The given expression is,
[tex]5(-7+3k)[/tex]Opening the brackets and multiplying each term inside the bracket with 5, we get,
[tex]\begin{gathered} \lbrack5\times(-7)\rbrack+(5\times3k)=-35+15\text{ k} \\ 15k=35 \\ k=\frac{35}{15}=2.33 \end{gathered}[/tex]The simplified expression is 15k = 35 and the value of k is 2.33.
Solve e–5x = 7.4 for x correct to four decimal places. –0.40030.40030.8692–0.8692
Question:
[tex]e^{-5x}=7.4[/tex]Step 1: Apply the exponent rule but taking ln of both sides
[tex]\begin{gathered} e^{-5x}=7.4 \\ -5x=\ln 7.4 \end{gathered}[/tex]Step 2:Divide both sides by -5
[tex]\begin{gathered} -5x=\ln 7.4 \\ \frac{-5x}{-5}=\frac{\ln 7.4}{-5} \\ x=\frac{\ln7.4}{-5} \end{gathered}[/tex]Hence,
The value of x is
[tex]\begin{gathered} x=\frac{\ln7.4}{-5} \\ x=-4.003 \end{gathered}[/tex]Hence,
The final answer is = -0.4003
126°r= 15 cmFind the arc length of the shaded sector.
To determine the arc length of the shaded area you have to use the following formula:
[tex]\text{arc.length}=2\pi r(\frac{\theta}{360º})[/tex]"θ" represents the measure of the central angle, in degrees
"r" represents the radius of the circle
We know that the arc measure is 126º, the central angle has the same measure as the intercepted arc, then its measure is also θ=126º
The radius of the circle is r=15cm
[tex]\begin{gathered} \text{arc.length}=2\pi\cdot15\cdot(\frac{126}{360}) \\ \text{arc.length}=30\pi\cdot\frac{7}{20} \\ \text{arc.length=}\frac{21}{2}\pi \\ \text{arclength}\approx32.98\approx33\operatorname{cm} \end{gathered}[/tex]Solve by graphing. If the population of a town is growing at a rate of 2.5% each year and the current population is 50,000. After how many years will the population reach 100,000 people. Round to the NEAREST whole number. Be sure to label your answer.
The situation describes an exponential growth, which can be expressed using the general formula:
[tex]y=a(1+r)^x[/tex]Where
a is the initial value
r is the growth rate, expressed as a decimal value
x is the number of times intervals
y is the final value after x time intervals
For the studied population, the growth rate is 2.5%, to express this number as a decimal value you have to divide it by 100:
[tex]\begin{gathered} r=\frac{2.5}{100} \\ r=0.025 \end{gathered}[/tex]The initial value is the current population of the town: a=50000
You can express the equation of exponential growth for this population as follows:
[tex]\begin{gathered} y=50000(1+0.025)^x \\ y=50000(1.025)^x \end{gathered}[/tex]We know that after x years the population will be y=100000, to determine how many years it will take to reach this value you have to equal the equation to 100000 and solve for x:
[tex]100000=50000(1.025)^x[/tex]-Divide both sides of the expression by 50000
[tex]\begin{gathered} \frac{100000}{50000}=\frac{50000(1.025)^x}{50000} \\ 2=(1.025)^x \end{gathered}[/tex]-Apply logarithm to both sides of the equal sign:
[tex]\begin{gathered} \log (2)=\log (1.025^x) \\ \log (2)=x\cdot\log (1.025) \end{gathered}[/tex]-Divide both sides by the logarithm of 1.025
[tex]\begin{gathered} \frac{\log(2)}{\log(1.025)}=\frac{x\cdot\log (1.025)}{\log (1.025)} \\ x\approx28.07\approx28 \end{gathered}[/tex]After approximately 28 years the population of the town will be 100,000.
Sketch a diagram showing VX intersectingUW at V so that VX is perpendicular toU and U, V, and W are collinear.
We have to do a diagram with the following characteristics.
• VX has to intersect UW at V.
,• VX is perpendicular to UW.
