Answer:
[tex]\large\boxed{y=2x^2+4}[/tex]
Step-by-step explanation:
The vertex form of a parabola:
[tex]y=a(x-h)^2+k[/tex]
(h, k) - vertex
We have the vertex at (0, 4) → h = 0 and k = 4.
Substitute:
[tex]y=a(x-0)^2+4=ax^2+4[/tex]
The point (-1, 6) is on the parabola. Put the coordinates of the point to the equation:
[tex]6=a(-1)^2+4[/tex] subtract 4 from both sides
[tex]2=a\to a=2[/tex]
Finally:
[tex]y=2x^2+4[/tex]
Solve 7x − 6 > 8 and 3x + 4 ≥ 22 for x.
Answer:
x ≥ 6
Step-by-step explanation:
Lets solve the first inequality:
7x - 6 > 8
7x > 8 + 6
7x > 14
x > 14/7
x > 2
And now the second inequality:
3x + 4 ≥ 22
3x ≥ 22 - 4
3x ≥ 18
x ≥ 18/3
x ≥ 6
So, from the 2 answers, which region is overlapping ?? x ≥ 6
So this is the solution.
Note: we disregard x from 2 to 6 because that region is ONLY solution to the first one
a survey of 2000 doctors showed that an average of 3 out of 5 doctors used brand x aspirin. how many doctors use brand x aspirin (solve for x)
Answer:
1,200 doctors use brand X aspirin
Step-by-step explanation:
Out of the 2,000 doctors, the survey showed that 3 out of 5 use brand X. So that means [tex]\frac{3}{5}[/tex] of 2000 doctors use Brand X. So the proportion will then be lke this:
[tex]\dfrac{3}{5} = \dfrac{x}{2000}[/tex]
So we can now solve for x using this equation:
[tex]\dfrac{3}{5} = \dfrac{x}{2000}\\\\\dfrac{(2000)(3)}{5} = x\\\\\dfrac{6000}{5} = x\\\\1200 = x[/tex]
Which statement is true about the sum of two rational numbers?
Answer:
So, adding two rationals is the same as adding two such fractions, which will result in another fraction of this same form since integers are closed under addition and multiplication. Thus, adding two rational numbers produces another rational number. Proof: "The product of two rational numbers is rational."
Sum of two rational numbers is always a rational number is always true .
What are rational numbers?A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. For example, −3/7 is a rational number, as is every integer
According to the question
The sum of two rational numbers :
Case 1: Consider rational numbers with different denominator : [tex]\frac{4}{5} , \frac{2}{3}[/tex]
Sum of both rational numbers
= [tex]\frac{4}{5} + \frac{2}{3}[/tex]
= [tex]\frac{12 + 10 }{15}[/tex]
= [tex]\frac{22}{15}[/tex]
Case 2:Consider rational numbers with same denominator : [tex]\frac{4}{5} , \frac{1}{5}[/tex]
= [tex]\frac{4}{5} + \frac{1}{5}[/tex]
= [tex]\frac{5}{5}[/tex]
= [tex]\frac{1}{1}[/tex]
= 1
Sum in both cases are rational numbers
Hence, Sum of two rational numbers is always a rational number is always true .
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Tom travels between the two mile markers shown and then finds his average speed in miles per hour. Select the three equations that represent this situation.
Answer:
1.5 hours is the correct answer !
Step-by-step explanation:
Speed is the rate of distance over time.
The equations are:
[tex]\mathbf{Speed = \frac{195\ miles}{3\ hours}}[/tex][tex]\mathbf{3\ hours \times Speed = 195\ miles}[/tex][tex]\mathbf{3\ hours = \frac{195\ miles}{Speed}}[/tex]The given parameters are:
[tex]\mathbf{(t_1,d_1) = (1:30pm,35miles)}[/tex]
[tex]\mathbf{(t_2,d_2) = (4:30pm,230miles)}[/tex]
So, the time difference is:
[tex]\mathbf{t=4:30pm - 1:30pm}[/tex]
[tex]\mathbf{t=3\ hours}[/tex]
The distance traveled is:
[tex]\mathbf{d = 230miles - 35miles}[/tex]
[tex]\mathbf{d = 195miles}[/tex]
Speed is calculated as:
[tex]\mathbf{Speed = \frac{Distance}{Time}}[/tex]
So, we have:
[tex]\mathbf{Speed = \frac{195\ miles}{3\ hours}}[/tex]
Multiply both sides by 3 hours
[tex]\mathbf{3\ hours \times Speed = 195\ miles}[/tex]
Divide both sides by Speed
[tex]\mathbf{3\ hours = \frac{195\ miles}{Speed}}[/tex]
Hence, the equations are:
[tex]\mathbf{Speed = \frac{195\ miles}{3\ hours}}[/tex]
[tex]\mathbf{3\ hours \times Speed = 195\ miles}[/tex]
[tex]\mathbf{3\ hours = \frac{195\ miles}{Speed}}[/tex]
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Mr and mrs Wilson hosted their daughter wedding they paid $575 to rent a banquet hall and $13 per person for a catered dinner in all there were 118 people at the wedding how much did the Wilson’s pay for the hall and the food use inverse operation to check your answer
Answer:
$2109
Step-by-step explanation:
We are given that Mr and Mrs Wilson payed a rent of $575 for the banquet hall and a per head of $13 for the catering dinner for their daughter's wedding.
We are to find the total amount they paid.
Amount paid for dinner for 118 people = [tex]118 \times 13[/tex] = $1534
Total amount payed by Mr and Mrs Wilson = $1534 + $575 = $2109
Inverse check:
2109 - 575 = 1534
1534/118 = 13
How much would $500 invested at 8% interest compounded continuously be
worth after 3 years? Round your answer to the nearest cent.
Answer:
[tex]\$635.62[/tex]
Step-by-step explanation:
The formula to calculate continuously compounded interest is equal to
[tex]A=P(e)^{rt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
e is the mathematical constant number
we have
[tex]t=3\ years\\ P=\$500\\ r=0.08[/tex]
substitute in the formula above
[tex]A=\$500(e)^{0.08*3}[/tex]
[tex]A=\$635.62[/tex]
What is the measure in degrees of angle 3
Answer: There is no picture ?
Step-by-step explanation:
Three ounces of cinnamon cost $2.40. If there are 16 ounces in 1 pound, how much does cinnamon cost per pound?
Jackrabbits are capable of reaching speeds up to 40 miles per hour. How fast is this in feet per second? (Round to the nearest whole number.)
5,280 feet = 1 mile
Answer:
80¢\lb.; 58 667\1000 ft.\sec.
Step-by-step explanation:
Divide the cost by three; multiply 40 by 1.466675.
what is 1/2 to the power of -2
Answer:
4
Step-by-step explanation:
=(1/2)^-2
=(2/1)^2
=2^2
=4
What is an statistics
Hello There!
Statistics is a tool used to help people process, summarize, analyze and interpret data for making better decisions.
It helps us with future events if we know what has happened in past.
Helps us make better decisions.
The better we know about the future of an outcome, the more possibility we have to work around it.
Answer:
Statistic is the art or science of collecting,analysing ,summarising and presenting data by using numbers.
solve -3(-8b+7)=3(2b-1)
Answer: [tex]b=1[/tex]
Step-by-step explanation:
Given the equation [tex]-3(-8b+7)=3(2b-1)[/tex] you need to solve for the variable "b".
You need to apply Distributive property on both sides of the equation:
[tex]-3(-8b+7)=3(2b-1)\\\\24b-21=6b-3[/tex]
Now you need to add 21 to both sides of the equation:
[tex]24b-21+21=6b-3+21\\\\24b=6b+18[/tex]
Subtract [tex]6b[/tex] from both sides:
[tex]24b-6b=6b+18-6b\\\\18b=18[/tex]
And finally, you can divide both sides of the equation by 18:
[tex]\frac{18b}{18}=\frac{18}{18}\\\\b=1[/tex]
Answer:
b=1
Step-by-step explanation:
You first need to multiply -3 and -8b. That will be 24b. Then you multiply -3 times 7. That will be -21. On the other side, you will multiply 3 times 2b which will equal 6b. Then you multiply 3 by -1. You will get -3. So at this point, the equation should look like this, 24b-21=6b-3. Then add 21 to both sides. You will have this equation, 24b=6b+18. Then subtract 6b from both sides, 18b=18. Finally, divide 18 from both sides to get your final answer of b=1.
The slope of a line is 5/8,(5 on he top and 8 on the bottom) and the line passes through the point .(−8,−4).
What is the slope-intercept form of the equation for this line?
Answer:
y=5/8 x+1
Step-by-step explanation:
so not 58 but 5/8 is the slope, okay... Did you try looking at your last question as an example for this one?
y=mx+b
we are given m=5/8 so plug in
y=5/8 x+b
You are given an (x,y) on the line which is (-8,-4) so plug in and find b
-4=5/8 (-8)+b
-4=-5+b
1=b
So the line y=5/8 x+1
9 to the third power
Answer:
729
Step-by-step explanation:
9 x 9 x 9
Answer:729
Step-by-step explanation:
third power means squared, and that means that you multiply the number by it's self three times, 9*9=81, that's once. then again 81*9 =728
Which equation has x=4 as the solution? A) ^log 4 (3x+4)=2 B) ^log 3 (2x-5)=2 C) ^log x 64=4 D) ^log x 16=4
ANSWER
[tex] \log_{4}(3x + 4) = 2[/tex]
EXPLANATION
Consider the equation:
[tex] \log_{4}(3x + 4) = 2[/tex]
When we rewrite this logarithmic equation in the exponential form, we obtain:
[tex]3x + 4= {4}^{2} [/tex]
Note that to write a logarithmic equation in exponential form, the base of the logarithm is still the base in the exponential form.
We now simplify the RHS.
[tex]3x + 4 = 16[/tex]
Group like terms
[tex]3x = 16 - 4[/tex]
This implies that
[tex]3x = 12[/tex]
Divide both sides by 3
[tex] \frac{3x}{3} = \frac{12}{3} [/tex]
Simplify to get;
[tex]x = 4[/tex]
Hence the equation that has x=4 as a solution is
[tex] \log_{4}(3x + 4) = 2[/tex]
Another way to do this is to substitute x=4 into each equation. The equation that is satisfied is the correct choice.
Answer:
(A)
Step-by-step explanation:
on edg 2021
PLEASE HELP ME RIGHT NOW!! 40 PTS.
The ceiling of Katie’s living room is a square that is 12 ft long on each side. To decorate for a party, she plans to hang crepe paper around the perimeter of the ceiling and then from each corner to the opposite corner. Katie can buy rolls that each contain 10 ft of crepe paper. What is the minimum number of rolls she should buy? Show your work.
Show work Please.
CREDIT BELONGS TO Sage24
I think that 3 rolls is wrong and that 6 rolls is right. If you create a 15 by 15 square and draw two lines through the center that connect to the opposite corner, you'll be able to use the Pythagorean Theorem.
Perimeter: 15+15+15+15=60ft.
Length of Line from Corner to Corner:
(15)(15)+(15)(15)=C^2
225+225=C^2
450=C^2
21.2=C
21.2(2)= 42.4ft.
42.4ft.+60ft.= 102.4ft.
102.4ft. divided by 20ft. = 5.12 = 6 rolls
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Which function is increasing and has a constant slope?
Answer:
We need to find the increasing function with constant slope.
Let us check each option one by one.
A) 6x -5y =10.
Let us solve it for y to get slope-intercept form
6x-5y =10.
-5y =-6x +10.
y =6/5 x-2.
Slope is 6/5 positive, therefore, it's an increasing function.
A linear function always has a constant slope.
Therefore, correct option is option A.
A. 6x -5y =10
All other options are incorrect.
Step-by-step explanation:
Please mark brainliest and have a great day!
which equation represents the line that is parallel to 3x-4y=7
Answer:
Option B (3x - 4y = -4).
Step-by-step explanation:
Parallel lines are the straight lines that never meet. This is only possible when the gradients of both the lines are same. This means that the slopes of all the parallel lines in a group can be calculated by calculating the slope of one of the lines. Therefore, the slope of the line that is parallel to the line 3x-4y=7 is the same as the original line. Hence, the gradient can be extracted from the original line by converting the equation in the form y=mx+c, where m is the slope.
3x - 7 = 4y.
y = (3/4)x - 7/4.
The slope of the line which has to be found is 3/4 and it passes through (x0, y0) = (-4, -2). Using the following formula:
(y - y0) = m*(x - x0).
(y + 2) = (3/4)*(x + 4)
Cross multiplying:
4y + 8 = 3x + 12.
3x - 4y = -4.
Hence, Option B is the correct choice!!!
A stereo salesman whose base pay plus commissions amounted to $37,625
last year earned a commission of 16.5% on each stereo sold. If each stereo
he sold cost $1500 and if his base pay was $33,170, how many stereos did
the salesman sell last year?
A. 17
B. 15
C. 18
D. 16
(APEX ANSWER) (you can answer anyways to rack up points but i mostly posted bc i dident see it when i looked for it)
Answer:
18
Step-by-step explanation:
thanks..
..
Answer:
C. 18
Step-by-step explanation:
Let x represent number of stereos.
We have been given that a salesman sold each stereo for $1500. He earned a commission of 16.5% on each stereo sold.
The amount of commission earned on each stereo would be 16.5% of 1500.
[tex]1500\times \frac{16.5}{100}=15\times 16.5=247.5[/tex]
The amount of commission earned on x stereos would be [tex]247.5x[/tex].
We are told his base salary is $33,170, so total salary of salesman would be [tex]247.5x+33,170[/tex].
We are also given that last year he earned $37,625. We can represent this information in an equation as:
[tex]247.5x+33,170=37,625[/tex]
[tex]247.5x+33,170-33,170=37,625-33,170[/tex]
[tex]247.5x=4455[/tex]
[tex]\frac{247.5x}{247.5}=\frac{4455}{247.5}[/tex]
[tex]x=18[/tex]
Therefore, the salesman sold 18 stereos last year.
What is the following product?
ANSWER
[tex]6 \sqrt{6} [/tex]
EXPLANATION
The given product is
[tex] \sqrt{12} \times \sqrt{18} [/tex]
We rewrite to get;
[tex] \sqrt{4 \times 3} \times \sqrt{9 \times 2} [/tex]
We split the radical sign to get:
[tex]\sqrt{4 } \times \sqrt{3} \times \sqrt{9} \times \sqrt{2} [/tex]
The perfect squares simplifies to:
[tex]2\sqrt{3} \times 3 \sqrt{ 2} [/tex]
This gives us :
[tex]2 \times 3 \sqrt{3 \times 2} [/tex]
This simplifies to;
[tex]6 \sqrt{6} [/tex]
prove that cos^2(45º – A ) - sin^2 (45º – A) = Sin2A
Answer:
see explanation
Step-by-step explanation:
Using the addition identity for sine
sin(x + y) = sinxcosy - cosxsiny
Consider the left side
cos²(45 - A) - sin²(45 - A)
cos²(45 - A) = 1 - sin²(45 - A), thus
1 - sin²(45 - A) - sin²(45 - A)
= 1 - 2sin²(45 - A) ← expand sin(45 - A)
= 1 - 2(sin45cosA - cos45sinA)²
= 1 - 2([tex]\frac{\sqrt{2} }{2}[/tex]cosA - [tex]\frac{\sqrt{2} }{2}[/tex]sinA)²
= 1 - 2([tex]\frac{1}{2}[/tex]cos²A - sinAcosA + [tex]\frac{1}{2}[/tex]sin²A)
= 1 - cos²A + 2sinAcosA - sin²A
= sin²A + 2sinAcosA - sin²A
= 2sinAcosA
= sin2A = right side ⇒ verified
By Using the addition identity for sine; sin(x + y) = sinx cosy - cosx siny.
It is proved that cos²(45 - A) - sin²(45 - A)= Sin2A.
How to convert the sine of an angle to some angle of cosine?We can use the fact that:
[tex]\sin(\theta ^\circ) = \cos(90 - \theta^\circ)[/tex]
To convert the sine to cosine (but the angles won't stay the same unless it's 45 degrees).
Using the addition identity for sine
sin(x + y) = sinx cosy - cosx siny
Now,
cos²(45 - A) - sin²(45 - A)
cos²(45 - A) = 1 - sin²(45 - A),
1 - sin²(45 - A) - sin²(45 - A)
= 1 - 2sin²(45 - A)
Expand sin(45 - A)
= 1 - 2(sin45cosA - cos45sinA)²
= 1 - 2(√2/2 cosA - √2/2 sinA)²
= 1 - 2(1/2 cos²A - sinAcosA + 1/2 sin²A)
= 1 - cos²A + 2sinAcosA - sin²A
= sin²A + 2sinAcosA - sin²A
= 2sinAcosA
cos²(45 - A) - sin²(45 - A) = sin2A = right side
Hence, it is verified.
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Add three hundreds to 85,670
Answer:
300+85670=85970
Answer:
85,970
Step-by-step explanation:
This is simple, just add 300 or 3 hundreds to 85,650 on a calculator to get 85,970. 6 + 3 = 9.
Help me I need to pass so I can go on to the next thing plz someone help me. Will give brainliest!!
Which of the following is the equation of a circle with center (5, - 2) and a radius of 3?
a.(x-5)^2+(y+2)^2=9
b.(x+5)^2+(y-2)^2=9
c.(x-5)^2+(y+2)^2=3
d.(x+5)^2+(y-2)^2=3
Answer:
option a
Step-by-step explanation:
we know the equation of a circle is:
(x-x1)^2 +(y-y2)^2= r^2
center= (x1,y2)
radius =r
in this case we have:
center= (5,-2)
r=3
so we have:
(x-5)^2 +(y-(-2))^2=9
finally we have:
(x-5)^2 +(y+2)^2=9
25POINTS!!Which expression is equivalent to 3 x 5 x 5 x 5 x 5 X 5 X 5?
15^6
15^7
3(5)^6
3(5)^7
Answer:
the third one
Step-by-step explanation:
count your factors of 5... I count 6
so the only answer that says you have a factor of 3 and 6 factors of 5 is the third one
Find the equation of the circle whose center and radius are given.
center (0,8), radius = 8
Answer:
[tex]x^2 +(y-8)^2=64[/tex]
Step-by-step explanation:
The equation of the circle with center at point [tex](x_0,y_0)[/tex] and radius r is
[tex](x-x_0)^2+(y-y_0)^2=r^2[/tex]
In your case,
[tex]x_0=0[/tex][tex]y_0=8[/tex][tex]r=8[/tex]So, the equation of the circle with center at (0,8) and radius r=8 is
[tex](x-0)^2+(y-8)^2=8^2\\ \\x^2 +(y-8)^2=64[/tex]
Answer: x² +( y - 8 )² =64
Step-by-step explanation: happy to help :)
Are the equations lxl – 3 = 7 and [x] = 10 equivalent?
They're not equivalent.
[tex]|x|[/tex] (vertical bars) represents the absolute value of x. How it works is that it turns negative numbers positive but leaves 0 and positive numbers alone (hence it gets a number's distance from 0 on the number line).
[tex][x][/tex] (square brackets) usually represents the floor function, which returns the largest integer that is less than or equal to x. (The floor of x can also be written as [tex]\lfloor x \rfloor[/tex] --- it depends on what your textbook/source says).
To solve [tex]|x| - 3 = 7[/tex], you first transform it into the equivalent equation [tex]|x| = 10[/tex]. Then by definition of absolute value, there are only two solutions for the first equation: x = 10 or x = -10.
[x] = 10 has infinitely many solutions. For example, the floor of 10 is 10, so [tex][10] = 10[/tex], thus a solution for the second equation is x = 10
The floor of 10.1 is 10, so [tex][10.1] = 10[/tex], thus another solution for the second equation is x = 10.1.
The two equations do not have the same solution set (as x = 10.1 does not solve |x| - 3 = 7 but solves [x] = 10), so they're not equivalent.
Yvette earns a $45,000 salary plus a 12% commission on any sales over $10,000. Last year Yvette made $30,000 in sales. How much did Yvette earn in salary plus commission ?
She earns commission on the amount of sales over $10,000
Subtract 10,000 from her sales to get the amount she earns commission on:
30,000 - 10,000 = 20,000.
multiply that by the percent:
20,000 x 0.12 = 2400
She earned $2,400 in commission.
Now add that to her salary to find her total pay:
45,000 + 2,400 = $47,400
Answer:
$47,400.
Step-by-step explanation:
We have been given that Yvette earns 12% commission on any sales over $10,000. Last year Yvette made $30,000 in sales.
The amount on which Yvette will get commission would be [tex]\$30,000-\$10,000=\$20,000[/tex].
Since Yvette gets 12% commission, so amount earned as commission would be 12% of $20,000.
[tex]\text{Commission}=\$20,000\times \frac{12}{100}[/tex]
[tex]\text{Commission}=\$20,000\times 0.12[/tex]
[tex]\text{Commission}=\$2,400[/tex]
Yvette also gets a salary of $45,000, so Yvette's total earnings would be $45,000 plus $2,400.
[tex]\text{Yvette's total earnings}=\$45,000+\$2,400[/tex]
[tex]\text{Yvette's total earnings}=\$47,400[/tex]
Therefore, Yvette's earned $47,400 in salary plus commission.
What is the domain of the function y=in(x+2) x<-2 x>-2 x<2 x> x<-2 x>-2 x<2 x>2
For this case we must find the domain of the following function:
[tex]y = ln (x + 2)[/tex]
By definition, the domain of a function is given by all the values for which the function is defined.
In this case, the argument of the expression must be greater than 0 to be defined.
[tex]x + 2> 0\\x> -2[/tex]
Thus, the domain of the function is given by all the values of x greater than -2.
Answer:
Domain: [tex]x> -2[/tex]
Please help me someone
Answer:
The correct answer option is D. He multiplied the divisor by 100 and dividend by 10.
Step-by-step explanation:
We are given that Miguel completed the division where initially he had to divide 754 by 0.52.
To make it easier, he multiplied both the divisor and the dividend by the same number to get rid of the decimal in the divisor.
If he multiplied the divisor by 100, he should have multiplied the dividend by 100 too. But instead, he mistakenly multiplied the divisor by 100 and dividend by 10.
A package of bacon holds 15 strips of bacon. The pancake house uses 17 packages of bacon in the morning and 21 packages in the afternoon. How many more strips were used in the afternoon than the morning?
Answer:
60 more strips were used in the afternoon
Step-by-step explanation:
Bacon used in the morning
17 packages * 15 strips/ package = 255 strips
Bacon used in the afternoon
21 packages * 15 strips/package = 315
Difference = 315-255 =60
60 more were used in the afternoon