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Karen will run more than 28
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Today's previewYou can solve this by rearranging to create asituation to use the method from the previouslesson, or you can solve this by thinking a littledifferently about how the variables below mightalso be described.... so solve it.y = 2x + 4x + y = 7
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Choose SSS, SAS, or neither to comparethese two triangles.A) SSSB) SASC) neither
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Answer:
C. Neither
Explanation:
The SSS Congruence Rule states that if the three sides of a triangle are equal to the three sides of another triangle, then the two triangles are congruent.
The SAS Congruence Rule states that if the two sides and the included angle of one triangle are equal to the two sides and the included angle of another triangle, then the two triangles are congruent.
Notice that in the given triangles, there are two congruent sides and a non-included angle, since this does not satisfy any of the rules stated above, SSS Congruence rule or SAS Congruence rule, we'll choose "neither" as the correct answer.
The graphs of the functions g and h are shown below. For each graph, find the absolute maximum and absolute minimum. If no such value exists, click on "None".
Assume that the dashed line shown is a vertical asymptote that the graph does not cross.
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For the graph g, the absolute maximum is 2 and the absolute minimum is -4.
Similarly, for graph h, the absolute maximum is 3 and the absolute minimum is -5.
Absolute Maximum of a Graph:
The absolute maximum of a graph is the point on the graph with the highest y-value. There can only be one absolute maximum of a graph.
Absolute Minimum of a Graph:
The absolute minimum of a graph is the point on the graph with the lowest y-value. There can only be one absolute minimum of a graph.
Given,
Here we have the two graph called g and h.
Now, we need to find the absolute maximum and minimum from it.
AS per the given definition, we know that,
For graph g,
The absolute maximum is 2 and the absolute minimum is -4.
Similarly, for graph h, the absolute maximum is 3 and the absolute minimum is -5.
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What is the slope of the line shown in the graph
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Step by step
We have the coordinate pairs of
(0, 3) and (-3, 5) as shown on the attachment
Slope is found by
y2 - y1 over x2 - x1
5 - 3 over -3 - 0
2 over -3
Slope is -2/3
You can also count from point to point y over x
Here we have -2 down and +3 over for a slope of -2/3
Remember if your line going left to right goes at a downward angle, it is a negative slope.
A ball is thrown from an initial height of 6 feet with an initial upward velocity of 21 ft/s. The ball's heighth (in feet) after t seconds is given by the following,6+21 167Find all values of t for which the ball's height is 12 feet.Round your answer(s) to the hearest hundredth(If there is more than one answer, use the "or" button.)
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The given expression in the question is
[tex]h=6+21t-16t^2[/tex]with the value of h given as
[tex]h=12ft[/tex]By equating both equations, we will have
[tex]\begin{gathered} 12=6+21t-16t^2 \\ 12-6-21t+16t^2=0 \\ 6-21t+16t^2=0 \\ 16t^2-21t+6=0 \end{gathered}[/tex]To find the value of t we will use the quadratic formula of
[tex]ax^2+bx+c=0[/tex]which is
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{where} \\ a=16 \\ b=-21 \\ c=6 \end{gathered}[/tex]By substitution, we will have
[tex]\begin{gathered} t=\frac{-(-21)\pm\sqrt[]{(-21)^2-4\times16\times6}}{2\times16} \\ t=\frac{21\pm\sqrt[]{441-384}}{32} \\ t=\frac{21\pm\sqrt[]{57}}{32} \\ t=\frac{21\pm7.5498}{32} \\ t=\frac{21+7.5498}{32}\text{ or t=}\frac{21-7.5498}{32} \\ t=\frac{28.5498}{32\text{ }}\text{ or }t=\frac{13.4502}{32\text{ }} \\ t=0.89\text{ or t=0.42} \end{gathered}[/tex]Alternatively, Solving the equation graphically we will have
Therefore,
The values of t( to the nearest hundredth) t= 0.89sec or 0.42sec
11. Jarrod's favorite movie is now on video at 15% off the originalprice. If he pays $17, what was the original price?
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original price = x
discount = 15%
price after discount = $17
Write an equation:
x (1-15/100) = 17
x (1-0.15 ) = 17
0.85x = 17
Solve for x:
x = 17/0.85
x = $20
Evaluate theexpression belowwhen x = = 3.<54 : 2.3 - 22Enter your answer inthe box below.
