Answer:
A
Step-by-step explanation:
Solving for x:
-3x + 8 ≥ 14
-3x ≥ 6
x ≤ -2
Notice the sign gets reversed when you divide or multiply by a negative number.
The only option less than -2 is -3, A.
Here's a tip: on multiple choice questions, sometimes it's faster to try each answer instead of solving the equation. This can save time on tests like the SAT or ACT.
Let's try it:
-3(-3) + 8 = 9 + 8 = 17
-3(-1) + 8 = 3 + 8 = 11
-3(0) + 8 = 0 + 8 = 8
-3(3) + 8 = -9 + 8 = -1
So you can see the answer is A.
in 2005, the total waste generated in a certain country was 3.474x10^9 pounds. also in 2005, the countrys population was 1.23x10^6 people. determine the garbage per capita (per person) in that country 8n the year 2005. the country produced _____ pounds of garbage per person in 2005.
Answer:
2824
Step-by-step explanation:
Take the number of pounds and divide by the number of people:
3.474×10⁹ / 1.23×10⁶
Divide the coefficients and subtract the exponents:
(3.474 / 1.23) × 10⁹⁻⁶
2.824×10³
So the country produced about 2,824 pounds of garbage per person in 2005.
What is the constant of variation, k, of the direct variation, y = kx, through (–3, 2)?
[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (-3,2)~~ \begin{cases} x=-3\\ y=2 \end{cases}\implies 2=k(-3)\implies -\cfrac{2}{3}=k[/tex]
To find the constant of variation k in the direct variation y = kx for the point (–3, 2), we substitute the point into the equation.
We get k = 2 / (–3), resulting in k = –rac{2}{3}.
Explanation:The constant of variation, k, in the direct variation equation y = kx can be found using the coordinates of a given point that lies on the line represented by this equation.
Given a point (–3, 2), we can substitute these values into the equation to find k:
y = kx
2 = k(–3)
To isolate k, we divide both sides of the equation by (–3):
k = 2 / (–3)
k = –rac{2}{3}
A four-person committee is chosen from a grous of eight boys and six girls.
If students are chosen at random, what is the probability that the committee consists of all boys?
The correct option is C.
Probability of selecting all boys from 8 boys and 6 girls for a 4-person committee is 10/143.
To find the probability that the committee consists of all boys, we need to calculate the probability of selecting 4 boys out of 8 boys and no girls out of 6 girls.
The total number of ways to choose a 4-person committee from 14 students (8 boys and 6 girls) is given by the combination formula:
[tex]\[ \text{Total number of ways} = \binom{14}{4} \][/tex]
The number of ways to choose 4 boys out of 8 is given by:
[tex]\[ \binom{8}{4} \][/tex]
And since we don't choose any gi-rls, the number of ways to choose 0 girls out of 6 is simply 1.
So, the probability of selecting all boys is:
[tex]\[ \text{Probability} = \frac{\binom{8}{4} \times \binom{6}{0}}{\binom{14}{4}} \][/tex]
Let's calculate this:
[tex]\[ \text{Probability} = \frac{\binom{8}{4} \times \binom{6}{0}}{\binom{14}{4}} = \frac{\frac{8!}{4!(8-4)!} \times \frac{6!}{0!(6-0)!}}{\frac{14!}{4!(14-4)!}} \][/tex]
[tex]\[ = \frac{\frac{8!}{4!4!} \times 1}{\frac{14!}{4!10!}} \][/tex]
[tex]\[ = \frac{\frac{8 \times 7 \times 6 \times 5}{4 \times 3 \times 2 \times 1}}{\frac{14 \times 13 \times 12 \times 11}{4 \times 3 \times 2 \times 1}} \][/tex]
[tex]\[ = \frac{70}{1001} \][/tex]
[tex]\[ = \frac{10}{143} \][/tex]
So, the correct answer is option C: [tex]\( \frac{10}{143} \)[/tex].
The complete question is here:
A four-person committee is chosen from a group of eight boys and six girls.. If students are chosen at random, what is the probability that the committee consists of all boys?
A. 4/1001
B. 15/1001
C. 10/143
D. 133/143
PLZ PLZ PLZ CAN SOMEONE HELP WITH MATHS DISTANCE TIME GRAPHS!!!
Answer:
Tbh I have no clue..
please help me out please
It’s > because when you square root 18 it’s 4.24264069
Answer:
The answer would be C, Greater Than, >.
Step-by-step explanation:
In this question, it is asked if 5 is equal to, less than or greater than the square root of 18. So we first need to find out the value of square root 18. We can do it manually or with a scientific calculator. If we do it with a calculator, we would come to know that the answer of square root 18 is 4. 24264068. Now we would compare it with 5. We will have to see if 5 is equal to, less than or greater than this value of square root of 18. So it is clear from the above answer of square root 18, that it is less than 5.
So the answer is C, that shows that 5 is greater than square root of 18, i-e 4.24264068.
The endpoints of the diameter of a circle are (-7,3) and (5,1) . What is the center of the circle
Answer:
The center is the point [tex](-1,2)[/tex]
Step-by-step explanation:
we know that
The center of the circle is equal to the midpoint of the endpoints of the diameter
so
The formula to calculate the midpoint between two points is equal to
[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
substitute the values
[tex]M(\frac{-7+5}{2},\frac{3+1}{2})[/tex]
[tex]M(\frac{-2}{2},\frac{4}{2})[/tex]
[tex]M(-1,2)[/tex]
therefore
The center is the point [tex](-1,2)[/tex]
Base=30cm
Heights=20cm
Find the X?
Answer: 25
Assuming the dotted line touches the middle of the base of the triangle,
Using Pythagoras Theorem,
(30/2)^2 + (20)^2 = x^2
x^2 = (15)^2 + 400
x^2 = 625
x = √625 or -(√625)
x = 25 or -25
But since x needs to be a positive value,
x = 25
Answer:
x = 25 cm
Step-by-step explanation:
Given the triangle is isosceles ( 2 equal sides )
Then the line from the vertex is a perpendicular bisector of the base
We can use Pythagoras' identity on the right triangle
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
where x is the hypotenuse and the legs are 15 and 20, so
x² = 15² + 20² = 225 + 400 = 625
Take the square root of both sides
x = [tex]\sqrt{625}[/tex] = 25
I PROMISE BRAINLIST; 5-STARS; THANKS!! IT'S VERY SIMPLE; BELIEVE ME
What type of trend does the scatter plot below show? What type of real-world situation might the scatter plot represent?
A. Positive trend; weight and height
B. Negative trend weight and height
C. No trend; the number of pets owned and the owner's height
D. Negative trend; The water level in a tank in the hot sun over time.
Answer:
Option A
Step-by-step explanation:
Positive trend will start from bottom to going upwards and negative trend will start from the top to bottom.
Weight and height is also logical because as height goes up, weight will follow up.
1) Which set of sides will make a triangle?
13 cm, 7 cm, 6 cm
10 cm, 9cm, 9 cm
4 cm, 8 cm, 14 cm
6 cm, 15 cm, 6 cm
Answer:
13cm, 7cm, 6cm
Step-by-step explanation:
To make a triangle you have to think about it in this way. The two smallest numbers should equal the largest number.
Answer:
13 cm, 7 cm, 6 cm
Step-by-step explanation:
The sum of the 2 shorter sides of the triangle has to be equal or longer than the longest side. In this case 7+6=13 which is equal.
You have $5000 to invest in two different accounts. In order to save the money you need for college, you need to average 6.9% interest. If the two accounts pay 5.5% and 8% interest, how much should you invest in each account?
A) $2400 in 5.5%, $2600 in 8%
B) $2500 in 5.5%, $2500 in 8%
C)$2200 in 5.5%, $2800 in 8%
D) $2800 in 5.5%, $2200 in 8%
Answer:
Amount invested at 8% = $2800
Amount invested at 5.5% = $2200.
Step-by-step explanation:
Let the amount invested at 8% = x
Then the amount invested at 5.5% = 5000-x
Then we get equation:
[8% of x] + [5.5% of (5000-x)] = [6.9% of 5000]
8(x) + 5.5(5000-x) = 6.9(5000)
8x + 27500 - 5.5x = 34500
8x - 5.5x = 34500-27500
2.5x = 34500-27500
2.5x = 7000
x = 7000/2.5
x = 2800
then the amount invested at 5.5% = 5000-x = 5000-2800 = 2200
Hence final answer is given by:
Amount invested at 8% = $2800
Amount invested at 5.5% = $2200.
Write two paragraphs reflecting on how food prices affect you or your family.
Answer:
One effect of higher food prices in a given country is higher consumer price index (CPI) inflation.However, higher food prices affect people in different economies differently.
The impact of rapidly rising food prices on CPI inflation is substantially larger in emerging market economies than advanced economies
This effect tends to be much greater for countries that are 1) large net importers of food, and 2) where households spend a greater percentage of their income on food (meaning that they have a much larger weighting of food in their CPI basket).
In short, higher food prices don't hurt everyone equally. Poorer, developing economies feel it much worse.
Step-by-step explanation:
Answer:
Here's some you can use below!:
Step-by-step explanation:
Oil is used in the processing of many food products. In additional, oil is used in the transportation of food. As a result, with oil price increases, the price of food increases as well.
The world population continues to grow, and with that comes increased demand of various food products. As a result, this rising demand directly leads to higher prices.
The increases in food prices have already taken effect and are not likely to improve in the near future. As of February 2011, the price of wheat has increased 83% and the price of corn has doubled since one year earlier. As feed becomes more expensive, the cost of beef products is expected to increase by almost 40%, leading to much higher prices for any meat eaters out there. With unemployment remaining at very high levels, these prices will serve to further put a dent in our wallets.
The situation is even more dire in poorer countries as many of their citizens spend about 80% of their income on basic food products. As a result, food price increases can be devastating to people in these countries, with an additional 44 million people already having been pushed into poverty. The food crisis has inspired riots in countries such as Egypt, Haiti, Tunisia, and Algeria.
(5x–7)–5(7x–12)+7=0
Help please
Answer:
x=2
Step-by-step explanation:
(5x–7)–5(7x–12)+7=0
5x-7-35x+60+7=0
-30x=-60
x=2
Answer:
The answer I got was x=2
During a field trip, 9 buses take 120 students to a museum. Some buses are short and hold 8 students each. Other buses are long and hold 20 students each.
All the buses are carrying as many students as they can hold. Complete the table and write a system of equations to represent the number of each type of bus.
See attached picture for the answers.
Answer:
Step-by-step explanation:
Find the surface area of a right prism whose bases are equilateral triangles with side lengths of 6 in. The height of the prism is 10in
Answer:
The surface area of the prism is [tex](18\sqrt{3}+180)\ in^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the triangular prism is equal to
[tex]SA=2B+PH[/tex]
where
B is the area of the triangular base
P is the perimeter of the triangular base
H is the height of the prism
Find the area of the base B
Applying the law of sines to find the area of a equilateral triangle
[tex]B=\frac{1}{2}b^{2} sin(60\°)[/tex]
we have
[tex]b=6\ in[/tex]
[tex]sin(60\°)=\sqrt{3}/2[/tex]
substitute
[tex]B=\frac{1}{2}6^{2}(\sqrt{3}/2)[/tex]
[tex]B=9\sqrt{3}\ in^{2}[/tex]
Find the perimeter P
[tex]P=3*6=18\ in[/tex]
we have
[tex]H=10\ in[/tex]
substitute the values
[tex]SA=2(9\sqrt{3})+(18)(10)=(18\sqrt{3}+180)\ in^{2}[/tex]
Let f(x) = 4 – x^2, g(x) = 2 – x. Find (f + g)(x) and its domain.
Step-by-step explanation:
[tex]f(x)=4-x^2,\ g(x)=2-x\\\\(f+g)(x)=f(x)+g(x)\\\\\text{therefore}\\\\(f+g)(x)=(4-x^2)+(2-x)=-x^2-x+(4+2)=-x^2-x+6\\\\\text{It's the quadratic function. The domain is the set of all real numbers}\ x\in\mathbb{R}[/tex]
PLEASE HELP 15 POINTS
Formula for area is:
A = pi*r^2
r = 28
so...
A = 3.14 * 28^2
A = 3.14 * 784
A = 2461.76 cm^2
Formula for circumference is:
C = 2*pi*r
r = 28
so...
C = 2*3.14* 28
C = 6.28*28
C = 175.84 cm
Hope this helped!
~Just a girl in love with Shawn Mendes
What is log15 2^3 rewritten using the power property?
ANSWER
[tex]log_{15}( {2}^{3} ) = 3 \: log_{15}( {2} )[/tex]
EXPLANATION
According to the power property of logarithms:
[tex] log_{x}( {y}^{n} ) = n \: log_{x}( {y} )[/tex]
The given logarithm is
[tex]log_{15}( {2}^{3} ) [/tex]
When we apply the power property to this logarithm, we get,
[tex]log_{15}( {2}^{3} ) = 3 \: log_{15}( {2} )[/tex]
Answer:
The required expression is [tex]3\log_{15}2[/tex].
Step-by-step explanation:
According to the power property of exponent,
[tex]\log_ax^b=b\log_ax[/tex]
The given expression is
[tex]\log_{15}2^3[/tex]
Here a=15, x=2, b=3.
Using power property of exponent the given expression can be written as
[tex]\log_{15}2^3=3\log_{15}2[/tex]
Therefore the required expression is [tex]3\log_{15}2[/tex].
F(x) is a function ?????????????????????????????????????
False because x should have only one y
What's greater 30% or 0.03
Answer:
30
Step-by-step explanation:
Answer:
30% is greater than 0.03
Step-by-step explanation:
30% = 0.3, which is greater than 0.03
8. A candle is 4 inches tall and burns at the rate of 0.6 inch per hour. If the height of the candle after x hours is 1.5 inches,
write an equation to represent the situation. Then use this equation to find the expected number of hours in which the candle
melted to 1.5 inches.
Answer with Step-by-step explanation:
A candle is 4 inches tall and burns at the rate of 0.6 inch per hour.
i.e. after 1 hour height of candle=4-0.6 inches
After 2 hours height of candle=4-0.6-0.6 inches
after x hours height of candle=4-0.6x
Also,
If the height of the candle after x hours is 1.5 inches
⇒ 4-0.6x=1.5
⇒ 0.6x=4-1.5
⇒ 0.6x=2.5
⇒ x=2.5/0.6
⇒ x=4.166
Hence, equation to represent the situation. is:
4-0.6x=1.5
and the expected number of hours in which the candle melted to 1.5 inches is:
4.166 hours
After defining and solving the linear equation representing the candle's height over time, it is determined that it will take approximately 4.17 hours for the candle to burn down to 1.5 inches.
Explanation:This is a problem about rates and linear equations in the subject of mathematics. The candle starts at 4 inches and burns at a rate of 0.6 inch per hour, which decreases the height of the candle. So, the equation would be: height = starting height - (burn rate)x(time), or H = 4 - 0.6x.
From the problem we know, that the height of the candle after x hours is 1.5 inches. So, we substitute H with 1.5: 1.5 = 4 - 0.6x.
To solve for x, first we can subtract 4 from both sides: -2.5 = -0.6x. Then, divide both sides by -0.6 to isolate x. So, x = -2.5/-0.6 which simplifies to approximately 4.17 hours. So, it will take around 4.17 hours for the candle to burn down to 1.5 inches.
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If f(x) = 4x + 12 is graphed on a coordinate plane, what is the y-intercept of the graph? 4 8 12 16
Answer:
The y-intercept would be 12.
Step-by-step explanation:
In the problem:
4x=slope
12=y-intercept
AnswBetty correctly determined that the ordered pair (–3, 5) is a solution to the system of linear equations 6 x + 5 y = 7 and x + 4y = 17. Based on this information, which statement is correct?
(–3, 5) satisfies neither the equation 6x + 5y = 7 nor the equation x + 4y = 17.
(–3, 5) satisfies the equation 6x + 5y = 7 but not the equation x + 4y = 17.
(–3, 5) satisfies the equation x + 4y = 17 but not the equation 6x + 5y = 7.
(–3, 5) satisfies both the equation 6x + 5y = 7 and the equation x + 4y = 17.
The question is in the picture please show work. If you know how to upload a file, doing the work on a piece of paper then uploading the answer is best, if you don't know how then just try doing it with keyboard
since TU is the midsegment in the triangle, then T and U are both midpoints.
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ R(\stackrel{x_1}{0}~,~\stackrel{y_1}{2b})\qquad Q(\stackrel{x_2}{-2a}~,~\stackrel{y_2}{0}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \stackrel{midpoint}{T}=\left( \cfrac{-2a+0}{2}~~,~~\cfrac{0+2b}{2} \right)\implies T=\left( \cfrac{-2a}{2}~,~\cfrac{2b}{2} \right) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill T=(-a,b)~\hfill[/tex]
I PROMISE THIS IS EASY I WILL GIVE BRAINLEST!!!!!!!!11 Add or subtract.
(8x – 2y) + (3x – 4y)
A.)11x + 8y
B.)4x – y
C.)11x – 6y
D.)5x + 2y
Answer:
11x-6y
Step-by-step explanation:
we ignore the parenthesis so we add 8x and 3x since they are both positive which adds up to 11x
for -2y and -4y we add, a negative and a negative equals negative therefor -2y+(-4y)= -6y
11x-6y
For this case we must add the following expressions:
[tex](8x-2y) + (3x-4y) =[/tex]
We eliminate the parentheses, taking into account that:[tex]+ * + = +\\+ * - = -\\8x-2y + 3x-4y =[/tex]
We add similar terms:
[tex]8x + 3x-2y-4y =[/tex]
Equal signs are added and the same sign is placed:
[tex]11x-6y[/tex]
Answer:
[tex]11x-6y[/tex]
Option C
Which equation represents a line that passes through (-2, 4) and has a slope
71
Step-by-step explanation:
The point-slope of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
We have the slope m = 71 and the point (-2, 4).
Substitute:
[tex]y-4=71(x-(-2))\\\\\bold{y-4=71(x+2)}[/tex]
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
Convert:
[tex]y-4=71(x+2)[/tex] use the distributive property
[tex]y-4=71x+142[/tex] add 4 to both sides
[tex]\bold{y=71x+146}[/tex]
The standard form of an equation of a line:
[tex]Ax+By=C[/tex]
Convert:
[tex]y=71x+146[/tex] subtract 71x from both sides
[tex]-71x+y=146[/tex] change the signs
[tex]\bold{71x-y=-146}[/tex]
The general form of an equation of a line:
[tex]Ax+By+C=0[/tex]
Convert:
[tex]71x-y=-146[/tex] add 146 to both sides
[tex]\bold{71x-y+146=0}[/tex]
what is 4.39 in a percent
Answer:The decimal 4.39 equals 439%
To convert from decimal to percent, just multiply the decimal value by 100. In this example we have: 4.39 × 100 = 439% (answer).
The ease way:
1) Move the decimal point two places to the right: 4.39 → 43.9 → 439.
2) Add a % sign: 439%
Answer: 439%
The equivalent value of the percentage is A = ( 4.39/100 ) = 4.39 %
Given data ,
Let the percentage be represented as A
Now , the value of A is
Let the numerator of the fraction be p
where the value of p = 4.39
Let the denominator of the fraction be q
where q = 100
Now , the fraction is A = p/q
On simplifying the expression , we get
So , the left hand side of the equation is equated to the right hand side by the value of p/q
A = 4.39/100
A = 0.0439
On further simplification , we get
A = 0.0439 = 4.39 %
So , the percentage is 4.39 %
Therefore , the value of A = 4.39 %
Hence , the expression is A = 4.39 %
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Find 0.1 more than 5.023.
A) 5.024
B) 5.033
C) 5.123
D) 5.134
C. the number goes up by one tenth. changing the 0 in the tenth place to a one.
Your answer would be
c. 5.123 since
5.023
+0.1
————
5.123
Use the distributive property to simplify expression (3b-2) (-3)
-9b + 6
Multiply the -3 by each term in the first parentheses.
(-3 * 3b) + (-3 * -2)
Now just simplify.
-9b + 6
Given the following graph, define a) the vertex, b) the intercepts, c) the axis of symmetry, and the sign of the lead coefficient.
Answer:
Vertex;
(2, -8)
The intercepts;
x-intercepts: (-2, 0) and (6, 0)
y-intercepts: (0, -6)
The axis of symmetry;
No axis of symmetry. X = 2 is a line of symmetry of the parabola
The sign of the lead coefficient;
Positive
Step-by-step explanation:
The graph shown in the attachment belongs to the parabola group of conic sections. The vertex of a parabola refers to the point where the parabola changes direction or also the lowest or the highest point on its graph. The graph is moving downwards from x = -4 to x = 2 and then starts moving upwards from x = 2 to x = 8. The vertex is thus located at the point x = 2. At this point, the y value is -8. Thus the vertex is located at (2, -8). This is the lowest point on the graph.
The intercepts refers to the points where the graph of a function crosses or cuts either the x or the y axes.
The parabola crosses the x-axis at two points;
x = -2 and x = 6
At these points the value of y is usually 0. The x-intercepts are thus;
(-2, 0) and (6, 0)
The parabola crosses the y-axis at the point where y = -6 and the corresponding x value is 0. The y-intercept is thus;
(0, -6)
Neither the x-axis nor the y-axis is an axis of symmetry of the parabola since neither of the axis divides the parabola into two identical portions. Nevertheless, the vertical line x = 2 passing through the vertex divides the parabola into two identical portions such that the left portion is a mirror image of the right portion. We can thus conclude that the vertical line x = 2 is a line of symmetry of the parabola.
The sign of the lead coefficient of a parabola determine whether the parabola opens upward or downward;
If the sign of the lead coefficient is positive, the parabola opens upward. If the sign of the lead coefficient is negative, the parabola opens downward.
The parabola in the attachment opens upward and thus the sign of its lead coefficient is positive.
Please help me I’m terrible at math
Answer:
...
Step-by-step explanation:
can you show us the options of the drop-down menus?
The number of Calories c that are burned by walking depends on t, the number of hours spent walking. If you burn 300 Cal/h, how many Calories do you burn in 2.5 hours of walking?
650 Calories
750 Calories
260 Calories
120 Calories
300/2.5= 120 Calories
Answer:
120 calories
Step-by-step explanation: