Step-by-step explanation:
the area of a triangle is
base × height / 2
in our case
base × height / 2 = 196 mm²
base × height = 392
base = height / 2
so, using that in our main equation :
(height / 2) × height = 392
height² = 784
height = sqrt(784) = 28 mm
base = height / 2 = 28/2 = 14 mm
Solve-ns16 Which of the following must be true about the inequality and the resulting graph? Select three
options.
ns<-24
n>-24
The circle is open.
The circle is closed.
The arrow points right.
By using the concept of inequality, the correct options are
2nd, 4th and 5th option
What is linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by [tex]> , < . \geq, \leq[/tex]
A one degree inequation is known as linear inequation.
Here,
The given inequation is
[tex]\frac{-2}{3}n \leq 16[/tex]
Now,
[tex]\frac{-2}{3}n \leq 16\\n \geq -16 \times \frac{3}{2}\\n \geq -24\\[/tex]
Since n is greater than or equal to 24, the arrow will point towards right
The circle will be closed as there is an equality
So the correct options are 2nd, 4th and 5th option
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Complete Question
The complete question has been attached here
Which of the following is the correct factorization 64x^3+8?
The correct factorization of the expression, [tex]64x^{3} +8[/tex], is 4[tex](2x-1)^{2}[/tex] (8x+2).
According to the question,
We have the following information:
[tex]64x^{3} +8[/tex]
The factors of this expression can be found using identity because 64[tex]x^{3}[/tex] is the whole cube of 4x and 8 is the cube of 2.
So, we have the following expression:
[tex](4x)^{3} + 2^{3}[/tex]
Now, we can use the following identity to factor the given expression:
[tex]a^{3} +b^{3} = (a+b) (a^{2} -ab+b^{2} )[/tex]
We have a = 8x and b = 2:
(8x+2) {[tex](4x)^{2}[/tex]-16x+[tex]2^{2}[/tex]}
(8x+2) (16[tex]x^{2}[/tex]-16x+4)
Taking 4 as the common factor from the second bracket:
4(8x+2) (4[tex]x^{2}[/tex]-4x+1)
Now, finding the factors of second bracket:
4(8x+2) ([tex]4x^{2}[/tex]-2x-2x+1)
4(8x+2) {2x(2x-1)-1(2x-1)}
4(8x+2) (2x-1) (2x-1)
4[tex](2x-1)^{2}[/tex] (8x+2)
Hence, the correct factorization of the expression, [tex]64x^{3} +8[/tex], is 4[tex](2x-1)^{2}[/tex] (8x+2).
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Alyson bought six packs of crayons for $19.50. What is the cost of a pack of crayons, in dollars, if all the packs cost the same? anyone got the answer 7th grade btw
Answer:
Answer would be $3.25
Step-by-step explanation:
First you would have to divide 19.5 by 6 to get 3.25 then check your answer by multiplying 3.25 by 6 which would be 19.50 .
5 red beads,3 blue,4 green probability of a blue bead
Answer:
3/12 or 40%
not 10000% sure on this tho
5. Given the following measurements in
parallelogram ABCD, find the PERIMETER of
CED.
AC 34 in. AB = 26 in. BD = 28 in.
P=
The Perimeter of triangle CED is 57 in.
What is a parallelogram?
A parallelogram is the name given to a quadrilateral in geometry. In a parallelogram, the opposing sides are parallel and of equal length. The rhombus, rectangle, and square are just a few shapes that are parallelograms.
Having two sets of parallel sides makes a quadrilateral a parallelogram. A parallelogram has opposite sides that are the same length and angles that are the same size. Additionally, the internal angles on the same transverse side are supplementary. 360 degrees are equal to the total of all internal angles.
Two parallel pairs of sides make up a parallelogram, a quadrilateral. Four right angles form a parallelogram called a rectangle.
Rhombus: An equal-length parallelogram with four sides.
The diagonals of a parallelogram bisect each other AC = 2 CE
Substitute AC= 34 into AC = 2CE =34 = 2CE
Calculate 34 = 2 CE=> CE = 17
The diagonals of a parallelogram bisect each other BD = 2DE
Substitute BD= 28 into BD = 2DE => 28 = 2DE
Calculate 28 = 2DE => DE = 14
Opposite sides of parallelogram are congruent AB = CD
Substitute AB = 26 into AB = CD => CD = 26
Perimeter of a triangle PΔCDE = CE + CD + DE
Substitute CE = 17, DE = 14, CD = 26.
PΔCDE = CE + CD + DE
PΔCDE = 17+ 26 + 14
PΔCDE = 57 in
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2a × ( 3 + b ) = 6a + 2ab is an example of the property
Answer:
It's an example of the distributive property
Solve the inequality4x + 13 ≥ 27
Work Shown:
4x + 13 ≥ 27
4x + 13-13 ≥ 27-13
4x ≥ 14
4x/4 ≥ 14/4
x ≥ 7/2
The inequality sign stays the same for each step. The inequality sign only flips if we were to multiply both sides by a negative number (or divide both sides by a negative number).
Note: 7/2 = 3.5
How would I solve this?
Answer:
y=2x-22
Step-by-step explanation:
lets make the equation into slope intercept form
-2x+y=-8 let's move the -2x to the other side we get
y=2x-8
now let's create our equation with the points given
to create the equation you want to make it point slope form with the point given
y-0=2(x-11) distribute the 2 and we can remove the 0
y=2x-22
Evaluate the power.
0.5² =
(Type a whole number or a decimal.)
What is 43+5673+20(1)
Answer:
5736
Step-by-step explanation:
calculator
Answer: 5736
Step-by-step explanation:
Can somebody please help me find a answer key for these
Answer:
Step-by-step explanation:
Lacey inherited some money from her grandfather and put it in a bank account that earns 4%
interest compounded monthly. After 2 years, Lacey had $700.00 in the bank account. How
much interest did she earn?
Round your answer to the nearest cent.
The interest eared from the given amount, rate of interest and time period is $426.883.
Given that, amount = $700, rate of interest = 4% and time period = 2 years.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest is [tex]Amount=Principal(1+\frac{r}{100})^{nt}[/tex]
Let the money deposited be x.
So, [tex]700=x(1+\frac{4}{100} )^{2\times12}[/tex]
⇒ [tex]700=x(1+0.04)^{24}[/tex]
⇒ [tex]700=x(1.04)^{24}[/tex]
⇒ 700 = 2.563x
⇒ x=700/2.563
⇒ x=$273.117
So, interest = 700-273.117
= $426.883
Therefore, the interest eared from the given amount, rate of interest and time period is $426.883.
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determine the midpoint of the line segment connecting (6,-5) and (-1,-6)
The midpoint of the line joining (6,-5) and (-1,-6) is (-5/2,-11/2).
How to determine the midpoint of the line joining two points (a,b) and (p,q)?
To get the midpoint of the line joining two points (a,b) and (p,q), we first have to add the x coordinates of two points and divide it by 2. So the midpoint's x coordinate will be (a+p)/2 . Similarly, we have to do the same with y. Then the midpoint of the line joining two points (a,b) and (p,q) will be [(a+p)/2,(b+q)/2}.
To get the midpoint of (6,-5) and (-1,-6) , first, we have to add the x coordinates and divide it by 2 . And have to do the same with y.
so, the midpoint will be [(6+(-5)]/2,[-5+(-6)]/2.
Hence ans will be ,(-5/2,-11/2)
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The graph of the absolute value parent function, f(x) = |x), is stretched
horizontally by a factor of 3 to create the graph of g(x). What function is g(x)?
OA. g(x)= x+3|
OB. g(x) = 31x1
C. g(x) = 13x1
OD. g(x)= |||
Option A is the correct answer g(x) = |x+3| by using the relation with the parent function.
Explain absolute value function.
A function that wraps an algebraic expression in absolute value symbols is known as an absolute value function. Remember that a number's distance from 0 on the number line represents its absolute value.
The definition of the absolute value parent function, f(x)=| x |, is as follows:
f(x) = [tex]\left \{ {{x ~, ~ x > 0} \atop {0 ~ , ~x = 0}} \atop {-x ~, ~x < 0} \right.[/tex]
Given parent function is f(x) = |x|
g(x) is obtained by stretching the graph of f(x) by a factor of 3.
