Answer:
The answer is $1250
Step-by-step explanation:
Solution,
Principle (P) = $ 5,000
Time (T) = 5 years
Rate(R) = 5 %
Simple Interest (I) = ?
Now,
We have,
Simple Interest (I) = P×T×R/ 100
= 5,000×5×5/100
= $1250
42. A triangle has an area of 14 square inches. The height of the triangle is three inches more than the
base. What are the base and height of the triangle?
43. Jill has a small treasure box that is 6 inches long. It can hold a volume of 72 inches cubed, and the
width of the box is 5 inches less than twice the height of the box. What are the dimensions of the box?
44. Jessie is mowing her back yard that is in the shape of a right triangle. The shortest side is 7 meters
shorter than the second side, and the hypotenuse is 13 meters long. What are the lengths of the two
sides?
Answer:
Question 42
area of a triangle = 1/2 × base × height
Given:
area = 14 in²height = x + 3base = xSubstituting given values into the formula:
⇒ 14 = 1/2 × x × (x + 3)
⇒ 28 = (x + 3)x
⇒ 28 = x² + 3x
⇒ x² + 3x - 28 = 0
⇒ (x - 4)(x + 7) = 0
⇒ x = 4, x = -7
As length is positive, x = 4 only.
⇒ height = 4 + 3 = 7 in
⇒ base = 4 in
-----------------------------------------------------------------------------------------
Question 43
volume of a cuboid = length x width x height
Given:
volume = 72 in³length = 6 inheight = xwidth = 2x - 5Substituting given values into the formula:
⇒ 72 = 6 × (2x - 5) × x
⇒ 12 = (2x - 5)x
⇒ 12 = 2x² - 5x
⇒ 2x² - 5x - 12 = 0
⇒ (x - 4)(2x + 3) = 0
⇒ x = 4, x = -1.5
As length is positive, x = 4 only.
⇒ height = 4 in
⇒ width = 2(4) - 5 = 3 in
-----------------------------------------------------------------------------------------
Question 44
Pythagoras' Theorem: a² + b² = c²
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
Given:
a = x - 7b = xc = 13 mSubstituting given values into the formula:
⇒ (x - 7)² + x² = 13²
⇒ x² - 14x + 49 + x² = 169
⇒ 2x² - 14x - 120 = 0
⇒ x² - 7x - 60 = 0
⇒ (x - 12)(x + 5) = 0
⇒ x = 12, x = -5
As length is positive, x = 12 only.
⇒ one leg = 12 m
⇒ other leg = 12 - 7 = 5 m
What is the factorization of the trinomial below?
3x^3 + 6x^2 - 24x
A. 3x(x - 2)(x + 4)
B. 3x(x - 2)(x - 4)
C. 3(x - 2)(x + 4)
D. 3(x^2 - 2)(x + 4)
Yolanda cut 2 2/3 yards of fishing line from a new reel. How much is this in inches?
Answer:
1 yard = 3 feet: 3.25 yards x 3 feet per yard = 9.75 feet. 1 foot = 12 inches: 9.75 feet x 12 inches per foot = 117 inches.
Step-by-step explanation:
1 yard = 3 feet: 3.25 yards x 3 feet per yard = 9.75 feet. 1 foot = 12 inches: 9.75 feet x 12 inches per foot = 117 inches.
A sample of radium has a weight of 1.5 mg and a half-life of approximately 6 years.
a. How much of the sample will remain after 6 years?
Answer:
0.75mg
Step-by-step explanation:
6 years is its half life, meaning that half of it will have iradiated by that point. 1.5 / 2 = 0.75
What is the mean of the data set?
21.2, 15.3, 20.5, 16.8, 30.2
Question 1 options:
19.2
20.8
21.5
Answer:
B. 20.8 (second option)Step-by-step explanation:
The mean is calculated by adding up their values, and then dividing them into elements of a set.
All of them should first be added together.
21.2+15.3+20.5+16.8+30.2
Solve.
[tex]\sf{21.2+15.3+20.5+16.8+30.2=104}[/tex]
The sum of the data set is 104.
The number of terms in the data set is n=5.
Therefore, the mean of the data set is 20.8, which is our answer.
I hope this helps you! Let me know if my answer is wrong or not.
Is x + 2 a factor of p(x) = x°- 3x² – 7x + 6 ? Explain your answer.
Answer:
True
Determine whether x+2 is a factor of x³-3x²-7x+6:
↓
[tex]True[/tex]
I hope this helps you
:)
Algebra: Right answer pls
Which statement about the graph of y = 4 (1.25)× is true?
The coordinates of the x-intercept are (4, 0)
The coordinates of the y- internet are (0, 4) (ʀɤɢʜʈ Åɴswɛɾ)
The equation of the asymptote is x = 4
The graph includes the point (0, 1.25)
Answer: B
Step-by-step explanation:
For the graphed function f(x) = (4)x - 1 + 2, calculate the average
rate of
change from x = 1 to x = 2.
