Answer:
16 x 32
Step-by-step explanation:
If you enlarge by 8 times, you are multiplying each dimension by 8. 2*8=16 and 4*8=32
By multiplying each dimension of the original photograph (2" x 4") by the scale factor (8), we get the dimensions of the enlarged photograph as 16" (length) and 32" (width)
Explanation:The problem you presented is a simple application of scale factors in math. You need to determine the new dimensions of the enlarged photograph. For a rectangular photograph with original dimensions of 2" x 4", if the photograph is enlarged by a scale factor of eight, we multiply each dimension by the factor 8.
So, for the length: 2" x 8 = 16"
And, for the width: 4" x 8 = 32"
Therefore, the dimensions of the new photograph after enlargement would be 16" by 32".
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What is the solution to sqrt 17-x=x+3? Show your work.
Answer:
[tex]x=1[/tex]
Step-by-step explanation:
Remember:
[tex](\sqrt[n]{a})^n=a\\\\(a+b)=a^2+2ab+b^2[/tex]
Given the equation [tex]\sqrt{17-x}=x+3[/tex], you need to solve for the variable "x" to find its value.
You need to square both sides of the equation:
[tex](\sqrt{17-x})^2=(x+3)^2[/tex]
[tex]17-x=(x+3)^2[/tex]
Simplifying, you get:
[tex]17-x=x^2+2(x)(3)+3^2\\\\17-x=x^2+6x+9\\\\x^2+6x+9+x-17=0\\\\x^2+7x-8=0[/tex]
Factor the quadratic equation. Find two numbers whose sum be 7 and whose product be -8. These are: -1 and 8:
[tex](x-1)(x+8)=0[/tex]
Then:
[tex]x_1=1\\x_2=-8[/tex]
Let's check if the first solution is correct:
[tex]\sqrt{17-(1)}=(1)+3[/tex]
[tex]4=4[/tex] (It checks)
Let's check if the second solution is correct:
[tex]\sqrt{17-(-8)}=(-8)+3[/tex]
[tex]5\neq-5[/tex] (It does not checks)
Therefore, the solution is:
[tex]x=1[/tex]
the only solution is x = 1.
To solve the equation sqrt(17-x) = x+3, we first eliminate the square root by squaring both sides of the equation. Doing so yields:
17 - x = (x + 3)2
17 - x = x2 + 6x + 9
Next, we rearrange the equation to set it equal to zero, thus forming a quadratic equation:
x2 + 6x + 9 + x - 17 = 0
x2 + 7x - 8 = 0
Now, we factor the quadratic:
(x + 8)(x - 1) = 0
Hence, the solutions are:
x = -8
x = 1
To verify that these solutions satisfy the original equation, we perform a check by substituting them back into the original equation. However, we notice that the solution x = -8 does not work because it would result in taking the square root of a negative number, which is not possible in real numbers. So the only solution is x = 1.
Please Help!!
Which function has zeroes at npi, where n is an integer? Select 2.
y=cos x
y=cot x
y=csc x
y=sec x
y=sin x
y=tan x
ANSWER
[tex]y = \sin(x) [/tex]
EXPLANATION
The trigonometric function that is zero at integral values is the sine function.
That is;
[tex]y = \sin(x) [/tex]
has x-intercepts at
[tex] n\pi[/tex]
where n is an integer.
In other words, the solution to the equation:
[tex] \sin(x) = 0[/tex]
is
[tex]x = n\pi[/tex]
where n is an integer.
Answer:
y=sin x
y=tan x
these are correct....
I have SAT's tomorrow and need help with math...
Antonina needs to have worked at least 90 volunteer hours to graduate. She has already volunteered with a housing organization over the summer for 52 hours. Antonina needs to tutor after school for 3 hours per week to complete the remainder of her volunteer hours. If w is the number of weeks that Antonina needs to tutor in order to complete her volunteer hours, which of the following inequalities best models the situation described above?
