Answer:
C) Triangular Prism
13.- La factorización correcta d
expresión 3x2- 24x + 21 es:
A) (3x-3)(x+7)
B) (3x+21)(x-1)
C) (3x+1)(x+21)
D) (3x-3)(x-7)
reción y
Answer:
Option (D)
Step-by-step explanation:
The given expression is,
3x² - 24x + 21
We will factorize the given expression by the following steps,
3x² - 24x + 21
= 3(x² - 8x + 7)
= 3(x² - 7x - x + 7)
= 3[x(x - 7) - 1(x - 7)]
= 3(x - 1)(x - 7)
= (3x - 3)(x - 7)
Therefore, factored form of the given expression is (3x - 3)(x - 7).
Option (D) will be the correct option.
An oblique prism has trapezoidal bases and a vertical height of 10 units. An oblique trapezoidal prism is shown. The trapezoid has base lengths of x and 2 x, and a height of x. The distance between the 2 trapezoid bases is 20. The vertical height of the prism is 10. Which expression represents the volume of the prism? 10x3 cubic units 15x2 cubic units 20x3 cubic units 30x2 cubic units
Answer:
volume of trapezoidal prism = 15x^2 cubic units
Step-by-step explanation:
First, area of the trapezoidal bases.
Parallel sides measure x and 2x, for an average of 1.5x.
Height = x
Area of trapezoidal base = 1.5x*x = 1.5x^2
Volume of prism = area base * height
(length does not matter, height does)
= 1.5x^2 * 10 = 15x^2
The volume of the prism is 15x² cubic units if the oblique prism has trapezoidal bases and a vertical height of 10 units option (B) 15x² cubic units is correct.
What is a trapezoid?It is defined as the quadrilateral having four sides in which two sides are parallel to each other, it is a 2-dimensional geometry.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
It is given that:
An oblique prism has trapezoidal bases and a vertical height of 10 units.
As we know, the area of the trapezoidal bases:
From the figure:
Height = x
Area of trapezoidal base = (1.5x)(x) = 1.5x²
The volume of prism = area base×height
= 1.5x²×10 = 15x² cubic units
Thus, the volume of the prism is 15x² cubic units if the oblique prism has trapezoidal bases and a vertical height of 10 units option (B) 15x² cubic units is correct.
Learn more about the trapezoid here:
brainly.com/question/8643562
#SPJ6
On the coordinate plane below, Point P is located at (2,-3), and point Q is located at (-4,4).
Find the distance between points P and Q Round your answer to the nearest whole number.
Answer:
9
Step-by-step explanation:
We can use the distance formula
d = sqrt ( ( y2-y1)^2 + ( x2-x1) ^2)
d = sqrt ( ( 4- -3)^2 + ( -4 -2) ^2)
= sqrt ( ( 7^2 + ( -6)^2)
= sqrt( 49+ 36)
= sqrt(85)
9.219544457
Rounding to the nearest whole number
= 9
The Department of Health in the United Kingdom wants to know whether the healthcare system is achieving its goals in Scotland. Much information about healthcare comes from patient records, but that source doesn't allow us to compare people who use health services with those who don't. Therefore, the Department of Health conducted the Scotland Health Survey, which was used to interview a random sample of 34,572 people who live in Scotland.
Part A: What is the population for this sample survey? What is the sample? (4 points)
Part B: The survey found that 70% of males and 87% of females in the sample had visited a general practitioner at least once during the past year. Do you think these estimates are close to the truth about the entire population? Explain. (6 points)
Answer:
A. the population for this sample survey is 34,572 people, and the sample is the people who live in Scotland.
B. The estimates are close to the truth about the entire population.
Step-by-step explanation:
A. According to the given data we have that it was used to interview a random sample of 34,572 people who live in Scotland, therefore, the population for this sample survey is 34,572 people, and the sample is the people who live in Scotland.
B. The estimates are close to the truth about the entire population becuase a large sample was conducted, hence we can make an aproximation that represents the population parameter.
Hi could somebody help me
Assuming both vertical lines are parallel and assuming I'm supposed to find all the unmarked angles...
Angle C:
Supplementary Angles.
x+36=180
180-36=x
x=144
Angle B:
Corresponding Angles.
Angle B ≅ Angle C
144
Angle A:
360 degrees in a quadrilateral
36+144+81+x=360
261+x=360
x = 99
Hope it helps <3
What is the simplified form of the equation fraction 4 over 5 n minus fraction 1 over 5 equals fraction 2 over 5 n?
n = −2
n = 4
n = fraction 1 over 2
n = fraction 2 over 3
Answer:
n=2
Step-by-step explanation:
⁴/5n-¹/5=²/5n
first we remove the denominators by multiplying all the numbers with their lcm
Lcm of 5n and 5 is 5n thus:
(5n×⁴/5n)-(¹/5×5n)=²/5n×5n
4-n=2
4-2=n
n=2
confirmationinsert 2 insted of n
⁴/5(2)-¹/5=²/5(2)
⁴/10-¹/5=²/10. simplify
²/5-¹/5=¹/5
¹/5=¹/5
so the correct value of n is 2
Sequences as Functions: Practice
Save and Exit
Question 8 of 8
Consider the geometric sequence below.
2, 12, 72, 432, ...
Select the explicit function which defines the sequence.
f(n) = 6.3(m – 1)
0 0
f(n) = 6.2(1 - 1)
f(1) = 3.2(0 - 1)
O f(x) = 2.6(n - 1)
Submit
Reset
Please answer it in two minutes
Answer:
2√3
Step-by-step explanation:
Since this is a 30-60-90 triangle, we can find s by finding the short leg (bottom), then the hypotenuse (s).
To find the short leg, we can divide the long leg (which is 3mm) by sqrt 3 (also √3, as any of them are fine), and we will have 3/√3. Since we don't want the square root on the bottom, we can multiply √3 on both sides, giving us 3√3/3, which is technically √3 because of simplifying.
Since you have the short leg now, you can find s. By finding s, you can multiply the short leg by 2, which will be √3 * 2 which is 2√3.
Explain why f(x) = x^2-x-6/x^2-9 is not continuous at x = 3.
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]f(x) = \frac{x^2 - x -6}{x^2 - 9}[/tex]
Required
Why is the function not continuous at x = 3
First substitute 3 for x at the denominator
[tex]f(x) = \frac{x^2 - x -6}{x^2 - 9}[/tex]
Factorize the numerator and the denominator
[tex]f(x) = \frac{x^2 - 3x+2x -6}{x^2 - 3^2}[/tex]
[tex]f(x) = \frac{x(x - 3)+2(x -3)}{(x - 3)(x+3)}[/tex]
[tex]f(x) = \frac{(x+2)(x - 3)}{(x - 3)(x+3)}[/tex]
Divide the numerator and denominator by (x - 3)
[tex]f(x) = \frac{x+2}{x+3}[/tex]
Substitute 3 for x
[tex]f(3) = \frac{3+2}{3+3}[/tex]
[tex]f(3) = \frac{5}{6}[/tex]
Because [tex]f(x) = \frac{x^2 - x -6}{x^2 - 9}[/tex] is defined when x = 3;
Then the function is continuous
Answer:
A: f is not defined at x = -3
Step-by-step explanation: EDGE 2020
What is the result of subtracting the second equation from the first? \begin{aligned} -2x+7y &= 10 \\\\ 3x+7y &= 2 \end{aligned} −2x+7y=10 3x+7y=2
Answer:
-5x = 8
Step-by-step explanation:
The result is shown here. The y-terms cancel.
[tex]\begin{array}{rccc}& -2x+7y &= &10 \\-&(\ \,3x+7y &= &2)\\\cline{1-4}&-5x+0y&=&8 \end{array}[/tex]
The simplified result is ...
-5x = 8
Answer:
The result is that 5x = -8
Step-by-step explanation:
Here, we want to subtract 3x + 7y = 2 from -2x + 7y = 10
Mathematically that would be;
(-2x+7y)-(3x+7y) = 10-2
-2x + 7y -3x -7y = 8
-2x -3x + 0 = 8
-5x = 8 or 5x = -8
among the following, a perfect number a) 6 b)28 c) 625 d) 100
this question comes under more than one correct answer
Answer:
28 and 6
Step-by-step explanation:
List the factors (excluding itself):
6: 1, 2, 3,
28: 1, 2, 4, 7, 14
Add them up!
1+2+3=6
1+2+4+7+14=28
if they add up to the original number then the number is perfect.
========================================
Explanation:
By definition, a perfect number is one where the factors smaller than itself add to the number in question.
The factors of 6, smaller than 6, are {1,2,3}. We can see that 1+2+3 = 6. Therefore, 6 is a perfect number.
Similarly, 1+2+4+7+14 = 28 showing that 28 is also a perfect number.
------
The factors of 625, that are smaller than 625, are 1,5,25,125. They add to 1+5+25+125 = 156. This isn't equal to 625, so 625 isn't a perfect number.
A similar issue happens with 100 as well. The smaller factors are 1,2,4,5,10,20,25,50, meaning we get a sum of 1+2+4+5+10+20+25+50 = 117, which is too large.
------
The first four perfect numbers are: {6, 28, 496, 8128}
For what value of x does 5^x-2 not equal zero?
a. all except 2
b. all except 0
c. all except -4
d. all except -2
e. all real numbers
Answer:
E: all real numbers
Step-by-step explanation:
☆*☆=3x, if x is even and negative OR ☆*☆=4x, if x is odd. Following the rule above, what is the value of ☆ - 23 ☆?
A. 92
B. -92
C. 529
D. -529
Answer:
okay... Thanks have a great day!
The points (- 1, – 2), (1, 0), (- 1, 2), (- 3, 0) forms a quadrilateral of type:
Answer:
A square.
Step-by-step explanation:
(1/16)^(x+3) = (1/4)^(x+1)
Answer:
x=-5
Step-by-step explanation:
The answer is x = -5. The explanation and answer is in the image below.
Find the ratio in which the line joining the points (2, 4, 16) and (3, 5, -4) is divided by the plane 2x – 3y+ z+ 6 = 0. Also find the co-ordinates of the point of division
Answer:
Step-by-step explanation:
let the plane intersects the join of points in the ratio k:1
let (x,y,z) be the point of intersection.
[tex]x=\frac{3k+2}{k+1} \\y=\frac{5k+4}{k+1} \\z=\frac{-4k+16}{k+1} \\\because ~(x,y,z)~lies~on~the~plane.\\2(\frac{3k+2}{k+1} )-3(\frac{5k+4}{k+1} )+\frac{-4k+16}{k+1} +6=0\\multiply~by~k+1\\2(3k+2)-3(5k+4)+(-4k+16)+6(k+1)=0\\6k+4-15k-12-4k+16+6k+6=0\\-7k+14=0\\k=2\\x=\frac{3*2+2}{2+1} =\frac{8}{3} \\y=\frac{5*2+4}{2+1}= \frac{14}{3} \\z=\frac{-4*2+16}{2+1} =\frac{8}{3}[/tex]
point of intersection is (8/3,14/3,8/3)
and ratio of division is 2:1
what is the product of (-a+3)(a+4)?
[tex](-a+3)(a+4)=-a^2-a+12[/tex].
Hope this helps.
Answer:
-a²-a+12
Step-by-step explanation:
-a²+3a-4a+12
-a²-a+12
Keats Library purchases a number of new books, all in the category of biography; the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 37.5% of the new total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased
Answer:
[tex]\large \boxed{87.5 \, \%}[/tex]
Step-by-step explanation:
Let x = the original number of books
Then 0.375x = the total number of biographies
and 0.20 x = the original number of biographies
[tex]\text{Percent increase} = \dfrac{\text{ New number - Old number }}{\text{Old number }} \times 100\, \%\\\\= \dfrac{0.375x - 0.20x}{0.20x} \times 100\, \% = \dfrac{0.175x}{0.20x} \times 100\, \% = 0.875 \times 100\, \% = \mathbf{87.5 \, \%}\\\\\text{The number of biographies has increased by $\large \boxed{\mathbf{87.5 \, \%}}$}[/tex]
i need help plzzzzz
Answer:
A
Step-by-step explanation:
Given
f(x) = [tex]\frac{3+x}{x-3}[/tex]
To evaluate f(a + 2), substitute x = a + 2 into f(x)
f(a + 2) = [tex]\frac{3+a+2}{a+2-3}[/tex] = [tex]\frac{5+a}{a-1}[/tex] → A
Jaden learns to perform 2 vocal pieces during each week of lessons . How many weeks of lessons will Jaden need before he will be able to sing a total of 24 pieces?
Answer:
12 weeks
Step-by-step explanation:
To solve this, all you need to do is divided 24 pieces by the two he learns per week. You'll then find it will take him 12 weeks
Please thank you! I will give brainleist to the first correct answer if it lets me
Answer:
x=10 y=12
Step-by-step explanation:
just multiply 15 and 18 by 1/3 because both triangle are similar.
Answer:
x = 10; y = 12
Step-by-step explanation:
find the scale factor ratio using corresponding sides: 9 / 6 = 3/2 so the ratio is 3:2
from large triangle to small triangle you will get:
1. 15 / x
2. 18 / y
to implement the ratio, set the side length ratio equal to the scale factor:
1. [tex]\frac{15}{x}[/tex] = [tex]\frac{3}{2}[/tex]
2. [tex]\frac{18}{y}[/tex] = [tex]\frac{3}{2}[/tex]
cross multiply:
1. 30 = 3x
2. 36 = 3y
divide:
1. x = 10
2. y = 12
Small roads with lower speed limits are known as:
O A. interstate highways.
O B. secondary roads.
C. streets
O D. county roads.
Answer:
B. secondary roads
Step-by-step explanation:
While all of streets, county roads, and secondary roads are generally designed to carry less traffic and/or have lower speed limits than interstate highways, the generic name for such roads is ...
secondary roads.
Can someone help me solve this :): ?
( brainliest to the correct answer/explanation)
Answer:
1and1/2yrs ago
Step-by-step explanation:
price dis year= 56545
reduction per year= 11309
...number of years ago = 73810-56545=17265
and is about 20% of annual deductions
so if 56545 +20% + 1/2 20% = 1nd1/2 yrs
Romain knows the following information about the 323232 classes he took in high school: He studied for but did not pass 333 classes. He passed 272727 classes in total. He studied for 262626 classes in total. Can you help Romain organize the results into a two-way frequency table?
Answer:
Classes studied for, Classes he did not study for Total
Classes Passed, 23 4 27
Classes Failed, 3 2 5
Total, 26, 6 32
Please find attached the two way frequency table formatted on Excel spreadsheet
Step-by-step explanation:
The given information are;
The total number of classes Romain took in high school = 32
The number of classes he studied for but did not pass = 3
The total number of classes Romain passed = 27
The number of classes Romain studied for = 26
Therefore;
The number of classes Romain studied for and passed = 26 - 3 = 23
The total number of classes Romain failed = 32 - 27 = 5
The total number of classes Romain passed but did not study for = 27 - (26 - 3) = 4
The number of classes Romain did not study for and failed = 5 - 3 = 2
The total number of classes Romain did not study for = 4 + 2 = 6
WILL GIVE BRAINLEIST!!!!!
Find the surface area of the right triangular prism shown below.
Answer:
144 units²
Step-by-step explanation:
Surface area of a traingular prism is given as:
Area = 2(B.A) + P*L
Where,
B.A = base area of the triangular prism = ½*b*h
b = base of the triangular base = 4 units
h = height of the triangular base = 3 units
Base Area (B.A) = ½*4*3 = 2*3 = 6 units²
P = Perimeter of triangular face = sum of all sides the triangle = 3 + 4 + 5 = 12 units
L = length or height of prism = 11 units
Plug in all values into the formula for surface area of triangular prism = 2(B.A) + P*L
[tex] Area = 2(6) + 12*11 [/tex]
[tex] = 12 + 132 [/tex]
[tex] Surface Area = 144 [/tex]
Surface area of the triangular prism = 144 units²
what is the domain of the function represented by the graph.?
Answer:
all real numbers
Step-by-step explanation:
There is nothing on the graph to indicate the function is undefined for any values of x. The domain is all real numbers.
Answer:
Domain is all real numbers.
Step-by-step explanation:
The domain of a quadratic function in standard form is always all real numbers, meaning you can substitute any real number for x.
11. How many kilometers is it from the main gate to Manatee Springs? (Hint: To convert from
yards to kilometers, multiply by 0.0009144). Round answer to the nearest hundredth kilometer.
Manatee Springs
Elephant
House
3,500 yds
4,200 yds
Train Depot
2,000 yds
Bird Sanctuary
Main Gate
(SHOW WORK)
Answer:
6 km
Step-by-step explanation:
Let us assume the following items
the Point at Train depot = T
The Point at Main gate = M
The Point at Bird sanctuary = B
The Point at Elephant house = E
The Point at manatee Springs = S
As we can see that there are two triangles namely TMB and TSE.
Mentioned that
MTB = ∠STE
∠TMB = ∠TSE
∠TBM = ∠TES.
According to the Angle-angle-angle (AAA similarity)
So, the triangles TMB and TSE are the same.
[tex]\frac{TM}{TS} = \frac{TB}{TE} \\\\ \frac{TM}{4,200} = \frac{2,000}{3,500}[/tex]
So, the TM is 2400 yds
Now the Distance between Main gate M and manatee Spring S is
MS = MT + TS
= 2,400 + 4200
= 6600 yds
Now the MS is
= 6600 × 0.0009144 km
= 6.035 km
≅ 6 km
Which statements are true regarding undefinable terms in geometry?
C. A line has one dimension, length.
E. A plane consists of an infinite set of lines.
(a) use the pythagorean theorem to determine the length of the unknown side of the triangle, (b) determine the perimeter of the triangle, and (c) determine the area of the triangle. the figure is not drawn to scale.
a. the length of the unknown side is ___
b. the perimeter of the triangle is ___
c. the area of the triangle is ___
Answer:
(A) 40 km
(B) 90 km
(C) 180 km²
Step-by-step explanation:
To find the missing side of this triangle, let's use the Pythagorean theorem.
[tex]a^2+b^2=c^2[/tex], assuming that a and b are legs, and c is the hypotenuse.
Assuming the 9km side is a, we need to find the value of b, so we can substitute into the equation.
[tex]9^2+b^2=41^2\\81+b^2=1681\\b^2=1681-81\\b^2=1600\\\\b = \sqrt{1600} \\b=40[/tex]
So, the length of the missing side is 40. Now that we know this piece of information, we can find the perimeter and area of the triangle.
The perimeter is all the sides added together, so [tex]41+9+40 = 90[/tex] km is the perimeter.
The area are the two legs multiplied divided by 2.
So,
[tex]\frac{9\cdot40}{2} \\\\\frac{360}{2}\\\\180[/tex]
So the area of this triangle is 180 cm²
I hope this helped!
A a supermarket sells the three bands of rice shown.
Answer:
the ansewr is b
Step-by-step explanation: