the cost of the bench is 350
Explanation
Step 1
let
x represents the cost of the garden table
y represents the cost of the bench
so
a)a garden table and a bench cost $613 combined.
[tex]x+y=613\rightarrow equation\text{ (1)}[/tex]b)the garden table cost $87 less then the bench,( in other words, you have to add 87 to the price of the garden table to obtain the cost of the bech)
[tex]\begin{gathered} x+87=y\rightarrow Equation(2) \\ \end{gathered}[/tex]Step 2
solve the equations
a)isolate x in equaiton (1) and replace in equation (2)
[tex]\begin{gathered} x+y=613\rightarrow equation\text{ (1)} \\ \text{subtrac y in both sides} \\ x+y-y=613-y \\ x=613-y \end{gathered}[/tex]now, replace in equation (2)
[tex]\begin{gathered} x+87=y\rightarrow Equation(2) \\ (613-y)+87=y\rightarrow Equation(2) \\ 700-y=y \\ \text{add y in both sides} \\ 700-y+y=y+y \\ 700=2y \\ \text{divide both sides by 2} \\ \frac{700}{2}=\frac{2y}{2} \\ 350=y \end{gathered}[/tex]it means, the cost of the bench is 350
A regular plot of land is 70 meters wide by 79 meters long. Find the length of the diagonal and, if necessary, round to the nearest tenth meter
Given :
The length is given l=79 m and width is given w=70m.
Explanation :
Let the length of diagonal be x.
To find the length of diagonal , use the Pythagoras theorem.
[tex]x^2=l^2+w^2[/tex]Substitute the values in the formula,
[tex]\begin{gathered} x^2=79^2+70^2 \\ x^2=6241+4900 \\ x^2=11141 \\ x=\sqrt[]{11141} \\ x=105.55m \end{gathered}[/tex]Answer :
The length of the diagonal is 105.6 m.
The correct option is D.
Graph the following:X>y^2 + 4y
Solution:
Given the inequality;
[tex]x>y^2+4y[/tex]The graph of inequality without an equal sign is done with broken lines,
The y-intercept is;
[tex]\begin{gathered} 0>y^2+4y \\ \\ 0>y(y+4) \end{gathered}[/tex]Thus, the graph is;
Hi , i need help with this question: what is the anwser to the division problem. 9÷4590
Problem
what is the anwser to the division problem.
9÷4590
Solution
We have the following number given:
[tex]\frac{9}{4590}[/tex]The first step would be simplify the fraction and we can divide both numbers by 9 and we got:
[tex]\frac{9}{9}=1,\frac{4590}{9}=510[/tex]So then our fraction becomes:
[tex]\frac{1}{510}[/tex]And if we convert this into a decimal we got 0.00196.
Find the remaining zer Degree 3; zeros: 5, 7- i The remaining zero(s) of f is
Answer:
The remaining zero is;
[tex]7+i[/tex]Explanation:
Given that two of the zeros of a polynomial are;
[tex]\begin{gathered} 5 \\ 7-i \end{gathered}[/tex]to get the remaining zero.
Recall that according to complex conjugates, complex roots/zeros comes in pairs;
[tex]\begin{gathered} a+bi \\ \text{and} \\ a-bi \end{gathered}[/tex]where a and b are real numbers.
Applying the rule to the given roots.
Since we have a complex root;
[tex]7-i[/tex]we must also have the other pair of the complex root;
[tex]7+i[/tex]Therefore, the remaining zero is;
[tex]7+i[/tex]20. Connie's pool has 50 cubic yards of water in it and is draining at a rate of 3 cubic yards per second. Paula's pool has 9 cubic yards of water currently in it and is filling at a rate of 4 cubic yards per second. After how many seconds will Connie's pool have less water than Paula's?
write the equation for the Connie's pool and Paula's pool
Connie's
[tex]y=50-3x[/tex]y=cubic yards of water remaining in the pool
x=time in seconds
Paula's
[tex]y=9+4x[/tex]y=cubic yards of water in the pool
x=time in seconds
write the inequality in order for connie's pool to have less water
[tex]\begin{gathered} 50-3x<9+4x \\ \end{gathered}[/tex]solve the inequality for x
[tex]\begin{gathered} 50-9<3x+4x \\ 41<7x \\ x>\frac{41}{7} \end{gathered}[/tex]After 41/7 seconds Connie's pool will have less water than Paula's.
7/8 = X/16 X=how do I solve it
x= 14
1) Let's solve this equation considering that we're dealing with two ratios.
Then we can cross multiply and simplify them this way:
[tex]\begin{gathered} \frac{7}{8}=\frac{x}{16} \\ 8x=16\cdot7 \\ \frac{8}{8}x=\frac{16\cdot7}{8} \\ x=2\cdot7 \\ x=14 \end{gathered}[/tex]2) So the answer is x= 14
Write the correct system of inequalities, by first defining x and y, that correctly models the situation. Then write the inequalities and then graph the situation stated below. For your stock portfolio, you have at most $4000 that you want to use to buy stock in two companies. One is a construction company, the other is a biotech company. You want to have at least 2 times as much in the construction company as you do in the biotech company. System of inequalities:
SOLUTION
Let x be a construction company,
Let y be a biotech company
From the question, we have that :
[tex]\begin{gathered} x\text{ + y }\leq\text{ 4000}\ldots\ldots..\ldots\ldots\ldots\ldots..equ\text{ 1 } \\ x\text{ }\ge\text{ 2y}\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots equ\text{ 2} \end{gathered}[/tex]
which of tje following proportion are true16/28=12/216/16=4/1430/40=24/3510/15=45/30
Notice that:
1)
[tex]\frac{16}{28}=\frac{4\cdot4}{7\cdot4}=\frac{4}{7}=\frac{4\cdot3}{7\cdot3}=\frac{12}{21}\text{.}[/tex]2)
[tex]\frac{6}{16}=\frac{2\cdot3}{2\cdot8}=\frac{3}{8}\ne\frac{2}{7}=\frac{2\cdot2}{2\cdot7}=\frac{4}{14}\text{.}[/tex]3)
[tex]\frac{30}{40}=\frac{10\cdot3}{10\cdot4}=\frac{3}{4}\ne\frac{2}{3}=\frac{12\cdot2}{12\cdot3}=\frac{24}{36}.[/tex]4)
[tex]\frac{10}{15}=\frac{5\cdot2}{5\cdot3}=\frac{2}{3}\ne\frac{9}{10}=\frac{5\cdot9}{5\cdot10}=\frac{45}{50}.[/tex]Answer: The only proportion that is true is the first one.
ubtract. - B the model to help
As you can see in the model
[tex]\frac{1}{2}=\frac{4}{8}[/tex]Then
[tex]\frac{5}{8}-\frac{1}{2}=\frac{5}{8}-\frac{4}{8}=\frac{5-4}{8}=\frac{1}{8}[/tex]This is the same as if you removed 4 pieces of 1/8 from the 5 pieces of 1/8, resulting in 1 piece of 1/8.
