept form of a line is y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept of the line.
What is the one-point formula of a straight line?The equation of a line passing through the point (x₁, y₁), having a slope m, is represented by the one-point formula: y - y₁ = m(x - x₁).
How do we solve the given question?We are asked to graph a line with a slope = -3, passing through the point (5, 1).
We use the one-point formula to determine the equation of this line, with slope m = -3, (x₁, y₁) = (5, 1).
Substituting these values in the equation y - y₁ = m(x - x₁), we get
y - 1 = -3(x - 5)
or, y = -3x + 15 + 1
or, y = -3x + 16.
or, 3x + y = 16
The equation of the line in the slope-intercept form is y = -3x + 16.
The equation of the line in the standard form is 3x + y = 16.
To graph this line we plot the points (5, 1) (as it is given that it passes through this point) and (0, 16) (as the y-intercept is at 16, so the line passes through the point (0, 16)). We join these points by a line and extend this line on both sides to get the required line.
Learn more about the graphing of a line at
https://brainly.com/question/4025726
#SPJ2
If line a has a greater slope than line b, is line a steeper than line b? Explain, giving examples to support your answer. ( PLEASE HELP)
Answer:
No a greater slope is not always steeper
Step-by-step explanation:
If line A has a slope of 10 and line B has a slope of 6. The slope of line A will definetely be steeper than line B. In a negative slope, if line A's slope is -20 and line b's slope is 5 the line A will be steeper even though it is actually less than 5.
Joel took out a car loan for 12000 he paid 4800 in interest at a rate of 8% per year how many year will it take him to pay off the loan.
Answer:
5 years
Step-by-step explanation:
Simple interest on a loan of P for t years at rate r per year is ...
I = Prt
4800 = 12,000(0.08)(t)
4800/960 = t = 5
It will take Joel 5 years to pay off the loan.
what does (x + 3)(x - 5)=
Can someone help me find the domain and range of this graph?
Answer:
Domain: (-5, 6]
Range: [-3, 6]
Step-by-step explanation:
Domain is all x-values that can be inputted into function f(x).
Range is all the y-values outputted by function f(x) when we plug in x.
We see that our x-values span from -5 to 6. Since -5 is a open dot, we cannot input -5. Therefore, we have:
Domain: (-5, 6]
Parenthesis on -5 shows that it is not included and bracket on 6 shows it is included.
We see that our y-values span from -3 to 6. Since both points are closed dots, we can include both. Therefore, we have:
Range: [-3, 6]
Brackets on both numbers signify that both values are included in the graph.
3х +3y-2х-у
I’m trying to combine like terms plz help
Answer:
1X+2Y
Step-by-step explanation:
3x - 2x = 1x
3y - 1y = 2Y
Answer:
3x+2y
Step-by-step explanation:
Let's simplify step-by-step.
3x+3y−y
=3x+3y+(−y)
Combine Like Terms:
=3x+3y+(−y)
=(3x)+(3y+(−y))
=3x+2y
Answer:
=3x+2y
HOPE THIS HELPS!!!!!! :)
<333333
Is (0,3), (0,7), (4,0) a function
Answer:
no because it has 2 of the same x-intercepts.
Step-by-step explanation:
r - 7 = 1
can someone help me with this
Answer:
[tex]r=8[/tex]
Step-by-step explanation:
[tex]r-7=1[/tex] add seven to both sides
[tex]r=1+7\\r=8[/tex]
Hope this helps
Answer:
The correct answer to this problem is r = 8.
Step-by-step explanation:
To solve this problem, we have to remember that our goal is to get the variable (in this case, r) by itself on one side of the equation. To do this, we have to get rid of the -7 on the left side of the equation. Therefore, our first step is to add 7 to both sides of the equation. This gives us:
r - 7 = 1
r - 7 + 7 = 1 + 7
r = 8
Thus, your answer is r = 8.
Hope this helps!
Consider the following set of data: 3, 6, 8, 15, 21, 22, 23 Define what is meant by “ measures of variation”. What is the interquartile range of data? What is the mean absolute deviation of the data?
