-5
Make the equation into slope-intercept form, which is y = mx + b, where m is the slope, and b is the y-intercept.
In the equation y = -5x - 2/3, the slope is -5 and the y-intercept is -2/3.
For this case we have that the equation of the line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cutoff point with the y axis
We have the following equation:
[tex]y = - \frac {2} {3} -5x[/tex]
Reordering:
[tex]y = -5x- \frac {2} {3}[/tex]
So, we have to:
[tex]m = -5\\b = - \frac {2} {3}[/tex]
Answer:
The slope is -5
Find the area of a parallelogram if a base and corresponding altitude have the indicated lengths.
Base 1 1/2 feet, altitude 6 inches.
Answer:
The area of the parallelogram is 108 inches² OR 0.75 foot²
Step-by-step explanation:
* Lets revise the properties of the parallelogram
- Each two opposite bases are are parallel
- Each two opposite bases are equal in length
- Each two opposite angles are equal in measure
- Each two adjacent angles are supplementary (their sum = 180°)
- Its two diagonals bisect each other
- Each base has an altitude (height) drawn from the opposite
base to it
* Look to the attached figure to more understand
- The area of the parallelogram is the product of the length of one
of its base and the corresponding altitude (height)
∵ Area = B1 × H1 ⇒ OR ⇒ Area = B2 × H2
∵ B1 = 1 1/2 feet
∵ H1 = 6 inches
- The base and the height have different units, so we must
change the unit of one of them to the other
∵ 1 foot = 12 inches
∵ B1 = 1 1/2 = 1.5 feet
∴ B1 = 1.5 × 12 = 18 inches
∴ A = 18 × 6 = 108 inches²
* The area of the parallelogram is 108 inches²
OR
∵ B1 = 1 1/2 = 1.5 feet
∵ H1 = 6 inches
∴ H1 = 6 ÷ 12 = 1/2 = 0.5 foot
∴ A = 1.5 × 0.5 = 0.75 foot²
* The area of the parallelogram is 0.75 foot²
Answer:
108 square inches
Step-by-step explanation:
We know that the formula of area of a parallelogram is given by:
A = base × altitude
Since here we have different units for base and altitude, so either we will change the base to inches or the altitude to feet.
Base = [tex]1\frac{1}{2} ft = 1.5 ft[/tex]
[tex]\frac{1}{1.5ft} =\frac{12inches}{x}[/tex]
Base (x) = 18 inches
Substituting the values in the above formula to get:
Area of parallelogram = 18 × 6 = 108 square inches
what is 6tens + 6 ones
Answer:
66
6 x 10=60
6 x 1=6
60+6=66
Have a good day!!! <3 Hope this helped ma dude :)
Need help! Geometry!
Answer:
(x, y) ⇒ (-y, x)
Step-by-step explanation:
You can see that the points (1, 2) and (3, 5) get mapped to (-2, 1) and (-5, 3), respectively. That is, the old value y, when negated, is the new value of x; and the old value of x is the new value of y.
___
I find it easier to think of a 270° CW rotation as being the same as a 90° CCW rotation.
Drag and drop a statement or reason to each box to complete the proof.
Given: parallelogram MNPQ
Prove: ∠N≅∠Q
Answer:
1. MN≅QP
MQ≅NP
2. MP≅MP
3. SSS congruence postulate
4. ∠N≅∠Q
5. CPCTC
Step-by-step explanation:
1. As per the property of parallelogram that opposite sides are congruent, in given case of parallelogram MNPQ the opposite sides
MN≅QP and MQ≅NP.
2. The reflexive property of congruence states that a line or a geometrical figure is reflection of itself and is congruent to itself. Hence in given case of parallelogram MNPQ
MP≅MP
3. SSS congruence postulate stands for Side-Side-Side congruence postulate, it states that when three adjacent sides of two triangle are congruent then the two triangles are congruent. In given case of parallelogram MNPQ, as the sides MN≅Q, MQ≅NP and MP≅MP hence
ΔMQP≅ΔPNM
5. As proven in part 4 that ΔMQP is congruent to ΔPNM, so as per the property of CPCTC (congruent parts of congruent triangles are congruent)
∠N≅∠Q
5. CPCTC stands for congruent parts of congruent triangles are congruent.
!
