We want to find the equation of the line with given slope and y-intercept.
The slope-intercept form of a line is:
[tex]y=mx+b[/tex]Where
m is the slope
b is the y-intercept (y-axis cutting point)
We are given the slope and y-intercept, so we simply substitute it. Steps are shown below:
[tex]\begin{gathered} y=mx+b \\ y=\frac{2}{5}x+(-7) \\ y=\frac{2}{5}x-7 \end{gathered}[/tex]The equation of the line is:
[tex]y=\frac{2}{5}x-7[/tex]In a recent survey of college-educated adults, 351 indicated that they regularly work more than 45hrs a week. If this represents 39% of those surveyed, how many people were in the survey?
Recall that the y% of x is given by the following expression:
[tex]x\cdot\frac{y}{100}\text{.}[/tex]Now, let S be the number of people that were in the survey, then, we know that 39% of S is 351, then we can set the following equation:
[tex]351=S\cdot\frac{39}{100}\text{.}[/tex]Multiplying the above equation by 100/39 we get:
[tex]\begin{gathered} 351\times\frac{100}{39}=S\cdot\frac{39}{100}\times\frac{100}{39}, \\ S=900. \end{gathered}[/tex]Answer: 900.
Indicate which property is illustrated in Step 6.Step 19 + 11x - 9 - 4x + 2=9 + (11x - 9) - 4x + 2Step 2=9 + (-9 + 11x) - 4x + 2Step 3=[9 + (-9)] + (11x - 4x) + 2Step 4=0 + (11x - 4x) + 2Step 5=(11x - 4x) + 2Step 6=(11 - 4)x + 2Step 7=7x + 2 A. additive inverse B. commutative C. associative D. distributive
step 6
(11 - 4)x + 2
the answer is option D.
distributive
Result is Result isRational IrrationalReason(a) 34 +O(Choose one)12(b)4+ -21(Choose one)17(c) ſo6 x 23(Choose one)13(d)8 x(Choose one)19
Firstly, rational numbers are numbers that can be express in the form of a ratio.
[tex]\begin{gathered} \frac{x}{y} \\ \text{where} \\ y\ne0 \end{gathered}[/tex]Irrational numbers are numbers that cannot be express in the form of a fraction. These numbers are non-terminating. Therefore,
a.
[tex]\begin{gathered} 34+\sqrt[]{7}=34+\sqrt[]{7} \\ 34\text{ is a rational number as it can be express in fraction} \\ \sqrt[]{7}\text{ is an irrational number. The square root of 7 is non-terminating.} \\ \text{The sum of a rational and an irrational number will }always\text{ be an irrational number} \end{gathered}[/tex]b.
[tex]\begin{gathered} \frac{12}{17}+\frac{4}{21}=\frac{252+68}{357}=\frac{320}{357}(rational) \\ \text{The sum of 2 rational numbers }produces\text{ a rational number.} \\ \text{Notice that the individual numbers can be express in fractions. This makes them rational.} \end{gathered}[/tex]c.
[tex]\begin{gathered} \sqrt[]{6}\times23=23\sqrt[]{6} \\ The\text{ product of the irrational number(}\sqrt[]{6}\text{) and rational number(23) will result in an irrational number.} \end{gathered}[/tex]d.
[tex]\begin{gathered} 8\times\frac{13}{19}=\frac{104}{19} \\ 8\text{ is rational number} \\ \frac{13}{19}\text{ is a rational number because it can be express in fraction.} \\ \text{The product of the 2 rational number will produce a rational number (}\frac{104}{19}\text{)} \end{gathered}[/tex]Write a transformation of a quadratic function with a vertical stretch by a factor of 2, followed by a horizontal shift of 3 units to the left and 5 units down.show workkkk!!!
The standard form of a quadratic function presents the function in the form
[tex]f(x)=a(x-h)^2+k[/tex]where (h, k) is the vertex.
The standard form is useful for determining how the graph is transformed from the graph of y = x^2. The figure below is the graph of this basic function.
You can represent a horizontal (left, right) shift of the graph of
by adding or subtracting a constant, h, to the variable x, before squaring. Here h = -3
[tex]y=(x+3)^2[/tex]The magnitude of a indicates the stretch of the graph. a = 2
[tex]y=2(x+3)^2[/tex]your budget is $80.00 to buy new clothes.what us the maximum whole dollar amount that you can spend on clothes, (bearing in mind that you will also have to pay 7.5 sales tax.)
We are told that the maximum amount to spend is $80 and that there is a 7.5% sales tax. If N is the amount we are going to spend then we need to have into account that we need to add the 7.5% of N and that should be at least equal to $80.
[tex]N+\frac{7.5}{100}N=80[/tex]Now we need to solve for N, to do that we add like terms:
[tex]\begin{gathered} (1+\frac{7.5}{100})N=80 \\ \frac{107.5}{100}N=80 \end{gathered}[/tex]Now we multiply both sides by 100:
[tex]107.5N=8000[/tex]Now we divide by 107.5:
[tex]N=\frac{8000}{107.5}[/tex]Solving the operations:
[tex]N=74.4\cong74[/tex]Therefore, the maximum amount to spend is $74
Recall that the formula for an area of a circle is A=πr^2 Find the radius of a circle whose area is 300 square meters. Give a decimal approximation rounded to 2 decimal places.raduis=_______meters
Given:
a.) Area of circle = 300 m²
Let's determine its radius,
[tex]\text{ Area = }\pi\text{r}^2[/tex][tex]\text{ }\pi r^2\text{ = Area}[/tex][tex]\text{ r}^2\text{ = }\frac{300}{3.1416}\text{ ; }\pi\text{ }\approx\text{ 3.1416}[/tex][tex]\text{ r = }\sqrt{\frac{300}{3.1416}}[/tex][tex]\text{ r = 9.77203881243 }\approx\text{ 9.77 m}[/tex]Therefore, the radius of the circle is approximately 9.77 m
An ice cream cone costs $3 plus 6% sales tax. How many ice creamcones can be purchased for $24270908
We know that
• Each ice cream costs $3.
,• Sales tax is 6%.
,• The total amount of money is $24.
Let's find the unit price including sales tax.
[tex]3+0.06(3)=3+0.18=3.18[/tex]So, each ice cream costs $3.18 with sales tax included. Now, we divide $242 by this price to get the total number of ice creams we can buy
[tex]\frac{24}{3.18}=7.5[/tex]Therefore, we can buy 7 ice creams.Hello not homework just review not worth any points question 9
We were given:
[tex]\begin{gathered} 74Dyani's age is not an even number. That means that:[tex]\begin{gathered} d=13\text{ or }15\text{ or }17 \\ \text{Dyani's age is the median} \\ \Rightarrow d=15 \\ \\ d=15 \end{gathered}[/tex]Dyani's age is halfway between Rachel & Shannon's:
[tex]\begin{gathered} d=\frac{r+s}{2} \\ 2d=c \\ 2(15)=r+s \\ 30=r+s \\ r+s=30 \\ \text{From the age set},\text{ the possible age of Rachel \& Shannon is 17 \& 13} \\ We\text{ were told that:} \\ sWe were given the inequality:[tex]\begin{gathered} sTherefore, the age of the girls are listed below:Shannon is 13 years old,
Mercedes is 14 years old
Dyani is 15 years old
Aisha is 16 years old
Rachel is 17 years old
6. A right triangle has legs of 4 and 5. What is the hypotenuse? Show your work.
Given:
The leg of 4 and 5
Find-:
The value of the hypotenuse
Explanation-:
The right triangle is:
Let the Hypotenuse is "x."
Use Pythagores theorm is:
[tex]\text{ Hypotenuse}^2=(\text{ Leg}_1)^2+(\text{ Leg}_2)^2[/tex]So the value of "x" is:
[tex]\begin{gathered} x^2=4^2+5^2 \\ \\ x^2=16+25 \\ \\ x^2=41 \\ \\ x=\sqrt{41} \end{gathered}[/tex]So value of hypotenuse is:
[tex]\begin{gathered} =\sqrt{41} \\ \\ \approx6.403 \end{gathered}[/tex]Find the value of x. 984 (149-x) 128 2x+4)
You have a pentagon. In order to determine the value of x for the given expression, of the measure of the angles, take into account that the sum of the interior angles of a pentagon is 540°.
Then, by using the given expressions you have:
(98) + (149 - x) + (2x + 4) + (114) + (128) = 540
To solve for x, proceed as follow:
(98) + (149 - x) + (2x + 4) + (114) + (128) = 540 eliminate parenthesis
98 + 149 - x + 2x + 4 + 114 + 128 = 540 simplify like terms left side
493 + x = 540 subtract 493 both sides
x = 540 - 493
x = 47
Hence, the value of x is x = 47
Use the Venn diagram shown to answer the question below.Which regions represent set B?
Answer
From the image attached, we can see that the regions in set B include
II
III
V
VI
Explanation
We are provided with the Venn Diagram for this question and asked to list the region spanned by set B.
For that, we will look at the circle representing the set B and easily list out the regions that exist in this circle.
From the image attached, we can see that the regions in set B include
II
III
V
VI
Hope this Helps!!!
need help with this
x=19 * sin(40)
x = 12.21
1) Since we have a right triangle and the opposite leg to angle 40º, then we can write the following trig ratio
[tex]\begin{gathered} \sin (40)=\frac{x}{19} \\ x=19\cdot\sin (40) \\ x=12.21296 \\ x\approx12.21 \end{gathered}[/tex]2) Then the equation for that is x= 19*sin(40) and the value of that leg is approximately 12.21 units
MAKE CONNECTIONSKatie is twice as old as her sister Mara. The sum of their ages is 24. Write a one-variable equation tosituation
Answer
3x = 24
Explanation
Let sister Maria's age be represented by x.
Katie is twice as old as her sister Mara
So Katie's age will be 2x.
If the sum of their ages is 24, it implies x + 2x =24
Therefore, a one-variable equation to the situation will be: 3x = 24
An item is regularly priced at $95. It is on sale for 60% off the regular price. How much (in dollars) is discounted from the regularprice?
We have to find the 60% of $95. Doing so, we have:
60/100*$95
0.6*$95 (Dividing)
$57 (Multiplying)
The discount is $57
Write the inequality shown by the shaded region in the graph with the boundary line 3x-y=9.
The equation given is,
[tex]3x-y=9[/tex]Since the boundary line is thick bold line and from the graph we can observe that the line (shaded portion) moves from the right to the left hand side.
Then the inequality of the shaded region is,
[tex]3x-y\leq9[/tex]Given a sphere with a diameter of 6.2 cm, find its volume to the nearest wholeknumberA. 998 cmB. 125 cmC. 39 cmD. 70 cm
The volume of a sphere of radius r is given by the following expression:
[tex]\frac{4}{3}\pi\cdot r^3[/tex]In this case the radius is equal to 6.2 cm so the volume of this sphere is:
[tex]\frac{4}{3}\pi\cdot6.2^3=\frac{4}{3}\pi\cdot238.328=998.3[/tex]If we round this to the nearest whole number we obtain 998 cm³. Then the answer is option A.
At the North Carolina Zoo there is a bucket that contains food for the gorillas and the grizzly bears. The gorilla food weighs 5.384 kg. The gorilla food weighs 0.796 kg more than the grizzly bear food. How much food for both gorillas and grizzly bears are in the bucket?
The food for both gorilla and grizzly bear in the bucket is 9.972 kg.
Given, at the North Carolina Zoo there is a bucket that contains food for the gorillas and the grizzly bears.
The gorilla food weighs 5.384 kg. The gorilla food weighs 0.796 kg more than the grizzly bear food.
Let the weight of the grizzly bear food be x,
According to the question,
weight of gorilla food = weight of grizzly bear food + 0.796 kg
5.384 = x + 0.796
x = 5.384 - 0.796
x = 4.588
So, the food for both gorilla and grizzly bear in the bucket is 9.972 kg.
Hence, the food for both gorilla and grizzly bear in the bucket is 9.972 kg.
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Can you provide an example of a number that is a perfect square
ANSWER
9
EXPLANATION
A perfect square is a number that can be expressed as the product of two equal integers.
For example, 9 is a perfect square because it can be expressed as the product 3 x 3 = 3² - which are two equal integers.
What is the coefficient and the constant of 5x+2-3x^2
Factor -1 out of the expression:
[tex]-1(3x^2-5x-2)[/tex]the coefficient of x² is 3 and the constant term is -2. The product of 3 and -2 is -6. The factors of -6 which sum to -5 are 1 and -6. Therefore:
[tex]undefined[/tex]5 A carpenter charges $720 for 18 hours of work. She charges the same amount of money foreach hour of work.Which table shows the relationship between the amount of time the carpenter works andamount of money she charges?theACarpenter's ChargesсCarpenter's ChargesAmountAmount ofAmountChargedTime WorkedCharged(dollars)(hours)(dollars)80375512571759225Carpenter's ChargesAmountCharged(dollars)720720720720Amount ofTime Worked(hours)2416062408320Carpenter's ChargesAmountCharged(dollars)720738756774Amount ofTime Worked(hours)19202122DAmount ofTime Worked(hours)14151617
Given:
A carpenter charges for 18 hours=$720.
Find:
We have to find the table which represents correct relationship between hours and charges.
Explanation:
A carpenter charges for 18 hours=$720.
A carpenter charges for 1 hour = 720/18 = $40.
Therefore, the charges of the carpenter for each hour is $40.
So, option A is correct option.
What is the area of this triangle? A=bh254 cm²90 cm²108 m²216 m²
Given:
A triangle with sides base 9 cm , height 12 cm and hypotenuse 15 cm.
Required:
What is the area of triangle?
Explanation:
The area of triangle is
[tex]A=\frac{1}{2}\times base\times height[/tex]We have base = 9 cm and height = 12 cm.
Now,
[tex]\begin{gathered} A=\frac{1}{2}\times9\times12 \\ A=54\text{ cm}^2 \end{gathered}[/tex]Answer:
Option A is correct.
Un gerente compró un total de 21 tazas de café y llaveros. Cada taza de café cuesta $8,50 y cada llavero cuesta $2,75. Si el gerente gastó un total de $132.50, ¿cuántas tazas de café compró el gerente?
Usemos la variable x para representar el número de tazas e y para el número de llaveros.
Si el número de artículos es 21, tenemos:
[tex]x+y=21[/tex]Si el costo total es 132.5, tenemos:
[tex]8.5x+2.75y=132.5[/tex]De la primera ecuación, podemos escribir:
[tex]y=21-x[/tex]Usando este valor de y en la segunda ecuación:
[tex]\begin{gathered} 8.5x+2.75(21-x)=132.5 \\ 8.5x+57.75-2.75x=132.5 \\ 5.75x=74.75 \\ x=13 \end{gathered}[/tex]Entonces la cantidad de tazas compradas es 13.
Which of the following is an infinite series?A) 3, –6, 12, –24, 48B) 2 − 6 + 18 − 54 + . . .C) 3, 13, 23, 33, . . .D) 4 + 8 + 16 + 32
SOLUTION
An infinite series is the sum of an indefinitely many numbers related in a given way. That is the addition of such number is continuos. So our answer should be between
B) 2 − 6 + 18 − 54 + . . . and
C) 3, 13, 23, 33, . . .
But, looking at both, C) is a sequence showing ordered list of numbers.
Hence B) is a showing series showing sum of a list of numbers or showing multiplication pattern.
Therefore, the correct answer is option B.
which one of these must be a correct congruence statement
Answer:
C. AB ≅ DE
Explanation:
If triangles ABC and DEF are similar, then the following holds:
[tex]\begin{gathered} \angle A\cong\angle D \\ \angle B\cong\angle E \\ \angle C\cong\angle F \end{gathered}[/tex]Likewise, the similar sides are:
[tex]\begin{gathered} AB\cong DE \\ AC\cong DF \\ BC\cong EF \end{gathered}[/tex]The correct choice is C.
In what quadrant of the complex plane is -10 + 23i - (20 - 171)
Simplify the expression -10+23i-(20-17i) implies,
[tex]-30+40i[/tex]The point (-30,40) lies in second quadrant.
Thus, the answer is second quadrant.
the graph to the right represents the cost of a taxi where X is distance in miles and y is cost $10 what conclusion can you make? A. the taxi will stop every two miles B. The taxi cost $2 per mile C. The taxi will stop after 5 miles D. The taxi cost $2 just to get into attacks
Explanation
Step 1
the graph to the right represents the cost of a taxi where X is the distance in miles and y is the cost.
if the cost is $10m it means,exist a x, that satisfies
[tex]f(x)=10[/tex]look for the y value = 10 in the graph
Step 2
down vertically for to find the x value
during the election of the last president 120 srudents voted fir Lindsey and 280 of the students voted for Sharif. 400 students total voted. What percentage voted for Lindsey
From a total of 400 students ,
120 votes for Lindsey
280 votes for Sharif
then 200 students = 50%
. 100 students= 25%
. 20 students = (50%)/10 = 5%
then 120 students (100+20) belows to 25%+5%= 30%
30% students voted for Lindsey
An object projected upwards with a velocity of 96 feet per second from a height of 6 feet above theground is modelled by the function ℎ() = −162 + 96 + 6 .A. [3 pts] How many seconds after launch will the object reach its maximum height? Round your answerto one decimal place.B. [3 pts] Find the maximum height that the object reaches. Round your answer to one decimal place.C. [3 pts] Find the x-intercept and explain its meaning on the context of the problem.D. [3 pts] After how many seconds will the object be 100 feet above the ground?E. [2 pts] Find the y-intercept and explain its meaning on the context of the problem
Given:
[tex]h(t)=-16t^2+96t+6[/tex]Find-:
(a) Maximum second after launch will the object reach its maximum height
(b) Find the maximum height that the object reaches.
(c) Find the x-intercept and explain its meaning in the context of the problem.
(d) After how many seconds will the object be 100 feet above the ground
(e) Find the y-intercept and explain its meaning on the context of the problem
Sol:
(a)
Maximum second after launch.
For maximum value derivative should be zero.
[tex]\begin{gathered} h(t)=-16t^2+96t+6 \\ \\ h^{\prime}(t)=-(16\times2)t+96 \\ \\ \end{gathered}[/tex][tex]\begin{gathered} -32t+96=0 \\ \\ 32t=96 \\ \\ t=\frac{96}{32} \\ \\ t=3 \end{gathered}[/tex]After 3-second the object reaches maximum height.
(b)
For maximum height is at t = 3
[tex]\begin{gathered} h(t)=-16t^2+96t+6 \\ \\ h(3)=-16(3)^2+96(3)+6 \\ \\ h(3)=(-16\times9)+(96\times3)+6 \\ \\ h(3)=-144+288+6 \\ \\ =150 \end{gathered}[/tex](c) x-intercept the value of y is zero that means:
[tex]\begin{gathered} h(t)=0 \\ \\ -16t^2+96t+6=0 \\ \\ -8t^2+48t+3=0 \\ \\ t=\frac{-48\pm\sqrt{48^2-4(-8)(3)}}{2(-8)} \\ \\ t=\frac{-48\pm48.98}{-16} \\ \\ t=6;t=-0.061 \end{gathered}[/tex]The negative value of "t" is not considered so at
x-intercept is 6 and -0.061
(d) Object be 100 feet above grounded is:
[tex]\begin{gathered} h(t)=-16t^2+96t+6 \\ \\ -16t^2+96t+6=100 \\ \\ -16t^2+96t-94=0 \\ \\ -8t^2+48t-47=0 \\ \end{gathered}[/tex]So, the time is:
[tex]\begin{gathered} t=\frac{-48\pm\sqrt{48^2-4(-8)(-47)}}{2(-8)} \\ \\ t=\frac{-48\pm\sqrt{800}}{-16} \\ \\ t=\frac{-48-28.28}{-16},t=\frac{-48+28.28}{-16} \\ \\ t=4.76,t=1.23 \end{gathered}[/tex]At t= 4.76 and t =1.23
(e)
For y-intercept value of "x" is zero.
[tex]\begin{gathered} h(t)=-16t^2+96t+6 \\ \\ h(0)=-16(0)^2+96(0)+6 \\ \\ h(0)=6 \end{gathered}[/tex]So, the y-intercept is 6.
balanced equation question for lrwctoce
Letter B is the correct answer.
2 Al 2
3 Ni 3
6 Br 6
The other equatins are unbalanced
i need help with math Will u
The value of 'w' for the two parallel lines are cut by the transversal is 52.
What is meant by the supplementary angles?The term "supplementary angles" refers to a pair of angles which always add up to 180°. These two perspectives are known as supplements. When supplementary angles are combined, they form a straight angle (180 degrees). In other words, so unless Angle 1 + Angle 2 = 180°, angles 1 and 2 are supplementary.For the given question
Two parallel lines are cut by the transversal.
Then,
w + (3w -28) = 180 (same side exterior angle of the traversal are supplementary)
Solve the equation;
4w - 28 = 180
4w = 208
w = 208/4
w = 52
Thus, the value of 'w' for the two parallel lines are cut by the transversal is 52.
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