Answer:
11, 71, 19, 67, 43.
Step-by-step explanation:
10
19 Solve the simultaneous equations.
You must show all your working.
x = 7 – 3y
x2 - y2 = 39
Answer:
x= -8 , y = 5
x= 25/4 , y = 1/4
Step-by-step explanation:
substitute first eqn into the second eqn:
(7 - 3y)^2 -y^2 = 39
49 - 42y + 9y^2 - y^2 = 39
8y^2 - 42y +10 =0
4y^2 - 21y + 5 = 0
(4y-1) (y-5) = 0
y= 1/4 , 5
when y=1/4
x = 7- 3/4
=25/4
when y= 5
x = 7- 15
= -8
The required solution of the given simultaneous equations are x = -8, 25/4 and y = 5, 1/4.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
x = 7 – 3y - - - - -(1)
x² - y² = 39 - - - - (2)
Put x from equation 1 in equation 2
(7 - 3y)² -y² = 39
49 - 42y + 9y² - y² = 39
8y² - 42y +10 =0
4y² - 21y + 5 = 0
(4y-1) (y-5) = 0
y= 1/4 , 5
Substitute this values in the equation 1,
x = -8 and 25/4
Learn more about simultaneous equations here:
https://brainly.com/question/16763389
#SPJ5
Ice cream beans are selling for $10 per pound and durians are selling for $9 per pound. If the market sold a total of $196 worth of durians and ice cream beans yesterday, and it sold 11 pounds of durian, which of the following is a good estimation of the total pounds of ice cream beans sold?
Answer:
I am not good at word problems but I think I found some good examples
Step-by-step explanation:
Durain beans cost $9 per pound and they sold 11 pounds.
Multiply the cost by the amount sold: 9 x 11 = $99
Subtract that from the total sold:
196 - 99 = $97
Now divide the amount left by the cost per pound for Ice cream beans:
97 / 10 = 9.7 pounds.
The projected worth (in millions of dollars) of a large company is modeled by the equation w = 221(1.09) t. The variable t represents the number of years since 2000. What is the projected annual percent of growth, and what should the company be worth in 2008? A. 19%; $479.99 million B. 19%; $240.89 million C. 9%; $404.00 million D. 9%; $440.36 million
Answer:
D. 9%, 440.36 million
Step-by-step explanation:
w = 221(1.09)t
9%, 440.36 million
What is the answer please
Answer:
I think it should be (C)
Answer:
B
Step-by-step explanation:
The fastest way to solve this would to plug in a number for x such as 1 in both equations to find which 2 are equivalent.
When you plug 1 into the top equation it equals 3.5, so now we need to find the correct equation below that equals 3.5 when 1 is plugged in for x.
When you plug 1 into equation B you are also left with 3.5.
Two trees are growing in a clearing. The first tree is 17 feet tall and casts a 10 foot shadow. The second tree casts a 35 foot shadow. How tall is the
second tree to the nearest tenth of a foot?
Answer:
59.5 feet
Step-by-step explanation:
The second tree is 59.5 feet tall.
GivenTwo trees are growing in a clearing.
The first tree is 17 feet tall and casts a 10-foot shadow.
The second tree casts a 35-foot shadow.
Let x be the tall is the second tree.
Then,
The ratio of the height of the tree is;
[tex]\rm \dfrac{17}{10} = \dfrac{x}{35}\\\\17 \times 35 = x \times 10\\\\595 = 10x\\\\x = \dfrac{595}{10}\\\\x = 59.5 \ feet[/tex]
Hence, the second tree is 59.5 feet tall.
To know more about Ratio click the link given below.
https://brainly.com/question/8677748
Answer for Brainiest, 25 points and 5 stars with thanks
Range: 71.9
Spread out above the median
The range is the biggest number minus the smallest number. This makes sense. The range here is 81.3 - 9.4 = 71.9.
Next, see the two middle groups? You can see the median, 45.5. Does the left or right side seem more spread out? It's the right side. 34.7 is closer to 45.5 than 63.6 is to 45.5.
