Answer:
Step-by-step explanation:
The diagonal of this rectangular box serves as the hypotenuse of the 2 right triangles that exist within this rectangle. The length is one leg, the hypotenuse is...well, the hypotenuse, so we need to use Pythagorean's Theorem to find the missing leg.
[tex]10^2=8^2+x^2[/tex] and
[tex]100-64=x^2[/tex] and
[tex]x^2=36[/tex] so
x = 6. The width is 6.
What is the minimum perimeter of a rectangle with an area of 625 mm^2
Question 2 options:
100 mm
125 mm
156.25 mm
312.5 mm
Show your work:
Answer:
100 mm
Step-by-step explanation:
Square root the area to find the length of each side
[tex]\sqrt[]{625} =25[/tex]
Multiply 25 by 4 to get the sum of all four sides for the perimeter
25 x 4 = 100
plz help me to do this
The graph of $y=ax^2+bx+c$ passes through points $(0,5)$, $(1,10)$, and $(2,19)$. Find $a+b+c$.
Answer:
[tex]a+b+c=10[/tex]
Step-by-step explanation:
We are given that the graph of the equation:
[tex]y=ax^2+bx+c[/tex]
Passes through the three points (0, 5), (1, 10), and (2, 19).
And we want to find the value of (a + b + c).
First, since the graph passes through (0, 5), its y-intercept or c is 5. Hence:
[tex]y=ax^2+bx+5[/tex]
Next, since the graph passes through (1, 10), when x = 1, y = 10. Substitute:
[tex](10)=a(1)^2+b(1)+5[/tex]
Simplify:
[tex]5=a+b[/tex]
The point (2, 19) tells us that when x = 2, y = 19. Substitute:
[tex](19)=a(2)^2+b(2)+5[/tex]
Simplify:
[tex]14=4a+2b[/tex]
This yields a system of equations:
[tex]\begin{cases} 5 = a + b \\ 14 = 4a + 2b\end{cases}[/tex]
Solve the system. We can do so using elimination (or any other method you prefer). Multiply the first equation by negative two:
[tex]-10=-2a-2b[/tex]
Add the two equations together:
[tex](-10)+(14)=(-2a+4a)+(-2b+2b)[/tex]
Combine like terms:
[tex]4 = 2a[/tex]
Hence:
[tex]a=2[/tex]
Using the first equation:
[tex]5=(2)+b\Rightarrow b=3[/tex]
Therefore, our equation is:
[tex]y=2x^2+3x+5[/tex]
Thus, the value of (a + b + c) will be:
[tex]a+b+c = (2) + (3) + (5) = 10[/tex]
A random sample of 13 teenagers were surveyed for a hypothesis test about the mean weekly amount spent on convenience goods. Researchers conduct a one-mean hypothesis test, at the 1% significance level, to test whether the average spent per week on convenience goods is greater than 50 dollars.
Answer:
Please find the complete question and the graph in the attached file.
Step-by-step explanation:
On the basis of the data,
The level of importance is [tex]\alpha = 0.01[/tex]
Freedom levels [tex]= n -1 = 13 -1 = 12[/tex]
For the right-tailed test, the critical value is [tex]t_c = 2.681[/tex]
(Partially t-table permitted [tex]\alpha = 0.01 \ and\ df =12[/tex])
Angles of triangle are in the ratio of 23:5. What is the Size of the smallest angle?
Answer:
ratio 2 : 3 : 5
size of smallest angle
[tex]180 \times \frac{2}{10} \\ = 36[/tex]
Answer:
The smallest angle of a triangle is 36°.
Step-by-step explanation:
Given, the ratio of angles of a triangle is 2 : 3 : 5
Let the angles of a triangle be ∠A, ∠B and ∠C.
∠A = 2x, ∠B = 3x, ∠C = 5x
∠A+∠B + ∠C= 180°
[sum of all the angles of a triangle is 180°]
2x + 3x + 5x = 180°
10x = 180°
x=180°/10 =18°
∠A=2x=2 x 18° = 36°
∠B = 3x = 3 x 18° = 54°
∠C = 5x = 5 x 18° = 90°
Hence, the smallest angle of a triangle is 36°.
HOPE IT HELPS!!!
(4 x 10 ^ 7) ÷ (8 x 10 ^ 4) in standard form PLZ ANSWER QUICK
Answer:
4.67×10
4
=4.67×10000=46700
[tex]4.67 \times {10}^{4} [/tex]
[tex] = \: 4.67 \times 1000[/tex]
[tex] = \: 46700[/tex]
What is the slope-intercept form is?
Question 2 of 10
What is the length of MN?
