Let m represent the number of apple pies Sam is making and
Let n represent the number of pumpkin pies Sam is making
If Sam sells a total of 80 pies, this can be represented by
m + n = 80 ------------------------------equation (1)
If she makes a total of $512 on the same day, this cost can be represented by
6m + 7n = 512 ----------------------------equation (2)
Solving both equations simultaneously
m + n = 80
6m + 7n = 512
from m + n = 80,
m = 80 - n
substitute m = 80 - n into equation (2)
we have
6(80 -n) + 7n = 512
480 - 6n + 7n = 512
480 + n = 512
n = 512 - 480
n = 32
Put n = 32 into m = 80 - n
we have
m = 80 - 32
m = 48
The number of apple pies Sam sell is 48
Brad expects that he will need $12,000 in 6 years to start an engineering consulting business. He has been offered an investment at 5%, compounded monthly. How much must he invest today to have enough money in 6 years? How much interest will he have earned?
Answer:
Invest today: $8895.36
Interest earned: $3104.64
Explanation:
The amount after t years can be calculated as:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where P is the initial amount invested, r is the interest rate and t is the number of years and n is the number of times the interest rate is compound. Solving the equation for P, we get:
[tex]P=\frac{A}{(1+\frac{r}{n})^{nt}}[/tex]Now, we can replace A by $12,000, r by 5% = 0.05, n by 12 because it is compounded monthly and t by 6
[tex]P=\frac{12000}{(1+\frac{0.05}{12})^{12(6)}}=8895.36[/tex]Therefore, he should invest $8895.36 today to have enough money in 6 years.
Finally, the interest earned is calculated as
$12000 - $8895.36 = $3104.64
So, the answers are:
Invest today: $8895.36
Interest earned: $3104.64
8i+ 5 - 2i equals 3i+ 23
We will have:
[tex]8i+5-2i=3i+23[/tex]We will operate like terms and solve for i, that is:
[tex]8i-2i-3i=23-5\Rightarrow3i=18\Rightarrow i=6[/tex]*Step by step:
[tex]8i+5-2i=3i+23\Rightarrow6i+5=3i+23[/tex][tex]\Rightarrow6i+5-5=3i+23-5\Rightarrow6i=3i+18[/tex][tex]\Rightarrow6i-3i=3i+18-3i\Rightarrow3i=18[/tex][tex]\Rightarrow\frac{3}{3}i=\frac{18}{3}\Rightarrow i=6[/tex]Select the correct answer.What are the asymptote and the y-intercept of the function shown in the graph?
Answer:
Explanation:
Here, we want to get the y-intercept and the asymptote of the shown function
The y-intercept is simply the point at which the curve crosses the y-axis
We can see this at the point y = 5 which is coordinate form is (0,5)
The asymptote is the point on the y-axis where the curve almost flattens out but will never touch
We have this at the point y = 2
1 Factor each polynomial over the set of realC)f(x) = x^4- 25x^2 + 144
Notice that:
[tex]\begin{gathered} x^4-25x^2+144=(x^2)^2+(-9-16)x^2+(-9)(-16) \\ =(x^2-9)(x^2-16)\text{.} \end{gathered}[/tex]Now, notice that:
[tex]\begin{gathered} x^2-9=x^2-3^2=(x+3)(x-3), \\ x^2-16=x^2-4^2=(x+4)(x-4)\text{.} \end{gathered}[/tex]Therefore:
[tex]x^4-25x^2+144=(x+3)(x-3)(x+4)(x-4)\text{.}[/tex]Answer:
[tex]x^4-25x^2+144=(x+3)(x-3)(x+4)(x-4)\text{.}[/tex]
Graph the equation after plotting at least three points. Y= -2/3x+4
Given the function:
[tex]y=-\frac{2}{3}x+4[/tex]It's required to graph the function by joining at least 3 points.
Let's select the points x = -3, x = 3, and x = 9.