Linear functions are expressed by the graph and
equation. Select all that apply.
(1)The slope is positive for both functions.
(2)The equation has a steeper slope than the line in
the graph.
(3) The y-intercept is the same for both.
(4) The graph and the equation express an equivalent
function.
8
4
y = -4x - 4
Answer:
C) The y-intercept is the same for both
D) The graph and the equation expression an equivalent function.
Step-by-step explanation:
We are given graph a linear function and a equation of line y = -4x - 4
From the given graph, let's find the equation.
From the graph, we know the slope = rise/run
Here rise = 4 and run -1
Slope = 4/-1 = -4
and
y-intercept is -4 (where the line cuts the y-axis)
The equation of graph of the line y = -4x - 4
So, the graph and the given equation are also the same.
Therefore, the answers are
C) The y-intercept is the same for both
D) The graph and the equation expression an equivalent function.
Answer:
(3) The y-intercept is the same for both.
(4) The graph and the equation express an equivalent
function.
Step-by-step explanation:
The slope of both functions is negative since in the graph the line is going down, then the Y intercept is the same for both because when X is 0, in the graph the line is located at Y=-4 and in the function you can set x to 0 and the function would be -4, then you can see that the function and the graph have the same slope and the same Y intercept that means that they express an equivalent function.
What is the premieter of this red polygon
Answer:
338 in
Step-by-step explanation:
If each of the measures shown is the measure from the vertex to the point of tangency, then that measure contributes twice to the perimeter (once for each leg from the vertex to a point of tangency).
2(22 in + 27 in + 22 in + 98 in) = 2(169 in) = 338 in
Select the margin of error that corresponds to the sample mean that corresponds to each population:
A population mean of 25, a standard deviation of 2.5, and margin of error of 5%
1. 30
2. 25
3. 20
Answer:
25
Step-by-step explanation:
Which relationship describes angles 1 and 2
Answer: First option and Third option
Step-by-step explanation:
You can observe in the figure that the angle 1 and the angle 2 have a common vertex and a common side. These kind of angles are known as "adjacent angles".
You can observe that the intersection of the lines forms four equal anles wich are right angles (Angles of 90 degrees). Thererefore, the angles 1 and 2 and also "complementary angles", because the sum of them is 90 degrees.
Then, the answers are the first option and the third option.
By 6 months, cubs can eat their adult diet of bamboo and fiber biscuits. An adult red panda might eat 1,100 grams of food per day made up of 23% biscuits, 73% bamboo, and the rest in fruit. Write and evaluate an expression to calculate how many grams of fruit an adult red panda eats in 3 weeks?
Explanation:
First we need to find the amount of the diet that is fruit. (It is what is not biscuits or bamboo.) The quantity is given per day, so we need to multiply that by the number of days in 3 weeks.
(1 - 23% -73%)·(1100 g/day)·(7 day/week)·(3 week) = (44 g/day)·(21 day)
= 924 g . . . . of fruit
Someone help please.
Answer:
$27
Step-by-step explanation:
If the table was marked up 125%, you can find the retail price of it this way:
20 + 1.25(20) = retail price
$45 = retail price.
To find 40% off of that, use
$45 - .4($45) = sale price
$27 = sale price (aka discount price)
Use the equation of the water level of the river represented by the equation y=-4x + 170, where x represents the
number of years and y represents the total feet. What points are located on the line?
Check all that apply.
(170,0)
(0,170)
(12, 126)
(50,30)
(5, 150)
(60,-70)
Answer:
(0,170) and (60,-70) and (5, 150)
Step-by-step explanation:
To see if a given point is on the line or not, you just have to enter the x value (first value in the parenthesis) and see if the function returns the correct y value (second number in the parenthesis).
f(x) = -4x + 170
(170,0) => -4 (170) + 170 = -680 + 170 = 510. NO, not equal to 0.
