Both Henry and Colin have a ratio of 4, so Colin gets the same amount as Henry, so we know Colin has 56.
Brian's ratio is 5, so for every 4 Colin gets, brian gets 5 ( 1 more).
Divide Colin's quantity by 4 :
56/4 = 14
Brain gets 14 more.
In the equation 3/4y+1/2=3 1/4, the fractional coefficient is what
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Given equation: [tex]\frac{3}{4}y + \frac{1}{2} = 3 \frac{1}{4}[/tex]
In the given equation, [tex]\frac{3}{4}[/tex] is a coefficient and y is the variable.
coefficient is a constant number or quantity multiplied to a variable in an algebric expression. Like in the above equation [tex]\frac{3}{4}[/tex] is a coefficient and y is the variable. We use term variable for y as its value may vary or change. If variable does not have any coefficient in any expression then in that case, we consider 1 as coefficient, for example: [tex]x+4[/tex], here variable have 1 as coefficient.
Hence, the fractional coefficient is [tex]\frac{3}{4}[/tex].
Assume that the quadrilateral shown is a parallelogram. Which expression represents the area of the parallelogram?
Answer:
B. x² + 16x + 15
Step-by-step explanation:
Area of parallelogram = base x height
A = (x + 15) (x + 1) = x² + 16x + 15
On a map, the distance from Los Angeles to San Diego is 6.35 cm. the scale is 1cm = 20 miles. What is the actual distance?
Answer:
The actual distance is 127 miles.
Step-by-step explanation:
Given:
On a map, the distance from Los Angeles to San Diego is 6.35 cm.
The scale is 1 cm = 20 miles.
Now, to find the actual distance.
Let the actual distance be [tex]x\ miles.[/tex]
And the distance on map is 6.35 cm.
So, 6.35 cm is equivalent to [tex]x\ miles.[/tex]
And as given on the scale 1 cm is equivalent to 20 miles.
Now, to get the actual distance by using cross multiplication method:
[tex]\frac{6.35}{x} =\frac{1}{20}[/tex]
By using cross multiplication we get:
⇒ [tex]127=x[/tex]
⇒ [tex]x=127\ miles.[/tex]
Therefore, the actual distance is 127 miles.
How does this polynomial identity work on numerical relationships?
(y + x) (ax + b)
Let us take 'a' in the place of 'y' so the equation becomes
(y+x) (ax+b)
Step-by-step explanation:
Step 1:
(a + x) (ax + b)
Step 2: Proof
Checking polynomial identity.
(ax+b )(x+a) = FOIL
(ax+b)(x+a)
ax^2+a^2x is the First Term in the FOIL
ax^2 + a^2x + bx + ab
(ax+b)(x+a)+bx+ab is the Second Term in the FOIL
Add both expressions together from First and Second Term
= ax^2 + a^2x + bx + ab
Step 3: Proof
(ax+b)(x+a) = ax^2 + a^2x + bx + ab
Identity is Found .
Trying with numbers now
(ax+b)(x+a) = ax^2 + a^2x + bx + ab
((2*5)+8)(5+2) =(2*5^2)+(2^2*5)+(8*5)+(2*8)
((10)+8)(7) =(2*25)+(4*5)+(40)+(16)
(18)(7) =(50)+(20)+(56)
126 =126
Alan is conducting a survey to find out the type of art preferred by students in the town’s high school. Identify the population of his survey and describe a possible sample of the population.
The other answer is wrong the following is the sample response.
Answer:
Sample Response: The population of Alan's survey is all the students at the town's high school. The sample must be representative of the population. A possible sample would be an equal number of freshman, sophomores, juniors, and seniors.
Step-by-step explanation:
just finished the assignment and this was the sample response.
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Have a great day!
Alan's survey population encompasses all students at the high school with art preferences. A sample could be randomly chosen from students from each grade or art class, reflecting the school's diversity and maintained by a random sampling method for fairness and representation.
Explanation:The population of Alan's survey is all the students at the town’s high school who have preferences for types of art. To conduct his survey, Alan needs to choose a sample, which is a smaller group from the population that can provide reliable information about the entire population's art preferences. An example of a possible sample would be selecting a certain number of students from each grade level or art class to ensure a variety of perspectives. It could also involve stratification by demographic characteristics such as age, gender, socioeconomic status, or ethnicity if these factors are believed to influence art preferences.
An efficient method to create a representative sample could be to use a random sampling technique where each student has an equal chance of being selected. For instance, Alan could use a random number generator to pick students from a list, or he might use a stratified random sampling by first dividing the student body into subgroups (such as by grade or art class) and then randomly selecting students from each subgroup.