Answer:
3w + 52 ≥ 90
Step-by-step explanation:
If she volunteers 3 hours per week for w weeks, then the number of hours from tutoring is 3w. Add the 52 hours from her summer volunteering, and her total hours is 3w + 52. This needs to be at least 90 hours for her to graduate, so:
3w + 52 ≥ 90
What is the sum of all the positive two-digit integers divisible by both the sum and product of their digits?
Answer:
72
Step-by-step explanation:
Exhaustive search shows the numbers to be 12, 24, 36. The sum of these three numbers is 72.
What else would need to be congruent to show that STU is congruent to JKL by SAS? tysm! :)
Answer:
Choice C.
Step-by-step explanation:
You already have two sides and two angles. Now you need the other two sides that include the angle. Choice C is correct.
Answer: C. [tex]\overline{SU}\cong\overline{JL}[/tex]
Step-by-step explanation:
SAS congruence postulate tells that if two sides and the included angle of a triangle are congruent to corresponding two sides and the included angle of other triangle, then the triangles are congruent.In the given picture , we have two triangles ΔSTU and Δ JKL , in which we have
[tex]\overline{ST}\cong\overline{JK}[/tex]
[tex]\angle{S}\cong\angle{J}[/tex]
To prove ΔSTU is congruent to Δ JKL, we need [tex]\overline{SU}\cong\overline{JL}[/tex] such that [tex]\angle{S}\text{ and }\angle{J}[/tex] becomes congruent the included angles between pair of congruent sides.
Hence, C is the right option.
Find the value of the indicated angles. PLEASE HELP!!
Answer:
Part 1) The measure of the angle is 47°
Part 2) The measure of the angle is 52°
Step-by-step explanation:
Part 1)
we know that
The inscribed angle is half that of the arc it comprises.
we have that
(12y-1)°=(9y+11)° ----> because the arc that the inscribed angles comprise is the same
Solve for y
12y-9y=11+1
3y=12
y=4°
Find the measure of the angle
(12y-1)°=12(4)-1=47°
Part 2)
we know that
The inscribed angle is half that of the arc it comprises.
we have that
2(3m+2)°=(4m+20)° ----> because the arc that the inscribed angles comprise is the same
Solve for m
6m+4=4m+20
6m-4m=20-4
2m=16
m=8
Find the measure of the angle
(4m+20)°=4(8)+20=52°
A bag contains 40 marble ,4 of which are blue , 10 are red ,25 are green , and 1 purple Shawna takes a marble out of the bag, records the color and returns it to the bag . How many green marbles should she exepect after 400 trials
She should expect 250 green marbles.
She has a 25 out of 40 chance of selecting a green marble each time since she is putting it back in the bag each time. 25/40 reduces to 5/8. Multiply 5/8 by 400 and you get 2000/8. Reduce the fraction to 250/1 or 250.
Jon has 15 coins in nickels and dimes.he has 3 more dimes than nickels.how many nickels and dimes dose he have
Answer: 6 nickels and 9 dimes
Step-by-step explanation:
15 coins - 3 extra dimes = 12
12 / 2 = 6
6 nickels
6 + 3 = 9 dimes
Identify the value of x and the length of each chord. HELP ASAP!!
Answer:
First option
x = 9.1, AB = 16.5, CD = 14.1
Step-by-step explanation:
5 * x = 13 * 3.5
5x = 45.5
x = 9.1
AB = 3.5 + 13 = 16.5
CD = 5 + 9.1 = 14.1
The value of x and the length of each chord is x = 9.1, AB = 16.5, CD = 14.1. Thus first option is correct.
What is the relation between line perpendicular to chord from the center of circle?If the considered circle has center O and chord AB, then if there is perpendicular from O to AB at point C, then that point C is bisecting(dividing in two equal parts) the line segment AB.
Or
|AC| = |CB|
Let x be the measure of the length of ED.
[tex]5 \times x = 13 \times3.5\\5x = 45.5\\x = 9.1[/tex]
Therefore,
AB = 3.5 + 13 = 16.5
CD = 5 + 9.1 = 14.1
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19. Heather invests $4,900 in an account with a 3.5% interest rate, making no other deposits or withdrawals. What will Heather’s account balance be after 5 years if the interest is compounded 2 times each year?