Answer:
Below.
Step-by-step explanation:
A measure of variation is an estimate of the spread of the numbers.
For example the set of numbers 1 2 3 19 78 has a greater measure of variation than the set 1 2 3 5 9.
The interquartile range and the mean absolute deviation are measures of variation.
3 6 8 15 21 22 23
The median of the data is the middle number 15..
The lower quartile is 6 and the higher quartile is 22
The interquartile range is 22 - 6 = 16.
The mean absolute deviation (M.A.D.) is calculated as follows:
Mean = (3+6+8+15+21+22+23) / 7 = 98/7
= 14.
List the absolute differences from the mean
14 - 3 = 11
14-6 = 8
15-14 = 1
21-14= 7
22-14 = 8
23-14 = 9 ( all these have to be positive)
The sum of the differences is 11+8+1+7+8+9 = 44
So the MAD = 44/7 = 6.3 to nearest tenth.
Sandy loves to ride her skateboard on her ramp. Sandy wonders how she could make her skateboard go faster. She thinks that the height of her ramp may play a role in the top speed reached by her skateboard. How should sandy set up her experiment to test her hypothesis? What would the independent variable be? What is the dependent variable?
Answer:
Null hypothesis : top speed = height
Alternative hypothesis : top speed ≠ height
Dependent variable : speed
Independent variable : Height
Step-by-step explanation: The experiment aims to determine the relationship between the height of ramp and the top speed reached by her skateboard.
The Null hypothesis: top speed = height
while the alternative hypothesis will negate the Null.
Alternative hypothesis : top speed ≠ height
The dependent variable in the experiment will be her top speed, because it is the variable we want to evaluate. We want to determine if thwre will be a change in the top speed of the skateboard if there is change in another variable 'height' of ramp. The variable which might cause a change in value of our dependent variable is called the independent or predictor variable, which in this case is the height variable.
1. There are 10 students in the class and 40 eggs. If
the eggs are divided equally among the students how
many does each student get?
Answer:
4 eggs
Step-by-step explanation:
40 divided by 10 = 4
Answer:
4
Step-by-step explanation:
40/10=4
Sophia manages a landfill. She decides to measure the rate at which trash increases in volume to fill the landfill as the number of households served increases.
Answer:
[tex]\frac{m^3}{h}, \frac{cm^3}{h}, \frac{km^3}{h}[/tex]
Step-by-step explanation:
If you look at the objects thrown as garbage, it's a two- or three-dimensional item that takes up space and also has mass and this is a solid waste.
And the landfill that dumps such garbage is also three-dimensional.
Hence, the volume module, if the object inside is a solid, either would be
[tex]m^3,cm^4,Km^3[/tex]
As household numbers rise, landfill space increases.
So,
[tex]household\ number = Proportionality\times landfill\ space[/tex]
If H represents the number of household keeps, then it will be a sufficient unit for the purpose of Sophia that is
[tex]\frac{m^3}{h}, \frac{cm^3}{h}, \frac{km^3}{h}[/tex]
Fully simplify.
-11xy2(13x2y3)
Answer:
-11xy\26x\2y\6
Step-by-step explanation:
write the verbal sentence as an equation. let y represent the number
the difference of 7 and the quotient of a number and 6 is -150
Answer:
Marcus is picking songs to play during a slideshow. The songs are each 3\dfrac123
2
1
3, start fraction, 1, divided by, 2, end fraction minutes long. The slideshow is 31\dfrac1231
2
1
31, start fraction, 1, divided by, 2, end fraction minutes long.
Step-by-step explanation:
Hi there, can anyone help me with this question?
A bag contains 1p, 2p and 5p coins. 2/5 of the bag are 2p coins. There are twice as many 1p coins than 5p coins in the bag. There are 630 coins in total. Work out the number of 5p coins in the bag.
Between which two consecutive whole numbers does the length of the diagonal fall?
Which whole number is it closer to? Use the drop-down menus to show your answer.