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Complete the equation of the line through (-8, -2) and (-4, 6)
Answer:
Equation of line is given by:
[tex]y=2x+14[/tex]
Step-by-step explanation:
Given points:
[tex](-8,-2)\ and\ (-4,6)[/tex]
Slope of line [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is a point on the line
[tex]m=\frac{6-(-2)}{-4-(-8)}[/tex]
[tex]m=\frac{6+2}{-4+8}[/tex]
[tex]m=\frac{8}{4}[/tex]
∴ [tex]m=2[/tex]
Point-slope equation of line is given by:
[tex]y-y_1=m(x-x_1)[/tex]
where [tex](x_1,y_1)[/tex] is a point on the line and [tex]m[/tex] is slope of line.
Using point [tex](-8,-2)[/tex] and slope [tex]m=2[/tex] point-slope equation of line is given by:
[tex]y-(-2)=2(x-(-8))[/tex]
Simplifying.
[tex]y+2=2(x+8)[/tex]
Using distribution.
[tex]y+2=2x+16[/tex]
Subtracting 2 to both sides.
[tex]y+2-2=2x+16-2[/tex]
[tex]y=2x+14[/tex]
Thus, equation of line is [tex]y=2x+14[/tex]
Aramp is 17 feet long, rises 8 feet above the floor, and covers a horizontal distance of 15 feet, as shown in the figure.
The ratio of
is equal to tan B.
The ratio of the vertical rise to the horizontal distance on the ramp is equal to tan B.
Explanation:The given figure represents a ramp with a length of 17 feet, rising 8 feet above the floor, and covering a horizontal distance of 15 feet. To find the ratio of the vertical rise to the horizontal distance (tan B), we can use the trigonometric function tangent (tan).
Tan B = vertical rise / horizontal distance = 8 feet / 15 feet = 0.5333
A bag contains 1 blue, 2 green, 3 yellow, and 3 red marbles, as shown.
What is the probability of drawing a red marble out of the bag without looking?
10
CVO
-10
-ICV
The probability of drawing a red marble out of the bag without looking is 1/3.
Explanation:The probability of drawing a red marble out of the bag without looking can be calculated by dividing the number of red marbles by the total number of marbles in the bag. In this case, there are 3 red marbles out of a total of 9 marbles, so the probability is 3/9, which simplifies to 1/3.
Ms. Fuller has 2 2/6 pies left over from her party. Write the number of pies left over as a fraction greater than 1.
Answer:
[tex]\frac{14}{6}[/tex]
Step-by-step explanation:
A mixed fraction of the form [tex]a\frac{b}{c}[/tex] can be converted into an improper fraction by writing it in the form [tex]\frac{(ac)+b}{c}[/tex] . By applying this formula , we can see that [tex]2\frac{2}{6} = \frac{12 +2}{6} =\frac{14}{6}[/tex] . As numerator is greater than the denominator , we can see that the answer is greater than one and thus it is an improper fraction.
i really need help with this angle of elevation and depression
Answer:
Step-by-step explanation
But the question does not say exactly what should be solve for.
On a bike trip, you traveled 21 miles on
the second day. On the 3rd day, you traveled 3
second day.
e trip, you traveled 21 miles on the first day, and n miles on
y. On the 3rd day, you traveled 5 miles less than on the rest
a. Write an expression for the number of miles traveled in three day
b. Simplify the expression. Explain each step.
c. Find the number of miles traveled in three days when you traveled
19 miles on the second.
Answer:
She traveled 13 23/56 miles on the third day.
Step-by-step explanation:
HOPE THIS HELPED ;3
plz hurry!!!! thank you!!!!
