Answer: [tex]x=2[/tex]
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
We know that the slope of this line is:
[tex]m=-\frac{3}{2}[/tex]
And the y-intercept is:
[tex]b=3[/tex]
Since the line intersects the x-axis when [tex]y=0[/tex], we can substitute values into [tex]y=mx+b[/tex]:
[tex]0=-\frac{3}{2}x+3[/tex]
The final step is to solve for "x", then:
[tex]-3=-\frac{3}{2}x\\\\(-3)(-2)=3x\\\\6=3x\\\\x=\frac{6}{3}\\\\x=2[/tex]
The x-intercept of the line is 2.
We must figure out the value of x when the y-coordinate is 0, in order to identify the x-intercept of a line.
We can express the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept,
Given that the slope of the line is -3/2 and the y-intercept is 3.
Substituting the given values into the equation, we have y = (-3/2)x + 3.
To find the x-intercept, we set y = 0 and solve for x:
0 = (-3/2)x + 3
Subtracting 3 from both sides:
(-3/2)x = -3
To isolate x, we multiply both sides by -2/3:
x = (-3)(-2/3)
x = 2
Therefore, the x-intercept of the line is 2.
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Dan spends 2/5 of his wages on rent and 1/2 on food. If he makes £540 per week, how much money does he have left?
Answer:
Dan has £54 left
Step-by-step explanation:
Dan's weekly wages are £540.
Then his spending includes (2/5)w + (5/10()w, or (9/10)w, and this is subtracted from Dan's wages: £540 - (expenses)
£540 - (9/10)(£540) = £54
Dan has £54 left after having spent 9/10 of his weekly wages on rent and food.
Solve 2x - 8 < 7.
{x | x < 1/2}
{x | x > 1/2}
{x | x < 15/2}
{x | x > 15/2}
The solution to the inequality is [tex]\( \{ x \,|\, x < \frac{15}{2} \} \),[/tex] indicating all real numbers less than [tex]\( \frac{15}{2} \).[/tex]
To solve the inequality [tex]\(2x - 8 < 7\)[/tex], we'll isolate x by adding 8 to both sides and then dividing both sides by 2.
Here's the step-by-step calculation:
Starting inequality:
[tex]\[ 2x - 8 < 7 \][/tex]
Add 8 to both sides:
[tex]\[ 2x - 8 + 8 < 7 + 8 \][/tex]
[tex]\[ 2x < 15 \][/tex]
Divide both sides by 2:
[tex]\[ \frac{2x}{2} < \frac{15}{2} \][/tex]
[tex]\[ x < \frac{15}{2} \][/tex]
So, the solution to the inequality is [tex]\(x < \frac{15}{2}\).[/tex]
Now, let's express the solution set in set-builder notation. The solution set for x consists of all real numbers less than [tex]\( \frac{15}{2} \)[/tex]. This can be written as:
[tex]\[ \{ x \,|\, x < \frac{15}{2} \} \][/tex]
So, the correct option is:
[tex]\[ \boxed{\{ x \,|\, x < \frac{15}{2} \}} \][/tex]
Which outcome is represented by X?
rolling a two and the coin landing on tails
rolling a three and the coin landing on tails
rolling a two and the coin landing on heads
rolling a three and the coin landing on heads
Answer:
A. rolling a two and landing on tails
What is the answer for 27^x=9^x-4
Answer:
x = -8
Step-by-step explanation:
We are given the following expression which we are to solve for [tex]x[/tex]:
[tex] 2 7 ^ x = 9 ^ { x - 4 } [/tex]
For this expression, we will make the bases same on both sides of the equation and then equate the exponents equal to each other.
