Answer:
The number of each size quilt is;
[tex]\begin{gathered} \text{ Number of large quilt = 9} \\ \text{ Number of small quilt = }6 \end{gathered}[/tex]Explanation:
Given that a large quilt requires 8 yards of fabric while the small quilt requires 3 yards of fabric.
Let x represent the number large quilt and y the number of small quilt.
If she used a total of 90 yards of fabric to make 15 quilts then we have;
[tex]\begin{gathered} 8x+3y=90\text{ ---------1} \\ x+y=15\text{ ----------2} \end{gathered}[/tex]let us solve the system of equations by substitution. From equation 2;
[tex]x=15-y[/tex]substituting into equation 1;
[tex]\begin{gathered} 8x+3y=90 \\ 8(15-y)+3y=90 \\ 120-8y+3y=90 \\ 120-5y=90 \\ 5y=120-90 \\ 5y=30 \\ y=\frac{30}{5} \\ y=6 \end{gathered}[/tex]substituting the value of y;
[tex]\begin{gathered} x=15-y \\ x=15-6 \\ x=9 \end{gathered}[/tex]Therefore; the number of each size quilt is;
[tex]\begin{gathered} \text{ Number of large quilt = 9} \\ \text{ Number of small quilt = }6 \end{gathered}[/tex]4. Taking a pill of Medicine A gives you 5 mg of an undesired substance, and a pill of Medicine B gives you 7 mg of the undesired substance. Let x be the number of A pills you take and y be the number of B pills you take. Define an objective function that could be used to minimize the amount of the undesired substance.z=
Answer:
z = 5x + 7y
Explanation:
If x is the number of A pills, the amount of undesired substance is 5 mg times x or
5x
In the same way, if y is the number of B pills, the amount of undesired substance is 7 mg per pill, so the total will be 7 mg times y or
7y
Then, the function that represents the amount of undesired substance will be
z = 5x + 7y
solve equation:3(2x-5)+4(6+x)=x+4with the steps please and thank you!
3(2x-5) + 4(6+x) = x + 4
3 * 2x - 3* 5 + 4 *6 + 4x = x + 4
6x - 15 + 24 + 4x = x + 4
Combine like terms
6x + 4x - x = 4 + 15 - 24
9x = -5
x = -5/9
Supplies for last year cost $1,477 which was $177 over ... to the nearest 1 % by what percent did the cost exceed the budgeted cost?
In order to determine the required percentage, calculate the quotient in between 177 and 1,477, and multiply the result of this by 100, as follow:
(177/1,477)(100) = 11.98 ≈ 12%
Hence, the cost exceeded 12% of the budgeted cost
with 6 seed packets how many total plants can joy have in her backyard
In the given graph the number if seeds are represnt along the x axis
and y axis represent the total number of plants
at x= 6
The line passes through y = 60
So, the number if plants are 60
Geometry Please help me!I was tested on this question and wasn’t sure what to do. I need a step by step tutorial and reasons! Thank you!
ANSWER
x = 4
EXPLANATION
Before, we begin solving, it will be helpful to make a quick sketch of the situation.
BD bisecting means that it divides
Therefore:
=> 7x - 10 = 4x + 2
Solve for x by collecting like terms:
=> 7x - 4x = 10 + 2
3x = 12
x = 12 / 3
x = 4
That is the value of x.
Which choice is equivalent to the fraction below when x2 1? Hint: Rationalize the denominator and simplify. 1 √x - √x-1 O A. - x - 1 - fx O B. x B. + VX-1 o + - 2x-1 O D. &x - √x-1
We have
[tex]\frac{\sqrt[]{8}}{\sqrt[]{2}-2}[/tex][tex]\frac{\sqrt[]{4\cdot2}}{\sqrt[]{2}-2}[/tex][tex]\frac{\sqrt[]{4}\cdot\sqrt[]{2}}{\sqrt[]{2}-2}[/tex][tex]\frac{2\sqrt[]{2}}{\sqrt[]{2}-2}[/tex]We rationalize the denominator
[tex]\frac{\sqrt[]{2}+2}{\sqrt[]{2}+2}\cdot\frac{2\sqrt[]{2}}{\sqrt[]{2}-2}[/tex]then we simplify
[tex]\frac{4+4\sqrt[]{2}}{-2}[/tex]Finally, we obtain
[tex]-2-2\sqrt[]{2}[/tex]I need help on this, this isn't a test or quiz its just an assignment
To indicate congruence of angles, we draw a semicircle-like along the angle. As we can see on the figure, angle A and angle D has one semicircle, hence, they are congruent. Angles B and E are also congruent because they both have two semicircle. Lastly, angles C and F are congruent with the same reasoning.
To indicate congruence on the lengths of the sides of the triangle, we put a line along the side. Based on this reasoning, side AB and side ED are congruent since these sides have one line.
Side CB has two lines. But the other triangle doesn't have any side that has 2 sides. But we can see on triangle ACB that the side CB is along angles C and B. This is congruent to the side EF with angles E and F. Hence, side CB is congruent with side EF.
Lastly, we have side CA which is not evaluated yet. It lies between angles A and C. This is the same as the side FD that lies between angles F and D. Hence, side CA is congruent with side FD.
Answer:
[tex]\begin{gathered} \angle A\cong\angle D \\ \angle B\cong E \\ \angle C\cong\angle F \\ CB\cong FE \\ AB\cong ED \\ CA\cong FD \end{gathered}[/tex]Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y = 57(1.05)x
You have the following exponential function:
y = 57(1.05)ˣ
the general form of an exponential function is given by:
y = abˣ
if b is greater than 1, then, the percentage rate increases, otherwise, decreases.
In this case, b = 1.05, and the rate of increase is given by 1.05 - 1.00 = 0.05
which is equivalent to an increase of 5%.
Then:
The rate of increase is 5% and the change represent a growth
Fred bought six new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only forty cards left. How many cards did Fred start with ? show work
EXPLANATION
Let's consider the facts:
Number of trading cards bought = 6
Then, he had 2x 29= 58 cards on the next day
Subtracting 6 from 58 give us:
58 - 6 = 52
Answer: Fred had 52 cards
Solve for all values of x in simplest form. -4|5x + 1| – 5 = -53
Simplify the equation -4|5x+1|-5=-53.
[tex]\begin{gathered} -4|5x+1|-5=-53 \\ -4|5x+1|=-48 \\ |5x+1|=\frac{-48}{-4} \\ |5x+1|=12 \end{gathered}[/tex]The equation |5x+1|=12 can be expressed as 5x+1=12 and 5x+1=-12.
Simpify the equation 5x+1=12 to obtain the value of x.
[tex]\begin{gathered} 5x+1=12 \\ 5x=11 \\ x=\frac{11}{5} \end{gathered}[/tex]Simplify the equation 5x+1=-12 to obtain the value of x.
[tex]\begin{gathered} 5x+1=-12 \\ 5x=-13 \\ x=\frac{-13}{5} \end{gathered}[/tex]So possible value of x is 11/5 and -13/5.
Team A won 102 games Team A lost 60 gamesWhat percentage of the games did Team A lose? (See 62.9%.) What's the sum of the win percentage & the loss percentage?
Let's calculate the percentage of games lost by team A.
[tex]\begin{gathered} \frac{60}{162} \\ 37.1\text{ \%} \end{gathered}[/tex]Team A's loss percentage is 37.1%.
The sum of the winning and losing percentages is 100%.
Question #18The graph shows the solution of a linear equation.Y1051010What is the linear equation?Аy=-43 +4By=-3x +4Cy=32 +2
Answer:
B. y = -3x + 4
Explanation:
To know the equation of a line, we need to find the slope m and the y-intercept b. Then, the equation of the line will be:
y = mx + b
So, the slope of the line can be calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x1, y1) and (x2, y2) are two points in the line.
So, replacing (x1, y1) by (0, 4) and (x2, y2) by (2, -2), we get:
[tex]m=\frac{-2-4}{2-0}=\frac{-6}{2}=-3[/tex]Then, the y-intercept is the point where the graph crosses the y-axis, in this case, the y-intercept is the point (0, 4) so the value of b is 4.
Therefore, the equation of the line is:
y = -3x + 4
So, the answer is:
B. y = -3x + 4
Find the Values of each of the angles marked z and y.Angles given are 70,50 and 28
First, we need to start off by finding the angle adjacent (next to) y.
We can find this angle because we know that the angles in a triangle add up to 180 degrees, and we are given 2 of the other angles.
We can find the last angle by subtracting the value of these angles from 180:
[tex]180-(70+50)=60[/tex]Now, we can find the measure of angle y by using the knowledge that the angle of a straight line is 180 degrees. If y and the angle 60 make up the line, then y must be equal to:
[tex]\begin{gathered} y=180-60 \\ y=120 \end{gathered}[/tex]The angle y is equal to 120 degrees.
Now that we have the angle y, we can find angle z by using the same method we did to calculate the missing angle on the lefthand side, next to y.
Let's add up angle y and 28 and subtract this from 180 degrees:
[tex]180-(120+28)=32[/tex]The angle z is equal to 32 degrees.