Substituting x = -3:
[tex]y=-\frac{2}{3}\cdot(-3)+4[/tex]Operating:
[tex]\begin{gathered} y=-\frac{-6}{3}+4 \\ y=2+4 \\ y=6 \end{gathered}[/tex]The first point is (-3,6)
Substitute x = 3:
[tex]y=-\frac{2}{3}\cdot3+4[/tex]Calculating:
[tex]\begin{gathered} y=-\frac{6}{3}+4 \\ y=-2+4 \\ y=2 \end{gathered}[/tex]The second point is (3,2)
Now for x = 9:
[tex]\begin{gathered} y=-\frac{2}{3}\cdot9+4 \\ y=-\frac{18}{3}+4 \\ y=-6+4 \\ y=-2 \end{gathered}[/tex]The third point is (9,-2).
Plotting the three points and joining them with a line, we get the following graph:
There are 364 people That have to go from the airport to the hotel. One sand can’t transfer 12 people have any vans are needed
To find the number of van that are needed you divide the number of people into the people that a van can transport:
As the result of division is a decimal number you approximate it to the next whole number (because you can not have 0.33 of a van)
Then, there are needed 31 vansa) which is equation of the parabola? b) name the focus and directrix ? c) name vertex and axis of symmetry?
The equation of the parabola whose axis of symmetry is parallel to x-axis is
[tex](y-k)^2=4p(x-h)[/tex]where the focus is
[tex]\text{focus}=(h+p,k)[/tex]and the directrix is
[tex]x=h-p[/tex]In our case, the focus is (6,1) and the directrix is x =2; therefore, we have
[tex](6,1)=(h+p,k)[/tex]and
[tex]h-p=2[/tex]These equations give
[tex]k=1,h=4,p=2[/tex]Hence, the equation of the parabola is
[tex](y-1)^2=8(x-4)[/tex]Find the formula for an exponential equation that passes through the points, (0,5) and (1,2). The exponential equation should be of the form y = ab^x
Answer:
[tex]y=5\cdot(\frac{2}{5})^x[/tex]Explanation:
The exponential equation has the form
[tex]y=a\cdot b^x[/tex]Since it passes through the point (0, 5). Let's replace (x, y) by (0, 5) to find the value of a
[tex]\begin{gathered} 5=a\cdot b^0 \\ 5=a\cdot1 \\ 5=a \end{gathered}[/tex]Then, the equation is
[tex]y=5\cdot b^x[/tex]To find the value of b, we will use the point (1, 2), so replacing x = 1 and y = 2, we get:
[tex]\begin{gathered} 2=5\cdot b^1 \\ 2=5\cdot b \\ \frac{2}{5}=\frac{5\cdot b}{5} \\ \frac{2}{5}=b \end{gathered}[/tex]Then, the exponential equation is:
[tex]a=5\cdot(\frac{2}{5})^x[/tex]Answer:
Step-by-step explanation: the answer is a= 5(2/5)^x
8+7i/4-6iI need the answer and how to solve asap!
ANSWER
[tex]\frac{1}{52}(-10\text{ + 76i) or }\frac{1}{26}(-5\text{ + 38i)}[/tex]EXPLANATION
We are given the fraction of complex numbers:
[tex]\frac{\text{8 + 7i}}{4\text{ - 6i}}[/tex]To simplify this, we will find the conjugate of the denominator and then multiply that with the numerator and denomiator.
The conjugate is gotten by changing the sign of the denominator. That is:
4 + 6i
So, we have:
[tex]\begin{gathered} \frac{\text{8 + 7i}}{4\text{ - 6i}}\cdot\text{ }\frac{4\text{ + 6i}}{4\text{ + 6i}} \\ =\text{ }\frac{(8\text{ + 7i) (4 + 6i)}}{(4\text{ - 6i) (4 + 6i)}} \\ =\frac{(8\cdot\text{ 4) + (8 }\cdot\text{ 6i) + (7i }\cdot\text{ 4) + (7i }\cdot\text{ 6i)}}{(4\cdot\text{ 4) + (6i }\cdot\text{ 4) - (6i }\cdot\text{ 4) - (6i }\cdot\text{ 6i)}} \\ We\text{ know that i = }\sqrt{i},\text{ so i }\cdot\text{ i = -1:} \\ \Rightarrow\text{ }\frac{\text{ }32\text{ + 48i + 28i - 42}}{16\text{ + 24i - 24i + 36}} \\ =\text{ }\frac{-10\text{ + 76i}}{16\text{ + 36}}\text{ = }\frac{-10\text{ + 76i}}{52} \\ =\text{ }\frac{1}{52}(-10\text{ + 76i) or }\frac{1}{26}(-5\text{ + 38i)} \end{gathered}[/tex]That is the answer.
can you help me is it < > or =
The correct answer is
[tex]\frac{1}{4}\times4\frac{1}{2}<4\frac{1}{2}[/tex]Tomas is leaving a tip of 18% of his original bill. If the amount of the tip is $2.34, which of the following equations can be used to find the amount of his original bill?0.18b = 2.34b - 0.18 = 2.342.34 x 0.18 = bb/2.34 = 0.18
Answer
0.18b = 2.34
Step-by-step explanation
Let's call b to the bill
The tip is 18% of the bill. To find the 18 percent of a number, we need to multiply this number by 18 and then divide by 100. In this case, the tip is:
[tex]\begin{gathered} tip=\frac{18}{100}b \\ tip=0.18b \end{gathered}[/tex]The amount of the tip is $2.34, then:
[tex]0.18b=2.34[/tex]a figure has vertices (-13,13), (26,52), (39,39) what would the new coordinates of the vertices to the nearest tenth if the image were reduced by a scale factor of 0.77 with the origin as the center of dilation
Explanation
Given that the figure has vertices (-13,13), (26,52), (39,39), to reduce the image by a scale factor of 0.77 with the origin as the center of dilation, we will multiply the x and y coordinates by the scale factors.
A bag of fertilizer covers 2,000 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn that is 29400 square feet.
Okay, here we have this:
Considering the provided information, we are going to calculate how many bags of fertilizer should be purchased to cover a rectangular lawn that is 29400 square feet, so we obtain the following:
Number of bags=Total space / Space per bag
Number of bags=29400ft² / 2000ft²
Number of bags=14.7
Number of bags≈15 bags of fertilizer.
Finally we obtain that rounded to the nearest unit, 15 bags of fertilizer are needed.
Determine the number of solutions for the following system of linear equations. If there is only onesolution, find the solution.x + 3y – 2z = 6- 4x - 7y + 3z = 3- 7x – 4y - 3z = -5AnswerKeypadKeyboard ShortcutsSelecting an option will enable input for any required text boxes. If the selected option does not have anyassociated text boxes, then no further input is required.O No SolutionO Only One SolutionX =y =Z=Infinitely Many Solutions
First, let's clear z from equation 1:
[tex]\begin{gathered} x+3y-2z=6\rightarrow x+3y-6=2z \\ \rightarrow z=\frac{1}{2}x+\frac{3}{2}y-3 \end{gathered}[/tex]Now, let's plug it in equations 2 and 3, respectively:
[tex]\begin{gathered} -4x-7y+3z=3 \\ \rightarrow-4x-7y+3(\frac{1}{2}x+\frac{3}{2}y-3)=3 \\ \\ \rightarrow-4x-7y+\frac{3}{2}x+\frac{9}{2}y-9=3 \\ \\ \rightarrow-\frac{5}{2}x-\frac{5}{2}y=12_{} \\ \end{gathered}[/tex][tex]\begin{gathered} -7x-4y-3z=-5 \\ \rightarrow-7x-4y-3(\frac{1}{2}x+\frac{3}{2}y-3)=-5 \\ \\ \rightarrow-7x-4y-\frac{3}{2}x-\frac{9}{2}y+3=-5 \\ \\ \rightarrow-\frac{17}{2}x-\frac{17}{2}y=-8 \end{gathered}[/tex]We'll have a new system of equations:
[tex]\begin{gathered} -\frac{5}{2}x-\frac{5}{2}y=12_{} \\ \\ -\frac{17}{2}x-\frac{17}{2}y=-8 \end{gathered}[/tex]Now, let's simplify each equation. To do so, we'll multiply the first one by -2/5 and the second one by -2/17. We'll get:
[tex]\begin{gathered} x+y=-\frac{24}{5} \\ \\ x+y=\frac{16}{17} \end{gathered}[/tex]Now, let's solve each equation for y to see them as a pair of line equations:
[tex]\begin{gathered} y=-x-\frac{24}{5}_{} \\ \\ y=-x+\frac{16}{17} \end{gathered}[/tex]Notice that this lines have the same slope. Therefore, they're parallel and do not intercept.
This way, we can conlcude that the original system has no solution.
Find the area bounded by the given curves. y=x², y=4 Options:32/3 31/3 34/3 37/3
We have to find the area within the given curves.
We have to integrate the difference between the two functions.
First, we have to find the intersections between the curves to know the interval for which we will integrate.
We then write:
[tex]\begin{gathered} y_1=y_2 \\ x^2=4\Rightarrow x_i=-2,x_f=2 \end{gathered}[/tex]We will integrate in the interval [-2, 2]. In this interval, the function y=4 is greater than y=x^2, so we will integrate the difference of the functions as:
[tex]\begin{gathered} A=\int ^2_{-2}\lbrack y_2(x)-y_1(x)\rbrack dx \\ A=\int ^2_{-2}(4-x^2)dx \\ A=4x-\frac{x^3}{3}+C \\ A=(4\cdot(2)-\frac{(2)^3}{3})-(4\cdot(-2)-\frac{(-2)^3}{3}) \\ A=(8-\frac{8}{3})-(-8+\frac{8}{3}) \\ A=8-\frac{8}{3}+8-\frac{8}{3} \\ A=16-\frac{16}{3} \\ A=\frac{48-16}{3} \\ A=\frac{32}{3} \end{gathered}[/tex]The area bounded by the curves y=x^2 and y=4 is A = 32/3.
2x^3 - 4x^2 - 50x + 100 factoring completely
The factor is 2(x−2)(x+5)(x−5).
From the question, we have
2x³−4x²−50x+100
=2(x−2)(x+5)(x−5)
Factors :
The positive integers that can divide a number evenly are known as factors in mathematics. Let's say we multiply two numbers to produce a result. The product's factors are the number that is multiplied. Each number has a self-referential element. There are several examples of factors in everyday life, such putting candies in a box, arranging numbers in a certain pattern, giving chocolates to kids, etc. We must apply the multiplication or division method in order to determine a number's factors.The numbers that can divide a number exactly are called factors. There is therefore no residual after division. The numbers you multiply together to obtain another number are called factors. A factor is therefore another number's divisor.
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Given the points A(-8,-7) and B(8,5) find the coordinates of point P on directed line segment AB that partitions AB into the ratio 3:1
Given the points A(-8,-7) and B(8,5) find the coordinates of point P on directed line segment AB that partitions AB into the ratio 3:1
step 1
Find the distance in the x-coordinate between A and B
dABx=(8-(-8)=8+8=16 units
Find the distance in the y-coordinate between A and B
dABy=5-(-7)=5+7=12 units
step 2
we know that
point P on directed line segment AB that partitions AB into the ratio 3:1
so
AP/AB=3/(3+1)
AP/AB=3/4
Find the x coordinate of point P
APx/ABx=3/4
substitute
APx/16=3/4
APx=16*(3/4)
APx=12 units
The x-coordinate of P is
Px=Ax+APx
where
Ax is the x-coordinate of P
Px=-8+12=4
step 3
Find the y-coordinate of P
we have that
APy/ABy=3/4
substitute
APy/12=3/4
APy=12*(3/4)
APy=9
The y coordinate of P is
Py=APy+Ay
where
Ay is the y-coordinate of P
Py=9+(-7)=2
therefore
the answer is
The coordinate of P are (4,2)Solve the system of equation graphed on the coordinate axed below y=-4/3x-1
Y=4/3x+7
Answer:
[tex]x=-3, y=3[/tex]
Step-by-step explanation:
The solution to a system is where the graphs intersect.
Using the image above, which of the following are opposite rays?A QP and PLB PL and PQC LP and QPD LQ and PQ
ANSWER
PL and PQ
EXPLANATION
We want to find which of the rays are opposite rays.
That means which of the rays are going in opposite direction and are the same length to one another.
We see different rays in the image. Some are going upward while some are going downward.
The ones going upward are:
LQ and PQ
The ones going downward are:
QL and PL
By observation, among all the options, we see that only PL and PQ are the same length and that are in opposite directions.