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The given expression is
[tex]54\frac{.}{.}2\times3-x^2[/tex]where x=3
the dot in the expression means multiplication
substitute into the expression above we have
[tex]\begin{gathered} 54\frac{.}{.}2\times3-3^2 \\ \end{gathered}[/tex]Applying BODMAS
[tex]27\times3-3^2[/tex][tex]\begin{gathered} 81-3^2 \\ 81-9 \\ 72 \end{gathered}[/tex]Therefore the value of the expression is 72
The table represents the amount of money in a bank account each month. Month Balance ($) 1 2,215.25 2 2,089.75 3 1,964.25 4 1,838.75 5 1,713.25 What type of function represents the bank account as a function of time? Justify your answer.
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The form of function that represents the bank account as a function of time is a linear function.
How to determine the type of function?The table of values is given as illustrated:
Month Balance ($)
1 2,215.25
2 2,089.75
3 1,964.25
4 1,838.75
5 1,713.25
From the above table of values, we can see that the balance in the bank account reduces each month by $125.5
So, we have
Difference = 1,838.75 - 1713.25 =125.5
Difference = 1,964.25 - 1,838.75 =125.5
Difference = 2,089.75 - 1,964.25 =125.5
Difference = 2,215.25 - 2,089.75 =125.5
This shows a linear function.
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4) Using the number line to help you, decide which fraction is larger or if they are equal: one/twos or three/fifths. Label each fraction on the number line.
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Explanation:
The number line is between 0 to 1. There are 10 smaller lines in between
Each of the small lines represent 1/10 or 0.1
one/twos is the same as 1/2 = 0.5
three/fifths is the same as 3/5 = 0.6
From the above, 0.6 is greater than 0.5
Showing both numbers on the number line:
What is the answer to 3/8 + 7 5/8
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Given the Addition:
[tex]\frac{3}{8}+7\frac{5}{8}[/tex]You can find the sum as follows:
1. Covert the Mixed Number to an Improper Fraction:
- Multiply the Whole Number part by the denominator of the fraction.
- Add the result to the numerator.
- The denominator does not change.
Then:
[tex]7\frac{5}{8}=\frac{5+(7\cdot8)}{8}=\frac{5+56}{8}=\frac{61}{8}[/tex]2. Rewrite the Addition:
[tex]=\frac{3}{8}+\frac{61}{8}[/tex]3. Since the denominators are equal, you only need to add the numerators:
[tex]=\frac{3+61}{8}=\frac{64}{8}[/tex]4. Simplifying the fraction, you get:
[tex]=8[/tex]Hence, the answer is:
[tex]=8[/tex]Please help with this practice question
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Explanation below:
The smaller of two similar balloons has a diameter of 10 inches. If it takes 12 (same sized) breaths to blow up the smaller balloon and 40.5 to blow up the larger, what is the diameter of the larger balloon?
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The smaller of two similar balloons has a diameter of 10 inches. If it takes 12 (same sized) breaths to blow up the smaller balloon and 40.5 to blow up the larger, what is the diameter of the larger balloon?
we have that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube.
so
Find the scale factor
ratio volumes=40.5/12=3.375
3.375=(scale factor)^3
[tex]\text{scale factor=}\sqrt[3]{3.375}[/tex]scale factor=1.5
To find out the diameter of the larger balloon multiply the scale factor by the diameter of the smaller balloon
so
1.5*(10)=15 inches
the answer is 15 inchesFind the surface area. Do not round please Formula: SA= p * h + 2 * b
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The shape in the question has two hexagonal faces,
The Area of each of the heaxagonal faces is
[tex]=42\text{ square units}[/tex]The shape also has 6 rectangular faces with dimensions of
[tex]8.2\times4[/tex]The area of a rectangle is gotten with the formula below
[tex]\text{Area}=l\times b[/tex]By substituting the values, we will have
[tex]\begin{gathered} \text{Area}=l\times b \\ \text{Area}=8.2\times4 \\ \text{Area}=32.8\text{square units} \end{gathered}[/tex]To calculate The total surface area of the shape, we will add up the areas of the hexagonal faces and the rectangular faces
[tex]\text{Surface area=}2\times(area\text{ of hexagonal faces)+ 6(area of rectangular faces)}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \text{Surface area=}2\times(area\text{ of hexagonal faces)+ 6(area of rectangular faces)} \\ \text{Surface area}=(2\times42)+(6\times32.8) \\ \text{Surface area}=84+196.8 \\ \text{Surface area}=280.8\text{ square units} \end{gathered}[/tex]Hence,
The Surface Area is = 280.8 square units
PLEASE ITS URGENT I NEED HELP!!! I BEG YOU GUYS PLEEAASEEE THANKS..
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Explanation
remember some properties of the exponents
[tex]\begin{gathered} a^m\cdot a^n=a^{m+n} \\ (a^m)^n=a^{m\cdot n} \\ a^{-m}=\frac{1}{a^m} \end{gathered}[/tex]then, to solve this solve each option and compare
Step 1
[tex]6^{-5}\cdot6^2[/tex]solve
[tex]\begin{gathered} 6^{-5}\cdot6^2=6^{-5+2}=6^{-3} \\ \end{gathered}[/tex]so, this is not an answer
Step 2
[tex](\frac{1}{6^2})^5[/tex]solve
[tex]\begin{gathered} (\frac{1}{6^2})^5=(6^{-2})^5=6^{(-2\cdot5)}=6^{-10} \\ \end{gathered}[/tex]so, this is an answer
Step 3
[tex]\begin{gathered} (6^{-5})^2 \\ \text{solve} \\ (6^{-5})^2=6^{-5\cdot2}=6^{-10} \end{gathered}[/tex]so, this is an answer
Step 4
[tex]\begin{gathered} \frac{6^{-3}}{6^7} \\ \text{solve} \\ \frac{6^{-3}}{6^7}=\frac{1}{6^3\cdot6^7}=\frac{1}{6^{3+7}}=\frac{1}{6^{10}}=6^{-10} \end{gathered}[/tex]so, this is an answer
Step 5
[tex]\begin{gathered} \frac{6^5\cdot6^{-3}}{6^{-8}} \\ \text{solve} \\ \frac{6^5\cdot6^{-3}}{6^{-8}}=\frac{6^{5-3}}{6^{-8}}=\frac{6^2}{6^{-8}}=6^2\cdot\frac{1}{6^{-8}}=6^2\cdot6^8=6^{10} \end{gathered}[/tex]so, this is not an answer
I hope this helps you
What are the domain and range of y = cot x? Select onechoice for domain and one for range.
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ANSWER:
A. Domain: x ≠ n
D. Range: All real numbers
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]y=\cot\left(x\right)[/tex]The domain of a function is the interval of input values, that is, the interval of x while the range is the interval of output values, that is, the interval of y.
In the cotangent function, x cannot take the value of radians (nor its multiples), since it is not defined, while the range is continuous on all real numbers.
That means the correct options are:
A. Domain: x ≠ n
D. Range: All real numbers
A person investigating to employment opportunities. They both have a beginning salary of $42,000 per year. Company A offers an increase of $1000 per year. Company B offers 7% more than during the preceding year. Which company will pay more in the sixth year? what will company A pay? and what will company B pay?
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qANSWER
Company B will pay more
Company A =
EXPLANATION
Both companies start by paying $42,000 per year.
Company A offers an increase of $1000 per year.
This means that after n years, he would have earned:
Earnings = 42000 + 1000n
where n = number of years after the first year
So, after 6 years, he would have worked 5 years after the first, so his earnings would be:
Earnings = 42000 + 1000(5) = 42000 + 5000
Earnings = $47000
Company B offers 7% more than the previous year. That means that his earnings are compounded.
His earnings can then be represented as:
[tex]\text{ Earnings = P(1 + }\frac{r}{100})^t[/tex]where P = initial salary = $42000
r = interest rate = 7%
t = number of years spent = 6 years
Therefore, his earnings after the 6th year will be:
[tex]\begin{gathered} \text{ Earnings = 42000(1 + }\frac{7}{100})^6 \\ \text{ Earnings = 42000(1 + 0.07)}^6=42000(1.07)^6 \\ \text{ Earnings = }42000\cdot\text{ 1.501} \\ \text{Earnings = \$63042} \end{gathered}[/tex]He would have earned $63042.
Therefore, Company B will pay more.
qANSWER
Company B will pay more
Company A =
EXPLANATION
Both companies start by paying $42,000 per year.
Company A offers an increase of $1000 per year.
This means that after n years, he would have earned:
Earnings = 42000 + 1000n
where n = number of years after the first year
So, after 6 years, he would have worked 5 years after the first, so his earnings would be:
Earnings = 42000 + 1000(5) = 42000 + 5000
Earnings = $47000
Company B offers 7% more than the previous year. That means that his earnings are compounded.
His earnings can then be represented as:
[tex]\text{ Earnings = P(1 + }\frac{r}{100})^t[/tex]where P = initial salary = $42000
r = interest rate = 7%
t = number of years spent = 6 years
Therefore, his earnings after the 6th year will be:
[tex]\begin{gathered} \text{ Earnings = 42000(1 + }\frac{7}{100})^6 \\ \text{ Earnings = 42000(1 + 0.07)}^6=42000(1.07)^6 \\ \text{ Earnings = }42000\cdot\text{ 1.501} \\ \text{Earnings = \$63042} \end{gathered}[/tex]He would have earned $63042.
Therefore, Company B will pay more.
Angie added a stone border 2 feet in width on all sides of her garden making her harder 12 by 6 feet. What is the area, in square feet, of the portion of the garden that excludes the border?
A. 4
B. 16
C. 40
D. 56
E. 72
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The area, in square feet, of the portion of the garden that excludes the border is 40.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
We have been given that Angie added a stone border of 2 feet in width on all sides of her garden making her harder 12 by 6 feet.
Length = 12 ft
Width = 6 ft
The dimension of the garden that excludes the border of 2 feet are;
Length = 12 ft- 2 = 10 ft
Width = 6 ft - 2= 4 ft
Thus, Area = length × Width
Area = 10 x 4
Area = 40 square feet
Hence, the area, in square feet, of the portion of the garden that excludes the border is 40.
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Hi there, I need help with this question. Thank you in advance!
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For the data given, we have 24 entries in all.
They are :
75, 36, 80, 49, 24, 61, 34, 39, 30, 76, 44, 44, 40, 35, 21, 89, 34, 70, 79, 65, 66, 53, 99, 11
(1) Minimum refers to the lowest data in the table. we can see out of all the data in the table, the lowest is 11. Therefore,
Min = 11
(2) Maximum refers to the highest data in the table.
The highest is 99.
Therefore,
Max = 99
(3) Range is defined as highest data minus lowest data
Range = 99 - 11
Range = 88
(4) Mean:
[tex]\begin{gathered} \text{ Mean =}\frac{\text{ sum of the data}}{total\text{ count}} \\ \operatorname{mean}\text{ = }\frac{75+36+80+49+24+61+34+39+30+76+44+44+40+35+21+89+34+70+79+65+66+53+99+11}{24} \\ \\ \text{Mean = }\frac{1254}{24} \\ =52.25 \end{gathered}[/tex]Therefore,
Mean = 52.25
(5) Standard deviation:
The steps to calculate the standard deviation in shown in the picture below.
The standard deviation = 22.8386..
To 2 decimal places, we have 22.84
Therefore,
Standard deviation = 22.84
please help me I dont understand A number is less than or equal to - 7 or greater than 12.
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To translate the sentence as an inequality, we have:
[tex]x\leq-7,x>12[/tex]Since the number is less or equal ( < = ) we use this symbol to represent it as inequality, and greater than using the symbol ( > ).
Then, we can answer the question as:
x < = -7 or x > 12.
Consider the two polynomials p(x), q(x) in Z[x] by p(x) = 1+2x+3x2, q(x) = 4+5x+7x3. Then p(x) + q(x) is
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The solution for polynomials p(x) + q(x) is 7x³ + 3x² + 7x + 5
Given,
The polynomials
p(x) = 1 + 2x + 3x²
q(x) = 4 + 5x + 7x³
We have to find the solution for p(x) + q(x)
Then,
p(x) + q(x) = (1 + 2x + 3x²) + ( 4 + 5x + 7x³)
p(x) + q(x) = 7x³ + 3x² + 2x + 5x + 1 + 5
p(x) + q(x) = 7x³ + 3x² + 7x + 5
That is,
The solution for polynomials p(x) + q(x) is 7x³ + 3x² + 7x + 5
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For the function f(x)=3x2−4x−4,a. Calculate the discriminant.b. Determine whether there are 0, 1, or 2 real solutions to f(x)=0.
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Answer:
a) Using the formula for the discriminant we get:
[tex]\begin{gathered} \Delta=(-4)^2-4(3)(-4), \\ \Delta=16+48, \\ \Delta=64. \end{gathered}[/tex]The discriminant is 64.
b) Based on the above result we know that the f(x)=0 has 2 real solutions,
For each set of three side lengths in the table, determine how many unique triangles can be formed. Select the appropriate circle in each row.
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The first one the 3 sides are equal to 1, this mean that it is a equilater triangle, so it is possible to made exactly one unique triangle.
now for the other triangles we will add the two shortest sides of the triangle, and if they are more than the greater side of the triangle, then it will be a unique triangle, if not there will be more than one triangle
for the second one:
[tex]3+4=7>5[/tex]so the second one have exactly one unique triangle.
for the number 3:
[tex]5+10=15=15[/tex]So in this case there is none unique triangles.
for the number 4:
[tex]6+16=22<26[/tex]So in this case there is none unique triangles.
and for the number 5:
[tex]10+50=60>55[/tex]So we hace exactly one unique triangle.
find the first term when the 31st 32nd and 33rd are 1.40, 1.55, and 1.70
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jadeymae06, this is the solution:
This is an arithmetic sequence, where d (common difference) = 0.15
(1.70 - 1.55) or (1.55 - 1.40)
•
,• a + 30d = 1.40
,• a + 30(0.15) = 1.4
,• a + 4.5 = 1.4
,• a = 1.4 - 4.5
,• a = -3.1
Jade, the first term is -3.1
Write the equation of the circle centered at (−4,−2) that passes through (−15,19)
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In this problem, we are going to find the formula for a circle from the center and a point on the circle. Let's begin by reviewing the standard form of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]The values of h and k give us the center of the circle, (h,k). The value r is the radius. We can begin by substituting the values of h and k into our formula.
Since the center is at (-4, -2), we have:
[tex]\begin{gathered} (x-(-4))^2+(y-(-2))^2=r^2 \\ (x+4)^2+(y+2)^2=r^2 \end{gathered}[/tex]Next, we can use the center and the given point on the circle to find the radius.
Recall that the radius is the distance from the center of a circle to a point on that circle. So, we can use the distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Let
[tex](x_1,y_1)=(-4,-2)[/tex]and let
[tex](x_2,y_2)=(-15,19)[/tex]Now we can substitute those values into the distance formula and simplify.
[tex]\begin{gathered} r=\sqrt{(-15-(-4))^2+(19-(-2))^2} \\ r=\sqrt{(-11)^2+(21)^2} \\ r=\sqrt{562} \end{gathered}[/tex]Adding that to our equation, we have:
[tex]\begin{gathered} (x+4)^2+(y+2)^2=(\sqrt{562})^2 \\ (x+4)^2+(y+2)^2=562 \end{gathered}[/tex]True or false? Based only on the given information, it is guaranteed thatAD EBDADGiven: ADI ACDBICBAC = BCBCDO A. TrueB. FalseSUBMIT
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According to the information given, we can assure:
For both triangles, two interior angles and the side between them have the same measure and length, respectively. This is consistent with the ALA triangle congruence criterion.
ANSWER:
True.
Can you please help me out with a question
Answers
right. the lateral area of a hemisfere is the curved area, wich is half the area of a complete sphere
area of a sphere:
4πr²
So, half the area is 1/2(4πr²)= 2πr²
Now, the total surface is the lateral area plus the area of the base. the base is a circle, so the area is equal to πr²
And the volume of a hemisfere is equal to half the volume of a sphere:
[tex](\frac{4}{3}\pi r^3)\cdot\frac{1}{2}\text{ =}\frac{2}{3}\pi r^3[/tex]So, the anwsers are:
[tex]2\pi r^{2}\text{ = }2\pi(24ft)^{2}\text{ = 1152}\pi ft^2[/tex][tex]\pi r^{2}\text{ = }\pi(24ft)^2\text{ = 576}\pi ft^2[/tex][tex]\frac{2}{3}\pi r^3\text{ = }\frac{2}{3}\pi(24ft)^3\text{ = 9216}\pi ft^3[/tex]The answers are in order
What is the distance from 7 to 0? O A. 7, because 171 = 7 Jurid O B. 7, because 171 = 7 O c. 7, because |-71 = -7 O D. -7, because [7] = -7
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The distance from 7 to 0 is 7 because the absolute value of 7 is 7.
Correct Answer: A
I wills send you a picture
Answers
Draw the tank
we can use the formula of the volume of a cylinder
[tex]V=\pi\times r^2\times h[/tex]we can repalce the value of the volume (320pi) and the height
[tex]\begin{gathered} 320\pi=\pi\times r^2\times20 \\ 320\pi=20r^2\pi \end{gathered}[/tex]now solve for r^2 dividing 20pi on both sides
[tex]\begin{gathered} \frac{320\pi}{20\pi}=r^2 \\ \\ r^2=16 \\ \end{gathered}[/tex]and solve for r using roots
[tex]\begin{gathered} r=\sqrt[]{16} \\ \\ r=4 \end{gathered}[/tex]the value of the radious is 4ft and the diameter double, then
[tex]\begin{gathered} d=2\times4 \\ d=8 \end{gathered}[/tex]diameter of the cylinder is 8 ft then rigth option is C
Hey I need help with my homework help me find the points on the graph too please Thankyouu
Answers
Given the function:
g(x) = 3^x + 1
we are asked to plot the graph of the function.
Using the table:
x y
-2 10/9
-1 4/3
0 2
1 4
2 10
The graph:
The expomential functions have a horizontal asymptote.
The equation of the horizontal asymptote is y = 1
Horizontal Asymptote: y = 1
To find the domain is finding where the question is defined.
The range is the set of values that correspond with the domain.
Domain: (-infinity, infinity), {x|x E R}
Range: (1, infinity0, {y|y > 1}.
Nov 28,Quadrilateral ABCD is dilated by a scale factor of to form quadrilateral A'B'C'D'.What is the measure of side DA?Dal1515301B2162А
Answers
The quadrilateral ABCD was dilated by a scale factor of 3/4 to form the quadrilateral A'B'C'D'
This means that each side of the quadrilateral was multiplied by 3/4 to make the dilation.
You know that the scale factor is 3/4 and the length of D'A' is equal to 30 units, then:
[tex]\begin{gathered} D^{\prime}A^{\prime}=\frac{3}{4}DA \\ 30=\frac{3}{4}DA \end{gathered}[/tex]Multiply both sides by the reciprocal of 3/4
[tex]\begin{gathered} 30\cdot\frac{4}{3}=(\frac{4}{3}\cdot\frac{3}{4})DA \\ 40=DA \end{gathered}[/tex]The length of side DA is 40 units.