Use the function g(x)=f(x−h) to translate the absolute value function f(x)=| x | horizontally.
The graph of f(x) is moved h units to the right to obtain g(x) for h>0
The graph of f(x) is translated h units to the left to obtain g(x) when h>0
Therefore, g(x) = |x+3|
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12u–9u–5u+13= -5
find u
I WILL GIVE BRAINLIEST!
Shamar belongs to a movie club that deducts $14 every month from his bank account. What is the change in Shamar's bank account after 7 months of paying for the movie club?
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The change in Shamar's bank account after 7 months is
x - 98.
Where x is the amount in the account initially.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Amount in the account = x
Amount deducted every month = $14
The change in the account after 7 months.
= x - 7 x 14
= x - 98
Thus,
The change in Shamar's bank account after 7 months is
x - 98.
Where x is the amount in the account initially.
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Two people are jogging around a circular track in the same direction one person can go to completely around the track in 21 minutes the second person takes 18th if they both start running in the same direction at the same time how long will it take them to be together at this place if they continue to run
Answer:
n * 21 = m * 18 one runs n laps and one runs m laps to again be together at the same place
7 n = 6 m divide by 3
one runs 7 * 18 = 126 min
the other runs 6 * 21 = 126 min
After 126 min they will be together at the start
How do I solve this ?
See attachment, this took me a while so please say thanks and rate <3
Kobe is 2.07 metres tall.
Marcus is 1.79 metres tall.
Stephen is taller than Marcus by half the difference between Kobe's height and
Marcus's height.
How tall, in metres, is Stephen?
Optional working
BD = 5, CX = 3, CD = 5
what does BC equal
Answer:
BC = 6
Step-by-step explanation:
since BD = CD then Δ BCD is isosceles.
the line a through D is a perpendicular bisector of BC, then
BX = CX = 3 , so
BC = BX + CX = 3 + 3 = 6
a bakery worker uses 175 cups of sugar to make 100 cinnamon rolls. at this rate, how many cups of sugar would be needed to make 1 cinnamon roll?
Aisha runs a tutoring business. With Plan 1, students may choose to pay $15 per hour. With Plan 2, they may follow the plan shown on the graph.
The student pay initial fess of $20 and addition $10 per hour.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx
where, m is the slope
Given:
Plan 1:
students pay = $15 per hour.
Plan 2:
From the graph we can see that
slope= Rise/ Run = 10/ 1= 10
and, the graph line starts from 20.
Hence, the student pay initial fess of $20 and addition $10 per hour.
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A ball is kicked with an initial velocity of 15 m/s in the horizontal direction and 18 m/s in the vertical direction. (Assume the ball is kicked from the ground.)
At what speed (in m/s) does the ball hit the ground?
For how long (in s) does the ball remain in the air?
What maximum height (in m) is attained by the ball?
A) The speed (in m/s) at which the ball hits the ground is; 23.43 m/s
B) The time (in s) that it takes the ball to remain in the air is; 3.67 s
C) The maximum height attained by the ball is; 16.51 m
How to solve projectile problems?
A) The motion of the ball on the vertical axis is basically uniformly accelerated motion, with acceleration g = 9.81 m/s² and initial vertical velocity v_y = 18 m/s, so the vertical position of the ball at time t is:
y(t) = v_y*t - ¹/₂gt²
The formula for time when the ball hits the ground is;
t = 2v_y/g
t = (2 * 18)/9.81
t = 3.67 s
Thus, vertical velocity at time t is given by the formula;
v_y(t) = v_y - gt
v_y(t) = 18 - (9.81 * 3.67)
v_y(t) = -18 m/s (which shows it is in the opposite direction because of the negative sign)
Thus, the speed at which the ball hits the ground is the resultant of the vertical and horizontal velocity at time t;
v = √(v_x² + v_yt²)
v = √(15² + 18²)
v = 23.43 m/s
b) From a above, the time that the ball remains in the air is the time it takes to hit the ground which is t = 3.67 s
c) The time to reach maximum height is half the time it takes to reach the ground. Thus;
t = 3.67/2 = 1.835 s
Thus maximum height is given by the formula;
y(t) = v_y*t - ¹/₂gt²
y(1.835) = 18(1.835) - ¹/₂(9.81)(1.835²)
y = 16.51 m
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Describe the slope of the line
Find the slope
m=??
Answer: 2.333333...
Step-by-step explanation:
If we apply rise over run, we see that it rises 3.5 spaces, and runs 1.5, which means that [tex]m = \frac{rise}{run} = \frac{3.5}{1.5} = 2.33333...[/tex]
Match each number on the left with the correct description of the number on the right.
Answer:a, c and d
Step-by-step explanation:bc i got it right on edge
A harbor seal dives 35 meters below the ocean's surface. Then it dives down an additional 12 meters Determine the seal's new position relative to the surface of the ocean
The seal's new position relative to the surface of the ocean is 47 meters below.
How to calculate the value?It is important to note that that question has to do with elevation which is the change in position with regards to the sea or ocean level.
In this case, the harbour seal dives 35 metres below the ocean's surface and then it dives down an additional 12 metres
The new position will be;
= -35 - 12
= -47
This implies that it's 47 meters below the ocean surface.
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Pedro walks 3/8 of a mile in a 1/4 of an hour. How many miles does he walk in an hour
Answer:
S=3/8 miles
T=1/4 hour
V=S/T = 3/8 ÷ 1/4 = (3×4)÷8 = 3/2 miles in an hour
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A dime is 1.35 x 10-3 meter thick. What would be the height, in
meters, of a stack of 1 million dimes?
A1.35 x 10^2meters
B 1.35 x 10^3meters
1.35 x 10^4 meters
1.35 x 10^9meters
Go Online You can complete an Extra Example online.
Show
your work
here
Answer:
Step-by-step explanation:
Square plank of 48 inches triangular base length of 12 inches height of 6 inches how much paper to cover
Applying the area of square and triangle, the amount of paper needed is: 180 inches².
What is the Area of a Square Shape and Area of a Triangular Shape?The area of a square shape = (side length of the shape)².
The area of a triangular shape = 1/2(base)(height)
The diagram that illustrates the problem given is shown in the image attached below, where the triangular paper to cover the triangular plank and the square paper for the square plank are shown also with their dimensions.
Therefore, the amount of paper that would cover the piece of art = area of the square shape + area of the triangular shape.
Area of the square shape = 12² = 144 inches²
Area of the square shape = 144 inches²
Area of the triangular shape = 1/2(12)(6)
Area of the triangular shape = 36 inches²
Amount of paper needed = 36 + 144
Amount of paper needed = 180 inches²
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Complete Question:
Theresa created a piece of art by attaching a square plank to a triangular plank. The square plank has a perimeter of 48 inches. The triangular plank has a base length of 12 inches and a height of 6 inches. She wants to cover the piece of art with colored paper.
How many square inches of paper are needed to cover Theresa's art piece?
Graph the function rule. Tell whether the graph is continuous or discrete. The height h, in inches, of the juice in a 20-oz bottle depends on the amount of juice j, in ounces, that you drink. This situation is represented by the function rule h=8−0.4j.
Upon graphing of the function rule h = 8 - 0.4j, we see that the graph is continuous.
We are given the function as; h = 8 - 0.4j
Let h represent the height in inches on the y-axis and let j represent the amount of juice in ounces on the x-axis.
We are told that the height of the juice in a 20-oz bottle depends on the amount of juice. This means that j is an independent variable and h is dependent variable.
The function represents the height of juice after drinking j ounces of juice. Therefore as the juice is being drank, the height of the juice in bottle will change continuously. Therefore, the graph of our given function will be continuous because we can drink fractions of an ounce juice.
The equation of a line in slope-intercept form is given as;
y = mx + b
where;
m is Slope of line
b is y-intercept
If we rewrite our function slope-intercept form of equation, we will get;
h = -0.4j + 8
Thus;
Slope = -0.3
y-intercept = 8.
The graph is as plotted in the attached file
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