Round all answers to the nearest hundredth, 2 places after the decimal. a. Find A ifr = 8. b. Find A if r = 14.62 c. Find A if d = 28 d. Find A if d = 15.4
What is the sum of 7 over 6 and 5 over 8
Given:
The sum of 7 over 6 and 5 over 8
To determine the sum of 7 over 6 and 5 over 8, we rewrite the given information first into:
[tex]\frac{7}{6}+\frac{5}{8}[/tex]Next, we note that the Least Common Denominator (LCD) of 6 and 8 is 24 and to make the denominators the same as the LCD:
[tex]\begin{gathered} \frac{7(4)}{6(4)}+\frac{5(3)}{8(3)} \\ \end{gathered}[/tex]Then, simplify:
[tex]\begin{gathered} =\frac{28}{24}+\frac{15}{24} \\ =\frac{43}{24} \end{gathered}[/tex]Therefore, the answer is 43/24.
Suppose you roll a special 8-sided die. What is the probability that the number rolled is a "1" OR a "2"? Round to 3 decimal places. Question
we have that
total numbers =8
The probability of getting any number is
P=1/8
so
The probability of getting a 1 or a 2 is
P=2/8 --------> 1/8+1/8=2/8
simplify
P=1/4
P=0.25pls help im really stuck on i’ll highly appreciated it
EXPLANATION :
From the problem, the taxi charges a flat rate of $3 and an additional $0.50 per mile.
Let x = number of mile
and y = total cost
The equation will be :
[tex]y=3+0.50x[/tex]Carl will take a taxi if the total cost is under $10.
Carl is 15 miles from home.
The inequality will be :
[tex]\begin{gathered} y\le10 \\ 3+0.50x\le10 \end{gathered}[/tex]For him to take a taxi, otherwise he will take a bus.
Substitute x = 15 miles :
[tex]\begin{gathered} 3+0.50(15)\le10 \\ 3+7.50\le10 \\ 10.50\le10 \\ False \end{gathered}[/tex]Since the total cost is greater than $10. He will take a bus.
ANSWER :
Carl will take a bus.
g(x)= 6/x find (g°g)(x)
Solution:
Give the function below
[tex]g(x)=\frac{6}{x}[/tex]To find (gog)
[tex]\begin{gathered} (g\circ g)=\frac{6}{\frac{6}{x}}=6\div\frac{6}{x}=6\times\frac{x}{6}=x \\ (g\circ g)=x \end{gathered}[/tex]Hence, the answer is x
The darkened sides in the figure are the edges of the roof this trim will be painted white find the length of each of these sides of the triangle explain or show work
a)
The given triangle is an isosceles triangle. A line is drawn to represent the perpendicular height as shown below
AD represents the height of the triangle.
AB = AC = sides of the triangle
Taking angle C as the reference angle,
AC = hypotenuse
CD = 8.5 = adjacent side
AD = opposite side
We would find AC by applying the cosine trigonometric ratio which is expressed as
Cos θ = adjacent side/hypotenuse
Cos36 = 8.5/AC
AC = 8.5/Cos36
AC = 10.51
The length of each side of the triangle is 10.51 m
b) Area of triangle = 1/2 x base x height
To find AB, we would apply Pythagorean theorem which is expressed as
hypotenuse^2 = opposite side^2 + adjacent side^2
10.51^2 = AB^2 + 8.5^2
AB^2 = 10.51^2 - 8.5^2 = 38.21
AB = √38.21 = 6.18
Area = 1/2 x 17 x 6.18
Area of triangle = 52.53 m^2
A toxic radioactive substance with a density of 2 milligrams per square centimeter is detected in the ventilatingducts of a nuclear processing building that was used 47 years ago. If the half-life of the substance is 20 years,what was the density of the substance when it was deposited 47 years ago? round to the nearest tenth.
The equation for calculating exponential decay is expressed as
A = Aox^t/T
where
A is the final amount after t years
Ao is the initial amount
x is the rate of change
t is the number of years
T is the time taken to achieve the change.
From the information given,
A = 2
t = 47 years
x = 1/2 = 0.5
T = 20
We want to find Ao
By substituting these values into the formula,
2 = Ao(0.5)^(47/20)
2 = Ao(0.5)^2.35
Dividing both sides by (0.5)^2.35, we have
Ao = 2/(0.5)^2.35
Ao = 10.2
the density of the substance when it was deposited 47 years ago is 10.2 milligrams per square centimeter
11. Which expression is equivalent to -2x + 5 ?10 - 4x - 5 + 2x3(2x + 1) - X-13x + 5- X - 10O -x - 9 + 4x + 4
Simplify each expression as follows:
[tex]\begin{gathered} 10-4x-5+2x=10-5-4x+2x \\ =(10-5)+(-4x+2x) \\ =5-2x \end{gathered}[/tex][tex]\begin{gathered} 3(2x+1)-x-1=3(2x)+3(1)-x-1 \\ =6x+3-x-1 \\ =6x-x+3-1 \\ =5x+2 \end{gathered}[/tex][tex]\begin{gathered} 3x+5-x-10=3x-x+5-10 \\ =2x-5 \end{gathered}[/tex][tex]\begin{gathered} -x-9+4x+4=-x+4x-9+4 \\ =3x-5 \end{gathered}[/tex]Therefore, the only expression that is equivalent to -2x+5 is 10-4x-5+2x.