Hope that helped,
-sirswagger21
determine the image of the point p[-3,10) under the translation [5,-7]
[tex](-3+5,10-7)=(2,3)[/tex]
Kelsey had $65 to spend on books. Each book cost $5.50, and there was a $7.50 fee for shipping. She let b equal the number of books she can purchase and wrote the inequality 5.50 b + 7.5 less-than 65 to represent the situation. Which statements describe the reasoning used to determine if Kelsey’s inequality is correct? Select two options. The inequality symbol is correct because she must spend less than $65. The inequality symbol is incorrect because she can spend up to and including $65. The expression 5.50b + 7.5 is correct because $5.50 per book is 5.50b and that is added to the shipping fee of $7.50 to determine the total purchase price. The expression 5.50b + 7.5 is incorrect because $5.50 per book and $7.50 should be combined to $9.50b to determine the total purchase price. The inequality symbol is correct because she cannot spend more than $65.
The statements that can be used to describe the reasoning used to determine if Kelsey’s inequality is correct include:
The inequality symbol is incorrect because she can spend up to and including $65. The expression 5.50b + 7.5 is correct because $5.50 per book is 5.50b and that is added to the shipping fee of $7.50 to determine the total purchase price.It should be noted that the inequality symbol is incorrect because she can spend up to and including $65.
Based on the information given, the correct expression that can be used to solve the question should be:
65 - (5.50b + 7.5)
In conclusion, the correct options are B and C.
Read related link on:
https://brainly.com/question/16904821
Answer:
B and C
Step-by-step explanation:
The altitude a
(in feet) of a plane i minutes after liftoff is given by
a = 34001 + 600. How many minutes
after liftoff is the plane
at an altitude of
21.000 feet?
Answer:
Step-by-step explanation:
a=3400t+600, we put in 21,000 for a. Because we have to find 't' when 'a' is 21,000.
which will give us 21,000 = 3400t+600.
Then,Subtract 600 to both sides to get 20,400 = 3400t
Divide both sides by 3,400 and you get 6 = t.
The ans is 6 minutes. The plane will take 6 min to reach the altitude 21,000 feet
What the answer question
Answer:
117.79
Step-by-step explanation:
solve for x 15x + 6 = 10x + 21
Answer:
15x+6=10x+21
15x-10x=21-6
5x=15
divide by 5
5x/5=15/5
x=3
Answer:
x=3
Step-by-step explanation:
15x+6=10x+21
-10x
5x+6=21
-6
5x=15
divided by 5
x=3
Zoologists are studying two newly discovered species of insects in a previously unexplored section of rain forest. They estimate the current population of insect A to be 1.3 million and the current population of insect B to be 2.1 million. As development is encroaching on the section of rain forest where these insects live, the zoologists estimate the populations of insect A to be reducing at a rate of 3.8% and insect B to be reducing at a rate of 4.6%.
Zoologists are studying two newly discovered species of insects in a previously unexplored section of rain forest. They estimate the current population of insect A to be 1.3 million and the current population of insect B to be 2.1 million. As development is encroaching on the section of rain forest where these insects live, the zoologists estimate the populations of insect A to be reducing at a rate of 3.8% and insect B to be reducing at a rate of 4.6%.
If P represents the population of each species of insect in millions, and t represents the elapsed time in years, then which of the following systems of equations can be used to determine how long it will be before the populations of the two species are equal?
Answer:
the system of equation that can be used to determine how long it will be before the populations of the two species are equal is :
[tex]\begin{cases} {\mathtt{P = 1.3 e^{-0.038 \ t}} & \\ \mathtt{P = 2.1 \ e^{-0.046 \ t}} & \end{cases}[/tex]
Step-by-step explanation:
Given that :
the current population of insect A to be 1.3 million
the current population of insect B to be 2.1 million.
As development is encroaching on the section of rain forest where these insects live, the zoologists estimate the populations of insect A to be reducing at a rate of 3.8% and insect B to be reducing at a rate of 4.6%.
The equation that can be used to determine how long it will be before the populations of the two species are equal is an equation for exponential decay, which can be represented as follows:
[tex]\mathtt{y = pe^{-rt}}[/tex]
where;
P represents the population of each species of insect in millions
t represents the elapsed time in years
r is the rate of decrease
So, we can have:
[tex]\mathtt{p_1 = 1.3 }[/tex] in million and [tex]\mathtt{p_2 = 2.1}[/tex] in million
Also for rate of decrease;
[tex]\mathtt{r_1 = 0.038}[/tex] and [tex]\mathtt{r_2 = 0.046}[/tex]
Therefore;
the exponential decay for Population of insect A can now be:
[tex]\mathtt{P = 1.3 e^{-0.038 \ t}}[/tex]
the exponential decay for Population of insect B can now be:
[tex]\mathtt{P = 2.1 \ e^{-0.046 \ t}}[/tex]
Hence, the system of equation that can be used to determine how long it will be before the populations of the two species are equal is :
[tex]\begin{cases} {\mathtt{P = 1.3 e^{-0.038 \ t}} & \\ \mathtt{P = 2.1 \ e^{-0.046 \ t}} & \end{cases}[/tex]
Answer:
A!
Step-by-step explanation:
Plato
Which system of linear inequalities is represented by
the graph?
Oy> x-2 and y < x + 1
O y< x-2 and y > x + 1
Oy x + 1
O y > x-2 and y < x + 1
Answer:
The correct option is;
y < x - 2, and y > x + 1
Step-by-step explanation:
The given graph of inequalities is made up of parallel lines. Therefore, the slope of the inequalities are equal
By examination of the graph, the common slope = (Increase in y-value)/(Corresponding increase in x-value) = (0 - 1)/(-1 - 0) = 1
Therefore, the slope = 1
We note that the there are three different colored regions, therefore, the different colored regions opposite to each inequalities should be the areas of interest
The y-intercept for the upper bounding linear inequality, (y >) is 1
The y-intercept for the lower bounding linear inequality, (y <) is -2
The two inequalities are y > x + 1 and y < x - 2
The correct option is y < x - 2, and y > x + 1.
The system of linear inequalities is represented by the graph is y> x-2 and y < x + 1
Inequalities is an expression that shows the non equal comparison of two or more variables and numbers.
Given that:
y and x are variables, plotting the inequalities using geogebra online graphing tool.The system of linear inequalities is represented by the graph is y> x-2 and y < x + 1
Find out more on linear inequalities at: https://brainly.com/question/21103162
Can u guys answer these 2 questions pls
Answer:
14) answer is 4
15) proved
Step-by-step explanation:
x=7-4√3 , √x +1/√x
√(7-4√3) +1/√7-4√3)=
8-4√x/√(7-4√3)= 4 ( use calculator)
(81/16)^-3/4*[(25/9)^-3/2 ÷(5/2)^-3]=(81/16)^-3/4= (9²/4²)^-3/4=(4^6/4)/(9^6/4)=8/(27)=8/27(25/9)^-3/2= (9^(3/2))/(25^3/2)=27/125(5/2)^-3=2³/5³ =8/125put the number to find the result:8/27[(27/125)÷(8/125)=8/27[(27/125)×125/8)]= 125 in nominator and dinaminotor=18/27[27/8]=1 provedI NEED HELP ANSWERING THESE QUESTIONS FIRST ANSWER GET BRAINLIEST!