Answer:
[tex]m\angle KLM=53.13^o[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find the measure of angle KOM
In the triangle KOM
we have
[tex]KO=MO=r=5\ units[/tex]
[tex]KM=8\ units[/tex]
Applying the law of cosines
[tex]8^2=5^2+5^2-2(5)(5)cos(KOM)[/tex]
[tex]64=50-50cos(KOM)[/tex]
[tex]50cos(KOM)=50-64[/tex]
[tex]50cos(KOM)=-14[/tex]
[tex]cos(KOM)=-14/50[/tex]
[tex]m\angle KOM=cos^{-1}(-14/50)[/tex]
[tex]m\angle KOM=106.26^o[/tex]
step 2
Find the measure of the arc KM
we know that
[tex]arc\ KM=m\angle KOM[/tex] ----> by central angle
we have
[tex]m\angle KOM=106.26^o[/tex]
so
[tex]arc\ KM=106.26^o[/tex]
step 3
Find the measure of angle KLM
we know that
The inscribed angle is half that of the arc comprising
[tex]m\angle KLM=\frac{1}{2}[arc\ KM][/tex]
we have
[tex]arc\ KM=106.26^o[/tex]
substitute
[tex]m\angle KLM=\frac{1}{2}[106.26^o][/tex]
[tex]m\angle KLM=53.13^o[/tex]
if sec thita . sin thita =0,then find the value of thita
Answer:
[tex]\large\boxed{\theta=k\pi,\ k\in\mathbb{Z}}[/tex]
Step-by-step explanation:
[tex]\sec\thets\cdot\sin\theta=0\iff \sec\theta=0\ \vee\ \sin\theta=0\\\\\sec\theta\neq0\ \text{for any value of}\ \theta\\\\\sin\theta=0\Rightarrow\theta=k\pi\ \text{where}\ k\in\mathbb{Z}[/tex]
57, 59, 64, 72, 76, 77, 77, 78, 85, 87, 88, 88, 88, 92, 94, 96, 98, 100
Find the Median of the data set
Answer:
82
Step-by-step explanation:
Mean of a set of data is simply the average. It's calculated by adding up all the numbers, then divide by how many numbers there are.
57 + 59 + 64 + 72 + 76 + 77 + 77 + 78 + 85 + 87 + 88 + 88 + 88 + 92 + 94 + 96 + 98 + 100 = 1,476
1476/18 = 82
Therefore 82 is the mean of the set of numbers
Answer:
Median = 86
Step-by-step explanation:
the middle of the data set is 85 and 87. to find the median you would do 85+87/2= 172/2 median = 86
Find the sum of the first 56 terms of the following sequence {-8, -1, 6, ...}
A. 10,332
B. 1,344
C. 10,584
Answer:
A
Step-by-step explanation:
Given sequence [tex]-8,\ -1,\ 6,\ ...[/tex]
In this sequence,
[tex]a_1=-8\\ \\a_2=-1\\ \\a_3=6\\ \\...[/tex]
Hence,
[tex]d=a_2-a_1=-1-(-8)=7\\ \\d=a_3-a_2=6-(-1)=7[/tex]
Find 56th term:
[tex]a_{n}=a_1+(n-1)\cdot d\\ \\a_{56}=-8+(56-1)\cdot 7\\ \\a_{56}=-8+385\\ \\a_{56}=377[/tex]
The sum of 56 terms is
[tex]S_n=\dfrac{a_1+a_n}{2}\cdot n\\ \\S_{56}=\dfrac{-8+377}{2}\cdot 56=\dfrac{369}{2}\cdot 56=369\cdot 28=10,332[/tex]
evaluate √7x(√x-7√7
pls & thanks!
Answer:
[tex]x\sqrt{7} - 49\sqrt{x}[/tex]
Step-by-step explanation:
[tex]\begin{array}{rcl}\sqrt{7x}(\sqrt{x} - 7\sqrt{7}) & = & \sqrt{7x}\times\sqrt{x}- 7\sqrt{7}\times\sqrt{7x} \\ & = & \sqrt{7}\times\sqrt{x}\times\sqrt{x} - 7\sqrt{7}\times\sqrt{7}\times\sqrt{x}\\& = & \sqrt{7}\times x - 7\times 7\times\sqrt{x}\\& = &\mathbf{ x\sqrt{7} - 49\sqrt{x}}\\\end{array}[/tex]
What expression will Help me find 4% of 25
Solve for m.
3.6m=14.4
Answer:
4
Step-by-step explanation:
3.6m = 14.4
m = 14.4 ÷ 3.6
m = 4
1/2(6 2/3+1/4)-5/24=
For this case we must simplify the following expression:
[tex]\frac {1} {2} (6 \frac {2} {3} + \frac {1} {4}) - \frac {5} {24} =[/tex]
We convert the mixed number to an improper fraction:
[tex]6 \frac {2} {3} = \frac {3 * 6 + 2} {3} = \frac {20} {3}[/tex]
So, by rewriting we have:
[tex]\frac {1} {2} (\frac {20} {3} + \frac {1} {4}) - \frac {5} {24} =\\\frac {1} {2} (\frac {4 * 20 + 3 * 1} {4 * 3}) - \frac {5} {24} =\\\frac {1} {2} (\frac {80 + 3} {12}) - \frac {5} {24} =\\\frac {1} {2} (\frac {83} {12}) - \frac {5} {24} =[/tex]
[tex]\frac {83} {24} - \frac {5} {24} =\\\frac {83-5} {24} =\\\frac {78} {24} =\\\frac {39} {12} =\\\frac {13} {4} =\\3 \frac {1} {4}[/tex]
Answer:
[tex]3 \frac {1} {4}[/tex]
Are the fractions 3/9, 3/10, 3/11, and 3/12 in order from least to greatest
Answer:
The fractions [tex]\frac{3}{9},\frac{3}{10},\frac{3}{11},\frac{3}{12}[/tex] are not in order from least to greatest.
