If x = 1/4 and Y = 3/7
Evaluate the following expression: 7x - 4y
[tex] \\ [/tex]
[tex] \rm{7 ( \frac{1}{4}) - 4( \frac{3}{7} ) } \\ [/tex]
Substitute the given value of x and y[tex] \rm { \orange{7 \times \frac{1}{4} }} - 4 \times \frac{3}{7} \\ [/tex]
Calculate the product of the rational numbers[tex] \rm{ \frac{7}{4} - \orange{ 4 \times \frac{3}{7 }} } \\ [/tex]
Calculate the product of the rational numbers[tex] \rm \orange{ \frac{7}{4} - \frac{12}{7} } \\ [/tex]
Find the difference between the two fractions[tex] = \small{\boxed{{\sf{ \frac{1}{28} }}}}[/tex]
Therefore, the answer is 1/28.
Answer:
Step-by-step explanation:
[tex]\text{Substitute the values of x and y in the expression}[/tex]
[tex]7x - 4y = 7*\dfrac{1}{4}-4*\dfrac{3}{7}[/tex]
[tex]\sf =\dfrac{7}{4}-\dfrac{12}{7}\\\\ [LCM \ of 4 \ and \ 7 = 28]\\\\ =\dfrac{7*7}{4*7}-\dfrac{12*4}{7*4}\\\\=\dfrac{49}{28}-\dfrac{48}{28}\\\\=\dfrac{1}{28}[/tex]
Algebra Find the value of x.
Answer:
x = 12
Step-by-step explanation:
Theorem of Thales
[tex]\frac{28}{12} =\frac{x+(x-3)}{x-3}[/tex]
[tex]\frac{28}{12} =\frac{2x-3}{x-3}[/tex]
[tex]28(x-3)=12(2x-3)[/tex]
[tex]28x-84=24x-36[/tex]
[tex]28x-24x=-36+84[/tex]
[tex]4x=48[/tex]
[tex]x=48/4[/tex]
[tex]x=12[/tex]
Hope this helps
Which ordered pair maximizes the objective function p = 3x 8y? (0, 0) (2, 7) (5, 6) (8, 1)
The ordered pair maximizes the objective function p = 3x + 8y will be (5, 6) .Option C is correct.
What is the objective function?The objective function is simply an equation that represents the goal production capability that relates to maximizing profits in relation to manufacturing.
On putting the values we will get the values one by one. We get;
1. (0, 0)
[tex]3 (0)+8(0) = 0[/tex]
2. (2,7)
[tex]3(2)+8(7)=62[/tex]
3. (5,6)
[tex]3(5)+8(6)=63[/tex]
4. (8,1)
[tex]3(8)+8(1)=42[/tex]
The maximum value obtained from the 63. Obtained from option C. The ordered pair maximizes the objective function p = 3x + 8y will be (5, 6)
Hence option C is correct.
To learn more about the objective function refer to the link;
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A figure is broken into a rectangle and a triangle. The triangle has a base of 2 and two-thirds feet and height of 3 feet. The rectangle has a base of 5 feet and height of 1 and one-third feet.
The irregular figure can be broken into a triangle and a rectangle as shown with the dashed line.
The length of b, the base of the triangle, is
ft.
The area of the triangle is
The area of the rectangle is
The area of the irregular figure is
Answer:
See belowStep-by-step explanation:
The length of b, the base of the triangle, is
5 - 2 1/3 = 3 - 1/3 = 2 2/3 ftThe area of the triangle is
A = 1/2*3*(2 2/3) = (3/2)(8/3) = 8/2 = 4 ft²The area of the rectangle is
1 1/3 * 5 = 4/3 * 5 = 20/3 = 6 2/3 ft²The area of the irregular figure is
4 + 6 2/3 = 10 2/3 ft²Answer:
[tex]b=2\frac23\:\sf ft[/tex]
Area of triangle = 4 ft²
Area of rectangle = [tex]6\frac23\: \sf ft^2[/tex]
Area of irregular figure = [tex]10\frac23\: \sf ft^2[/tex]
Step-by-step explanation:
[tex]\begin{aligned}\sf Base\:of\:triangle\:(b) & = 5-2\frac13\\\\& = \dfrac{15}{3}-\dfrac73\\\\ & = \dfrac83\\\\ & = 2\frac23\:\sf ft \end{aligned}[/tex]
[tex]\begin{aligned}\sf Area\:of\:a\:triangle & =\dfrac12 \sf \times base \times height\\\\& = \dfrac12 \times b \times 3\\\\ & = \dfrac12 \times \dfrac83 \times \dfrac31\\\\ & = \dfrac{24}{6}\\\\ & = 4\: \sf ft^2\end{aligned}[/tex]
[tex]\begin{aligned}\sf Area\:of\:rectangle& =\sf length \times width\\\\& = 5 \times 1\frac13\\\\ & = \dfrac51\times \dfrac43\\\\& = \dfrac{20}{3}\\\\ & = 6\frac23\: \sf ft^2\end{aligned}[/tex]
[tex]\begin{aligned} \sf Area\:of\:irregular\:figure & = \sf area\:of\:triangle+area\:of\:rectangle\\\\ & = 4 + 6\frac23\\\\ & = 10\frac23\: \sf ft^2\end{aligned}[/tex]
Teresa makes $26.4 from selling $52.8 ounces of lemonade. Find the unit price in dollars per ounce. If necessary, round your answer to the nearest cent.
Hi There! Hope you are having a great day! As you know, you need to find the unit rate of the problem. In order to do that you must divide how much ounces there is, (52.8) and divide that integer by how much money she made (26.4) leaving you with a unit rate of 2. Hope this helps! :)
A right rectangular prism is sliced perpendicular to its base.
What is the shape of the resulting two-dimensional cross section?
trapezoid
rectangle
triangle
Answer:
rectangle!
Step-by-step explanation:
Just finished the test for k-12
Answer:
Rectangle
Step-by-step explanation:
WILL GIVE BRAINLEIST!!!
What is the best way to describe the center of the data represented in this line plot?
Select from the drop-down menus to correctly complete the statement.
The Choose...is Mean or median Choose.... 2 inches 2.5 inches 3 inches or 3.2 inches
Considering that the data has no outliers, the mean of 3.2 inches should be used to describe the center of the data represented in this line plot.
What measure should be used to describe the center of a data-set?It depends if the data-set has outliers or not.
If it does not have outliers, the mean should be used.If it has, the median should be used.The dot plot gives the number of times each measure appears. Since there is no outliers, that is, all values are close, the mean should be used. It is given by:
M = (2 x 1 + 3 x 2 + 2 x 3 + 1 x 5 + 1 x 6 + 1 x 7)/(2 + 3 + 2 + 1 + 1 + 1) = 3.2 inches.
The mean of 3.2 inches should be used to describe the center of the data represented in this line plot.
More can be learned about the mean of a data-set at https://brainly.com/question/24628525
Answer: median 2.5
Step-by-step explanation:
PLS HELP WILL MARK YOU BRAINLIEST! NO FAKE ANSWERS!
Answer:
See below ~
Step-by-step explanation:
We know the sum of the interior angles is 720° for a hexagon.
Finding x
2(90)° + 2(5x + 10)° + 136° + 134° = 720°180° + 10x° + 20° + 270° = 720°10x° + 470° = 720°10x° = 250°x = 25Finding m∠ABC
∠ABC = 5x + 10∠ABC = 5(25) + 10∠ABC = 125 + 10∠ABC = 135°What is the value of t?
What is the volume of the right triangular prism in cubic meters
Answer: 24 cubic meters
Step-by-step explanation:
The formula for the volume of a triangular prism is [tex]\frac{1}{2}[/tex]bhl
Where
b is the base (3 for this)
h is the height (2 for this)
and l is the length (8 for this)
Sub the values into the formula and solve
[tex]\frac{1}{2}bhl\\\frac{1}{2}(3)(2)(8)\\\frac{1}{2}(3)(16)\\\frac{1}{2}(48)\\24[/tex]
What is the Median of the numbers 20, 18, 14, 7, 15, 5
Answer:
The answer should be 14.5
Step-by-step explanation:
Hope This Helps
Have A great day
~Zero~
Which is true?
A) 36 feet = 3 inches
B) 36 inches = 3 feet
C) 36 yards = 3 feet
D) 36 feet = 3 yards
Answer:
option D
Step-by-step explanation:
becuase 36=3 feet
What are the coordinates of the y-intercept of the graph of y=–4x+5? (0, 5) (0, -5) (-5, 0) (5, 0)
Answer:
(0, 5)
Step-by-step explanation:
y = mx + b <== slope-intercept form of a straight line
m <== slope of the line
b = y-intercept (when x = 0)
y = -4x + 5
Therefore, for this line, the y-intercpet is (0,5)
Hope this helps!
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The solutions are all the points strictly larger than 5, to represent this, we draw an open circle at x = 5, and a bold line that points to the right.
How to represent the inequality?
Here we have the inequality:
–3(2x – 5) < 5(2 – x)
First, we need to isolate x in one side of the inequality, we will get:
-6x + 15 < 10 - 5x
15 - 10 < -5x + 6x
5 < x
Then the solutions are all the points strictly larger than 5, to represent this, we draw an open circle at x = 5, and a bold line that points to the right.
If you want to learn more about inequalities, you can read:
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What is 77x145 ?What do I do??
Answer:
11165
Step-by-step explanation:
77*145= 11165
Hope this helps. :D
Which statements are true about the polynomial 28vw 49v 35w? check all that apply. the coefficients have no common factors other than 1. there are no common variables among all three terms. the gcf of the polynomial is 7v. each term written as the product, where one factor is the gcf, is 7(28vw) 7(49v) 35(w). the resulting expression when factoring out the gcf is 7(4vw 7v 5w).
The statements that are true about the considered polynomial are:
Option 2: There are no common variables among all three termsOption 5: The resulting expression when factoring out the gcf is 7(4vw+7v+5w)How to find Greatest common factor?Greatest common factor, as the name implies, is greatest among all common factors among the quantities given.
We can factorize the quantities in smallest relative factors possible (one level of factors over which all quantities can form themselves), and collect as many common factors as we could. Those will together compose GCF(Greatest common factor).
The considered polynomial is: 28vw + 49v + 35w
Checking all the options:
Option 1: The coefficients have no common factors other than 1False.
Coefficients are numbers in multiplication with variables in each term.
The coefficients of the considered polynomial are 28, 49, 35
They are all multiple of 7 and 1, so the common factor is 7 too, along with 1.
Option 2: There are no common variables among all three termsYes its true.
It is because none of the variables v, or w are in all the three terms.
Option 3: The gcf of the polynomial is 7v.False.
First term = 28vw = [tex]7\times 4 \times v \times w[/tex]Second term = 49v = [tex]7\times 7 \times v[/tex]Third term = 35w = [tex]7 \times 5 \times w[/tex]Thus, the greatest factor that is common in all three terms is 7 and not 7v.
Option 4: Each term written as the product, where one factor is the gcf, is 7(28vw) 7(49v) 35(w)False.
Because, each term written as product of gcf gives:
First term = 28vw = [tex]7\times 4vw[/tex]Second term = 49v = [tex]7\times 7v[/tex]Third term = 35w = [tex]7 \times 5w[/tex]Option 5: The resulting expression when factoring out the gcf is 7(4vw+7v+5w)True.
It is because:
[tex]7(4vw+7v+5w) = 28vw + 49v + 35w[/tex] = the considered polynomial, and that 7 is the gcf.
Thus, the statements that are true about the considered polynomial are:
Option 2: There are no common variables among all three termsOption 5: The resulting expression when factoring out the gcf is 7(4vw+7v+5w)Learn more about greatest common factor here:
https://brainly.com/question/207329
Answer:
The coefficients have no common factors other than 1.
There are no common variables among all three terms. <----
The GCF of the polynomial is 7v.
Each term written as the product, where one factor is the GCF, is 7(28vw) + 7(49v) + 35(w).