Answer:
3 - b=12
4- b=14.1
Step-by-step explanation:
Area of the bookshelf=864 square inches
the book shelf is a rectangular prism
if we have height=4b, width=3b, length=b
then the area=length * width
A=(l*w)*2 ( we have 2 shelves)
864=(b*3b)*2
864=6b²
b²=864/6=144
b=√144= 12 inches
4- to cover the sides :
(height * length)*2 ( we have 2 sides)
(4b*b)×2=1600
8b²=1600
b²=1600/8=200
b=√200=14.1
Answer:
Question #3: b = 12 in
Question #4: b = 14.1 in
Step-by-step explanation:
Please see in the image attached the actual proportions that the furniture manufacturer uses to build the furniture in question:
Height = 4 b
Width = 3 b
Depth = b
So for question #3, given that the customer wants a total surface of the shaded shelves to be 864 [tex]in^2[/tex]
we can write that one wants twice the area of each rectangle of width 3 b and depth b to total 864:
[tex]2\,(3b\,*\,b)=864\\6 b^2=864\\b^2=864/6\\b^2=144\\b=12\,\,in[/tex]
Question # 4:
The total lateral surface to be covered by the silk is 1600 [tex]in^2[/tex], therefore if we consider the surface of each lateral plank as:
Area of each lateral plank :
[tex](4b)\,(b) = 4\,b^2[/tex]
Then twice these is: [tex]8\, b^2[/tex]
So we can solve for be requesting that these total surface equal the amount of silk:
[tex]8\,b^2=1600\\b^2=1600/8\\b^2=200\\b=\sqrt{200} \\b\approx 14.1421\,\,in[/tex]
which rounded to the nearest tenth of an inch gives:
[tex]b\approx 14.1\,\,in[/tex]
help meh wit this bruh♂️
Answer:
a) m∠BPD = 120°
b) m∠BC + m∠AD = 120°
Step-by-step explanation:
a) To solve for question a, we make use of a theorem called the intersecting chord theorem. This states that:
The measure of the angle formed by two chords that intersect inside a circle is the average of the measures of the intercepted arcs.
The Interior angle =( The larger exterior arc + The smaller exterior arcs) ÷ 2
The larger exterior arc (m∠BD) = 170°
The small exterior arc (m∠CA) = 70°
m∠BPD = m∠BD + m∠CA/2
m∠BPD = 170° + 70°/2
= 240°/2
= 120°
b) We are to find m∠BC + m∠AD
The sum of exterior angles in a circle = 360°
360° = m∠BD + m∠CA + m∠BC + m∠AD
360° = 170° + 70° + m∠BC + m∠AD
360° = 240 + m∠BC + m∠AD
360 - 240° = m∠BC + m∠AD
Thererefore,
m∠BC + m∠AD = 120°
Answer:
1. m∠BPD = 120°
2. m∠BC + m∠AD = 120°
Figure a is a scale image of figure b. Figure a maps to figure b with a scale factor of 0.75 What is the value of x? please answer asap!
Answer:
x = 7.5
Step-by-step explanation:
Step 1: Create a fraction with the known sides
[tex]\frac{x}{10}[/tex]
Step 2: Set the fraction equal to the scale factor
[tex]\frac{x}{10}=\frac{0.75}{1}[/tex]
Cross multiple to solve for x
[tex]x = 7.5[/tex]
Therefore x is equal to 7.5
Answer:
7.5
Step-by-step explanation:
did it on khan
A Food Marketing Institute found that 35% of households spend more than $125 a week on groceries. Assume the population proportion is 0.35 and a simple random sample of 75 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is between 0.36 and 0.42
Answer:
The probability that the sample proportion of households spending more than $125 a week is between 0.36 and 0.42 is 0.3115
Step-by-step explanation:
From the question, we can deduce the following;
n = 75
p = 0.35
where q = 1-p = 1-0.35 = 0.65
To compute the probability that the sample proportion of households spending more than $125 a week is between 0.36 and 0.42, we start by calculating the standard deviation of sample proportion.
Mathematically;
Standard deviation of sample proportion = √pq/n
SD = √(0.35)(0.65)/75 = 0.055 which is approximately 0.06
Let’s now compute the z-scores
For 0.36, we have ; (0.36-0.35)/0.06 = 0.01/0.06 = 0.17
For 0.42, we have; (0.42-0.35)/0.06 = 0.07/0.06 = 1.17
So the probability we want to calculate is :
P(0.17<z<1.17) = P(z<1.17) - P(z < 0.17) = 0.8790 - 0.5675 = 0.3115
Determine algebraically whether f(x) = x2(x2 + 9)(x3 + 2x) is even or odd.
Answer:
[tex]f(x) = x^{2}\cdot (x^{2}+9)\cdot (x^{3}+2\cdot x)[/tex] is an odd function.
