Answer:60 and 80
Step-by-step explanation:
O EQUATIONS AND INEQUALITIESSolving a word problem using a quadratic equation with rationa...
Answer:
[tex]\begin{gathered} length\text{ = 8 m} \\ width\text{ = 5.5 m} \end{gathered}[/tex]Explanation:
Here, we want to get the dimensions of the rectangle
Let us represent the length by l and the width by w
From the question:
The length of the rectangle is 3 m less than double the width
Mathematically:
[tex]l\text{ = 2w-3}[/tex]The product of the two represents the area
[tex]\begin{gathered} A\text{ = l }\times\text{ w} \\ lw\text{ = 44} \end{gathered}[/tex]Now, let us substitute the first equation with the second:
[tex]\begin{gathered} w(2w-3)\text{ = 44} \\ 2w^2-3w\text{ = 44} \\ 2w^2-3w-44\text{ = 0} \end{gathered}[/tex]Solving the quadratic equation, we have:
[tex]\begin{gathered} 2w^2-11w+8w-44\text{ = 0} \\ 2w^2+8w-11w-44\text{ = 0} \\ 2w(w\text{ + 4\rparen -11\lparen w+4\rparen = 0} \\ (2w-11)(w+4)\text{ = 0} \\ 2w=\text{ 11} \\ w\text{ = }\frac{11}{2} \\ \\ w\text{ = 5.5} \end{gathered}[/tex]Recall:
[tex]\begin{gathered} lw\text{ = 44} \\ 5.5l\text{ = 44} \\ l\text{ = }\frac{44}{5.5}\text{ = 8 } \end{gathered}[/tex]An architect plans to buy 5 stone spheres and 3 stone cylinders. For the same amount, he can buy 2 stone spheres and 7 stone cylinders. If one stone cylinder costs $32.73 how much does
each stone sphere cost?
Answer:
Each stone sphere costs $43.64Step-by-step explanation:
Let the cost of stone sphere is s and stone cylinder is c.
According to question we have equation:
5s + 3c = 2s + 7cSolve it for s:
5s - 2s = 7c - 3c3s = 4cSubstitute the value of c:
3s = 4*32.733s = 130.92s = 130.92/3s = 43.64True or False: The set of whole numbers is closed under multiplication.
Explanation:
Take any two whole numbers you want. Multiplying them together always result in some (other) whole number.
Examples:
2*3 = 65*7 = 3511*12 = 132In other words,
(whole number)*(whole number) = whole number
This is why we consider the set closed under multiplication.
Please help ㅤㅤ
What is the value of this expression
ㅤ
PLUG IN THE VALUES OF THE VARIABLES IN THE RIGHT POSITIONS AND SIMPLIFY.
[tex] \frac{1}{2} (12 - 4) \times \frac{1}{4} \\ = \frac{1}{2} (8) \times \frac{1}{4} \\ = \frac{8}{2} \times \frac{1}{4} \\ = \frac{8}{8} \\ = 1[/tex]
THE ANSWER IS OPTION B.
10-9x24/8x6 (pemdas)
Answer:
-152
Step-by-step explanation:
1. Parenthesis
2. Exponents
3. Multiplication/Division (left to right)
4. Addition/Subtraction (left to right)
Always look left to right.
The first thing is 9x24=216 (3. multiply)
10-216/8x6
Then 216/8=27 (3. divide)
10-27*6
Then 27*6=162 (3. multiply)
10-162
Then finally 10-162=-152 (4. subtract)
The expression 10 - 9 x 24/8 x 6 following (PEMDAS/BODMAS) is 5.5.
We have,
To solve the expression using the order of operations (PEMDAS/BODMAS), follow these steps:
Perform multiplication and division from left to right:
10 - 9 x 24/8 x 6 can be rewritten as 10 - (9 x 24) / (8 x 6).
Perform the multiplication inside the parentheses:
10 - (9 x 24) / (8 x 6)
10 - 216 / (8 x 6).
Perform the multiplication in the denominators:
10 - 216 / (8 x 6)
10 - 216 / 48
Perform the division:
10 - 216 / 48
10 - 4.5
Perform the subtraction:
10 - 4.5
5.5
Therefore,
The expression 10 - 9 x 24/8 x 6 following (PEMDAS/BODMAS) is 5.5.