Answer:
4 and 5, closer to 4
Step-by-step explanation:
From the diagram above,
length of the diagonal = √18
√18 = 4.2426406871192
√18 is between 4 and 5
√18 is more than 4 by .2426406871192 but not up to 5
Rounding up 4.2426406871192 to an 1 significant figure,
We have 4
This means, the length of the diagonal, √18 is between 4 and 5 but it is closer to 4
Answer:
4 and 5, closer to 4
Step-by-ste
[tex]\sqrt18=4.24\\[/tex]
4.24 is closer to 4 than to 5
Joshua is preheating his oven before using it to bake. The initial temperature of the
oven is 75º and the temperature will increase at a rate of 25° per minute after being
turned on. What is the temperature of the oven 7 minutes after being turned on?
What is the temperature of the oven t minutes after being turned on?
Temp after 7 minutes:
Temp after t minutes:
Answer:
1) [tex]\huge\boxed{ 250\°}[/tex]
2) [tex]\huge\boxed{75\° + 25\°t }[/tex]
Step-by-step explanation:
Initial Temperature = 75°
Per minute Increase = 25°
After 7 minutes:
=> 75 + 25 ( 7 )
=> 75 + 175
=> 250°
After t minutes:
=> 75 + 25 (t)
=> 75° + 25°t
Answer:
[tex]\Large \boxed{\mathrm{a) \ 250\° \ \ \ b) \ 75\° +25\°t}}[/tex]
Step-by-step explanation:
Before baking, Joshua preheats the oven at an initial temperature of 75°. The temperature increases at a rate of 25° per minute.
Temperatute after 7 minutes,
[tex]75 \° + 25 \°(7)=75\° +175 \° =250 \°[/tex]
Tempertaure after t minutes,
[tex]75 \° +25 \° t[/tex]
i know im dumb srry but help plz....
If two angles are complementary, then the
sum of their measures is 90 degrees.
We can find the m<B by taking 90 minus the measure of <A.
So here, we have 90 - 15 which is 75.
So m<A is 75 degrees.
Given g(x)=3x2+3 evaluate f(0) Please help me with this.
Answer:
Assume you meant: [tex]g(x) = 3x^{2}+3[/tex]
Answer is 3
Step-by-step explanation:
Replace x with 0:
[tex]g(0) = 3(0)^{2} +3[/tex] zero squared is zero
[tex]g(0) = 3(0) + 3[/tex]
[tex]g(0) = 0 + 3[/tex]
[tex]g(0) = 3[/tex]
Step-by-step explanation:
[tex]\huge\underline\bold\blue{ƛƝƧƜЄƦ}[/tex]
we have
[tex]g(x) = {3x}^{2} + 3[/tex]
in this we have x = 0
[tex]g(0) = 3( {0})^{2} + 3[/tex]
[tex]g(0) = 0 + 3[/tex]
[tex]g(0) = 3[/tex]
so we have x =3
Hope it helps
Help ASAP!! I’m confused on only this question!
Answer:
Second choice
Step-by-step explanation:
f(x) = (1/4)(x + 4)^2 - 9
f(x) = (1/4)(x^2 + 8x + 16) - 9
f(x) = (1/4)x^2 + 2x + 4 - 9
f(x) = (1/4)x^2 + 2x - 5
(1/4)x^2 + 2x - 5 =
= (1/2 x + 5)(1/2 x - 1)
Answer: Second choice
4 + 6x + 5 = 7x Could someone help me? Thanks :) And could you also show how u did it
Answer:
x=9
Step-by-step explanation:
combine like terms
[tex]4+6x+5=7x[/tex]
4+5=9
9+6x=7x
to get 6x with 7x subtract 6x from both sides as its positive
6x-6x=0
7x-6x=x
9=x
x=9
Naya sells half the paintings in her collection and gives one-third of her paintings to friends, while she keeps the remaining paintings for herself. What fraction of her original collections does she keep?
Answer:
[tex]R = \frac{1}{6}[/tex]
Step-by-step explanation:
Given that she sold half the paintings and gives out one-third
Required
Determine the fraction left with her
The relationship between the paintings is as follows;
Sold Paintings + Giveaway Paintings + Remaining Paintings = 1
From the question;
Sold Paintings = 1/2
Giveaway = 1/3
Represent Remaining Paintings with R
Substitute these values in the above formula
[tex]\frac{1}{3} + \frac{1}{2} + R = 1[/tex]
Take LCM
[tex]\frac{2+3}{6} + R = 1[/tex]
[tex]\frac{5}{6} + R = 1[/tex]
Make R the subject of formula
[tex]R = 1 - \frac{5}{6}[/tex]
Take LCM
[tex]R = \frac{6-5}{6}[/tex]
[tex]R = \frac{1}{6}[/tex]
Hence, the fraction of the paintings left with her is [tex]\frac{1}{6}[/tex]
The midpoint of JK is M(8,9). One endpoint is J(10, 10). Find the coordinates of the other
endpoint K.
Write the coordinates as decimals or integers.
K= (1,7)
Answer:
[tex]K(6,8)[/tex]
Step-by-step explanation:
Given
Midpoint, M = (8,9)
J = (10,10)
Required
Find K
The midpoint of segments is calculated using;
[tex]M(x,y) = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})[/tex]
Where [tex]x = 8[/tex] and [tex]y = 9[/tex]
Take J as J(x1,y1);
So:
[tex]x_1 = 10[/tex] [tex]y_1 = 10[/tex]
Substitute values for x and y in the given formula
[tex](8,9) = (\frac{10 + x_2}{2}, \frac{10 + y_2}{2})[/tex]
Solving for x2, we have
[tex]8 = \frac{10 + x_2}{2}[/tex]
Multiply both sides by 2
[tex]2 * 8 = \frac{10 + x_2}{2} * 2[/tex]
[tex]2 * 8 = 10 + x_2[/tex]
[tex]16 = 10 + x_2[/tex]
Make x2 the subject of formula
[tex]x_2 = 16 - 10[/tex]
[tex]x_2 = 6[/tex]
Solving for y2
[tex]9 = \frac{10 + y_2}{2}[/tex]
Multiply both sides by 2
[tex]2 * 9 = \frac{10 + y_2}{2} * 2[/tex]
[tex]2 * 9 = 10 + y_2[/tex]
[tex]18 = 10 + y_2[/tex]
Make y2 the subject of formula
[tex]y_2 = 18 - 10[/tex]
[tex]y_2 = 8[/tex]
So,
[tex](x_2,y_2) = (6,8)[/tex]
So, the coordinates of K is
[tex]K(6,8)[/tex]
Prove that “The sum of the angles in a triangle is 180“.
Answer
See below :)
Step-by-step explanation:
Experimental Verification
Step 1 : Three triangles with different shapes and sizes are drawn. Suppose the name of each triangle is ABC.
( Draw the triangles in such a way that you can each angle by using a protractor )
( See attached picture )
Step 2 : Measure each angle of these three triangles with the help of protractor and fill up the following table.
_________________________________
Figure < A < B < C < A + <B + <C Result
-------------------------------------------------------------
( i ) 180°
--------------------------------------------------------------
( ii ) 180°
-------------------------------------------------------------
(iii) 180°
________________________________
Conclusion : The sum of the angles of any triangle is equal to 180°
Theoretical proof
( See attached picture )
Given : <ABC , <BCA and <BAC are the angles of ∆ABC.
To prove : <ABC + <BCA + <BAC = 180°
Construction : Through the vertex A , a straight line XY parallel to BC is drawn.
Proof :
_________________________________
Statements Reasons
------------------------------------------------------------
1. < XAB = <ABC 1. XY // BC and alternate
angles
------------------------------------------------------------
2. <YAC = <BCA 2. XY//BC and alternate
angles
------------------------------------------------------------
3. <XAB + <BAC + 3. whole part axiom
<YAC = <XAY
----------------------------------------------------------
4. <XAB + <BAC + 4. < XAY is a straight angle.
<YAC = 180°
-------------------------------------------------------------
5. <ABC + <BAC + 5. from statements ( 1 ),
<BCA = 180° ( 2 ) and (4)
_______________________________
Proved
Hope I helped!
Best regards!!