Step-by-step explanation:
Let be [tex]f(x) = x^{2}\cdot (x^{2}+9)\cdot (x^{3}+2\cdot x)[/tex], by Algebra this expression can be rewritten as:
[tex]f(x) = x^{3}\cdot (x^{2}+9)\cdot (x^{2}+2)[/tex]
Where [tex]x^{2} + 9[/tex] and [tex]x^{2}+ 2[/tex] are even functions, because they satisfy the condition that [tex]g(x) = g(-x)[/tex], whereas [tex]x^{3}[/tex] is an odd function, as the condition of [tex]h(-x) = - h(x)[/tex] is observed. Then, the overall function is odd.
A water park has 28 water attractions: pools, game areas, and water slides. There are P pools and P +2 games areas. If 50% of the attractions are water slides, how many games areas are there?
Answer:
8
Step-by-step explanation:
total: 28 water attractions
pools: p
game areas: p + 2
water slides: 50% of 28 = 14
14 + p + p + 2 = 28
2p = 12
p = 6
game areas:
p + 2 = 6 + 2 = 8
0 is the multiplicative identity of the set of rational numbers true or false
if [tex] x\times e=x[/tex] for all x, then e is the Multiplicative Identity.
is this enough for you to get the answer?
Answer:
FALSE.
Step-by-step explanation:
1 is the multiplicative identity of the set of rationals.
What is the width of the rectangle shown below?
4x + 3
A = 8x2 – 10x – 12
Answer:
2x-4Step-by-step explanation:
Area of a rectangle = Length * Width
Given parameters
Area A = 8x2 – 10x – 12
Length of the rectangle = 4x+3
Required
Width of the rectangle.
Substituting the given parameters into the formula
8x2 – 10x – 12 = (4x+3)*width
width = 8x2 – 10x – 12 /4x+3
S
Factorizing the numerator
8x² – 10x – 12
= 2(4x²-5x-6)
= 2(4x²-8x+3x-6)
= 2(4x(x-2)+3(x-2))
= 2(4x+3)(x-2)
Width = 2(4x+3)(x-2)/4x+3
Width = 2(x-2)
Width = 2x-4
Hence the width of the rectangle is 2x-4
Simplify the expression. (3x2 – 4x + 1) + (-x2 + x – 9)
Answer: 2x2−3x−8
Step-by-step explanation:
or what value of g does the function f(g) = g2 + 3g equal 18?
Answer:
The 2 values that makes the function equal to 18 is 3 and -6
Step-by-step explanation:
First you can convert the quadratic equation from standard form to root form
Step 1: Substitute f(g) = 18
Step 2: Move 18 to the other side to create
0 = g² + 3g - 18
Step 3: Now we rearrange equation from standard form into root form
Step 4: Find what adds to 3 and multiples to -18
-3 and 6 adds to 3 and multiples to -18
Step 5: Now we substitute -3 and 6 into the root equation
0 = (g-3)(g+6)
Step 6: Set the brackets to 0 and solve
g - 3 = 0
g = 3
g + 6 = 0
g = -6
A square has an area of 18.49 square yards. What is the length of each side in yards?
Answer:
4.6225
Step-by-step explanation: It would be too long to get an exact
Answer:
Step-by-step explanation:
Area of square = 18.49 square yards
side² = 18.49
side = √18.49
side = 4.3 yards
i will mark brainlist!!
Answer:
3/5 + 2 3/4 = 3 7/20
Step-by-step explanation:
2 = 8/4
2 3/4 = 2 + 3/4
then:
3/5 + 2 3/4 = 3/5 + 8/4 + 3/4
= 3/5 + (8+3)/4
= 3/5 + 11/4
3/5 = 12/20
11/4 = 55/20
then:
3/5 + 11/4 = 12/20 + 55/20 = 67/20
67/20 = 60/20 + 7/20 = 3 + 7/20
= 3 7/20
Figure A is a scale image of figure B. Figure A maps to figure B with a scale factor of 2/7 What is the value of x?
Answer:
42
Step-by-step explanation:
If the scale factor is 2/7 divide 12 by 2 which is 6. 6 is 1/7 and if Figure a is 7/7
multiply 6 by 7 to get x. That would be 42.
Answer:
42
Step-by-step explanation:
Since the scale factor is [tex]\frac{2}{7}[/tex], we know that the bigger shape went to the smaller shape.
If we know that the smaller shape's side, 12, is [tex]\frac{2}{7}[/tex] of the bigger one, we can make the equation
[tex]\frac{2}{7}x = 12[/tex].
To solve for x, we can divide both sides by [tex]\frac{2}{7}[/tex].
[tex]x = 12\div{\frac{2}{7}}[/tex]
We can multiply by the reciprocal:
[tex]\frac{12}{1} \cdot \frac{7}{2} = \frac{84}{2} = 42[/tex]
Hope this helped!
Consider an experiment in which a marble is tossed into a box whose base is shown in the figure. The probability that the marble will come to rest in the shaded portion of the box is equal to the ratio of the shaded area to the total area of the figure. If the probability is equal to 3/10, find the positive value of x.
Answer:
x = 2
Step-by-step explanation:
Probability that the marble comes to rest in the shaded region is equal to the ratio of the shaded area to the total area.
Probability 'P' = [tex]\frac{A'}{A}[/tex]
Area of the shaded region (A')= (x + 1)(x + 2)
Total area of the figure (A) = (2x + 1)(3x + 2)
P = [tex]\frac{(x+1)(x+2)}{(2x+1)(3x+2)}=\frac{3}{10}[/tex]
10(x + 1)(x + 2) = 3(2x + 1)(3x + 2)
10(x² + 3x + 2) = 3(6x² + 7x + 2)
10x² + 30x + 20 = 18x² + 21x + 6
(18x² - 10x²) + (21x - 30x) + (6 - 20) = 0
8x² - 9x - 14 = 0
x = [tex]\frac{9\pm\sqrt{(-9)^2-4(8)(-14)} }{2(8)}[/tex]
x = [tex]\frac{9\pm \sqrt{81+448}}{16}[/tex]
x = [tex]\frac{9\pm 23}{16}[/tex]
x = -[tex]\frac{7}{8}, 2[/tex]
Therefore, positive value of x = 2 will be the answer.
En una empresa trabajan 60 personas. Usan gafas el 16% de los hombres y el 20% de las mujeres. Si el número total de personas que usan gafas es 11. ¿Cuántos hombres y mujeres hay en la empresa?
Pregunta completa:
En una empresa trabajan 60 personas. Usan gafas el 16% de los hombres y el 20% de las mujeres. Si el numero total de personas que usan gafas es 11. ¿Cuantos hombres y mujeres hay en la empresa?
Responder:
Hombres = 25
Mujeres = 35
Explicación paso a paso:
Dado lo siguiente:
Número de personas que trabajan en la empresa = 60
Porcentaje de hombres que usan anteojos = 16%
Porcentaje de mujeres que usan anteojos = 20%
Número total de personas que usan anteojos = 11
Suponga, Número de hombres en la empresa = m
Número de mujeres = número total - número de hombres = 60 - m
Por lo tanto,
16% de los hombres = 0,16 m
20% de mujeres = 0,2 (60 - m) = 12 - 0,2 m
Por lo tanto,
0,16 m + 12 - 0,2 m = 11
- 0,04 m = 11 - 12
-0,04 m = - 1
m = 1 / 0.04 = 25
Por tanto, Número de hombres en la empresa = m = 25
Número de mujeres en la empresa = (60 - m) = (60 - 25) = 35 mujeres
he Boston public school district has had difficulty maintaining on-time bus service for its students. Suppose the district develops a new bus schedule to help combat chronic lateness on a particularly woeful route. Historically, the bus service on the route has been, on average, 10 minutes late. After the schedule adjustment, the first 36 runs were an average of eight minutes late. As a result, the Boston public school district claimed that the schedule adjustment was an improvement using a two tailed test—students were not as late. Assume a population standard deviation for bus arrival time of 10 minutes. The test statistic is 1.20 based on this and an alpha of .05 which of the following statements is not correct?
Answer:
Fail to reject the null hypothesis.
Step-by-step explanation:
The hypothesis test is conducted for Boston public school. They have used z-value table and the value of test statistics is 1.20. AT the significance level of 0.05, the null hypothesis is accepted. We cannot reject the null hypothesis. The p-value is greater than alpha so there is no evidence to support the claim of Boston Public School.