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Use the Rational Zeros Theorem to list all possible zeros of the function below.
f(x) = 11x³ 2x² + x + 10.
-
[Enter all possible zeros predicted by the Rational Zero Theorem individually and separated by commas
(1,-1,-1/2,1/2,etc.) Note: You do not need to factor the polynomial.]
The all possible zeros predicted by the Rational Zero Theorem individually and separated by commas are ±1/1, ±1/11, ±2, ±2/11, ±5, ±5/11, ±10, ±10/11.
P(x) = 11x³ + 2x² + x + 10
The factors of the constant term 10 is ±1, ±2, ±5, ±10 (=p)
The factors of leading coefficient are ±1, ±11 (= q)
The possible rational zeros are p/q : ±1/1, ±1/11, ±2/1, ±2/11, ±5/1, ±5/11, ±10/1, ±10/11.
After simplification the possible roots are ±1/1, ±1/11, ±2, ±2/11, ±5, ±5/11, ±10, ±10/11.
Therefore, ±1/1, ±1/11, ±2, ±2/11, ±5, ±5/11, ±10, ±10/11. are the all possible zeros predicted by the Rational Zero Theorem individually and separated by commas.
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7 ft
9 ft
26 ft
What is the area?
The total area of the figure is 298.17 ft².
What is termed as the area of the figure?The total space occupied by a flat (2-D) surface or the shape of an object is defined as its area.Sketch a square on a paper piece with a pencil. It is a two-dimensional figure. The area of the shape just on paper is referred to as its Area.For the given question;
Let divide the given the figure in three parts;
RectangleTrianglesemi circleThe dimensions of the rectangle is;
Length = 26 - 9 = 15 ft
Breadth = 9 ft
Area = length x breadth
Area = 15 x 9
Area = 135 ft²
The dimension of the triangle is-
Base = 9 ft
Height = 15 - 7 = 8 cm
Area = (1/2) base x height
Area = (1/2) x 9 x 8
Area = 36 ft²
The dimension of semi circle is -
Radius = 9 ft
Area = πr²/2
Area = 3.14 x 9² / 2
Area = 127.17 ft²
Total area = rectangle +triangle + semicircle
Total area = 135 + 36 + 127.17
Total area = 298.17 ft²
Thus, the total area of the figure is 298.17 ft².
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Subtract and simplify:
PLEEEEASE HEEEEELP ASAP
8 1/2 − 5 2/3 = _____
Responses
A 16/6
B 3 1/3
C 2 5/6
D 3 1/6
Answer:
C
Step-by-step explanation:
8.5 - 5.6666= 2.83
Answer:
C. 2 5/6
Step-by-step explanation:
8 1/2 - 5 2/3 1. convert mixed numbers into an improper fraction
17/2 - 17/3 2. convert fractions into 2 numbers that can be subtracted
51/6 - 34/6 3. subtract
17/6 4. convert to mixed number
2 5/6
Solve for x to the nearest tenth.
Answer:
x = 11,2 inchs
Step-by-step explanation:
I infer that the units are in inches.
8-3 = 5
Then:
By the Pythagorean Teorem:
x² = 10² + 5²
x² = 100 + 25
x² = 125
√x² = √125
x = 11.18
to the nearest tenth:
x = 11.2 inches
1.5x+0.5y=12
a. solve for y
b. find ordered pairs for the function
Answer:
Step-by-step explanation:
y=-3x+24
(0,24)
The slope of line ℓ
is greater than 0 and less than 1. Write an inequality for the slope of a line perpendicular to ℓ
.
By properties of perpendicular lines and algebra properties, the slope of the line perpendicular to line ℓ is represented by m' > 1.
How to represent an inequality associated with a line perpendicular to another line
Let m be the slope of a line, in accordance with analytic geometry, the slope of line perpendicular to the first one is equal to m' = - 1 / m. The statement can be summarized by the following inequality:
0 < m < 1
Then, by algebra properties for inequalities we find that that slope for the perpendicular line is:
0 < m · m⁻¹ < m⁻¹
0 < 1 < m⁻¹
1 < m⁻¹
- m⁻¹ > 1
- 1 / m > 1
m' > 1
The slope of the line perpendicular to line ℓ is represented by m' > 1.