Therefore, the result of the subtraction is
[tex]\frac{1}{8}[/tex]What are the solutions to the following system?{-2x+y=-5y=-3x2 + 50 (0, 2)O (1, -2)o (12.-1) and (- 12.-1):o 15.-10) and (-75-10
Answer:
[tex](\sqrt[]{2\text{ }},-1)\text{ and (-}\sqrt[]{2\text{ }}\text{ ,-1)}[/tex]Explanation:
Here, we want to solve the system of equations
Since we have y in both equations, let us start by rewriting the second equation to look like the first
We have that as:
[tex]\begin{gathered} -2x^2+y\text{ = }-5 \\ y+3x^2\text{ = 5} \end{gathered}[/tex]Subtract equation ii from i
We have it that:
[tex]\begin{gathered} -5x^2=\text{ -10} \\ 5x^2=10 \\ x^2=\text{ 2} \\ \\ x\text{ = }\pm\sqrt[]{2} \end{gathered}[/tex]when x = positive root 2, we have it that:
[tex]\begin{gathered} -2x^2+y\text{ = -5} \\ -2(\sqrt[]{2\text{ }})^2+y\text{ = -5} \\ -4+y\text{ = -5} \\ y\text{ = -5+4} \\ y\text{ = -1} \end{gathered}[/tex]when x = negative root 2:
We will still get the same answer as the square of both returns the same value
Thus, we have the solution to the system of equations as:
[tex](\sqrt[]{2\text{ }},-1)\text{ and (-}\sqrt[]{2\text{ }}\text{ ,-1)}[/tex]Does the function f(x) or g(x) have a greater value at x=2? f(x)=4∙2^x
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
graph: g(x)
function: f(x) = 4 * 2 ^ x
Step 02:
greater value ==> x = 2:
graph: g(x)
x = 2 , y = 18
g(2) = 18
function: f(x) = 4 * 2 ^ x
[tex]f(2)\text{ = 4 }\cdot2^2=\text{ 4 }\cdot\text{ 4 = 16}[/tex]The answer is:
g(x) has a greater value at x = 2
Below is a model of the infield of a baseball stadium. How long is each side of the field Hurry pleaseee
We have the following:
[tex]\begin{gathered} A=s^2 \\ s=\sqrt{A} \end{gathered}[/tex]A = 81, replacing:
[tex]A=\sqrt{81}=9[/tex]therefore, each side measures 9 in
1 + xThe function g is defined by g(x)=7+2xFind g(a+5).
The function is given as:
[tex]g(x)=\frac{1+x}{7+2x}[/tex]We need to find the expression g(a + 5).
This means that we are going to plug in "a + 5" into "x" of the function. So, substituting, it gives us,
[tex]\begin{gathered} g(x)=\frac{1+x}{7+2x} \\ g(a+5)=\frac{1+(a+5)}{7+2(a+5)} \end{gathered}[/tex]Now, we need to simplify the expression. Steps are shown below:
[tex]\begin{gathered} g(a+5)=\frac{1+(a+5)}{7+2(a+5)} \\ =\frac{1+a+5}{7+2a+10} \\ =\frac{6+a}{17+2a} \end{gathered}[/tex]Answer[tex]\frac{6+a}{17+2a}[/tex]can you please help me solve this? i can't solve this question.
To solve this question, we have to relate period (seconds to make a cycle) and its length.
We can relate them as:
[tex]T=2\pi\sqrt[]{\frac{L}{g}}[/tex]where g is the acceleration due to gravity and L the length of the pendulum.
If T1=2.00 and T2=1.99, we can relate them as:
[tex]\begin{gathered} \frac{T_2}{T_1}=\sqrt[]{\frac{L_2}{L_1}} \\ \frac{L_2}{L_1}=(\frac{T_2}{T_1})^2=(\frac{1.99}{2.00})^2=0.995^2=0.990025 \\ L_1=\frac{L_2}{0.990025}\approx1.01L_2 \end{gathered}[/tex]Then, we know that the length of should be 1% larger than it actually is.
As we do not know the actual length, we will use the first equation to calculate the actual length first and then the correct length for a period of 2 seconds.
[tex]\begin{gathered} T=2\pi\sqrt[]{\frac{L}{g}} \\ \frac{T}{2\pi}=\sqrt[]{\frac{L}{g}} \\ L=g(\frac{T}{2\pi})^2 \\ L=9.81\cdot(\frac{1.99}{2\cdot3.14})^2=9.81\cdot0.3167^2=9.81\cdot0.1=0.981\text{ m} \end{gathered}[/tex]NOTE: all the variables and constants are in meters and seconds.
As the correct length is 1% larger than 0.981 m, we can calculate the increase in length as:
[tex]\Delta L=0.01\cdot L_2=0.01\cdot0.981m=0.00981\text{ m}[/tex]Answer: 0.00981 m
Drag and drop a phrase to make the statement true. TrianglesABC and DEF are Response area.similar or not similar
Solution:
Given two triangles;
Triangle ABC and DEF are similar only if;
[tex]\begin{gathered} \angle A\cong\angle D \\ \angle B\cong\angle E \\ \angle C\cong\angle F \end{gathered}[/tex]Thus, we have;
[tex]\begin{gathered} \angle A=180^o-80^o-60^o \\ \angle A=40^o=\angle D \end{gathered}[/tex]Also,
[tex]\angle B=\angle E=80^o[/tex]Also,
[tex]\begin{gathered} \angle F=180^o-80^o-40^o \\ \angle F=60^o=\angle C \end{gathered}[/tex]FINAL ANSWER: Triangle ABC and DEF are similar triangles
f(x)=x^3-4x^2+x+6 find all the real zeros of the function
The zeroes of the polynomial f(x)= x³ - 4x² + x + 6 = 0 are x - 1, x = 2
and x = 3.
We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given, f(x)= x³ - 4x² + x + 6 = 0.
Now, zeroes of the polynomial should be factors of 6 they are ±1, ±2. ±3, ±6.
Now at x = 1 f(x) = 4 so not a zero, at x = - 1, f(x) = 0 so x = - 1 a zero
at x = 2 f(x) = 0 so x = 2 is a zero,
at x = 2 f(x) = so x = 3 is a zero.
learn more about polynomials here :
https://brainly.com/question/20121808
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Evaluate with no calculator sin(sin^-1(3/8))
Since the sine ratio is opposite side/hypotenuse
Then in
[tex]\sin (\sin ^{-1}\frac{3}{8})[/tex]This means the angle has opposite side 3 and hypotenuse 8 in a right triangle
Then use this rule to evaluate without a calculator
[tex]\sin (\sin ^{-1}\frac{a}{b})=\frac{a}{b}[/tex]Because sin will cancel sin^-1
[tex]\sin (\sin ^{-1}\frac{3}{8})=\frac{3}{8}[/tex]The answer is 3/8
Use Cramer's Rule to solve the system. You may use the calculator for computations only - do not use any matrix functions. Show all work
Solution
Therefore the value of
[tex]\begin{gathered} x=-1 \\ y=\frac{5}{2}=2.5 \end{gathered}[/tex]What is the speed of a jet plane that flies 8100 km in 9 hours (in km/hr)
V = d/t
Speed = distance/time
V = 8100km/9hr = 900Km/hr
Answer:
V = 900 km/h
TASK 8 Michael has made a scale drawing of his classroom. The scale for his drawing is 0.5 in.: 3 ft. a. The length of the classroom is 30 ft. The length of the room on the scale drawing is 6 in. Is this correct? Explain why or why not. b. One of the student tables is 6 ft long. How long should it be on the drawing? Explain how you got your answer. c. Write your own problem concerning Michael's drawing. Solve and explain your answers.
The scale drawing is
Inches : Feet
0.5 : 3
We need to find the length of the classroom on the drawing if it is 30 feet
Let us use the ratio above to find it
Inches : Feet
0.5 : 3
x : 30
by using cross multiplication
[tex]x\times3=0.5\times30[/tex]3x = 15
Divide both sides by 3 to find x
[tex]\frac{3x}{3}=\frac{15}{3}[/tex]x = 5
The length on the drawing must be 5 inches
a) 6 inches is incorrect because the length on the drawing must be 5 inches
b) The student is 6 ft long
let us use the ratio above to find his length on the drawing
Inches : Feet
0.5 : 3
y : 6
By using cross multiplication
[tex]\begin{gathered} y\times3=0.5\times6 \\ 3y=3 \end{gathered}[/tex]Divide both sides by 3 to find y
[tex]\begin{gathered} \frac{3y}{3}=\frac{3}{3} \\ y=1 \end{gathered}[/tex]b) his length on the drawing is 1 inch
for number c) choose any length by feet and use the ratio to find its length on the drawing
Your height is 8 feet
Let us find it in the drawing
Inches : Feet
0.5 : 3
h : 8
By using cross multiplication
[tex]\begin{gathered} h\times3=0.5\times8 \\ 3h=4 \end{gathered}[/tex]Divide both sides by 3 to find h
[tex]\begin{gathered} \frac{3h}{3}=\frac{4}{3} \\ h=\frac{4}{3} \end{gathered}[/tex]c) Your height on the drawing is 4/3 inches
Drag and drop numbers into the equation to complete the equation of the line in slope-intercept form.The line passes through (8, 19) and (5, 1).
we are given two points
(8,19) and (5,1)
firstly, we need to calculate the slope
slope = y2 - y1 / x2 - x1
from the points
x1 = 8, y1 = 19, x2 = 5, y2 = 1
slope = 1 -19 / 5 - 8
slope = -18/-3
negative will cancel each other
slope = 18/3
slope = 6
slope intercept equation is
y - y1 = m(x - x1)
m = slope = 6
y1 = 19 and x1 = 8
y - 19 = 6(x - 8)
open the parentheses
y - 19 = 6*x - 6*8
y - 19 = 6x - 48
make y the subject of the formula
y = 6x - 48 + 19
y = 6x - 29
General MathematicsProblem:What interest rate would yield ₱1,200 interest on ₱10,000 in 2 years?
Answer
Interest rate = 6%
Explanation
From the information given in the question,
Interest, I = ₱1,200
Principal, P = ₱10,000
Time, T = 2 years
Interest rate, R = ?
Using Simple Interest formula:
[tex]I=\frac{PRT}{100}[/tex]Since I, P and T are know, we shall substitute these values into the formula to get R.
[tex]\begin{gathered} 1200=\frac{10000\times R\times2}{100} \\ 1200=200R \\ \text{Divide both sides by 200} \\ \frac{1200}{200}=\frac{200R}{200} \\ R=6 \end{gathered}[/tex]Therefore, the interest rate is 6%
A company charges (c) a flat fee of $4 for shipping plus $0.85 per pound (p). Which equation expresses this relatioship?
The cost of shipping is the flat rate plus the cost per pound times the number of pounds
c = flat rate + rate* pounds
c = 4 + 0.85*p
The write the second part in the opposite order
c = 0.85p +4
When we add the order doesn't matter
Answer B c = 0.85p + 4
Fergus gets paid $5.25 an hour with time-and-a-half for overtime(over 40 hours). How much did he earn one week when he worked 48hours?a. $63.04b. $190.90c. $210d. $273.04
The correct answer is d. $273
Fergus worked 48 hours in the week. This means that for 40 hours he was paid $5.25 per hour; And for 8 hours he was paid 150% of the normal (150% is one and a half time)
Then for the regular paid hours:
$5.25 per hour by 40 hours => 5.25*40= $210
Now for the 8 remaining hours we need to calculate how much Fergus is paid by hour.
Then 50% of $5.25 is the same as 5.25 divided by 2: 5.25/2 = $2.625
Then the 150% is equal to 100% + 50%. The 100% is $5.25 and the 50% is $2.625
5.25 + 2.625 = $7.875
This is what Fergus gets paid for every overtime hour. This week he worked 8 overtime hours.
Then, $7.875 * 8 = $63
Now the total earning of the week is equal to $210 + $63 = $273 and that's option D.
I need to find out which ones are true and which ones I have to change to get the answers correct please help me.
Solution
- In order to solve this question, we need to apply the following rules:
[tex]\begin{gathered} Given \\ f(x)=ax^2+bx+c \\ \\ |a|>1:\text{ } \\ \text{ The graph gets narrower the larger }|a|\text{ gets} \\ \\ 0<|a|<1: \\ \text{ The graph gets wider the closer }|a|\text{ is to zero} \\ \\ a<0: \\ \text{ The graph has a peak} \\ \\ a>0: \\ \text{ The graph has a valley} \end{gathered}[/tex]- Applying this rule, we can proceed to solve this question.