(0,170) => -4 (0) + 170 = 0 + 170 = 170. YES
(12, 126) => -4 (12) + 170= -48 + 170= 122. No, not equal to 126.
(50,30) => -4(50) + 170 = -200 + 170 = 130. No, not equal to 30.
(5, 150) => -4(5) + 170 = -20 + 170 = 150. YES
(60,-70) => -4(60) + 170 = -240 + 170 = -70. YES
Answer:
(0,170) and (60,-70) and (5, 150)
Step-by-step explanation:
Find the coordinates of the points of intersection of the graphs without building them: 5x–4y=16 and x–2y=6
[tex]\bf \begin{cases} 5x-4y=16\\ \cline{1-1} x-2y=6\\ \boxed{x}=6+2y \end{cases}~\hspace{7em}\stackrel{\textit{substituting \underline{x} in the first equation}}{5\left( \boxed{6+2y} \right)-4y=16} \\\\\\ 30+10y-4y=16\implies 30+6y=16\implies 6y=-14 \\\\\\ y=-\cfrac{14}{6}\implies y=-\cfrac{7}{3}\implies \blacktriangleright y=-2\frac{1}{3} \blacktriangleleft \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{since we know that}}{x=6+2y}\implies x=6+2\left( -\cfrac{7}{3} \right)\implies x=6+\left(-\cfrac{14}{3} \right) \\\\\\ x=6-\cfrac{14}{3}\implies x=\cfrac{18-14}{3}\implies x=\cfrac{4}{3}\implies \blacktriangleright x=1\frac{1}{3} \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left( 1\frac{1}{3} ~,~-2\frac{1}{3}\right)~\hfill[/tex]
Use substitution to solve each system of equations.
x – 5y = –3
–7x + 8y = –33
A(2, 7)
B(–5, 1)
C(7, 2)
D(1, –5)
I think it’s C sorry if I’m wrong
For this case we have a system of sos equations with two unknowns:
[tex]x-5y = -3\\-7x + 8y = -33[/tex]
We clear "x" from the first equation:
[tex]x = -3 + 5y[/tex]
We substitute in the second equation:
[tex]-7 (-3 + 5y) + 8y = -33\\21-35y + 8y = -33\\-27y = -33-21\\-27y = -54\\y = \frac {-54} {- 27}\\y = 2[/tex]
We find the value of "x":
[tex]x = -3 + 5 (2)\\x = -3 + 10\\x = 7[/tex]
ANswer:
(7,2)
Option C
Mrs. Varner deposited q dollars in a bank account that has been earning annual interest. The total value of the account is based on the function f(x) = q • 1.025x, where x represents the number of years the money has been in the account. If no deposits or withdrawals are made after the initial deposit, which equation represents the total value of the account 5 years from now? f(x) = q • 1.025x + 5 f(x) = q • 1.025x + 5 f(x) = q • 1.025x – 5 f(x) = q • 1.025x – 5
Answer:
f(x) = q • 1.025x + 5
Step-by-step explanation:
Mrs. Varner deposited q dollars in a bank account that has been earning annual interest.
The total value of the account is based on the function f(x) = q • 1.025x
where x represents the number of years the money has been in the account.
If no deposits or withdrawals are made after the initial deposit, the equation that represents the total value of the account 5 years from now is :
f(x) = q • 1.025x + 5
Answer:
b
Step-by-step explanation:
solve the system of equations using elimination. –9x – 2y = –115 –6x + 2y = –110
The answers are:
[tex]x=15\\y=-10[/tex]
Why?Solving systems of equations using elimination means multiplying/dividing the factors of the given equations in order to reduce variables and make the isolating process simpler, so, solving we have:
We are given the equations:
[tex]\left \{ {{-9x-2y=-115} \atop {-6x+2y=-110}} \right.[/tex]
We have that the terms that contains the variable "y" are equal with opposite signs, so, we can eliminate both directly, and then, isolate the variable "x", so, solving we have:
[tex]\left \{ {{-9x-2y=-115} \atop {-6x+2y=-110}} \right\\\\\left \{ {{-9x=-115} \atop {-6x=-110}} \right\\\\-9x-6x=-115-110\\\\-15x=-225\\\\x=\frac{-225}{-15}=25[/tex]
Now, that we know "x" we need to substitute it into any of the given equations in order to find "y", so, substituting we have:
[tex]-9x-2y=-115\\\\-9*(15)-2y=-115\\\\-135+115=2y\\\\2y=-20\\\\y=\frac{-20}{2}=-10[/tex]
Hence, we have that:
[tex]x=15\\y=-10[/tex]
Have a nice day!