[tex](3^3)^x = (3^2)^{x-4}[/tex]
Multiplying the exponents and equating them to get:
[tex] 3 x = 2 ( x - 4 ) [/tex]
[tex] 3 x = 2 x - 8 [/tex]
[tex] 3 x - 2 x = - 8 [/tex]
x = -8
For this case we must solve the following equation:
[tex]27 ^ x = 9 ^ {x-4}[/tex]
We rewrite:
[tex]27 = 3 * 3 * 3 = 3 ^ 3\\9 = 3 * 3 = 3 ^ 2[/tex]
So:
[tex]3^{3(x)}=3^{2(x-4)}[/tex]
Since the bases are the same, the two expressions are only equal if the exponents are also equal. So, we have:
[tex]3 (x) = 2 (x-4)\\3x = 2x-8[/tex]
Subtracting 2x on both sides:
[tex]3x-2x = -8\\x = -8[/tex]
Answer:
[tex]x = -8[/tex]
Lucinda wants to make $6.00 on every arrangement of flowers she sells. If it costs her $10.00 to prepare an
arrangement, by what percentage will she mark up the price?
a.60%
b.70%
c.59%
d.167%
Answer:60%
Step-by-step explanation:
Final answer:
Lucinda will mark up the price of her flower arrangements by 60% to make a $6.00 profit on each one, which costs her $10.00 to prepare. The correct answer is option a.
Explanation:
Lucinda wishes to make a profit of $6.00 on each flower arrangement she sells, on top of the $10.00 it costs her to prepare one. To calculate the percentage markup, we use the formula: Markup Percentage = (Profit / Cost) × 100%. In Lucinda's case, the profit is $6.00 and the cost is $10.00.
So, the calculation will look like this:
Markup Percentage = ($6.00 / $10.00) × 100% = 0.6 × 100% = 60%.
Therefore, Lucinda will mark up the price by 60% to achieve her desired profit. The correct answer to the question is option a.
Which of the following equations is an example of inverse variation between
the variables x and y?
A. Y=x+5
B. Y=5x
C. Y=5/x
D. Y=x/5
[tex]\bf \qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ k=5\qquad \qquad y=\cfrac{5}{x}[/tex]
Answer:
C. Y=5/x
Step-by-step explanation:
Inverse variation is given by
xy = k where k is a constant
Divide each side by x
xy/x = k/x
y = k/x where k is a constant
Let k=5
y = 5/x is an equation that is inverse variation
Simplify -4 + (-3) + 6.
Answer:
-1
Step-by-step explanation:
-4 + -3 = -7
-7 + 6 = -1
-7 + 6 = -1 because when you are adding a positive and negative number you subtract and then add the sign of the bigger number.
1. You have a piece of land where you want to grow a garden. You only
have 20 yards of fencing to surround the garden. Work through the steps
below to figure out the maximum space you can create to grow plants.
A) you decide to make the width 2 yards
What is the length? ___ yards
Check: is the perimeter 20? _____
What is the area? ____ square yards
Factor the expression below.
x2 - 18x+81
O A. (x - 3)(x - 27)
O B. (x+9)(x+9)
O C. (x+3)(x+ 27)
O D. (x - 9)(x-9)
You must remember that a polynomial is written like so...
ax^2 + bx + c
In this case...
a = 1
b = -18
c = 81
To factor you must find two numbers who both add up to b (-18) AND multiply to c (81)
-9 + -9 = -18
-9 * -9 = 81
so...
D. (x - 9)(x - 9)
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:B (x+9)(x+9)
Step-by-step explanation: just did it and (x-9)(x-9) is the WRONg answer. the correct answer is B (x+9)(x+9)
is 1 greater than 5/3
Answer: No
Step-by-step explanation: 5/3 is greater than 1 because 1 is the same as 3/3 and 5/3 is greater than 3/3 making 5/3 greater than 1.
Analyze the diagram below and complete the instructions that follow.
A. 3/22
B. 3/7
C. 8/15
D.8/11
1. This question refers to conditional probability and is asking us to find the probability of Q occurring, given that R occurs. What this means is that we must divide the probability of Q and R occurring by the probability of R occurring (this is because we have the condition that R occurs). This may be written as such:
Pr(Q|R) = Pr(Q ∩ R) / Pr(R)
2. Now, the first step is to find Pr(Q ∩ R). This is given by the value in the centre of the Venn Diagram (ie. in the cross-over between the two circles) divided by the total of all the values:
Pr(Q ∩ R) = 3/(8 + 3 + 4 + 22)
= 3/37
3. The next step is to find Pr(R). This is given by the value in the circle denoted R (including the cross-over with Q) divided by the total of all the values.