- Based on these rules above, we can select the correct options as follows:
One friend claims that to find the height of the platform, you need to use the tangent ratio. Explain why her approach is or is not a reasonable approach to finding the height of the platform.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the trigonometric ratios
[tex]\begin{gathered} \sin\theta=\frac{opposite}{hypotensue} \\ \cos\theta=\frac{adjacent}{hypotenuse} \\ \tan\theta=\frac{opposite}{adjacent} \end{gathered}[/tex]STEP 2: Analyze the given scenario to get the details given
We were given the length of the piece of wood needed to make the ramp as 3.5m long, this implies that the length of the side is 3.5m. From the given image, this is the hypotenuse.
[tex]hypotenuse=3.5m[/tex]The angle of elevation is 28 degrees,
[tex]\theta=28\degree[/tex]The height of the platform from the image will be opposite since it is the side that is facing the angle 28 degrees.
[tex]opposite=height\text{ }of\text{ }platform[/tex]Joining all these together, we have a right-angled triangle given below:
From the given ratios in step 1, since we know tha hypotenuse and the opposite and also the theta, therefore the correct ratio to use is:
[tex]\begin{gathered} \sin\theta=\frac{opposite}{hypotenuse} \\ \\ \sin28=\frac{height}{3.5} \\ height=3.5\times\sin28 \end{gathered}[/tex]Therefore, the given claim of needing tangent ratio to find the height of the platform is not a reasonable approach because the adjacent which is the base is not given.
does any know how to find the variance using n=122 p= 0.64
The formula to find the variance of a binomial distribution given the values n and p is:
[tex]\begin{gathered} \sigma^2=n\cdot p\cdot q \\ \text{ Where} \\ q=1-p \end{gathered}[/tex]In this case, you have:
[tex]\begin{gathered} n=122 \\ p=0.64 \\ q=1-p \\ q=1-0.64 \\ q=0.36 \end{gathered}[/tex]Then
[tex]\begin{gathered} \sigma^2=n\cdot p\cdot q \\ \sigma^2=122\cdot0.64\cdot0.36 \\ \sigma^2=28.11 \\ \text{ Rounding to the nearest tenth} \\ \sigma^2=28.1 \end{gathered}[/tex]Now, the standard deviation is the square root of the variance. So, you have
[tex]\begin{gathered} \sigma=\sqrt[]{\sigma^2} \\ \sigma=\sqrt[]{28.1} \\ \sigma=5.3 \end{gathered}[/tex]Therefore, the variance and standard deviation of the binomial distribution with the given values n y p are
[tex]\begin{gathered} \sigma^2=28.1\Rightarrow\text{ Variance} \\ \sigma=5.3\Rightarrow\text{ Standard deviation} \end{gathered}[/tex]If ST = x + 4, TU = 10, and SU = 9x + 6, what is ST?
Given:
[tex]\begin{gathered} ST=x+4 \\ \\ TU=10 \\ \\ SU=9x+6 \end{gathered}[/tex]Find-:
The value of "x."
Explanation-:
The line of property
[tex]SU=ST+TU[/tex]Put the value is:
[tex]9x+6=x+4+10[/tex][tex]\begin{gathered} 9x+6=x+14 \\ \\ 9x-x=14-6 \\ \\ 8x=8 \\ \\ x=\frac{8}{8} \\ \\ x=1 \end{gathered}[/tex]So, the value of "x" is 1.
Kevin went for a drive in his new car. He drove for 377.6 miles at a speed of 59 miles per hour. For how many hours did he drive ?
We know that the average speed (v) can be calculated as the quotient between the distance D and the time t.
As v = 59 mi/h and D = 377.6 mi., we can calculate the time as:
[tex]v=\frac{D}{t}\longrightarrow t=\frac{D}{v}=\frac{377.6\text{ mi}}{59\text{ mi/h}}=6.4\text{ h}[/tex]Answer: he drove for 6.4 hours.
y = 3x ÷ 9 and x = -6 what is the output?
y = 3x ÷ 9 and x = -6
y = 3(-6) ÷ 9 = -18 ÷ 9 = -2
y = -2
Answer:
y = -2