Answer:
y = - [tex]\frac{5}{6}[/tex] x + 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - [tex]\frac{5}{6}[/tex] , then
y = - [tex]\frac{5}{6}[/tex] x + c ← is the partial equation
to find c substitute (6, 1 ) into the partial equation
1 = - 5 + c ⇒ c = 1 + 5 = 6
y = - [tex]\frac{5}{6}[/tex] x + 6 ← equation of line
ABC has vertices at a(11,6), B(5,6), and (5,17).
The correct statements regarding the congruent triangles are given as follows:
Triangle ABC and triangle MNO are congruent by a sequence of rotations and translations.Triangle JKL and triangle ABC are congruent by a single rotation.What are congruent triangles?Congruent triangles are triangles in which the outer side lengths have the same measure.
Then the triangles ABC and triangle MNO are congruent by a sequence of rotations and translations, as both are right triangles.
Triangle JKL and triangle ABC are congruent by a single rotation, as the distances between the vertices of each triangle are equal.
Missing InformationThe problem is given by the image shown at the end of the answer.
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On a scale drawing of a horse, the scale is 1 in: 10 ft. If the real horse is 25 ft tall, how tall is the horse on the scale drawing?
Answer: 2.5 inch
Step-by-step explanation:
Given the system below,
9x+3y=-18
y=x+7
What is the ordered pair for the intersection
)?
Answer:
(-3.25,3.75)
Step-by-step explanation:
Thuis can be answered with either of two approaches: Graphing and Matematical. We'll do both:
Graphing
Graph both equations. It is helpful to use a free online graphing utility: DESMOS.
The attached graph reveals the intersection of the lines at point (-3.25, 3.75).
Matematical
Solve the equations be using substitution. Rearrange either equation to isolate one of the two variables (x or y).
Lets use the second, since y is already isolated, making the task simple and fast. But the other equation could also be used, if desired.
y=x+7
Now use this expression of y in the other equation:
9x+3y=-18
9x+3(x+7)=-18
9x +3x +21 = -18
12x = -39
x = -(39/12)
x = -3 - (3/12)
x = -3.25
Now use x= -3.25 in either equation tand solve for y:
y=x+7
y=(-3.25)+7
y = 3.75
The solution to this series of equations is (-3.25,3.75)
A bank features a savings account that has an annual percentage rate of r=3.5% with interest compounded quarterly. Althea deposits $3,500 into the account.
What values should be used P, r, and n?
How much money will Althea have in the account in 8 years? Round to the nearest penny.
Althea will have a $4625.32 compound amount in the account in 8 years.
What is compound interest?
The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. Compound interest is computed as interest on the initial principal plus any accrued interest from prior periods.
Given,
Principal (P) = $3,500
rate of interest (r) =3.5% = 0.035
for compounded quarterly (n) = 4
time (t) = 8 years
The compound amount is given by
[tex]A = P(1+\frac{r}{n})^{nt}\\A = 3500(1+\frac{0.035}{4})^{4*8}[/tex]
A = 4625.32
Hence, Althea will have $4625.32 in the account in 8 years.
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What is the perimeter of triangle mno
Answer:
[tex]\huge{\boxed{82.8\text{ units}}}[/tex]
Step-by-step explanation:
Because the triangles have all of the same angles, similarity can be proven via AAA.
Now that ΔJKL ~ ΔMNO, the sides must be proportional.
Because the sides are proportional, the following equation can be made:
[tex]\frac{24}{20}=\frac{x}{22}[/tex]
Via cross-multiplication, the equation simplifies to:
20x = 24 * 22
20x = 528
x = 26.4
Now, because perimeter is simple the sum of all sides, the perimeter of ΔMNO is simply 32.4 + 24 + 26.4, or 82.8.
Hope it helps :) and let me know if you want me to elaborate.
If g(x)=x^2+6 and f(x)=2x-4, find g(f(x))
The value of the function g(f(x)) is 2x² - 8x + 11.
What is function?
In the composition of functions, we completely swap out one function for another. The function f with g has the notation (fg)(x)=f(g(x)) and is read as f of g of x. It signifies that the function g(x) is substituted for every instance of an x in the function f.The combination of two functions is frequently referred to as a "function of a function," and g*f is sometimes represented as g.f.g(x) = x² + 6
f(x) = 2x - 4
g(f(x)) = (2x-4)² + 6
= 4x² - 16x + 16 + 6
= 4x² - 16x + 22
= 2x² - 8x + 11
Hence, the value of the function g(f(x)) is 2x² - 8x + 11.
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help: find the measure of each angle indicated
Answer: 27
Step-by-step explanation:
You know that the whole shape equals 180. So you add 133+20=153 then subtract that from 180 and that should give you 27.
Hope that helps!
Hello, can someone help me out with these two questions please!?!?!?
Answer: No solution
Step-by-step explanation:
3(2x + 3) - 3x = 9 + 3x
6x + 3 - 3x = 9 + 3x - 3x
6x + 3 - 6x = 9
3 = 9
No solution
fraction find the missing number 1/2 of 30= 1/4=
The missing number in the equation 1/2 of 30 = 1/4 is 60
How to determine the missing number?From the question, we have the following parameters that can be used in our computation:
1/2 of 30 = 1/4
This equation can be properly expressed as
1/2 of 30 = 1/4 of __
Represent the blank with a variable x
So, we have the following representation
1/2 of 30 = 1/4 of x
Express as products
1/2 * 30 = 1/4 * x
Multiply both sides by 4
This gives
x = 4 * 1/2 * 30
Evaluate
x = 60
Hence, the missing number is 60
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is x^4+2x^3-x^2+7x+11 a quintic binomial
On solving the provide question, we got that - [tex]x^4+2x^3-x^2+7x+11[/tex] is not a quintic binomial
What is quintic polynomial?A mathematical word raised to the fifth power of the independent variable. B. Or 5th order polynomial in the form of 5th order or 5th order for 5th order (not equivalent).
What is an example of a quintic polynomial?A polynomial of degree 5. Examples: x5 – x3 + x, y5 + y4 + y3 + y2 + y + 1, and 42a3b2.
[tex]x^4+2x^3-x^2+7x+11[/tex] is not a quintic binomial
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Convince me that...
the √(25) is 5.
Step-by-step explanation:
The square root of 25 is 5. It is the positive solution of the equation x2 = 25. The number 25 is a perfect square.
Answer:
Yeah, √(25) is 5.
Step-by-step explanation:
Given problem,
→ √(25) = 5
Checking the equation,
→ √(25) = 5
→ 25 = (5)²
→ 25 = 25
→ LHS = RHS
Thus, equation is proved.
Unit 3 Lesson 8 Cumulative Practice Problems
1. This is an invalid proof that all isosceles triangles are similar. Explain which step is
invalid and why.
1. Draw 2 isosceles triangles ABC and DEF where AC = BC and DF = EF.
2. Dilate triangle ABC to a new triangle A'B'C using center C and scale factor de so
that A'C = B'C = DF = EF.
3. Translate by directed line segment CF to take A'B'C to a new triangle A"B" F.
Since translation preserves distance, A" F = A'C= DF and B" F = BC = EF.
4. Since A" F = DF, we can rotate using center F to take A" to D.
5. Since B" F = EF, we can rotate using center F to take B" to E.
6. We have now established a sequence of dilations, translations, and rotations that
takes A to D, B to E, and C to F, so the triangles are similar.
Answer:
Step-by-step explanation:
Let ABC be an isosceles triangle with lateral sides AB and AC, a base of BC, and medians of AC and AB, respectively, at BD and CE.
In △ACE and △ABD ,
AB≅AC lateral sides of isosceles triangle
∠A≅∠A common angle
AE≅AD half segments of equal lateral sides
As a result, ACE ≅ABD according to the side angle side theorem. as a result, median BD is consistent with median CE.
If any two figures can be positioned exactly over one another, the congruence between them can be seen. The relationship between two figures is referred to as their congruence, and is expressed using the word "congruence".
In other terms, two geometric figures are said to be congruent if they can be superimposed on one another.
All figures, including triangles, quadrilaterals, and other shapes, have this feature. Along with figures, line segments and angles that have the same measure are also said to be congruent. To comprehend what congruent figures represent, look at the following figure.
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Will mark as brainiest. Please help more points!
The total area of the two shaded faces of the cuboid below is = 112[tex]cm^{2}[/tex]
Since the two shaded faces of the cuboid shown are adjutant to each other and are of the same dimensions so according to the calculations -
Let us consider only one side of the shaded portion-
The length of the shaded part = 8cm
The width of the shaded portion = 7cm
So it appears that due to the uneven measure of length and breath this is a rectangle, so the area of a rectangle
= [ length (l) x width(w) ]
= 8cm x 7cm
= 56[tex]cm^{2}[/tex]
Since the question asks the total area of both sides so because both the shaded sides are equal then total area = 56 x 2 = 112 [tex]cm^{2}[/tex]
Therefore, the total area of the shaded faces of the cuboid = 112[tex]cm^{2}[/tex]
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Calcula el número si 30 menos el triple del número es cuatro veces la diferencia del triple del número más 10
Answer:Calcula el número si 30 menos el triple del número es cuatro veces la diferencia del triple del número más 10
Step-by-step explanation:
the number of cells in a specimen of bacteria doubles every hour. what type of function best represents the growth of the bacteria?