ANSWER
(15,-10)
EXPLANATION
The given equations are:
–9x – 2y = –115 ...(1)
–6x + 2y = –110...(2)
Add equation (1) from equation (2) to eliminate y.
-9x+-6x=-110+-115
This implies that,
-15x=-225
Divide both sides by -15
[tex]x = 15[/tex]
Put the value of x into equation (2) to find y.
[tex] - 6(15 ) + 2y = - 110[/tex]
[tex] - 90+ 2y = - 110[/tex]
[tex]2y = - 110 + 90[/tex]
[tex]2y = - 20[/tex]
[tex]y = - 10[/tex]
The solution is (15,-10)
Graph the image of the figure after a dilation with a scale factor of 2 centered at (−7, −2) .
Use the Polygon tool to graph the quadrilateral by connecting all its vertices.
Answer:
See image and explanation
Step-by-step explanation:
Point (-7,-2) is the center of dilation. The scale factor is 2.
If point A has coordinates (-3,-2), then its image point H has coordinates (1,-2).
If point B has coordinates (-6,2), then its image point E has coordinates (-5,6).
If point C has coordinates (-4,3), then its image point F has coordinates (-1,8).
If point D has coordinates (-1,1), then its image point G has coordinates (5,4).
Answer:
hope this helps :)
Step-by-step explanation:
Help me with ixl please
Answer:
$5.82
Step-by-step explanation:
A markup or markdown of p% on a price causes that price to be multiplied by ...
(1 + p/100)
The price after the markup 115% is ...
$7.74(1 + 115/100)
And the price after that has been marked down 65% is ...
$7.74(1 +115/100)(1 -65/100) = $7.74×2.15×0.35 ≈ $5.82
The discount price was $5.82.
write a function to model the situation.
a box is w inches wide. the box is twice as long as it is wide and 3.5 times as tall as it is wide. write a function to model the volume (v) of the box in cubic inches as a function of its width.
please help and thank you!
Answer:
v(w) = 7w³
Step-by-step explanation:
The formula for the volume of a cuboid (rectangular prism, or box) is ...
V = LWH . . . . . . where L represent length, W represents width, and H represents height
The problem statement tells you that for a box of width w (in inches), the length is 2w, and the height is 3.5w. Using these values in the formula, we have ...
V = (2w)(w)(3.5w)
V = 7w³
Written as a function v(w), volume as a function of width, this is ...
v(w) = 7w³
Which number line represents the solutions to |–2x| = 4?
Answer:
I want to say its b
Answer:
the answer is C
Step-by-step explanation:
A sixth grade teacher can grade 25 HW assignments in 20 minutes. Is he working at a faster rate or slower rate than grading 36 HW assignments in 30 minutes?
Answer:
im not sure but he is grading assignments at a faster rate
Step-by-step explanation:
25/20=1.25 so 1.25 mins per hw assignment
36/30=1.20 so 1.20 mins per hw assignment
it takes him 5 more seconds to grade 36 hw assignments so he's going at a faster rate
hope this helps :)
a car gets 36 miles to the gallon. How many miles can the car travel on six and ¾ gallon of gasoline?
For this case we have a mixed number given by:
[tex]6 \frac {3} {4} = \frac {6 * 4 + 3 * 1} {4} = \frac {27} {4}[/tex]
We make a rule of three to get the miles that the car can travel.
