When Akbar is 9 years older than Yasir and Hamid is 2 years younger than Yasir then, the expression for their sum of ages is 3x+7
What are linear equations?A linear equation is a mathematical equation that describes a straight line. It is a first-degree polynomial equation, which means that the largest exponent of the variables is 1. Since a and b are constants and x and y are variables, linear equations have the general form ax+by=c. A straight line forms on a coordinate plane when the values of x and y fulfil the expression. The connection between two variables or the price of a product are two examples of real-world events that are frequently modelled using linear equations. Solving a linear equation entails determining the values of the variables that make the equation true. Different techniques, such graphing, substitution, or elimination, can be used to accomplish this.
How to solve?
Let x be Yasir's age
Akbar is x+9
Hamid is x-2
The sum of their ages is x+(x+9)+(x-2)
=3x+7
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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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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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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
Tarzan loaded 4 trucks every 8 hours At this rate, how may would he load in 4 hours?
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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The enrollment at a local business school has been increasing linearly. In 2001, there were 940 students enrolled. By 2009, there were only 1324 students enrolled. Determine the average rate of change of the enrollment during this time period.
The average rate of change= ?
The average rate of change of the enrollment during this time period is increasing with 48 students/year.
What is rate of change?
The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function. A method that determines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.In 2001, there were 940 students.
In 2009, there were 1324 students.
Represent year with y and students with x.
Average rate of change = (x₂ - x₁) / (y₂ - y₁)
= (1324 - 940) / (2009 - 2001)
= 384/ 8
= 48
Average rate of change = 48 students/year
Hence, the average rate of change of the enrollment during this time period is increasing with 48 students/year.
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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]Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y-3)² = 36
The standard form for finding the equation of a circle is expressed as;
[tex](x-a)^{2} + (y-b)^{2} = b = r^{2}[/tex]
where;
(a, b) is the center of the circle
r is the radius of the circle
Given the following
diameter = 12 units
radius = 12/2 = 6 units
If the centre lies on the y-axis, the center will be at (0, 3).
Substituting into the formula, we will have[tex](x-0)^{2} + (y-3)^{2} = (6)^{2}[/tex]equivalent to x²+ (y-3)² = 36
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17
Select the correct answer from each drop-down menu.
Rita is planting saplings along her garden fence. When she started, she had x packages of saplings with 5 saplings per package. She planted 15
saplings and has at most 20 left. How many packages of saplings did she start with? What would the solution look like on a number line graph?
When Rita started, she had
with an arrow to the
packages of saplings. The solution can be represented as
Reset
Next
Note that:
When Rita started, she had 7 packages;The solution can be represented on a number line graph, it will begin at 4 (the number of packages Rita still has) and progress to the right to 7, the number of packages when Rita began planting if we plot x (the number of sapling packages).What is the rationale for the above answer?Recall that we are given the following:
To determine the number of packages Rita started with, we must resolve:
(Number of saplings planted by Rita + Number of saplings left)/Number of saplings per package
that is:
x = (15 + 20)/5
x = 35/5
x = 7
Thus, when she started, she actually had 7 packages. By the time she was done, she had 4.
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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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Question 30
Write y - 4 =(x-3) in slope-intercept form.
Answer: To write the equation in slope-intercept form, we need to isolate the y term on one side of the equation. We can do this by adding 4 to both sides of the equation:
y - 4 + 4 = x - 3 + 4
Combining like terms on each side, we get:
y = x - 3
This is the slope-intercept form of the equation. The slope of the line is 1, and the y-intercept is -3. The slope-intercept form of the equation is y = 1x - 3.
Answer: y = x + 1
Step-by-step explanation:
Write y - 4 =(x-3) in slope-intercept form
This is in Point Slope Form.
y - 4 =(x-3)
We add 4 to both sides
==> y - 4 + 4 = x-3 + 4
==> y = x + 1
This is slope intercept form, since it resembles the equation, y = mx + b, but m equals zero.
what do you think the true slope is? you do not need an exact number. hint: can you provide an interval that you think the true slope falls in?
A line's equation can be written as y = mx + b, y = ax + b, or y = a + bx. As may be seen, the equation for the regression line is similar as true slope.
Explain the term true slope?Understanding the distinction between negative, positive, zero, and undefinable slopes is crucial.
In summary, the function operates "uphill" if the slope equals positive and y rises as x rises (going left to right). If a slope is negative, the function is downward-sloping because y falls off as x rises. If the slope is zero, y remains constant—a horizontal line—and does not vary. Problematic vertical lines are those in which x remains constant. Because it is divided by zero, our formula is therefore undefinable. Some people will refer to this situation as having an infinite slope, but we are unable to determine whether it is negative or positive infinity!As a result, the rather perplexing term "no slope" is also frequently used in this context.
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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!!
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:
$6,000 at 5% compounded daily for 3 years
6000 dollars at 5% compounded daily for 3 years will amount to $6,970.93.
How to solve compound interest?Compound interest is the interest you earn on interest. In other words, compound interest is the interest calculated on the principal and the interest accumulated over the previous period.
Compound interest formula can be use to find the amount of the money after 3 years.
Using the compound interest formula,
[tex]A = p(1 + \frac{r}{n} )^{nt}[/tex]
where
p =principalr = raten = number of timest = time in yearsA = amountTherefore,
p = 6000 dollars
rate = 5% = 0.05
n = 365
t = 3
Hence,
[tex]A = 6000(1+\frac{0.05}{365} )^{(365)(3)}[/tex]
A = 6,000.00(1 + 0.00013698630136986)¹⁰⁹⁵
Therefore,
A = $6,970.93
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Determine whether the following statement is true or false. In a normal distribution, the z-score for the mean is 0. Choose the correct answer below. * OA. The statement is true because a z-score describes how many standard deviations a data item in a normal distribution lies above or below the mean. B. The statement is false. The z-score for the standard deviation is 0. OC. The statement is false. The z-score for the mean is always 1. D. The statement is false. The z-score for the mean depends on the data item.
The statement "In a normal distribution, the z-score for the mean is 0" is true. A z-score describes how many standard deviations a data item in a normal distribution lies above or below the mean. Since the mean of a normal distribution is defined as the value at which the distribution is centered, a data item with a value equal to the mean will have a z-score of 0.
Therefore, the correct answer is option A: "The statement is true because a z-score describes how many standard deviations a data item in a normal distribution lies above or below the mean." Option B, C, and D are all false because they do not accurately describe the relationship between z-scores and the mean in a normal distribution.
Pleaseee help! I don’t really get math
Answer:
GE is congruent to GE
Step-by-step explanation:
This is true because both triangles use this same line, so it is referred to as the reflexive property.
pls help ill give brainliest to whoever is correct
Answer:
12.1 cm (nearest tenth)
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Sine Rule} \\\\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c} $\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]
From inspection of the given triangle:
A = 81°a = 13.5 cmc = 8.2 cmSubstitute the values into the sine rule to find the measure of angle C:
[tex]\implies \dfrac{\sin A}{a}=\dfrac{\sin C}{c}[/tex]
[tex]\implies \dfrac{\sin 81^{\circ}}{13.5}=\dfrac{\sin C}{8.2}[/tex]
[tex]\implies \sin C=\dfrac{8.2\sin 81^{\circ}}{13.5}[/tex]
[tex]\implies C=\sin ^{-1} \left(\dfrac{8.2\sin 81^{\circ}}{13.5}\right)[/tex]
[tex]\implies C=36.86482816..^{\circ}[/tex]
Interior angles of a triangle sum to 180°.
[tex]\implies A+B+C=180^{\circ}[/tex]
[tex]\implies 81^{\circ}+B+36.86482816...^{\circ}=180^{\circ}[/tex]
[tex]\implies B=62.13517184...^{\circ}[/tex]
Substitute the found value of angle B into the sine rule and solve for b:
[tex]\implies \dfrac{\sin A}{a}=\dfrac{\sin B}{b}[/tex]
[tex]\implies \dfrac{\sin 81^{\circ}}{13.5}=\dfrac{\sin 62.13517184...^{\circ}}{b}[/tex]
[tex]\implies b=\dfrac{13.5\sin 62.13517184...^{\circ}}{\sin 81^{\circ}}[/tex]
[tex]\implies b=12.08347925...[/tex]
Therefore, the measure of b is 12.1 cm (nearest tenth).
Please Answer Correctly.
Answer:
10 should be the correct answer
Step-by-step explanation:
im sooooo sorry if its wrong :|
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.
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 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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10y + 21 = 951 what is the variable of y
Answer: y= 93
Step-by-step explanation:
10y + 21 = 951
10y = 930
y= 93
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!
You and your friends decide to take a road trip to Florida for Winter Break. It will cost you $60 per day to visit Orlando and $100 per day to visit Tampa. You have $760 to spend on this trip and will stay for 10 days. What two equations could help you determine how many days you can afford to stay in each city?
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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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
8. In a local election, one candidate received 45% of the votes. A total of 440 votes were cast. How many votes did this candidate receive?
The vote received by the candidate if he receives 45 % of the votes and a total of 440 votes were cast is 198.
What is percentage?A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is.
Given:
The Total vote of the election = 440,
The vote received by one candidate = 45 % of total votes,
Solve the expression as given below,
The vote received by one candidate = 45 % of 440
The vote received by one candidate = 45 / 100 × 440
The vote received by one candidate = 0.45 × 440
The vote received by one candidate = 198
Therefore, the vote received by the candidate if he receives 45 % of the votes and a total of 440 votes were cast, is 198.
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What is the relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean?.
Answer: With a 95 percent confidence interval, you have a 5 percent chance of being wrong. With a 90 percent confidence interval, you have a 10 percent chance of being wrong. A 99 percent confidence interval would be wider than a 95 percent confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent)
Step-by-step explanation:
All hats are on sale for 22.5% off the original price.
Abrien is buying a hat that is originally priced at h.
Sales tax is 8.875%.
Part A: Which expression would calculate the final price
of a hat?
Part B: If the original price of a hat is $42, what is the
final price of buying four hats after the discount and
sales tax? (round your answer to the nearest dollar) Untitled Title
A. Part A: h(0.225)(0.08875)
Part B: 41
B. Part A: 4h(0.775)(1.08875)
Part B: $142
C. Part A: h(0.775)(1.08875)
Part B: $142
D. Part A: h(0.775)(0.08875)
Part B: $156
The expression for the final price of a hat would be h(0.775)(0.08875) and the final price of buying four hats after the discount and sales tax would be $142.
Option (C) is correct.
What is a discount?
A discount is a reduction in the price of a product or service. It can be offered for a variety of reasons, such as to encourage customers to make a purchase or to clear inventory. Discounts can be expressed as a percentage off the original price, or as a fixed dollar amount.
Part A: The expression that would calculate the final price of a hat is h(0.775)(1.08875). This takes into account the 22.5% discount by multiplying the original price by 0.775, and then adds the 8.875% sales tax by multiplying the discounted price by 1.08875.
Part B: If the original price of a hat is $42, then the final price of buying four hats after the discount and sales tax would be $42 x 4 x 0.775 x 1.08875 = $142.
Hence, the expression for the final price of a hat would be h(0.775)(0.08875) and the final price of buying four hats after the discount and sales tax would be $142.
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