Step-by-step explanation:
Given order of fractions from least to greatest:
[tex]\frac{3}{9},\frac{3}{10},\frac{3}{11},\frac{3}{12}[/tex]
To check if the fractions are in correct order.
Solution:
The fractions given have same numerators but different denominators.
For fractions the higher the denominator the lower is the value of that fraction.
Thus, in the given list the least value fraction will be the fraction with the greatest denominator which is [tex]\frac{3}{12}[/tex] and the greatest value fraction will be the fraction with the least denominator which is [tex]\frac{3}{9}[/tex]
So, the order of the fractions from least to greatest is not correct. Instead the order is from greatest to least.
The correct order from least to greatest should be:
[tex]\frac{3}{12},\frac{3}{11},\frac{3}{10},\frac{3}{9}[/tex].
trapizoid figure STUV is scaled version of figure WXYZ. The scale factor of figure STUV to figure WXYZ is 3:1. If ST= 117 mm and SV= 153 mm, what is the length of side WZ?
Answer:
39mm
Step-by-step explanation:
Final answer:
Using the scale factor of 3:1, the length of side WZ from trapezoid WXYZ can be calculated by dividing the known length of side SV from trapezoid STUV by the scale factor. The length of WZ is found to be 51 mm.
Explanation:
If trapezoid STUV is a scaled version of trapezoid WXYZ with a scale factor of 3:1, we can use this scale factor to determine the length of side WZ given the lengths of ST and SV. To find the length of WZ, we divide the length of SV by the scale factor. Since SV = 153 mm and the scale factor is 3, we perform the division 153 mm / 3 to get 51 mm as the length of WZ.
A proportion is a mathematical statement that two ratios or fractions are equal. It is used to express the equality of two fractions that compare two numbers or quantities to each other. For example, if we have two fractions a/b and c/d, a proportion states that these two fractions are equivalent: a/b = c/d. Proportions are fundamental in various branches of mathematics and applications, including solving problems involving scales, maps, and ratios in real-life scenarios.
10 POINTS!!! will give Brainliest
Find the volume of the prism. Round to the nearest tenth if necessary.
Answer:
The volume of the prism will be given by 204.7 cubic cm.
Step-by-step explanation:
The area of a triangle whose three side lengths are given is equal to
Δ = [tex]\sqrt{s(s - a)(s - b)(s - c))}[/tex] .......... (1)
Where, a, b, and c are the three side lengths and s is the half perimeter i.e.
[tex]s = \frac{a + b + c}{2}[/tex] ......... (2)
Now, in our case, [tex]s = \frac{6 + 7 + 6}{2} = 9.5[/tex] {From equation (2)}
So, Δ = [tex]\sqrt{9.5(9.5 - 6)(9.5 - 7)(9.5 - 6)} = 17.05[/tex] sq. cm.
{From equation (1)}
Hence, the volume of the prism will be given by (17.05 × 12) = 204.7 cubic cm. (Answer)
The mass of two sacks of potatoes is 168 grams. One-eight of the mass of Sack A and three-quarter of the mass of Sack B is 76 grams. Write an equation to find the mass of Sack A.
Answer:
1/8(A)+(3/4)(168-A)=76 is an equation to find the mass of A, the mass of A is 80 grams.
Step-by-step explanation:
What do we know?
Both sacks together are 168 grams. Therefore;
A+B=168
One eighth of sack A and three quarters of sack B is equal to 76 grams. Therefore;
1/8(A)+(3/4)B=76
Let's solve using the substitution method to find A. First, we need to isolate and then substitute B for an expression containing A.
A+B=168
B=168-A
Now that we have isolated B, we can substitute '160-A' for B in the other equation.
1/8(A)+(3/4)(168-A)=76
1/8(A)-3/4(A)+126=76
1/8(A)-3/4(A)+126=-50
-5/8(A)=-50
A=80
the area of a rectangular dog pen is 8 1/2 square feet. if the width is 3 2/5, what is the length, in feet?
Answer:
2 1/2 or 2.5
Step-by-step explanation:
The area is the length times the width. To solve for the length, you have this equation using the data you already have. 8 1/2 = 3 2/5 x length. 8 1/2 / 3 2/5 = length. 8.5/3.4 = length. length = 2.5 OR to do this fraction wise, you can make them fractions and divide, making 8/1 -> 16/2 + 1/2 = 17/2 and 3/1 - 15/5 + 2/5 = 17/5 and divide those, which ends up at 2 1/2 but fraction wise makes it more complicated
Given ƒ(x) = −12x + 72, find x when ƒ(x) = 24. A) 1 B) 3 C) 4 D) 6
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Answer:
if f(x)=24
24=-12x+72
24-72=-12x
-48=-12x
x=48/12
x=4
so it's (C)
Answer:
x=4; Option C is your answer.
Step-by-step explanation:
Plug in 24:
[tex]f(x)=24\\[/tex]
[tex]24=-12x+72[/tex]
Solve For X:
[tex]-12x+72-72=24-72\\-12x=-48\\\frac{-12x}{-12} =\frac{-48}{-12}\\ x=4[/tex]
what is the differance look at the link
Answer:
The difference is [tex]\frac{3}{4}[/tex] inches.
Step-by-step explanation:
See the attached number line where the worm lengths in inches are plotted.
From the number line plotted in the attached photo, it is clear that the shortest worm has the length of [tex]\frac{3}{4}[/tex] inches and the longest worm has the length of [tex]1\frac{1}{2}[/tex] inches i.e. [tex]\frac{3}{2}[/tex] inches.
Therefore, the difference in length between the shortest and longest worm is [tex](\frac{3}{2} - \frac{3}{4}) = \frac{3}{4}[/tex] inches. (Answer)
Jenni wrote a rational number that is positive. Which of the following is not a possible number that she wrote?
51/4
0
7/8
1
Answer:
There is no answer.
0 is rational since it can be written as a fraction (0/5, 0/69)
1 is obviously rational. 7/8 is .875 and 5 1/4 is 5.25
What percent of 500 is 150
Answer:
30%
Step-by-step explanation:
We can translate the question into an equation.
500x=150
x=150/500
x=3/10=30%
answer: 30%
Rewrite the equation by completing the square. x^2-20x+100 = 0
By completing the square, the equation x²- 20x + 100 = 0, we get, (x-10)²=0
Here, we have,
To rewrite the equation x² - 20x + 100 = 0 by completing the square, we can follow these steps:
Step 1: Move the constant term to the right side of the equation:
x² - 20x = -100.
Step 2: Take half of the coefficient of the x-term (-20/2 = -10) and square it to get (-10)² = 100.
Step 3: Add the result from step 2 to both sides of the equation:
x² - 20x + 100 = -100 + 100.
Simplifying:
x² - 20x + 100 = 0.
Step 4: Factor the left side of the equation. In this case, the left side is a perfect square trinomial:
(x - 10)² = 0.
Therefore, by completing the square, the equation x²- 20x + 100 = 0,
we get, (x-10)²=0
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Final answer:
The equation [tex]x^2 - 20x + 100 = 0[/tex] is already a perfect square and does not need to be completed. However, completing the square involves moving the constant to the other side, squaring half the coefficient of x, and solving for x, which leads us back to the original equation [tex](x - 10)^2 = 0[/tex] and reveals that x = 10.
Explanation:
The equation given is [tex]x^2 - 20x + 100 = 0[/tex]. This equation appears to already be a perfect square, as the constant term (100) is the square of half the coefficient of the x term (which is 10), thus completing the square is actually not needed. However, to illustrate the method of completing the square, let's ignore for a moment that it's already a perfect square and proceed with the steps:
Move the constant term to the right side of the equation: [tex]x^2 - 20x = -100.[/tex]Take half of the coefficient of x, which is -10, and square it, giving us 100.Add this square (100) to both sides of the equation, which yields [tex]x^2 - 20x + 100 = 0[/tex], the same as we started with.Now the left side is a square of (x-10): [tex](x - 10)^2[/tex] = 0.To solve for x, take the square root of both sides, giving us x - 10 = 0, which simplifies to x = 10.We've found that x = 10 is the solution to the equation, which is the same result you would get by recognizing the equation was already a perfect square in its original form.
Adam burns 225 calories per 30 minutes of bicycling how many calories in 10 mins.
Answer:
7.2
Step-by-step explanation:
You divide 225 by 30 and get 7.2
Answer:
c
Step-by-step explanation: