The Pythagorean theorem is used to prove that a triangle is a(n) triangle.
Answer:
Right
Step-by-step explanation:
The average rate of change from x = 0 to x = 15 is about −4.667. How does the average rate of change from x = 0 to x = 20 compare to this number?
Suppose that the height of the slide is 2 feet, when x = 20. What is the average rate of change over the entire slide?
The average rate of change over the entire slide is -0.05.
The average rate of change from x = 0 to x = 15 is calculated by finding the slope of the secant line that intersects the graph of the function at x = 0 and x = 15.
The slope of the secant line is:
m = ([tex]y_2[/tex] - [tex]y_1[/tex])/([tex]x_2[/tex] - [tex]x_1[/tex])
= (-2 - 15)/(15 - 0)
= -17/15
= -1.133
The average rate of change from x = 0 to x = 20 is calculated by finding the slope of the secant line that intersects the graph of the function at x = 0 and x = 20.
The slope of the secant line is:
m = ([tex]y_2[/tex] - [tex]y_1[/tex])/([tex]x_2[/tex] - [tex]x_1[/tex])
= (2 - 15)/(20 - 0)
= -13/20
= -0.65
The average rate of change from x = 0 to x = 20 is smaller than the average rate of change from x = 0 to x = 15.
This is because the slope of the secant line is getting closer to 0 as the interval gets larger.
If the height of the slide is 2 feet when x = 20, then the average rate of change over the entire slide is:
m = ([tex]y_2[/tex] - [tex]y_1[/tex])/([tex]x_2[/tex] - [tex]x_1[/tex])
= (2 - 1)/(20 - 0)
= -1/20
= -0.05
The average rate of change over the entire slide is also negative, but it is much smaller than the average rate of change from x = 0 to x = 15.
This is because the slope of the secant line is getting closer to 0 as the interval gets larger.
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Delia spent 45 minutes working on her book report. She finished the report at 6:10 p.m. at what time did Delia start working on her report
5.65 times 3.4 estimate
Jesse has a storage container in the shape of a right rectangular prism. The volume of the container is 43.875 cubic meters, the length is 5 meters and the width is 3.9 meters.
What is the height of Jesse's storage container?
I NEED HELP!!!!!!!!!!!!!!!!!!!!!!! :(
Answer:
2.25 meters
Step-by-step explanation:
all you have to do is divide the volume of the container (43.875) by 5 (length) and 3.9 (width) because the formula for the volume of a rectangular prism is V=lwh. So the answer/height of the storage container is 2.25 meters.
Convert. Into degrees
Chang and Cal both collect pearls. Chang has three more pearls in her collection than Cal. Write an expression to represent the total number of pearls in both collections.
Simplify this power raised to a power: (54)4
The value of [tex]$\left(5^4\right)^4$[/tex] simplified to [tex]$5^{16}$[/tex], meaning x = 16.
To simplify [tex]$\left(5^4\right)^4$[/tex], we first expand it as [tex]$5^4 \cdot 5^4 \cdot 5^4 \cdot 5^4$[/tex], using four factors of [tex]$5^4$[/tex].
Applying the product of powers rule, we add the exponents together: [tex]$5^{4+4+4+4}$[/tex]. This simplifies to [tex]$5^{16}$[/tex].
In essence, raising a power to another power involves multiplying the exponents.
In this case, we have four factors of [tex]$5^4$[/tex], which means we multiply 4 by 4, resulting in [tex]$5^{16}$[/tex].
So, the value of x in the simplified power [tex]$5^x$[/tex] is 16.
Complete Question:
Simplify this power raised to a power: [tex]$\left(5^4\right)^4$[/tex]
1. Expand using four factors of [tex]$5^4$[/tex] : [tex]5^4 \cdot 5^4 \cdot 5^4 \cdot 5^4[/tex]
2. Apply the product of powers rule: [tex]5^{4+4+4+4}[/tex]
3. Simplify: [tex]5^x[/tex]
What is the value of x in the simplified power?
in circle P, chord AB is 3 inches from the center and chord CD is 5 inches from the center. Chord CD is ____ than chord AB.