36 ---------> 1
x ------------> [tex]\frac {27} {4}[/tex]
Where "x" represents the variable that gives the number of miles that the car can travel with [tex]\frac{27}{4}[/tex]gallons of gasoline
[tex]x = \frac {\frac {27} {4} * 36} {1}\\x = 243[/tex]
So, the car can travel 243 miles
ANswer:
243 miles
PLEASE HELP AND THANK YOU
Answer:
• n(t) = 150·2^t . . . . . . . . . . . . number of cells after t minutes
• a(t) = π(0.25 +0.50t)^2 . . . . area in cm^2 after t minutes
• d(t) = n(t)/a(t) = (2400·2^t)/(π(1+2t)^2)
Step-by-step explanation:
The number of cells (n(t)) is described by an exponential function of time (t) with an initial value of 150 and a growth factor of 2 each minute:
n(t) = 150·2^t . . . . . . n in cells; t in minutes
___
The area of the culture is given by ...
a(t) = π·(r(t))^2 . . . . where r(t) is the radius as a function of time.
The radius is linearly increasing with a rate of increase of 0.50 cm/min, so can be described by ...
r(t) = 0.25 +0.50t
Then the area is ...
a(t) = π·(0.25 +0.50t)^2
A factor of 0.25 can be removed from inside parentheses to make this be ...
a(t) = (π/16)(1 +2t)^2 . . . . . a in cm^2; t in minutes
___
The density is the number of cells divided by the area:
d(t) = n(t) / a(t) = 150·2^t/((π/16)(1 +2t)^2)
Simplifying a bit, this is ...
d(t) = (2400/π)(2^t)/(1 +2t)^2 . . . . . d in cells/cm^2; t in minutes
Which of the following formulas could be used to find the perimeter, P, of a regular octagon? P = 6s P = 7s P = 8s P = 9s
Answer: P=8s
Perimeter of octagon=8sides(unit value of side)
Answer:
P=8s
Step-by-step explanation:
we know that
The perimeter of a regular figure is equal to multiply the number of sides by the length of one side
In this problem
A regular octagon has 8 sides
Let
s-----> the length of one side
The perimeter is equal to
P=8s
Solve the exponential equation. 125^7x-2 = 150.
A.) -0.1375
B.) 2.1483
C.) 0.4234
D.) 0.4340
Answer:
D
Step-by-step explanation:
You need to get the x out of the position in which is currently sitting, which is exponential. The only way to get an exponent out from that position is to take the log of both sides. The power rule of logs allows us to move the exponent down in front of the log. Like this:
7x - 2 log (125)=log(150)
Now you want to divide both sides by log(125) to get the 7x - 2 all by itself:
[tex]7x-2=\frac{log(150)}{log(125)}[/tex]
Do that on your calculator and you'll get this:
7x - 2 = 1.037760918
Add 2 to both sides to get
7x = 3.037760918
then divide both sides by 7:
x = .4339 which rounds to .4340
Answer:
D.) -0.1375
Step-by-step explanation:
Solve the systems of substitution(find out what number x is and what number y is)
y=2x+5
y=3x+11
Answer:
(x, y) = (-6, -7)
Step-by-step explanation:
Substitute for y:
2x +5 = 3x +11 . . . . . use the first expression for y in the second equation
0 = x +6 . . . . . . . . . . subtract 2x+5
-6 = x . . . . . . . . . . . . add -6
y = 2(-6) +5 = -7 . . . .substitute for x
The solution is x = -6, y = -7.
A man standing on the roof of a building 64.0 feet high looks down to the building next door. He finds the angle of depression to the roof of that building from the roof of his building to be 34.7°, while the angle of depression from the roof of his building to the bottom of the building next door is 63.3°. How tall is the building next door? (Round your answer to the nearest tenth.)
