Given:
The objective is to explain the method of solving pi equations.
The term with pi can be solved
which function is equivalent to y = 3(x + 4)² + 5?A) y = 3x² + 21B) y = 3x² + 24x + 63C) y = 3x² + 24x + 53D) y = 3x² + 8x + 21
Given: The function
[tex]y=3(x+4)^2+5[/tex]To Determine: The equivalent function of the given function
Solution:
Step 1: Expand the parenthesis
[tex]\begin{gathered} y=3(x+4)^2+5 \\ (x+4)^2=(x+4)(x+4) \\ (x+4)^2=x(x+4)+4(x+4) \\ (x+4)^2=x^2+4x+4x+16 \\ (x+4)^2=x^2+8x+16 \end{gathered}[/tex]Step 2: Substitute the expanded into the function
[tex]\begin{gathered} y=3(x+4)^2+5 \\ y=3(x^2+8x+16)+5 \\ y=3x^2+24x+48+5 \\ y=3x^2+24x+53 \end{gathered}[/tex]Hence, the equivalent function to the given is y = 3x²+24x+53, OPTION C
Can you help me with this question? I have no other information.
Given,
The number of lawn mowed by Thomas is 35.
The amount of tip thomas got is $150.
The number of lawn mowed by Candice is 30.
The amount of tip Candice got is $275.
They charged equal price to mow each lawn.
Consider,
The amount of mowing the one lawn is x.
According to the question,
[tex]undefined[/tex]Find the missing side length and angles of ABC given that m A = 41°, b = 4, and c = 10.
To solve this question, we would use cosine rule which is given as
[tex]a^2=b^2+c^2-2bc\cos A[/tex]Our values have been defined for us and we will proceed to evaluate
[tex]\begin{gathered} a^2=4^2+10^2-2(4)(10)\cos 41 \\ a^2=16+100-80\cos 41 \\ a^2=116-60.376 \\ a^2=55.624 \\ \text{take the square root of both sides} \\ a=\sqrt[]{55.624} \\ a=7.458\approx7.5 \end{gathered}[/tex]From the calculations above, the value of the missing side a is 7.5 units
To find angle B,
we can use sine rule
[tex]\begin{gathered} \frac{a}{\sin A}=\frac{b}{\sin B} \\ \frac{7.5}{\sin 41}=\frac{4}{\sin B} \\ \sin B=\frac{4\times\sin 41}{7.5} \\ \sin B=0.3498 \\ B=\sin ^{-1}0.3498 \\ B=20.5^0 \end{gathered}[/tex]We can still approach C with sine rule or sum of angle in a triangle
[tex]\begin{gathered} A+B+C=180 \\ 41+20.5+C=180 \\ c=118.5^0 \end{gathered}[/tex]From the calculations above, the value of a = 7.5 , B = 22⁰ and C = 118.5⁰ respectively which is option B
Identify the function shown in this graph. 5 4 3 2 과 2 பான் O A. y = x + 4 ос B. y=-x+4 C. y= x-4 D. y=-x-4
Given the graph of the line passes through the points ( -4 , 0 ) and ( 0 , 4 )
The general form of the line is : y = mx + b
where m is the slope and b is y-intercept
The slope will be calculated as following:
[tex]\text{slope}=m=\frac{y2-y1}{x2-x1}=\frac{4-0}{0-(-4)}=\frac{4-0}{0+4}=\frac{4}{4}=1[/tex]b = y intercept = ( the value of y when x = 0 )
So, as the line pass through the point ( 0 , 4 )
b = 4
so, the equation of the line is:
[tex]y=x+4[/tex]The empty gas tank of a truck needs to be completely filled. The tank is shaped like a cylinder that is 4 ft long with a diameter of 1.6 ft. Suppose gas is poured into the tank at a rate of 1.9 ft^3 per minute. How many minutes does it take to fill the empty tank?
Use the value 3.14 for pi, and round your answer to the nearest minute. Do not round any intermediate computations.
Hence, the minutes it take to fill the empty tank is [tex]8.0384min[/tex].
What is the volume of cylinder?
The volume of a cylinder is the capacity of the cylinder which calculates the amount of material quantity it can hold.
In geometry, there is a specific volume of a cylinder formula that is used to measure how much amount of any quantity whether liquid or solid can be immersed in it uniformly.
Here given that,
The empty gas tank of a truck needs to be completely filled. The tank is shaped like a cylinder that is [tex]4[/tex] ft long with a diameter of [tex]1.6[/tex] ft. Suppose gas is poured into the tank at a rate of [tex]1.9ft^3[/tex] per minute.
Here,
[tex]d=1.6ft\\r=0.8ft\\h=4ft[/tex]
The general formula for the volume of cylinder is
[tex]V=\pi r^2h\\V=(3.14)(0.8)^2(4)\\V=(3.14)(0.64)(4)\\V=8.0384min[/tex]
Hence, the minutes it take to fill the empty tank is [tex]8.0384min[/tex].
To know more about the cylinder
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The percent markup on the cost price of a dress is the same as the cost price in dollars. If the dress is sold for $24, what was the cost price of the dress ?
Markup is the difference between a product's selling price and cost as a percentage of the cost.
If we call the cost of the dress as x, the markup is given by the following expression
[tex]markup=\frac{24-x}{x}\times100[/tex]The percent markup on the cost price of a dress is the same as the cost price in dollars, therefore, we can rewrite the previous expression as:
[tex]x=\frac{(24-x)\cdot100}{x}[/tex]Solving for x, we have:
[tex]\begin{gathered} x=\frac{(24-x)\cdot100}{x} \\ x^2=2400-100x \\ x^2+100x-2400=0 \\ \implies x=-120\:or\:x=20 \end{gathered}[/tex]Since we can't have a negative cost price, the markup is 20% and the cost price of the dress is $20.
Which of the following represents the synthetic division form of the long division problem below? x - 3x+4/ x-5
The number on the left in the synthetic division form is the root of the divisor polynomial. The root of x-5 is 5
The numbers on the right are the coefficients of the dividend polynomial: 1 -3 4
The correct answer is option B
What is the inequality shown?
The inequality shown is -4 ≤ x ≤ 3.
In graph, as we can see the dots are solid that means inequality is not strict which leads to use of equal sign as well.
In graph, the line is from -4 to 3, that means the number exists between or equals to -4 and 3.
Hence, inequality is -4 ≤ x ≤ 3.
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Drag the red and blue dots along the x-axis and y-axis to graph 8x+2y=10
Solution
Writing in the form
[tex]\begin{gathered} y=mx+x \\ \\ \Rightarrow4x+y=5 \\ \\ \Rightarrow y=-4x+5 \end{gathered}[/tex]A company installs a rectangular septic tank 10 ft long by 15 ft wide and 8 ft deep. Calculate the capacity of the tank in gallons. (Use 1ft^3 = 7.48 gal.)The capacity of the tank is:enter your response here gallons. (Round to the nearest gallon as needed.)
To find the capacity in gallons we firs need to find the volume.
The volume is given by:
[tex]V=lwh[/tex]Plugging the values given we have:
[tex]V=(10)(15)(8)=1200ft^3[/tex]Now that we know that we need to convert it, to do this we multiply by the factor given:
[tex]1200(7.48)=8976[/tex]Therefore the capacity of the tank is 8976 gal
Jeremiah wants to send some of his shirts to a dry cleaner. He usually takes his shirts
to Spot-Less Dry Cleaners, where he pays $4.50 per shirt. He sees a sign at No Mess
or Stress Dry Cleaners that says it's $21.00 to have 4 shirts cleaned. Which is the
better deal?
Answer: Spot-less dry cleaners
Step-by-step explanation:
21/4=$5.25
$4.50<$5.25
Identify an equation in point-slope form for the line parallel to y = 1/2x - 7 thatpasses through (-3,-2).
ANSWER:
D.
[tex]y+2=\frac{1}{2}(x+3)[/tex]EXPLANATION:
Given:
[tex]y=\frac{1}{2}x-7[/tex]Recall that the slope-intercept form of the equation of a line is generally given as;
[tex]y=mx+b[/tex]where;
m = slope of the line
b = y-intercept of the line
Comparing both equations above, we can see that the slope(m) of the line is 1/2 and the y-intercept(b) is -7
Recall that parallel lines have the same slope. So the line that is parallel to the given line will have the same slope(m) of 1/2
Given the point (-3, -2), we can go ahead and write the equation of the parallel line in point-slope form as seen below;
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-2)=\frac{1}{2}[(x-(-3)] \\ y+2=\frac{1}{2}(x+3) \end{gathered}[/tex]INSTRUCTIONS: JCTIONS: e slope of the line er it here:m=1/3 Find the slope of the line and enter it here: 4 ey-intercept of & enter it Find the y-intercept of the line & enter it here: Write the equation of the line in form y=mx+b + he equation of in form y=mx +b /3x + 2 30 म
The equation of a line in the slope intercept form is expressed as
y = mx + b
where
m represents slope
b represents y intercept
The formula for finding slope is
m = (y2 - y1)/(x2 - x1)
From the graph,
When x1 = 1, y1 = - 2
when x2 = 2, y = 1
Slope = (1 - - 2)/(2 - 1) = 3/1
Slope = 3
The y intercept is the value of y at the point where the line cuts through the y axis. Thus, y intercept = - 5
To write the equation of the line, we would substitute m = 3 and b = - 5 into the slope intercept equation. Thus, the equation of the line is
y = 3x - 5
Which statement justifies why ∠ABF measures 130°?Given: angles ABD and DBC are complementary
SOLUTION:
We are to find the statement that justifies why
Given that
50 degrees +
In conclusion, the justified statement is "a linear pair is two adjacent, supplementary angles.
Answer:
B
Step-by-step explanation:
another person person said it was n had 5stars
is (18,302) a solution to the equation y=300?
No
Explanations:Note that:
the solutions to an equation are the values, if substituted into the equation, that will make the equation true.
The given equation is:
y = 300
(18, 302) means that x = 18, y = 302
Since the equation given is y = 300 and not y = 302, the point (18, 302) is not a solution to the equation.
The total points scored in the games of an NBA playoff series:195 177 215 200 189 232 201 199 192 201 Round any of the following answers to 1 decimal if needed. If there is no mode type NONE in the answer box.Mean = Median = Mode = Maximum = Minimum =
Solution
Step 1:
Arrange the number in ascending order of magnitude.
177, 189, 192, 195, 199, 200, 201, 201, 215, 232
Step 2:
[tex]\begin{gathered} Mean=\frac{177+189+192+195+199+200+201+201+215+232}{10} \\ \\ Mean\text{ = }\frac{2001}{10} \\ \\ Mean\text{ = 200.1} \end{gathered}[/tex][tex]\begin{gathered} Median\text{ = }\frac{199+\text{ 200}}{2}\text{ } \\ \\ Median\text{ = }\frac{399}{2} \\ \\ Median\text{ = 199.5} \end{gathered}[/tex]Mode is the most occurring number.
Mode = 201
Maximum = 232
Minimum = 177
give the function f(x)=-2x-5 determine the value of f(-3)
We have the next function
[tex]f(x)=-2x-5[/tex]And we must calculate f (-3).
To calculate it we must replace x = -3 in the function.
[tex]f(-3)=-2(-3)-5[/tex]Finally, we must simplify the answer
[tex]f(-3)=6-5=1[/tex]So, the answer is
[tex]f(-3)=1[/tex]For questions 7-8: P is the center of a circle with diameter KR.7. If P(7,-5) and R(4,-2), find the coordinates of point K.8. What is the length of the radius to the nearest hundredth?
Answer:
7.) The coordinates of point K are (10,8)
8.) The length of the radius, to the nearest hundreth, is of 4.24 units.
Step-by-step explanation:
P is the center of a circle with diameter KR:
This means that P is the midpoint between K and R.
I will see that the points are:
[tex]P(x_P,y_P),K(x_K,y_K),R(x_R,y_R)[/tex]Since P is the midpoint:
[tex]x_P=\frac{x_K+x_R}{2},y_P=\frac{y_K+y_R}{2}[/tex]P(7,-5) and R(4,-2)
This means that:
[tex]x_P=7,y_P=-5,x_R=4,y_R=-2[/tex]7. If P(7,-5) and R(4,-2), find the coordinates of point K
[tex]x_P=\frac{x_K+x_R}{2}[/tex]Substituting:
[tex]7=\frac{x_K+4}{2}[/tex][tex]x_K+4=14[/tex][tex]x_K=10[/tex]Now we do the same for y:
[tex]y_P=\frac{y_K+y_R}{2}[/tex]Replacing with what we have
[tex]-5=\frac{y_K-2}{2}[/tex][tex]y_K-2=-10[/tex][tex]y_K=-8[/tex]The coordinates of point K are (10,8)
8. What is the length of the radius to the nearest hundredth?
The radius is half the diameter(distance between KR divided by 2). It can also be the distance between an endpoint of the circle and the centre(Distance between P and K, or between P and R).
I am going to calculate the distance between P and R.
P(7,-5) and R(4,-2). So
[tex]R=\sqrt{(7-4)^2+(-5-(-2))^2}=\sqrt{3^2+(-5+2)^2}=\sqrt{9+9}=\sqrt{18}=4.24[/tex]The length of the radius, to the nearest hundreth, is of 4.24 units.
Express the answer in terms of a natural logarithm. Y= (do not simplify)
Solution
Exponential expressions with natural base e are of the form
[tex]y=a.e^{kx}[/tex]The value of 'a' is already set to be 96 since this is the coefficient of the given equation. We just need to find k
so set 3.8^x as e^kx and solve for k
[tex]\begin{gathered} 3.8^x=e^{kx} \\ 3.8^x=(e^k)^x \\ 3.8=e^k \end{gathered}[/tex]The two sides have the same exponent of x. So the two bases are 3.8 and
e^k must be equal to
[tex]\begin{gathered} e^k=3.8 \\ k=ln(3.8) \\ k=1.335 \end{gathered}[/tex]This means
[tex]e^{kx}=e^{1.335x}[/tex]and we replace the
[tex]3.8^x=e^{1.335x}[/tex]to go from
[tex]y=96(3.8)^x[/tex]to
[tex]y=96.e^{1.335x}[/tex]Therefore the correct answer is
[tex]y=96.e^{1.335x}[/tex]what is the prescribed dosage for a 4 yr old child, if the adult dosage is 180 milligram
In order to calculate the child's dosage, let's use the value of n = 4 and M = 180 in the formula, then we calculate the value of D:
[tex]\begin{gathered} D=\frac{n}{n+12}\cdot M \\ D=\frac{4}{4+12}\cdot180 \\ D=\frac{4}{16}\cdot180 \\ D=\frac{1}{4}\cdot180 \\ D=\frac{180}{4} \\ D=45 \end{gathered}[/tex]So the child's dosage is 45 milligrams.
What is the value of h? 48 sqrt 3168 sqrt 2
From definition:
[tex]\sin (angle)=\frac{\text{opposite side}}{\text{ hypotenuse}}[/tex]From the picture:
[tex]\begin{gathered} \sin (45)=\frac{8}{h} \\ \frac{1}{\sqrt[]{2}}=\frac{8}{h} \\ h=8\cdot\sqrt[]{2} \end{gathered}[/tex]Find the value of x that will make A B5x + 20А.B3x + 60x = [?]
x = 20
Using the alternate exterior angles theorem, it was stated the exterior ang
Hi, can you help me answer this question, please, thank you!
Given:
mean, u = 0
standard deviation σ = 1
Let's determine the following:
(a) Probability of an outcome that is more than -1.26.
Here, we are to find: P(x > -1.26).
Apply the formula:
[tex]z=\frac{x^{\prime}-u}{\sigma}[/tex]Thus, we have:
[tex]\begin{gathered} P(x>-1.26)=\frac{-1.26-0}{1} \\ \\ P(x>-1.26)=\frac{-1.26}{1}=-1.26 \end{gathered}[/tex]Using the standard normal table, we have:
NORMSDIST(-1.26) = 0.1038
Therefore, the probability of an outcome that is more than -1.26 is 0.1038
(b) Probability of an outcome that
Needing help with this practice problem please. Also, I need to show all work
ANSWER
L = 24 inches
W = 14 inches
EXPLANATION
Given tat
The length of the rectangular painting is 10 inches more than the width
Let the width of the rectangular painting be x
Recall, that the frame is 2 inches thick. This implies that there re 2 inches to the left ogf the length and 2 inches to the right of the length. So, there are more 4 inches to the length of the picture
Hence, the new length is
L = (x + 10) + 4
L = x + 10 + 4
L = x + 14
Also, for the width of the painting, we have
w = x + 4
Recall, that the area of a rectangle is given below as
Area = L x W
[tex]\begin{gathered} \text{ Area of a rectangle = L x W} \\ \text{ L = x + 14, and W = x + 4, and A = 336 in}^2 \\ \text{ 336 = \lparen x }+\text{ 14\rparen \lparen x }+\text{ 4\rparen} \\ \text{ Open the parentheses} \\ \text{ 336 = x}^2\text{ + 4x + 14x + 56} \\ \text{ 336 = x}^2\text{ + 18x + 56} \\ \text{ x}^2\text{ + 18x + 56 = 336} \\ \text{ x}^2\text{ + 18x + 56 - 336 =0} \\ \text{ x}^2\text{ + 18x - 280 = 0} \end{gathered}[/tex]Find the value of x by using factorizatin method
[tex]\begin{gathered} \text{ x}^2\text{ }+\text{ 28x - 10x - 280 = 0} \\ \text{ x\lparen x + 28\rparen - 10\lparen x + 28\rparen = 0} \\ \text{ \lparen x - 10\rparen \lparen x + 28 \rparen = 0} \\ \text{ \lparen x - 10\rparen = 0 or \lparen x + 28\rparen = 0} \\ \text{ x = 0 + 10 or x = 0 - 28} \\ \text{ x = 10 or x = -28} \end{gathered}[/tex]Find the length and the width of the rectngular painting
L = x + 14
L = 10 + 14
L = 24 inches
width
W = x + 4
W = 10 + 4
W = 14 inches
2) Chang saves up enough money to surprise his momand buy her a new blouse for her birthday. The blousecosts about $70 and he uses a coupon for 20% off. Howmuch does he save by using the coupon?
2) Chang saves up enough money to surprise his mom and buy her a new blouse for her birthday. The blouse costs about $70 and he uses a coupon for 20% off. How much does he save by using the coupon?
_________________________________
coupon for 20% off
20% = 0.2
The total of 100% of the price minus the discount =
100% - 20% = 80% or 1- 0.2 = 0.8
So then,
$70* 0.8 = $ 56 he pays
70 - 56 = 14 he saves
__________________________
Answer
He saves 14 by using the coupon
____________________
70*0.2= 14
Evaluate the function f(x) = 5 -√x at each specified value and simplify. 1. f(9)
Answer:
f(9)=2
Explanation:
The function f(x) is defined as follows:
[tex]f(x)=5-\sqrt[]{x}[/tex]To find the value of f(9), we substitute 9 for x in f(x) as follows:
[tex]\begin{gathered} f(9)=5-\sqrt[]{9} \\ =5-3 \\ =2 \end{gathered}[/tex]100 + (n - 2) ^ = 149 how do I solve this what is the first step??
The given expression is
[tex]100+(n-2)^2=149[/tex]First, we have to subtract 100 on each side
[tex]\begin{gathered} 100-100+(n-2)^2=149-100 \\ (n-2)^2=49 \end{gathered}[/tex]Hence, the answer is the first option, that's the first step.The reason for this first step is because we can't take a square root without getting rid of the terms 100, otherwise, the process would be wrong.
If you toss two dice, what is the probability that the sum of the dots is either 7 or 11?
sum of 7:
there are 6 combinations: (1,6) (6,1) (2,5) (5,2) (3,4) and (4,3)
[tex]=6\times\frac{1}{36}=\frac{6}{36}[/tex]sum of 11:
there are 2 combinations: (5,6) and (6,5)
[tex]=2\times\frac{1}{36}=\frac{2}{36}[/tex]thus the probability is
sum of 7 + sum of 11
[tex]\begin{gathered} =\frac{6}{36}+\frac{2}{36} \\ =\frac{8}{36} \\ =\frac{2}{9} \end{gathered}[/tex]therefore = 22%
write an equation for the graph below in terms of xy=______
Given the graph of a line.
We will write the equation of the line using two points lying on the line
As shown, the line passes through the points (0, 1) and (-1, 3)
The general equation of the line is: y = m * x + b
Where (m) is the slope and (b) is the y-intercept
We will find the slope as follows:
[tex]slope=m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{3-1}{-1-0}=\frac{2}{-1}=-2[/tex]And the value of b = the value of (y) when x = 0
So, b = 1
So, the answer will be, the equation of the line:
[tex]y=-2x+1[/tex]To solve the equation 2x - 6 = 30 by balancing, what would be step?
Given the equation
[tex]2x-6=30[/tex]To solve the equation means to determine the value of x, so your objective will be to isolate the x term in one side of the equal sign.
To do this using the balancing method, you have to "pass" all unrelated terms to the other side if the equal sign by performing the oposite operation.
So, first step is to pass -6 to the other side by adding it to both sides of the equation
[tex]\begin{gathered} 2x-6+6=30+6 \\ 2x=36 \end{gathered}[/tex]Next, the x term is being multiplied by 2, to cancel this multiplication you have to divide it by 2. And, to keep the equality valid, any operation performed in one side of the equal sing must be performed on the other side so, divide 36 by 2 too.
[tex]\begin{gathered} \frac{2x}{2}=\frac{36}{2} \\ x=18 \end{gathered}[/tex]