An example of an exponential function is the growth of bacteria. the growth of the bacteria is by exponential growth in the number of cells in a specimen of bacteria doubles every hour.
Some bacteria double her size every hour. Starting with 1 bacterium, every hour he doubles, after x hours he doubles as bacterium. This can be written as f(x) = 2x.
Bacteria replicate by binary fission, the process by which one bacterium divides into two. Bacteria therefore multiply in number by a geometric progression, doubling the population with each generation. The binary fission is the actual multiplication procedure of the cells division where cells grows fastly and further divided itself into other groups or colony.
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Determine whether the following statement is true or false. In a normal distribution, the z-score for the mean is 0. Choose the correct answer below. * OA. The statement is true because a z-score describes how many standard deviations a data item in a normal distribution lies above or below the mean. B. The statement is false. The z-score for the standard deviation is 0. OC. The statement is false. The z-score for the mean is always 1. D. The statement is false. The z-score for the mean depends on the data item.
The statement "In a normal distribution, the z-score for the mean is 0" is true. A z-score describes how many standard deviations a data item in a normal distribution lies above or below the mean. Since the mean of a normal distribution is defined as the value at which the distribution is centered, a data item with a value equal to the mean will have a z-score of 0.
Therefore, the correct answer is option A: "The statement is true because a z-score describes how many standard deviations a data item in a normal distribution lies above or below the mean." Option B, C, and D are all false because they do not accurately describe the relationship between z-scores and the mean in a normal distribution.
Find the correct answer & explaining why
The line segment will be needed to create step 4 is 30. Hence option D is the correct option.
What is line segment?
Line segment is line whose distance fixed. There are two fixed end points. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.
The number of line segment in step 1 is 2.
The number of line segment in step 2 is 6.
The number of line segment in step 3 is 14.
Now finding the pattern:
Step 2: 6 = 2 × 2 + 2
Step 3: 14 = 6 × 2 + 2
The number of line segment is equal to 2 more than 2 times the number of line segment of previous step.
According to this pattern,
step 4: 14 × 2 + 2 = 30
The number of line segment is 30.
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a study was made of seat belt use among children who were involved in car crashes that caused them to be hospitalized. it was found that children not wearing any restraints had hospital stays with a mean of 7.37 days and a standard deviation of 2.75 days with an approximately normal distribution. (a) find the probability that their hospital stay is from 5 to 6 days, rounded to five decimal places.
Therefore, the probability that their hospital stay is from 5 to 6 days is 0.03310 .
What exactly is probability?Probability deals with calculating or making estimates of how probable or "possible" an event is to occur. To convey the probability of an event occurring, words like "certainly," "impossible," or "likely" might be employed. Probabilities are always represented in mathematics as fractional, decimals, or percentages, with values that range from 0 to 1.
Here,
Given:
Mean, μ =7.37 days
Standard Deviation, σ = 2.75 days
Given: hospital stays are distributed in a bell-shaped manner, which is a typical distribution.
Formula:
Z = [tex]\frac{x-u}{\alpha }[/tex]
a) P( 5 to 6 days are spent in the hospital.)
P(5≤x≤6)
=>P([tex]\frac{5-7.37}{2.75}[/tex] ≤x≤ [tex]\frac{6-7.37}{2.75}[/tex])
=>P(-0.861≤x≤-0.498)
=>P(Z≤-0.498) - P(Z<-0.861)
=>0.034 - 0.001 = 0.03310
=> P(5≤x≤6) =3.3%
Therefore the probability that their hospital stay is from 5 to 6 days is 3.3%.
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A cyclist rides her bike at a speed of 18 miles per hour. What is this speed in kilometers per hour? How many kilometers will the cyclist travel in 5 hours? In your
computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
Speed: Distance traveled in 5 hours:
The speed in kilometres per hour is 28.8 km/hr.
The distance in kilometres the cyclist will travel in 5 hours is 144 km.
How to find speed and distance?A cyclist rides her bike at a speed of 18 miles per hour. The speed in kilometres per hour an be calculated as follows;
1 miles = 1.6 km
18 miles = ?
cross multiply
distance in km = 18 × 1.6
distance in km = 28.8 km
Therefore, the speed in kilometres per hour is 28.8.
The kilometres the cyclist will travel in 5 hours can be calculated as follows;
speed = distance / time
28.8 = d / 5
cross multiply
distance travelled in km = 28.8 × 5
Therefore,
distance travelled in km = 144 km
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Consider the system of equations
5x+3y=30
−5x−2y=−25
Part A: Solve the system. Show your work.
Part B: Use the solution to your equation to find the value of x – y. Show your work.
x−y =
A translation stretches or compresses the graph of a function.
True false question.
