The factors of 45 are 9 and 5.
A number divisible by 45 needs to be divisible by both 9 and 5.
For a number to be divisible by 9 the sum of the digits must also be divisible by 9 and the number needs to end with either a 0 or a 5 to be divisible by 5.
This means the number needs to end with the 0 so cross out the last number (4)
Now find a sum of 5 remaining numbers divisible by 9.
5 + 1 + 4 + 8 + 0 = 18 which is divisible by 9
Cross out 9,7 and the last number 4 to get the number: 51480
The diagram shows that `/_A cong /_D` and `bar(AB) cong bar(DE)`. Which other statement do you need to prove triangle congruency through the SAS criterion?
A. /_C cong /_F
B. bar(BC) cong bar (EF)
C. /_B cong /_E
D. bar(AC) cong bar(DF)
Answer:
Option D
Step-by-step explanation:
In the given triangles ΔABC and ΔDEF,
∠A ≅ ∠D
AB ≅ DE
By SAS property of congruence of two triangles,
Two sides and the included angle of one triangles should be congruent to corresponding two sides and the included angle of the other triangle.
Therefore, AC ≅ FD will be the desired property to prove the given triangles congruent.
Option D will be the correct option.
Answer:
Step-by-step explanation:
Given the function, calculate the following values...
f(0) = 56
f(2) = 42
f(-2) = 70
f(x+1) = 7|x-7|
f(x²+2) = 7|x²-6|
Answered by GAUTHMATH
Find the area of the figure
Please help :)
9514 1404 393
Answer:
66.5 cm²
Step-by-step explanation:
A horizontal line at the "knee" on the right will divide the figure into a 4 cm by 2 cm rectangle, and a trapezoid with bases 4 cm and 9 cm, and height 11-2 = 9 cm. Then the total area of the figure is ...
A = LW + 1/2(b1 +b2)h
A = (4 cm)(2 cm) + (1/2)(4 cm +9 cm)(9 cm) = 8 cm² +58.5 cm²
A = 66.5 cm² . . . . area of the figure
RESUELVE USANDO LAS PROPIEDADES DE LA POTENCIA
PLISSSSSSSSS CON PROCEDIMIENTOOOOOOO
Answer:
Tenemos dos propiedades de la potencia en este caso:
Para un numero real A:
[tex]A^0 = 1[/tex]
[tex](A^n)^m = A^{n*m}[/tex]
En este caso nuestra ecuación es:
[tex][ [(\frac{0.1234}{-3.2098})^4]^3]^0[/tex]
usando la segunda propiedad, podemos reescribir como:
[tex][ [(\frac{0.1234}{-3.2098})^4]^3]^0 = (\frac{0.1234}{-3.2098})^{4*3*0} = (\frac{0.1234}{-3.2098})^0[/tex]
Y acá tenemos un numero real a la potencia 0, sabemos que esto es igual a 1, entonces:
[tex](\frac{0.1234}{-3.2098})^0 = 1[/tex]
Please help NO LINKS
[tex]\bar{x} = 0[/tex]
[tex]\bar{y} =\dfrac{136}{125}[/tex]
Step-by-step explanation:
Let's define our functions [tex]f(x)\:\text{and}\:g(x)[/tex] as follows:
[tex]f(x) = x^2 + 1[/tex]
[tex]g(x) = 6x^2[/tex]
The two functions intersect when [tex]f(x)=g(x)[/tex] and that occurs at [tex]x = \pm\frac{1}{5}[/tex] so they're going to be the limits of integration. To solve for the coordinates of the centroid [tex]\bar{x}\:\text{and}\:\bar{y}[/tex], we need to solve for the area A first:
[tex]\displaystyle A = \int_a^b [f(x) - g(x)]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\int_{-\frac{1}{5}}^{+\frac{1}{5}}[(x^2 + 1) - 6x^2]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\int_{-\frac{1}{5}}^{+\frac{1}{5}}(1 - 5x^2)dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\left(x - \frac{5}{3}x^3 \right)_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]
[tex]\:\:\:\:\:\:\:= \dfrac{28}{75}[/tex]
The x-coordinate of the centroid [tex]\bar{x}[/tex] is given by
[tex]\displaystyle \bar{x} = \dfrac{1}{A}\int_a^b x[f(x) - g(x)]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:= \frac{75}{28}\int_{-\frac{1}{5}}^{+\frac{1}{5}} (x - 5x^3)dx[/tex]
[tex]\:\:\:\:\:\:\:=\dfrac{75}{28}\left(\dfrac{1}{2}x^2 -\dfrac{5}{4}x^4 \right)_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]
[tex]\:\:\:\:\:\:\:= 0[/tex]
The y-coordinate of the centroid [tex]\bar{y}[/tex] is given by
[tex]\displaystyle \bar{y} = \frac{1}{A}\int_a^b \frac{1}{2}[f^2(x) - g^2(x)]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\frac{75}{28}\int_{-\frac{1}{5}}^{+\frac{1}{5}} \frac{1}{2}(-35x^4 + 2x^2 + 1)dx[/tex]
[tex]\:\:\:\:\:\:\:=\frac{75}{56} \left[-7x^5 + \frac{2}{3}x^3 + x \right]_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]
[tex]\:\:\:\:\:\:\:=\dfrac{136}{125}[/tex]
Please help me figure out if this truth table is equivalent or not. People who show their work and give a proper answer shall receive brainliest
Answer:
The statements are logically equivalent.
The 6th column is:
F T F F
The 7th column is:
F T F F
Step-by-step explanation:
The 6th column is just the opposite of the 5th column
The 7th column is T only if both the 1st and 4th are T
She uses a scale of 1 centimeter to 6 inches
the scale drawing of the front face is
Answer:
change inches into centimeter and then divide it
hope this help
The volume, V, of a sphere in terms of its radius, r, is given by , V(r)=4/3(pie)r^3. Express r as a function of V, and find the radius of a sphere with volume of 150 cubic feet. Round your answer for the radius to two decimal places.
r(V)=
A sphere with volume 150 cubic feet has radius
_________ feet.
Step-by-step explanation:
If
[tex]V=\dfrac{4\pi}{3}r^3[/tex]
then we can solve for r as
[tex]r = \sqrt[3]{\dfrac{3V}{4\pi}}[/tex]
If the volume of the sphere is 150 ft^3, then the radius is
[tex]r = \sqrt[3]{\dfrac{3(150\:\text{ft}^3)}{4\pi}} = 3.30\:\text{ft}[/tex]
The radius of the given sphere with a volume of 150 cubic feet is 2.29 feet, correct to two decimal places.
Given that
the volume of a sphere = 150 cubic feet.
the radius of the sphere=????
what is a Sphere?a round solid figure, or its surface, with every point on its surface equidistant from its center.
as we know,
the volume of a sphere
[tex]V=\frac{4}{3} *\pi *r^3[/tex]
[tex]r = \sqrt[3]{\frac{3V}{4\pi } }[/tex][tex]r = \sqrt[3]{\frac{3*150}{4\pi } }[/tex][tex]=2.29 feet[/tex]
therefore, the radius of the given sphere is 2.29feet
to get more about sphere refer to the link,
https://brainly.com/question/22807400
A roasted turkey is taken from an oven when its temperature has reached 185° Fahrenheit and is placed on a table in a room where the temperature is 75° Fahrenheit. Provide your answers accurate to at least 2 decimal places. (a) If the temperature of the turkey is 146° Fahrenheit after half an hour, what is its temperature after 45 minutes? Fahrenheit (b) When will the turkey cool to 100° Fahrenheit? hours.
Step-by-step explanation:
a the rate of changes = (185-146)/30
= 1.3° /minutes.
after 45 minutes = 1.3 ×45 = 58.5°
so, the temperature = 185 - 58.5
= 126.50°F
b. the time to reach 100°F =
(185-100)/ (1.3)
= 85/(1.3) = 65.38
after 65.38 minutes
Which shows the best estimate of the quotient of 4,346 ÷ 82?
between 50 and 60
between 60 and 70
between 500 and 600
between 600 and 700
Answer:
Between 50 and 60
Step-by-step explanation:
4,346/82 is 53 which is between 50 and 60.
Hope this helps!
If f (x)=3x-2 and g(x) =6-4 find f(x) + g(x)
Answer:
3x
Step-by-step explanation:
Joaquin drew the triangle below.
On a coordinate plane, triangle K L J has points (3, 6), (4, 0) and (negative 5, 0).
Which statement must be true about a figure that is congruent to Joaquin’s triangle?
It has two angles on the x-axis.
It has a side that is 9 units long.
It has a side that lies on the x-axis.
It has an obtuse angle.
Answer:
It has a side that is 9 units long.
Step-by-step explanation:
Answer:
B) It has a side that is 9 units long.
Step-by-step explanation:
Since it does not have two angles on the X-axis, a side that lies on the X-axis, or an obtuse angle the reasonable answer would be B as it is true, and all of the others are false.
What is the following product? Assume x>0 and y>0 v5x^8y^2•v10^3•v12y
Answer:
[tex]10x^{5}y \sqrt{6xy}[/tex]
Step-by-step explanation:
Find the length of side ab, give your answer to 1 decimal place 62 and 12
Answer:
Huh? is it triangle? and right triangle? if it is its 62^2 = 12^2 + x^2
Step-by-step explanation:
A closed, rectangular-faced box with a square base is to be constructed using only 36 m2 of material. What should the height h and base length b of the box be so as to maximize its volume
Answer:
[tex]b=h=\sqrt{6}[/tex] m
Step-by-step explanation:
Let
Bas length of box=b
Height of box=h
Material used in constructing of box=36 square m
We have to find the height h and base length b of the box to maximize the volume of box.
Surface area of box=[tex]2b^2+4bh[/tex]
[tex]2b^2+4bh=36[/tex]
[tex]b^2+2bh=18[/tex]
[tex]2bh=18-b^2[/tex]
[tex]h=\frac{18-b^2}{2b}[/tex]
Volume of box, V=[tex]b^2h[/tex]
Substitute the values
[tex]V=b^2\times \frac{18-b^2}{2b}[/tex]
[tex]V=\frac{1}{2}(18b-b^3)[/tex]
Differentiate w. r.t b
[tex]\frac{dV}{db}=\frac{1}{2}(18-3b^2)[/tex]
[tex]\frac{dV}{db}=0[/tex]
[tex]\frac{1}{2}(18-3b^2)=0[/tex]
[tex]\implies 18-3b^2=0[/tex]
[tex]\implies 3b^2=18[/tex]
[tex]b^2=6[/tex]
[tex]b=\pm \sqrt{6}[/tex]
[tex]b=\sqrt{6}[/tex]
The negative value of b is not possible because length cannot be negative.
Again differentiate w.r.t b
[tex]\frac{d^2V}{db^2}=-3b[/tex]
At [tex]b=\sqrt{6}[/tex]
[tex]\frac{d^2V}{db^2}=-3\sqrt{6}<0[/tex]
Hence, the volume of box is maximum at [tex]b=\sqrt{6}[/tex].
[tex]h=\frac{18-(\sqrt{6})^2}{2\sqrt{6}}[/tex]
[tex]h=\frac{18-6}{2\sqrt{6}}[/tex]
[tex]h=\frac{12}{2\sqrt{6}}[/tex]
[tex]h=\sqrt{6}[/tex]
[tex]b=h=\sqrt{6}[/tex] m
Put the equation y = x^2- 14x + 48 into the form y = (x-h)^2+k
please help me!
Answer:
Step-by-step explanation:
Answer:
[tex]y=(x-7)^2-1[/tex]
Step-by-step explanation:
We want to convert the equation:
[tex]\displaystyle y=x^2-14x+48[/tex]
Into vertex form, given by:
[tex]\displaystyle y=a(x-h)^2+k[/tex]
Where a is the leading coefficient and (h, k) is the vertex.
There are two methods of doing this. We can either: (1) use the vertex formulas or (2) complete the square.
Method 1) Vertex Formulas
Let's use the vertex formulas. First, note that the leading coefficient a of our equation is 1.