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need this asap 50 points for it
Answer:
the subtraction property of equality
Step-by-step explanation:
trust
Answer:
Subtraction
Step-by-step explanation:
Which of the following properly describe
"slope"? Select all that apply.
0
A)
ratio of the change in y-values
(rise) for a segment of the graph to
the corresponding change in x-
values (run)
OB) x₂-x₂
y₂-M1
C) ₂-₁
x₂-x₂
D) run/rise
☐ E) rise/run
What is the arithmetic mean between 15 and 7?
Answer:
11
Step-by-step explanation:
How to find the arithmetic mean:
Add all numbers together, and divide by the amount of numbers.
Ans: 15 + 7 = 22
22 ÷ by amount of numbers =
22 ÷ 2 =
11
Ans = 11
if 63 Naira is shared in the ratio 4 ratio 5 what is the larger share
Answer:
35
Step-by-step explanation:
sum the parts of the ratio, 4 + 5 = 9 parts
divide 63 by 9 to find the value of 1 part of the ratio
63 ÷ 9 = 7 , then
4 parts = 4 × 7 = 28
5 parts = 5 × 7 = 35 ← larger share
please help me with this question !!
Answer: The perimeter of the triangle is 69 cm.
Step-by-step explanation:
Let us consider the side of the triangle be 3x ,4x and 5x.
According to the question,
The longest side of the triangle be 30 cm.
. 5x=30cm
x=6 cm
So the side of the triangle are 18cm ,24 cm and 30 cm.
The perimeter of the triangle is the sum of sides of the triangle.
so perimeter is =15+24+30=69 cm
a fence is to be built to enclose a rectangular area of 280 square feet. the fence along three sides is to be made of material that costs 6 dollars per foot, and the material for the fourth side costs 13 dollars per foot. find the dimensions of the enclosure that is most economical to construct.
Fencing of any rectangular region is basically represent perimeter of that rectangular region.
For most economical fencing, length L = 21.05 feet and width W = 13.301 feet.
How to estimate the length and width of the rectangular region?Area of rectangular region is 280 square feet.
And length is L and width is W.
Area of rectangular region = L × W=280 square feet
W=280 / L
Since, The fence along three sides is to be made of material that costs 6 dollars per foot, and the material for the fourth side costs 14 dollars per foot.
Therefore, Total cost, C = 6(2L + W) + 13W = 12 L + 19 W
Total cost, C = 12 L+ 5,320 / L
To find most economical cost, differentiate above function and equate to zero.
C' = 12 - 5,320 / L²
simplifying the above equation, we get
⇒ 12 - 5,320 / L² = 0
⇒ L² = 5,320 / 12
L = 21.05 feet
Therefore, L = 21.05 feet
Substituting value of L in area equation.
We get, W = 13.301 feet.
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-2 = y + 5/6 solve for y and simplify your answer as much as possible
Step-by-step explanation:
Solve for y: -2 = y + 5/6
-2 = y + 5/6 subtract 5/6 from both sides:
-2 - 5/6 = y + 5/6 - 5/6
-2 - 5/6 = y
combine left side:
-17/6 = y
so:
y = -17/6
OR:
[tex]y = -2\frac{5}{6}[/tex]
twelve hungry teenagers can devour a very large pizza in $20$ minutes. how many teenagers would it take to finish a very large pizza in $15$ minutes? (assume that all teenagers eat pizza at the same rate.)
It would take 9 Teenagers to finish a very large pizza in $15$ minutes.
From the knowlegde of Propotional method/ subject formular in mathematics;
From the questions:
12 Teens finished a very large pizza in $20$ minutes.
The number of teens to finish a very large pizza in $ 15 minutes would calculate thus,
12 Teens=$20$ minutes.
x Teens=$15$ minutes.
then we cross multiply:
x Teens × $20$ minutes =$15$ minutes × 12 Teens
making x Teens subject of the formula we have;
x Teens=$15$ minutes × 12 Teens/$20$ minutes
x Teens=9 Teens
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(7, 8) and (-1, 0)find the distance between the two points?
