Select the correct answer from each drop-down menu.Phyllis bought 21 feet of wood to frame a window. If she makes a triangular window, what is the greatest area the window can have?For a given perimeter, the triangle with the largest perimeter isv triangle. Using this type of triangle, the sides wouldmeasureSo, the greatest area the window could be is aboutsquare feet
Answers
Equilateral Triangles
An equilateral triangle has all of its three sides of the same measure. Suppose the side length of an equilateral triangle is L.
The perimeter of such a triangle is:
P = 3L
Phyllis bought 21 feet of wood to frame a triangular window. This corresponds to the perimeter of the triangle, so we can calculate the side length:
L = P/3
L = 21 feet / 3
L = 7 feet.
Now we know the length of the side of the triangle, we calculate the area by using the formula:
[tex]A=\frac{\sqrt[]{3}}{4}L^2[/tex]Substituting L = 7 feet:
[tex]\begin{gathered} A=\frac{\sqrt[]{3}}{4}(7ft)^2 \\ A=\frac{\sqrt[]{3}}{4}49ft^2 \\ \text{Calculating:} \\ A\approx21.22ft^2 \end{gathered}[/tex]Related Questions
Up: How Many?If the hexagon is one whole, how many one-thirds (3s) are in 12/3?Explain how the model shows the problem and thesolution.How many 1/3 are in 1 and 2/3?
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so we have to divide 5/3 by 1/3
[tex]\frac{\frac{5}{3}}{\frac{1}{3}}=\frac{5}{3}\cdot\frac{3}{1}=5[/tex]so there are 5 1/3's in 1 2/3
Determine a series of transformations that would map Figure 1 onto Figure J. y 11 Figure J NOW ona 00 05 15 1 -12-11-10-9-8-7-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 -2 Šť b bo v och t co is with Figure I -11 -12 A followed by a o
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EXPLANATION
The transformations that would map Figure 1 onto Figure J are:
A rotation followed by a translation
Estimate the amount of money he will have after paying these bills each month
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First, add all those bills.
[tex]undefined[/tex]find the absolute extrema for the function on the given inveral
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In order to find the minimum and maximum value in the given interval, first let's find the vertex coordinates:
[tex]\begin{gathered} f(x)=3x^2-24x \\ a=3,b=-24,c=0 \\ \\ x_v=\frac{-b}{2a}=\frac{24}{6}=4 \\ y_v=3\cdot4^2-24\cdot4=3\cdot16-96=-48 \end{gathered}[/tex]Since the coefficient a is positive, so the y-coordinate of the vertex is a minimum point, therefore the absolute minimum is (4,-48).
Then, to find the maximum, we need the x-coordinate that is further away from the vertex.
Since 0 is further away from 4 than 7, let's use x = 0:
[tex]f(0)=3\cdot0-24\cdot0=0[/tex]Therefore the absolute maximum is (0,0).
The following table gives the frequency distribution of the ages of a random sample of 104 Iris student
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Given:
The frequency values are given for class interval of N = 104 IRSC students.
The objective is to find cumulative frequency, cumuative relative frequency and cumulative percentage.
Cumulative frequency is addition of the previous frequency values.
So, the cumulative freqency values can be cclculated as,
The formula to find the cumulative relative frequency is,
[tex]\text{CRF}=\frac{CF}{N}[/tex]Now, the cumulative relative frequency can be calculated as,
Now, the formula to find the Cumulative percentage is,
[tex]\text{Cumulative \% = CRF }\times100[/tex]Then, the table values for Cumulative percentage will be,
Hence, the required cumulative frequency, cumuative relative frequency and cumulative percentage values are obtained.
Simplify the rational expression. 16b2+40b+25/4b+5 Enclose numerators and denominators in parentheses. For example, (a−b)/(1+n).
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Given the rational expression;
[tex]\frac{16b^2+40b+25}{4b+5}[/tex]We shall begin by factorizing the numerator as follows;
[tex]\begin{gathered} 16b^2+40b+25 \\ \text{Note that the coefficient of b}^2\text{ is greater than 1} \\ \text{Therefore we shall multiply the constant by the coefficient of b}^2 \\ \text{That gives us;} \\ 16\times25=400 \\ We\text{ shall now use the sum-product method, which is;} \\ \text{The factors of the constant 400} \\ S\text{hall also sum up to the coefficient of b } \\ \text{These factors are +20, +20} \\ \text{Therefore;} \\ 16b^2+40b+25\text{ becomes;} \\ 16b^2+20b+20b+25 \\ \text{Factorize by groups of two and we'll have} \\ 4b(4b+5)+5(4b+5) \\ \text{This becomes;} \\ (4b+5)(4b+5) \end{gathered}[/tex]The rational expression now becomes;
[tex]\frac{(4b+5)(4b+5)}{(4b+5)}[/tex]The perimeter, P, of a rectangle is the sum of twice the length and twice the width. P= 21+ 2w units P= 2([+w) units P= 2(x+3) units P= 2(5)-2(9) units P= 4 x units
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We can see the problem states that P = 2(x+3) and also states that P=4x
Those equations lead to the expression
2(x+3)=4x
Operating
2x+6=4x
Subtracting 2x
6 = 2x
Solving for x
x = 6/2 = 3
Thus, the perimeter is
P = 2(3+3) = 12 units
Part A: Solve the following equation: 8 + 2(x - 3) = 3x - 3
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We need to solve the following equation:
[tex]8+2(x-3)=3x-3[/tex]First we distribute the product in the left side:
[tex]\begin{gathered} 8+2(x-3)=3x-3 \\ 8+2x-6=3x-3 \end{gathered}[/tex]Then we pass all the terms with an x to the left side and all the constant terms to right side:
[tex]\begin{gathered} 8+2x-6=3x-3 \\ 2x-3x=6-3-8 \\ -x=-5 \\ x=5 \end{gathered}[/tex]So the answer is x=5.
These trianglesare congruent bythe trianglecongruencepostulate [?].A. AASB. ASAC. Neither, they are not congruent
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At the point of intersection, the angles are equal because they are vertically opposite. This means that in both triangle, there are two congruent angles and a congruent sides. Recall,
if any two angles and the side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are congruent by the (Angle side angle) ASA rule
Since the given triangles obey this rule, then the correct option is B
Compute.
\[ \left(\dfrac 8 3\right)^{-2} \cdot \left(\dfrac 3 4\right)^{-3}\]
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[tex]\left(\cfrac{8}{3}\right)^{-2} \left(\cfrac{3}{4}\right)^{-3}\implies \left(\cfrac{3}{8}\right)^{+2} \left(\cfrac{4}{3}\right)^{+3}\implies \cfrac{3^2}{8^2}\cdot \cfrac{4^3}{3^3}\implies \cfrac{4^3}{8^2}\cdot \cfrac{3^2}{3^3} \\\\\\ \cfrac{64}{64}\cdot \cfrac{1}{3}\implies 1\cdot \cfrac{1}{3}\implies \cfrac{1}{3}[/tex]
Evaluate the following expression.12!
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Explanation
Factorial, in mathematics, the product of all positive integers less than or equal to a given positive integer and denoted by that integer and an exclamation point.
[tex]a![/tex]so, to evaluate the expression we need to apply the definition
hence
[tex]\begin{gathered} 12\text{ ! = 12}\cdot11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1 \\ 12\text{ ! =}479001600 \end{gathered}[/tex]I hope this helps you
Write the fraction as decimal 182/1000182/1000 written as decimal is ?
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Let's convert the following number into a decimal:
[tex]\text{ }\frac{182}{1000}[/tex]182 has 3 digits
1000 has 3 zeros
For this fraction with a denominator of 10, 100, 1000, 10000 and so on.
Converting its decimal form, we just have to count the number of zeros they have. Once we got the number of zeros, that's the number of places we move to put the decimal point in the numerator from right to left.
Let's now answer this to better understand the rule.
Since 1000 has 3 zeros, we move the decimal point 3 places from right to left of 182.
Therefore, the answer is 0.182
so i have to factor x(3x+10)=77
Answers
SOLUTION
Given the equation as seen below, we can use the following steps to get the factors
[tex]x(3x+10)=77[/tex]Step 1: Remove the bracket by multiplying the value outside the bracket with the one inside the bracket using the distributive law. We have:
[tex]\begin{gathered} x(3x)+x(10)=77 \\ 3x^2_{}+10x=77 \\ 3x^2+10x-77=0 \end{gathered}[/tex]Step 2: Now that we have a quadratic equation, we solve for x using the quadratic formula:
[tex]\begin{gathered} 3x^2+10x-77=0 \\ u\sin g\text{ the form }ax^2+bx+c=0 \\ a=3,b=10,c=-77 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ =\frac{-10\pm\sqrt[]{10^2-4(3)(-77)}}{2(3)} \\ =\frac{-10\pm\sqrt[]{100+924}}{6} \\ =\frac{-10\pm\sqrt[]{1024}}{6} \\ =\frac{-10+32}{6}\text{ or }\frac{-10-32}{6} \\ \frac{22}{6}\text{ or -}\frac{42}{6} \\ =\frac{11}{3}\text{ or }-7 \end{gathered}[/tex]Hence, it can be seen from above that the factors will be -7 or 11/3.
what is the sum(add) of 2.31 and .21
Answers
what is the sum(add) of 2.31 and .21
we have
2.31+0.21=2.52
Remember that
2.31=2+0.31
so
2+0.31+0.21=2+0.52=2.52
Hi! I am having trouble with A assignment called "TIME TO SHOP!" I just need answers.
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The total item price is $265.50 while the total price with sales tax inclusive is $282.76
Here, we want to determine the sales price of each of the individual items, the total price of all and the appropriate sales tax
To get the price of each, we find the discount off the price of each
Mathematically, that would be;
[tex]\text{Price - (discount percentage }\times\text{ price)}[/tex]We follow through each of the chosen items as follows
1) Blu-Ray player
[tex]\begin{gathered} 42-(12\text{ percent of 42)} \\ =\text{ 42-(}\frac{12}{100}\text{ }\times\text{ 42)} \\ =\text{ 42- 5.04 = \$36.96} \end{gathered}[/tex]2) Jeans
[tex]\begin{gathered} 18.50-(20\text{ percent of 18.50)} \\ =\text{ 18.5 - }(\frac{20}{100}\times18.50) \\ =\text{ \$14.80} \end{gathered}[/tex]3) Set of Books
[tex]\begin{gathered} 15-(15\text{ percent of 15)} \\ =\text{ 15-(}\frac{15}{100}\times15) \\ =\text{ \$12.75} \end{gathered}[/tex]4) Sneakers
[tex]\begin{gathered} 39.5-(32\text{ percent of 39.5)} \\ =\text{ 39.5 - (}\frac{32}{100}\text{ }\times\text{ 39.5)} \\ \\ =\text{ \$26.86} \end{gathered}[/tex]5) Cell Phone
[tex]\begin{gathered} 199-(12.5\text{ percent of 199)} \\ 199-(\frac{12.5}{100}\times\text{ 199)} \\ =\text{ \$174.125} \end{gathered}[/tex]Now, we proceed to get the total of all the items
This is simply obtainable by adding up all the calculated prices
Mathematically, that would be;
174.125 + 26.86 + 12.75 + 14.8 + 36.96 = 265.495
This is a total of $265.50
Now, we want to calculate the total price with the value of the sales tax inclusive
Mathematically, that would be;
[tex]\begin{gathered} \text{Total price + (sales tax percentage of Total price)} \\ =\text{ 265.50 + (}\frac{6.5}{100}\text{ }\times\text{ 265.5)} \\ \\ =\text{ 282.7575 } \\ =\text{ \$282.76} \end{gathered}[/tex]if you receive a 175.84 cents on 314 invested at a rate of 7% for how long did yo invest the principle
Answers
Answer:
The number of years you should invest the principal is;
[tex]8\text{ years}[/tex]Explanation:
Given;
[tex]\begin{gathered} \text{Interest i = \$175.84} \\ \text{ Principal P = \$}314 \\ \text{Rate r = 7\% =0.07} \end{gathered}[/tex]Recall that the formula for simple interest is;
[tex]\begin{gathered} i=P\times r\times t \\ t=\frac{i}{Pr} \\ \text{where;} \\ t=\text{time of investment} \end{gathered}[/tex]substituting the given values;
[tex]\begin{gathered} t=\frac{i}{Pr} \\ t=\frac{175.84}{314\times0.07} \\ t=\frac{175.84}{21.98} \\ t=8 \end{gathered}[/tex]Therefore, the number of years you should invest the principal is;
[tex]8\text{ years}[/tex]We can also solve as;
[tex]\begin{gathered} i=P\times r\times t \\ 175.84=314\times0.07\times t \\ 175.84=21.98t \end{gathered}[/tex]then we can divide both sides by 21.98;
[tex]\begin{gathered} \frac{175.84}{21.97}=\frac{21.98t}{21.98} \\ 8=t \\ t=8\text{ years} \end{gathered}[/tex]Cuanto es : Siente mas que cuatro veces un número igual a 13?
Answers
Respuesta:
O número es 1.5
Explicacion paso-a-paso:
No sabemos cual o número, entonces o llamamos de x.
Siente mas que cuatro veces un número
7 + 4x
Igual a 13:
7 + 4x = 13
4x = 13 - 7
4x = 6
x = 6/4
x = 1.5
O número es 1.5
Evaluate the function at the given x-value.5. f(x) = -4x + 5 ; f(3)
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Answer: f (3) = -7
Instructions: Find the surface area of each figure. Round your answers to the nearest tenth, if necessary. 8 cm. 5 cm. 9 cm. 4 cm. 10 cm. Surface Area: cm2
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Solution
Step 1
State the number of shapes in the figure
The shape is made up of
2 triangles
and
3 rectangles
Step 2
State an expression for the area of a triangle and find the area of the triangle
[tex]\text{The area of a triangle ( A}_1)\text{ = }\frac{1}{2}\times base\text{ }\times height[/tex]Where the base = 10cm
height = 4cm
The area of the triangle after substitution is
[tex]\begin{gathered} A_1=\frac{1}{2}\times10\times4 \\ A_1=20cm^2 \end{gathered}[/tex]Since there are two triangles total area of the triangles = 2 x 20 = 40cm²
Step 3
State the expression for the area of a rectangle
[tex]\text{Area of a rectangle = Length }\times width_{}[/tex]Where
For rectangle 1
length = 8cm
width = 9cm
Area of rectangle 1 after substitution = 8 x 9 = 72cm²
For rectangle 2
length = 10cm
width= 9cm
Area of rectangle 2 after substitution = 9 x 10 = 90cm²
For rectangle 3
length = 5cm
wiidth = 9cm
Area of rectangle 3 after substitution = 9 x 5 = 45cm²
Step 4
Find the total area of the shape
[tex]\text{Total surface area of the shape = 45 +90 +}72+40=247cm^2[/tex]Therefore the surface area of the shape = 247cm²
Jake wanted to buy candy for $4.87 with a 6% sales tax. He has a $5.00 bill. Does he have enough for his candy?Yes or No
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The candy cost $4.87, and the sales tax is 6%, which means the sales tax can be calculated as follows;
[tex]\begin{gathered} \text{Cost}=4.87 \\ \text{Sales tax}=4.87\times\frac{6}{100} \\ \text{Sales tax}=4.87\times0.06 \\ \text{Sales tax}=0.2922 \end{gathered}[/tex]Therefore, the total cost inclusive of sales tax would be;
[tex]\begin{gathered} \text{Cost}+\text{Sales tax}=4.87+0.2922 \\ \text{Cost}+\text{Sales tax}=5.1622 \end{gathered}[/tex]ANSWER:
The total cost would be $5.1622
Hence, Jake does not have enough for his candy
The answer is NO
On a coordinate plane, point J is located at (-1, units, from point J to point K? 2) and point K is located at (8, 10). What is the distance, in Enter your answer in the space provided.
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The expression for the distance between two coordinates are express as :
[tex]\text{ Distance=}\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substitute the values of the coordinates:
[tex]\begin{gathered} (x_1,y_1)=(-1,-2) \\ (x_2,y_2)=(8,10) \end{gathered}[/tex][tex]\begin{gathered} \text{ Distance=}\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{Distance}=\sqrt[]{(8-(-1))^2+(10-(-2))^2} \\ \text{Distance}=\sqrt[]{(8+1)^2+(10+2)^2} \\ \text{Distance}=\sqrt[]{9^2+12^2} \\ \text{Distance}=\sqrt[]{81+144} \\ \text{Distance}=\sqrt[]{225} \\ \text{Distance}=15\text{ unit} \end{gathered}[/tex]So, distance between two points (-1,-2) & (8,10) is 15
Answer : Distance between two points (-1,-2) & (8,10) is 15.
6 points 3 The coordinates of the vertices of the triangle shown are P (2,13), Q (7,1), and R (2, 1). 14 13 12 11 10 9 8 6 5 3 2. 1 R Q 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 2 7 8 What is the length of segment PQ in units?
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We have the following:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]replacing:
P (2,13) = (x1,y1)
Q(7,1) = (x2,y2)
[tex]\begin{gathered} d=\sqrt[]{(7-2)^2+(1-13)^2} \\ d=\sqrt[]{5^2+12^2} \\ d=\sqrt[]{25+144} \\ d=\sqrt[]{169} \\ d=13 \end{gathered}[/tex]The answer is 13 units
An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. If 240 feet of antique picket fencing are to be used to enclose the garden, find the dimensions of the garden. What is the length of the garden? The length of the garden is What is the width of the garden? The width of the garden is
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STEP 1:
We'll derive an expression for the width and the length
[tex]\begin{gathered} w=\frac{2l}{3}\text{ where} \\ w\text{ = width} \\ l=\text{ length} \end{gathered}[/tex]STEP 2:
Next, We then derive an expression for the perimeter substituting w as a function of l
[tex]\begin{gathered} \text{Perimeter = 2(l+w)} \\ 240=2(l+\frac{2l}{3}) \end{gathered}[/tex]STEP 3:
Solve for l and subsequently w
[tex]\begin{gathered} \text{Perimeter}=\text{ 240 = 2(}\frac{2l+3l}{3})=2(\frac{5l}{3}) \\ 240=\frac{10l}{3} \\ \text{Cross multiplying gives 240}\times3=5l \\ l=\frac{240\times3}{10}=72ft \\ w=\frac{2l}{3}=\frac{2\times72}{3}=48ft \end{gathered}[/tex]Therefore, length = 72 ft and width = 48ft
17) A father gave $500 to his two sons. He gave x dollars to one son. Which of the following expressions correctly shows the amount he gave to the other son . *
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Total amount given by father = $500
He gave an amount of $x to his first son
then father will left with $500- $x amount
So, He will pay an amount of (500-x) to his other son
Answer : d) 500 - x
Select all the answers that are congruent to angle 6.
Answers
∠2 and ∠6 are corresponding angles
∠3 and ∠6 are alternate angles
∠6 and ∠7 are vertical angles
Step by step
First we see ∠7 and ∠6 are vertical angles, so they are congruent or the same.
Then we see ∠2 is a complementary angle to ∠6 which means it’s in a similar position so it is congruent or the same.
Last we see ∠3 is a vertical angle to ∠2, which is congruent to ∠6, so it’s also the same.
What is the equation of the line? −x−2y=4x + 2y = 4−x+4y=2x−4y=2
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We can write the line equation as:
[tex]y=mx+b[/tex]And to find the values of the coefficients 'm', and 'b', we can use the intercepts(where the line cuts the x and y axis) on the graph. Looking at the graph, we have the following interceptions:
[tex]\lbrace(0,2),(4,0)\rbrace[/tex]Plugging those values in our equation, we have:
[tex]\begin{cases}2=b \\ 0=4m+b\end{cases}\Rightarrow4m=-2\Rightarrow m=-\frac{1}{2}[/tex]Writing the line equation in slope intercept form, we have the following:
[tex]y=-\frac{1}{2}x+2[/tex]Rewriting this equation:
[tex]\begin{gathered} y=-\frac{1}{2}x+2 \\ \Rightarrow\frac{1}{2}x+y=2 \\ \Rightarrow x+2y=4 \end{gathered}[/tex]And this is our final answer. The line equation is
[tex]x+2y=4[/tex]this one is super hard
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we have the expression
[tex]d\log a+\log c[/tex]Apply property of log
[tex]d\log a+\log c=\log (a^d\cdot c)[/tex]Determine if the sequence below is arithmetic or geometric and determine thecommon difference / ratio in simplest form.4,2,1,...
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An arithmetic progression is a progression where the next term is found by multiplying the previous by a constant number called the common ratio, for the given progression:
[tex]4,2,1[/tex]If we use 1/2 as a common ratio we get:
[tex]\begin{gathered} 2=\frac{4}{2} \\ 1=\frac{2}{2} \end{gathered}[/tex]Therefore this is an arithmetic progression and its common ratio is 1/2
The value of a baseball players rookkie card began to increase once the player retired.When he retired in 1995 hid card was worth 9.43.The value has increased by 1.38 each year since then.Yall I really need help I dont get this at all
Answers
Given that,
The value of card starts increasing after 1995. In this question, we have to find the value of card at present (2020).
Initial worth = I = 9.43
Final worth = F = ?
Total years = 2020 - 1995 = 25 years
Increasing rate = r = 1.38
The final worth of a card after 'n' years is calculated as:
F = I * r^n
F = 9.43 * (1.38)^25
F = 9.43 * 3140.34
F = 29613.43
Hence, the value of the card in 2020 would be 29613.43.
Exactly 25% of the marbles in a bag are black. If there are 8 marbles in the bag, how many are black?
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Let the total number of marbles in the bag be 'x'.
Given that exactly 25% of the total marbles are black,
[tex]\begin{gathered} \text{ No. of black marbles}=25\text{ percent of total marbles} \\ \text{ No. of black marbles}=25\text{ percent of x} \\ \text{ No. of black marbles}=\frac{25}{100}\cdot x \\ \text{ No. of black marbles}=0.25x \end{gathered}[/tex]Also, given that there are total 8 marbles in the bag,
[tex]x=8[/tex]Then the number of black marbles will be obtained by substituting x=8,
[tex]\begin{gathered} \text{ No. of black marbles}=0.25(8) \\ \text{ No. of black marbles}=2 \end{gathered}[/tex]Thus, there are 2 black marbles in the bag.