,• U, V, and W are collinear.
Based on the given information, we have the following diagram
The image above shows the answer.
The values of x and y
The values of x and y are 26° and 54° respectively.
Consider the triangle with x is triangle 1
Triangle with y is triangle 2
In triangle 1
Since it is a right angled triangle one angle is already known
Another angle is 64°
We know the sum of interior angles of a triangle is equal to 180
Hence 90 + 64 +x = 180°
154 + x = 180°
x= 180 - 154
x = 26°
From triangle 2 it is evident that x and y are complementary angles which means they sum up to 90°
Hence x + y = 90°
26 + y = 90
y = 90 - 26
y = 54°
Hence the value of x and y are 26° and 54° respectively
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Find the coordinates of the points of intersection of the graphs with coordinate axes: y= -1/4x+2
Answer:
Solutions below.
Step-by-step explanation:
This question is asking us to find the points of intersection, which means its asking to find the x-intercept abd y-intercept.
To find the x-intercept, we know that y = 0.
Therefore we can substitute y = 0 into the line equation:
[tex]0 = - \frac{1}{4} x + 2 \\ - \frac{1}{4} x = - 2 \\ x = - 2 \div - \frac{1}{4} \\ = 2 \times 4 \\ = 8[/tex]
Therefore the point of the x-intercept is (8,0).
Likewise to find the y-intercept, we know x = 0.
Therefore we can substitute x = 0 into the line equation:
[tex]y = - \frac{1}{4} (0) + 2 \\ = 0 + 2 \\ = 2[/tex]
Therefore the point of the y-intercept is (0,2).
Answer:
x-intercept: (8, 0)
y-intercept: (0, 2)
Step-by-step explanation:
Given equation:
[tex]y=-\dfrac{1}{4}x+2[/tex]
The graph intersects the y-axis when x = 0.
To find the graph's y-intercept, substitute x = 0 into the equation and solve for y:
[tex]\begin{aligned}x=0 \implies y&=-\dfrac{1}{4}(0)+2\\y&=0+2\\y&=2\end{aligned}[/tex]
Therefore, the coordinates of the point of intersection with the y-axis are:
(0, 2)The graph intersects the x-axis when y = 0.
To find the graph's x-intercept, substitute y = 0 into the equation and solve for x:
[tex]\begin{aligned}y=0\implies \-\dfrac{1}{4}x+2&=0\\-\dfrac{1}{4}x&=-2\\x&=8\end{aligned}[/tex]
Therefore, the coordinates of the point of intersection with the x-axis are:
(8, 0)bvhftfgtfygygfygygftfghh vv g f f fyk jf khvy. ynnnnnnnnnnnnnn
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At preseident Obama's inauguration in 2013 the newspaper head lines stated there were about 800.000 people in attendance if the newspaper rounded to the nearest hundred thousand what is the largest number and smallest number of people who could have been there
The smallest whole number is 750,000, while the largest whole number is 849,999.
Consider the facts offered.
We must determine the smallest whole integer that, when rounded to the nearest hundred thousands, equals 800,000
Rounding a numerical rule
If the number on the right side of the rounding digit is 0, 1, 2, 3, 4, there is no need to modify the rounding digit and replace the remainder of the digit on the right with 0.
If the number on the right side of the rounding digit is 5, 6, 7, 8, 9, the rounding digit rounds up by one number and replaces the remainder of the digit on the right with 0.
Consider the number 800,000 for a moment.
Because we want the smallest number possible, the number at the hundred thousand place should be 7.
As a result, the smallest whole number is 750,000.
We now want the largest whole number that rounds to 800,000
Similarly, the biggest whole number must be bigger than 800,000 We don't want to raise the number at the hundred thousand place, hence the best ten thousand place option is 4. Put 9 at the rest locations to get the highest number.
As a result, the biggest whole number is 849,999.
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What is the area of this figure?
5 mm
19 mm
36 mm
7 mm
8 mm
7 mm
13 mm
9 mm
Write your answer using decimals, if necessary.
9 mm
11 mm
(2a² + 7a - 10) (a – 5)
2a³ - 3a² - 45a + 50 is the simplified form of the expression ( 2a² + 7a - 10 )( a - 5 ) using FOIL method.
What is the simplified form of the given expression?Given the expression in the question;
( 2a² + 7a - 10 )( a - 5 )
To expand ( 2a² + 7a - 10 )( a - 5 ), multiply each term in the first expression by each term in the second expression.
( 2a² + 7a - 10 )( a - 5 )
a( 2a² + 7a - 10 ) -5( 2a² + 7a - 10 )
a×2a² + a×7a + a×-10 -5×2a² -5×7a -5×-10
Multiply a and 2a²
2a³ + a×7a + a×-10 -5×2a² -5×7a -5×-10
Multiply a and 7a
2a³ + 7a² + a×-10 -5×2a² -5×7a -5×-10
Multiply a and -10
2a³ + 7a² - 10a -5×2a² -5×7a -5×-10
Multiply -5 and 2a²
2a³ + 7a² - 10a - 10a² -5×7a -5×-10
Multiply -5 and 7a
2a³ + 7a² - 10a - 10a² - 35a -5×-10
Multiply -5 and -10
2a³ + 7a² - 10a - 10a² - 35a + 50
Collect and add like terms
2a³ + 7a² - 10a² - 10a - 35a + 50
2a³ - 3a² - 45a + 50
Therefore, the simplified form of the expression is 2a³ - 3a² - 45a + 50.
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in January 2008, the temperature in parts of Minnesota fell from 41 degrees to -13 degrees over a 24 hour period. what was the average temperature change per hour?
We need to find the average termperature change per hour during January 2008.
We have the information that Minnesota fell from 41 degrees to -13 degrees over 24 hours.
Then, 41 degrees to -13 degrees, there is a difference of 41+13 = 54 degrees over 24 hours.
If the difference is over 24 hours, then:
54 degrees / 24 hours =2.25 F is the rate of change.
However, the termperature is decreasing, so the rate of change must be negative.
Hence, the rate of change = -2.25 F.
The correct answer is the third option.
f(x)= -2x-1
h(x)= -x+5
(hf)(6)=??
Answer:
[tex]f(x) = - 2x - 1 \\ h(x) = - x + 5 \\ \\ The \: \: value \: \: of \: \: \: f(6) = ( - 2) \times 6 - 1 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - 13 \\ \\ as \: we \: know ,\: \\➪(hf)(x) = h(f(x)) \\ so \:➪( hf)(6) = h(f(6)) \\ \\ put \: the \: value \: \: of \: f(6) \: we \: \: get \\ \\➪ (hf)(6) \: = h( - 13) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - ( - 13) + 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 13 + 5 \\ \: \: \: \: \: \: \: = 18[/tex]
Tʜᴀɴᴋs Hᴏᴘᴇ ɪᴛ ʜᴇʟᴘs..4. There are 6 red, 5 white, 3 blue, and 4 green marbles in a bag. What is the probability of selecting a red marble, given that a blue marble was already selected?5. While playing Blackjack, an Ace is dealt. To get Blackjack, or 21, a card worth 10 is needed. This could be a 10, Jack, Queen, or King. What is the probability of not getting Blackjack?
How does a reflection affect the properties of a two dimensional
Reflection:
A reflection is a transformation that flips a figure across a line.
Properties of reflection:
• The length remains the same, the angles remain the same.
,• This means that the image and the pre-image have the same size and shape only the orientation changes.
,• The line segment which connects the corresponding parts of the image and pre-image is perpendicular to the line of reflection.
,• The distance from the line of reflection of the corresponding parts of the image and pre-image is the same.
Following is an example of a reflection
This is called a horizontal reflection since the image and the pre-image is flipped across the x-axis. The line of reflection is the vertical line.
Let sin 0 = 4/9. Find the exact value of cos 0.
we have the following
[tex]\sin \theta=\frac{4}{9}[/tex]sin of an angle is the same as:
[tex]\sin \theta=\frac{opposite}{hypotenuse}[/tex]therefore we can create the following right triangle:
we can calculate the adjacent side using the pythagorean theorem
[tex]h^2=a^2+b^2[/tex]where h is the hypotenuse, a is the adjacent side and b the opposite side to the angle.
thus, the adjacent side is:
[tex]a=\sqrt[]{h^2-b^2}=\sqrt[]{9^2-4^2}=\sqrt[]{81-16}=\sqrt[]{65}[/tex]Using that value, we can now calculate cos of the angle
[tex]\cos \theta=\frac{adjacent}{hypotenuse}[/tex][tex]\cos \theta=\frac{\sqrt[]{65}}{9}[/tex]which can't be simplify, thus that is the answer for the exact value
Jessica evaluates √2 on her calculator which
shows a value of 1.4142136.
She then writes √/2 =1.4142136.
Is she correct explain
Generally, one should not write down values such as this directly from a calculator. √2 is an irrational number, which means that instead of writing it as a terminating decimal, it is best to write it in its exact form (√2) to ensure accuracy for further calculations.
Sketch a graph representing f(x), indicating all intercepts and min or max points.
Given the function below;
[tex]f(x)=4-\frac{x^2}{8}[/tex]The x-intercept is the point where f(x) = 0 as shown:
[tex]\begin{gathered} 0=4-\frac{x^2}{8} \\ 0=32-x^2 \\ x^2=32 \\ x=\pm\sqrt{32} \\ x=\pm5.66 \end{gathered}[/tex]The x-intercept of the graph will be at (5.66, 0) and (-5.66, 0)
The y-intercept occurs at the. point where x = 0 to have:
[tex]\begin{gathered} f(0)=4-\frac{0^2}{8} \\ f(0)=4 \end{gathered}[/tex]The y-intercept is (0, 4)
The equivalent graphis as shown below
The graph shows that the function has a maxmum point at (0, 4) with no minimum point.
. Lisa, Bret, and Gary harvested apples.
Lisa filled 3 carts with apples. Bret also
filled 3 carts with apples. Gary filled
another 3 carts with apples. Write a
multiplication equation and a division
equation for this story.
Multiplication:
Lisa, Bret, and Gary harvested apples. If they each harvested 3 carts of apples, how many carts did they harvest in total?
--> 3 * 3 = 9 carts in total
Division:
Lisa, Bret, and Gary harvested apples. If all three of them harvested 9 carts of apples in total, how many carts did each person harvest.
--> 9 / 3 = 3 carts per person
The length of the base of an isosceles triangle is 49.96 meters. Each base angle is 31.43°. Find the length of each of the two equal sides of the triangle. Round to the hundredths place.
Given that:
- The triangle is isosceles.
- Its base is 49.96 meters.
- Each base angle is 31.43°.
You can draw the triangle. See the picture shown below (it is not drawn the scale):
Notice that the Isosceles Triangle can be divided into two equal Right Triangles. Then, you know that:
[tex]CD=BD=\frac{49.96m}{2}=24.98m[/tex]Since it is isosceles, the sides AB and AC have equal length.
Then, you can choose one of the equal Right Triangles and use the following Trigonometric Function in order to find the length of each equal side:
[tex]\cos \beta=\frac{adjacent}{hypotenuse}[/tex]In this case, you can set up that:
[tex]\begin{gathered} \beta=31.43\degree \\ adjacent=24.98 \\ hypotenuse=AC \end{gathered}[/tex]Therefore, substituting values and solving for AC, you get:
[tex]\begin{gathered} \cos (31.43\degree)=\frac{24.98}{AC} \\ \\ AC\cdot\cos (31.43\degree)=24.98 \end{gathered}[/tex][tex]\begin{gathered} AC=\frac{24.98}{\cos (31.43\degree)} \\ \\ AC\approx29.28 \end{gathered}[/tex]Hence, the answer is:
The length of the two equal sides of the triangle is:
[tex]length\approx29.28m[/tex]
Donna and her husband are each starting a saving plan. Donna will initially set aside S50 and then add $20.55 every week to the savings. The amount A (in
dollars) saved this way is given by the function = 50+20.55N, where N is the number of weeks she has been saving.
Her husband will not set an initial amount aside but will add $80.55 to the savings every week. The amount B (in dollars) saved using this plan is given by the
function B=80.55 N.
Let T be total amount (in dollars) saved using both plans combined. Write an equation relating T to N. Simplify your answer as much as possible.
The total amount (in dollars) saved using both plans combined is T = 50 + 101.1N.
How to illustrate the equation?Based on the information, the function = 50+20.55N.
where N is the number of weeks she has been saving.
For the second function, this is illustrated as:
function B = 80.55 N.
Therefore, the total of the plans combined will be:
T = 50 + 20.55N + 80.55N
T = 50 + 101.1N
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Complete the function for this graph.
Enter the correct
symbol,+ or -.
y = [?] |x|
Answer:
Step-by-step explanation:
y = -|x|
The graph is facing downwards, meaning it is negative.
The students in Cassie's class got to choose between pizza and burgers for the celebration on the last day of school. 8 students picked the pizza. If there are 10 students in all in Cassie's class, what percentage of the students picked the pizza? Write your answer using a percent sign (%).
There is a total of 10 students in Cassie's class.
8 students choose Pizza
So, the percentage of the students who picked the pizza is 80%.
[tex]Percentage\%= \frac{Students who picked Pizza}{Total number of students in class} *100[/tex]
[tex]Percentage\%= \frac{8}{10}*100\%[/tex]
[tex]=\frac{800}{10}\%[/tex]
[tex]=80\%[/tex]
And 20% of students picked Burgers.
About Percentage
The Latin adverb "percent" means "by the hundred." The 16th century saw its invention. The abbreviation was later changed to %. Later, the period was eliminated, and the two words were merged to form the term "percent." Brief explanations employ the annotation sign %. Calculate your percentage of marks by comparing your final score to your overall score.
The percentage is a fraction or a ratio in which the value of the whole is always 100. For example, if Sam scored 30% marks in his math test, it means that he scored 30 marks out of 100. It is written as 30/100 in the fraction form and 30:100 in terms of ratio.
Percentage Definition:
The percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
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{2x + 3y = 5}{ y= 5 x -4}
Solve the system using substitutions:
[tex]\begin{gathered} 2x+3y=5 \\ 2x+3(5x-4)=5 \\ 2x+15x-12=5 \\ 17x=5+12 \\ 17x=17 \\ x=\frac{17}{17} \\ x=1 \end{gathered}[/tex]x has a value of 1. Use this value to find the value of y.
[tex]\begin{gathered} y=5x-4 \\ y=5\cdot1-4 \\ y=5-4 \\ y=1 \end{gathered}[/tex]y has a value of 1.
x=1
y=1
Using the table, what is the average daily balance of the credit card for the May 1 - May 31 billing period? Round your answer to the nearest cent. Do not include a dollar sign or comma in your answer. For example, $5,678.00 should be entered as 5678.00.
The average daily balance for the credit card for the may 1 - may 2 billing period was 1566.13
From the table given, we have
The balance of the credit card from May 1 - May 5 was 2000 which is 5 days, from may 6- may 10 was 1600, which is again 5 days, from may 11 to may 20 was 1350, the interval is 10 days and 21 to may 31, 11 days the balance was 1550.
The avergae daily balance was
=[tex]\frac{(Balance (number of days))}{Total number of days}[/tex]
= [tex]\frac{2000(5)+1350(10)+1550(11)}{5+5+10+11}[/tex]
=[tex]\frac{48550}{31}[/tex]
=1566.13
So The average daily balance for the credit card for the may 1 - may 2 billing period was 1566.13
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Which of the following numbers represents the place the digit 8 as 80?
2x+2y = 4 2x + 2y = 3 One Solution No Solutions Infinitely Many Solutions
The system has no solutions
Here, we want to solve the system of linear equations
As we can see, the exact expression is what we have on the left side of both equations
The only different thing is what we have on the right hand side
What this mean is that no values of x and y can satisfy both equations
With that in mind, we have it that the system of equations has no solutions
pls help l need to finish this
The equation of the linear function represented by the table below in slope-intercept form is y = -3x + 5
The linear function that will be obtained by using these values of x and y will be a Equation of line.
The slope-intercept form of line looks like this,
y = mx + c
where,
m is the slope.
c is the y intercept,
Firstly, to find the slope we can use any two points,
we will use (1,2) and (2,-1)
Hence, slope m,
m = (-1-2)/(2-1)
m = -3
Putting the value of slope in equation y = mx + c,
y = -3x + c
To fin the value of c,
Using the coordinate (1,2) and putting the values of x and y,
2 = -3 + c
c = 5.
Putting the values of c and m in the equation,
we get,
y = -3x + 5.
The required equation of the line in slope-intercept form is y = -3x + 5
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Type the correct answer in each box. Use numerals instead of words.Consider this expression,-412 + 21 - 5(1 + r)What expression is equivalent to the given expression?12 + I +ResetNext
To answer this question, we need to expand the original equation, and then simplify to obtain the equivalent expression as follows:
[tex]-4x^2+2x-5(1+x)=-4x^2+2x-5(1)-5(x)[/tex]We used the distributive property for -5 (1 + 5).
Then, we have:
[tex]-4x^2+2x-5-5x=-4x^2+2x-5x-5[/tex]Adding like terms:
[tex]-4x^2-3x-5[/tex]In summary, therefore, the equivalent expression is:
[tex]-4x^2-3x-5[/tex]At an animal shelter, 3/8 of the animals are dogs. Of the
dogs, 2/5 have spots. What portion of the animals at the
shelter are dogs that have spots?
At an animal shelter, 3/8 of the animals are dogs, of the dogs, 2/5 have spots, 3/20 portion of the animals at shelter are dogs that have spots. A fraction, which derives from Latin word fractus, which means "broken," is a portion of whole or, more broadly, any number of equal pieces.
What is a fraction?A fraction, which derives from Latin word fractus, which means "broken," is a portion of a whole or, more broadly, any number of equal pieces. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of particular size there are when stated in ordinary English. A common, vulgar, or simple fraction is one that has a non-zero denominator that is displayed below (or after) line on which the numerator is shown. Compound fractions, complicated fractions, and mixed numeral fractions are the examples of uncommon fractions that use numerators and denominators.
The numerator and the denominator of positive common fractions are both natural integers. The denominator shows how many of numerator's equal parts make up a unit or whole, and the numerator reflects the number of equal parts. Since there can never be zero components in a whole, denominator cannot be zero. For instance, numerator 3 in the fraction 3/4 denotes that the fraction is made up of 3 equal parts, while denominator 4 denotes that the fraction is made up of 4 parts altogether.
Let, [tex]\frac{3}{8} x[/tex] animals are dogs,
[tex]\frac{2}{5} * \frac{3}{8}x = \frac{3}{20}x[/tex]
Therefore, [tex]\frac{3}{20}[/tex] of the animals at shelter are dogs that have spots.
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Ai Mi was out at a restaurant for dinner when the bill came. Her dinner came to $9. After adding in a tip, before tax, she paid $11.79. Find the percent tip.
The percent tip which Ai mi added to the $9 dinner as required in the task content is; 31%.
What percent tip did Ai mi add to the dinner as described?It follows from the task content that the percent tip which Ai mi added to the dinner is to be determined by evaluation.
Since the dinner itself costs; $9 and she paid $11.79 after adding tip, it follows that the percent tip is the percentage change in price paid per unit original price as follows;
Percent tip = { ( 11.79 - 9 ) / 9} × 100%
Percent tip = 2.79/9 × 100%
Percent tip = 31%.
Therefore, the percent tip added by Ai mi to the original price of dinner is ; 31%.
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