The distance (d) between two points is computed as follows:
[tex]d\text{ = }\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}^{}[/tex]where (x1, y1) and (x2, y2) are the points of interest. In this case, the points are (7, 8) and (-1, 0). Replacing into the equation:
[tex]d\text{ = }\sqrt{(-1-7)^2+(0-8)^2\text{ }}[/tex][tex]d\text{ = }\sqrt{(-8)^2+(-8)^2}=\sqrt{128}[/tex]which of the following additional statements would you need to prove these two triangles are by SAS similarity?
∠I ≅∠L
1) Given that the triangles are similar, then we can write:
[tex]\begin{gathered} \frac{KL}{HI}=\frac{JL}{GI} \\ \frac{18}{12}=\frac{27}{18}\text{ =}\frac{3}{2} \end{gathered}[/tex]Notice that the sides are proportional to k=3/2.
2) Since we need to prove that these triangles are similar under SAS -Side, Angle Side, examining the picture we can state that one of their corresponding angles are congruent so
[tex]\begin{gathered} \angle I\cong\angle L \\ \end{gathered}[/tex]3) Having one of these angles as congruent would fit to prove that these triangles are similar by SAS similarity.
Answer:
∠I ≅∠L
Step-by-step explanation:
Can someone help me with my practice? I am having trouble with this question.
We are to solve an inequality and give the answer in graph form.
The inequality is:
[tex]6-5+n\ge\text{ 18}[/tex]Let's solve for n in order to be able to answer the question.
we start by trying to isolate n on one side of the inequality symbol. So first combine 6-5 = 1 and re-write the inequality:
[tex]1+n\ge18[/tex][tex]\begin{gathered} n\ge18-1=17 \\ n\ge17 \end{gathered}[/tex]Now, subtract 1 from both sides, and you get the final answer:
n must be larger than or equal to 17. WHich agrees with the first answer option provided by the problem.
Funds are distributed to five families affected by floods in the ratio 5:12:2:15:29. The total amount that the five families received was $630.
a) The first family received _____
b) The difference between the amount of money the first and last family received was _____
c) A sixth family joins. They receive n amount of money and the average amount of money donated to all six families becomes 140. How much money does the sixth family receive?
Step-by-step explanation:
We must first add up the ratios:5+12+2+15+29 = 63, this will be the total ratio the money was shared Then we pick out the ratio for each family accordingly:For the first family, 5 out of the total ratio = 5/63
For the second family, 12 out of the total ratio = 12/63
For the third family, 2 out of the total ratio = 15/63
For the fifth family, 29 out of the total ratio = 29/63
a) The first family = 5/63 of the money, $630
we can therefore say the money they received is
= 5/63 ×630
= $50
b) The last family = fifth family = 29/63 of the money, 630
= 29/63 × 630
= $290
recall that the first family received $50 , the positive difference between the money received by both the first and last family
= $290 - $50
= $240
c) Since another family joins in, the total number of families become 6
the money the received is nwe can't find the average without knowing what the second, third, and fourth family received out of that money
we apply the same stepthe second family = 12/63 ×630
= $120
the third family = 2/63 × 630
= $20
the fourth family = 15/63 × 630
= $150
Average generally is = total sum/ frequency or number of occurrences or peoplein this case, we were told the average became $140
which means that
sum of money received by the families/ the number of families involved in the sharing = $140
( $50+$120+$20+$150+$290+n)/6 = $140($630+n)/6= $140
now the plan would be to make n subject of formula
multiply both sides of the equation by 6, the equation will become$630+n = $840
take $630 to the other side, it becomes -$630
n = $840-$630
n = $210
therefore the newly added family received $210
I honestly hope I explained it properly...thank you
If a rectangle is drawn and another rectangle is drawn so that the sides are twice asbig as the first rectangle, what happens to the area? (remember k^2 for area)A.) quadruplesB.) doublesC.) triplesD.) not enoughInformation
Let the rectangle with side as x and y.
Determine the area of the rectangle.
[tex]\begin{gathered} A=x\cdot y \\ =xy \end{gathered}[/tex]The sides of the rectangle is increased by twice means that new sides are 2x and 2y.
Determine the area of new rectangle.
[tex]\begin{gathered} A^{\prime}=2x\cdot2y \\ =4xy \\ =4A \end{gathered}[/tex]So new area is four times the previous rectangle.