Which letter on the diagram below repersents the name of the circle
A circle is named by its center. For the given diagram, the center is point A. Hence, it has a name circle A
Answer: Option C
Which of the following exponential functions represents the graph below?O A. f(x) = 5 •3*OB. f(x) = 3.5xOC. f(x) = 5.(1)OD. f(x) = 3.(3)540-5105
Answer: D.
Explanation
The exponential function:
[tex]f(x)=a^x[/tex]Has the form:
Thus, if we evaluate the graph given, we would see that instead of going to the right as the function above, it goes to the left, meaning that whole numbers do not represent our function.
Additionally, we can see that the function represented in the graph has a y-intercept at (0,3):
Meaning that when x = 0, y must be equal to 3.
If we set x = 0 in function C and D we would see that:
[tex]f(0)=5\cdot(\frac{1}{3})^0=5[/tex][tex]f(0)=3\cdot(\frac{1}{5})^0=3[/tex]Therefore, our function is:
[tex]f(x)=3\cdot(\frac{1}{5})^x[/tex]find sum of arithmetic series where a1 = 7, n=31, an=127
2077
Explanation
To find the sum of an arithmetic sequence, use the formula
[tex]\begin{gathered} S_n=n(\frac{a_1+a_n}{2}) \\ \text{where} \\ n=the\text{ number of terms being added} \\ a_1=the\text{ firs term} \\ a_n=the\text{ nth term}(\text{ last term)} \end{gathered}[/tex]Step 1
Let
[tex]\begin{gathered} a_1=7 \\ n=31 \\ a_n=127 \end{gathered}[/tex]now, replace and calculate
[tex]\begin{gathered} S_n=n(\frac{a_1+a_n}{2}) \\ S_n=31(\frac{7+127}{2}) \\ S_n=31(\frac{134}{2}) \\ S_n=31(67) \\ S_n=2077 \end{gathered}[/tex]therefore, the answer is
2077
I hope this helps you
The slope of the given line is: 2. 4. -2. None of these choices are correct.
great, with the graph and the line equation
y=mx+b
m is the slope and b is, in this case, b= 4 (where the line cross the x=0)
so know we have y=mx+4
we know the line cross over the point x=2 y=0
so if we replace it on the equation we will find the slope
0=m*2+4
-4=m*2
-4/2=m
m=-2
the answer is m= -2
please i need help with a question i need to know are 3/8 and 3/4 equivalent fraction? draw a number line to decide.
For this problem, we need to know whether the numbers 3/8 and 3/4 are equivalent fractions. And we need to draw a number line to decide.
This is done below:
As we can see from the lines above, the two numbers are in different positions, therefore they are not equivalent fractions.
See your levelsDEA 9-pack of plastic flower pots costs $9.72. What is the unit price?per pot
The unit price can be calculated as:
[tex]\text{unit price=}\frac{\text{ cost of the pack}}{\text{units on the pack}}[/tex]Since every pack costs $9.72 and there are 0 plastic flower pots per pack, the unit price is:
[tex]\text{unit price = }\frac{9.72}{9}=1.08[/tex]Answer: $1.08 per pot
12^x = 94Solve the equations and check for extraneous solutions
Given
[tex]12^x=94[/tex]Solve for x as shown below
[tex]\begin{gathered} \Rightarrow ln(12^x)=ln(94) \\ \Rightarrow xln(12)=ln(94) \\ \Rightarrow x=\frac{ln(94)}{ln(12)}\approx1.8284 \end{gathered}[/tex]The exact answer is x=ln(94)/ln(12). There are no extraneous solutions.
2. What is a solution of x2 + 6x = -5? (1 point)
x= -6
x=-1
Ox=1
x=6
So, the two possible solutions are -1 and -5
0.36 and 1/2 to a percent
Solution
Step 1
To convert a number to percent, multiply the number by 100
step 3
[tex]0.36\text{ x 100 = 36\%}[/tex][tex]\frac{1}{2}\times\text{ 100\% = 50\%}[/tex]