Answer:
The height of the next door building is 41.7 feet
Step-by-step explanation:
* Lets study the situation in the problem
- The man standing on the roof of a building 64.0 feet high
- The angle of depression to roof of the next door building is 34.7°
- The angle of depression to the bottom of the next door building
is 63.3°
- We need to find the height of the next door building
* Lets consider the height of the man building and the horizontal
distance between the two building formed a right triangle and the
angle of depression is opposite to the side which represented the
height of the building
- Let the horizontal distance between the two buildings called x
# In the triangle
∵ The length of the side opposite to the angle of depression (63.3°)
is 64.0
∵ The length of the horizontal distance is x which is adjacent to the
angle of depression (63.3°)
- Use the trigonometry function tanФ = opposite/adjacent
∴ tan 63.3° = 64.0/x ⇒ use cross multiplication
∴ x (tan 63.3°) = 64 ⇒ divide both sides by (tan 63.3°)
∴ x = 64.0/(tan 63.3°)
∴ x = 32.1886 feet
- Lets use this horizontal distance to find the vertical distance between
the roofs of the two buildings
* Lets consider the height of the vertical distance between the roofs
of the two buildings and the horizontal distance between the two
building formed a right triangle and the
angle of depression is opposite to the side which represented the
vertical distance between the roofs of the two buildings
- Let the vertical distance between the roofs of the two buildings
called y
# In the triangle
∵ The vertical distance between the roofs of the two buildings is y
and opposite to the angle of depression (34.7°)
∵ The horizontal distance x is adjacent to the angle of
depression (34.7°)
∴ tan (34.7°) = y/x
∵ x = 32.1886
∴ tan 34.7° = y/32.1886 ⇒ use the cross multiplication
∴ y = 32.1886 (tan 34.7°)
∴ y = 22.2884 ≅ 22.3 feet
∴ The vertical distance between the roofs of the two
buildings is 22.3 feet
- The height of the next door building is the difference between the
height of the man building and the vertical distance between the
roofs of the two buildings
∴ The height of the next door building = 64.0 - 22.3 = 41.7 feet
Final answer:
This answer explains how to calculate the height of a building using trigonometry based on given angles of depression.
Explanation:
To determine the height of the building next door, we need to use trigonometric functions. Specifically, the tangent of an angle in a right triangle relates the angle to the ratio of the opposite side to the adjacent side.
The total height of the building next door will be H + D.
From the top of the 64.0 feet building, looking down with an angle of depression of 34.7° to the roof of the building next door gives us:
Tan(34.7°) = D/Distance
Similarly, looking down with an angle of depression of 63.3° to the bottom of the building next door gives us:
Tan(63.3°) = (H + D)/Distance
By creating a right triangle for each angle, we can establish the relationships to find the height, which turns out to be around 52.0 feet.
(6x – 4) – (2x + 8) is equivalent to:
A. 4(x + 4)
B. 4(x – 1)
C. 4(x – 3)
D. 4(x – 12)
Show Your Work
Answer:
C. 4(x – 3)
Step-by-step explanation:
(6 x - 4) - (2 x + 8)
6 x - 4 - 2 x - 8
4 x - 12
Factor
4 ( x - 3 )
A bus picks Trish up at 9 o’clock. She ate breakfast one hour and 30 minutes earlier. What time did Trish eat breakfast?
Trish ate her yummy breakfast at 7:30 :)
Answer:
7:30 am
Step-by-step explanation:
Subtract 90 minutes from 9:00 am to determine what time Trish ate breakfast.
quadratic function has x intercepts of (0,0) and (10,0) what is the x value of the minimum of the parabola explain how you know
ANSWER
x=5
EXPLANATION
The given quadratic function has x intercepts of (0,0) and (10,0) .
The x-value of the minimum point lies on the axis of symmetry of this graph.
The axis of symmetry is the midline of the x-intercepts
[tex]x = \frac{0 + 10}{2} [/tex]
The x-value of the minimum point is
[tex]x = 5[/tex]
Amira pulls a 3 pound wagon 4 feet. How much work has she done?
3 ft-lbs.
4 ft-lbs.
7 ft-lbs.
12 ft-lbs.
Answer:
12 ft-lbs is your answer
12ft-lbs that she has done