Recall that the vertex is given by:
[tex]\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = 1, b = -14, and c = 48. Find the x-coordinate of the vertex:
[tex]\displaystyle x=-\frac{(-14)}{2(1)}=7[/tex]
To find the y-coordinate, substitute this value back into the equation. Hence:
[tex]y=(7)^2-14(7)+48=-1[/tex]
Therefore, our vertex (h, k) is (7, -1), where h = 7 and k = -1.
And since we already determined a = 1, our equation in vertex form is:
[tex]\displaystyle y=(x-7)^2-1[/tex]
Method 2) Completing the Square
We can also complete the square to acquire the vertex form. We have:
[tex]y=x^2-14x+48[/tex]
Factor out the leading coefficient from the first two terms. Since the leading coefficient is one in this case, we do not need to do anything significant:
[tex]y=(x^2-14x)+48[/tex]
Now, we half b and square it. The value of b in this case is -14. Half of -14 is -7 and its square is 49.
We will add this value inside the parentheses. Since we added 49 inside the parentheses, we will also subtract 49 outside to retain the equality of the equation. Hence:
[tex]y=(x^2-14x+49)+48-49[/tex]
Factor using the perfect square trinomial and simplify:
[tex]y=(x-7)^2-1[/tex]
We acquire the same solution as before, with the vertex being (7, -1).
Which ordered pair makes both inequalities true?
y> - 2x + 3
ysx-2
- + -3 2-1
X
Answer:
Step-by-step explanation:
On the graph of two inequalities, solution of two inequalities is defined by the common shaded area.
That means all the points which lie in this area will satisfy both the inequalities.
From the graph attached,
Points given in the options (0, 0), (0, -1) and (1, 1) are not lying in the solution area.
Since, ordered pair given in 4th option is not clear in the picture, Option (4) may be the answer.
What is the range of g?
y
--
.
9
7.
6+
5+
4+
3+
2+
1+
.
3
{4}}
-7 -6 -5 -4 -3 -2
+++
2 3 4 5 6 7
-2
-3
-4+
-5
-6+
7
7
Answer:
y 9 5 473648
Step-by-step explanation:
Private nonprofit four-year colleges charge, on average, $26,208 per year in tuition and fees. The standard deviation is $7,040. Assume the distribution is normal. Let X be the cost for a randomly selected college. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(
26208
Correct,
7040
Correct)
b. Find the probability that a randomly selected Private nonprofit four-year college will cost less than 22,924 per year.
c. Find the 60th percentile for this distribution. $
(Round to the nearest dollar.)
Answer:
#########
Step-by-step explanation:
A circle has a circumference of 2cm. Which statement about the circumference and area is true?
A comparison of the area and circumference is not possible since the area cannot be determinec
The numerical values of the circumference and area of the circle are equal.
The numerical value of the circumference is greater than the numerical value of the area.
The numerical value of the circumference is less than the numerical value of the area.
ОО
Answer:
The numerical values of the circumference and area of the circle are equal.
NO LINKS OR ANSWERING WHAT YOU DON'T KNOW!!!!!
7. Suppose y varies inversely with x, and y = 39 when x = 1/3. What is the value of y when x = 26.
a. 3
b. 2
c. 1/2
d. 13
8. Suppose y varies inversely with x, and y = 25 when x = -1/5. What inverse variation equation relates x and y?
a. y = 5/x
b. y = -5/x
c. y = 5x
d. y= -5x
Answer:
Problem 7) C
Problem 8) B
Step-by-step explanation:
Recall that inverse variation has the form:
[tex]\displaystyle y=\frac{k}{x}[/tex]
Where k is the constant of variation.
Problem 7)
We are given that y = 39 when x = 1/3. Thus:
[tex]\displaystyle 39=\frac{k}{{}^{1}\!/ \!{}_{3}}[/tex]
Solve for k:
[tex]\displaystyle k=\frac{1}{3}(39)=13[/tex]
Hence, our equation is:
[tex]\displaystyle y=\frac{13}{x}[/tex]
Then when x = 26, y equals:
[tex]\displaystyle y=\frac{13}{(26)}=\frac{1}{2}[/tex]
Problem 8)
We are given that y = 25 when x = -1/5. Thus:
[tex]\displaystyle 25=\frac{k}{-{}^{1}\!/ \!{}_{5}}[/tex]
Solve for k:
[tex]\displaystyle k=-\frac{1}{5}(25)=-5[/tex]
Hence, our equation is:
[tex]\displaystyle y=-\frac{5}{x}[/tex]
The asymptote of the function f(x) = 3x + 1 – 2 is . Its y-intercept is
Answer:
-1
Step-by-step explanation:
1-2=-1
y=mx+b
b= y intercept
Answer:
-1
Step-by-step explanation:
40 points! Need help finding.
The cordent plan of the answer is 2
Answer:
The scale factor will just be 2
Step-by-step explanation:
The length of PQ is twice as larger than the length of AB.
so from 12 to 6 or 6 to 12, we multiply 6 by 2 which equals to 12
Create your own proportion problems?
Answer:
See Explanation
Step-by-step explanation:
Required
Proportion problems
An example is:
y is directly proportional to x such that: y=4 when x = 2;
Derive the equation
For direct proportions, we have:
[tex]y\ \alpha\ x[/tex]
This gives:
[tex]y = kx[/tex]
Make k the subject
[tex]k = y/x[/tex]
So:
[tex]k = 4/2 =2[/tex]
So, the equation is:
[tex]y = kx[/tex]
[tex]y = 2x[/tex]
Assume the above question is for inverse proportion
The variation will be:
[tex]y\ \alpha\ \frac{1}{x}[/tex]
This gives:
[tex]y\ = \frac{k}{x}[/tex]
Make k the subject
[tex]k =x*y[/tex]
[tex]k =2* 4 = 8[/tex]
So, the equation is:
[tex]y\ = \frac{k}{x}[/tex]
[tex]y = \frac{8}{x}[/tex]
Simplify the radical expression below square root of 5/64
A square root 5/8
B 5/64
C square root 5/64
D 5/8
Answer:
a
Step-by-step explanation:
square root distribute to numerator and denominator so both get square rooted [tex]\sqrt{5}[/tex]/8
Tyler and Elena are on the cross country team. Tyler’s distances and times for a training run are shown on the graph. Elenas distances and times for a training run are given by the equation y=8.5x, calculate Tyler’s pace per minute
Answer:
8.2 miles per minute
Step-by-step explanation:
Given
See attachment for graph
Required
The rate of Tyler's graph
This means that we calculate the slope (m) of the graph using:
[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]
So, we have:
[tex](x_1 ,y_1) = (0,0)[/tex]
[tex](x_1 ,y_1) = (1,8.2)[/tex]
So, we have:
[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]
[tex]m = \frac{0 - 8.2}{0 - 1}[/tex]
[tex]m = \frac{-8.2}{- 1}[/tex]
[tex]m = 8.2}[/tex]
f(x)=3x+2 what is f(5)
Answer:
17
Step-by-step explanation:
Substitute.
f(x)=3(5)+2
=15+2
=17
I hope this helps!
Step-by-step explanation:
if the equation if f(x) = 3x + 2, then f(5) would be equal to 3*5 + 2 = 17.
Please help ASAP. No links
Hello my dear friend of USA !!!
DB/AD = BE/EC
=> 6/4 = x+1/x
=> 6x = 4x + 4
=> 2x = 4
=> x = 2
So x = 2
I am from INDIA.
Lots of love ❤️!!!
Have a great day ahead!
Answer:
x = 2
Step-by-step explanation:
[tex]\frac{6}{4} = \frac{x+1}{x}[/tex]
6x = 4x + 4
2x = 4
x = 2
what can you infer about angles w and z based on the information in the other triangles?
Answer:
They are supplementary and their sum is 180°
w = 45 + 60 or w = 105
z = 180 - 105 or z = 75
Tonya wants to estimate what proportion of the students in her dormitory like the dorm food. She interviews a simple random sample of 50 students living in the dormitory. She finds that 14 think the dorm food is good. Find a 90% confidence interval for the true proportion of students that think the dorm food is good.
a. 0.176 to 0.384
b. 28%
c. 0.28 +/- 0.03
d. 0.156 to 0.404
Answer:
Step-by-step explanation:
The solution of the problem has been solved on paper and attached in the attachment section. Kindly refer to that and feel free to ask any doubt.