True
False
Answer:
False, a transformation is the one that stretches or compresses the graph. A translation just shifts the graph up, down, left, or right.
Answer: False
Step-by-step explanation:
A translation is just moving the graph up, down, left, and right! It doesn't make a graph bigger or smaller, so this is a False
Clayton place towel I pell the word time and a bowl. He draw one tile from the ball and then without replacing it draw another child. What i the ample pace of doe it repreent in the letter picked him to
On solving the question, The possible combinations when choosing two letters randomly are: T-I, T-M, T-E, I-T, I-M, I-E, E-T, E-M, E-I, M-I, M-T, M-E.
What is combination ?When the order of selection is irrelevant, the mathematical operation of combining counts the number of possible configurations for a set of elements.
[tex]Letters are given as - T I M E[/tex]
Given that there is no alternative for the choice, we have the following number of possibilities:
[tex]= > n = 4^2\\[/tex]
here -
4 =the number of letters
2 =the number of selection
so, n= 16
The choices are then shown as follows:
TI, TM, TE
IT, IM, IE
MT, MI, ME
ET, EI, ET
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The cubic polynomial | f(x) = 6x ^ 3 - 7x ^ 2 - 11x + d has a 2 factor (x-1)
(a)Find the value of d
( b )Find the remainder when the polynomial is divided by (x + 2)
Answer:
d=12 and the remainder is -42
Step-by-step explanation:
a.
put x=1 into f(x)
6(1)³-7(1)²-11(1)+d=0
6-7-11+d=0
-12+d=0
d=12
b.
Put x=-2 into the polynomial
6(-2)³-7(-2)²-11(-2)+12
6(-8)-7(4)+22+12
-48-28+22+12
-42
Simplify [tex]\sqrt[3]{125z}[/tex] - [tex]\sqrt[3]{64z}[/tex]
Answer:
[tex] \sqrt[3]{z} [/tex]
Step-by-step explanation:
[tex] \sqrt[3]{125z} = \sqrt[3]{ {5}^{3} z} = 5 \sqrt[3]{z} [/tex][tex] \sqrt[3]{64z} = \sqrt[3]{ {4}^{3}z } = 4 \sqrt[3]{z} [/tex][tex]5 \sqrt[3]{z} - 4 \sqrt[3]{z} = \sqrt[3]{z} [/tex] Select the statement that correctly describes the
solution to this system of equations,
18x-2y=-4
4x-y=-2
There is exactly one solution at (2.0),
There is no solution,
There is exactly one solution at (0-2).
There are infinitely many solutions.
HELP ASAP
The solution of the equations 18x - 2y = -4 and 4x - y = -2 is (0,-2). Hence option c is the correct option.
What is an equation?
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Given pair of equations is
18x - 2y = -4 ....(i)
4x - y = -2 .....(ii)
To solve the equation apply elimination method.
Multiply equation (ii) by 2 and subtract it from (i):
18x - 2y = -4
8x - 2y = -4
(-) (+) (+)
_________
10x = 0
x = 0
Putting x = 0 equation (ii)
0 - y = -2
y = 2
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Pleaseee help! I don’t really get math
Answer:
GE is congruent to GE
Step-by-step explanation:
This is true because both triangles use this same line, so it is referred to as the reflexive property.
2. Multiply the polynomials (4a³-5a - 3) and (2a² - 7a+ 3). Simplify the answer. Show your work.
Can the answer be given by hand please
Answer:
Step-by-step explanation:
(25 points)
Which inequality is represented by this number line?
Answer:
C
Step-by-step explanation:
Pick point 7 and sub into the equations
eq 1 not equal to 10
eq 2 not equal to 12
eq 3 is equal to 15
eq 4 not equal to 18
Now sub in the value of -3 into equation 3 Yes equal to 15
so answer is eq 3
numbers greater than 7 and less than -3 are also true ....
A 140 ft diameter helicopter pad covers an area of about how many square feet? What value did you use for pi and why did you choose it?
15,386 ft² an area of helicopter pad covers .
What does a circle's area mean?
The area a circle occupies in a two-dimensional plane is known as the area of the circle. It can be simply calculated using the formula A = r2, (Pi r-squared), where r is the circle's radius.
Area is measured in square units, such as m2, cm2, etc. Where = 22/7 or 3.14, the area of a circle is equal to r2 or d2/4, in square units.
D = 140
r = 140/2 = 70
area of helicopter = πr²
= 3.14 ×70 × 70
= 15,386 ft²
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Classify the given angle.
right angle
obtuse angle
acute angle
straight angle
Answer: Acute Angle
Step-by-step explanation: It is less than 90 degrees (right angle) so it is an acute angle
Answer:
Step-by-step explanation:
Acute Angle 100% Correct!!