Pr(R) = (4 + 3)/(8 + 3 + 4 + 22)
= 7/37
4. Thus, we can now subtitute the probabilities we defined in 2. and 3. into the formula for conditional probability we defined in 1.:
Pr(Q|R) = (3/37) / (7/37)
= 3/7
Thus, the answer is B.
Note that technically there is no need to write out the full probabilities before coming to this answer. The same exact answer could be found by using Pr(Q ∩ R) = 3 and Pr(R) = 7. This works because they are part of the same universal set - in other words, since the total of all the values in the Venn Diagram remains constant, the denominators of the two probabilities would be the same (given that no cancelling is done) and these denominators would be cancelled out when dividing Pr(Q ∩ R) by Pr(R). This can be particularly useful for a multiple choice question such as this one.
Find the value of y and
simplify completely.
y =
?
Answer:
y=9.01
Step-by-step explanation:
In this question you apply the Pythagoras Theorem to generate relationships which will enable you to form equations and solve for the unknown.
The Pythagoras Theorem states that when you have a right-angle triangle and squares are made at each of the three sides, the sum of squares of the two small sides will equal the square of the longest side.
It is expressed as a²+b²=c² where;
a and b are the shortest sides of the triangle, where b is the heightc is the longest side of the triangle/hypotenuseIn the question we can use three triangles to form expressions using this theorem
First triangle
That one with a height of y, short side of 3 and hypotenuse of zThe relationship you can form is;
[tex]3^2+y^2=z^2\\9+y^2=z^2\\y^2=z^2-9------------------------(1)[/tex]
In this equation you make y² the subject of the formula
Second Triangle
The second triangle is that with a base of 27 as the (a), a height of y as the (b) and the hypotenuse of x as the (c)Hence the relationship you can form is
[tex]27^2+y^2=x^2\\729+y^2=x^2\\y^2=x^2-729[/tex]
In this equation you make y² the subject of the formula
Third Triangle
The third triangle is that one with a base of z as (a) , x as (b) which is the height and 30(3+27) as the (c) which is the hypotenuseThe relationship you can form is;
[tex]z^2+x^2=30^2\\x^2=30^2-z^2---------------------(3)[/tex]
Here x² is the subject of the formula
Equations
[tex]y^2=z^2-9\\y^2=x^2-729\\x^2=900-z^2[/tex]
Substitute equation 3 in equation 2
[tex]y^2=x^2-729-------------2\\\\x^2=900-z^2-------------3\\\\y^2=900-z^2-729\\\\y^2=171-z^2---------------4[/tex]
Substitute equation 4 in equation 1
[tex]y^2=171-z^2---------------4\\\\y^2=z^2-9------------1\\\\z^2-9=171-z^2\\\\2z^2=171+9\\\\z^2=180\\\\z=\sqrt{180} \\\\z=9.487\\\\z=9.5[/tex]
Use the value of z in equation 1 to get value of y
[tex]z^2-3^2=y^2\\\\9.5^2-9=y^2\\\\90.25-9=y^2\\\\81.25=y^2\\\\\sqrt{81.25} =y\\\\y=9.01[/tex]
How do you do this problem
Find the area of rectangle ABCD with vertices A(-4, 0), B(2, 2), C(3, -1), and D(-3, -3)
Answer:
18 square units.
Step-by-step explanation:
graph the square or find the difference then multiply the base by the hight.
A field is 910 yards by 300 yards. What is the greatest number of rectangle lots of 120 yards by 65 yards that can be places on the field?
Let R = greatest number of rectangular lots.
R = (910 • 300)/(120 • 65)
R = 273,000 ÷ 7800
R = 35
The graph below corresponds to the equation y=x2+bx+c, what are the values of b and c?
Answer:
C) B= -1 C= -2
Step-by-step explanation:
Determine the domain of the function.
f(x)= sqrt of 7+x
Answer:
Df=[-7,∞)
Step-by-step explanation:
Answer:
x∈R {x ≥ -7}
Step-by-step explanation:
The domain of the function can only include real numbers. This means whatever happens under the square root sign (i.e. the radicand) cannot be less than 0 (since you can't take the square root of a negative number).
To find the domain, set the radicand ≥ 0:
7 + x ≥ 0
x ≥ -7
What is the value of x:
2 + x = 8
A cash register contains 10$ bills and 20$ bills total value of 340 if there are 23 bills total then how many of each does the register contains
Answer:
There are 12 bills of 10$ and 11 bills of 20$
Step-by-step explanation:
Let
x ------> number of 10$ bills
y -----> number of 20$ bills
we know that
x+y=23 -----> x=23-y -----> equation A
10x+20y=340 ----> equation B
substitute equation A in equation B and solve for y
10(23-y)+20y=340
230-10y+20y=340
10y=340-230
y=110/10=11
Find the value of x
x=23-y ----> x=23-11=12
therefore
There are 12 bills of 10$ and 11 bills of 20$
2.3 +0.02(x + 20) - 4.8= -9
Answer:
x = -345
Step-by-step explanation
2.3 + .02x + .4 - 4.8 = -9
2.7 - 4.8 + .02x = -9
-2.1 + .02x = -9
.02x = 6.9
x = -6.9 / .02
x = -345
Answer: x = -345
Step-by-step explanation:
2.3 + .02(x + 20) - 4.8 = -9
2.3 + (.02x + .4) - 4.8 = -9
-2.1 + .02x = -9
+2.1 +2.1
.02x = -6.9
.02/.02 -6.9/.02
x = -345
Juan is hiking up a mountain starting at an elevation of 800 feet. Every hour, he is 2000 feet higher in elevation.
Which function, h(t), where t is time in hours, represents Juan's height over time?
1. h(t)=2800t
2. h(t)=800t+2000
3. h(t)=2000t
4. h(t)=2000t+800
Answer:
4. h(t)=2000t+800
Step-by-step explanation:
800 is his starting elevation we dont not multiply it
every hour he gains 2000ft in elevation and t shows the hours 2000ft * t (hours) + 800
A circle has an arc whose measure is 80° and whose length is 88π, What is the diameter of the circle?
Answer:396
Step-by-step explanation:Arc length = radius * angle in radians
you know radius = Diameter/2 = D/2
80 deg = (80pi/180) rad
then,
88 pi = (D/2) * (80 pi /180)
sloving for D
D = 396
The diameter of the circle which measures is 80° and length arc is 88π is 396
Length of arc formula
length of arc = ∅ / 360 × 2πr
where
r = radius
∅ = centre angle = 80°
length of arc = 80 / 360 ×2πr
length of arc = 88π
Therefore,
88π = 16 / 36 πr
cross multiply
88π × 36 = 16πr
3168π = 16πr
divide both sides by 16π
198 = r
Recall
diameter = 2(radius)
Therefore,
diameter of the circle = 2 × 198
diameter of the circle = 396
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I’m stuck, please help ASAP. Will give brainliest!
Answer:
C) 35 Degrees
Step-by-step explanation:
To find the degree of an exterior angle, subtract the larger arc, DE, degree by the smaller arc, BC, and then divide by 2! Which is 35. 118-48/ 2 = 35.
What is the slop of the line containing the points (4,-10 2/3), (-3,1)
let's firstly convert the mixed fraction to improper fraction.
[tex]\bf \stackrel{mixed}{10\frac{2}{3}}\implies \cfrac{10\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{32}{3}} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{4}~,~\stackrel{y_1}{-\frac{32}{3}})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-\left( -\frac{32}{3} \right)}{-3-4}\implies \cfrac{1+\frac{32}{3}}{-7}\implies \cfrac{\frac{3+32}{3}}{-7}[/tex]
[tex]\bf \cfrac{~~\frac{35}{3}~~}{\frac{-7}{1}} \implies \cfrac{\stackrel{5}{~~\begin{matrix} 35 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}~~}{3}\cdot \cfrac{1}{~~\begin{matrix} -7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies -\cfrac{5}{3}[/tex]
A taxi company charges passengers $1.75 for a ride, no matter how long the ride is, and an additional $0.40 for each mile traveled. The rulec
= 0.40m + 1.75 describes the relationship between the number of miles m and the total cost of the ride c.
a. What is the charge for a 1-mile ride?
b. What is the charge for a 2.7-mile ride?
A. $2.15; $2.83
B. $0.40; $5.13
C. $1.75; $2.15
D. $0.40; $1.08
Answer:
A
Step-by-step explanation:
For a 1 mile ride, plug in 1 into m.
Total = 0.40(1) + 1.75
= 0.40+1.75 = 2.15.
Because no other answer but A has 2.15, you're answer is A
Answer:A
Step-by-step explanation:
Samuel consumed 2129 calories of food on Monday, 2348 calories on Tuesday, and 1863
calories on Wednesday. In order for Samuel's average calorie intake to equal a daily
average of 2200 calories, how many calories of food must he consume on Thursday?
Answer: 2460 calories
Step-by-step explanation:
2129 + 2348 + 1863 = 6340
2200 x 4 = 8800
8800 - 6340 = 2460
Final answer:
Samuel must consume 2460 calories on Thursday to achieve his target average daily calorie intake of 2200 over the four days.
Explanation:
To find out how many calories Samuel must consume on Thursday to have an average daily intake of 2200 calories, we first calculate the total number of calories he should have consumed over four days. This is done by multiplying the desired daily average (2200 calories) by the number of days (4), which equals 8800 calories.
Next, we add the calories Samuel consumed from Monday to Wednesday, which amounts to 2129 (Monday) + 2348 (Tuesday) + 1863 (Wednesday) = 6340 calories.
To find the calories for Thursday, we subtract the total consumed so far (6340 calories) from the desired four-day total (8800 calories). This gives us 8800 - 6340 = 2460 calories.
Therefore, Samuel must consume 2460 calories on Thursday to achieve an average of 2200 calories per day over the four days.
Apartment rentals in Fairview run approximately $0.90 per square foot. Jillian has determined that she can afford $630 per month for rent. What is the largest apartment, in square feet, she should consider at the given rate?
Answer:
700 square feet
Step-by-step explanation:
We can simply divide 630 by 0.9 to find the value:
[tex]\frac{630}{0.90}=700[/tex]
Checking, if she goes for 700 sq ft at $0.90 per square feet, she would need:
700 * 0.90 = $630
Yes, that's the max, so 700 sq. feet apartment is what she can afford.
Can someone Help me please
Answer:
x<3
Step-by-step explanation:
The circle is open and the arrow is going left so its going to be less then. The circle is on 3 so the answer is c. x<3.
A line passes through the given points. Write an equation for the line in
point-slope form. Then rewrite the equation in slope-intercept form.
(4, -2), (9, -8)
4-9=5
-2--8=6
y=mx+b
slope/mx=6/1
base/y intercept=5
Answer: The equation for the line in point-slope form :[tex] (y+2)=\dfrac{-6}{5}(x-4)[/tex]
The equation in slope-intercept form : [tex]y=\dfrac{-6}{5}x+\dfrac{14}{5}[/tex]
Step-by-step explanation:
The equation of a line in point slope form passing through points (a,b) and (c,d) is given by :-
[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]
Now, the point slope form passing through points (4, -2) and (9, -8) is given by :-
[tex](y-(-2))=\dfrac{-8-(-2)}{9-4}(x-4)\\\\\Rightarrow (y+2)=\dfrac{-6}{5}(x-4)[/tex]
The equation for the line in point-slope form :[tex] (y+2)=\dfrac{-6}{5}(x-4)[/tex]
Further if we simplify the equation , we get
[tex] y+2=\dfrac{-6}{5}x+\dfrac{24}{5}\\\\\Rightarrow\ y=\dfrac{-6}{5}x+\dfrac{24}{5}-2\\\\\Rightarrow\ y=\dfrac{-6}{5}x+\dfrac{14}{5}[/tex]
The equation in slope-intercept form : [tex]y=\dfrac{-6}{5}x+\dfrac{14}{5}[/tex]
Find the radius of K
Answer:
6 ft.
Step-by-step explanation:
solution :
360 degree = pie r².
1 degree =pie r²/360
50degree=5pie r²/36
5pie = 5 pie r²/36
r²=36
r=6
Therefore radius = 6 ft.