Given
The polynomial function,
[tex]f\mleft(x\mright)=(x+2)²\left(x-4\right)³\left(x−3\right)[/tex]To find: The x-intercepts.
Explanation:
It is given that,
[tex]f\mleft(x\mright)=(x+2)²\left(x-4\right)³\left(x−3\right)[/tex]That implies,
The x-intercept is determined by setting f(x)=0.
Then,
[tex]\begin{gathered} f\mleft(x\mright)=0 \\ (x+2)²\left(x-4\right)³\left(x−3\right)=0 \\ (x+2)^2=0,\text{ }(x-4)^3=0,\text{ }x-3=0 \\ x+2=0,\text{ }x-4=0,\text{ }x-3=0 \\ x=-2,\text{ }x=4,\text{ }x=3. \end{gathered}[/tex]Hence, the x-ntercepts are (-2,0), (4,0), (3,0).
A bookstore spent $241 to send a group of students to a readingcompetition. Each student who won was given a $5 gift certificate. Anda personalized bookmark that cost $2. Included in the $241 was $45 forthe salary of a staff member who accompanied the students to thecompetition. How many students won prizes?
A bookstore spent $241 to send a group of students to a reading
competition. Each student who won was given a $5 gift certificate. And
a personalized bookmark that cost $2. Included in the $241 was $45 for
the salary of a staff member who accompanied the students to the
competition. How many students won prizes?
Let
x -----> number of students that won prizes
we have that
the equation that represents this situation is
241=(5+2)x+45
241=7x+45
solve for x
7x=241-45
7x=196
x=28
therefore
28 students won prizesA petrified stump that is 4 ft tall casts a shadow that is 2 ft long. Find the height of a tent that casts a 5 ft shadow
The petrified stump is 4 ft tall and cast a shadow that is 2 ft long .
2 ft shadow has a 4 ft height
5 ft shadow will have ? height
cross multiply
[tex]\begin{gathered} \text{height of tent = }\frac{5\times4}{2} \\ \text{height of tent = }\frac{20}{2} \\ \text{height of tent = 10 ft} \end{gathered}[/tex]Height: Suppose you are 5 feet 8 inches tall. Give your height in meters and centimeters.For example, "9'2" = 2.8 meters = 2 meters and 80 centimeters."You are meters andcentimeters.
Height is 5 feet 8 inches.
1 feet is 12 inches. So,
(5*12) + 8 = 68 inches
Now, let's convert to meters.
We know:
1 inch = 0.0254 meters
So, 68 inches would be:
68 * 0.0254 = 1.7272 meters
We would need to convert the fractional part (excess of 1, which is 0.7272) to cm.
We know:
1 m = 100 cm
So,
0.7272 m is:
0.7272 * 100 = 72.72 cm
Hence,
The answer is:
1 meters and 73 centimeters (rounded to neaerest cm)Work out the rage 51,38,48,36,39,40,39,47
The range of the given data set will be 15.
What is the range?When the sample maximum and minimum are subtracted, the range of a collection of data is the difference between the greatest and lowest values. It uses the same units as the data to express itself.Find the biggest observed value of a variable (the maximum) and subtract the smallest observed value to determine the range (the minimum).The range is the range of values, from lowest to highest. Example: The lowest value in 4, 6, 9, 3, and 7 is 3, while the highest value is 9. The range is therefore 9 - 3 = 6.So, the range of the given data:
In increasing order: 36, 38, 39, 39, 40, 47, 48, 51The range will be:
51 - 3615
Therefore, the range of the given data set will be 15.
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Correct questions:
Work out the range 51,38,48,36,39,40,39,47
A customer wants to leave a 15% tip. The bill was $35. How much should the customer leave as a tip?
The customer wants to leave 15% tip, if the bill is $35, then the tip is
[tex]=15\text{ \% of 35}[/tex][tex]=\frac{15}{100}\times\text{ \$35}[/tex][tex]=\text{ \$5.25}[/tex]Therefore, the customer should leave $5.25 as a tip.
$480 invested at 15% compounded quarterly after a period of six years
Answer: $1161
Step-by-step explanation: The equation for compound interest is A=P(1+r/n)^n*t. P is the principal, in this case, being $480 originally invested, r is the rate, in this case being 15% or 0.15, and n is 4 because it is compounded quarterly. t is 6 because the period invested is 6 years. A=480(1+0.15/4)^4*6. This can simplify to 480(1.0375)^24, which equals approximately $1161 dollars. If the question requires to the tenths, it is $1161.3, and for the hundredths, $1161.33.
2 5/6 divided by 1 3/4
Find the quotient. If possible, rename the quotient as a mixed number or a whole number. Write your answer in simplest form, using only the blanks needed.
The quotient is 113/21.
What is a mixed number?It is formed by combining three parts a whole number, a numerator and a denominator. Here, the numerator and denominator are a part of the proper fraction that makes the mixed number. These are also known as mixed fractions. It contains both an integer or a whole number. A mixed fraction or number is therefore a product of a whole number and a proper fraction.
2 5/6 = (2·6 +5)/6 = 17/6
1 3/4 = (1·4 +3)/4 = 7/4
Here 17/6 is dived by 7/4,we get
(17/6) ÷ (7/4) = (17/6) × (4/7) = (17×4)/(6×7) = (17×2)/(3×7) = 34/21
Here 34/21 is converted into a mixed number.
34/21 = (21 +13)/21 = 1 13/21
Therefore, the quotient is 113/21
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A group of 30 students rented small canoes and large canoes at a river park.
• The group
rented twice as many small canoes as large canoes.
• There were 3 students in each small canoe.
• There were 4 students in each large canoe.
Let x represent the number of small canoes and let y represent the number of large canoes
Create a set of equations that can be used to determine the number of each type of canoe the group rented.
Answer:
Im taking the test ill give the answers in 5 minutes
Step-by-step explanation:
Find value of x. Math 80 I know it’s something to do with sine right?
Given
To find the value of x.
Explanation:
It is given that,
[tex]\theta=34\degree[/tex]Then,
[tex]\begin{gathered} \sin34\degree=\frac{x}{29} \\ 0.55919\times29=x \\ x=16.21659 \\ x=16.22 \end{gathered}[/tex]Hence, the value of x is 16.22.
The expression 12x+6 can be used to describe a sequence algebraically. Which of the following could be the first five numbers in this sequence?A. 18, 36, 54, 72, 90B. 6, 12, 18, 24, 30C. 18, 30, 42, 54, 66D. 6, 18, 24, 36, 42
We need to find the first five numbers of a sequence determined by the expression:
[tex]12x+6[/tex]Notice that each time we increase the value of x by 1 unit, we add 12 to the previous result. Thus, subsequent terms in the sequnce differ by 12 units.
From the options, the only one with all the terms differing by 12 units is the beginning at x=1:
[tex]\begin{gathered} x=1:12(1)+6=18 \\ \\ x=2:12(2)+6=30 \\ \\ x=3:12(3)+6=42 \\ \\ x=4:12(4)+6=54 \\ \\ x=5:12(5)+6=66 \end{gathered}[/tex]Therefore, the answer is: C. 18, 30, 42, 54, 66
Use the graph to find the slope and y-intercept of the line. Compare the values to the equation y= -3x+ 1
The y-intercept is at the point where the line cut the y-axis.
Hence, the y-intercept is 1
[tex]\begin{gathered} \text{Slope}=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{3-0}{-1-0} \\ m=\frac{3}{-1}=-3 \end{gathered}[/tex]
Hence, the slope is -3
Comparing the values to the equation y = =-3x +1, the equation is valid for the line.
i need help with math
Answer:
7
Step-by-step explanation:
opposite angles are the same
8z+18=74
8z=56
z=7
Answer:
7 is my final answer thank you
Step-by-step explanation:
set as brainliest
which statements and reason complete steps 3 , 4 and 6 of the proof ?
Statement 1:
ΔABC ≅ ΔCBD ≅ ΔACD
Reason: Given
_________________________________
Statement 2:
b/c = y/b; a/x = x/a
Reason: corresponding sides of similar triangles are proportional
(we want to have to have in the next statement that b² = cy; a² = cx
and proportionality is usually represented as fractions, if we observe the figure, the fractions of this statement correspond to the division of similar sides of the triangles)
________________________
Statement 3:
b² = cy; a² = cx
Reason: cross product property
(if we multiply both sides of b/c = y/b by b, we obtain b² = cy, and if we do the same for a/x = x/a we obtain a² = cx, since we are multiplying, it is called product, then, the option that best fit this field is cross product property)
_______________________________
Statement 4:
a² + b² = cx + cy
Reason: addition property of equality
(we want to prove that a² + b² = c², from the previous statement we can add both equalities so we obtain a² + b² , which is nearer to the conclusion we want to prove)
____________________
Statement 5:
a² + b² = c(x + y)
Reason: factor
(we find the common factor of cx and cy, it is c, then cx + cy = c(x + y))
___________________________
Statement 6:
c = x + y
Reason: Segment addition postulate
(we almost have the conclusion in the previous statement except for the (x + y) of the right part of the equality, since in the figure we observe that c = x + y, then we can use it to replace (x + y))
___________________________
Statement 7:
a² + b² = c²
Reason: substitution
(we substitute c by (x + y) of the statement 5)
⊕
h(x) = 10x - x^2 find h(4)
We have the following expression
[tex]h(x)=10x-x^2[/tex]In our case x is equal to 4, then, we will evalute the given function h(x) when x is 4. It yields,
[tex]h(4)=10(4)-(4)^2[/tex]which gives
[tex]\begin{gathered} h(4)=40-16 \\ h(4)=24 \end{gathered}[/tex]Therefore, the asnswer is h(4)=24
Please help me with this question:Graph the function F(x) = x^2 + 4x - 12 on the coordinate plane by finding the important points below.Be sure to show all steps in your calculations.(a)What are the x-intercepts?(b)What is the y-intercept?(c)What is the maximum or minimum value?(d)Use the points to graph the function.
Given the function:
[tex]f(x)=x^2+4x-12[/tex]Let's graph the function.
Let's find the following:
• (a). x-intercepts:
The x-intercepts are the points the function crosses the x-axis.
To find the x-intercepts substitute 0 for f(x) and solve for x.
[tex]\begin{gathered} 0=x^2+4x-12 \\ \\ x^2+4x-12=0 \end{gathered}[/tex]Factor the left side using AC method.
Find a pair of numbers whose sum is 4 and product is -12.
We have:
6 and -2
Hence, we have
[tex]\begin{gathered} (x+6)(x-2)=0 \\ \\ \end{gathered}[/tex]Equate the individual factors to zero and solve for x.
[tex]\begin{gathered} x+6=0 \\ Subtract\text{ 6 frm both sides:} \\ x+6-6=0-6 \\ x=-6 \\ \\ \\ x-2=0 \\ Add\text{ 2 to both sides:} \\ x-2+2=0+2 \\ x=2 \end{gathered}[/tex]Therefore, the x-intercepts are:
x = -6 and 2
In point form, the x-intercepts are:
(x, y) ==> (-6, 0) and (2, 0)
• (b). The y-intercept.
The y-intercept is the point the function crosses the y-axis.
Substitute 0 for x and solve f(0) to find the y-intercept:
[tex]\begin{gathered} f(0)=0^2+4(0)-12 \\ \\ f(0)=-12 \end{gathered}[/tex]Therefore, the y-intercept is:
y = -12
In point form, the y-intercept is:
(x, y) ==> (0, -12)
• (c). What is the maximum or minimum value?
Since the leading coefficient is positive the graph will have a minimum value.
To find the point where it is minimum, apply the formula:
[tex]x=-\frac{b}{2a}[/tex]Where:
b = 4
a = 1
Thus, we have:
[tex]\begin{gathered} x=-\frac{4}{2(1)} \\ \\ x=-\frac{4}{2} \\ \\ x=-2 \end{gathered}[/tex]To find the minimum values, substitute -2 for x and solve for f(-2):
[tex]\begin{gathered} f(-2)=(-2)^2+4(-2)-12 \\ \\ f(-2)=4-8-12 \\ \\ f(-2)=-16 \end{gathered}[/tex]Therefore, the minimum value is at:
y = -16
Using the point form, we have the minimum point:
(x, y) ==> (-2, -16).
• (d). Use the points to plot the graph.
We have the points:
(x, y) ==> (-6, 0), (2, 0), (0, -12), (-2, -16)
Plotting the graph using the points, we have:
Which inequality represents all values of x for which the quotient below is defined? (Division)
We want to calculate the following quotient
[tex]\frac{\sqrt[]{28(x-1)}}{\sqrt[]{8x^2}}[/tex]Note that using properties of radicals, given non zero numbers a,b we have that
[tex]\frac{\sqrt[]{a}}{\sqrt[]{b}}=\sqrt[]{\frac{a}{b}}[/tex]So, using this fact, our quotient becomes
[tex]\sqrt[]{\frac{28(x-1)}{8x^2}}[/tex]As we are taking the square root, this opearation is only valid if and only if the expression inside the square root is a non negative number. That is, we must have that
[tex]\frac{28(x-1)}{8x^2}\ge0[/tex]As this is a quotient, we should also that the quotient is defined.
To understand this last point, we should make sure that we are not dividing by 0. So first, we want to exclude those value s of 0 for which the denominator becomes 0. So we have the following auxiliary equation
[tex]8x^2=0[/tex]which implies that x=0.
So, the second quotient is always defined whenever x is different from 0. However, assuming that x is not 0 we want to find the value of x for which
[tex]\frac{28(x-1)}{8x^2}\ge0[/tex]To start with this problem, we solve first the equality. So we have
[tex]\frac{28(x-1)}{8x^2}=0[/tex]since x is not 0, we can multiply both sides by 8x², so we get
[tex]28(x-1)=0\cdot8x^2=0[/tex]If we divide both sides by 28, we have that
[tex]x-1=\frac{0}{28}=0[/tex]now, by adding 1 on both sides we get that
[tex]x=1[/tex]so, whenever x=1, we have that the quotient inside the radical becomes 0.
Now, we will solve the inequality, that is
[tex]\frac{28(x-1)}{8x^2}>0[/tex]Note that on the left, we are mostly dividing two expressions. Recall that the quotient of two expressions is positive if and only if both expressions have the same sign.
Note that the expression
[tex]8x^2[/tex]is the product of number 8 (which is positive) with the expression x², which is also always positive for any value of x. This means that the expression 8x² is always positive.
So, taking this into account, we should focus on those values of x for which the numerator is positive, as the denominator is always positive. So we end up with the following inequality
[tex]28(x-1)>0[/tex]If we divide both sides by 28 we get
[tex]x-1>\frac{0}{28}=0[/tex]So, if we add 1 on both sides, we get
[tex]x>1[/tex]So, whenever x is greater than 1, the expression inside the radical is positive.
This means that the original quotient is defined whenever x=1 and whenever x>1. Thus, we would have
[tex]x\ge1[/tex]A school librarian would like to buy subscriptions to 7 new magazines. Her budget however, will allow her to buy only 4 new subscriptions. How many different groups of 4 magazines can she chose from the 7 magazines?
The number of groups of 4 magazines can she choose from the 7 magazines is 35
Total number of magazines that school librarian would like to buy subscription = 7 magazines
The number of subscription that she can afford = 4 new subscription
The different groups of 4 magazines can she choose from the 7 magazines = [tex]7C_4[/tex]
The combination is the method of selecting a particular items or objects from the group of collection. The combination can also be defined as the number of possible arrangement from the collection.
Then the value of
[tex]7C_4[/tex] = 7! / 4!(7 - 4)!
= 7! / (4! × 3!)
= (7 × 6 × 5 × 4!) / (4! × 3!)
= (7 × 6 × 5) / 3!
= (7 × 6 × 5) / 3 × 2 × 1
= 210 / 6
= 35
Hence, the number of groups of 4 magazines can she choose from the 7 magazines is 35
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Use the given triangle to fill in the blank.bCasin BB
We can apply trigonometric ratios, on this case we ned to use sine
[tex]\sin (\alpha)=\frac{O}{H}[/tex]Where alpha is th reference angle, O the opposite side from the reference angles and H the hypotenuse of the triangle
On our case O is b and H is c, then replacing
[tex]\sin (B)=\frac{b}{c}[/tex]then sinB is b/c, then right option is first
What is the area of the rectangle whose coordinates are at A(-1,4), B(3, 2), Clo,-4) and D(-4,-2) (Round to the nearest whole number.)
Answer:
Explanation:
The area of the rectangle with the given coordinates is:
[tex]undefined[/tex]Evaluate ( (dx-4) dx 16 S (WX - 4) dx = ( (Type an exact answer in simplified form) 9
Can someone please help me with this math, thank you
Given data:
The given growth rate is r=7.8%=0.078.
The final number of bacteias in terms of initial is P'=2P.
The expression for the bacterias growth rate is,
[tex]P^{\prime}=P(1+r)^t[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} 2P=P(1+0.078)^t \\ 2=(1.078)^t \\ \ln (2)=t\ln (1.078) \\ t=\frac{\ln(2)}{\ln(1.078)} \\ =9.23\text{ hours} \end{gathered}[/tex]Thus, after 9.23 hours population of the bacterias doubled.
Choose the median for the set of data. 99 95 93 92 97 95 97 97 93 97 a. 7b. 95.5 c. 96d. 97
The median is the middle of a sorted list of number. So, we need to place the number in value order, that is,
[tex]92,93,93,95,95,97,97,97,97,99[/tex]then, the middle is between the 5th and 6th number:
then, we need to find the mean value of these numbers. So, the median is
[tex]\text{ median=}\frac{95+97}{2}=96[/tex]Therefore, the answer is option C.
write the equation for this line in slope intercept form.y= ? × + __ a) -4 b) 2c) -2 d) -1/2
we know that
the equation in slope intercept form is equal to
y=mx+b
In this problem
we have
b=-4 ------> because the y-intercept is (0,-4)
Find the slope
we need two points
we take
(-2,0) and (0,-4)
so
m=(-4-0)/(0+2)
m=-4/2
m=-2
therefore
y=-2x-4PLSSS ANSWER ASAP PLS!!!! Solve y3 = 27.A. y = 9 B. y = 3 y= 3 C. y = 3 D. y = 5.2
A chemist is using 383 milliliters of a solution of acid and water, If 17.3% of the solution is acid, how many milliliters of acid are there? Round your answer to the nearest tenth.
A chemist is using 383 milliliters of a solution of acid and water.
If 17.3% of the solution is acid, how many milliliters of acid are there?
We basically need to calculate 17.3% of 383 milliliters.
[tex]\begin{gathered} acid=17.3\%\: of\: 383\: mL \\ acid=\frac{17.3}{100}\times383 \\ acid=0.173\times383 \\ acid=6.3\: mL \end{gathered}[/tex]Therefore, the solution has 6.3 milliliters of acid.
lines m and n are paralle. Find the measures of angles x, y, and z in the figure
Explanation
From the image, angle x and 65 degrees form angles on a straight line. We will recall that the sum of angles on a straight line sums up to 180 degrees.
Therefore,
[tex]\begin{gathered} x+65^0=180^0 \\ x=180^0-65^0 \\ x=115^0 \end{gathered}[/tex]Angle y and 65 degrees form alternate angles, we will recall that alternate angles are equal
Therefore,
[tex]y=65^0[/tex]Angle x and angle z form corresponding angles, we will recall that corresponding angles are equal.
Therefore,
[tex]z=115^0[/tex]Answer:
[tex]x=115^0,y=65^0,z=115^0[/tex]Which expression is equivalent to 6x + 7- 12.2 - (32 + 2) - x?(A)7x - 28B7x - 21©5x - 28D5x - 21please hurry
Suppose a sample of 879 new car buyers is drawn. Of those sampled, 288 preferred foreign over domestic cars. Using the data construct a 95% confidence interval for the population proportion of new car buyers who prefer for foreign cars over domestic cars. Round your answers to three decimal places
To find the confidence interval for a proportion, we use the following formula:
[tex]Confidence\text{ }interval=p\pm z\cdot\sqrt{\frac{p(p-1)}{n}}[/tex]Where:
p is the sample proportion
z the chosen z-value
n sample size
Since we want to make a confidence interval of 95%, we need to use z = 1.96. The sample size is n = 879.
We can use cross multiplication to find p, which is the percentage of the total sample size that preferred foreign cars:
[tex]\begin{gathered} \frac{879}{288}=\frac{100\%}{x} \\ . \\ x=100\%\cdot\frac{288}{879} \\ . \\ x=32.765\% \end{gathered}[/tex]p is the proportion in decimal, we need to divide by 100:
[tex]p=\frac{32.765}{100}=0.32765[/tex]Now, we can use the formula:
[tex]Confidence\text{ }interval=0.32765\pm1.96\sqrt{\frac{0.32765(1-0.32765)}{879}}=0.32765\pm0.031028[/tex][tex]\begin{gathered} Lower\text{ }endpoint=0.32765-0.031028=0.296616 \\ Upper\text{ }endpoint=0.32765+0.031028=0.35867 \end{gathered}[/tex]Thus, the answer is:
Lower endpoint: 0.297
Upper endpoint: 0.359
Describe the shape of the graph of the cubic function by determining the end behavior and number of turning points. y=2x^3-x-1 What is the end behavior of the graph of the function?
Solution
What is the end behavior of the graph of the function?
[tex]y=2x^3-x-1[/tex]The end behaviors of the function describe the functions of x as it approaches +∝ and as x approaches -∝
Therefore the correct answer is
Option D
Final answer = Down and Up
Turning points = 2
Find the slope and the y-intercept of the line. 4x + 2y= -6 Write your answers in simplest form. Undefined 08 slope: . X ? y -intercept: 0
Transform equation form Ax + By = C
to y = ax + b
THen
4x + 2y = -6
A= 4. B= 2. C= -6
y = (-A/B)•x +(D/B)
y= (-4/2)•x + (-6/2)
y = -2x -3
Therefore in new equation
Slope a = -2
Y intercept b = -3