Answer:
y+4
Step-by-step explanation:
The piecewise function h(x) is shown on the graph.
What is the value of h(3)?
-2
ch
0-1
0 1
02
2.
-5 4 -3 -2 -14
2 3 4 5 x
-2
2
-3
-5
Answer:
1
Step-by-step explanation:
Let's say we have y=f (x)
It denotes the y value that corresponds to x.
When x=3, we can see from the graph that
The matching y value for x=3 =1
As a result, h(3)=1
The value of h(3) can be estimated from the piecewise function curve is 1. so option c is correct.
What is piecewise function?A function that is composed of several smaller functions, each with a distinct domain, is said to be piecewise. The term "piecewise" refers to the way in which these sub-functions are defined in terms of various intervals or "pieces" of the function's overall domain.
Given that,
The graph of the piecewise function
The function is divided into two piece
Interval-1 x ∈ [-4, -1)
Interval-2 x ∈ [-1, 4]
The value of the function when x is equal to 3,
In the graph it is clearly mention that for x =3
the output value of the function is 1
Hence, the output value is 1
To know more about piecewise function check:
https://brainly.com/question/12561612
#SPJ5
A manager drew this box-and-whisker plot to represent the number of minutes each of his 27 employees took on their break. Each employee took a different amount of time.
How many employees took a break longer than 49 minutes?
Enter your answer in the box.
Answer:
6
Step-by-step explanation:
Longer than 49 is only 25% percentile.
27 X .25 = 6.75
Employees are whole numbers, therefore the answer is 6.
Answer:
6
Step-by-step explanation:
A rectangle has a length of √ 72 meters and a width of √ 18 meters. Find its perimeter in exact and approximate forms, and then find its area.
The exact perimeter is _________ meters.
This is approximately ___________ meters. (Round your answer to the nearest tenth)
The area of the rectangle is ____________ square meters.
Answer:
The exact perimeter is [tex]18\sqrt{2}[/tex] meters.
This is approximately 25.5 meters (nearest tenth).
The area of the rectangle is 36 square meters.
Step-by-step explanation:
Area of a rectangle = width × length
Perimeter of a rectangle = (2 × width) + (2 × length)
Given:
length = [tex]\sqrt{72}[/tex] mwidth = [tex]\sqrt{18}[/tex] mPerimeter
[tex]\textsf{Perimeter}=2 \sqrt{18} +2\sqrt{72}[/tex]
[tex]=2 \sqrt{9 \cdot 2} +2\sqrt{36 \cdot 2}[/tex]
[tex]=2 \sqrt{9} \sqrt{2}+2\sqrt{36}\sqrt{2}[/tex]
[tex]=2 \cdot 3 \sqrt{2}+2\cdot 6\sqrt{2}[/tex]
[tex]=6 \sqrt{2}+12\sqrt{2}[/tex]
[tex]=18\sqrt{2} \textsf{ m}[/tex]
The exact perimeter is [tex]18\sqrt{2}[/tex] meters.
This is approximately 25.5 meters (nearest tenth).
Area
[tex]\textsf{Area}=\sqrt{18} \times \sqrt{72}[/tex]
[tex]=\sqrt{9 \cdot 2} \times \sqrt{36 \cdot 2}[/tex]
[tex]=3\sqrt{2} \times 6\sqrt{ 2}[/tex]
[tex]=18\sqrt{2}\sqrt{ 2}[/tex]
[tex]=18 \cdot 2[/tex]
[tex]=36 \textsf{ m}^2[/tex]
The area of the rectangle is 36 square meters.
Which statement about these triangles is true.
Picture Below
Answer:
For me I think it is a number 3
Step-by-step explanation:
The statement about these triangles which is true there are exactly three isosceles triangles, the correct option is B.
What is the right triangle?A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse. The angle of a right angle is always 90 degrees.
We are given that;
4 triangle figure
we can answer the question by counting how many triangles belong to each category. We have:
Three acute triangles: B, D, and E.
Three isosceles triangles: A, D, and E.
Two right triangles: A and C.
Two scalene triangles: B and C.
Therefore, the statement that is true about these triangles is:
Therefore, by the given triangle answer will be There are exactly three isosceles triangles.
Learn more about a right angle triangle;
https://brainly.com/question/7116550
#SPJ2
1. Find the area of the polygon
2. Find the area of the polygon
A=__ sq. un
3. In the figure, each of the small squares has an area of 1. What is the area of the shaded region?
(A) 50
(B) 45
(C) 100
(D) 55
Answer:
1. A = 40 units²
2. A = 72 units²
3. B) 45
Step-by-step explanation:
1. This shape comprises 4 congruent triangles with base of 5 units and height of 5 units.
Area of a triangle = 1/2 x base x height
Therefore, area of polygon = 4(1/2 x 5 x 4)
= 40 units²
2. This shape comprises two pairs of congruent triangles.
Area of a triangle = 1/2 x base x height
Therefore, area of polygon = 2(1/2 x 2 x 6) + 2(1/2 x 10 x 6)
= 72 units²
3. Count the number of shaded squares:
9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45 units²
Solve for x 5x + 15 = 28
o
ol
43
5
13
5
O 13
043
Answer:
[tex]\boxed{\sf{x=\dfrac{13}{5}=2.6 }}[/tex]Step-by-step explanation:
To solve for x, you have to isolate it on one side of the equation.
First, subtract by 15 from both sides.
[tex]\sf{5x+15-15=28-15}[/tex]
Solve.
28-15=13
Rewrite the problem down.
5x=13
Divide by 5 from both sides.
[tex]\sf{\dfrac{5x}{5}=\dfrac{13}{5} }[/tex]
Solve.
You can also divide the numbers from left to right.
13/5=2.6
[tex]\boxed{\sf{x=\dfrac{13}{5}=2.6 }}[/tex]
Therefore, the correct answers is x=13/5=2.6.I hope this helps you! Let me know if my answer is wrong or not.
[tex]\rightarrow \sf 5x + 15 = 28[/tex]
[tex]\rightarrow \sf 5x + 15 -15= 28-15[/tex]
[tex]\rightarrow \sf 5x = 13[/tex]
[tex]\rightarrow \sf \dfrac{5x}{5} = \dfrac{13}{5}[/tex]
[tex]\rightarrow \sf x = \dfrac{13}{5}[/tex]
[tex]\rightarrow \sf x = 2\dfrac{3}{5}[/tex]
[tex]\rightarrow \sf x = 2.6[/tex]
how many millions are there in 1 core?
Answer:
10 million
Step-by-step explanation:
HELP 50pts!!!!!!!!!!
Answer:
2.5, which would be 2:30 hours
Step-by-step explanation:
time/distance:
22.5/9 = 2.5
9 x 2.5 = 22.5
so the answer is 2.5
Answer:
2.5 hours
Step-by-step explanation:
[tex]\sf time \ taken = \dfrac{distance}{speed}[/tex]
Here:
distance : 22.5 kmspeed : 9 km/hr[tex]\hookrightarrow \sf \dfrac{22.5}{9}[/tex]
[tex]\hookrightarrow \sf 2.5[/tex]
15 Mary needs to work out the size of angle x in this diagram.
DO NOT WRITE IN THIS AREA
63°
X
B
С
She writes
x = 63° because base angles of an isosceles triangle are equal.
Mary is wrong.
(a) Explain why.
Mary is wrong because ∠A = ∠B = 63°, while ∠C = x ≠ 63°
What is a triangle?
A triangle is a polygon with three sides and three angles. Types of triangles are equilateral, isosceles and right angled.
An isosceles triangle is a triangle in which two sides and two angles are equal.
From the diagram:
∠A = ∠B (base angles)
Mary is wrong because ∠A = ∠B = 63°, while ∠C = x ≠ 63°
Find out more on triangle at: https://brainly.com/question/17335144
Megan purchased a used car for $6,200. Her state charges 6% tax for the car, $57 for registration, $60 for a new title certificate, and $40 for a state safety and emissions inspection. Show all work. a. How much does Samantha need to pay for these extra charges, not including the price of the car? b. How much does she need to pay in total, for the car and extra charges? Show oyur work.
If A:B = 7:8 an B:C =12:7,find
In the polynomial below, what number should replace the question mark to produce a difference of squares?
x^2 + ?x - 36
A. 12
B. 36
C. 6
D. 0
Answer:
Step-by-step explanation:
c
Help help help help help
[tex]\mathbf{m}=-\frac{1}{2}[/tex]
Step-by-step explanation:⇒ Find the slope of the line that is perpendicular to y = 2x + 7 :
↓
[tex]\mathbf{m}=-\frac{1}{2}[/tex]
I hope this helps you
:)
Suppose a math class has 18 females (2 of whom speak French) and 13 males (5 of whom speak French).
Compute the probability that a randomly selected student is male, given that the student speaks French.
Round your answer to three decimal places.
18 females, 13 males, total: 31 students.
•female french students: 2
•male french students: 5
probability: male french = 5/31,
total students
edit: as a percentage, 16.129 %
the question is below please help by monday
Complete the table below with the amounts of raspberry juice, apple
juice and soda needed to make the different quantities of Fruit Fizz.
mixture must taste exactly the same each time.
What is 5 1/3% converted into a fraction?
Answer: [tex]\frac{4}{75}[/tex]
To Know: A percent (%) divided by 100 becomes a decimal / fraction.
Step-by-step explanation:
[tex]5\frac{1}{3}[/tex]% [tex]/100[/tex]
[tex]5\frac{1}{3}[/tex]%[tex]*\frac{1}{100}[/tex]
[tex]\frac{16}{3}[/tex]%[tex]*\frac{1}{100}[/tex]
[tex]\frac{16*1}{3*100} =\frac{16}{300} =\frac{8}{150}=\frac{4}{75}[/tex]
Leaving us with an answer of [tex]\frac{4}{75}[/tex]
What type of function is f(x) = 2x3 – 4x2 + 5?
it's a cubic function
The given function f(x) = 2x³ – 4x² + 5 is a cubic function.
What is a cubic polynomial?A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
A cubic polynomial is a sort of polynomial that is based on the variable's largest exponent, or degree, in mathematical terms. As a result, a cubic polynomial is one in which the degree or maximum power of the variable is 3.
It is observed that the given function is a cubic function as its highest power of the variable is three.
Therefore, the given function f(x) = 2x³ – 4x² + 5 is a cubic function.
To know more about cubic polynomials follow
https://brainly.com/question/20896994
#SPJ5
Jodi has a collection of 153 shells. She gives 39 shells to her sister Sherri. Then their mother gives each sister 28 shells.
Part A
How many shells does Sherri have now?
A.
28
B.
67
C.
142
D.
181
Part B
How many shells does Jodi have now?
A.
28
B.
67
C.
142
D.
181
Answer:
Part-A= C
Part-B= B
Step-by-step explanation:
153-39=114
114+28=142
39+28=67
Answer:
Part A is b and Part B is c good luck
What is the domain and range of the graph below?
Answer:
Domain = [-7,4]
Range = [-4,8]
Step-by-step explanation:
Domain= all values of x
Range= all values of y
becuase there are no values going to infinity and they all end, we can just look at our end points.
Graph the following function:
f(x) = x2 + 5x – 6
Answer:
The graph is in the image below
Step-by-step explanation:
you can use an online graphing calculator like Desmos to graph questions like this
I'm not sure if the x2 is x^2 but I will assume
-
Angle A and B are vertical angles. If Angle A = (5x – 3)° and Angle B = (4x + 21)°,
then find the measure of Angle A.
Answer:
Angle A=87°
Step-by-step explanation:
(5x-3)°+(4x+21)°=180°
9x°+18°=180°
9x°+18°-18°=180°-18°
9x°=162°
9x°/9°=162°/9°
x=18°
Angle A=(5x18-3)°
(90-3)°
Angle A=87°
Find the angle between vectors a=(1,2) and b=(1,-1/2).
Answer:
[tex]90^{\circ}[/tex]. In other words, these two vectors are perpendicular (orthogonal) to one another.
Step-by-step explanation:
Let [tex]\|a\|[/tex] and [tex]\|b\|[/tex] denote the magnitudes of vector [tex]a[/tex] and vector [tex]b[/tex]. The dot product between these two vectors is represented as [tex]a^{T}\, b[/tex]. Let [tex]\theta[/tex] denote the angle between the two vectors. The cosine of this angle would be equal to:
[tex]\begin{aligned}\cos(\theta) &= \frac{a^{T}\, b}{\|a\| \|b\|}\end{aligned}[/tex].
The dot product between vector [tex]a = \langle 1,\, 2\rangle[/tex] and [tex]b = \langle 1,\, -1/2\rangle[/tex] is:
[tex]\begin{aligned}a^{T}\, b &= {\begin{bmatrix}1 \\ 2\end{bmatrix}}^{T}\, \begin{bmatrix}1 \\ -1/2\end{bmatrix} \\ &= 1 \times 1 + 2 \times \left(-\frac{1}{2}\right) \\ &= 0\end{aligned}[/tex].
The magnitudes of the two vectors are:
[tex]\begin{aligned}\| a \| &= \sqrt{1^{2} + 2^{2}} \\ &= 5\end{aligned}[/tex].
[tex]\begin{aligned}\| b \| &= \sqrt{1^{2} + \left(-\frac{1}{2}\right)^{2}} \\ &= \frac{1}{2}\, \sqrt{5}\end{aligned}[/tex].
Therefore:
[tex]\begin{aligned}\cos(\theta) &= \frac{a^{T}\, b}{\|a\| \|b\|} \\ &= \frac{0}{5 \times (\sqrt{5} / 2)} \\ &= 0\end{aligned}[/tex].
Among all angles between [tex]0^{\circ}[/tex] and [tex]180^{\circ}[/tex], the only angle with a cosine of [tex]0[/tex] is [tex]90^{\circ}[/tex]. Therefore, the angle between vector [tex]a[/tex] and vector [tex]b[/tex] must be [tex]90^{\circ}\![/tex]. Hence, these two vectors are perpendicular to one another.