That means that the answer is PL and PQ
1. find the sum of the first 7 terms of the following sequence round to the nearest hundredth if necessary 18,-6,22. Find the sum of the first 6 terms of the following sequence to the nearest hundredth:324, 54, 9
You can find the sum of the first n terms of a geometric sequence using the formula:
[tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex]1. First, let's calculate r:
[tex]\begin{gathered} r_1=18-(-6)=24 \\ r_2=-6-2=-8 \\ r=-\frac{8}{24}=-\frac{1}{3} \end{gathered}[/tex]Replacing the values in the formula, (n=7 , r=-1/3) we get that:
[tex]S_n=13.51[/tex]2. Let's calculate r:
[tex]\begin{gathered} r_1=324-54=270 \\ r_2=54-9=45 \\ r=\frac{r_2}{r_1}=\frac{45}{270}=\frac{1}{6} \end{gathered}[/tex]Using the formula with the data we have, (n=6 , r=1/6) we get that
[tex]S_n=388.79[/tex]x^2+x^2=11.3^2 solve using the pathogen theorem
The value of x in the given expression is 8.
What is Pythagoras theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (a² + b² = c²).
Given an expression, x²+x² = 11.3²
2x² = 11.3²
[tex]\sqrt{2}[/tex]x = 11.3
x = 7.99 = 8
Hence, The value of x in the given expression is 8.
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A hummingbird can travel up to 15 meters per second.What is the hummingbird's speed in miles per hour?1 mile ≈ 1609 meters Enter your answer, as a decimal to the nearest tenth, in the box. mph
SOLUTION
The speed of the hummingbird is giving as
[tex]\text{ 15meter/seconds }[/tex]Recall that
[tex]1\text{mile}\approx1609\text{ meters }[/tex]Hence
[tex]\begin{gathered} 15\text{meters will be }\frac{15}{1609}miles\text{ } \\ \\ \end{gathered}[/tex]Recall that
[tex]3600\text{ seconds =1hour }[/tex]Hence
the speed of the hummingbird in miles per hour will be
[tex]\begin{gathered} \frac{15}{1609}\times\frac{3600}{1}=\frac{54000}{1609}=33.56\text{miles per hour } \\ \\ \end{gathered}[/tex]Therefore the speed in miles per hour to the nearest tenth is 33.6mph
There is a bag full of 30 different colored and/or patterned balls. How many different three ball combinations can you have if you pull three balls out of the bag?Part 2: Write down (in factorial form) the total number of possible combinations there are if you draw all the balls out of the bag one at a time.I am really stuck on part 2
a) 4060 different combinations
b) 30!
Explanation:Given:
Total balls of different patterns = 30
To find:
a) the different three-ball combinations one can have if 3 balls are pulled out of the bag
b) the total number of possible combinations there are if you draw all the balls out of the bag one at a time in factorial form
a) To determine the 3-ball combinations, we will apply combination as the order they are picked doesnot matter
[tex]\begin{gathered} for^^^\text{ the 3 ball comination = }^nC_r \\ where\text{ n = 30, r = 3} \\ \\ ^{30}C_3\text{ = }\frac{30!}{(30-3)!3!} \\ ^{30}C_3\text{ = }\frac{30!}{27!3!}\text{= }\frac{30\times29\times28\times27!}{27!\times3\times2\times1} \\ \\ ^{30}C_3\text{ = 4060 different combinations} \end{gathered}[/tex]b) if you are to draw all the balls one at a time, then for the 1st it will be 30 possibilities, the next will reduce by 1 to 29 possibilities, followed by 28 possibilities, etc to the last number 1
The possible combination = 30 × 29 × 28 × 27 × 26 × 25 ......5 × 4 × 3 × 2 ×1
The above is an expansion of a number factorial. the number is 30
30! = 30 × 29 × 28 × 27 × 26 × 25 ......5 × 4 × 3 × 2 ×1
Hence, the total number of possible combinations when you draw all the balls out of the bag one at a time in factorial form is 30!
Use the drawing tool(s) to form the correct answer on the provided graph.
Graph the solution to this system of inequalities in the coordinate plane.
3y>2x + 122x + y ≤ -5Having trouble rewriting in form. Graphing once in form okay.
Explanation
We are given the following system of inequalities:
[tex]\begin{gathered} 3y>2x+12 \\ 2x+y\leqslant-5 \end{gathered}[/tex]We are required to graph the given system of inequalities.