The resulting expression when factoring out the GCF is 7(4vw + 7v + 5w).
^^^^
Step-by-step explanation:
B and E i just did it on edg
I don’t know it and need help with this problem.
Emilio is helping pass out modeling clay in art class. He takes three 2-pound bricks of clay
from the supply shelf. His job is to give each student 4 ounces of clay, but he runs out before
he can finish. If his class has a total of 28 students, how many more ounces of clay does he
need?
Answer:
16 ounces
Step-by-step explanation:
1 pound = 16 ounces. Each clay block is 2 pounds so each of them are 32 ounces.
32 x 3 = 96
Divide 96 by the 4 ounces for each student, 96 ÷ 4 = 24
The clay is only enough for 24 students, leaving 4 students out, each need 4 ounces, so multiply the 4 students by the 4 ounces.
4 x 4 = 16
Therefore, 16 ounces are needed. Hope this helped!
A small box in the shape of a cube for packaging has a volume of 64 cubic inches.
For a medium box, the length, width, and height are all doubled. What is the ratio of the sides, area of the bases, and volumes of the boxes? Show your work.
What is the volume of a medium box? Show your work.
Ratios
Sides:
Area:
Volume:
What are the ratio of the small box to the medium box?
The first step is to determine the side lengths of the small box.
Side length = ∛64 = 4 in
Side lengths of the medium boxes = 4 x 2 = 8 inches
Volume of the medium box = 8³ = 256 cubic inches
The ratio of the sides of the small box to the medium box = 4 : 8 = 1:2.
The ratio of the area of the small box to the medium box= (4 x 4) : (8 x 8) = 1:4.
The ratio of the volume of the small box to the medium box = 4³ : 8³ = 1 : 8.
To learn more about the volume of a cuboid, please check: https://brainly.com/question/26406747
Find the
volume of a
rectangular prism
with dimensions of
12 ft. high, 14 ft.
wide, and 9 ft. long.
*Don't forget units.
Answer:
1,512 ft cubed
Step-by-step explanation:
Volume Formula is Length times Width times Height.
Do 9ft x 14ft x 12ft = n ft cubed
**n is a variable used**
1,512 ft cubed is the correct answer.
-
If sec 0= √ 2, find the two values of O between
0° and 360°.
[tex]\sec \theta = \sqrt 2\\\\\implies \cos \theta = \dfrac 1{\sqrt 2}\\\\\implies \theta = 2n\pi \pm \dfrac{\pi}4\\\\\\\text{In the interval}~ 0 < \theta < 2\pi, \\\\\theta = \dfrac{\pi}4, \dfrac{7\pi}4~~ \text{or}~~ \theta = 45^{\circ}, 315^{\circ}[/tex]
For each expression, select all equivalent expressions from the list.
(a) 11x - 4x + 10x
O 7x + 10x
0 17 + x
10x - 7x
17x
(b) 2(1+8y)
2+1.2 +8y
2 +16y
02.1+2.8y
O2 + 8y
I can’t figure them all out please help.
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's find the equivalent expressions ~
#1. PROBLEM
[tex]\qquad \tt \dashrightarrow \:11x - 4x + 10x[/tex]
[tex]\qquad \tt \dashrightarrow \:21x - 4x[/tex]
[tex]\qquad \tt \dashrightarrow \:17x[/tex]
#2. PROBLEM
[tex]\qquad \tt \dashrightarrow \:2(1 + 8y)[/tex]
[tex]\qquad \tt \dashrightarrow \:(2 \times 1) + (2 \times 8y)[/tex]
[tex]\qquad \tt \dashrightarrow \:2 + 16y[/tex]
Find the circumference of circle, in terms of pi, if the diameter is 23.7 feet. a
Answer:
I believe the answer is 74.557 I apologize if I am incorrect
Step-by-step explanation:
Which dot plot has the least number of sites
represented?
Shield Darter
Zebra Mussel
Number of Sites
Number of Sites
:
1 2 3 4 5 6 7 8 9 10
2
3
4
5
6
7 8 9 10
Number of Shield Darter
Number of Zebra Mussel
Blueback Herring
Calico Crayfish
Number of Sites
Number of Sites
2.