A. longer
B. congruent
C.shorter
D. proportional
Explain when you know you need to rename a mixed number to subtract.
Madame pompadour recently purchased velvet-lined doggy basket and a Diamond studded flea collar as a birthday gift for her beloved pet poodle. If the two items cost $3,215.90 and $ 5,850.25 Respectively what was the total bill
The equation of the quadratic function represented by the graph y=a(x-3)-1 what is the value of a
why is one half of the Box wider than the other half of the box
Dora is purchasing a $162,000 home with a 30-year mortgage at 5.15%. What is her monthly principal and interest payment?
A. $829.23
B. $884.56
C. $807.81
D. $876.09
Answer:
B . $ 884.56
Step-by-step explanation:
Since, monthly payment formula of a loan,
[tex]P=\frac{PV(\frac{r}{12})}{1-(1+\frac{r}{12})^{-12t}}[/tex]
Where,
PV = principal value,
r = annual rate of interest,
t = number of years,
Here,
PV = $ 162,000,
r = 5.15% = 0.0515,
t = 30,
Hence, the monthly payment would be,
[tex]P=\frac{162000(\frac{0.0515}{12})}{1-(1+\frac{0.0515}{12})^{-360}}[/tex]
[tex]=\$ 884.562485827[/tex]
[tex]\approx \$ 884.56[/tex]
OPTION B is correct.
Factor 64 – x15. (4 – x3)(16 + 4x3 + x3) (4 – x3)(16 + 4x3 + x6) (4 – x5)(16 + 4x5 + x5) (4 – x5)(16 + 4x5 + x10)
Answer:
Option d) [tex](4-x^5)(16+x^{10}+4x^5)[/tex]
Step-by-step explanation:
We are given the following in the question.
[tex]64-x^{15}[/tex]
We have to factorize the given expression.
Using the algebraic identity:
[tex]a^3 - b^3 = (a-b)(a^2+b^2+ab) = (a-b)^3 +3ab(a-b)[/tex]
[tex]64-x^{15}\\\\(4)^3 - (x^5)^3\\\\(4 - x^5)(4^2 + (x^5)^2 + 4x^5)\\\\(4-x^5)(16+x^{10}+4x^5)[/tex]
Hence, the factors of given expression is given by option d) [tex](4-x^5)(16+x^{10}+4x^5)[/tex]
Gabriel wants to solve the equation 5/8 m=25. What step should he do to get m by itself on one side of the equation?
Final answer:
To solve the equation 5/8 m = 25, Gabriel needs to multiply both sides of the equation by the reciprocal of 5/8, which is 8/5, to isolate m on one side. The result after simplification is m = 40.
Explanation:
To solve the equation 5/8 m = 25, Gabriel needs to isolate the variable m on one side of the equation. He should start by multiplying both sides of the equation by the reciprocal of the fraction that is multiplied by m, which is 8/5. Here's the step-by-step process:
Multiply both sides of the equation by 8/5 to cancel out the 5/8 on the left side:
(8/5) × (5/8) m = (8/5) × 25
Simplify the left side by canceling out the common factors in the fraction:
1 m = (8/5) × 25
Next, multiply the number 25 by 8/5 to find the value of m:
m = 25 × (8/5) = 40
Thus, the solution to the equation is m = 40.
studying for the act and I'm really bad at math, please help!
Is the system of equations is consistent, consistent and coincident, or inconsistent? y=4x−4 y=−4x+4 Select the correct answer from the drop-down menu.
If a system has exactly one or infinite number of solutions then it will be a consistent system.
So, we can solve the given system of equation to get the answer.
y=4x−4 ................(1)
y=−4x+4...............(2)
After equating both the equations we will get,
4x-4= -4x+4
4x-4+4x=4 (Adding 4x to each sides).
8x-4=4
8x=4+4 (Adding 4 to each sides).
8x=8
8x/8=8/8 ( Dividing each sides by 8).
x=1
Now pluging x=1 in equation (1). So,
y=4x−4
=4(1)-4
=4-4
=0
Hence the solution of the given system is (1, 0) which also means that the two equations is intersecting at a point(1,0).
So, the given system is consistent and coincident.
Answer:
The answer is " Consistent And Independent"
Why? :
When 2 Lines intersect at one point it means it Consistent and Independent
and When the Lines are the same exact thing its Consistent and Dependent
But, when 2 lines don't intersect at all its inconsistent. :)
I also Took The 5.11 Unit Test :)
In 7 minutes, Jo swims 12 laps. If she maintains the same pace, how long will it take Jo to swim 30 laps? SHOW ALL WORK. Answer the question using a complete sentence PLEASE...
A car maintains a speed of 23 mi/h for 5 seconds. It then accelerates to a speed of 46 mi/h in 5 seconds. It maintains that speed for the next 5 seconds. Which graph shows the car’s speed over time?
(80 points)
A car maintains a speed of 23 mi/h for 5 seconds. It then accelerates to a speed of 46 mi/h in 5 seconds. It maintains that speed for the next 5 seconds. Which graph shows the car’s speed over time?
Solution:
The graph is Time versus Speed.
In figure (a), the graph has a speed or y-axis=23mi/h for time or x-axis=5seconds.
The car maintains a speed of 23mi/h for 5 seconds.
For next 5 seconds, in figure a the graph increases linearly or we have a acceleration and reaches to 46mi/h.
It accelerates to a speed of 46 mi/h in 5 seconds.
It maintains that speed for the next 5 seconds. In figure (a), after we reach speed=46mi/h, there is a straight line for 5 seconds at speed=46mi/h.
So, Answer Graph a
Use the net to compute the surface area of the three-dimensional figure. A) 210 units2 B) 225 units2 C) 240 units2 D) 280 units2
The surface area of the given three-dimensional figure is 210 square units.
Option A will be the correct answer.
Surface Area of CuboidA cuboid is a three-dimensional figure having length, width and height. The surface area of a cuboid can be calculated by adding together the areas of the six faces.
For the given cuboid, length l = 8 , width w = 5 and height h = 5.
Area of Cuboid = 2 lw + 2 lh + 2 wh
[tex]A = 2\times l\times w + 2 \times l\times h + 2\times w\times h[/tex]
Substituting the values in the above formula, the area will be,
[tex]A = 2 \times 8 \times 5 + 2 \times 8 \times 5 + 2\times 5\times 5[/tex]
[tex]A = 210 \;\rm {units}^2[/tex]
Hence, the surface area of the cuboid is 210 square units.
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a dog pen measures 4 meters wide and has an area of 20 square meters. what is the perimeter of the pen in meters
Jake purchased a box of 1000 candy guitar lollipops to sell in the bakery for20. 00 how much did you pay for each lollipop
Ellen is drawing two polygons one of the polygons has 3 more angles than the other what shape could she be drawing
Answer:
Step-by-step explanation:
The attachment shows different types of polygons.
Now depending on these we have following five possibilities:
Case 1: Triangle and hexagon
If first polygon is triangle with three angles, the second will have 6 angles and the second polygon will be hexagon.
Case 2: Quadrilateral and heptagon
If first polygon is quadrilateral with 4 angles, the second will have 4+3 =7 angles and the second polygon will be heptagon.
Case 3: Pentagon and Octagon
If first polygon is pentagon with 5 angles, the second will have 5+3=8 angles and the second polygon will be octagon.
Case 4: Hexagon and Nonagon
If first polygon is hexagon with 6 angles, the second will have 6+3=9 angles and the second polygon will be nonagon.
Case 5: Heptagon and Decagon
If first polygon is Heptagon with 7 angles, the second will have 7+3=10 angles and the second polygon will be decagon.
Depend on the possibilities, which figure Ellen is drawing.
What is polygon?A closed, two-dimensional form with straight line segments is called a polygon. It does not have three dimensions. A polygon has flat surfaces throughout. A polygon must have three sides at a minimum. Only at its terminal must each side of a line segment cross another line segment. Depending on a polygon's number of sides.
Given Ellen is drawing two polygons one of the polygons has 3 more angles than the other,
Now, based on these, there are the five options listed below:
Case 1: Hexagon and triangle
If the first polygon is a triangle with three angles, the second polygon will be a hexagon with six angles.
Case 2: Heptagon and quadrilateral
If the first polygon has a quadrilateral shape and four angles, the second polygon will have four plus three more angles, making it a heptagon.
Pentagon and Octagon in Case 3
If the first polygon has a pentagon shape with five angles, the second will have an octagon shape with five plus three equals eight angles.
Hexagon and Nonagon in Case 4
If the first polygon has a hexagon shape and 6 angles, the second will have 6 + 3 = 9 angles and be a nonagon.
Heptagon and Decagon in Case 5
if the initial polygon is a hexagon, then The first polygon has 7 angles, the second has 7+3=10 angles, and the third is a decagon.
Hence the shape of polygon depend on these possibilities.
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You buy 8 packs of markers with 20 markers in each pack. You already had 10 markers. Which equation shows how to calculate the total number of markers, m, you have?
Answer: [tex]m= 8(20)+10[/tex]
Step-by-step explanation:
Given : The number of markers in each of 8 pack = 20
Then, the number of markers in 8 packs = 8 x 20 = 8(20)
Also, You already had 10 markers.
Then, the total markers you have now = Number of markers in 8 packs+ 10
= 8(20)+10
If we denote the total number of markers be 'm'.
Then, the required equation will be :-
[tex]m= 8(20)+10[/tex]
Hence, the equation shows how to calculate the total number of markers, m, you have : [tex]m= 8(20)+10[/tex]
PLZ HELP Harry baked a cake in the shape of a right rectangular prism and cut it in half parallel to the base of the cake. The base is 6 inches long and
4 inches wide, and the cake is 5 inches tall. Harry puts icing on the surface of each half of the cake. What is the shape of the cross section? What is the total area that is iced?
The cake’s cross section is a . The total area that is iced is square inches.
1/a.rectangle.b.square.c.kite.d.trapezoid
2/a.40.b.48.c.60.d.84
The answer is B, a square. I don't know about the area though.
Kasimir rode his bike 34,478 centimeters. He converts the distance to kilometers. His work is shown below.
A.Kasimir should have divided by 10,000.
B.Kasimir should have multiplied by 100.
C.Kasimir should have divided by 100,000.
D.Kasimir should have multiplied by 0.001.
Answer:
c) Kasimir should have divided by 100,000.
Step-by-step explanation:
Given that Kasimir rode his bike 34,478 centimeters.
We have the table
10 mm=1 cm
10 cm =1dm
10dm = 1 m
...
Hence we have 100 cm = 1 m
100x1000 cm = 1 km
1 km = 34478/100000 = 0.34478
Hence C) is right
Kasimir should have divided by 100,000.
The movie theater received a shipment of candy boxes in a carton that has a volume of about 64,000 cubic inches. Each candy box is 6 inches by 5 inches by 1/2 inch. The carton is completely full. About how many candy boxes are in the carton?
About 2,000
About 10,000
About 1,000
About 4,000
Look at the following math problems. 10 + 2 = 12 12 − 2 = 10 What are these operations called?
They are called inverse operations:
a triangle has a base of 15 in. and an area of 82.5 square inches. what is the height of the triangle? please explain how u found the answer out :)