This is achieved thus:
- First, we determine two coordinates from the given inequalities:
[tex]\begin{gathered} 3y>2x+12 \\ \text{ Suppose }3y=2x+12 \\ \text{ Let x = 0} \\ 3y=12 \\ y=4 \\ Coordinate:(0,4) \\ \\ \text{Suppose }3y=2x+12 \\ \text{ Let y = 0} \\ 0=2x+12 \\ 2x=-12 \\ x=-6 \\ Coordinate:(-6,0) \end{gathered}[/tex]- Now, we plot the points on a graph. Since the inequality is "strictly greater than", the line drawn will be broken. The graph is shown below:
- Using the second inequality, we have:
[tex]\begin{gathered} 2x+y\leqslant-5 \\ \text{ Suppose }2x+y=-5 \\ \text{ Let y = 0} \\ 2x=-5 \\ x=-2.5 \\ Coordinate:(-2.5,0) \\ \\ \text{Suppose }2x+y=-5 \\ \text{ Let x = 0} \\ y=-5 \\ Coordinate:(0,-5) \end{gathered}[/tex]The graph becomes:
Combining both graphs, we have the solution to be:
The solution is the intersection of both graphs as indicated above.
Bailey wants to buy a house, paying approximately $1000 per month. The bank estimates a 4.5% annual interest rate for 15 years. Which formula approximates the total value of a house Bailey can afford?
Data:
Amount per month: $1000
Interest rate: 4.5% annual for 15 years
As Bailey wants to pay approx. $1000 per month, in a year he wants to pay approx.: $12000
[tex]1000\cdot12=12000[/tex]is the least common denominator of two fractions always greater than the denominators of the fractions
The least common denominator of two fractions is not always greater than the denominators of each fraction because sometimes the least common denominator is equal to the greater denominator. For example, if we have the fractions
[tex]\frac{4}{5}-\frac{1}{5}[/tex]In this case, since you have equal denominators, the least common factor would be 5, not greater than 5.
Another example could be
[tex]4+\frac{2}{9}[/tex]In this case, the least common denominator is 9, not greater than 9.
Therefore, the least common denominator is not always greater than the denominator of the fractions.Which equation is true when the value of x is -12
We are told to check for the correct equation that satisfies when the value of x = -12.
Let us resolve that by picking one of the options and testing it to confirm if it satisfies the value of x = -12.
Starting with OPTION B
[tex]15-\frac{1}{2}x=21[/tex]Solve for x
Subtract 12 from both sides
[tex]\begin{gathered} 15-15-\frac{1}{2}x=21-15 \\ -\frac{1}{2}x=6 \end{gathered}[/tex]Multiply both sides by 2
[tex]\begin{gathered} 2\times-\frac{1}{2}x=2\times6 \\ -1x=12 \end{gathered}[/tex]Divide both sides by -1
[tex]\begin{gathered} \frac{-1x}{-1}=\frac{12}{-1} \\ x=-12 \end{gathered}[/tex]From the solution, we can conclude that the above equation is true when the value of x = -12.
The correct option is Option B.
Simplify each expression by using The Distributive Property and combine like terms to simplify the expression.4(3х - 2)
The given expression is
[tex]undefined[/tex]Instructions: Find the missing side of the triangle. tion 24 x 7 2 =
We are given a right-angled triangle.
Two of the side lengths are given and the third is missing.
We can us the Pythagorean theorem to find the missing side of the triangle.
[tex]c^2=a^2+b^2[/tex]Where c is the longest side, a and b are the shorter sides of the triangle.
[tex]\begin{gathered} c^2=a^2+b^2 \\ x^2=7^2+24^2 \\ x^2=49^{}+576 \\ x^2=625 \\ x^{}=\sqrt[]{625} \\ x^{}=25 \end{gathered}[/tex]Therefore, the missing side of the triangle is 25
Anna found that there are 3^4 options for pizzas with different loppings at her local are there for pizzas? B. 12 c. 64 D.BA ker notes
As there are 3^4 options for pizzas, we can calculate this as:
[tex]3^4=3\cdot3\cdot3\cdot3=81[/tex]Answer: 3^4 options is equivalent to 81 options (option D).