3
4 5 6 7 8 9 10
2 3 4 5 6 7 8 9 10
Number of Calico Crayfish
Number of Blueback Herring
The dot plot with the least number of sites has the least frequency
The dot plot has the least number of sites is the Shield Darter
How to determine the dot plot?To determine the dot plot with the least number of sites, we simply calculate the total frequency of each dot plot
So, we have:
Shield Darter = 3 + 1 + 4 + 2 + 3 + 1 + 1
Shield Darter = 15
Calico Crayfish = 1 + 1 + 3 + 4 + 1 + 2 + 4 + 2
Calico Crayfish = 18
Zebra Mussel = 1 + 3 + 2 + 5 + 1 + 1 + 2 + 3 + 2
Zebra Mussel = 20
Blue back Herring = 3 + 3 + 2 + 1 + 3 + 1 + 4
Blue back Herring = 17
From the computation above, the least frequency is
Shield Darter = 15
Hence, the dot plot has the least number of sites is the Shield Darter
Read more about dot plots at:
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Please help and explain with a bit of work
Problem: Y = 3x² - 3x + 2
Discriminant: b²-4ac = 9 - 4 (3)(2) = -15
Explain why this has no solution/ 0 real solutions. Explain the discriminant.
Answer:
Given:-
Y = 3x² - 3x + 2
Find : - Discriminant
Y = ax² - bx + c
Discriminant is : - Y = b² - 4ac
So, Discriminant is :-
(-3²) - 4 (3) (2)
= 9-24
=-15
If b² - 4ac < 0.
The equation has no real solution but it does have complex solution.
A lab is monitoring the population of mice in a sample. Scientists noticed the number of mice triples every week. If there were initially 4 mice in the sample, how many mice will there be after 6 weeks?
A. 324 Mice
B. 972 Mice
C. 2916 Mice
D. 8748 Mice
C. 2916 Mice
Step-by-step explanation:
4 x 3^6 = 2916
Because as the mice increases, you triple that amount, instead of tripling 4 & multiplying by 6.
So, you're doing this instead:
4 x 3 = 12 (1 wk)
12 x 3 = 36 (2 wk)
36 x 3 =108 (3 wk)
108 x 3 = 324 (4 wk)
324 x 3 = 972 (5 wk)
972 x 3 = 2916 (6 wk)
Hope this helps!
if you were a quadrilateral what quadrilateral are you?why?
Answer:
I would be a diamond because diamonds are one of my favorite shapes.
Step-by-step explanation:
Diamonds are a girl's best friend
Hope it Helps
Roberta's monthly bank statement says that she has a balance of 386.29, but roberta's check register says that her balance is 370.77. which of the following are still outstanding? i. a $78.17 check to the electric company ii. a $16.15 deposit from roberta's roommate iii. a $22.67 check to the grocery store iv. a $62.65 deposit from roberta's tax return a. i and ii b. ii and iii c. ii and iv d. i and iv please select the best answer from the choices provided a b c d
Answer:
D
Step-by-step explanation:
I and IV
A movie premiere had a full house of 350 film buffs. The price of the tickets was $6 for adults and $4 for underage. The income from ticket sales was $1,600. What is the number of adult's, x, who attended?
A 80
B 140
C 100
D 250
Answer:
C
Step-by-step explanation:
let x be number of adults and y the number of underage , then
x + y = 350 → (1)
6x + 4y = 1600 → (2)
multiplying (1) by - 4 and adding to (2) will eliminate y
- 4x - 4y = - 1400 → (3)
add (2) and (3) term by term to eliminate y
(6x - 4x) + (4y - 4y) = 1600 - 1400
2x + 0 = 200
2x = 200 ( divide both sides by 2 )
x = 100
the number of adults who attended is 100
from the number of card numbered from 1 to 15 orchid is drawn from random find the probability of getting a card having a prime number
Answer:
The total number of outcomes is 15.
favourable outcomes =6 (2,3,5,7,11,13)
prime number probability = 6/15