Thus correct answer is option A quadruples.
Graph line with slope 1/2 passing through the point (-1,3)
Answer:
Step-by-step explanation:
First, graph your first point at (-1,3) Then, take your slope which is 1/2 and use rise over run. So from your point of (-1,3) go up 1 in your y coordinate, and 2 in your x coordinate. So your next point should be at (1,4)
hassan is cooking some rice.
the recipe says he needs 450 granms of rice for 6 people
how many kilograms of rice would he need for 18 people
Answer:
Round 1350 to decimal form and your answer should be 1.35 kg.
A triangle has two sides of length 12 and 12. What is the largest possible whole-number length for the third side?
The largest possible whole-number length for the third side of the triangle is 23.
The total of any two sides in a triangle with sides a, b, and c MUST be less than the length of the third side.
You have a line segment, not a triangle if the third side's length equals the sum of the other two sides' lengths.
Here, the sum of the two sides of the triangle is 12 + 12 = 24.
Therefore, the length of the third side should be less than 24, and the whole number which is less than 24 is 23.
Hence, the length of the third side is 23.
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brainly 100!!! Which of the following functions is graphed below?
The function that is represented on the graph is (a) y = x^2 + 4, x < 2 and y = x + 4, x ≥ 2
How to determine the graphed function?The graph represents the given parameter
From the graph, we have the following function types
Whole graph: Piecewise functionQuadratic function to the leftLinear function to the rightUsing the options as a guide, we have the equations to be
Quadratic function: y = x^2 + 4Linear function: y = x + 4Next, we calculate the domain
The quadratic function stops at x = 2 with an open circle
So, the domain is x < 2
The linear function starts at x = 2 with a closed circle
So, the domain is x ≥ 2
Hence, the graphed function is (a)
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The table lists recommended amounts of food to order for 19 party guests. Nathan and Sydney are hosting a graduation party for 40 guests. They know there will also be guests stopping by who may have come from other parties. For ordering purposes, they will count each of these "drop-in" guests as half a guest. How much of each food item should Nathan and Sydney order for a graduation party with 15 drop-in guests?table: fried chicken =28 meats =4 1/3 lasangnia = 10 3/4
For the graduation party, Nathan and Sydney should order pieces of 70 fried chicken , 11 pounds of meats and 36 pounds of lasangnia .
In the question ,
it is given that
there are 15 drop in guests , and drop in guests are counted as half a guest .
So , the number of half guests = 15/2 = 7.5
number of guests for the party = 40 guests
So , total number of guests = 40+7.5 = 47.5
From the table , we can see that
19 party guests need 28 pieces of fried chicken .
So , 1 party guests will need 28/19 pieces of fried chicken .
so, 47.5 guests will need [tex]47.5*\frac{28}{19}[/tex] pieces of fried chicken
[tex]47.5*\frac{28}{19}[/tex] = 70
hence , 70 pieces of fried chicken is needed .
From the table , we can see that
19 party guests need [tex]4\frac{1}{3}[/tex] = 13/3 pounds of meats .
so, 1 party guests will need 13/(3*19) pounds of meats .
So, 47.5 guests will need [tex]47.5*\frac{13}{3*19}[/tex] pounds of meats .
[tex]47.5*\frac{13}{3*19}[/tex] = 10.833
≈ 11
hence , 11 pounds of meats is needed .
From the table , we can see that
19 party guests need [tex]10\frac{3}{4}[/tex] = 43/3 pounds of lasangnia .
So , 1 party guests will need 43/(3*19) pounds of lasangnia .
So, 47.5 guests will need [tex]47.5*\frac{43}{3*19}[/tex] pounds of lasangnia .
[tex]47.5*\frac{43}{3*19}[/tex] = 35.8333
≈ 36
hence , 36 pounds of lasangnia is needed .
Therefore , For the graduation party Nathan and Sydney should order 70 pieces of fried chicken , 11 pounds of meats and 36 pounds of lasangnia .
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Hello I'm trying to figure out this math problem can anyone help me
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
Earnings:
January = $2350
February = january + $500
March = twice as much (february)
Step 02:
March's earnings:
February = $2350 + $500 = $2850
March = 2 * $2850 = $5700
The answer is:
She earned $5700 in March