M
4x
x + 3
250"
50
N
A. 4
o
B. 1
C. 7
ОО
D. 8
Answer:
4
Step-by-step explanation:
Since the base angles are the same, the side have to be the same
ML = MN
4x = x+3
Subtract x from each side
4x-x = x+3-x
3x= 3
Divide by 3
3x/3 = 3/3
x = 1
We want the length of MN
MN = x+3 = 1+3 = 4
The measurement of MN side is 4
What are the properties of Triangle?The properties of the triangle are:
1. The sum of all the angles of a triangle (of all types) is equal to 180°.
2. The sum of the length of the two sides of a triangle is greater than the length of the third side.
3. In the same way, the difference between the two sides of a triangle is less than the length of the third side.
Since the base angles are the same, the side have to be the same
ML = MN
4x = x+3
Subtract x from each side
4x-x = x+3-x
3x= 3
Divide by 3
3x/3 = 3/3
x = 1
We want the length of MN
MN = x+3 = 1+3 = 4
Learn more about triangles here:
https://brainly.com/question/2773823
#SPJ7
If Q = 5+2i, E = i, and D = 5-2i, find Q.E.D
Answer:
Q.D.E=(5+2i).(5-2i).i = (25-4i²)i = 25i-4i³
Step-by-step explanation:
Analyze the diagram below and complete the instructions that follow.
Quadrilateral LMNO is a rectangle. Find MN.
A.
7
B.
10
C.
18
D.
27
Answer:
there is no diagram ......
What is the area of trapezoid DEFG with coordinates D (4, 3), E (4, 0), F (2, 1), and G (2, 3)?
10 square units
5 square units
3 square units
2 square units
The area of the trapezoid is 10 square units
How to find the area of a trapezoid?The formula for finding the area of the trapezoid is expressed as:
A = 0.5(a+b)h
where:
a and b are the sides
h is the height
Given the following
a = 3
b = 2
h = 4
Determine the requried volume of the trapezoidSubstitute
A = 0.5(3 + 2)*4
A = 0.5(20)
A = 10 square units
Hence the area of the trapezoid is 10 square units
Learn more on area of trapezoid here: https://brainly.com/question/1463152
Answer:
B) 5 Square Units
Step-by-step explanation:
Answered from another colleague :)
B1 = 2
B2 = 3
H = 2
A = 1/2 (B1 + B2) H
1/2 (2+3) 2
1/2 (5) 2
(2.5)2
5
Help me plss I’m lost ☺️❤️
Answer:
there is only one way to to roll a 3
1/36 = .044 = 4.4%
Step-by-step explanation:
Abel bought a mini hi-fi set for S600.
He sold it to Bob at a loss of 20%.
Bob sold it to Charles and made a profit of 5%. How much did Charles pay for it?
Answer:
$504
$600* .8 = $480
$480 * 1.05 = $504
Step-by-step explanation:
Answer:
Step-by-step explanation:
Abel:
Cost price = $ 600
Loss = 20%
Selling price = [tex]\frac{100-loss}{100}*Cost \ price[/tex]
[tex]= \frac{(100-20)}{100}*600\\\\=\frac{80}{100}*600[/tex]
= 80 * 6 = $ 480
Cost price for Bob = Selling price of Abel = $ 480
Bob's cost Price = $480
Selling price = [tex]\frac{100+Profit}{100}*CP\\\\[/tex]
[tex]= \frac{100+5}{100}*480\\=\frac{105}{100}*480[/tex]
= $ 504
Amount paid by Charles =$ 504
reciprocal of. 0×7/11
Answer:
it doesn't exist
Step-by-step explanation:
the expression 0×7/11 is equivalent to 0. 1/0 isn't possible, so its reciprocal doesn't exist.
25)
Jackson's current salary is $36,000 per year. Each year his salary is 1.04 times the previous yeal's salary. What
will his salary be in his 5th year?
OA) $42,214.92
OB) $42,114.91
Answer:
$43,799.50
Step-by-step explanation:
USing the formula:
A = P(1+r)ⁿ
n is the time = 5
1 + r = 1.04
P = 36,000
Substitute the values into the formula
A = 36000(1.04)⁵
A = 36,000(1.2166529024)
A = 43,799.50
Hence the value in the fifth year will e $43,799.50
Use the cross product property to determine witch of the following equalities are proportions:
6.6/1.1 = 0.3/0.05
Answer:
proportion
Step-by-step explanation:
6.6/1.1 = 0.3/0.05
Using cross products
6.6 * .05 = 1.1 * .3
.33 = .33
Since this is a true statement, the statement is a proportion
10. A rectangle whose length is twice its width has a diagonal equal to one side of a given square. The ratio of the area of the rectangle to the area of the square is
Answer:
2/5
Step-by-step explanation:
First, we can draw the rectangle out, as shown. The length is twice the width, and the diagonal, y, cuts across the rectangle. This forms a right triangle, and using the Pythagorean Theorem, we can say that
y² = x² + (2x)²
y² = x² + 4x²
y² = 5x²
square root both sides
y=√(5x²)
The diagonal, or y, is equal to √(5x²). This is equal to one side of the square
The area for the rectangle, which we need to find for the ratio, is length * width = x * 2x = 2x²
The area for the square, which we also need to find for the ratio, is (side length)² = √(5x²) = 5x²
The ratio for the area of the rectangle to the area of the square is therefore 2x²/5x² = 2/5 (crossing out the x² in both the numerator and the denominator). We know to put the rectangle on top because of the specific wording of "the ratio of the area of the rectangle to..."
Which of the following statements does not prove that ABCD is a parallelogram.
Given: A(-4, 7), B(3,0), C(2,-5) and D(-5, 2).
Answer:
answer A
Step-by-step explanation:
A=(-4,7)
C=(2,-5)
midpoint = U=((-4+2)/2, (7+(-5))/2)=(-1,1))
B=(3,0)
D=(-5,2)
midpoint = V=((3+(-5))/2,(0+2)/2)=( -1,1)
Diagonals have the same middle, the quadrilater is a parallogram.
A 90 ° angle is divided into 2 angles.
Find the size of the angles.
5x+10 and 6x-41
Answer:
So required ans is 5*11+10=65 6x-41=25
Step-by-step explanation:
You can do as,
5x+10+6x-41=90
11x-31=90
11x=31+90
11x=121
x=121/11
x=11
4. If 2 Cos A-1 = 0, then the value acute value A is
Answer:
[tex]A=60^{\circ}[/tex]
Step-by-step explanation:
Given [tex]2\cos A-1=0[/tex],
Add 1 to both sides:
[tex]2\cos A=1[/tex]
Divide both sides by 2:
[tex]\cos A=\frac{1}{2}[/tex]
Take the inverse cosine of each side (note that the question stipulates that A is acute):
[tex]\arccos(\cos A)=\arccos(\frac{1}{2})[/tex]
[tex]A=\arccos(\frac{1}{2}), A\in (0^{\circ}, 90^{\circ}),\\A=\boxed{60^{\circ}}[/tex]
TRIANGLES please help!! :)
Answer:
A
Step-by-step explanation:
First, the list of congruence theorems are:
SSS
SAS
ASA
AAS
HL
SSA is not on the list, so we can cross that out
Next, ASA implies that two angles are congruent, but we only know that one pair of angles (the right angles) are congruent, so we can cross that out
After that, the angle is not connecting the congruent sides, so D is not an option
Finally, we know that the longest sides (AD / AC) are congruent to each other, one other pair of legs/sides are congruent, and the triangles are both right triangles. Therefore, we can apply HL here
What is Index Law 1?
please give a definition
Answer:
LAW 2: The second law of indices tells us that when dividing a number with an exponent by the same number with an exponent, we have to subtract the powers. In algebraic form, this rule is as follows . ... Example: In this example, the powers were multiplied together to give the answer which is 3 to the power of 6.
Find x in the right triangle (not drawn to scale):
Find the general term of the ap whose 7th term is -1 and 16th term is 17? (pls Hurry up I will mark you Brainliest and don't reply in a silly way or I'll report you)
Answer:
The answer is -13.
Step-by-step explanation:
The formula of the nth term of an AP(arthimetic progression) is a+(n-1)d.
So the 7th term will be a+6d= -1 ---(1)
The 16th term will a+15d=17 ---(2)
Subtract (2) and (1)
a+15d-(a+6d)=17-(-1)
=a+15d-a-6d=17+1
9d=18
d=18/9
d=2.
Substitute d in eq (1)
a+6(2)= -1
a+12=-1
a= -1-12= -13
Thus the general term of the ap is -13
does anyone know this?
Answer:
The volume is approximately 50 m^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h where r is the radius and h is the height
The radius is 1/2 of the diameter r = 8/2 = 4
V = pi ( 4)^2 (1)
V = 16 pi
Letting pi be approximated by 3.14
V = 3.14 * 16
V = 50.24
The volume is approximately 50 m^3
Solve for x.
x – 42 = 98 – 9x
X = [?]
Answer:
x = 14
Step-by-step explanation:
x - 42 = 98 - 9x
+42 +42
x = 140 - 9x
+9x +9x
10x = 140
/10 /10
x = 14
10 fracciones que generen decimales exactos 10 fracciones que generen decimales inexactos puros y 10 fraccionarios que generen decimales periódicos mixtos
Answer:
Un número decimal exacto es algo de la forma:
3.27
Para reescribir este número como una fracción, podemos ver que tiene dos dígitos luego del punto.
Entonces podemos multiplicar y dividir por 100 (misma cantidad de ceros que dígitos luego del punto decimal)
así obtenemos:
3.27*(100)/(100) = 327/100
Entonces la fracción 327/100 genera un decimal exacto.
Así, encontrar 10 fracciones es trivial, 10 ejemplos son:
7/10 = 0.7
314/100 = 3.14
27/10 = 2.7
27/100 = 0.27
2/10 = 0.2
25/100 = 0.25
31/10 = 3.1
12/10 = 6/5 = 1.2
131/10 = 13.1
142/100 = 1.42
Ahora, un decimal inexacto puro es algo de la forma:
3.33...
donde el 3 se repite infinitamente.
Tratemos de reescribir este número como una fracción:
primero debemos ver la cantidad de dígitos que se repiten, en este caso es uno solo, el 3, entonces multiplicamos por 10:
3.33*10 = 33.33...
Ahora, podemos restar el numero original:
33.333... - 3.333... = 30
Entonces tenemos que:
3.33*9 = 30
3.33 = 30/9
La fracción:
30/9 nos da in decimal inexacto puro.
Ahora que sabemos construirlas, 10 ejemplos pueden ser:
30/9 = 3.33....
1/3 = 0.33...
40/9 = 4.44...
50/9 = 5.55...
60/9 = 6.66...
70/9 = 7.77...
20/9 = 2.22...
55/9 = 6.11...
544/99 = 5.5959...
10/9 = 1.11...
Finalmente, un periódico mixto es algo de la forma:
1.2343434...
Es decir, el 34 se repite infinitamente, pero también tenemos un 2 luego del punto decimal, por lo que este número no es puramente periódico.
Para construirlos, podemos tomar una fracción exacta, como
1.1 y una periódica, como 1.11...
Si las sumamos, obtenemos:
1.1 + 1.11... = 2.211...
donde el uno se repetirá infinitamente.
Así, simplemente sumando las fracciones del primer caso con las del segundo, obtendremos decimales periódicos mixtos, por ejemplo:
7/10 + 55/9 = 613/90 = 0.7 + 6.11... = 6.8111....
7/10 + 10/9 = 163/90 = 0.7 + 1.11... = 1.811....
31/10 + 10/9 = 379/90 = 3.1 + 1.11... = 4.2111...
31/10 + 20/9 = 479/90 = 3.1 + 2.22... = 5.322...
31/10 + 30/9 = 579/90 = 3.1 + 3.33... = 6.4333...
27/10 + 20/9 = 443/90 = 2.7 + 2.22... = 4.922...
37/10 + 20/9 = 533/90 = 3.7 + 2.22... = 5.922...
4/10 + 10/9 = 136/90 = 0.4 + 1.11... = 1.511....
3/100 + 10/9 = 1027/900 = 0.03 + 1.11... = 1.14111...
4/10 + 20/9 = 236/90 = 0.4 + 2.22... = 2.622....
The difference between the square of two numbers is 11. Twice the square of the first number increased by the square of the second number is 97 find the numbers
Answer:
Below in bold.
Step-by-step explanation:
x^2 - y^2 = 11
2x^2 + y^2 = 97
From the first equation:
y^2 = x^2 - 11
Substituting in the second equation:
2x^2 + x^2 - 11 = 97
3x^2 = 108
x^2 = 36
x = 6, -6.
Substituting for x in the first equation:
(6)^2 - y^2 = 11
y^2 = 36 - 11 = 25
y = 5, -5.
El periodo de un movimiento circular uniforme es de
8 segundos. ¿Cuál es su velocidad angular?
Answer: I dont understand what your saying im sorry, I'd really like to help but I cant :(
Can someone help me with this math homework please!
Answer:
10
Step-by-step explanation:
f ( 1 ) = 18
First term ( a ) = 18
f ( n + 1 ) = f ( n ) - 2
When, n = 1
f ( 1 + 1 ) = f ( 1 ) - 2
f ( 2 ) = 18 - 2
f ( 2 ) = 16
f ( 2 ) - f ( 1 )
= 16 - 18
= - 2
Common difference ( d ) = - 2
f ( 5 )
= a + 4d
= 18 + 4 ( - 2 )
= 18 - 8
= 10