Answer:
[tex]\$5,828.28[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/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
n is the number of times interest is compounded per year
in this problem we have
[tex]t=5\ years\\ P=\$4,900\\ r=0.035\\n=2[/tex]
substitute in the formula above
[tex]A=\$4,900(1+\frac{0.035}{2})^{2*5}[/tex]
[tex]A=\$4,900(1.0175)^{10}=\$5,828.28[/tex]
Answer:
5,828.28
Step-by-step explanation:
Our basketball team has 10 players. we need to divide into two teams of 5 for an intra-squad scrimmage. in how many ways can we do this without restriction?
There are 252 ways to divide the 10 players into two teams of 5 without any restriction.
To determine the number of ways you can divide 10 players into two teams of 5 without any restriction,
Using the formula, C(n, k) = [tex]\frac{n!}{k!(n-k)!}[/tex]
By finding the number of ways to choose 5 players out of 10, which is the same as choosing the other 5 players who are not on the first team.
Where n = 10
k = 5
C(10, 5) = [tex]\frac{10!}{5!(10-5)!}[/tex]
C(10, 5) = [tex]\frac{10!}{5!(5)!}[/tex]
C(10, 5) = 10*9*8*7*6*5*4*3*2*1/5*4*3*2*1(5*4*3*2*1)
C(10, 5) = 30240/5*4*3*2*1
C(10, 5) = 252 ways
Therefore, there are 252 ways to divide the 10 players into two teams of 5 without any restriction.
An object moves along a circular path with radius 10 inches and makes 5 revolutions in 1 minute. What is the linear velocity, in inches per minute, of a point on the edge of the wheel?
10π
20π
50π
100π
Answer:
100π
Step-by-step explanation:
step 1
Find the circumference
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=10\ in[/tex]
substitute
[tex]C=2\pi (10)[/tex]
[tex]C=20\pi\ in[/tex]
step 2
we know that
An object moves along a circular path and makes 5 revolutions in 1 minute
Remember that
[tex]1\ rev=2\pi r[/tex] ----> circumference of the circle
therefore
[tex]5\ rev=5(20\pi)=100\pi\frac{in}{minute} [/tex]
For what value of y must QRST be a parallelogram?
A: 1
B: 2
C: 3
D: 0.5
Answer:
A
Step-by-step explanation:
Diagonals of a parallelogram bisect each other.
3x = 3
x = 1
y = x
y = 1
In a parallelogram, the parts in which each diagonal cuts the other are congruent.
This means that we must have
[tex]\begin{cases}3=3x\\x=y\end{cases}[/tex]
From the first equation we can deduce x=1, and thus y=x=1.
Yvonne is a salesperson who earns a fixed amount of $1,850 per month. She also earns a commission of 4% on the amount of goods that she sells. If she wants to earn more than $2,300 in one month, how many dollars (x) in goods must she sell?
Answer: $11,250
1850 + (4/100)x = 1850 + 0.04x.
1850 + 0.04x > 2300
0.04x > 2300 - 1850
0.04x > 450
x > 450 / 0.04
x > $11,250
Answer
x> 11,250
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The person at (0, 1) needs a bottled water. He moved to the right on a slope of -4. Where can you find him to give him the water he ordered
Final answer:
To locate the person who moved from (0, 1) with a slope of -4, we need to know the specific horizontal distance they moved. Without this, we can only say they moved downward 4 units for every 1 unit they moved to the right.
Explanation:
The student's question involves determining the position of a person who has moved along a slope on a coordinate plane. Since the individual started at the point (0, 1) and moved to the right with a slope of -4, we can assume they are moving in the negative y-direction (downward), as the negative slope indicates a decrease in y for every increase in x. The specific horizontal distance isn't given, so we cannot provide an exact new coordinate without more information. However, if we had a specific horizontal distance the person moved, we could calculate the new position using the slope (-4), which means for every 1 unit moved horizontally to the right, the person would move 4 units down.
You are getting ready to watch a fireworks display and are sitting about 300 feet away from the launch pad. The angle for you to see the fireworks is about 35°. If the fireworks are launched vertically into the sky, what is the height of the fireworks when they explode?
Answer:
210.06 feet
Step-by-step explanation:
This is a classic right triangle trig problem. The distance from the launch pad is the measure of the base of the right triangle. The angle of elevation, 35, is the base angle (not the right angle). How high the fireworks go up is the height of the triangle. You have the reference angle of 35, the side adjacent to it, 300, and you're looking for the side length across from it, y. The trig ratio that relates a reference angle to the sides opposite it and adjacent to it is the tangent ratio. Setting that up:
[tex]tan(35)=\frac{y}{300}[/tex]
Solving for y:
y = 300 tan(35)
On your calculator in degree mode find y to be 210.06 feet.
By using basic trigonometry, specifically the tangent of the viewing angle, we can determine that the height of the fireworks when they explode is approximately 210 feet.
Explanation:You are asking how to use trigonometry to find the height of the fireworks when they explode. If we combine your conditions that the launch was vertical and the viewing angle was 35°, we can use the tangent of that angle to find the height of the fireworks. The tangent of an angle in a right triangle is the opposite side (height in this case) divided by the adjacent side (distance from the launch, 300 feet in this case). So setting up the equation, we have: tan(35°) = height / 300. Solving for 'height', we get: height = 300 * tan(35°). Using a calculator, we find that tan(35°) is roughly 0.70021. Multiplying that by 300, we find that the height of the fireworks when they explode is approximately 210 feet.
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Which two events have the same probability the spinner is divided into 8 equal sections
Answer:
N/A
Step-by-step explanation:
Not enough context is given for the problem.
Just remember, though:
And = Multiplication
Or = Addition
1/8 chance for each section
Answer:
(A) P(gray), P(green)
Step-by-step explanation:
Notice that there are 2 tiles in each, so it should be A as the answer.
Please mark me brainiest!
Hope you have a good day!
70 POINTS!!!!!!!!!! Given: E, F, Q, D∈k(O),O ∈ ED, m∠DFQ = 10°, measure of arc EF = 28° Find: Angles of △EFQ
Answer:
The measures of angles of triangle EFQ are
1) [tex]m\angle EFQ=100\°[/tex]
2) [tex]m\angle FEQ=66\°[/tex]
3) [tex]m\angle EQF=14\°[/tex]
Step-by-step explanation:
step 1
Find the measure of arc QD
we know that
The inscribed angle is half that of the arc it comprises.
[tex]m\angle DFQ=\frac{1}{2}(arc\ QD)[/tex]
substitute the given value
[tex]10\°=\frac{1}{2}(arc\ QD)[/tex]
[tex]20\°=(arc\ QD)[/tex]
[tex]arc\ QD=20\°[/tex]
step 2
Find the measure of arc FQ
we know that
[tex]arc\ QD+arc\ FQ+arc\ EF=180\°[/tex] ---> because ED is a diameter (the diameter divide the circle into two equal parts)
substitute the given values
[tex]20\°+arc\ FQ+28\°=180\°[/tex]
[tex]arc\ FQ=180\°-48\°=132\°[/tex]
step 3
Find the measure of angle EFQ
we know that
The inscribed angle is half that of the arc it comprises.
[tex]m\angle EFQ=\frac{1}{2}(arc\ QD+arc\ ED)[/tex]
substitute the given value
[tex]m\angle EFQ=\frac{1}{2}(20\°+180\°)=100\°[/tex]
step 4
Find the measure of angle FEQ
we know that
The inscribed angle is half that of the arc it comprises.
[tex]m\angle FEQ=\frac{1}{2}(arc\ FQ)[/tex]
substitute the given value
[tex]m\angle FEQ=\frac{1}{2}(132\°)=66\°[/tex]
step 5
Find the measure of angle EQF
we know that
The inscribed angle is half that of the arc it comprises.
[tex]m\angle EQF=\frac{1}{2}(arc\ EF)[/tex]
substitute the given value
[tex]m\angle EQF=\frac{1}{2}(28\°)=14\°[/tex]
Help with this question, please!!
Answer:
(x +8)² +(y +1)² = 9
Step-by-step explanation:
The formula for a circle with center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
Filling in your given numbers gives ...
(x -(-8))² +(y -(-1))² = 3²
Simplifying that results in ...
(x +8)² +(y +1)² = 9
What will happen to the mean if the outlier is removed?
4, 5, 5, 7, 9, 17
It will not change.
It will be the same as the median.
It will decrease.
It will increase.
The mean is the average. The outlier is a number way bigger or smaller than the rest of the data. The outlier here would be 17. If you remove 17 and then find the average again, it will be smaller because all the numbers left are around the same range.
Answer: It will decrease
Kylie started basketball practice at 2:30 p.m and finished at 6:00 p.m how long was kylie at basketball practice
Answer:
3 hours and 30 minutes
Step-by-step explanation:
Since both of these times are in the P.M., each hour has 60 minutes and 2:30 is half, add 30 minutes to get 3:00 P.M. and then add 3 hours to get 6:00 P.M. . 3 hours and 30 minutes added to 2:30 P.M. equals 6:00 P.M. :)
Answer:
3 hours and 30 minutes
Step-by-step explanation:
Kylie started basketball practice at 2:30
Kylie finished basketball practice at 6:00
Time duration = 3 hours and 30 minutes
2 : 30 → 3 : 00
( 30 minutes )
3 : 00 → 6 : 00
( 3 hours )
3 hours + 30 minutes = 3 hours and 30 minutes
Express the product as a sum containing only sines or cosines. 64) sin (5θ) cos (2θ)
[tex]\bf \textit{Product to Sum Identities} \\\\sin(\alpha)cos(\beta)=\cfrac{1}{2}[sin(\alpha+\beta)\quad +\quad sin(\alpha-\beta)] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin(5\theta )cos(2\theta )\implies \cfrac{1}{2}[sin(5\theta +2\theta )+sin(5\theta -2\theta )]\implies \cfrac{sin(7\theta )+sin(3\theta )}{2}[/tex]
The required value of trigonometry expression is the product as a sum [sin(7θ) + sin(3θ)] / 2.
What is the product to sum Identities?The product-to-sum formulae are used to represent the sum of the sine and cosine functions. These are generated from trigonometry's sum and difference formulae.
sin A cos B = (1/2) [ sin (A + B) + sin (A - B) ]
The trigonometry expression is given in the question
sin (5θ) cos (2θ)
According to the product to sum Identities
sin A cos B = (1/2) [ sin (A + B) + sin (A - B) ]
Here A = 5θ and B = 2θ
sin (5θ) cos (2θ) = (1/2) [sin(5θ + 2θ) + sin(5θ - 2θ)]
sin (5θ) cos (2θ) = (1/2) [sin(7θ) + sin(3θ)]
sin (5θ) cos (2θ) = [sin(7θ) + sin(3θ)] / 2
Thus, the required value of trigonometry expression is the product as a sum [sin(7θ) + sin(3θ)] / 2.
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Please help me out please
Answer:
20°
Step-by-step explanation:
40=2x,x=20°
find the vertex : f(x)=3x^2-18x+10
f(x)=3x^2-18x+10
a = 3, b = -18 and c = 10
The vertex of a parabola is in form a(x+d)^2 + e
d = b/2a = -18/2(3) = -18/6 = -3
e = c-b^2/4a = 10 - -18^2/4(3) = 10-27 = -17
Now the vertex form of the parabola becomes 3(x-3)^2 -17
Use the vertex form of the parabola in the vertex form of y = a(x-h)^2 +k
Where a = 3, h = -3 and k = -17
Now you have y = 3(x-(-3))^2 +(-17)
Simplify: y = 3(x+3)^2 -17
The vertex becomes the h and k values of (3,-17)
Please answer this correctly
The answer is 8......
Answer:
The answer is 8
Step-by-step explanation:
Just add the rest of the numbers and then subtract from the answer
Can someone show me the steps to do this :( please
Answer:
Step-by-step explanation:
Use the sum of angle formula:
cos(a+b) = cos(a)cos(b) -sin(a)sin(b)
This gives you ...
cos(x)cos(-π/6) -sin(x)sin(-π/6) = 1 + cos(x)cos(π/6) -sin(x)sin(π/6)
Subtracting the right-side trig function terms and factoring, we have ...
cos(x)(cos(-π/6) -cos(π/6)) -sin(x)(sin(-π/6) -sin(π/6)) = 1
Since the cosine is an even function, cos(-π/6) = cos(π/6). Since the sine is an odd function, sin(-π/6) = -sin(π/6). This gives us ...
cos(x)·0 -sin(x)(-2sin(π/6)) = 1
sin(x) = 1/(2·sin(π/6)) = 1/(2·1/2) = 1
x = arcsin(1)
x = π/2
_____
When solving these by using a graphing calculator, it is convenient to subtract one side of the equation so you have a function of x that you want to find the zeros of. Here, we subtracted the right side. The graph shows the result is zero for x=π/2, as we know.
Please help me out!?????
Answer
[tex]\frac{121}{4} \pi mm^2[/tex]
Explanation
Find the radius
11/2 = 5.5
The formula to find the area of a circle is [tex]\pi r^2[/tex]
[tex]\pi 5.5^2[/tex] = [tex]30.25\pi[/tex]
Convert number into fraction.
[tex]30.25 \rightarrow \frac{121}{4} \pi[/tex]
Area = [tex]\frac{121}{4} \pi mm^2[/tex]
Answer:
30.25π mm²
Step-by-step explanation:
The area (A) of a circle is calculated using the formula
A = πr² ← r is the radius
here diameter = 11 and radius is half of the diameter. thus
r = 5.5
A = π × 5.5² = 30.25π mm²
use an appropriate technology to simulate 35 rolls of a six sided number cube according to this data,what is the experimental probability of a roll of 3? what is the theoretical probability that a roll of the number cube will yield a result of 3? explain any differences between the theoretical probability and the experimental probability.
Explanation of experimental and theoretical probability of rolling a 3 on a six-sided number cube.
The experimental probability of rolling a 3:
Simulate 35 rolls of a six-sided number cube to get results.
Count the number of times a 3 is rolled and calculate the experimental probability by dividing the number of 3s rolled by 35.
The theoretical probability of rolling a 3:
Theoretical probability = Number of favorable outcomes / Total number of outcomes = 1/6 (since there is 1 favorable outcome out of 6 possible outcomes).
Differences between theoretical and experimental probabilities:
Theoretical probability is based on calculations and assumptions, while experimental probability is based on actual observations. Discrepancies between the two can occur due to sample size, random variations, or errors in the simulation.
Please help me with these 2
explain the step plz
thanks
1)when we know x+y=90* the sine of x is equal to cosine of y , so the solution of the first is 0.6 again!
Answer:
Left diagram cos(y) = 0.6
Right diagram x = 5 makes the equation true.
Step-by-step explanation:
Left diagram
Both the sin(x) and the Cos(y) use the same side as the non hypotenuse side.
Therefore they most be equal.
So if sin(x) = 0.6, then cos(y) = 0.6
=========================
Right diagram
You can factor this to get the answer.
From the first 2 terms, take out x^2. From terms 3 and 4 take out 2.
x^2(x - 5) + 2(x - 5) = 0
Take out the common factor of (x - 5)
(x^2 +2)(x - 5)
x^2 + 2 yields a complex answer (which doesn't matter for this question)
x - 5 = 0
x = 5
please help me with this geometry question
image attached
15/17. The value (ratio) of cos A is 15/17.
The trigonometric ratios of an acute angle are, basically, the sine, the cosine and the tangent. They are defined from an acute angle, α, of a right triangle, whose elements are the hypotenuse, the leg contiguous to the angle, and the leg opposite the angle.
-The sine of the angle is the opposite leg divided by the hypotenuse.
-The cosine of the angle is the adjacent leg divided by the hypotenuse.
-The tangent of the angle is the opposite leg divided by the adjacent leg or, which is the same, the sine of the angle divided by the cosine of the angle.
cos A = adjacent leg/hypothenuse = BC/AC = 15/17